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ORDNANCE AND GUNNERY
A TEXT- BOOK
PREPARED FOR THE CADETS OF THE
UNITED STATES MILITARY ACADEMY, WEST POINT
BY
ORMOND M. LISSAK
LIEUTENANT-COLONEL, ORDNANCE DEPARTMENT, UNITED STATES ARMY, RETIRED^
LATE PROFESSOR OF ORDNANCE AND THE SCIENCE OF GUNNERY
AT THE UNITED STATES MILITARY ACADEMY
FIRST EDITION
THIRD THOUSAND
NEW YORK
JOHN WILEY & SONS, INC.
LONDON: CHAPMAN & HALL, LIMITED
1915
Copyright, 1907
BY
ORMOND M. USSAK
PRESS OF
BRAUNWORTH & CO.
BOOKBINDERS AND PRIN1
BROOKLYN, N. Y.
PREFACE.
THE material of war has undergone greater changes in the
past thirty years than in the previous hundreds of years since
the introduction of gunpowder. The weapons of attack and
defense have become more numerous, more complicated, and
vastly more efficient. The appurtenances to their use are more
elaborate. The science of gunnery constantly requires of the
officer greater knowledge and higher attainments, that he may
thoroughly understand the powerful and important instruments
that are put under his control and be prepared to obtain from
them, in time of need, their full effect.
I have attempted in this text to set before the Cadets of the
Military Academy the subjects of Ordnance and Gunnery in such
manner as to give to the Cadets a thorough appreciation of the
fundamental principles that underlie the construction and effective
use of the instruments of war, and such practical knowledge of
the material of today as should be possessed by every army
officer.
The purpose held in view in the preparation of the text has
been to present, in order, the theories that apply in the use of
explosives and in the construction of Ordnance material, the
methods pursued in the construction of the material, descriptions
of the material, and the principles of its use.
The applications of the theoretical deductions to the investi-
gation of the action of gunpowders and other explosives and to
the construction and use of Ordnance material, are extensively
illustrated by problems fully worked out in the text; the idea
being that these solutions, in addition to making evident to the
student the practical use of the theories, will serve as guides in
solutions of similar problems encountered in practice.
v
359940
Vi PREFACE.
When, the theoretical deductions are applicable to other than
ordnance constructions other problems inserted in the text indicate
their more extended field.
In the chapter on interior ballistics, which is taken princi-
pally from the writings of Colonel James M. Ingalls, United States
Army, the deduction and application of Colonel Ingalls' latest
interior ballistic formulas are fully set forth. The determina-
tions from these formulas have been found in practice to be more
closely in accord with the actual results obtained in firings, than
determinations from any ballistic formulas hitherto in use.
In the chapter on explosives the theoretical determination of
the results from explosions, including the quantity of heat, l the
volume of the gases, the temperature, the pressure, etc., is ex-
plained and illustrated by examples. This demonstration has not
hitherto been available in English.
A simplification has been introduced, by the author of the
text, into the gun construction formulas of Clavarino. The sim-
plification materially shortens these extended formulas and reduces
the labor required in their application.
The graphic system of representing the pressures and shrink-
ages in cannon, devised by Lieut. Commander Louis M. Nulton,
United States Navy, is also explained in connection with the
deduction and application of the formulas of gun construction.
The graphic system is a material help toward a ready understand-
ing of the subject.
In the subject of exterior ballistics sufficient problems are
introduced and fully worked out to illustrate the processes fol-
lowed in the solutions of the principal problems of gunnery. This
course has been adopted with the purpose of removing to a large
extent the difficulties usually encountered in the practical appli-
cation of the formulas of exterior ballistics.
An appendix to the chapter on exterior ballistics contains
the deduction of the author's formulas for double interpolation.
The formulas are more accurate and more convenient in applica-
cation than the interpolation formulas previously in use. Explan-
ation of the use of the ballistic tables to which the interpolation
formulas apply, follows the deduction of the formulas.
The chapter on armor contains information as to the general
PREFACE. vn
arrangement and thickness of the armor on ships of war, the
expected targets of the heavy artillery.
A chapter on submarine mines, torpedos, and submarine
torpedo boats concludes the text.
Acknowledgment is due for much assistance obtained from
the text-book on Ordnance and Gunnery, by Captain L. L. Bruff,
Ordnance Department, that has been in use at the Military
Academy for the past eleven years. The plan of that work has
been largely followed, many of its illustrations appear in this
volume, and assistance has been derived from its text throughout.
I desire to express my indebtedness to Captain Edward P.
O'Hern, Ordnance Department, Principal Assistant in the Depart-
ment of Ordnance and Gunnery, whose valuable suggestions and
helpful criticism have been of marked benefit to the text. Lieu-
tenants Ennis, Bryant, and Selfridge, Artillery Corps, Assistant
Instructors of the Department, have also, by their suggestions,
added to the value of the text.
I desire, too, to thank Sergeant Carl A. Schopper, of the West
Point Ordnance Detachment. The illustrations in the text are
the products of his skill as a draftsman, of his knowledge of the
illustrative arts, and of his unremitting labor.
ORMOND M. LISSAK.
WEST POINT, May 24, 1907.
CONTENTS.
CHAPTER I.
PAGE
Gunpowders ............................................ 1
Definitions, 1. History, 2. Charcoal powders, 4. Smokeless pow-
ders, 5. Guncotton, 6. Nitroglycerine small-arm powder, 7. Manu-
facture of nitrocellulose powder, 9. Other smokeless powders, 10.
Proof of powders, 11. Advantages of smokeless powder, 12. Pow-
der charges, 14. Blank charges, 15.
COMBUSTION OP POWDER UNDER CONSTANT PRESSURE, 16. Constants
of form of powder grains, 18. Emission of gas by grains of different
forms, 24. Considerations as to best form of grain, 27.
VARIOUS DETERMINATIONS, 28. The number of grains in a pound, 28.
The dimensions of irregular grains, 28. Comparison of surfaces, 28.
Density of gunpowder, 29.
CHAPTER II.
Measurement of Velocities and Pressures .................... 32
Measurement of velocity, 32. Le Boulenge chronograph, 32. Measure-
ment of very small intervals of time, 40. Schultz chronoscope, 41.
Sebert velocimeter, 42. Methods of measuring interior velocities, 43.
Measurement of pressures, 44. Initial compression, 45. Small-arm
pressure barrel, 45. The micrometer caliper, 46. Dynamic method,
of measuring pressures, 46. Comparison of the two methods, 47.
CHAPTER III.
Interior Ballistics .................................... .... 4&
Scope, 49. Investigations, 49. Gravimetric density of powder, 52.
Density of loading, 53. Reduced length of powder chamber, 55.
Reduced length of initial air space, 55. Problems, 56.
PROPERTIES OF PERFECT GASES, 57. Mariotte's law, 57. Gay Lussac's
law, 58.- Characteristic equation of the gaseous state, 58. Prob-
lems, 60. Thermal unit, 61. Specific heat, 62. Relations between
heat and work in the expansion of gases. 63. Isothermal expansion,
65. Adiabatic expansion, 65.
NOBLE AND ABEL'S EXPERIMENTS, 67. Apparatus, 67. Results of the
experiments, 68. Relation between pressure and density of load-
ix
CONTENTS.
ing, 69. Temperature of explosion, 70. Relations between volume
and pressure in the gun, 71. Theoretical work of gunpowder, 73.
FORMULAS FOR VELOCITIES AND PRESSURES IN THE GUN, 74. Prin-
ciple of the co volume, 75. Differential equation of the motion of a
projectile in a gun, 76. Dissociation of gases, 78. Ingall's formulas,
79. Combustion under variable pressure, 82. Velocity of the pro-
jectile while the powder is burning, 85. Velocity after the powder
is burned, 85. Pressures, 87. Values of the constants in the equa-
tions, 90. The force coefficient, 93. Values of the X functions, 94.
Interpolation, using second differences, 95. Characteristics of a
powder, 97.
APPLICATION OF THE FORMULAS, 97.
DETERMINATIONS FROM MEASURED INTERIOR WELOCITIES, 102. Prob-
lem 1, 102. Problem 2, 113. The action of different powders, 117.
Quick and slow powders, 120. Effects of the powder on the design
of a gun, 121.
DETERMINATIONS FROM A MEASURED MUZZLE VELOCITY AND MAXIMUM
PRESSURE, 122. Problem 3, 122. The force coefficient, 131. Prob-
lem 4, 132.
TABLE OF UNITED STATES ARMY CANNON, 135.
CHAPTER IV.
Explosives 136
Effects of explosion, 136. Orders of explosion, 137. Vielle's classifi-
cation of nitrocelluloses, 138. Conditions that influence explosion,
139. Uses of different explosives, 140. Bursting charges in projec-
tiles, 141. Exploders, 143. Explosion by influence, 144.
THEORETICAL DETERMINATION OF THE RESULTS FROM EXPLOSIONS, 145.
Specific heats of gases, 145. Specific volumes of gases, 146. Classi-
fication of gases, 147. Quantity of heat, 147. Heats of formation,
148. Quantity of heat at constant pressure, 149. Quantity of heat
at constant volume, 151. Potential, 154. Volume of gases, 154.
Temperature of explosion, 155. Pressure in a closed chamber, 157.
Complete calculation of the effects of explosion. 161.
CHAPTER V.
Metals Used in Ordnance Construction 163
Stress and strain, 163. Physical qualities of metals, 163. Strength of
metals, 164. Testing machine, 166. Copper, . brass, bronze, 167.
Iron and steel, 167. Hardening and tempering steel, 169. Anneal-
ing, 174. Uses, 175. Gun steel, 175.
MANUFACTURE OF STEEL FORCINGS FOR GUNS, 176. Open hearth
process, 176. Other processes, 180. Casting, 180. Defects in in-
gots, 181. Whitworth's process of fluid compression, 181. Processes
after casting, 183. Strength of parts of the gun, 187.
CONTENTS. xi
CHAPTER VI.
Guns 188
ELASTIC STRENGTH OF GUNS, 188. The elasticity of metals, 188.
Hooke's law, 188. Equations of relation between stress and strain,
190. Problems, 190. Stresses and strains in a closed cylinder, 191.
Lamp's laws, 192. Basic principle of gun construction, 195. Sim-
plification of the formulas of gun construction, 196. Stresses in a
simple cylinder, 198. Limiting interior pressures, 202. Graphic
representation, 204. Limiting exterior pressure, 205. Thickness of
cylinder, 206. Longitudinal strength, 206. Problems, 207. Com-
pound cylinder, Built-up guns, 208. System composed of two
cylinders, 209. Application of formulas to outer cylinders, 210.
System in action, 212. System at rest, 213. Graphic representa-
tion, 215. Shrinkage, 217. Radial compression of the tube, 219.
Prescribed shrinkage, 220. Application of the formulas, 220. Prob-
lems, 222. Curves of stress in section, 227. Systems composed of
three and four cylinders, 229. Minimum number of cylinders for
maximum resistance, 230. Graphic construction, three cylinders, 230.
Wire wound guns, 234.
CONSTRUCTION OF GUNS, 236. General characteristics, 236. Opera-
tions in manufacture, 239. Gun lathe, 240. Boring and turning
mill, 241. Assembling, 242. Rifling the bore, 244.
MEASUREMENTS, 245. Necessity of accurate measurements, 245. Ver-
nier caliper, 245. Measuring points, 246. The star gage, 247.
Calipers, 248. Standard comparator, 249.
RIFLING, 250. Twist, 250. Increasing twist, 251. Equation of the
developed curve of the rifling, 251. Problems, 252. Service rifling,
254.
BREECH MECHANISM, 255. General, characteristics, 255. Slotted
screw breech mechanism, 256. Bofors breech mechanism, 258. The
Welin breech block, 259. Obturation, 260. The De Bange obtura-
tor, 260. The Freyre obturator, 262. Firing mechanism, 263. Slid-
ing wedge breech mechanism, 265. Older forms of breech mechan-
ism, 266. 12-inch mortar breech mechanism, 268. Automatic and
semi-automatic breech mechanisms, 269.
CHAPTER VII.
Recoil and Recoil Brakes 274
Stresses on the gun carriage, 274. Velocity of free recoil, 274. Deter-
mination of the circumstances of free recoil, 276. Retarded recoil,
279. Recoil brakes, 280. Hydraulic brake with variable orifice, 281.
Total resistance to recoil, 281. Values of the total and partial
resistances, and velocities of recoil, 283. Resistance of the hy-
draulic brake, Pressure in the cylinder, 286. Relation between the
pressure, area of orifice, and velocity of recoil, 286. Brake with
variable pressure, 288. Constant pressure. 288. Brake with con-
Xii CONTENTS.
stant pressure, 289. Profile of the throttling bar, 290. Neglected
resistances, 291. Recoil system of seacoast carriages, 291. Modi-
fication of recoil system, 293. Wheeled carriages, Recoil, 294.
Design of a field carriage, 300. 3-inch field carriage recoil system,
301. Recoil system of other carriages, 303.
CHAPTER VIII.
Artillery of the United States Land Service 304
Mobile artillery, 304. Advantages of recent carriages, 306. The
mountain gun, 307. Field artillery, 310. The 3-inch field gun, 311.
Field howitzers and mortars, 319. Siege artillery, 320. The 4. 7-inch
siege gun, 321. The 6-inch siege howitzer, 324. Siege artillery in
present service, 330. Seacoast artillery, 332. Seacoast guns, 333.
Seacoast gun mounts, 333. Pedestal mounts, 335. The balanced
pillar mount, 337. Barbette carriages for the larger guns, 339.
Disappearing carriages, 341. 12-inch disappearing carriage, model
1901, 342. Modification of the recoil system, 346. 6-inch experi-
mental disappearing carriage, model 1905, 346. Seacoast mortars,
349. The 12-inch mortar carriage, model 1896, 350. The 12-inch
mortar carriage, model 1891, 352. Subcaliber tubes, 353. Drill
cartridges, projectiles, 'and powder charges, 355.
CHAPTER IX.
Exterior Ballistics 357
Definitions, 357. The motion of an oblong projectile, 358. Deter-
mination of the resistance of the air, 360. Mayevski's formulas for
resistance of the air, 362. Trajectory in air, Ballistic formulas, 363.
The ballistic coefficient, 367. The functions, 368. Formulas for
the whole range, 370. The ballistic elements, 371. The rigidity of
the trajectory, 371. Secondary functions, 372. Ballistic tables, 375.
Exterior ballistic formulas, 376. Interpolation in Table II, Double
interpolation formulas, 378. The solution of problems, 380. Prob-
lems, 381. Correction for altitude, 383. The effect of wind, 387.
The danger space, 392. Method of double position, 393. The
danger range, 396. Curved fire, 398. High angle fire, 401. Calcula-
tion of the coefficient of reduction, 410. Perforation of armor, 411.
Range tables, 412. Curvature of the earth, 413.
ACCURACY AND PROBABILITY OF FIRE, 413. Accuracy, 413. Prob-
ability of fire, 415. Probability curve, 417. Probable zones and
rectangles, 420. Probability of hitting any area, 420.
A/PENDIX. THE USE OF TABLE II, INGALL'S BALLISTIC TABLES 421
Description of Table II, 421. Deduction of formulas for double inter-
polation, 422. Double interpolation formulas, 425. Double inter-
polation in simple tables, 426. Use of the formulas, 427.
CONTENTS. Xiii
CHAPTER X.
Projectiles 438
Old forms of projectiles, 438. Modern projectiles, 440. Form of pro-
jectile, 442. Canister, 443. Shrapnel, 444. The bursting of shrap-
nel, 446. Shot and shell, 448. Armor piercing projectiles, 449.
Action of the cap, 451. Deck piercing and torpedo shell, 454. Latest
form of base of shell, 454. Shell tracers, 454. Hand grenades, 455.
Volumes of ogival projectiles, 455. Weights of projectiles, 456.
Thickness of walls, 456. Sectional density of projectiles, 458.
MANUFACTURE OF PROJECTILES, 460. Cast projectiles, 460. Chilled
projectiles, 461. Forged projectiles, 461. Requirements in manu-
facture, 462. Inspection of projectiles, 462. Ballistic tests, 464.
The painting of projectiles, 464.
CHAPTER XI.
Armor 46G
History, 466. Harvey and Krupp armor, 467. Manufacture of armor,
467. Armor bolts, 469. Ballistic test of armor, 471. Characteristic
perforations, 471. Armor protection of ships, 472. Chilled cast-iron
armor, 475. Gun shields, 475. Field gun shields, 476.
CHAPTER XII.
Primers and Fuses for Cannon 477
Common friction primer, 477. The service combination primer, 478.
Other friction and electric primers, 481. Percussion primers, 481.
20-grain saluting primer, 483. 110-grain electric primer, 484. Com-
bination electric and percussion primer, 484. Igniting primers, 484.
Insertion of primers in cartridge cases, 485.
FUSES, 486. Percussion fuse, 486. Point percussion fuse, 487. Base
percussion fuses, 489. Combination time and percussion fuses, 492.
Service combination fuse, 492. Combination fuse, old pattern, 495.
Ehrhardt combination fuse, 497. Detonating fuses, 498. The fuse
setter, 499. Arming resistance of fuse plungers, 501. Problems, 501.
CHAPTER XIII.
Sights 505
Principle and methods, 505. Graduation of rear sights, 506. Correc-
tion for drift, 507. Correction for inclination of site, 507. Sights
for mobile artillery, 509. The adjustable or tangent sight, 509. The
panoramic sight, 512. The range quadrant, 514. Telescopic sights,
517. Telescopic sight, model 1904, 517. Telescopic sight, model
1898, 520. The power and field of view of telescopes, 522. Aiming
mortars, 522. The gunner's quadrant, 523.
CONTENTS.
CHAPTER XIV.
Range and Position Finding 525
Range finders, 525. Depression range finders, 526. Swasey depres-
sion range and position finder, 526. The plotting room, 527. Field
range and position finding, 528. The Weldon range finder, 528. The
battery commander's telescope, 531. The battery commander's
ruler, 532. Plotting board for mobile artillery, 537. Other range
finders, 538. The Berdan range finder, 538. The Barr and Stroud
range finder, 538. The Le Boulenge telemeter, 540.
CHAPTER XV.
Small Arms and their Ammunition 541
Service small arms, 541. The 38-caliber revolver, 541. The Colt auto-
matic pistol, 544. Modern military rifles, 546. Requirements, 547.
Life of the rifle. Erosion, 549. The U. S. magazine rifle, model 1903,
550. Appendages, 554. Deviation. Drift, 555. The 22-caliber gal-
lery practice rifle, 556.
AMMUNITION FOR THE 30-CALiBER MAGAZINE RIFLE, 556. The ball
cartridge, 556. Bullets, 559. The Blank cartridge, 560. The
dummy cartridge, 561. The guard cartridge, 561. Proof of ammu-
nition, 562.
CHAPTER XVI.
Machine Guns 564
Service machine guns, 564. The Gatling machine gun, 565. The
Maxim automatic machine gun, 569. The Maxim one-pounder auto-
matic gun, 574. The Colt automatic machine gun, 575.
CHAPTER XVII.
Submarine Mines and Torpedoes. Submarine Torpedo Boats . . 576
SUBMARINE MINES AND TORPEDOES, 576. History, 576. Confederate
mines, 578. Spanish mechanical mine, 580. Electric mines, 581.
Buoyant mines, 581. Ground mines, 582. The explosive, 582. The
charge, 583. Defensive mine systems, 583. Countermining, 585.
The removal of mines, 585. Mobile and automobile torpedoes, 586.
The Sims-Edison torpedo, 586. The Whitehead torpedo, 586. The
Bliss-Leavitt torpedo, 588. The Howell torpedo, 589.
SUBMARINE TORPEDO BOATS, 590. The Holland submarine torpedo
boat, 591. The Lake submarine torpedo boat, 592.
TABLES.
Table I. LOGARITHMS OF THE X FUNCTIONS 596
Table II. HEATS OF FORMATION OF SUBSTANCES 590
Table III. SPECIFIC HEATS OF SUBSTANCES 601
Table IV. DENSITIES AND MOLECULAR VOLUMES OF SUBSTANCES 602
Table V. ATOMIC WEIGHTS 603
Table VI. CONVERSION; METRIC AND ENGLISH UNITS, TEMPERATURES.. 604
Ji
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ORDNANCE AND GUNNERY.
CHAPTER I.
GUNPOWDERS.
i. Definitions. Explosion, in a general sense, may be defined
as a sudden and violent increase in the volume of a substance.
In a chemical sense, explosion is the extremely rapid conversion
of a solid or a liquid to the gaseous state, or the instantaneous
combination of two or more gases accompanied by increase of
volume. Chemical explosion is always accompanied by great
heat.
An explosion due to physical causes alone, as when a gas
under compression is suddenly released and allowed to expand,
causes cold.
The explosion of gunpowder may be divided into three parts:
ignition, inflammation, and combustion.
Ignition is the setting on fire of a part of the grain or charge.
Gunpowder is ignited by heat, which may be produced by
electricity, by contact with an ignited body, f by friction, shock,
or by chemical reagents.
An ordinary flame, owing to its slight density, will not ignite
powder readily. The time necessary for ignition will vary with
the condition of the powder. Thus damp powder ignites less
easily than dry; a smooth grain less easily than a rough one; a
dense grain less easily than a light one.
" ORDNANCE AND GUNNERY.
Powder charges in guns are ignited by primers, which are fired
by electricity, by friction, or by percussion.
Inflammation is the spread of the ignition from point to point
of the grain, or from grain to grain of the charge.
With small grain powders the spaces between the grains are
small, and the time of inflammation is large as compared with the
time of combustion of a grain; but with modern large grain powders
the facilities for the spread of ignition and the time of burning of
the grain are so great that the whole charge is supposed to be
inflamed at the same instant, and the time of inflammation is not
considered.
Combustion is the burning of the inflamed grain from the sur-
face of ignition inward or outward or both, according to the
form of the grain.
Experiment shows that powder burns in the air according to
the following laws:
1. In parallel layers, with uniform velocity, the velocity being
independent of the cross section burning.
2. The velocity of combustion varies inversely with the density
of the powder.
When a charge of powder is ignited in a gun inflammation of
the whole charge is rapidly completed. The gases evolved from
the burning grains accumulate behind the projectile until the
pressure they exert is sufficient to overcome the resistance of the
projectile to motion. The accumulated gases, augmented by
those formed by the continued burning of the charge, expand into
the space left behind the projectile as it moves through the bore,
exerting a continual pressure on the projectile and increasing its
velocity until it leaves the muzzle.
History. The Chinese are said to have employed an explo-
sive mixture, very similar to gunpowder, in rockets and other
pyrotechny as early as the seventh century.
The earliest record of the use in actual war of the mixture of
charcoal, niter, and sulphur called gunpowder, dates back to the
fourteenth century. Its use in war became general at the begin-
GUNPOWDERS 3
ning of the sixteenth century. Until the end of the sixteenth
century it was used in the form of fine powder or dust. To over-
come the difficulty experienced in loading small arms from the
muzzle with powder in this form, the powder was at the end of
the sixteenth century given a granular form. With the same
end in view attempts at breech loading were made, but without
success, as no effective gas check, which would prevent the escape
of the powder gases to the rear, was devised.
No marked improvement was made in gunpowder until 1860,
win 'ii General Rodman, of the Ordnance Department, U. S. Army,
discovered the principle of progressive combustion of powder, and
that the rate of combustion, and consequently the pressure exerted
in the gun, could be controlled by compressing the fine grained
powder previously used into larger grains of greater density.
The rate or velocity of combustion was found to diminish as the
density of the powder increased. The increase in size of grain
diminished the surface inflamed, and the increased density
diminished the rate of combustion, so that, in the new form,
the powder evolved less gas in the first instants of combustion,
and the evolution of gas continued as the projectile moved through
the bore. By these means higher muzzle velocities were attained
with lower maximum pressures. To obtain a progressively
increasing surface of combustion General Rodman proposed the
orated grain, and the prismatic form as the most convenient
for building into charges. As a result of his investigations powder
was thereafter made in grains of size suitable to the gun for which
intended, small grained powder for guns of small caliber, and
large grained powder for the larger guns. The powders of regu-
granulation, such as the cubical, hexagonal, and sphero-hex-
agonal, came into use, and finally for larger guns the prismatic
powder in the form of perforated hexagonal prisms.
A further control of the velocity of combustion of powder
obtained in 1880 by the substitution of an underburnt char-
coal for the black charcoal previously used. The resulting powder,
called brown or cocoa powder from its appearance, burned more
4
ORDNANCE AND GUNNERY.
slowly than me black powder, and wholly replaced that powder
.in the larger guns.
A still further advance in the improvement of powder was
brought about in 1886 by the introduction of smokeless powders.
These powders are chemical compounds, and not mechanical mix-
tures like the charcoal powders; they burn more slowly than the
Sphero-hexagonal. Prismatic.
charcoal powders, and produce practically no smoke. Smokel*
powders have now almost wholly replaced black and brown pow-
ders for charges in guns. Black powder is used in fuses, primer s
and igniters, in saluting charges, and as hexagonal powder
the smaller charges for seacoast mortars.
2. Charcoal Powders. COMPOSITION. Black gunpowder is
a mechanical mixture of niter, charcoal, and sulphur, in the
proportions of 75 parts niter, 15 charcoal, and 10 sulphur.
The niter furnishes the oxygen to burn the charcoal and sul-
phur. The charcoal furnishes the carbon, and the sulphur gives
density to the grain and lowers its point of ignition.
The distinguishing characteristic of charcoal is its color, being
brown when prepared at a temperature up to 280, from this to
340 red, and beyond 340 black.
Brown powder contains a larger percentage of niter than
black powder, and a smaller percentage of sulphur. A small
percentage of some carbohydrate, such as sugar, is also added.
Its color is due to the underburnt charcoal.
GUNPOWDERS. 5
MANUFACTURE. The ingredients, purified and finely pulver-
ized, are intimately mixed in a wheel mill under heavy iron rollers.
The mixture is next subjected to high pressure in a hydraulic
press. The cake from the press is broken up into grains by rollers,
and the grains are rumbled in wooden barrels to glaze and give
uniform density to their surfaces. The powder is then dried in
a current of warm dry air, and the dust removed. The powder
is thoroughly blended to overcome as far as possible irregularities
in manufacture.
For powders of regular granulation the mixture from the
wheel mill was broken up and pressed between die plates con-
structed to give the desired shape to the grains. Prismatic
powder was made by reducing the mill cake to powder and press-
ing it into the required form.
Smokeless Powders. There are two classes of smokeless
powders used in our service: nitroglycerine powder in small
arms, and nitrocellulose powder in cannon. They are both made
from guncotton, to which is added for the small-arm powder
about 30 per cent by weight of nitroglycerine.
COMPARISON OF NITROGLYCERINE AND NITROCELLULOSE POW-
DERS. The temperature of explosion of nitroglycerine powder is
higher than that of nitrocellulose powder. As the erosion of the
metal of the bore of the gun is found to increase with the tem-
perature of the gases, greater erosion follows the use of nitro-
glycerine powder. The endurance, or life, of a modern gun is
dependent on the condition of the bore, and on account of the
great cost of cannon erosion becomes a more serious defect in
cannon than in small arms. On this account, therefore, nitro-
cellulose powder is more suitable than nitroglycerine powder for
cannon.
To produce a given velocity a larger charge of nitrocellulose
than of nitroglycerine powder is required. This necessitates for
nitrocellulose powder a larger chamber in the gun, and the increase
in size of the chamber involves increased weight of metal in the
gun. This is more objectionable in a small arm than in cannon,
6 ORDNANCE AND GUNNERY.
for the increased weight of the gun and of the charge adds to
the burden of the soldier. For this reason nitroglycerine powder
is more suitable than nitrocellulose powder in the small arm.
In the manufacture of nitroglycerine powders for cannon, a
satisfactory degree of stability under all the conditions to which
cannon powders are exposed was not obtained. In time the
powder deteriorated, and exudation of free nitroglycerine oc-
curred. Detonations and the bursting of guns followed. In the
small-arm cartridge the powder is hermetically sealed, and as
now manufactured appears to possess a satisfactory degree of
stability.
For these reasons nitroglycerine powder has been selected for
use in small arms in our service, and nitrocellulose powder for
use in cannon.
A disadvantage attending the use of nitrocellulose powder
arises from the fact that in the explosion there is not a suffi-
cient amount of oxygen liberated to combine with the carbon
and form C02. The reaction on explosion is approximately
represented by the following equation.
2(C 6 H 7 2 )0 3 (N0 2 ) 3 = 9CO+3C0 2 +7H 2 0+3N.
A large quantity of CO, an inflammable gas, is often left in the
bore. On opening the breech more oxygen is admitted with
the air, and should a spark be present the CO burns violently,
uniting with the oxygen and forming C0 2 . This burning of the
gas is called a flareback. An instance of it has occurred with
disastrous results in a turret gun aboard one of our men-of-war,
the Missouri.
3. Guncotton. Guncotton forms the base of most smoke-
less powders. When dry cotton, C 6 H 10 5 , is immersed in a
mixture of nitric and sulphuric acids part of the hydrogen of
the cotton is replaced by N0 2 from the nitric acid. The sul-
phuric acid takes up the water formed during the reaction and
prevents the dilution of the nitric acid. The nitrated cotton,
GUNPOWDERS. 7
or nitrocellulose, may be of several orders of nitration, depending
on the strength and proportions of the acids, and the tempera-
ture and duration of immersion; as mononitrocellulose, di-
nitrocellulose, trinitrocellulose, according as one or more atoms
of hydrogen are replaced. All nitrocellulose is explosive, and
the order of explosion produced is higher as the nitration is higher.
Dinitrocellulose and trinitrocellulose are used in the manu-
facture of smokeless powders. The lower orders of nitrocellulose,
containing less than 12.75 per cent of nitrogen, are soluble in,
a mixture of alcohol and ether. Trinitrocellulose contains a
higher percentage of nitrogen, and is insoluble in alcohol and
ether but soluble in acetone.
MANUFACTURE OF GUNCOTTON FOR SMOKELESS POWDERS.
The process followed is practically the same for all varieties, the
nitration being stopped at the point desired in each case.
The cotton used is the waste or clippings from cotton mills.
It is first finely divided and then freed from grease, dirt, and other
impurities by boiling with caustic soda. After cleansing it is
passed through a centrifugal wringer and then further dried in
a dry-house.
The dry cotton is immersed in a mixture of about three parts
sulphuric acid and two parts nitric acid for about fifteen minutes;
after which the cotton is run through a wringer to remove as
much acid as possible. It is then thoroughly washed or drowned.
After this washing the guncotton is reduced to a pulp and
further washed to remove any trace of acid which may have been
freed in pulping, carbonate of soda being added to neutralize
the acid.
The water is then partially removed from the pulp by hy-
draulic pressure, and the dehydration is completed by forcing
alcohol under high pressure through the compressed cake.
4. Nitroglycerine Small-arm Powder. Laflin and Rand,
W. A. In the manufacture of this pow r der highly nitrated gun-
cotton called insoluble nitrocellulose is used. It is insoluble in
ether and alcohol but soluble in acetone.
8 ORDNANCE AND GUNNERY.
The powder is composed of
Insoluble nitrocellulose 67.25 per cent
Nitroglycerine 30.00 per cent
Metallic salts 2.75 per cent
Forty pounds of acetone serve as solvent for 100 pounds of the
above mixture.
The nitroglycerine and acetone are first mixed. The acetone
makes the nitroglycerine less sensitive to pressure or shock, and
therefore less dangerous to handle in the subsequent operations.
The dried guncotton is spread in a large copper pan, the finely
ground metallic salts are sifted over it, and the mixed nitrogly-
cerine and acetone are sprinkled over both. The whole is mixed
by hand by means of a wooden rake for a period of about ten
minutes, the object of the mixing being to thoroughly moisten
the guncotton for the purpose of eliminating the danger from
the presence of dry guncotton in the next operation. The mixed
mass is put into a mixing machine, where it is mechanically mixed
for a period of three hours. It comes from the mixing machine
in the form of a colloid or jelly like paste. It is then stuffed
and compressed into brass cylinders, from which it is forced by
hydraulic pressure through dies fitted with mandrels. It comes
from the die in the form of a long hollow string or tube, and is
received on a belt which carries it over steam pipes into baskets.
The drying which it receives while on the belt strengthens the
tube, and after remaining half an hour in the baskets it becomes
sufficiently tough to be cut into grains. This is done in a machine
provided with revolving knives. The resulting grains are bead-
shaped single perforated cylinders and have a length of about
one twentieth of an inch. The powder is dried for two or three
weeks at a temperature not to exceed 110 F. It is then thor-
oughly mixed twice in the blending barrels and graphited at the
same time. It is carefully screened to remove large grains, dust,
and foreign matter, and is packed in muslin bags in metallic
barrels holding 100 pounds.
GUNPOWDERS. 9
Cordite. This is an English nitroglycerine powder, composed
of 58 per cent of nitroglycerine, 37 per cent of guncotton, and
5 per cent of vaseline. The vaseline serves to render the powder
water proof and improves its keeping qualities. For small arms
the powder is made in the form of slender cylindrical rods, the
length of the chamber of cartridge. For cannon it is in thicker
and longer rods, in tubular form, or in the form of perforated
cylinders. For heavy guns a powder called Cordite M. D.
has lately been introduced. The composition (30 parts nitro-
glycerine, 65 parts guncotton, 5 parts vaseline) is very simi-
lar to that of our small-arm powder. The reduction in the per-
centage of nitroglycerine was made for the purpose of lowering
the temperature of explosion and reducing the erosion in the
bore.
Wetteren Powder. A nitroglycerine powder manufactured at
the Royal Belgian Factory at Wetteren. The solvent used is
amyl acetate.
5. Manufacture of Nitrocellulose Powder. The guncotton
used contains 12.65 per cent of nitrogen, and is soluble in the
ether-alcohol mixture. It is prepared as previously described,
the dehydration with alcohol being so conducted that when com-
pleted the proper proportion of alcohol for solution remains in
the cake. The guncotton cake is broken up and ground until
it is free from lumps, and is then placed in a mixing machine
with the proper amount of ether, tw r o parts of ether to one of
alcohol. During the mixing the temperature is kept at 5 C.
to prevent loss of the solvent.
The powder comes from the mixing machine as a colloid, and
the remaining processes are similar to those described for nitro-
glycerine powder.
After graining, the solvent is recovered by forcing heated air
over the powder. The ether and alcohol vapors are collected
and afterwards condensed for further use. The powder is dried
for a period varying from six weeks to three months, depending
on the size of the grain. The drying is never complete, a small
10
ORDNANCE AND GUNNERY.
percentage of the solvent always remaining, but care is taken
that the remaining percentage shall be uniform.
In the manufacture of all powders uniformity in the product
can only be obtained by the strictest uniformity in the quantities
and quality of the substances used, and in the conduct of the
various processes.
Cannon powders are, as a rule, not graphited.
Other Smokeless Powders. The length of time requii
for the drying of nitrocellulose powders has led to the develop-
ment of other powders that require little or no time to dry.
Two such powders have been tested. One, stabilite, is com-
posed of nitrocellulose with or without nitroglycerine and a sol-
vent that is itself an explosive and not volatile. The other is
similar to the present nitrocellulose powders except that dinitro-
cellulose is used in its manufacture instead of trinitrocellulose.
To make up for the insufficiency of oxygen in nitrocellulose,
already referred to, a number of smokeless powders are made
by a combination of nitrocellulose with nitroglycerine or with
the nitrates of barium, potassium, and sodium. The nitroglyc-
erine or the metallic nitrates furnish the oxygen which is deficient
in the nitrocellulose.
E. C. Powder. This powder contains both soluble and insolu-
ble nitrocellulose and the nitrates of barium, potassium, anc
sodium. It is yellow in color and of fine granulation. It is
easily ignited quick burning powder and is used in our service i]
blank small-arm cartridges.
Schultze Powder, the type of smokeless sporting powders, is oi
constitution similar to that of E. C. powder.
Troisdorf Powder, used in the German service, and B. N. PC
der, in the French service, are other powders similarly constituted.
All these powders differ principally in the proportion of the ingre-
dients, and also in the organic substance used as a cementing
agent.
Maxim Powder is composed of nitrocellulose, both soluble and
insoluble, nitroglycerine, and a small percentage of sodium carbonate.
GUNPOWDERS. 11
Form and Size of Grain. For most cannon in our service
the powder is formed into a cylindrical grain with seven longi-
tudinal perforations, one central and the other six equally dis-
tributed midway between the center of the grain and its circum-
ference. A uniform thickness of web is thus obtained. The
powder is of a brown color and has somewhat the appearance
of horn. The length and diameter of the grain vary in powders
for different guns, the size of grain increasing with the caliber
of the gun. For the 3-inch rifle the grain has a length of about
| of an inch and a diameter of T 2 g- of an inch. For the 12-inch
rifle the length is 1J inches and the diameter of an inch. For
some of the smaller guns the grains are in the form of thin flat
squares.
In other services cannon powders are made into grains of
various shapes. Cubes, solid and tubular rods of circular cross
section, flat strips, and rolled sheets are among the forms that
have been used.
6. Proof of Powders. All powders used by the Army are
furnished by private manufacturers. The materials and processes
employed in the manufacture are prescribed by the Ordnance
Department in rigid specifications, and the manufacture in all
its stages is under the inspection of the Department. The proof
of the powder consists of tests made to determine its ballistic
qualities, its uniformity, and its stability under various condi-
tions. Its ballistic qualities and uniformity are determined from
proof firings made in the gun for which the powder is intended.
The required velocity must be obtained without exceeding the
maximum pressure specified. The mean variation in velocity
in a number of rounds must not exceed, in the small arm 12 feet
per second, in cannon 1 per cent of the required velocity.
The stability of the powder under various conditions is deter-
mined by heat tests, and by a number of special tests. For small-
arms powder the heat test consists in subjecting the powder,
pulverized, to a temperature of 150 to 154 F. for 40 minutes.
It must not in that time emit acid vapors, as indicated by the
12 ORDNANCE AND GUNNERY.
slightest discoloration of a piece of iodide of potassium starch
paper partially moistened with dilute glycerine. The other tests
consist in exposing the powder both loose and loaded in car-
tridges, to heat, cold, and moisture, for periods varying- from six
hours to one week. When fired the variations in velocities and
pressures must not exceed specified limits.
Nitrocellulose cannon powders are subjected to a heat of
135 C. (275 F.) for five hours. Acid fumes, as indicated by
the reddening of blue litmus paper, must not appear under expcK
sure of an hour and a quarter, nor red nitrous fumes under two
hours. Explosion must not occur under five hours. Other tests
are made for the determination of the loss of weight when sub-
jected to heat, of the moisture and volatile matter in the powder,
of the quantities of nitrogen in the powder, and of ash in the
cellulose.
For the proper regulation of the evolution of gas in the gun
it is important that the grains of smokeless powder retain their
general shape while burning. If they break into pieces under the
pressure to which they are subjected, the inflamed surface is
increased, gas is more quickly evolved, and the pressure in the
gun is raised. The powder is therefore subjected to a physical
test to determine that the grain has sufficient strength and tough-
ness. The grains are cut so that the length equals the diameter,
and are then subjected to slow pressure in a press. The grain
must shorten 35 per cent of its length before cracking.
Powder grains incompletely burned, that have been recovered
after firing, show that the burning proceeds accurately in parallel
layers. The outer diameter of the grain is reduced and the diam-
eter of the perforations increased in exactly equal amounts.
7. Advantages of Smokeless Powder. The advantages ob-
tained by the use of smokeless powder are due almost wholly
to the fact that the powder is practically completely converted
into gas. The experiments of Noble and Abel show that the
gases evolved by charcoal powders amount to only 43 per cent
of the weight of the powder, and part of the energy of this quan-
GUNTOWDERS. 13
tity of gas is expended in expelling the residue from the bore. A
smaller quantity of smokeless powder will therefore produce an
equal weight of gas, and with smaller charges we may give to
the projectile equal or higher velocities. The smokelessness of
the powder and the absence of fouling in the bore are also due
to the complete conversion of the powder into gas.
Ignition and Inflammation of Smokeless Powder. Though
the temperature at which smokeless powder ignites, about 180
C., is much lower than that required for the ignition of black
powder, 300 C., the complete inflammation of a charge com-
posed only of smokeless powder takes place more slowly than
the inflammation of a charge of black powder. This is due to
the slower burning of the smokeless powder and the consequent
delay in the evolution of a sufficient quantity of the heated gas
to completely envelop the grains composing the charge. In the
long chamber of a gun the gases first evolved at the rear of the
charge may, in expanding, acquire a considerable velocity. The
pressure due to their energy is added to the static pressure due
to their temperature and volume, thus increasing the total pres-
sure in the gun. The movement of the gases back and forth
causes what are called wave pressures, and if the complete ignition
of the charge is delayed until the projectile has moved some
distance down the bore, there may result at some point in the
gun a higher pressure than the metal of the gun at that point
can resist.
For this reason and in order to insure the practically instan-
taneous ignition of the whole charge, small charges of black powder
are added to every smokeless powder charge. The priming
charges of black powder insure against hang-fires and misfires,
arid by producing uniformity of inflammation assist toward uni-
formity hi the ballistic results.
In addition, in order to prevent as far as possible the pro-
duction of wave pressures, the charge of powder, whatever its
weight, is given when practicable a length equal to the length
of the chamber.
14 ORDNANCE AND GUNNERY.
8. Powder Charges. The powder for a charge in the gun is
inserted in one or more bags, depending upon the weight of the
charge. The bags are made of special raw silk and are sewed
with silk thread. The ends of each bag are double, and between
the two pieces at each end is placed a priming charge of black
powder, quilted in in squares of about two inches and uniformly
spread over the surface.
The charge is inserted through an unsewed seam at one end,
and the seam is then sewed. The bag, purposely made large,
is then drawn tight around the charge by lacing drawn with a
needle between two pleats on the exterior. Two priming pro-
tector caps are then drawn over the ends of the bag and fastened
by draw strings. In the bottom of each cap is a disk of felt which
serves to keep moisture from the priming charge and prevents
the loss of the priming through wearing of the bottom of the
bag. For convenience in handling the charge a cloth strap is
attached to each protector cap. By means of the straps the pro-
tector caps may be pulled off without undoing the draw strings
when the charge is to be inserted in the gun.
The illustrations show a bag filled ready for lacing, and a
bag filled and laced and provided with the priming protector
caps.
The weight of each portion of the charge should not be
greater than can be readily carried by one man. Thus the charge
of 360 pounds for the 12-inch rifle is put up in four bags each hold-
ing 90 pounds.
As previously stated, the charge whatever its weight is made
up if practicable of a length nearly equal to that of the cham-
ber, with a minimum limit of nine tenths of that length.
Raw silk does not readily hold fire. With powder bags made
of cotton cloth it occasionally happens that a fragment of the
bag remains burning in the s bore, and to this fact is ascribed the
flarebacks that have occurred. Powder bags treated with chem-
icals to render them non-inflammable have also been tried. Am-
monium phosphate is found to be the best agent for this purpose.
Bag filled ready
for lacing
Bag laced and provided
with priming pro-
tector caps.
SECTION OF POWDER CHARGE FOR HEAVY GUNS.
GUNPOWDERS. 15
A nitrocellulose cloth which will burn up completely and leave
no residue has been used as a material for powder bags, but
as the charge of powder enclosed in this material is much more
subject to accidental ignition by a chance spark, the nitrocellu-
lose cloth is not generally adopted.
The powder charge in fixed ammunition is placed loose in
the cartridge case.
In fixed ammunition for cannon one or two wads of felt
placed on top of the powder fill the space in the case behind the
projectile. The priming charges of black powder are contained
in the primer, which is inserted in the head of the cartridge case,
and between two disks of quilted crinoline at the forward end
of the charge.
Blank Charges. If the same smokeless powder that is pre-
scribed for use with the projectile in any piece is used in a blank
charge, the grains are not subjected to the pressure under which
they were designed to burn, and consequently they burn very
slowly and many of them are ejected from the bore only partially
consumed. The report made by the explosion under these cir-
cumstances is unsatisfactory for saluting purposes.
To produce a sharper report a more rapid evolution of gas is
necessary, which requires, if smokeless powder is employed, the
use of a smaller grain, or one that is porous through imperfect
colloiding. It has been found that a satisfactory report can be
obtained from a blank charge of smokeless powder only by the
use of a grain so small or of such a nature that the rate of evolu-
tion of the gas becomes excessive. This has resulted, in several
instances, in the bursting of the gun.
For this reason black powder only has been used in saluting
charges. A nitrocellulose powder, called the Thorn smokeless
saluting powder, has recently given satisfactory results in blank
charges. The powder is in flat cross-shaped grains, about f of
an inch in length and breadth. It is of low density and has the
appearance of blotting-paper.
16
ORDNANCE AND GUNNERY.
COMBUSTION OF POWDER UNDER CONSTANT
PRESSURE.
9. Quantity Burned when any Thickness has Burned.
Under constant pressure, as in the air, a grain of powder burns
in parallel layers and with uniform velocity, in directions per-
pendicular to all the ignited surfaces.
Under the variable pressure in the gun powder burns with
a variable velocity, but, as has been previously stated, modern
smokeless powders burn accurately in parallel layers in the gun.
A determination of the volume burned when any thickness of
layer is burned will therefore be useful when we come to con-
sider the burning of the powder in the gun.
Powders of irregular granulation may be considered as com-
posed of practically equivalent grains of regular form.
Let IQ be one half the least dimension of the grain,
I the thickness of layer burned at the time t,
So the initial surface of combustion,
S the surface of combustion at the time t, when a thick-*
ness I has been burned,
S' the surface of combustion when Z = Zo,
VQ the initial volume of the grain,
V the volume burned at the time t,
F = V/V the fraction of grain burned at the time t.
The least dimension of the grain, 21 , is called the web of the
grain. As the burning proceeds equally in directions perpen-
dicular to all the surfaces, the grain will, in most instances, be
about to disappear when the thickness of layer burned is nearly
equal to 1 . The surface ', corresponding to this thickness, is
therefore called the vanishing surface.
A general expression may be written for the burning surface
of a grain when a thickness I has been burned. Since a surface
is a quantity of the second degree the expression will be of the
form,
GUNPOWDERS. 17
in which a and b are numerical coefficients whose values depend
on the form and dimensions of the grain.
For grains that burn with a decreasing surface the sign of
a in this equation will later be found to be negative, and for those
that burn with an increasing surface the sign of b becomes nega-
tive
The volume burned when any thickness I has been burned is
And substituting for S its value from equation (1),
~
(2)
Dividing both members by F and introducing 1 by multiplica-
tion and division we have, for the fraction of the grain burned,
V o V ^0 [ ^^0 ^0 OOQ'
and making
a=S Q lo/V * = al /2So fjL = bl 2 /3S Q (3)
we obtain
This equation gives the value for the fraction of the grain
burned when a length I has been burned; and as each grain in
a charge of powder burns in the same manner, the equation also
expresses the value for the fraction of the whole charge burned.
The quantities a, A, and p. are called the constants of form
of the powder grain. Their values depend wholly on the form
and relative dimensions of the grain.
18
ORDNANCE AND GUXXERY.
When l = k the whole grain is burned, F becomes unity, and
we have the relation
l= a (l + X+p) (5)
which may always serve to test the correctness of the values
of these constants as determined for any grain.
10. Determination of the Values of the Constants of Form
for Different Grains. In the values of a, X, and //, equations (3),
the quantities So, IQ, and V are known for any form of grain.
We must know in addition the values of a and 6.
When 1 = 1 the volume burned is the original volume V
and equation (2) becomes
The burning surface at this time, designated by S', is, from
equation (1),
The values of a and 6, if desired, may be derived from these
two equations.
Combining the two equations with equations (3) we obtain
the following values for a, ^, and p.
a = S l /V
(6)
The Vanishing Surface. The quantity S', which represents
the vanishing surface, or surface of combustion when l = lo, re-
quires explanation. A spherical grain burning equally along all
the radii becomes a point as I becomes equal to 1 . S' for a
sphere is therefore 0, and similarly for a cube. A cylindrical
grain, of length greater than its diameter, becomes a line when
l = k. S' is therefore for this cylinder. A flat square grain
GUNPOWDERS. 19
remains flat throughout the burning, its thickness being reduced
until as I becomes equal to Z there are two burning surfaces with
no powder between them. S', in this case, is the sum of these
two surfaces.
PARALLELOPIPEDON. Let 21 be the least dimension, and m
and n the other dimensions of the grain of powder, m being the
longer.
So = 4? w -f 4Z n + 2mn
S'=2(m-2Z )(n-2/o)
FO = 2l Q mn
Make x and y the ratios of the least dimension to the other dimen-
sions of the grain
x = 2l /m y
With these values we get from (3) for a
Eliminating the common factors in the values of S' and So
we have,
S' mn- 2l n-2l m+4lo 2
S ~ 2l Q m+2l n+mn
and dividing each term by mn,
S' l-2l /m-2l /n+4l<?/mn l-x-
S 2/o/n+2/oM+l 1 + x+y
Substituting in equations (6),
, x+y+xy
~ l + *+2/
**~l + x + y
20 ORDNANCE AND GUNNERY.
For the parallelopipedon grain, the general expression for the
fraction of the grain burned when a thickness I has been burned
therefore becomes, by equation (4),
U xyxyl_ xy _g_| ( .
' 1 + x+y k * ' ~' "
And by giving various values to x and y this equation may be
applied to any form of the parallelepiped.
ii. Cube. For instance, for the cube m = n = 2l Q , and x and y
are unity. Therefore
a = 3 A=-l / = l/3
and
(8)
Strip. For strips or ribbons of square cross section n = 2Zo
and 2/ = l,
l + 2x x
" 2 + x fi ~2 + x
If the strip is very long in comparison with the edge of cross
section, x is practically zero and
Square Flat Grains. For square flat grains x = y and
x(2 + x) x 2
If the grains are very thin, x is small compared with unity and
As the surface and volume of a burning sphere of powder vary
with the diameter in precisely the same manner that the surface
GUNPOWDERS. 21
and volume of a cube vary with the edge of the cube, the values
a, A, and /*, see equations (6), will be the same for the sphere
as for the cube. And similarly the values of these constants for
a cylinder of length greater than its diameter will be the same as
for the strips of square cross section, and the values for a flat
cylinder will be the same as for the flat square grain.
SPHERE. For the sphere,
the same as for the cube.
12. SOLID CYLINDER. For the solid cylinder of length greater
than the diameter, d = 2l and x = 2lo/m,
If the diameter is very small compared with the length, as in
the slender cylinders or threads of cordite, 21 is small with respect
to m, x is small compared with unity, and approximately
a =2 A =-1/2 jf =
Therefore for cordite
(9)
FLAT CYLINDER. 2Z = thickness, d = diameter, x=2l t) /d,
x(2 + x) x*
A= -
the same as for the flat square grain.
SINGLE PERFORATED CYLINDER. Let R be the outer radius of
the grain, r the radius of the perforation, and m the length of the
22 ORDNANCE AND GUNNERY.
grain. Make x=2l Q /m. By proper substitution we find, for the
tubular grain in general,
If the grain is very long compared with its thickness of wall,
x is small compared with unity. We then have
A=0
and
(10)
This indicates for long tubes with thin walls a constant emis-
sion of gas during the burning of the grain, since F now varies
directly with I.
13. MULTIPERFORATED CYLINDER. A section of the service
multiperf orated grain before burning is shown in Fig. 1. The
FIG. 1.
FIG. 2.
perforations are equal in diameter and symmetrically distributed.
The web, 2fo, is the thickness between any two adjacent circum-
ferences. When this thickness has burned the section is as shown
in Fig. 2.
There remain now six interior and six exterior three-cornered
pieces, called slivers, which burn with a decreasing surface until
completely consumed.
The method previously followed cannot be used to find the
value of F for the multiperf orated grain because the law of burn-
GUNPOWDERS.
23
ing for this grain changes abruptly when the grain is but partially
consumed.
To find the value of F for this grain we proceed as follows.
Let R be the radius of the grain, r the radius of each perfora*
tion, m the length of the grain.
I^or the initial volume we have
V Q = 7tm(R 2 -7r 2 )
When a thickness I is burned, R, r, and m become respectively
R I, r+l, and m2l, and the volume remaining is obtained from
the above equation by making these substitutions. The differ-
ence between the two volumes will be the volume burned, and
dividing this resulting volume by V we have the value of F.
This may be reduced to
F =
m(R 2 -7r 2 )
For the service multiperf orated grain we therefore have
m(R 2 -7r 2 )
R 2 -7r 2 +
(12)
Equation (11) applies only while the web of the grain is burn-
ing and does not apply to the slivers.
The thickness of web bears the following relation to R and r
24 ORDNANCE AND GUNNERY.
in our service grains, as may be readily seen by drawing a diam-
eter through any three perforations, Fig. 1.
We will take a specific grain for use later to illustrate the
burning of the multiperf orated cylinder. The grains of a lot of
powder for the 8-inch rifle had the following dimensions, in inches.
# = 0.256 r = 0.0255 m = 1.029
Therefore, from (13), 1 Q = 0.044875.
Substituting in (11), we obtain for this grain
F = 0.72667^-1 1 + 0.19590^ 0.02378^-1 (14)
When l = lo, that is, when the grain is reduced to slivers,
7^ = 0.85174
from which we see that the slivers form about 15 per cent of this
particular grain.
14. Emission of Gas by Grains of Different Forms. As
the velocity of combustion under constant pressure is uniform,
the time of burning will be proportional to the thickness of layer
burned.
We may conveniently show the manner of burning of the
different grains by dividing the half web into five layers of equal
thickness, that is, by giving to the ratio 1/1 , in the value of the
fraction burned, the values 1/5, 2/5, etc., in succession, and
then tabulating the resulting values of F. The successive values
of F obtained will be the fractional parts burned in 1/5, 2/5,
etc., of the total time of burning; and the differences of the suc-
cessive values of F will be the fractions burned in the successiva
intervals of time.
GUNPOWDERS.
25
The following table is formed from equations (8), (9), and
(14). For the multiperf orated grain the fractions 1/1 are frac-
tions of the web onlv.
I 'Jo
Cube.
Slender Cylinder.
Multiperforated Cylinder.
F.
Difference.
F.
Difference.
F.
Difference.
0.0
0.000
0.00
0.00
0.49
0.36
0.15
0.2
0.49
0.36
0.15
0.29
0.28
0.16
0.4
0.78
0.64
0.31
0.16
0.20
0.17
0.6
0.94
0.84
0.48
0.05
0.12
0.18
0.8
0.99
0.96
0.66
0.01
0.04
0.19
1.0
1.00
1.00
1.00
1.00
Web 0.85
0.85
0.15
Whole grain 1 . 00
1.00
Regarding the columns of differences in the table we see
that nearly half of the cubical grain is burned in the first layer,
and that the volume burned in the successive layers decreases
continuously. The slender cylinder emits at first a less volume
of gas than the cube and later a greater volume, that is, its burn-
ing is more progressive. We have seen, equation (10), that the
long tubular grain burns with a constant surface. The quantity
of gas given off in the burning of each layer is therefore the same,
and the grain is more progressive than the slender cylinder. The
multiperforated cylinder burns with a continually increasing
surface until the web is consumed, and the volume of gas given
off increases for each layer burned.
Whether the burning surface of the multiperforated grain
increases or decreases depends on the relation between the length
of the grain and the radii of the grain and of the perforations.
Referring to equation (11) it will be seen that when
(15)
26 ORDXANCE AXD GUXNERY.
the secoad term within the brackets disappears, m is the length
of the grain. Giving to the multiperf orated grain considered in
equation (14) the length indicated in the last equation, we get
m = 0.29, and the value of F becomes
' I - x-x rx^- r^ A *
1 O I
F = 0.94892-H1- 0.08134 ,
to I to" J
A table formed from this equation will show that this grain
burns with a continuously decreasing surface; the fractional
volumes burned in the successive intervals being 0.189, 0.186,
0.178, 0.167, and 0.152. The sum of these, 0.872, is the frac-
tion of the grain burned when the web ceases to burn.
It is apparent that since the manner of burning of a multi-
perforated grain depends upon the relation expressed in equa-
tion (15), a grain may start to burn with an increasing surface,
and change, as the length is diminished, to burn with a decreas-
ing surface.
The multiperforated grains used in our service are of lengths
considerably greater than that indicated in equation (15). The
length of the grain is about 2J times the outer diameter. The
diameter of the perforations is about 1/10 the exterior diameter
of the grain. The grains burn with a continuously increasing
surface until the web is burned, and then with a decreasing sur-
face.
The Weight of Charge Burned. Assuming instant ignition
of the whole charge, equation (4) expresses the value of the frac-
tion of the charge burned when any thickness, Z, has burned.
Let (i) be the weight of the charge,
y the weight burned at any instant.
The fraction of the charge burned is therefore ?//#, which
we may write for F in equation (4), and obtain
GUNPOWDERS. 27
15. Consideration as to Best Form of Grain. It would
appear that the most desirable form of powder grain would be
one that gives off gas slowly at first, starting the projectile before
a high pressure is reached, and then with an increased burning
surface and a more rapid evolution of gas maintaining the pres-
sure behind the projectile as it moves down the bore.
It is this consideration that has led to the adoption in our
service of the multiperforated grain, which in the preceding
discussion is shown to be the only practicable form of grain that
burns with an increasing surface emitting successively increasing
volumes of gas. The facilities for complete inflammation of the
charge are not as great in this grain as in some others, as the
grains assume all positions in the cartridge bag, and do not pre-
sent unobstructed channels to the flame from the igniter. We
have seen, page 13, that when there is delay in the complete
inflammation of the charge, excessive pressures, called wave pres-
sures, may arise, due to the velocity acquired by the gases first
formed.
The single perforated cylinder, or tubular grain, offers advan-
tages in this respect. This grain when its length is great com-
pared to the thickness of web, as when cut hi lengths to fit the
chamber, burns with a practically constant surface, as we have
seen, equation (10). The charge is readily prepared by bind-
ing the grains in bundles, and when so prepared offers perfect
facilities for the prompt spread of ignition through the uniformly
distributed longitudinal air spaces within and between the grains.
While larger charges of powder in this form may be required,
to produce a desired velocity, the advantages of greater uni-
formity in velocities and pressures, and decreased likelihood of
excessive pressures, will probably be obtained by its use.
In the process of drying the tubular grain in manufacture
the grain will warp excessively if too long with reference to its
diameters. On this account and in order that the grain may
serve for convenient building into charges its length is limited.
The requirement of prompt ignition throughout the length of tho
28 ORDNANCE AND GUNNERY.
grain also limits its length. Good results have been obtained wil
grains whose length was 85 times the outer diameter.
VARIOUS DETERMINATIONS.
16. To Determine the Number of Grains in a Pound. Lei
n be the number of grains in a pound of powder,
VQ the volume of each grain in cubic inches,
d the density of the powder.
The volume occupied by the solid powder in one pound is
evidently n7 ; the volume of one pound of water is 27.68 cu.
in. ; and the volumes being inversely proportional to the den-
sities, we obtain
-?Sr (17]
and when the number of grains in a pound is known, we have
for the density
d = ^T (18)
To Determine the Dimensions of Irregular Grains. Irreg-
ular grains may be considered as spheres, and the mean radius
may be determined as follows. Retaining the above significa-
tions of n and V , let r be the mean radius of the grains in inches.
Then 7 = 4^r 3 /3. Substituting this in the above equation
and solving for r we obtain
1.8766
Comparison of Surfaces. Let Si be the total initial surface
of the grains in a pound of powder. As S is the initial surface
of each grain,
GUNPOWDERS.
29
Substituting the value of n from (17) and the value of So from
the first of equations (3) we obtain
- c
(19)
From which it appears that for two charges of equal weight,
made up of grains of the same density and thickness of web,
the initial surfaces of the two charges are to each other as the
values of a for the two forms of grain. For charges of equal
weights composed of grains of the same shape and density the
initial surfaces will be inversely proportional to the least dimen-
sions of the grains.
17. Density of Gunpowder. The density, or specific gravity,
of gunpowder is the ratio of the weight of a given volume of solid
powder to the weight of an equal
volume of water. The density of
charcoal gunpowders is determined
by means of an instrument called
the mercury densimeter, in which is
obtained the weight of a volume of
mercury equal to the volume of the
powder. From the known specific
gravity of the mercury that of the
powder is readily determined. Mer-
cury is used in the instrument instead
of water because mercury possesses
the property of closely enveloping
the grains of powder without being
absorbed into their pores, and it
not dissolve the constituents of
the powder.
The densimeter is shown in the
accompanying figure. The glass globe FlG 3
a is connected with an air pump by
the rubber tube c. The lower outlet of the globe is immersed
in mercury in the dish d.
30
ORDNANCE AND GUNNERY.
As the globe is exhausted of air by means of the air pump, the
mercury is drawn upward until it fills the globe and stands at a
certain height in the glass tube e. The globe is then detached,
full of mercury, and weighed. It is then emptied, and a given
weight of powder placed in it. The globe is then returned to its
original position, the air again exhausted, and mercury allowed to
enter until it stands at the same height as before. The globe,
now filled with mercury and powder, is again detached and weighed.
With the difference of the two weights we may arrive at the
weight of the mercury whose volume is equal to that of the powder,
in the following manner.
Let w be the weight of the powder,
P the weight of the vessel filled with mercury,
P' the weight of the vessel filled with mercury and powder,
D the density of the mercury, about 13.56,
d the density of the powder.
Then P' w = the weight of the mercury and vessel when the
latter is partially filled with powder,
P (P f w) = the weight of the volume of mercury displaced
by the powder.
Since the weights of equal volumes are proportional to the
densities, we have
w \P-P'
:D
or
wD
P-P'+w
The density of charcoal powders varies between 1 68 and
1.85.
SMOKELESS POWDER. The nitrocellulose smokeless powders
are affected by mercury; therefore if the densimeter is used in
the determination of the densities of these powders, water must
be used in the instrument in place of mercury. The density of
large grained powders may be determined by weighing a grain
GUNPOWDERS. 31
of the powder in air and in water. The difference of the weights
in air and water is the weight of a volume of water equal to the
volume of the grain. The density is then the weight in air divided
by the difference of the weights.
The density of smokeless powders varies from 1.55 to 1.58.
CHAPTER II.
MEASUREMENT OF VELOCITIES AND PRESSURES.
1 8. Measurement of Velocity.
In measuring the velocity of a pro-
jectile the time of passage of the
projectile between two points, a
known distance apart, is recorded
by means of a suitable instrument.
The calculated velocity is the mean
velocity between the two points,
and is considered as the veloc-
ity midway between the points. In
order that this may be done without
material error, the two points must
be selected at such a distance apart
in the path of the projectile that the
motion of the projectile between th
points may be considered as uni-
formly varying, and the path a right
line.
Le Boulenge Chronograph. The
instrument generally employed for
measuring the time interval in the
determination of velocity was in-
vented by Captain Le Boulenge of
the Belgian Artillery, and is called
the Le Boulenge Chronograph. It
has been modified and improved by
Captain Breger of the French ArtP-
32
FIG. 4.
MEASUREMENT OF VELOCITIES AND PRESSURES. 3tf
lery. The brass column, a Fig. 4, supporting two electromagnets, I
and c, is mounted on the triangular bedplate d which is provided with
levels and leveling screws. The magnet b supports the long rod e>
called the chronometer, which is enveloped when in use by a zinc or
copper tube /, called the recorder. A nut above the recorder, shown
in Fig. 10, holds the recorder fixed in place on the chronometer rod.
The magnet c which supports the short rod g, called the registrar,
is mounted on a frame which permits it to be moved vertically
along the standard. Fastened to the base of the standard is the
Hat steel spring h which carries at its outer end the square knife i.
The knife is held retracted or cocked by the trigger / which is
acted upon by the spring k. The chronometer e hangs so that one
element of the enveloping tube or recorder is close to the knife.
When the knife is released by pressure on the trigger it flies out
under the action of the spring h and indents the recorder. The
registrar g hangs immediately over the trigger. When the electric
circuit through the registrar magnet is broken the registrar falls
on the trigger and releases the knife. The tube / supports the
registrar after it has fallen through it. Adjustable guides are
provided to limit the swing of the two rods when first suspended.
The stand or table on which the instrument is mounted is pro-
vided with a pocket which receives the chronometer when it
fulls, at the breaking of the circuit that actuates its magnet.
A quantity of beans in the bottom of the pocket arrests the fall
of the chronometer without shock.
In the use of the chronograph in measuring the velocity of
a shot the following accessory apparatus is required: targets,
itats, disjunctor, and measuring rule.
Targets. Two wire targets, each made of a continuous wire,
Fi<r. r>. are erected in the path of the projectile. The targets
form purls of. electric circuits which include the electromagnets
of the chronograph. Each magnet has its own target and its
own circuit independent of the other. The circuit from the nearer
or first target includes the chronometer magnet; the circuit from
34
ORDNANCE AND GUNNERY.
FIG. 5.
the second target includes the registrar magnet. On the passage
of the projectile through the first target the circuit
is broken, the chronometer magnet demagnetized,
and the long rod, or chronometer, falls. When the
projectile breaks the circuit through the second tar-
get the short rod, or registrar, falls and, striking
the trigger, releases the knife, which flies out and
marks the recorder at the point which has been
brought opposite the knife by the fall of the chro-
nometer.
In some instruments the chronometer circuit is.
led through a contact piece not shown, carried by the spring h,
and so arranged that the chronometer circuit cannot be close(
until the knife is cocked. This arrangement prevents the loss of
a record through failure to cock the knife when suspending the
rods before the piece is fired.
The first target must always be erected at such a distance
from the gun that it will not be affected by the blast. For small
arms it is placed three feet from the muzzle and consists of fine
copper wire wound backward and forward over pins very close
together. For cannon it is placed from 50 to 150 feet from the
muzzle, depending upon the size of the gun. For the measure-
ment of ordinary velocities the targets are usually placed 1(
feet apart for small arms and 150 feet for cannon.
The second target for small arms consists of a steel plate
stop the bullets, having mounted on its rear face, and insulal
from it by the block w, Fig. 6,
a contact spring s, contact pin p,
and their binding screws. When
the bullet strikes the plate the
shock causes the end of the spring
to leave the pin, and thus breaks
the circuit, which is immediately reestablished by the reaction of
the spring. By means of this device constant repairing of the
target is avoided.
w
FIG. 6.
MEASUREMENT OF VELOCITIES AND
35
1 9. The Rheostat. Both circuits are led independently
through rheostats, by means of which the resistance in the cir-
cuits may be regulated, and the
strength of the currents through
the two magnets equalized. One
form of rheostat is shown in
Fig. 7. The current passes through
the contact spring a and through
a German silver wire wound in
grooves on the wooden drum b.
By turning the thumb nut c the
contact spring is shifted, and more
or less of the wire is included in
the circuit.
Another form of rheostat,
through which both circuits pass
FIG. 7.
independently, is shown in Fig. 8.
Each current passes through a strip of graphite, a, and the resist-
ance in the circuit may be increased or diminished by sliding the
FIG. 8.
contact piece b so as to include a greater or less length of the
graphite strip in the circuit.
The Disjunctor. Both circuits also pass independently through
an instrument called the disjunctor, by means of which they may
be broken simultaneously. The disjunctor is shown in elevation
and part section in Fig. 9. The two halves of the instrument are
exactly similar. The two contact springs c, weighted at their
free ends, bear against insulated contact pins e, supported in the
same metal frame d. The frame is pressed upward against the
36
ORDNANCE AND GUNNERY.
spring catch h by two other contact springs, /. The electric cir-
cuit passes from one binding post through the parts /, e, c, and a
to the other binding post.
On the release of the spring catch h the frame d flies upward
under the action of the springs / until stopped by the pin g.
FIG. 9.
At the sudden stoppage of the movement the weighted ends of
the contact springs simultaneously leave the contact pins, thus
breaking both circuits momentarily. Mounted on a shaft are two
hard rubber cams, b, which bear against other springs, a, in the
two circuits. On turning the cam shaft the connection between
the parts a and c is broken, breaking both electric circuits, but
not necessarily simultaneously. The circuits are habitually
broken in this manner except when taking disjunction or records
in firing.
20. Disjunction. By means of the disjunctor both circuits
are broken at the same instant. The mark made by the knife
under these circumstances is called the disjunction mark, and its
height above a zero mark made by the knife when the chronometer
is suspended from its magnet is evidently the height through which
a free falling body moves in the time used by the instrument in
making a record. This time includes any difference in the times
required for demagnetization of the two magnets; the time occu-
MEASUREMENT OF VELOCITIES AND PRESSURES. 37
pied by the registrar in falling, and the time required for the
knife to act.
From the height as measured we obtain the corresponding
time from the law of falling bodies,
Now when the circuits are broken by the projectile the chro-
nometer begins to fall before the registrar. The mark made by
the knife will therefore be found above the disjunction mark. If
we measure the height of this second mark above the zero, the
corresponding time is the whole time that the chronometer was
falling before the mark was made, and to obtain the time between
the breaking of the circuits we must subtract from this time the
time used by the instrument in making a record, or the time cor-
responding to the disjunction. Let hi and h 2 represent the heights
of the disjunction and record marks respectively, t\ and t 2 the
corresponding times. Let t be the time between the breaking of
screens, then
It will be seen by the equation that the difference of the times, and
not the difference of the heights, must be taken.
FIXED DISJUNCTION. For the velocity at the middle point
h. -tween targets we have, representing by s the distance between
f .he targets,
v = s/t
Substituting for t its value, w r e have
(2h 2 /g)*~
this equation we see that if the value of s, and of (2h\/g)* t
unction, be fixed, the values of v can be calculated for
all values of h 2 within the limits of practice, and tabulated. This
has been done for the values s = 100 feet and (2/ii /</)* = 0.1 5 sec-
3S
ORDNANCE AND GUNNERY.
FIG. 10.
onds. This value of (2hi/g)* is called the fixed dis-
junction. If such a table is not at hand, the fixed
value of the disjunction avoids the labor of calculating
(2/ii/gf)* for each shot.
In this case
In ordinary practice it is better to take the disjunc-
tion at each shot, and to keep the disjunction mark
near the disjunction circle, but not necessarily on it.
The times corresponding to the heights of the disjunc-
tion and record marks are both read from the table, and
with the difference of these times the velocity is taken
from another table.
Measuring Rule. For measuring the height of the
mark on the recorder above the zero mark there is pro-
vided with the instrument a rule graduated in milli-
meters, and with a sliding index and vernier, the least
reading being -J^- of a millimeter. The swivelled pin at
the end of the rule, Fig. 10, is inserted in the hole through
the bob of the chronometer, and the knife edge of the
index is placed at the lower edge of the mark whose
height is to be measured. The height is then read from
the scale. Tables are constructed from which can be
directly read the time corresponding to any height in
millimeters within the limits of the scale. The maxi-
mum time that can be measured with this chronograph
is limited by the length of the chronometer rod, and is
about 0.15 of a second.
21. Adjustments and Use. The instrument must
be properly mounted on a stand at such a distance from
the gun that it will not be affected by the shock of dis-
charge. The electrical connections with the batteries
and targets, through the rheostats r and disjunctor d,
are made as shown in Fig. 11.
To adjust the instrument, first level it by the level*
MEASUREMENT OF VELOCITIES AND PRESSURES.
39
ing screws, cock the knife, and suspend the chronometer rod, en-
veloped by the recorder, from its magnet. See that the recorder
hangs close to the knife and that no part of the base of the rod
touches any part of the instrument. The guides must be close to.
but not touching, the bob of the chronometer. Depress the
FIG. 11.
trigger. The knife will mark the recorder near the bottom. This
mark is the zero from which all heights are measured, and the
knife edge on the measuring rule index must be so adjusted that
the zero of the vernier shall coincide with the zero of the scale
when the knife edge is in the mark. The adjustment of the knife
is made as follows. Place the sliding index so that the zero of the
vernier is at the zero of the scale on the rule. Clamp the index
and apply the rule to the chronometer. Loosen the screws that
hold the knife and adjust the knife edge to the zero mark on the
recorder. Tighten the knife screws. After this adjustment,
slide the index to the mark Disjunction on the rule, and letting
the knife edge bear against the recorder turn the recorder around
the chronometer rod. The knife edge will scribe a circle on the
recorder, and the mark made at disjunction should fall on or near
this circle.
40 ORDNANCE AND GUNNERY.
To regulate the strength of the magnets each of the rods is
provided with a tubular weight, one tenth that of the rod. Place
the proper weight on each rod and suspend the rods from their
magnets. Increase the resistance in each circuit by slowly mov-
ing the contact piece of the rheostat until the rod falls. Remove
the weights from the rods and again suspend the rods. Take
the disjunction. If the bottom of the mark made by the knife
does not lie on or near the circle previously scribed on the recorder,
raise or lower the registrar magnet until coincidence is nearly
obtained.
Test the disjunctor by shifting the two circuits. The height
of disjunction should remain the same.
Test the circuits by suspending the rods and causing the
circuits to be broken successively at the two targets. Note that
the proper rod falls as each circuit is broken.
Always suspend the chronometer rod with the same side of
the bob to the front, and always, before suspending it, press
the recorder hard against the bob. After each record turn the
recorder slightly on the rod to present a new element to the knife.
Circuits should always be broken at the disjunctor when
the rods are not actually suspended, and the rods should be
allowed to remain suspended as short a time as possible.
Measurement of Very Small Intervals of Time. For the
measurement of very small time intervals the registrar mag-
net is raised to near the top of the standard and placed in the
circuit with the first target. The chronometer magnet is put
in the circuit with the second target. Under this arrangement
the disjunction mark will be made near the top of the recorder
and the record mark under the disjunction. The interval of
time measured is obtained by subtracting the time corresponding
to the height of the record mark, from the time of disjunction.
The object of this arrangement is to obtain the record when the
chronometer has acquired a considerable velocity of fall, so that
the scale of time will be extended, and small errors of reading
will not produce large errors in time.
MEASUREMENT OF VELOCITIES AND PRESSURES.
41
22. Schultz Chronoscope. The Le Boulenge chronograph
measures a single time interval only. When it is desired to
measure the intervals between several successive events an instru-
ment that provides a more extensive time scale is required.
The Schultz Chronoscope is an instrument of this class. An
electrically sustained tuning fork, c, Fig. 12, whose rate of vibra-
tion is known, carries on one tine a quill point b which bears
against the blackened surface of the revolving cylinder a and
marks on it a sinusoidal curve which is the scale of time. By
FIG. 12.
FIG. 13.
giving motion of translation to the cylinder past the fork the
time scale may be extended helically over the whole length of
the cylinder. The records of events, such as the passage of the
shot through screens, are made by the breaking of successive
circuits which pass through the Marcel Deprez registers shown
at e, Fig. 12, and in Fig. 13. When the circuit is broken the
magnet e, Fig. 13, is demagnetized, and the spring g rotates the
armature / and the quill h attached to it. This marks a bend
or offset in the trace of the quill on the revolving cylinder, and
t he point of the bend referred to the time scale marks the instant
of the breaking of the circuit.
42
ORDNANCE AND GUNNERY.
It will be noted that the tuning fork has a constant lead with
respect to any register. The point of the time scale that corre-
sponds to any point on a register record is found at the length of
this lead from the point on the time scale opposite the given point
on the register record.
The Sebert Velocimeter. This instrument is used to record
the movement of the gun in recoil. A blackened steel ribbon, S,
-r
FIG. 14.
Fig. 14, is attached by the wire T to a bolt projecting from the
trunnion of the gun. As the gun recoils it pulls the ribbon past
the registers R and the tuning fork A, whose rate
of vibration is known. The quill on the tuning
fork marks the time scale on the blackened rib-
bon as shown by the curve t, Fig. 15. The time
occupied by the gun in traversing any length is
obtained by laying off this length on the time
scale and counting the vibrations and parts of a
vibration included. The right line through the
centre of the time scale is made by pulling the
ribbon past the fork when the fork is not vibrating.
The line assists in the count of the number of
double vibrations in any length.
The time scale is therefore a complete record of the move-
ment of the gun; and by measuring from it the length travelled
by the gun during any vibration of the fork the velocity of the
gun at the middle instant of the vibration may be determined.
FIG. 15.
MEASUREMENT OF VELOCITIES AND PRESSURES.
When the gun moves in free recoil, that is, when it is so mounted
that it recoils horizontally and with very little friction, the ve-
locities of the projectile may be determined from the velocities
of the gun; and the ^ essures necessary to produce these veloci-
ties in the prc
The registe
recoil proper, I
while the recoL
parture of the \
and independent
between points i
hav
ms
cor
ect
ty then be determined.
10 function in the measurement of the
DC used to record any event happening
3 being made. The instant of the de-
F rom the bore is usually thus recorded,
ment of the velocity of the projectile
bore may also be made.
Two register records are shown by the lines r, Fig. 15, the
event recorded by each register having occurred when the offset
at s was made. The time that elapsed between the beginning
of movement and the occurrence of the event recorded is obtained
by laying off on the time scale the length from the origin of the
register record to the offset.
Methods of Measuring Interior Velocities. Two methods
that have been used in determining the instant of the projec-
FIG. 16.
tile's passage past selected points in the bore are shown in Figs. 16
and 17.
Y I 1
:
BREECH
'! T n
$&#'#&*&: "\
T^
=>
\^
FIG. 17.
iSome circuit breaking device is used at the points selected,
and the electric wires are led to any suitable velocity instru-
ment.
44
ORDNANCE AND GUNNERY.
FIG. 18.
23. Measurement of Pressures. Pressures in cannon are di-
rectly measured by means cf the pressure gauge shown in Fig. 18.
In the steel housing h are assembled the steel piston p and the
copper cylinder c, which is centered by the steel spring or rubber
washer w. The housing is closed by the scre"\
plug s. A small copper obturating cup o prc
vents the entrance of gas past the piston, am
a copper washer performs the same office at
the joint between the housing and the closi]
plug. A series of grooves a, called air packing,
is sometimes cut near the bottom of the pistol
and assists in obturation in the case of a defecl
in the copper cup. Any gas that may pj
the cup has its tension materially reduced by expansion into the
successive grooves.
In another form of gauge the housing is threaded on the
exterior and the gauge is screwed into a socket provided in the
head of the breech block.
The gauge is placed in the gun behind the powder charge,
or is inserted in its socket in the breech block. When the gui
is fired the pressure of the powder gases is exerted against the
end of the piston and the copper cylinder is compressed. The
compression is manifestly due to the maximum pressure exerted
in the gun. The length of the cylinder is measured both befoi
and after firing, and the compression due to the pressure is deter-
mined. With the compression thus obtained the pressure
square inch that produced it is read at once from a tarage table
previously constructed.
The Tarage Table. The copper cylinders are cut in half-
inch lengths from rods very uniformly rolled and carefully an-
nealed. The compression of the cylinders under different 1<
is determined in a static pressure machine. It is assumed thai
the compression obtained in firing is due to a load on the piston
of the pressure gauge equal to the load that produced the same
compression in the static machine. The pressure per square
MEASUREMENT OF VELOCITIES AND PRESSURES. 45
inch in the gun may therefore be obtained by dividing the static
load that corresponds to the observed compression by the area
of the piston in the pressure gauge. Knowing the area of the
piston used, the table of compressions and corresponding pres-
sures per square inch is readily constructed from the results
obtained in the machine.
The area of piston in cannon gauges is Vio of a square
inch, and in the small-arm pressure barrel, 1 / 30 of a square
inch.
Initial Compression. When the pressure in the gun is high
the compression of the copper is considerable, and the piston
acquires an appreciable velocity during the compression. The
energy of the piston due to this velocity adds to the compres-
sion that would result from the pressure alone, and consequently
the measured compression is greater than the compression that
corresponds to the true pressure. The energy of the piston
may be reduced in two ways: by reducing its weight, and by
limiting its travel and accompanying velocity. The piston is
made as light as possible consistent with the duty it has to per-
form. To limit its travel the copper cylinders are initially com-
pressed before using, by a load corresponding to a pressure
somewhat less than that expected in the gun. Further com-
pression of the copper will not occur until the load applied in the
gun is close to that used in the initial compression.
The general practice is to use a copper initially compressed
by a load corresponding to a pressure about 3000 Ibs. less than
that expected in the gun. Thus if a pressure of 35,000 Ibs. is
expected, a copper initially compressed by a load correspond-
ing to 32,000 Ibs. per square inch is used.
Small-arm Pressure Barrel. In the measurement of pres-
sures in small arms a specially constructed barrel whose bore
is the same as that of the rifle barrel is used. The piston of the
pressure gauge passes through a hole bored through the barrel
over the chamber, and a steel housing erected over this part of
the barrel serves as an anvil for the copper cylinder.
46
ORDXANCE AND GUNNERY.
A. hole is bored through the metallic cartridge case to per-
mit the powder gases to act directly on the end of the
piston.
24. The Micrometer Caliper. The micrometer caliper, Fig.
19, is used for measuring the lengths of the copper cylinders
before and after firing. This instrument is used generally for the
measurement of short exterior lengths.
FIG. 19.
The movable measuring point p has a screw thread of fort?
turns to the inch cut on its shaft. One turn of the attach(
micrometer head m therefore moves the point one fortieth
25 thousandths of an inch. By means of the scale on th(
spindle and the 25 divisions on the micrometer head m the
tance that separates the measuring points can be read to th(
one-thousandth of an inch, and by further subdividing the divi-
sions on the head by the eye, readings to the ten-thousandth of
an inch may be made. The figure represents the points as sepa
rated by 0.2907 inches.
The Dynamic Method of Measuring Pressures. This con
sists in determining the velocities of the gun in recoil, as b)^ the
Sebert velocimeter, or of the shot at different points of the bore
The differences of the velocities divided by the corresponding
differences of the times give the accelerations, and the corre-
sponding pressures are obtained by multiplying the accelera-
tions by the mass. A pressure obtained in this manner is
evidently only the pressure required to produce the observed
MEASUREMENT OF VELOCITIES AND PRESSURES. 47
acceleration in a body whose mass is that of the gun or of
the projectile. That part of the pressure expended in over-
coming the friction of the projectile in the bore and in giving
rotation to the projectile is neglected. The measured pressure
is consequently less than the true pressure exerted in the
gun.
Comparison of the Two Methods. When the same pressure
in the bore is measured by the dynamic method and by the pres-
sure gauge the result obtained dynamically is usually the greater,
and this notwithstanding the fact, as just explained, that the
dynamically measured pressure is less than the true pressure.
This causes doubt as to the correctness of the pressures recorded
by the gauge.
In the gun the compression of the copper is effected in a very
small fraction of the time required in the static machine that
produced the tarage, and as the maximum pressure in the gun
is instantly relieved, it is held that the metal of the copper cylinder
has not time to flow under this pressure, and consequently that
the compression is less than it would-be under the same load
in the static machine. The pressure as obtained from the com-
pression in the gauge is therefore less than the true pressure in
the gun.
On the other hand Sarrau, an eminent French investigator,
concludes from many experiments that with gunpowder, when
the pressure gauge is placed in rear of the projectile, the com-
pressions will agree with the tarage. The maximum pressure
in the gun is reached in a very short time, but the time is appre-
ciable. Therefore the application of the pressure resembles in
some degree that of the force producing the tarage. When
high explosives are used, or when with gunpowder the pressure
gauge is placed anywhere in front of the base of the projectile so
that the gas strikes it suddenly upon the passage of the projectile,
the rate of application of the force is so great that as a general
rule the true pressure is measured by the tarage corresponding to
half the actual compression of the cylinder.
48 ORDNANCE AND GUNNERY.
Though these differences of opinion as to the correctness of the
pressure gauge exist, the gauge itself is in general use. It affords
the most convenient method of getting a measure of pressure, and
serves to compare the measured pressure with what is known
from experience to be a safe pressure in the gun.
CHAPTER III.
INTERIOR BALLISTICS.
25. Scope. Ballistics is the science that treats of the motion
of projectiles.
Interior ballistics is concerned with the motion of the projectile
while in the bore of the gun, and includes a study of the condi-
tions existing in the bore from the moment of ignition of the
powder charge to the moment that the projectile leaves the muz-
zle. The circumstances attending the combustion of the powder,
the pressures exerted by the gases at different points of the bore,
and the velocities impressed upon the projectile are the subjects
of investigation; and the practical results of the study lie in the
application of the deduced mathematical formulas which connect
the travel of the projectile with the velocities and pressures. By
means of the formulas we may deter mine the stresses to which a
gun Is subjected from the pressure of the powder gases, and the
dimensions of chamber and of bore, and the weight of powder, to
produce hi a given projectile a desired velocity. The action of
different powders may be compared and the most suitable powder
selected for a particular gun. The interior pressures at all points
along the bore being made known, the thickness required in the
walls of the gun to safely withstand these pressures are deter-
mined from the principles of gun construction, to be studied
later.
Early Investigations. In 1743 Benjamin Robins described,
before the Royal Society of England, experiments that he had
made to determine the velocities of musket balls when fired with
50 ORDNANCE AND GUNNERY.
given charges of powder. To measure the velocities he invented
the ballistic pendulum, which consisted simply of a large block of
wood suspended so as to move freely. The bullet was fired into
the block of wood, and the velocity impressed upon the pendulum
was measured. By equating the expressions for the quantities
of motion in the bullet before striking the pendulum, and in the
pendulum after receiving the bullet, the velocity of the bullet was
obtained. The gun pendulum, which consisted of a gun mounted
to swing as a pendulum, was also invented by Robins. Among
other deductions made from his experiments Robins announced
the following. The temperature of explosion is at least equal to
that of red-hot iron; the maximum pressure exerted by the powder
gases is equal to about 1000 atmospheres; the weight of the per-
manent gases is about three tenths that of the powder, and their
volume at atmospheric temperature and pressure about 240 times
that occupied by the charge.
Dr. Charles Hut ton, Professor in the Royal Military Academy,
Woolwich, continued Robins's experiments, 1773 to 1791, improv-
ing and enlarging the ballistic pendulum so that it could receive
the impact of one-pound balls. He verified Robins's deductions
as to the nature of the gases, but put the temperature of explosion
at double that previously deduced, and the maximum pressure at
2000 atmospheres. Hutton produced a formula for the velocity
of a spherical projectile at any point of the bore, upon the assump-
tion that the combustion of the charge is instantaneous and that
the expansion of the gas follows Mariotte's law, no account
being taken of the loss of heat due to work performed a principle
which, at that time, was unknown.
In 1760 the Chevalier D'Arcy made the first attempt to deter-
mine dynamically the law of pressure in the bore by successively
shortening the length of the barrel and measuring the velocity of
the bullet for each length. The pressures were determined from
the calculated accelerations.
In 1792 Count Rumford, born in the United States, endeavored
to make direct measurement of the pressure exerted by fired gun-
INTERIOR BALLISTICS. 51
powder by measuring the maximum weights lifted by different
charges fired in a small but very strong wrought iron mortar, or
eprouvette. He determined a relation existing between the pres-
sure of the powder gases and their density. The maximum pres-
sure that would be exerted by the gases from a charge that com-
pletely filled the chamber was, as calculated by Rumford, about
100 tons to the square inch. Noble and Abel, in their later
experiments, arrived at 43 tons per square inch as the maximum
pressure under these conditions. Their value is now accepted as
being very near the truth. The great difference in the two deter-
minations is probably due to the fact that Rumford deduced his
value for the maximum pressure from experiments with small
charges that did not fill the chamber, so that the energy of the
gasfs was greatly increased by the high velocity they attained
before acting on the projectile.
Later Investigations. In the years 1857 to 1860 General Rod-
man of the Ordnance Department, United States Army, conducted
the experiments that resulted in the change of form of powder
grains and their variation in size according to the caliber of the
gun. He devised the pressure gauge for directly measuring the
maximum pressures of the powder gases. His gauge differed from
the pressure gauge now in use, only in the method employed to
record the pressure. The piston of the gauge carried at its inner
end a V-shaped knife, and the amount of the pressure was read
from the length of the cut made by the knife in a disk of copper.
General Rodman was also the author of the principle of interior
cooling of cast iron cannon, by the application of which principle
the metal surror/nding the bore of a gun was put under a perma-
nent compressive strain which greatly increased the resistance of
the gun to the interior pressures.
In 1874 Noble and Abel announced the results of their experi-
ments on the explosion of gunpowder in closed vessels. As the
ballistic formulas now in use are based largely on the results of
Noble and Abel's experiments, these will later be more fully
described.
54 ORDNANCE AND GUNNERY.
Let C" be the volume in cubic inches occupied by the solid
powder of the charge; d the density of the powder. dC f will
then be the volume of an equal weight of water, and
= aC'/27.68 (24)
which, substituted in equation (22), gives
A = dC'/C (25)
The accompanying figure will serve to illustrate the difference
between density, gravimetric density, and density of loading. The
figure represents a section of the whole chamber
of a gun charged with powder to the line A. The
density of loading is in this case the weight of
powder below the line A divided by the weight of
water that will fill the whole chamber. The gravi-
metric density is the weight of the powder divided
by the weight of water that will fill all that part
of the chamber below the line A. Now consider-
ing the powder charge as compressed into a solid mass at the
bottom of the chamber, represented by the black portion, the
density of the powder will be its weight divided by the weight of
water that will fill this black portion. As the weight of water
that will fill each volume is equal to the volume in cubic inches
divided by 27.68, we have :
P. ., , T ,. 27.68w
Density of Loading, J = -. , ,
vol. of chamber
Gravimetric Density, r = i * r~
vol. of charge
Density, - 27 - 68(S
vol. of solid powder
"Using metric units the factor 27.68 will be omitted.
INTERIOR BALLISTICS. 55
28. Reduced Length of Powder Chamber. For convenience in
the mathematical deductions the volume of the powder chamber
is reduced to an equal volume whose cross section is the same as
the cross section of the bore. The length of this volume is called
the reduced length of the powder chamber.
Let u be the reduced length of the chamber,
w the area of cross section of the bore,
C the volume of the chamber,
d the diameter of the bore.
Then
C = u Q a> = u 7:d 2 /4:
and
Wo = 4CVW2 (26)
Reduced Length of Initial Air Space. The air space in the
loaded chamber, which includes all the space in the chamber not
occupied by solid powder, is also reduced to a volume whose
cross section is that of the bore. The length of this volume is
called the reduced length of the initial air space,
Let ZQ be the reduced length of the initial air space, in inches.
Then, since C is the volume of the chamber and C" the volume
of the solid powder,
Substituting for C and C' their values from equations (22)
and (24)
*G-J)
Make a = -J- (27)
Then z w=27.6Saa> (23)
56 ORDNANCE AND GUNNERY.
and since w
z = 35.2441a d>/d 2 = [1 .54709]atf/d 2 (29)
the number in square brackets being the logarithm of 35.2441.
Problems. 1. The volume of the chamber of the 3-inch field
rifle is 66.5 cu. in. The weight of the charge is 26 oz. Density
of the powder 1.56. .What is the density of loading, and what is
the reduced length of the initial air space?
Ans. J= 0.6764,
2 = 5.33 inches.
2. If the gravimetric density of the powder in the last example
is unity, how many pounds will the chamber hold?
2.4 Ibs.
3. The reduced length of the initial air space in the 8-inch
rifle loaded with 80 Ibs. of powder, density 1.56, is 43.72 inches.
What is the capacity of the chamber?
C = 3617cu. in.
4. The 5-inch siege gun has a chamber capacity of 402.5 cu.
in. What is the density of loading with a charge of 5.37 Ibs.?
J= 0.3693.
5. The 4-inch rifle when loaded with 12 Ibs. of sphero-hex-
agonal powder has a density of loading of 0.915. What is the
chamber capacity?
C = 363 cu. in.
6. The 12-inch rifle has a chamber capacity of 17487 cu. in.
The density of loading is 0.5936. What is the weight of the
charge, and what is the volume of the solid powder in the charge?
d = 1.56.
a* = 375 Ibs.
Solid volume = 6654 cu. in.
7. What is the reduced length of the initial air space in the
last example?
0o = 95.79 inches.
INTERIOR BALLISTICS. 57
8. The chamber capacity of the 6-inch rifle is 2114 cu. in.
What is the reduced length of the chamber?
w = 74.77 inches.
PROPERTIES OF PERFECT GASES.
29. Marietta's Law. At constant temperature the tension, or
pressure, of a gas is inversely as the volume it occupies.
As the density of a gas is inversely as its volume, this law may
also be expressed: At constant temperature the pressure of a gas
is proportional to its density.
Let v be the volume of a given mass of gas,
p its pressure in pounds per unit of area.
Then if the volume occupied by the gas be changed to VQ, the
temperature of the gas being kept constant, the pressure will
change according to the law
vp = constant
Let p Q represent the normal atmospheric pressure, barometer
30 inches;
p Q = 14.6967 pounds per square inch,
or 103.33 kilograms per square decimeter;
i'o the volume of unit weight of a gas at C. under normal
atmospheric pressure.
Then by Mariotte's law, at C.,
vp = Vopo (3C )
Specific Volume. The specific volume of a gas is the volume
of unit weight of the gas at zero temperature and under normal
atmospheric pressure. v in the above equation is the specific
volume of the gas.
In English units the specific volume of a gas is the number of
58 ORDNANCE AND GUNNERY.
cubic feet occupied by a pound of the gas under the above condi-
tions.
Specific Weight. The specific weight of a gas is the weight of
a unit volume of the gas at zero temperature and under normal
atmospheric pressure. It is the reciprocal of the specific volume.
Gay-Lussac's Law. The coefficient of expansion of a gas is
the same for all gases; and is sensibly constant for all tempera-
tures and pressures.
Let VQ be the specific volume of a gas, v t its volume at any
temperature t, and a the coefficient of expansion. Then the
variation of volume under constant pressure by Gay-Lussac's law
will be expressed by the equation
or v t
The value of a is approximately 1/273 of the specific volume
for each degree centigrade. The above equation may therefore be
written
/ / \
(31)
30. Characteristic Equation of the Gaseous State. The last
equation, which expresses Gay-Lussac's law, may be combined
with Mariotte's law, introducing the pressure p.
Let x be the volume that v t would become at C., under the
pressure p t . Then by Gay-Lussac's law
but by Mariotte's law
Ptx
whence, eliminating x,
p t v t = p Q v (l + at}
INTERIOR BALLISTICS. 59
Since po^o/273 is constant for any gas, put
R = p Q v /273 (32)
whence, dropping the subscripts as no longer necessary,
The temperature (273 -H) is called the absolute temperature
of the gas. It is the temperature reckoned from a zero placed 273
degrees below the zero of the centigrade scale. Calling the abso-
lute temperature T there results finally
pv = RT (33)
which is called the characteristic equation of the gaseous state, and is
simply another expression of Mariotte's law in which the tem-
perature of the gas is introduced.
Equation (33) expresses the relation that always exists between
the pressure, volume, and absolute temperature of a unit weight
of gas. To apply it to any gas, substitute for v in the value of
R, equation (32), the specific volume of the particular gas.
For any number w units of weight occupying the same volume
the relation evidently becomes
pv = wRT (34)
A gas supposed to obey exactly the law expressed in equation
(33) is called a perfect gas, or is said to be theoretically in the per-
fectly gaseous state. This perfect condition represents an ideal
state toward which gases approach more nearly as their state of
rarefaction increases.
For a temperature T' equation (34) becomes
60 ORDNANCE AND GUNNERY.
Dividing equation (34) by this equation we obtain
^--- (351
p'v'~ T'
from which we readily see that if the pressure of any mass of gas
is constant the volume of the gas will vary with the absolute tem-
perature, and if the volume is constant the pressure will vary with
the absolute temperature.
Problems. Equations (30) to (34) are used in solving the
following problems.
Specific volumes : Air V Q = 12.391 cu. ft.
Hydrogen v = 178.891 cu. ft.
Coal gas VQ= 24.6 cu. ft.
Water gas V Q = 18.09 cu. ft.
1. A volume of 3 cubic feet of air, confined at 59 F. (15 C.)
and 30" barometer, is heated to a temperature of 300 C. What
pressure does it exert?
Vol. of 1 Ib. air at 15, equation (31), v t = v Q 2SS/273.
3/v t = w
Equation (34), p = wRT/v = 29.24: Ibs. per sq. in.
2. Two pounds of air confined in a volume of 1 cubic foot
exerts a gauge pressure of 679.76 Ibs. per square inch. What is
its temperature by the centigrade and Fahrenheit scales?
The total pressure p is the gauge pressure plus the atmospheric
pressure,
p = 679.76 +14.70 = 694.46
Equation (34), T = pv/wR = 520.54
3. A spherical balloon 20 feet in diameter is to be inflated with
hydrogen at 60 F., barometer 30.2 inches, so that gas may not
be lost on account of expansion when the balloon has risen unti/
INTERIOR BALLISTICS. 61
the barometer is at 19.6 inches and the temperature 40 F. How
many cubic feet of gas must be put in the balloon?
The gas pressure in the balloon is in equilibrium with the atmos-
pheric pressure. The weight of gas occupying the balloon must
be such that at 40 F. the pressure will be in equilibrium with a
barometric pressure of 19.6 inches.
p = poX 19.6/30 v = volume of balloon
Equation (34), w = pv/RT = 15.05 Ibs.
Volume of w at 60 F. and 30".2 barometer:
p = p X 30.2/30
v = wRT/p = 2827A cubic feet
4. What is the lifting power at 70 F. (21.ll C.) and 30 in.
barometer of 1000 cubic feet of each of the gases whose specific
volumes are given?
Air
Vol. 1 lb. at 70.
Equation (31).
.. . 13.35
Pounds in
1000 cu. ft.
74.91
Lifting power
1000 cu. ft.
Ibs.
Hvdrogen .
. .. 192.73
5.19
6972
Coal gas
26.5
37.73
37 18
Water gas..
19.49
51.31
23.60
5. The balloon in which Wellman intends to seek the North
Pole has a capacity of 224,244 cubic feet, and weighs with its car
and machinery 6600 Ibs. What will be its lifting capacity when
filled with hydrogen at 10 C. and 30 inches barometer?
Ans. 9647 Ibs.
31. Thermal Unit. The heat required to raise the tempera- 1
ture of unit weight of water at the freezing point one degree of the
thermometer is called a thermal unit.
Mechanical Equivalent of Heat. The mechanical equivalent
of heat is the work equivalent of a thermal unit, that is it is the
62 ORDNANCE AND GUNNERY.
work that can be performed by the amount of heat required to
raise the temperature of unit weight of water one degree. It will
be designated by E. The unit weight of water being one pound,
the value of E for the Fahrenheit scale is 778 foot-pounds; and
for the centigrade scale, 1400.4 foot-pounds.
In metric units the value of E is 425 kilogr ammeters.
Specific Heat. The quantity of heat, expressed in thermal
units, which must be imparted to unit weight of a given substance
in order to raise its temperature one degree of the thermometer
above the standard temperature is called the specific heat of the
substance.
The specific heat of a gas may be determined in two ways:
under constant pressure, and under constant volume.
Suppose heat to be applied to a unit weight of gas retained in
a constant volume whose walls are impermeable to heat. The
whole effect of the heat will be to raise the temperature of the
gas. If, however, the gas is enclosed in an elastic envelope, sup-
posed to maintain a constant pressure on the gas, the gas will
expand on the application of heat, and part of the heat applied
will perform the work necessary to expand the envelope. There-
fore to raise the temperature of the gas one degree, a greater
amount of heat must be applied when the gas is under constant
pressure than when under constant volume; and the difference of
these quantities, that is, the difference between the specific heat
under constant pressure, c p , and the specific heat under constant
volume, c v , will be the heat that performs the work of expansion.
The mechanical equivalent of a heat unit being represented by E,
we may write
Work of expansion = (c p c v )E
Actually, part of the work that we have included in the work
of expansion is internal work, used in overcoming the attractions
between the molecules; but the quantity of work so absorbed is
small and is omitted in the discussions.
The work of expansion is equal to the constant resistance mul-
tiplied by the path. We will assume the constant resistance to
INTERIOR BALLISTICS. 63
be the atmospheric pressure, p . The path is measured by the
increase of volume of the gas. To determine the path we have
from Gay-Lussac's law, for the centigrade scale equation (31),
v t -v Q = tvo/273
and therefore for an increase of temperature of one degree there
is an increase of volume equal to vo/273. The work of expansion
for one degree is therefore p Q v /273. Referring to equation (32),
p v Q /273 = R
The quantity R is therefore the external work of expansion
performed under atmospheric pressure by unit weight of gas when
its temperature is raised one degree centigrade. But this work of
expansion has been found above to be equal to (c p c v )E. There-
fore we may write
(c p - c v )E = R = poVo/273 (36)
From the definition of specific heat we deduce that the quan-
tity of heat necessary to raise the temperature of unit weight of
gas any number of degrees, as /, will be
Q = ct (37)
c representing either c p or c v .
Ratio of Specific Heats. In the study of interior ballistics the
particular values of c p and c v for the different gases which are
formed by the explosion of gunpowder are of little importance.
It suffices to know their ratio, which is constant for perfect gases
and approximately so for all gases at the high temperature of
combustion of gunpowder.
The ratio of the specific heats, c p /c v , is subsequently designated
by n.
32. Relations between Heat and Work in the Expansion of
Gases. The relation which exists between the heat in a unit
64 ORDNANCE AND GUNNERY.
weight of gas and the work performed in the expansion of the gas
may now be determined from equation (33),
which cor tains the three variables p, v and T. If we suppose an
element of heat, dq, to be applied to the gas, the effect will be
generally an increase in the temperature, accompanied by an in-
crease in the pressure, or in the volume, or in both the pressure
and the volume.
Considering p constant, and differentiating, we get
dT = pdv/R
and the quantity of heat communicated to the gas will be, equa-
tion (37),
Considering v constant we obtain similarly
dq = c v vdp/R
If p and v both vary, we obtain from the sum of the partial
differentials, still representing by dq the element of heat applied
to the gas,
1
dq = ft(c p pdv + c v vdp) (38)
The differential of equation (33) is
RdT = pdv+vdp (38')
Eliminating vdp between the last two equations we have
'-p-^pdv (39)
INTERIOR BALLISTICS. 65
The quantity pdv represents the elementary work of the elastic
force of the gas, while its volume increases by dv. The integral of
pdv is therefore the total external work between the limits con-
sidered.
Representing by W the total external work we have
= fpdv
(40)
Represent by TI and T the initial and final temperatures.
Integrating equation (39) between the limits T and TI we
obtain, since c v , c p , and R are constant for the same gas,
(41)
Isothermal Expansion. If we suppose the initial temperature
TI to remain constant, that is, that just sufficient heat is imparted
to the gas while it expands to maintain its initial temperature,
the quantity T TI in equation (41) becomes 0, and solving with
respect to W we obtain
We see that in this case, since R, c p , and c v are constant for the
same gas, the external work done is proportional to the quantity
of heat absorbed by the gas.
Making q equal to one thermal unit, W becomes E, and we
obtain, as before in equation (36),
E(c p -c v ) = R
33. Adiabatic Expansion. If a gas expands and performs
work in such a manner that it neither receives heat from any
extraneous body nor gives out heat to an extraneous body, the
66 ORDNANCE AND GUNNERY.
transformation is said to be adiabatic. In this case part of the
heat in the gas is converted into work, the temperature and pressui e-
of the gas both diminish, and the work performed will be less than
for an isothermal expansion.
Since no heat is gained or lost, q becomes in equation (41)
and we have
C p C v
Make c p /c v =n
Then W = ^<Ti - T) (42)
This equation gives the value of the external work done by a
unit weight of gas whose temperature is reduced from TI to T in
an adiabatic expansion. It will be seen that the external work
done is proportional to the fall of temperature.
LAW CONNECTING THE VOLUME AND PRESSURE. In the adia-
batic expansion, as no heat is received from an external source,
dq in equation (38) becomes 0, and we have
= c p pd ; + c v vdp
Dividing through by c v pv we find, since c p /c,=n
A^-ot
V p
and integrating, n log e v + log e p = log^ c
whence v n p = constant =
P-PV/ (43)
This equation expresses the relation between the volumes and
pressures of a gas in an adiabatic expansion.
INTERIOR BALLISTICS.
67
NOBLE AND ABEL'S EXPERIMENTS.
34. In 1874 and again in 1880 Captain Noble of the English Army
and Sir Frederick Abel published the results of their experiments
on the explosion of gunpowder in closed vessels. The purpose of
their experiments was to determine definitely the nature of the
products of combustion, the volume and temperature of the gases,
and the pressures with different densities of loading.
Apparatus. The steel vessel in which the powder was ex-
ploded was of great strength and capable of resisting very high
pressures.
The charge of powder was introduced through the opening a
which was then closed with a taper screw-plug. A pressure gauge
n
d was inserted in the plug c and an outlet was provided at e through
which the gas could be drawn off if desired. The charge was fired
by electricity.
The vessels were of two sizes. In the larger one a charge of
2.2 pounds of powder was fired, and the gases wholly retained.
Black powder was used in the experiments.
The gravimetric density of the powder iiscsl was unity, so that
68 ORDNANCE AND GUNNERY.
when the chamber was completely filled the density of loading
was also unity.
Results of the Experiments. Character of the Products. The
products of combustion were found to consist of about 43 per cent
by weight of permanent gases, and about 57 per cent of non-gaseous
products. The non-gaseous products ultimately assume the solid
form, but are liquid at the moment of the explosion. This was
determined by tilting the vessel at an angle of 45 degrees, one
minute after the explosion. Forty five seconds later it was re-
turned to its original position. On opening the vessel the solid
residue was found inclined to the walls at the angle of 45 degrees.
The permanent gases are principally C0 2 , N, and CO, and the
solids K 2 C0 3 , K 2 S, K 2 S0 4 , and S. With the exception of the
K 2 S and the free sulphur, the products agree in character with
those expressed in the formula generally adopted as approximately
representing the reaction of black powder on explosion.
The formula, however, gives 35} per cent by weight of per-
manent gases and 64 J per cent of solids.
It was found, as was to be expected, that in a closed vessel
variations in the size, form, or density of the grains had practically
no effect on the composition of the products of combustion, or on
the pressures.
Volume of Cases. Noble and Abel found that the gases, when
brought to a temperature of C. and under atmospheric pressure,
occupied a volume of about 280 times the volume- of the unex-
ploded powder.
Specific Volume of Gunpowder Gases. To simplify somewhat
the discussions concerning the gases of fired gunpowder we will use
as the specific volume the volume, at C. and under atmospheric
pressure, of the gases produced by the combustion of unit weight
of powder. That is, we will consider this weight of gas as unit
weight.
INTERIOR BALLISTICS. 69
35. Relation between Pressure and Density of Loading.
The relation between the pressure, volume, and absolute tem-
perature of the gases from <D units of weight of powder at the
moment of explosion is given by equation (34).
Make f = RT (44)
and we obtain from (34), for the pressure exerted by the gases from
(ij pounds of powder, the gases occupying the volume v at the
temperature of explosion,
p = f<i>/v (45)
FORCE OF THE POWDER. If we make both d) and v unity in this
equation, p becomes equal to /. / is therefore the pressure per
unit of surface exerted by the gases from unit weight of powder,
the gases occupying unit volume at the temperature of explosion.
/ is called the force of the powder.
Let a be the volume of the residue from unit weight of powder,
C the volume of the chamber.
Then the volume occupied by the gas from a> units of powder will
be
V = C CCd)
We may introduce the density of loading, using metric units
by substituting for C in this equation its value &/J from equation
(23), and obtain
Substituting this value of v in (45) we obtain
(46)
This equation expresses the relation between the pressure of the
gases from & units of weight of powder and the density of loading.
ORDNANCE AND GUNNERY.
When = l > that 1S > when J = (46/)
Comparing the value of J in equation (46') with the general
value, J = u/C, we see that in (46') the weight of powder is unity,
and the volume of the chamber l + a. The volume occupied by
the gas is therefore also unity. The pressure therefore becomes
in this case the force of the powder as defined above.
By substituting in equation (46) two observed values of p cor-
responding to different values of J, the values of a and / were
determined. As the means of many observations Noble and
Abel finally adopted the values:
a =0.57;
/= 18.49 tons per square inch
=291200 kilograms per square decimeter
The pressure for any density of loading is given by the equation
j
p = 18.49^- n -_ . tons per square inch
1 U.o/^i
When A = \ the equation gives p = 43 tons per square inch.
The value of a, 0.57, means that the volume occupied at the
temperature of explosion by the liquid residue from one kilogram
of powder is 57/100 of one cubic decimeter. With gravimetric
density unity one kilogram of powder occupies one cubic decimeter.
Referring now to equation (21), we see that the solid powder, of
ordinary density and of gravimetric density unity, occupies 57/100
of the volume of the charge in granular form. The volume of the
residue at the temperature of explosion is therefore practically
equal to the volume of the solid powder in the charge.
36. Temperature of Explosion. The temperature of explosion
may now be determined from equation (44), which with (32) gives
(47)
INTERIOR BALLISTICS. 71
VQ is the volume occupied by the gas from unit weight of pow-
der. Since the volume of this quantity of gas is 280 times the
volume of the powder, and one kilogram of powder occupies one
cubic decimeter, v = 280 cubic decimeters. p , the atmospheric
pressure, is 103.33 kilograms per square decimeter. Substituting
these with the value of /, 291200 kilograms per square decimeter,
we find J F = 2748 C. As this is the absolute temperature, subtract-
ing 273 we find the temperature of explosion to be 2475 C.
(Vptain Noble later considered the absolute temperature as
2505 C.
The approximate correctness of these temperatures was verified
by the introduction of pieces of fine platinum wire into the explo-
sion chamber. The platinum, which melts at about 2000 C.,
was partially fused.
Mean Specific Heat of Products. The quantity of heat given
off by one kilogram of powder was found to be 705 calories, that
is, the heat necessary to raise 705 kilograms of water one degree
centigrade. From the relation Q = ct, equation (37), t being the
actual temperature of explosion, not the absolute, a value was
found for the mean specific heat of the products:
705 =0.316
2505-273
Relations between Volume and Pressure in the Gun.
Noble and Abel found, contrary to their expectations, that the
pressures in closed vessels did not differ greatly from the pres-
sures in guns when the powder in the gun was wholly consumed
oi f nearly so. They concluded from this that the expansion of
the gases in the gun did not take place without the addition of
heat; but that the gases received during the expansion the heat
stored in the finely divided liquid residue.
Let Ci be the specific heat of the residue, assumed to be con-
stant. The elementary quantity of heat given up by each unit
weight of residue will then be CidT. If there are ivi units of weight
72 ORDNANCE AND GUNNERY.
of residue, WiCidT units of heat will be yielded to the gases; and
if there are w 2 units of weight of gas, each unit will receive, in heat
units,
ft being the ratio Wi/w 2 , and the negative sign being used be
cause T decreases while q increases.
Substituting this value of dq in equation (39) it becomes
C,
Eliminate RdT by means of (38'); divide through by pv, and
integrate, considering c p , c v , GI and /? constant. We will obtain
(48)
When there is no residue /? is 0, and the equation becomes
identical with equation (43), which was deduced for an adiabatic
expansion. In both these equations Vi and v are the volumes
actually occupied by the gases, exclusive of the residue.
Assume the gravimetric density and density of loading to be
unity, that is, the chamber is filled with powder, and that the
powder is all burned before the projectile moves. Then Vi in
equation (48) will be the volume occupied by the gases in the
chamber of the gun, and pi the corresponding pressure. If we
call v f the volume of the chamber, av' will be the volume of the
residue, and i/ av' = vi the volume of the gases; and if we call
v" the volume behind the projectile at any instant, the volume
v occupied by the gases becomes v" av' = v. Equation (48)
therefore becomes
INTERIOR BALLISTICS. 73
These values for the constants were determined in the experi-
ments.
pi = 13 tons per square inch
a =0.57 i/= 27.68 CD
= 1.2957 c p = 0.2324
ci=0.45 c,= 0.1762
From these values we find the ratio of the specific heats,
c P /Ct, = n = 1.32. The value of the exponent in (48') is 1.074.
37. Theoretical Work of Gunpowder. The general expression
for the work done by a gas expanding from a volume Vi to a vol-
ume v is
W= Tpdv
Jvi
Substituting for p its value from (43) and integrating,
Assuming that the powder is all burned before the projectile
moves, and that the gravimetric density and density of loading
are unity, the values vi and v in this equation may be replaced
as indicated in equation (480, and we obtain
w
\v"-av'
*l
\
This is the expression for work under the adiabatic expansion
for which n = 1.32. If we substitute for n the value 1.074, which is
the value of the exponent in equation (480, the equation will then
apply to Noble and Abel's hypothesis.
Work at Infinite Expansion. When the length of the bore is
infinite, v", which is the volume behind the projectile, is infinite,
and we have
n-l
74 ORDNANCE AND GUNNERY.
To obtain the work of the gases from one pound of powder
make v' = 27.68 cubic inches, the volume occupied by one pound,
the gravimetric density being unity. Make ft = 1.32, and substi-
tute for the other constants the values given on page 73. Divide
by. 12 to reduce from inch-tons to foot-tons.
We find for the work of one pound of powder expanding adi-
abatically to infinity
W = 133.3 foot-tons per pound.
Substituting for n the value of the exponent in equation (480,
1.074, we obtain, under Noble and Abel's hypothesis that the gases
received heat from the residue,
W = 576.35 foot-tons per pound.
FORMULAS FOR VELOCITIES AND PRESSURES IN
THE GUN.
38. Elements Considered. Assumptions. Formulas connect-
ing the velocity of the projectile with its travel in the bore may
be deduced from the relations we have established involving the
work of the powder; but these formulas, while they include the
force of the powder, do not include consideration of the individual
characteristics of different powders, such as form and size of grain,
density, and velocity of combustion in the air; nor consideration
of the effect on the combustion of the variable pressure in the gun.
M. Emile Sarrau, engineer-in-chief of the French powder fac-
tories, was the first to include these elements in ballistic formulas.
He considers the progressive combustion of the charge under the
influence of the varying pressure in the gun, regarding the powder
as a variable in the formulas. The individual characteristics of
the powder employed enter the formulas, which thereby become
applicable to the determination, in advance, of the proper weight
of charge, the kind of powder, the best form and size of grain to
produce desired results in a given gun.
INTERIOR BALLISTICS. 75
Sarrau assumes that the time required for complete inflam-
mation of the charge is negligible compared with the time of
combustion. He also assumes an adiabatic expansion of the
gases.
This latter assumption, while incorrect according to the ex-
periments of Noble and Abel, is now generally made by writers
on interior ballistics; and whatever error is introduced through
the assumption is later corrected in the determination, by experi-
ment, of the constants in the formulas.
Principle of the Covolume. Another assumption of important
bearing in the deduction of the ballistic formulas will now be
explained.
The characteristic equation for perfect gases, equation (33),
combined with equation (47) gives for the pressure from unit
weight of gas confined in the volume v,
p = f/v
But it has been found by experiment that for the gases of
explosion the law expressed by this equation does not hold, and
that to obtain the true value of the pressure we must diminish the
volume v, which is the volume of the explosion chamber. The
true equation must therefore be of the form
(49)
v a
We may call the volume v a. the effective volume of the gas.
Theoretical deductions indicate that the subtractive volume a.
is the actual volume of the incompressible molecules in a unit
weight of powder gas; that is, it is the limiting volume beyond
which a unit weight of gas cannot be compressed.
The volume a is called the covolume. Sarrau determined
by experiment with different gases that the mean value of
the covoiume is one one-thousandth of the specific volume of
the gas. Other writers take, for convenience, the reciprocal
76 ORDNANCE AND GUNNERY.
of the density of the powder as the covolume, this value
not differing greatly from the other. We have seen, equation
(20), that when the gravimetric density is unity the volume of the
solid powder in unit volume of the charge is the reciprocal of
the density of the powder. The assumption of the reciprocal of
the density as the covolume is equivalent therefore to considering
the covolume as the volume originally occupied by unit weight
of solid powder.
Under this assumption the volume v a, equation (49), which
is the effective volume of unit weight of the powder gases, becomes
the volume of the powder chamber minus the volume of the solid
powder in unit weight of the charge.
The effective volume of the gases from the whole charge will
therefore be the volume of the powder chamber minus the volume
of the solid powder in the whole charge.
But this is the initial air space in the chamber. Therefore
the effective volume occupied by the powder gases in the chamber is
the initial air space.
If the powder leaves a non-volatile residue, the volume of this
residue at the temperature of explosion must be added to the
covolume of the gases formed, a in equation (49) will then
represent the covolume of the gases from unit weight of powder
plus the volume of the residue from unit weight of powder.
39. Differential Equation of the Motion of a Projectile in a
Gun. Let
y be the weight of powder burned at the time t,
TI the absolute temperature of combustion,
T the absolute temperature of the gas at the time t.
The work of a unit weight of gas in an adiabatic expansion
between the temperatures TI and T is given by equation (42).
For a weight of gas y we have
INTERIOR BALLISTICS. 77
From equation (44), since T\ now represents the temperature
of explosion, the value for the force of the powder is f = RTi;
and from equation (34), pv = yRT. With these substitutions the
above equation becomes
(n-l)W = fy~pv (50)
In this equation v is the volume occupied by the gases at the
temperature T and at the time t.
Let u be the distance traveled by the projectile at the time t,
w the cross section of the bore,
ZQ the reduced length of the initial air space.
Under the assumption of the volume originally occupied by
unit weight of solid powder as the covolume of the gases, the
initial air space in the chamber becomes the volume occupied by
the powder gases in the chamber.
We therefore have, for the volume occupied by the gases at
the time t,
Substituting this value in equation (50) we have
(51)
an equation expressing the relation at each instant between the
weight of powder burned, the pressure, the travel of the projectile,
and the external work performed.
In introducing the velocity of the projectile we will assume that
the whole work of the gas is expended in giving motion of transla-
tion to the projectile. Making w the weight of the projectile,
and representing now by v the velocity of the projectile,
w w /du
p in (51) is the pressure per unit of area; cup the total pressure
78 ORDNANCE AND GUNNERY.
on the base of the projectile. The acceleration of the projectile is
dPu/dt 2 . The total pressure on the base of the projectile is equal
to the product of the mass by the acceleration. Therefore
w d 2 u
w-
Substituting these values of W and cup in (51) we have
d 2 u nl/du 2 .
(53)
which is Sarrau's differential equation of the motion of a projectile
in the bore of a gun.
In deducing this equation there were neglected the following
energies.
The heat communicated by the gases to the walls of the gun,
The work expended on the charge, on the gun, and in giving
rotation to the projectile,
The work expended in overcoming passive resistances, such as
the forcing of the band, the friction along the bore, and the resist-
ance of the air.
Dissociation of Gases. The error committed by the omission
of these energies may not be as great as would at first appear,
for we have also omitted from consideration the heat supplied by
the phenomenon called dissociation. According to Bcrthelot the
composition of the complex gases from fired gunpowder is not
permanent, and at the high temperature during the first instants
of explosion these gases decompose into more simple combinations,
perhaps into their elements. The increase in volume due to the
displacement of the projectile causes a reduction in the tempera-
ture, which permits the dissociated gases to combine again with a
consequent development of heat. The theory of dissociation
forms the basis for the assumption of some writers on ballistics,
notably Gokmel Mata of the Spanish artillery, that by reason of
this phenomenon the expansion of the gases in the gun takes place
1XTERIOR BALLISTICS. 79
as though the gases received heat from the exterior, and not
adiabatically.
It will be seen, however, from the form of equation (53) that
the errors of assumption may be allowed for by giving to / a suit-
able value, and this without changing the form of the differential
equation of motion. The force of the powder as it appears in
equation (53) can therefore be considered only as a coefficient
whose value must be determined by experiment.
Sarrau deduced from the differential equation of motion for-
mulas for the velocity and pressure as functions of the travel of
the projectile.
40. Ingalls' Formulas. We will now follow Colonel Ingalls,
United States Army, in the deduction of his formulas. These
formulas are considered as giving more accurate results than
Sarrau's formulas, for the velocity and pressures produced by
modern powders in the bore of the gun; and the use of Sarrau's
formulas is generally limited to the determination of muzzle
velocities and maximum pressures.
Let v be the velocity of the projectile in the bore at the time t.
Then
du
3f= v
and
d?u dv vdv d(v*)
dP~df~ du~ 2du
Substituting these values in equation (53) it becomes
The true value of n, the ratio of the specific heats, c p /c t , is un-
certain. For perfect gases its value is 1.41. Regarding the pow-
der gases at the high temperature of explosion as perfect gases,
earlier writers assumed this value for n. Recent investigations
80 ORDNANCE AND GUNNERY.
have shown that the value of 1.41 is too great. Some recent
writers adopt the value unity for n. As we have seen, equation
(35), the work of expansion is directly proportional to the differ-
ence of the specific heats; and if their ratio is unity and the differ-
ence between them zero, there can be no external work performed.
The assumption of the value unity is made for convenience, and
the error due to the assumption is compensated for, with the other
errors, in the experimental determination of the values of the
constants.
Ingalls assumes the value n = 4/3, which is practically the
value deduced from the experiments of Noble and Abel, see page
73.
Making n = 4/3 in equation (55) we obtain
(56)
Make
x = U/ZQ (57)
Under the assumption made that the covolume of the gases is
equal to the volume occupied by the solid powder in the charge,
the initial air space is the volume occupied by the gases in the
powder chamber. Considering 2 , which is the reduced length of
the initial air space, as the measure of this volume, x in equation
(57), X = U/ZQ, becomes the number of expansions of the volume
occupied by the powder gases in the chamber, when the projectile has
traveled the distance u.
It is important to bear in mind that x represents a number of
expansions, and u the distance traveled by the projectile.
Making x = u/z , equation (55) becomes
m
y, the weight of powder burned, is a function of the time and
also of the travel u, and of x. The integration of this equation
BALLISTICS. 81
even when the simplest admissible form of y as a function of x is
assumed has not yet been possible.
Considering y constant the equation may be integrated. Re-
! arranging it,
V 2 -
w
And integrating,
V 2 L
II
When =-0, v=0, and C=-6fgy/w. Therefore
} (59)
Making i/ constant in equation (58) is equivalent to assuming
instantaneous combustion for that part of the charge that has
burned at the time t. We know this to be in error since the com-
bustion of the charge is progressive. If, however, we determine
the values of the constants in the equations by substituting meas-
ured values of v, we obtain an equation that is true for the meas-
ured values, and may be true for other values of v at other points
in the bore. Only by experiment can we determine whether re-
sults obtained under this supposition are correct; and experiment,
as stated by Colonel Ingalls, is the final test of nearly all physical
formulas.
41. Velocities in the Bore. To make equation (59) applicable
to points in the bore we must determine a relation between the
quantity of powder burned at any instant and the corresponding
travel of the projectile, that is, we must determine the value of y
as a function of u or x. Then substituting for y in the equation
this value, which for any powder will contain x as the only varia-
ble, we will have the desired equation expressing the relation
between the velocity of the projectile and its travel in the bore.
82 OKDNAXCE A\D GUNNERY.
Combustion under Variable Pressure. We have previously
deduced, page 26, an expression for the quantity of the powder
burned, under constant pressure, as a function of the thickness of
layer burned. This relation is given by equation (16) on that
page.
in which y is the weight of the powder burned when a thickness of
layer I has been burned, <D is the weight of the charge, 1 is half the
least dimension of the powder grain, and a, A, and /* are constants
of form of the grain.
Representing by r the time of combustion in air of the whole
grain, or charge, the uniform velocity of combustion will be IQ/T.
In the gun the powder burns under variable pressure, and the
velocity of combustion is expressed by dl/dt. Assuming that tho
velocity of combustion varies as some power of the pressure, and
representing by p the pressure of the atmosphere under which the
velocity of combustion is IQ/-C, we obtain the equation
dt T \po
in which p represents the pressure on the base of the projectile at
any instant.
The exponent <j> is given different values by different writers.
Sarrau assumes = 1/2. Recent experiments indicate a mean
value of 0.8. The value unity is assumed by other writers. In-
galls assumes the value 1/2 with Sarrau.
The pressure per unit of area on the base of the projectile is,
from equation (52),
Substituting this value of p in equation (61) and using equation
INTERIOR BALLISTICS. 83
(54) and the relations
dx__l du_v_
dt Zodt ZQ
and
dt~ dxdt ~dxz
equation (61) may be brought to the form
dx~ T\2gajpo/ \ dx / v
Integrating and dividing by 1 ,
lo~ T \2gojpJ J \ dx i v
Make
(63)
Then l/l Q = KXo (65)
Substituting this value in (60) we have
y = tfaKXo i 1 + IKX Q + fi(KX ]*} (66)
42. DISCUSSION OF VALUES. The value of K in this equation
is composed wholly of constants, a, A, and ft are the constants of
form of the powder grain. By the differentiation of equation
(59) and substitution in (64), see foot-note, page 84, we find for
the value of X
(67)
84 ORDNANCE AND GUNNERY.
X is therefore a function of x only, and x from its value, x =
is itself a function of the travel of the projectile. Equation (66)
therefore expresses, for powder of any particular granulation, the
relation between the weight burned at any instant and the corre-
sponding travel of the projectile.
This equation may be put into another form.
At the instant that the powder is all burned in the gun, y = &
and I = IQ. We will distinguish the particular values of the various
quantities at the instant that the burning of the powder is com-
pleted by putting a dash over the symbol.
When y = a> and I = IQ, equations (65) and (66) then become
KX = 1 (68)
This last relation has been previously established in equa-
tion (5).
Substituting the value of K from (68) in (66), we obtain
v . . . (69)
^0
We have now, in X Q , introduced into the value of y the travel
of the projectile at the specific instant that the burning of the
charge is complete.
*-. f 1 \
(59)
'Fran equation (64),
INTERIOR BALLISTICS. 85
Make
(70)
and X 1 /X = X 2 (71)
whence x a -i___ (72)
From equation (59) we obtain for the velocity at the instant
that the burning of the charge is complete,
(73)
43. Velocity of the Projectile while the Powder is Burn-
ing. Substituting in equation (59) the value of Qgf from (73) and
the value of y from (69), using equation (71), and making
*>- (74)
AQ
equation (59) reduces to the form
v* = MXi { 1 + NX + N'X<? | (75)
This equation expresses the value of the velocity of the pro-
jectile at any instant while the powder is burning, in terms of the
variable travel of the projectile, and of its velocity and travel at
the instant of the complete burning of the charge.
Velocity after the Powder is Burned. Distinguish with the
subscript a the values of v and p after the charge is completely
burned, y is then equal to w, and equation (59) when combined
with (73) and (72) becomes
X 2 (76)
86 ORDNANCE AND GUNNERY.
and making F x 2 = v 2 /X 2 (77)
we have v a 2 = VJX 2 (78)
which is the formula for the velocity after the powder is all burned.
This equation is identical with equation (59), if in the latter
we make y = &. Vi 2 = 6fga>/w, see (73) and (77), and X 2 is an
abbreviation for the quantity in brackets, see (72).
As explained under equation (59), equation (78) is therefore
the equation of the velocity under the supposition that the powder
is all burned before the projectile moves.
The Velocity Vi. From equation (78) we see that Vi is what
v a becomes when X 2 is equal to unity; and, equation (72), X 2 is
unity when x is infinite. V\ is therefore the velocity corresponding
to an infinite travel of the projectile.
44. Relation between the Velocities Before and After the
Burning of the Charge. Make
Jc = y/a> = fraction of charge burned.
Replacing M, N, and N' in equation (75) by their values, and
combining with equations (69), (70), and (76) we may establish
the relation
v = v a Vk (79)
That is, the velocity of the projectile before the charge is con-
sumed is equal to what the velocity w r ould have been at the same
point if all the charge had been burned before the projectile moved,
multiplied by the square root of the fraction of charge burned.
Relation between the Weight of Powder Burned and the
Velocity and Travel of the Projectile. Replacing v a in equation
(79) by its value from (78) we obtain
* or y = a>v*/VJX 2 (80)
equations that will be found convenient for determining the frac-
INTERIOR BALLISTICS. 87
tion of charge or weight of powder burned when the velocity and
travel of the projectile are known.
By reason of the form assumed by the value of k for certain
grains very simple relations may be established, for these grains,
between the fraction of charge burned and the travel of the pro-
jectile.
CUBICAL, SPHERICAL, AND SPHEROIDAL GRAINS. For cubical
grains a = 3, A= -1, and /* = l/3 (see page 20). These values
apply also to spherical and spheroidal grains. Substituting them.
in equation (69) we obtain
/i X
= l ( 1 =-
V X
(81)
and X = X l-l
From the first equation we may obtain the fraction of charge
burned for any travel of the projectile, and the converse from the
second.
SLENDER CYLINDRICAL AND PRISMATIC GRAINS. For long
slender cylinders
(82)
which also apply to grains in the form of long slender prisms of
square cross- sec tion.
For other forms of grain the solution of a complete cubic equa-
tion is necessary to determine XQ when A; is known.
45. Pressures. The general expression for the pressure per
unit of area on the base of the projectile is given in equation (62).
Transforming this equation by means of (54) and (57) we obtain
w
By substituting in succession the values of d(v*)/dx obtained
ORDNANCE AND GUNNERY.
from the equations for velocity before and after the complete
burning of the charge we will obtain the values of p that apply
before and after the charge is burned.
Pressure While the Powder is Burning. Finding the value of
d(v*)/dx from equation (75), see foot-note, and making
(84)
(85)
we obtain for the pressure per unit of area on the base of the pro-
jectile while the powder is burning
(86)
It will be observed that X s , X, and X 5 are all functions of x
only. The logarithms of their values for various values of x will
be found in Table I at the end of the volume.
Pressure After the Powder is Burned. Finding the value of
d(t?)/dx from equation (78), Vi 2 being constant, we obtain with
the aid of (72)
d(v t ?)Vi*dX 2 V?
dx
dx
(75}
Make
INTERIOR BALLISTICS. 89
Substituting in (83) and making
we obtain for the pressure per unit of area on the base of the pro-
jectile after the powder is all burned
(88)
46. Maximum Pressure. The maximum pressure in a gun
occurs when the projectile has moved but a short distance from
its seat, or when u and x are small. The position of maximum
pressure is not fixed, but varies with the resistance encountered.
As a rule it will be found that the less the resistance to be over-
come by the expanding gases the sooner will they exert the maxi-
mum pressure and the less the maximum pressure will be. By
the differentiation of equation (86) we may obtain the value for
the maximum, but it is too complicated to be of practical use.
Examination of the table of the X functions shows that ^3 is a
maximum when = 0.65, nearly, while X^ and X 5 increase indefi-
nitely. The functions XB, X 4 , and X 5 are found to vary in such
a manner that when A, and therefore N, see (74), is negative, that
is, when the powder burns with a decreasing surface, p will be a
maximum when x is less than 0.65; and when A and N are positive
or when the powder burns with an increasing surface, p will be a
maximum when x is greater than 0.65.
A function at or near its maximum changes its value slowly.
Therefore a moderate variation of the position of maximum pres-
sure will have no practical effect on the computed value of the
pressure. It has been found by experiment that if we take a: = 0.45
for the position of maximum pressure when A is negative, and
x = 0.8 when A is positive, no material error results.
Therefore to obtain the maximum pressure make x=0.45, in
equation (86) when the powder burns with a decreasing surface,
90 ORDNANCE AND GUNNERY.
and make x = 0.8 when the powder burns with an increasing sur-
face.
The Pressure P'. Combining equations (87), (77), and (73) we
obtain
Comparing this with equation (45) we see that since z Q a> is the
initial air space in the chamber, P' is the pressure of the gases from
cj pounds of powder occupying the volume behind the projectile before
the projectile has moved from its seat. This volume is 7 the initial
air space. Equation (88) is therefore the equation of the pressure
curve under the supposition that the powder is all burned before
the projectile moves.
47. Values of the Constants in the Equations for Velocity,
Pressure, and Fraction of Charge Burned. We have now these
equations which express the circumstances of motion of the pro-
jectile, and the fraction of charge burned at any instant. The
original numbers of the equations are given on the left.
While the powder burns,
(75) vZ^MX^l + NXo+N'XJ} (90)
(86) p = M'X 3 {l + NXt+N'X 6 \ (91)
After the powder is burned
(78) v a ^ = V 1 2 X 2 (92)
(88) p- (93)
The fraction of charge burned, substituting A r and N' for their
values,
(69) = x ! l + NX + N ' x <> 2 {
INTERIOR BALLISTICS. 91
The quantities M, N, N', M', V i} P f and X Q in these five equa-
tions are constant for any experiment, and their values must be
determined before the equations can be used. It will be seen in
the equations that express the values of these constants, equations
(74), (77), (85), and (87), that the quantities entering the values
are of two kinds : the known elements of fire by which is meant
the constants of the powder, of the gun, and of the projectile and
quantities such as v, XQ, Xi, etc., that involve the velocity and
travel of the projectile at the instant that the powder is all
burned.
When M and N are known all the constants are known.
The value of M given in equation (74) may be reduced by
means of (77) and (71) to
M = aV l 2 /X (95)
We have, equation (74),
(96)
M and N being known, X and Vi 2 are determined from these
equations, and N', M', and P' become known from (74), (85), and
(87).
Therefore when M and N are known the five equations, (90)
to (94), are fully determined, and all the circumstances attending
the movement of the projectile become known from them. For
any assumed travel of the projectile u, the number of expansions,
x = u/z , is obtained, and with this value of x the functions XQ to
A's are obtained from Table I. These substituted with the con-
stants in the equations give the values of v, p, and y. Proceeding
in this manner for a number of points along the bore complete
curves may be constructed showing the values of v, p, and y for
any point in the bore of the gun.
The value of x corresponding to X is obtained from the table.
The value of u follows from the equation u = xz . This value u
is the distance that the projectile has travelled at the moment
92 ORDNANCE AND GUNNERY.
that the charge is completely burned. For values of u less than
this, equations (90), (91), and (94) apply; for greater values of
u equations (92) and (93) apply.
48. Determination of the Constants by Experiment. Regarding
equation (90) and noting from equations (74) that N' is a function
of N, it will be seen that if we measure two velocities at known
points in the bore of the gun we can determine M and N from
equation (90). x being known for each of the points the X func-
tions are obtained from the table. With the two measured values
of v we then form two equations in which M and AT are the only un-
known quantities. Determining M and N the other constants
become known.
In using this method care must be exercised that the measured
velocities are taken at points passed by the projectile before the
powder has completely burned. If the powder is not wholly
burned when the projectile leaves the gun one of the measured
velocities may be taken at the muzzle.
Since M' is also a function of M, equation (85), we may make
use of the two equations (90) and (91), or (92) and (91), and with
a single measured velocity and a measured pressure determine M
and N from these equations. But it has been shown in the chapter
on powders that there is room to believe that the pressures as ordi-
narily measured with the crusher gauge are not reliable. There-
fore results obtained in this way are not likely to be as satisfactory
as those obtained from measured velocities, which can be deter-
mined with a high degree of accuracy.
It is found in fact that while the velocities obtained from the
formulas agree very closely with those actually measured in prac-
tice, there is not as satisfactory an agreement between the pres-
sures. The pressures are obtained in the formulas by the dynamic
method and are usually higher than the measured pressures.
This is in accord with what has already been said in our previous
consideration of the subject of pressures, and adds to the evidence
against the accuracy of the crusher gauge.
When r and f are known all the constants are known.
INTERIOR BALLISTICS. 93
From equations (63) and (68) we obtain
From equations (73) and (77)
(98)
from which can be determined .Y and V\ 2 . M and N follow from
equations (95) and (96).
T, the time of burning of the whole grain in air, is constant for
the same powder.
The value of /, equation (98), is dependent on the value of V\,
a quantity determined by experiment in the gun. / for any pow-
der is therefore constant, within the limits explained below, in the
same gun only. It is practically constant for guns that do not
differ greatly in caliber. Consequently when T and / have once
been determined for a powder and a gun, we may at once form the
equations of motion and pressure for different conditions of load-
ing, involving differences in the form and size of grain of the pow-
der, in the weight of the charge, in the weight of the projectile,
and in the size of the chamber and length of the gun.
49. The Force Coefficient /. The quantity / at its first intro-
duction, equation (45), was shown to be the pressure exerted by
the gases from unit weight of powder, the gases occupying unit
volume at the temperature of explosion. It was called the force
of the powder. But in the ballistic formulas it has been affected
by whatever errors there are in the assumptions made in deducing
the formulas. It can consequently be regarded only as a coeffi-
cient, and it may conveniently be called the force coefficient.
Its value, when determined by experiment, may be considered
constant in the same gun for charges of the same powder not
differing in weight by more than about 15 per cent from the
charge used in determining its value. The effective value of the
force coefficient is measured in the formulas by projectile energy,
94 ORDXANCE AND GUNXERY.
and there has been omitted in deducing the formulas all considera-
tion of the force necessary to start the projectile. As the charge
decreases the portion of the developed force necessary to start the
projectile bears a larger relation to the total force exerted; and if
the charge is sufficiently small the projectile will not start at all.
The effective force for a small charge must therefore be proportion-
ally less than for a large charge, and the value of / determined
from one charge must be modified for use with another that differs
greatly in weight. The formula used by Ingalls for this modifica-
tion will be found in equation (137), problem 3 of the applications
which follow.
Values of the X Functions. We may simplify the value of
X by means of circular functions. In equation (67) make
sec =
we may then deduce, see foot-note,
dd
The value of this integral, designated as (6), is given in Table V
of the book of ballistic tables for every minute of arc up to 87
degrees. We therefore have, simply
Differentiating the equation sec 6= (1-f #)i
dsec 6 = sec 6 tan 6 dd=}(l + x)~*dx=dx/6 sec 8
From the second and fourth members,
dx=Q sec 6 6 tan Odd
tan 6= (sec 2 0-l)*=
Equation (67) becomes
y /*6 sec 6 tan 6 dd
*'"V sec3 e tanfl
INTERIOR BALLISTICS. 95
From the equations giving the values of the various X func-
tions, (70), (71), and (84), first making
X
we may now deduce the following values:
i
The logarithms of the values of the X functions for various
values of x are found in Table I at the end of the volume.
The argument in the table is x. The value of is obtained
from the equation x = u/Zo, in which u is the travel of the projectile
and ZQ the reduced length of the initial air space. Knowing z
and assuming the travel we obtain x and from the table find the
corresponding values of the functions.
Interpolation, Using Second Differences. It will often be
necessary in determining values of the functions for values of x
not given in the table to employ second differences in order to get
the desired accuracy in the interpolated values of the functions.
In a table containing values of a function, the first differences
are the differences between the successive values of the function.
The second differences are the differences between the successive
values of the first differences. Thus if the successive values of
an increasing function are a, a', and a" , the first differences
are a' a = Ji, and a" a' = Ji'. The second difference is then
J l '-J l = J 2 -
The interpolation may be effected by the following formula.
The sign of the last term in this formula is made + so that, in
this particular table, only the numerical values of the second
differences need be considered.
ORDNANCE AND GUNNERY.
, (99)
in which x is the given value of the argument, lying between the
tabular values x a and z& ;
h = Xb~ x a ,
A\ and ^2 are the first and second differences of the func-
tion under consideration,
X a the tabular value of the function corresponding to
X a ,
X the interpolated value of the function corresponding
to x.
It will be observed that the difference between successive values
of x varies in different parts of the table. In applying the formula
we must use the same value of h in getting the two first differences
from which the second difference is obtained.
The lower sign of the second term of the second member must
be used when the function decreases as x increases. This sign will
only be required for the values of the function X 3 when the value
of x is greater trj^n 0.65.
EXAMPLES. 1. What is the value of log X corresponding to
1st diff. 2d diff.
Z = logX (z = 1.15) 0.52960 792 = 4 36 = J 2
log X (x = 1.20) 0.53752 756
log X (x = 1.25) 0.54508
X = (0.52960) + f 792 + f x f X 36 = (0.52960) + 316.8+8.6
The parentheses around 0.52960 indicate that this number
is to be treated as a whole number in applying the corrections.
Therefore
0.52960
316.8
8.6
X-log X (x = 1.17) =0.53285
INTERIOR BALLISTICS. 97
2. What is the value of log Xi when x = 0.563?
Ans. Log Xi= 9.53337.
3. Log X 3 for x = 0.275. Log X 3 = 9.82216.
4. Log .Y 3 for x = 2.18. Log X 3 = 9.76089.
5. Log X 5 for x = 0.772. Log X 5 = 1.15879.
50. The Characteristics of a Powder. The quantities/, r, a, Jl,
and /* were called by Sarrau the characteristics of the powder,
because they determine its physical qualities. Of these factors, /,
the force coefficient of the powder, depends principally upon the
composition of the powder. In the same gun it is practically
constant for all powders having the same temperature of com-
bustion. It increases with the caliber of the gun, and for this
reason its value determined for one caliber cannot be depended
upon for another. The factor T, the time of combustion of the
grain in air, depends upon the least dimension of the grain and
upon the density ; also, in smokeless powders, upon the quantity of
solvent remaining in the powder. The factors a, X, and /z depend
exclusively upon the form of the grain, and for the carefully pre-
pared powders now employed their values can be determined with
precision. They are constant as long as the burning grain retains
its original form.
APPLICATION OF THE FORMULAS.
For convenience of reference the notation employed in the
deduction of the formulas is here repeated, and the units custom-
arily employed in our service are assigned to the different quan-
tities. For most of these quantities specific units have not here-
tofore been designated.
a denned by equation (101) below.
C volume of powder chamber, cubic inches.
d caliber in inches.
DI outer diameter of powder grain, inches.
98 ORDNANCE AND GUNNERY.
di diameter of perforation of powder grain, inches.
/ force coefficient of the powder, pounds per square inch.
F fraction of grain burned.
g acceleration due to gravity, 32.16 foot-seconds.
Jc = y/a } fraction of charge burned.
I thickness of layer burned at any instant, inches.
Z one half least dimension of grain, inches.
L constant logarithms in the ballistic equations.
m length of powder grain, inches.
M ballistic velocity constant, foot-seconds.
J!/' ballistic pressure constant, pounds per square inch.
N, N' ballistic constants.
n number of powder grains in one pound.
P' ballistic pressure constant, pounds per square inch.
p pressure while powder burns, pounds per square inch.
p a pressure after powder is burned, pounds per square inch.
p m maximum pressure, pounds per square inch.
PQ standard atmospheric pressure, 14.6967 Ibs. per square
inch.
$1 initial surface of a pound of powder, square inches.
u travel of projectile, inches.
U total travel of projectile, inches.
v velocity of projectile while powder burns, foot-seconds.
v a velocity of projectile after powder is burned, foot sees.
V muzzle velocity of projectile, foot-seconds.
Vi ballistic constant, velocity at infinity, foot-seconds.
v e velocity of combustion of powder, foot-seconds.
VQ specific volume of a gas, cubic feet.
V initial volume of a powder grain, cubic inches.
w weight of projectile, pounds.
x number of expansions of volume of initial air space.
XQ, Xi, X2, Xs, X, X 5 , functions of x.
y weight of powder burned at any instant, pounds.
Zo reduced length of initial air space, inches.
INTERIOR BALLISTICS. 99
ffl
A | constants of form of powder grain.
*J
d density of powder.
J density of loading.
(I) weight of powder charge, pounds.
T time of burning of whole grain in air, seconds.
aj cross section of bore, square inches.
Quantities topped with a bar, as v, x, u } X2, etc., designate
the particular values of the quantities at the instant of com-
plete burning of the powder charge.
With the units assigned above the following working equa-
tions are, with the aid of equation (28), derived from the equa-
tions whose numbers appear on the left. The numbers in brackets
are the logarithms of the numerical constants after reduction to
the proper units.
(22) J = [1.44217]0/C (100)
(27) a = d ~
(29) 2 = [1.54708]a<D/cP (102)
(57) x = u/z (103)
(73) v 2 = [4.44383] / X 2 a/w (104)
(85) M' = [3.82867]Mw/a<o (105)
(87) P f = [S.35155] V^w/ocD (106)
(89) P' = [1.79538] //a (107)
(97) T = [2.56006]v / a^DX /d 2 (108)
(98) / = [5~.55617]Fi 2 w>/a> (109)
100 ORDNANCE AND GUNNERY.
In addition to the above working equations the following
formulas are needed or are useful in the solution of most problems.
(74) M=av 2 /X l N=X/X N f = ii/X<? (110)
(95) M = aV l 2 /X (111)
(75) v^MXiil + NXo+N'Xo 2 } (112)
(86) p = M'X 3 {l + NXt+N'X 5 \ (113)
(78) vJ-VJX* (114)
(88) Pa =i (115)
(80) k = y/a> = v*/V l 2 X 2 (116)
(124)
(137)
(138)
51. Transformation of the Formulas into the Forms (104)
to (109). In the deduction of the formulas the quantities
have been expressed in general terms, no units having been
assigned.
In assigning now to the velocity v the foot-second unit and to
the weights the pound unit, we fix the units in the formulas as
the foot, the pound, and the second. All dimensional quantities
in the formulas must then be considered as expressed in feet,
square feet, or cubic feet; pressures in pounds per square foot, and
time in seconds. As appears on page 98, we intend now to pre-
INTERIOR BALLISTICS. 101
serve the footrsecond as the unit of velocity, but to express the
dimensional quantities, such as d, aj, z , u, etc., in terms of the inch
as the unit, and the pressures in pounds per square inch. We must
therefore introduce into the formulas such factors as will make
them applicable to the new units.
This is accomplished as follows.
Equation (104). In the value of v 2 , equation (73), g is already
in feet, a> and w in pounds; X2 is dependent only on x, which is a
ratio independent of the unit. /, which we now express in pounds
per square inch, must, before being substituted for / pounds per
square foot in (73), be converted into pounds per square foot by
multiplying by 144. We therefore get for the numerical factor
whose logarithm appears in (104) the quantity 6 g 144.
Equation (105). The quantity ZQOJ in (28) is expressed in
cubic inches, and before substituting its value for Z Q CJ cubic feet
in the formulas we must divide the value by 1728. This sub-
stitution is made in equation (85). M' is a pressure in pounds
per square foot, as may be seen by substituting for M its value
from (74). Equation (85) then becomes M' = (wv 2 /2g)Xa/Xiajz ,
work divided by a volume, or pressure, see equation (40). To
reduce M' to pounds per square inch in order to convert into
pounds per square inch the pressures determined from equation
(86) we must divide it by 144. With these two operations we
obtain, for the numerical factor in (105),
17287(144X20 27.68) =Q/g 27.68
Equation (106). Substitute for ZQOJ in (87) its value from
(28) divided by 1728, and divide the value of P by 144 to
reduce P' to pounds per square inch. The numerical factor is
2/g 27.68.
Equation (107). Substitute for Z Q OJ in (89); multiply /
now in pounds per square inch by 144, and divide by 144 to
reduce P f to pounds per square inch. The numerical factor is
1728/27.68.
102 'ORDNANCE AND GUNNERY.
Equation (108). From (97), multiplying and dividing b> a>*.
/ 27.68ati>\*
The numerical factor becomes
Equation (109). Reduce (98) to pounds per square inch by
dividing by 144. The numerical factor is l/6# 144.
DETERMINATION OF THE BALLISTIC FORMULAS
FROM MEASURED INTERIOR VELOCITIES.
52. As a test of the formulas that have been determined, and at
the same time to illustrate their extensive use, we will follow Colonel
Ingalls in his application of these formulas to the experiments
made by Sir Andrew Noble in 1894 with a six-inch gun. The
normal length of the gun was 40 calibers, but it could be lengthened
as desired to 50, 75, or 100 calibers.
The length of a gun when expressed in calibers ordinarily means
the length measured from the front face of the closed breech block
to the muzzle of the gun. The travel of the projectile is the distance
passed over by the base of the projectile, measured from its posi-
tion in the gun when loaded. The length of the gun in calibers is
therefore equal to the travel of the projectile plus the length of the
powder chamber.
By means of a chronoscope not differing in principle from tl
Schultz chronoscope that has been described, the velocity of the
shot could be measured at sixteen points in the bore. Noble gives
the mean instrumental error of the chronoscope as three one-
millionths of a second.
Problem i. A 100-pound projectile was fired from this 6-incl
gun with a charge of 2?i Ibs. of cordite. Diameter of grain 0".'
INTERIOR BALLISTIC*. 103
density 1.56. Velocities measured at points corresponding to the
different positions of the muzzle were as follows.
u = 199.2 inches r = 2794 f . s.
259.2 " 2940 "
409.2 " 3166 "
559.2 " 3284
The volume of the chamber was 1384 cu. in.
Determine all the circumstances of motion.
Constants of the gun. Constants of the powder.
= 1384 d> = 27.5
d = 6 3 = 1.56
17 = 559.2 a = 2 1
A= -} (see page 21)
From equation (100), J = 0.55
(101)., log a = 0.07084
(102), Iogz = 1.50096
Zo-31.693
METHOD OF PROCEDURE. With Z Q we may determine from equa-
tion (103) the value of x corresponding to any travel of the pro-
jectile, and with x we may obtain from Table I the corresponding
values of the X functions.
We have now all the necessary data for the solution of the
problem, and from this data we must determine the values of
the constants in the five formulas (112) to (116). The pro-
cedure is as follows.
A. 1. Select two of the measured velocities and the corre-
sponding values of the travel u, and assume that the velocities
were reached before the powder was all burned.
2. Substitute successively in (112) the selected values of v
104 ORDNANCE AND GUNNERY.
with the values of the X functions obtained with the corresponding
travels.
We have then two equations in which only the constants are
unknown. As N' is a function of N, there are but two constants,
M and N, to be determined from the two equations.
8. Determine M and N from the two equations.
4. With the value of N find from the second of equations (110)
the value of XQ, and with this determine from the table the value
of x, and from (103) the value of u.
5. The powder was all burned at this travel u, and if the
values of u corresponding to the selected velocities are less than
u, we were right in assuming these two velocities as having been
reached before the powder was all burned.
Our determinations of M and N are therefore correct, and,
as explained on page 91, all the other constants may be deter-
mined from these two.
53. B. If, however, one or both of the selected velocities were
reached at a travel greater than u, our assumption that they
were both reached before the powder was burned was wrong and
our values of M, N, and u obtained under that assumption are
wrong.
We must therefore determine new values of M and N as
follows.
Substitute the first of the selected velocities with the corre-
sponding values of the X functions in (112) as before. Sub-
stitute the second selected velocity in (114) with the value of X 2
corresponding to the travel.
Determine Vi.
Replace N, N f , and M in_ (112) by their values from (110)
and (111). Then in (112) X is the only unknown quantity,
and its value can be determined.
With XQ and V : the values of M and N are readib
found.
C. The constants cannot be determined if both the selecl
velocities were reached after the powder was wholly burn<
INTERIOR BALLISTICS. 105
Equation (114) should give the same value of Vi for both the
selected velocities.
Now to revert to the problem, which will be solved after the
first method, designated A, and the steps of the solution will
be numbered as in the explanation above.
We have to determine the ballistic constants for use in the
velocity and pressure formulas.
Since /* = we see from equation (110) that
tf'-O
and that since A is negative N is also negative.
Velocity formula (112) therefore becomes for this powder
(117)
from which with two measured values of v and the correspond-
ing values of u, and hence of X\ and X 0) we may determine M
and N. We must use for this purpose two values of v while the
powder is burning.
1. We will take the two measured values 2794 and 3166 and
determine afterwards whether we are right in the selection.
2. The ^Y functions for u = 199.2 corresponding to v = 2794
are found as follows.
Equation (103), x = 6.2853, for u = 199.2.
From the table of X functions, using first differences only,
log X = 0.821 10
In the same way the other functions for this value of x, and
the functions for the values of x corresponding to the other given
values of u, are obtained from the table.
u
x
v
log A'
log*,
log*,
199.2
6.2853
2794
0.82110
0.50606
1.68496
259.2
8.1784
2940
0.86213
0.58011
1.71799
409.2
12.9112
3166
0.93117
0.69774
1.76657
559.2
17.6446
3284
0.97710
0.77150
1.79440
106 ORDNAXCE AND GUNNERY.
In equation (117), using two values v and v' and the values
of X and Zi corresponding to each, and solving for N and M,
we obtain
N =
v 2
3. Making v = 2794 and i/ = 3166, we obtain with the corre-
sponding values of X Q and Xi
log M = 6.59155
log # = 2.75465
With these, as has been shown on page 91, all the other ballistic
constants are determined.
4. We will first determine from the second of equations (110)
log X = 0.94432
and from the table find the corresponding value of x by inter-
polation, using first differences only,
From equation (103) ^ = 447.19, that is, the burning of the
powder was completed at the instant that the shot had travelled
447.19 inches.
5. The values of u for the points selected for the determina-
tion of the constants in the equations being less than u we find
ourselves justified in the selection of these points.
From equation (105) log M f = 4.91005
(111) log 7i 2 = 7.23484
(106) logP' =5.07622
INTERIOR BALLISTICS. 107
We now have all the constants that enter the equations (112)
to (116) for velocity and pressure and fraction of charge burned.
These equations become for this round
v 2 = [6.59155JY! (1 - [2.75465]X ) (118)
p = [4.91005PT 3 (1 - [2.75465]X 4 ) (119)
(120)
2 (122)
With these five equations we can determine the velocity,
pressure, and weight of powder burned as the projectile passes
any point in the bore, by substituting the values of the X func-
tions determined from Table I for the value of x corresponding
to the travel of the projectile at the point.
In this way we find from equation (118) for u = 259.2, for which
x = 8.1784, (the symbol L indicates a constant logarithm in the
equation),
log^o 0.86213
L 2.75465
0.41379 1.61678
0.58621 1.76805
logA'i 0.58011
L 6.59155
log v 2 0.93971
log v 3.46985
v = 2950 foot-seconds
This differs from the measured velocity by 10 feet.
To find the velocity at the muzzle, for comparison with the
measured velocity, we must make use of equation (114), since the
powder was all burned before the projectile reached the muzzle.
108 ORDNANCE AND GUNNERY.
log 7i 2
log X 2
logF 2
log V
7 =
7.23484
1.79440
7.02924
3.51462
3270.5 foot-seconds
This differs but 13.5 feet from the measured velocity of 3284
feet. The difference, T \ of one per cent of the measured velocity,
is negligible.
In the same way the velocity at any point may be determined
and the curve v in Fig. 20 plotted.
54. Pressures. The pressure at any point may be similarly
obtained from equations (119) and (121). The pressures so ob-
tained are plotted in the curve p, Fig. 20.
MAXIMUM PRESSURE. As the cylindrical grain burns with a
decreasing surface the maximum pressure is obtained as explained
on page 89 by making a; = 0.45 in equation (119),
for x=0.45 log X 3 = 1.85640 log X 4 = 0.48444
With these values we get from equation (119)
p m = 48,276 Ibs.
Weight of Powder Burned. From equation (122) we obtain
the curve y, Fig. 20, which shows the weight of powder burned at
each point of the travel. From this curve it is seen that at the
point of maximum pressure, for which u = 14.26 inches, about 12
of the 27.5 pounds of the charge were consumed. The charge was
half consumed when the travel was 18 inches, and three-quarters
consumed at a travel of about 68 inches.
The following table obtained from the three equations, (118),
(119), and (122), is represented by the curves v, p, and y in Fig.
INTERIOR BALLISTICS.
109
110
ORDXAXCE AXD GUNNERY.
Travel
Veolcity
Pressure
Powdei burned
X
u
V
P
y
inches.
ft. -sees.
pounds.
pounds.
0.2
6.34
564.99
43929
8.669
0.4
12.67
876.56
48183
11.597
0.6
19.02
1109.1
47558
13.584
0.8
25.36
1295.2
45569
15.097
1.0
31.69
1449.8
42S95
16.315
1.5
47.54
1747.9
36632
18.589
2.0
63.38
1967.2
31386
20.209
2.5
79.24
2138.0
27158
21.442
3.0
95.08
2276.1
23738
22.419
4.0
126.77
2488.0
18600
23.873
5.0
158.46
2644 . 2
14975
24.898
6.2853
199.2
2794.0
11642
25.822
8.1784
259.2
2950.0
8329
26.677
12.9112
409.2
3166.0
3840
27.475
14.1100
447.2
3198.0
3191
27.500
17.6446
559.2
3271.0
2411
In the figure the curve y stops at the travel u because equation
(122) can only apply as long as the powder is burning. The pow-
der, wholly burned at u, is of course wholly burned at every point
beyond u.
The curves v a and p a in Fig. 20 are similarly obtained from
equations (120) and (121). They represent the velocity and pres-
sure under the supposition that the powder was wholly burned
before the projectile moved, and from them are obtained the
velocities and pressures in the gun after the powder is all burned,
that is, after the travel u.
The size of the page does not permit the representation of the
first part of the curve p a . This curve intersects the vertical axis
at a point obtained by making z = in equation (121), for which
value p a = 119,180 Ibs. per sq. in. = P', see (115). As explained on
page 90, P f is the pressure per unit of surface exerted by d> pounds
of powder confined in a volume equal to the initial air space.
The Force Coefficient / and Constant T. From equation
(109) / =2247.4 Ibs. per sq. in.
(108) T = 0.50486 seconds
INTERIOR BALLISTICS. Ill
/ was originally considered as the force of the powder or, in the
units assigned, the pressure exerted by a pound of a gas occupying
a cubic foot at the temperature of explosion, see equation (45).
But it has been affected by whatever errors there are in the as-
sumptions made in the deduction of the formulas. It can conse-
quently be regarded only as a coefficient, called the force coefficient.
T is the total time of burning of the grain in air. The velocity
of burning in air is, therefore, for this grain,
ZO/T = 0.39615 inches per second.
55. Velocity of Combustion. The velocity of combustion of
the powder at any instant may be obtained from equation (61).
(123)
by substituting the value of p corresponding to any point in the
travel of the projectile.
Thus at the moment of maximum pressure, p m = 48,276, and
v c = 22.7 inches per second.
At this rate of burning the charge would be consumed in about
nine one-thousandths of a second.
Thickness of Layer Burned. Combining equations (65) and
(68) we obtain
l = loX /Xo (124)
Substituting for any point the value of XQ we obtain Z.
Thus for u = 199.2, log X = 0.82110, and for the thickness of
layer burned at this travel
1 = 0.1506 inches.
Variation in Size of Grain. The thickness of layer burned at
any travel of the projectile is evidently the half thickness of web
112 ORDNANCE AND GUNNERY.
of some whole grain of the same shape that would be completely
burned at that point. We may therefore write in equation (124)
1 Q ' for I and X ' for X and form the equation
2Zo' = 2ZoXo7-Xo (125)
The web of a grain designed to be completely burned at any
travel of the projectile under the same conditions of loading as
in problem 1 will therefore have a thickness equal to twice the
thickness of layer burned at the travel as obtained in that problem.
For u = 199.2, 2/ ' = 0.3012 inches,
which is twice the value we found for I at this length of travel.
Variation in Initial Surface of Charge for Same Shape of
Grain. From equations (19) and (125) we obtain
St'-SiXo/Xo' (126)
For the grain whose web we have just determined the initial
surface of the charge would have the following relation to the
same weight of charge of the powder used in problem 1.
&'- 1.322 &
56. Variations in Gun, Powder, or Projectile. Having
once determined the constants r and / for any powder in a gun
of any caliber, we may assume any variation in the gun except
in caliber, or any variation in the powder or in the projectile,
and determine the effect of the variation on the circumstances
of motion. T, the time of complete burning of the grain in air, is
proportional to the web thickness. Its value for the same powder
in grains of any other shape or size is equal to the determined
value multiplied by the ratio of the web thicknesses of the new
grain and of the grain used in the determination. For any as,
sumed size of the chamber and fixed weight of charge or density
INFERIOR BALLISTICS. 113
of loading v/e may proceed exactly as in problem 1. For changes
in the weight of the charge or of the projectile the procedure is
the same as in that problem. For changes in the shape of the
powder grain the method to be pursued will be best understood
from an example.
Problem 2. Suppose that the powder used in problem 1
instead of being made up into cylindrical grains was made into
ribbons 0".4 thick, 2" wide, and 8" long, of the same density
as the cylindrical grains.
Determine the circumstances of motion with the same weight
of charge, 27J pounds, as in that problem.
The thickness of web, 0".4, is the same as for the cordite
cylinder.
The values of the constants of form for the parallelepiped
grain are, see page 19,
a=l+x+y
_x + y+xy
" l + x+y
xy
in which x = 2l G /m and y = 2lo/n.
Making x = 0.4/8 = 0.05 and y= 0.4/2 =0.2 we find for the
ribbon grain assumed in this problem
a = 1.25, A=- 0.208, /i = 0.008.
As the initial surfaces of two charges of equal weight com*
posed of the same powder in grains of different shapes are to
each other as the values of a for the two forms of grain, see equa-
tion (19), the initial surface of this charge will be 1.25/2 = 5/8
of the initial surface of the charge in problem 1, and as the maxi-
mum pressure is dependent upon the initial surface we may expect
a lower maximum pressure from this charge than from the first.
The values of / and T determined in problem 1, being constant
for the same powder and gun, are applicable to this round, and
it will be seen from equations (100) to (109) that J, a, z , v 2 ,
P', Xo, and V\ 2 have the same values as in that problem.
lit
Therefore from equations (110), (111), and (105) we obtain
at once the values of the constants in the formulas for velocity
and pressure.
log M= 6.38743
log AT =2.37374
log N f =4.01445
log M'= 4.70593
and with these values we may write the formulas for velocity
and pressure while the powder is burning.
^ = [6.38743]X 1 {1-[2.37374]X + [4.01445]X 2 },
p = [4.70593]X 3 !l-[2.37374]X 4 + [I.01445]Z 5 |.
The formula for the weight cf powder burned is the same
as in problem 1, equation (122), but since the value of v for any
value of x is now different the weights burned at the different
travels will also be different.
The formulas for velocity and pressure after the charge is all
burned are the same as in problem 1, equations (120) and (121),
and the velocities and pressures beyond the point of complete
consumption are the same. The point of complete consumption
is the same as in that problem, since XQ has the same value.
The velocities and pressures and weight of powder burned
under the conditions of this problem are shown in the subjoined
table and in Fig. 21.
Powder
Travel
Velocity
Pressure
burned
X
u
V
P
y
inches.
f. s.
pounds.
pounds.
0.2
6.34
458.86
29584
5.718
0.4
12.67
720.16
33587
7.828
0.6
19.02
919.33
34089
9.333
0.8
25.36
1081.6
33381
10.528
1.0
31.69
1218.6
32220
11.527
1.5
47.54
1489.7
28926
13.503
2.0
63.38
1696.1
25922
15.024
2.5
79.24
1862.3
23390
16.269
3.0
95.08
2005.6
21278
17.326
4.0
126.77
2223.2
18001
19.062
5.0
158.46
2397.2
15600
20.465
6.2853
199.2
2576.0
13324
21 . 947
8.1784
259.2
2780.3
10977
23.697
12.9112
409.2
3131.0
7559
26.871
14.1100
447.2
3198.0
7091
27.500
17.6446
559:2
3271.0
2411
INTERIOR BALLISTICS.
115
116
ORDNANCE AND GUNNERY.
Comparing this charge, by means of the tables or of the curves,
with the charge in problem 1 we see that while the muzzle velocity
is the same the maximum pressure is reduced from about 48,000
to about 34,000 Ibs. The pressures along the chase are increased.
The total area under the pressure curves, which represent the
work expended upon the projectile, must be equal.
It is apparent from the powder curves that the powder burned
more progressively in the second charge than in the first. This
was to have been expected, for if we compare the rate of burning
of the two grains in air by means of equations (9) and (7), dividing
the half thickness of web into five equal parts, we find for the
fraction burned in each layer:
Cordite grains ....
Ribbon grains ....
0.36 0.28 0.20 0.12 0.04
0.24 0.22 0.20 0.18 0.16
57. Velocities and Pressures after the Powder is Burned.
We have seen, pages 86 and 90, that equations (114) and (115)
are the equations for the velocity and pressure under the supposi-
tion that the powder is all burned before the projectile moves.
The curves v a and p a in Figs. 20 and 21 are calculated from
equations (120) and (121) for both shapes of grain. They are
alike in the two figures since the weight of charge is the same.
The curve v a , from equation (120), shows what the velocities
would be if the 27 J pounds of powder were all burned before the
projectile moved, and the curve p a shows the pressures under
the same condition.
We find in practice that the velocities measured beyond the
point where the powder is all burned agree with the velocities
obtained from the v a formula. We are therefore warranted in
using this formula for determining velocities after the powder
is burned. And if the correct velocities are given by the v a for-
mula, the pressures obtained from the p a formula must also be
correct.
Therefore velocities and pressures after the powder is all
burned are taken from the v a and p a curves or formulas.
INTERIOR BALLISTICS. 117
From the manner of deduction of equations (112) and (114)
these two equations will give the same value v for the value u.
The curves v a and v therefore coincide at that value of the travel.
It will be observed, however, in Fig. 21, that the curves p a and p
for the ribbon grain do not coincide at the travel u.
It may be shown analytically that these curves coincide only
for grains of such form that the vanishing surface is zero; such
as the cube, sphere, or solid cylinder, see page 18. The vanishing
surface of the ribbon grains of this problem is a finite surface
that suddenly becomes zero at the travel u. Coincidence of the
two curves at this point could therefore not be expected.
The curves p a and p in Fig. 20, for the cordite grain, coincide
at u, since the vanishing surface of the cordite grain is zero.
58. The Action of Different Powders. In Fig. 22 the curves of
velocity, pressure, and weight of powder burned, from problems
1 and 2, are shown together. This figure serves well to illustrate
the action of different powders in the gun.
The curves with the subscript 1 are taken from problem 1,
in which the charge was 27.5 Ibs. of cordite. The curves with
subscript 2 are from problem 2, in which the charge was of
the same weight as in problem 1 and of powder of the same com-
position, but made up into ribbon-shaped grains with the same
thickness of web as the cordite.
Regarding the curves y\ and 7/2 we see that the burning of
the charge of powder was completed in each case at the same
point of travel, u = 447.2 inches. The quantity burned at any
travel less than u was less for the ribbon grain than for the cordite.
The rate of emission of gas as a function of the travel of the
projectile is shown by the tangents to the curves yi and y 2 . For
equal travels of the projectile the ribbons gave off gas less rapidly
at first and until the projectile had traveled about 63 inches, at
which point the curves yi and y 2 are farthest apart. From this
point on the ribbon grains emitted gas more rapidly than the
cordite.
We consequently find in the pressure curves lower pressures
118
ORDNANCE AND GUNNERY.
r 7f*-
i i < i | i i i < O '
INTERIOR BALLISTICS. 119
from the ribbon grains over this part of the bore. The maximum
pressure is lower and occurs later than the maximum pressure
from the cordite. After the travel of* 63 inches the pressure is
better maintained by the more rapid evolution of gas from the
ribbon grains and we find that the pressure curve p 2 falls off more
slowly than the curve pi, so that the two curves rapidly approach
each other, and later cross at a travel of about 130 inches.
At the instant before the travel u is reached the area of the
burning surface of the ribbon grains has a considerable value.
It may readily be determined, from the given dimensions and
density of the ribbon grains, that there are 76 of these grains
in the charge of 27 J Ibs. The initial surface of the charge is 3040
square inches.
The vanishing surface of each grain, determined by mensu-
ration or by making 1 = 1 in equation (1), is 24.32 square inches,
and for the 76 grains, 1848 square inches. This is more than 6/10
of the original surface.
At the travel u this large burning area suddenly becomes zero.
There is a sudden cessation of the emission of gas and a sharp
drop in the pressure. As the burning surface of the cordite
grain approaches zero gradually the pressure curve pi of this grain
is continuous.
Since at the travel u the projectile has the same velocity
from the two charges, the work done upon it is the same in each
case, and the areas under the pressure curves to this point must
be equal.
Corresponding with the sudden change in pressure at the
travel u we find in the curve v 2 a sudden variation in the rate
of change of the velocity of the projectile as a function of the
travel, represented by the tangent to the curve.
The above considerations apply to the 100 caliber length of
the gun.
Now if we consider the gun as 40, 50, or 75 calibers in length
neither charge would have been wholly consumed in the bore;
and we see from the curves that in each case the muzzle velocity
120 ORDNANCE AND GUNNERY.
would be less from the slower burning powder. It is therefor
apparent that to produce in the gun of any of these lengths a give
muzzle velocity, vi, taken "from the cordite curve, a larger cfo
of the slower powder would be required.
The maximum pressure from the larger charge of slow powd(
would remain less than that from the quicker powder, since
area under the two pressure curves must be equal and the pn
curve of the slow powder would be the higher at the muzzle.
As the gun is longer the difference in the weight of the
charges of the quick and slow powder that produce the same
muzzle velocity is less, until at some length the difference becomes
zero. The advantage of lower maximum pressure always remains
with the slower powder.
59. Quick and Slow Powders. It is apparent from Fig. 22 that
if the maximum pressure and the muzzle velocities obtained from
the cordite in the 40 and 50 caliber guns are satisfactory, the
muzzle velocities produced by the same charge of powder in the
form of ribbons would be too low. This powder would be too slow
for guns of those lengths, while for the guns of 75 or more calibers
it would be satisfactory.
The powder for a gun of any caliber and length has the greatest
efficiency when in grains of such shape and dimensions that the
charge of least weight produces the desired muzzle velocity within
the allowed maximum pressure. The powder that produces
these results may be considered the standard powder for the
gun.
The maximum pressure is dependent on the initial surface of
the powder charge. A powder with greater initial surface than the
standard powder, that is a powder of smaller granulation, will
produce a greater maximum pressure and therefore will be a quick
powder for the gun, and a powder of larger granulation will be a
slow powder.
In powder grains that are similar in shape but of different
dimensions, the thickness of web will vary as the square root of
the surface. We may therefore judge as to whether the powder
INTERIOR BALLISTICS. 121
is quick or slow for any gun by comparing its web thickness with
that of the standard powder of the same shape.
It is also found that usually a powder that is satisfactory in a
gun of a given caliber is slow for a gun of less caliber and quick
for a gun of larger caliber. Therefore, as has been shown in the
chapter on gunpowders, a special powder is provided for each
caliber of gun and for markedly different lengths of the same
caliber.
Effects of the Powder on the Design of a Gun. In the
design of a gun, the caliber, weight of projectile, and muzzle velocity
being fixed, consideration must be given to the powder in order
that the size of chamber, length of gun, and thickness of walls
throughout the length may be determined. We have seen that to
produce a given velocity in any gun we require a larger charge of
a powder that is slow for the gun than of a quicker powder. The
larger charge will require a larger chamber space, and will thus
increase the diameter of the gun over the chamber. The maximum
pressure being less than with the quicker powder the walls of the
chamber may be thinner. The slow powder will give higher pres-
sures along the chase, therefore the walls of the gun must here be
thicker. The weight of the gun is increased throughout its
length.
If we do not wish to increase the diameter of the chamber we
must, for the slow powder, lengthen the gun in order to get the
desired velocity.
On the other hand, with a powder that is too quick for the gun
very high and dangerous pressures are encountered, requiring ex-
cessive thickness of walls over the powder chamber. The difficul-
ties of obturation are increased. Excessive erosion accompanies
the high pressures and materially shortens the life of the gun.
The gun may be shorter and thinner walled along the chase.
It is evident from the above considerations that each gun
must be designed with a particular powder in view, and that a
gun so designed and constructed will not be as efficient with any
other powder.
122 ORDNANCE AND GUNNERY.
DETERMINATION OF THE BALLISTIC FORMULAS FROJ
A MEASURED MUZZLE VELOCITY AND MAXIMUM
PRESSURE.
60. In the previous problems we determined the constants in the
ballistic formulas by means of measured interior velocities. This
method will usually not be available, as interior velocities can be
measured only by special apparatus not usually at hand. The
usual data observed in firing are the muzzle velocity and the
maximum pressure.
The method of determining the constants with this data is
illustrated in the following problem, and at the same time the
method of applying the formulas to the multiperf orated grain.
Problem 3. Five rounds were fired from the Brown 6 inch
wire wound gun at the Ordnance Proving Grounds, Sandy Hook.
March 14, 1905. The projectiles weighed practically 100 Ibs.
each. The charge was 70 Ibs. of nitrocellulose powder in multi-
perforated grains, with two igniters, each containing 8 ounces of
black powder, at the ends of the charge. The multiperf orated
grains weighed 89 to the pound. They were of the form described
on page 22. Their dimensions, corrected for shrinkage, were
Di=Q"M2 di=0".051 m = l".029
The mean muzzle velocity of the five rounds was 3330.4 f . s.
The measured maximum pressure was 42,497 Ibs. per sq. in.
The capacity of the powder chamber was 3120 cubic inches.
The total travel of the shot w r as 252.5 inches.
Determine the circumstances of motion.
Before we can proceed with the solution of the problem we
must determine the constants of the powder. We will make no
distinction between the two different kinds of powder, but con-
sider the weight of charge as 71 pounds of multiperforated powder.
Dimensions of grains, Di = 0".512, di = 0".051, m=l".029.
Weight of grain, 89 to 1 pound.
We will first determine the constants of form of the powder
grain.
INTERIOR BALLISTICS. 123
From equation (13)
2Z = O.OS975
and from equations (12) we find a = 0.72667, A = 0. 19590, // = 0.02378.
Equation (11), in which F is the fraction of grain burned when
the web is burned, therefore becomes for this grain
F=0.72667/- j 1 + 0.19590^-0.02378^ 1 (127)
to I /o to 2 j
Making 1 = 1 ,
F = 0.85174 (128)
the fraction of grain burned when the burning of the web is com-
pleted. The slivers therefore form 0.14826 of this particular grain.
FICTITIOUS MULTIPERFORATED GRAIN. The body of the grain
burns with an increasing surface, while the slivers burn with a
decreasing surface. To avoid the difficulties that would follow
from the introduction of the two laws of burning into the ballistic
formulas, we will substitute for the real grain a fictitious grain
with such a thickness of web that when the web is burned the
same weight of powder is burned as when the whole of the real
grain is burned; that is, the body of the fictitious grain is equiv-
alent to the whole of the real grain.
For the body of the fictitious grain F in the formula of the
fraction burned must be unity when 1 = 1 . Making F = l in
equation (127) and solving the cubic equation by Horner's Method,
as explained in the algebra, we obtain for 1/1 Q
l/fc -1.1524
The value of 1/1 that will make F = l in equation (127) can
be obtained more simply and with sufficient accuracy by trial as
follows.
We have determined that when 1 = 1 Q and l/l Q = l, 1^ = 0.85174.
This value is less than unity by 0.148. For a first trial we will
increase the value of 1/1 by 0.148 and obtain from (127),
with l/lg = 1.148 F = 0.99568
124 ORDNANCE AND GUNNERY.
an increase in the value of F of 0.144. Therefore if we further
increase l/lo by 0.005 we will get a value of F near unity;
with l/k = 1-153 F = 1.0006
Interpolating, by the rule of proportional parts, between these two
sets of values we find that for F = 1
= 1.1524
Substituting this value in (127) it becomes
1 = 0.837416(1 + 0.22573 - 0.031581)
Comparing this with equation (5), 1 =a(l + A+ //), which is derived
from the formula for the fraction burned by making 1 = 1 , and
which expresses the relations existing between the constants of
form of the powder grain, we see that for the fictitious grain
a = 0.837416 A = 0.22573 //=- 0.031581
The new value of Zo must be the former value multiplied by
the above ratio, Z/Z = 1.1524, since we have multiplied all the
quantities in equation (127) by this ratio to make .F = l. There-
fore Z = 0.044875 X 1 .1524 = 0.051714.
The volume of the real grain is
7 = fr(Di 2 - 7di 2 )m = 0.197144
Whence from equation (18) with n = 89, d = 1.5776.
61. Solution. We have now all the data necessary for the
solution of the problem. For convenience it is repeated here.
Constants of the Gun. Constants of the Powder.
C = 3120 = 71
d = 6 d= 1.5776
17- 252.5 a= 0.837416
w-100 A= 0.22573
Measured Data. p = - 0.031581
7 = 3330.4 Z = 0.051714
p m = 42497
INTERIOR BALLISTICS. 125
From equation (100) J = 0.6299
(101) log a= 1.97940
(102) Iogz = 1.82144
On account of the thinness of web of the powder grain, and the
high pressure, we may be certain that the. charge was wholly con-
sumed in the bore. Assuming that the maximum pressure was
the maximum pressure on the base of the projectile we then have
a pressure while the powder was burning and a velocity after the
charge was all burned. As explained on page 92, equations (92)
and (91), or (114) and (113), are applicable in this case.
METHOD OF PROCEDURE. The procedure is as follows.
1. Substitute in (114) the measured muzzle velocity and the
value of X 2 taken from the table with the value of x corresponding
to the travel of the projectile at the muzzle.
2. Determine V\.
3. Substitute in (113) the measured value of the maximum
pressure and the values of the X functions corresponding to x = 0.8
or z = 0.45, according as the grain burns with an increasing or
decreasing surface.
4. Assume a value for the travel at the moment of complete
combustion and determine for this travel the values of x and X .
5. With this value of X and the value of FI, previously deter-
mined, find values for N, N', and M' from (110), (111), and (105).
6. Substitute these values in the second member of (113).
7. If the second member has then the same value as the first
member, which is the measured maximum pressure, our assump-
tion of the travel u is correct. If not we must make new assump-
tions for u and determine new values for M, N, and N' until we
find values that will satisfy equation (112).
The successive steps of the solution which follows are num-
bered as in the preceding paragraph.
.1. For the muzzle 17 = 252.5 and, equation (103),
x = 3.8091
From the table, for this value of x
log X 2 = 1.61019
J26 ORDNANCE AND GUNNERY.
Therefore equation (114) becomes for the muzzle
v a 2 = (3330.4) 2 = TV [1.61019] (131)
from which
2. log 7i 2 = 7.43481
3. It was shown on page 90 that with a grain burning with an
increasing surface the maximum pressure may be taken as occur-
ring when
z = 0.8
which for this round corresponds to a travel u = 53.03 inches, see
equation (103).
For this value of x we find from the table
log .Y 3 = 9.S6027 log X 4 = 0.60479 log .Y 6 = 1.17352
Equation (113) therefore becomes, since /* and N' are negative,
p m = 42497 = [I.86027JM' 1 1 + [0.60479]]V- [1 .17352]tf ' } (129)
From equation (105) we determine for this problem
M' = [3.99801] M
and substituting this value of M' in equation (129) it becomes
p m = 42497 - [3.85828]M { 1 + [0.60479] N - [1 .1 7352]#' } (130)
4. The proper values of M, N, and N' must satisfy equation
(130). But we see that equations (110) and (111) express fixed
relations between these constants and V\ at the moment of com-
plete burning of the charge.
Therefore we will assume the travel at the moment of com-
plete consumption, and with the corresponding value of x, and
therefore of X , determine N and N' from equations (110) and M
from (111).
Then substituting this set of values in equation (130) we will
determine whether the values satisfy that equation. If not we
will make other assumptions for x and proceed in the same way
until we find satisfactory values of the constants.
INTERIOR BALLISTICS. 1*27
The value of x at the muzzle is 3.8091. The value x must be
less than this since we are assuming that the charge was all con-
sumed in the gun. Let us assume x = 2.
5. Taking from the table the corresponding value of log XQ
we find from equations (110) and (111) values of M, N, and N'.
6. These substituted in equation (130) make the second mem-
ber equal to 45,746.
7. This is greater by 3249 pounds than the measured maximum
pressure, 42,497 pounds; and we therefore conclude that we have
assumed a too rapid combustion of the powder. The true value
of x is therefore greater than 2.
Assume next Z = 2.3
From the table log X = 0.65467
From equation (111) logM =6.70307
From equation (110) log AT =2.69892
log N' = 3.19009
With these values in equation (130) we get
p m = 42,909 pounds
As this differs from the given pressure, 42,497 pounds, by less than
one per cent, we may without material error use these values of
the constants as the true values.
The assumed value = 2.3, by means of which the constants
were determined, gives, from equation (103)
& = 152.5 inches
We have from equations (105) and (106)
log A/' =4.70108
log P' = 4.95570
We may now from equations (112) to (116) form the five
equations applicable to this round.
V 2 = [6.70307]*! 1 1 + [2.69892]A~ - [3.19009]AVI (132)
p = [4.70108]AT 3 j 1 + [2.69892]A r 4 - [3.19009]A', | (133)
r 2 = [7.43481 ].Y, (134)
128
ORDNANCE AND GUNNER!.
[4.95570]
P =
(135)
(136)
With these equations we may determine the velocity, pressure,
and weight of charge burned at any point in the bore. For any
travel less than 152J inches equations (132) and (133) apply
for the velocity and pressure, and equation (136) for the weight
of powder burned. For any travel greater than 152J inches,
equations (134) and (135) apply.
The table and curves which will follow are derived from these
equations.
A convenient method of performing the work in constructing
the table or curves is here shown. It is always best to assume
values of x that are given in the table, rather than values of u,
which would require interpolation in the table to find the values
of the X functions.
The symbol L in the following work is used to designate the
various constant logarithms in equations (132) to (136).
We will take for example the value x = 0.8, corresponding to
the travel at which we found the maximum pressure.
From the table:
log X Q = 0.46075
log X 3 = 9.86027
Equation (103)
logX
logZ
log x
logzo
1=9.71100
4 = 0.60479
1.90309
1.82144
logX 2
logX 5
= 9.25025
= 1.17352
Equation (132)
log u
log TV
1.72453
o 0.46075
2.69892
1.031 inches
log Xi 1.71100
log M 6.70307
+ 1
1.15967
1.14443
log*
o 2 0.92150
' 3.19009
6.41407
0.01293 . ,
. 2.11159
0.05365. .
1.13150
log v 2 6.46772
log v 3.23386
v = 1713.4 foot seconds
INTERIOR BALLISTICS. 129
log X 5 1.17352
logJV' 3.19009
2.36361
Equation (133)
log X 3 1.86027
log M' 4.70108
4.56135
log X 4
L
+ 1
0.60479
2.69892
1.30371
1.20124
0.02310
0.07120 . .
1.17814
log p m 4.63255
p m = 42909 Ibs.
per sq. in.
Equation (136)
log v 2
L
colog X 2
log?/
6.46772
6.41645
0.74945
1.63392
= 43.045 Ibs.
And if we desire the values of v a and p ,
Equation (134) log F t 2 7.43481 Equation (135) log 1.8 0.25527
logX 2 1 . 25025 X4/3 0.34036
log % 2 6.68586 log P f " 4.95570
log v a 3 . 34253 log p a 4.61 534
y a =2200.5 f. s. p a =41,2421bs. per sq. in.
These values of v a and p a are what the velocity and pressure
would have been had the powder all burned before the projectile
moved.
The calculations for velocity and pressure at any point of
the bore beyond the point of complete combustion of the charge
are extremely simple, being limited to the solving of the two
equations (134) and (135), which require from the table the
function X 2 only.
Proceeding as above for different values of x we obtain the
data collected in the table on page 130, from which the curves
in Fig. 23 are constructed.
62. Pressure Curves for Real and Fictitious Grains. We
have used in the deduction of the equations from which the table
is produced a fictitious multiperforated grain the body of which,
without the slivers, equals the whole of the real grain. The
body of the real grain was, as shown by equation (128), 85.174
per cent of the whole grain, the slivers forming 14.826 per cent
of the whole. The table and curve p show discontinuity of
130
ORDNANCE AND GUNNERY.
Travel
Powder
burned
Velocity Pressure Velocity Pressure
1
00000
26018
33698
40316
42500
42909
42500
41223
39659
38052
36002
26.5 53.0 106.0 152.5 Travel, Inches. 2525
FIG. 23. Charge, 71 pounds, Multiperforatod Grains.
INTERIOR BALLISTICS. 131
the pressure at the travel 152.5 inches when the burning of the
whole charge is completed.
Actually there is no discontinuity in the true pressure curve.
The web of the real grain was burned when 85.2 per cent of the
body of the fictitious grain, or of the whole charge, was burned.
This portion of the charge, 60.5 Ibs., was burned at a travel of
about 109 inches, as may be seen from the table. The charge
burned with an increasing surface up to this point of travel and
then with a decreasing surface which gradually approached the
vanishing surface zero.
The pressure would therefore, at a travel of 109 inches, begin
to fall off more rapidly, making a point of inflection in the true
pressure curve. From this point, as the slivers burn, the pressure
curve should gradually approach the curve p a and join it at some
point beyond the theoretical a = 152.5 inches, since the slivers,
burning with a constantly decreasing surface, will require a longer
time for complete consumption than the same weight in the
body of the fictitious grain.
The Constant r for this Powder. From equation (108),
r = 0.37477 seconds
This is the time of burning of the whole grain in air.
The velocity of burning of this grain in air, Z /r, =0.138 inches
per second.
The velocity of combustion in the gun is given by equation
(123), and the thickness of layer burned at any travel by equa-
tion (124).
The Force Coefficient /.From equation (109),
/= 1379.5 Ibs. per sq. in.
It has been previously stated that / is constant for any powder
in a given gun for charges not differing greatly in weight. The
effective value of /, as measured in the formulas by projectile
energy, must decrease as the charge decreases, for we have omitted
in the formulas all consideration of the force necessary to start
the projectile. It is apparent that if the charge were sufficiently
132
ORDNANCE AND GUNNERY.
reduced the projectile would not move, and / in the formula woulc
be zero.
Therefore for any charge differing materially in weight froi
the charge used in the determination of / the value of / must
modified.
Ingalls adoots provisionally, this relation.
(is;
in which WQ is the weight of charge used in the determination
/ ; / is the modified value of / for the charge d>; a is any char^
differing in weight from the charge d> by 15 per cent or more.
The value of / will be modified also by a marked change
the weight of the projectile. Ingalls uses for / in this case tl
value
/-*'
and if both & and w change sufficiently,
With the modified value of / from equation (137) we
now determine the velocities produced by reduced charges.
63. Problem 4. What muzzle velocities should be exped
from the 6 inch gun of problem 3, with charges (including igniters
of 59 and 33 J Ibs. of the powder used in that problem?
As these charges differ in weight by more than 15 per cenl
of the charge of 71 Ibs. used in problem 3, we will obtain the
value of / from equation (137), using for a> and / the valu(
of problem 3.
We have as before
C = 3120 5 = 1.5776 U = 252.5
The work may be conveniently performed as follows.
INTERIOR BALLISTICS.
133
Equation (137)
Equation (109)
Equation (100)
Equation (101)
Equation (102)
Equation (103)
From the table
Equation (114)
Charge, 59 Ibs.
log (D 1.77085
log w Q 1.85126
-3 1.91959
1.97320
log /o 3.13972
log / 3.11292
log (D/w 1.77085
L 4.44383
log Vi 2 7.32760
J =0.5234
log a =0.10605
logzo =1.86768
Z Q =73.736
for the muzzle,
x =3.4244
logX 2 1.59202
log 7j 2 7.32760
logv a 2 6.91962
log v a 3.45981
7 = 2883f.s.
Charge, 33\ Ibs.
1.52179
1.85126
1.67053
1.89018
3.13972
3.02990
1.52179
4.44383
6.99552
0.2950
0.44028
1.95285
89.712
2.8146
1.55630
6.99552
6.55182
3.27591
F = 1888f.s.
The muzzle velocities actually obtained with charges of the
above weights w r ere 2879 and 1913 f. s. respectively. The calcu-
lated velocities show differences of 4 and 25 f. s. respectively.
The latter difference, though practically not very great, shows
that the modified value of / determined from the value deduced
from one charge gives only approximate results when the second
charge is, as in this case, less than 47 per cent of the first.
64. Problem 5. What muzzle velocities should be cxpcctrd
from the 6 inch gun of problem 3, with charges (including igniters)
of 68 and 75 Ibs. of the powder used in that problem?
As these charges differ but little in weight from the charge
of 71 Ibs. used in problem 3, the value of / there determined will
serve in this problem.
134
ORDNANCE AND GUNNERY.
1379.5 C = 3120, 5 = 1.5776 7 = 252.5
Charge, 68 Ibs.
Equation (100) A = 0.6033
Equation (101) log a =0.01016
Equation (102) log Z Q = 1 .83344
Equation (103) x =3.7052
Equation (109) log Fi 2 = 7.41606
From the table log X 2 = 1.60555
Equation (114) V =3242 f. s.
Charge, 75 Ibs.
0.6654
1.93901
1 .80486
63.806
3.9573
7.45861
1.61648
V = 3448 f. s.
The measured muzzle velocities with these charges were,
respectively, 3236 and 3455 f. s. The differences between th(
calculated and measured velocities are immaterial.
We may make for this powder and gun any desired assum]
tion as to the form of the powder grain, weight of charge, weighl
of projectile, size of powder chamber or length of gun, and with
the values of / and r from problem 3, determine the full circum-
stances of motion under the assumption.
Sufficient illustration has now been given of the remarkable
accuracy, the simplicity and extensiveness of application of the
ballistic formulas deduced by Colonel Ingalls. By their use we
may obtain a more intimate knowledge of the conditions existing
in the bore of a gun than has heretofore been attainable; and
the knowledge so obtained will be applied in the manufacture of
powder and of guns, and will result in the production of more
efficient weapons.
United States Army Cannon. A table containing data con-
cerning the principal cannon now in service follows. The bursting
charges for projectiles as given in the table are of rifle powder
for the 1.457 inch and 3.2 inch guns, the 3.6 inch mortar, the
6 inch howitzer, and the two subcaliber tubes. For all other
projectiles the bursting charges are of high explosive.
INTERIOR BALLISTICS.
135
O CO i-i O iO
t>- oo **< Ci i-i oo <M co o eo <o cC
''t'ococoodcaoooc
<M CO i i Tt< 00 i
:j
^COiOCOcOiO^CO'
;fc
t^ t^oco-tooooci
14 t^ 00 O^ CO l^ CO ^
-H O> CO
00 < '
O CO
oooo o
1 1
88888:
OOOOO<^^>_/ . ^_, ,..
lOOO't-f-tcOcOOOXCCOOt^CO
C4i (COCOCOCOCOCOCOCOCO7''ICOi
88S88i88i||8
8
g:
CJS
11
1
rHOOCOlO'-OOOCCCO
T-* CO
00
- t^ (M C4 (M t^ ^
COiOt^CO'-i C^COOS
a
1C
t^ -t >0 CO
CO i I CO i i ^ CO O >O
dd^dd<
iO <M 00 C^
00 CO CO CO 00
O
>o
QO o oo 'O c^ co -" r
CM^HCOCJ-NcOt- COC
OcOOS-t'l-ICOOcO'f
-ICOOcO'f
- C5 CO 1-1 r-t
05 lO(MrH
r-< 10 co
OO ^
O iO CO CO (M
t> o>
'-t'Mr^.O't 1 !^
t i-O 00 i
(N-HCOQCt
-i C^4 CO O >-i t>-
OcOOOOQ^^iO
~S I-H CO -t< 00 (
i U5 i i iO
?OCO CM
' p < 5 ^ 10 8gi8SS855Sa
-i(MOOcO' i TlXl^TOO^-
ioiS;
IJD^ 1 '
'"*' Q ^^^ WJ fS fct i( N WJ ^^
I fljri. < 228l.tf! 9 J
....
to co to OQ
-- -_- -
C ^? ^^"ar * S * o o *c"
CHAPTER IV.
EXPLOSIVES.
65. Explosive and Explosion. An explosive is a substanc
that is capable of sudden change from a solid or liquid state to
gaseous state, or a mixture of gases whose chemical combination,
suddenly effected, results in a great increase of volume. A chem-
ical explosion is always attended by the emission of great heat.
An explosion due to physical causes alone, as when a gas und<
compression is suddenly released and allowed to expand, cai
cold.
Effects of Explosion. The effects of an explosion are depend-
ent on the quantity of gas evolved, on the quantity of heat, an<
on the rapidity of the reaction.
QUANTITY OF GAS. PRESSURE. The volume of gas at th(
temperature of explosion determines the pressure exerted ag*
the walls of the vessel containing the explosive.
Force. The pressure per unit of surface exerted by the
from unit weight of the explosive, the gases occupying unit volui
at the temperature of explosion, is called the force of the explosive.
The unit volume occupied by the gases is exclusive of the c<
volume of the gases and the volume of any residue.
QUANTITY OF HEAT. WORK. The quantity of heat determines
the quantity of work that may be effected by the explosion. The
bursting of the walls of the containing vessel and the projectioi
of the fragments, or the projection of the shot from a gun,
effects produced by the conversion of the heat of explosioi
mto work.
Potential. The total work that can be performed by th<
gas from unit weight of the explosive under indefinite adiabat
expansion measures the potential of the explosive.
136
EXPLOSIVES. 137
The theoretical potential of an explosive is never reached in
practice. The potentials, however, afford the means of comparing
the maximum theoretical quantities of work to be obtained from
different explosives. The maximum practical effect obtained
from explosives in firearms is from \ to J of the potential.
RAPIDITY OF REACTION. An explosion starts with the ex-
plosion of a single molecule, or particle, of the explosive. The heat
generated and the shock developed by the explosion of the first
molecule are communicated to the surrounding molecules and by
the explosion of these molecules are transmitted further into the
mass.
The rapidity with which the explosive reaction is transmitted
through the mass varies greatly in different explosives.
The explosion of gunpowders does not differ in principle from
the burning of a piece of wood or other combustible. As we have
seen in the chapter on gunpowders the combustion proceeds from
layer to layer and the rate of combustion, in 'air and in the gun,
and the quantity of powder burned at any time, may be deter-
mined by means of the formulas of interior ballistics.
The explosion of nitroglycerine, of guncotton, and of other
explosives of like nature is effected with very much greater
rapidity than the explosion of gunpowder. The theory of Berthelot
is that in these explosives the spread of the explosive reaction is
riot confined to the exposed surfaces, but that the explosion of the
initial molecule gives rise to an explosive wave which is trans-
mitted with great velocity in all directions through the mass
and causes the almost instantaneous conversion of the whole
body into gas. The velocity of propagation of the explosive wave
through a mass of guncotton has been determined experimentally
by Sebert to be from 16,500 to 20,000 feet per second.
The progressive emission of gas from gunpowder produces a
propelling effect by causing a gradual increase of pressure on thy
base of the projectile, while the sudden conversion into gas of nitro-
glycerine or guncotton produces the effect of a blow of great in-
tensity.
66. Orders of Explosion. The differences in the rapidity of
reaction give rise to the division of explosives into two groups,
high explosives and low or progressive explosives. Explosions
138
ORDNANCE AND GUNNERY.
are designated as detonations or explosions of the first orde
and progressive explosions or explosions of the second order.
The high explosives are those of great rapidity of reactioi
Their complete explosions are of the first order, and produce b]
reason of their quickness a crushing or shattering effect on any
material exposed to them.
The principal high explosives in general use are nitroglycerine,
the dynamites, guncotton, picric acid and its salts, the Sprengel
mixtures, and the fulminate of mercury.
The cadets of the Military Academy have studied in theii
course in chemistry (Descriptive General Chemistry (Tillman),
pages 369 to 385) the constitution, method of production, and
characteristics of the principal high explosives. It is therefc
unnecessary to further describe these explosives here.
The progressive explosives are those that consume an apprecu
time in the explosion. They produce explosions of the second
order. The explosion is slow, comparatively, and progressive,
produces a propelling or pushing effect.
The various gunpowders are progressive explosives. Gi
powders have been fully described in Chapter I.
Nitrocellulose. The classification by Vielle of the nitrocelh
loses of various degrees of nitration is shown in the following table
The higher the degree of nitration of the cellulose the greater is
the power of its explosion.
VIELLE'S CLASSIFICATION OF NITROCELLULOSES.
Formula.
Designation.
c.c. of
NO 2 .
Per Cent
of N.
C2 4 HO a (NO a ) 4
C. 4 H 35 20 (N0 2 ) 6
C 24 H 34 20 (N0 2 ) B
Tetra-n.c.
Penta-
Hexa-
108
128
146
6.76
8.02
9.15
C 24 H3Ao(N0 2 ) 7
Hepta-
162
10.18
C 24 H 32 20 (N0 2 ) 8
Octo-
178
11.11
C^O^CNOa
CaH.O.CNO.X
C^HaAoCNCU,
Ennea-
Deca-
Endeca-
190
203
214
11.96
12.75
13.47
Remarks.
Only slightly attacked by '
acetic ether and ether-
alcohol.
Becomes gelatinous in
acetic ether and ether-
alcohol.
Soluble in ether-alcohol. Infe
colloid.
\ Highly soluble in ether-alcol
/ Superior colloid.
Insoluble in ether-alcohol. Soli
ble in acetone. Guncotton.
EXPLOSIVES. 139
It will be observed that the general formula for nitrocellulose
isC 24 H4o_n0 20 (N0 2 ) n .
The last four nitrocelluloses of the table are used in the manu-
facture of gunpowders.
67. Conditions that Influence Explosions. The character of
the explosion produced by any explosive is influenced by the
physical condition of the explosive, by the external conditions,
and by the nature of the exciting cause.
PHYSICAL CONDITION. The influence of the physical condition
of the explosive is seen in the sputtering of damp black powder
when ignited, and in the insensitiveness to explosion of nitro-
glycerine when frozen.
EXTERNAL CONDITIONS. External conditions influence the
explosion chiefly by the amount of confinement they impose.
Confinement is necessary to obtain the full practical effect of all
explosives. The more rapid the reaction the less the degree of
confinement required. Thus blocks of iron may be broken by the
explosion of nitroglycerine upon their surfaces in the open air. In
this case the air imposes sufficient confinement, as the explosion is
so quick that its effect on the iron is produced before the air has
time to move.
Gunpowder, on the other hand, requires strong confinement if
its complete explosion is desired. Thus, in firing a large charge
of gunpowder under w r ater, unless the case is strong enough to
retain the gases until the reaction is complete the case will he
broken by the pressure of the gases first given off, and a por-
tion of the charge will be thrown out unburned. Large powder
grains are frequently thrown out of the gun not wholly
burned.
The confinement required by the slower explosives may be
diminished by igniting the charge at many points, so that less
time is required for the complete explosion.
EXCITING CAUSE. Heat is the immediate cause of all explo-
sions, whether communicated to the explosive directly by a flame
or heated wire, or indirectly through friction, or percussion, or
chemical action. Each explosive has a specific temperature of
explosion, to which one or more of the molecules must be rai- >1
before the explosion can begin. The heating of the initial mole-
^iO ORDNANCE AND GUNNERY.
cule to the exploding point is not of itself sufficient to cause ex-
plosion of the entire mass, but this temperature must be trans-
mitted from molecule to molecule throughout the mass.
The method of producing the explosion of the initial molecule
has with many explosives an important influence on the character
of the explosion. Nitroglycerine when ignited in small quantities
burns quietly, but when struck it explodes violently. Similarly,
guncotton when ignited by a flame burns progressively and the
combustion may be extinguished by water, but when detonated
by an explosive cap the explosion is of the first order. Most of the
high explosives produce either detonations or explosions of lower
order, depending upon the manner in which the explosion is ini-
tiated, and it is stated by Roux and Sarrau that even black gun-
powder may be detonated by the use of nitroglycerine as an
ploding charge.
Flame is sufficient to cause the complete explosion of the pi
gressive explosives, though it may be necessary with some expl(
sives that the flame be continuously applied. For some of th(
high explosives a percussive shock suffices to induce an explosion
of the first order, while other high explosives are practically in-
sensitive to shock and require for their explosion an initial explo-
sion of some detonating substance.
68. Uses of Different Explosives. It is apparent from what
has been said concerning the differences in rapidity of reaction of
the various explosives and the influences of external conditions
that each class of explosives has its particular field of usefulness.
Thus the progressive explosives are more suitable for use in
guns where a propelling rather than a shattering effect is desired
from the explosion. A high explosive acts so quickly that if used
in a gun its explosion would be completed practically before the pro-
jectile moved, with the result that the whole of its enormous force
would be exerted upon the walls of the gun to produce rupture.
For the movement of masses of earth the slow explosive is
better than the more rapid one, for here also a propelling rather
than a shattering effect is desired.
In submarine mines the best results are obtained from dynamite
No. 1, a dynamite consisting of 75 parts by weight of nitroglyc-
erine absorbed into the pores of 25 parts of the siliceous
EXPLOSIVES. 141
called kieselguhr. The effect of the inert substance is to retaro!
the explosion of the nitroglycerine, and the retarded explosion is
of greater effect in a yielding substance like water than the more
rapid explosion of pure nitroglycerine.
In hard rocks and metals the quickest explosive will give the
best results, as in these hard substances the greatest intensity of
blow is required to produce the shattering effect desired. Dyna-
mite is ordinarily used for blasting purposes on account of its con-
venient form, its comparative safety in handling, and its ease of
ignition.
Bursting Charges in Projectiles. The explosives used as burst-
ing charges in armor piercing projectiles must have a great shatter-
ing effect in order to break the projectile into fragments and to
project the fragments with force; and at the same time the ex-
plosive must be practically insensitive to shock, so that it will
not be exploded by the shock of discharge in the gun or the shock
of impact on the ship's armor. The explosion of the bursting
charge of an armor piercing projectile is effected by a detonating
fuse so arranged as to cause the projectile to burst after it has
perforated the armor.
The explosives used by the various foreign nations as bursting
charges in projectiles are all composed principally of picric acid
or its derivatives. The French melinite, the English lyddite, the
Japanese shimose powder are examples.
Some of the picrates, as the picrates of lead, calcium, mercury,
and others, are more sensitive to friction and percussion than
picric acid itself. In order to prevent the formation by chemical
action of any of these sensitive compounds when tho bursting
charge is composed of picric acid or of any of its derivatives, the
walls of the projectile and all metal parts that come in contact
with the bursting charge are covered with a protecting coat of
rubber paint.
The walls of the cavity of the shell, the base plug, and the
body of the fuse are so painted; also the screw threads of the base
plug and fuse. Red or white lead or other metal lubricant must
not be used on the screw threads.
69. Requirements for High Explosives for Projectiles.
The following requirements are considered essential for :i
142
ORDNANCE AND GUNNERY.
explosive to be used in filling shell. They have been found nec<
sary as a result of a long series of tests.
SAFETY AND INSENSITIVENESS. The explosive should be
reasonably safe in manufacture and free from very injurious effects
upon the operatives.
It must show a relatively safe degree of insensitiveness in an
impact testing apparatus.
It must withstand the maximum shock of discharge unc
repeated firings in the shells for which it is intended.
It must withstand the shock of impact when fired in unfused
shell, as follows:
(a) Field Shell. With maximum velocity, against 3 feet of
oak timber backed by sand. With the remaining velocity for full
charge at 1000 yards range, against a seasoned brick wall.
(b) Siege Shell. Against seasoned concrete thicker than the
shell will perforate with remaining velocity for full charge at
500 yards range.
(c) Armor Piercing Shell. Against a hard faced plate
thickness equal to the caliber of the projectile.
DETONATION AND STRENGTH. It must be uniformly
completely detonated with the service detonating fuse.
It should possess the greatest strength compatible with
satisfactory fragmentation of the projectile. The average frag-
ment of a projectile should be effective against the vulnerable
material of a ship, such as the mechanisms of guns, gun mounts,
engines, boilers, electric installations, and the like. With very
quick and powerful explosives, as explosive gelatin and picric
acid, the shattering effect is excessive and the fragments of the pi
jectile are too small.
STABILITY. It must not decompose when hermetically seal<
and subjected to a temperature of 120 F. for one week.
It should preferably be non-hygroscopic, and its facility f(
detonation must not be affected by moisture that can be absorl
under ordinary atmospheric exposure necessary in handling.
It must not deteriorate or undergo chemical change in stoi
GENERAL CONDITIONS. Loading must not be attended wit
unusual danger and should not require exceptional skill or tedioi
methods.
EXPLOSIVES. 143
The explosive should be obtainable quickly in large quantities
and at reasonable cost.
REMARKS. The explosives used as shell fillers are more stable
under severe heat treatment than the service smokeless powders.
The explosives should therefore be correspondingly safer to store
in large quantities.
Explosive D, used in our service, invented by Major Beverly W.
Dunn, Ordnance Department, is safer to handle than black powder.
70. Exploders. Fulminate of mercury is one of the most
violent explosives. By reason of its sensitiveness to explosion
by heat or percussion, and the intensity of the shock obtained by
its explosion in small quantities, the fulminate of mercury is the
most suitable substance for use in initiating detona-
tions or explosions in other explosives.
It forms the principal or the only ingredient of the
detonating composition in explosive caps, primers, and
fuses. Other ingredients may be potassium chlorate
or nitrate, or bisulphide of antimony, the proportions
differing hi order to produce the best results from the
particular explosive with which the exploder is to be
used.
DETONATORS. A commercial detonating cap or fuse
is shown in the accompanying figure. The fulminate of
mercury, or detonating composition, B, is enclosed in a
copper case closed with a plug of sulphur through which
pass the bared ends of the electric wires. A platinum
bridge connects the ends of the wires, and the heating
of the bridge by the electric current fires the detonator.
In order to secure the best results it is necessary
that the detonator be in intimate contact with the
explosive. It is therefore usually placed in the midst
of the mass, and the explosive is packed closely
around it.
PRIMERS FOR GUNPOWDERS. For the ignition of
charges of gunpowder a large body of flame is of more advantage
than an intense shock. Consequently in small-arm primers
mercury fulminate has been replaced by a less violent composition
of chlorate of potash and bisulphide of antimony, which produces
144
ORDNANCE AND GUNNERY.
a larger body of flame and is at the same time less sensitive
percussion and therefore safer for use in a small-arm cartridge.
In primers for cannon the large body of flame is produced by
the use of black powder for the priming charge in the primer,
the ignition of the black powder being effected by the explosion
of a small percussion cap or by the electric ignition of a small
quantity of loose guncotton.
Explosion by Influence. The detonation of a mass of ex-
plosive may under certain circumstances induce the explosion of
another mass of the same or of a different explosive not in contact
with the first. The induced explosion is called an explosion by
influence or a sympathetic explosion.
The ability of one explosive to induce the sympathetic explo-
sion of another not in contact with it appears to depend on the
character of the shock communicated by the first explosive. Abel
found that while the detonation of guncotton would cause the
sympathetic detonation of nitroglycerine in close proximity to it,
the detonation of nitroglycerine would not cause the detonation
of guncotton, although nitroglycerine is more powerful than gun-
cotton.
In explanation of this difference in action Abel advanced the
theory of synchronous vibrations. It is a well established fact that
certain vibrations will induce the decomposition of chemical com-
pounds whose atoms are in a state of unstable equilibrium; and
according to Abel sympathetic explosion is produced when the
first explosive sets up in the connecting medium vibrations that
are synchronous with those that would result from the explosion of
the second explosive.
This theory is questioned by later investigators, and it is n<
generally held that sympathetic explosion is due to the ir*
mission of a shock of sufficient intensity.
EXPLOSIVES. 145
THEORETICAL DETERMINATIONS OF THE
RESULTS FROM EXPLOSIONS.
71. In the theoretical determinations of the results from explo-
sions metric units and the centigrade thermometric scale are
usually employed.
Definitions. CALORIE. A small calorie is the quantity of heat
required to raise the temperature of 1 gram of water (1 cubic centi-
meter) from degrees to 1 degree centigrade.
A large calorie is the quantity of heat required to raise the
temperature of 1 kilogram of water (1 liter, 1 cubic decimeter)
from degrees to 1 degree. A large calorie is equal to 1000 small
calories.
EXOTHERMIC AND ENDOTHERMIC REACTIONS. An exother-
mic reaction gives off heat, an endothermic reaction absorbs
heat.
MOLUGRAM. The term rnolugram is used to designate a
weight of as many grams as there are units in the molecular weight
of the substance. Thus, the molugram of hydrogen, H 2 , is 2 grams.
Water or water vapor, H 2 0, has a molecular weight of 18. The
molugram of water is therefore 18 grams. The molugram of nitro-
glycerine, C 3 H5(NO 2 )30 3 , is 227 grams.
The molugram of a mixture has a weight in grams equal to the
sum of the molecular weights of as many molecules of each con-
stituent as appear in the formula for the mixture. Thus, the
molugram of 10KN0 3 + 3S + C is 1119 grams.
Specific Heats of Gases. The specific heat of a gas at constant
pressure is the number of calories required to heat 1 gram of the
gas from to 1 while the gas is permitted to expand under the
constant pressure.
The specific heat of a gas at constant volume is the number of
calories required to heat 1 gram of the gas from to ], the volume
of the gas remaining unchanged.
When large calories are used the unit weight of gas is 1 kilo-
gram.
MOLECULAR HEAT. The molecular specific heat of a gas, or
more simply the molecular heat, is the number of calorie* required
to heat a molugram of the gas from to 1.
146 ORDNANCE AND GUNNERY.
The molecular heat is obtained by multiplying the specific heat
of the gas by its molecular weight. The molecular heat may be
under constant pressure or under constant volume, depending upon
whether the specific heat used as a multiplier is the specific heat
at constant pressure or at constant volume.
Thus, carbon dioxide, C02 ; ' molecular weight, 44.
At constant pressure, specific heat, 0.2169; molecular h<
0.2169X44 = 9.5436.
At constant volume, specific heat, 0.172; molecular
0.172X44 = 7.568.
72. Specific Volumes of Gases. The specific volume of a gas
is the volume in cubic decimeters (liters) of 1 gram of the gas at
temperature and under atmospheric pressure (barometer, 760
millimeters; pressure, 103.33 kilograms per square decimeter).
MOLECULAR VOLUME. The molecular volume is the volume, at
and 760 mm. pressure, of a molugram of the gas. It is obtained
by multiplying the specific volume by the molecular weight.
Thus, C0 2 , specific volume, 0.5073, molecular volume, 44 X
0.5073=22.32 cubic decimeters or liters.
The molecular volumes of all gases are the same, 22.32 litei
as will be shown.
LAW OF AVOGADRO. Alt gases under the same conditions of
pressure and temperature have the same number of molecules in
equal volumes.
It follows from this law that the single molecules of all gases,
whether simple or compound, occupy equal volumes under the
same conditions of pressure and temperature.
The volume of the hydrogen atom is taken as the unit volume.
The molecule of hydiogen and the molecules of the other simple
gases as well are composed of two atoms. A molecule of any
therefore occupies 2 unit volumes.
In the following reaction the number of volumes appears un
each of the symbols
N + H 3 - NH 3
1 vol 3 -vols 2 vols.
That is, 1 volume of N combining with 3 volumes of H forms 2
volumes of ammonia, NH 3 . The volumes may be expressed in
any unit, as liters or cubic feet.
EXPLOSIVES. 147
The atomic weight of nitrogen is 14 and of hydrogen 1. There
are therefore in the molecule of NH 3 17 parts by weight occupying
the same volume as 2 parts of hydrogen alone. The specific volume
of NH 3 , the volume of unit weight, is therefore 1/17 of the molec-
ular volume of hydrogen, and the molecular volume of NH 3 ,
which is the specific volume multiplied by the molecular weight, 17
in this case, is the molecular volume of hydrogen.
As the same is true for any other gaseous compound, it follows
that the product of the specific volume of a gas by its molecular
weight is a constant and is equal to the molecular volume of
hydrogen.
The molecular volume of all gases is 22.32 liters.
By means of the molecular volume we may determine the
volume of any weight of gas, or the weight of any volume,
since we know that a molugram of any gas occupies 2J.."J
liters.
The specific volume, the number of liters occupied by 1 gram,
is equal to 22.32 divided by the molecular weight.
The specific weight, the number of grams occupying one HNT,
is the reciprocal of the specific volume, or the molecular weight
divided by 22.32.
Classification of Gases. Compound gases such as C02, NH 3 ,
2!^, whose molecules contain more than two atoms, are called
gases with condensation, as in their formation more than two atoms
are condensed into the volume of two simple atoms. Compound
gases such as CO, HC1, whose molecules contain two atoms, ;uv
called gases without condensation. Oxygen, hydrogen, and nitrogen
are simple or perfect gases.
In the following determinations of the effects of explosion we
will follow the methods described by Leon Gody in his work en-
titled Matieres Explosives.
73. Quantity of Heat. The heat given off in explosions can
be measured experimentally by means of special calorimeters.
Roux and Sarrau made use of a very strong cylindrical bomb,
similar to the apparatus of Noble and Abel, illustrated on page 67.
The bomb, charged with a few grams of explosive, was immersed
in a known volume of water. After the explosion of the charge,
148 ORDNANCE AND GUNNERY.
effected electrically, the increased temperature of the body of
water was noted and the quantity of heat necessary to produce
the rise in temperature calculated.
The theoretical determination of the quantity of heat resulting
from an explosion involves the application of certain principles of
thermochemistry established by Berthelot.
PRINCIPLE OF THE INITIAL AND FINAL STATE. The heat liber-
ated (or absorbed) in any modification of a system of simple or
compound bodies, effected under constant pressure or at constant
volume and without any external mechanical effect, depends solely
on the initial and final states of the system. It is completely inde-
pendent of the series of intermediate transformations.
From this principle it follows that the heat liberated in any
transformation accomplished through successive reactions is the
algebraic sum of the heats liberated in the different reactions.
We may consider the formation of an explosive as an inten
diate reaction in the formation of the products of explosion
simple elements. If we then subtract from the total heat of
formation of the products of explosion the heat of formation of the
explosive, the difference will be the heat liberated in the reaction
of explosion.
PRINCIPLE OF MAXIMUM HEAT. All chemical changes effected
without the intervention of external energy tend toward the forma-
tion of the body or the system of bodies that liberates the most
heat.
The quantity of heat liberated or absorbed in a reaction is inde-
pendent of the time occupied in the reaction.
74. Heats of Formation. The heats of formation at constant
pressure of the principal explosives and of the gases resulting from
explosion are given in Table II at the end of the volume. The
heats are given in large calories for the molugram of each substance.
Thus hydrochloric acid gives off in its formation 22 large calories;
that is, 1 gram of hydrogen and 35.5 grams of chlorine in com-
bining give off sufficient heat to raise the temperature of 22 kilo-
grams of water from to 1. The heat of formation of 36.5
gr&ms of HC1 is therefore 22 large calories.
The heats of formation of endothermic bodies are preceded
the minus sign in the table.
EXPLOSIVES. 149
The atomic and molecular weights in Tables II, III, and IV
are those that were in use at the time these tables were formed.
Atomic weights according to the latest determinations are given
in Table V. In the examples which follow, involving the use of
Tables II, III, and IV, the atomic and molecular weights as given
in those tables are used.
Quantity of Heat at Constant Pressure. In order to determine
the quantity of heat given off in any chemical change the chemical
reaction must be known. The composition of explosives is gen-
erally known and the products of explosion can be predicted,
under the principle of maximum heat, when the body undergoes
complete combustion; that is, when it contains sufficient oxygen
to form stable compounds of the maximum oxidation.
The sum of the heats of formation of the products of explosion
that appear in the formula for the reaction, minus the heat of
formation of the explosive, is the quantity of heat liberated by the
explosion.
Example i. As an example we will find the heat given off in
the explosion of nitroglycerine under constant pressure, as in the
open air.
The equation of the reaction is as follows :
2C 3 H 5 (N0 2 )303 = 6C0 2 + 5H 2 + 3N 2 + J0 2
454 264 90 84 16
With the heats of formation from Table II for the molugram
of each substance we obtain, for the numbers of molecules in the
reaction,
2C 3 H 5 (N0 2 )303, 2X98 =196,
6C0 2 , 6X94.3 = 565.8,
5H 2 0, 5X58.2 = 291.
The nitrogen and oxygen being simple elements add no heat.
We therefore have for the heat given off by the explosion under
constant pressure of 2X227 grams of nitroglycerine
(565.8 + 291) -196 = 660.8 1. cal. *
* In other works the abbreviation used to designate a large calorie is cal. k. d.
(kilogram-degree), and for a small calorie, cal. ;/. </. (-nnn^lcgree). The ab-
breviations /. cal. and s. cal. are used here, as they more plainly indicate the
words abbreviated.
150
ORDNANCE AND GUNNERY.
and for the heat given off by 227 grams of the explosive, a mol
gram,
Q mp = 660.8/2 = 330.4 Leal.
For the heat given off by a kilogram of the explosive,
330.4X1000
227
= 1455.5 1. cal.
75. When Solid Products are Formed. If the explosion
produces solid products the heats of formation of these bodies
are added to the heats of formation of the gases in the determina-
tion of Q mp and Q kp .
Example 2. A mixture of nitrobenzol with sufficient pol
sium chlorate to make the combustion of the nitrobenzol com-
plete is exploded.
The reaction is
2C 6 H 5 N0 2
1266.8
= 12C0 2 + 5H 2 O + N 2 + - 2 /KC
528 90 28 620.8
A molugram of a mixture is the sum of the molecular weights
in grams of as many molecules of each of the constituents as
appear in the reaction. The molugram of this explosive mixture
is therefore 2 X 123 + ^X122.5 = 1266.8 grams.
Heats of formation :
12C0 2 ,
5H 2 0,
KC1,
2C 6 H 5 N0 2 ,
12 X 94.3 = 1131.6
5X 58.2= 291
- 2 /Xl05 = 875
2297.6
2X 4.2= 8.4
X 94.6= 788.3
2297.6-796.7 =
1500.9X1000
~ 1266.8
796.7
. cal.
EXPLOSIVES. 151
Incomplete Combustion. When an explosive does not con-
tain sufficient oxygen for complete combustion the products
formed vary with the temperature, the pressure, and the density
of loading. Therefore no fixed formula can be written for the
reaction. The products of combustion of these explosives are
determined by analysis, and the heat given off may then be deter-
mined as above.
The explosion of guncotton under atmospheric pressure gives
the following reaction.
ii = 15CO + 9C0 2 + 9H 2 O + 5.5H 2 + 5.5N 2
Under high pressure the reaction is as follows.
C 24 H 29 2 o(N0 2 )ii = 12CO + 12C0 2 + 6H 2 + 8.5H 2 + 5.5N 2
76. Quantity of Heat at Constant Volume. If the decom-
position takes place at constant volume, for instance in a closed
vessel, the heat developed is greater than in the open air under
constant pressure. The gases developed in the open air perform
the work of driving back the air, and this work absorbs some
of -the heat.
Let Q mp be the heat given off by the molugram of the substance
in the reaction at constant pressure at the surround-
temperature t,
Q mv the heat given off by the molugram of the substance
in the reaction at constant volume at the surround-
ing temperature t,
W the work of expansion at constant pressure,
E the mechanical equivalent of heat, 425 kilogram-
meters.
Then W/E is the heat expended in performing the work of driving
back the air, and
Q mv = Q mp +W/E (1)
But the work W due to the pressure of the gas against the
constant pressure p is, as shown by equation (40), page 65,
W= I l pdv = p I l dv
J Vb J Vb
152
ORDNANCE AND GUNNERY.
v b and Vi representing the volumes of the gas before and afl
expansion.
Performing the indicated integration,
Taking the molecular volume at and 760 mm., 22.32 lil
as the unit volume,
Let rib represent the number of unit volumes before expansion,
HI the number of unit volumes after expansion to normal
atmospheric conditions.
n\ will also represent the number of gaseous molecules, since afl
expansion to the normal atmospheric conditions of temperati
and pressure each unit volume is occupied by a molugram.
Then from Gay-Lussac's law, page 58, we have at the tei
perature t
Substituting these values in equation (2) we have
Whence
W
j- = 22.32 (n,-n b )(l+at)
The value 425 for E, the mechanical equivalent of heat, is
expressed in kilogr ammeters. We must therefore express p,
the normal atmospheric pressure in kilograms per square meter,
103.3X100, and the volume 22.32 liters (cubic decimeters) in
cubic meters, 22.32/1000.
Equation (3) then becomes
TP 1033 0X22.32
E~ 425X1000 (Ul
or W/E = 0.5424(m - n b ) (I + at)
a = 1/273 and 1/273 X 0.5424 - 0.002, nearly
Therefore
EXPLOSIVES. 153
In the case of explosives the volume v b is generally negligible
with respect to Vi, v b represents the volume of the explosive for
those explosives that are completely converted into gas. n b is
therefore negligible with respect to ni, and equation (4) becomes
W/E = 0.5424/1! + 0.002M
Substituting this value in equation (1)
Qmv = Qm P + 0.5424ft! + 0.002rii t
We will make Z = 15, since the heats of formation in Table II
have been determined for that temperature, and Q mp and Q^ in
the above equation will be determined from the table. We have,
then, finally,
Qm* = Qm P + 0.5724ft! (5)
for the quantity of heat given off at constant volume by the molu-
gram of the explosive.
77. Example 3. Take, for example, nitroglycerine,
2C 3 H 5 (N0 2 )303 = 6C0 2 + 5H 2 + 3N 2 + J0 2
454 2G4 90 84 16
We have found at constant pressure, example 1,
Q mp = 330.4 l.cal.
From the reaction we see that 2 molugrams of the explosive give
off 6 + 5 + 3 + 0.5 = 14.5 molecular volumes of gas. 1 molugram,
therefore, gives
ni = 7.25 volumes
Substituting in equation (5) we obtain
Q mv = 330.4 + 0.5724 X 7.25 = 334.5 1. cal.
For 1 kilogram of the explosive, example 1,
^4. ^
Q kv = --X 1000 = 1473.6 l.cal.
We found at constant pressure
Q kp = 1455.5 l.cal.
154
ORDNANCE AND GUNNERY
Potential. The potential has been defined as the total work
that can be performed by the gas from unit weight of the explosive
under indefinite adiabatic expansion. The kilogram is taken
the unit weight in the determination of the potential, and th<
meter as the unit of length. The work unit is therefore the kilc
gr ammeter. The total work from one kilogram of the explosive
is equal to the maximum quantity of heat given off by one kilc
gram multiplied by the mechanical equivalent of heat.
The mechanical equivalent of heat is 425 kilogrammetei
Therefore representing the potential, the total work from a kilc
gram of the explosive, by Wk we have
Wk = Qhv X 425 kilogrammeters
78. Volume of Gases. The volume of gases produced by ex-
plosion may be measured experimentally, the gases being drawi
off from the calorimetric bomb for this purpose.
The volume of the gases may also be determined theoretically
from the reaction.
As previously explained, the molecular volume (the volume
the molugram) of any gas, simple or compound, is 22.32 litei
Therefore in any reaction the molecular volume, at standard tei
perature and pressure, of the evolved gases is very simply obtainc
by multiplying the number of gaseous molecules in the formi
for the reaction by 22.32.
Example 4. A formula for the explosion of black gunpowde
is
10KN0 3 + 3S + 8C = 3K 2 S0 4 + 2K 2 C0 3 + 6C0 2 + 5N 2
1010 96 96 522 276 204 140
The first two products of the reaction are solid. The gaseous pi
ucts are 6 molecules of C0 2 and 5 of N. Therefore the molecuh
volume of the gases from 1202 grams of the explosive is, at an<
760 mm.,
7 OT = 11X22.32 = 245.52 liters
and from 1 kilogram of explosive
V k =
245.52X1000
1202
= 204.26 liters
EXPLOSIVES. 155
The volumes at any other pressure or temperature may be ob-
tained by means of equations (31) and (34), Chapter III.
79. Temperature of Explosion. The method of Mallard and
Le Chatelier for calculating the temperature of explosion at con-
stant volume in a closed vessel is as follows.
The quantity of heat liberated by the explosion of the molu-
gram of the explosive would, if the specific heat of the products
were constant, be equal to the molecular specific heat multiplied
by the rise in temperature. We would then have
Qmv^CmvXk (7)
from which h, the rise in temperature, could be obtained. Assum-
ing 15, an ordinary temperature, as the temperature of the ex-
plosive when fired, the temperature of explosion would then be
t = ti + 15 (8)
But it is known that the specific heat increases with the tem-
perature. Assuming that the specific heat varies with the tem-
perature in the manner represented by the linear expression,
Cm.- a + 6*1 (9)
the values of a and 6, and the consequent values of C mv , have
been deduced for certain gases as follows. The values are given in
small calories.
a b
For C0 2 , SO 2 , 6.26 0.0037 C m * = 6.26 + 0.0037 ti
For H 2 0, 5.61 0.0033 C mv = 5.61 + 0.0033 h
For gases without
condensation, 4.80 0.0006 Cm, = 4.80 -f 0.0006 k
The values of a are the molecular heats of the gases in small
calories at the temperature 15, and the values of b are the incre-
ments of the molecular heats for each degree of rise in temperature.
Suppose that the products of an explosion are as follows :
156
ORDNANCE AND GUNNERY.
P representing a molecule of a perfect gas. The coefficients a
and 6 for the products of explosion will then be
a = 6.26 a + 5.61/2+ 4.8 d
b = 0.0037 a + 0.0033/2+ 0.0006 d
(K
Combining equations (7) and (9) and multiplying Q mv by 1000,
since it has been determined in large calories, and a and b are ]
in small calories, we obtain
Solving this equation for t\ and substituting the resultii
value in equation (8), we obtain, for the temperature of explosioi
mv
-+15
80. Example 5. Nitroglycerine. Q mv = 334.5 1. cal. (see 62
ample 3).
454
264
90
84
16
Since the products, as given in the formula, are from two molecuk
of the explosive,
.5 = 82.41
26 = 0.0037 X 6 + 0.0033 X 5 + 0.0006 X (3 + 0.5) = 0.0408
a = 41. 205 6 = 0.0204
and from equation (12)
, -41 .205 + V41.205 2 + 4000x0.0204X334.5
2X0.0204
81. Temperature when Solid Products are Formed. If the
explosion gives rise to solid products the heat absorbed in raisii
the temperature of these products must be considered. In eqi
EXPLOSIVES. 157
tion (7) C mv must be the mean specific heat of the products of
the explosion of a molugram of the explosive.
Suppose that in addition to the gaseous products assumed
above, page 155, we have x molugrams of a solid product having
a specific heat h referred to its molecular weight. Then a, equa-
tion (10), becomes
The specific heat of a solid product is assumed not to vary
with the temperature, therefore the value of b as given by equa-
tion (11) is not affected.
The specific heats of substances will be found in Table III at
the end of the volume.
Example 6. Determine the temperature of explosion of the
mixture of nitrobenzol and potassium chlorate of example 2.
The reaction is
2C 6 H 5 N0 2 + VKClOa = 12C 2 + 5H 2 + N 2 + VKC1
1266.8 528 90 28 620.8
From example 2, Q mp = 1500.9 1. cal.
equation (5), Q mv =Q mp +0.5724n!
page 152, n! = 12 + 5 + l = 18
Q m ,= 1511.2
From Table III, molecular specific heat of KC1, 12.89
eq. (13), a = 6.26X12 + 5.61X5 + 4.8 +12.89X25/3 = 215.39
eq. (11), 6 = 0.0037X12 + 0.0033X5 + 0.0006=0.0615
- 215.39 + v / 2l5^9 2 + 4000X0.0615X151 1.2
1-< 12 >' 2X0.0615
= 3521.
82. Pressure in a Closed Chamber. The pressure of the gases
produced by explosion is a function of the volume occupied by
the gases. In a closed chamber the volume available for the gases
depends upon whether the products of explosion are wholly gaseous
or whether they contain non-gaseous matter as well.
158
ORDNANCE AND GUNNERY.
PRODUCTS WHOLLY GASEOUS. We have deduced inequati<
(47), Chapter III, the following value for the force of an explosiv<
f = p v T/273
in which, in the metric units that have been chiefly used in tl
previous calculations, the kilogram and the decimeter,
/ is the pressure per square decimeter of the gases from 1 kik
gram of explosive, the gases occupying at the tempen
ture of explosion a volume of 1 cubic decimeter.
PQ the normal atmospheric pressure, 103.3 kilograms per squa
decimeter,
VQ the specific volume of the gas, now taken as the volume
cubic decimeters occupied by 1 kilogram of the gas at
and 760 mm.,
T the absolute temperature.
The volume V '&, as determined on page 154, is the volume
cubic decimeters, or liters, of the gaseous products from 1 kilo^
of the explosive. Therefore
= v k
The absolute temperature T = 273 + t, in which t, the temp*
ture of explosion, is taken as the rise in temperature due to tl
explosion plus 15, which is the assumed temperature of th(
explosive when fired.
Substituting the values of p , V Q , and T in equation (14)
obtain for the force of the powder
. 103.3y(273 + Q .
' 273 kilograms per sq. dec.
RELATION BETWEEN PRESSURE, FORCE OF EXPLOSIVE, AND
DENSITY OF LOADING. We have, equation (49), Chapter III, for
the pressure from unit weight of gas confined in the volume v,
f
va
in which a is the covolume of the gas.
EXPLOSIVES. 159
By the process followed in Chapter III in deducing equation
(46) from equation (45) this equation may be put in the form
(18)*
in which P is the pressure per unit of surface of the gases from
(i) units of weight of explosive,
A is the density of loading.
According to Sarrau the covolume is 1/1000 of the specific
volume of the gases. Therefore when the products are wholly
gaseous we have from equation (15)
a = F,/1000 (19)
83. Non-gaseous Products. When solid or liquid products
result from the explosion, these products occupy part of the
volume in the chamber and diminish the volume occupied by the
Let y be the weight of gas from unit weight of explosive,
w Q the volume at and 760 mm., occupied by the gas from
unit weight of explosive,
a' the volume, at temperature and pressure of explosion, of
the non-gaseous residue from unit weight of explosive.
In this case if we consider as the specific volume of the gas
the volume MO occupied by the gas from unit weight of the ex-
plosive instead of the volume VQ occupied by unit weight of the
gas, /, equation (14), becomes for the new specific volume
(20)
And if we consider that a, the subtractive term in equation (14),
includes the volume of the residue from unit weight of explosive
as well as the covolume of the gases for the new specific volume,
a = a' + wo/1000 (21)
*This equation is identical with equation (46), Chapter III, deduced by
Noble and Abel. They considered a as the volume of the solid residue from
unit weight of powder, but later investigations show, as explained in Chapter
III, that the covolume of the gases must appear in the equation. When solid
products result the value of a must be modified to include the volume occupied
by the solid products.
160
ORDNANCE AND GUNNERY.
By definition we have
G
With these new values of / and a equation (17) gives the
pressure due to the gases from unit weight of the explosive, and
equation (18) may be deduced from it as before.
Therefore when non-gaseous products result from the
plosion the pressure is obtained from equation (18) by substituting
for / and a the values given in equations (20) and (21).
The volume of the solid matter is easy to calculate, as from
the formula of the decomposition we may obtain the weight of the
residue from 1 kilogram of the explosive, and it is only necessary
to divide this weight by the density.
The densities of substances are given in Table IV at the end
of the volume.
84. Example 7. What is the pressure in a closed chamber
of a charge of the explosive of example 6, the density of loading
being 0.9?
The reaction is
2C 6 H 5 N0 2 + - 2 /KC10 3 = 12C0 2 + 5H 2 + N 2 + VKC1
1266.8 528 90 28 620.8
From example 6, Q mp = 1500.9
Q mv = 1511.2
3794
Following example 4,
V k = 18 X 22.32 X 1000/1266.8 = 317.15 = v , equation (15)
KC1.
Gas.
1266.8 kilos explosive produce, kilos 620.8 646
1 kilo explosive produces, kilos 0.49 0.51 = y
Divide by density KC1, 1.94, Table IV .... 0.2526 = '
Eq. (22), wo
Eq. (21), a = 0.2526 + 0.1617 = 0.4143
EXPLOSIVES. 161
Eq. (20), / = 103.3X161. 75X3794/273 = 232210 kilos per sq. dec.
Eq. (18), P =
For A = 1, P = 3964GO kilos per sq. dec.
SPECIFIC HEATS AND DENSITIES OF NON-GASEOUS PRODUCTS.
It is assumed in the above discussion that the specific heats and
densities of the non-gaseous products remain constant. This
assumption is generally inaccurate, and the calculated values of
force and pressure for explosives that yield non-gaseous products
are therefore uncertain. For these explosives the most satis-
factory determinations are made by experiment. Two or more
charges of the explosive are exploded in a closed chamber and
the values of P measured. Substituting these with the corre-
sponding known values of A in equation (18) the values of / and
a are determined.
85 Complete Calculation of the Effects of Explosion.
The formula of the reaction for the complete combustion of
Sprengel's explosive acid, a mixture of picric acid and nitric acid,
is as follows.
5C 6 H 2 (N0 2 ) 3 OH + 13HN0 3 = 30C0 2 + 14H 2 + 14N 2
1145 819 1320 252 392
The molecular weight is 1145 + 819 = 1964.
In the work that follows, the number of the page on which the
process is explained, or the number of the equation from which
the value is derived, appears on the left.
146, Q mp = (30X94.3+14X58.2)- (5X49.1 + 13X41.6)
= 2857.5 1. cal.
1000
150, Q kp = 2857.5 X = 1454.9 1. cal.
(5) Q mr = 2S57.5 + 0.5724(30 + 14 + 14) =2890.7 1. cal.
1000
53, Q kv = 2890.7X^5 = 1471 .8 Leal.
(6) W k = 1471 .8 X 425 = 625515 kgm.
162 ORDNANCE AND GUNNERY.
154, V m = (30+14+14)22.32 = 1294.56 liters
154, V k = 1294.56 X jg^ = 659.14 liters
a = 6.26 X 30 + 5.61 X 14 + 4.8 X 14 = 333.54
b = 0.0037 X 30 + 0.0033 X 14 + 0.0006 X 14 = 0.1656
(10)
(11)
(12)
(18)
-333.54+v / 333.54 2 + 40QQx0.1656x2890.7
L-kv , f\ -//> + J.O
2X0.1656
3306
(16) / =
103.3x659.14(273 + 3306)
273
= 892650 kgm. per sq.
APJQ 14
(19) a = -r^- = 0.65914
1000
892650J
1- 0.65914 J kll S rams P er S( l- dec -
For J = 0.8, P = 1510700 kilograms per sq. dec.
CHAPTER V.
METALS USED IN ORDNANCE CONSTRUCTION.
86. Stress and Strain. A proper understanding of these terms
will be helpful in what follows.
When a force is applied to a body the effect produced depends
upon whether or not the body is free to move. A force applied
to a free body produces motion of the body. A force applied to a
fixed body produces change of form of the body.
Stress is the name given to any force or part of a force that
produces change of form of the body. The component forces or
pressures induced in the interior of the body are also called stresses.
Strain is the effect of the force as measured by the change in
form of the body to which the stress is applied.
Stresses are of different kinds, depending on the manner of ap-
plication of the force; as tensile stress, compressive stress, tor-
sional stress. A torsional stress is a compound stress and may be
resolved into a tensile stress on some elements of the material and
a compressive stress on others.
Each kind of stress produces a corresponding strain, or effect
on the material, the tensile stress producing elongation, the com-
pressive stress compression. As all stresses may be resolved into
tensile and compressive stresses, all strains may be resolved into
elongation and compression.
Physical Qualities of Metals. The following qualities of metals
are those with which we are most concerned in ordnance construc-
tion.
Fusibility. The property of being readily converted into the
liquid form by heat.
Malleability. The property of being permanently extended in
all directions without rupture when hammered or rolled.
Ductility. The property of being permanently extended with-
out rupture by a tensile stress, as in wire-drawing.
163
164 ORDNANCE AND GUNNERY.
Hardness. The property of resisting change of form under
compressive stress. A hard metal offers great resistance to such
a stress, while a soft metal yields readily and changes its form
without rupture. The terms hardness and softness are of course
comparative only.
Toughness. The property of resisting fracture under change of
form produced by any stress.
Elasticity. The property of resisting permanent deformation
under change of form. This is one of the most important proper-
ties of gun metals, which under the high stresses due to the ex-
plosion are subjected to extensive deformation. Through this
property the deformations disappear on the cessation of the stress
and the metal resumes its original dimensions.
Strength of Metals. The strength of metals is ordinarily de-
termined by physical tests in a testing machine. As the tensile
strength of metals is less than the compressive strength, usually a
tensile test only is applied. A test specimen is cut from the metal
to be tested and is prepared in suitable form to be inserted in the
machine. The area of the cross section of the test specimen is
usually a square inch or some aliquot part of a square inch.
In the machine the test piece is subjected to a tensile stress,
the amount of which is recorded by a sliding weight on a scaled
beam. The test piece stretches under the applied stress. With
elastic metals it will be found that up to the application of a
certain stress the test piece will resume its original length if
the stress is removed, but on the application of a stress
greater than this the test piece will remain permanently elongated.
When permanent distortion occurs the metal is said to have
permanent set.
ELASTIC LIMIT. The stress per square inch applied at
moment that the permanent set occurs is called the elastic limit
the metal. Within this limit the metal has practically perfe
elasticity and does not suffer permanent deformation.
As the stress increases beyond the elastic limit the metal stretcl
permanently and more rapidly, the cross section at the weak(
point reduces, and finally the test piece ruptures.
The elastic strength of metals will be found more fully treat
in the discussion of the elastic strength of guns in Chapter VI.
METALS USED IN ORDNANCE CONSTRUCTION.
165
87. TENSILE STRENGTH. The stress per square inch that pro-
duces rupture of the metal is called the tensile strength.
ELONGATION AT RUPTURE AND REDUCTION OF AREA. In ord-
nance structures the stresses are not expected to exceed the elastic
limit of the metal, but should they by any chance exceed this limit
the tensile strength of the metal and its capacity to permanently
elongate before rupture become of importance. The permanent
elongation will serve as a warning that the elastic strength has
been exceeded. The reduction of area of cross section is intimately
connected with the elongation. In the tests of metals for ordnance
purposes these particulars are therefore always noted and limits are
prescribed. For the measurement of the elongation at rupture the
parts of the ruptured test piece are brought together and the dis-
tance is measured between two punch marks that were made on
the test piece before insertion in the testing machine.
The tensile test therefore includes the determination of the
elastic limit, the tensile strength, the elongation at rupture, and the
reduction of area of cross section. The last two are recorded in
percentages of the original dimensions.
The following table shows the physical requirements demanded
by the Ordnance Department in the principal metals used in ord-
Elastic
Limit.
Tensile
Strength.
I\ln Cation
:it Rupture.
Contraction
of Area.
Copper
Ibs. per sq. in.
Ibs. per sq. in.
32,000
per cent.
22.0
per cent.
Bronze \o 1 ....
IN ,000
Bronze No 4
60,000
20.0
Tobin bronze
60,000
25.0
Ton No 1
22,000
on No 2
* 28,000
\\ ioii""ht iron
22,000
50,000
25.0
35.0
seel No 1 . .
25000
60,000
16.0
24.0
jteel \o :i
45,000
85,000
12.0
18.0
! sled. No. 1
For"vd steel (caps) .
27,000
60,000
1 60 ,000
28.0
30.0
40.0
45.0
i steel (tubes)
46,000
86,000
17.0
30.0
1 steel (jackets)
48000
90,000
16.0
27.0
: si eel ( hoops)
Forged steel, D
53,000
100,000
93000
120,000
14.0
14.0
20.0
30.0
Nickel steel. . . .
65,000
95,000
18.0
30.0
Steel wire (guns)
100,000
160,000
* Cast iron No. 2 must not show a tensile strength of more than 39,000
pounds per square inch.
fThe tensile strength of steel used in caps for armor piercing projectile*
must not exceed 60,000 pounds.
166
ORDNANCE AND GUNNERY.
nance construction, the requirements varying for each kind
metal according to the use to which it is destined.
Testing Machine. The standard government testing machine
is at Watertown Arsenal, Mass. It has a testing capacity of
800,000 Ibs.
A smaller testing machine, with a capacity of 50,000 Ibs., is
shown in Fig. 26. The specimen of the metal to be tested is turned
to the shape shown by the piece marked 1. The ends of the test
specimen are grasped by clamps fixed in the upper fixed head, /,
of the machine and in the lower movable head m. Four hea
vertical screws pass through the corners of the movable head, a
by their means the movable head is moved toward or from t
fixed head, exerting on the specimen held between the clamps
force of compression or of extension as desired. The amount
this force is measured by a sliding weight, w, on a scaled beam i
the same manner as a weight is determined on an ordinary sc
The total force divided by the area of cross section of the
specimen gives the force exerted per square inch.
A graphic representation of the relation between the fo
exerted and the change in length of the test specimen is made on
the indicator card, c. An indicator card, showing the results of
tensile tests on specimens of several metals, is shown in Fig. 25.
Within the elastic limit of the metal the elongation of the
test piece is proportional to
the tensile stress. Up to this
point, therefore, the line made
by the indicator will be a straight
line. At the elastic limit, whei
the bends occur in Fig. 25, pei
manent set occurs, and the
piece thereafter elongates moi
rapidly than the stress in-
creases.
To prevent injury to the ii
dicating apparatus by the shock
that occurs when the test piece
breaks, the indicator is usually
disconnected after the elastic limit has been registered.
0.2 0,3 0..4
FIG. 25.
METALS USED IN ORDNANCE CONSTRUCTION. 167
Broken test-pieces are shown at 2 and 3 in Fig. 26. Comparing
these with test piece 1, the effects of the test, the elongation at
rupture, and the contraction of area are apparent.
88. Copper, Brass, Bronze. Pure copper is used for the bands
of projectiles. In alloys, as brass and bronze, it enters into the
construction of parts of guns and gun carriages not usually sub-
jected to great stress. In this form, too, it is extensively employed
in the manufacture of cartridge cases, fuses, primers, gun sights,
and instruments. Brass is an alloy of copper with zinc. Bronze
is an alloy of copper with tin and usually a small quantity of zinc.
The addition of zinc or tin produces a harder and stronger metal
better suited than the soft copper for the uses to which these alloys
are applied. By the addition of aluminum or manganese in the
alloy the strong hard bronzes known as aluminum bronze and
manganese bronze are produced.
Iron and Steel. When iron ore is melted in the furnace the
product obtained, called pig iron, is an alloy of iron with carbon,
the carbon content being about 5 per cent. This alloy may be
readily fused and cast, and is then called cast iron. By various
processes in the furnace the amount of carbon in the iron may be
reduced. When the quantity of contained carbon is between two
per cent and two tenths of one per cent the product is steel. When
there is less than two tenths of one per cent of carbon we have
wrought iron.
As the amount of carbon is reduced the qualities of the metal
change in a marked degree. Cast iron is easily fusible, is hard and
not malleable or ductile, cannot be welded, and has a crystalline
structure. Wrought iron, on the other hand, is practically infusi-
ble, is soft, and possesses great malleability and ductility. It is
easily welded and has a fibrous structure.
The properties of steel lie between those of wrought iron and
cast iron, and the steel partakes of the characteristics of one or
the other according to the percentage of carbon contained. Thus
low steel, that is, steel low in carbon, is comparatively soft and
may be readily welded or drawn into wire, while high steels are
harder and more brittle and weld with difficulty.
CHIEF CONSTITUENTS. When examined under the microscope
iron and steel are found to be conglomerate in structure, consisting
168 ORDNANCE AND GUNNERY.
of microscopic particles chiefly of the following substances
widely varying proportions.
1. Pure or nearly pure metallic iron, called ferrite; soft, weak,
and very ductile.
2. A definite iron carbide, Fe 3 C, called cementite, which is ex-
tremely hard and brittle, but probably very strong under a tens-
stress.
The character of the iron or steel depends upon the proportions
of these two chief constituents. The steels which are especially
soft and ductile, as rivet and boiler plate steels, consist chiefly of
the soft ductile ferrite, the proportion of cementite in these st
not exceeding perhaps 1 per cent. The harder steels, like
steels, which are called upon to resist abrasion, contain a mu
larger percentage of cementite, about 7 per cent, and about 93
cent of ferrite. As the proportion of cementite increases
that of ferrite decreases the hardness increases and the ductili
diminishes. The tensile strength increases to a maximum when
the cementite amounts to about 15 per cent of the whole, and
then decreases.
The percentage of carbon in the metal is T V the percentage of
cementite the molecular weight of Fe 3 C being ISO, of which 12 parts
are carbon.
GRAPHITE. CAST IRON. In gray cast iron there is present, in
addition to the ferrite and cementite, a quantity of nearly pure
carbon in the form of graphite. The graphite is in thin flexible
sheets which form a more or less continuous skeleton running
through the mass of gray cast iron. The graphite makes the metal
weak and brittle.
White cast iron contains but little graphite, but has a much
higher percentage of cementite than either gray cast iron or steel.
The large percentage of cementite, over 60 per cent, brings the
carbon content to about 4J per cent, making the iron extremely
hard and brittle.
SLAG. WROUGHT IRON. Wrought iron contains, in addition to
the matrix of ferrite and cementite common to all irons, a small
quantity of slag, a silicate of iron formed in the process of pud-
dling. The presence of this slag forms the chief difference be-
tween wrought iron and the low carbon steels.
:
METALS USED IN ORDNANCE CONSTRUCTION. 169
89. Hardening and Tempering Steel. The distinguishing char-
acteristic of steel when compared with cast or wrought iron is the
property it possesses of hardening when cooled quickly after being
heated to a red heat, and of subsequently losing some of its added
hardness when subjected to a lower heat.
There is more or less confusion in the use of the terms applied
to the two processes. By some the first process, quick cooling
from a high heat, is called tempering, and the second process, re-
heating to a lower heat, is called annealing. By others the first
process is called hardening or quenching, and the second process,
which mitigates or lets down the hardness, is called tempering.
The more recent tendency is toward the use of the latter
terms, and following what is perhaps the better practice, we
will call the first process hardening and the second process
tempering.
EFFECT OF HEAT. In order to get a comprehensive idea of the
processes of hardening and tempering it will be necessary to go
somewhat further into the constitution of steel and to learn how
its constitution is affected by heat. As before stated, the chief
constituents of steel are ferrite (iron) and cementite (Fe 3 C).
These exist in different proportions, and the behavior of the metal
under heat treatment is dependent to a certain extent on the pro-
portions of these substances. The amount of carbon in the steel
depends on the proportion of cementite. The results attending
the application of heat to steel are chiefly due to the effect of the
heat on the condition of the carbon.
Austenite. When steel is heated to a temperature of from 700
to 1000 degrees centigrade, depending on the quantity of carbon
contained, the ferrite and cementite of which it is composed are
converted into a substance called austenite, which, according to
Howe, Professor of Metallurgy in Columbia University and an
eminent writer on steel, is a solid solution of carbon in iron. He
defines a solid solution as a solid that bears the same relation to
the definite solid chemical compounds that a liquid solution, salt
water for instance, bears to the definite liquid chemical com-
pounds, as water.
Austenite is a distinct substance with properties of its own.
When it contains 0.75 per cent or more of carbon it is extremely
170
ORDNANCE AND GUNNERY.
hard and brittle. Its hardness and brittleness are approximately
proportional to the percentage of carbon contained.
The temperature at which austenite forms depends upon the
proportions of ferrite and cementite in the metal. When these
proportions are such that there is 9/10 of 1 per cent of carbon in the
metal, that is when the metal consists of 0.9X15 = 13.5 per cent
of cementite and 86.5 per cent of ferrite, the transformation of
these constituents into austenite takes place at a lower temperature
than when they are present in any other proportions.
Pearlite. Eutectoid. The mixture of ferrite and cementite
containing 0.9 per cent of carbon is given a specific name, pearlit
and is characterized as a eutectoid, which means a solid mixture ii
the particular proportions that give to the mixture the lowest
iransformation point under the action of heat. The correspond!]
term applied to a liquid solution is eutectic. Thus the eutectic soli
tion of salt in water contains 23.6 per cent of salt. When this
percentage of salt is present the solution forms at the lowest t<
perature, and conversely the salt remains longest in solution
the temperature is lowered.
Steel containing less than 0.9 of one per cent of carbon
considered to be composed of pearlite and an excess of ferril
while the steels higher in carbon contain pearlite and an excess
cementite.
Now referring to Fig. 27 we will see at what temperature the
various mixtures are transformed into austenite. The proportions
of carbon and iron in the metal are shown on the horizontal axis.
The curves are worded to show the transformations that occur as
the metal cools from the molten state.
When there is 0.9 per cent of carbon in the metal we hai
pearlite, which is converted into austenite at a teraperature
about 680 C., as shown in the figure by the intersection of the lii
AI at the point S. In the steels lower in carbon , which are com-
posed of pearlite and an excess of ferrite, the pearlite is trans-
formed at the same temperature as before, but the excess of ferrite
requires a higher temperature, as shown by the line SA 3 , so that the
transformation is not complete for any particular composition until
that temperature is reached which is indicated by the intersection
of the ordinate representing the composition with the line SA 3 .
METALS USED IN ORDNANCE CONSTRUCTION.
171
1600
1500-
1400-
1300-
1200-
1100-
1000 2
A 3 -
800-
700-
Molten Cast Iron
-v\
Austenite
Austenite and Graphite Eutectoid Forms.
Austenite + Graphite
i
E
Cementite begins to Form
1 /
\ x *
% /
Austenite
H /
/
4- Cementite
/
+ Graphite
Austenite Resolved into Ferrite and Cementite
Pearlite
4-
Pearlite
Ferrite
+
Cementite
Pearlite
4 Cementite
Blue
"Oxide
+ Graphite
m
_Straw
"Oxide
i
1
i i
i t I 1 ! 1
600-
500-
400 2
300
200-
loo 1 !
oc
Carhon,
Iron
0.5
99.0
1.5 2.0 2.5 3.0
98.0 'J7.0 y.
27. Effect of Heat on Iron and Steel
95.0
172 ORDNANCE AND GUNNERY.
And similarly for the higher carbon steels containing an excess
of cementite; and for the cast irons, which, containing more than
2 per cent of carbon, are composed of pearlite, cementite, and
graphite.
90. Hardening. It will now be easy to understand the process
of hardening steel by means of high heat followed by quick cooling.
The high heat causes the formation of austenite in the metal. If
the metal is allowed to cool slowly the austenite is retransformed
into ferrite and cementite. This transformation requires an ap-
preciable time, and if the metal is suddenly cooled from its high
temperature the retransformation is prevented, and the hard
austenite is preserved in the cold metal.
The change in the character of steel being due principally to
the change in the condition of the carbon between its states in
pearlite and cementite and in austenite, the effect of the heat
treatment is greater as the proportion of carbon in the metal is
greater. Thus the low-carbon steels containing from 0.06 to 0.10
per cent of carbon are in general but little affected by heat treat-
ment and are practically incapable of being hardened, while the
high-carbon steels and some cast irons are greatly affected and may
be given extreme hardness.
The hardness and brittleness induced increase with the rapidity
of cooling without limit, but they are apparently nearly inde-
pendent of the temperature from which the sudden cooling begins,
provided that this temperature is above the line of complete trans-
formation, the line A 3 SE, Fig. 27. If the metal is suddenly cooled
from temperatures between the beginning and end of the trans-
formation, that is at temperatures between the lines AI and
A 3 SE, the hardening increases as the quenching temperature rises.
The range of temperature between the lines AI and A 3 SE is called
the critical range. In this range the hardness increases with the
quenching temperature, but above the critical range the hardness
is independent of the temperature.
The hardening of steel greatly increases its tensile strength and
elastic limit, but it makes the steel brittle, thus reducing its tough-
ness, as shown in test pieces by reduced elongation at rupture and
diminished contraction of area of cross section.
The tensile strength of low-carbon steels increases with the
METALS USED IN ORDNANCE CONSTRUCTION.
173
rapidity of cooling without limit. In high-carbon steels the ten-
sile strength at first increases with the rapidity of cooling, but
-lies a maximum and then declines; that is, there is a certain
rapidity of cooling that will give to any one of these steels its
maximum tensile strength. This may be due to the fact that
rapid cooling induces internal strains that may become so great as
to be destructive.
The following table, taken from Iron, Steel, and other Alloys, by
Henry Marion Howe, LL.D., well shows the effects of differences in
the rapidity of cooling of steel containing 0.21 per cent of carbon.
Cooled in
Tensile
Strength.
Elastic
Limit.
Elongation.
Contraction of
Area.
loed brine
Ibs. per sq. in.
237,555
Ibs. per sq. in.
237,170
per cent in 2 in.
2
per cent.
1 30
Cold water
216,215
1.5
1.67
Oil
174 180
2 9
1 403
Air
86,797
54342
27.76
57 829
In furnace.
80 103
44 091
28 15
54 749
91. Tempering. Hardened steel is tempered by slight reheat-
ing, say to 200 or 300 C. This process lessens the hardness and
brittleness of the steel, and thus increases its toughness. The aus-
tenite of the hardened steel is in a stable condition only when
above the transformation temperature. As the temperature of the
steel diminishes the austenite tends to change into ferrite and
cementite. In the hardening process this tendency is resisted by
the frictional resistance due to the sudden cooling, and the aus-
tenite is retained in an abnormal condition in the cold metal. The
reheating of the metal in tempering appears to lessen the molec-
ular rigidity of the austenite, and to afford opportunity for part
of the austenite to follow the course that it would have taken in
slow cooling through the transformation range and thus to be
converted into pearlite. The higher the reheat ing the more does
the change occur.
The rate of cooling after tempering has no effect on the
since the highest temperature of reheating lias determined how far
the change from austenite to pearlite may proceed, and no further
change can occur at a lower temperature. It is therefore imma-
terial whether the cooling after tempering be slow or rapid.
174 ORDNANCE AND GUXNERY.
Tempering has the effect of reducing somewhat the tensile
strength and elastic limit of hardened steel, while it increases its
toughness, as shown in test specimens by increased elongation
rupture and increased contraction of area of cross-section.
It will be seen that by proper regulation of the temperatures i
the processes of hardening and tempering an extensive control
the properties of the metal is obtained, permitting the productio
of metal of the quality best suited to any particular purpose.
The tempering temperatures may be judged within limits by
the color given to the steel, as it is heated, by the various oxides
that form successively on the surface. The following table shows
the temperatures at which the colors appear, and the temperin
points for steels for various purposes.
220 C., straw; razors, surgical instruments.
245 yellow; penknives, taps, dies.
255 brown; cold chisels, hatchets.
265 brown with purple spots; axes.
275 purple; table knives, shears.
295 violet; swords, watch springs.
320 blue; saws.
525 incipient red.
700 dark red.
950 bright red.
1100 luminous yellow.
1300 : incipient white.
1500 white.
Gun steel is tempered at temperatures between 600 and 6
Annealing. If the steel after being hardened is reheated to i
critical temperature and then cooled slowly the austenite is co
pletely converted into pearlite and ferrite or cementite, and the
steel reverts to its original condition, losing all its added hardness
and brittleness. This process is called annealing.
92. Other Substances. In addition to the carbon in the metal,
there are other substances, some of which are always present and
others that may be added, that affect the qualities of steel.
Sulphur, phosphorus, manganese and silicon are usually present
to a greater or less extent in all steels. If present in too large
argea
METALS USED IN ORDNANCE CONSTRUCTION. 175
percentage sulphur produces what is called hot shortness in the metal,
that is brittleness when hot, while phosphorus makes the metal
cold diort, or brittle when cold. Manganese and silicon when
present in proper percentages improve the qualities of the metal.
Chromium and tungsten give hardness to the steel without
brittleness.
Xfc/cel also greatly increases the toughness of the steel. Nickel
steel for guns contains about 3J per cent of nickel-.
Uses. Cast iron, wrought iron, cast steel and forged steel are
all used in ordnance constructions. Cast iron on account of its
cheapness and ease of manufacture in irregular shapes is used when
practicable wherever great strength is not required, as in project-
iles for the smaller guns and in parts of carriages not subject to
wear or to high stresses.
Wrought iron is not now extensively used in ordnance con-
structions. The older seacoast carriages were almost wholly
made of this metal.
Wherever great strength is required steel is employed. Cast
steel is used in those parts that do not require the greater strength
of forged steel, or that on account of their irregular shapes cannot
be readily produced as forgings, such as the chassis and top car-
riages of seacoast gun carriages. Cast steel has also been used for
projectiles and for guns, but without great success.
In structures or parts of structures requiring great strength, or
subject to wear, forged steel only is used. Guns and armor and
armor-piercing projectiles are now made of forged steel only, and
the operative parts of gun carriages and of other structures are
principally of this metal.
Gun Steel. Of two steels, one high in carbon and the other
low in carbon, the steel with the higher percentage of carbon will,
with similar treatment, have the higher elastic limit. Since the
elastic limit of the metal is the limit of the strength considered in
the construction of guns, it would appear that the metal with the
highest elastic limit would be the most desirable. But high steel
is more difficult to manufacture than low steel, and in large pi
there is much greater liability to flaws, strains, and incipient cracks.
After passing the elastic limit the hard steel has little remaining
strength and breaks without warning, while the low steel, due to
176
ORDNANCE AND GUNNERY.
its greater toughness, yields considerably without fracture. For
these reasons a low steel containing about one half of one per cei
of carbon is used in the manufacture of guns.
MANUFACTURE OF STEEL FORCINGS FOR GUNS.
93. Open Hearth Process. All gun steel at the present day is
made by the open hearth process, which derives its name from the
fact that the receptacle in which the steel is melted is open at
the top and exposed to the flarne of the fuel, which plays over the
surface and performs a principal part in the formation of the steel.
The product is called Siemens or Siemens-Martin steel, according
to the ingredients contained.
The open hearth furnace, invented by Dr. Siemens, consists of
the following essential parts:
1. The gas producer;
2. The regenerators;
3. The furnace proper.
THE GAS-PRODUCER. The fuel used in the Siemens furnace is
gaseous, and. is obtained from ordinary fuel by subjecting the
fuel to a preliminary process
in the gas producer. This ap-
paratus, Fig. 28, consists of
a rectangular chamber of fire-
brick, one side, B, being inclined
at an angle of from 45 to 60 de-
grees. A is the grate. The fuel,
which may be of any kind, is
fed into the producer through
the hopper C. As the fuel slowly
FIG. 28.
burns, the C0 2 rises through the
ing
mass above it and absorbs an additional portion of C, becomi
converted into 2CO. This gas passes out of the opening D into
a flue. In order to cause it to flow toward the furnace it is 1
through a long pipe, E, where it is partially cooled, and then
scends the pipe F leading to the furnace. The gas in F bei
cooler than that in E and D, a constant flow of gas from produc
to furnace is maintained.
I.IETALS USED IN ORDXAXCE CONSTRUCTION.
177
Tin: RKGENERATORS. The gas entering the furnace is, as has
been stated, CO. To burn it to C0 2 , air must be mixed with it.
This mixture is made in the furnace proper, the CO and air being
kept separate till they reach the point where they are to burn.
The CO is cooled to some extent, as shown, before being admitted
to the furnace.
To heat both air and CO before they are mixed and burned,
and to accomplish this economically, and raise the gases to a high
temperature, the waste heat of the furnace is employed. The
heating of the gases is accomplished by means of the regenerators,
Fig. 29. They consist of four large chambers, usually placed below
FIG. 29.
the furnace, filled with fire-brick. The fire-brick is piled so that
there are intervals between the bricks to allow the passage of gas
and air. When the furnace is started, CO is admitted through A
and air through B, both A and B being cold. The gases pass
between the fire-bricks in A and B and through flues at the top,
and flow into the furnace proper, where they aw lighted. The
products of combustion are caused to pass through C and D,
which are similar chambers. In doing so these products heat the
lire-bricks in C and D. After some time about one hour gener-
ally by the action of valves controlled by the workmen, the CO
and air are caused to enter the furnace through D and C respec-
tively, and the products of combustion to pass out through A and
B. In this case the CO and air, entering the heated chambers D
and C, are raised to a high temperature before ignition, and the
temperature of the furnace is thereby givntly increased. It is also
ITS
ORDNANCE AND GUNNERY,
evident that A and B will be more highly heated than C and D
were, and therefore when the next change is made, the gas and
air passing through A and B will be more highly heated than when
they passed through D and (7, and so on.
The action of the furnace is therefore cumulative, and its onb
limit in temperature is the refractoriness of the material. B
regulating the proportions of gas and air, which is readily done
the temperature may be kept constant.
94. THE FURNACE. The furnace proper, Fig. 30, is a chambei
situated above the regenerating chambers. The dish-shaped casl
FIG. 30.
iron vessel D, lined with refractory sand S, constitutes the hearth
of the furnace. The iron vessel is supported in such a manner
that the air may circulate freely around it and keep it from melting.
The iron that is to be converted into steel is piled on the hearth of
the furnace.
The gaseous fuel and air enter by the flues F, and the products
of combustion escape by the flues F', or the reverse, according to
the position of the regulating valves. The gases are ignited as
they enter the furnace. The sloping roof R, lined with fire-brick,
deflects the flames over the metal on the hearth.
At opposite ends of the furnace are a charging door for admis-
sion of the metal, and a tap hole, closed with a plug of fire-clay,
for drawing off the finished steel.
OPERATION. The process consists in the decarbonizing of cast
iron to the point at which the metal contains only that percentage
of carbon that is desired in the steel, and in the partial removal
from the iron of those impurities, such as silicon, manganese, and
METALS USED IN ORDNANCE CONSTRUCTION. 179
phosphorus, that arc injurious to the steel if present in too large
quantities.
Pig cast iron heated to a red heat in a separate furnace is piled
on the hearth of the Siemens furnace, and a quantity of steel or
wrought iron scrap is usually added to the charge to reduce the
percentage of carbon in the mass.
By the action of the furnace the charge is soon melted. Under
the influence of the heat the carbon oxidizes to carbonic oxide gas,
which escapes; the silicon oxidizes to silica and the manganese to
manganous oxide. The silica and manganous oxide unite with the
slag which floats in a thin layer on the molten metal.
The percentage of carbon in the steel at any stage of the proc-
ess is determined by taking samples from the metal, cooling them,
and observing their fracture on breaking; and by dissolving por-
tions of the specimens in nitric acid and comparing the color with
the colors of standard solutions of steel containing different per-
centages of carbon. In this way the composition of the steel can
be exactly regulated, for the metal can be kept in a melted state
without damage for a considerable time, and the character of the
flame can be made oxidizing or reducing at will, according to
the relative amounts of air and CO admitted.
The decarbonizing process is often continued until the percent-
age of carbon remaining in the steel is less than the percentage
desired. The desired percentage is then obtained by the addition
of pig iron containing a known percentage of carbon, such as
spiegeleisen or ferromanganese, or by the addition of ore.
The lining of the hearth, 8 Fig. 30, is of sand when the iron to
be reduced does not contain a harmful percentage of phosphorus.
The process is then called the acid process, from the silicious or
acid nature of the slag. When the iron contains a larger percent-
age of phosphorus a basic lining, as magnesia or calcined dolomite,
is required for the removal of the phosphorus. The slag formed in
the basic process is strongly retentive of phosphorus and removes
the excess of this substance from the metal.
The reduction of a charge of metal in the Siemens furnace or-
dinarily takes about eight hours.
When the steel has attained its desired composition the furnace
is tapped and the metal cast into ingots.
180
ORDNANCE AND GUNNERY.
FIG. 31.
95. Other Processes. The crucible process is used to some extent
by Krupp in the production of gun steel. The ingredients of the steel
are melted together in crucibles, and the resulting steel is poured from
the crucibles into a common reservoir from which the ingots are cast.
The Bessemer Process, though important and producing large
quantities of steel, is not used in making gun steel.
Casting. The molten metal is drawn into an iron ladle which
depends from a crane in front of the furnace. The ladle, Fig. 31,
is lined with refractory sand. It is provided with trunnions, T' ',
so that it may be tipped for pouring the
metal into the mold, or it may have a
tap hole, T, in the bottom, closed with a
plug of fire-clay. The plug is lifted and
replaced by means of a rod R also encased
in refractory sand. There is an advan-
tage in drawing the metal from the bot-
tom of the ladle in that the scoria and
impurities that float on the surface may
be kept out of the mold. The metal if
Very hot is poured slowly into the mold in a thin stream, thus
^allowing opportunity for escape of
the gases that it contains. If at
a lower temperature it may be
poured more quickly. It is fre-
quently allowed to cool to the
desired temperature in the ladle.
Molds. In the casting of ordi-
nary ingots, the iron or steel molds
into which the metal is poured from
the ladle are slightly conical in
shape, Fig. 32, to facilitate their
removal from the ingot. They are
of various cross sections, depending
on the shape of the ingot desired.
The interior surface is covered
with a wash of clay or plumbago.
Sinking Head. In all castings, w r hether of iron, steel, or nth
metal, an excess of metal, called the sinking head, is left at t
SOLID.,
SPLIT.
FIG. 32.
METALS USED L\ ORDNAXCE CONSTRUCTION. 181
top of the mold. The pressure due to the weight of this metal
gives greater density to the casting. The sinking head also se.
to collect the scoria and impurities which rise to the top, and
it provides metal to fill any cracks or cavities that may form in
the cooling of the ingot.
Defects in Ingots. Blow Holes. The gases in the melted
metal, unable to escape from the mold, form holes in the ingot,
called blow holes. These cannot be detected, nor can they rx> re-
moved by forging. Forging changes their form only without giv-
ing continuity to the metal. Blow holes are more* prevalent in
Bessemer than in open hearth steel and are more apt to occur at
low temperatures of casting, when the metal hardens before the
gas can escape.
Pipes. The metal in contact with the molds cools first and
solidifies. As the cooling and consequent contraction extends
toward the center, the liquid metal is drawn away from the center,
leaving cavities called pipes along the axis of the ingot. Pipes
most frequently occur when the metal is cast too hot. Thus on the
one hand too low a temperature causes blow holes and too high a
temperature pipes.
Segregation. As the various constituents of the steel (iron,
silicon, manganese, etc.) solidify at different temperatures, it fre-
quently happens that they separate from each other as the ingot
cools, forming what is called segregation. This gives a different
structure to the metal and greatly weakens it. Segregation is
more likely to be found toward the center of the ingot and in the
upper portions.
96. Whitworth's Process of Fluid Compression. The \ ui
of this process, invented by Sir Joseph Whitworth of England, is to
remove as far as possible the blow holes, pipes, and other defects
from the ingot and to give the metal greater solidity and uniformity
of structure than can be obtained in tin; ordinary method of
easting The object is. accomplished, to a lar^e extent, by the
application of enormous pressure on the metal uhile in the
fluid state in molds so constructed as to allow free escape of
the gases.
The flask, / Fig. 33, made of cast steel, is of groat strength to
withstand the givat pressure. It is built up of cyKndric-.l sections
182
ORDNANCE AND GUNNERY.
t
or
i
which are bolted together to the desired length. The interior of
the flask is lined with vertical wrought iron bars, 6, whose long
edges are cut away or beveled to form channels, a, by means of
w 7 hich the gas may escape: the interior and exterior channels
. _ thus formed being connected by
grooves, r, cut in the sides of the
bars at short intervals. The cylin-
der formed by the interior surfaces
of the bars is lined with refractory
sand. A cast iron plate, d, through
which are continued the longitudi-
nal gas channels closes the mold at
the bottom. The mold rests on a
^ ~ car in the bottom of a pit.
D Q When the mold is filled with
^1 T"\
metal the car is run into a hydraulic
press with an adjustable head. The
head, p, of the press, of diameter
only slightly less than the interior
of the mold, is brought down
against the molten metal and
locked in that position. The metal
wells up around the head of the
press and, quickly cooling, forms
a solid mass which with the head
completely closes the top of the
mold.
The press is constructed with its
piston at the bottom so that the
pressure may be applied on the
bottom of the car that carries the
mold.
By the pressure on the bottom
of the car, gradually applied until
a pressure of six tons to the square
inch is reached, the car and mold are slowly forced upward.
The molten metal is compressed by the applied pressure, and the
gas, forced through the sand lining and the channels betw<
d
FIG. 33.
between
METALS USED IN ORDNANCE CONSTRUCTION. 183
the lining bars, issues from the top mid bottom of the mold
in a violent flow of flame. The pressure is continued until
the column of metal has shortened one eighth of its length.
A uniform pressure of about 1500 pounds to the square inch is
then left on the ingot while it cools, to follow up the metal as
it contracts and prevent the formation of cracks.
07. Processes After Casting. The specifications for gun forg-
ings require that the forgings be made from that part of the ingot
that remains after 30 per cent by weight has been cut from the
top of the ingot and 6 per cent from the bottom. These parts
are cut off, as they are likely to contain most of the defects in
the ingot.
For hollow forgings the center of the part selected is then bored
out in a heavy lathe, or punched out if the ingot is short.
Heating. The ingot is then heated preparatory to forging.
The heating is accomplished in a furnace erected near the forging
hammer or press, and is conducted with great care. The cooling
of the ingot in the mold has left in the metal strains due to tilt-
successive contraction of the interior layers. Assisted by unequal
expansion in heating the strains may cause cracks to develop in the
ingot. Great care is therefore exercised that the heating shall pro-
ceed slowly and uniformly, thus avoiding the overheating of the
exterior layers of metal before the heat has thoroughly penetrated
to the interior.
Forging. The heated ingot is forged either by blows delivered
by a steam hammer or by pressure delivered by a hydraulic forg-
ing press. Under the slow pressure of the forging press the metal
of the forging has more time to flow, the effect of the treatment is
more evenly distributed, and the metal is more uniformly strained.
This process is therefore preferred in the manufacture of gun
forgings.
34 is a reproduction from a photograph of a 5000-ton
hydraulic forging press at the works of the Bethlehem Steel Co.
The print shows a bored ingot for the tube of a 12-inch gun being
forged on a mandrel. The outer diameter of the ingot is reduced
by the forging and the length of the ingot increased. The diameter
of the bore remains practically unchanged. The outer end of the
ingot is supported from an overhead crane.
184 ORDNANCE AND GUNNERY.
The ingot is turned on the anvil of the press, and advanced when
desired, by means of the chain seen through the press. The method
of turning is better shown in the plate following.
The movements of the head of the press are controlled by means
of levers situated at a short distance to the right of the press. The
operator at the lever sees recorded on the dial the pressure exerted
at any instant.
Fig. 35 shows a 10-ton steam hammer forging a solid ingot for
a 3-inch gun. The ingot is supported from an overhead crane and
is nearly balanced in the sling chain by the bar of iron, called a
porter bar, clamped to the ingot and extending to the rear. By
bearing down on the porter bar the ingot is lifted off the anvil and
may then be moved by the crane back and forth under the ham-
mer. The ingot is turned under the hammer from the crane by
means of the gearing shown in the upper part of the picture.
The movements of the hammer are controlled by the man at the
left through the levers shown at his hand.
98. Hollow Forgings. In forging bored ingots a solid steel
shaft called a mandrel is passed through the bore of the heated
ingot, and the method pursued in forging depends upon whether
the length of the ingot is to be increased without change of interior
diameter, as in forging a gun tube, or whether the diameters of the
ingot are to be enlarged, as in forging hoops. In the first case the
ingot, on a mandrel of proper diameter, is placed directly on the
anvil of the press, as shown in Fig. 34. The effect of forging is
then to increase the length of the ingot and decrease the outer
diameter while maintaining the interior diameter unchanged.
The mandrel is withdrawn from the forging by means of a
hydraulic press.
In forging hoops, the mandrel rests on two supports on either
side of the head of the press, Fig. 36, and is itself the anvil on
which the forging is done. By turning the mandrel new surfaces
of the hoop are presented to the press. The walls of the hoop are
reduced in thickness by the forging, the diameters of the hoop
being increased, while the length is not materially changed.
The specifications for gun forgings require that the part of a
solid ingot used for a tube forging shall have before forging an
area of cross section at least four times as great as the maximum
FIG. 34. 5,000-ton Hydraulic Forging Press.
FIG. 35. 10-ton Steam Hammer.
METALS USED L\ OJW\A.\('E COXSTRUCTIOX.
185
area of cross section of the rough forging when finished, and for a
jacket forging 3J times as great. For forgings for guns 12 inches
or more in caliber these figures are reduced to 3.J and :> respectively.
Forgings for lining tubes must be reduced 6 times in area.
If bored ingots are used the wall of the ingot must be reduced
at least one half in thickness.
Annealing. The w.orking of the ingot in forging and the irreg-
ular cooling leaves the metal in a state of strain. The strains
are removed by the process of annealing. For this purpose the
FRONT ELEVATION.
SIDE ELEVATION.
FIG. 30.
forging is usually laid in a brick-walled pit or furnace, and slowly
and uniformly heated by wood fires, the burning logs being di>-
tributed along the pit as required to heat the forging uniformly.
When the proper heat, usually a bright red, has been attained, the
fires are allowed to die out, or are drawn, and the ingot remains
in the furnace until both are cold. Three or four days may be
required for the slow cooling of a large forging.
99. Hardening in Oil or Water. Annealing removes the in-
ternal strains that exist in the forging, but. as before explained, it
greatly reduces the tensile strength and elastic limit of the metal.
To restore the strength to the metal and to produce in it the quali-
ties required in gun forgings, the forging is next subjected to the
process of hardening. Before hardening it is machined in a lathe
nearly to finished dimensions. Specimens for tests are cut from
the ends, and from their behavior in the testing machine the re-
quirements of the subsequent treatment are determined.
1S6
ORDNANCE AND GUNNERY.
The forging is then slowly and uniformly heated throughout.
Large forgings, such as tubes and jackets, are heated in vertical
furnaces, great care being exercised that the heating shall be uni-
form throughout the length of the piece in order that undue warp-
ing may not occur in the subsequent cooling. When the forging
is at a uniform red heat the side of the furnace is opened and the
forging is lifted out by a crane and immersed in a deep tank of oil
or of water alongside the furnace. The oil tank is surrounded by
another tank through which cold water is constantly running.
The heat of the forging passes to the oil and thence to the water,
and is thus gradually conducted away.
The Bethlehem Steel Co. of Bethlehem, Penn., and the Midvale
Steel Co. of Philadelphia, the two principal manufacturers of gun
forgings in this country, use different oils for oil tempering. The
Bethlehem Co. uses petroleum oil once refined. The Midvale Co.
uses cottonseed oil with flashing point not less than 360 degrees
centigrade.
The temperature of the forging when immersed is very high
compared with that of the oil. The cooling is therefore sudden at
first, but as oil is a poor conductor of heat the heat of the forging
is carried away slowly, leaving the metal with greater toughness
than it would have if hardened in water and cooled more quickly.
Oil is customarily used in the hardening of gun forgings. Occa-
sionally the qualities of the metal are such that better results are
obtained by the quicker cooling in water.
Tempering. The process of hardening greatly increases the
elastic strength of the metal but reduces its toughness. At the
same time it produces internal strains due to contraction in cool-
ing. The strains are removed, the hardness reduced, and the
toughness restored by the process of tempering, conducted in the
same manner as the previous annealing, but at a low r er heat, so
that the gain in elastic strength is reduced but slightly and not
entirely lost. The tempering temperature for gun forgings lies
between 600 and 675 degrees centigrade, 1100 to 1250 degrees
Fahrenheit.
Specimens are again taken from the ends of the forging and
broken in the testing machine. If the specimens do not fulfil the
requirements of the specifications the forging is again hardened
MI'TALS USED IX ORDNANCK COXSTItUCTIOX. Is7
and tempered, the temperature and conduct of the processes being
so regulated as to improve those qualities in which the metal has
proved defective in the tests.
Strength of Parts of the Gun. The requirements in steel forg-
ings for guns over 8 inches in caliber are shown in the table on
page 165. It will be observed that the strength of the metal in-
creases as we proceed outward from the center of the gun. Thus
the elastic limit of the tube is 46,000 Ibs., of the jacket 48,000, and
of the hoops 53,000. It would be better if the strongest metal
wore in the tube, which has to endure the greatest strain. But tin-
production of the high qualities required is much more difficult in
large forgings than in smaller ones, and for this reason the require-
ments for the tubes and jackets must be lower than for the hoops.
An additional reason for the difference in requirements is found in
the fact that the metal of the tube has the advantage of greater
elongation before rupture, as may be seen in the table on page
165. The greater elongation is difficult to produce with the higher
elastic limit.
The tubes and jackets of guns under 8 inches in caliber have
an elastic limit of 50,000 Ibs.
Forged steel that has an elastic limit of over 110,000 Ibs. is now
produced.
CHAPTER VI.
GUNS.
ELASTIC STRENGTH OF GUNS.
100. The Elasticity of Metals. In the chapter on metals the
elastic limit of a metal has been defined as the minimum stress per
unit of area of cross section that will produce in the metal a per-
manent set. For each kind of stress, whether of extension or coi
pression, the metal has a distinct elastic limit. The elastic limit
extension, or the tensile elastic limit, is usually less than the elastic
limit of compression. In gun steels the difference is not great anc
the two are considered equal. The tensile elastic limit is ordi-
narily used, as it is the limit usually measured.
Hooke's Law. A tensile stress applied to a bar of metal cau
elongation of the bar, and it is found by experiment that under
stresses less than the elastic limit of the metal the elongation if
proportional to the stress. In other words, within the elastic limit
of the metal the ratio of the stress to the strain is constant. This
law is known as Hooke's law, and is often expressed ut tensio sic
vis.
Modulus of Elasticity. If we measure the elongation of a
caused by a tensile stress, and divide the measured elongation
the original length of the bar, we will obtain the elongation pel
unit of length, expressed as a numerical fraction.
Now if we divide any stress per unit of area within the elastic
limit of the metal by the elongation per unit of length the resull
will be the constant ratio of stress to strain within the elastic limit.
This ratio is called the modulus of elasticity.
Let E be the modulus of elasticity of the metal,
the elastic limit of the metal,
7- the elongation per unit of length at the elastic limit.
188
GUNS.
By definition we have
E=e/ r (i)
If we assume that the elasticity of the metal continues in-
definitely we see, by making 7- equal to unity in the above equa-
tion, that the modulus of elasticity is the stress per unit of area
that would extend a bar to twice its length.
When the clastic limit is expressed in pounds per square inch
the modulus of elasticity of steel may, without sensible error, be
taken as 30,000,000.
The modulus of elasticity is really a stress per unit of area, but
it had best be considered as the abstract ratio between stress and
strain.
Since by Hooke's law the ratio of the stress to the strain is con-
stant within the elastic limit, we may write for 6 and 7- in equa-
tion (1) any other stress within the elastic limit and its correspond-
ing strain.
Let S be a stress per "unit of area within the elastic limit,
I the strain per unit of length due to the stress.
Then E = S/l and l = S/E (2)
That is, the strain per unit of length due to any stress per unit
of area within the elastic limit is equal to the stress divided by the
modulus of elasticity.
loi. Strains Perpendicular to the Direction of the Stress.
In the previous paragraphs we have considered only the strain
produced in the direction of the stress. Rut we have seen in the
chapter on metals that a tensile stress produces a reduction in
of cross section, and it is found by experiment that, for steel, the
strain at right angles to the direction of a stress within the elastic
limit of the metal is equal to one ^ ^
third of the strain in the direction of
the stress. If the cube in Fig. 37 is
subjected to the tensile stress rcprc-
J
sented by p, the edges, aa, bb, etc.,
parallel to the direction of the stress
will be elongated, and the edges, ab,
ac, etc., perpendicular to this direction will be shortened by an
amount equal to one third the elongation of the parallel
1%
ORDNANCE AND GUNNERY.
Equations of Relation between Stress and Strain. If we con-
sider that the cube is subjected at once to tensile stresses applied
in the three directions perpendicular to its faces, the strain in each
direction due to the stress in that direction will be diminished by
the contrary strains due to the perpendicular stressevS.
Let X, Y, and Z be three independent extraneous tensile
forces perpendicular to the faces of the cube;
l x , ly, and l z the strains in the directions of X, Y, and Z re-
spectively.
The strain in the direction X due to the force .Y is from equa-
1 Y 1 Z
tion (2) X/E. It is diminished by ~--~ and by -^. Therefore,
for the total strains in the three directions, we have
t -l(V-*-a
l * E\ 3 3/
Problems. 1. A steel test specimen has an elastic limit of
59,000 Ibs. What will be its elongation per unit of length at the
elastic limit? 0.00197
2. The original diameter of the specimen being 0.505 inches,
what is its diameter when the piece is stretched to its elastic limit?
0.5047 inches.
3. A vertical steel rod 20 feet long and J inch square sustains
at its lower end a load of 6000 Ibs. The elastic limit of the steel is
72,000 Ibs. What will be the elongation caused by the load?
0.192 inches.
4. Taking the modulus of elasticity of copper as 16,000,000,
what will be the elongation of a copper bar 1 inch square and 10
feet long supporting a load of 5000 Ibs.? 0.0375 inches.
102. Principal Stresses and Strains. Since every stress applied
to a solid produces stresses in directions perpendicular to the direc-
tion of the applied stress, at any point in a solid under stress there
are always three planes at right angles to each other upon each of
GUNS. 191
which the stress is normal. Thus in the cube we have just con-
sidered, the stresses at any point in the cube are normal to three-
planes parallel to the faces of the cube. The normal stresses are
called the principal stresses at the point; and it may be shown by
the ellipsoid of stress that one of the principal stresses is the great-
est stress at the point. The corresponding strains are called the
principal strains.
Stresses and Strains in a Closed Cylinder. The following dis-
cussion of the elastic strength of cylinders is based on the theory
of Clavarino, published in 1879, and modified through the results
of experiments by Major Rogers Birnic, Ordnance Department,
U. S. Army.
Consider a hollow metal cylinder, closed at both ends, to be
subjected to the uniform pressure of a gas confined in the cylinder.
The pressure acting perpendicularly to the cylindrical walls will
tend to compress the walls radially. If we consider a longitudinal
section of the cylinder by any plane through the axis, the pressure
acting in both directions perpendicular to this plane will tend to
disrupt or pull apart the cylinder at the section, and will therefore
produce a tensile stress in a tangential direction on the metal
throughout the section. The pressure acting against the ends of
the cylinder will tend to pull it apart longitudinally.
The metal of any elementary cube in the cylinder is therefore
subjected to three principal stresses: a radial stress of compression,
a tangential stress of extension, and a longitudinal stress of ex-
tension.
If the cylinder be subjected to a uniform exterior pressure
stresses will be similarly developed in the three directions.
In the following discussion we will always understand by the
term stress, the stress per unit of area, and by the term strain, the
strain per unit of length, unless these terms are qualified by the
word total or other qualifying word.
Assume a closed cylinder affected by uniform interior and ex-
terior pressures. At any point of the cylinder
Let t be the tangential stress,
p the radial stn
q the longitudinal stress.
Substituting these letters in equations (3) for A", Y, and Z,
192
ORDNANCE AND GUNNERY.
respectively, and changing the sign of F, since the interior anc
exterior pressures act toward each other radially, so that the
stress, p, acts in a direction opposite to that assumed for Y in
deducing equations (3), we obtain the following equations.
(4)
which express the values of the strains in the directions of
three stresses. These values may be positive or negative, depend-
ing upon the resultant of the stresses. A positive value of a strain
represents elongation and a negative value contraction, as a posi-
tive value of a stress represents a tensile stress and a negative
value a compressive stress.
103. Relations between the Stresses /, p, and q. Lame's
Laws. The stresses and strains in equations (4) form six unknown
quantities which cannot be determined from the three equations.
Lame, a distinguished investigator in the subject of elasticity
of solid bodies, has established relations between the stresses, by
means of which the equations may be solved and the values of the
stresses and strains determined. He assumes that the longitudinal
stress q and the longitudinal strain l q are constant throughout the
cross section. The last of equations (4) may then be written
t p = 3(q l q E) = constant
which equation is true whether q has a value or is zero. As t and
p apply to any point in the walls of the cylinder, we have Lame's
first law.
In a cylinder under uniform pressure the difference between th
tangential tension and the radial pressure is the same at all points
in the section of the cylinder.
.
GC7.YN. 193
Now let us consider a right section of the cylinder, of unit
length, Fig. 38.
Let P be the pressure per unit of
area acting on the in-
terior of the cylinder,
PI the pressure per unit of
area on the exterior,
R Q the interior radius of the
cylinder,
Ri the exterior radius,
r the radius of any point in
the cylinder.
The total interior pressure acting
normally on either side of the diametral plane be is 2P R . The
total pressure acting on the outer circumference on either side of
the plane and normal to it is 2P t Ri. The difference of these pres-
sures is the resultant pressure acting on the metal in the sectional
plane be. The total tangential stress on the metal at the section
will therefore be
FIG. 38.
But since t represents this stress per unit of area, the total
stress is equal to 2 I / dr. Therefore
\j RQ
r*i
I t dr
JR O
Assuming that t is a function of r, it must be such a function
that t dr when integrated between the limits Ri and A'o will be
equal to P R P\Ri. t dr must then be equal to -d(pr) because
the integral of this expression taken between the given limits is
PuRoPiRi. The substitution of the pressures P and PI for the
/>, in integrating the expression d(j)r), may be made
. as will be 1'oun I later, p varies proportionately with P
and /',.
We therefore have
tdr= r'(pr) = jxlr rdp
194
ORDNANCE AND GUNNERY.
From which by combination with equation (5) and integratl
see foot note, we obtain
in which C is a constant.
Equation (6) expresses Lame's second law:
In a cylinder under uniform pressure the sum of the tangential
tension and the radial pressure varies inversely as the square of the
radius.
Both laws are based on the assumption that the longitudi
stress is constant or zero.
104. Stresses in the Cylinder. By means of Lame's laws we
may now determine the values for the stresses at all points in the
cylinder. We may write for t, p, and r in equations (5) and (6)
the coordinate values referring to any point in the cylinder and
thus form the equations
l/rfcv
-
Eliminating T and
PoRo
from these equations we may obtain
'
Ri 2 -R 2 r 2
72oW(Po-Pi)l
From equation (5)
Therefore
Integrating
t dr= pdr rdp
-(t+p}dr=rdp
t+p=2p+k
dr d
= loge (2p+ A;) + log e A
Replacing 2p+ k by its value t+ p we obtain
GUXS.
From these equations we may obtain the values of the tangen-
tial and radial stresses at any point in the section of the cylinder
by substituting for r its value for the point.
Longitudinal Stress. The longitudinal stress has been as-
sumed as constant over the cross section of the cylinder. Under
tliis assumption when applied to a gun the total longitudinal
36 due to the pressure on the face of the breech block is dis-
tributed uniformly over the cross section of the gun, producing a
stress per unit of area that is small compared with the tangential
and radial stresses. In the present discussion of the stresses act-
ing on the cylinder the longitudinal stress will therefore be neg-
lected, and q in equations (4) will be considered as zero. Later
the value of the longitudinal stress will be deduced.
105. Resultant Stresses in the Cylinder. Making q = Q in
equations (4) and substituting for t and p their values from (7) and
(8) we obtain
J-7J ^ _ . /Q\
btt^&t^^ ) 2 D 2 " O D~2 D 2 1^
j3 (io)
In the above equations the first members are the respective
strains multiplied by the modulus of elasticity. Referring to
equation (2) we see that each product is equal to the stress which
acting alone would produce the strain. The equations then irive
th<; values of the simple stresses that would produce the same
ins as are caused by the stresses p and t acting together. Their
values at any point in the cylinder are obtained from the above
dions by giving to r the value for the point.
Basic Principle of Gun Construction. The following principle
is the foundation of the modern theory of gun construction.
No fiber of any cylinder in the gun must be strained beyond the
clastic limit of the metal of the cylinder.
This principle is strictly adhered to in the construction of guns
built up wholly of steel forging. In the construction of wire-
196
ORDNANCE AND GUNNERY.
wound guns the tube is, in some constructions, purposely coi
pressed beyond its elastic limit by the pressure exerted upon it
the wire.
The principle fixes a limit to the stresses to which any cylim
that forms part of a gun may be subjected. If we represent by
the tensile elastic limit of the metal,
p the compressive elastic limit of the metal,
the stresses represented by the first members of equations (9) to
(11) may never exceed either 6 or p, depending on whether the
stress is one of extension or of compression; and the interior and
exterior pressures, represented by PQ and PI in those equatioi
must never have such values as to cause the stresses to exceed th(
limits.
1 06. Simplification of the Formulas of Gun Construction.-
The formulas of gun construction are deduced from equations (9),
(10), and (11). Heretofore, in the deduction, these equations have
been used in the form in which they appear above, and the for-
mulas resulting from them have been similarly extended and
equally formidable in appearance, and much labor has been ex-
pended in writing them out.
We will introduce here, for the first time in any text, a sim-
plification of equations (9), (10), and (11), which will result in a
marked simplification of all the formulas of gun construction,
making the formulas easier to handle, and greatly reducing the
labor required in their use.
We will express in equations (9), (10), and (11) Ri 2 in terms of
Ro 2 , and in the future deductions we will always express R, Rs 2 ,
R n 2 in terms of R 2 .
(12)
Make R 1 2 = aR 2 or a = R^
b = R 2 2 /R Q 2
For convenience in future discussion we will call a, 6, c, n the radius
ratios.
GUNS. 197
Now if we divide numerator and denominator of each term of
equations (9), (10), and (11) by R 2 and substitute for Ri 2 /R 2 its
value a from equations (12) we obtain
- 4a(P -P 1 )fl 2
* 3 a-1 7^
2 (Po-aPQ 4
^ = S p = j (a-1) 3 Ca-1) "?
Ft 1 2 (P ~ aPl)
^ = ^=-3 (a _ 1}
RULES FOR TRANSFORMATION. We will notice here, with
reference to the transformation, two facts on which we will base
rules for future transformations. In what follows we will under-
stand by the words term factor a factor that affects a whole term,
in contradistinction to a factor that affects a part of a term only.
Comparing the first term of the second member of equation (13)
with the corresponding term of equation (9) we can write the first
rule.
Rule 1. The non-appearance of Ro 2 in any term involving the
radius ratios indicates that the term from which it was formed
had in the numerator the same number of term factors involving
the squares of the limiting radii as in the denominator.
In the first term of the second member of equation (9) the
numerator contains a single term factor involving the square
the radii. The denominator similarly contains but one such term
factor.
Comparing the last terms of equations (13) and (0) we
Rule 2. When Ro 2 appears in the numerator of a term involving
the radius ratios, it indicates that (he original term contained in
the numerator one more term factor involving the squares of the
''nig radii, than in the denominator.
Though the last term of equation (13) contains in numerator
and denominator the same number of term factors that involve
the radius ratios, the presence of Ro 2 in the numerator indicates
that the term from which it was formed had one more such term
factor. That factor was R 2 , and since R 2 /R Q 2 = 1 the factor has
disappeared from equation (13).
198
ORDNANCE AND GUNNERY.
107. Stresses in a Simple Cylinder. In a cylinder forming a
part of a gun we have three cases to consider. There may be a
pressure on the interior of the cylinder and none on the exterior, the
atmospheric pressure being considered zero. There may be a pi
sure on the exterior of the cylinder and none on the interior,
both exterior and interior pressures may be acting at once, tl
interior pressure being usually the greater. We will consider tl
simple cylinder under these circumstances.
Differentiating equation (13) we obtain
dS t
dr
and differentiating again,
a-l
r 3
(H
dr 2 aI r 4
Similarly from equation (14) we obtain
dp__8 a(P -Pi)#o 2
dr 3 a 1 r 3
a-l
(II
(II
First Case. Interior Pressure Only. Making PI =0 in equa-
tion (13) and remembering that r may vary between the limits
RO and RI we see that the smaller the value of r the greater will be
the value of the resultant tangential stress. This is more readily
seen in equation (16) in which the first differential coefficient of
the stress as a function of the radius is negative when Pi=0,
showing that S t decreases as r increases. R being the least value
of r the tangential stress is greatest at the interior of the cylinder.
Since, when Pi=0, St in equation (13) is positive for all values of
r, the stress is one of extension throughout the cross section of the
cylinder. When Pi=0 in equation (17) the second member is
positive, showing that the curve of stress is concave upwards, tl
axis of r being taken as horizontal. The curve of tangential sti
due to an interior pressure only may then be represented in gen-
GUNS.
199
cral hy the curve ti in Fig. 39, the ordinates being the values of
the stress, the abscissas the values of the radius.
The numbers at the extremities of the curve are the actual
due to an interior pressure P = 36,000 pounds per square
inch in a cylinder one caliber thick. They are calculated from
equation (13) by making Pi=0 and R 1 =3R . When Ri=3R we
have a = Ri 2 /R Q 2 = 9. The equation becomes with these substitu-
tions
(20)
Making P = 36,000 and r = R we obtain , = 57,000; and for
r = 3# , , = 9000.
Similarly from equations (14), (18), and (19) we determine for
the radial stress produced by an interior pressure the general curve
FIG. 39.
p } , Fig. 39, which shows radial compression throughout the cross
;<>n with the greatest stress at the interior. Equations (14)
and (15) become for the cylinder one caliber thick
(21)
(22)
and comparing these with equation (20) we see that for equal
values of r the radial stress from an interior pressure is alxvuys less
200
ORDNANCE AND GUNNERY.
The longitudinal stress is less than
ed
36,000 are note
than the tangential stress,
either.
The radial stresses produced by a pressure P
on the curve pi.
We may observe from equations (20), (21), and (22) that the
thickness of the cylinder being expressed in calibers, or, what is the
same thing, in terms of the interior radius, the stresses developed by
an interior pressure are entirely independent of the caliber, and
are the same for all cylinders the same number of calibers thick.
1 08. Second Case. Exterior Pressure Only. Making P =
in equations (13) to (19) we may determine the curves of stress fo
an exterior pressure acting alone. In this case the value of
equation (13), is always negative. The stress is therefore com
pressive throughout the cylinder. dS t /dr, equation (16), is posi-
tive. S t therefore increases algebraically with r. d 2 S t /dr 2 , equa-
tion (17), is negative. The curve is therefore concave downwards.
The general curve fe, in Fig. 40, therefore results.
33000
FIG. 40.
In the same way the general curve p 2 is obtained from equa-
tions (14), (18), and (19).
The numbers on the curves are the values for the stresses caused
by an exterior pressure PI =36,000 Ibs. on a cylinder one caliber
thick, for which Ri=3R and a = Ri 2 /R 2 = 9.
We see as before that the greatest stresses are at the interior of
the cylinder, and that the tangential stress is greater than the
radial. The tangential stress is one of compression throughout.
GUNS.
201
The radial stress is one of compression on the exterior and of ex-
trusion on the interior.
109. Third Case. Interior and Exterior Pressures Acting.
Tlu? curves of stress due to interior and exterior pressures acting at
once may be found from the equations, or by combination of the
curves of stress due to the pressures acting separately. Thus in
Fig. 41 , in which the curves from Figs. 39 and 40 are repeated, the
lines /) 3 and / ;{ represent the stresses due to the equal interior and
srior pressures, P = Pi =36,000 Ibs.
The position of the resultant curves of stress from interior and
exterior pressures acting together will, of course, depend on the
relative values of the two pressures. In Fig. 41 the pressures are
FIG. 41.
equal. In Fig. 42 are shown the curves resulting when the interior
pressure is twice the exterior pressure; P = 36,000, PI = 18,000.
\Ve may see at once from these figures that the tangential re-
nce of a cylinder to an interior pressure may be greatly in-
rd by the application of an exterior pressure. Assuming that
the maximum ordinates of the curves ti and /o, in Fig. 41, are the
elastic limits and p respectively, the interior pressure acting alone
would produce the limit of tangential extension. But with the
exterior pressure acting the interior pressure has first to overcome
the existing compression, and as p is usually greater than the in-
terior pressure required to produce the stress p + 6 would be more
than twice as great as the pressure required to produce the str
alone. That is to say, that by the application of an exterior pres-
202
ORDXANCE AND GUNXERY.
sure we may more than double the tangential resistance of a cylii
der to an interior pressure.
Similarly it is seen that the tangential resistance of a cylim
to an exterior pressure is increased by the application of an interi<
pressure.
no. Limiting Interior Pressures. In determining the ma:
mum safe pressure that can be applied to the interior of a cylinder
there are two cases to be considered; for, as we have just seen, a
greater interior pressure may be applied when there is an exterioi
pressure acting than w r hen the interior pressure acts alone.
INTERIOR AND EXTERIOR PRESSURES ACTING. In Figs. 41 am
42 we see that when both interior and exterior pressures are actii
FIG. 42.
on a given cylinder the maximum values of the resultant tangential
and radial stresses depend upon the relative values of the pres-
sures. In Fig. 41 the maximum values of the two resultant stresses
are equal. In Fig. 42 the resultant radial stress of compression
has a greater maximum value than the resultant tangential stress
of extension. Therefore when both pressures are acting, in order
to determine the maximum permissible interior pressure we must
find the values of the interior pressures that will produce the limit-
ing stresses both of extension and of compression, and then adopt
the smaller value as the greatest permissible pressure. The maxi-
mum stress in either case occurs when r = R . Therefore make this
substitution in equations (13) and (14). Write for S t and p for
S p and solve the equations for P . The negative sign is given to
GCNS. 203
si MCI /; is an absolute value only, while S p now represents a stress
of compression, which is negative.
=
4a-2
P Q9 is the interior pressure that acting with the exterior
sure PI will produce the limiting tangential stress of extension 6:
and P 0f) is the interior pressure that acting with the exterior pres-
sure PI will produce the limiting radial stress of compression p.
The lesser of these two values should, according to our prei:
always be used, but it will be seen later that in practice it is usual
to neglect consideration of P 0p and to make use of P oe even when
it is the greater. Assuming that 6 = p we will find by equating the
< >nd members of the above equations that P Qo will be less than,
equal to, or greater than P 0p as follows.
^o*~/V as aP,=lO
^ **>
in. TXTKRIOR PRKSSURE ONLY.- We have seen in Fig. 39 that
the greatest stress from an interior pressure acting alone is a tan-
gential stress of extension at the interior of the cylinder. This
must never exceed 0, the elastic limit for extension. Therefore to
find the greatest permissible value of an interior pressure acting
alone make S t = in equation (13), PI =0, r = R 0} and solve for P .
/v=^0 cay
If the cylinder is one caliber thick 7,'i :>#. n -',). and
If the cylinder has infinite thickness ^=00 and
Po* = 0.750 (27)
From which we conclude that the greatest possible safe value
for an interior pressure acting alone in a simple cylinder is <'
204 ORDNANCE AND GUNNERY.
and also that comparatively little benefit is derived by inc
the thickness of the cylinder to more than one caliber.
Now if we assume an exterior force applied to the cylinder and
assume the effect of this force to be the stress p of compression,
the tangential stress that must be produced by the interior pres-
sure to reach the limit of safety becomes p+6, and this being sub-
stituted for 6 in equation (26) it becomes
(28
From equations (26) and (28) the advantage derived by the
interior cooling of cast guns formed of a single cylinder becomes
apparent. When the gun is cooled from the interior the layer of
metal immediately surrounding the bore cools first and contracts.
The cooling and contraction of the subsequent layers then pro-
duce a stress of compression on the layers of metal immediately
surrounding the bore similar to the stress that would be produced
by the application of an exterior pressure. The limiting interior
pressure in this case would be obtained by substituting for p in
equation (28) the value of the stress resulting from the initial com-
pression.
112. Graphic Representation of Limiting Interior Pressures.
The system of graphics devised by Lieutenant Commander Louis
M. Nulton, U. S. Navy, for the representation of the relation be-
tween the pressures and the shrinkages in cannon helps materially
towards a ready understanding of the subject.
We will begin the study of the graphic system with the repre-
sentation of the limiting interior pressures whose values are given
by equations (23) and (24).
We will consider, as is customary in gun construction, that 6 = p.
Equations (23) and (24) may be put in the following forms,
which A, B, C, and D are constants for any given cylinder-
(23o)
P 0fi = C+DP 1 (24o)
These are the equations of right lines that- do not pass through the
origin of coordinates. The lines may be constructed, as shown
GUNS.
from
Fig. 43, from the axes of P and P r , the line marked PI
quation (23a) and the line PiPo P from (24a).
The abscissa of any point of the line PiPo* is the value of P ,
which, acting together with the pressure PI, whose value is repre-
sented by the ordinate of the point, will produce the limiting in-
terior tangential stress of extension 6. Similarly the abscissa and
ordinate of any point of the line PiP , represent the pressures
P and PI that acting together on the cylinder will produce the
limiting interior radial stress of compression p.
FIG. 43.
For any given value of cither interior or exterior pressure. / ) o
or PI, we may at once determine from the figure the value <>f the
corresponding exterior or interior pressure, PI or P , that will
produce the limiting strain of compression or of extension.
For /'<, -\0 the pressure I\, whose value is then
equation C2~>), will produce in the interior of the cylinder the maxi-
mum permissible stresses both of extrusion and compression.
The figure also shows that the resistance of the cylinder to an
interior pressure is increased by the application of an exterior ;
sure, since /',, has its least value for Pi=0.
113. Limiting Exterior Pressure. This is deduced only for the
of an exterior pressure acting alone, as we will have no occa-
sion to use the limiting values of the exterior pressure when both
interior and exterior pressures are acting.
From Fig. 40 we see that the great* j from an exterior
pressure is a tangential stress of compression at the interior of the
206
ORDNANCE AND GUNNERY.
cylinder. This must not exceed p, the elastic limit for compres-
sion. Therefore make S t =p in equation (13), Po = 0, r = R 0)
and solve for PI.
PI P being the exterior pressure that acting alone will produ<
the limiting tangential stress of compression p.
For the cylinder one caliber thick Ri = 3R in equation (29]
p lp = 0.44 ( o
For the cylinder of infinite thickness RI = oo ; and
P, n '
1 u.f
again showing how little is gained by increasing the thickness
the cylinder beyond one caliber.
114. Thickness of Cylinder. The thickness H needed in a sin
pie cylinder to withstand an interior pressure Pee is obtained
replacing a in equation (26) by its value Ri 2 /R 2 , solving the
tion for RI and then subtracting R from each member.
06
Similarly the necessary thickness to withstand an exterior pi
sure PI P is obtained from equation (29).
t-Ro-H-Ro^ _2p -l)
Longitudinal Strength of a Simple Closed Cylinder. The
total pressure acting on each of the end walls is 7iR 2 P . This
is assumed to be uniformly distributed over the cross section of
the cylinder, n(R 1 2 R 2 ). The longitudinal stress per unit of
area is therefore
o-l
GUNS. 207
Substituting this value of q in the third equation (4), and for
t and /> their values from (7) and (8), we obtain for the longitudinal
stress in the cylinder
Giving El q its maximum value, or p, and solving for P ,
using we obtain
Po*-3(a-l)0+2aPi
for the interior pressure that will produce the maximum permissible
longitudinal stress.
If P!=O
a value considerably greater than that expressed in equation (26).
Problems. 1. What is the maximum permissible interior pres-
sure on a steel gun hoop the interior diameter of which is 20 inches
and the exterior diameter 28 inches, the elastic limit of the metal
being 60,000 pounds per square inch?
Ans. 17,561 Ibs. per sq. in.
2. The steel tubes of a water tube boiler are 2 inches in interior
diameter and 2.4 inches in exterior diameter. The elastic limit of
the metal is 30,000 Ibs. per sq. in. What is the limiting interior
water pressure? Ans. 5103.2 Ibs. per sq. in.
3. Using a factor of safety of 1J, what is the limiting interior
pressure in an air compressor tank with interior and exterior diam-
8 of 15 and 17 inches respectively? The elastic limit of the
.1 is 30,000 Ibs. per sq. in. . 2391 Ibs. per sq. in.
1. An iron tube 3 inches in interior diameter is subjected to
:ior pressure, 1326.5 Ibs. per sq. in. The elastic limit of the
metal is 20.000 Ibs. per sq. in. What must be the exterior diam-
eter of the tube in order that it may safely with>tai:d the j
sure? An*. -'5.2") inches.
.">. The 6-inch wire-wound gun has the following dimensions at
the powder chamber: /2o = 4.5 inches, R\ = \2 inches. If the <nm
were constructed of a single forging with an elastic limit of 60,000
Ibs. per sq. in. what would be the maximum permissible powder
pressure? Ans. 36,132 Ibs. pers<j. in.
6. A boiler 6 feet in interior diameter is required to withstand
208 ORDNANCE AND GUNNERY.
a steam pressure of 350 Ibs. per sq. in. The elastic limit of the
metal is 20,000 Ibs. per sq. in. What is the maximum thickness
required in the shell? Ans. 0.64 inches.
7. The cylinder of a hydraulic jack has an interior diameter of
10 inches and a maximum working pressure of 10,000 Ibs. per sq.
in. The elastic limit of the metal is 40,000 Ibs. per sq. in. What
thickness of wall is required in order that the factor of safety
may be 1J? Ans. 2.9 inches.
115. Compound Cylinder, Built-up Guns. It has been shown
that the resistance of a cylinder to an interior pressure may be
greatly increased by the application of pressure on the exterior of
the cylinder. This is accomplished in practice by shrinking a
second cylinder over the first. The shrinkage causes a uniform
pressure over the exterior of the inner cylinder and an equal uni^
form pressure on the interior of the outer cylinder.
The exterior pressure strengthens the inner cylinder against an
interior pressure, and at the same time weakens the outer cylinder.
That the full strength of the compound cylinder may be utilized
it is important that the shrinkage, and therefore the pressure at the
surfaces in contact, be so regulated that under the action of an in-
terior pressure the interior of the weakened outer cylinder will not
be stretched to its elastic limit before the inner cylinder has reached
that limit. Otherwise we cannot employ the full strength of the
inner cylinder. And if the inner cylinder is strained to the elastic
limit before the outer cylinder, we cannot employ the full strength
of the outer cylinder.
We have seen in Fig. 39 that the tangential stress produced in a
single cylinder by an interior pressure diminishes in value as the
thickness of the cylinder increases. It is therefore apparent that
the stress transmitted to the outer cylinder may, by giving proper
thickness to the inner cylinder, be so reduced that when added to
the initial stress existing in the outer cylinder this cylinder will
not be strained beyond its elastic limit. And by adjusting the
thicknesses of the two cylinders and the pressure produced by the
shrinkage, the system may be so constructed that the cylinders
composing it will both be strained to the elastic limit at the
same time.
There is evidentlv then a relation between the thicknesses of
CC/.VS. 209
the cylinders and the shrinkage that must be applied in order that
the inner and outer cylinders shall be stretched to their elastic
limits by the same interior pressure. This relation must be estab-
lished if we desire to utilize the full elastic strength of the cylinders.
And if a third and a fourth cylinder are added the proper relation
between the thickness and the shrinkage must be established
for these as well.
A modern gun is built up of a number of cylinders assembled
by shrinkage, the number of the cylinders, from two to four, de-
pending upon the size and power of the gun. The shrinkage of
each cylinder is so adjusted that under the action of the powder
pressure, if the pressure becomes sufficiently great, all the cylinders
will be strained to the elastic limit at once.
When the powder pressure is acting in a compound cylinder the
system is said to be in action. When the powder pressure is not
acting the system is at rest. In action each elementary cylinder
except the outer one is subjected to both interior and exterior pres-
sures. At rest the inner cylinder is subjected to exterior pressure
only, the outer cylinder -to interior pressure only, and the inter-
mediate cylinders to both pressures.
1 1 6. System Composed of Two Cylinders. Assume a system
so assembled that under the action of an interior pressure both
cylinders will be strained to their elastic limits.
Let #o, Ri, #2, Fig. 44, be the radii of the successive surfaces
from the interior outwards,
PO, PI, P 2 , the normal pres-
sures on the successive sur-
faces when the system is in
action,
PO, Pi, P2, variations in P , PI,
P%, as the system passes
from a state of action to a
state of rest,
, #ir the tensile elastic limits
of the inner and outer cyl-
inders respectively,
p Q , />j, the compressive elastic FIG. 44.
limits.
210 ORDNANCE AND GUNNERY.
E } the modulus of elasticity, assumed the same for bo
cylinders,
Pis, the normal pressure at the surface of contact wh
the system is at rest.
Application of Formulas to Outer Cylinders. It will be well
before proceeding further, to show how the formulas deduced f
a single cylinder are made applicable to outer cylinders in com-
pound systems.
Thus equation (23)
:
-
4a + 2
gives the value of the limiting pressure in a single cylinder wh
the pressure PI acts on the exterior.
Let us make this apply to the second cylinder of a compound
system.
Substituting for a its value R^/Rf and clearing of fractions
numerator and denominator,
Now to apply this equation to the second cylinder change all
zero subscripts to 1, and subscripts 1 to 2. Making these changes,
dividing numerator and denominator by R 2 , we obtain, since
R 1 2/R Q * = a and R 2 2 /R 2 = b,
Ple=
Comparing this equation with (31), from which it has been de-
duced, we see that the transformation may be immediately made
by substituting b for a, and by writing a after the numerical quan-
tities that are affected when we substitute R^/Rf for a and clear
of fractions.
We have made this transformation under transformation rule
1, page 197. In equation (31) the numerator forms but one term
factor and the denominator another. As R 2 does not appear in
GUNS. 211
(31) we know that the equation from which it is derived, equation
(32), is of the same form.
The following equation, which refers to pressures in the inner
cylinder of a compound system,
(b-a) a(c-b)
PI = J^1) PO beC meS P2== b(^) pl
for the second cylinder, since the absence of R 2 in the first equa-
tion indicates that its original equation had two term factors in-
volving the squares of the radii in the numerator as well as in the
denominator. Therefore consider 1 = R Q 2 /R Q 2 as present as a
term factor in the numerator of the first equation, change to
Ri 2 /Ro 2 , and write a for this quantity in the second equation.
The equation
becomes, if made applicable to the second cylinder,
since the absence of R 2 indicates that the original equation had
one term factor in the denominator as well as in the numerator.
Equation (13) is, for the first cylinder,
2(P -aP 1 ) 4a(P -P 1 W
3(a-l) 3(o-l) 7^
and becomes for the second cylinder
l 3(6-a) 3(6-o) ~F
Under transformation rule 2 the presence of R 2 in the nu-
merator of the last term indicates that the original term had two
term factors involving the squares of the limiting radii in the
numerator and one in the denominator. Therefore supply the
missing factor l = # 2 /Ro 2 , change to 7?i 2 //? 2 , write a in (36) for
212
ORDNANCE AND GUNNERY.
this quantity and change the a in (13) to b. Ro 2 is itself not
affected in the transformation, as in reality it disappears during
the transformation and reappears later by reinsertion.
Whenever in doubt as to a transformation replace the radi
ratios by their values, clear the resulting fractions, make the tra
formation, and rewrite the ratios.
117. System in Action. When the system is in action t
outer cylinder is strained to its elastic limit by an interior
pressure. The limiting pressure is given by equation (26), changi
the subscripts to conform to the nomenclature above.
3(&-a)
:
The pressure Pi e will extend the inner layer of the outer cylin-
der to its elastic limit. It is therefore the greatest safe pressure
that can be applied to the interior of this cylinder.
The pressure P\ g just found also acts upon the exterior of the
inner cylinder, and the pressure P upon the interior. For the
limiting values of the interior pressure we have, under these cir-
cumstances, from equations (23) and (24),
(38)
4a+2
4a-2
The smaller of these values as determined by the test, equation
(25), must be used as the limiting interior pressure. Acting with
the pressure PU it brings the inner layer of the inner cylinder to
its elastic limit of tension or compression according as P os or P 0f
is the less. At the same time the pressure P\ stretches the inner
layer of the outer cylinder to its elastic limit.
Equation (37), containing in the second member known quai
tities only, is solved first, and the value of Pi e obtained is sul
stituted in equation (38) or (39) as determined by the test. The
maximum permissible value of P results.
GUNS. 213
1 18. System at Rest. We have seen in Figs. 40 and 41 that an
exterior pressure acting alone on a cylinder may produce a greater
stress than when an interior pressure is also acting.
It may be, therefore, that the pressure P u deduced as a safe
pressure for the system in action may produce a higher pressure
than the inner cylinder can safely withstand when the system is
at rest, that is, when the interior pressure P is zero. This must
be determined before we can assume, as safe values for the pres-
sures, the values obtained from the consideration of the system in
action.
As the system passes from a state of action to a state of rest
variations occur in the pressures acting, and consequent variations
in the stresses at the various surfaces, po and pi represent the
variations in the pressures P and PI respectively. Since the in-
terior pressure changes from P to we have
Po=-Po (40)
because PQ Po = 0; that is, the algebraic sum of the pressure in
action and the variation in the pressure is the pressure at rest.
The variations in the tangential stresses due to the variations
in the pressures may be determined from equation (13). For the
exterior of the inner cylinder, the pressures P and pi acting,
write PO for P , pi for PI and make r = Ri.
It will be noticed that when r = R l in equations (13) and (14)
the last factor becomes R 2 /Ri 2 or I/a, which cancels the a in the
numerator of the last term.
-6Po-(2a+4) Pl
3(a-l)
For the outer cylinder equation (13) takes the form of equa-
tion (36). For the interior of the outer cylinder, the pressure
pi acting alone, write p^ for I\, make P2 = 0, and r = R\.
3(6-o)
As the surfaces of contact of the two cylinders form virtually
one surface the two values for the variation in the stivss at this
214
ORDNANCE AND GUNNLRY.
surface must be equal. Equating the second members of equj
tions (41) and (42) and solving for p i} we obtain
(b-a)P
which expresses the relation between the variations in pressure
the interior and exterior of the inner cylinder.
We have designated the pressure at the surface of contact
the two cylinders, system at rest, by P Js . The variation in pi
sure from the state of action to the state of rest must therefore
because P 19 - (Pi,- PI.) =Pi s . Solving (44) for P ls
and substituting the value of pi from equation (43) we obtain
(6-a)P
for the value of the pressure on the exterior of the inner cylindei
system at rest.
119. This value of P is must not exceed the maximum permit
sible value of an exterior pressure acting alone on the inner cyl
inder, as given by equation (29).
P -
If it does the inner cylinder at rest will be crushed by the pressi
applied to strengthen it in action.
The condition that P J8 shall not exceed P lp may be expressed
(6-a)P
-
(4-
If the values of P le from equation (37) and of P from (38) 01
(39) do not fulfill the above conditions these values for the pressures
cannot be used for the system in action.
GUNS. '215
To find the safe values for the pressures in this case we must
reduce the value of the first member of (47), P lf , until it is equal
to the second member, PI P . P^ becomes then PI and we have
This is the relation that must exist between PI and P in order
that these pressures may be safe for the system at rest.
Equations (38) and (39) express the relations between the safe
pressures for the system in action.
If therefore we substitute the lesser value, PI from (48), forP^
in equations (38) and (39) and solve for P we will obtain the
values of PQ that willpDe safe both in action and at rest.
3(a- ,
b-a
(50)
The lesser of these two values will !><> the limiting safe interior
pressure that can be applied to the system.
lining and p equal, we will find by equating the second
members of equations (49) and (50) that P oe will be less than,
equal to, or greater than P 0f> according as
a(6-l)P lp (a-l)^ (51)
120. Graphic Representation. System at Rest and in Ac-
tion. Equation (43) expresses the value of the variation pi in the
rior pressure for a variation P in the interior pressure. Drop-
ping the negative sign for convenience this equation may In-
written, for a given cylinder.
Pi A*/',,
216
ORDNANCE AND GUNNERY.
and may be represented by the line piP in Fig. 45. The variation
in exterior pressure increases directly with the interior pressure at
a rate represented by the inclination of the line piPo.
The lines PiP and P\Po p represent, as in Fig. 43, the coordi-
nate limiting pressures for the inner cylinder. P le is the limiting
pressure at the surface of contact in action obtained from equaticn
(37). Considering only the tangential stresses, the abscissa of the
point c, PQ = 42,955, is the limiting value of the interior pressure in
action. As the system passes from action to rest the exterior
pressure falls at the rate represented by the inclination of the line
y
-0085
28969
$0 42956
19911
FIG. 45.
Therefore drawing through c a line parallel to piPo, the
point where it cuts the axis PI will be the value of Pfj, the pres-
sure at rest, P being zero at this point. If the value of P ]s is
less than P J/0 , the limiting value of the pressure at rest calculated
from equation (46), the value P lo is a safe value. If P\ s is
greater than P\ p we cannot use PI O in action. In this case we
would find the permissible value of PI in action by drawing a line
from PI P parallel to piPo. Its intersection with P\Poe would give
the values of the coordinate limiting exterior and interior pres-
sures in action.
121. Maximum Value of the Safe Interior Pressure in a
Compound Cylinder. The stresses and strains produced by any
pressure applied to a compound cylinder are exactly the same as
would be produced by the same pressure applied to a single cyl-
inder of the same dimensions.
GUNS. 217
The resultant stresses in the compound cylinder are the alge-
braic sums of the stresses already existing in the cylinder and
those induced by the application of the pressure, and similarly for
the strains.
As the resultant stresses may never exceed the elastic limits of
extension and compression, the maximum permissible pressure in
any cylinder is given by equation (28).
Changing a into b to make of the compound cylinder a single
cylinder whose outer radius is R 2 , we have
Making R 2 = <*>, and therefore b=R 2 2 /Ro 2 =<x>, we obtain
which is the greatest possible value of the safe interior pressure in
a compound cylinder.
The same result is obtained by substituting OQ-\- po for 6 in
equation (27).
122. Shrinkage. The absolute shrinkage is the difference be-
tween the exterior diameter of the inner cylinder and the interior
diameter of the outer cylinder before
heated for assembling, 2ab, Fig. 46.
The relative shrinkage is the absolute
shrinkage divided by the diameter, or
the shrinkage per unit of length, ab/Ri.
The shrinkages are so small that it is
unnecessary to distinguish between the
lengths of the radii as affected by the
shrinkage.
The shrinkage diminishes the exterior radius of the inner cyl-
inder, when cold, and increases the interior radius of the outer cyl-
inder, so that the radius RI of the surfaces in contact is of a length
intermediate between the lengths of the original radii.
The relative shrinkage is, Fig. 46,
(5 2)
218
ORDNANCE AND GUNNERY.
The relative compression ci/Ri is the strain per unit of length
produced by the pressure PI S acting on the exterior of the inner
cylinder. As the circumference is proportional to the radius the
diminution of the circumference per unit of length will be the same
as the unit shortening of the radius, and the value of the tangential
strain produced by the pressure PI S may be obtained from equa-
tion (13), by making P = and r = Ri.
(2a + 4)P la
Lt 3E(a-l)
The negative sign is omitted, as it simply indicates compressi<
The tangential strain co/Ri at the interior of the outer cylinde
is similarly obtained from equation (13), which for the second cyl
inder takes the form of equation (36). Making Pi = P lt ,
and r=Ri,
Therefore from equation (52) we have for the relative shrinl
E(a-l)(b-a)
The absolute shrinkage is
E(a-l)(b-a)
The exterior diameter of the inner cylinder before shrinkage
should be
RI representing here the interior radius of the outer cylindt
before assembling.
The relative tangential compression of the bore due to the
shrinkage pressure P ls is found from equation (13) by making
Po^O, Pi = Pi s , and r = R .
E(a-l)
GUNS. 219
Substituting the value of P^ from equation (54) and reducing
we have
(6-1)2^
from which we may obtain at once the tangential compression when
the absolute shrinkage is known.
Since, equation (13), El t =S t the tangential stress on the bore
in pounds per square inch is found by multiplying the relative com-
pression by the modulus of elasticity; 30,000,000 for gun steel.
123. GRAPHIC SHRINKAGE. Equation (54) becomes for a given
compound cylinder
It is represented in Fig. 45 by the line SiPi 8 , the axis of Si coin-
ciding with the axis of P . Different scales are used on these
two axes. The coordinates of any point of the line SiPi, repre-
sent, for the given compound cylinder, absolute shrinkage and
the pressure produced by it at the surface of contact. Therefore
to find the shrinkage necessary to produce the required pressure
at rest, PU, draw the horizontal line from P\ 8 and the vertical
line from its intersection with S\P\ 8 . The intercept on the axis
of Xi is the value of the absolute shrinkage that will produce the
pressure 7^. Si = 0.0085 in the case illustrated.
124. Radial Compression of the Tube. The value of the
pressu re on the exterior of the inner cylinder at rest is given l>y
equation (45),
(b-q)Po
I { will be seen from this equation that the larger the value of
P Q used the less'will be the value of 7*1.,; and from equation (54
we Bee that the less the value of PI, the less will be the shrinka^-.
Therefore if when 7% is greater than PQ P we use PO* in equa-
tion (45), the resulting shrinkage will be less than if P 0p were
used, and as may be shown by equation (14) the resulting radial
stress at the inner surface of the inner cylinder, system in action,
will be increased. Now in deducing the value for the shrinkage
\ve have used the pressures calculated t<> strain the metal to
220 ORDNANCE AND GUNNERY.
its elastic limit. Therefore with reduced shrinkage the pressure
P Qp will produce a stress of radial compression at the inner sur-
face of the tube greater than the 'elastic limit of the metal.
But it is found that the metal of the inner cylinder supported
as it is by the outer cylinder has greater strength to resist radial
compression than is indicated by the tests of the detached speci-
mens of the metal used in determining the elastic limits; and
as the reduced shrinkage resulting from the use of P oe in equa-
tion (45) reduces all the stresses on the system in a state of rest,
and those on the outer cylinder in a state of action, it is the prac-
tice to use PQO instead of PQ P in calculating the shrinkage.
Guns as constructed yield by tangential extension, and the
radial over-compression if it exists does not determine rupture.
Consequently the tangential elastic resistance of the gun, even
though frequently greater than the radial elastic resistance, is
taken as the elastic strength of the gun.
125. Prescribed Shrinkage. Equation (54) expresses the re-
lation between the shrinkage and the pressure that it produces.
When for any reason the compound cylinder is not assembled
in such a manner as to offer the maximum elastic resistance,
as, for instance, when a certain shrinkage less than the maximum
permissible shrinkage is prescribed, the pressure due to the pre-
scribed shrinkage may be found by solving equation (54) for
PI S . The elastic resistance of the compound cylinder assembled
with the prescribed shrinkage will then be found from equations
(49) and (50) by substituting for P 1/} , which represents the pressure
at rest, the value of P i8 from equation (54), which is the actual
pressure applied.
The prescribed value of Si will give in equation (56) the re-
sulting relative tangential compression of the bore.
GRAPHIC REPRESENTATION. In Fig. 45 let the point 0.008
be the value of the prescribed shrinkage. By following the broken
lines from this point we find on the axis PI the resulting pressure
at the surface of contact, system at rest; and at b. on the line
PiPoe the point whose coordinates are the limiting interior and
exterior pressures, system in action.
126. Application of the Formulas. Assuming the caliber
of the bore and the thicknesses of the cylinders, to determine
GUNS.
221
the shrinkage and the permissible pressures in the compound
cylinder assembled to offer the maximum resistance.
The formulas usually required for a system composed of two
cylinders are here assembled for convenience.
P
^ i
3(o- l)0p + 6oPi
4a + 2
4o-2
(b-a)
0(6-1) 2a ^ '
#(0-1X6-0)
lt== " (6-1)2^
3(o-
Po- =
(12)
(37)
(38)
(39)
(43)
(47)
(54)
(56)
(49)
(50)
EL.-S
2(P -oPi) ^(Pp-Pj)
3(o-l) 3(o-l)
2(P -oPi) 4a(P -Pi)
p *J P
r 2
(13)
(14)
222
ORDNANCE AND GUNNERY.
In equation (43) above, PO has been replaced by its vf
p from equation (40) in order to make the equation general.
PO is a particular value of
In the first member of (47) P <? is written for P to make the
equation conform to the practice of using P oe in determining the
shrinkage.
PROCESS. Use the values of 6 and p determined in the testing
machine.
Find PU from equation (37).
Find PO* and P 0p from (38) and (39).
Make the test indicated in (47) and if either of the conditions
are met use the value of the first member of (47) for P ls in (54)
and find Si.
The values already found for P^ and P are then the limil
ing safe pressures.
If the first member of (47) is greater than the second,
Find P oe and P 0f from (49) and (50).
Use PI, from (47) for P is in (54) to find Si.
The stresses and strains produced by any pressures are founc
by means of equations (13) and (14); the tangential stresses and
strains from equation (13), the radial from equation (14).
127. Problem i. The dimensions of the 4.7 inch siege rifle, at
the section marked IV in Fig. 47, are :
#o = 2.35 inches, #i = 3.86, R 2 = 6. The prescribed elastic
limit for both tube and jacket is 50,000 Ibs. per sq. in. What
will be the shrinkage when the cylinders are assembled to offer
the maximum resistance, and what will be the maximum per-
missible interior pressure?
We have a
b = R 2 2 /R<? = 6.5187
6-a = 3.8207
Equation (37) P le
3X3.8207
: 26.0748 +5.396
50000 = 18210
/OQN z> 3X1.698X50000 + 6X2.698X18210 ._-
06 = 12 792~ =42956
GUNS. 223
5.094 X 50000 + 5.396x18210
* = s 792~~
3.8207X42956 1.698
Pn-18210-
4X3.86X2.698X5.5187X7187
30,000,000X1.698X3.8207
The outer diameter of the tube must therefore be 0.0085
inches greater than the inner diameter of the jacket before
assembling.
If PO, were used in place of P 00 in the determination of P u ,
equation (47), we would obtain P ls = 7909, and from (54) 1 =
0.00934.
128. GRAPHIC SOLUTION. In Fig. 45 is shown the graphic
solution of Problem 1. For this problem the equations take
form as follows.
(38) P ,= 19910 +1.325Pi
(39) P 0o = 28968 + 0.614PJ
(43) pi=0.2566P
(47) Si= 0.00001 18Pi.
These equations are represented by the lines of the figure
drawn to scale. Determine from equation (37) the limiting
interior pressure on the jacket, P ig . From this point on the
axis of PI draw the horizontal line. It cuts PiP at the point c,
for which P = 42956. Passing from action to rest the pressure
PI varies at the rate indicated by the inclination of the line p\P Q .
Therefore draw from c a line parallel to this line. It cuts the
axis of PI at PI,, which is the pressure at rest. P lf is less than
P lp , equation (47), also represented in the figure. Therefore P ltf
in action is a safe pressure. Drawing the horizontal line from
P l8 and the vertical line from its point of intersection with SiPi 9
we find that the absolute shrinkage that will produce the pressure
p lt is Si = 0.0085.
129. Problem 2. What are the stresses on the inner and
outer surfaces of the tube of the gun in the last problem, both
224 ORDNANCE AND GUNNERY.
at rest and in action, assuming the gun to be assembled with the
shrinkage determined in that problem, and using the pressui
P 0p = 40146, equation (39), as the interior pressure in action?
The pressure at rest, Pi s = 7187, determined in Problem
acts alone.
Tangential stresses, (13), S t (R ) = -22839 S t (Ri) = - 1325;
Radial stresses, (14), S P (R ) = + 7613 S P (Ri) = - 1970
In Problem 1 in determining by equation (47) the pressure
rest we used PO<? = 42956 Ibs. as the pressure in action. Tl
pressure at the outer surface of the tube in action as given b]
equation (37), PIO = 18210, will therefore be produced only
the interior pressure P 0g . An interior pressure P 0p = 40146 11
less than Po e , will produce a pressure on the exterior of the tul
less than 18210 Ibs. Equation (43) gives the value of the variatic
in the exterior pressure due to any variation p in the interic
pressure. Making p = 42956 -40146 = 2810 in equation (43)
find pi = 721. The pressure PI in action, due to the interic
pressure P 0f3 , is therefore 18210-721 = 17489 Ibs.
Making P = 40146 and PI = 17489 we find
Tangential stresses, (13), S t (Ro) = + 45236 S t (Ri) = + 15027
Radial stresses, (14), S P (R ) = -50764 S p (Ri) = -20555
Had the shrinkage in Problem 1 been determined by the use
of PO P = 40146 in equation (47), that pressure in action wou
have compressed the inner layer of the tube radially to its elasti
limit, 50000 Ibs. But with the reduced shrinkage due to the
of PQQ in equation (47) the pressure of 40146 Ibs. exerts a radi
stress on the inner layer of the tube of 50764 Ibs., which is in ex
of the elastic limit.
130. GRAPHICALLY. The pressure PI in action, used in de
mining the stresses from equations (13) and (14), may be o
tained from Fig. 45. The shrinkage being 0.0085, PI is th
pressure at rest. From P la follow the line of variation in pressure
to the point a, whose abscissa is P 0j0 = 40146. The ordinate of
this point is the pressure PI in action when P = 40146. The
fore P! = 17489.
here-
GUNS. 225
131. Problem 3. The shrinkage actually prescribed at the
section of the 4.7 inch rifle used in Problem 1 is 0.008 of an inch.
What is the elastic resistance of the gun, tangential and radial,
at the section, and what is the relative compression of the bore
and the stress of tangential compression at the surface of the
bore?
_ 0.008 X 30,000,000 X 1 .698 X 3.8207
4X3.86X2.698X5.5187
P ^3X
3 X 1 .698 X 50000+2 X 2.698 X 6773
- =
(13) S t = El t
132. GRAPHICALLY. From the point 0.008, Fig. 45, on the
axis of Si follow the broken lines and obtain successively the values
found above for PI S , P 0p , and P oe .
133. Curves of Elastic Resistance. In the same way the
elastic resistances are found at various sections of the gun, and
the curves of elastic resistance shown in Fig. 47 are constructed.
By comparing the ordinates of these curves with the corresponding
ordinates of the curve of powder pressures it will be seen that
the gun has a factor of safety of about 1J over the part of its
length that is subjected to the maximum pressure.
Problem 4. What will be the tangential stresses in the system
assembled as in Problem 3 under a powder pressure of 32,000 Ibs.
per sq. in.?
R = 2.35 Ri = 3.86 R 2 = 6 (See Problem 1)
The pressure at rest, P u = 6773, determined in Problem 3,
produces stresses as follows, equations (13) and (36).
Tube, (13), S t (R ) = -21523 S t (Ri) = -12493
Jacket, (36), S t (R ) = + 18596 S t (Ri) = + 9566
StUONVSnOHl N31
6NOISS33dWOO'13 JO 31VDS
Kl OSM3d SaTOOOI-30NVlSIS3M 3I1SV13JO 31V3S
** -V
t\ M
GUNS. 227
The stresses within the elastic limit produced by an interior
or exterior pressure on a compound cylinder are exactly the same
as would be produced by the same pressure on a simple cylinder
of the same dimensions. If therefore we consider the gun as a
simple cylinder and calculate the stresses due to an interior pressure
of 32,000 Ibs., these stresses will be the variations in the stresses
in the compound cylinder as it passes from rest to action, and the
algebraic sums of the stresses at rest and the variations will be the
siressrs in action.
Considering the gun as a simple cylinder acted on only by the
interior pressure, 32,000 Ibs., we obtain from equation (13) for
the stresses at the surfaces for which r = R = 2.35, r = 3.86, and
r = #i = 6:
Inner surface of cylinder, S t = + 54265
At r = 3.86, <=+ 22546
Outer surface of cylinder, S t = + 11597
Taking the algebraic sums of these stresses and those above
determined for the system at rest, we find for the stresses in action:
Tube, S t (Ro) - +32742, S t (Ri) = + 10053
Jacket, S t (R ) = +41142, S t (Ri) = +21163
134. GRAPHICALLY. As in the graphic solution of* Problem 2,
the pressure PI corresponding to the interior pressure P = 32,000
is found from Fig. 45 by following the line of variation of pressure
for /->!. = 6773 to the point d whose abscissa is P = 32,000. The
ordinate of this point is PI, and this being substituted with PQ
in equations (13) and (14), the values of the stresses are derived.
135. Curves of Stress in Section. The curves of tangential
stress in a section of a gun composed of two cylinders assembled
to offer the maximum resistance are shown in Fig. 48. The curves
s show the stresses in the cylinders produced by the shrinkage, the
system being at rest. The curves r show the stresses in the
cylinders for the system in action. The curve p shows the
stresses that would result from the pressure P in a single cylinder.
228
ORDNANCE AND GUNNERY.
In each cylinder the ordinates of the curve r are the algebraic
sums of the ordinates of the curves p and s.
The gain and loss of strength in the compound cylinder as
compared with the single cylinder are shown in Fig. 49. The
curve t is the curve of tangential stress due to the maximum
permissible interior pressure in
the single cylinder. The gain
in strength in each cylinder of
the compound cylinder is shown
by the cross-shaded area marked
FIG. 48.
FIG. 49.
with the plus sign, and the loss in strength by the single-
shaded area marked with the minus sign. The total tangential
stress in the single cylinder is the area between the curve t
and the horizontal axis. The inner cylinder of the compound
cylinder gains over an equal portion of the single cylinder the
shaded area below the axis, representing the compressive stress
due to the shrinkage; and loses the area between the curves t
and r, since the single cylinder would be under the stress t while
the compound cylinder is subjected only to the lower stress r
The outer cylinder at rest being under the stress of extension
represented by the area under the curve s, that area is lost to it in
action, as compared with the single cylinder, while it gains the
area lying between the curves r and t.
136. Problems. 5. A section of the 2.38 inch experimental
field rifle, model of 1905, has the following dimensions: R = 1.19
GUNS. 229
inches, #i = 1.95, # 2 = 3. What is the elastic resistance of this
section assembled to offer the maximum resistance, and -what
is the absolute shrinkage? The elastic limit of the metal, nickel
steel, is 65,000 Ibs. per sq. in.
Pie = 23243 Ibs. * P oe = 55184 Ibs.
P Qp = 51875 Ibs.
P lt = 9158 Ibs. Si = 0.00554 in.
6. The prescribed shrinkage for the above section is 0.005 of
an inch. What is the elastic resistance of the section with this
shrinkage and what is the stress of tangential compression on
the bore?
Pi. = 8271 Ibs. P oe = 53527 Ibs.
l t = 0.000879 in. S t = 26360 Ibs.
137. Systems Composed of Three and Four Cylinders.
The construction and elastic strength of the larger guns built
up of three or four cylinders are determined by considerations
similar to those explained in the foregoing discussion. Precau-
tion is taken, by modifying the shrinkages if necessary, that the
inner cylinders at rest shall not be injured by the shrinkage pressures
of the outer cylinders. The elastic strength of the system, that
is, the maximum permissible interior pressure, is the pressure that
will bring any one of the elementary cylinders to its elastic limit
of extension or compression. In a proper construction the tube
is subjected to the greatest pressures both at rest and in action,
and consequently if the elastic strength of the gun is exceeded
by the powder pressure the tube will yield first.
In Fig. 50 are shown the curves of stress in a section through
the powder chamber of the 8 inch gun, model of 1888.
The curves si show the stresses due to the assembling of the
jacket on the tube, the curves 2 the stresses due to the shrinkage
of the outer hoop. The curves s r show the resultant stresses
due to both shrinkages.
The numbers on all curves are the actual values of the
stresses in tons per square inch due to an interior pressure
P = 23.2 tons.
230
ORDNANCE AND GUNNERY.
36.1
The curve p shows the stresses that would be produced
by this pressure in a single cylinder of the same dimensions
as the compound cylinder.
The curves r, the stresses in ac-
tion, are the resultants of the curves
s r and p in -each cylinder.
The curve t shows the stresses
resulting in a single cylinder from the
maximum interior pressure, 12.4 tons,
permissible in a single cylinder of
these dimensions.
The area between the curves p
and t represents the gain in strength
52 due to the compound construction.
Minimum Number of Cylinders
for Maximum Resistance. It will
be noticed in Fig. 50 that although in
action all the cylinders are stretched
to their elastic limits the compression
of the tube at rest is less than the
elastic limit of compression p, assumed
equal to 6. In this construction
therefore there was not obtained the
maximum resistance that the metal was capable of offering. The
same conditions exist in the two cylinder gun, as may be seen in
Problem 2. The stress of tangential compression at the surface
of the bore at rest is found in that problem to be 22,839 Ibs., while
the elastic limit of the metal is 50,000 Ibs.
It may be shown by the equations that in a two or three cylinder
gun whose parts have essentially the same elastic limits the con-
ditions that the parts shall be strained to the elastic limit in
action and that the tube shall be compressed to its elastic limit
at rest are incompatible. That both- these conditions may be
fulfilled the compound cylinder must be composed of at least
four parts.
138. Graphic Construction. Three Cylinders. The equations
'deduced for the compound cylinder of two parts are used for the
cylinder of three parts, the subscripts and radius ratios in these
FIG. 50.
GUNS. 231
equations being changed as required. Due to the application of
the third cylinder the relation between the variations in pressure
in the bore and at the first contact surface, equation (43), takes
the form
7>
and between the first and second contact surfaces, see equation (34),
a(c-b)
P2 ~b(c-a)
Pi (58)
The shrinkage at the second surface of contact, equation (54),
becomes
-l)
- 2 >
In addition we need for the graphic representation the pressure
at the first contact surface due to the shrinkage pressure at the
second surface. This is given by the equation
in which pi2 represents that part of the pressure at the first contact
surface that is due to P^ s only.
Equation (60) also gives the value of the variation in the pres-
sure at the first contact surface due to a variation in P 2a . The
equation is deduced by equating the stresses at R due to the
pressures Pi2 and P^-
With the above equations we may now proceed to the graphic
representation of the pressures and shrinkages shown in Fig. 51.
We will call the three cylinders in order from the center outwards
the tube, the jacket, and the hoop.
The first quadrant of the figure, similar to Fig. 45, refers
to the tube and the shrinkage at the first contact surface. The
second quadrant shows the pressures on the surface of the jacket.
The shrinkage at *the second contact surface is put in the
third quadrant for convenience. The numbers of the equations
232
ORDNANCE AND GUNNERY.
GUNS. 233
from which the lines are derived are shown on the lines. It will
be understood that the subscripts and radius ratios in any equa-
tion must be such as make the equation refer to the particular
cylinder to which it is applied.
P 2e is first determined from equation (37). It will stretch
the inner surface of the hoop to its elastic limit in action. It is
therefore the greatest pressure that may be permitted on the
exterior of the jacket. Draw ab, to P 2 Pio, and be. c is the pres-
sure PI that, acting on the interior of the jacket, will produce the
limiting pressure P 2g on the exterior. Draw cd, to PiP Qej and
de. e is the value of PQ in action that will produce the value
c of PI and therefore the limiting pressure P 2e on the interior of
the hoop.
When the system passes from action to rest the pressure on
the outer surface of the tube falls along the line df drawn parallel
to P\PQ. J is the total pressure on the exterior of the tube at
rest. It is composed of the pressure PI S due to the first shrinkage
and the pressure pi 2 due to the second shrinkage.
The pressure on the outer surface of the jacket falls along the
line bg parallel to p 2 p\, which line shows the relation existing
between the variations in pressure at the two surfaces of the
jacket. As the change in interior pressure on the jacket stops
at / the change in the exterior pressure stops at g, and projecting
g to h on the axis of P 2 we find the pressure P 28 on the exterior
of the jacket at rest. This is the shrinkage pressure, and drawing
hi and ij we find the shrinkage / that will produce the pressure
P 28 .
The total pressure / on the exterior of the tube is composed
of the pressure due to the first shrinkage and the pressure due
to the second shrinkage. The variation in interior pressure on
the jacket due to variation in the exterior pressure is given by
equation (60), which is represented in the figure by the line pi 2 P 2s .
If therefore we draw gk parallel to this line the point k will be the
interior pressure on the jacket when the exterior pressure is 0,
that is before the second shrinkage. The pressure k is therefore
the pressure due to the first shrinkage only, and the shrinkage
that will produce it is obtained by drawing the lines kl and Im.
For the system to be safe the total pressure / on the exterior
234 ORDNANCE AND GUNNERY.
of the tube must be less than the maximum permissible pressure
as given by the last half of equation (47). We will now designate
the maximum permissible pressure on the exterior of the tube
by Pi(max)> since P ip designates now an interior pressure on the
jacket.
The values of the pressures and shrinkages marked on the
figure apply to the chamber section of the 6-inch rifle, model
1905, the section being assembled to offer the maximum resistance.
For the section,
#o = 4 inches = 46000 Ibs. per sq. in.
R! = 5.9 01=48000
R 2 = 8.35 6 2 = 47700 assumed, 53000 actual
#3 = 12 = P
The equations become with this data,
(37) P 2 g - 14857 (38) P 00 = 15159 + 1 .2 197P t "
(38) Pie = 14425 + 1.2003P 2 .(39) P 0p = 24205 +0.64920A
(39) Pi, - 24023 +0.6664P 2 (57) p l = 0.39209P
(43) p 2 = 0.33963p k (54) P la = 446400Si '
(60) p 12 = 0.70129P 2 . (47) P ls(max) = 12428
(59) P<2s = 401610S 2
139. Wire Wound Guns. As shown in Fig. 50 the various
cylinders of a built up gun are strained to the elastic limit at the
interior surfaces only. It is apparent that if the same thickness
of wall is composed of a greater number of cylinders, each cylinder
being brought to its elastic limit at the interior surface, more of the
total strength of the metal will be utilized. It follows that
with a greater number of cylinders the gun may be given the same
elastic strength with less thickness of wall.
The most convenient method of increasing the number of cylin-
ders is by winding wire under tension around the tube of the gun.
The tension of the successive layers of wire may be so regulated
that each layer will be strained to its elastic limit when the system
is in action. Usually, however, the wire is wound with uniform
GUXS.
tension. In the form of wire the metal in the gun is much more
likely to be free of defects, and can be given a much higher elastic
limit than when in the form of forged hoops. An elastic limit of
over 100,000 pounds is obtained in steel gun wire.
But the elastic strength of the gun is determined by the elastic
strength of the tube that forms the bore of the gun; and if the
tube is worked only within its elastic limit the wire wound gun
cannot be stronger than the built up gun. In the Brown wire
wound gun shown in Fig. 5 on page 238, the wire is wound with
a tension of 112,000 Ibs. per sq. in., compressing the inner surface
of the tube beyond its elastic limit without apparent injury. This
gun is composed of a lining tube about which are wrapped over-
lapping sheets of steel 1/7 of an inch thick and of the shape
shown in Fig. 6 on page 238. The steel sheets form, about the
lining tube, an outer tube which is afterwards wrapped with wire
from breech to muzzle. The wire wrapped overlapping sheets
give longitudinal stiffness to the gun. Over the wire is shrunk
a steel jacket with just sufficient tension to prevent its rotation
upon the tube. The jacket is not depended upon to add to the
tangential strength of the gun. It takes, however, a part of the
longitudinal stress.
The Ordnance Department 6 inch wire wound gun is shown
in Fig. 4, page 238. The wire, 1/10 of an inch square, is wound
with a uniform tension of 47,400 Ibs. per sq. in., much less than in
the Brown gun. The wire winding extends over the breech and
half way along the chase of the gun.
After 31 rounds had been fired from each of these guns with
velocities of about 3280 feet and pressures of about 45,000 pounds,
it was reported that the most notable result observed in the test of
the guns was the considerable wear of the rifled bore near the
seat of the projectile and near the muzzle of the gun. The wear
of the bore was much greater than in built up guns of the same
caliber fired with velocities of 2600 and 3000 feet.
This indicates that the life of the wire wound gun will be very
short if fired with the higher velocities and pressures. In other
words we are unable at present to take economical advantage of
the greater strength of these weapons. The wire wound gun has,
however, a greater reserve of strength when fired under ordinary
236 ORDNANCE AND GUNNERY.
pressures than has the gun of the same dimensions built up wholly
of steel forgings.
No wire wound guns have yet been put in service in the United
States. They have been extensively used for some years by the
British Government.
CONSTRUCTION OF GUNS.
140. General Characteristics. The smaller guns in our service,
such as the mountain gun, the field and siege howitzers and
mortars, are made from single forgings. All other guns are built
up. The smaller built up guns of caliber up to 5 inches consist of
a central tube (see opposite page), a jacket surrounding the breech
end of the tube, and a locking ring which locks the tube and
jacket together. Guns of caliber greater than 5 inches have one
or more layers of hoops surrounding the tube and jacket. The
bore of the tube forms the powder chamber, the seat of the pro-
jectile, and the rifled bore. The jacket embraces the tube from
the breech end forward nearly half the length of the tube and
extends to the rear of the tube a sufficient distance to allow the
seat of the breech block to be formed in the bore of the jacket.
Through the bearing of the breech block in the jacket the longi-
tudinal stress due to the pressure of the powder gases is trans-
mitted to the jacket and the metal of the tube is thus relieved
from this stress.
All guns of 6 inch caliber and above are hooped to the muzzle.
The 6 and 8 inch guns have a single layer of hoops over the jacket.
Guns of caliber larger than 8 inches have two layers of hoops
over the jacket.
The construction of the several classes of guns and mortars
of the latest models may be seen in the illustrations, pages 237
and 238.
The forward end of the jacket of the field and siege rifles is
threaded with a broad screw thread. The rear end of locking
hoop is provided with a similar female thread, and the locking
hoop is both screwed and shrunk on the jacket. The hoop is also
shrunk to the tube, and by means of a bearing against a shoulder
GUNS.
237
on the tube just forward of the jacket it holds the tube and jacket
firmly together.
CO
8,
A noteworthy difference will be observed in the construction
of the two 12 inch rifles, Figs. 1 and 2, page 238. While the gun
I
lit
'1!
GUNS 239
of the older model, 34 calibers long, is composed of a tube and
jacket and 17 hoops, the gun of later model, 40 calibers long, -is
composed of tube and jacket and but 7 hoops. The reduction in
the number of the hoops by increasing their lengths has been
made possible by the great advances that have been made in
recent years in the production of large masses of steel of the
requisite high quality. The improvement has been largely due
to the demand of the Ordnance Department, and to the stringent
and increased requirements in successive specifications for gun
forgings.
By the increase in the size of the hoops there has been gained,
in addition to ease and economy of manufacture, largely in-
creased longitudinal strength and stiffness in the gun, which
permits the construction of a longer gun without the tendency to
droop at the muzzle.
The D hoop shown in Fig. 2, page 238, locks together the jacket
and the C\ hoop; and these, bearing against shoulders on the
tube, in rear and in front, hold the tube firmly in place. The
space behind the D hoop, left to accommodate the increase of
length of the hoop when heated for shrinking, is filled with a steel
filling ring as noted in the 1888 model. The joint between the
Ci and C 2 hoops is coned, as shown exaggerated in Fig. 52. Four
securing pins passing through the 2 hoop near the muzzle assist
in preventing forward movement of the
hoops under the vibration set up in the
gun by the shock of discharge.
As the metal at the muzzle receives FlG - 52>
support from one side only the gun is thickened there to make
the section of equal strength with those near it. The thickening
of the metal produces what is called the swell of the muzzle.
141. Operations in Manufacture. The steel forgings from
which the parts of the guns are made are manufactured by private
concerns and are delivered rough bored and turned to within
about 3/10 of an inch of finished dimensions.
As the parts of the gun are of a genera] cylindrical form the
principal operations in preparing them for assembling are the
operations of boring and turning.
In making long bores of comparatively small diameter, as in
240 ORDNANCE AND GUNNERY.
the tubes of guns, special tools are necessary in order to insure
straightness of the bore.
The tube is carefully mounted in the lathe and so centered that
any bending or warping that may exist in the long forging will be
wholly removed in the operations of boring and turning. The
bore is started true with a small lathe tool and continued for a
length of about three calibers. The tool shown in Fig. 53 is then
FIG. 53.
used to continue the bore. This tool, called a reamer, has a semi-
cylindrical cast iron body, or bit, A, carrying the steel cutting
tool B. It is supported in the boring bar C, which is pushed
forward by the feed screw of the lathe. The semi-cylindrical bit
exactly fits in the bore already started. As the tube rotates, the
pressure against the cutting edge B forces the bit against the
bottom of the bore. This together with the length of the bit
prevents deviation of the cutting edge as the tool advances down
the bore, and makes the bore a true cylinder.
In order to make the surface of the bore smooth and uniform
the light finishing cuts are made with a packed bit or wood reamer,
shown in Fig. 54.
FIG. 54.
The cast iron bit A carries two cutters, b, at opposite ex-
tremities of a diameter. Two pieces D of hard wood packing are
bolted to the bit and serve to guide the cutters accurately. The
tool fits tightly in the bore. The light cut taken and the pressure
of the oiled wood packing leaves the surfaces of the bore very
smooth and uniform and highly polished.
142. Gun Lathe. The general features of the lathe, by means
of which the larger forgings are bored and turned, are shown in
GUNS.
241
Fig. 55. The principal parts are: the bed, B, made very strong
and much larger than for the ordinary lathe; the head stock -and
cone pulley C; the face plate F, to which the work T is clamped;
the slide rest S, carrying a cutting tool; the back rests R, forming
intermediate supports for the tube T; the boring bed 0, supported
on the bed proper, B, and carrying the boring bar P with its
tool Q; the feed screw V, which lies inside the boring bar P; and
the gears W, by which the feed screw is driven.
Motion is communicated to all the parts by the belt X, acting
on the cone pulley. This causes the face plate and tube to rotate
and also communicates motion to the long shaft, not shown in
the figure, upon the end of which is the lower gear wheel W".
The motion is transmitted through W to W , and thence to
FIG. 55.
the feed screw V. By changing the gears any ratio between the
velocity of rotation of the tube and that of translation of the tool
Q can be obtained. It is necessary that there be only one source
of motion, since if the feed screw or slide rest were driven inde-
pendently of the cone pulley which drives the work, a change in
the speed of one would not cause a corresponding change in the
speed of the others, and damage to the tools, the work, or the
machine might result.
The slide rest S is driven by a second feed screw not shown.
The back rests R can be adjusted to any diameter of forging.
The lathe is supplied with an oil pump, by means of which a
stream of oil is forced into the bore while the work is in progress.
The chips or cuttings come out at the opposite end of the tube
from that at which the tool enters.
Boring and Turning Mill. The smaller hoops are usually
machined on a vertical boring and turning mill, shown in Fig. 56.
The work is bolted to the slotted table t. The cutting tools
are carried in the tool holders o at the lower ends of the boring
242 ORDNANCE AND GUNNERY.
bars a. In the illustration one of the boring bars is shown in a
vertical position and the other inclined. The table rotates,
carrying the work with it. By means of the feed mechanism
the cutting tools are fed either vertically or horizontally or at an
%ngle as desired.
On account of the greater difficulty of boring than of turning
to prescribed dimensions, the bored shrinkage surface is always
finished first. Allowance may then be made in turning the male
surface for any slight error in the diameter of the bored surface.
The desired shrinkage is thus obtained.
143. Assembling. The interior diameter of the jacket, when
bored to finished dimensions, is less than the exterior diameter
of the tube by the amount of the shrinkage prescribed. In order
to assemble the jacket on the tube it is therefore necessary to
expand the jacket sufficiently to permit its being slipped over
the tube into its place. The expansion is accomplished by heat.
The jacket is placed in a vertical furnace heated by oil or other
fuel to a temperature varying from 600 to 750 degrees Fahrenheit,
depending upon the thickness of the forging and the amount of
expansion required. Great care is exercised that the heating
shall be uniform throughout the length of the forging. The
requisite expansion, which in general is about 0.004 of an inch
per inch of diameter, is determined by a gauge set to the exact
diameter to which the bore should expand. The gauge, held at the
end of a long rod, is tried in the bore of the forging in the furnace.
When it enters the bore properly the requisite expansion has
been attained. Care is taken to avoid overheating which might
injuriously affect the qualities of the metal.
When the desired expansion has been attained the jacket is
hoisted vertically from the furnace. It will be seen by reference
to the figures on page 238 that the shoulders on the tubes of the
12-inch guns are so arranged that the jacket must be slipped over
the breech end of the tube, while the arrangement of the shoulders
on the wire wrapped tubes of the 6-inch guns require that the
tube be inserted into the breech end of the jacket.
The method of assembling is called breech insertion or muzzle
insertion according as the breech or muzzle end of the jacket first
encircles the tube. For breech insertion, as in wire wrapped
Fia. 56. Vertical Boring and Turning Mill, 37-inch.
GUNS.
243
guns, the jacket after being lifted from the furnace is placed up-
right on a strong iron shelf supported at the mouth of a deep~pit,
Fig. 57. The tube is then carefully lowered into its seat in the
jacket. For muzzle insertion, as in the 12-inch guns, the tube
is supported upright in the pit, the breech end up, and the jacket
is lowered over the tube.
Cooling of the heated jacket is accomplished by means of
sprays of water directed against the forging from an encircling
pipe as shown at D in Fig. 58. The cooling is begun at the section
of the jacket which it is desired should take hold of the tube first,
TUBE.
J-
I
FIG. 57.
FIG. 58.
as at the shoulder C, Fig. 58. As the cooling of the remainder of
the jacket progresses the metal is drawn toward the section first
cooled, and thus a tight joint at the shoulder is insured. After
the jacket has gripped at the shoulder the cooling pipe is moved
very gradually upward toward the breech, care being exercised
that the jacket shall grip at successive sections in order that longi-
tudinal stresses due to unequal contraction may not be developed
in the metal.
The shrinking on of hoops is conducted in practically the same
manner as the shrinking of the jacket. When the hoops are small
and can be handled quickly they are often assembled to the gun
in a horizontal position. Cooling of the hoop is begun at the end
244 ORDNANCE AND GUNNERY.
toward the jacket, or toward the hoop already in place, in order
that contraction shall take place in that direction and make a
tight joint between the parts.
When the assembling of all the parts is completed the tube is
finish smooth-bored and the exterior of the gun turned to pre-
scribed dimensions.
144. Rifling the Bore. The rifling of the bore is effected in
the rifling machine, which is essentially similar to the boring
and turning lathe previously described. The gun does not rotate
in the rifling machine, but the cutting tool is given the combined
movement of translation and rotation necessary to cut the spiral
grooves in the bore. The rifling bar takes the place of the boring
bar, P Fig. 55. The rifling bar, m Fig. 59, carrying at its forward
1F>(OJGUN.
FIG. 59.
end the rifling tool g provided with cutters for the grooves, is moved
forward and backward by means of the feed screw b. The desired
motion of rotation is given to the rifling bar by means of the
pinion c and the rack d, which engages on a guide bar e bolted to
a table made fast to the side of the rifling bar bed. The bar e
is flexible and is given the shape of the developed curve of the
rifling. As the rack travels forward with the rifling bar it is forced
to the left by the guide bar, imparting the proper amount of
rotation to the rifling bar and cutting tools.
Cutting tools are carried at both ends of a diameter of the
rifling tool. At the end of a cut the cutting tools are automatically
withdrawn toward the center of the bar and the bar retracted for
a new cut.
When a number of guns of the same design are to be manu-
factured, a spiral groove is cut in the rifling bar itself. A stud
fixed in the forward support of the rifling bar works in the groove
and gives to the bar the proper movement of rotation. The guide
bar with rack and pinion is not then used.
GUNS.
245
MEASUREMENTS.
145. Necessity of Accurate Measurements. In order that the
gun may be assembled with the required shrinkages the surfaces of
the various cylinders composing the gun must be accurately turned
and bored to the prescribed dimensions. The dimensions of all
parts of the gun must be in accord with the design. The toler-
ances, or allowed variations from prescribed dimensions, are in
general two thousandths of an inch for the diameters of shrinkage
surfaces, and one hundredth of an inch in lengths.
Accurate measurements of the various dimensions of every
part of a gun are therefore essential.
The exact length of any dimension of a forging is usually
obtained by means of one of two instruments, called measuring
points and calipers. The points of the instrument used are
adjusted until the distance between them is the exact length of
the dimension to be determined. The length between the points
of the instrument is then measured in a vernier caliper.
Vernier Caliper. The vernier caliper is shown in Fig. 60.
The steel blade a graduated in inches and decimal divisions is pro-
o a
liiiiliiiiliiiiliiiiIiiiiiiiiiliiiiliniliiM
*|
1 III!
Illlllll
y
2,
iliiiilii!i!iii|liin!
ii!n
d
3 |
lIlllllllllIlllllllllllllllllU
\r
'"'f
1
[o' r
jp
m
6
T
c
J
e
f
FIG. 60.
vided with a fixed jaw 6 and movable jaw c. By means of the
clamp d and small motion screw e the movable jaw may be brought
accurately to any distance from the fixed jaw. The distance
between the jaws is read from the scale and vernier. The least
reading of the vernier is one thousandth of an inch. The ends of
the jaws b and c are usually one eighth of an inch wide so that the
measurement between their outer edges is a quarter of an inch
greater than the reading of the scale.
246
ORDNANCE AND GUNNERY.
Measuring Points. The measuring point consists ordina-
rily of a rod of wood into the ends of which are set metal points,
Fig. 61. One of these points at least is capable of a small move-
ment out and in. The rod is of wood in order that the heat of
the hand may not affect its length. One of the metal points may
FIG. 61.
be provided with a micrometer head from which the movement
of the point out and in from a fixed length may be read at once.
Measuring points are used in determining interior diameters
and the distance between surfaces that face each other. In
measuring an interior diameter at any point in a bore, as at a, Fig.
62, one end of the measuring point is placed at a. As the diam-
eter is the longest line in the cross section, the end b must be
moved out until the rod cannot be revolved about the end a in
the plane of the cross section.
To determine, when touch is made at b, that the rod is truly in
the cross sectional plane the rod must be revolved in a direction
at right angles to this plane, for as seen in Fig. 63 the diameter is
a
FIG. 62.
FIG. 63.
the shortest line in the longitudinal plane, and the rod when set
to the proper length must be capable of revolution in that plane,
touching only at the point b. In other words the measuring
point has the length of the diameter when the measuring point
is incapable of revolution in the cross sectional plane and at the
same time capable of revolution in the longitudinal plane.
GUNS.
24?
Similarly when applying the rod to the vernier caliper to read
the length of the rod, the movable jaw of the caliper must" be
brought to such a distance from the fixed jaw that the rod when
revolved about one end in two planes at right angles to each other
will touch at one point only in each plane of movement. The
length of the interior diameter may then be correctly read from
the scale of the caliper.
In making measurements the sense of touch is depended upon
to determine when contact exists. When the distance that
separates a measuring point from a surface is so minute that light
cannot be seen between the point and the surface, the lack of
contact can be unerringly detected by the touch.
146. The Star Gauge. In the case of long tubes all parts of
which are not readily accessible some means must be adopted of
making the measurements at a distance from the operator. The
instrument used for this purpose is called a star gauge.
Its general features are shown in Fig. 64. The long hollow
FIG. 64.
rod or staff a carries at its forward end the head 6. Embracing
the rear end of the staff is the handle c to which is attached the
square steel rod /. The handle has a sliding motion or screw
motion on the end of the staff, and any movement of the handle
is communicated through the rod / to the cone g in which the
square rod terminates at its forward end.
The head b has three or more sockets, d, which are pressed in-
ward upon the cone g by spiral springs not shown in the figure.
Into these sockets are screwed the star gauge points e. Three
points are generally used, 120 apart. The points are of different
lengths for the different calibers to be measured.
Any movement of the cone forward or backward causes a cor-
responding movement of the measuring points out or in. The
cone has a known taper, and the change in its diameter under the
248 ORDNANCE AND GUNNERY.
measuring points due to any movement of the handle is marked
on a scale at the handle end of the staff. The handle carries a
vernier by means of which the scale may be read to a thousandth
of an inch. The reading of the scale is the change in length of
the diameter that is measured by the points when the handle is
at the zero mark.
The staff a and rod / are made in sections, usually 50 inches
long, so that the gauge may be given a length convenient for the
measurement of any length of bore.
The star gauge is set for any measurement by means of a stand-
ard ring of the proper diameter. The standard rings are of steel,
hardened and very carefully ground to the given diameter. If it
is desired to measure a 10-inch bore for instance, measuring points
of the proper length are inserted in the sockets d of the star gauge.
The 10-inch ring is held surrounding the points, and the handle c
of the star gauge is pushed in until the points touch the inner sur-
face of the ring. The handle is then adjusted until the reading of
the scale is zero. The instrument is now ready for use.
The gun or forging whose bore is to be measured is supported
so that its axis is horizontal. The star gauge is also carefully
supported in the axis of the bore prolonged, and in the bore when
necessary. The distance of the measuring points from the face
of the bore is read from a scale of inches marked on the staff. At
each selected position of the gauge the handle is pushed forward
until the measuring points touch the surface of the bore. The
difference between the diameter of the bore at this point and the
standard diameter for which the gauge is set is then read from
the scale at the handle in thousandths of an inch.
147. Calipers. For the measurement of outside diameters
calipers are used. The ordinary calipers for measurement of short
exterior lengths are shown in Fig. 65. For the measurement of
the large exterior diameters of gun forgings, calipers as shown in
Fig. 66 are employed. One of the points a or b is movable and
may be provided with a micrometer head. As in the case of inte-
rior measurements the caliper must be revolved in two planes about
the end that is held at the point from which the diameter is to be
measured, and the distance between the points of the caliper must
be adjusted until touch is made at one point only in each plane.
GUNS.
249
The distance between the points of the caliper, as determined
by the length between the outer edges of the jaws of the vernier
caliper, is then the true length of the exterior diameter.
FIG. 65.
FIG. 66.
The frames of the large exterior calipers required for gun meas-
urements must be made heavy in order that the calipers shall have
sufficient stiffness and not be subject to change of form. In
R
FIG. 67.
use these calipers are therefore supported from above by a
spring connection with a frame that is secured to the piece being
measured, Fig. 67.
Standard Comparator. In order to insure accuracy in all
measurements, all measuring scales are compared w r ith a common
standard. For this purpose the standard comparator is provided.
250
ORDNANCE AND GUNNERY.
A heavy metal bar very accurately graduated in inches and deci-
mal divisions rests in a very stiffly constructed cast iron bed.
Sliding heads on the bed, one of which carries a reading microscope,
may be set accurately at any determined distance apart.
RIFLING.
148. Purpose. The purpose of the rifling in a gun is to give to
the projectile the motion of rotation around its longer axis neces-
sary to keep the projectile point on in flight. The rifling consists
of a number of spiral grooves cut in the surface of the bore. The
soft metal of a band on the projectile is forced into the grooves
by the pressure of the powder gases, whereby a rotary motion is
communicated to the projectile.
Twist. The twist of the rifling at any point in the bore is the
inclination of the tangent to the groove, at that point, to the axis
of the bore. Twist is usually expressed in terms of the caliber,
as one turn in so many calibers. If the inclination of the groove
is constant the rifling is of uniform twist. If the inclination of
the groove increases from breech to muzzle the rifling has an
increasing twist.
Let a, Fig. 68, be the development of one turn of a groove with
uniform twist, n the twist in calibers, or the number of calibers in
which the groove makes a complete turn, and r the radius of the
bore. Then AB = 2nr, BC = 2nr, and we have
(61)
tan (j> = 2nr/2nr = n/n
for the value of the tangent of the angle of the rifling. For the
groove with increasing twist (f> is variable, but at any point its
tangent is n/n.
.GUNS. 251
Let v denote the velocity of the projectile at any point of the
bore, in feet per second,
</> the angle made by the tangent to one of the grooves
with an element of the bore,
co the angular velocity of the projectile,
r the radius of the bore, in feet.
The velocity of the projectile along the groove is the resultant
of two components, v and v tan </>, at right angles to each other.
The actual velocity of rotation of a point on the surface of the
projectile is cur = cud/2, and this is equal to the component v tan <.
Therefore
vtan< and <u = 2v tan^/d (62)
Increasing Twist. When the twist is uniform the inclination
of the grooves to the axis of the bore is the same throughout
the length of the bore, and therefore it is greater at the breech
than the inclination of the grooves of an increasing twist that is
equal to the uniform twist at the muzzle. The pressure required
to cause the projectile to take the grooves is therefore greater in
the case of the uniform twist, and the greater resistance offered to
the starting of the projectile serves to increase the maximum pres-
sure in the gun. The total energy absorbed by the projectile in
taking the rifling is greater with an increasing twist than with the
uniform twist on account of the increased frictional resistance due
to the continual change in the inclination of the grooves. The
total energy absorbed is, however, small compared with that
required to give the projectile its velocity of translation.
149. Equation of the Developed Curve of the Rifling. If
the twist increases from zero at the breech uniformly to the muzzle,
the equation of the developed curve of the rifling will be of the
form
y = ax+bx 2
which being differentiated twice gives
That is, the rate of change in the tangent to the groove is constant.
A twist of this form would offer less resistance than the uni-
form twist to the initial rotation of the projectile. But to still
252 ORDNANCE AXD GUNNERY.
further diminish this resistance, a twist that is at first less rapid
than the uniformly increasing twist and later more rapid has
been generally adopted for rifled guns. The equation of the
semicubic parabola
(63)
is generally adopted for the developed curve of the rifling. The
twist is assumed at breech and muzzle and the curve between
these points is obtained from the above equation.
The tangent to the curve at any point makes with the axis of z
an angle whose tangent is dy/dx. The value of the tangent of
the angle at any point is n/n, see equation (61), n representing
the twist in calibers, the number of calibers in which the groove
makes a complete turn.
Therefore, differentiating equation (63),
dy/dx = tan < = 3x*/4p = TI/U (64)
Problem i . Determine the equation of the developed rifling
curve, and the part of the curve to be used, for the 3 inch rifle,
model 1905. The twist is at the breech end, 1 turn in 25
calibers at a point 12.52 inches from the muzzle, and from this
point uniform to the muzzle. The length of the rifled bore is
72.72 inches.
The twist at the breech is 0, or one turn in an infinite number
of calibers. Therefore n in equation (64) is infinite, tan <f> is
and = 0; and from equation (63) y is also 0. The origin of the
curve is therefore at the breech.
At 12.52 inches from the muzzle, x = 72.72 -12.52 -60.2, and
the twist n = 25.
Substituting these values in equation (64) and solving for p,
p = 3(60.2)^25/4^ = 46.31
Substituting in (63) we have for the equation of the developed
groove of the rifling from the breech to a point 12.52 inches from
the muzzle
and the part of the curve to be used lies between the origin and
the ordinate for which the abscissa is x = 60.2. From this point
GUNS. 253
to the muzzle the curve is a straight line making with the axis
of x an angle whose tangent is rc/25.
The curve is shown numbered 1 in Fig. 69.
150. Problem 2. Determine the equation of the developed
rifling curve, and the part of the curve to be used, for the 4.7
inch Armstrong gun, 50 calibers long. The twist is 1 turn in
600 calibers at the breech, and 1 turn in 30 calibers at the muzzle.
The length of the rifled bore is 203.12 inches.
At the breech ?i = 600 and tan < = 7r/600
At the muzzle tan (f> = ;r/30
The curve represented by equation (64) passes through the
origin of coordinates.
|0 I ^
I
_ I _
60.2 72.72 203,12
FIG. 69.
Let xi be the abscissa of the point of the curve at which the
tangent is Tr/600. Then x 2 = xi +203.12 will be the abscissa of
the point at which the tangent is ;r/30.
From equation (64)
7T/600 = 3*i */4p 7T/30 = 3(zi + 203.12
We have two equations involving x\ and p. Solving we find
p = 102.2 zi=0.51 x 2 = 203.63
The equation of the developed curve of the rifling is, equation (63),
x* = 204: Ay
And the abscissas of the extremities of the part of the curve to be
used are the values determined for Xi and x 2 .
The curve is shown numbered 2 in Fig. 69.
254
ORDNANCE AND GUNNERY.
Service Rifling. An increasing twist is adopted for the
guns in our service. In all guns of recent model the twist is one
turn in 50 calibers at the breech, and increases to one turn in 25
calibers at a point about 2J calibers from the muzzle. The pur-
pose of the uniform twist for a short length at the muzzle is to
give steadiness to the projectile as it issues from the bore.
A right handed twist is used in all guns in our service.
The number of grooves depends on the caliber of the gun. In
the siege and seacoast guns the number is six times the caliber of
the gun in inches. Thus the 5 inch gun has 30 grooves and the
10 inch gun 60. The 3 inch field rifle has 24 grooves.
The shape of the grooves is shown in Fig. 70. The widths of
FIG. 70.
land and groove noted in the figure are the same for all guns of
5 inch caliber and greater. The depth of the groove varies from
0.03 of an inch in the 3 inch gun to 0.06 in the seacoast rifles, and
0.07 in the seacoast mortars.
A form of groove called the hook section groove, used in Navy
rifles, is shown in Fig. 71. The view is from the breech end.
FIG. 71.
The driving edge of the groove makes a sharp angle with the
Surface of the bore, and the other edge has a gradual slope to
that surface.
The depth of the groove in the larger naval guns is 0.05 of an
inch.
In the service 30 caliber rifle the depth of the grooves is 0.004
of an inch. It is desirable in small arms to limit the depth of
the grooves to the minimum, in order to lessen the thickness of
GUNS. 255
barrel and to permit ready cleaning of the bore. There are four
grooves each 0.1767 inches wide. The lands are one third as wide.
The twist is uniform, one turn in 10 inches.
BREECH MECHANISM.
151. General Characteristics. The breech mechanism com-
prises the breech block, the obturating device, the firing mechan-
ism, and the mechanism for the insertion and withdrawal of the
block.
The breech block closes the bore after the insertion of the charge
and transmits the pressure of the powder gases as a longitudinal
stress to the walls of the gun.
There are two general methods of closing the breech. In the
first method the block is inserted from the rear. The block is pro-
vided with screw threads on its outer surface which engage in cor-
responding threads in the breech of the gun. In order to facilitate
insertion and withdrawal of the block the threads on block and
breech are interrupted.
The surface of the block is divided into an even number of
sectors and the threads of the alternate sectors are cut away.
Similarly the threads in the breech are cut away from those
sectors opposite the threaded sectors on the block. The block
may then be rapidly inserted nearly to its seat in the gun, and
when turned through a comparatively small arc, say 1/8 or 1/12
of a circle, depending upon the number of sectors into which the
block is divided, the threads on the block and in breech are fully
engaged and the block locked.
In the second method a wedge-shaped block is seated in a
slot cut in the breech of the gun at right angles to the bore, and
slides in the slot to close or open the breech.
Variations of these two methods will be noted in the descrip-
tions of the breech mechanism of some of the guns in service.
The breech block is usually supported in the jacket of the gun
or in a base ring screwed into the jacket. The seat in the jacket
being of greater diameter than could be provided in the tube,
the bearing surface of the screw threads on the block is increased,
and the length of the block may be diminished.
256
ORDNANCE AND GUNNERY.
p IG 72. Breech Mechanism for Heavy Guns.
GUNS. 257
The Slotted Screw Breech Mechanism. The slotted screw
breech mechanism is better adapted than any other for use hi
heavy guns. It is also used in most of the field and siege guns
of our service. The form used in the field and siege guns is de-
scribed with the 3-inch field gun in Chapter VIII.
An example of the slotted screw breech mechanism as used
in the heavier guns is shown in Figs. 72 to 74, which represent
the breech mechanism of the 12-inch rifle. The breech block
B has six threaded and six slotted sectors. When the breech is
closed the threads on block engage with the threads in the breech.
The breech is opened by turning the crank K mounted on the shaft
W. The movement of the crank is transmitted through the
worm gear to the hinge pin HP, and through the compound gear
CG to the rotating lug rl formed on the rear of the block. The
block is thus rotated one twelfth of a turn, and its threaded sectors
then lie in the slotted sectors of the breech. Further movement
of the crank causes the teeth of the compound gear CG to engage
in the teeth of the translating rack tr cut in a slotted sector of the
block. The block is thereby caused to slide to the rear on to the
tray T, the guide rails of the tray engaging in the grooves g g in
the block. When the block is sufficiently withdrawn the bottom
of the block depresses the rear end of the tray latch L and lifts
the forward end of the latch out of the catch A, where it has been
held by the pressure of the spring s. The tray is now unlocked
from the breech. The upper front toe of the latch L engages
in a groove in the breech block, locking the block and tray
together. The further action of the compound gear on the last
teeth of the translating rack tr then causes the tray to swing to the
right about the hinge pin, carrying the block clear of the breech.
As the tray swings clear of the breech the locking bolt Ib forces
forward the operating stud os and enters a seat in the latch. The
latch is thus locked in its raised position and secures the breech
block against being pushed forward off the tray when open.
In closing the breech the operations are reversed hi order.
When the tray comes in contact with the face of the breech the
operating stud os forces the locking bolt Ib from its seat in the
latch. The latch is depressed by the spring s and thus unlocks
the block from the tray.
258
ORDNANCE AND GUNNERY.
The two plugs shown in the obturator head of the breech
mechanism, Fig. 74, are in the seats provided for the insertion of
pressure gauges when it is desired to measure the pressure in the
gun.
In recent mechanisms of this type there is added a locking
device which locks the block in position when closed and insures
against the opening of the block by the pressure of the powder
gases. The locking bolt is withdrawn by hand before opening
the block.
152. Bofors Breech Mechanism. The mechanism shown in
Figs. 75 to 78, known as the Bofors breech mechanism, is most
suitable for guns of medium caliber. It is applied to the 6-inch
gun in our service. The block, b Fig. 75, is ogival in shape and
FIG. 75.
has six threaded and six slotted sectors. With the ogival shape
a very small retraction to the rear is necessary before the block
may be swung open. In the 6-inch gun this retraction is 1.2
inches, just sufficient to withdraw the obturator o from its seat
in the bore. The block is supported when the breech is opened by
the block carrier c provided with a central tube which embraces
a spindle s formed in the block.
FIG. 73. Closed.
FIG. 74. Open.
BREECH MECHANISM FOR HEAVY GUNS.
FIG. 76. Closed.
FIG. 77. Block Unlocked, Ready
to Swing Open.
FIG. 78. Open.
BOFORS RAPID FIRE BKEECH MECHANISM.
GUNS.
259
This mechanism is not applicable to the larger guns because
the greater weight of the breech blocks in these guns requires
better support than can be conveniently given by this method.
The mechanism is actuated by means of the lever I, Fig. 76,
which is attached to the lower end of the hinge pin. A spool p
mounted on the hinge pin has teeth cut near its lower end which
engage in the rack r. The rack slides in a horizontal groove cut
in the block carrier c, and the teeth at its left mesh with corre-
sponding teeth on the hub of the breech block which projects
through the rear face of the carrier.
When rotation of the block is completed a lug, u Fig. 75, on
the spool engages in a slot at the rear end of the block and trans-
lates the block slightly to the rear. Before this translation is
complete the block carrier is unlocked from the gun, and swings to
FIG. 79.
the rear with the block, fully uncovering the bore. The loading
tray, shown in Fig. 78, the purpose of which is to protect the
threads of the breech from injury as the shot is put into the bore,
remains permanently in the breech. When the block is entered
and rotated the tray is pushed aside by the threads on the block
until it covers the slotted sector. On opening the block it is
brought back into the position shown.
In the breech mechanism shown in Fig. 74 the loading tray is
a separate piece placed in the breech by hand when loading, and
removed before closing the block.
153. The Welin Breech Block. The Welin breech block,
largely used in naval ordnance, has the threaded sectors arranged
in steps at different distances from the center of rotation, as shown
260
ORDNANCE AND GUNNERY.
FIG. 80.
in Figs. 79 and 80. By this means the threaded area may cover
two thirds, three fourths, or even a
larger portion of the surface of the
block. A large increase in threaded
area is thus secured over that obtained
on a cylindrical block with alternate
threaded sectors, and the block may
therefore be made smaller. The amount
of rotation required in locking and un-
locking is also diminished, one twelfth
of a turn sufficing for the block shown
in Fig. 79, and one sixteenth for the
block of Fig. 80.
Obturation. There must be provided at the breech of the
gun some device that will prevent the powder gases from passing
to the rear into the threads and other parts of the breech mechan-
ism. If any passage is open to the gases they are forced through
it with great velocity by the high pressure existing in the bore.
Their velocity together with their high temperature gives to them
great erosive power, and the threads and other parts of the breech
mechanism subject to their action are eroded, channeled, and
worn away to such an extent that the breech mechanism is soon
ruined and the gun is rendered useless.
In guns that use fixed ammunition the obturation is performed
by the cartridge case, which expands under the pressure in the
bore to a tight fit against the walls of the gun. The breech mechan-
ism of these guns contains, therefore, no obturator parts.
With the slotted screw breech block two systems of obturation
are used. They are known by the names of their inventors,
DeBange and Freyre.
154. The DeBange Obturator. This system is in the most
general use. It is seen at o, Figs. 72 and 75, in the breech mechan-
isms already described. The details are shown in Fig. 81. The
obturator consists of the steel mushroom head h with the spindle
s, the pad p, the split steel rings r, and the steel filling-in disk d.
The pad p is made of asbestos, tallow, and paraffine or other
substance, that together form a plastic mixture that melts only
at a high heat. The ingredients are mixed and then pressed into
GUNS.
261
shape under a hydraulic press and protected by a cover made of
canvas or of asbestos wire cloth. The split rings, r Fig. 81 and
TUBE.
FIG. 81.
Fig. 82, are hardened, and their outer surfaces, which are coned
toward the front, are very care-
fully ground, so that their diameters
when the rings are free are 0.01
of an inch larger than the diam-
eters of the conical seat in the
bore. The edges of the rings
therefore* always bear against the
walls of the bore.
The pressure of the gases
against the mushroom head com-
presses the elastic pad and further
presses the split rings against the
walls of the bore, thus effectually preventing the passage of
to the rear.
The smaller split ring surrounding the spindle serves to pre-
FIG. 82.
262
ORDNANCE AND GUNNERY
vent escape of the pad composition between the filling-in disk and
the spindle.
The spindle s passes through a central hole in the breech
block. The obturator parts are held in place by the split nut n
clamped on the spindle. The nut bears against a shoulder in the
block through the ball bearing b. It will be seen that the breech
block may rotate independently of the obturator parts, so that
in opening the breech the rotation of the block is not affected by
any sticking of the obturator to its seat in the gun. On retraction
of the block the obturator is readily withdrawn from its conical
seat.
A vent is drilled the full length of the obturator spindle to
afford a passage for the flames from the primer to the powder
charge in the gun. The two grooves at the rear end of the spindle
serve for the attachment of the firing mechanism.
The Freyre Obturator. The Freyre obturator shown in Fig.
83 is used in the 3.6 inch field mortar. The head g is cone shaped.
FIG. 83.
In rear of it resting against the head of the breech block h is
the cone shaped steel ring /. The head g is constantly pressed
forward by the spring e. Under the action of the powder pressure
the head is forced to the rear and expands the ring / against the
walls of the bore.
With this obturator the breech mechanism is comparatively
short and light in weight, which is an important advantage iu
GUNS.
263
field mortar. The obturator ring with its thin front edge is, how-
ever, readily subject to accidental injury, which would render the
obturation imperfect.
155. Firing Mechanism. A seat for the firing mechanism is
formed on the rear end of the obturator spindle by two grooves, g
Fig. 84, cut in the spindle. A hinged collar k embraces the end of
the spindle. The housing h screws over the collar and is locked
l>
FIG. 84.
to it by the spring pin p. The ejector e pivoted in the housing
has at its lower end a forked seat for the head of the primer.
Projecting ribs on the front face of the housing form guides for
the slide, d Fig. 84 and Fig. 85. The slide is moved up or down
by means of the handle b, the catch lever a being first pressed to
release a holding catch. Pivoted at o in the slide is the slotted
firing leaf I, which carries the insulated brass contact clip c and
is provided with an eye into which the hook of the lanyard
engages.
264 ORDNANCE AND GUNNERY.
The slide being at its uppermost position, the primer r is inserted
in the vent in the obturator spindle, the head of the primer resting
in its seat in the ejector. The slide is then pushed down. The
firing leaf I, by means of the slot, embraces the insulated primer
wire just in front of the button at its outer end. The two halves
of the contact clip c spring apart and embrace the uninsulated
button.
If the breech is closed, a pull on the lanyard rotates the firing
leaf I about its axis o, drawing out the primer wire and firing the
primer by friction; or the closing of the electric circuit, which
enters the mechanism through the electric terminal n, will fire
the primer electrically. The electric current passes through
insulated parts to the platinum firing bridge inside the primer
and thence through the body of the primer to the metal of the
gun and to the ground.
Fifing by either of these methods cannot be accomplished
unless the slide d is all the way down and the breech is fully closed.
A safety lug on the right side of the housing engages in a
groove in the firing leaf and prevents the latter being drawn to
the rear before the slide is all the way down. The contact clip
engages the primer button only in the last part of the downward
movement of the slide.
The inner end of the safety bar, s Fig. 85, also engages the
firing leaf. The outer end of the safety bar embraces a stud pro-
jecting from the safety bar slide, i Fig. 87, and the safety bar slide
carries at its outer end a stud that engages in a groove cut in the
gun. The groove is so shaped as to withdraw the safety bar only
at the last part of the movement of the block in closing. At this
moment also the parts of the electric circuit breaker, fixed one to
the block and the other to the gun, Fig. 87, come into contact.
It will be seen therefore that the primer cannot be fired until
the breech block is locked.
We have seen that the breech block rotates independently of
the obturator spindle. In order then that the firing mechanism
may always be in an upright position when the breech is closed, a
guide bar, m Fig. 87, fixed at one end to the housing and at the
other end to the block, causes the mechanism to rotate on the
spindle with the block.
FIG. 85. Slide Raised and
Primer Inserted.
FIG. 86. Slide Lowered Ready
for Firing.
FIG. 87. Breech Partially Unlocked. Safety Bar Forced in by Cam Slot,
and Electric Circuit Broken.
FIRING MECHANISM FOR HEAVY GTTNS,
GUNS.
265
The fired primer is ejected by lifting the slide. The lug on the
slide, dFig. 84, strikes the upper part of the ejector lever, giving
to the lower end a sharp movement to the rear, which throws the
primer clear of the piece.
156. Sliding Wedge Breech Mechanism. The method of
closing the breech by means of a sliding wedge-shaped block is
used principally by Krupp, and
to some extent by other makers.
The jacket of the gun, a Fig. 88,
extends to the rear of the tube, and
the bore of the gun is continued
through the extension. A slot
cut transversely through the jacket
just in rear of the tube forms a
seat for the sliding breech block
k. The front surface of the slot
is a plane surface perpendicular
to the axis of the bore, the rear
surface is cylindrical and inclined
to the axis of the bore. Two
guides b b f similarly inclined guide
the breech block in its movements.
The breech block is of the same
shape as the slot and slides in and
out to close and open the breech.
The greater part of the movement
of the block is accomplished
rapidly by means of the transla-
ting screw c, which is held in two
bearings at the ends of the block
and works in a half nut d on the
gun. The screw is turned by means of the handle e, which is
removed from the position in which it is shown and applied to the
end of the screw c. The final movement in closing and the initial
movement in opening are effected more slowly and more power-
fully by the locking screw g. A nut / carried on the locking screw
locks the block when closed.
Obturation. Obturation is effected with the sliding breech
FIG. 88.
265
ORDNANCE AND GUNNERY.
BREECH BLOCK.
TUBE
j ^
-o
; c
\
6
a
e
6
i
^-^
FIG. 89.
block by means of a steel obturator plate, b Fig. 89, carried in the
block, and a steel cup-shaped ring, a,
called the Broadwell ring, seated in the
end of the bore. The pressure of the
gases forces the ring back tightly
against the plate and at the same time
presses the thin lip c against the walls
of the bore. The grooves shown in the
rear surface of the ring serve as air
packing and also to collect any dirt that
may be on the surface of the plate. The
hollow e in the plate also serves to
collect fouling and to remove it
from the bearing surface. The plate
is forced tightly against the ring by
the last movement of the locking
screw in closing.
This mechanism is better adapted to small than to large guns.
The light breech block of a small gun may be pushed to its seat by
hand. Only a limited screw motion is then necessary to firmly
seat and lock the block. Better obturation is also obtained when
a cartridge case is used with this mechanism than when dependence
is placed on the Broadwell ring.
In guns using fixed ammunition, if the breech block closes from
the rear less care is required in inserting the round than if the
breech is closed from one side. In the latter case if the round is
not sufficiently inserted, the block in closing strikes the cartridge
case and a temporary jamming of the mechanism occurs.
157. Older Forms of Breech Mechanism. There are mounted
in our fortifications many guns equipped with the breech mechan-
ism shown in Fig. 90.
The block is revolved by means of one crank fixed to the gun,
and withdrawn and swung aside by a second crank attached to
the tray. The shaft of the revolving crank carries at its end the
pinion p, Fig. 91, which works in the rack of the rotating ring b.
The rotating ring revolves in bearings provided in the face plate,
and communicates its motion of rotation to the block through the
lug a, which engages in one of the slotted sectors. When the rota-
GUNS.
267
tion of the block is completed the translating stud at the bottom
of the block has entered one of the threads of the double threaded
translating roller. The other thread of the roller works in a
corresponding thread cut in the tray. Rotation of the translating
FIG. 90.
crank causes the block to move to the rear with a movement
equal to the sum of the movements due to each of the two
threads. When the front of the roller passes to the rear of
the stud shown acting on the tray latch, the block is brought
268
ORDNANCE AND GUNNERY.
to a stop on the tray, and the shock of its arrest is sufficient
to release the tray latch from its hold on the lip of the recess in
the gun. The tray then swings
aside, carrying the block clear
of the breech.
The tray is similar in general
shape to the tray of the more
modern mechanism shown in
Fig. 72.
i2-inch Mortar Breech
Mechanism. The 12-inch mor-
tars are provided with the
mechanism shown in Fig. 92.
It differs from the mechanism
just described only in the
method of rotating the breech
Fia 91 block. A steel plate k is
fixed to the rear face of the
breech block and extending upwards provides journals for the
pinions a, b, and c of the rotating gear. The pinion c meshes in
the rack e fixed to the gun, and when the crank d is turned the
FIG. 92.
block is rotated to open or close. The block is withdrawn on a
tray as described above. The translating stud that engages in
the translating roller is seen at the bottom of the block.
GUNS. 269
The vent shield /, cut shorter than shown in the figure, is pro-
vided with a stud at its lower end that engages with the safety
bar of the firing mechanism already described. The stud at its
upper end works in the groove g cut in the gun, withdrawing the
safety bar as the breech is fully closed.
Automatic and Semi-automatic Breech Mechanisms. In
guns provided with automatic breech mechanism the energy of
recoil or the pressure of the powder gases is utilized to open the
breech, withdraw the fired shell, insert a new cartridge and close
the breech. After the firing of the first round the only operation
necessary for firing the succeeding rounds is pulling the trigger.
The automatic mechanism is at present applied only to guns of
small caliber that use the small arm cartridge or fire a projectile
weighing not more than a pound.
The semi-automatic mechanism is applied to guns of medium
caliber, up to 6 inches, and efforts are being made to adapt it to
the larger guns. The breech is opened by mechanism that is
operated during the recoil or counter recoil of the piece, and if
fixed ammunition is used the fired shell is ejected. At the same
time power is stored in a spring to be later used in closing the breech.
In some mechanisms the insertion of the succeeding round
by hand operates the breech closing mechanism. In others the
pulling of a lever after the insertion of the round actuates this
mechanism.
158. THE 2.38-iNCH FIELD GUN BREECH MECHANISM. The
semi-automatic breech mechanism of the 2. 38-inch light field gun
is shown in Figs. 93 to 95.
The wedge shaped breech block b is seated in a vertical slot
cut through the extension of the jacket. Projecting guide ribs, t
Fig. 94, in the slot engage in grooves cut in the sides of the block.
The block is lowered or raised to open or close the breech by means
of the crank c. A stud at the end of the crank engages in the cam
groove g on the right side of block, the groove being so shaped
that the crank gives vertical movement to the block. On the
outer end of the crank shaft is the operating lever, I Fig. 95, attached
to which is the operating bar r, and the coiled operating spring.
The forward end of the operating bar embraces the pin pro-
truding from the sliding piece s, which slides in an undercut groove
270
ORDNANCE AND GUNNERY.
2.38-inch Field Gun, Semi-automatic Breech Mecnanism,
GUNS. 271
v in the locking ring of the piece. The pawl p, pivoted on the same
pin, has at its upper end a stud which rests on a shoulder above
the groove. The end of a spring pin, e, in the pawl works in a
slot cut in the sliding piece s and limits the motion of the pawl.
The mechanism above described is fixed to the piece and
moves with the piece in recoil.
A stud, d, is fixed on the recoil cylinder of the carriage. When
the piece recoils, carrying the mechanism with it, the pawl p is
lifted by the stud and falls back into the position shown as soon
as it has passed the stud. As the piece returns in counter recoil
the pawl is engaged by the stud and held. The piece continues
its forward movement. The slide s moves, relatively, to the rear
in its slot, causing the bar r to rotate the operating lever I against
the tension of the coiled spring.
The rotation of the lever lowers the breech block and opens
the breech. The block in the last part of its movement oper-
ates the forked extractor x which ejects the empty cartridge
case.
The stud on the upper end of the pawl p has now moved up
the incline at the rear end of the shoulder on which it slides, lift-
ing the pawl, disengaging it from the stud d on the carriage, and
allowing the piece to finish its movement into battery. The pawl
p being disengaged from the stud the breech block moves upward
under the action of the operating spring until the curved locking
studs o on each arm of the extractor, Fig. 94, engage in the cor-
responding recesses cut in the sides of the block. The curved
shape of the locking studs and recesses, together with the direc-
tions in which the engaging parts are constrained to move, prevent
further movement of the parts and the block is therefore locked
open against the tension of the operating spring.
The rear part of the jacket extension is trough shaped to permit
the ready insertion of the cartridge into the breech. As the
cartridge is pushed into the breech with force its flanged head
engages the extractor arms and forces the locking studs o out of
the recesses. The action of the operating spring through the
lever I and the crank c then lifts the block and closes the breech.
The firing mechanism is similar to that of the 3-inch field gun
which is fully described in Chapter VIII.
272
ORDNANCE AND GUNNERY.
159. THE 3-iNCH SEACOAST GUN BREECH MECHANISM. The
operating parts of the U. S. Ordnance Co.'s semi-automatic breech
mechanism, applied to the 3-inch seacoast gun, are shown in Figs.
96 and 97. Attached to the gun is the actuating rod a, its front
FIG. 93.
end provided with three twisted ribs which are practically screw
threads with a very long pitch. The nut n similarly threaded
is held in the bearing b which is fixed on the recoil cylinder c of
the carriage.
FIG. 97.
When the gun recoils the nut n is turned through 128 degrees
by the actuating rod, but in counter recoil the nut is held by a
pawl and the actuating rod turns clockwise, looking from the
rear, in passing through the nut. The turning of the actuating
rod operates the miter gears at its rear end and through them
opens the breech and ejects the fired shell.
GUNS. 273
The operating spring, one end of which is held in the adjusting
nut d which is carried hi a bearing on the gun, is wound up" by
the movement of the actuating rod during counter recoil, and the
energy stored in the spring is later utilized to close the breech.
A small hydraulic buffer, /, modifies the action of the spring and
relieves the mechanism of violent shock. The block is held open
by the lug I, which under the action of a spring falls inside the
carrier when the breech is open.
After the insertion of the cartridge, hand pressure on the trip-
ping lever t lifts the lug I from inside the carrier. The operating
spring, then free to act, closes the breech block.
The firing mechanism is similar to that described in Chapter
VIII in the 3-inch field gun. The trigger is seen at r, Fig. 97.
Automatic breech mechanisms are described in Chapter XVI,
in the descriptions of the guns in which they are used.
CHAPTER VII.
RECOIL AND RECOIL BRAKES.
160. Stresses on the Gun Carriage. The stresses to which a
gun carriage is subjected are due to the action of the powder gases
on the piece. Gun carriages are constructed either to hold the
piece without recoil or to limit the recoil to a certain convenient
length. In the first case the maximum stress on the carriage is
readily deduced from the maximum pressure in the gun. In the
second case it becomes necessary to determine all the circum-
stances of recoil in order that the force acting at each instant may
be known, and the parts of the carriage designed to withstand
this force and to absorb the recoil in the desired length.
Velocity of Free Recoil. Suppose the gun to be so mounted
that it may recoil horizontally and without resistance. On ex-
plosion of the charge the parts of the system acted upon by the
powder gases are the gun, the projectile, and the powder charge
itself, the latter including at any instant both the unburned and
the gaseous portions. While the projectile is in the bore, if we
neglect the resistance of the air, none of the energy of the powder
gases is expended outside the system. The center of gravity of the
system is therefore fixed and the sum of the quantities of motion
in the different parts is zero. The -movement of the powder gases
will be principally in the direction of the projectile. We may
therefore write
(1)
in which M, ra, and are the masses of the gun, projectile, and
charge of powder, respectively; and v f , v, and v c the velocities of
274
RECOIL AXD RECOIL BRAKES. 275
the same parts. The mass of the charge is the same whether the
charge is unburned or partially or wholly burned.
The velocity of the projectile at any point in the bore of the
gun may be determined from the formulas of ulterior ballistics,
equations (112) to (115), page 100. The velocity of the center
of mass of the products of combustion is unknown. The velocity
of the products varies from zero near the breech to v at the base
of the projectile, and we may, without material error, consider
the velocity of the center of mass of the products as equal to half
the velocity of the projectile.
Writing v/2 for ?; c in equation (1), replacing masses by weights,
and solving for v f we obtain
H-J<o
V '=-W~ V (2)
W, w, and < being the weights of the gun, projectile, and charge.
At the muzzle of the gun v becomes the initial velocity F, and
for the velocity of free recoil at that instant
(3)
This value vf is not the maximum velocity of free recoil,
though it is the maximum value reached while the velocities of
the gun and of the projectile are connected. At the departure of
the projectile the bore of the gun is still filled with gases under
tension, which continue to exert pressure on the breech and in-
crease the velocity of recoil. The value vf obtained by the above
equation is about 7/10 of the maximum velocity of free recoil.
It has been determined by experiment with the Sebert veloci-
meter that the maximum velocity of free recoil may be obtained
from equation (3) by substituting for the quantity Jo>F the quan-
tity 4700d>. The equation then becomes
(4)
being the maximum velocity of free recoil.
276 ORDNANCE AND GUNNERY.
The coefficient 4700 applies to smokeless powders. The co-
efficient for black powders was 3000.
161. Determination of the Circumstances of Free Recoil.
In the above equations the velocity of free recoil is expressed as a
function of the velocity of the projectile, and we have in the bal-
listic formulas the velocity of the projectile expressed as a func-
tion of the travel of the projectile. We might therefore now
determine the velocity of free recoil as a function of the travel of
the projectile. But in the determination of all the circumstances
of recoil it is necessary to know the relations between the velocity,
time, and length of recoil; and in order to arrive at these relations
by means of equation (2), we must obtain an expression for the
velocity of the projectile as a function of the time.
With the velocity of the projectile expressed as a function of
the time, equation (2) will then express the velocity of free recoil
as a function of the time, and with the velocity of recoil so ex-
pressed we may obtain the length of recoil from the equation
* (5)
x representing the length of free recoil.
We thus obtain the complete relations between the velocity,
time, and length of free recoil.
162. Velocity of the Projectile as a Function of the Time.
The velocity of tha projectile as a function of the time is obtained
in the following manner. Representing the travel of the pro-
jectile by u, we have
/I
~du
(6)
That is, t is the area under the curve whose ordinates are values
of 1/v and whose abscissas are values of u.
Therefore if we construct such a curve the area under the
curve from the origin to any ordinate will be the time correspond-
ing to the velocity whose reciprocal is represented by the ordinate.
Construct the curve v, Fig. 98, from the ballistic formulas,
the abscissas representing travel, the ordinates velocity of the
projectile.
RECOIL AND RECOIL BRAKES.
277
Take the value of v as expressed by any ordinate and lay off
its reciprocal on the same ordinate, to any convenient scale. The
curve l/v in the figure is obtained in this way. Its ordinates are
values of 1/r, its abscissas are values of u. The areas under the
curve are therefore values of t, equation (6).
For very small values of v the ordinates l/v will be very large
and will not fall within the limits of an ordinary drawing. We
cannot determine, then, from the drawing, the area under the first
part of the curve. But we can obtain a sufficiently close approxi-
mation to this area in the following manner. We may assume,
FIG. 98.
without material error in the determination of this small area,
that the velocity of the projectile as a function of the time is ex-
pressed by the equation of a parabola
v = \/2pi
Multiplying by dt and integrating, we have, since J v
(7)
(8)
At the instant at which the shot leaves the bore, v in equation
(7) becomes the initial velocity V, and denoting the corresponding
time by t' we obtain from that equation
or
278 ORDNANCE AND GUNNERY.
Substituting this value of (2p)* in equation (8), t in that equa-
tion becoming if and u the total travel of the projectile U, we
obtain
,_3ff
~2 V
t' is then the total area under the curve 1/v, Fig. 98, and sub-
tracting from t' the area that can be measured we obtain the area
under that part of the curve near the origin that is not plotted.
Having now from the v curve the values of v=*f(u) and from
the areas under the l/v curve the values of = /(w) we may, by
combination, determine the desired values of vf(t).
Using as abscissas the areas under the curve l/v, which are the
values of t, and as ordinates the corresponding ordinates of the
curve v, which are the velocities, we obtain the
curve of the velocity of the projectile as a function
of the time, Fig. 99.
Since the velocity of free recoil as given by
equation (2) is equal to the velocity of the pro-
jectile multiplied by a constant, the curve in
Fig. 99 becomes at once the curve of velocity
of free recoil, if we consider the scale of the
p IG 99 ordinates as multiplied by the coefficient of r in
equation (2).
163. Maximum Velocity of Free Recoil. The curve shown
in Fig. 99 gives the velocity of free recoil only while the pro-
jectile is in the bore, and as previously explained the velocity
of recoil has not reached its maximum when the projectile leaves
the piece. The value of the maximum velocity of recoil is given
by equation (4). With this value as an ordinate, Fig. 100, draw a
line parallel to the axis of t and continue the curve of velocity
already drawn until it is tangent to this line. It is reasonable to
infer that the rate of change in the curvature of the curve of recoil
will continue uniform from the point corresponding to the muzzle
of the gun to the point of maximum velocity, and the curve so
continued will with sufficient exactness express the circumstances
of motion. A slight error made in the selection of the point of
tangency will be without practical effect on the determinations to
RECOIL AND RECOIL BRAKES.
279
be later made from this curve. The abscissa of the point of J^an-
gency is the time corresponding to the maximum velocity of free
recoil.
As, by assumption, there is no resistance to recoil, the maximum
velocity attained will never be reduced, and the curve will extend
indefinitely parallel to the axis of t.
The tangent to the curve at any point is a value of dv f /dt, and
therefore represents the acceleration at the instant of time repre-
sented by the abscissa of the point. The tangent has a maximum
value at the point of inflexion of the curve, the point where the
curve ceases to be convex toward the axis of t, and becomes con-
cave. This point is therefore the point of maximum acceleration.
f
*
FIG. 100.
The maximum acceleration being due to the maximum powder
pressure in the gun the abscissa of the point of inflexion is the time
of the maximum pressure.
Since, equation (5), x = Jv f dt, the area under the curve v f , Fig.
100, from the origin to any ordinate is the length of free recoil
corresponding to the velocity represented by the ordinate.
Retarded Recoil. In the discussion thus far we have neglected
all resistances and have considered the movement of the gun in
recoil as unopposed. When the gun is mounted on a carriage the
recoil brakes, of whatever character, begin to act as soon as recoil
begins, and consequently the velocity of recoil is less at each in-
stant than the velocity shown by the curves just determined.
The manner of obtaining the velocity of retarded recoil will be
explained later.
280 ORDNANCE AND GUNNERY.
Recoil Brakes. To absorb the energy of recoil and to bring the
gun to rest in a convenient length, all gun carriages which permit
movement of the gun in recoil are provided with recoil brakes.
These are of two general classes, friction brakes and fluid brakes.
Friction brakes were formerly used on seacoast carriages, but are
now confined exclusively to wheeled carriages. Fluid brakes are
either hydraulic or pneumatic. Pneumatic brakes, depending
for their resistance on the compression of air, have been used in
England to some extent on seacoast carriages. On account of the
difficulty of preventing loss of pressure in the brakes through
leakage of the air these brakes are not satisfactory.
164. Hydraulic Brakes. A hydraulic recoil brake consists of a
cylinder filled with liquid, and a piston. Relative movement is
given to the cylinder and piston by the recoil, and provision is
made for the passage of the liquid from one side of the head of the
piston to the other by apertures cut in the piston or in the walls of
the cylinder. The power of the brake lies in the pressure produced
in the cylinder by the resistance offered by the liquid to motion
through the apertures.
If the area of the apertures is constant it is evident that the
resistance to flow will be greater as the velocity of the piston or
the velocity of recoil is greater. Therefore the pressure in the
cylinder, which measures the resistance offered, will vary with the
different values of the velocity of recoil. If, however, the aper-
tures are constructed in such a manner that the area of aperture
increases when the velocity of the piston increases and diminishes
when that velocity diminishes, the variation in the area of aperture
may be so regulated that the pressure in the cylinder will be con-
stant or will vary in such a manner as to keep the total resistance
to recoil constant.
Both of these methods have been used in the construction of
recoil brakes for gun carriages. The brakes with constant orifices
and variable pressures were used on the old carriages for 15-inch
smooth bore guns.
For a fixed length of recoil a constant resistance will have a
lower maximum value than a variable resistance, and consequently
will produce a less strain on the gun carriage. For this reason and
for other advantages that will appear in the discussion which fol-
RECOIL AND RECOIL BRAKES.
281
lows, the brake with variable orifices, and constant or variable
pressure as circumstances may require, is at present used to the
exclusion of all others on gun carriages.
Hydraulic Brake with Variable Orifice. The mode of action
of the hydraulic brake with variable orifices will be understood
m%^/7M#%#%%%^
FIG. 102.
FIG. 101.
from Fig. 101, which represents a longitudinal section through a
recoil cylinder of the form used in our seacoast carriages.
Fig. 102 represents a cross section through the cylinder.
To the w r alls of the cylinder c are fastened two
bars o called throttling bars, of varying cross sec-
tion as shown. The piston p is stationary, the
piston rod r being fixed to a stationary part of the
carriage. The cylinder c is attached to the gun
and moves to the rear in recoil.
The direction of the movement of the cylinder
is to the right in the figure. The figure shows the relative positions
of cylinder and piston at the beginning of recoil.
Through the piston head are cut two slots or apertures, s,
through which the liquid is forced from one side of the piston to
the other as the cylinder moves in recoil. Each slot has the dimen-
sions of the maximum section of the throttling bar, with just enough
clearance to permit operation. The area of orifice open for the
flow of liquid at any position of the piston is therefore equal to
the area of the slots minus the area of cross section of the throt-
tling bars at that point; and the profile of the throttling bars is
so determined that the resistance to the flow of the liquid, or the
pressure in the cylinder, is made constant or variable as desired.
165. Total Resistance to Recoil. The total resistance to
recoil is composed of the resistance opposed by the brake, the re-
sistance due to friction, the resistance either plus or minus due
282 ORDNANCE AND GUNNERY.
to the inclination of the top of the chassis, and the resistance due to
the counter recoil springs if there are such included in the recoil
system. The function of the counter recoil springs is to return the
gun to battery after recoil.
The resistance of the counter recoil springs varies with the
degree of compression. Therefore to maintain a constant total
resistance when springs are included in the system the resistance
of the brake must also vary, the other resistances being constant.
Let W be the weight of the moving parts,
M the mass of the moving parts,
/ the coefficient of friction,
a the angle of inclination of the chassis rails,
S the resistance of the springs at any time t,
P the total resistance of the hydraulic brake, or the total
pressure in the cylinder, at the time t,
R the total resistance to motion,
v r the velocity of retarded recoil at the time t,
V r the maximum velocity of retarded recoil.
The resistance due to friction will be fWcos a ; that due to the
inclination of the chassis rails will be W sin a. The total resist-
ance at the time t is therefore
R = W(sma + fcosa) + S+P (9)
Dividing the total resistance by the mass, we have, for the
retardation,
-dv/dt = R/M (10)
When the total resistance to recoil is constant, the retardation
R/M is constant, and we may substitute it for g in the equation
that expresses the law of constant forces,
Assuming the origin of movement as at the maximum velocity
of recoil, V r , and designating by V the length of recoil from this
point to the end, the above equation becomes
or l' = V r *M/2R (11)
RECOIL AND RECOIL BRAKES. 283
V is the length in which the constant resistance R will overcome a
velocity of recoil V r .
For the velocity at any point whose distance from the origin is
x } we have the relation
(12)
since I' x is the length in which the constant resistance must over-
come the velocity v r .
Values of the Total and Partial Resistances and Velocities
of Recoil. In the construction of a gun carriage the length of
recoil is usually fixed by the design of the carriage. We will
therefore assume a length I as the total length of recoil. We must
now determine the total constant resistance that will restrict the
recoil to this length and then determine the portion of this resist-
ance that is to be contributed by the brake. In so doing we will
arrive at the values of the velocities of recoil at all points in the
path.
1 66. Total Constant Resistance. The curve v f in Fig. 103,
which as far as the point m is the curve v/ in Fig. 100 drawn to a
FIG. 10J.
different scale, represents the velocity of free recoil as a function
of the time. We have seen that the tangent to the curve at any
point represents the acceleration at that point.
We may represent the negative velocities due to a constant
resistance by the ordinatos of some straight line oc, whose ab-
scissas are the corresponding times. The tangent of the constant
284 ORDNANCE AND GUNNERY.
angle toe is therefore equal to dv/dt, the retardation due to the
force.
The line oc is for convenience drawn above the axis of t. As
its ordinates represent the negative velocities due to the resistance
the line properly belongs below the axis.
Now if we subtract from the velocities of free recoil, repre-
sented by the ordinates of the curve v } , the velocities due to the
retarding force, the ordinates of oc, the ordinates of the resulting
curve v rt will be the velocities of retarded recoil. The curve v rt is
therefore the curve of the velocity of retarded recoil as a function
of the time. The abscissas of the curve being values of t, the area
under the curve will be the total length of retarded recoil, see
equation (5).
We have assumed a total length of recoil, I, and if the area
measured under the curve of retarded recoil, as obtained above,
does not give this length, we must change the angle toe, draw a new
line oc, and construct a new curve. After a few trials the proper
direction of oc will be determined and the area under the curve of
retarded recoil, v rt Fig. 103, will be the length I.
Then the retardation represented by the line, oc is given, see
equation (10), by the equation
- tan toe = - dv/dt = R/M (13)
from which, after measuring the angle toe, we may determine R,
the total constant resistance that will limit the recoil to the length L
The length of retarded recoil corresponding to any velocity of
retarded recoil represented by an ordinate of the curve i>e is the
area under the curve from the origin to the given ordinate.
We may now construct the curve of retarded recoil as a function
of the distance recoiled. To construct a point of the curve meas-
ure the area under the curve v rt in Fig. 103 from the origin to any
ordinate; use the value of this area as an abscissa, and use the
selected ordinate of the curve v rt as an ordinate. The curve v rx in
Fig. 104, constructed in this manner from the curve v n in Fig. 103,
represents the velocity of retarded recoil as a function of the dis-
tance recoiled.
Minor Constant Resistance. The total resistance R is com-
posed, equation (9), of the constant part W(sm a + fcosa)=k
RECOIL AND RECOIL BRAKES. 285
and the two variable parts S and P. The value of TF(sin a + f cos a)
may be readily determined. The retardation due to this resistance'
is equal to k/M, and is represented in Fig. 103 by a line ok drawn
so that the tangent of the angle tok is equal to k/M.
FIG. 104.
167. Resistance of the Spring. The resistance S of a coiled
spring varies directly with the compression of the spring.
Representing by G the force required to compress the spring,
when free, over the first unit of length, the resistance of the spring
at any length of compression x is
If the spring has an initial compression so that it exerts a
resistance G', the resistance after further compression over a
length x becomes
(14)
For the counter recoil springs of a gun carriage, G' represents
the residual pressure in the spring when the gun is in battery, and
x represents any length of recoil.
The resistance of the spring at any point may therefore be
determined from equation (14).
To find the velocities taken out of the system by the spring,
we proceed as follows.
Representing by v r the velocity in the mass M due to the
spring alone, the retardation due to the spring is
286 ORDNANCE AND GUNNERY.
In order to integrate we must express dt in terms of dx.
dx = v'dt. Therefore
dt = dx/v',
and - dv'/dt = - v'dv'/dx = (G f + Gx)/M
and integrating,
- v' 2 /2 = (G'x + Gx 2 /2)/M
the constant of integration being 0, since when x is 0, v f is 0.
The values of i/ are obtained from this equation in terms of
x. We may find from the curves v rx and v rt the value of t corre-
sponding to any value of x. The values of v' obtained above may
then be laid off in Fig. 103 as the true ordinates of the curve os.
These ordinates are laid off in the figure from the line ok so that in
the figure the ordinates of os are the sums of the true ordinates of
ok and os. The ordinates of os are therefore the velocities taken
out of the system by resistances other than the hydraulic brake.
As the ordinates of the line oc are the velocities taken out by
the total constant resistance, the ordinates between the lines os
and oc represent the velocities to be taken out of the system by
the brake alone.
Resistance of the Hydraulic Brake, Pressure in the Cyl-
inder. The pressure in the brake cylinder at any point of the
recoil may now be determined from equation (9)
P = R-W(sma + fcosa)-S (15)
if we substitute for R its constant value from equation (13), for S
its value at the given point from equation (14), and for the remain-
ing term its constant value.
1 68. Relation Between the Pressure, Area of Orifice, and
Velocity of Recoil. In this discussion we will designate by the
term aperture the cut through the piston, and by the term orifice
that portion of the aperture open to the flow of the liquid ; and we
will consider for simplicity that there is but one aperture and one
orifice.
Let A be the effective area of the piston in square feet, that is,
the area of the piston minus the area of the piston rod and aper-
ture. The square foot is taken as the unit of area, because in the
RECOIL AND RECOIL BRAKES. 287
velocities involved in the discussion the foot is the unit of
length.
Let a be the area of the orifice at any time t,
Vr the maximum velocity of retarded recoil,
v r the velocity of retarded recoil at any time t,
vi the velocity of the liquid through the orifice at the time t,
T the weight of a cubic foot of the liquid,
P the total pressure on the piston at the time t.
The cylinder being full of liquid the volume that passes through
the orifice is the volume displaced by the piston. We therefore
have at any instant
v r A =
or, tor the velocity of flow,
vi = VrA /a (16)
From Torricelli's law for the flow of liquids through orifices
we know that the pressure required to produce this velocity of
flow is the pressure due to a column of liquid whose height h is given
by the equation
(17)
Substituting for v the value of vi from equation (16) and solving
for h we obtain
h = v r 2 A 2 /2ga 2 (18)
The weight of a cubic foot of the liquid being ?, the weight of
the column whose area of cross section is unity will be fh, and the
weight of the column whose area of section is equal to that of the
piston will be Afh. Afh is therefore the pressure on the piston, and
substituting in this expression the value of h from equation (18) we
have, for the total pressure on the piston, for any velocity v r
P= r A 3 Vr 2 /2ga 2 (19)
This equation * is general and expresses the relation that exists
between P, A, and a for any given velocity of recoil.
Solving for a 2 we obtain
(20)
288 ORDNANCE AND GUNNERY.
169. Area of Orifice. With the relations established in equa-
tions (14), (15), and (20), which are here repeated, and the curve
v rx in Fig. 104, we are now prepared to determine the variable area
of orifice in the piston.
(14) S
(15) P = R-W(sma + fcosa)-S
(20) a?
The dimensions of the recoil cylinder will be fixed within
narrow limits by the design of the carriage, and by the requirement
that the pressure per unit of area must not be so great as to render
difficult the effective packing of the stuffing boxes through which
the piston rod passes. We will therefore assume that the diam-
eters of the cylinder and piston rod are given, and as the rela-
tion between the total area of piston and the effective area may be
readily established we will assume that the effective area A of the
piston is known.
Brake with Variable Pressure. The value of P at any
point in the cylinder, for which the length of recoil is z, is obtained
from equation (15), the proper value of S for the point having been
first determined from (14). The value of v r is taken from the
curve v rx in Fig. 104 at the ordinate whose abscissa is x. The values
of P and v r thus determined are substituted in equation (20).
The resulting value of a is the area of orifice at the given point.
170. Constant Pressure. If P in equations (19) and (20) is
constant we will have in a given cylinder, for any other values of
v r and a, as V r and a , respectively the maximum velocity of recoil
and the maximum area of orifice
a 2 = r A 3 Vr 2 /2gP (21)
and by combining equations (20) and (21) we obtain for any given
cylinder
v r /Vr (22)
from which we see that to maintain a constant pressure in the
cylinder the area of the orifice must vary directly with the velocity
of recoil.
RECOIL AND RECOIL BRAKES. 289
Assuming the maximum velocity of recoil as the origin_pf_
movement and substituting in equation (22) the value of v r /V r
obtained by combining equations (11) and (12), in which l f repre-
sents the total length of recoil after the maximum velocity has been
reached, we obtain
(23)
that is, with constant pressure in the cylinder the area of orifice
varies as the ordinates of a parabola.
Equation (23) and all equations in which Z' appears refer only
to that part of the recoil from the maximum velocity to the end of
recoil.
Brake with Constant Pressure. When there are no springs
or other variable resistance in the recoil system, S becomes in
the value of P, equation (15), and a constant resistance will be
required in the brake.
To determine the area of orifice we have, for this case,
P = R- W(sin a + f cos a)
(21) af
(22) a/a
Find the value of P from the first equation in the manner
already explained on page 286.
The maximum ordinate of the curve v rx , Fig. 104, is the value
of V r in equation (21). A is known. The maximum area of ori-
fice a may be now determined from equation (21) and the area of
orifice at all other points more simp'y by means of equation (22),
using the values of v r taken from the curve v rx . The areas from the
maximum velocity to the end may also be obtained from equation
(23).
Horizontal Chassis. If the chassis rails are horizontal and the
top carriage is mounted on rollers, so that we may neglect the
friction, the term W (sm a + f cos a) in the value of P, equation
(15), also becomes zero, and P reduces to R. Substituting for R
in equation (11) the value of P from (21) and solving for a we
obtain
(24)
290
ORDNANCE AND GUNNERY.
The maximum area of orifice is in this case independent of the
velocity of recoil, and is dependent only on the length of recoiL
Therefore for a given maximum area of orifice the length of recoil
will be the same no matter w r hat the initial velocity of the projectile r
the charge of powder, or the angle of fire ma}^ be.
Under these conditions the brake requires no adjustment for
varying conditions of fire, and in this respect it possesses further
advantage over the brake with constant orifices and variable
pressure.
The explanation of the independence, under the given condi-
tions, of the length of recoil and the velocity will appear if we sub-
stitute P for R in equation (11). We obtain
In equation (21) we see that for a given maximum area of
orifice the pressure P must vary directly as V r 2 varies. Therefore
in (25), P varying with Vr 2 , I' will remain constant.
171. Profile of the Throttling Bar. Suppose there are n similar
apertures cut in the piston. The area of each orifice at any point
in the cylinder will then be a/n,
a being determined for the par-
ticular point from equation (20).
Let 6, Fig. 105, be the width and d
the depth of each aperture. The
throttling bar has the same depth,
and a variable width y.
Then for the area of each orifice
at the given point in the cylinder
w r e have
^^
FIG. 105. a/n = d(b y)
For the brake with constant pressure the profile of the throttling
bar from the point of maximum velocity to the end will be a par-
abola. Its equation, obtained by substituting the value of a from
the above equation in equation (23) and reducing, is
RECOIL AND RECOIL BRAKES. 291
I
Neglected Resistances. In the foregoing discussion we have
neglected the resistance due to the friction of the liquid and the
contraction of the liquid vein. It has been found by experiment
that the error due to the neglect of these resistances may be cor-
rected by assigning to vi, the velocity of the flow through the ori-
fices, equation (16), a value greater than the actual value as ex-
pressed in equation (17). The value to be substituted is deter-
mined by experiment for each class of carriage and takes the form
Vs = avi + b, a and b being constants. The result of the substitution
is an increase in the area of orifice for any given pressure in the
cylinder, see equation (20).
172. Recoil System of Seacoast Carriages. The arrangement
of the parts of the recoil system on our seacoast disappearing car-
riages, and on barbette carriages for guns 8 inches or more in
caliber, is shown in Fig. 106.
The two cylinders c are integral parts of the top carriage, the
top carriage, including the cylinders, forming a single steel casting
in the sides of which above the cylinders are trunnion seats, for the
gun trunnions in a barbette carriage, and for the gun lever trun-
nions in a disappearing carriage.
The piston rods of the recoil cylinders are fixed to the chassis in
front and supported in the rear. They enter the cylinders through
stuffing boxes. On discharge of the piece the top carriage and
recoil cylinders move to the rear with the gun, forcing the liquid
in the cylinders through the orifices in the stationary pistons.
The direction of the movement of the cylinders is to the right in
Fig. 106.
To equalize the pressure in the two cylinders their interiors are
connected at the front by the pipe a and at the rear by the two
pipes d and /. Each half of the pipes d and / has unobstructed
communication with the other half of the same pipe through a
valve box v. A cross pipe b connects the pipe a with the valve
box. A path is afforded through the pipes a, 6, and d and / for the
flow of liquid from one side of the piston to the other, which path,
as well as the orifices in the pistons, must be considered in deter-
mining the area of orifice.
The area of orifice, and consequently the length of recoil, is
calculated for standard conditions of loading. Any variation in
292
ORDNANCE AND GUNNERY.
^^>x%
~^-0>^_^-X_^:
FIG. 106. Recoil System, Seacoast Carriages.
RECOIL AND RECOIL BRAKES. 293
these conditions will vary the length of recoil, and thus, hi disap-
pearing carriages, vary the height of the breech of the gun above
the loading platform. Standard conditions of loading do not
always exist, and it is therefore desirable to have means for varying
the resistance hi the cylinders in order that the prescribed length
of recoil may be obtained under any conditions, as for instance
when reduced charges are being used.
For the purpose of varying the area of orifice, and therefore
the resistance in the cylinders, adjustable valves called throttling
valves are provided at Vi and v 2 . The flow from the pipe 6 into the
pipe d communicating with the body of the cylinder is regulated
by the valve v i} and the area open to the flow is affected to increase
or diminish the pressure in the cylinder as desired. The pipe d
and its valve Vi are for the control of the recoil.
To control the counter recoil and to bring the gun and top
carriage to rest without shock as they come into battery under the
action of gravity, the counter recoil buffer is provided. The rear
cylinder head is provided with a cylindrical recess into which the
enlargement n of the piston rod, just in rear of the piston, enters
as the carriage approaches its position of rest in battery. The
lug n is slightly conical, so that the escape of the liquid from the
recess is gradually obstructed. The pipe / with its valve v 2 assists
in the regulation of this part of the counter recoil.
The valves v\ and v 2 are moved to increase or diminish the area
of orifice by means of the handles seen hi the rear view, at the
right of Fig. 106.
The cylinders are filled, through holes provided in the top,
with a mineral oil called hydroline. The freezing point of the oil
is below F. Its specific gravity is about 0.85. The oil may be
drawn off through a hole e in the valve box, ordinarily stopped
with a screw plug.
The throttling bars are fastened to the cylinders by screw bolts
through the cylinder walls, as shown in Fig. 106.
Modification of Recoil System. In the recoil system just
described it will be noticed that, at the beginning of recoil, as the
enlargements n of the piston rods emerge from the recesses in the
rear cylinder heads there is around the enlargements but little
clearance by which the oil displaced by their bulk in the cylinders
294 ORDNANCE AND GUNNERY.
proper may enter the vacated recesses. Consequently if the
cylinders are full of oil the liquid will be forced with great velocity
through the clearances, and the pressure in the cylinders will be
correspondingly high.
To prevent this high pressure, oil is withdrawn from the cyl-
inders in sufficient quantity to leave an air space in the cylinders
nearly equal to the space occupied by the enlargements of the
piston rods, and on emerging from the recesses the enlargements
occupy the air space without giving to the liquid an excessive
velocity of flow.
The removal of oil from the cylinders is objectionable in that
if the cylinders are not completely filled with oil the uncovered
parts of the piston and of the cylinder walls are attacked by
rust.
It will be noticed, too, that any movement of either of the
throttling valves that control the recoil and counter recoil affects
the area of orifice. Therefore the regulation of the counter recoil
affects also the recoil.
For these reasons it has been found desirable to separate the
two systems so as to have independent control of both recoil and
counter recoil; and in a 6-inch disappearing carriage now being
tested an additional recoil cylinder is fixed in the counterweight of
the carriage. The control of the recoil is effected wholly by this
large cylinder, and the counter recoil is controlled by smaller cyl-
inders whose pistons are acted on by the top carriage in the last
part of its movement into battery.
Other advantages of this arrangement will appear in the de-
scription of the carriage in the next chapter.
173. Wheeled Carriages, Recoil. To arrive at the effect of the
recoil on a wheeled carriage we must consider the effects of all the
forces that act upon the carriage. These forces include the weight
of the system composed of the carriage and gun, and the various
forces developed by the transmission of the powder pressure to the
points of support of the carriage.
In Fig. 107 is represented the trail of a wheeled carriage with
the wheel and spade. For the purpose of discussion we will as-
sume that the carriage is a rigid body, that the wheels are locked,
and that the pressure developed in the gun, or the pressure de-
RECOIL AND RECOIL BRAKES.
295
veloped in the recoil system when the gun recoils on the carriage,
is transmitted to the carriage at the point o.
The points of application and the directions of the forces
acting on the carriage and of the reactions at the points of support
are represented in the figure.
(f) is any angle of elevation,
P the transmitted pressure.
Let M be the mass of the system composed of the gun and
carriage,
W its weight,
F = F' ' + F", the total friction on the ground.
The center of gravity of the system is represented at c.
The forces acting on the carriage are symmetrically disposed
with respect to the axial plane, and therefore their resultant acts
in that plane.
A system of forces acting in a plane is completely known when
its components in the direction of two rectangular axes in the
plane and the moments about any axis perpendicular to the plane
are determined.
We will assume the rectangular axes as horizontal and vertical,
the vertical axis through the center of gravity and the horizontal
axis on the surface of the ground.
The effect of the forces acting on the carriage will be, under
296 ORDNANCE AND GUNNERY.
the most general consideration, a movement of the carriage to the
rear, and at the same time, since the resistance to motion is great-
est at the point of support of the trail, there will occur a movement
of rotation of the carriage about the point of support.
Applying to the carriage, in the manner shown in Fig. 107, all
the forces that act upon it, we may consider the carriage as a free
body and may then determine the values that the forces must haye
in order to produce in the free body the actual movement of the
carriage in recoil.
The movement of a free rigid body acted on by forces may be
considered as composed of a movement of translation of the
center of gravity and a movement of rotation of the body about the
center of gravity. The movements of translation and of rotation
may be considered separately.
We have for the equations of motion of the center of gravity
Pcosd>-F-S d 2 x
(26)
M dt 2
p + T-W-Psm<j> _d?y
M = dP
(27)
The sum of the moments of the applied forces with reference
to an axis through the center of gravity is the same whether the
center of gravity is in motion or at rest, and is equal to the product
of the acceleration of rotation into the moment of inertia of the
body about the axis. Therefore, representing with small letters
the lever arms of the forces with respect to an axis through the
center of gravity, we have the equation
Pp+Ff+Dd+Ss-Tt _ d 2
= ~
ki representing the principal radius of gyration of the body.
174. CONDITION OF MOVEMENT. Now to introduce into the
three general equations of motion, (26), (27), and (28), the condi-
tion that the movement of the free body shall be the same as the
movement of the carriage in recoil, we may write
y = I sin 6
RECOIL AND RECOIL BRAKES. 297
since this condition holds in the actual movement of the carriage;
that is, as long as the point of the trail is on the ground the center
of gravity is at the distance I sin 6 from the ground.
Differentiating y twice we obtain
dy = I cos Odd
d 2 y = lcosdd 2 d-lsmddd 2
and dividing by dt 2
d 2 y Q d 2 n dP
= l cos d -lsmO W2
dO/dt is the angular velocity of the carriage about the point of
the trail. IdO/dt is therefore the linear velocity of the center of
gravity about the same point. Representing this linear velocity
by v we obtain from the above equation after multiplying the last
term by l/l
This equation expresses that the vertical acceleration of the
center of gravity rotating about the point of the trail is equal to
the vertical component of the linear acceleration Id 2 d/dt 2 about
that point, see Fig. 107, minus the vertical component of the
acceleration along the radius I.
Any change in the angle that the trail makes with the ground
is accompanied by an equal change in the angle of revolution of
the body about the center of gravity, see the two angles 6 in Fig.
107. Therefore the quantities d 2 6/dt 2 in equations (29) and (28)
are the same.
Substituting the value of d 2 y/dt 2 from equation (29) in equa-
tion (27) we introduce into the general equations the actual condi-
tion of motion. We then have, for the gun carriage, the three
equations
M = dt 2
W-Psmt -d 2 v 2 .
~~ - = Zcos0--sm0 (31)
Pp+Ff+Dd+Ss-Tt d 2 6
= dt 2
298 ORDNANCE AND GUNNERY.
We may determine any three of the quantities in these equa-
tions if we establish, or assume, values for the other quantities;
and in this way we may determine the effects that follow from
variations in the values of any of the quantities that enter the
equations.
The above equations are applicable only while y = lsmO',
that is, as long as the point of the trail remains on the
ground.
As the linear velocity of ths center of gravity is usually small
the value of the term v 2 sin 6/1 in equation (31) is veiy small and
is generally neglected in computations. In the computations of
the stresses before movement begins v is 0.
175. Application of the Equations. The general equations
(26), (27), and (28) are applicable in the solution of all problems
that involve the determination of the stresses, and of the move-
ment, produced by the application of a force or a system of forces
to any body or structure.
The equations have been deduced under the most general
considerations, and while the number of quantities that appear in
them is greatly in excess of the number of equations, it will be
found, in practical application under given conditions, that equa-
tions of relation between the various quantities may be readily
established in sufficient number to reduce the number of unknown
quantities in the equations to three, whose values may then be
determined.
Thus to apply the general equations, under given conditions,
to any given construction, such as the gun carriage represented
in Fig. 107.
The intensity and direction of the applied force or forces are
usually known or assumed. We will therefore assume that in
equations (26), (27), and (28) P and (f> are known.
For the gun carriage, the condition y = lsmO eliminates the
quantity d 2 y/dt 2 and brings the equations into the forms (30),
(31), and (32). A similar condition of restraint will ordinarily be
found in all constructions that are free to move in given directions
only.
In the modified equations, P, (/>, W, and M are known. All
dimensional quantities such as /, p, t, etc., are determined from
RECOIL AND RECOIL BRAKES. 299
the known dimensions of the construction, ki may be determined.
6 is known.
D and T being parallel forces their intensities have a relation
to each other dependent on the distances of their points of ap-
plication from the directions of the vertical components of the
applied forces, which relation may be determined from the known
dimensions of the construction.
Representing by /' the coefficient of friction we have
F = F' + F" = f'D + f'T. This equation and the established rela-
tion between D and T provide two equations by means of which
two of the quantities, D and F for instance, may be expressed in
terms of the third, T.
Neglecting the term v 2 sin 6/1, there are now left unknown in
the original equations the quantities T, S, d 2 x/dt 2 , d 2 6/dt 2 .
If a value of any one of these quantities is established by the
given conditions the values of the others may be determined from
the equations. For instance, the problem may specify that the
pressure on the spade shall not exceed a certain limit. Then S
would be known. Or it may be specified that there shall be no
horizontal movement. This would make d 2 x/dt 2 = Q. Or that
there shall be no rotation; d 2 6/dt 2 = Q.
Integrating the expression for the value of d 2 x/dt 2 we obtain
dx/dt = v, the velocity in the direction of a: as a function of the
time, and integrating again we obtain x, the distance passed over,
also as a function of the time. Similarly, if the term d 2 y/dt 2
remains among the unknow r n quantities.
Integrating d 2 6/dt 2 we obtain the velocity of rotation, and
integrating a second time we obtain the angular displacement,
both as functions of the time.
The problem is now completely solved.
If there is no movement of the body the problem is much
simplified, as under that condition the terms involving the dif-
ferentials and the velocity v become 0.
The equations are also applicable in determining the relations
that must exist, in order that any given condition may be ful-
filled, between the dimensions and weight of a construction and
the forces applied to it. This will be shown in the following
problem.
300 ORDNANCE AND GUNNERY.
176, Problem. Determine, for the 3-inch field carriage, the
relations that must exist between the constant resistance in the
recoil system and the weight and dimensions of the carriage in
order that there may not be any movement of the carriage when
the firing is at zero elevation.
In the three equations (30) to (32), 0, the angle of elevation,
becomes 0; and since there is to be no movement of the carriage
the terms involving the accelerations and the linear velocity
become 0. Without movement there will be no friction and F
will also be 0.
The three equations then reduce to
P-S=Q
D+T-W =
Pp + Dd+Ss-Tt =
which express the relations that must exist between the resistance
P to recoil, the weight, and the dimensions of the carriage under
the condition of stability imposed.
As the center of gravity of the system moves to the rear when
the gun recoils on the carriage, the most unfavorable position of
the center of gravity must be used in the equations. This will be
the rearmost position.
Design of a Field Carriage to Fulfil the above Conditions.
Using the equations established in the preceding problem, W, the
weight of the system composed of the gun and gun carriage must
be such that when the weight of the limber filled with ammunition
is added, the weight behind each horse of the team shall not exceed
650 pounds. The length of the trail I will be limited by considera-
tions of draft and of the turning angle of the limbered carriage.
The height of the carriage, /+P(^=o)> must be such that the gun
niay be readily served and not too easily overturned. The area
of the spade must be such that the pressure against it will not
exceed 80 pounds per square inch, as it is found that in average
ground the spade will not satisfactorily prevent movement of the
carriage when the pressure against the spade exceeds this limit.
Therefore the area of the spade = /80.
By carefully weighing these and other considerations, and
assuming successive values for the various quantities in the estab-
RECOIL AND RECOIL BRAKES.
301
lished equations, satisfactory dimensions for the carriage as a
whole are finally determined.
Similar equations are established for each of the individual
parts of the carriage in exactly the same manner as explained for
the carriage as a whole. The stresses to which each part is sub-
jected and the necessary strength and best form of the part to
perform its functions are thus determined.
The pressure P determined from the above equations is the
greatest pressure that may be transmitted to the carriage under
the condition of stability imposed. The 3-inch gun recoils on its
carriage and the recoil is controlled by a hydraulic brake and
counter recoil springs. If we neglect the friction of the moving
parts, P becomes at once the maximum constant resistance that
may be permitted in the recoil controlling system. It is a value
of R in equations (9) and (15). We will then determine, as ex-
plained under hydraulic brakes, the length of the recoil when op-
posed by this resistance, and the length so determined will be the
minimum length of recoil that may be permitted on the carriage.
177. 3-inch Field Carriage Recoil System. A longitudinal
section through the gun recoil system of the 3-inch field carriage
is shown in Fig. 108, drawn to a distorted scale in order to show,
the parts more clearly.
FIG. 108.
A cylindrical cradle d, of cross-section as shown in Fig. 109, is
pintled by the pintle p in a part of the carriage called the rocker,
not shown. The grooves a of the pintle are engaged by clips
provided on the rocker. The rocker embraces the axle of the
carriage and has a movement in elevation which is transmitted
to the gun by the cradle.
302
ORDNANCE AND GUNXERV.
The gun is provided with clips k which engage the upper
flanges of the cradle: and when fired, the gun slides to the
rear on the upper surface of the cradle. The lug Z, Fig.
108, is an integral part of the gun.
The counter recoil buffer u is at-
tached to the lug by a bolt t, and the
recoil cylinder c is attached to the
same bolt by means of the screw v.
Integral with the walls of the cyl-
inder are three throttling bars o.
The piston head s is provided with
three corresponding apertures, Fig.
109.
The hollow piston rod r is held
to the front end of the cradle by a
nut screwed on the forward end of
the rod. The rod terminates at its
rear end in the piston head s. The
outer shoulder formed on the front
head / of the recoil cylinder receives
the thrust of the counter recoil springs m transmitted through the
annular spring support n, w r hich also serves to center the cylinder
in recoil. The flat coiled springs m extend continuously from the
front end to the rear end of the recoil cylinder.
The gun in recoiling draws with it, by means of the lug Z, the
recoil cylinder c, filled with oil, and the counter recoil buffer u.
The piston, attached to the cradle, does not move. When the
forward end e of the curve of the throttling bar reaches the piston
head s, the apertures in the piston are completely closed against
the flow of the liquid, and recoil ceases. The counter recoil buffer
u has now been drawn all the way out of the piston rod.
Under the action of the springs m, which have been com-
pressed by the recoil, the gun returns to battery. The first part
of the counter recoil, during which the counter recoil buffer is out
of the hollow piston rod, is unobstructed. When the buffer enters
the piston rod the escape of oil from inside the rod is permitted only
through the narrow clearance between the rod and the buffer.
The resistance thus offered gradually diminishes the velocity of
FIG. 109.
RECOIL AXD RECOIL BRAKES. 303
counter recoil and brings the gun to rest without shock as it comes
into battery. The buffer is cylindrical for the greater part of its
length, with a clearance in the piston rod of 0.025 of an inch on the
diameter. The diameter of the buffer gradually enlarges over a
length of three inches at the rear until the clearance is but 1/1000
of an inch on the diameter.
The pressure on the piston due to the recoil is transmitted
through the cradle to the pintle p and thence to the carriage.
The length of recoil is 45 inches.
Recoil System of Other Carriages. The recoil-controlling parts
of the carriages for siege guns, and of the barbette carriages for
seacoast guns six inches or less in caliber, embody the same prin-
ciples as the system described above.
CHAPTER VIII.
ARTILLERY OF THE UNITED STATES LAND SERVICE.
178. Classification. Service artillery may be broadly divided
into two classes : mobile artillery and artillery of position.
Mobile artillery consists of the guns designed to accompany or
to follow armies into the field, and comprises mountain, field, and
siege artillery.
Artillery of position consists of the guns permanently mounted
in fortifications. As the fortifications of the United States are all
located on the seacoasts, the guns that form their armament are
usually designated seacoast guns.
Mobile Artillery. The mobile artillery of the United States as
at present designed will consist of the following guns :
Gun. Caliber. Projectile.
Mountain gun 2.95 inch 18 Ibs.
Light field gun 2 . 38 inch 7 J Ibs.
Field gun 3.0 inch 15 Ibs.
Field howitzer 3.8 inch 30 Ibs.
Heavy field gun 3.8 inch 30 Ibs.
Heavy field howitzer 4 . 7 inch 60 Ibs.
Siege gun 4 . 7 inch 60 Ibs.
Siege howitzer 6.0 inch 120 Ibs.
The selection of these calibers is based on the following prin-
ciples. The field gun, the principal artillery weapon of an army
in the field, must have sufficient mobility to enable it to accom-
pany the rapidly moving columns of the army. Long experience
indicates that to attain the desired degree of mobility the weight
behind each horse of the team should not exceed 650 pounds. A
ARTILLERY OF THE UNITED STATES LAND SERVICE. 305
six horse team is used with the field gun. The total weight of the
gun, carriage, limber, and equipment, with a suitable quantity ot
ammunition, is therefore limited to 3900 pounds. Limited by this
requirement the power of the gun should be as great as it can be
made. The shrapnel being the most important projectile of the
field gun the caliber of the gun should be such as to give the
shrapnel the greatest efficiency. Consideration of these require-
ments has led to the adoption of the 3-inch caliber for the field
gun of our service.
A gun of greater power will, on those occasions when it can be
brought into action, be more effective than the 3-inch gun. The
heavy 3.8-inch field gun, firing a 30-pound projectile and possessing
sufficient mobility to enable it to accompany the slower moving
columns of the army, is therefore provided. The weight behind
the six horse team is limited to 4800 pounds. With this weight
the gun is capable of rapid movement for short distances.
The caliber of the siege gun is limited by the requirement that
the weight of the gun shall not exceed the draft power of an eight
horse team. The draft power of this team, for the siege gun, is
taken as 8000 pounds.
Allowing for bad roads and rough usage and for the occasional
necessity of covering considerable distances at high speed, the
draft power of a horse for artillery purposes is taken as consider-
ably less than the draft power of the horse used in ordinary com-
merce.
The guns above named are intended for the attack of targets
that can be reached by direct fire, that is, by fire at angles of
elevation not exceeding 20 degrees. For the attack of targets that
are protected against direct fire and for use in positions so shel-
tered that direct fire cannot be utilized, curved fire, that is, fire
at elevations exceeding 20 degrees, is necessary. There is there-
fore provided, corresponding to each caliber of gun, a howitzer of
an equal degree of mobility. The howitzer is a short gun designed
and mounted to fire at comparatively large angles of elevation.
In order to reduce to the minimum the number of calibers of
the mobile artillery and thus simplify as far as possible the supply
of ammunition in the field, the calibers of the guns and howitzers
have been so selected that, while both guns and howitzers fulfil
306 ORDNANCE AND GUXXERY.
the requirements as to weight and power for each degree of mobil-
ity, the caliber of each howitzer is the same as that of the gun of
the next lower degree of mobility. That is, the howitzer corre-
sponding in mobility to one of the guns is of the same caliber as
the next heavier gun and uses the same projectile.
As there may be occasions when profitable use can be made
of a gun throwing a lighter projectile than that of the 3-inch
field gun, the light field gun, 2.38-inch caliber, is provided. The
weight of the projectile is 7J pounds, this weight being considered
the lowest limit for an efficient shrapnel. The 2.38-inch gun will
probably be used for the movable defense of seacoast fortifica-
tions.
179. Advantages of Recent Carriages. The chief difference
between the latest and earlier designs of carriages for mobile
artillery lies in the provision made in the later carriages for recoil
of the gun on the carriage. By this means a part of the force
produced by the discharge is absorbed in controlling the recoil of
the gun on the carriage, leaving only a part available to produce
motion of the carriage; and by the addition to the end of the trail
of a spade which is sunk in the ground the carriage is enabled to
withstand the transmitted force without motion to the rear.
When the spade is once fixed firmly in the earth further firing of
the gun does not produce recoil of the carriage. Rapidity of fire
is thereby greatly increased, and the soldier is relieved from the
fatiguing labor of running the carriage back into battery after
each round.
Rapidity of fire is also increased by the use of fixed ammuni-
tion, and by the provision for a slight movement in azimuth of the
gun on the carriage. The movement in azimuth permits a change
in the pointing of the gun of three or four degrees to either side
without disturbing the carriage after the spade is set in the ground.
In addition, the gun sights on all modern constructions are
fixed to some non-recoiling part of the carriage so that they are
not affected by the recoil. The operation of sighting may there-
fore go on continuously, independently of the loading and firing.
Our service, field and siege carriages, with the exception of the
6-inch siege howitzer carriage, are so designed that the wheels will
not be lifted from the ground under firings at zero elevation.
FIG. 110. 2.95-inch Mountain Gun.
FIG. 111. Transport of Trail.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 307
The Mountain Gun. For mountain service the system oorn-^
posed of gun and carriage must be capable of rapid dismantling
into parts, no one of which will form too heavy a load for a pack
mule. The weight of the load, including the saddle and equip-
ment of the mule, should not exceed 350 pounds. The system
must be capable of rapid reassembling for action.
The mountain gun used in our service, originally made by
Vickers Sons and Maxim of England, has a caliber of 75 milli-
meters, or 2.95 inches, and fires projectiles weighing 12J and 18
pounds. The caliber of this piece will probably soon be changed
to 3 inches so that it may use the same projectile as the 3-inch
field gun.
The gun is made from a single forging, and weighs complete
with breech mechanism 236 pounds. Fixed ammunition is used
in it. The breech mechanism, Fig. 110, is of the interrupted
screw type. The block has two threaded sectors separated by
flat surfaces. It is provided with percussion firing mechanism so
arranged that the gun cannot be fired until the breech block is
fully closed and locked. The trigger to which the firing lanyard
is attached is seen to the left in the figure outside the breech. In
case of a misfire the mechanism may be recocked without opening
the breech.
1 80. The Carriage. A low wheeled carriage is provided for the
mountain gun. The wheels are 36 inches in diameter and have
a track of 32 inches. The principal parts of the carriage are the
cradle, the trail and elevating gear, the wheels and axle.
THE CRADLE. The cradle is a bronze casting, with a central
cylindrical bore and a smaller cylinder on each side. The central
cylinder embraces the gun to within a few inches of the muzzle
and forms a support in which the gun slides in recoil. The side
cylinders are hydraulic buffers the piston rods of which are secured
to lugs on the gun by interrupted screws so that the gun may be
readily separated from the cradle. Grooves of varying width and
depth cut in the interior walls of the buffer cylinders allow passage
of oil from one side of the piston to the other in recoil. Constant
pressure is maintained in the cylinder throughout the length of
recoil, 14 inches. Spiral springs surrounding the piston rods
return the gun to battery.
308 ORDNANCE AND GUNNERY.
The cradle is secured to the trail by a bolt, seen above the
axle in Fig. 110, which passes through two lugs formed on the
under side of the cradle, the outer ends of the bolt fitting into
two bearings or sockets provided at the forward upper end of the
trail. The cradle moves in elevation about this bolt.
Light lifting bars are provided for use in dismantling and
assembling the gun and carriage. They are passed through the
two eye bolts on the top of the cradle, and through one on the gun.
Front and rear sights are 'attached to the cradle. The rear
tangent sight is detachable.
THE TRAIL. The trail consists of two outside plates or flasks
of steel joined together by a shoe and three transoms. The shoe
is provided with a spade on the under side to assist in checking
recoil, and with a socket on the upper side, in which a handspike
may be fitted, or the shafts attached when traveling on wheels.
At the front end of the trail are the bearings for the cradle bolt
and further to the rear are bearings for
the axle. The bearings are open at the
top, Fig. 112, the openings having a
width less than the diameter of the
bearing. The cradle bolt and axle tree
are cylindrical, with flats cut on them
so that they can only enter their bear-
ings at a certain angle. When in position in the bearings they are
turned through 90 degrees and thus secured. The crank secured
to the axle at the right, Fig. 110, is for the purpose of turning the
axle, in dismantling the carriage, to bring the flats of the axle in
line with the openings of the bearings. When assembled the axle
is locked in position by a spring latch bolt in the crank handle
which engages in a slot provided in the trail.
THE ELEVATING GEAR. The elevating gear is permanently
attached to the trail. Motion of the hand wheel, Fig. 110, is com-
municated to the gun through bevel gears, b Fig. 113, a worm,
w, and a toothed quadrant, q, attached at its rear end to the
cradle. An arm formed on the forward end of the quadrant em-
braces the cradle bolt and revolves around it. A cross bar, c t
on each side near the upper end of the arm keeps the quadrant in
ft central position, and two spiral springs fastened to the front
ARTILLERY OF THE UNITED STATES LAND SERVICE. 309
transom and acting on the arm maintain practically a uniform,
weight on the elevating gear while the gun is being elevated
or depressed. CRADLE
The gun may move in eleva-
tion from minus 10 degrees to
plus 27 degrees.
181. Ammunition. Fixed
ammunition is used. The charge
is about 8 ounces of smokeless
powder. The 1 10-grain percussion
primer is used in the cartridge
case and a front igniter of about
J ounce of black rifle powder.
Three kinds of projectiles are pro-
vided: canister, shrapnel, and FlG 113
high explosive shell. The canis-
ter and shrapnel weigh 12J Ibs., the high explosive shell 18 Ibs.
The canister contains 244 cast iron balls each f of an inch in
diameter. The shrapnel contains 234 balls. The bursting charge
for the shell is 2.07 Ibs. of high explosive.
The muzzle velocity of the 12J-lb. projectile is 850 feet. The
maximum pressure in the bore is 18,000 Ibs.
The gun has an effective range of about 4000 yards.
Transportation. For purposes of transportation the gun and
carriage, with tools, implements, and equipments, are divided into
four loads, the principal items of which are the gun, the cradle,
the trail, the wheels and axle. These loads,' without the pack
equipment, weigh approximately 250 Ibs. each. The pack saddle
and equipment weigh 90 Ibs., so that the total weight carried by
the mule is about 340 Ibs.
The trail, which forms the most inconvenient load, is shown
in Fig. Ill, loaded on the pack animal.
The ammunition is carried in nine loads of 10 or 12 rounds
each, according as the projectiles weigh 18 or 12J Ibs. A box
holding 5 or 6 rounds is slung on hooks on each side of the pack
saddle by loops formed in wire straps about the box. The boxes
open at the end so that the ammunition may be removed from
them without disturbing the pack.
310
ORDNANCE AND GUNNERY.
Field Artillery. The field artillery as at present designed will
consist of the 2. 38-inch gun, the 3-inch gun, the 3. 8-inch gun,
and the 3.8-inch and 4.7-inch howitzers. It is also the intention to
modify the carriage of the mountain gun so that the piece may
be fired at high angles of elevation and be used as a light field
howitzer. The caliber of the gun will then be changed to 3 inches
so that the projectiles of the 3-inch field gun may be used in it.
There is also at present in service a 3.6-inch field mortar.
Fixed ammunition is used in all field pieces except the mortar.
The following table contains data relating to the guns and
carriages of the field artillery.
Guns.
Howitzers. Mortar.
Caliber inches
2.38
1905
0.72
7.5
0.8
9.5
118
1700
33000
2400
15
19 4
3
1905
3.8
1905
3.8
1906
4.7
1906
1.3
60
3.1
65
1063
900
15000
4800
45
37.4
7,32
6850
3.6
1890
0.38
20
0.6
690
17000
45
21.2
515
3360
Date of Model
Charge Ibs . .
1.G2
15
0.82
18.75
252
1700
33000
3900
15 ;
21 9
3
30
2.1
38
526
1700
33000
4800
15
21
769
6900
1.2
30
2.1
35
526
900
15000
3900
45
36.3
707
6300
Projectile Ibs .
Bursting charge, Ibs
Cartridge complete Ibs
Shrapnel balls number
Muzzle velocity f s
Maximum pressure Ibs
Weight limbered Ibs
AT MAXIMUM ELEVATION.
Elevation degrees
Time of flight seconds
Remaining velocity f s .
664
5800
737
6100
Range yards
Other data concerning the guns of the field artillery will be
found in the table on page 135.
The velocities and pressures are fixed at the low figures given
in the table in order that the guns and carriages may be kept within
the limits as to weight.
With velocities of 400 feet the service shrapnel balls are effec-
tive against men, and with velocities of 880 feet, against animals.
As the velocity of the balls is increased by from 250 to 300 feet at
the bursting of the shrapnel, it will be seen from the table that
shrapnel fire from the field pieces is effective at all ranges.
The designs of the field guns of different caliber, with their
mounts, differ 'practically only in thfc size of the parts. A de-.
scription of one will therefore answer for all,
ARTILLERY OF THE UNITED STATES LAND SERVICE. 311
182. The 3-inch Field Gun. The 3-inch field gun is the
ipal weapon of the field artillery. The gun, of nickel steel, is
built up in the manner described on page 236. A hoop called the
clip is shrunk on near the muzzle. On the under side of this hoop,
and of the locking hoop and jacket, are formed clips, k Fig. 117,
which embrace the guide rails of the cradle of the carriage. The
gun slides in recoil on the upper surface of the cradle. A down-
wardly extending lug, I Figs. 116 and 117, at the rear of the jacket
serves for the attachment of the recoil cylinder, which moves with
the gun in recoil.
THE BREECH MECHANISM. The breech mechanism, model
1904. is shown in Fig. 114, in the locked position. The mechan-
ism is of the slotted screw type.
FIG. 114.
The breech block 6 is cylindrical with four threaded and four
slotted sectors. It is mounted on a hollow spindle s formed on
the carrier c, to which it is held by the lug n, which engages in a
slot cut in the enlarged base of the spindle. On a semi-circular
boss formed on the rear face of the block is cut a toothed rack,
312
ORDNANCE AND GUNNERY.
outlined at z, Fig. 117. The teeth of a bevel pinion formed on the
inner end of the operating lever g mesh in the teeth of the rack.
The lever is pivoted on a pin which passes through two lugs formed
on the rear face of the carrier. On grasping the handle of the
lever the pressure against a latch t in the handle unlocks the lever
from the face of the breech. Swinging the lever to the rear ro-
tates the block until it is stopped by a lug inside the carrier and
locked in position by the spring stud a. Further movement of the
lever causes both block and carrier to rotate together about the
hinge pin h. When the movement is nearly complete the surface
o of the carrier bears against the arm of the extractor lever y,
which causes the extractor x to move sharply to the rear and
eject the empty cartridge case.
183. THE FIRING MECHANISM. The firing mechanism, Fig.
115, is contained in the firing lock case /, which is inserted into the
b
FIG. 115.
hollow spindle from the rear, the interrupted lugs d on the lock
case engaging behind corresponding interrupted lugs c on the
carrier. Assembled in the lock case are the firing pin p, the spiral
firing spring, the firing pin sleeve w, and the trigger fork v, the
latter fitting over the squared end of the trigger shaft h, which is
journaled in an arm of the lock case /, Fig. 117, extending down-
ward and to the right outside the carrier.
At the lower end of the trigger shaft h, Fig. 117, are two levers
at right angles to each other, one marked trigger provided with
ARTILLERY OF THE UNITED STATES LAND SERVICE. 313
an eye for the hook of the lanyard, the other acted upon by_an_
upwardly extending lug on the end of the firing lever shaft.
A narrow section of the forward end of the lock case, Fig. 115,
is cut out for the flat sear spring r. A notch in the sear engages
the shoulder formed on the firing pin. The sleeve w at its rear
end bears upon the last coil of the firing pin spring. When the
trigger shaft h is turned by a pull on the lanyard, or by means of
the firing lever, the trigger fork v forces the sleeve w to the front,
compressing the firing spring. The forward end of the sleeve
pushes the sear spring aside from its engagement on shoulder of
firing pin, and the compressed spring then drives the firing pin
forcibly forward until arrested by the shoulder striking the inner
surface of the spindle. When the pull on the lanyard has ceased,
the firing spring, still compressed, exerts a pressure against the
rear end of the sleeve w, thence on the fork v, and on the head o of
the firing pin; and the construction of these parts is such that
the spring can regain its extended length only when the parts are in
the position shown in the figure. The firing pin is therefore im-
mediately withdrawn, on the cessation of the lanyard pull, until
caught again by the sear.
The system of cocking and firing the piece by one movement
is called the continuous pull system. The firing spring is com-
pressed only at the moment of firing, whereas in the mechanism
that is cocked in opening the breech the firing spring is com-
pressed whenever the breech is opened and may remain com-
pressed for a long time.
SAFETY DEVICES. Safety against discharge before the breech
is fully closed is secured as follows. The axis of the spindle 5
on the carrier, Fig. 114, lies -f$ of an inch below and y^ of an inch
to the right of the axis of the gun. The breech block which re-
volves on this spindle is therefore eccentric with the bore. The
firing mechanism is eccentric with the block, the axis of the firing
mechanism being fixed in the axis of the bore. When the. block
is locked the hole in its front end through which the firing pin
protrudes in firing is also in the axis of the bore, but as the block
is rotated in opening, the hole rotates out of the axis of the bore
and the flat surface at its rear end comes in front of the firing pin
and prevents movement of the firing pin until the breech is locked.
314 ORDNANCE AND GUNNERY.
The headed spring pin u, Fig. 117, enters a hole in the carrier
and retains the firing mechanism in its position in the carrier.
By withdrawing this pin and rotating the firing lock case / upward
through 45 degrees the interrupted lugs d, Fig. 115, on the firing
lock case disengage from behind the interrupted lugs c on the
carrier, and the firing mechanism may be withdrawn from the gun.
The breech block is then readily removed. The breech mechan-
ism may thus, without the use of tools, be readily dismantled for
repair, or the gun may be quickly disabled in the event of imminent
capture.
Four holes are drilled rearwardly through the breech block, b
Fig. 114, to permit the escape of gas without injury to the screw
threads of the mechanism in case the primer in the cartridge is
punctured by the blow of the firing pin.
THE 3-iNCH GUN, MODEL 1905. The 3-inch gun, model 1905,
is 50 Ibs. lighter than the 1902 and 1904 models, the outside diam-
eters being slightly diminished. The twist of the rifling, which
in the earlier models increases from 1 turn in 50 calibers at the
breech to 1 in 25 at the muzzle, increases from zero at the breech
to 1 in 25 at 9| inches from the muzzle, from which point it is
uniform to the muzzle. The purpose of the change in twist is
to diminish the resistance encountered by the projectile in the
first part of its movement and thereby diminish the maximum
pressure. The short length of uniform twist at the muzzle steadies
the projectile as it issues from the bore.
184. The Carriage. The principal parts of the carriage are the
cradle, the rocker, the trail, the wheels and axle.
THE CRADLE. The cradle, c Figs. 116 and 117, is a long steel
cylinder, which contains the recoil controlling parts. These parts
are fully described in the chapter on recoil, and illustrated in
Figs. 108 and 109 of that chapter. The gun slides in recoil on the
upper surface of the cradle, the clips of the gun, k Fig. 117, en-
gaging the flanged edges. A pintle plate fastened to the bottom
of the cradle is provided with the pintle p, Fig. 117, and the
grooved arc a, which serve to connect the cradle to the rocker.
THE ROCKER. The rocker r embraces the axle between the
flasks of the trail by the bearings at its ends. The cradle pintle
fits in a seat provided in the rocker above the axle, and the clips
ARTILLERY OF THE UNITED STATES LAND SERVICE. 315
n
FIG. 116.
FIG. 117.
316 ORDNANCE AND GUNNERY.
on the rocker engage in the grooved arc a of the cradle. This con-
struction permits movement of the cradle and gun in azimuth on
the rocker, while the rocker itself revolves about the axle and thus
gives movement in elevation to the cradle and the gun. The
movement in azimuth, 4 degrees either way, is produced by a
screw on the shaft of the hand wheel t, Fig. 116. The shaft is
fixed in bearings in the rocker arms and the screw works in a nut
pivoted in a bracket fastened under the cradle.
The double elevating screw, actuated by either of the crank
shafts e fixed in bearings in the trail, rotates the rocker and cradle
about the axle. The bevel pinion on the end of each shaft e rotates
the bevel pinion b in its bearings. The pinion b is splined to the outer
screw m and causes the outer screw to turn in the fixed nut q which
is supported below the pinion & by a transom. The outer screw m
has a left handed thread on the exterior and a right handed thread
in the interior. When turned it travels up or down in the nut q,
and at the same time causes the inner screw n to move into or out
of the outer screw, the inner screw being prevented from turning
by its connection with the rocker arms, r Fig. 116. The move-
ment of the inner screw for each turn of the pinion b is thus equal
to the sum of the pitches of the outer and inner screws.
THE TRAIL. The trail, Fig. 119, composed of two flanged steel
flasks connected by transoms and top and bottom plates, ter-
minates at its lower end in a fixed spade provided with a float or
wings which prevent excessive burying of the spade in the ground.
The lower edge of the spade is of hardened steel riveted on so that
it may be readily replaced when worn out. The lunette, a stout
eye bolt fixed in the end of the trail, engages over the pintle of the
limber when the carriages are connected for traveling. Seats for
two cannoneers who serve the piece hi action are attached to the
trail one on either side near the breech of the piece; and two other
seats on the axle, facing toward the muzzle, are occupied in trav-
eling by two cannoneers, one of whom manipulates the lever of
the wheel brakes.
THE WHEELS AND AXLE. The axle of forged steel is hollow.
The axle arms are given a set so as to bring the lowest spoke of
each wheel vertical.
The wheels are a modified form of the Archibald pattern, 56
ARTILLERY OF THE UNITED STATES LAND SERVICE. 317
FIG. 118.
The hollow axle forms a reservoir for
inches in diameter with 3-inch tires. The hub, Fig. 118, eonsists
of a steel hub box h and hub ring r
assembled by bolts through the
flanges, between which the spokes
of the wheel are tightly clamped.
The hub box is lined with a bronze
liner forced in. A steel cap c is
screwed on the outer end of the
hub box. Riveted to the cap is a
self closing oil valve, by means of
which the wheels are oiled without
removal from the axle.
the oil.
The wheels are secured to the axle by the wheel fastening, a
bronze split ring, hinged for assembling around the axle. The
ring revolves freely in a groove in the axle. Interrupted lugs on
its exterior engage behind corresponding interrupted lugs, I Fig.
118, in the inner end of hub box, and hold the wheel on the axle.
A hasp connects the hub and the wheel fastening so that they
cannot revolve independently and disengage the lugs.
185. THE SHIELD. The cannoneers serving the piece are pro-
tected by a shield of hardened steel r 2 F of an inch thick. It is in
three parts. One part, the apron, depends from the axle and is
swung up forward under the cannoneers' seats when traveling.
The main shield, rigidly attached to the frame of the carriage,
extends upwards from the axle, to 2J inches below the tops of the
wheels. The top shield is hinged to the main shield. When
raised its upper edge is 62 inches from the ground, a height suffi-
cient to afford protection from long range and high angle fire to
cannoneers on the trail seats. In traveling the top shield is folded
over so that should the carriage turn over on the march the shield
is partially protected from injury. Each shield before being at-
tached to the carriage is tested at a range of 100 yards with a
bullet from the service rifle. The plate must not be perforated,
cracked, broken, or materially deformed in the test.
SIGHTS. The piece is provided with three different means of
sighting. Two fixed sights, on the upper element of the gun,
Fig. 116, determine a line of sight parallel to the axis, for use in
318 ORDNAXCE AND GUNXERY.
giving general direction to the piece. For more accurate sighting
a tangent rear sight and a front sight with crossed wires are pro-
vided. They are seated in brackets attached to the cradle. A
telescopic panoramic sight is seated on the stem of the tangent
sight. This sight is used for direct aiming and for indirect aiming,
which consists in pointing the gun by means of a line of sight con-
siderably divergent from the line of fire. By means of the pano-
ramic sight any object in view from the gun may be used as an
aiming point.
A range quadrant, seated on the cradle of the carriage, pro-
vides the means of determining the elevation in indirect fire.
The sights are fully described in the chapter on sights, Chapter
XIII, and the range quadrant in Chapter XIV.
The Limber. The limber, Fig. 120, is practically wholly of
metal, the neck yoke and pole, and spokes and felloes of the
wheels, being the only wooden parts. The body of the limber is a
steel frame, composed of three rails riveted to lugs formed on the
axle and braced by steel tie rods. The middle rail is in the form
of a split cylinder, one half passing below the axle and the other
above. The halves unite in front forming a socket for the pole,
which is held firmly in place by a clamp. Similarly in the rear the
middle rail forms a seat for the pintle hook. The pintle hook is
swiveled in its seat, so that if at any time the gun carriage turns
over the pintle will turn without overturning the limber as
well.
The ammunition chest, of sheet steel, is fastened to the outer
rails. The front of the chest and the door which forms the rear
are strengthened by vertical corrugations. The door opens down-
ward and is then supported by chains. The metallic ammunition
is supported in the chest by three diaphragms each perforated
with 39 holes. The middle and rear diaphragms are connected by
flanged brass tubes cut away on top to reduce the weight. The
tubes support the front ends of the cartridge cases and enable
blank ammunition and empty cases to be carried.
Seats made of sheet steel are provided for three cannoneers on
the limber chest, and a steel foot-plate rests on the rails in front
of the chest.
The wheels of the limber and the wheels of all other carriages
FIG. 119. 3-inch Field Gun, Model 1902.
FIG. 120. 3-inch Field Limber.
Fig. 121. 3-inch Field Gun, Limbered.
FIG. 122. 3-inch Field Caisson.
FIG. 123. 3-inch Field Battery Wagon.
FIG. 124. 3-inch Field Store Wagon.
ARTILLERY OF r HE UNITED STATES LAXD SERVICE. 319
that form part of a field battery are interchangeable with the
wheels of the gun carriage.
1 86. The Caisson and other Wagons. The construction of
the caisson, Fig. 122, does not differ materially from that of the
limber. The ammunition chest is larger and carries 70 rounds of
ammunition. The front of the chest is of armor plate -$ of an
inch thick; and the door at the rear, which opens upward to an
angle of about 30 degrees above the horizontal, is of armor plate
yW of an inch thick. A T \-inch plate also depends from the axle
as in the gun carriage. The cannoneers serving the caisson are
thus afforded protection for a height of 63 inches from the ground.
Attached to the caisson by a hinged bracket at the rear is an
automatic fuse setter, by means of which the cannoneer at the
caisson may quickly set the fuse of the projectile to the time of
burning corresponding to any range ordered by the battery com-
mander. The fuse setter is described in the chapter on primers
and fuses, and is illustrated in Fig. 229.
Three 'caissons with their limbers accompany each gun into
the field.
The wagons of a battery include also the forge limber, which,
as its name indicates, carries a blacksmith's forge and set of tools;
and the battery wagon, Fig. 123, which carries carpenter's and
saddler's tools and supplies; materials for cleaning and preserva-
tion; spare parts of gun, of carriage, and of harness; tools and
implements; miscellaneous supplies and two spare wheels.
A wagon called the store wagon, Fig. 124, is for use in carrying
such stores, spare parts, and materials as cannot be carried in the
battery wagon.
Experiments are now being conducted toward the develop-
ment of an automobile battery wagon.
Field Howitzers and Mortars. The 3. 8-inch and 4.7-inch
field howitzers have not yet been constructed. The principles of
construction of the guns and carriages will be understood from the
description of the 6-inch howitzer and carriage which follows later.
There is at present in service a 3. 6-inch field mortar shown in
Fig. 125. The piece is a short gun intended for vertical fire against
troops protected by intrenchments or other shelter. The Freyre
obturator described on page 262 is used in the breech mechanism
320
ORDNANCE AND GUNNERY.
to save weight. The gun weighs 245 Ibs. and its mount 300 Ibs.
more, so that the gun with its mount may be readily moved in the
field. The mount is a single steel casting. The gun is held at any
desired elevation by means of a clamp which acts on a steel arc
attached to the under side of the gun.
When in use the carriage rests on a wooden platform, and
recoil is checked by a heavy rope attached to stakes driven into
the ground in front.
187. Siege Artillery. The new siege artillery comprises the
4.7-inch gun and the 6-inch howitzer. The older siege pieces now
in service are the 5-inch gun, the 7-inch howitzer, and the 7-inch
mortar.
The following table contains data relating to the guns and
carriages of the siege artillery.
Guns.
Howitzers.
Mortar.
1892'
Caliber inches
4.7
1904
5
1898
6
105
7
1898
Date of model
Charge, Ibs
5.94
60
3.1
73|
1063
1700
33000
8000
15
21.8
971
7600
5.37
45
1.75
1830
35000
8800
31
38.2
638
10000
4
1LO
3.86
2150
900
15000
7900
45
37.5
764
7000
4.6
105
7.4
lioo
_8000
35
34.3
749
7700
4.0
125
11.9
800
20000
45
32.9
641
5200
Projectile Ibs
Bursting charge Ibs . .
Cartridge complete, Ibs . .
Shrapnel balls, number .
Muzzle velocity, f. s.
Maximum pressure Ibs
Weight limbered Ibs
AT MAXIMUM ELEVATION.
Elevation, degrees
Time of flight seconds
Remaining velocity f s
Range, yards
ARTILLERY OF THE UNITED STATES LAND SERVICE. 321
Other data concerning the guns of the siege artillery will be
found in the table on page 135.
The 4.7-inch Siege Gun. The gun is similar in construction
and in breech mechanism to the 3-inch field gun. Fixed ammu-
nition is used in it.
THE CARRIAGE. The carriage is, in general, similar in con-
struction to the 3-inch field carriage. The greater weight of the
gun and the increased force of recoil render necessary certain
changes in the parts. In the 3-inch carriage the recoil cylinder
and counter recoil springs are assembled together in a single cyl-
inder in the cradle. The cradle of the 4.7-inch carriage, Figs. 127,
128, and 129, consists of three steel cylinders bound together by
broad steel bands, the middle band provided with trunnions.
The middle cylinder contains the mechanism for the hydraulic
control of recoil. Each of the outer cylinders contain three con-
centric columns of coiled springs for returning the gun to battery.
The front end of each of the outer two spring columns is connected
to the rear end of the next inner column by a steel tube, flanged
outwardly at the front end and inwardly at the rear end. A
headed rod passes through the center of the inner coil and is fixed
to a yoke that is fastened to the lug at the breech of the gun, see
Fig. 128. The head of the rod acts on the inner coil only, and the
pressure is transmitted through the flanged tubes or stirrups to
the outer coils. In this way the
springs work in tandem and have a
long stroke with short assembled
length.
The arrangement of the springs
will be understood by reference to
Fig. 126, in which r represents the
headed rod, s the tubular stirrups, and
c the walls of the cradle cylinder.
The length of recoil is 66 inches.
The gun is supported, and slides in recoil, on rails r fixed on
top of the spring cylinders. The distance apart of the rails broad'
ens the bearing of the gun and gives it steadiness both in action
and in transportation. An extension piece, bolted to the front
end of the cradle and readily detachable, continues the rails to
FIG. 126.
322
ORDNANCE AND GUNNERY.
the front clip of the gun. When traveling this extension piece
is detached and carried in fastenings under the trail.
THE PINTLE YOKE. The cradle is trunnioned in a part called
the pintle yoke, y Fig. 127, which is itself pintled in a seat, p,
called the pintle bearing, mounted between the forward ends of
the trail flasks, its rear end embracing the hollow axle x. A
traversing bracket, 6, is attached to the bottom of the pintle yoke
and extending to the rear under the axle forms a support for the
FIG. 127.
traversing shaft t and for the elevating mechanism. The rear end
of the traversing bracket slides on supporting transoms between
the flasks of the trail, motion being given to the bracket by means
of a screw on the traversing shaft which works in a nut suitably
attached to the trail. The gun may be moved in azimuth on the
carriage 4 degrees either way. The elevating mechanism is car-
ried on the traversing bracket and moves with the gun in azi-
muth. It is therefore not subjected to any cross strains. The
gun may be moved in elevation from minus 5 to plus 15 degrees.
1 88. THE WHEELS AND THE TRAIL. The w r heels are 60 inches
in diameter with 5-inch tires. Exhaustive tests recently con-
eg
S 1
e.
ARTILLERY OF THE UNITED STATES LAND LER~\ ICE. 323
eluded indicate that no practical advantage is gained by tEe use
of wider tires on vehicles of this class and weight.
The trail is of the usual construction, two pressed steel flasks
of channel section tied together by transoms and plates. The
front ends of the flasks are riveted to cast steel axle bearings
which extend to the front of the axle and support between them
the pintle bearing p. The location of the pintle socket in front
of the axle permits the use of a shorter trail and reduces the weight
at end of trail to be lifted in limbering.
Bearings are provided at about the middle of the trail, in the
opening seen in Fig. 128, for a detachable geared drum which is
used in giving initial compression to the counter recoil springs in
assembling, and in withdrawing the gun to its traveling position.
When not in use the drum is kept in the tool-box in the trail.
The spade with its horizontal floats is hinged to the trail on
top. For traveling it is turned up and rests on top of the trail,
see Fig. 129; for firing it is turned down. In either position it is
locked in place by a heavy key bolt.
A bored lunette plate is riveted to the bottom of the trail, for
engagement on the pintle of the limber.
The Limber. The limber, Fig. 130, is merely a wheeled turn-
FIG. 130.
table for the support of the end of the trail in traveling. It has
the usual arrangements for the attachment of the team. Its
wheels are interchangeable with those of the carriage. The
turntable, shaped to fit the end of the trail, is mounted on a frame
324 ORDNANCE AND GUNNERY.
fixed to the axle. It forms a seat for the trail. The seat is
pivoted at the rear end and its front end rests on rollers which
travel on a circular path on the limber. A pintle on the seat en-
gages in the lunette in the bottom of the trail.
When traveling, in order to distribute the weight as evenly as
possible between the front and rear wheels of the limbered carriage,
the gun is disconnected from the piston rod and spring rods, and
drawn back 40 inches to the rear, Fig. 129. In this position the
recoil lug is secured between two stout braces attached to a heavy
trail transom. The breech of the gun is thus supported and
rigidly held in traveling, and the elevating and traversing mech-
anisms are relieved from all strains. The braces referred to are
pivoted in the trail, and when not in use are turned down inside
the trail.
189. Weights. The weight of the gun carriage complete is
4440 Ibs., and that of the gun and carriage, 7170 Ibs. The weight
at the end of the trail, gun in firing position, or the weight to be
lifted in limbering, is 400 Ibs. ; with the gun in traveling position,
this is increased to 1150 Ibs., which is the part of the weight of
the gun carriage sustained by the limber.
Siege Limber Caisson. For the transportation of ammuni-
tion for siege batteries there is provided a vehicle called the siege
limber caisson. As the name indicates, this vehicle is composed of
two parts. Each part supports an ammunition chest arranged to
carry 28 rounds of 4.7-inch ammunition or 18 rounds of 6-inch
ammunition, thus making 56 rounds of 4.7-inch ammunition or
36 rounds of 6-inch ammunition per vehicle. For each siege
battery of 4 guns 16 limber caissons are provided.
The 6-inch Siege Howitzer. This is a short piece, 13 calibers
long, mounted on a wheeled carriage so constructed that the
piece can be fired at angles of elevation from minus 5 to plus 45
degrees. This wide range of elevation on a wheeled mount in-
troduces into the carriage requirements not encountered in the
construction of the carriages previously described, which provide
for a maximum elevation of 15 degrees.
The piece is made from a single forging, Fig. 131. A lug, /,
extends upward from its breech end for the attachment of the
recoil piston rod and the yoke for the rods of the spring cylinders.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 325
Flanged rails r formed above the piece support it on the cradle of
the carriage, on which the piece slides in recoil.
The operating lever of the breech mechanism of the gun, Figs.
132 and 133, is above the axis of the gun instead of below it as
in other guns. It is so placed for the purpose of increasing the
clearance in recoil and for convenience in operating.
FIG. 131.
190. The Carriage. The cradle, Figs. 132 and 133, is pro-
vided with recoil and spring cylinders. The arrangement of the
springs in the spring cylinders is the same as shown in Fig. 126
for the 4.7-inch siege gun. The gun is placed below the cylinders
in order that the center of gravity of the system may be as low as
possible. The trunnions of the cradle rest in beds in the top
carriage, which in turn rests on and is pintled in the part called
the pintle bearing. Flanges on the top carriage engage under
clips on the pintle bearing. The forward ends of the trail flasks
are riveted to the pintle bearing, which forms a turntable on which
the top carriage, and the parts supported by it, have a movement
of three degrees in azimuth to either side. The traversing is ac-
complished by means of the hand-wheel t on the left side. The
traversing shaft is supported in a bracket, a, fixed to the left flask,
and its worm works in a nut, o, pivoted to the top carriage.
THE ROCKER. The rear part of the rocker is a U-shaped piece
that passes under the gun and is attached to the cradle by the hook
k, pivoted in the cradle. Arms extend forward from the sides of
the U and embrace the cradle trunnions between the cradle and
the cheeks of the top carriage, so that the rocker may rotate
about the cradle trunnions. The sights are seated on a bar sup-
ported on the left vertical arm of the rocker. The upper end of
the elevating screw n is attached to the bottom of the rocker,
while the lower end of the screw and the elevating gear are sup-
326
ORDNANCE AND GUNNERY.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 327
ported by trunnions in lugs on the under side of the tup~car-
riage. The rocker therefore moves in elevation in the top carriage
and gives elevation to the gun-supporting cradle fastened to the
rocker by the hook k. The elevating apparatus is operated by a
hand-wheel e on either side.
THE TRAIL. The flasks of the trail extend separately to the
rear a sufficient distance to permit free movement between them
FIG. 133.
of the gun in recoil at any elevation. They are then joined by
transoms and top and bottom plates, and terminate in a detachable
spade which is secured to the top of the trail when traveling.
Sockets are provided for two handspikes at the end of the trail.
Two lifting bars are also fixed to the trail. In order to permit the
328 ORDNANCE AND GUNNERY.
desired movement of the cradle in elevation the axle is in three
parts, the middle part lower than the two axle arms. The three
parts are held by shrinkage in cylinders formed in the sides of the
pintle bearing.
The wheel brakes, used both in firing and in traveling, are
manipulated by hand-wheels b in front of the axle.
1 91. RECOIL CONTROLLING SYSTEM. The feature of this car-
riage which chiefly differentiates it from other carriages described
is the provision for the automatic shortening of recoil as the ele-
vation of the gun is increased. From minus 5 degrees to eleva-
tion the gun has a recoil of 50 inches. As the elevation increases
from to 25 degrees the length of recoil diminishes continuously
from 50 inches to 28 inches. For elevations between 25 and 45
degrees the length of recoil rmeains at 28 inches. The variation
in length of recoil is necessitated by the approach of the breech to
the transoms and to the ground as the piece is elevated.
The automatic regulation of recoil is produced in the following
manner. Four apertures are cut in the piston of the recoil cyl-
inder and two longitudinal throttling grooves in the walls of the
cylinder. The total area of apertures and deepest section of the
grooves is the proper maximum area of orifice for the 50-inch
length of recoil, while the grooves alone furnish the proper con-
tinuous area of orifice for a recoil of 28 inches. A disk rotatably
mounted on the piston rod against the front of the piston, and
provided with apertures similar to those in the piston and similarly
placed, is rotated on the piston rod during the recoil of the piece
by two lugs projecting into helical guide slots cut in the walls of
the recoil cylinder. The rotating disk gradually closes the aper-
tures in the piston, and the twist of the guiding slots is such that
the area of orifice is varied as required for limiting to 50 inches the
recoil of the gun when fired at elevation.
The recoil cylinder is rotatably mounted in the cradle. Teeth
cut on its outer surface, Fig. 134, mesh in the teeth of a ring sur-
rounding the right spring cylinder, and the teeth of the ring also
mesh, at any elevation between and 25 degrees, in a spiral
gear cut on the cylindrical block s, which is seated in the
hollow trunnion of the cradle and is fast to the right cheek
of the top carriage. As the gun is elevated from to 25
ARTILLERY OF THE UNITED STATES LAND SERVICE. 329
degrees the spiral teeth of the gear cause the ring to rotate
clockwise and the cylinder counter
clockwise. The rotating recoil
cylinder carries with it the disk
in front of the piston, causing the
disk to close the piston apertures
more and more until at 25 degrees
elevation they are completely
closed. The throttling grooves
in the walls of the cylinder
then provide the proper area
of orifice for the 28-inch length FIG. 134.
of recoil permitted to the gun at elevations between 25 and 45
degrees.
LOADING POSITION. To load the piece after firing at high an-
gles the hook k, which holds the cradle to the rocker, is disengaged
by means of a handle, h, conveniently placed on top of the cradle,
and the cradle and gun are swung by hand to a convenient position
for loading. The center of gravity of the tipping parts is in the axis
of the trunnions. A pawl, 3, attached to the cradle automatically
engages teeth, 4, on the top carriage and retains the gun in the
loading position until released by means of the same handle h
that was used to disengage the cradle hook.
As the sights and elevating screw are attached to the rocker,
their positions are not affected by the position of the piece in load-
ing. The operations of laying the piece may therefore be per-
formed at the same time as the loading.
STABILITY OF THE CARRIAGE. The piece is set low in the car-
riage to diminish as far as possible the overturning moment; but
the maximum velocity of free recoil of this light piece is so great
that stability of the carriage at all angles of elevation could not
be obtained without exceeding the limit of weight and making the
recoil unduly long. The carriage will be stable for angles of eleva-
tion greater than about 10 degrees. The wheels are expected to
rise from the ground in firings at angles of elevation less than 10
degrees.
THE LIMBER. The limber is the same as the limber of the
4.7-inch siege carriage previously described. When limbered the
330
ORDNANCE AND GUNNERY.
rear end of the cradle is locked to the trail in order to relieve the
elevating and traversing mechanisms from strain. The short
length of the howitzer renders it inadvisable to move the gun to a
more rearward traveling position.
WEIGHTS. The weight of gun and carriage is about 6900
pounds, and the weight of the limber 1000 pounds. The total
FIG. 136.
weight is slightly less than the limit of 8000 pounds, considered as
a maximum load for a siege team.
192. Siege Artillery in Present Service. The wheeled siege
pieces in present service are the 5-inch gun, shown in Fig. 135,
and the 7-inch howitzer, Fig. 136.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 331
When emplaced in a siege battery the carnage for either piece
rests on a wooden platform. Recoil is limited by means of a
hydraulic buffer attached to the trail and pintled in front to a
heavy pintle fixed to the platform. The howitzer also recoils on
the carriage, the recoil of the piece being controlled by hydraulic
buffers one on each side in front of the trunnions. Springs, strung
on rods in rear of the trunnions, return the gun to the firing posi-
tion. The springs are either coiled or Belleville springs, the latter
being saucer shaped disks of steel strung face to face and back to
back.
The pieces are mounted at a height of about six feet above the
ground to enable the guns to be fired over a parapet of sufficient
height to shelter the gunners.
For traveling, the guns are shifted to the rear into trunnion
beds provided in the trail.
The 7-inch siege mortar and carriage are shown in Fig. 137.
- J
FIG. 137.
The carriage rests on three traverse circle segments / bolted to
the platform. It is held to the paltform by the overhanging
flanges of the segments g. Elevation is given to the gun by means
of the handspike /, which, for the purpose, is seated in a slot in the
trunnion; and direction is given by means of the handspikes /
which are engaged against lugs on the carriage. The means of
332 ORDNANCE AND GUNNERY.
controlling the recoil of the piece are similar to those employed
with the 7-inch howitzer.
193. Seacoast Artillery. Comprised in the seacoast artillery
are guns ranging in caliber from 2.24 inches to 16 inches, their
projectiles ranging in weight from 6 pounds to 2400. The 2.24-inch
and 3-inch guns, called the 6-pounder and the 15-pounder, are used
for the defense of the sea fronts of fortifications against landing
parties and for the defense of the submarine mine fields. The
guns of medium caliber, from 4 to 6 inches, are best used for the
protection of places subject to naval raids, and for the defense of
mine fields at distant ranges. Their fire is effective against un-
armored or thinly armored ships.
The 8- and 10-inch guns are effective against armored cruisers
and against the thinly armored parts of battleships.
The proper target for guns 12 inches or more in caliber is the
heavy water line armor of the enemy's battleship.
The 12-inch gun is the largest gun at present mounted in our
fortifications. One 16-inch gun has been manufactured and satis-
factorily tested, but no guns of this caliber are mounted. The
latest model of 12-inch gun was designed to give the 1000 pound
projectile a muzzle velocity of 2550 feet, which would insure per-
foration, at a range of 8700 yards, of the 12-inch armor carried by
the latest type of battleship. But it has been found that in the
production of this high muzzle velocity in a heavy projectile the
erosion due to the heat and great volume of the powder gases is
so great as to materially shorten the life of the gun. It has been
decided therefore as a measure of economy to reduce the muzzle
velocities of the larger guns from 2550 feet to 2250, and to build
for the defense of such wide waterways as cannot be properly
defended by the 12-inch guns with the reduced velocity, 14-inch
guns which will give to a 1660-pound projectile a muzzle velocity
of 2150 feet, sufficient to insure perforation of 12-inch armor at a
range of 8700 yards.
The wide channels that exist at the entrances to Long Island
Sound, Chesapeake Bay, Puget Sound, and Manila Bay will require
these 14-inch guns for their defense.
The table following contains data relating to seacoast
guns.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 333
1
oi
<M
A
For Maximum Range.
Gun.
Date of
1
*i
6
B
|
b
Model.
of
I
*j G3
ll
P X
U
III
jfc
3
3
3*^
1
a 10
1*
H
2.24-inch
19JO
1.35
6
0.25
2400
34000
18
7600
25.1
695
3-inch
1903
6.06
15
0.35
3UOO
34000
15
8500
24.1
776
4. 72- inch
Armstrong
10.5
45
1.96
2600
34000
15
10COO
26.4
718
5-inch
1900
26
58
2.75
3000
36000
15
10900
27.0
865
6-inch
1905
42
106
4.6
2900
36000
15
12400
29.4
926
8-inch
1888
80
316
19
2200
38000
12
nooo
23.5
1080
10-inch
1900
224
604
33
2500
38000
12
12300
24.7
1148
12-inch
1900
367
1046
58.3
2500
38000
10
11600
21.5
1269
14-inch
1906
280
1660
58.5
2150
36000
10
11300
20.9
1302
16-inch
1895
612
2400
139.3
2150
38000
10
12800
22.4
1373
Mortar.
10 inch
1890
34
604
33
1150
33000
45
11 SCO
48.1
97-5
12-inch
1890
54
1016
58.3
1150
33000
45
13400
52.7
1055
The bursting charges given in the table are for shell. The bursting charge
for a shot is about one third of the bursting charge for a shell of the same caliber.
Other data concerning the seacoast guns will be found in the
table on page 135.
Seacoast Guns. The seacoast guns and mortars are con-
structed as shown on pages 237 and 238. As the considerations
that limit the weights of the guns of the mobile artillery do not
apply to seacoast guns mounted on fixed platforms, and as with
longer guns higher muzzle velocities may he obtained without
increasing the maximum pressure, the seacoast guns are much
longer, in calibers, than are the field and siege pieces. This may
be noted in the table on page 135.
All seacoast guns up to 4.7 inches in caliber use fixed ammuni-
tion. In guns of greater caliber the projectile is inserted first and
is followed by the powder charge made up in one or more bags.
In general the breech mechanism of the guns using fixed ammuni-
tion is of the type described with the 3-inch field gun. Guns
five and six inches in caliber are provided with the Bofors of simi-
lar mechanism. Larger guns have the cylindrical slotted screw
mechanism described on page 256.
194. Seacoast Gun Mounts. The mounts for the seacoast guns,
commonly called carriages, are distinguished as barbette or dis-
appearing carriages according as they hold the gun always ex-
posed above the parapet or withdraw the gun behind the parapet
334 ORDNANCE AND GUNNERY.
at each round fired. The disappearing carriage has the advantage
of excellent protection for the carnage and gun crew, and, for guns
of the larger calibers, the added advantage of greatly increased
rapidity of fire. The increased rapidity of fire is due to the lower-
ing of the gun to a height convenient for loading, so that the heavy
projectiles and charges of powder need not be lifted in loading.
On high sites the disappearing carriage is not necessary to secure
protection for the gunners, for behind the parapets the gunners
can only be reached by high angle fire from the enemy's ship, and
on account of the excessive strain on the decks that would accom-
pany such fire guns aboard ship are not so mounted that they can
be fired at high angles. Disappearing carriages, emplaced, are
more costly than barbette carriages, but the advantage of the
more rapid fire from the disappearing carriage has determined its
use in this country for all seacoast guns above six inches in caliber,
on high sites as well as on low sites.
Many of the 6-inch guns and all guns below six inches in caliber
are mounted on barbette carriages provided with shields of armor
plate for the protection of the gunners.
Seacoast guns being permanently emplaced the weights of the
gun and the carriage, and simplicity of mechanism in both gun and
carriage, are not matters of .such importance as they are in the
field and siege artillery. We consequently find adapted to the
seacoast guns and carriages every mechanism that will assist in
increasing the rapidity of fire. Fixed ammunition is used in guns
up to 4.7 inches in caliber and its use will probably be extended to
larger calibers. Experiments are being made with mechanisms
for the automatic or semi-automatic opening and closing of the
breech. The mechanisms for elevating the gun and for traversing
the carriage are arranged to be operated from either side of the
carriage, and in the carriages for the larger guns provision is made
for the operation of these mechanisms both by hand and by electric
power. Sights are provided on both sides of the gun, and the
operations of aiming and loading may proceed together.
Finally the magazines and shell rooms in the walls of the
fortifications are so arranged with regard to the gun emplacement,
and so equipped, as to insure a rapid delivery of ammunition to
every gun.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 335
The seacoast gun mounts differ for guns of different caliber.
A description of one mount of each distinct type will follow and
will serve to show the principles that govern in similar construc-
tions.
GENERAL CHARACTERISTICS. In general, the mount consists of
a fixed base bolted to the concrete platform of the emplacement,
and of a gun-supporting superstructure resting on the base and
capable of revolution about some part of it. The superstructure
supports, in addition to the gun, all the recoil controlling parts
and the necessary mechanisms for elevating, traversing, and re-
tracting the gun.
Fastened to the fixed base or to the platform around the base
is an azimuth circle graduated to half degrees, and on the movable
part of the carriage is fixed a pointer, with vernier reading to
minutes, that indicates the azimuth angle made by the gun with a
meridian plane through its center of motion. '
The gun, supported by means of its trunnions on the super-
structure of the carriage or contained in a cradle which is itself so
supported, has movement in elevation about the axis of the trun-
nions. The elevating mechanisms, or the sights, are provided
with graduated scales which usually indicate the range correspond-
ing to each position of the gun.
Protecting guards are provided wherever necessary for the
protection of the gunners against accident, or for the protection
of the mechanisms of the carriage against the entrance of dust or
water.
195. Pedestal Mounts. Seacoast guns up to six inches in
caliber are mounted in barbette on carriages similar in construction
to the carriage shown in Figs. 138 and 139.
A conical pedestal of cast steel, p Fig. 138, is bolted to the
concrete platform. A pivot yoke y free to revolve is seated in the
pedestal. In the upwardly extending arms of the pivot yoke
are seats for the trunnions of the cradle c. The gun is sup-
ported and slides in recoil in the cradle. The weight of all
the revolving parts is supported by a roller bearing r on
a central boss in the base of the pedestal. In the lower rear
portion of the cradle are formed a central recoil cylinder and two
spring cylinders, Fig. 139, similar to the corresponding cyl-
336
ORDNANCE AND GUNNERY.
inders described in the 4.7-inch siege carriage, but much shorter.
As the seacoast gun mounts are firmly bolted to platforms and as
they may be made as strong as
desired without limit as to
weight, these mounts will stand
much higher stresses, without
movement or rupture, than can
be imposed on a wheeled
carriage. We therefore find
that shorter recoil is allowed
to the seacoast guns than to
the lighter field and siege
guns. Thus the recoil of the
5-inch gun on the pedestal
FlG 138 mount is but 13 inches, and
of the 6-inch gun 15 inches,
while the 4.7-inch siege gun recoils 66 inches on its carriage and
the 3-inch field gun 45 inches.
Bolted to the arms of the pivot yoke, on each side, are brack-
ets to which are attached platforms for the gunners. The plat-
forms move with the gun in azimuth and carry the gunners un-
disturbed in the operations of pointing and of manipulating the
breech mechanism.
The carriage may be traversed from either side. The shafts
of the traversing hand-wheels extend downward toward the
pedestal and actuate a horizontal shaft held in bearings on the
pivot yoke. A worm on this shaft acts on a circular worm-wheel
surrounding the top of the pedestal, t Fig. 138.
Elevation is given by the upper hand-wheel, on the left side
only. The elevating gear is supported by a bracket bolted to the
platform bracket and works on an elevating rack attached to the
cradle, the center of the rack being in the axis of the trunnions.
The traversing rack, or worm-wheel, surrounding the upper
part of the pedestal is held to the pedestal by an adjustable friction
band; and a worm-wheel in the elevating gear, contained in the
gear casing fixed to the elevating bracket, Fig. 139, is held between
two adjustable friction disks. These friction devices are so ad-
justed as to enable the gun to be traversed or elevated without
ARTILLERY CF THE UNITED STATES LAND SERVICE 337
slipping of the mechanism, and yet to permit slipping in casenndue
strain is brought on the teeth of the worm-wheels.
A shoulder guard is attached to the cradle on each side of the
gun to protect the gunners from injury during movement of the
piece in recoil.
Open sights and a telescopic sight are seated in brackets on
the cradle on each side of the gun. Dry batteries in two boxes
held in brackets secured to the platform brackets supply electric
power for firing the piece and for lighting the electric lamps of the
sights.
The shield, of hardened armor plate, 4J inches thick, is fast-
ened by two spring supports to the sides of the pivot yoke. The
bolt holes for the shield support are seen in Fig. 139. The shield is
pierced with a port for the gun and with two sight holes, and is
inclined at an angle of 40 degrees with the horizon, see Fig. 201.
196. The Balanced Pillar Mount. A variation of the mount
just described is found in the balanced pillar mount, also called
the masking parapet mount. This mount is constructed for guns
up to 5 inches in caliber. The purpose of this mount is to afford a
means of withdrawing the gun, when not in use, behind the para-
pet and out of the view of the enemy. The gun is withdrawn
behind the parapet only after the firing is completed, and ;not
after each round. Guns mounted on the disappearing carriages
later described are withdrawn from view after each round fired.
The construction of the balanced pillar mount will be under-
stood from Fig. 140. The pintle yoke, with all the parts sup-
ported by it, rests on the top of a long steel cylinder which has
movement up and down in an outer cylinder. The base of the
pintle yoke is circular. It embraces a heavy pintle formed on the
top of the cylinder and rests on conical rollers which move on a
path provided on the cylinder top. Clips attached to the base of
the pivot yoke engage under the flanges of the roller path and
hold the top carriage to the cylinder.
Imbedded in the concrete of the platform is the outer cast iron
cylinder in which the inner cylinder slides up and down. The
weight of the inner cylinder and supported parts is balanced by
lead and iron counterweights strung on a central rod which is
connected to brackets on the inside of the inner cylinder by three
ORDNANCE A^D Gl'XXLKY.
chains. The pulleys over which the chains pass are supported on
posts that pass through holes in the counterweight and rest in
sockets formed in the bottom of the cylinder. For lifting and
lowering the inner cylinder with the gun and top carriage, a ver-
tical toothed rack is fixed to the exterior of the inner cylinder. A
pinion is seated in bearings provided at the top of the outer cyl-
inder and engages in the rack. The pinion is turned by means
of two detachable levers mounted on the ends of the pinion shaft.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 339
By means of a friction clamp the pinion is made to hold the ele-
vated carriage against any sudden downward shock.
The construction permits a vertical movement of the gun and
carriage of about 3J feet.
When firing, the muzzle of the gun projects over the parapet;
and before lowering, the gun is turned parallel to the parapet.
In a similar mount provided for 3-inch guns the outer cylinder
is a double cylinder. The counterweight is annular and occupies
the space between the two cylinders composing the double outer
cylinder. The lifting levers are applied directly to the shaft of
one of the chain pulleys, over which pass the chains that connect
the counterweight to brackets on the outside of the inner cyl-
inder. The brackets move in slots provided in the interior of the
double cylinder.
197. Barbette Carriages for the Larger Guns. Guns from 8
to 12 inches in caliber are mounted in barbette on carnages similar
in construction to that shown in Fig. 141. The carriages are made
FIG. 141.
principally of cast steel, all the larger parts with the exception of
the base ring being of that metal. The cast iron base ring, A
Pig. 142, has formed on it a roller path, b, on which rest the live
conical rollers E of forged steel. The rollers are flanged at their
inner ends and kept at the right distance apart by outside and
inside distance-rings B. The central upwardly extending cylinder
c forms a pintle about which the upper carriage revolves. Em-
340
ORDNANCE AND GUNNERY.
bracing the pintle and resting on the rollers is an upper circular
plate called the racer. Clips attached to the racer, see Fig. 141,
and engaging under the flange of the lower roller path hold the
parts together under the shock of firing. The two cheeks,
Fig. 141, of the chassis are cast in one piece with the racer for the
FIG. 143,
ULI
smaller carriages and separately for the larger carriages, and are
connected together by transoms and strengthened by inner and
outer ribs. A groove or recess is
formed in the upper part of each
cheek, see Fig. 143, for the series of
rollers seen in Fig. 141, on which the
top carriage moves in recoil. The
axles of the rollers are fixed in the
walls of the grooves at such a height
that the tops of the rollers are just
above the top of the chassis.
The top carriage, D Fig. 141 and a Fig. 143, rests on the rollers
and is held to the chassis by means of the clips d, Fig. 143. The
top carriage is cast in one piece. It consists of two side frames
united by a transom a passing under the gun. The side frames
contain the trunnion beds c for the gun trunnions and the two
recoil cylinders b. The piston rods of the recoil cylinders are
held in lugs formed on the front of the chassis.
Elevation from minus 7 to plus 18 degrees is given by means
of the hand-wheel seen near the breech of the gun, Fig. 141, or by
the hand-wheel just under the top carriage. The carriage is
traversed by means of the crank handle in front of the chassis.
Through a worm and worm-wheel the crank actuates a sprocket-
wheel fixed in bearings on the chassis. A chain that encircles the
base ring and that is fast to the base ring at one point passes over
ARTILLERY OF THE UNITED STATES LAND SERVICE. 341
the sprocket-wheel. When the sprocket-wheel is turned it pulls
on the chain and causes the chassis to revolve.
In later carriages the chain is replaced by a circular toothed
rack attached to and surrounding the base ring, and the sprocket-
wheel is replaced by a gear train whose end pinion meshes in the
rack. There is less friction and less lost motion with this construc-
tion.
The shot is hoisted to the breech by means of a crane attached
to the side of the carriage.
When the gun is fired, the gun and top carriage recoil to the
rear on the rollers. The length of recoil is limited by the length
of the recoil cylinder, and on this type of carriage is about five
calibers. The recoil is absorbed partly in lifting the gun and top
carriage up the inclined chassis rails and partly by friction, but
principally by the resistance of the recoil cylinders, as explained in
the chapter on recoil.
On cessation of the recoil the gun returns to battery under the
action of gravity, the inclination of the chassis rails, four degrees,
being greater than the angle of friction.
198. Disappearing Carriages. The importance of the func-
tion of the heavy seacoast guns, the difficulty in the way of quick
or extensive repairs to their mounts, the great cost of the guns
and their carriages, are all considerations that point to the desira-
bility of giving to these guns and carriages the greatest amount
of protection practicable.
The guns are therefore emplaced in the fortifications behind
very thick walls of concrete, which are themselves protected in front
by thick layers of earth. Additional protection is obtained by
mounting the guns on carriages which withdraw the guns from
their exposed firing position above the parapet to a position
behind the parapet and below its crest, where the gun and every
part of the carriage except the sighting platforms and sight stand-
ards are protected from a shot that grazes the crest at an angle of
seven degrees with the horizontal.
An additional and very important advantage gained by the
use of these carriages is the increased rapidity of fire obtained
from the guns mounted upon them. The guns in their lowered
positions are at a convenient level for loading, and the time and
342 ORDNANCE AND GUNNERY.
labor that must be expended in lifting the heavy projectiles and
powder charges to the breech of a gun of the same caliber mounted
in barbette are practically eliminated.
12-inch Disappearing Carriage, Model 1901. The annular base
ring, b Fig. 144, surrounds a well left in the concrete of the em-
placement. The racer a rests on live rollers on the base ring and
is pintled on a cylinder formed by the inner wall of the base ring.
The racer supports the superstructure as in the carriage just de^
scribed. It is held to the base ring by clips c, which engage under
a flange on the inside of the pintle. A working platform, or floor,
of steel plates is fixed to brackets x fastened to the racer, and
moves with the carriage in azimuth.
The forward ends of the chassis cheeks are continued upward,
and on the inside of the cheeks and of the upward extensions are
formed vertical guideways for the crosshead k, from which the
counterweight w is suspended.
GUN LIFTING SYSTEM. The top carriage, similar in construc-
tion to that of the barbette carriage, rests on flanged live rollers
which roll on the rails of the chassis. The rollers are connected
together by side bars in which the axles of the rollers are fixed.
The gun levers / are trunnioned in the trunnion beds of the top
carriage. They support the gun between their upper ends, and
between their lower ends, the crosshead k from which the counter-
weight is suspended.
The crosshead is provided with clips that engage the vertical
guides formed on the inside of the chassis cheeks. Cut on the
front faces of the clips of the crosshead are ratchet teeth in which
pawls p engage to hold the counterweight up after the gun has
recoiled. The pawls are pivoted on the chassis. Levers v pivoted
on the ends of a shaft across the front of the chassis serve as means
for releasing the pawls when it is desired to put the gun in
battery.
The counterweight consists of 102 blocks of lead of varying
size, weighing approximately 164,700 pounds. It is piled on the
bottom plate m, which is suspended by four stout rods from the
crosshead. The preponderance of the counterweight may be ad-
justed, within limits, by the addition or removal of small weights
at the top.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 343
344 ORDNANCE AND GUNNERY.
199. ELEVATING SYSTEM. The gun elevating system consists
of the band n dowelled to the gun and provided with trunnions
that are engaged by the forked ends of the elevating arm h. The
elevating arm has at its lower end a double ended pin which ro-
tates in bearings in the elevating slide s. The elevating slide has a
movement up and down on an inclined guideway machined on the
rear face of the rear transom. Movement is given to the slide by
means of a large axial screw on which the slide moves as a nut
prevented from turning. The screw is turned by gearing on the
shaft e actuated by hand-wheels outside the carriage. In order
to counterbalance the weight of the elevating arm and band, and
to equalize the efforts required in elevating and depressing the
gun, a wire rope passes from the elevating slide over pulleys and
supports a counterbalancing weight g. The gun moves in eleva-
tion from minus 5 degrees to plus 10 degrees.
TRAVERSING SYSTEM. Crank-handles on the traversing shaft
t actuate, through gearing, a vertical shaft carrying at its lower
end a pinion o which works in a circular rack on the inside of the
base ring. In a convenient position on the racer near the azimuth
pointer is placed the lever of a traversing brake, not shown, which
works against the base ring. By its means traversing is retarded
as the carriage approaches any desired azimuth.
RETRACTING SYSTEM. Means are provided to bring the gun
down from its firing position when for any reason it has been ele-
vated into battery and not fired. Detachable crank-handles
mounted on the ends of the shaft r turn two winding drums on
the shaft u inside the chassis. A wire rope y leads from each
drum arour-d a pulley at the rear end of the chassis to the top of
the gun lever, a loop in the end of the rope engaging over the hook
of the lever.
SIGHTING SYSTEM. Elevated platforms are provided on each
side of the carriage. The telescopic sight, see Fig. 145, is mounted
above the left platform on a hollow standard that rises from the
floor of the racer. A vertical rod passing through the standard is
connected at the top to a pivoted arm carrying the sight, and at
the bottom the rod is so geared to the elevating shaft that the
same movement in elevation is given to the sight arm as is given
to the gun. Within reach of the gunner at the sight are two
ARTILLERY OF THE UNITED STATES LAND SERVICE. 345
crank-handles, at the upper ends of vertical shafts, by means of
which the gunner has electric control of the elevating, traversing,
and retracting mechanisms.
Trials are being made of the panoramic sight fitted to disap-
pearing carriages. The vertical tube of the sight is made very
long and the sight is attached to the side of the carriage in such a
position that the eye piece is convenient to the gunner standing
on the racer platform, while the head piece of the sight is above
the parapet.
OPERATION. The operation of the carriage for firing is as
follows. The gun is loaded in its retracted position, Fig. 145,
being held in that position by the pawls p engaged in the notches
on the crosshead k. After the gun is loaded the tripping levers v
are raised, releasing the pawls from the notches in the crosshead.
The counterweight falls and the top carriage moves forward on
its rollers, the last part of its motion being controlled by the
counter-recoil buffers in the recoil cylinders, so that the top carriage
comes to rest without shock on the chassis. By the movement of
the gun levers the gun is lifted to its elevated position above the
parapet.
When the piece is fired the movements are reversed in direc-
tion. The recoil forces the gun to the rear, the top carriage rolls
back on the chassis rails and the counterweight rises vertically
under the restraint of the guides engaged by the crosshead.
In the movement either way the upper end of the gun lever de-
scribes an arc of an ellipse. The path of the muzzle of the gun,
indicated in Fig. 144, is affected by the constraint of the elevating
arm. The ellipse is the most favorable figure to follow in the
movement of a gun on a disappearing carriage. From the firing
position the movement of the gun is at first almost horizontally
backward, and the movement downward occurs principally in the
latter part of the path. Therefore the carriage that moves the
gun in an elliptical path can be brought nearer to the parapet and
thus receive better protection than any other carriage.
The recoil is controlled principally by the recoil cylinders, and
the shock at the cessation of motion is mitigated by two buffers /
which receive the ends of the gun levers. The buffers are com-
posed of steel plates alternating with sheets of balata.
346 ORDNANCE AND GUNNERY.
Balata is a substance that resembles hardened rubber. It has
not as great elasticity as rubber but does not deteriorate as rapidly
under exposure to the weather.
200. Modification of the Recoil System. In the chapter on
recoil it was pointed out that there is a disadvantage in having the
control of the counter recoil in the same hydraulic cylinders that
control the recoil. The adjustment of the counter-recoil system
affects the adjustment of the recoil system.
It will also be observed in the carriage just described that in
the latter part of the movement in recoil the gun is moving
almost vertically downward. Consequently the movement of the
top carriage to the rear is very slight during this part of the recoil,
and the slight movement affords little opportunity for the close
control by the recoil cylinders of the final movement of the gun.
But it is in the last part of the recoil that complete control of the
movement of the gun is most desirable, in order that the gun may
be brought to rest at any desired position for loading, and without
shock to the carriage.
While the movement of the top carriage is least rapid at the
latter end of recoil the counterweight has then its most rapid move-
ment. Therefore a recoil cylinder fixed so as to move with the
counterweight will afford the best control of the final movement
of the gun.
The top carriage has its most rapid movement at the latter
part of the movement of the gun into battery, while the counter-
weight has its least rapid movement at that time. The control
of the counter recoil is therefore best effected through the top
carriage.
By retaining therefore, to act on the top carriage, recoil cyl-
inders adapted for the control of the counter recoil only, and by
adding to the counterweight a cylinder adapted for control of the
recoil, we will obtain the advantage of completely separating the
two systems, thus making them capable of independent adjust-
ment, and the advantage of obtaining from each system the
greatest control of the movement to which it is applied.
201. 6-inch Experimental Disappearing Carriage, Model
1905. The modification of the recoil system as above indicated
has been applied to a 6-inch experimental carriage.
ARiILLERY OF THE UNITED STATES LAND SERVICE. 347
The recoil cylinder is held in the center of the counterweight,
Fig. 146. The lower end of the piston rod is fixed in the lower
member d of a frame whose sides / are bolted to the bottom of the
racer a, as shown in the left and rear views. Grooves cut in the
walls of the recoil cylinder permit the flow of the liquid from one
side of the piston to the other. For the regulation of the extent
of the recoil, and therefore of the height of the gun when in load-
ing position, two diagonal channels pass through the center of the
piston head from one face to the other, and the flow through them
is controlled by a conical valve enclosed in the upper piston rod,
which is hollow. The stem of the valve projects above the end of
the piston rod.
The counter recoil is checked by the short cylinders s mounted
on each chassis rail in front of the top carriage. The pistons of
the counter-recoil cylinders are not provided with apertures for
the flow of the liquid from one side of the piston to the other, but
the flow of the liquid takes place through the pipes p which are led
from both cylinders to a valve v, by which the area of orifice is
controlled and through which the pressure in the two cylinders is
equalized. The pressure in the counter-recoil cylinders does not
exceed 500 pounds per square inch, while the pressure in the recoil
cylinder is 1800 pounds.
As the top carriage comes into battery the front of the carriage
strikes the rear end o of the piston rod and forces the piston through
the cylinder against the liquid resistance and against the action
of springs g mounted on each side of the cylinder. The springs
act on central rods connected to the forward end of the piston,
and as the top carriage moves from battery the springs move the
piston to the rear in position to be acted on by the top carriage
as it comes back into battery.
There are other points of difference between this carriage and
the carriage last described.
The retraction of the gun from the firing position is accom-
plished without the use of wire ropes by the vertical racks 6, shown
in the left and rear views, attached to bars that connect the cross-
head k and the bottom section m of the counterweight. The end
pinions 5 of two trains of gears, one on each side, mesh in the rack,
the gear trains bem actuated by the cranks on the shaft r. The
348
ORDNANCE AND GUNNERY.
Left View.
Rear View.
FIG. 146. 6-inch Experimental Disappearing Carriage, Model 1905.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 349
retracting mechanism is partially shown in the smaller views.
The parts are similarly numbered in all the figures. The mechan-
ism is thrown out of gear when not in use.
The rollers of the top carriage are geared to the top carriage
so that they are compelled to move with the top carriage and
there can be no slipping of the top carriage on the rollers. In
present service carriages this slipping sometimes occurs as the gun
recoils, so that on counter recoil the rollers reach their position in
battery before the top carriage, and prevent the top carriage from
coming fully into battery.
The sight standard is moved to the front of the chassis in order
to get better protection for the gunner, for the sight, and for the
elevating and traversing mechanisms under control of the gunner.
Through the upper hand-wheel e and the shafts and gears also
marked e the gunner has control of the elevating mechanism;
and through another hand-wheel at his right hand, covered by the
wheel e in the figure, and the shafts and gears marked t he con-
trols the traversing mechanism.
Firings from this 6-inch carriage have shown that the gunner
on the sighting platform is so near the muzzle of the gun that he
is injuriously affected by the blast. The sighting platforms will
therefore be removed to the rear end of the carriage, in which
position they will also afford means of access to the breech when
the gun is up.
202. Seacoast Mortars. The thick armored sides of ships of
war protect the ships to a greater or less extent against the direct
fire from high powered guns. The great weight of armor that
would be required for complete deck protection is prohibitive.
The decks of war ships are therefore thin and practically un-
armored, the heaviest protective deck on any battleship being not
more than two inches thick over the flat part. The decks there-
fore offer an attractive target.
As the elevation above sea level of the sites of the guns in most
fortifications is not sufficient to permit direct fire against the
decks, there are provided for use against this target the 12-inch
seacoast mortars, short guns so mounted that they can be fired at
high angles only. The heavy projectiles fired from these guns
carry large bursting charges of high explosive. Descending
350
ORDNANCE AND GUNNERY.
almost vertically on the deck of a ship they easily overcome the
slight resistance offered, and penetrating to the interior of the
ship burst there with enormous destructive effect.
The mortar carriages permit firing only at angles of elevation
between 45 and 70 degrees. With a fixed charge of powder a lim-
ited range only would be covered by fire between these angles.
Charges of several different weights are therefore used in the
mortars. With each charge a certain zone in range may be cov-
ered by the fire, and the charges are so fixed that the range zones
overlap. Any point within the limits of range may thus be
reached by the projectile. The least range with the smallest
charge provided is about a mile and a half. Mortar batteries are
therefore usually erected at not less than this distance from the
channels or anchorages that are under their protection.
The 12-inch Mortar Carriage, Model 1896. The construction
of the 12-inch mortar carriage, model 1896, will be understood
from Fig. 147. The mortar is supported by the upper ends of the
KW//////7/////////W
FIG. 147.
two arms of a saddle d which is hinged on a heavy bolt to the
front of the racer. The arms of the saddle are connected by a
thick web. Extending across under the web is a rocking cap-
piece, c, against which five columns of coiled springs act, sup-
porting the gun in its position in battery and returning it to bat-
tery after recoil.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 351
The lower ends of the springs rest in an iron box trunnioned in
two brackets bolted to the bottom of the racer. The box oscil-
lates as required during the movement of the saddle in recoil and
counter recoil. Holes in the bottom of the box and in the cap-
piece arid saddle web permit the ends of the rods on which the
springs are strung to pass through during the movement.
The recoil cylinders h are trunnioned in bearings fixed to the
top of the racer. Bolted to the top of each cylinder is a frame /
which serves as a guide for the crosshead o at the upper end of
the piston rod. The crosshead embraces the stout pin r which
extends outward from the trunnion of the mortar and communi-
cates the motion of the piece in recoil to the piston rod.
The provision for the flow of liquid in the
recoil cylinder from one side of the piston to
the other differs in this carriage from that
described in other carriages. A small cyl-
inder, A Fig. 148, is formed outside the re-
coil cylinder proper, H. Holes a, bored
through the dividing wall, form passages
through which the oil may pass from the
front of the piston to the rear. The piston
head in its movement closes the holes suc-
cessively. Thus as the velocity of recoil de-
creases the area open to the flow of the liquid
is reduced. The area of aperture is also
regulated by screw throttling plugs b that
are seated in the outer wall of the small cyl-
inder. These plugs have stems of different
diameters, and are used to partially or
wholly close any of the passages in the
proper regulation of the recoil. The recoil
cylinders on each side of the carriage are con-
nected by the equalizing pipe p.
The counter recoil is checked and the gun
brought into battery without shock by the FlG 14g
counter-recoil buffer s, an annular projection
formed on the cylinder head surrounding the piston rod. The buffer
enters, with a small clearance, an annular cavity in the head of
352
ORDNANCE AND GUNNERY.
the piston, and the liquid in the cavity escapes slowly through the
clearance. As an added precaution against shock when the gun
returns to battery, buffer stops composed of alternate layers of
balata and steel plates are held between the crosshead guides of
the frame /, Fig. 147, under the cap.
The gun is elevated by the mechanism shown mounted on the
saddle, Fig. 147, and traversed by means of the crank shaft and
mechanism supported in a vertical stand on the racer. A pinion
p on the end of a vertical shaft engages in a circular rack bolted
to the inner surface of the base ring.
The movement of the saddle in recoil causes the gun to rotate
on its trunnions. To prevent excessive rotation of the gun and
excessive strain on the elevating mechanism, a friction collar is
provided in the large gear wheel of the elevating mechanism.
The collar slips in the gear wheel when the strain is ex-
cessive.
For determining elevation, a quadrant, similar to the gun-
ner's quadrant described in the chapter on sights, is permanently
attached to a seat prepared on the right rim base of the mortar.
FIG. 149.
203. The 12-inch Mortar Carriage, Model 1891. The 12-inch
mortar carriage, model 1891, on which many 12-inch mortars are
mounted in our fortifications, is shown in Figs. 149 and 150.
ARTILLERY OF THE UNITED STATES LAND SERVICE. 353
-r
The spring cyl'nders E are formed in the vertical cheeks bolted
to the racer. Inside the cheeks are inclined guideways for sliding
crossheads G. The crossheads receive the
trunnions of the gun. The pistons h of the
recoil cylinders project downward from the
crossheads and enter the recoil cylinders H
attached to the lower parts of the spring cyl-
inders. The recoil cylinders are of the type
shown in Fig. 148. The crosshead G has at its
upper end an arm, r Fig. 150, which projects
outwardly into the spring cylinder and carries
at its outer end the adjusting screw k, which
rests on top of the column of springs. The
springs are compressed when the gun recoils,
and return the gun to battery on the cessation
of recoil. By means of the adjusting screw k
the height of the trunnion carriages G may be
adjusted to bring the mortar to the proper
height for loading.
The hand-wheel g, Fig. 149, works the shot
hoist a, by means of which the shot is lifted to
the breech of the gun for loading.
204. Subcaliber Tubes. For the purpose of
enabling troops to become familiar with the
operation of the guns and carriages by actual
firing, yet without the expense attendant upon
the use of the regular ammunition, there are provided for use
inside the various service guns smaller guns or gun barrels called
subcaliber tubes. These are seated in the bores of the larger guns
in such position that the breech of the subcaliber tube is just in
front of the breech block of the gun when closed. The sub-
caliber tube is loaded with fixed ammunition arranged to be fired
by the firing mechanism of the larger gun. Three calibers of sub-
caliber tubes are provided: one of 0.30-inch caliber, using the
small arm cartridge, for guns that use fixed ammunition; one of
1.475-inch caliber, using 1-pounder ammunition, for use in all
guns 5 inches or more in caliber; and one of 75 mm. (2.95 inches)
caliber, using 18-pounder ammunition, for use in the 12-inch mortar.
FIG. 150.
354
ORDNANCE AND GUNNERY.
For those guns that use fixed ammunition the 30-caliber sub-
caliber tube, a 30-caliber rifle barrel, is fixed in a metal mounting
that has the shape and dimensions of the complete cartridge used
in the piece. Fig. 151 shows the subcaliber tube for the 3-inch
rifle.
FIG. 151.
The 30-caliber small arm cartridge is inserted in the barrel b
and is fired by the percussion firing mechanism of the piece. It
is extracted, far enough to be grasped by the hand, by the ex-
tractor, two bowed springs s which are under compression when
the small arm cartridge is forced to its seat by the breech block
of the gun. A special primer is used in the small arm cartridge,
strong enough to withstand without puncture the heavy blow of
the firing pin of the gun.
The head of the subcaliber cartridge is permitted longitudinal
movement in the body in order to allow for expansion of the 30-
caliber barrel in firing.
FIG. 152.
The 1-pounder tube is provided with different fittings to adapt
it to the particular gun in which it is to be used. It is fitted in
the gun in the manner shown in Fig. 152, which represents the
75 mm. subcaliber tube in the 12-inch mortar.
The 75 mm. tube is a gun similar to the mountain gun, without
ARTILLERY OF THE UNITED STATES LAND SERVICE. 355
its breech mechanism. The cartridges for the mountain gun are
used in it.
The wheel-shaped fittings, called adapters, are screwed on the
gun. The front adapter fits against the centering slope in the
bore for the band of the projectile. The outer rim of the rear
adapter is cut through at the top and the rim is expanded against
the sides of the bore by the wedge w, which is forced between the
parts of the rim by means of the screw seated in one of them.
The tube is prevented from turning in the adapters by the clamp
screw c.
The firing mechanism of the guns in which the two larger
subcaliber tubes are used is not of the percussion type. The
cannon cartridges used in these two tubes are therefore provided
with the 110-grain igniting primer, described in the chapter on
primers, in place of the usual percussion primer. The igniting
primer in the cartridge is ignited by the flame from the ordinary
primer seated in the rear end of the breech mechanism of the
gun.
Drill Cartridges, Projectiles, and Powder Charges. For ordi-
nary use at drill, without firing, dummy cartridges are provided
for guns that use fixed ammunition, and dummy projectiles and
powder charges for other guns. The dummies have the dimen-
sions and weights of the parts they represent.
The drill cartridge for guns using fixed ammunition are hollow
bronze castings, Fig. 153, of the shape of the service cartridge
FIG. 153.
loaded with shrapnel. For the instruction of cannoneers in fuse
setting there is fitted at the head of the cartridge a movable ring
graduated in the same manner as the time scale on the combina-
tion time and percussion fuse.
Drill projectiles, for guns separately loaded, are of the con-
struction shown in Fig. 154. A bronze band, &, is inset at the
bourrelet to prevent wearing of the rifling in the gun by frequent
356
ORDNANCE AND GUNNERY.
insertion of the projectile. The rotating band r, made in two or
more sections with spaces between, is pressed to the rear on a
sloping seat by springs s. When the projectile is rammed with
force into the gun the band is likely to stick in its seat and thus
to resist efforts to withdraw the projectile. The method of at-
tachment of the band is for the purpose of affording a means of
readily overcoming this resistance. The extractor, a hook on the
FIG. 154.
end of a pole ; is engaged over the inner lip I. A pull on the pole
will, if the band is stuck, first move the remainder of the projectile
to the rear until it strikes and dislodges the band.
The dummy powder charge, Fig. 155, circular in section, is
FIG. 155.
made up of a core of metal surrounded by disks of wood, the
whole covered with canvas. The parts are assembled by means
of a central bolt. An inner lip / formed in the hollow metal base
piece is engaged by the hook of the extractor.
CHAPTER IX.
EXTERIOR BALLISTICS.
205. Definitions. Exterior Ballistics treats of the motion of a
projectile after it has left the piece.
In the discussions the dimensions of the gun are considered
negligible in comparison with the trajectory.
The Trajectory, bdf, Fig. 156, is the curve described by the
center of gravity of the projectile in its movement.
FIG. 156.
The Range, bf, is the distance from the muzzle of the gun to
the target.
The Line of Sight, abf, is the straight line passing through
the sights and the point aimed at.
The Line of Departure, be, is the prolongation of the axis of
the bore at the instant the projectile leaves the gun.
The Plane of Fire, or Plane of Departure, is the vertical plane
through the line of departure.
357
358 ORDNANCE AND GUNNERY.
The Angle of Position, s, is the angle made by the line of sight
with the horizontal.
The Angle of Departure, <j>, is the angle made by the line of
departure with the line of sight.
The Quadrant Angle of Departure, <j>+ e, is the angle made by
the line of departure with the horizontal.
The Angle of Elevation, <', is the angle between the line of sight
and the axis of the piece when the gun is aimed.
The Jump is the angle / through which the axis of the piece
moves while the projectile is passing through the bore. The
movement of the axis is due to the elasticity of the parts of the
carriage, to the play in the trunnion beds and between parts of the
carriage, and in some cases to the action of the elevating device as
the gun recoils. The jump must be determined by experiment
for the individual piece in its particular mounting. It usually
increases the angle of elevation so that the angle of departure is
greater than that angle.
The Point of Fall, f, or Point of Impact, is the point at which
the projectile strikes.
The Angle of Fall, w, is the angle made by the tangent to the
trajectory with the line of sight at the point of fall.
The Striking Angle, w, is the angle made by the tangent to the
trajectory with the horizontal at the point of fall.
Initial Velocity is the velocity of the projectile at the muzzle.
Remaining Velocity is the velocity of the projectile at any point
of the trajectory.
Drift, kf, is the departure of the projectile from the plane of
fire, due to the resistance of the air and the rotation of the pro-
jectile.
Direct Fire is with high velocities, and angles of elevation not
exceeding 20 degrees.
Curved Fire is with low velocities, and angles of elevation not
exceeding 30 degrees.
High Angle Fire is with angles of elevation exceeding 30
degrees.
206. The Motion of an Oblong Projectile. The projectile
as it issues from the muzzle of the gun has impressed upon it a
motion of translation and a motion of rotation about its longer
EXTERIOR BALLISTICS. 359
axis. The guns of our service are rifled with a right handed twist,
and the rotation of the projectile is therefore from left to right
when regarded from the rear. After leaving the piece the pro-
jectile is a free body acted upon by two extraneous forces, gravity
and the resistance of the air.
When the projectile first issues from the piece, its longer axis
is tangent to the trajectory. The resistance of the air acts along
this tangent, and is at first directly opposed to the motion of
translation of the projectile.
The longer axis of the projectile being a stable axis of rotation
tends to remain parallel to itself during the passage of the pro-
jectile through the air, but the tangent to the trajectory changes
its inclination, owing to the action of gravity. The resistance of
the air acting always in the direction of the tangent, thus becomes
inclined to the longer axis of the projectile, and in modern pro-
jectiles its resultant intersects the longer axis at a point in front
of the center of gravity.
In Fig. 157, G being the center of gravity, and R the resultant
FIG. 157.
resistance of the air, this resultant acts with a lever arm Z, and
tends to rotate the projectile about a shorter axis through G per-
pendicular to the plane of fire.
The resultant effect of the resistance of the air on the rotating
projectile is a precessional movement of the point of the projectile
to the right of the plane of fire. After the initial displacement of
the point to the right the direction of the resultant resistance
changes slightly to the left with respect to the axis of the pro-
jectile, and produces a corresponding change in the direction of the
precession, which diverts the point of the projectile slightly down-
ward.
If the flight of the projectile were continued long enough
the point would describe a curve around the tangent to the
360 ORDNANCE AND GUNNERY.
trajectory; but actually the flight of the projectile is never
long enough to permit more than a small part of this motion
to occur.
The precession of the point is greater as the initial energy of
rotation is less. It is therefore necessary to give to the projectile
sufficient energy of rotation to make the divergence of the point
small. Otherwise the precessional effect may be sufficient to cause
the projectile to tumble.
When the point of the projectile leaves the plane of fire the
side of the projectile is presented obliquely to the action of the
resistance of the air, and a pressure is produced by which the pro-
jectile is forced bodily to the right out of the plane of fire. It
is to this movement that the greater part of the deviation of
the projectile is due.
DRIFT. The departure of the projectile from the plane of
fire, due to the causes above considered, is called drift.
207. Form of Trajectory. It may be shown analytically that
the drift of the projectile increases more rapidly than the range.
The trajectory is therefore a curve of double curvature, convex
to the plane of fire.
The trajectory ordinarily considered is the projection of the
actual curve upon the vertical plane of fire. This projection so
nearly agrees with the actual trajectory that the results obtained
are practically correct; and the advantage of considering it,
instead of the actual curve, is that we need consider only that
component of the resistance of the air which acts along the longer
axis of the projectile and which is directly opposed to the motion
of translation.
Determination of the Resistance of the Air. The relation
between the velocity of a projectile and the resistance opposed
to its motion by the air has been the subject of numerous experi-
ments.
In the usual method of determining this relation the velocity
of the projectile is measured at two points in the trajectory.
The points are selected at such a distance apart that the path
of the projectile between them may be considered a right line,
and the action of gravity may be neglected. The resistance of
the air is then regarded as the only force acting to retard the
EXTERIOR BALLISTICS. 361
projectile, arid is considered as constant over the path between
the two points.
The loss of energy in the projectile, due to the loss of velocity,
is the measure of the effect of the resistance of the air, and is
equal to the product of the resistance into the path. The resist-
ance thus obtained is the mean resistance, and corresponds to
the mean of the two measured velocities.
EARLY EXPERIMENTS. The first experiments were those of
Robins in 1742. For the measurement of velocities he used the
ballistic pendulum. His conclusions were, that up to a velocity
of 1100 foot seconds the resistance is proportional to the square
of the velocity; beyond 1100 f. s. the resistance is nearly three
times as great as if calculated by the law of the lower velocities.
Hutton in 1790, with the improved ballistic pendulum, made
numerous experiments with large projectiles. His conclusions
were that the resistance increases more rapidly than the square
of the velocity for low velocities, and for higher velocities that
it varies nearly as the square.
General Didion made a series of experiments at Metz in 1840
with spherical projectiles of varying weights. His conclusions
were that the resistance varied as an expression of the general
form a(v 2 + bv 3 ), a and b being constants. This formula held for
low velocities only.
Experiments were again made at Metz in 1857. Electro-ballis-
tic instruments were now used for the measurement of velocities.
The conclusions from these experiments were that the resistance
varies as the cube of the velocity. Experiments by Prof. Helie
at Gavre in 1861 gave practically the same results.
The experiments above described were made principally with
spherical projectiles. The difference in the nature of the resistance
experienced by oblong and spherical projectiles, together with the
difference in the velocities, then and later, may account for the
wide difference in the results obtained from these and from later
experiments.
LATER EXPERIMENTS. The Rev. Francis Bashforth made
exhaustive experiments in England, in 1865 and again in 1880,
using comparatively modern projectiles and accurate ballistic
instruments. His conclusions were, that for velocities between
362 ORDNANCE AND GUNNERY.
900 and 1100 f. s. the resistance varied as the sixth power of
the velocity; between 1100 and 1350 f. s., as the cube of the
velocity; and above 1350 f. s., as the square of the velocity.
The most recent experiments are those made by Krupp in
1881 with modern guns, projectiles, and velocities. The results of
these experiments were used by General Mayevski in the deduc-
tion of the formulas for the resistance of the air which are now
generally used.
CONCLUSIONS FROM THE EXPERIMENTS. The experiments have
shown that the resistance of the air varies with the form of the
projectile, with its area of cross section, with the velocity of the
projectile, and with the density of the air. Considering the form
of the projectile the resistance is affected principally by the shape
of the head, and by the configuration at the junction of the head
and body. The ogival head encounters less resistance than any
other form of head. The resistance was found to increase directly
with the area of cross section of the projectile, and directly with
the density of the air.
208. Mayevski's Formulas for Resistance of the Air. In
expressing the relation between the resistance of the air and the
velocity of the projectile, General Mayevski placed the retarda-
tion, as determined in Krupp 's experiments, equal to an expres-
sion which involves, together with an unknown power of the
velocity, quantities whose values are dependent on the weight,
form, and cross section of the projectile, and on the density of
the air.
Calling p the resistance of the air,
w the weight of the projectile in pounds,
g the acceleration of gravity,
the retardation is pg/w
Representing by R the retardation of the projectile, make
R = pg/w = vA/C (1)
in which A is a constant and n some power of the velocity, both
to be determined from the experiments.
THE BALLISTIC COEFFICIENT, C. The quantity C in the equa-
tion was given a value
r = ^
9 cd*
EXTERIOR BALLISTICS.
363
in which di is the standard density of the air,
d the density at the time of the experiment,
c the coefficient of form,
d the diameter of the projectile in inches,
w the weight of the projectile in pounds.
By the introduction of this coefficient into the value of the retarda-
tion, the effect of variations in weight, form, and cross section
of the projectile, and in the density of the air, may be considered.
The coefficient of form c was taken as unity for the standard
projectiles. For projectiles of a form that offers greater resistance
the value of c will be greater than unity. Examination of equa-
tion (1) shows that as c increases, and C decreases, the retardation
is increased; a result also obtained by increase in d or d, that is
in the cross section of the projectile or in the density of the air;
while by an increase in w, C is increased and the retardation is
diminished. The coefficient C is therefore the measure of the bal-
listic efficiency of the projectile.
The value of c for all projectiles in our service is usually taken
as unity.
The density of the air is a function of the temperature and
of the atmospheric pressure. The values of di/d for different
atmospheric pressures and temperatures are found in Table VI
of the ballistic tables.
Mayevski determined, from Krupp's experiments, values for n
and A for different velocities as follows.
Velocities, f. s.
n
log A
Velocities, f . s.
n
log 4
Above 2600
1.55
3.6090480
1230 to 970
5
14.8018712
2600 to 1800
1.7
3.09ol978
970 to 790
3
8.7734430
1800 to 1370
2
4.1192596
Below 790
2
5.6698914
1370 to 1230
3
8.9809023
209. Trajectory in Air. Ballistic Formulas. In the deduc-
tion of the ballistic formulas the trajectory is considered as a
plane curve. The line of sight is taken as horizontal. The angle
of elevation is taken as the angle of departure, and the striking
angle becomes the angle of fall.
The trajectory so considered is called The Horizontal Trajec-
tory.
364 ORDNANCE AND GUNNERY.
Considering the motion of translation only, and that the
resistance of the air is directly opposed to this motion, let, Fig. 158,
R be the retardation due to the resistance of the air, its
value being given by equation (1);
V, the initial velocity;
v, the velocity at any point of the trajectory whose co-
ordinates are x and y,
Vi, the component of v in the direction of x;
<f>, the angle made with the horizontal by the tangent to the
trajectory at the origin, or the angle of departure;
6, the value of <j) for any other point of the trajectory;
w, the angle of fall;
x and T/, the co-ordinates of any point of the trajectory, in feet;
X, the whole range, in feet.
EQUATIONS OF MOTION. The only forces acting on the pro-
jectile after it leaves the piece are the resistance of the air and
gravity.
The resistance of the air is directly opposed to the motion of the
projectile, and continually retards it. Gravity retards the pro-
jectile in the ascending portion of the trajectory, while it acceler-
ates it in the descending portion.
Considering the ascending portion of the trajectory, the velocity
in the direction of x is
v cos 6 = vi = dx/dt dx = vidt (2 )
The velocity in the direction of y is
v sin 6 = Vi tan 6 = dy/dt dy = Vi tan 6 dt (3)
The retardation in the direction of y is therefore
- d(vi tan d)/dt = gRsm6 (4)
EXTERIOR BALLISTICS. 365
Since gravity has no component in a horizontal direction, the
retardation in the direction of x is
- dvi /dt = # cos dt=- dvi /R cos 6 (5)
Substituting this value of dt in (2), (3), and (4), and performing
the differentiation indicated in (4), d tan 6 being dd/cos 2 6, we
obtain
dx = - Vidvi/R cos (6)
= v 1 tan 6 dvi /R cos 6 (7)
(8)
The four equations (5) to (8) are the differential equations of
motion of the projectile, and if they could be integrated directly
they would give the values of t y x, y, and 6 for any point of the
trajectory. But as they are expressed in terms of R, v, and 6,
three independent variables, the direct integration is impossible.
The value of R is given by Mayevski's formulas, R = Av n /C }
n representing the exponent of v for any particular velocity. Sub-
stituting this value of R in (6), the equation may, by means of
the relation v cosO = Vi, be put in the form
dx= -C cos n - 1 6dv l /Av 1 n - 1 (9)
The second member would be an exact integral were it not
for the factor cos n ~ 1 d. In direct fire cos 6 differs but little from
unity, and it might be taken as unity without appreciable error.
cos n ~ l O would then be unity and the expression w r ould be integrable.
A closer approximation, however, as shown by Siacci, results
from making
Making this substitution equation (9) may be brought by
reduction, see foot note, to the form
C
A Oi sec -i
cos n ~(>=
c& is constant, therefore sec (j>dv i = d(Vi sec ok).
366
Make
ORDNANCE AND GUNNERY.
Vi sec <j> = v cos 0/cos (j> = u
V i sec = V cos (/cos </> = V
Making these substitutions in equation (10) and integrating
between the limits u and V we obtain
T
2)A\u-* ' V n ~
(11)
And similarly equations (5) and (8) may be brought to the forms
C
(nl)A cos
_l L_l
u- L F- 1 J
tan <> tan ^=
nA cos 2 Lw n
nA cos^
210. To simplify equations (11) to (13), make
Q
(12)
(13)
I
1
itt + Q
: i Qf
(n-l)Au n - 1
9n
- + Q"
(14)
nAu"
The reason for the addition of the constants will appear.
Making these substitutions, equations (11) to (13) become
x = C{S(u)-S(V)} (15)
C
t =
cos
\T(u)-T(V)\
C
(16)
(17)
tan = tan <f>-^ cQg2 ,\I(u)-I(V)}
Making in the last equation tan = dy/dx, and making
4(*)-./^r (14')
j\J U n
EXTERIOR BALLISTICS. 367
i
equation (17) may be brought to form, see foot note,
Equations (15) to (18), with the equations
cos 6
U = V cosl> ' ^
and
/?, in
(20)
are the fundamental equations of Exterior Ballistics, and con-
stitute the method of Siacci, an eminent Italian ballistician. The
essence of the method lies in the use of u, called by Siacci the
pseudo velocity, for v, the actual velocity.
In all problems of direct fire, since the difference between (f>
and 6 is not great, u may be used for v with sufficient accuracy.
In problems in curved and high angle fire, and in direct fire when
greater accuracy is desired, we pass from the value of u to the
value of v by means of equation (19). It will be seen from this
equation that, since ucos <f> = v cos 0, u is the component of v
parallel to the line of departure.
The Ballistic Coefficient. The ballistic coefficient, like the
force coefficient in the interior ballistic formulas, affords a con-
venient means of introducing into the exterior ballistic formulas
any correction necessary to make the formulas applicable to con-
ditions differing from the conditions for which the formulas were
deduced.
From (17),
dy=tan <f>dx- -^{I( u )dx-I(V)dx\)
From (10), and v, sec <j>=u, dx=Cdu/Au n ~ 1
Substitute this value in the second term of the second member of (17a).
Integrate the equation between the limits u and V with the help of (14'X and
divide through by x.
x 2 cos- (j) (
Substitute for C/x its value from (15).
368 ORDNANCE AND GUNNERY.
For general use with the formulas of exterior ballistics
Mayevski's value for C, page 362, is changed by the introduction
of two quantities, / and ft, so that the value of the ballistic
coefficient takes the form written in equation (20).
/ is called the altitude factor, and brings into consideration the
diminution in the density of the air as the altitude of the tra-
jectory increases. The value of / is greater than unity and de-
pends upon the mean altitude of the trajectory, which is taken
as two-thirds of the maximum altitude.
ft is an integrating factor, and corrects for the error due to cer-
tain assumptions made in deducing the primary equations, when
these equations are applied to a trajectory whose curvature is
considerable, ft is approximately unity in all problems of direct
fire. The product ftc is called the coefficient of reduction.
When in the statements of ballistic problems the data required
to determine $i/d, ft or c is not given, the value unity is assumed
for the factor, f is also assumed as unity unless a correction for
altitude is desired. When all these factors are unity the ballistic
coefficient becomes
C=w/d 2
2ii. The Functions. The functional expressions inequations
(15) to (18) are called: S(u) the space function, T(u) the time
function, I(u) the inclination function, and A(u) the altitude
function. Their values are given by the equations (14) and (14').
The values of these functions for values of u from 3600 to 100
foot seconds have been calculated, and form Table I of the Bal-
listic Tables.
Since V is a particular value of u the values of the functions
of V are included in the table as values of the functions of u.
For example, to find the value of S(V), V being given, enter
the table with the value of V as a value of u and take out the
corresponding value of S(u).
The quantities Q, ()', and Q", in the values of the functions,
equations (14), are arbitrary constants ; and the purpose of includ-
ing them is to provide a means for avoiding abrupt changes in
the tables at those points where in Mayevski's formulas the values
of A and n change.
EXTERIOR BALLISTICS. 369
CALCULATION OF THE FUNCTIONS. The method of employing
the constants in forming the tables is best shown by an example.
The value of the S function is, equation (14),
For va'ues of v greater than 2600 f. s., we have from May-
evski's formulas, n = 1.55. Therefore for a velocity greater than
2600 f . s.
In order to avoid the use of large numbers Table I of the lat-
est ballistic tables, published in 1900, is so constructed that the
S, A, and T functions reduce to zero for ^ = 3600. I(u) reduces
to. zero for u= <x>. We have then for S(u), when w
and therefore
For any other value of u down to 2600
S(u) = - L (360(f 45 - w- 45 ) =K-KW M (21)
For velocities between 2600 and 1800 f. s., n = l.7 f and
Qz must have such a value as to make the value of S(u) for
w = 2600 the same as the value determined from equation (21)
with this value of u. Therefore
0.45
from which the value of Q 2 can be determined.
The same process is followed at each change in the values of
n and A.
37U ORDNANCE AND GUNNERY.
When n = 2 equation (11) becomes indeterminate and the
values of the functions cannot be determined as above; but
making n = 2 in equation (10) and integrating we obtain
C
S(u) becomes in this case
INTERPOLATION IN TABLE I. This is effected by the ordinary
rules of proportional parts. The difference between successive
values of u varies from unity in one part of the table to 2, 5, and
10 in other parts. This difference must be carefully noted in
interpolating.
212. Formulas for the Whole Range. Designate the whole
range, Fig. 158, by X, the corresponding time of flight by T, the
angle of fall (considered positive for convenience) by a>, and use the
subscript u to designate the values of u and v at the point of
fall.
At the point of fall y = Q and 0= &>; and after combining
equations (17) and (18) to eliminate 7(7) from (17), equations (15)
to (19) become, respectively,
(22)
(23)
C f T A(u u )-A(V)}
u u = v w cos co/cos (j> (26)
At the summit of the trajectory = 0. Using the subscript,,
to designate the summit, equations (17) and (19) become, after
reduction,
(27)
(28)
EXTERIOR BALLISTICS. 371
Combining (27) and (25) we have
o ~S(uJ-S(V)
Therefore (24) and (25) become
tan o, = !/(*O-/W{ (30)
(31)
213. The Ballistic Elements. The quantities C, u, V, <f>,
0, cu, T, and X in the previous equations are called the ballistic
elements. When referring to the end of the range they are
written as capitals, or with the subscript w . For any other point
of the trajectory they are written as small letters, with suitable
subscript if desired. The subscript always refers to the summit
of the trajectory. The equations, by reason of Siacci's assump-
tion for the value of cos n ~ 1 0, express the relations existing between
these elements in direct fire only.
When three or more of the elements are given the others may
be determined.
The Rigidity of the Trajectory. According to the principle
of the rigidity of the trajectory, which is mathematically demon-
strated, the relations existing between the trajectory and the
chord representing the range are sensibly the same whether the
chord be horizontal or inclined to the horizon, provided that the
quadrant angle of departure and the angle of position are small
or that the difference between them is small. That is to say
that, considering <+e and as small, in Fig. 156, if the trajec-
tory bdf and its chord bf were revolved about the point b until bf
were horizontal, the relation of the trajectory to bf would not
change. A trajectory calculated for a horizontal range equal to bf
would then answer as the trajectory for the actual inclined range &/.
Therefore when the quadrant angle of departure, <f>+ e, is
small we may consider bf, or any other chord of the trajectory,
as a horizontal range; and we may apply to the trajectory sub-
tended by the chord the formulas deduced for a horizontal range.
If however the quadrant angle of departure is large, the prin-
372 ORDNANCE AND GUNNERY.
ciple of the rigidity of the trajectory applies only when the angle
of position is also large, that is when (j>+e does not differ much
from e. Therefore in any complete high angle trajectory for a
horizontal range the principle of the rigidity of the trajectory
applies only to a part of the trajectory near the origin. This
part may be treated as a horizontal range whose angle of departure
is the difference between the quadrant angle of departure of the
horizontal trajectory and the angle of position.
When the difference between (/> + e and e is small, (j> must
be small. It is therefore evident that, in direct fire, the principle
of the rigidity of the trajectory applies whenever the angle of
departure is small.
This principle enables us to use the elements calculated for a
horizontal range when firing at objects situated above or below
the level of the gun.
214. Use of the Formulas. The method of using the formulas
may best be shown by considering a problem.
Problem i. What is the time of flight of a 3-inch projectile
weighing 15 Ibs., for a range of 2000 yards; muzzle velocity, 1700
f. s.?
The given data are C = 15/9, 7=1700, and Z = 6000, the
range being always taken in feet. T is required.
These formulas apply:
\T(u.)-T(V)\ (23)
COS .
(25)
X = C\S(uJ-S(V)} (22)
Take the T 7 , S, A, and / functions of V from Table I.
Determine S(u v ) from (22).
Find u a from Table I, and take from the Table T(u a ) and
Find $ from (25).
Find T, required, from (23). Ans. 7* = 4.48 seconds.
215. Secondary Functions. The most important problems in
gunnery may be solved by means of equations (22) to (31) and
EXTERIOR BALLISTICS. 373
ballistic Table I, but some of the solutions are indirect and ten-
tative and therefore very laborious. The processes of solution
have been greatly abbreviated and the labor greatly reduced
by the introduction of secondary functions, whose values, for all
the requirements of modern gunnery, have been calculated and
collected in Table II of the ballistic tables.
The development of the science of exterior ballistics to its
present accuracy and comparative simplicity is principally due
to Colonel James M. Ingalls, U. S. Army, whose interior ballistics
are set forth in Chapter III.
From equation (15) we have
S(u)=x/C+S(V)
and substituting the values of S(u) and S(V), see (14),
(n-2)Au n ~ 2 C T (n-2)AV n ~ 2
From this equation it is apparent that the value of the pseudo
velocity u, at any point, is a function of x/C and V only, and is
independent of the height of the point in the trajectory.
Make
z = x/C Z=X/C
It will be seen in equations (16), (17), and (18) that t, 6, and y
are functions of u and therefore also functions of z and of V.
The secondary functions, whose values are here given, are all
functions of Z and V, and are tabulated with Z and V as arguments.
A(u)-A(V)
A =
B
T' = T(u)-T(V)
S(u)-S(V)
A(u)-A(V)
S(u)-S(V)
(32)
The subscripts are dropped in these expressions since they
only serve to indicate particular values of u, while the table
contains the values of A, B } etc., for all the values of u.
374 ORDNANCE AND GUNNERY.
The table also contains, in the column u, the values of u for
all values of Z and F.
Equations (23), (24), and (25) may now be put, by reduction,
into the following exceedingly simple forms.
T = CT'/cos<f> (33)
sin 2 < = AC (34)
tan & = BC/2 cos 2 <j> = E' tan </> (35)
Equations (17) and (18) may also be put in the forms
(A-a') (36)
y = ^ (A . a ) (37)
In these equations a and a' are the values of A and A' corre-
sponding to z = x/C for the particular point of the trajectory con-
sidered, while A and A' are the values corresponding to Z = X/C
for the whole range.
216. At the summit tan 6 reduces to zero; and we obtain from
equation (36), writing a ' for a! at the summit,
o' = A (38)
Equation (37) then becomes
(38')
From the third equation (32) we have for the summit
6o = o / CLQ. With this relation and the relation z = x /C, and
making
equation (38') reduces to the form
yo = a "C tan < (39)
t/o representing the maximum ordinate.
To obtain ao" for use in this equation we find in Table II,
in the A' column, the value of A as determined for the whole
EXTERIOR BALLISTICS. 375
range. With this value as A' and the given value of V we find
GO" in the A" column.
Write Z=X/C (40)
v = u cos </cos 6 (41)
[3.79239] CPD'/cos* < (seacoast guns)
(43)
[3.92428] C 2 D'/cos 3 < (field guns)
which is Mayevski's formula for drift, abbreviated for tabulation
by Colonel Ingalls. The values of D' are found in Table II.
We have in the equations (33) to (43) the principal formulas
required for the solution of nearly all the problems of direct fire.
While the formulas apply strictly to direct fire only, where the
values of <j> and 6 are such as to permit the use of Siacci's value
of cos n ~ l d without appreciable error, they give sufficiently accu-
rate results for curved fire, and they are used for curved fire as
well.
They are made applicable to high angle fire by giving to the
coefficient c in the ballistic coefficient such values as will make the
results obtained from the formulas agree with the results obtained
in actual firings. For the low velocities used in mortars and
howitzers the formulas are simplified, as will later be shown.
Ballistic Tables. The Ballistic Tables, which are issued by
the War Department, consist of three volumes, entitled: Ar-
tillery Circular M, Series of 1893 (printed in 1900), Supplement to
Artillery Circular M (1903), and Supplement No. 2 to Artillery Cir-
cular M (1904). The supplements extend Tables II, IV, and V of
Artillery Circular M.
In addition there has appeared a simplification of Table IV in
the Journal of the United States Artillery, number for January and
February, 1905.
Artillery Notes, No. %5, issued by the War Department, 1905,
contains a corrected table to replace Table VI of Artillery Circular
M, the latter table having been found to be based on incorrect data.
The ballistic formulas are found assembled on page VIII of the
376 ORDNANCE AND GUNNERY.
first book of tables, Artillery Circular M, so that the books of
tables contain all that is needed for the solution of most of the
problems of gunnery.
Under the heading Formulas to be used ivith Table II, on page
VIII of Artillery Circular M, appears the formula
which is another form of
This formula, which is sometimes convenient to use, requires the
use of Table I.
To understand the additional formulas under this heading on
page VIII of the ballistic tables it is only necessary to know that
e represents the angle of position of a target, not on the same level
with the gun, whose horizontal distance from the gun is x, and
that <f> x is the angle of departure for the horizontal range x. a is
the particular value of A that corresponds to the value of x.
These formulas express the relations that exist between <f>, e,
and (/> x . They are used to determine the quadrant angle of elevation
for a target situated so much above or below the level of the gun
and at such a range that the principle of the rigidity of the trajectory
cannot be applied.
EXTERIOR BALLISTIC FORMULAS.
The formulas required in the solutions of most ballistic prob-
lems are here assembled for convenience. There are included the
formulas already deduced and others which are deduced later.
DIRECT FIRE.
7>825f. s. 0<20
tf=/|j (42) Z = X/C (40)
sin 2 <j> = AC (34) T = CT'/co8<fr (33)
tan (u = B' tan < (35) v = u cos </cos 6 (41)
y = x tan < (A - a) /A (37) a ' = A = sin 2 <f>/C (38)
tan 6 = tan < (A - a')/ A (36) y = a " C tan (39)
EXTERIOR BALLISTICS. 377
CORRECTION FOR ALTITUDE.
log (log /) =log T/o+5.01765 (44)
DANGER SPACE AND DANGER RANGE.
(51) / = / + - (/,-/<>) (53)
AX=X-x (54) a r ao // = 2 2 / /C 2 (55)
DRIFT.
Seacoast Guns. Drift (yds.) = [3.79239]C 2 D'/cos 3 < 1
Field Guns. Drift (yds.) = [3.92428]C 2 D7cos 3 <j> j
WIND EFFECT RANGE.
AV = W p cos<f> (45) V' = VJV (46)
sin 4<f> = W p sin <f>/V (47) <' = 0T^ (48)
AX (ft.)=X'~ (XW P T) (49)
WIND EFFECT DEVIATION FOR 8, 10 7 12-INCH PROJECTILES.
(T f SPO ") \ 2
33QQQ+Z(yds.)) (50)
CURVED FIRE.
Always correct for altitude.
For 7>825 f. s. and <, 20 to 30, use formulas for direct fire.
Use the following formulas when
F<825f. s.
C = / (42) Z-X/0 (40)
log (log /) = log i/o+5.01765 (44)
sin 2 < = [5.80618] AC/V 2 (56) tan cj = B' tan <f> (35)
v u = [3.09691K cos </> V/cos aj (57)
T = [2.90309] CT'/V cos (58)
378 ORDNANCE AND GUNNERY.
HIGH ANGLE FIRE.
Always correct for altitude.
When the coefficient of reduction c is known use Table IV.
When the coefficient of reduction is not known use the formulas
for direct fire and Table II, or Table I in those problems for
which Table II is not sufficiently extended.
CURVATURE OF EARTH.
Curvature (f t.) = [7.33289JZ 2 (yds.) (59)
217. Interpolation in Table II. Exact formulas for inter-
polation in Table II are deduced and explained in the appendix
to this chapter. These formulas greatly facilitate the solution of
ballistic problems. A thorough understanding of the interpola-
tion formulas, and facility in their use, should be acquired before
proceeding further. These formulas, which are here written, will
be used in place of the interpolation formulas given on page VIII
of the ballistic tables, as the latter formulas are approximate only.
Double Interpolation Formulas Ballistic Table II.
/ = non-tabular value of any function corresponding to the non-
tabular values V and Z.
/o = tabular value of function corresponding to tabular values VQ
and Z always next less than V and Z.
h = difference between velocities given in caption of table.
Jv Q and AZQ = tabular differences for /Q.
Jvi = tabular difference next following Jv in same table.
/(+zj indicates that function decreases as V increases, and increases
as Z increases.
Use the following formulas for the functions A, A', B, T', log
C", .and D' throughout the table. They also apply for some values
of the functions A" and log B' when F>2500.
-Z V-Vp Z-Z F-T
EXTERIOR BALLISTICS. 379
Q (Avi AVQ)
Use the following formulas for the functions A" and log B f
when F<2500, and for some values beyond that point.
Z-Z V-
Xh
X100
Use the following formulas for the function w.^
y-F Z-Zp V-Vp
Inspect the tables to determine how the function varies with V
and Z, and select the proper group of formulas.
380 ORDNANCE AND GUNNERY.
Exercise great care in the use of the plus and minus signs.
As the numbers in the difference columns of the table are
written as whole numbers we must, when using the interpolation
formulas, treat the tabular values of the functions as whole num-
bers, and afterwards put the decimal point where it belongs.
Regarding the interpolation formulas we will note that the pro-
portional parts of the differences Az Q and Av Q are always applied
to the tabular value of the function, / , with a sign indicated by
the manner of variation of the function with Z and V respectively;
positive if the function is increasing, negative for a decreasing
function. The sign of the last term of the / formulas is positive if
the signs of the preceding terms are similar, and negative if they
are dissimilar.
In the formulas for V and Z the fractional coefficients of h and
y _ y 17 _ >7
100 are equal respectively to and ~~~^ These coefficients
will always indicate by their values whether we are working with
the proper tabular values. Numerator and denominator of the
fraction should always be positive, and the value of the fraction kss
than unity.
218. The Solution of Problems. With the ballistic formulas
and the tables, the solutions of the problems of gunnery become
very simple. We will remember that all the functions in Table II
are functions of V and of Z = X/C, the arguments of the table.
Therefore, given any two of the three quantities, F, Z, and a value
of a function, the third may be determined from the table, and
also the corresponding value of any other function in the table.
For instance, suppose V and A f are given and the corresponding
values of A", log E r and T r are required. With V and A' we may
obtain Z from the table, and with V and Z we obtain A", log B'
and T'.
Inspecting the formulas, pages 376 and 377, we select those that
contain the given quantities, and such other formulas as, with
Table II, will enable us to pass to the formula containing the
required quantity.
It must be remembered that in the formulas the large letters
represent values of the quantities for the whole range, or complete
horizontal trajectory; while the small letters represent values of
EXTERIOR BALLISTICS. 381
the same quantities for particular points of the trajectory. In the
tables all these values are gathered in columns headed with the
large letters, which are thus used in a general sense.
In what follows, either in general discussions or when demon-
strating the use of the tables, the large letters will be used.
To show the advantages derived from the use of Table II with
the abbreviated formulas, let us consider the problem whose solu-
tion by means of Table I has been indicated on page 372.
219. Problem i. What is the time of flight of a 3-inch pro-
jectile weighing 15 Ibs., for a range of 2000 yards; muzzle velocity,
1700 feet?
C = 15/9, 7 = 1700, and X = 6000 are given. T is required.
These formulas apply: T = CT'sec $ (33)
sm2<j> = AC (34)
Z = X/C (40)
Determine Z from (40).
With Z and V take A and T from Table II.
Determine < from (34).
Determine T from (33). Ans. T = 4A8 seconds.
Compare this with the process indicated on page 372.
To show the most convenient method of performing the work,
the solution of a problem is here given in full.
220. Problem 2. A 575 Ib. projectile is fired from a 10-inch
gun at a target 8000 yds. distant; muzzle velocity, 2540 f. s. As-
suming the atmospheric conditions as normal, determine the angle
of elevation required and the other ballistic elements.
No data being given for the determination of $i/d, and the
correction for altitude not being required, the value C = w/d 2 is
taken for the ballistic coefficient.
log w 2.75967
2 log d 2.00000
log C 0.75967
= X/C logZ 4.38021
log Z 3.62054
Z = 4173.9
382 ORDNANCE AND GUNNERY.
To find the angle of departure, use sin 2 (j>
From Table II, with F = 2540 and Z = 4174,
^ = (0.03054) + .74X107 -.4X243 -.3X10 = 0.03033
The inclusion of the number in parentheses is to indicate that
in applying the corrections this number is treated as a whole
number.
log A 2.48187
log C 0.75967
log sin 2 <f> 1. 24154 2 < = 10 2'.6
<= 5!'
<j>, after being accurately determined, is used to the nearest
minute only.
To find the time of 'flight, use T = CT' sec <.
From Table II, with V and Z,
.74X68-.4X89-. 3X3 = 2.1588
log?" 0.33421
logC 0.75967
1.09388
log cos <f> 1.99833
log T 1 . 09555 T = 12 . 46 seconds
To find the angle of fall, use tan a) = B' tan <f>.
From Table II, with V and Z, (4v 1 Jv ) being negative,
log ' = (0.1513) + . 74X38-. 4X12 + . 3=0.15366
log' 0.15366
log tan <j> 2.94340
log tan co 1 . 09706 ai = 7 8'
To find the striking velocity, use v = u cos </> sec 6.
6 in this case becomes aj. From Table II, with V and Z,
u = 1481 - .74 X 20 + .4 X 66 = 1492.6
logu 3.17394
log cos < 1.99833
3.17227
log cos co 1.99663
log v 3.17564 r = 1498f. s.
EXTERIOR BALLISTICS. 383
It is evident from these values of u and v that no material error
is made by considering, for this shot, that u = v.
To find the maximum ordinate, use ?/o = o" C tan $.
As already explained, see equation (39), we find the value of
a " in this equation by means of the value A obtained from the
equation sin 2 (j> = AC. At the summit, see equation (38),
This value of A is therefore the value of A r for the summit.
Using this value of A in the A' column of Table II, with the given
value of V, we obtain from the A" column the value of ao".
The value of A obtained above is 0.03033
From Table II, with 7 = 2540 and A' = 0.0303,
2200
Z-Z Q 303-(300-.4X24)_
100 18- .4
a " = 1200 + .71X59 = 1241.9
Ioga " 3.09409
log C 0.75967
log tan 2.94340
log 2/0 2.79716 y = 626 . 8 f eet
221. Problem 3. Compute the drift for the shot in Problem 2.
Use Mayevski's formula, D (yds.) = [3.79239] C 2 Z)'/cos 3 <.
F = 2540 Z = 4174 < = 51' log C = 0.75967
From Table II D' = 81 + .74X5-.4X6 = 82.3
log Z>' 1.91540
2 log C 1.51934
const.log 3.79239
1.22713
3 log cos <f> 1.99499
logD 1.23214 D = 17 yards
222. Correction for Altitude. The altitude factor / in the bal-
listic coefficient, see equation (42), takes into account the diminution
in the density of the air as the projectile rises, and it corrects with
sufficient exactness for the error that arises from the use of the
384 ORDNANCE AND GUNNERY.
standard density with which Table II is computed. When accu-
racy is desired the altitude factor is calculated and applied to the
ballistic coefficient in all firings at angles greater than about 5
degrees.
Under the assumption of the mean height of the trajectory as two
thirds of the maximum ordinate, the value of the altitude factor is
given by the equation
log (log /) =log 7/0+5.01765 [44]
The summ'.t ordinate is, equation (39),
2/o = tto" C tan (j>
As C enters the value of yo we must assume, tor an approxi-
mation in the determination of the altitude factor by means of
equations (39) and (44), the value of C obtained by considering
the altitude factor as unity. Call this value Ci. With Ci com-
pute <j> as explained in Problem 2, determine yo from equation (39)
and / from (44). Call these values <i, y olt and fa. Then applying
the value /i, thus determined, to the assumed value C\, a new
value of C, C c , is obtained. This value C c will be close to the true
value and may usually, with sufficient accuracy for practical pur-
poses, be used as C. If greater accuracy is desired a second deter-
mination (of <p c , yo c , and f c ) is made. The resulting value, / c , is
applied to the value Ci first assumed, and the process is repeated
until there is no material change between the corrected values of
Ci resulting from the last two operations. The final corrected
value is then used as C.
223. Problem 4. Correct the ballistic coefficient for altitude,
and determine the angle of elevation required in order that a
1048 Ib. projectile fired from the 12 inch rifle with a muzzle velocity
of 2350 f. s. may strike a target distant 12,000 yds.; the atmos-
pheric conditions at the time of firing being barometer 29".5,
thermometer 67 F.,
X = 36000 7=2350
The process may be indicated as follows :
C=f^^ Z = X/C Table II, A, a " sm2<f>
o ca
t/ =ao" C tan < log (log /) =log y +E. 01765
EXTERIOR BALLISTICS. 385
Table VI V* = 1-037- 0.5 (1.037 -1.003) = 1.02
- 00860
Consider c = 1 log 10 3 . 02036
3.02896
logd 2 2.15836
log Ci . 87060 (1st approximation)
Z=X/C logX 4.55630
log Z 3.68570 Z = 4849.5
Table II, A = (0.04589) + .495 X 146- .5 X 396- .248 X 13 = . 044601
While using the table we will take out for future use the value of
ao" corresponding to ao' = A = 0.044601.
With ao' =0.044601, we obtain from the A' column
2600
Z-Z Q 446 - (447-. 5 X 38) _
100 24-. 5X2
Note tnat in this operation we have taken a tabular value
0.0447 for A larger than the given value 0.0446 because the tabular
value when corrected for the variation in V becomes less than the
given value.
a " = 1444+ .783X61 = 1491.8
sin20 = A<7 log A 2.64934
logCi 0.87060
log sin 20! 1 . 51994 2 fa = 19 20M
0i = 9 40'
2/o = o" C tan log tan 0! 1 . 23130
logCi 0.87060
log OQ" 3.17371
log 2/01 3.27561
386 ORDNANCE AND GUNNERY.
log 2/01 3.27561
log (log /)=log 2/0+5.01765 5.01765
log (log A) 2.29326
log /i 0.01965
. logCi 0.87060
Jog C c 0.89025 (1st correction)
With the corrected value of C we repeat the process followed
after the determination of Ci, the first approximation.
Z=X/G logZ 4.55630
logC c 0.89025
log Z 3.66605 Z=4635
Table II, ^ = (0.04306) + .35X140 -.5X372 -.175X12 =0.041669
Take out for future use the value of a " corresponding to a</ =
A =0.04167
2500
Z-Z Q 416.7- (424-. 5X36)
100 23-. 5X2
a " = 1383 + .486 X 61 = 1412.6
sm2<t> = AO log A 2.61981
logC c 0.89025
.486
log sin 2 < c 1.51006 2 < c = 18 53' .0
< c = 926'.5
2/o = a " C tan <f> log tan < c 1 . 22088
logC c 0.89025
Ioga " 3.15002
Iog7/o c 3.26115
log (log /)=log 2/0+5.01765 5.01765
log (log f e ) 2.27880
log/c 0.01900
logCi 0.87060
log C cc . 88960 (2d correction)
EXTERIOR BALLISTICS. 387
As this value of log C cc does not differ greatly from the value
log C c = 0.89025, obtained by the first correction, further correction
is unnecessary and we will use log C cc as log C in determining the
angle of departure.
Z = X/0 Table II, A sm2<f> =
logZ 4.55630
log C 0.88960
logZ 3.66670 2 = 4641.9
A = (0.04306) -f .419 X 140 - .5 X 372 - .21 X 12 = 0.041761
sin 2 <= AC log A 2.62077
log C 0.88960
log sin 2 <f> 1 . 51037 2 < = 18 53'.8
(= 926'.9
This value of < is practically the same as the value <j> c pre-
viously obtained. It is obvious therefore that we have carried
the correction for altitude sufficiently far.
224. ANGLE OF DEPARTURE CONSTANT. When the angle of
departure < is fixed, instead of the range X as in the last problem,
the correction for altitude is made and the range found as here
indicated.
tf-/~ A = sin 2 <f>/G Table II, a " 2/o=ao" tan
log (log /) =log 7/0+5.01765 X=ZO
Determine Ci from C=wdi/dd 2 , as in Problem 4 (1st approxima-
tion).
Find a ' = A from sin 2 <j> = AC
Find ao" corresponding to ao' from Table II
Find ?/oi from T/O = &o" C tan (j>
Find /i from log (log /)=log 7/ + 5.01765
Find <7 C from C c = faCi (1st correction)
and proceed in the same way to find C cc or C 3c as required.
Find the range from X = ZC with the final corrected value of C.
22$. The Effect of Wind. In considering the wind we assume
that the air moves horizontally, and that the effect on the velocity
of the projectile is due to the component of the wind in the plane
388 ORDNANCE AND GUNNERY.
of fire only. We also assume as practically correct that the time
of flight of the projectile is not influenced by the wind.
Let W be the velocity of the wind in foot seconds,
W p the component of W in the plane of fire,
a the angle, reckoned from the target, between the direc-
tion of the wind and the plane of fire.
Then
W P = W cos a.
Call W p positive for a wind opposed to the projectile, and nega-
tive for a wind with it.
THE EFFECT ON RANGE. Ingall's Method. We will assume that
the effect of the wind component, W p , is simply to increase or
diminish the resistance encountered by the projectile; and that
therefore this resistance, instead of being due to the velocity v, is
due to the velocity (vW p ). Represent by AX the correction to
be applied to the range in a calm to produce the true range, this
correction being the variation in range, with its sign changed,
caused by the wind. We may put equations (23) and (22), when <
is small and cos (f> nearly unity, in the following forms, using the
upper signs when the direction of W p is toward the gun and the
lower signs when it is toward the target.
= T/C+T(VW p )
JX=C{S(vW p )-S(VW p )l-(XTW p )
in which T(vW p ) and S(vW p ) are the T and S functions in
Table I.
Compute the range X and the time of flight T without consider-
ing the wind. Then from the first of the foregoing formulas find
v W p , and from the second the desired value of AX.
226. Another Method. Let ob, Fig. 159, represent the initial
direction of the projectile and its velocity V. Let be represent the
velocity W p of the wind component in the plane of fire, reversed
in direction While the projectile moves from o to b the air par-
ticle b moves to the left a distance equal to be. The direction of
movement of the projectile relative to this particle of air is there-
fore oc, which is also the relative velocity, V, of the projectile.
$ is the relative inclination, and A(j> the relative change in inclina-
EXTERIOR BALLISTICS.
389
tion. Draw cd perpendicular to ob, and call bd JF. Then, using
the upper signs only,
A ~\T TT/^ ^L. ( A C \
(nearly)
F'sin J<> =
(46)
(47)
(48)
FIG. 159.
Referring to Fig. 160, let b represent the position of the gun,
and bd the range X in calm air. In the head wind the range is
reduced to be. cd is therefore the variation in range due to the
wind. While the projectile travels from b to c the air particle
travels from b to a, the distance W P T. ac, or X', is therefore the
distance that separates the projectile and the air particle at the
-X-
-X-
FIG. 160.
end of the time T] that is, it is the relative range of the projectile
with respect to the air particle. The relative initial velocity of
the projectile is as shown in Fig. 159, its velocity in a calm, V, in-
creased by the component AV of the air's velocity in the direction
of motion. V' = V+4V is therefore the initial velocity necessary
to produce the relative range, and similarly <j>' = <{>J(f> is the
necessary angle of departure.
390 ORDNANCE AND GUNNERY.
It is apparent from Fig. 160 that
cd = bdbc = bd(ac ab)
or cd = X-(X'-W p T)
and calling cd with its sign changed 4X, we have
Compute the relative range X' with the values V and </>' f using
the formulas with Table II. While the projectile is traversing this
relative range the air particle moves over a distance W P T. The
actual range traversed by the projectile is therefore X' =F W P T, and
the variation in range due to the wind is
Changing the sign and rearranging, we get
) (49)
in which X and T are computed from V and & without considering
the wind.
The upper signs in the above equations apply when the wind
blows toward the gun ; the lower signs when it blows toward the
target.
APPLICATION OF METHODS. The first method of obtaining the
variation in range due to wind is useful only when the angle of
departure is small. The second method may be used in all prob-
lems of direct fire.
227. Problem 5. What will be the effect of a one o'clock wind,
blowing 30 miles an hour, on the range of the shot in Problem 1 ?
Velocity in miles per hour X 44/30 = velocity in foot seconds.
TF = 30X44/30 = 44f. s. a = 30
W P = W cos a = 38.1f. s.
From Problem 1: log C = 0.22185, Z = 6000,
(T = 4.48, < = 2 42'
Therefore W P T = 170.7, and X+W P T
First Method. V+ W p = 1738 . 1
EXTERIOR BALLISTICS. 391
From Table I, (1738 . 1) = 6220 . 2 - . 81 X 43 . 8 = 6184 .7 '-
7X1738.1) = 2. 508-.81X. 025=2. 4878
log? 7 0.65128
log C 0.22185
log T/C . 42943 T/C = 2. 6880
T(1738.1) 2.4878
T(v+W p ) 5.1758
From Table I,
5.189-5.176
V \~ rr 7J J- J- JL ~T~ /\ *J
.018
and (1113. 4) =9860. 0-^X20. 6 = 9845. 6
(1113.4) 9845.6
(1738.1) 6184.7
log 3660.9 3.56359
log<? 0.22185
log 6101.5 3.78544
X+W P T 6170.7
JX=-69.2 feet
228. Second Method. Find
Equation (45) J7 = 38.06
(46) F = 1738.1
(47) J0 = 3'.6
(48) <' = 238'.4
Fromsin20' = A(7 ; A = 0.05521
From Table II Z = 3671.5
= ZC X' = 6119.1
Equation (49) AX = - 51 . 6 feet
Note the difference in the results of the two methods. Neither
method is wholly satisfactory.
392 ORDNANCE AND GUNNERY.
229. THE EFFECT OF WIND ON DEVIATION. The component of
the wind perpendicular to the plane of fire, W sin a, is alone con-
sidered as producing deviation. The deviation due to the wind
can only be determined by experiment for each kind of projectile.
The following formula for the deviation of 8, 10, and 12 inch
projectiles is given, in another form, in the Coast Artillery Drill
Regulations.
(seo \ 2
33QQO-U(vds.)/ (50)
in which W is the velocity of the wind in miles per hour,
a its angle with the plane of fire,
T is the time of flight in seconds,
X the range in yards.
Problem 6. Compute the deviation of the shot in Problem 2
for a two o'clock wind blowing 20 miles an hour.
F = 20m.p.h. a = 60 W sin a = 17.32 T = 12.46
12 46 \ 2
(
3
3000 +8oob
230. The Danger Space. The danger space is the horizontal
distance over which an object of a given height will be struck. It
is the horizontal length of those portions of the trajectory for which
the ordinates are equal to and less than the given height. Usually
the danger space at the further end of the range is alone con-
sidered.
The elements of the trajectory are assumed to be known.
Let abc, Fig. 161, be the known trajectory for the range X, and
U X
FIG. 161.
let y represent the height of the object for which the danger space
is to be determined. The danger space for this height is evidently
so much of the range as lies beyond the ordinate y. It is equal to
EXTERIOR BALLISTICS.
393
the whole range minus the abscissa x corresponding to the ordinate
y. Calling the danger space AX we obtain AX = Xx.
The problem of determining the danger space therefore con-
sists in finding the value of x corresponding to the given value of
y and subtracting from the given range.
Substituting Cz for x in equation (37) and combining with
equation (34) we obtain
(A - a)z = 2y cos 2 </C 2 (51)
in which A is the value of the function for the whole range X, and
a the particular value of the same function for the abscissa x cor-
responding to the ordinate y. The elements of the whole range
being known, and y given, the second member of the above equa-
tion is known, and A in the first member. There remain two
quantities, a and 2, to be determined from the equation. This is
done by applying the method of double position.
231. METHOD OF DOUBLE POSITION. Enter Table II with the
known value of V. Inspect the table and find a value of Z which
when substituted with its corresponding value of a from the A
column in the first member of equation (51) will give to that
member a value close to the known value of the second member.
The difference between the first and second members is the error.
Repeat this operation until two successive values of Z are found,
ZQ and Zi, that give values for the first member, one value greater
and one less than the value of the second member.
Let ZQ and Z b Fig. 162, represent these values of Z; FQ and FI
the resulting values of the first member of equation (51); and S
the known value of the second
member. e and e will represent
the errors obtained with FQ and
FI. It is evident from the figure
that the true value of Z lies be-
tween ZQ and Z l and that its dis-
tance from the smaller trial value z
ZQ is given by the proportion FIG. 162.
Solving for Z
(52)
394 ORDNANCE AND GUNNERY.
In the application of this method to equation (51) we are assuming
that (Aa)z varies proportionately with z between the values Z
and Z\. This is not a true assumption, but the results are suffi-
ciently approximate for practical use.
To make this demonstration general we may consider that z
and (A a) in equation (51) represent any two functions, / and f,
whose product is known. We then have
We may write either / or f for Z in equation (52) and obtain
the general formula
-/o) (53)
We may now, employing the method of double position, deter-
mine from equation (52) the value of z in (51), and from the equa-
tion z = x/C we obtain the value of x corresponding to the given
ordinate y. We then have for the danger space
AX=X-x (54)
232. Problem 7. What is the danger space, for an infantry-
man, in the 1000 yard trajectory of the service 0.30 caliber rifle;
muzzle velocity, 2700 f. s.; bullet, 150 grains?
This assumes that the rifle is fired from the ground.
The height of a man is assumed at 5' 8" = 5.67 feet = y.
The value of the coefficient of form c, in the ballistic coefficient,
as determined by experiment for the 150 grain bullet is c = 0.5694,
see foot-note.
w = 150/7000 d = 0.3 7=2700 X = 3000
The coefficient of form is determined for the small arms bullet by means of
actual measurements of the velocity of the bullet at the ends of a long range,
as, for instance, 500 yards. With the measured values of V and v, the latter
corrected for the effect of wind if there is any, and the measured range, the
value of C is determined from the equation x=C{S(v) S(V}\ by means of
ballistic Table I. The coefficient of form c is then obtained from the equation
r-^i
~ d cd*
For the projectiles of large guns the coefficient c is determined by means
of measured values of <, V, and X, see Problem 12.
EXTERIOR BALLISTICS. 395
The steps in the operation are indicated as follows:
C = w/cd 2 Z = X/C Table II, A sm2<j>
(A-a)z = 2ycos 2 (t>/C 2 x = zC AX=X-x
C = w/cd? log 7000 3 . 84510
logc 1.75542
logd 2 2.95424
2.55476
log 150 2.17609
= X/0 log C 1.62133
logX 3.47712
log Z 3.85579 Z = 7174. 5
Table II, A = (0.06201) + 0.745X158 = 0.063187
sin 2 0=4(7 log A 2.80063
log C 1.62133
log sin 2 <t> 2 . 42196 20 = 1 30'.8
= 45'.4
(A - a)z = 2i/ cos 2 0/C 2 log 2y 1 . 05461
log cos 2 1.99992
1 05453
logC 2 1.24266
1.81187 (A-a)z = 6
Applying the method of double position to find the values of
z and a that will satisfy this equation, we find by inspection of
Table II for 7 = 2700 that the value of Z = 6500 with the corre-
sponding value of A, 0.05307, will when substituted in the last
equation give a close approximation to 64.844.
With Z = 6500 we obtain
(0.063187-0.05307)6500 = 65.761
e = 65.761 - 64.844 = 0.917
With Z = 6600
(0.063187-0.05449)6600 = 57.4
^ = 64.844-57.4 = 7.444
ORDNANCE AND GUNNERY.
The results obtained with these values of Z are greater and less
than 64.844.
Then from Z =
x=zC log z 3.81365
log C 1.62133
logo; 3.43498 z = 2722.6
AX = X- x AX = 3000 - 2722.6 = 277.4 ft. = 92.5 yds.
For 7 = 2700 we will also find that the value Z = 1122.7 with
the corresponding value of a will nearly satisfy the equation
(A a)z = 64.844. This value of z gives x = 469.5 feet, which is
at once the danger space at the inner end of the trajectory, see
Fig. 161.
233. The Danger Range. When the danger space is con-
tinuous and coincides with the range it is called the danger range.
Thus the danger range for an infantryman is the range at every
point of which an infantryman would be struck. The maximum
ordinate of the trajectory is therefore 5 feet 8 inches.
To determine the danger range we compute the horizontal tra-
jectory whose maximum ordinate yo is given.
Combining equations (34) and (39) and making cos < unity,
since < for all danger ranges is very small, we obtain
a 'ao" = 2y /C 2 (55)
From this we determine a ' by trial by the method of double
position, using the A! and A" columns of Table II. Since at the
summit ao'=A, see (38), with this value of a</ w r e go to the A
column of Table II for the given value of V and find the correspond-
ing value of Z, from which the required X is obtained.
234. Problem 8. What is the danger range, for a cavalryman,
of the service rifle fired from the ground? The height of a cavalry-
man is assumed as 8 feet.
log C= 1.62133 y = 8
EXTERIOR BALLISTICS. 397
The successive steps are indicated as follows :
27/o/C 2 Table II, Z X= ZO
a 'a " = 2y Q /C* log 2y 1.20412
log C 2 1.24266
log ooV 1 . 96146 aoW = 91 .508
By inspection of Table II for 7 = 2700 we find that the product
of a ' and a " for Z = 3400 will give a close approximation.
For Z = 3400 a 'a " = . 0467 X 1938 = 90 . 504
e =91.508-90.504 = 1.004
For Z = 3500 a V = . 0488 X 2002 = 97 . 697
ei = 97.697-91.508 = 6.189
The first product obtained is less than 91 . 508 and the second
product greater. In / = /o + - (/i /o) write a ' for /; 0.0467,
#0 i ^1
the smaller trial value of ao', for /o; and 0.0488 for fa.
or it may sometimes be more convenient to find the value of Z and
then the value of a</. Thus
and oo' = (0 . 0467) +.14X21=0. 04699
Using this value of a ' in the A column, we obtain
X=ZG log Z 3.78178
log C 1.62133
logZ 3.40311
X = 2529. 9 ft. =843. 3 yds.
398 ORDNANCE AND GUNNERY.
The trajectory for this range is, at its highest point, 8 feet from
the ground. A cavalryman at any point of the range would there-
fore be struck.
235. Curved Fire. Problems involving angles of departure
less than 30 degrees, and initial velocities less than 825 f. s., are
solved by means of the first part of Table II, pages 14 to 16, Bal-
listic Tables. The formulas to be used are collected on page VIII
of the tables under the heading " Formulas to be used with the
first part of Table II." They will also be found under the heading
Curved Fire on page 377, ante.
For velocities less than 825 f. s. the resistance of the air is
assumed to vary as the square of the velocity, or, as it is called,
according to the Quadratic Law of Resistance. Under this law the
formulas for direct fire are capable of modification into the forms
that we are now considering.
It may be shown that under the quadratic law of resistance
the function A, for the same value of Z = X/C, that is, for the
same range and projectile, will vary for different values of V in
the ratio Vi 2 /V 2 . If therefore we obtain the values of A with the
value Vi and all the necessary values of Z, we can pass by means
of the above ratio to the value of A for any other velocity. The
value Fi=800 was used in calculating the part of Table II that
refers to velocities less than 825 f. s.
The value of sin 20, see equation (34), calculated for Fi=800
becomes for any other velocity
AC 1
(56)
the form in which it appears among the formulas we are consider-
ing.
Under the quadratic law the other functions vary according to
different ratios of V t and F, as shown by the formulas in which
they appear. Under this law the function B r becomes independent
of the muzzle velocity, and therefore V does not appear in the
formula for tan a>.
CORRECTION FOR ALTITUDE. In curved fire the correction of the
ballistic coefficient for altitude is made by the same process as in
EXTERIOR BALLISTICS. 399
direct fire, but using the value of sin2< given by equation (56)
instead of that given by equation (34).
236. Problem g. A shot is fired from the 4.7 inch siege how-
itzer at a target 4000 yards distant; w = 60 Ibs., 7 = 820 f. s., ba-
rometer 29". 6, thermometer 63. Correct the ballistic coefficient
once for altitude and find the angle of departure and the time of
flight.
The process of correcting for altitude may be indicated as
follows :
C = f-j ^ Z = X/C Table II, A, a " sin 2<f> = [5.8061 8] AC/V*
2/ = a "C tan < log (log /) = log y + 5.01765
Table VI, o x /o = 1.029- 0.6(1.029- 0.994) = 1.008
0.00346
/ = ! c = l logw 1.77815
1 . 78161
logd 2 1.34420
log Ci 0.43741 (1st approximation)
Z=X/0 logZ 4.07918
log Z 3.64177 Z=4383
Table II, A l = (0 . 24821) + . 83 X 662 = . 25370
A = a r With a ' = . 25370 find a ".
2200
Z-Z 2537-2456
100 123
a " = 1138+ .66X53 = 1173
log A 1.40432
logCi 0.43741
const. 5.80618
5.64791
400 ORDNANCE AND GUNNERY.
logF 2 5.82762
log sin 20 1 . 82029 20i = 41 23'.2
0!=2041'.6
Ioga " 3.06930
logCi 0.43741
log tan 0i 1 . 57719
log T/oi 3.08390
log Gog /) =log 2/o+.01765 5 .01765
log (log A) 2.10155
log /! 0.01263
logCi 0.43741
log(7 c 0.45004
We will use this as log C in determining the angle of departure and
time of flight.
Z=X/C Table II, A, T'
sin 20 = [5.80618]AC/T 2 7 7 =[2.90309]C7 7 V7 cos
Z=X/C logX 4.07918
log C 0.45004
log Z 3.62914 Z = 4257.4
Table II, A = (0 . 24163) + . 574 X 658 = . 24541
log A 1.38989
log C 0.45004
const. 5.80618
5.64611
logF 2 5.82762
log sin 2 1 . 81849 20 = 41 10'.7
= 20 35' .4
7 T =[2.90309]C7 v /Fcos0
EXTERIOR BALLISTICS. 401
Table II, T' = (5 . 801) + . 574 X 152 = 5 . 8882
log 2" 0.76998
logC 0.45004
const. 2.90309
4.12311
log F cos ^ 2.88514
logT 7 1.23797
!T = 17.3secon\is
237. High Angle Fire. Problems in high angle fire are solved
by means of Table IV. This table was computed under the quad-
ratic law of resistance and is practically a range table, for veloci-
ties less than 825 feet, for a projectile whose ballistic coefficient is
unity. To make it applicable to other projectiles the tabular
numbers involve the value of the ballistic coefficient with the
values of the different elements. Therefore with C known, and
applied as indicated in the headings of the columns, we may, with
any other known element of the trajectory in addition to the ele-
vation, obtain from the different columns the values of the remain-
ing elements.
Thus (7, <f>, and V being known, find V/\/C and take out of
Table IV, for the particular value of <, the values of X/C, T/^C,
etc., corresponding to V/\/C as obtained. X } T, etc. may then
be obtained. If < is not a tabular value, solve the problem for
the tabular values of $ on either side of the given value and
interpolate between the results.
To correct for altitude use the formulas log (log /) given at
the head of each table. The value of the maximum ordinate is
also there given in the terms of the range.
THE COEFFICIENT OF REDUCTION. While the quadratic law of
resistance applies to velocities less than 825 f. s., Table IV may be
used for the higher velocities now obtained from our mortars by
the introduction of the coefficient of reduction c into the ballistic
coefficient. Compensation may thus be made for the errors arising
from the use of the table for higher velocities. The coefficient of
reduction is actually a quantity required to make the results
402
ORDNANCE AND GUNNERY,
obtained from the formulas and Table IV agree with the results
obtained in experiment.
The values of c for the 1046 Ib. mortar projectile have been
calculated from actual firings for different ranges and angles of
elevation. The determinations were made from firings with the
12 inch cast iron steel hooped mortar. The values of c which are
given in the following table therefore apply only to projectiles
fired with the velocities used in this mortar. In the steel mortar,
model 1890, higher velocities are attained.
The method employed in the calculation of the coefficient of
reduction is shown in Problem 12.
VALUES OF THE COEFFICIENT OF REDUCTION, c, FOR THE 1046 LB.
PROJECTILE IN THE 12 INCH MORTAR; DETERMINED FROM
ACTUAL FIRINGS.
Elevation,
Range in
Yards.
Degrees.
3000
4000
5000
6000
7000
8000
45
1.59
2.11
.93
1.76
1.53
1.25
46
1.77
2.20
.94
1.76
1.55
1.28
47
1.93
2.28
.94
1.77
1.57
1.32
48
2.07
2.34
.95
1.78
1.59
1.36
49
2.19
2.38
.95
1.79
1.61
1.40
50
2.29
2.41
1.96
1.80
1.63
1.44
51
2.39
2.42
1.97
1.81
1.66
1.48
52
2.48
2.42
1.98
1.82
1.68
1.52
53
2.56
2.42
1.99
1.83
1.71
.56
54
2.62
2.42
1.99
1.84
1.74
.61
55
2.66
2.42
2.00
1.85
1.77
.65
56
2.65
2.41
2.01
1.86
1.79
.70
57
2.64
2.40
2.02
1.87
1.82
.75
58
2.62
2.38
2.04
1.88
1.85
.80
59
2.59
2.37
2.05
1.89
1.88
1.85
60
2.56
2.35
2.07
1.90
1.91
1.91
61
2.53
2.34
2.09
1.92
1.95
1.97
62
2.49
2.32
2.11
1.94
1.99
2.04
63
2.45
2.30
2.13
1.97
2.04
2.11
64
2.41
2.28
2.15
2.01
2.09
2.18
65
2.37
2.26
2.17
2.07
2.15
2.25
238. Problems in High Angle Fire. When C, <f>, and V or X
are given, to determine the remaining elements.
I. Given C, V, and X, to determine <j> and the other elements.
EXTERIOR BALLISTICS. 403
METHOD. 1. With the given data find Ci =w/d 2 , V/Vcl~ and
2. With the value of V/VCi enter Table IV and find by in-
spection in consecutive tables two values of X/C, one value greater
and one value less than the trial value already determined.
3. Assume the lesser of the elevations for the two tables as a
first trial value of <j), determine / from the formula at the top of
the table for this value of <f> and compute C c from C c =fw/cd 2 .
4. Then, using the value of C c as C, redetermine V/VC and
X/C.
5. With these values reenter Table IV and redetermine as
before a second trial value of (f>.
6. With this value of < and the given value of X compute V.
7. If the computed value be greater than the given value, re-
compute with the next lesser value of <f>-, if less, recompute with
the next greater value. The given value of V will usually lie be-
tween the two values thus computed, if not continue the process
until this result is attained.
8. Then interpolate for <, assuming it to vary directly with V.
9. To find the other elements, T, CD, and v w , use the tables for
the values of < on each side of the value just determined. Find
the values of these elements from each table, and interpolate be-
tween the values so determined for the values corresponding to
the determined value of <j>.
Problem 10. A projectile weighing 1046 Ibs. is to be fired
from a 12 inch mortar, model 1888, to reach a target at a range of
7180 yards. Assuming the muzzle velocity to be 950 f. s., deter-
mine the angle of elevation required.
w = 1046 d = 12 7 = 950 X = 21540
1. d=w/d 2 log Ci =0.86117
V/VCi = 352 . 48 X/Ci = 2965 . 4
2. From Table IV,
for 0=59 and F/\/C = 352 . 48 X/C =2971. 7
= 60 F/\/C = 352.48 X/C = 2914
180
3. Assume = 59 Page 402, c = 1 . 88 - r^ X . 03 = 1 . 8746
404 ORDNANCE AND GUNNERY.
log (log /)= log X- 5. 32914 log X 4.33325
const. 5.32914
log* (log/) 1.00411
log/ 0.10095
G=fw/d 2 c \ogw/d 2 0.86117
0.96212
logc 0.27291
log(7 c 0.68921
4. log V 2.97772
log\/C c 0.34461
2.63311 7/\/C = 429.65
logZ 4.33325
logC c 0.68921
logX/C 3.64404 Z/(7 = 4406
5. From Table IV,
for< = 55 and 7/VC = 429 . 65 X/C = 4436.1
^ = 56 7/\/C = 429.65 X/C = 4375.1
Computed F/\/C = 429.65 X/C = 4406.0
6. Assume ^> = 55 c= 1. 77- .18X .12 = 1.7484
log ( lo g /) = lo g x ~ 5 40257 log X 4 . 33325
const. 5.40257
log (log/) 2.93068
log/ 0.08525
C=}w/d 2 logw/d 2 0.86117
0.94642
logc 0.24264
logC c 0.70378
logZ 4.33325
logZ/C 3.62947 X/C = 4260.6
EXTERIOR BALLISTICS. 405
Table IV, V/VU = 410 + ~~ X 10 = 419 . 33
2.62256
logVC c 0.35189
log V 2.97445 7 = 942.87
7. Assuming = 56 c = 1. 79- .18X .09 = 1.7738
log (log /) = log X - 5 . 38029 log X 4 . 33325
const. 5.38029
log (log/) 2.95296
log/ 0.08974
G=jw/d 2 c fogw/d 2 0.86117
0.95091
logc 0.24890
log(7 c 0.70201
logX 4.33325
logX/C 3.63124 Z/C=4278
Table IV, 7/x/C = 420 + ^ X 10 = 423 . 87
, 2.62723
logVC' c 0.35101
log V 2.97824 7 = 951.13
8. For 7 = 942.87, < = 55 > and for 7 = 951.13, = 56.
Therefore for 7 = 950
713
= 55 + i_ X 60' = 55 51'.8
9. To obtain the values of T, to, and v w , corresponding to
= 5551'.8, enter Table IV for ^ = 55 and < = 56, using as
arguments the values of V/\/C obtained above in steps 6 and 7.
For < = 55: For = 56:
V/VC_ = 419 . 33 V/VC = 423 . 87
T/VC = 19. 81 + 0. 93X0. 44 = 20. 219 !T/v / C = 20.656
a> = 58 59' + . 93 X 10' = 59 8'.3 w = 60 7'.9
JVC = 355 + . 93 X 6 = 360 . 58 vjV~C= 364 . 73
406 ORDNANCE AND GUNNERY.
From these values we derive, using the values of \/C as deter-
mined in steps 6 and 7,
T = 45.462 !F = 46.351
w = 598'.3 w = 607'.9
1^ = 810.76 ?^ = 818.43
Interpolating between these values, that correspond to ^> = 55
and = 56, we find for </> = 55 51'.8
T = 45. 46+^(46. 35-45. 46) =46. 2 seconds
,= 59 8'.3+^X59'.6 = 59 59'.8
51 8
v = 810 . 8+ -gjj- X 7 . 61 = 817 . 4 f oot seconds
239. II. Given C, V, and <j>, to determine X and the other ele-
ments.
METHOD. To determine the value of the coefficient c from the
table on page 402 we must know both (/> and X. In this problem
X is unknown.
1. \Ve will therefore first determine from Table IV an approxi-
mate value of X, designated XL, using for this purpose Ci=w/d 2
and the tabular value of <f> next greater than the given value.
2. Take from the table for c the value of c corresponding
to the value Xi and to the value of used in step 1. Call this
value ci.
3. Determine a second approximate value for the ballistic co-
efficient C2 = w/Cid 2 . Correct for altitude by means of Table IV,
using (f> as in step 1 ; and with the corrected coefficient, (7 3 , deter-
mine a corrected range, X 2 . This corrected range will be suffi-
ciently close to the true range to enable us to obtain approxi-
mately the correct values of c from the table. This has been the
object of the foregoing steps.
4. With the corrected range, X 2 , and the tabular values of <
on each side of the given value take new values of c from the table.
Call these values c 2 and determine with them two new values for
C, designated C 4: =w/c 2 d 2 .
EXTERIOR BALLISTICS. 407
5. By means of Table IV, for the values of <j> on each side of
the given value, correct both values of 4 for altitude. Call the
resulting values C 5 .
6. Using the values 5 as C find the corresponding values of
V/\/C and then, from Table IV, the corresponding values of X
and the other elements.
7. Interpolate between the values thus found for the values
corresponding to the given value of 0.
Problem 1 1 . Assume d = 12 inches, w = 1046 Ibs.
< = 55 40' 7 = 950f. s.
Determine X, T, a>, and v w .
1. d=w/d 2 = [0.86117]
log^F 2.97772
logVCi 0.43059
2.54713 7/Ci = 352 . 48
With this value we find from Table IV, for < = 56,
.25X156 = 3123
logX/Ci 3.49457
logCi 0.86117
logXi 4.35574 X r = 22685 ft.
= 7561.7 yds.
2. From the table of values of c, with X = 7562 yds. and < = 56,
C = 1.79-. 562X0. 9 = 1. 739
3. C 2 =w/c 1 <P = C l /ci =[0.62087]
For use in Table IV, log T 2 . 97772
0.31044
log7/\/C 2 2.66728 7/VC 2 =464.81
From Table IV, for < = 56,
X/C 2 = 4890 + . 48 X 1 73 = 4973
logZ/C 2 3.69662
logC 2 0.62087
logZ 4.31749
408 ORDNANCE AND GUNNERY.
log (log /) = log X- 5 . 38029 5 . 38029
log (log/) 2.93720
log/ 0.08654
logC 2 0.62087
logC 3 0.70741
Determine V/VC 8 logF 2.97772
7* 0.35371
2.62401
From Table IV, for < = 56,
.07X168 = 4224.8
logZ/C 3 3.62581
log C 3 0.70741
log X 2 4 . 33322 X 2 = 21539 ft.
= 71 79.7 yds.
4. Since, in mortar fire, X will vary but little for a variation of
one degree in <, we may without material error use this value X 2
in the determination of c for 55 as well as for 56.
Therefore, from the table of values of c, with X = 7180 yds. and
<j6 = 55, = 56,
c 2 = 1.77-.18X.12 = 1.748 c 2 = l. 79- .18X .09 = 1.774
C 4 = w/c 2 d 2 = Ci /c 2 - [0 . 61863] C 4 = [0 . 61222]
5. For use in Table IV,
log V 2.97772 log V 2.97772
0.30932 loVC^ 0.30611
2.66840 log V/VC 4 2.67161
i = 466 . 02 V/VC 4 = 469 . 47
EXTERIOR BALLISTICS. 409
From Table IV,
= 4959 + . 6 X 176 = 5064 . 6 X/C 4 = 5060 . 4
log.Y/C 4 3.70455 logZ/(7 4 3.70418
logC 4 0.61863 log<7 4 0.61222
logZ 4.32318 logZ 4.31640
const. 5.40257 const. 5.38029
log (log/) 2.92061 log (log /) 2.93611
log/ 0.08329 log/ 0.08632
log<7 4 0.61863 logC 4 0.61222
logC 5 0.70192 logC 5 0.69854
6. For use in Table IV,
log V 2.97772 log V 2.97772
0.35096 logVC 0.34927
2.62676 logV/VU 2.62845
V/VC = 423 . 41 V/VC = 425 . 06
From Table IV,
X/C = 4272 + . 34 X 170 = 4329 . 8 X/C = 4298 . 7
= 20.25+ .34X .43 = 20.396 T/VU = 20 . 704
= 59 9'+ .34X10^ = 59 12'.4 oj = QQ 9'.1
= 361 + . 34 X 7 = 363 . 38 v^/x/C = 365 . 57
From the above values we derive
Z = 21797 Z = 21472
^ = 45.763 !T = 46.272
7. Interpolating between these values, that correspond to
= 55 and c = 56, we find for < = 55 40'
X = 21580 ft. = 7193 . 3 yards
T = 46.1 seconds
w-5946'.9
v w = 816.5 foot seconds
410 ORDNANCE AND GUNNERY.
It will be seen that the approximate range, X 2 = 7179.7 yards,
used in determining the value of c, is very close to the true range,
7193.3 yards.
240. Calculation of the Coefficient of Reduction. A recent
addition to Table IV, printed in the Journal of the United
States Artillery, Jan.-Feb., 1905, provides a simple method of
computing the coefficient of reduction for any projectile, when
<f>, V, and X are determined from actual firings.
A column containing values of V 2 /X, obtained by combining
the two columns V/V~C and X/C, is added to the table. With <
and V 2 /X as arguments, we may obtain C from the value in the
column VI\^C. The value of C thus obtained is the complete
value, C = f~j~;]2- Determine / from the formula at the head of
the table, and di/d from Table VI. c is then readily determined.
When the additional column giving the values of V 2 /X is not
at hand, the value of V '/V C corresponding to any value of V 2 /X
may be readily determined from Table IV by trial. Square the
values in the V/\/C column and divide by the corresponding
values in the X/C column until two values of V 2 /X are found,
one value greater and one less than the given value. By inter-
polation the value of F/vC corresponding to the given value of
V 2 /X may then be found.
241. Problem 12. The range of the 1046 Ib. projectile from
the 12 inch steel mortar, model 1890 MI, is limited to 11,215 yards.
The muzzle velocity of the projectile is 1150 feet, the velocity
being limited by the requirement that the maximum pressure
shall not exceed 33,000 Ibs. In order to extend the range of the
mortar a projectile weighing 824 Ibs. is provided, for which, with-
out exceeding the allowed pressure, the muzzle velocity is in-
creased to 1325 feet and the range to 12,713 yards.
Compute the value of the coefficient of reduction, c, for that
projectile with the following data obtained in experiment.
d-12 ^ = 824 7 = 1325 < = 45 Z=38,139feet
Barometer, 30".5 Thermometer, 65 F.
The process of solution is indicated as follows:
EXTERIOR BALLISTICS. 411
V*/X Table IV, C from V/VC, log (log /) = log X- const, log.
_
"
From the given data, V 2 /X = 46 . 03
From Table IV we find with this value
logF 3.12222
2.80567
logVC 0.31655
logC c 0.63310
log (log /)= log X- 5. 55099 log.Y 4.58137
const. 5.55099
log (log/) 1.03038
log/ 0.10725
log*i/* 1.99211
logw 2.91593
3.01529
logCd 2 2.79146
loge 0.22383 c = 1.6743
242. Perforation oi Armor. The following empirical formulas
are used by the Ordnance Department, U. S. Army, for calculating
perforation of the earlier Krupp armor.
Uncapped projectiles,
Capped projectiles,
irP'^V
^=[3.84060]^
in which t = thickness perforated, in inches;
w= weight of projectile, in pounds;
v = striking velocity, in foot seconds;
d = diameter of projectile, in inches.
412 ORDNANCE AND GUNNERY.
The following formula has been proposed by the Ordnance
Board for capped projectiles against thin plates:
t \' 7 w' 5 v
. 926651
J
. 0-
sin a I J d' 75
in which a is the angle of impact, that is to say, the angle between
the axis of the projectile and the face of the plate. This formula
is applicable to tempered nickel steel plates from 3 to 4J inches
thick, and for angles of impact varying from normal to 50 degrees.
The following formulas are used by the Bureau of Ordnance,
U. S. Navy, for calculating the perforation of face hardened armor
without backing. They apply to Harvey armor only. No for-
mula satisfactory to the Bureau has yet been developed for the
perforation of the most modern Krupp armor.
Uncapped projectiles,
v=[3. 34512]
Capped projectiles,
in which the letters represent the same quantities as in the for-
mulas above.
The formula for capped projectiles is tentative only.
Range Tables. The elements of the trajectories for different
ranges are calculated for each gun in the service and embodied
with other information in a range table. The standard muzzle
velocity and standard weight of projectile are used in the con-
struction of the table for each gun. The range is the argument in
the table, the successive entries in the range column differing from
each other by 200 yards. The perforation of armor, and the
logarithm of the ballistic coefficient corrected for altitude at stand-
ard temperature and pressure, are entered at intervals of 1000
yards.
The construction of range tables will be understood from the
following data taken from the first line of the range table for the
10-inch rifle.
EXTERIOR BALLISTICS. 413
Muzzle Velocity, %%50 /. s. Projectile, capped, 60J, Ibs.
Range, X 1000 yards
Angle of departure, < 34M
Change in elevation for 10 yds. in range 0'.4
Time of flight, T 1.37 seconds
Angle of fall, a> 36'
Slope of fall 1 on 95
Maximum ordinate, y Q 8 feet
Striking velocity, v 2116 f. s.
Perforation of Krupp armor, impact normal 13.3 inches
" " " 30 with normal 11. 2 inches
Ballistic coefficient, log C 0.78112
Curvature of the Earth. The angle of elevation is affected by
the curvature of the earth about 15 seconds of arc for each 1000
yards of range.
The amount of curvature, in feet, is approximately two thirds
the square of the range in miles, or
Curvature (ft.) = [7 . 33289]Z 2 (yds.) (59)
ACCURACY AND PROBABILITY OF FIRE.
243. Accuracy. The accuracy of a gun at any range and under
any given conditions of loading and firing is determined as follows.
A number of shots are fired under the given conditions, care
being exercised to make the circumstances of all the rounds as
nearly alike as possible. The point of fall of each shot is plotted
on a chart or marked on the target when practicable. The target
may be either horizontal or vertical. We will assume a vertical
target.
The coordinates x and y of each shot-mark, or impact, are
measured with respect to two rectangular axes X and Y drawn
through an assumed origin conveniently placed. The sum of the
abscissas divided by the number of shots, which is the mean
abscissa, and the sum of the ordinates divided by the same num-
ber, the mean ordinate, are the coordinates of the mean point of
fall, called the center of impact.
414
ORDNANCE AND GUNNERY.
A representation of a target of 8 shots from the 10-inch rifle is
shown in Fig. 163. The range was 3000 yards. The center of
impact is at the center of the crossed circle.
The distance, in the direction of the axis of Y, of any impact
from the center of impact is the vertical deviation for the shot.
The deviation is plus if the shot-mark lies above the center of
impact, and minus if below. The distance of the shot-mark from
the center of impact in the direction of the axis of X is the lateral
deviation of the shot, plus if to the right, minus if to the left.
ii
14.
FIG. 163.
The numerical sum of the horizontal deviations divided by the
number of shots is the mean horizontal deviation. The mean
vertical deviation is similarly obtained from the numerical sum of
the vertical deviations.
The actual distance of each shot from the center of impact is
the absolute deviation for the shot, and the mean of the absolute
deviations is the mean absolute deviation for the group.
The mean absolute deviation is usually computed from the
mean horizontal and vertical deviations by taking the square root of
the sum of their squares. The value computed in this more con-
venient way differs slightly from the mean of the absolute devia-
tions.
By comparing the mean absolute deviations of different groups
of shots we may arrive at the comparative accuracy of different
guns or of the same gun under different conditions of loading or
filing.
EXTERIOR BALLISTICS.
415
The measure of the ability of a gunner is the absolute distance
of the center of impact of the group of shots from the point of the
target aimed at.
244. EXAMPLE. In a test of the 10-inch rifle for accuracy 8
shots were fired at a vertical target distant 3000 yards. The co-
ordinates of the shots measured from a point on the target, see
Fig. 163, are given below. Find the center of impact and the
mean absolute deviation.
Coordinates, Feet.
Deviations.
No. of
Shot.
Horizontal.
Vertical.
Horizontal.
Vertical.
1
12.20
11.00
0.80
1.65
2
11.50
9.90
0.10
0.55
3
13.30
9.75
1.90
0.<iO
4
11.70
9.10
0.30
0.25
5
13.20
9.15
1.80
0.20
6
9.00
9.55
2.40
0.20
7
11.05
7.15
0.35
2.20
8
9.25
9.20
2.15
0.15
8
91.20
74.80
9.80
5.60
11.40
9.35
1.23
0.70
The coordinates of the center of impact are: horizontal, 11.40
feet; vertical, 9.35 feet.
The mean deviations from the center of impact are : horizontal,
1.23 feet; vertical, 0.70 feet.
The mean absolute deviation
feet.
245. Probability of Fire.* Suppose that a large number of
shots have been fired at a target, under conditions as nearly alike
as possible, and that the center of impact of the group of shot-
marks on the target has been determined.
If we count the number of impacts that lie within any given
distance from the center of impact and divide this number by the
* The greater part of the discussion of the subject of Probability of Fire
follows the method set forth by Professor Philip R. Alger, U. S. Navy, in an
article appearing in the Proceedings of the U. S. Naval Institute, Whole No. 108,
1903, and in the Journal of the United States Artillery, March-April, 1904.
416
ORDNANCE AND GUNNERY.
whole number of shots, the resulting fraction will express the
probability that any shot will fall within the given distance.
Probability is thus always expressed as a fraction of unity. If
an event may happen in a ways and may fail in b ways, the prob-
ability of its happening is a/ (a + 6), and of its failing to happen,
b/(a+b). The sum of these two fractions, unity, represents the
certainty that the event will either happen or fail. Unity there-
fore indicates certainty.
By examination of many groups of shots we learn that as we
approach the center of impact the impacts become more numerous,
also that both the vertical and horizontal deviations are as likely
to be on one side of the center of impact as on the other.
We also learn that the vertical and horizontal deviations are
entirely independent of each other, and that any vertical deviation
is just as likely to occur with one horizontal deviation as with
another. This makes it necessary in considering probabilities
that we consider the horizontal and vertical deviations separately.
Let 0, Fig. 164, represent the center of impact of any group of
/
/
^
=-^
N
\
/
\
/
\
o a
FIG. 164.
shots used as a criterion. Considering only lateral deviations, lay
off on the axis of X successive distances representing lateral de-
viations.
Count the number of impacts on the target that lie within the
distance Oa to the right of the center of impact. Erect at a an
ordinate of such length that the area of the rectangle between the
ordinate and the axis of Y represents the number of impacts
found within the distance.
Proceed in the same manner for the distance ab and for the
other distances represented by the other divisions of the axis of X.
The area of any rectangle divided by the area of all the rect-
angles will then be the probability that any shot will lie within the
EXTERIOR BALLISTICS. 417
limits of deviation between the limiting ordinates. As the total
area of all the rectangles is a constant, the probabilities with re-
spect to deviations within any limits represented by different por-
tions of the axis of X are proportional to the rectangles erected on
those portions.
246. Probability Curve. If we consider that a very large
number of shots have been fired and make the rectangles very
small, so that the base of each becomes dx, we obtain the area in
the figure bounded by the curve and the axis of X.
The curve is called the probability curve and the area under any
part of it divided by the whole area is the probability that any
shot will deviate from the center of impact within the limits be-
tween the limiting ordinates.
If we consider the whole area under the curve as unity, the area
under any part of the curve will represent at once the probability
of a deviation within the limits between the limiting ordinates.
As the ordinates may be considered as areas infinitely small in
width any ordinate will represent the probability of a specific devia-
tion represented by the abscissa; that is, it will represent the proba-
bility that a shot will fall at a specific distance on either side of
the center of impact. The area of the ordinate being infinitely
small the chance that a shot will have any specific deviation is
infinitesimal and not worthy of consideration. If we were deal-
ing with events that could happen only in a finite number of ways,
each ordinate would be an area that would have a finite relation
to the sum of all the ordinates or areas, and would then represent
the probability of the happening of a particular event.
CHARACTERISTICS. The curve is symmetrical with respect to
the axis of Y, since the probability is the same for equal deviations
on either side. The ordinate has its greatest value at the center of
impact, since the center of impact is the mean position of all the
shots and the probability of the deviations increases continuously
as the deviations are less. The curve is theoretically an asymptote
to the axis of X, since all deviations between + oo and oo am
possible. Practically it may be considered as meeting the axis of
X at a short distance from the center, since with events happening
under the same conditions large variations from the mean are not
to be expected.
418 ORDNANCE AND GUNNERY.
While the curve as deduced applies to the deviations, or errors,
of shot, the laws that are expressed by it are general in character
and apply to accidental errors of any kind.
247. Equation of the Probability Curve. The equation of
the curve must be such as to express the characteristics just enu-
merated. Deduced by means of the theory of accidental errors,
taking as its basis the axiom that the arithmetical mean of observed
values of any quantity, the values occurring under similar circum-
stances, is the most probable value of the quantity, the equation
takes the form
y = e- x2 ^ (60)
nr
in which ? is the mean error, in our case the mean deviation, and
e = 2.71828 the base of the Napierian system of logarithms. The
factor 1/7:7- i g introduced to make the whole area under the curve
/ /* +0 \
unity, ( / e~ s l/nrZ dx = nfj, thus obviating the necessity of
dividing a partial area by the whole area whenever a probability
is to be computed.
As stated above, the area under any part of the curve divided
by the whole area under the curve is the probability that the
deviation of any shot will lie between the limits of deviation
represented by the part of the axis of X between the limiting ordi-
nates. The area under the curve is j ydx } and since we have
introduced into y in equation (60) the factor required to make the
whole area unity, the integral taken between limits will represent
at once the probability for any limit of deviation.
Thus the probability that any shot will have a deviation less
than the numerical value Oa, Fig. 164, is
P = 2/V** = -Te-^dx (61)
*/ ''/ yo
the factor 2 appearing since the ordinate at the end of the distance
Oa occurs at equal distances on either side of the center.
The values of P in this equation for various values of a and r
are arranged in the following table with a I? as an argument.
Knowing the mean lateral or vertical deviation 7-, to find the prob-
EXTERIOR BALLISTICS.
419
ability of a shot striking within the distance a to the right or left
of the center of impact, it is only necessary to take from the table
the value of P that corresponds to the argument a/f.
PROBABILITY OF A DEVIATION LESS THAN a IN TERMS OF THE
RATIO a/r-
a
r
P
a
r
P
a
r
P
a
r
P
0.1
0.064
1.1
0.620
2.1
0.906
3.1
0.987
0.2
0.127
1.2
0.632
2.2
0.921
3.2
0.990
0.3
0.189
1.3
0.700
2.3
0.934
3.3
0.992
0.4
0.250
1.4
0.735
2.4
0.945
3.4
0.994
0.5
0.310
1.5
0.768
2.5
0.954
3.5
0.995
0.6
0.368
1.6
0.798
2.6
0.962
3.6
0.996
0.7
0.424
1.7
0.825
2.7
0.969
3.7
0.997
0.8
0.477
1.8
0.849
2.8
0.974
3.8
0.998
0.9
0.527
1.9
0.870
2.9
0.979
3.9
0.998
1.0
0.575
2.0
0.889
3.0
0.983
4.0
0.999
248. ILLUSTRATION OF THE USE OF THE TABLE. On December
17, 1880, at Krupp's proving ground at Meppen, 50 shots were
fired from a 12 cm. siege gun at 5 elevation, giving a mean range
of 2894.3 meters. The points of fall were marked on the ground
and their distances from assumed axes measured. The center of
impact was thus determined. The lateral deviations were meas-
ured from the center of impact. The mean lateral deviation was
1.07 meters.
We will find from the table the probability that any shot should
have a deviation of less than one meter from the center of impact.
The deviation is a = l. The mean lateral deviation is 7- = 1.07.
Therefore a/j- = l/1.07 = 0.935, and from the table, P = 0.544, the
probability that any shot will fall within 1 meter of the center of
impact.
For 50 shots the probability is that PX50 shots will be found
within this limit of deviation, Px 50 = 0.544X50 = 27. This num-
ber of shots actually fell within the limit of deviation of 1 meter in
the experiment.
Making a = 2 meters, a/r= 2/1.07 = 1.87, P= 0.864, and
50X0.864 = 43. The probability is that 43 shots out of the 50 will
be found within 2 meters, laterally, of the center of impact.
Forty-three shots were actually so found.
420 ORDNANCE AND GUNNERY.
249. Probable Zones and Rectangles. Since P is the prob-
ability that the deviation of any shot will not be greater than a,
100P represents the number of shots in 100 that will probably fall
on both sides of the mean impact within the limit of the deviation
a. It is therefore the percentage of hits that will probably be
found in the zone defined by the limits at the distance a in both
directions from the center of impact. From the table we find that
for P = 0.25, or 100P = 25 per cent, a/r = 0.4, or a = 0.4;-. The
half width of the zone that probably contains 25 per cent of hits
is therefore 0.4^ and the full width of the zone is 2a = 0.8?-.
This zone is called the 25 per cent zone.
Similarly for the zone that probably contains 50 per cent of
hits, the 50 per cent zone, a = 0.846?- and 2a = 1.697-.
Knowing the mean deviation, vertical or horizontal, we may at
once from these relations find the width of either zone.
The 50 per cent zone is also called the probable zone and its
half width is the probable error , or deviation, since it is the error
that is just as likely to be exceeded as not to be exceeded.
The 25 per cent rectangle is the rectangle formed by the inter-
section of the 50 per cent zones for lateral and vertical deviations.
The probability of each of these zones being 1/2 the probability
of the rectangle will be 1/2X1/2.
Similarly the 50 per cent rectangle is that formed by the inter-
section of the zones for each of which P=v / l/2. It is also called
the probable rectangle.
COMPARISON OF THE ACCURACY OF GUNS. The rectangles of
probability may be used in comparing the accuracy of different
guns. The probable rectangle is generally used when this method
is employed.
For small arms and high powered guns using direct fire the
probable rectangle is taken in the vertical plane, since the targets
for these guns usually offer a vertical front.
For guns using curved or high angle fire the probable rectangle
is taken in the horizontal plane.
Probability of Hitting any Area. The probability of hitting
any area whose width is 26 and whose height is 2h, and which is
symmetrical with respect to the center of impact, as the area abed,
Fig. 165, assuming as the center of impact, is equal to the product
EXTERIOR BALLISTICS.
421
of the two values of P taken from the table with b/f x and h/r v as
arguments, the subscripts indicating lateral and vertical deviations.
If the center of impact lies in the l
given area, or on its edge, the proba- *
bility of hitting the area is readily
obtained by dividing the area into parts
by lines passing through the center of
impact and taking the sum of the prob-
abilities of hitting the parts.
Thus the probability of hitting the
area efgh, Fig. 165, is the sum of the e
probabilities of hitting the four rect- d
angles into which it is divided by lines
through the center of impact. The
probability for any one of these rectangles is 1/4 the probability
for the area, symmetrical to the center of impact, that is formed
by four rectangles equal to the one considered.
If the center of impact lies wholly without the area, the proba-
bility of hitting the area is obtained by extending the area to
include the center of impact and then taking the difference of the
probabilities for the whole area and for the part added to the
original area.
Thus the probability for the rectangle bg is equal to the proba-
bility for the rectangle og minus the sum of the probabilities for
the rectangles ol and bk.
FIG. 165.
APPENDIX TO CHAPTER IX.
THE USE OF TABLE II INGALLS' BALLISTIC TABLES.
250. Description of Table II. The several functions in this
table are functions of two independent variables, V and Z. Each
function varies with V and Z according to the law expressed by
the equation which gives the value of the function, and the several
functions vary differently. Thus the functions A and A' and
others decrease as V increases and increase as Z increases through-
out the table. The functions A" and log B' increase with V and
422 ORDNANCE AND GUNNERY.
increase with Z up to a value of F = 2500, beyond which point
they will be found to increase with V for certain values of Z and
to decrease with V for other values of Z. The function u in-
creases with V and decreases with Z throughout the table.
The values of any function given in the table are the computed
values obtained by assuming successive values for V and Z in the
equation of the function. The constant difference 100 is taken
between the successive values of Z. As most of the functions vary
more rapidly when V is small, the computed values are taken
close together for the lower values of V and at greater intervals
for the larger values of V. Thus for values of V below 1000 the
computations were made for values of V differing from each other
by 25. Between 7 = 1000 and F = 2000, the difference between
the tabular values of V is 50, and above F = 2000 the difference is
100. The purpose of this course was to obtain in the tables cor-
rect values of the functions so close to each other as to permit the
assumption, without material error, that the function varies uni-
formly between the tabulated values. This assumption enables us
to interpolate between the given values with comparative ease.
251. Deduction of Formulas for Double Interpolation. To
obtain a formula for interpolation we will proceed as follows. A
function of two independent variables may be graphically repre-
sented by the length of a line drawn perpendicular to the plane
which contains the axes of the variables. The variables in the
tables are V and Z. Let us take from the table a value of any one
of the functions, as A, and call this value / , the corresponding
values of V and Z being called 7 and Z . Let the axis of V be
horizontal and the axis of Z vertical. From the point VoZ on
the plane, Fig. 166, draw a line perpendicular to the plane, and
lay off on it the length / equal to the value of the function taken
from the table. Lay off the distance ZoZ 2 parallel to the axis of
Z and equal to 100. From Z 2 draw a line perpendicular to the
plane and lay off on it the value of the function given in the same
table for the next greater value of Z. Lay off VoV 2 parallel to
the axis of V and equal to the difference between the two velocities
given in the caption of the table, and call this distance h. On a
perpendicular to the plane at V 2 lay off the value of the function
taken from the next succeeding table for the first value of Z, and
EXTERIOR BALLISTICS.
423
from a point at a distance of 100 below V 2 lay off the next suc-
ceeding value of the function from this table. Complete the figure
shown by the heavy lines. The solid represented by this figure is
made up of all the values of the function lying between the four
tabular values.
...... >
n
*
100 i
FIG. 166.
Let us cut the solid by a plane through V in the figure at a
distance V V from 7 , and by another plane through Z in the
figure at a distance Z Z from Z . The intersection of these two
planes, /, will be the value of the function corresponding to the
values V and Z. In the column marked 4z in the table, opposite
the value of each function, appears the difference between this
424 ORDNANCE AND GUNNERY.
value and the value next below. This difference for / , called
Jz , is represented in the figure; and similarly the corresponding
difference in the Av column, which is the difference between the
values of the function for the same value of Z and successive
tabular values of F, is shown as 4v in the figure; and the next
succeeding difference in the same column is shown as Av^ at the
bottom of the figure. Draw vertical lines from c, m, and Z.
From the figure:
h:Jv ::VV :dc dc =
From the triangle cnm we have:
WQ:nm::Z-Z :ab
Z-Z
~m~ nm
ml = 7 -
,
. J-
= ^00~ ~ ^ l ~~ ^ h
The above expression having been deduced under the condi-
tions that the function decreases with V and increases with Z, we
will indicate this by writing / ( ( ~^ } for /. Transposing the terms
of this formula, for convenience, it may be written:
EXTERIOR BALLISTICS. 425
and by changing the signs according to the manner of the variation
of the function with V and Z, we may write the formulas for those
functions that vary in a different manner.
The formula gives the value of the function corresponding to
the values of V and Z between the tabular values. If we solve it
for V we obtain an expression for the value of V when non-tabular
values of the function and of Z are given; and similarly, solving
it for Z, the resulting formula will give the value of Z correspond-
ing to non-tabular values of the function and of F.
The formulas will be of the form given below.
252. Double Interpolation Formulas Ballistic Table II.
/ = non-tabular value of any function corresponding to the non-
tabular values V and Z.
/o = tabular value of function corresponding to tabular values VQ
and ZQ, always the nearest values less than V and Z.
h = difference between velocities given in caption of table.
JVQ and AZQ = tabular differences for / .
Avi = tabular difference next following Ji> in same table.
/["^ indicates that function decreases as V increases and increases
as Z increases.
Use the following formulas for the functions A, A', B, T', log
C', and D' throughout the table. They also apply for some values
of the functions A" and log & when F>2500.
Z-Zp V-Vo. Z-Zp V-Vp
100
F=F +
v _ v
Az Q - (Jvi-
xioo
Use the following formulas for the functions A" and log B f
when F<2500, and for some values beyond that point.
426 ORDNANCE AND GUNNERY.
" " F-Fo, , Z-Z F-Fo
AV Q + (Al\-
Use the following formulas for the function u.
V-V
_Z-Z (
V = V +
Inspect the tables to determine how the function varies with
V and Z, and select the proper group of formulas.
Exercise great care in the use of the plus and minus signs.
Double Interpolation in Simple Tables. Regarding Fig. 166,
from which the above formulas have been deduced, we will see that
the interpolated value / of the function may be obtained from the
four tabular values represented by the four heavy corner lines of
the figure. Interpolating by the rule of proportional parts be-
tween the value /o of the function and the value immediately
below it in the same table for V, which value is represented at Z 2
in the figure, we obtain the value of the function at VoZ in the
figure. Proceeding in the same manner in the table for the next
value of V we obtain the value of the function at V 2 Z in the figure.
EXTERIOR BALLISTICS. 427
Interpolating between the values at VoZ and V^Z we obtain the
desired value /.
This method is the most convenient method of double inter-
polation in simple tables, such as Table VI of the Ballistic Tables.
The numbers in that table are simple and the data is all found
together on one page.
USE OF THE FORMULAS.
253. Given Non-Tabular Values of V and Z, to Find f.
Select the / formula applicable to the particular function. Take
from the table the value of the function corresponding to the
tabular values of V and Z next less than the given values. The
tabular values of V and Z are VQ and ZQ in the formula. Express
-rr _ TT y _ y
the fractions r and ..-.-. decimally. If we take from the
table at the same time with the function the corresponding num-
bers in the Az and Av columns, also the number next following in
the Av column, called respectively Az, AVQ, and Avi in the formula,
we have all the data necessary for the solution of the problem.
The numbers in the different columns of the table are obtained
by considering the values of the functions as whole numbers.
The corrections therefore must be applied to the function as if it
were a whole number.
In the examples which follow we will indicate by enclosing the
decimal values of functions in parentheses that they are to be con-
sidered as whole numbers in applying the corrections.
EXAMPLE.
1. Given V = 1015 Z = 37^ What is the value of A't
/=(0.2946) + .42X96-.3X223-.42X.3X7
= (0.2946) + 40.32 - 66.9 - .88
= (0.2946) -27.5
=0.29185
428 ORDNANCE AND GUNNERY.
2. Given V=887 Z = 7275 What is the value of log B'f
V-Vo 12 Z-Z _
A ~25~ 100 :
/= (0.09779) + . 75X133 + . 48X59-. 75X. 48X1 =0.099067
To help in fixing the formulas for / in the mind, we will note
that the correction for Az is applied with a positive sign if the func-
tion increases with Z, and with a negative sign if the function
decreases with Z. The correction for Av is similarly applied ac-
cording as the function varies with V. The sign of the last term
is positive if the signs of the two preceding terms are similar, and
negative if they are dissimilar. The difference between the two
values of Av in the last term is usually positive and no attention
need be paid to the sign of this difference except when dealing
with the functions log B' and log C'.
The formulas used in the above examples, which we will call
the / formulas, and which give the values of the functions for non-
tabular values of V and Z, indicate the simplest and quickest
method of arriving at the correct value of an interpolated func-
tion. This method should therefore always be followed in solving
problems of this nature.
3. Given 7 = 1630 Z = 3781 Find D f Ans. 155.9
4. Given V = 972. 4 Z = 9569 Find A Ans. 0.464181
5. Given V = 2790 Z = 1255 Find log C f Ans. 4.65946
6. Given V = 2790 Z = 8473 Find log C r Ans. 4.97732
Note the difference in the signs of the last term of the formula
in the two preceding examples; also the sign of the same term in
the following example.
7. Given 7 = 1217 Z = 8778 Find log B' Ans. 0.138514
Note that in the following example A" decreases with 7.
8. Given 7 = 3040 Z - 4926 Find A" Ans. 2952.4
254. Given Non-Tabular Values of the Function and of V,
to Find Z. Select the Z formula applicable to the particular
function. Inspect the table on the page that contains the given
value of 7 to find the proper values to substitute in the formula
EXTERIOR BALLISTICS. 429
for /o, Z , and the tabular differences. To arrive at accurate re-
sults this requires some little care, and is best done in the following
manner. By rapid inspection of the table find the two values of
the function between which the given value lies. Apply to the
tabular value corresponding to the larger value of Z the correc-
tion r 4v . By comparing the corrected tabular value with
IV
the given value we determine on which side of the corrected
tabular value the given value lies, and thereby determine which
value of Z to use for / and the differences in the formula. An
example will illustrate this.
9. Given A = 0.06121 V = 2192 Find Z.
Looking in the table for 7=2100 we find that the given value
of A lies between the values corresponding to Z = 5100 and
= 5200. Applying to the value of the function corresponding to
the larger value of Z the correction T ^ = . 92X571 =525
we have (0.06263) -525 = 0.05738 as the value of the function for
F = 2192 and Z = 5200. This value is less than the given value by
about 380, and as the function increases with Z the given value
lies below it in the table.
The tabular Az for the value of the function, 0.06263, that we
have taken from the table, is about 190; that is the function is here
increasing by about 190 for each tabular value of Z. The tabular
function when corrected gave us a value too small by 380. Con-
sequently if we take the second value of Z greater than 5200, the
one we have used, we shall probably have the value we seek.
We will therefore take the function for Z = 5400 and apply the
correction to get its value for F = 2192. The corrected value is
(0.06639) -.92X602 = 0.060852. As this is less than the given
value of A and close to it, we know that the given value lies
between Z = 5400 and Z = 5500, and we will use Z = 5400 and the
corresponding tabular values in the formula.
It will be observed in each of the formulas for Z and V that,
in the numerator of the last term, there is a term in parentheses
430 ORDNANCE AND GUNNERY.
containing / plus or minus a correction. This term in paren-
theses is the tabular value of the function corrected for the differ-
ence between the given value of V or Z and the next less tabular
value. It is essential, in order to arrive at correct results, that the
value of this term be found first; for, as shown above, it is only by
this means that we can determine the true tabular values of Z or
V between which the required value lies. It will be shown later
that without these values correct results cannot be obtained.
In this example we have found the value of the term in paren-
theses to be (0.06639) -.92X602 = 0.060852. Using this in the
formula with the given value of the function and the tabular
quantities corresponding to /o, the process becomes exceedingly
simple, and the required value is easily and quickly and accu-
rately obtained.
/ = 0.06639 Jz
oco
Z ==5400 + 100 = 5420.1
If we had not pursued the above course, but had used for Z
the smaller value of Z obtained at our first inspection of the table,
the result would have been as follows.
The difference in the results is due to the fact that in using
the value Z = 5100 we assume that the function varies uniformly
between this value and the obtained value, a difference of 332,
while our process of interpolation is based on the assumption that
the variation is uniform for a difference in Z of 100 only.
The effect of the difference in the values of Z obtained by the
two methods may be seen in the problem from which the above
data were taken. The value of the ballistic coefficient, (7, was
4.7859 and the range X was required. X = ZC.
With Z = 5420.1 X = 25940 ft.
With Z = 5432.6 X = 26000 ft.
EXTERIOR BALLISTICS. 431
It may sometimes be more convenient, after having found the
proper value of Z for -use in the formula, to obtain from the table
the corrected values of the function for that value of Z and for
the next greater value of Z. The given value of the function will
lie between these two corrected tabular values, and the true value
of Z may be found by the method of proportional parts.
For 7 = 2192 Z = 5400 A = (0.06639) -.92X602 =0.060852
Z = 5500 A = (0.06832) - .92 X 618 =0.062634
1782
A, given, .06121
.060852
OKO
7=5400+^,100 =
The results given by the two methods are the same. Indeed
the methods are the same, for through the agency of 4z and Avi
in the formula we make use of the tabular values of the function
corresponding to the second value of Z. It will be seen in the
examples above that the fractions to be reduced are exactly alike.
In problems in the text books on exterior ballistics the value
of Z is nearly always determined to the nearest tenth. This in-
dicates that it is important to obtain the correct value. The
correct value can be obtained, from the tables, only by inter-
polating between the nearest tabular values on each side. The
importance of the preliminary application of the correction
V V
T 4v Q to the tabular values of the function, for the purpose of
determining the proper value of Z to use, is therefore apparent.
In using the formulas for Z and V the fractional coefficients
of 100 and of h in the last terms will always inf onn us whether we
are in the proper place in the tables. Both numerator and
denominator of the fraction must be positive, and the
value of the fraction must be less than unity. A negative
value of the fraction or a value greater than unity indicates that
we have not used the nearest values of / and V or Z and the
differences. The result is therefore approximate only, and the
432 ORDNANCE AND GUNNERY.
degree of approximation varies with the number of units in the
value of the fraction.
The formulas for V and Z may be easily fixed in the memory
if we observe that the numerator of the last term is the difference
between the given value of the function and the nearest corrected
tabular value, the correction being applied to the tabular value
with a sign indicated by the mariner of variation of the function
with Z or V. The first term of the denominator is Jv in the V
formulas, and Az Q in the Z formulas. The sign of the second term
of the denominator is the same as the sign inside the parentheses
of the numerator. The value of the second term of the denomi-
nator is positive for all the functions except log B' and log C 1 '. For
some value of log B', and for most values of log C', Jvi is less
than Jv , so that (dvi 4v ) becomes negative and causes a change
of sign for the second term of the denominator in the V and Z
formulas, and for the last term in the / formulas.
10. Given u = 991 V ' = 1630 Find Z.
V-Vo 30
This value of u apparently lies between the values of Z
V-V
and Z = 4700, but applying the correction 7 Av Q = . 6X15 = 9
to 987, the tabular value of the function for Z = 4700, adding it
since u increases with V, we find that the value of u for F = 1630
and Z = 47QO is 996. This being greater than our given value,
and the function decreasing with Z, the given value corresponds
to a value of Z greater than 4700. Similar inspection shows that
the proper value of Z is less than 4800. We therefore use the
values for Z = 4700 in the formula.
/ = 987 4z = 6 4v = 15 Jvi = 15
QQfi_QQ1
z = 4700 + loo = 4783 ' 3
11. Given A" =2158 V ' = 979 Find Z.
V-V
h
= .16
EXTERIOR BALLISTICS. 433
The change in the function here is very slight for a change m
7, and we see at once that this value of A" lies between Z = 4000
and Z = 4100.
Z = 4000 + ^^ 5 100=4034.2
57 +
12. Given 5 = 0.0341 7 = 2763 Find Z Ans. 4053.4
13. Given D f = 790 7 = 1784.6 Find Z Ans. 7278.1
14. Given log B f = 0.07140 7 = 1146 Find Z Ans. 3894.9
15. Given A' = 0.2252 7 = 970 FindZ Ans. 2813.1
255. Given Non-Tabular Values of the Function and of Z,
to Find V. This problem is slightly more troublesome than the
one just explained, because as 7 is not given we cannot turn
directly to the page on which the nearest tabular value of the
function will be found.
Select the 7 formula applicable to the particular function.
With the next tabular value of Z less than the given value look
through the table until two consecutive tables are found which,
for this value of Z, give values of the function less and greater
17 17
than the given value. Apply the correction - Jz to the
1UU
tabular value corresponding to the larger value of 7 and deter-
mine, from the corrected tabular value, the side on which the
given value lies, and the proper table to use.
16. Given B = 0.32386 Z = 5887 FindV.
1oo~ = - 87
Inspecting the tables with the value Z = 5800 we find that
tabular values of the function greater and less than the given
value are found in the consecutive tables for 7 = 900 and 7 = 925,
these values being respectively 0.3388 and 0.3230. Apparently
then the value of 7 for the given function lies between 900 and
925, and the values for / , 7 , etc., in the formula, should be taken
from the table for 7 = 900. But applying the correction
17 >7
-^^Az Q = . 87X77 = 67 to the tabular value of the function for
100
Z = 5800 and 7 = 925, adding it since B increases with Z, we obtain
434 ORDNANCE AND GUNNERY.
for the function at 7 = 925 and Z = 5887, the value 0.3297, which
is greater than the given value. Since B decreases with V the
given value must therefore lie to the right of the value for V = 925,
and as the difference between the two is considerably less than
the Av in the table, 144, we know without further inspection that
the value for V lies between 925 and 950, and in the formula we
will use the quantities taken from the table for 7 = 925.
7 = 925 Z = 5800 / = 0.3230
3297-3238.6 584
' 144+3X.87 2 ' + 2t
In a manner similar to that explained in the first problem under
the previous heading this same value of V can be obtained, after
having found the value of the function for Z = 5887 and V = 925, by
finding the value of the function corresponding to Z = 5887 and
the next tabular value of V, 950, and determining the true value
of V by the method of proportional parts.
For Z = 5887 V = 925 B = (0.3230) + .87 X 77 =0.3297
7 = 950 B= (0.3086) + .87X74 =0.31504
1466
3297
B, given, 32386
584
17. Given T' = 9.130 Z = 9378 Find 7.
Z ~ Z - 78
Too"
Inspecting the table with Z = 9300, we find that the given
value of T f lies between the tabular values for 7 = 1600 and
7 = 1650. Adding to 9.046, the value of T' for the larger value of 7,
the correction .78X128, we find that T' for Z = 9378 is 9.146. We
know then that the value of 7 sought is greater than 1650; and
since 9.146-9.130 is less than the Jv in the table, 152, we know
EXTERIOR BALLISTICS. 435
that V lies between 1650 and 1700. We therefore use in the
formula the values from the table for F = 1650.
18. Given log B' =0.165% 2=4.625 FindV.
Z ~ Z - 25
~~m~
From the value of tan aj, equation (35), we have B'=- -- -7.
tan (p
The same range may be attained by different shots fired with
different velocities at different angles of elevation. The angles of
fall will also be different. But the changes in the angle of eleva-
tion and angle of fall may be such that the ratio of the tangents of
the angles will remain constant. We may therefore get similar
values for B', and for its logarithm, with one value of X and widely
different values of V. When, therefore, log B' is given and a
value of Z, since Z contains X as a factor, we may find in the
tables more than one value of V corresponding to these given
values. Should this case be encountered in the solution of a
ballistic problem, the proper value of V to use would be deter-
mined after consideration of the other data of the problem.
With the data given above we find the two following solutions,
hi the tables for F = 1900 and 7 = 2900 respectively; using in the
first the formula for V when log B' corresponds to a value of
V < 2500, and in the second the formula for V when log B' corre-
sponds to a value of F>2500.
As we have before noted, the functions A" and log B f , for some
values of Z, increase with V when F<2500 and decrease with V
beyond that point. Therefore we may expect to find, for these
436 ORDNANCE AND GUNNERY.
values of Z, equal values of either function on both sides of
7=2500.
19. Given u = 931. 3 Z = 8122.7 Find V Ans. 2187.5
20. Given B= 0.16801 Z = 6345 Find 7 Ans. 1832.0
21. Given? 7 ' = 3.7943 Z = 4852 Find 7 Ans. 1747.0
22. Given log B' = 0.23376 Z = 7318 Find 7 Ans. 2226.0
256. Given One Function and V or Z, to Find the Corre-
sponding Value of Another Function. Inspecting the formulas
for 7 and Z we see that the fractional coefficients of h and 100,
77 ZZ
in the last terms, are respectively equal to -r-~ and - ~.
fi 00
We therefore take out this coefficient from the Z formula if 7 is
given with the function, and from the 7 formula if Z is given,
using the formula applicable to the given function. Substitute
r? f7 -rr TT
the value thus obtained for J or for 7- in the / formula
applicable to the required function, using for / and the differ-
ences in this formula the tabular values for the required function
corresponding to the same values of 7 and Z as were used in the
previous operation.
23. Given A" = 3150 V = 1929 .5 Find u.
7-7
h
= .59
From the Z formula for A" when 7 < 2500
5200
- (3116 + 5.9)
100 65 +.59
It will always be well when taking from the table the quanti-
ties required in computing the coefficient (Z-Z )/100 from the Z
formula to write above Z the tabular value used, as it is written
in the above equation. This will serve as a memorandum as to
what value of Z Q to use when computing the value of the required
function.
The memorandum is not necessary when computing (7 Vo)/h,
as the value of 7 is indicated on the page at which the table is
open.
EXTERIOR BALLISTICS. 437
Substituting the value of this coefficient, obtained above, in
the / formula for the function u, and using for / and the differ-
ences in this formula the tabular quantities for the function u for
the same values of V and Z used in computing the coefficient,
u = 1041 -.43X8+. 59X14- = 1045.8
24. Given D' = 125 7 = 3018 Find A".
5500
, n , Z-Zp 125-120.4
forZ)' -: 7 _ 18 =.67
Since V is greater than 2500 we must inspect the table to see
how A" varies for the value of Z used. We find that A" is here
diminishing with V and increasing with Z. The first of the /
formulas is therefore appropriate.
A" = 3364+. 67X73-. 18X6-0 = 3411.8
25. Given A' = O.OJ+01 Z = 51+0 Find T '.
Z-Zo
100
For = 500 this value of A' lies between the values given for
7 = 900 and 7 = 925. Applying the correction for Z to the value
corresponding to 7 = 925, we find that 925 is the proper value of
7 to use in the formula.
V-Vo 418-401
h "19 + 4X.4"
T' = (0.548) + .4X 111-. 825X 14-. 4X. 825X3 =0.5799
26. Given log B' = 0.0809 Z = $565 Find log C'.
Z-Z Q
100
= .65
7-7 809-786.65
for log R = _____ .493
log C f = (5.3076) + .65 X 34 - .493 X 274 - .65 X .493 X 2 = 5.29624
27. Given A' = 0.2485 7 = 2180.4 Find B Ans. 0.15578
28. Given r = 7.698 Z = 5728 Find D r Ans. 1013.3
29. Given log F = 0.1832 7 = 1832 Find u Ans. 954.2
30. Given A =0.01669 Z = 1224.5 Find log C" Ans. 5.1347
CHAPTER X.
PROJECTILES.
257. Classification. Projectiles are classed as shot, shell, and
case shot. The shell is a hollow shot designed to be filled with a
bursting charge that by means of a fuse may be exploded at a
selected time. The case shot consists of a number of shot held
together by an enclosing envelope which may be ruptured by the
shock of discharge or by a bursting charge in flight. The en-
velopes of canister and grape shot are ruptured by shock in the
gun. The envelope of shrapnel is ruptured by a bursting charge.
Old Forms of Projectiles. In the old smooth bore cannon
round cast iron shot and shell of diameter nearly equal to the caliber
of the gun were used. The grape, canister, and shrapnel for these
nrr
t ; -S
rntrr
m
GRAPE.
CANISTER.
guns are shown in the illustrations. The shrapnel was invented
about 1803 by Colonel Shrapnel of the British Army. In its first
form it contained a number of lead balls with loose powder in the
interstices. The walls of the shell were made thick to resist def-
ormation by the movement of the contained balls. In its later
forms the spaces between the balls were filled with melted sulphur,
438
PROJECTILES.
439
and a chamber for the bursting charge was provided as shown.
By this arrangement the walls were no longer subject to the im-
pact from the loose balls, and therefore could be made thinner,
SHRAPNEL.
thus providing room for a greater number of bullets. The con-
fining of the bursting charge in a chamber made its explosive effect
greater and permitted a reduction in its weight.
Chain shot and bar shot, made up of two projectiles connected
by a chain or bar, were occasionally used in early times; and in-
STUDDED.
EUREKA.
BUTLER.
cendiary shell, called carcasses, which were ordinary shell filled
with combustible material, the flames from which issued through
holes drilled through the walls of the shell.
Smooth bore guns were succeeded by muzzle loading rifled
guns. The introduction of rifling brought about the use of elon-
gated projectiles of increased weight. The capacity of the gun in
weight of metal thrown was largely increased and much greater
accuracy of fire was obtained.
440
ORDNANCE AND GUNNERY.
For the projectiles for the muzzle loading rifled cannon some
device was necessary to cause the projectile to take the rifling.
The several devices that were employed are shown in the illustra-
tions on the preceding page.
The studs on the projectile shown in the first figure were fitted
into the grooves of the rifling as the projectile was inserted at the
muzzle. In the other projectiles shown the parts a are of brass,
and in firing were expanded outward into the rifling by the pres-
sure of the powder gases. Other means that were employed are
shown in Figs. 167, 168, and 169.
FIG. 167.
FIG. 168.
FIG. 169.
Fig. 167 shows the Hotchkiss projectile. The parts a and b
are of iron and are held apart by the ring of lead c. The gas pres-
sure acting on the part 6 forced the lead outward into the rifling.
Fig. 168 shows the Whitworth projectile. The bore of the
Whitworth gun was a twisted prism of hexagonal cross section as
shown in Fig. 169. The projectile was fashioned to fit the bore,
its sides being provided with surfaces of a similar prism.
258. Modern Projectiles. BANDING. With the introduction
of breech loading in arms of all kinds the problem of giving rota-
tion to the projectile was much simplified As the chamber of
the gun is larger than the bore, a projectile provided with a soft
metal band, b Fig. 170, of diameter larger than the diameter of
the bore, may be inserted through the chamber. On the explosion
of the charge the pressure causes the sloping ends*d of the lands
of the rifling to force their way through the rotating band, causing
the band to conform in shape to the section of the rifling, and
PROJECTILES.
441
assuring the proper rotation in the projectile. As the band com-
pletely fills the cross section of the bore it serves also as a check
to prevent the escape of gas past the projectile, and in addition it
-6
a
FIG. 170.
serves to center the projectile in the bore, and to determine a
fixed position of the projectile when rammed into the gun.
The banding of projectiles is practically the same for all cali-
bers. An undercut groove, b Fig. 171, is cut around the projec-
tile near the base. A straight band of
copper, of cross section as shown at a, is
hammered into the groove and com-
pletely fills it, as shown at e. The ends
of the band are beveled lengthwise and
make a scarf joint where they meet. The
bands for projectiles of small caliber are
solid rings of metal forced into the grooves
of the projectile under hydraulic pressure.
The bottom of the groove b is scored with
vertical cuts into which the copper enters
when the band is hammered on. These
prevent the rotation of the band independently of the projectile.
The width of the band depends upon the caliber of the projectile
and is greater for the larger calibers. The outer surface of the
band is smooth in projectiles for siege and smaller caliber guns.
In the wider bands of the larger projectiles a number of grooves are
cut, as shown in section at e, Fig. 170, to diminish the resistance to
FIG. 171.
442
ORDNANCE AND GUNNERY.
forcing and to provide space for the metal forced aside by the
lands of the rifling.
In the latest 6-inch wire wound guns, in which velocities of over
3400 feet have been produced, difficulty has been experienced on
account of the tendency of the jointed rotating bands to strip
from the projectile during flight, due to the effect of the centrif-
ugal force. A band made by winding a thin copper ribbon on
edge and filling the groove has been tried with these projectiles
but without success.
It is probable that the method of banding with solid rings
seated by hydraulic pressure will ultimately be used with these and
with larger projectiles.
259. FORM OF PROJECTILE. With the exception of the can-
ister all modern projectiles are of the same general shape, a cylin-
drical body with ogival head. The ogival head is found by ex-
periment to be the most advantageous, as it offers little resistance
to the air and at the same time provides enough metal at the point
of the projectile to give to the point the requisite strength to per-
form the work of penetration.
The ogive is struck from a center on a line perpendicular to the
axis of the projectile, Fig. 172, and with a radius usually ex-
BODY.
i
i u
C /K^
*}
I UJ
I
f <
|
g m
1 i
HEAD.
I
1
/
I
/
t
^ -
I
I
0*"
I
^
FIG. 172.
pressed in calibers. The radius of the head varies in different
projectiles from 1J to 3 calibers.
The lower part of the ogive is turned off to make a cylindrical
bearing surface for the front part of the projectile. This surface,
PROJECTILES.
443
called the bourrelet, has a diameter 1/100 of an inch less than the
diameter of the gun.
Below the bourrelet the diameter of the projectile is diminished,
for ease of manufacture and to prevent bearing in the gun, to
about 7/100 of an inch less than the caliber. The band is placed
from 1J to 2J inches from the base, depending on the caliber, the
greatest diameter of the band exceeding the caliber by from 1/10
to 3/10 of an inch.
The length of projectile varies between 2J- and 5 calibers. The
length of most of the seacoast projectiles is 3J calibers.
Canister. Canister projectiles are for use at very short range >
when the guns of a battery are being charged by the enemy. The
projectile consists of a number of small balls
contained in a metallic envelope so con-
structed that it will break into pieces at the
shock of discharge. In our service, canister
are provided for the mountain guns only.
The canister for the 75 m|m Vickers Maxim
gun is shown in Fig. 173.
The case, c, made of malleable iron, is solid
at the bottom and open at the top. It is
weakened by two series of cuts, s, each series
consisting of three oblique cuts, each of which
extends over an arc of 120 degrees. The case
contains 244 iron balls f of an inch in diameter
and weighing 30 to the pound. The balls are
confined in the case by the tin cup, a, riveted
in. Three holes, h, drilled through the bottom
of the case admit the powder gases to assist
in rupturing the case. The metallic cartridge
case is attached to the projectile by being
crimped at several points into the groove r.
The copper band, b, forms a stop for the
head of the cartridge case, and serves as a FIG. 173.
gas check in the gun. The groove g, in other projectiles, is filled
with grease for the purpose of preventing the entrance of moisture
into the cartridge case.
It is the present intention of the Ordnance Department not to
b
444 ORDNANCE AND GUNNERY.
manufacture any more canister. Their place will be taken by
shrapnel, which are so constructed that they may be burst within
25 feet of the muzzle of the gun.
260. Shrapnel. The modern shrapnel is a projectile designed
to carry a number of bullets to a distance from the gun and there
to discharge them with increased energy over an extended area.
It is particularly efficacious against troops in masses and is not
used against material. The shrapnel is the principal field artillery
projectile. It is also provided for mountain and siege artillery
and for use in the small caliber guns in seacoast fortifications in
repelling land attacks.
In the earlier models the case of the shrapnel was so con-
structed as to break into a number of fragments on explosion of
the bursting charge, with the idea of thus practically increasing
the number of bullets carried. With the same end in view the
spaces between the balls were filled with the parts of cast metal
diaphragms that separated the layers of balls and broke up into
additional fragments at the bursting of the projectile. The
bursting charge was placed sometimes in the head and sometimes
in the base of the projectile. It was found with these shrapnel
that a very large percentage of the numerous fragments had not
sufficient energy to inflict serious injury. The shrapnel is there-
fore at present constructed of a stout case w r hich, except for the
blowing out of the head, remains intact at the explosion of the
bursting charge, and from which the balls are expelled in a forward
direction and with increased velocity by the bursting charge in
the base. By these means, while the number of fragments is
less, a greater number possess the required energy and the
effective range of these is increased.
Fig. 174 represents the shrapnel for the 3-inch field gun.
The case, c, is a steel tube drawn in one piece with a solid
base. A steel diaphragm, d, rests on a shoulder near the base,
forming a chamber for the bursting charge in the base of the
projectile, and a support for a central steel tube which extends
through the head, h. A small quantity of guncotton in the
bottom of the tube is ignited by the flame from the fuse, and
in turn ignites the bursting charge. The balls, of lead hardened
with antimony, are 252 in number. Each ball is 49/100 of an
PROJECTILES.
445
inch in diameter and weighs approximately 167 grains, or 42 to
the pound. After the balls are inserted a matrix of mono-nitro-
naphthalene is poured into the case, filling
the interstices between the balls in the lower
half of the case. When cool this substance
is a waxy solid. It gives off a dense black
smoke in burning. The purpose of its in-
troduction is to render the burst of the
shrapnel visible from the gun so that the
gun commander may determine whether his
projectiles are attaining the desired range.
Kesin is used as the matrix in the forward
half of the case.
The matrix forms a solid mass with the
balls and prevents their deformation by the
pressure that they would exert upon each
other, on the shock of discharge in the gun,
if they were loose in the case. Resin gives
better support to the balls than naphthalene
and therefore no more of the naphthalene is
used than is necessary to produce the desired
amount of smoke.
On being expelled from the case the
matrix burns and breaks up, leaving the
balls free.
To prevent rotation of the contained mass in the case the interior
of the case is fluted lengthwise, so that its cross section is as shown
in Fig. 175; and to reduce the friction to a
minimum, particularly in the chamber for the
bursting charge, the interior of the case is coated
with a smooth asphalt lacquer.
The head, h, of steel is given a cellular form
to make it as light as possible. The weight of
the projectile complete is fixed at 15 Ibs., and
weight is saved as far as possible in all parts of
the case in order that the greatest number of balls may be carried.
The head is screwed into the body and fixed by two brass pins, p.
The combination time and percussion fuse, /, is screwed into the
-d
FIG. 174.
FIG. 175.
446 ORDNANCE AND GUNNERY.
head. It is protected against injury or tampering by the spun
brass cap, 6, soldered on to the head of the projectile.
The projectile is fixed in the cartridge case as explained for the
canister.
Shrapnel forms 80 per cent of the ammunition supply of the
field gun.
261. The Bursting of Shrapnel. When the shrapnel bursts
the balls are expelled forward with increased velocity, and as they
have at the same time the movement of rotation of the projectile
they are dispersed more or less to the right and left. Their paths
form a cone, called the cone of dispersion, about the prolongation
of the trajectory. The section of' this cone at the ground is an
irregular oval with its longer axis in the plane of fire. The dimen-
sions of the area will vary, as is evident from Fig. 176, with the
FIG. 176.
angle of fall, the height of burst, and the relation between the
velocities of translation and rotation at the moment of burst.
It is assumed that when a shrapnel ball has an energy of 58 foot
pounds it has sufficient force to disable a man, and with 287 foot
pounds of energy it will disable a horse. These energies corre-
spond in the service shrapnel bullet to velocities of about 400 and
880 foot seconds. An increased velocity of from 250 to 300 feet is
imparted to the balls by the bursting charge. Knowing the ve-
locity of the projectile and the weight of the balls the space within
which the balls will be effective may be determined for any range.
POINT OF BURST. The best point of burst for a shrapnel is
assumed to be that point from which the burst of the shrapnel will
produce practically one hit per square yard of vertical surface at
the target. It is determined from the cone of dispersion by find-
ing the right section that contains as many square yards as there
are bullets in the shrapnel. The distance in front of the target
at which the burst occurs is called the interval of burst. On ao
PROJECTILES.
447
count of the variation at different ranges in the velocities of trans-
lation and of rotation the interval of burst which will produce one
hit per square yard of vertical surface at the target varies with
the range, decreasing as the range increases.
Practically it is found best to consider the height of burst
rather than the interval of burst, since the battery commander can
more readily estimate the height than the interval. Suitable
cross hairs in the field of the battery commander's telescope facili-
tate this estimation.
In our service a height of 3/1000 of the range, called 3 mils, is
adopted as the most favorable mean height of burst. The point
of burst at this height gives, over a large part of the range, very
approximately the correct interval of burst. For short ranges
this height of burst is excessive, and for long ranges it is insuffi-
cient.
The following table shows for the 3-inch shrapnel the results
obtained at different ranges from bursts at the correct interval of
burst, and also at a height of burst of 3 mils. The front of target
that should be covered depends upon the number of balls in the
shrapnel For the 3-inch shrapnel with 270 bullets, a former
model, the front to be covered with one hit per square yard is 18.5
yards.
One Hit per Square Yard.
Height of Burst, 3 Mils.
Range.
Interval.
Front Covered.
Interval.
Front Covered.
Yards.
Yards.
Yards.
Yards.
Yards.
H)OU
81.4
18.5
116. Z
27.0
2000
73.0
18.5
83.4
21.2
2500
68.98
18.5
73.5
19.55
3000
65.84
18.5
66.6
18.76
3500
63.28
18.5
60.9
18.84
4000
61.07
18.5
56.4
17.12
4500
58.97
18.5
51.3
16.13
It will be observed that between 2000 and 4500 yards the
height of burst of 3 mils gives approximately the desired density
of fire at the target. At ranges less than 2000 yards the front
covered is largely increased and the density of fire therefore dimin-
ished.
The figures refer to a single shrapnel bursting at the mean
448 ORDNANCE AND GUNNERY.
point of burst. In a group of shrapnel the bursts above and below
the mean point would largely make up the discrepancies in dis-
tribution and density.
FUSE. The fuse used in the shrapnel is the combination time
and percussion fuse of which a full description will be found in the
chapter on fuses. The fuse is arranged in such a manner that if
the projectile is not burst in flight it will be burst soon after im-
pact, a short time being allowed by the delay element in the fuse,
during which the projectile may rise on a graze and its burst be
accomplished in the air.
The fuse is also constructed to permit of using the shrapnel as
canister. When the fuse is set at zero of the time scale, the pro-
jectile will burst within 25 feet of the muzzle of the gun.
262. Shot and Shell. Solid shot are no longer used in modern
cannon except for target practice, at least in our service. Certain
hollow projectiles with thick walls designed principally for the
perforation of armor are denominated shot to distinguish them
from shell, which name is given to thinner walled projectiles that
have not as great a penetrative power but carry larger bursting
charges, and have consequently greater destructive effect after
penetration.
Shell were formerly made of cast iron, being cast in one piece
and subsequently bored for the fuse, Fig. 177.
FIG. 177.
With the adoption of high explosives for bursting charges,
greater strength in the walls of shell became desirable in order to
insure against accidental explosion of the projectile while in the
gun. With the exception of some of the projectiles for guns of
minor caliber in which black powder is used for the bursting charge,
all projectiles are now made of forged steel.
Fig. 178 represents a steel shell for the 5-inch siege rifle. The
steel projectiles for mountain, field and siege artillery are similarly
constructed.
PROJECTILES.
449
The base of the shell is closed by a steel base plug, p, which is
screwed in after the explosive charge has been packed in the pro-
jectile. The plug is bored and tapped for the base fuse, /, which
when inserted is flush with the rear surface of the projectile. The
wrench holes in base plug and in head of fuse are filled with lead in
order to make a continuous bearing surface for the copper cup, c.
The cup is applied to the base of the shell to prevent the powder
gases in the gun from penetrating to the interior of the projectile
by way of the joints of the screw threads. The edge of the cup
D
FIG. 178.
fits into the circular undercut groove, g, and the joint there is
sealed and the cup held in place by lead wire hammered in.
Armor Piercing Projectiles. Armor piercing projectiles are of
the same general construction as the steel shell just described.
Their distinguishing feature is a soft metal cap embracing the
point of the projectile for the purpose of increasing the power of
the projectile in the perforation of hard armor.
The head and point of an armor piercing projectile are ex-
tremely hard, the hardness being attained in the process of manu-
facture by any one of several secret tempering processes. The
metal of the projectile before being subjected to the secret process
has a tensile strength of about 85,000 pounds per square inch,
which is undoubtedly increased by the tempering. The cap, on the
other hand, has a tensile strength not exceeding 60,000 pounds, with
a large percentage of elongation, and reduction of area, as may be
seen in the table on page 165. The metal of the cap is therefore
very soft compared with the metal in the head of the projectile.
A 10-inch armor piercing shot is shown in Fig. 179 and a '10-
inch shell in Fig. 180.
The shot has thicker walls and head, and a less capacity for
450
ORDNANCE AND GUNNERY.
FIG. 179.
IQ-in. Armor Piercing Shot.
FIG. 180.
10-in. Armor Piercing Shell.
PROJECTILES.
451
the bursting charge. The outer diameters of the two projectiles
are the same, and the weight of each when ready for firing is the
same, 604 pounds. To maintain uniformity of weight the shot is
made about 4J inches shorter than the shell.
The cap is fixed to the head of the projectile by means of the
circular groove, a, cut around the head of the projectile. The cap
before affixing is of the shape shown half in section and half in
elevation in the figure between the projectiles. A shallow recess,
6, is filled with graphite to lubricate the projectile as it passes
through the cap and armor. To fasten the cap, the projectile with
the cap on its point is put in a lathe, and the excess metal at the
base of the cap is hammered into the groove of the projectile by
means of pneumatic hammers.
In naval projectiles the caps are sometimes fastened on by
passing two wires through holes drilled in the cap and notches cut
in the projectile.
263. Action of the Cap. The soft steel cap increases the
power of penetration to the projectile in hard faced armor, at
FIG. 181.
normal impact and up to an angle of 30 degrees from the normal,
about 15 per cent with respect to the velocity of the projectile
and more than 20 per cent with respect to the thickness of plate.
Among the several theories advanced as to the action of the
cap, the following appears the most satisfactory.
When an uncapped projectile strikes the extremely hard face
of a modern armor plate, the whole energy of the projectile is
applied at the point, and the high resistance of the face of the
plate puts upon the very small area at the point of the projectile a
452
ORDNANCE AND GUNNERY.
stress greater than the metal can resist, however highly tempered
it may be. The point is therefore broken or crushed and the head
of the projectile flattened, Fig. 181. The flattening of the head
brings loss of penetrative power, and the energy of the projectile
is expended largely in shattering the projectile itself. The head
of the projectile adheres to the plate and is practically welded
to it.
The effect on a plate of thickness equal to the caliber of the
projectile may be the partial or complete punching out of a cylin-
drical piece, Fig. 182. But even if the plate
is completely perforated, the projectile does
not get through as a whole; and behind the
plate are found only fragments of the pro-
jectile and of the metal forced from the
plate.
When a projectile provided with a cap
strikes a hard faced plate, the pressure due to the resistance of the
plate is not confined simply to the point of the projectile, but is
distributed uniformly over a comparatively large cross section. In
FIG. 182.
FIG. 183.
addition the point of the projectile is firmly supported on all sides
by the metal of the cap. As a consequence the point is not de-
formed, and passing easily through the cap it finds the hard face
PROJECTILES.
453
of the plate dished and severely strained and more or less crum-
bled by the impact of the cap. The unexpended energy of the
projectile forces the point through the weakened face and through
the softer metal of the back.
The face of the plate is crumbled, and a conical hole made
through the softer metal, through which the projectile passes
practically intact and in condition for effective bursting, Fig. 183.
The form of the cap has not apparently a great effect on the
results. Many different shapes are used by different manufac-
turers, some of which are shown in Fig. 184.
FIG. 184.
The cap increases the biting angle of the projectile, the limiting
angle of impact at which the projectile will perforate the plate.
The following results have been obtained in comparative tests
of capped and uncapped projectiles against tempered nickel steel
plates. The angle of impact is measured from the normal to the
plate.
Gun.
Thick-
ness of
Plate.
Angle
of
Impact.
Strik-
ing Ve-
locity.
Projectile.
Effect.
8-inch rifle
Inches.
3 5
Degrees
60
1074
Capped
Perforated plate
60
1073
Un capped
Indented plate inch
12-inch mortar. . .
4.5
65
65
40
40
1066
1077
711
711
Capped
Uncapped
Capped
Perforated plate
Indented plate 1 inches
Nearly perforated. In-
dentation 6 inches deep.
Fragment nearly punched
out
Glanced from plate In*
dentation If inches deep
It is stated that the addition of the cap to the projectile and
the consequent moving of the center of gravity of the projectile
454 ORDNANCE AND GUNNERY.
toward the point favorably influences the trajectory, increasing
both the accuracy and range.
All projectiles for seacoast guns above 3 inches in caliber will
probably be provided with caps.
264. Deck Piercing and Torpedo Shell. These projectiles are
provided for the 12-inch mortars. The torpedo shell is longer
and of greater interior capacity than the deck piercing shell, and
carries a larger bursting charge of high explosive. The bursting
charge for the deck piercing shell is 64 pounds and for the torpedo
shell 134 pounds.
Latest Form of Base of Shell. A form of base with which
good results have been obtained is shown in Fig. 185. The metal
of the shell is cut away, beginning at a short
distance behind the band, leaving only a narrow
ring to support the band. In the perforation
of armor the band and the supporting ring are
sheared off, thus relieving the projectile of the
resistance due to the greater diameter of the
band.
Shell Tracers. Experiments are now being
conducted toward the development of a pro-
~FiG~i85~ " J ect ^ e tnat w ^ indicate its line of flight by the
emission of flame, or by the emission of some
substance that will be visible from the gun; the purpose of the
projectile being to enable the gun commander to follow the flight
of a projectile from his gun and thus determine whether the gun
is properly directed.
The tracer for use at night consists of a short metal cylinder
filled with a slow burning substance that emits a bright flame
during the flight of the projectile through the air. It may be
screwed into a seat prepared in the base of any projectile. Igni-
tion of the compound occurs in the gun.
For day tracing a special shell is prepared. The cavity of the
shell is partly filled with a mixture of lampblack and water, the
mixture having the consistency of thick paint. A small orifice is
made through the base of the projectile on one side. The powder
gases enter this orifice under the pressure in the -gun, and filling the
cavity in the shell force from the orifice during flight a spray of
PRDJEC1ILES.
455
black liquid. In recent experiments the flight of a 6-inch day
tracing shell was followed for over 7200 yards.
Hand Grenades. The hand grenade is a metal bomb filled with
high explosive and provided with one or more percussion caps or
fuses, which cause its explosion on striking after being thrown.
Hand grenades were effectively used by both sides in the Russo-
Japanese war.
265. Volumes of Ogival Projectiles. Assume a solid cylinder,
Fig. 186, of the length and diameter of a given solid shot.
Let d represent the diameter of the shot, usu- "T
ally taken as equal to the caliber of
the gun,
L, the length of the shot in calibers.
The volume of the cylinder is (xd 2 /4)Ld.
Let B represent, in calibers, the length of a Ld\
cylinder . whose diameter is d and wiiose volume,
(7rd 2 /4)Bd, is equal to that part of the cylinder
in Fig. 186 that is outside the shot.
Subtracting this volume from the volume of
the whole cylinder and representing by V 8 the
volume of the solid shot, we have
xd 2 , ,
FIG. 186.
(LB)d, or L B calibers, is the length of a solid cylinder whose
diameter is the diameter of the shot and whose volume is equal to
the volume of the shot. L B is called the reduced length of the
projectile in calibers, as it is the length of a cylinder of equal
diameter and volume.
B is a function of the radius of the ogive expressed in calibers.
Its value, obtained by means of the calculus, is given by the equa-
tion
B = 2n 2 (2n-l)sin- 1
6n 2 -2n-
2n
in which n is the radius of the ogive in calibers. When n=2, the
usual radius of head in seacoast projectiles, 5 = 0.58919.
456 ORDNANCE AND GUNNERY.
For cored shot the reduced length is less than for solid shot by
the length of the cylinder whose volume is that of the interior
cavity. Representing by B f the length of this cylinder in calibers,
the solid volume of the cored shot, or volume of the metal, is given
by the equation
Weights of Projectiles. Representing the reduced length by
I, and dividing the expression for the volume of one projectile by
a similar expression for another, we have
Since the weights are proportional to the volumes :
The weights of ogival projectiles are proportional to the prod-
ucts of the cubes of their diameters by their reduced lengths.
The weights of ogival projectiles of the same caliber are propor-
tionate to their reduced lengths.
As the standard projectiles for most of our guns are similar,
their dimensions when expressed in terms of the caliber are the
same. The reduced length is therefore the same for all these
projectiles, and the weights of the projectiles are proportional to
the cubes of the calibers.
266. Thickness of Walls. The maximum stress sustained in
the gun by the walls of a cored projectile, at any section of the
projectile, is due to the pressure to which the walls are subjected in
transmitting to that part of the projectile in front of the section
the maximum acceleration attained in the gun. The maximum
acceleration is due to the maximum pressure in the gun; and this
pressure being known the acceleration is determined by dividing
the pressure by the mass of the projectile.
a = P/M = Pg/w
a being the acceleration, P the total maximum pressure on the
base of the projectile, arid w the weight of the projectile. Substi-
tuting the values of the known quantities a may be determined.
a being known, if we substitute for w the weight of that part
of the projectile in front of the given section and solve the equa-
PROJECTILES. 457
tion for P, the value obtained, which we will call PI, will be the
pressure sustained by the walls of the section. The area of the
section is n(R 2 r 2 ). The pressure per unit of area is therefore PI
divided by x(R 2 -r 2 ).
This pressure must not exceed the elastic limit of the metal for
compression, divided by a suitable factor of safety; nor must it
cause excessive flexure in the walls. If it does the walls must be
made thicker.
Thickening the walls will increase the weight in front of the
section and therefore a new value of w must be obtained for a
second determination.
In shrapnel it is desirable to make the walls as thin as possible
in order to increase the number of bullets that may be carried.
The longitudinal pressure of the contained bullets is borne by the
thicker base of the projectile, and the walls sustain only the pres-
sure due to the centrifugal force and that proceeding from the
weight of the head and fuse. Their thickness will therefore be
determined by the requirement that they must resist rupture by
the pressure exerted by the gases from the bursting charge when
the head of the projectile is blown off. The pressure required to
blow off the head is equal to the resistance offered to shearing by
the screw threads and shear pins of the head.
A much greater thickness of wall than is needed in the gun is
required to enable a projectile to withstand the shock of impact on
the face of an armor plate. The retardation in this case is much
greater than the acceleration in the gun and consequently the
stresses on the walls are correspondingly greater. As there is no
means of determining the retardation at impact, the proper thick-
ness of walls of armor piercing projectiles cannot be calculated,
but must be determined by experiment.
We may, however, by assuming that the plate offers a constant
resistance to the penetration of the projectile, determine the thick-
ness of wall necessary in the projectile to enable it to pass through
the plate and have any required velocity on emerging.
Thus, to determine the thickness of wall of an armor piercing
shell that is required, with a striking velocity v, to perforate an
armor plate of given thickness and to have on emerging a re-
maining velocity Vi.
458 ORDNANCE AND GUNNERY.
Let S be the constant resistance offered by the plate
I the thickness of the plate, in feet,
a the constant retardation of the projectile during pene^
tration.
The work performed by the resistance over the path I is equal to
the energy abstracted from the projectile while traversing this
path. Therefore
The retardation due to the resistance is equal to the resistance
divided by the mass. Therefore
S V 2 -V! 2
= ~"
The pressure sustained by any section of the projectile during
penetration is equal to the mass of that portion of the projectile
behind the section multiplied by the retardation. Denoting by w f
the weight of that part of the projectile behind any given section,
we have for the pressure sustained per unit of area at the section
w f a w'(v 2 Vi 2 }
R and r must be given such values, that is, the thickness of the
walls must be such that p will not exceed the elastic limit of the
metal for compression, or that the flexure of the walls, considering
the shell as a hollow column, will not be sufficient to cause rupture.
267. Sectional Density of Projectiles. It has been found by
experiment, as explained in exterior ballistics, that the retardation
in the velocity of a fired projectile, due to the resistance of the air,
is expressed by an equation that, for any fixed atmospheric condi-
tions and standard form of projectile, may be put in the form
R representing the retardation, A a constant, d the diameter of the
projectile, w its weight, and f(v) some function of its velocity*
PROJECTILES. 459
For a given velocity it is apparent that the retardation will in-
crease directly with the square of the diameter of the projectile and
inversely with its weight; or, more concisely, the retardation will
increase directly with the fraction d?/w.
The reciprocal of this fraction, or w/d 2 , will therefore be the
measure of the capacity of the projectile to resist retardation, that
is, to overcome the resistance of the air.
The fraction io/d 2 is called the sectional density of the projectile.
w/\nd 2 is the weight of the projectile per unit area of cross section,
and w/d 2 is taken as the measure of this weight, ?r/4 being con-
stant.
The sectional density is of importance in considering the mo-
tion of the projectile both in the air and in the gun.
EFFECT ON THE TRAJECTORY. The greater the sectional den-
sity of the projectile, the less the value of its reciprocal, the factor
d 2 /w in the above equation, and consequently the less is the value
of the retardation of the projectile.
Of two projectiles fired with the same initial velocity and eleva-
tion, the projectile with the greater sectional density will therefore
lose its velocity more slowly and will attain a greater range. For
any given range it will be subjected for a less time to the action of
gravity and other deviating causes, and will therefore have a
flatter trajectory and greater accuracy.
The advantages of increased sectional density are therefore
increased range, greater accuracy, and a flatter trajectory.
The sectional density may be increased by increasing the
weight of the projectile or by decreasing its diameter. The
weight of a projectile for any gun may be increased by increasing
its length. This has been done with modern projectiles for large
guns until the length is from 3J to 4 calibers. In small arms the
weight is increased by the use of lead in the bullet. Increase in
sectional density by decrease in diameter is found in the modern
small arms of reduced caliber, the weight and diameter of the
projectile having been reduced in such proportions as to increase
its sectional density.
EFFECT ON THE GUN. An increase in the weight of the pro-
jectile requires an increased pressure in the bore of the gun if the
initial velocity is to be maintained. The maximum pressure for
460 ORDNANCE AND GUNNERY.
any gun being fixed, it has been possible to increase the weight and
sectional density of projectiles only by the use of improved pow-
ders, which while they exert no greater maximum pressures exert
higher pressures along the bore of the gun. The mean pressure on
the projectile is therefore greatly increased, and to withstand the
increased pressure the chase of the gun is made stronger.
MANUFACTURE OF PROJECTILES.
268. Cast Projectiles. A wooden pattern of the shape of the
projectile is first made, the dimensions of the pattern being slightly
greater than the dimensions desired in the projectile, in order to
allow for contraction of the metal in cooling. The pattern is in
one or more parts, depending upon its size. The pattern shown in
Fig. 187 is in two parts separated at the line b. The parts are
slightly coned from this line to facilitate withdrawal from the
mold. For hollow projectiles a core box is also made similar in
its interior dimensions to the cavity in the shell. The core, e Fig.
187, made of core sand mixed with adhesives, is formed in the
core box around a hollow metal spindle wound with tow. The
heat of the casting burns the tow, and the gases from the core
pass out through the hollow spindle.
Fig. 188 shows a mold prepared for casting a shell. The outer
box, called the flask, is in two sections parting at the line xy. In
the lower part the sand is molded around the pattern, which is
also divided into two parts on the same line. In the upper part
of the flask the remainder of the mold is made and the core at-
tached in its proper position by means of the frame a bolted to
the flask. The gate b and the riser c are also formed in the mold,
the riser being considerably greater in diameter than shown in the
figure. The patterns are withdrawn and the parts of the mold
brought together and bolted.
The molten metal enters through the gate b, generally in a
tangential direction, so that the metal hi the mold has a circular
motion which assists in the escape of the gases and brings the
impurities to the center and top. The mold is filled with the
metal to the top of the riser, where the impurities collect. The
pressure of the liquid metal in the riser assists in making the cast-
PROJECTILES.
461
ing sound, and affords a means of adding molten metal as the
casting shrinks in cooling.
Solid shot are cast head down in order that the dense metal
may be in the head of the shot. Shells are cast base down, that the
base of the shell may be sound and free from cavities that would
allow the powder gases to pass into the interior and ignite the
bursting charge.
-6
FIG. 187.
FIG. 188.
Chilled Projectiles. For use against wrought iron armor the
heads of cast projectiles were hardened in casting by the process
of chilling. A comparatively thin iron mold the shape of the
head and in contact with it was fixed in the sand around the head
of the projectile. This served to rapidly conduct the heat away
from the head of the projectile, causing it to cool rapidly and
giving it great hardness. These projectiles are no longer used.
Forged Projectiles. The steel for a forged projectile is cut
from a cast ingot, and is then bored, forged, and turned to finished
dimensions. Armor piercing projectiles are in addition treated
462 ORDNANCE AND GUNNERY.
with some secret process of tempering to give them the hardness
and toughness necessary for the perforation of armor.
269. Requirements in Manufacture. The qualities of the
metal of the projectile are prescribed as follows: For cast iron,
tensile strength 27,000 Ibs. per square inch; for steel, in what are
called common shell, that is, those of the smaller calibers, tensile
strength 85,000 Ibs. For armor piercing projectiles the tensile
strength or elastic limit is not specified, further than by the re-
quirement that the projectiles in a lot shall not vary in tensile
strength by more than 20,000 Ibs. The strength of these shells is
determined by actual firing against armor. The cap must be of
steel whose tensile strength does not exceed 60,000 Ibs., with an
elongation at rupture of 30 per cent, and a reduction in area of
45 per cent.
The base plugs of all projectiles are made of forged steel.
Inspection of Projectiles. The dimensions of the projectiles
are tested by means of calipers, and profile and ring gauges. The
slight variations, called tolerances, allowed from the standard
dimensions are specified for each dimension, and the gauges for
any projectile are constructed for the maximum and minimum
of the particular dimension. Thus for the diameter of the band
there are two ring gauges, one a maximum, the other a minimum,
and similarly for other diameters. Maximum and minimum plug
gauges are applied to the threads of the fuse hole. A ring gauge
is shown in Fig. 189. A profile gauge or templet is shown at a in
Fig. 190.
FIG. 189. FIG. 190.
Eccentricity in the cavity of the projectile is determined by
rolling the projectile along two rails, a Fig. 191, placed on a flat
surface. Irregular movement of the projectile denotes eccen-
tricity, which may be measured by means of the calipers, d, shown
in the figure.
PROJECTILES.
463
For the detection of holes or cracks through the walls of hollow
projectiles all such projectiles are subjected to an interior hy-
draulic pressure. A pressure of 500 Ibs. per sq. in. is applied for
one minute to steel projectiles, and a pressure of 300 Ibs. for two
minutes to those of cast iron.
To determine whether the treatment received by the armor
piercing shot in the tempering process has left in the shot initial
strains that might cause rupture in store or in firing, these shot are
cooled to a temperature of 40 degrees F. and then suddenly heated
FIG. 191.
by being plunged into boiling water. When thoroughly heated by
the water, the projectile is suddenly cooled by being half inserted,
with its axis horizontal, in a bath of water at 40 degrees F. After
a brief interval it is turned 180 degrees for a like immersion of the
other half. Three days must elapse after the tempering of the
projectile before this test is applied. The necessity of the test is
indicated by the not infrequent bursting of the projectiles in the
shops after tempering. This test is not applied to armor piercing
shell. The thinner walls of these projectiles are more uniformly
affected by the tempering process.
464 ORDNANCE AND GUNNERY.
The interior walls of hollow projectiles are coated with a lacquer
of turpentine and asphalt for the purpose of making them smooth
and of reducing the friction between the walls and the bursting
charge.
Ballistic Tests. Each class of projectile is subjected to a
' allistic test under conditions assimilating the conditions of ser-
vice. For the purpose of the test two or more projectiles are
selected from each lot presented. The projectiles tested are filled
with sand in place of a bursting charge, and after the test must be
in condition for effective bursting.
Armor piercing shot are fired against hard faced Krupp armor
plate, from 1 to 1J calibers thick, secured to timber backing. The
striking velocities of the shot from 8, 10, and 12 inch rifles
against plates one caliber thick are near to 1750 feet, which corre-
sponds to ranges of about 3000, 4000, and 5000 yards, respectively^
from the three guns. The shot is required to perforate the plate
unbroken and then be in condition for effective bursting.
Armor piercing shells must meet similar conditions, the thick-
ness of the plate being one half the caliber of the shell, and the
striking velocities, 1420 f. s. for 5-inch shell, 1220 f. s. for 6-inch
shell, and 920 f . s. for 8-, 10-, and 12-inch shell.
12-inch deck piercing shell must perforate a 4J-inch nickel
steel protective deck plate at an angle of impact of 60 degrees.
12-inch torpedo shell are fired into a sand butt from a gun in
which the chamber pressure must be 37,000 Ibs.
Common steel shell for seacoast guns of small caliber are
tested with service velocities against tempered steel plates from 3
to 5 inches thick, depending on the caliber and service velocity of
the projectile.
The shell for field and mountain guns are fired into sand, with
a pressure in the gun 12 per cent greater than the service pressure
and with at least the service velocity.
Tests are also made to determine whether the fragmentation of
the projectile on bursting is satisfactory.
The Painting of Projectiles. Projectiles are so painted as to
indicate the metal of which they are formed and the character of
the bursting charge. The greater part of the body is black. A
broad colored band around the projectile over the center of gravity
PROJECTILES. 465
indicates by the color whether the projectile is of iron, cast or
chilled, or of steel, cast or forged.
The color of the base indicates whether the projectile is charged
with powder or with high explosive. In assembled ammunition
the base color is painted in a band just above the band of the
projectile.
CHAPTER XI.
ARMOR.
270. History. The use of armor for the protection of ships of
war began in France in 1855 and soon became general. The first
armor was of wrought iron. This metal opposed a sufficient re-
sistance to the round cast iron projectiles of that time and to the
elongated cast iron shot of a later date. As the power of guns
increased and chilled projectiles came into use wrought iron armor
became ineffective. It was replaced about 1880 by compound
armor, which consisted of a wrought iron back and a hard steel
face. Compound armor wa,s made either by running molten steel
on the previously prepared wrought iron back or by welding a
plate of steel to another of wrought iron by running molten steel
between them, both plates being previously brought to a welding
heat. The hard steel face opposed a great resistance to penetra-
tion of the shot and caused the shot to expend its energy in shatter-
ing itself. At the same time it distributed the stress over an in-
creased section of the iron back, and the toughness of the wrought
iron served to hold the plate together. The chief defect of the
compound plate was due to the difficulty of obtaining intimate
union between the two metals, and lay in the tendency of the steel
face to flake off over considerable areas. The basic principle of
this armor, the hard face and the tough back, is still maintained
in the construction of the most modern armor.
NOTE. This chapter is largely derived from the chapter on armor by
Lieutenant Commander Cleland Davis, U. S. Navy, in Fullam and Hart's
Text Book of Ordnance and Gunnery, 1905.
466
ARMOR. 467
At the same time that the compound plate was used by Great
Britain and other powers the all steel plate was being used by
France, the effectiveness of the two plates being about equal.
In 1889 the homogeneous nickel-steel plate, markedly superior
to the steel plate in toughness and resisting power, was introduced.
The Harvey treatment of the nickel-steel plate, developed in the
United States in 1890, still further increased the resisting power
of armor, and in 1895 the Krupp process followed with further
improvement.
Harvey and Krupp Armor. The principle employed in the
manufacture of armor by these two processes is the same. In
both, the face of the plate is made extremely hard by supercarbon-
ization and subsequent chilling. The superiority of the Krupp
plate appears to be due to the composition of the steel. The
Harvey plate is made of a manganese nickel steel, while in the
Krupp plate chromium is also present, and in greater quantity
than the manganese. The composition of the two plates, in per-
centages, is given as follows:
C. Mn. Si. P. S. Ni. Cr.
Harvey 0.30 0.80 0.10 0.04 0.02 3.25 0.00
Krupp 0.35 0.30 0.10 0.04 0.02 3.50 1.90
The nickel, and to a certain extent the manganese, give great
strength and toughness to the metal, while the chromium makes
the metal more susceptible to the treatment that gives the desired
qualities to the finished plate. First, it permits the attainment of
a very tough fibrous condition throughout the body of the plate
that makes it less liable to crack; second, it gives the metal an
affinity for carbon which enables supercarbonization to a greater
depth; third, it increases the susceptibility of the metal to tem-
pering, which gives a greater depth of chill. These are the quali-
ties that mark the superiority of Krupp armor.
Even when carbonization of the plates is effected in the same
manner, carbon will be absorbed to a greater depth in the Krupp
than in the Harvey armor, giving a greater depth of hardened face
and an increased resistance to penetration of about 20 per cent.
271. Manufacture of Armor. The steel, of proper composi-
tion, is made in the open hearth furnace and cast into an ingot of
the shape shown in Fig. 192. The head of the ingot affords a
468
ORDNANCE AND GUNNERY.
means for the attachment of the chains of the cranes employed in
handling it. A long heavy beam is used to counterbalance the
weight of the plate when slung in the chains.
When stripped from the mold and cleaned, the ingot is heated
in a furnace and then forged, as shown in Fig. 193, under an
immense hydraulic press capable of exerting a total pressure of
about 15,000 tons. The forging reduces the thickness of the plate
\
244'
130"-
FIG. 192.
and increases its length and breadth. The plate is then rough
machined approximately to finished dimensions.
CAKBONIZING. The carbonization of the face of the plate is
effected by one of two methods: the cementation process, or the
gas carbonizing process. The cementation process consists in
covering the surface of the plate with carbonaceous material,
usually a mixture of wood and animal charcoal, heating the plate
to a temperature of about 1950 degrees, and maintaining it at
this temperature for a sufficient time to accomplish the required
ARMOR. 469
degree of carbonization. A covering of sand protects the face of
the plate and the carbonizing material from the flames of the
furnace, and excludes the air. From four to ten days, depending
on the thickness of the plate, are required to bring the plate to the
desired temperature, and a further period of from four to ten days
to effect the carbonization of the face. Under the action of the
heat the carbon is absorbed into the face of the plate, and pene-
trates into the interior, the quantity of the absorbed carbon dimin-
ishing from the surface inward.
The gas carbonizing process consists in passing coal gas along
the face of the plate heated in a furnace to about 2000 degrees.
The heat decomposes the gas, which deposits carbon on the face
of the plate, and the carbon is absorbed as in the cementation
process.
REFORGING AND BENDING. After being cleaned of the scale
that is formed on it in the process of carbonization the plate is re-
forged to its final thickness. It is then annealed and bent to the
desired shape in a hydraulic press. The operation of bending an
armor plate in a 9000 ton press is shown in Fig. 194.
HARDENING. For tempering, the plate is uniformly heated to
a high temperature and quickly cooled or chilled by cold water
sprayed upon it under a pressure of about 23 pounds to the square
inch.
In Krupp plates as first made the tempering produced cracks
over the whole hard surface of the plate, some of them a quarter
of an inch wide and extending some distance into the plate. The
cracks were characteristic of the plate and were not considered
abnormal, the resistance of the plate even with the cracks being
greater than that of plates made by other processes. With im-
provement in the process of manufacture smoother plates were
produced, and in many of the latest plates the surface appears
continuous to the naked eye. When etched with acid, however,
the face is found to be covered with a network of fine lines and
presents an appearance similar to that of crackled glass.
272. Armor Bolts. The armor plates are fastened to the sides
of ships by means of nickel-steel bolts. These are of such strength
that they are not broken by the impact of projectiles that badly
crack the plate. The bolts pass through the sides of the ship and
470
ORDNANCE AND GUNNERY.
are screwed into the soft back of the armor plate. To insure a
good fit of the plate, and at the same time to lengthen the armor
bolt so that its deformation per unit of length under the stresses
of impact may not be excessive, wood backing is used between
the armor plate and the ship's side. The wood backing is being
reduced in thickness and the tendency is to discard it altogether.
Figs. 195 and 196 show types of bolts for armor with and without
wood backing.
FIG. 195.
The threads on the bolts are all plus threads, so that the bolt is
of uniform strength. A calking of marline or oakum surrounds
the bolt to prevent leakage through the
bolt hole. A steel washer is under the
head of the bolt. A rubber washer has
also been used under the steel washer
to diminish the suddenness of any
strain on the bolt head.
Armor bolts vary in diameter from
1.5 inches for plates 5 inches thick or
less to 2.4 inches for plates 9 inches
FlG 196 thick and upward.
In number they are provided one
for every five square feet of surface as far as the framing of the
ship will permit.
ARMOR. 471
Ballistic Test of Armor. The U. S. Navy specifications re-
quire as a test, before acceptance of Krupp and Harvey armor,
three impacts of capped shells against a specimen plate, with
velocities as given in the following table.
Caliber Capped Plate Striking
of Gun, Projectile, Thickness, Velocity,
Inches. Pounds. Inches. f . s.
6 105 5 1416
6 105 6 1608
6 105 7 1791
7 165 6 1416
7 165 7 1578
7 165 8 1732
8 260 . 7 1412
8 260 8 1552
8 260 9 1685
10 510 9 1458
10 510 10 1569
10 510 11 1676
12 870 11 1412
12 870 12 1501
The first impact in the center of the plato must not develop
a through crack to an edge of the plate, and no part of the pro-
jectile shall get entirely through the plate and backing. On the
second and third impacts no part of the projectile shall get en-
tirely through the plate and backing. The impacts shall not be
nearer than 3J calibers to each other or to an edge of the plate.
Comparing the requirements for plates attacked by the 8, 10,
and 12 inch guns with the requirements of the ballistic tests of
armor piercing projectiles for the land service, page 464, it will be
seen that the armor plates one caliber thick are tested with
velocities about 200 feet less than those at which the projectiles
from land guns are required to perforate similar plates.
Characteristic Perforations. Characteristic perforations in
hardened and unhardened armor are shown in Figs. 197 and 198,
the front face of the plate being uppermost in each figure. The
face of the hardened armor, Fig. 197, breaks and crumbles under
impact, while the metal of the unhardened plate, Fig. 198, being
softer and more tenacious, flows under the pressure of the projec-
tile in the direction of least resistance and forms a combing in
472
ORDNANCE AND GUNNERY.
front of the plate. When the projectile reaches the back of the
hardened armor the metal of the back, being prevented from
flowing by the hard face, breaks out in one or more pieces, leaving
FIG. 197.
a broad based conical hole through the back and producing but
slight bulging of the rear surface of the plate.
As the metal of the imhardened plate is of the same constitu-
tion throughout, the perforation does not exhibit the marked
FIG. 198.
differences shown in the hardened plate. The metal of the back
part of the plate flows to the rear, producing a greater bulging of
the rear surface.
273. Armor Protection of Ships. The armor carried by ships
of war is of various thicknesses, depending upon the size and pur-
pose of the ship and on the position of the armor on or in the ship.
The thickest armor is used to protect the water line and the vital
parts of battleships. The present practice in the United States is
to protect the whole length of the water line with a belt of armor
8 feet wide extending 4J feet above the water line and 3J feet
below it.
ARMOR. 473
This belt, see Fig. 199, has its maximum thickness over that
part of the ship that contains the machinery and the magazines.
The thickness diminishes from the mid-ship section and is least at
the bow and stern.
The gun turrets are protected in front by the thickest armor.
Armor of less thickness covers the casemates, barbettes, and sides
of the turrets, the thickness depending upon the importance of
the part protected and upon its exposure to hostile fire.e.
An armored deck of a thickness to prevent penetration by the
fragments of exploded shell extends the whole length of the ship.
This deck, the berth deck, Figs. 199 and 200, is flat over the
machinery and boiler spaces and slopes downward at the sides
and at the bow and stern to the bottom of the belt armor. On
the heaviest ships the armored deck has a thickness of two inches
over the flat part and four inches on the slopes, the thickness
being reduced over the flat part in order to reduce the weight.
The gun deck, next above the armored deck, is sometimes an
armored splinter deck one inch thick.
Across the main body of the ship, bow and stern, extends
heavy athwartship armor, which, with the armored barbettes and
turrets, provides protection to the body of the ship from fire from
the front or rear. Thus with the side armor the main body of
the ship becomes an armored box, within which the crew, the
machinery, the magazines, and the guns are protected.
With the improvements that have taken place in armor within
the last fifteen years there has been a gradual reduction in the
thickness of armor carried by ships of the various classes.
The battleship Oregon, built in 1893, has a water line belt 18
inches in thickness, while the battleship Connecticut, commis-
sioned in September, 1906, has but 11 inches of armor at her water
line.
The arrangement of the armor on the battleship Connecticut
is shown in Figs. 199 and 200.
Definitions. The following definitions will assist toward a
ready understanding of the figures.
TURRET. A revolving armored structure in which one or two
guns are mounted. The guns revolve with the turret and are
completely enclosed with the exception of the chase of the gun,
474
ORDNANCE AND GUNNERY.
ARMOR.
475
which projects through a port hole in the front plate of the
turret.
BARBETTE. A fixed circular structure, armored, which pro-
tects the mechanism for the
ammunition supply of the gun
mounted above it and the
mechanism of the turret con-
taining the gun.
CASEMATE. An isolated gun
position for a broadside gun
with fixed armor protection.
The casemate completely en-
closes the gun with the excep-
tion of the chase, which projects
through a port hole.
CENTRAL CITADEL. Armor
enclosing a series of broadside
guns. There may or may not
be splinter bulkheads between
the guns. With the bulkheads
completely enclosing the guns the citadel becomes a series of
casemates.
274. Chilled Cast Iron Armor. This armor on account of its
thickness and great weight is used only on land. It is manu-
factured by Gruson of Germany. It is cast in large blocks whose
outer faces are made very hard by chilling. The fclocks are then
built into turrets, usually of rounded shape.
On account of the great weight and hardness of the metal and
the rounded shape of the turrets, this armor affords better pro-
tection than any other armor.
Gun Shields. Guns of 6 inches caliber and less mounted in
barbette in seacoast fortifications are provided with shields per-
manently attached to their carriages. The shields are made of
Krupp plate 4J inches thick. The requirements of the ballistic
test for these shields are as follows.
The shield, firmly supported by a backing of oak timbers, is
subjected to three shots from a 5-inch gun. The striking velocity
of the shot is 1500 feet and the impact normal. On the first im-
FIG. 200.
476 ORDNANCE AND GUNNERY.
pact, near the center of the shield, no portion of the projectile
shall get through the shield, nor shall any through crack develop to
an edge of the shield. The other two impacts are so located that
no point of impact shall be less than three calibers of the projectile
from another point of impact or from an edge of the shield. At
the second and third jmpacts no projectile or fragment of projectile
shall go entirely through the shield.
The supports that hold the shield to the carriage are very heavy
ribbon-shaped springs, which reduce the stress on the carriage from
the impact on the shield. The springs are of great strength in
order to withstand the shock of impact. They are made of steel
with a tensile strength of 110,000 Ibs., elastic limit 75,000 Ibs.,
e ongation at rupture 15 per cent, contraction of area 25 per cent.
The fastening bolts must have a tensile strength of 80,000 Ibs.,
and an elongation at rupture of 27 per cent.
The shields are curved around the front of the carriage and are
inclined upward and to the rear at an angle of 40 degrees. The
chase of the gun protrudes through a hole in the shield and other
holes are provided for sighting purposes.
Fig. 201 shows the arrangement of the shield on a 6-inch bar-
bette carriage.
Shields will probably be provided for all barbette carriages.
It is still a matter of discussion as to whether advantage is
derived by the use of gun shields, for while they serve to keep
out the smaller .projec tiles they also serve to determine the burst-
ing of larger projectiles whose destructive power may be sufficient
to disable the gun and wholly destroy the gun detachment. With-
out the shields these projectiles would in many instances pass by,
doing little or no harm.
Field Gun Shields. Shields of hardened steel plate two-
tenths of an inch thick are attached to the gun carriage and caisson
for the 3-inch field gun. These shields are tested by firings, at a
range of 100 yards, with the 30 caliber rifle, using steel jacketed
bullets with 2300 feet muzzle velocity. The plate must not be
perforated, cracked, broken, or materially deformed.
The front of the caisson chest is made of the same material as
the shields and has the same thickness. The door of the chest,
which opens upward to an angle of 30 degrees, is made of hardened
steel plate T VV of an inch thick.
I
3
8
2
PH
O
1
f
CHAPTER XII.
PRIMERS AND FUSES FOR CANNON.
275. Classification. Primers are the means employed to
ignite the powder charges in guns.
They may be divided, according to the method by which
ignition is produced, into three classes:
Friction primers,
Electric primers,
Percussion primers.
Combination primers are those so constructed that they may
be fired by any two of the above methods. Primers that close
the vent against the escape of the powder gases are called ob-
turating primers.
All primers should be simple in construction, safe in handling,
certain in action and not liable to deterioration in store. Electric
primers in addition should be uniform as to the electric current
required for firing.
Common Friction Primer. The primer known as the common
friction primer, formerly used in all cannon, is shown in Fig. 202.
The body b and the branch d are copper tubes. The tube b is
filled with rifle powder, and is closed at its lower end by a wax
stopper a. The tube d is filled with the friction composition,
whose ingredients are chlorate of potash, sulphide of antimony,
ground glass, and sulphur mixed with a solution of gum arabic.
Imbedded in the friction composition is the serrated end of the
copper wire c, the other end of the wire being formed into a loop
for attachment of the hook of the lanyard. The outer end of the
tube d is closed over the flattened end of the wire, which is bent
over into a hook, as shown, and serves to hold the wire securely in
477
478
ORDNANCE AND GUNNERY.
place except when a stout pull is given to the lanyard. The pull
on the lanyard straightens out the hook and draws the serrated
wire through the friction composition, igniting it. The fire is
communicated to the rifle powder in the tube 6, and thence through
the vent to the powder charge in the gun.
For use in axial vents, in order to prevent the primer being
blown to the rear among the men of the gun detachment, a coiled
copper wire e is added to the primer, one end of the wire being
FIG. 202.
made fast to the top of the primer body, the other end to the loop
for lanyard hook. The coil is extended by the pull of the lanyard,
and the primer when blown to the rear remains attached to the
lanyard.
Service Primers. The. primer above described is blown out of
the gun by the explosion of the powder charge, leaving the vent
open for the escape of gas. This disadvantage is overcome in
modern practice by the use of obturating primers. The breech
mechanisms of all guns now made are adapted to obturating
primers, and the primer just described is no longer used in service
cannon.
The firing mechanism described in the chapter on guns, page
263, is fitted to most of the cannon in our service that do not use
fixed ammunition. The firing mechanism is adapted to receive
the primer and hold it firmly, and is provided with means for
firing the primer either by the pull of a lanyard or by electricity.
276. The Service Combination Primer. The principal primer
used in our service is a combination primer which is arranged to
PRIMERS AND FUSE FOR CANNON.
479
be fired either by friction or by electricity. The primer is shown
complete in Fig. 203. The igniting elements are shown on a larger
b c d e f g hk
FIG. 204.
PIG. 203.
scale in Fig. 204. The igniting elements are assembled in the
brass case /, which is screwed to its seat in the primer.
FRICTION ELEMENTS. For firing by friction there is pressed
into the case / an annular pellet of friction composition, shown in
black in Fig. 204, which rests on a vul-
canite washer, g. The washer supports the
composition and prevents it from crum-
bling when the pull which fires the primer is
applied. The inner end of the firing wire,
k, is loosely surrounded by the serrated
cylinder h, which is imbedded up to the
serrations in the friction composition. The
headed inner end of the firing wire fits in a seat inside the
serrated cylinder, and the parts are held securely in place by the
forked metal support e and the closing nut 6.
When the firing wire is pulled the serrated cylinder is drawn
through the composition and ignites it. The conical end of the
cylinder h is drawn to its seat in the rear part of the primer and
prevents escape of gas to the rear. The flame from the friction
composition passes through vents in the closing nut, 6, and ignites
the priming charge of compressed and loose black powder in the
body of the primer.
The mouth of the primer is stopped by the brass cup, a, shel-
lacked in place. This cup is blown out by the explosion of the
primer charge, and the flames from the primer pass through the
vent in the breech block and ignite the powder charge in the gun.
The pellet of powder near the mouth of the primer is also blown
through the vent and insures the ignition of the charge in the gun.
480 ORDNANCE AND GUNNERY.
ELECTRIC ELEMENTS. For electric firing the wire k is covered
with an insulating paper cylinder j and enters the primer body
through a vulcanite plug i. The wire is in electric contact with
the serrated cylinder h, Fig. 204, but this is insulated from the
primer body by the vulcanite washer g and the pellet of friction
composition, a non-conductor of electricity.
The electrical elements of the primer are assembled in the
metal case /. The head of the forked metal support e is in contact
with the headed end of the wire k, but not fastened to it. The
forked end of the support is held in the vulcanite cup c. The
brass contact nut b, screwed into the end of the case /, presses the
assembled parts into intimate electrical contact. A platinum wire
d is soldered to the head of the support e and to the contact nut b.
An igniting charge of guncotton surrounds the wire.
When the primer is inserted in the gun the uninsulated button
at the end of the wire j is grasped by the parts of an electric contact
piece through which the electric firing current passes. The cur-
rent passes through the wire j, the platinum bridge, and the body
of the primer to the walls of the gun and thence to the ground.
The passage of the electric current heats the platinum wire,
igniting the guncotton and the priming charge of powder.
It will be observed that the friction elements of the combina-
tion primer are independent of the electrical elements, and that
when one of these primers fails to fire by electricity it may still be
fired by friction.
If, however, the primer fails in an attempt to fire it by friction,
it will not generally be possible to fire it electrically since the
cylinder A, which has been pulled into the head of the primer, is
out of contact with the part e and the platinum wire bridge. The
current will then pass directly from h through the primer body
and gun to the ground.
The primer should in this case be at once removed from the
vent and not be again used.
The outer button and wire k may be turned without danger of
breaking the platinum wire bridge d.
When an electric or friction primer fails to fire it should be
removed from the vent and the wire bent down and around the
primer to prevent attempts to use it again.
PRIMERS AND FUSES FOR CANNON.
481
The metal parts of the primer are tinned to prevent corrosion.
Other Friction and Electric Primers. Primers arranged for
firing by friction alone are shown in Figs. 205 and 206. The primer
FIG. 205.
shown in Fig. 206, of simple and cheap construction, is for drill
purposes only.
FIG. 236.
The friction primer shown in Fig. 207 and the electric primer
FIG. 207.
shown in Fig. 208 are for use in the 3.6-inch and 7-inch mortars,
FIG. 208.
The
these guns not being provided with firing mechanisms,
primers are screwed into the vents in the breech blocks.
277. Percussion Primers. The friction and electric primers
described are used in guns in which the projectiles and powder
charges are loaded separately, the primer being separately in-
serted in the breech block. Percussion primers, and the electric
primer described with them, are, on the other hand, inserted in
cartridge cases, in which are usually assembled both the projectile
and the powder charge.
482 ORDNANCE AND GUNNERY.
The essential parts of a simple percussion primer such as the
cap in a small arm cartridge, are the primer cup, the anvil, and
the percussion composition.
Formerly the percussion composition of all service primers
contained a large percentage of fulminate of mercury. On ac-
count of the danger involved in handling mixtures containing
the fulminate of mercury, its use as a primer ingredient in service
primers manufactured at the Frankford Arsenal has been aban-
doned, and a mixture known as the H-48 composition is now em-
ployed.
This mixture contains the same ingredients as the friction com-
position, but in different proportions, as follows :
Chlorate of potash, 49.6. Ground glass, 16.6.
Sulphide of antimony, 25.1. Sulphur, 8.7.
To insure the practically instantaneous ignition of smokeless
powder charges, the addition of a small charge of quick-burning
black powder is required. This may be inserted in the base of the
smokeless powder charge, or may be contained in the primer. It
is desirable, on account of the smoke produced by black powder
and the fouling of the bore, that the quantity of black powder
used be limited to the smallest amount that will produce prompt
and complete ignition of the smokeless powder. The minimum
amounts required for different charges have been determined and,
for fixed ammunition, are contained in the percussion and igniting
primers. These primers are inserted in the head of the cartridge
case, in the position occupied by the primer in the small arm
cartridge.
Two sizes of percussion primers, the 110-grain and the 20-
grain, have been adopted for all guns from the 1-pounder to the
6-inch Armstrong inclusive.
110-GRAiN PERCUSSION PRIMER. The body / is of brass, 2.93
inches long, Fig. 209. A pocket is formed in the head of the case
for the reception of the metal cup e containing the percussion com-
position d. Projecting up from the bottom of the pocket is the
anvil c against which the percussion composition is fired. Two
vents are drilled through the bottom of the pocket. The priming
charge consists of 110 grains of black powder inserted under high
PRIMERS AND FUSES FOR CANNON.
483
pressure into the primer body around a central wire. The with-
drawal of the wire after the compression of the powder leaves a
longitudinal hole the full length of the primer. Six sets of radial
holes are drilled through the walls of the primer and through the
compressed powder. The compression of the powder increases the
time of burning of the priming charge and causes the primer to
burn with a torch-like rather than an explosive effect, making the
HhHhH
FIG. 209.
ignition of the smokeless powder charge more complete. The
holes through the priming charge increase the surface of com-
bustion and the mass of flame, and direct the flames to different
parts of the charge of powder, thus facilitating its complete igni-
tion. The paper wad, a, shellacked in the mouth of the primer
and the tin-foil covering, 6, serve to keep out moisture and to
protect the primer from the impact of the powder grains when
transported assembled in cartridge cases.
This primer is used in cartridge cases for guns from the
6-pounder to the 6-inch Armstrong gun, inclusive.
20-GRAiN PERCUSSION PRIMER. The 20-
grain percussion primer, shown in Fig. 210,
length 1.1 inches, is used in cartridge cases for
1-pounder subcaliber tubes, 1-pounder machine
guns, and 1.65-inch Hotchkiss guns.
20-grain Saluting Primer. This primer, Fig. 211, costing less
to manufacture than the 110-grain primer, is to be used in place
of the latter with blank charges only. The
primer contains a charge of 20 grains of loose
rifle powder. As black powder only is used
in blank charges, a smaller igniting charge
FIG. 211 answers.
FIG. 210.
484
ORDNANCE AND GUNNERY.
no-grain Electric Primer. This primer, Fig. 212, is similar
in form to the 110-grain percussion primer just described, and has
the same priming charge similarly ar-
ranged. Ignition is produced electrically
through the brass cup g, to which one
en d f the platinum wire e is soldered.
A small quantity of guncotton surrounds
the wire. Electric contact is made with
the cup g by the insulated firing pin of
the gun. The cup is insulated from the
body of the primer by the cylinder / and
bushing d, both of vulcanite. The brass
c d e f g
FIG. 212.
FIG. 213.
contact bushing c, to which the other end of the platinum wire
is soldered, completes the electrical connection.
278. Combination Electric and Percussion Primer. In Fig.
213 is shown a combination electric and percussion primer used in
rapid-fire guns in the U. S. Navy. Its
construction can be readily understood
from the figure. The insulation is
shown by the heavy black lines. When
fired by percussion the percussion cap
'.s not directly struck by the firing pin,
but by the point of a plunger forced inward by the blow.
Igniting Primers. The igniting primers are for use in car-
tridge cases for subcaliber tubes for seacoast cannon not provided
with percussion firing mechanism. They contain no means of
ignition within themselves, but require for their ignition an aux-
iliary friction or electric primer which is inserted in the vent of the
piece in the same manner as for service firing. The flame passes
from the service primer through the vent in the breech block to
the igniting primer in the head of the cartridge case. The flame
from the service primer would not be sufficient to ignite properly
the smokeless powder charge in the cartridge case, and therefore
the igniting primer is added.
The 110-grain and the 20-grain igniting primers, Figs. 214 and
215, differ from the corresponding percussion primers in the sub-
stitution of the obturating cup a and obturating valve 6, both of
brass, for the percussion cup and anvil. The obturating cup a is
PRIMERS AND FUSES FOR CANNON.
485
provided with a central vent to allow passage for the flame from
the auxiliary primer. The obturating valve b is cup-shaped, and
has three sections of metal cut away from its top and sides to
allow passage of the flame. The valve b has a sliding fit in the
cup a, and when the pressure is greater in front of the valve than
behind it, the valve is forced to the rear and the solid top of the
valve closes the vent in the outer cup.
The valve is shown in section in Fig. 214, in the position it
assumes after firing; and in elevation in Fig. 215, in its position
before firing.
FIG. 214.
FIG. 215.
Insertion of Primers in Cartridge Cases. The percussion
primers and igniting primers and the electrical primers of the same
form are so manufactured as to have a driving fit in their seats in
the cartridge cases to which they are adapted, the diameter of the
primer being from one-and-a-half to two thousandths of an inch
greater than the diameter of the seat. Special presses for the in-
sertion of the primers are provided. The primer must no.t be
hammered into the cartridge case. The primer seats in all car-
tridge cases using these primers are rough bored to a diameter
about 20 per cent less than the finished size, and then mandrelled
to finished dimensions with a steel taper plug, to toughen the metal
of the cartridge case around the primer seat. The toughening is
necessary to prevent expansion of the primer seats under pressure
of the powder gases, and consequent loose fitting of the primers in
subsequent firings.
486 ORDNANCE AND GUNNERY.
FUSES.
279. Classification. Fuses are the means employed to ignite
the bursting charges of projectiles at any point in the flight of the
projectile, or on impact.
They are of three general classes:
Time fuses,
Percussion fuses,
Combination time and percussion fuses.
All fuses should be simple in construction, safe in handling,
certain in action, and not liable to deterioration in store. In
addition the rate of burning of the time train of the fuse must be
uniform.
The time fuse alone, that is, without percussion element, is no
longer used in modern ordnance.
Percussion Fuses. A percussion fuse is one that is prepared
for action by the shock of discharge, and that is caused to act by
the shock of impact.
When ready to act, as after the shock of discharge, the fuse is
said to be armed.
Percussion fuses are inserted at the point or in the base of the
projectile. In the projectiles for 1- and 2-pounder guns the fuse
is inserted at the point. The percussion fuses for field, siege, and
seacoast projectiles are base insertion fuses.
The percussion fuse consists essentially of the case or body, of
brass, which contains and protects the inner parts and affords a
means of fixing the fuse in the projectile; the plunger, carrying
the firing pin and provided with devices to render the fuse safe in
handling; the percussion composition, which is fired by the action
of the plunger on impact; and the priming charge of black gun-
powder.
The percussion composition of all service fuses manufactured
at Frankford Arsenal is the same. The ingredients are chlorate of
potash, sulphide of antimony, sulphur, ground glass, and shellac.
The thoroughly pulverized ingredients are mixed dry, and alcohol
is added to dissolve the shellac. The percussion pellets are formed
by pressing the mixture while in a plastic state into the percussion-
PRIMERS AND FUSES FOR CANNON.
487
primer recess. Upon the evaporation of the alcohol the shellac
causes the pellet to adhere to the metal of the recess.
A fulminate of mercury percussion composition was formerly
used in fuse primers, but on account of the danger incident to
handling this compound it has been abandoned as a primer in-
gredient.
It is still used abroad, and the percussion composition of both
the Ehrhardt and Krupp combination time and percussion fuses
contains fulminate of mercury.
Point Percussion Fuse. Point percussion fuses are adapted
to the projectiles for 1-pounder and 2-pounder guns only.
-\ a
_A_ :
1
/ \
Pi
1 1
1 1
Tl
i i
S-i-J-
r*
p|
pi
FIG. 216.
FIG. 217.
The body, a Fig. 216, is of brass. The percussion composition
and the priming charge of black powder are assembled in a
vented case, e, which is screwed into a recess formed in the head of
the fuse. A thin brass disk, the primer shield, protects the per-
cussion composition from the firing pin in the body of the fuse. It
prevents any dislodgment of the composition during transporta-
tion or by shock of discharge and also restrains the firing pin during
the flight of the projectile.
Contained in the body of the fuse is the plunger, which consists
of the firing pin /, the cylindrical sleeve h, and the split-ring spring k,
all of brass. The firing pin has an enlarged rear part joined to the
forward part by a conical slope and provided near the bottom
with a groove, /, of diameter slightly larger than the diameter of
the forward part of the pin. A radial hole, i, through the pin near
488 ORDNANCE AND GUNNERY.
its forward end, and an axial hole from this point to the rear end
of the pin, provide a passage for the flame from the priming charge.
The rear part of the bore through the sleeve h is of diameter just
sufficient to admit the spilt ring which rests against the forward
shoulder of the counterbored recess in the sleeve and holds the
firing pin so that its point is wholly within the sleeve. The front
part of the sleeve is counterbored to permit ready entrance of the
flame from the priming charge into the passage through the firing
pin. The plunger thus assembled is placed in the fuse body,
which is closed by the brass closing screw m provided with a cen-
tral vent which is in turn closed by the brass disk n. To prevent
pressure of the closing screw on the plunger, which might cause
expansion of the split ring and the arming of the fuse, the plunger
is allowed a longitudinal play in the fuse body of from one to two
hundredths of an inch. With the parts of the fuse in this position
the point of the firing pin is prevented from coming into contact
with the percussion composition, and therefore the fuse cannot be
fired.
If sufficient force is applied rearwardly to the sleeve A, the split
ring k will be forced over the enlarged portion of the firing pin until
it rests in the groove I near the bottom; and the sleeve, moving to
the rear, will expose the point of the firing pin. The fuse is then
armed, as shown in Fig. 217.
To insure arming of the fuse when fired the resistance of the
split ring to expansion is made less than the force necessary to
give the sleeve the maximum acceleration of the projectile. There-
fore when the piece is fired and while the projectile is attaining its
maximum acceleration, the pressure of the sleeve will force the
ring over the enlarged part of the firing pin into the groove at the
rear.
The diameter of this groove being greater than the diameter of
the front part of the firing pin, the ring is now expanded into the
counterbored recess in the sleeve and locks the sleeve and firing
pin together, with the point of the firing pin projecting beyond the
sleeve.
As the plunger of the fuse does not encounter the atmospheric
resistance which retards the projectile in its flight, it is probable
that during the flight of the projectile the plunger moves slowly
PRIMERS AND FUSES FOR CANNON.
489
forward until the point of the firing pin rests against the brass
primer shield.
At impact of the projectile the combined weight of the plunger
parts acts to force the point of the firing pin through the primer
shield and into the percussion composition, igniting the composi-
tion.
The flame from the priming charge passes through the forward
vents, through the passages in the plunger, and through the vent
in the closing screw, blowing out the closing disk and igniting the
bursting charge in the shell.
280. Base Percussion Fuse, for minor caliber shell. This
fuse, as well as the point percussion fuse, is adapted to the pro-
jectiles for 1-pounder and 2-pounder guns. The fuse for the pro-
jectiles of the 6-pounder gun and of the 2.38-inch field gun is
similar in construction.
The fuse, Fig. 218, is similar in construction and action to the
point percussion fuse. As the primed end of the fuse is toward the
interior of the shell the flame from the priming
charge passes directly to the bursting charge in
the shell without passing through the body of
the fuse. The flame passages through the
plunger parts are therefore omitted. The pri-
mer cup b, containing the percussion composi-
tion and priming charge, is closed at its outer
end by the brass disk a, which is secured in
place by crimping over it a thin wall left on the
brass closing cap screw c.
The act of arming a ring-resistance percus- FlG - 218 -
sion fuse shortens the plunger and increases materially its longitu-
dinal play in the fuse body. This fact permits a ready and simple
means of inspecting for premature arming without dismantling the
fuse. If the fuse be held close to the ear and shaken, the marked
difference between the play of the plunger in an armed fuse and in
an unarmed one can be readily discerned.
Centrifugal Fuses. The centrifugal fuse of service pattern is
the result of a long series of experiments made for the purpose of
developing a fuse that would fulfill the requirements of absolute
safety in handling and transportation, and certainty of action.
490 ORDNANCE AND GUNNERY.
In the case of ring-resistance fuses, or any fuse the action of
which depends on the longitudinal stresses developed by the pres-
sure in the gun, the conditions of safety in handling and certainty
of action are opposing ones.
It was impossible to meet successfully both sets of conditions
in all cases, the stress developed in the direction of the axis by
accidental dropping of a fuse being in many cases higher than that
developed in the gun.
A fuse which is armed by the centrifugal force developed by the
rotation of the projectile, and which is safe until the maximum
velocity of rotation is nearly attained, has been developed at the
Frankford Arsenal and is now used in the projectiles for low
velocity guns; the mountain gun, and all howitzers and mortars.
In these guns the maximum acceleration of the projectile in the
bore is so low that the ring-resistance fuse must be very sensitive
in order to insure arming, with the result that it becomes too sen-
sitive for safety in handling and transportation. For the projec-
tiles of other guns the fuses are similar, but are provided with ring-
resistance plungers instead of centrifugal plungers.
The centrifugal fuse, before arming, is shown in Fig. 219.
Fig. 220 is a view of the plunger after arming.
The fuse body, or stock, and the primer parts of the centrifugal
fuse do not differ materially from the corresponding parts of the
ring-resistance fuses. To better protect the priming charge the
closing cap screw b is lengthened and the vented primer-closing
screw a is added.
The body of the centrifugal plunger is in two parts, nearly semi-
cylindrical in shape, which when the fuse is at rest are held to-
gether by the pressure of a spiral spring g contained in the cylin-
drical bushing e which is secured to one of the plunger halves. The
spring exerts its pressure on the other half of the plunger through
the bolt /. Pivoted in a recess in one half of the plunger is the
firing pin d, which when the fuse is at rest is held with its point
below the front surface of the plunger by the lever action of the
link c which is pivoted in the other half. Under the action of the
centrifugal force developed by the rapid rotation of the projectile
the two halves of the plunger separate. The separating move-
ment causes the rotation of the firing pin d, the point of which is
PRIMERS AND FUSES FOR CANNON.
491
now held in advance of the front surface of the plunger, Fig. 220,
ready, on impact of the projectile, to pierce the brass primer
shield and ignite the percussion composition. When the fuse is
armed the end of the link c rests on the pivot of the firing pin,
thus affording support to the firing pin when it strikes the per-
cussion primer. The separation of the plunger parts is limited by
the nut i coming to a bearing on a shoulder in the bushing e, so
FIG. 219.
FIG. 220.
FIG. 221,
as not to permit the diameter of the expanded plunger to equal
the interior diameter of fuse stock, see Fig. 222.
A rotating piece, h Figs. 219 and 221, screwed into head of fuse
stock, engages in a corresponding slot cut through the bottom
of both plunger-halves and insures rotation of the plunger with the
shell.
The strength of the spring g is so adjusted that the fuse will
not arm until its rapidity of revolution is a certain percentage of
that expected in the shell in which it is to be used, and that it will
certainly arm when the rapidity of revolution approximates that
expected in the shell. Should the parts of the plunger be acci-
dentally separated and the fuse armed by a sudden jolt or jar in
transportation or handling, the reaction of the spring will imme-
diately bring the plunger to the unarmed condition.
The fuse just described is called the F fuse.
492
ORDNANCE AND GUNNERY.
FIG. 222.
The fuse shown in Fig. 222, the S fuse, is for use with 3.6- and
7-inch mortar shell, powder-charged. The additional priming
in end of fuse gives a greater body of
flame than is emitted from the F fuse.
A similar fuse of larger size is used
in powder-charged shell of 8-inch caliber
and over.
A fuse, called the 12 M fuse, is pro-
vided for use in the 12-inch mortar deck-
piercing and torpedo shell. This fuse is
similar in construction to the other
centrifugal fuses, but on account of the
low velocity of rotation of mortar pro-
jectiles and their low striking velocity
a much heavier plunger is needed to
provide the force necessary for arming
the fuse, and for puncturing the primer-
shield on impact.
281. Combination Time and Per-
cussion Fuses. All combination fuses used in the service are point
insertion and combine the elements of time and percussion ar-
ranged to act independently in one fuse body.
Combination fuses contain two plungers and two primers.
One plunger, the time plunger, is armed by the shock of discharge
and fires its primer immediately, igniting the time train of the
fuse. The other plunger, the percussion plunger, is also armed by
the shock of discharge but fires its primer on impact of the pro-
jectile.
Service Combination Fuse. The upper part of the fuse, Fig.
223, contains the time elements, the lower part the percussion ele-
ments. The time elements consist of the concussion or time
plunger 6, the firing pin c, and the time train. The firing pin is
fixed in the body of the fuse, and the plunger carries the percus-
sion composition and a small igniting charge of black powder.
The plunger is held out of contact with the firing pin by the split
resistance-ring a. On the shock of discharge the inertia of the
plunger acting through the conical surface in contact with the
split ring expands the ring so that the plunger can pass
PRIMERS AND FUSES FOR CANNON
493
through it and carry the percussion composition to the firing
pin.
The time train of the fuse is composed of two rings of powder,
/ and h, contained in grooves cut in the two time-train rings m
and n. The grooves are not cut completely around the rings, but
a solid portion is left between the ends of the groove in each ring.
FIG. 223.
Mealed powder is compressed into the grooves under a pressure of
70,000 pounds per square inch, forming a train 7 inches long, the
combined length of the two grooves.
The flame from the percussion composition passes through
the vent d, igniting the compressed tubular powder pellet e, which
in turn ignites one end of the upper time train /. When the fuse is
set at zero the flame passes immediately from the upper time train
through the powder pellet g to one end of the lower time train h]
thence through the pellet i and vent / to the powder k in the an-
nular magazine at the base of the fuse.
Under each of the time rings is a felt washer, o and p, that
closes the joint under the ring against the passage of flame, except
through the hole in the washer directly over the vent in the part
below. The upper washer o is glued to the upper corrugated surr
face of the lower time ring n and moves with that ring. The lower
washer p is glued to the fuse body and is stationary. The upper
494
ORDNANCE AND GUNNERY.
time ring m is fixed in position by two pins I halved into the fuse
body and the ring. The lower time ring is movable, and any of
the graduations on its exterior, see Fig. 224, which correspond to
\
k
'" r*> f (T^ ttt
FIG. 224.
seconds and fifths of seconds of burning, may be brought to the
datum line marked on body of fuse below the ring. The ring is
moved, in setting, by means of a wrench applied to the projecting
stud w.
To set the fuse for any time of burning, say 20 seconds, move
the lower time ring n until the mark 20 is over the datum line.
On ignition of the primer the flame ignites the upper time train /,
which burns clockwise, looking from base to point of fuse, until
the hole through the washer over the zero mark of the lower ring
n is encountered. The flame then passes through the vent g to
the lower time train n, which burns anti-clockwise until the mark
20 is reached. This mark being over the vent i in the body of
fuse, the flame now passes to the magazine k. The setting of the
fuse consists in fixing the position of the passage from the upper
to the lower time train, so as to include a greater or less length
of each train between the vent e and the vent i.
In each time ring a vent opens from the initial end of the
powder train to the exterior. The vent contains a pellet of pow-
der and is covered by a thin brass cup. The vent in the lower
PRIMERS AND FUSES FOR CANNON. 495
time ring is seen at x in Fig. 223. The caps, x, of both vents are
shown in Fig. 224. The blowing out of the cap affords a passage
to the open air for the flame from the burning time train, thus
preventing the bursting of the fuse by the pressure of the con-
tained gases.
When the fuse is set at safety, indicated by the letter S stamped
on the lower time ring, the position shown in Fig. 224, the solid
metal between the ends of the upper time train is over the vent g
to the lower train, and the solid metal between the ends of the
lower train is over the vent i leading to the magazine. In case of
accidental firing by the time plunger, the upper train will be com-
pletely consumed without communicating fire to the lower train
and to the magazine. The fuse is habitually carried at this setting,
which serves also when it is desired to explode the shell by impact
only.
For percussion firing the fuse is now provided with a ring-
resistance plunger similar to that shown in Fig. 218. Better
results are obtained with the ring-resistance plunger than with the
centrifugal plunger, which was formerly used in these fuses and
is shown at r in Fig. 223. A vent s leads from the percussion
primer to the annular magazine k. A thin brass cap t separates
the lower plunger-recess from the powder in the four radial cham-
bers v cut in the bottom closing screw. The central vent in the
closing screw is closed by a piece of shellacked linen, held in place
by a brass washer.
These fuses are issued fixed in the loaded projectiles. For
protection in transportation the fuse is covered by a spun brass
cap, soldered on to the head of the projectile. The soldering strip
is torn off and the cover removed before using the projectile.
A 21-second fuse of this pattern is now in service, and a 31-
second fuse is being developed.
282. COMBINATION FUSE, OLD PATTERN. As the former model
of combination fuse may perhaps still be encountered in service,
it is illustrated here. The time train, b Fig. 225, is made by
filling a lead tube with mealed powder and then drawing the filled
tube through dies until its diameter has been reduced to the de-
sired dimension. The powder train is thereby given practically
uniform density, so that it burns more uniformly than the time
496
ORDNANCE AND GUNNERY.
trains of previous fuses. The results, however, were not so good
as the results obtained with fuses of the present service model.
The time train, b, incased in the lead tube, is wound spirally
around the lead cone c. To set the fuse for any time of burning
the time train and lead cone are punctured, by means of a tool
provided for the purpose, at the point on the scale marked on the
cover of fuse corresponding to the time of burning desired. The
puncture passes completely through the time train and the lead
cone behind it, forming a channel from the annular space in which
FIG. 225.
the letter b appears to the powder in the time train. When the
projectile is fired the flame from the percussion composition ignites
the compressed powder ring d, and the flame from this ring ignites
the time train at the point at which it has been punctured. The
safety pin a retains the time plunger in its unarmed position, and
must be withdrawn before placing the projectile in the gun.
Two fuses of this pattern were made, one with a 15-second time
train and the other with a 28-second time train.
PRIMERS AND FUSES FOR CANNON.
497
EHRHARDT COMBINATION FUSE. This fuse is similar in con-
struction to the Frankford Arsenal fuse, latest pattern, described
above and differs only in details.
The arming of the time plunger of the Ehrhardt fuse, Fig. 226,
is resisted by the U-shaped spring a, the upper ends of which are
sprung out into a counterbored recess in the closing cap, and by
FIG. 226.
the slender brass pin b, which passes through the plunger and
both sides of the closing cap. At discharge of the piece the inertia
of the plunger shears the pin b and straightens the U-shaped
spring a, permitting the plunger to strike the firing pin.
In the percussion mechanism the composition is carried in the
plunger and the firing pin is fixed in the diaphragm d in body of
fuse. The plunger is held away from the firing pin, before firing,
by the brass restraining pin c. The pin is let into a hole in the
diaphragm d, the head of the pin abutting against a shoulder near
the bottom of the hole. The restraining pellet of powder e is
pressed in to fill the recess above the pin. A perforated brass
disk and a piece of linen close the hole at its upper end and pre-
vent the powder pellet from being jarred out of place. The burn*
498
ORDNANCE AND GUNNERY.
ing of this pellet on ignition from the time plunger leaves the
restraining pin and percussion plunger free to move forward at
impact.
A compressed charge of black powder, g, is inserted into the
extension of the closing screw / to reinforce the magazine charge
and effectually to carry the flame to the base charge in the shrapnel.
The Krupp combination fuse does not differ essentially from the
Ehrhardt fuse. The shear pin through time plunger is omitted,
the U-shaped spring being made strong enough to offer sufficient
resistance against accidental arming. The percussion plunger,
carrying the percussion composition, is held away from the firing
pin, before firing, by a sleeve and an inverted U-shaped resistance
spring. A spiral spring between plunger and firing pin prevents
the creeping forward of the plunger during the flight of the pro-
jectile.
Detonating Fuses. These fuses are for use in shell containing
high explosives.
4.29-]
FIQ. 227.
Fig. 227 shows the form of detonating fuse for point insertion
in field shell. Fig. 228 shows the form of fuse for base insertion
in siege and seacoast projectiles.
9 .35
FIG. 228.
In order to prevent the unscrewing of the fuse during flight of
the projectile, all point insertion fuses are provided with right-
PRIMERS AND FUSES FOR CANNON. 499
handed screw threads and base insertion fuses with left-handed
threads.
283. The Fuse Setter. The fuse setter is a device for the
rapid and accurate setting of the time fuse in the field gun pro-
jectile. It is attached to a hinged bracket on the caisson for the
field gun, see Fig. 122, in a position convenient for the cannoneer
who serves the caisson.
The base of the fuse setter, Fig. 229, is fixed to the bracket on*
the caisson. Mounted on the base are two movable rings called
the corrector ring and range ring. The range ring carries the
range scale graduated in yards, and the corrector ring carries an
index or pointer that moves between the corrector scales that are
fastened to the fixed cover. The base and the two rings are bored
out conically to fit over the combination time and percussion fuse
used in the 3-inch projectile. The corrector ring is notched to
receive the rotating stud, w Fig. 224, which projects from the
time train ring of the fuse. A spring plunger projects inwardly
from the range ring of the fuse setter.
A guide fixed to the base serves to direct the point of the pro-
jectile into the socket of the fuse setter and to support the car-
tridge during the operation of fuse setting.
To set the fuse for the time of burning corresponding to any
range, as 1000 yards, the range ring is turned by means of the
range-worm handle until the 1000 mark on the range scale is
opposite the datum line marked on the corrector scale, see Fig.
229. The weather-proof cover of the time fuse in the projectile is
stripped off and the point of the projectile is then placed in the
fuse setter, the rotating stud on the fuse engaging in the notch in
the corrector ring. The cartridge is then turned slowly in a clock-
wise direction until the spring plunger, which has been pushed in
by the insertion of the fuse in the fuse setter, is forced out into a
notch prepared for it in the body of the fuse. The plunger pre-
vents further rotation of the cartridge, the time fuse of which has
now been set to the proper time of burning for 1000 yards.
The rate of burning of different fuses of the same lot will be
uniform, but it may vary slightly from the rate of burning used in
the graduation of the scale of the fuse setter. This must be deter-
mined by actual firings, and if after a few shots it is found that
500
ORDNANCE AND GUNNERY.
the projectiles burst short of or beyond the range for which the
time fuse is set, or if the height of burst is not exactly as desired,
^ _ Cbtsrecfvt' fncteoc
s
/
Corrector Scales
Corrector Worm
Notch for Rotating Pin efJte*
>-
\. tfamptng UoltJ
FIG. 229. Fuse Setter for 3-inch Projectiles.
a correction is made in the setting of the fuse by means of the
corrector ring in the fuse setter.
The height of burst may be increased or diminished by turning
PRIMERS AND FUSES FOR CANNON. 501
the corrector ring, by means of the corrector-worm thumb nut.
to increase or diminish the corrector scale reading.
A point on the corrector scale corresponds to a difference of
one mil in the height of burst.
The fuse setters now issued are provided with two corrector
scales, one for use with Frankford Arsenal and Krupp fuses, and
the other for use with Ehrhardt fuses.
284. Arming Resistance of Fuse Plungers. RING RESIST-
ANCE FUSES. The arming resistance of the ring resistance fuse,
Fig. 216, is the resistance offered by the split ring k to movement
over the enlarged base of the firing pin.
As the projectile is accelerated in the bore of the gun the split
ring imparts the acceleration to the sleeve h of the plunger. If
the resistance that the split ring offers to rearward motion over
the slope of the firing pin is less than the pressure that the ring
must impart to the sleeve to give to the sleeve the maximum
acceleration of the projectile, the rearward movement of the ring
will occur and the fuse will arm.
Problem 1. Determine the maximum permissible arming re-
sistance for the ring-resistance fuse in the projectile for the 3-inch
gun, for which we have the following data.
Maximum pressure, P = 33,000 Ibs. per sq. in.
Weight of projectile, ^ = 15 Ibs.
Weight of plunger sleeve, w 8 = 464 grains = 464/7000 Ibs.
Diameter of projectile, d = 3 inches.
Neglecting friction and the rotation of the projectile we will
assume that the pressure is wholly employed in giving motion of
translation to the projectile.
The maximum acceleration of the projectile is
w
If the split ring of the fuse plunger imparts this acceleration to
the sleeve, the pressure on the ring will be
w. 500120X464
502 ORDNANCE AND GUNNERY.
Therefore the plunger with sleeve weighing 464 grains will arm in
the gun if the arming resistance of the fuse is anything less than
1030.8 pounds.
285. Problem 2. The actual arming resistance of the fuse for
the 3-inch projectile is 220 pounds. What pressure per square
inch is required in the gun in order to arm the fuse?
Equating the values of a in the equations established in the
preceding problem, and writing p for P to indicate any pressure
per square inch, we obtain
s?!.^
P 4 w w t
The total pressure on the projectile at any instant divided by
the weight of the projectile is equal to the pressure on the sleeve
at the instant divided by the weight of the sleeve.
Making F = 22Q, and substituting for the other quantities the
values as given in the preceding problem, we find
4X15X220X7000
P= ^X9X464 = '043 Ibs. per sq. in.
The fuse w r ill arm under any pressure in excess of this.
Problem 3. What is the minimum effective powder pressure
that will arm the ring-resistance fuse described below, when fired
from the 6-inch gun?
Weight of projectile, w = 106 Ibs.
Weight of plunger sleeve, w s = 70Q grains = 0.1 Ibs.
Ring resistance to arming, =220 Ibs.
Ans. p = 8248 Ibs. per sq. in.
286. CENTRIFUGAL FUSE. The arming resistance of the cen-
trifugal fuse, Fig. 219, is the pressure exerted by the spring g,
which holds the plunger halves together. The centrifugal force
due to the rotation of the projectile tends to separate the plunger
halves. In order that the fuse may be armed when the projectile
strikes, the arming resistance must be less than the centrifugal
force developed by the rotation in the projectile at impact. For
simplicity we will consider that the projectile's velocity of rota-
tion at impact is the same as at the muzzle of the gun.
PRIMERS AND FUSES FOR CANNON. 503
Problem 4. Determine the maximum permissible arming re-
sistance for the centrifugal fuse in the 12-inch mortar projectile,
for which we have the following data.
Weight of plunger complete, 660 grains.
Weight of plunger half, w 9 = 330 grains = 330/7000 Ibs.
Radius of center of gravity of plunger half, r 0.4 ins. =0.4/12 ft.
Twist at muzzle, n = 25.
Muzzle velocity of projectile, F = 950 f. s.
Diameter of projectile, d = 12 inches = 1 ft.
Combining equations (62) and (61), page 250, we find for the
velocity of rotation of the projectile at the muzzle
w = 2Vn/dn = 2 x 950/25 = 238.76
The centrifugal force acting on each plunger half is
in which v is the linear velocity of the center of gravity of the
plunger half, due to the rotation,
r the radius of the center of gravity,
p the radius of its path.
At the beginning of movement p = r, and we have
330X238. 76 2 XO. 4
F = w.<*r/g= 7QQQX32 . 16X12 =2.79 Ibs.
for the force tending to move each plunger half.
If the resistance of the spring is less than 2.79 Ibs. the fuse will
start to arm.
As the plunger halves separate, the resistance of the spring
increases in the manner shown by equation (14), page 285.
S = G'+Gx
It will be seen, from the value of F above, that F increases
directly with r. In order that the fuse, after starting to arm, may
arm completely, the values of G r and G must be such, that is, the.
spring must be of such construction, that S will not increase more
rapidly than F.
504 ORDNANCE AND GUNNERY.
287. Problem 5. Assume that the spring in the plunger of the
fuse for the 12-inch mortar projectile is under a tension of 1J Ibs.
What muzzle velocity is required in the projectile to arm the fuse?
We have
from which
co = (Fg/w s r)* = 2V7t/dn
Solving for V
dn(Fg\*
* r x-k 1
2n \w s r/
The force required for arming is in this case 1.5 pounds. Sub-
stituting 1.5 for F, and for the other quantities the values as given
in the preceding problem, we have
25/1. 5X32. 16X7000X12V
= S\ 330X0.4 -) -697.14 f.s.
The fuse will arm for any muzzle velocity of the projectile ex-
ceeding 697.14 foot seconds.
Problem 6. What is the minimum muzzle velocity that will
arm the centrifugal fuse described below, when fired from a 6-
inch howitzer?
Weight of plunger half, w s = 40Q grains = 4/70 Ibs.
Radius of center of gravity of plunger half, r = 0.5 in. =0.5/12 ft*
Spring resistance to arming, F = 2 Ibs.
Twist of rifling at muzzle, n = 25.
Diameter of projectile, d = 6 in. =0.5 ft.
Ans V = 327 foot seconds*,
CHAPTER XIII.
SIGHTS.
288. Purpose. It has been shown in exterior ballistics that
in order that the projectile from any gun may hit the target the
gun must be fired at a certain angle of elevation, depending upon
the range and upon the relative level of the gun and target, and
nmst be given such direction to the right or left of the target as
to neutralize the deviation of the shot from the plane of fire due
to the drift and wind.
The elevation in the plane of fire and the allowance for devia-
tion from the vertical plane containing gun and target are deter-
mined beforehand either by calculation or estimate. Direction is
given to the axis of the gun by whatever means may be provided.
The axis of the gun when given the determined elevation and
deviation has a fixed relation to the line from the gun to the target.
The sights of the gun provide the means of determining when
the axis of the gun has the predetermined direction with respect
to the line from gun to target.
Principle and Methods. The principle of sighting is simple.
It consists in determining, by means of the sights, a line to which
the axis of the gun has the fixed relation already determined as
being required between the axis and the line to the target; and
then, by looking through the sights, making the line of the sights
and the line to the target coincide.
The line of sight on a gun may be fixed in one of two ways:
first, by means of two plain or open sights, the rear one of which
has a peep or notch capable of adjustment in vertical and hori-
zontal directions; second, by means of a telescope, whose axis or
line of collimation may be given any direction desired.
505
506 ORDNANCE AND GUNNERY.
In Fig. 230 represents the peep of the rear sight in its zero
position, the line from to the front sight A being parallel to the
axis of the piece. Or the line OA may represent the line of colli-
ination of a telescope, the telescope being pivoted at A. If now
we calculate that to reach the target at F, under the conditions
prevailing, a certain angle of elevation is required and a certain
deviation to the left, we lift the peep of the rear sight to the point
C so that OAC is the required angle of elevation, and then move
the peep horizontally from C to E to obtain the required deviation.
The line of sight is now the line EA, and if the gun is maneuvered
so that this line is made to pass through the target, the axis has
FIG. 230.
then the elevation and deviation required under the existing
conditions.
The gun is aimed at the target F, but its axis, parallel to the
line CB, is practically pointed at B, which is above F by the
vertical distance BD and to the left of F by the horizontal distance
DF.
TARGET NOT IN VIEW. In the foregoing the target has been
assumed to be in view. If the target is not in view the required
position of the axis of the gun with respect to a horizontal line in
the vertical plane through gun and target is determined. The
vertical angle betw r een this line and the axis is the angle of eleva-
tion. This angle is laid off by the sights as before and the gun is
elevated until the line of sight AC is horizontal as determined by
means of a spirit level mounted on the rear sight. Other means
must be employed for determining the direction in this case.
289. Graduation of Rear Sights. The graduations of the
rear sight for elevation may be, and often are, in degrees and
minutes of arc, the center of the arc being at the center of motion
SIGHTS. 507
of the rear sight. But as the powder charges of guns are made
up to give certain fixed muzzle velocities to the projectiles, the
angle of elevation required to attain any range with the given
muzzle velocity under standard atmospheric conditions may be
determined in advance, and the rear sight be graduated for range
instead of angular elevation.
The range graduation is the more convenient, for the range
may usually be readily determined, and the graduation on the
rear sight indicates at once the proper elevation.
The horizontal deflection scale, by means of which allowance is
made for deviation to the right or left, is graduated, in sights for
field artillery, to thousandths of the range. These graduations
are called mils, from the French millikmes. It is apparent from
Fig. 230 that if EC is n thousandths of AC, the horizontal dis-
tance DF will be n thousandths of AD and practically of the range
AF. In sights for seacoast artillery the least division of the
deflection scale is three minutes of arc, which corresponds to a
deflection of 0.00087 of the range, approximately 1/1000.
Correction for Drift. The deviation of the projectile due to
drift, which is caused by the rotation of the projectile and the
resistance of the air, may be determined for any range by the
formulas of exterior ballistics, and thus the curve of drift may be
constructed for any gun. If then the rear sight is so constructed
that as the peep is lifted in elevation to any range it is automatic-
ally moved horizontally just enough to compensate for the drift
at that range, the sight makes automatic correction for the drift,
and need be further adjusted only for the wind or other atmos-
pheric deviating influences.
In all service guns the drift of the projectile is to the right.
The drift increases with the range. The rear sight with automatic
drift correction therefore moves to the left as it is raised in eleva-
tion. In our service, automatic drift correction will be found only
in sights for small arms.
It is well to bear in mind that the projectile follows the move-
ment of the rear sight, going higher as the sight is raised, and to
the right or left as the sight is moved to the right or left.
290. Correction for Inclination of Site. The angle of eleva-
tion of a gun is the angle, in a vertical plane, that the axis of the
508
ORDNANCE AND GUNNERY.
gun makes with the horizontal. In Fig. 231 let r be the point to
which the rear sight must be raised, in the vertical plane of the
axis, to give to the gun a desired angle of elevation equal to o/r, /
representing the front sight, h is a horizontal line in the vertical
plane of the axis. Now suppose the gun to be revolved to the
left about its axis. The axis of the gun remains in the vertical
plane, but the points r, o, and / revolve to the left out of the plane;
and as r is farther from the center than o and /, its movement is
greater than the equal movements of o and / . We may therefore
consider that, relatively to o and /, r takes some position r' '. Pro-
FIG. 231.
jecting r' on the vertical plane, at r", we see that the angle of
sight o/r' produces an angle of elevation ofr" ', which is less than the
desired angle ofr. It is apparent too that the line of sight through
f f will cause the gun to be pointed to the left of the plane of o/r.
If, however, the sight is pivoted at o so that it has movement
in a plane perpendicular to the axis of the gun, we are enabled,
when the gun has been revolved, to make the sight arm or' ver-
tical; and since the points o and / have revolved together, of,
now coincident with or, will subtend the desired vertical angle o/r.
It is therefore essential that the rear sights for guns that are
likely to be fired on uneven sites shall be so constructed that the
sight arm may revolve about the zero point of the elevation scale in
a plane perpendicular to the axis of the gun. We w y ill find that
the rear sights for all guns mounted on wheeled carriages are
constructed in this manner.
Guns of position are mounted on carriages that rest on level
platforms, and their sights are so adjusted as to always move in a
vertical plane.
SIGHTS. 509
Location of Sights. Sights for all guns are now placed on
some non-recoiling part of the gun carriage, and the elevating and
traversing mechanisms are under the control of the cannoneer at
the sights, so that the operation of sighting may go on continuously
during the loading arid firing of the piece.
LINE SIGHTS. Most guns are provided with line sights fixed
to the gun. They serve only to give general direction to the piece,
and consist of a front stud with conical point, and a notched bar
on the top of the breech. The line extending from a point over
the center of the notch at the level of the top of the bar to the
point of the front sight is parallel to the axis of the piece.
The most recent service sights and other appliances used in
gun pointing will now be described. The sights mounted on the
various guns of older model will readily be understood after a
study of these.
291. Sights for Mobile Artillery. The appliances provided
for sighting the 3-inch field piece, and other pieces on wheeled
carriages, include line sights, the adjustable or tangent sight, the
panoramic sight and the range quadrant.
The line sights are fixed to the gun as already de-
scribed.
The Adjustable or Tangent Sight. The adjustable sight con-
sists of a fixed front sight and an adjustable rear sight.
The front sight, supported in a bracket on the cradle, is a short
tube, Fig. 232, whose axis is marked by the intersection of two
cross wires set in the tube at angles of
45 degrees with the horizon. A bead on
top of the tube serves for approximate
determination of direction.
The rear sight, Fig. 233, is shown
viewed from the left in the left-hand
figure, and from the rear in the figure on
the right. The rear sight bracket is seated
in a socket attached to the cradle of the
carriage, on the left side. At the upper end of the bracket two
seats are formed for the attachment of the socket for the sight.
The seats are faced in a plane perpendicular to the axis of the
510
ORDNANCE AND GUNNERY.
piece and circular guides are cut on them, with the zero index of
the elevation scale as a center.
The shank socket which holds the rear sight is mounted on the
bracket and has circular motion on the guides under the action of
the transverse leveling screw. This arrangement permits the
correction for inclination of site by revolution of the rear site in a
plane perpendicular to the axis of the gun until the sight is ver-
tical, as indicated by the transverse level fixed to the socket.
SIGHTS. 511
The sight shank is an arm curved to the arc of a circle whose
center is the front sight. The shank slides up and down in guides
in the socket, its movement being effected by the thumb nut,
called the elevating gear hand wheel, through a scroll gear wheel
which acts on the teeth of the rack cut on the right face of the
shank. The scroll gear is held in mesh by a spring. By pulling
out the thumb nut the gear is disengaged from the rack, and a
large change in elevation may then be rapidly made by sliding the
shank through the socket by hand.
The range scale is marked on the rear face of the shank, and is
read at the index at the upper end of the socket. The smallest
division of the scale corresponds to 50 yards of range, but this may
be readily subdivided by the eye.
On the upper end of the shank is a frame in which is mounted
the peep of the rear sight. The peep is moved to the right or left
by means of the deflection screw. The peep hole is 1/10 of an
inch in diameter. The divisions of the deflection scale correspond
to one mil, 1/1000 of the range. The scale is marked from left to
right as follows:
40 30 20 10 90 80 70 6360
The deflection readings arc uniform with those of the pano-
ramic sight and battery commander's telescope. They will be
explained later in the description of the panoramic sight.
The sight is continued upward above the seat for the peep to
form a seat for the panoramic sight.
The axis of the clinometer level is parallel to the line of sight,
and thus permits the use of the sight as a quadrant in giving ele-
vation to the piece when the target is not in view.
In the sight for the 6-inch howitzer, see Fig. 132, the front
sight is mounted on the same bar as the rear sight, and the bar
revolves in elevation about a point between the two sights. The
rear sight has a sliding movement in deflection on the end of the bar.
The adjustable sight is often called a tangent sight from its
similarity to the sights with straight shanks formerly much used
with cannon. The peep of the tangent sight moves on the tan-
gent of an arc instead of on the arc itself. The rear sight for the
30-caliber rifle is a tangent sight.
512 ORDNANCE AND GUNNERY.
For field howitzers the seats for the front and rear sights are
alike, so that the positions of the sights may be reversed for in-
direct sighting, which consists in directing the line of sight at any
object other than the target.
292. The Panoramic Sight. The fire from modern field guns
is so accurate and destructive that it has been found necessary in
recent battles to establish field batteries always in positions out
of view of the enemy, in order to protect the batteries from the
fire of the enemy's guns.
Indirect sighting becomes then of necessity the usual method
of sighting guns in battle.
The panoramic sight affords the means of aiming the gun by
directing the line of sight on any object in view from the gun.
At the same time it offers the advantages of a telescopic sight in
direct or indirect aiming.
The panoramic sight is a telescope so fitted with reflectors and
prisms that a magnified image of an object anywhere in view
may be brought to the eye without change in the direction of
sight.
The panoramic sight for the field and siege guns is shown in
Fig. 234. The rays of light from the object viewed enter the
sight through the plain glass window 7 in the head piece and are
bent downward by the prism of total reflection A, rectified ver-
tically by the prism B, focussed by the object lens C, and rectified
laterally by the gabled prism D, so that there is presented to the
eyepiece E a rectified image of the object, which image is magni-
fied by the two lenses of the eyepiece.
The magnifying power of the instrument is 4 and the field of
view is 10 degrees.
THE ROTATING PRISM. The interior tube containing the prism
B and the objective C is mounted so that it may rotate in the
body of the telescope.
The prism B is rectangular in cross section. Its upper and
lower faces are oblique to its axis, and its length is such that a ray
that enters the prism axially emerges axially. Every ray entering
parallel to the axis therefore emerges at an equal distance on the
other side of the axis. A vertical ray entering the prism at a, Fig.
235, is reflected by the back of the prism and emerges at c. Now
SIGHTS.
513
FIG. 235.
if the prism is revolved through any angle, say 45 degrees, as repre-
sented in the figure by the position shown in broken lines, the ray
a will emerge at e, the back of the prism now being at the angle
of 45 degrees with its original position; and the
angle through which the ray has moved, measured
from the axis of the prism, which is the axis of
rotation, is 90 degrees. The angular movement of
the ray is therefore double the angular movement
of the prism. Consequently the image of an object
seen through the prism rotates through twice the
angle of rotation of the prism.
The head piece containing the prism A is also
mounted to rotate on the body of the telescope,
and in order to counteract the doubled angular
movement of the image by the prism B, the head
piece is made to rotate twice as fast as the prism.
The image of any object then rotates through the
same angle as the head piece, and the relative positions of objects
in the field of view are not changed.
The different movements of A and B are accomplished by
means of one tangent screw through gearing contained in the
cylindrical casing seen at the junction of the rotating parts.
THE GRADUATED SCALE. The angular movement of the head
piece is indicated by a graduated scale on its perimeter, visible
through a window in the rear of the casing. When the index on
the casing is at the zero of the scale, the line of sight of the pano-
ramic sight is in the vertical plane parallel to the axis of the piece.
If at the same time the tangent sight on which the panoramic sight
is mounted is at the zero of the elevation scale, the line of sight of
the panoramic sight is parallel to the axis of the piece.
In the scale on the head piece the circle is divided in 64 equal
parts, numbered clockwise. One complete turn of the tangent
screw moves the head piece through one of these angles. A
micrometer scale mounted on the shaft of the tangent screw has
100 equal divisions. A movement of the tangent screw through
one of the divisions of the micrometer scale therefore moves the
head piece through 1/6400 of a circle, which angle corresponds
very closely to 1/1000 of the range. The reading of the scales is
514 ORDNANCE AND GUNNERY.
in 6400ths of the circle. The hundreds are read from the scale
on the head piece, and tens and units from the scale on the tangent
screw. Thus if the index has passed the mark 27 on the head
scale, and the index of the micrometer scale stands at 18, the
reading is 2718.
Referring now to the readings on the deflection scale of the
tangent sight, page 511, we see that the first reading to the left
of the zero, which is 10, indicates a position of the tangent sight
parallel to the position of the panoramic sight when the index of
the scale on the head of the panoramic sight is between and 1
of the scale, and the index of the micrometer scale is at 10. Simi-
larly the reading 90, to the right of the zero, indicates the position
of the panoramic sight between 63 and 64 of the head scale with
the micrometer scale at 90. The reading of the panoramic sight
is then 6390.
USE AS A RANGE FINDER. As horizontal angles may be
measured with the panoramic sight the sight may be used as a
range finder. Using the line between the sights of the flank guns
of a battery as a base the triangle formed by the two sights and
the target may be determined.
ON SEACOAST CARRIAGES. Trials are now being made of the
panoramic sight applied to disappearing carriages. The sight is
attached to the left cheek of the chassis with the eye end of the
sight at a height convenient for the gunner standing on the racer
platform. The vertical tube of the sight is of length sufficient to
bring the head of the sight above the crest of the parapet.
293. The Range Quadrant. In rapid firing, the duties of
setting the sight for range and deflection, and laying the piece by
manipulating the elevating and traversing mechanisms would, if
attended to by a single cannoneer, frequently delay the firing
much beyond the time required to load. Since in the carriages for
mobile artillery the elevating and traversing mechanisms are
entirely independent of each other, the pointing of the piece may
be much simplified and the time required be considerably lessened
by assigning to one cannoneer the pointing of the piece for direc-
tion and to a second the elevation of the piece for range. Such a
division of duties is provided for by the elevating crank at the
right side of the trail and by the range quadrant attached to the
SIGHTS.
515
right of the cradle. By this arrangement, the gunner on the left
of the piece, using the open or panoramic sight, lays for direction
only, "While the cannoneer on the right of the piece gives quadrant
elevations.
The range quadrant, Fig. 236, is supported in a bracket on the
right side of the cradle of the carriage with its axis parallel to the
vertical plane containing the axis of the piece: and provision is
516 ORDNANCE AND GUNNERY.
made for rotation of the quadrant about its axis in order that the
curved rocker arm of the quadrant may be made vertical when the
wheels of the carriage are on different levels. The vertical posi-
tion of the quadrant arm is indicated by the transverse level.
The quadrant consists of a fixed arm of which the rocker arm
is a part; and a movable arm, in front of the fixed arm in the
figure, carrying a range disk, a clinometer level, and the mechanism
for elevating the movable arm. The fixed arm has at the rear an
upwardly extending arc, called the rocker arm, with toothed
racks on front and rear edges. The movable arm, pivoted at the
front to the fixed arm, is given motion about its pivot by a gear
actuated by the elevating hand wheel and meshing in the rearmost
rack. A pinion on the shaft of the range disk meshes in the for-
ward rack, and the movement of the arm in elevation is indicated
by the scale on the range disk in terms of the corresponding
range.
THE CLINOMETER. The clinometer level is pivoted on the axis
of the movable arm, arid may be moved relatively to the arm by
the clinometer level screw, the upper end of which carries a microm-
eter scale. A short circular scale is marked on the left edge of the
piece carrying the level. The level scale is in 64ths of a circle, and
the micrometer scale in 6400ths, similar to the scales of the pano-
ramic sight.
The purpose of the clinometer is to make correction for differ-
ence in level of the gun and target. The angle subtended at the
target by the difference in level is called the angle of site, as may
be seen by the words on the clinometer level in the figure. In
exterior ballistics we have called this angle the angle of position,
\vhich is a better term, first in better expressing what is meant,
and second in not leading to confusion through similarity to the
word sight, and to the term angle of sight, in frequent use.
The readings on the clinometer scale are 2, 3, and 4, read 200,
300, and 400, to which are added the readings of the micrometer
scale. 300 corresponds to the horizontal position of the axis of
the gun. The angle of position, expressed in 6400ths of the circle,
is obtained by subtracting the reading of the scales from 300. If
the reading is greater than 300 the result is negative and the target
is above the gun.
SIGHTS. 517
294.. USE OF THE QUADRANT. The quadrant is used as follows,
The gun is pointed at the target by means of the line sights, the
quadrant being set at the zero of the range scale. The quadrant
is leveled transversely, and the clinometer level is leveled by
means of its screw. The angle indicated on the clinometer scale is
the angle of position of the target. Further movement of the gun
in elevation is, by means of the clinometer, measured from this
position of the gun as zero. The movable arm of the quadrant is
elevated until the range of the target is recorded on the range
scale. The piece is then elevated until the clinometer level is
again level. The piece has now the proper angle of elevation for
the range increased or diminished by the angle of position, accord-
ing as the target is higher or lower than the gun.
It will be noted that in the use of the clinometer in correcting
the angle of elevation by adding or subtracting the angle of posi-
tion we are applying the principle of the rigidity of the trajectory.
The Battery Commander's Telescope and Ruler. The bat-
tery commander's telescope and the battery commander's ruler,
used as aids in determining the elements of sighting for pieces
employed in indirect fire, should perhaps be classed as range and
position finders rather than as appliances for sighting. They will
be described in the chapter on range and position finding, which
follows- this chapter.
Telescopic Sights. The advantages gained by the use of a
telescope in laying a piece consist in an increased power of vision
and a large decrease in personal error. The telescope renders dis-
tinct an object that may be barely visible to the naked eye and
enables the gunner to lay the gun on such an object with accuracy
and facility.
Telescopic sights are now used on all guns of position. They
are fixed to the non -recoiling cradle of the barbette mount, and
to the chassis of the disappearing mount. Hand wheels, or electric
controllers, for the manipulation of the mechanisms for laying the
piece are in positions convenient to the gunner at the sight, and in
addition an electric firing pistol is placed at his hand so that all the
operations of aiming and firing the piece are under his control.
295. Telescopic Sight, Model 1904. The latest pattern of
telescopic sight, model 1904, for guns mounted on disappearing
518 ORDNANCE AND GUNNERY.
carriages, is shown in Fig. 237; see also Fig. 145. Sights of the
same model are provided also for barbette carriages. They differ
from the sight described only in the method of attachment to the
carriage.
The sight arm a is pivoted at its forward end on the sight
standard of the carriage and is supported, by a pin through the
hole near its rear end, on a vertical rod so connected with the
elevating mechanism of the gun that it gives to the sight arm the
same movement in elevation that is given to the gun, see Figs.
145 and 146. A curved guide g, moving in a groove in the stand-
ard, keeps the sight arm in the vertical plane. A cradle c carry-
ing the telescope t is pivoted to the forward end of the sight arm
in such a manner that the cradle has both vertical and horizontal
movement about its pivot. Vertical movement is given by the
hand wheel e which actuates a gear mounted on the sight arm
and meshing in the rack on the shank s. The cradle is given
horizontal movement on the head of the shank by the deflection
screw d. On the rear face of the shank is an elevation scale
graduated to degrees and minutes of arc, the least reading being
6 minutes. A deflection scale on the rear end of the cradle under
the telescope extends over 4 degrees of arc. The degree marks are
numbered from 1 on the right to 5 on the left, the 3-degree mark
corresponding to no deflection. The least reading of the deflection
scale is 3 minutes, which corresponds approximately to a deflec-
tion of one mil.
"When the sight is set at the zero of the elevation and deflection
scales the axis of the telescope is parallel to the axis of the piece.
A range drum m connected with the elevating gear of the sight
indicates the range corresponding to any position of the sight.
The range drum contains a coiled ribbon spring arranged to equal-
ize the efforts in elevating and depressing the sight.
A peep sight p is mounted above the eye end of the telescope,
and an open front sight /, with crossed wires, is mounted above the
forward end of the cradle.
Electric lamps I illuminate, in night sighting, the elevation
and deflection scales and the cross hairs in the telescope.
THE TELESCOPE. The construction of the telescope will be
understood from Fig. 238. The achromatic object glass o, com-
SIGHTS.
519
posed of three lenses, has a clear aperture 3 inches in diameter
and a focal length of 17.25 inches. The length of the telescope is
diminished and an erect image presented to the eyepiece by means
of the two Porro prisms p. In the figure the prisms appear to be
so placed that each intercepts a ray of light entering or issuing
from the other, but in reality the prisms are offset from each other
so that the light has unobstructed passage to and from them.
One prism is horizontal and the other stands vertically. The
lower prism by its inclined surfaces bends the ray twice through
angles of 90 degrees, reflecting it back to the upper prism, which
again bends it twice and reflects it into the field of the eyepiece.
The image, rectified horizontally and vertically by the prisms, is
FIG. 238.
focussed in a plane marked by horizontal and vertical cross wires
r carried in a ring, and is magnified by the two lenses of the eye-
piece. The ring carrying the cross wires is mounted in a tube d
called the draw tube which may be given movement in and out
by rotation of the focussing ring /. The eyepiece has a screw
motion out and in.
Two different eyepieces are provided with the telescope, their
magnifying powers being 12 and 20 diameters respectively. The
field of view of the telescope with the 12-power eyepiece is 3.6
degrees, and with the 20-power eyepiece 2.6 degrees.
In the use of the instrument the eyepiece is first adjusted until
the cross wires are distinctly defined. The cross wires are then
brought into the focal plane of the objective by turning the focus-
sing ring until the object viewed is also distinctly defined and
does not appear to move w r hen the ej^e is shifted from side to side.
An objective once focussed is correct for all observers, but the
eyepiece requires focussing for each individual.
Small electric lamps of about 2 candle power, I Fig. 237, illu-
520
ORDNANCE AND GUNNERY.
minate, in night sighting, the cross wires at r and the elevation
and deflection scales in the vicinity of the indexes. The lamp
that illuminates the cross wires is attached outside the draw tube
and its light is reflected by two mirrors through two slits cut
through the tube at right angles to each other. The light from
each mirror is thrown upon the full length of a cross wire, and the
wires appear as bright lines in a dark field.
296. Telescopic Sight, Model 1898. The telescopic sight,
model 1898, illustrated in Fig. 240, is provided for the 8-, 10-, and
12-inch barbette carriages and for disappearing carriages of the
earlier models. A seat for the sight is attached to the chassis.
When mounted in this seat the sight is used to give to the gun
direction in azimuth only.
A seat is also provided on the trunnion of the gun, and in this
seat the sight may be used in giving both elevation and direction.
The bracket 6, Fig. 240, is screwed to the trunnion. The tele-
scope is mounted in a frame whose trunnions t rest in notches in
the bracket. The frame and telescope are leveled transversely by
the screw / which bears against a lug projecting from the trun-
nion shaft of the frame.
ERECTING PRISMS. To rectify the image of the object there is
mounted in the telescope between the objective and the eyepiece
a Hastings- Brashear compound erecting prism, Fig. 239. The
FIG. 239.
compound prism is composed of two prisms, o, whose angles are
30, 60, and 90 degrees, laid with their 30-degree angles toward
each other on a parallel-sided glass plate b. On the other side of
the plate is fixed a gabled prism c with a 90-degree angle. The
upper prisms rectify the image vertically, and the lower prism
GG
tfe'
SIGHTS. 521
horizontally, as may be seen by following the course of the ray of
light shown in the figure.
The telescope is pivoted at its forward end to the frame and is
given movement in elevation by the screw e, Fig. 240. The ele-
vation scale is read to one minute by a micrometer scale under
the screw head.
Deflection is given by moving the vertical cross wire in the
telescope to the right or left by means of the deflection screw d,
and then moving the gun until the intersection of the vertical and
horizontal cross wires covers the point aimed at.
There are two deflection scales, one inside the telescope and
one outside. The inside scale, of horn, is in the focal plane of the
telescope and is seen at the same time with the object viewed.
The scale is graduated in divisions of 3 minutes, and the degrees
are numbered from 1 on the right to 5 on the left as in the model
1 904 telescopic sight. The cross wires in the telescope appear in
front of the scale. The vertical cross wire is attached to a sliding
diaphragm which is actuated by the deflection screw d and
moves the vertical wire to any desired degree of deflection to the
right or left.
In sighting, the intersection of the cross wires is brought in line
with the object sighted.
The outside deflection scale, s Fig. 240, corresponds in move-
ment with the scale inside the telescope. Both scales are read to
minutes by the graduations on the micrometer head d.
In a telescopic sight the cross wires inside the telescope form
virtually the front sight, and the aperture of the eyepiece forms
the rear sight. With the telescope just describedd eflection is
given by moving the vertical cross wire to the right or left, and
this movement is equivalent to moving the front sight to the
right or left. We have seen on page 507 that with the front
sight fixed the projectile follows the movement of the rear sight.
When the rear sight is fixed a movement of the front sight is
equivalent to a movement of the rear sight in the opposite direc-
tion. Therefore with the telescopic sight, model 1898, the pro-
jectile will be moved to the right by movement of the vertical
cross wire to the left, and to the left by movement of the vertical
wire to the right.
522 ORDNANCE AND GUNNERY.
297. The Power and Field of View of Telescopes. The power
of a telescope, the ratio of the apparent angle subtended by any
object to the actual angle which the object subtends, may be ob-
tained by dividing the aperture of the object lens by the aperture
of the eye lens. The telescope of the model 1904 sight has an
objective with an aperture of 3 inches. The eye lens of one of the
eyepieces provided has an aperture of J of an inch. The power
of the telescope with this ej^epiece is therefore 12. In the telescope
of the model 1898 sight the aperture of the objective is 1J inches
and of the eye lens J of an inch. The telescope has therefore
approximately a power of 8.
The eye receives the maximum amount of light through a tele-
scope when the diameter of the pencil of light emerging from the
eyepiece is equal to the diameter of the pupil of the eye. In the
normal eye the diameter of the pupil varies approximately from
J of an inch to \ of an inch, according as there is much light or
little.
The field of view of a telescope is equal to the field of the eye-
piece divided by the power of the telescope. The telescope of the
model 1898 sight has a power of 8 and its eyepiece has a field of
48 degrees. The field of view of the telescope is therefore 6 de-
grees.
The field of view of the same telescope with different eyepieces
varies practically in inverse ratio to the power of the telescope.
298. Aiming Mortars. Mortars, both field and seacoast, are
as a rule located out of view of their targets and usually behind
high shelter. Seacoast mortars are permanently emplacecl. Their
carriages are provided with graduated azimuth circles by means of
which the piece may be laid at any given angle with the meridian
plane. The angle made with the meridian plane by the line to
the target is determined by means of range and position finders.
The piece is then laid at that angle by means of the graduations
on the azimuth circle, and correction is made for drift and devia-
tion due to the wind.
For giving direction to field and siege mortars the vertical plane
through gun and target is established by stakes, or by trestles with
plumb lines, set up either in front of or behind the mortar in such a
position that both gun and target are in view. The axis of the
SIGHTS. 523
mortar is brought into this plane or into any determined position
with respect to the plane, and the first round is fired. Correction
for error in direction is afterwards made by means of marks on
the platform.
The Gunner's Quadrant. Elevation is given to mortars by
means of the gunner's quadrant shown in Fig. 241. The movable
e -Elevation,. // .
-Depression.. ^ "\ \^^
FIG. 241.
arm b carries a spirit level and may be set at any desired angle
with the base of the instrument up to 65 degrees. The notched
scale fixes positions for the arm b at whole
degrees. Minutes are obtained by sliding
the level along the scale on the curved arm
b. The principle of the sliding level on the
curved arm will be readily understood by
reference to Fig. 242.
The quadrant may be used to measure
angles of elevation or of depression from F IG 242.
to 65 degrees.
The quadrant, set to any desired angle of elevation, is placed
on the gun on a seat prepared for it parallel to the axis of the
piece. The instrument is so placed that the proper arrow on its
524 ORDNANCE AND GUNNERY.
base points in the direction of the line of fire. The piece is then
elevated until the bubble of the level is in the middle of the tube.
By placing the instrument on a vertical seat, as for instance
the face of the breech or muzzle of a gun, angles greater than 25
degrees from the vertical may be measured. The angle is ob-
tained by subtracting the reading of the quadrant from 90 degrees.
To facilitate the elevating of the mortar the quadrant is now,
on mortars mounted on the model 1896 carriage, permanently
fixed to a seat provided on the right rimbase of the mortar. The
level is fixed on the movable arm of the quadrant, and minutes of
elevation are obtained through movement of the arm by means of
a tangent screw at its end.
CHAPTER XIV.
RANGE AND POSITION FINDING.
299. Definitions. A range finder is an instrument for deter-
mining the range from the observer to any distant object.
A position finder is an instrument for determining the position
of an object with respect to any plane or line, as the meridian plane
for guns of position or the front of a battery for mobile artillery.
An instrument adapted to perform both functions becomes a
range and position finder.
Range Finders. With all practical range finders the deter-
mination of the range comes from the solution of a triangle. The
target is the apex of the triangle. The base of the triangle is laid
off either vertically or horizontally from the instrument, and the
angles at the extremities of the base are determined, one or both
of them, by means of the instrument.
In determining any fixed range the effect of an error in thfc
measurement of an angle at the base of the triangle will diminish
as the length of the base increases. This is
apparent from Fig. 243. A given range ot
is less affected by an angular error the
made at the end of the base ob than by an
equal error tac made at the end of the
a n
shorter base oa. FlG 943
It is therefore always desirable to use as
long a base as can be conveniently obtained. For this reason
horizontal base lines are preferred, since the vertical base of any
range finder is limited in length to the height of the instrument
above the water.
525
526 ORDNANCE AND GUNNERY.
Consequently in seacoast fortifications, if the surroundings
afford convenient sites for the angle measuring instruments, the
range finding system consists of two transits or azimuth instru-
ments established at the ends of a long base. Observations are
made on the target from both ends of the base. The position of
the target is plotted on a chart, and its range and position deter-
mined for any gun. If the target is moving, simultaneous obser-
vations are made from both ends of the base at periodic intervals.
The readings of the instruments are transmitted by telephone or
telegraph to a plotting room in the fortification, where the succes-
sive positions of the target are marked on the chart. From the
plotted course prediction may be made as to the position the
target will occupy at some determined instant in advance, and
the range and azimuth of the target at the selected instant may
be determined for any gun or battery in the fortification.
300. Depression Range Finders. The principle employed in
the depression range finder will be understood from Fig. 244.
The instrument, at a known height
above the sea level, measures the
vertical angle to any object. From
FIG 244 the fixed height each angle corre-
sponds to a certain length of base,
which is the horizontal range to the object.
The range in yards is indicated on a scale which is moved past
an index by the same mechanism that gives angular movement to
the line of sight.
A difference in the sea level due to the action of tides will
affect the height of the instrument above the sea level and conse-
quently the range corresponding to any angle, t and l\ Fig. 244.
Means are therefore provided for adjustment of the instrument
for variations in its height above sea level.
The instrument is made a position finder by being mounted so
as to revolve on a fixed base which is graduated in degrees and
hundredths, the zero graduation being placed in the meridian
plane.
Swasey Depression Range and Position Finder. The de-
pression range arid position finder now used in our sendee is shown
in Fig. 245. The observing telescope, similar in construction to
RANGE AND POSITION FINDING. 527
the telescope of the model 1904 sight, is mounted in a frame which
revolves about a central spindle s projecting upward from the
pedestal. The telescope is pivoted near its front end, and is sup-
ported near its rear end by the attached bar v which rests on a stiul
projecting from the carriage a. The carriage a is mounted on the
forward arm of a bent lever I which is pivoted at o. The lower
vertical arm of the lever is connected by gearing with the operating
shaft, not seen in the figure. Turning the operating shaft moves
the lower end of the lever /, and thus gives vertical movement to
the telescope about its forward pivot. The range drum enclosed
in the casing d, and visible through the window 7 w in the casing,
is given motion by the same shaft, and the scale on the drum in-
dicates the range corresponding to any position of the telescope.
The azimuth is read from a graduated scale seen through the
window z.
The carriage a may be moved along the upper arm of the
lever to adjust the position of the telescope for any height above
sea level. The height scale along which the carriage moves reads
from 40 to 400 feet. Corrections may be made, by moving the
carriage, for the change in height of the instrument due to the
change in sea level caused by the tides.
301. The Plotting Room. The range and azimuth of any se-
lected target, as determined by either range finder system, is com-
municated to the plotting room. In this room are assembled all
the instruments necessary for the complete determination of the
elements of sighting for the directing gun in the battery whose fire
is directed from the room. The corrections to be applied to the
observed range to compensate for the effect of the wind, of the
thermometric and barometric conditions, of differences in tide
level, and of the motion of the target, are quickly determined from
the instruments for a predicted position of the target at some in-
stant in advance. The deviation due to the wind and drift and
motion of the target are also determined. The corrected range,
azimuth, and deviation are sent to the gun, and the gun is then
pointed according to the instructions received. The command to
fire is given at such a moment as to cause the shot to arrive at the
predicted position of the target at the same instant as the target.
The instruments used are as follows.
528 ORDNANCE AND GUNNERY.
The wind component indicator gives the components of the wind
for range and deflection for use on the range and deflection boards.
The azimuth of the wind's direction, taken from the wind dial, and
the velocity of the wind, taken from an anemometer, are laid off
on the instrument. The azimuth of the target is also laid off, and
the instrument then indicates by a pointer the range and deflection
components of the wind with respect to the line from the gun to
the target.
The atmosphere board indicates the correction to be applied
at the range board for thermometric and barometric changes.
The range board, with the data supplied by the foregoing instru-
ments and other data indicated below, gives the corrections in
yards to be applied to the range for wind, atmosphere, tides, and
variations from the standard muzzle velocity, and indicates the
sum of these corrections.
The plotting board converts the range and position of the target
as determined from the reports of the range and position finders,
to the range and position for the particular battery or gun, with
the correction for range determined by the range board.
The deflection board indicates, for the corrected range and azi-
muth from the plotting board, the sum of the deflections to be
applied to the sight, or to the azimuth of the piece, to correct for
the deviating effect of wind, drift, and the motion of the target.
By means of these instruments, which have been devised by
artillery officers of our army, the correct setting of a gun may be
determined, the gun aimed, and the shot sped on its way, in an
interval of 15 seconds. The instruments are simple in construc-
tion and manipulation, and their use is entrusted to the enlisted
soldier.
302. Field Range and Position Finding. For range and posi-
tion finding in the field there are provided the Weld on range finder,
the battery commander's telescope, the battery commander's
ruler, and the field plotting board. The uses of these instruments
will be understood from their descriptions.
The Weldon Range Finder. The Weldon range finder, Fig.
246, consists of three triangular prisms mounted in a metal frame.
The silvered base of each prism rests against the metal. The angle
at the apex of each prism is as follows.
RANGE AND POSITION FINDING.
529
The upper or first prism, 90 degrees
The second prism, 88 51' 15"
The third prism, 74 53' 15"
Now if we construct, as in Fig. 247, the first two of the above
angles at the end of a base whose length is unity, and the third
FIG. 247.
FIG. 246.
FIG. 248.
angle as shown in the figure, the sides of the resulting triangles will
be of the lengths marked on them in the figure, the sides being
proprtional to the sines of the opposite angles.
Each prism diverts a ray of light through an angle equal to the
angle at its apex, as may be seen from Fig. 248. A ray entering
the first prism from I or a issues from the prism in a direction per-
pendicular to its original direction. And similarly a ray will issue
from the second prism at an angle of 88 51' 15" with its original
direction.
530 ORDNANCE AND GUNNLRt.
Standing at a, Fig. 249, and looking into the first prism, we see
the image of the object t in the direction ad, perpendicular to at,
and at the same time looking over
the prism we see the object d in line
with the image of t. Now moving
back on the line da there will be
some point b on this line where the
target t, seen in the second prism,
will again align with the object d seen over the prism. The angle
iba is then 88 51/ 15" and a^the range to the target, is 50 times
the base ab, see Fig. 247.
The second prism' may be used at both ends of the base. The
triangle obt will then be an isosceles triangle, the angle at a being
equal to the angle at 6, and the length of the sides at and bt will
be 25 times the length of the base.
The third prism is provided for use when the base ab is incon-
veniently long or when through the interposition of a gulch or
other obstacle the length of the base can not be directly
measured.
The points a and b, Fig. 249, having been determined, the ob-
server moves on the line tb to some point c from which, looking in
the third prism, he sees the image of the point a covering the object
at t seen over the prism. The angle at c is then 74 53" 15', and
as shown in Fig. 247 the base cb is one quarter of the base ab or
1/200 of the range at.
It is apparent from Fig. 248 that the instrument may be used
with the apex of the prism toward the eye or toward the target,
since both t and a may represent either target or eye. The posi-
tion of the image in either case with respect to the apex of the
prism is indicated in the figure.
The true refracted image may always be distinguished from im-
ages reflected from the face of a prism by revolving the instrument
about a vertical axis. Reflected images revolve with the instru-
ment, but as the lateral refraction is a fixed one the refracted image
remains stationary when the instrument is revolved.
When the instrument is held with the compass needle pointing
north, the bottoms of the two notches in the middle of the cover
mark the east and west line; and these two notches together with
RANGE AND POSITION FINDING.
531
the two at the end of the cover mark diagonal lines running north-
east and northwest.
303. The Battery Commander's Telescope. The battery com-
mander's telescope, Fig. 250, is mounted on a tripod in the same
-Azimuth Tangent feme*-. *
FlG. 250.
manner as the telescope of a transit instrument. It has movement
about horizontal and vertical axes. The amounts of the move-
ments about the axes are indicated by scales graduated to 6400ths
of the circle, or mils, corresponding for horizontal movement to
the deflection scale of the panoramic sight, and for vertical move-
ment to the clinometer scale of the range quadrant.
The telescope forms an erect magnified image of the object.
The ray of light enters the window in front of the objective prism,
is reflected downward by this prism, which is one of total reflection,
532 ORDNANCE AND GUNNERY.
passes through the objective, is rectified by the two Porro prisms,
and forms the image in the plane of the cross hairs in front of the
eyepiece.
The objective has a clear aperture of If inches, and a focal
length of 11 inches. The power of the telescope is 10, and the
field of view is 4 degrees.
The battery commander's telescope is used for measuring both
horizontal and vertical angles ; horizontally, the azimuths between
the target, gun, and aiming point, the azimuth of the front of a
hostile position, the correction in azimuth required to bring the
shots from a battery on to the target ; and vertically, the angle of
position of the target, the correction in elevation required to bring
the projectile to the target or the burst of the shrapnel to the
proper height above the target.
304. The Battery Commander's Ruler. The battery com-
mander's ruler, Figs. 251 and 252, constructed after the manner
of the slide rule, provides on the front, Fig. 251, a scale for quickly
measuring azimuths and a slide rule for determining the height
of the trajectory in mils at any point of the range, and on the back,
Fig. 252, a table of parallaxes, computed for a base of 20 yards, for
several ranges and for different angles of obliquity of base to
.range.
The instrument is of brass about 6 inches long, 1 inch wide, and
J of an inch thick.
A cord about 2 feet long passes through a hole in the ruler.
One end of the cord is fastened to a button on the observer's coat
so that when the ruler is held out until the cord is taut the ruler
is 20 inches from the observer's eye.
The scales on either edge of the front of the ruler are graduated
to read azimuths in mils. To measure any angle in azimuth, as
for instance from the target to the aiming point, the ruler is held
horizontally at the length of the cord with the zero at the end
marked T in line with the target. The 'azimuth to the aiming
point is indicated on the scale at the point where the line from the
eye to the aiming point cuts the edge of the ruler. It will be seen
that azimuths to the right of the target read from to 300, and
azimuths to the left read from 6100 to 6400, corresponding to the
deflection scales of the sights. The ruler is always held with that
RANGE AND POSITION FINDING.
533
L_
-
? %
! L
i
b
5
534 ORDNANCE AND GUNNERY.
edge up that will give a reading in the desired direction from the
mark T on the scale. All desired azimuths are similarly measured.
The ruler will be used for these measurements when the more
accurate battery commander's telescope is not at hand.
THE SLIDE. The slide and the adjacent range scale on the
ruler provide the means for determining the height of the trajectory
in mils at any given point of the rangel This information may be
frequently required for use in ascertaining whether an intervening
obstacle such as a hill, or woods, or a tower, will interfere with
the fire at a given target, or in determining the extent behind the
obstacle that is masked from the fire of the gun. The slide is
graduated in mils from -24 through to -f 284. The adjacent
range scale on the ruler is in hundreds of yards.
To use the instrument, first determine the angle of position of
the target, in mils, by the battery commander's telescope or other-
wise. Move the slide so as to place the slide graduation that in-
dicates the angle of position of the target over the range of the
obstacle as indicated on the range scale. The height of the tra-
jectory at the obstacle, in mils, is then indicated on the slide
opposite the range of the target on the range scale. If the height
indicated is greater than the angle of position of 'the obstacle,
obtained in the same manner as the angle of position of the target,
the projectile will clear the obstacle.
The principle involved in the use of the slide will be under-
stood from Fig. 253, in which the 6000- yard trajectory of the 3-
FIG. 253.
inch rifle is represented. The angular heights of the successive
points of the trajectory, measured from the origin, evidently
diminish from the angle of departure < at the origin to zero at the
end of the range. Under the principle of the rigidity of the tra-
RANGE AND POSITION FINDING. >35
jectory we may assume with sufficient exactness that within the
limits of direct fire any portion of the trajectory from the origin is
the true trajectory for the range represented by its chord. We
may therefore assume the portion of the trajectory subtended by
the shorter chord in the figure as the true trajectory for the range
3200 yards, and from the figure we see that the angular height of
the 6000-yard trajectory at 3200 yards is the angle of departure
<p for 6000 yards minus the angle of departure tV for 3200 yards.
On the range scale under the slide, Fig. 251, the zero of the two
scales being together, each range is indicated opposite its corre-
sponding angle of departure as indicated in mils on the slide.
Thus the angle of departure for a range of 3200 yards is nearly 100
mils, 100/6400 of 360 degrees, or 5 37'.
A movement of the slide in either direction will cause the read-
ing above any range to be increased or diminished, that is, the
movement adds an angle to the angle of departure for the range,
or subtracts an angle. If the zero of the slide is moved to the
3200-yard mark on the range scale, the angle of departure for
3200 yards is subtracted from the reading over every range on
the scale. Therefore the angle of departure for, say, the 6000-
yard range is diminished by the angle of departure for 3200 yards,
and as shown in Fig. 253 this difference, indicated on the slide
over the 6000-yard mark on the range scale, is the height of the
6000-yard trajectory at 3200 yards.
Now if we assume that the line od, Fig. 253, is horizontal and
that the target at c is elevated above d by the angle of position e,
say 20 mils, it is evident that 20 mils must be added to every
reading on the slide. We therefore move the zero of the slide back
until the 20 on the slide instead of the zero is now T over the range
3200. The reading over every range is increased by 20.
We have now put the angle of position of the target over the
range of the obstacle, and over the range of the target we read the
height of the trajectory at the obstacle.
305. THE PARALLAX TABLE.- On the back of the ruler, Fig.
252, is inscribed what is called the parallax table. By parallax is
meant here the angle, in mils, subtended by the front of a
platoon, 20 yards, from any point outside the battery. Thus
in Fig. 254, a being the aiming point and t the target, the
\a
536 ORDNANCE AND GUNNERY.
parallax of the aiming point is the angle at a subtended by the
two guns, and the parallax of the target is the angle at t sub-
tended by the guns.
The parallax of a point that
lies in a direction normal to the
front of the battery is, since 1
$J>^ mil is 1/1000 of the range, equal
to 20 divided by the number of
thousands of yards in the range.
FIG. 254. Thus for 4000 yards the parallax
is 5 mils. If the point lies in a
direction oblique to the front of the battery, the parallax is equal
to the normal parallax multiplied by the cosine of the angle which
the direction of the point makes with the normal to the battery
front.
The parallax has been calculated for different ranges and
different directions of the point and tabulated on the back of the
ruler. The upper two lines of the table, Fig. 252, give the angles
of obliquity in hundreds of mils in the two quadrants in front of
the battery, the lower two lines give similar angles for the two
quadrants in rear. The parallax of any point at any one of the
four ranges marked at the left is found in the line of the range and
in the column that indicates, to the nearest hundred mils, the
obliquity of the point's direction. The parallax in any fixed
direction is an inverse function of the range, therefore for any
range not given in the table it may be readily determined by means
of the parallax for some range in the table. Thus the parallax for
3000 yards is half that for 1500 yards or that for 1000 yards.
By means of the parallax the proper setting of the sight in in-
direct firing may be determined for one gun from the sighting of
the adjacent gun. Thus in Fig. 254 if the gun on the right has
found the target, at the angle a from the aiming point, the angle
/? for the second gun is readily obtained. Representing by p a and
p t the parallax angles at a and / respectively, we see from the figure
that, since
RANGE AND POSITION FINDING.
537
306. Plotting Board for Mobile Artillery. The plotting board,
Fig. 255, 16 inches wide by 39 inches long, is covered with rubber
cloth. Across the middle of the board is a grooved guideway g,
its edges graduated in yards. The protractor o slides in the guide-
way. The protractor is graduated in 64ths of a circle and by a
vernier may be read to mils. The outer graduated rim of the
protractor turns about the fixed central part. Fixed to the outer
rim of the protractor is the arm /, and pivoted to the center of the
protractor is the arm m, both graduated in yards. On each arm
FIG. 255.
is a sliding index, a and I, provided with a pin which may be
stuck into the board to hold the index in a fixed position.
The plotting board is used at the observing station to deter-
mine, for the directing gun, the position of the target with respect
to the point selected as an aiming point. Thus in Fig. 254, o is
the observing point from which the aiming point a, the target /,
and the directing gun are visible. The ranges from the observer
to the three points are determined, and the angles made by the
lines to the points with the line from the observer to the gun.
This line to the gun is the datum line, and is represented on the
plotting board by the center line of the grooved guideway. The
scale on the edge of the guideway is graduated to yards.
With the protractor in the center of the board, o Fig. 255, the
ami m is placed at an angle with the guideway equal to the angle
d+ e, Fig. 254, and the sliding index on the arm is placed at the
range oa on the scale. Similarly the arm / is revolved to make the
angle d with the guideway, and its index is placed at the range ot
on the scale. The pins of the two indexes are stuck into the board.
The protractor is now moved along the guideway to the point
OKDNANW A'ND QJJNN&&Y.
on the guideway scale, o' Fig. 255, that marks the distance
from the observer to the gun. The two arms slide through the
indexes and assume the positions of the lines from the gun to the
aiming point and to the target, Fig. 254. The angle a between
the arms is read from the protractor, and the ranges from the gun
to the aiming point arid target are read from the scales on the
arms.
307. Other Range Finders. Other range finders have been
constructed on the principle of the Weldon range finder, using
prisms with different angles or producing the deflection of the ray
by means of mirrors.
The Berdan Range Finder. The Berdan range finder consists of
two telescopes permanently mounted 6 or 12 feet apart on the bed of
a wagon, and provided with graduated circular bases by means of
which the angles between each of the telescopes and the base are
measured. The short base renders excessive the effect of a slight
error in the measurement of an angle, and for this reason prin-
cipally the instrument has not been found satisfactory in service.
The Barr and Stroud Range Finder. The Barr and Stroud
range finder, used on the ships of our own and foreign navies, and
now being tested for our field service, is constructed, optically, in
the manner shown in Fig. 256. The tube containing the optical
1
\ 1
1 1
1
1 1
I
tt
J. JL
pk"(
FIG. 256.
parts is so mounted on the deck of the ship, that the target may be
kept in view during heavy rolling or pitching of the ship.
Two reflectors r, marking the ends of a base line 4| feet long,
divert the rays from the target through the objectives o and
thence through the prisms p to the observer's right eye at e. The
field of view of the right eyepiece is divided horizontally by a dark
RANGE AND POSITION FINDING.
539
line, Figs. 258 and 259. The image from the objective on the
right is formed above this line and that from the left below it.
A deflecting prism, d Fig. 256, has a sliding movement in the
right telescope. When in position at d the prism has no deflecting
effect on the ray from the objective, and in this position of the
prism the parallel rays a from an object at a great distance, as
from the sun or moon, will form a continuous image in the field of
the right eyepiece. Now if a nearer object, on the same line from
the left reflector, be viewed, the direction of the ray to the light
reflector will be changed from a to s and the image from the righ:
telescope will not be continuous with that from the left, Fig. 259.
FIG. 257.
FIG. 258.
FIG. 259.
FIG. 260.
Continuity in the image is obtained by sliding the deflecting
prism d to the position c. The amount of the movement of the
deflecting prism is dependent on the range to the object; and the
ranges corresponding to the various positions of the prism are
marked on a scale that is carried by the prism. A movement of
the deflecting prism over a length of six inches corresponds to a
change in range from infinity to 250 yards.
The observer looks with his left eye through the eyepiece Z,
Fig. 256, and through the finder objective / opposite. The left
eyepiece and the object lens / form a low powered telescope with
a large field of view. The object viewed, Fig. 257, is seen through
this telescope, and in the field of view above the object appear a
pointer and a portion of the scale that is attached to the deflecting
prism d. The range to the object is read from the scale at the
pointer.
For use at night in obtaining the range to any target that bears
a light an optical appliance called an astigmatizer is provided in
the instrument. The astigmatizer lengthens the images of a point
of light into vortical streaks, Fig. 260, and the streaks are brought
540 ORDNANCE AND GUNNERY.
into coincidence. The astigmatizer is moved aside when not in
use.
The Le Boulenge* Telemeter. The Le Boulenge telemeter is
an instrument by means of which the velocity of sound is used for
measuring distance. The instrument is a glass tube filled with
liquid. In the tube is a loose glass piece or traveler whose specific
gravity is but slightly greater than that of the liquid, so that when
the tube is held vertical the traveler falls through the liquid slowly
and with approximately uniform motion. The time between the
flash of a gun and the arrival of the report is measured by turning
the tube from a horizontal to a vertical position when the flash is
seen, and back to the horizontal when the report is heard. The
range corresponding to the distance that the traveler has fallen
in the interval is read from a scale on the tube.
As the velocity of sound, 1100 feet per second in calm air,
varies with the velocity and direction of the wind, this method of
measuring ranges is not satisfactory.
CHAPTER XV.
SMALL ARMS AND THEIR AMMUNITION.
308. Service Small Arms. The present service small arms
are the .38 caliber revolver, model 1903, and the .30 caliber rifle,
model 1903. Automatic pistols have been issued to the service
for trial within recent years, but the results of the trials have not
been sufficiently favorable to bring about the adoption of any of
these arms for the military service. Automatic and semi-auto-
matic rifles have also been submitted to the Ordnance Depart-
ment for test. The tests are now in progress.
The .38 Caliber Revolver. The service revolver is made by the
Colt's Patent Fire Arms Manufacturing Co. of Hartford, Conn., and
is known as the Colt's double action revolver, caliber .38.
A double action revolver is one that may be fired in either of
two ways: by separately cocking the hammer and pulling the
trigger^ or by performing both operations with a single pull on the
trigger. When the separate movements are employed the piece
is said to be used in single action; and in double action, when
cocked and fired by the pull on the trigger alone. The service
revolver may be used either in single action or in double action.
Much greater rapidity of fire can be attained using the revolver in
double action, but on account of the increased effort required in
firing in this manner, and the consequent unsteadiness of the
hand holding the revolver, the fire is not likely to be as accurate
as when the revolver is fired in single action.
The mechanism of the revolver is shown in Fig. 261. The
operation of the mechanism is briefly as follows. In single action
541
542
ORDNANCE AND GUNNERY.
the piece is cocked by pressure of the thumb on the head of .the
hammer, 18. The lower end of the hammer moves the upper
end of the trigger forward and upward until the upper edge of
the trigger engages under the lip at the lower end of the hammer
and holds the hammer in the cocked position. A pull on the
trigger will then release the hammer, which, under the action of
the mainspring 32, falls and explodes the cartridge. The pressure
on the trigger being released, the rebound-lever spring 37
FIG. 261.
acting on the rebound-lever 34 moves the hammer back slightly
to its safety position and at the same time moves the trigger
forward.
When fifing in double action the pull on the trigger causes the
upper end of the trigger to bear against the end of the strut 10
which is pivoted on the pivot of the hammer and bears against the
hammer above the pivot. The pull on the trigger thus lifts the
hammer until, when the hammer is nearly at full cock, the strut
escapes from the end of the trigger and the hammer falls. As
the rear part of the trigger moves upward, whether in single or
in double action, the upper end of the hand 25 engages in a notch
on the rear face of the cylinder and causes the cylinder to revolve
through one-sixth of a turn. At the last part of the movement
SMALL ARMS AND THEIR AMMUNITION. 543
of the trigger a projecting lug forward on its upper surface passes
through a slot in the frame and engaging in a notch in the cylinder
prevents further movement of the cylinder.
The mechanism includes safety devices which allow the piece
to be cocked only when the cylinder is fully closed and latched in
the proper position.
309. THE MAINSPRING TENSION SCREW. The mainspring ten-
sion screw 33 is an important part of the mechanism whose func-
tions are not usually understood. Its purpose is to vary the ten-
sion of the mainspring in order to adjust the force of the blow
delivered by the hammer on the primer of the cartridge. When
the revolver is used in double action the hammer is not retracted
as far as in single action and consequently delivers a lighter blow
on the primer. It is a difficult matter to manufacture a primer
suitable for both methods of firing. If the cap of the primer is
made thin enough to insure firing of the primer under the lighter
blow in double action, the metal of the cap is likely to be pierced
by the point of the hammer under the heavier blow in single
action. The pierced primer allows the powder gases to escape to
the rear, perhaps to the injury of the soldier. If on the other
hand the primer cap be made sufficiently thick to insure its not
being punctured by the heavier blow, the primer may not be
sufficiently sensitive to be always fired by the lighter blow. The
importance of a proper adjustment of the tension of the main-
spring is therefore apparent. If it is found that failures to fire in
double action are frequent the screw 33 should be screwed in
slightly to increase the tension of the mainspring and produce a
heavier blow of the hammer. But the tension must not be in-
creased more than absolutely necessary, for otherwise puncture
of the primer may occur when the revolver is fired in single
action.
THE BARREL. The barrel of the revolver has a length of 6
inches, and a diameter between the lands of the rifled bore of
0.357 of an inch. It is rifled with 6 grooves 0.003 of an inch deep
and with a uniform twist of one turn in 16 inches. The rifling has
a left handed twist in order that the drift of the bullet to the left
may counteract to some extent the tendency that exists to pull
to the right in firing.
544 ORDNANCE AND GUNNERY.
AMMUNITION AND BALLISTICS. The ball and blank cartridges
used in the revolver are shown in Fig. 262. The charge in the
ball cartridge is about 3J grains of a nitroglycerine powder, and
produces in the bullet a muzzle velocity of 750
feet. The bullet, of lead, weighs 148 grains.
Its greatest diameter is 0.357 of an inch, which
is the diameter between the lands of the rifled
bore. The powder gases entering a conical
cavity in the base of the bullet expand the
base of the bullet into the grooves of the rifling.
The grooves of the bullet are filled with Japan
wax as a lubricant. The wax also serves, to-
gether with the crimping of the front end
of the cartridge case against the bullet, to keep out moisture and
render the cartridge waterproof.
While the bullet has sufficient energy to inflict a disabling
wound at a range of 200 yards, the revolver cannot be relied upon
for accurate firing beyond 75 yards.
The blank cartridge contains 7 grains of E. C. powder held in
the case by a paper wad crimped in place and shellacked.
310. The Colt Automatic Pistol. In the Colt automatic
pistol the recoil of a movable barrel .and slide is utilized to eject
the fired shell, cock the firing mechanism, and load a new car-
tridge into the barrel; so that after the first shot is fired the only
operation necessary to fire the remaining cartridges in the maga-
zine is a pull of the trigger for each cartridge.
The pistol is made in three calibers, .32, .38, and .45. The
magazines of the two smaller pistols hold 8 cartridges; that of
the .45 caliber pistol holds 7 cartridges. The .45 caliber pistol is
represented in Figs. 263 to 265. The rear part of the frame or
receiver r forms a hollow handle which encloses the magazine
and the firing mechanism. The magazine, Fig. 264, is a light metal
case containing a spring and follower. The cartridges are in-
serted one at a time by sliding in at the top. The sides of the
magazine curve slightly over the upper cartridge, which may be
removed only by being pushed out to the front. The magazine
when filled is inserted into the handle of the pistol from below
and is held in place by a spring catch.
FIG. 265.
Colt Automatic Pistol, Caliber .45.
SMALL ARMS AND THEIR AMMUNITION. 545
The forward extension of the receiver r contains the retractor
spring g arid has formed on its sides guides for the reciprocating
slide s. The barrel b is attached to the receiver by two links o.
The forward part of the slide 5 covers the barrel, and the rear
part forms the breech bolt and carries the firing pin. Three lugs
formed on the top of the barrel engage in notches in the slide and
lock barrel and slide together. The slide lock c, a straight bar,
holds the slide to the receiver. It passes through longitudinal
slots in the sides of the receiver, and its ends are engaged in
notches in the slide. The head of the retractor-spring follower
/ presses against a recessed seat in the middle of the slide lock
*, and thus holds slide and barrel in firing position.
OPERATION. The operation of the pistol when fired is as
follows. The powder gases acting rearwardly against the bolt
force the slide to the rear against the pressure of the retractor
spring. The barrel, carried to the rear with the slide, revolves
about the lower pivots of the two links o, its axis always remain-
ing parallel to the top of the receiver. The downward movement
of the barrel soon disengages it from the slide, but not until after
the bullet has left the muzzle. The momentum acquired by the
slide causes it to continue to the rear. Its rear end cocks the
hammer h. An extractor carried by the slide withdraws the
fired shell which, striking an ejector, is thrown out to the right
through a slot in the slide. When the front of the bolt has passed
to the rear of the top cartridge in the magazine this cartridge is
forced upward into the path of the bolt by the magazine
spring.
As the slide returns under the action of the retractor spring
the bolt forces the top cartridge forward out of the magazine
into the barrel in its lowered position, and then raises the barrel
into its locked position for firing. A pull on the trigger now causes
the cocked hammer to strike the firing pin and fire the cartridge.
When the last cartridge has been fired the slide remains to the
rear, thus warning the soldier that the magazine is empty.
The safety lever, / Fig. 263, prevents movement of the trigger
until the slide and barrel are in proper position for firing.
To load the first cartridge into the barrel, the rearward move-
ment of the slide is produced by hand, the slide being grasped by
546 ORDNANCE AND GUNNERY
the disengaged hand at the roughened surfaces on its sides, and
pulled to the rear.
The necessity of using two hands to load the first cartridge into
the barrel is one objection to the pistol as a military arm.
HOLSTER. The pistol holster is a light steel frame covered with
leather, and is arranged to be attached to the butt of the pistol
in such a manner as to serve as a stock by means of which the
pistol can be fired from the shoulder.
AMMUNITION. The .45 caliber bullet, of lead with a cupro-
nickel jacket, weighs 200 grains. The charge of powder is 5.1
grains. The muzzle velocity of the bullet is 900 feet.
Five shots may be fired from the pistol in a second.
311. Modern Military Rifles. The modern military rifle
differs from its predecessors chiefly in caliber and in the use of
the magazine. The caliber of the rifle in our service has been
reduced from 0.45 to 0.30 of an inch, with an accompanying reduc-
tion in the weight of the bullet from 500 grains to 220 grains, and
recently to 150 grains. The maximum pressure in the bore has
been increased, with the change in caliber, from 25,000 pounds
per square inch to 44,000 pounds.
INCREASED VELOCITY. The increased pressure, better sus-
tained along the bore by modern powders, produces in the lighter
bullet a velocity very much greater than that attained in the
rifles of larger caliber. The muzzle velocity of the bullet from
the .45 caliber rifle was 1300 feet per second, while the present
sendee rifle gives to the 220-grain bullet a muzzle velocity of 2200
t feet, and to the 150-grain bullet a muzzle velocity of 2800 feet.
At the same time, since the weight of the gun has not materially
changed, the ratio of weight of bullet to weight of gun has greatly
diminished. On this ratio principally depends the maximum
velocity of free recoil of the gun for any given velocity of the
projectile, see equation (4), page 275. We may consider the
velocity of recoil, or better its square, as a measure of the shock
of recoil. In the modern rifle the ratio of weight of bullet to
weight of gun is diminished to such an extent that, even with the
increased velocity of the bullet, the velocity of recoil is dimin-
ished. In consequence of the lighter shock of recoil on the soldier's
shoulder, he is enabled to longer continue his fire without fatigue.
SMALL ARMS AND THEIR AMMUNITION. _547
OTHER ADVANTAGES. The increased muzzle velocity in-
creases the range and accuracy of the rifle and flattens the trajec-
tory, thus increasing the danger space for any range. The in-
creased velocity has been attained with a shorter barrel, thus
diminishing the weight of the gun and facilitating the handling of
the gun by the soldier.
The reduced weight of the bullet and of the charge of
powder reduces the weight of the cartridge, thereby enabling
the soldier to carry a greater number of cartridges on his
person.
THE JACKETED BULLET. In order that the metal of the bullet
shall not be stripped by the rifling as the bullet passes with high
velocity through the bore, it is necessary to cover the soft lead of
the bullet with a jacket of tougher material. The modern bullet
is therefore composed of a lead core enclosed in a jacket made of
cupro-nickel or of nickeled steel. The lead gives weight to the
bullet and increases its sectional density, see page 458, while the
tougher jacket enables the bullet to take the rifling without ma-
terial deformation, and also gives to the bullet greater penetra-
tion hi any resisting material.
THE MAGAZINE. Ease and rapidity of fire are greatly increased
by the use of the magazine. At the first introduction of magazine
guns the cartridges in the magazine were considered as in reserve,
to be used only in cases of emergency. The gun was habitually
used as a single loader. In the latest weapons the filling of the
magazine may be accomplished more readily than the insertion
of a single cartridge into the barrel, since the cartridges are carried
by the soldier in packets adapted to magazine loading only. Maga-
zine fire is therefore used habitually, though the guns are adapted
for single loading as well.
The mechanism of the magazine is usually arranged to lock
the bolt of the gun open when the magazine is empty, so that in
the excitement of battle the soldier may not continue to go through
the motions of firing with an unloaded gun.
312. Requirements. That the military arm may stand the
rough usage incident to service in war it is essential that it be
strongly constructed. Its mechanisms must be strong, simple,
and easily dismantled for repair in the field without the use of
548 ORDNANCE AND GUNNERY.
tools. The mechanisms must not be seriously affected by a mod-
erate amount of rust or dust.
To lessen the chances of injury to the rifle as few of the parts
as possible should project beyond its general outline. This latter
consideration forms one of the objections to the attachment to
military rifles of telescopic sights and other devices for increasing
the accuracy of fire. The military rifle can rarely get the care
necessary to keep the more delicate and more complicated sporting
and target rifles in condition. Especially is this so in time of war
when armies, those of the United States particularly, are largely
composed of untrained volunteers most of whom have never pre-
viously carried a rifle. The arm that is put into their hands must be
of such a character that it will be serviceable under almost all con-
ditions, and as accurate as it may be made under this requirement,
Tests. Before the adoption into our service of a rifle of new
model the arm is subjected to tests as follows.
ENDURANCE TEST. The arm is tested for endurance by firing
from each of several rifles 5000 rounds, in forty lots of 100 rounds
each and two lots of 500 rounds each.
At various stages of the endurance test the ballistic qualities
of the arm are tested by firing for velocity and accuracy, and the
working of the mechanism by tests for rapidity of fire.
DUST TEST. The rifle, with the breech block closed, is sub-
jected to a blast of fine sand for two minutes, first with the maga-
zine empty and again with the magazine filled with cartridges.
After each exposure to the blast the surplus sand is removed by
blowing, by wiping with the bare hands only, and by tapping the
butt and muzzle on the ground. The rifle must then be capable of
operation in single loading and in magazine fire.
RUST TEST. The rifle is thoroughly cleaned and all oil and
grease removed by washing in soda water. The muzzle and
chamber are tightly corked and the rifle is immersed in a saturated
solution of sal ammoniac for ten minutes and then exposed to a
damp atmosphere for 48 hours. The rifle must then be capable
of operation as before.
DEFECTIVE CARTRIDGE TEST. Cartridges cut through at the
head, others cut through at the extractor groove, and others slit
throughout their length are fired in tho rifle.
FIRED FROM NEW BARREL INTO SAWDUST.
RRED INTO SAWDUST FROM BARREL PREVIOUSLY
FIRED 3500 TIMES.
FIRED INTO SAWDUST FROM BARREL PREVIOUSLY
FIRED 4500 TIMES.
FIG. 267. Effects of Erosion on Bullets.
SMALL ARMS AND THEIR AMMUNITION. __ 549
EXCESSIVE CHARGE TEST. Five rounds are fired with car-
tridges loaded to produce a maximum pressure in the chamber
one third greater than the maximum pressure attained in service.
313. Life of the Rifle. Erosion. Although the rifle remains
serviceable, as far as the operation of its mechanism is concerned,
after endurance tests of 5000 rounds or more, its accuracy dimin-
ishes markedly after a number of rounds considerably less than
5000, the number depending on the conditions of the firing. With
its accuracy seriously impaired the rifle ceases to be suitable for
service. The service life of the rifle must therefore be measured
by the number of rounds that can be fired from it with accuracy,
and not by the number fired in tests for endurance.
The accuracy of the rifle is principally affected through the
erosion of the barrel by the powder gases. The gases, highly
heated and moving with high velocity under great pressure, at-
tack the walls of the bore, which are probably softened by the
great heat, and cut irregular channels in the metal, destroying the
surface of the bore and the rifling. The erosion is greatest at the
seat of the bullet immediately in front of the cartridge case, and
extends forward into the barrel for several inches. Beyond this
the walls of the bore are practically unaffected.
The effect of erosion is well shown in the enlarged photographs,
Fig. 266, of rifle barrels from which 3500, 4000, and 5000 rounds
have been fired.
When the erosion has become marked, the bullet is forced
against an irregular surface and the metal of the bullet jacket,
probably also softened by the heat, is unequally stretched on
different sides, producing a decided eccentricity of the point of
the bullet and great irregularity of the base. The sides of the
bullet are deeply scored by the powder gases escaping past the
bullet and by the irregularities of the bore.
In Fig. 267 are shown enlarged photographs of a service 220-
grain bullet, model 1903, recovered after being fired into sawdust
from a new rifle barrel, and of bullets fired from barrels that had
been previously fired 3500 and 4500 times.
The deformation of the bullet is the chief cause of its inaccuracy.
At the same time its muzzle velocity is reduced by the escape
of the gases past the bullet in the bore.
550 ORDNANCE AND GUNNERY.
VELOCITY AND PRESSURE. The erosive effect of the gases ap-
pears to depend more on their velocity than on the maximum
pressure. Thus in tests that were made with the service rifle with
220-grain bullets fired with muzzle velocities of 2300 and 2200
feet, the maximum pressures in the two cases not being very
different, the first appreciable falling off in accuracy occurred
after 2000 rounds with the 2300-foot velocity and after 4000 rounds
with the velocity of 2200 feet; and the accuracy after 7000 rounds
with the lower velocity was better than after 4000 rounds with the
higher.
Ammunition loaded to produce a muzzle velocity of 2300 feet
was originally used in the service rifle, but after the above men-
tioned tests the muzzle velocity was reduced to 2200 feet and the
accuracy life of the rifle increased from 2000 to 4000 rounds.
The 150-grain bullet recently adopted for the new rifle was
intended originally to have a muzzle velocity of 2800 feet, the
maximum pressure being considerably less than with the 220-
grain bullet. It is doubtful whether, on account of the rapid
erosion, this high velocity can be fixed as the standard.
Erosion, the cause of the reduction in the muzzle velocity in
the small arm, is also the cause of the recent reduction of the
muzzle velocities in the 10- and 12-inch seacoast guns from 2500
to 2250 feet.
314. The U. S. Magazine Rifle, Model 1903.- The present
'service rifle fulfils all the requirements enumerated in a previous
paragraph as essential for a military rifle. As the Cadets of the
Military Academy are armed with the rifle and familiar with its
operation through daily use, an extended description of the
weapon is not necessary here. Consideration of some of its parts
may be of advantage.
Two views of the mechanism of the rifle, with bolt in closed
position, are shown in Fig. 268.
THE RECEIVER. The receiver is that part of the gun that
contains the breech closing bolt. It is held to the stock by the
two guard screws, front and rear. The barrel is screwed into the
front of the receiver.
TRIGGER PULL. It will be observed that the rounded upper
edge of the trigger bears against the bottom of the rear part of the
SMALL ARMS AND THEIR AMMUNITION
552 ORDNANCE AND GUNNERY.
receiver, against which it is held by the. pressure of the sear spring,
the trigger being pivoted in the slotted sear. When the trigger is
pulled it has comparatively free movement until the rear point,
or heel, of the trigger bears against the receiver. The nose of the
sear, its rear part which projects upward through a slot in the re-
ceiver, is by this movement partially withdrawn from the sear notch
in the cocking piece. When the heel of the trigger bears against
the receiver the trigger leverage is reduced and a short but more
decided pull is required to further withdraw the sear from the
sear notch. The purpose of the first movement of the trigger,
against slight resistance, is to prevent accidental discharge of the
piece as the soldier first feels the trigger, and to increase the accu-
racy of fire by enabling the soldier to partially withdraw the sear
while aiming, and to complete its withdrawal at the proper mo-
ment by a slight movement of the ringer.
CAMS. In the operation of the mechanism the most decided
resistances are encountered in the compression of the mainspring
and, at times, in the insertion of a cartridge into the barrel and
in the extraction of the fired shell. In order that these opera-
tions may be accomplished with the least fatigue to the soldier
they are all performed by means of cams.
The mainspring is partially compressed in the movement of
unlocking the bolt by the action of a cammed surface of the bolt
against the cocking cam on the firing pin, and the compression of
the spring is completed on the closing of the bolt by the action of
the two locking lugs at front end of bolt against the cammed
locking shoulders in the receiver. The cammed movement of
rotation also forces the cartridge to its seat in the chamber. In
the rotation of the bolt in opening, the extracting cam at upper
end of bolt handle works against a cammed surface in the receiver
and moves the bolt slightly to the rear, starting the fired shell
from the chamber.
THE BARREL. The rifling of the barrel consists of four grooves
0.004 of an inch deep. The grooves are three times as wide as
the lands. The twist is uniform, one turn in 10 inches, and right
handed. The length of the barrel, measured from end to end, is
24.206 inches, a length that permits the use of this arm by the
cavalry, and makes their fire as efficient as that of the infantry.
SMALL ARMS AND THEIR AMMUNITION. 553
Formerly the cavalry were provided with carbines, short guns
with the same mechanism as the longer rifle and using the same
ammunition.
The muzzle of the barrel is rounded to protect the rifling.
Any irregularity of the muzzle end of the bore will seriously affect
the accuracy of the arm by causing unequal pressure on the sides
of the bullet as it is about to leave the bore.
315. THE SIGHTS, MODEL 1905. The sight seats or bases for
front and rear sights are bands that encircle the barrel, to which
they are fixed by splines and pins. This method of attachment
is preferable to the method formerly employed of screwing the
sight seats directly to the barrel, as the sights are now more se-
curely held and there is less likelihood of their adjustment being
disturbed.
The windage screw, Fig. 258, which gives the movement in
deflection to the rear sight, is acted on by a spring which prevents
lost motion due to wear in the parts of the rotating mechanism.
Each division or point of the deflection scale of the rear sight
corresponds to a lateral deviation of 4 inches in 100 yards.
The leaf of the sight is graduated for elevations from 100 to
2500 yards, the sight for the latter range being taken through the
notch on upper end of leaf.
With the leaf down the sights are set at 400 yards, battle range,
at all positions of the slide on the leaf.
In the movement of the slide up the leaf, the drift slide, Fig.
268, in which are cut the sighting notches and peep, follows a
drift curve cut in the leaf and thus compensates for the lateral
deviation of the trajectory from the line of sight as adjusted on
the piece. Explanation of the drift and of the adjustment of the
line of sight will be found in a later paragraph entitled Deviation.
The front sight is fitted in a stud that before being screwed to
its seat is adjusted laterally to its proper position on the indi-
vidual rifle. The proper adjustment is obtained by actual firing
with each rifle. The firings are done by expert marksmen over a
covered 200-yard range provided at the armory.
The sight radius of the piece, the horizontal distance between
the point of the front sight and the rear edge of the notch or peep
of the rear sight, is 22.3251 inches.
554
ORDNANCE AND GUNNERY
RAPIDITY OF FIRE. With single loading,
23 aimed shots have been fired from the rifle
in one jninute, and with magazine fire, 25
shots in one minute. With the rifle held at
the hip, 27 unaimed shots, loaded singly, have
been fired in one minute, and with magazine
fire, 35 shots.
THE BAYONET. The tang B of the bay-
onet, Fig. 269, is of one piece with the blade.
In a recess in the tang is mounted the catch
H which engages under the bayonet stud on
the gun, locking the bayonet to the gun; and
the catch E which secures the bayonet in its
scabbard by engaging a hook provided in the
scabbard . Ei ther catch is released by pressure
on the thumb piece E.
Appendages. Among the appendages
provided for the care of the piece is a bullet
jacket extractor,
Fig.270, a cylin-
drical steel plug
rifled on the ex- FIG. 270.
terior to fit the bore. This is pushed down
the bore from the muzzle until it rests on the
bullet jacket, which may then be forced out
of the barrel.
A headless shell extractor consists of a steel
plug, Fig. 271 of the general shape of the
FIG. 269.
FIG. 271.
inside of the cartridge case, with a head like
that of the cartridge. A steel ball rolls freely
in a groove at the point, the groove being
inclined outward toward the point. The
extractor is roughened on the side opposite
the groove. The extractor is pushed into the
SMALL ARMS AND THEIR AMMUNITION. 555
headless shell by the bolt of the gun, the gun being held with
the muzzle up. The muzzle of the gun is then pointed down
and the bolt withdrawn, extracting the extractor and the headless
shell.
An aiming device is also provided for purposes of instruction
in aiming. It consists of the circular steel clip a, Fig. 272,
w r hich embraces the gun in rear of the rear sight and
supports the standard b to which the cage c may be
fixed at any desired height. The cage contains a reflector
so arranged that the instructor sees in the reflector the
images of the gun sights and of the object aimed at.
He may therefore correct the soldiers' aim.
A cleaning thong and brush are contained in a
metal case carried in the butt of the stock. The case
is arranged to contain also a quantity of oil and a
metal oil-dropper. A brass cleaning rod, a steel front
sight cover, and a suitable screw driver are provided
with each piece.
316. Deviation. Drift. The rifle has a right-handed twist.
The drift proper is therefore to the right. But at the moment that
the bullet leaves the bore the muzzle of the gun is actually pointed
to the left of its aimed position. The movement of the muzzle is
probably due to vibrations of the barrel caused by the passage of
the bullet through the bore. The barrel being held firmly at the
bands the vibrations will take place about these points as nodes.
The vibratory movement of the barrel is such that at the moment
that the bullet leaves the bore the muzzle is pointed to the left
of its aimed position.
The horizontal deviation of the bullet from the axial plane of
sight is therefore the resultant of the drift due to the rifling and
the deviation due to the vibration of the barrel. Following
custom, we will call the resultant horizontal deviation the drift.
As determined by experimental firings the drift of the 220-
grain bullet, fired from the service rifle, is to the left of the axial
plane of sight up to a range of 850 yards, and beyond that range
the drift is to the right.
In order to minimize the deviation at the most important
ranges the drift slot in the leaf of the model 1.905 sight is so cut
556 ORDNANCE AND GUNNERY,
as to make the trajectory cross the adjusted line of sight at a range
of 1530 yards. Within that range the drift is to the left of the
line of sight, its maximum value being 1.8 inches at the range of
1200 yards. After the trajectory crosses the line of sight the
drift is to the right and increases rapidly from 1.1 inches at 1600
yards to 39.4 inches at 2500 yards.
VERTICAL DEVIATION. The angles of elevation of the rifle as
determined from actual firings at different ranges are all greater
than the computed angles of elevation, for the ranges. This in-
dicates that at the moment that the bullet leaves the bore the posi-
tion of the muzzle due to the vibratory movement of the barrel is
below as well as to the left of its aimed position. The difference
between the observed and computed elevations increases with the
range, as it should since the effect of a constant difference of the
angles will be less as the range increases.
The .22-caliber Gallery Practice Rifle. The gallery practice
rifle differs from the U. S. magazine rifle, model 1898, known as
the Krag-Jorgensen rifle, only as to the barrel and the receiver.
The barrel of the gallery practice rifle is a .22-caliber rifled barrel
adapted to fire commercial .22-caliber, rim-fire, short or long
cartridges. The barrel is issued assembled with a suitable ex-
tractor to a modified receiver. Any model 1898 rifle may be con-
verted into a gallery practice rifle by dismounting the .30-caliber
barrel and receiver and mounting in their stead the .22-caliber
barrel and receiver.
With .22 caliber long cartridges, a range of 50 feet requires the
sight to be set at 100 yards, and a range of 100 feet requires a
sight setting of 225 yards.
AMMUNITION FOR THE .30=CAL. MAGAZINE RIFLE.
317. The Ball Cartridge. The ball cartridge, Fig. 273, con-
sists of the cartridge case, the primer, the charge of powder, and
the bullet.
THE CARTRIDGE CASE. The cartridge case is made f .com a
circular disk of brass cut from a flat ribbon 0.13 of an inch thick.
The disk is first bent into the form of a cup and then drawn out in
successive operations by being forced by punches through dies
SMALL ARMS AND THEIR AMMUNITION. 557
successively diminishing in diameter. In each draw press the
length of the cartridge is increased and its diameters and thick-
ness of wall diminished. Six draws are required to bring the car-
tridge to the desired size. After the cupping operation and after
FIG. 273.
each of the first four draws the case is softened by annealing,
which removes the brittleness of the metal caused by the drawing
process. The cases are trimmed as required. The head of the
cartridge case and the primer pocket are formed in a press. The
mouth of the case is then annealed and the reduction of the neck
and shoulder is accomplished in three operations in another press.
The extractor groove is turned in the head, and the vent is punched
through the bottom of the primer pocket.
BODY. The body of the cartridge is of greater diameter than
the rifled bore of the gun, in order to provide the necessary chamber
space in the shortest practicable length. The enlarged body is a
disadvantage in that it increases the bulk of the cartridge, and
requires a larger chamber in the gun and greater thickness in the
working parts of the gun. But in the present development of
powders it has not yet been possible to produce from a cylindrical
cartridge of reasonable length the desired ballistics for the rifle.
HEAD SPACE. The space in the rifle between the head of the
bolt and the surface against which the cartridge bears is called
the head space. The head space in the rifle is of a length to allow
proper clearance between the bolt and the head of the cartridge
when the cartridge is fully inserted in the chamber. The head of
the cartridge should always occupy the same position in the rifle,
in order that the blow of the firing pin on the primer may be
uniform, thus reducing the chances of misfires and punctured
primers.
In order that the position of the primer in the gun shall vary
the least the head space should be as short as possible, that is, the
bearing surface of the cartridge should be close to the head of the
558 ORDNANCE AND GUNNERY.
cartridge, since in the manufacture of the cartridge the variations
in a short dimension are likely to be less than in a longer one.
The cartridge 'with flanged head, Fig. 274, used in former
service rifles, has an advantage over the present cartridge in this
respect. The head space with the flanged cartridge measured from
the seat for the front edge of the flange, was about T V of an inch
FIG. 274.
long, while the head space in the present rifle which is measured
from the seat for the sloping shoulder of the cartridge, is nearly
two inches long. In addition the bearing surface of the present
cartridge is sloped, so that more extensive variations in the posi-
tion of the head of the cartridge are likely to occur.
THE PRIMER. The primer, Fig. 273, consists of the cup, the
anvil, and the percussion composition. A pellet of moist percussion
composition is put into the cup which is previously shellacked
so that the composition will adhere. A shellacked disk of paper is
pressed in tightly over the composition to keep out moisture. The
anvil of hard brass is then forced into the cup. The primers are
dried for several days in a dry house.
The cup of the primer is made of gilding metal, an alloy of
copper much softer than the brass of the cartridge case. The
metal of the cup must be sufficiently soft, and of the proper thick-
ness, to permit a large part of the blow of the firing pin to be
transmitted to the percussion composition, thus insuring explo-
sion of the primer. At the same time the metal must be suffi-
ciently hard to resist puncture by the firing pin. The firing pin
strikes the primer with an energy of about 17 inch-pounds.
The priming composition is as follows:
Chlorate of potash, 632 parts
Sulphide of antimony, 320 parts
Ground glass, 212 parts
Sulphur, 110 parts
SMALL ARMS AXD THEIR AMMUNITION. 559
The finely pulverized ingredients are thoroughly mixed wet,
and the composition is always handled wet, in which condition it
is safe to handle. The composition is called the H 48 composition.
This composition is safe, sufficiently sensitive, and emits a
large bod}^ of flame. The large bod}^ of flame makes the composi-
tion superior for use with smokeless powders to the fulminate of
mercury formerly used in all primers and still largely used in the
primers in sporting cartridges and others.
The primer is seated slightly below the head of the cartridge in
order to diminish the liability to accidental explosion of the car-
tridge in handling.
THE POWDER CHARGE. The powder charge consists of about
51 grains of nitroglycerine powder. The weight of powder re-
quired to produce the muzzle velocity of 2800 feet varies in dif-
ferent lots of powder. The weight of charge therefore varies
slightly in different cartridges.
318. Bullets. The core of the bullet, Fig. 273, is an alloy of
16 parts of lead and one part of tin. The jacket, of cupro-nickel,
is drawn from a disk in the same manner as the cartridge case.
The lead slug is forced into the jacket, the point of the bullet
shaped in a press, and the rear end of jacket turned squarely over
the base of the bullet.
The 220-grain bullet is shown in Fig. 275, and the recently
adopted 150-grain bullet in Fig. 276. The 220-grairi bullet had a
muzzle velocity of 2200 feet, the maximum x-x
pressure in the bore of the rifle being about
49,000 Ibs. The 150-grain bullet is given a
muzzle velocity of 2800 feet with a maximum
pressure of 45,600 pounds. The great in-
crease in the muzzle velocity makes the
trajectory of the lighter bullet very much
flatter than that of the 220-grain bullet, and
thus correspondingly increases the accuracy FlG> 2 ' 5 ' FlG> 27G -
of the rifle. It might be expected that the lighter bullet would
suffer greater retardation in flight from the resistance of the air,
but this bullet with its sharp point encounters less resistance
than the heavier bullet with its rounded point. Greater accuracy
at all ranges therefore results from the lighter bullet, with its
higher velocity and sharp point.
A
560 ORDNANCE AND GUNNERY.
The bearing surface of a bullet, that part of the bullet that
comes in contact with the walls of the bore, should end abruptly,
in order that as the bullet leaves the muzzle the bearing against
the walls of the bore will cease at the same instant on all sides,
and the bullet will not be deflected by the longer contact of any
one point with the walls of the bore. The bearing surface of the
service bullet terminates at the base. The base of the bullet
should therefore be square with the axis, and the edge of the base
should be as sharp as the metal of the jacket will permit.
In Fig. 277 is shown in full size a bullet recently tested. The
bullet, of copper, weighed 175 grains. The bearing surface began
about f of an inch from the point and extended to about
J of an inch from the base, terminating on the rear
slope of the bullet, the diameter of the base being less
than the caliber. In tests for comparative accuracy at
500 yards the radius of the circle of shots was 4.2
inches for the 150-grain service bullet, 5.6 inches for
the 220-grain service bullet, and 25.6 inches for the
experimental copper bullet. On examination of the
copper bullets, recovered after firing, the marks of the
rifling were found extending farther to the rear on one
side of the bullet than on the others. The difference
in length of bearing on the different sides is sufficient to account
for the inaccuracy.
319. The Blank Cartridge. The bullet of the ball cartridge
guides the cartridge from the magazine into the chamber of the
rifle. In order that blank cartridges may be loaded from the
magazine, a hollow paper bullet, Fig. 278, replaces the metal bullet
FIG. 277.
FIG. 278.
of the ball cartridge. The paper bullet is charged with 5 grains
of E. C. powder held in place by a drop of shellac. The bullet is
made by rolling a strip of paper into a tube of proper length, the
end of the tube being afterwards closed into the rounded head
SMALL ARMS AND THEIR AMMUNITION. 561
by pressure in a machine. The strip of paper that forms the tube
is gummed only on the outside edge so that the charge may readily
burst the bullet at the muzzle of the gun. If the paper were
gummed over its entire length the bullet would be so stiff that it
might act as a rocket and do injury at some distance from the
muzzle.
The propelling charge in the cartridge case is 10 grains of E. C.
powder.
The blank cartridge is made T V of an inch shorter than the ball
cartridge, to prevent the accidental assembling of a ball cartridge
into a clip with blank cartridges. The machine in which this
operation is performed is adapted for cartridges of one length only.
The Dummy Cartridge. In order that the dummy cartridge,
Fig. 279, may be readily distinguished from the ball cartridge both.
FIG. 279.
by sight and touch, the case of the dummy cartridge is tinned and
corrugated, and three holes are bored through the bottoms of the
corrugations. These are means intended to diminish the chances
of the insertion of a ball cartridge in the rifle when drilling with
dummy cartridges.
The Guard Cartridge. The long range of the bullet of the
ball cartridge and its great penetrative power render the ball
cartridge unsuitable for the use of guards in times of peace, and
for use in cities or other crowded places at times of riot and dis-
FIG. 280.
turbance. The guard cartridge, Fig. 280, is provided for these
uses. The nn jacketed lead bullet weighs 117 grains and is given
a velocity of 1150 feet. The cartridge gives good results at JOO
yards and has sufficient accuracy for use at 150 and 200 yards.
562
ORDNANCE AND GUNNER*.
The lead bullet is deformed on striking and has little pene-
trative power, so that it is not likely to cause injury at a distance
to innocent persons,
320. Proof of Ammunition. Ammunition is proved by
velocity and accuracy tests made with the arm in which the
ammunition is to be used. Service rifle cartridges are also tested
to determine whether they are waterproof.
VELOCITY TEST. The velocity is measured at 53 feet frcm the
muzzle, the first velocity screen being placed 3 feet from the
muzzle and the two screens 100 feet apart. The mean velocity of
10 shots must not differ more than 15 feet from the standard.
ACCURACY TEST. The accuracy test for rifle ammunition con-
sists of several series of 10 shots each fired at a target 500 yards
from the muzzle. The gun is fixed in a rest. The target is a
heavy steel plate about 20 feet square, painted white and marked
with horizontal and vertical black lines 2 feet apart.
The horizontal and vertical coordinates of each shot mark are
measured from a convenient origin. The means of the horizontal
and vertical coordinates are respectively the horizontal and ver-
tical coordinates of the center of impact.
The distance of each shot from the center of impact is measured
and the mean of these distances is the wean radius of the group of
shots, or, as it is sometimes called, the radius of the circle of shots.
The mean of the vertical distances of the shots from the center
of impact is the mean vertical deviation, and the mean of the hori-
zontal distances from the center of impact is the mean horizontal
deviation.
In the proof of ammunition the mean horizontal deviation is
not measured, as the horizontal deviation depends upon the
atmospheric conditions rather than upon the ammunition.
The results of recent comparative tests of the 220-grain and 150-
grain bullets in the service rifle are shown in the following table.
Bullet.
Charge,
Grains.
Pres-
sure,
Lbs.
Velocity, f. s.
Accuracy
500 Yards.
Pene-
tration
500
Yards,
Inches.
Muzzle.
1000
Yards.
Had.
M.<V. D.
220-grain 1903
44
51
49000
45000
2200
2730
980
1130
5.6
4.2
4.2
2.5
23.3
32.5
150-grain 1906
SMALL ARMS AND THEIR AMMUNITION. _ 563
Equipment for Accuracy Test. As it would often be most in-
convenient to make on the target the measurements necessary for
the determination of the mean radius and deviations of a group of
shots, the ammunition proof range is provided with a camera
obscura in a building in front and to one side of the target and near
it. The lens of the camera forms an image of the target on a
paper facsimile of the target constructed to the proper scale so
that the lines of the image coincide with the lines of the target
facsimile. An observer in the camera marks with a pencil the
image of each shot mark made on the target, and the desired
measurements are then conveniently made from the paper fac-
simile.
WATERPROOF TEST. Cartridges from each lot manufactured
are immersed in water at a depth of 8 inches for a period of 24 or
48 hours, and are then tested for velocity. There must be no fall-
ing off in velocity due to the entrance of moisture into the case.
CHAPTER XVI.
MACHINE GUNS.
321. Service Machine Guns. The machine guns in our service
are the Gatling machine gun and the Maxim automatic machine
gun. The guns are of the same caliber as the infantry rifle and
use the same ammunition.
In the Gatling machine gun the operations of loading, firing,
and extracting the empty shell are effected through mechanisms
actuated by a crank. The crank is turned by the gunner at a rate
to produce any desired rapidity of fire. The greatest efficiency is
obtained from the gun at a rate of fire of 600 rounds per minute.
In an emergency this rate can be greatly increased.
In the Maxim automatic machine gun the operating mechanism
is actuated by the recoil, so that after the first shot is fired the
firing continues without effort on the part of the gunner as long
as the trigger is pressed. The rate of fire from the gun depends
upon the condition of the barrel and mechanism. In a new gun
250 cartridges in a single belt are fired at the rate of 650 shots a
minute. After 8000 rounds this rate is reduced to about 325
shots a minute. In the continuous firing of 1000 rounds the rate
of fire from a new gun is about 400 rounds a minute.
The Gatling gun has the advantages of a more rapid rate of
continuous fire, and of a complete control of the rate of fire at all
times. The fire of the automatic gun is however sufficiently rapid,
the aiming is not interfered with by the operation of a crank, and
the gun is lighter and more readily transported. It has therefore
been adopted as the principal machine gun for our service.
Machine gun fire has recently become of such importance io
564
SMALL ARMS AND THEIR AMMUNITION.
565
battle that a machine gun platoon, armed with two automatic
machine guns, is organized in each battalion of infantry and in
each squadron of cavalry, so that six machine guns now accom-
pany each regiment into the field.
The Gatling Machine Gun. Fixed to a central shaft 8, Fig.
281, are the ten ,30-caliber rifled barrels B held in the barrel
S G
FIG. 281.
plates P\ the carrier block C, provided with grooves which re-
ceive the cartridges successively and guide them into the barrels,
the lock cylinder L, provided with guide slots in which the breech
blocks for the barrels slide to close and open the breech; and the
worm wheel G, by means of which the shaft and attached parts
are rotated. The shaft is supported at each end in a frame, the
sides of which also support the shaft of the rotating crank K.
The parts behind the rear barrel plate are completely inclosed
in a cylindrical bronze casing which keeps out dust and protects
the operating parts against injury. Within the casing is a hollow
cylinder, called the cam cylinder, on the interior surface of which
a continuous cam groove is cut.
The breech bolt, Fig. 282, one for each barrel, carries the firing
FIG. 282.
pin a, and its spring, and the extractor d. The guide rib e at
the bottom of the bolt engages in a guide slot of the lock cylinder,
L Fig. 281. The lug c on top of the bolt engages in the cam
groove cut in the walls of the cam cylinder.
566
ORDNANCE AND GUNNERY.
The cam groove, represented in Fig. 283 as though visible
through the casing and cam cylinder, extends continuously around
the interior of the cylinder. The top and
bottom parts of the groove, a and b, follow
lines cut from the cylinder by planes at right
angles to its axis. These parts of the groove
are joined by the inclined parts cd. The cam
cylinder is fixed to the casing and does not
revolve.
322. OPERATION. As the lock cylinder, L Fig. 281, rotates
with the barrels in a clockwise direction, the uppermost breech
bolt is in its rearmost position, being held there by the lug c of the
bolt moving in the circular part a of the groove. While the bolt
.is in this position a cartridge is placed by the feed mechanism in
the top groove of the carrier block C in front of the bolt. As
the bolt in its rotation moves downward on the right side it is
FIG. 283.
FIG. 284.
moved forward by the cam groove cd and pushes the cartridge
into the barrel. During this movement the cocking head of the
firing pin, b Fig. 282, is caught by a grooved rib, R Figs. 283 and
284, and the firing pin is prevented from moving forward with the
bolt. The method of operation will be understood from Fig. 284,
which shows a development of the cam groove and rotating parts.
The lines dd and cc in Fig. 284 represent respectively the develop-
ments of the parts a and b of the groove as shown in Fig. 283.
MACHINE GUNS.
567
When the barrel is in its lowest position the head of the firing
pin leaves the rib R, and the firing pin, under the action of its
spring, strikes and fires the cartridge. As the breech bolt moves
upward on the left side it is drawn to the
rear by the cam groove, extracting the fired
shell from the barrel and ejecting it to
the left through a slot in the casing.
THE FEED. A hopper is formed in the
top of the bronze casing immediately over
the carrier block, C Fig. 281 and e Fig. 285.
The device, called the Bruce feed, for
feeding cartridges to the gun, is fixed in
a socket at the mouth of the hopper.
Pivoted on the standard, ac Fig. 285, is
a swinging piece b, provided with two
flanged grooves which engage the heads of
the cartridges: by the flange of the 1898
cartridge, and by the groove of the 1903
cartridge. The grooves in b are quickly
filled by stripping the cartridges from the
paper boxes in which they are packed.
The cartridges from one of the grooves in
b pass immediately through the groove in
c and are fed one at a time to the 'carrier
block e by the wheel d which is caused to
revolve by the carrier block. When one
of the grooves in b is empty the weight
of the cartridges in the other groove
causes the piece b to swing to one side and
bring the full groove over the groove in c.
MOUNTS. The Gatling gun is mounted,
for field service, on a shielded wheeled car-
riage with limber. When mounted in the
casemates of permanent or temporary fortifications for use in
repelling landing parties and in protecting the land approaches, a
fixed mount is provided.
Blank Cartridge for Gatling Gun. When the blank cartridge
for the infantry rifle is used in the Gatling gun the blunt end of
FIG. 285.
568
ORDNANCE AND GUNNERY.
MACHINE GUNS.
569
the paper bullet often catches on a shoulder at the rear end of the
barrel, thus preventing insertion of the cartridge and causing the
mechanism to jam.
A special blank cartridge is therefore
made for the gun. The cartridge case
is extended to the length of the com-
plete ball cartridge and, after the inser-
tion of the powder charge, the mouth
of the case is closed into the rounded
form of the point of the 220- grain bullet.
323. The Maxim Automatic Machine
Gun. The Maxim automatic machine
gun has a single barrel, arid the recoil
of the barrel and attached mechanism is
utilized to perform the operations neces-
sary in continuous firing.
The barrel, 32 Fig. 286, is inclosed in
a cylindrical water jacket 97, and slides
in its bearings in stuffing boxes at each
end of the water jacket. Fixed to the
rear end of the water jacket is the
breech casing 55, a rectangular steel box
that incloses the operating mechanism
and provides means, 35 and 54, for the
attachment of the gun to its mount.
METHOD OF ACTION. The barrel and
the breech mechanism recoil together
until after the bullet has left the bore.
When the barrel has reached the end
of its recoil the breech mechanism
continues to the rear, opens the breech,
and extracts the fired shell; and, re-
turning under the action of a spring,
inserts a new cartridge in the barrel and
fires the piece. These actions are re-
peated as long as the trigger is pressed.
The cartridges are fed to the gun in a belt, see Fig. 291, which
is automatically drawn through the feed mechanism above the
570
ORDNANCE AND GUNNERY.
breech in such manner as to present a new cartridge after each
discharge.
RECOILING PARTS. The recoiling parts, Fig. 287, comprise the
barrel a, the two recoil plates 6 fixed to the breech of the barrel,
the operating crank shaft e fixed in bearings in the recoil plates,
and the breech mechanism which slides between the recoil plates
and is operated by means of the crank shaft e.
The recoil plates slide in grooves provided in the sides of the
breech casing 55, Fig. 286. The left recoil plate extends to the
front of the breech and operates the feed mechanism above the
barrel. The crank shaft 75 projects on both sides through slots
79 in the casing. The movement of the recoiling parts to the
FIRJNGjPOSITJON,
FIG. 288.
rear is stopped when the crank shaft strikes the rear edges of the
slots. Fixed to the right end of the shaft is the cam lever 57.
During the recoil, and after the shot has left the bore, the lower
surface of the cam lever bears on the roller 58, and as the recoil
continues the cam lever, riding on the roller, is rotated upward,
thus producing a downward movement to the crank on the shaft
between the recoil plates. The crank is seen in Fig. 287 and at i
Figs. 288 and 289. Attached by links to the fusee, g Fig. 287,
on the crank shaft outside the breech casing, is the operating
spring h which at its f orward end is attached to the breech casing.
On recoil and rotation of the shaft the spring is extended, and at
the end of the recoil the reaction of the spring returns the parts to
the firing position.
324. THE BREECH MECHANISM. The breech mechanism is
MACHINE GUNS.
571
shown in Figs. 288 and 289. It consists of the lock k which con-
tains the firing mechanism; the carrier n, a narrow piece which
slides up and down the front of the lock and is provided in front
with a flanged groove to engage the head of the cartridge; and
the forked link j pivoted at its rear end to the crank i on the
operating shaft e. The breech mechanism slides back and forth
between the recoil plates b in grooves cut in the sides of the
recoil plates.
The parts being in the firing position the flanged groove of the
carrier n engages the head of a cartridge in the feed belt above
the barrel and also the head of the cartridge in the barrel. When
the piece is fired the barrel and breech mechanism start to the
FIG. 289.
rear together. At the end of the movement of the barrel, the
breech mechanism is drawn farther to the rear between the recoil
plates by the rotation of the crank i as shown in Fig. 289.
In this movement the carrier n is guided by its bearings q
which move on the upper surfaces of solid cams, 37 Fig. 286,
fixed to the side plates of the breech casing. The movement of
the carrier is at first straight to the rear withdrawing the cartridge
from the belt and the fired shell from the chamber. The carrier is
then depressed by a guide lug, 43 Fig. 86 and p Figs. 288 and
289, attached to the top plate of the breech casing. The loaded
cartridge is thus brought opposite the barrel and the fired shell
opposite the ejector tube 33. The reaction of the coiled spring
now returns the parts to the firing position, the carrier n, Figs.
288 and 289, moving straight to the front in its depressed position.
After the cartridge has boon placed in the chamber, the carrier is
572
ORDNANCE AND GUNNERY.
slid upward by the action of the finger o against the lifting lever
o', the finger o being fixed to the link j. The carrier leaves the
fired shell in the ejector tube where it is held by a spring to prevent
its falling back into the mechanism. It is ejected from the tube
by the next succeeding shell.
THE FIRING MECHANISM. The firing mechanism, shown in Fig.
290, is contained between two plates k. The solid part of the
forked link j acts in its downward movement against the pro-
jecting end of the tumbler c, withdrawing the firing pin until it is
caught by the safety catch e. At the same time the sear d en-
FIG. 290.
gages in the notch of the tumbler where it is held by one leaf of the
spring b. The trigger h is placed at the rear outside the breech
casing, between the two gun handles. A forward pressure against
its upper end moves the trigger bar g to the rear. When the
trigger is pressed the lug on the trigger bar that engages the sear
d releases the sear from the notch in the tumbler as the breech
mechanism moves forward in closing, and holds it released after
the breech is closed. After the release of the sear the firing pin
is held back by the safety catch e. The link ; in the last part of
its movement upward lifts the projecting end of the safety catch
and releases the firing pin, which under the action of the spring
b flies fonvard and fires the cartridge.
MACHINE GUNS. 573
The trigger is constantly pressed to the rear by the spring i
and is provided with a safety catch to guard against accidental
firing. The trigger cannot be pressed forward for firing until
the safety catch is lifted.
325. THE WATER JACKET. In continuous firing the barrel of
an automatic rifle becomes very highly heated and if not cooled in
some way may even attain a red heat. The walls of the bore are
so softened by the heat that the lands of the rifling are soon worn
away and the gun loses its accuracy. The accuracy is completely
destroyed after about 1000 rounds fired with the water jacket
empty. The necessity of cooling the barrel during firing is therefore
apparent, and the gun should never be fired, except in emergency,
without water in the jacket.
The water jacket of the Maxim gun holds 12 pints of water.
The barrel of the gun is coated with copper on the exterior as a
protection against rust. The stuffing boxes through which the
barrel passes are packed with asbestos packing.
A steam tube, 89 Fig. 286, is fitted in the upper part of the
water jacket to provide a means of escape for the steam that is
formed in the water jacket during continuous firing. Near each
end of the steam tube is a hole 89 for the admission of steam,
and at the front end a hole 99 through both tube and water jacket
permits escape of steam to the exterior. The steam tube is sur-
rounded by the tubular valve 96 which slides on the steam tube
and closes the forward or rear steam port according as the gun is
depressed or elevated, thus preventing the entrance of water into
the steam tube while permitting the entrance of steam.
THE CARTRIDGE BELT. The cartridge belt, Fig. 291, is formed
of two pieces of flax webbing connected by brass strips and eyelets
between adjacent cartridges, every third strip projecting about an
inch beyond the bullet edge of the belt to guide the belt properly
through the feed mechanism of the gun. A flat brass handle 4
inches long is attached to each end of the belt.
Each belt holds 250 cartridges.
The cartridges are quickly and evenly inserted into the belt
pockets by means of a small belt-filling machine, Fig. 292, which
is attached to a bench and operated by hand.
MOUNTS. For service with the infantry and cavalry the auto-
&74 ORDNANCE AND GUNNERY.
matic gun is mounted on a tripod, Figs. 291 and 293. It is trans-
ported by means of pack animals. For transportation the legs of
the tripod fold together and the rear leg telescopes. A complete
outfit consists of five packs. The gun and tripod form one pack
which weighs, with the equipment of the animal, 275 pounds.
Each of the other four packs consists of 1500 rounds of ammuni-
tion, and accessories for the gun including water for refilling the
water jacket. These packs weigh complete about 290 pounds
each.
The gun with tripod, and water jacket filled with water, weighs
152 pounds. It may therefore be readily transported by hand
over short distances in the field. The legs of the tripod fully
extended to the front and rear form convenient shafts for carrying.
For use in fortifications the gun is mounted on a two-wheeled
carriage provided with shields. The parts of the mount connecting
with the gun are alike in the carriage and in the tripod mount, so
that the guns may be fitted to either type of mount as desired.
BLANK FIRING ATTACHMENT. The pressure produced in the
discharge of a blank cartridge is not sufficient to operate the
mechanism of the gun. There is therefore provided for use in
drill with blank cartridges an attachment called the drill and
blank firing attachment. The attachment, Fig. 293, is affixed to
one of the rear gun handles and acts, through the continuous
turning of a crank by hand, to operate the crank shaft of the
recoil mechanism in the same manner as when operated by the
explosion of a ball cartridge.
326. The Maxim One-pounder Automatic Gun. This gun,
called the Pompom from the noise of its explosions, is constructed
on the same principles as the ,30-caliber automatic gun above de-
scribed.
On account of the greater size and weight of the parts and the
increased total force of recoil, an additional coiled recoil spring, s
Fig. 294, surrounds the barrel in the water jacket. The spring, as
well as the barrel, is coated with copper. A small hydraulic
cylinder c also assists in checking the recoil. The cylinder is
held in the rear plate of the breech casing, the piston p of the
cylinder being connected with a cross bar x held between the
rear ends of the recoil plates.
FIG. 292. Belt Filling Machine.
FIG. 293. Attachment for Firing Blank Cartridges.
MAXIM .30-CALiBER AUTOMATIC MACHINE GUN.
MACHINE GUNS. 575
The caliber of the gun is 1.457 inches. It fires a shell weighing
one pound, with a bursting charge of 4/10 of a pound.
The Colt Automatic Machine Gun. The operation of the Colt
automatic machine gun, Fig. 295, is effected through the direct
action of the powder gases on the end of a swinging lever I. A
vent is cut through the bottom of the stationary barrel a short
distance in rear of the muzzle. When the bullet has passed the
vent a portion of the powder gases enter the vent and impinge on
a piston p attached to the lever I. The blow on the piston causes
the lever to revolve downward and to the rear against the action
of a coiled spring s which at the end of the movement returns the
lever to its former position.
The movement of the lever is communicated by the connecting
bar c to the mechanisms in the rear, and actuates these mechan-
isms to perform the successive operations necessary for the main-
tenance of continuous fire.
The cartridges are fed to the gun in a belt similar to that
described for the Maxim gun. The feeding of the belt is accom-
plished by the feed wheel w under the rear end of the barrel.
CHAPTER XVII.
SUBMARINE MINES AND TORPEDOES. SUBMARINE
TORPEDO BOATS.
327. Submarine Mines and Torpedoes. A submarine mine is
a charge of explosive confined in a strong case anchored in posi-
tion under the surface of the water.
A torpedo is a submarine vehicle charged with explosive. The
term torpedo formerly included fixed as well as moving mines,
and still includes, to a certain extent, both these classes.
History. The first recorded experiments with submarine
mines were made by David Bushnell of Connecticut, in 1775.
His mines contained charges of black powder, and explosion was
effected by means of clockwork, which, after being set in motion,
allowed sufficient time before the explosion for the operator to get
clear.
Bushnell also constructed a submarine boat for the purpose of
conveying his mines to hostile vessels. The boat, Fig. 296, was
formed of two sides, each shaped like the upper shell of a tortoise.
Entrance was gained through a hatch in the top. It carried but
one operator, who moved the craft by means of screw propellers.
The explosive was carried in a case with the firing mechanism, on
the back of the boat, and was fastened by a rope to the stem of a
wood screw which projected through the top of the boat. The
operator was expected to bring the craft under the hostile ship,
and fasten the wood screw in the ship's wooden bottom. This
effected, the moving away of the submarine boat would release
the mine and set the clockwork in motion, to explode the charge
after a sufficient interval of time.
576
SUBMARINE MINES AND TORPEDOES.
577
An attempt was actually made in 1776 with this boat against
the English man-of-war Eagle in the harbor of New York. The
operator claimed that he found the vessel, and that in attempting
to fasten the screw in her bottom he struck iron. In looking for
a, better location he lost the vessel. He released the magazine in
the harbor, and an hour afterward the explosion occurred.
Bushnell also attacked the English fleet, at Philadelphia in
1777, with drifting torpedoes. This attempt was also unsuccessful.
FIG. 296.
Robert Fulton experimented with torpedoes from 1797 to 1810.
In 1801 he succeeded in sinking the first vessel, a small one, with a
submarine mine. The mine contained 20 pounds of gunpowder.
In 1804 he conducted, for the English, an unsuccessful attack with
mines against the French fleet in the harbor of Boulogne. The
mines exploded but did no harm to the French ships.
In 1842 Samuel Colt applied electricity to the firing of sub-
marine mines, and in the following years was successful in numer-
ous experiments in the explosion of mines at great distances from
the operator.
Mines and torpedoes were first successfully used in war by the
Confederates in our Civil War. With imperfect appliances they
578
ORDNANCE AND GUNNERY.
succeeded in sinking or seriously damaging more than thirty
United States ships. Their success attracted the attention of the
world to this method of naval attack and defense, with the result
that there has followed great improvement in the appliances and
methods employed, and the means for submarine warfare are now
given earnest consideration by all maritime nations.
328. Confederate Mines. The mines used by the Confederates
were of various forms. The simplest and one of the most effective
mines was made of a barrel, which was partially filled with black
gunpowder. The charge was usually about 100 pounds. The
barrel, Fig. 297, was provided with pointed ends to prevent its
being overturned by the current. It was moored to float 5 or 6
FIG. 297.
feet below the surface of the water, and a depending weight kept
the top of the barrel uppermost. Screwed into sockets on top of
the barrel were a number of percussion or chemical fuses. A
vessel striking one of these would explode the mine.
The chemical fuse consisted of a small glass tube filled with
sulphuric acid and surrounded by a mixture of chlorate of potash
and white sugar, the whole enclosed in an outer lead tube. The
lead tube was crushed by the blow of a striking vessel and the
glass tube broken. The action of the sulphuric acid on the mixture
of chlorate of potash and white sugar produced fire, which was
communicated to the powder charge of the mine by a priming of
black powder.
Another very effective buoyant mine, known as the Singer
mine, is shown in Fig. 298. The case, made of tin, was of size
sufficient to hold from 50 to 100 pounds of gunpowder, and to
provide sufficient air space a for flotation. A percussion cap was
held in a cup in the lug e in the midst of the powder charge, and
SUBMARINE MINES AND TORPEDOES.
579
the upper end of the rod d was close to the cap. A firing bolt b
was held back against the pressure of a spiral spring by the pin g.
A heavy iron cap c, connected by a wire to
the pin, rested on the top of the mine. When
the mine was struck the cap was knocked off.
The cap in falling pulled out the pin g. The
firing mechanism would then act and explode
the mine.
In shallow waters, frame and spar, or pile,
toipedoes were used. The frame torpedo,
Fig. 299, consisted of a number of inclined
timbers framed together and supporting at
their upper ends explosive shell provided
with percussion caps.
Two forms of the spar torpedo are shown
in Figs. 300 and 301. The spar torpedo was
also used for offensive operations in boats.
The spar, with torpedo at the end, was
carried projecting from the bow of a launch.
The most noteworthy exploit with a spar torpedo was that of
Lieut. W. B. Gushing, U. S. Navy, who in 1864 attacked in a
launch the Confederate ironclad Albemarle which was tied to a
dock in the river at Plymouth, N. C. The Albemarle was sunk by
FIG. 298.
FIG. 299.
the explosion of the torpedo. So was the launch. Lieutenant
Cushing and one member of his crew of thirteen escaped.
The Confederates also made use of submarine boats carrying
torpedoes, and they sunk by these means the Unitod States
580
ORDNANCE AND GUNNERY,
frigate Housatonic in Charleston Harbor in 1864. The submarine
boat used on this occasion was worked by a crew of nine men who
FIG. 300. FIG. 331.
operated the propellers by hand. The boat and her crew were
carried down with the Housatonic.
Spanish Mechanical Mine. Fig.
302 represents a Bustamente contact
mine. Seventeen of these mines were
removed by our Navy from the harbor
of Guantanamo, Cuba, after the cap-
ture of the harbor in 1898.
The mine is circular in cross sec-
tion. It carried a charge of 100
pounds of wet guncotton hi the
cylinder a and a priming charge of
dry guncotton in the chamber b.
Against the chemical fuse c, a bottle
containing sulphuric acid and sur-
rounded by a mixture of chlorate of
potash and sugar, rest the ends of
six iron rods or plungers d whose
outer ends are connected to the six
pivoted contact arms e. A blow on any one of the arms e would
cause a plunger to break the fuse. Ignition of the priming charge
and explosion of the bursting charge would follow.
SUBMARINE MINES AND TORPEDOES.
581
329. Electric Mines. Mechanical mines such as those de-
scribed above, when once planted, render the waterways dangerous
to friend and foe alike. This great disadvantage is overcome in
modern practice by the use of electrically controlled mines which
may be made instantly operative or harmless at the will of an
operator on shore.
MOORINjVRpPt-
SWfcLE CONBVCTOR CABUC
5HACKLE
SOCKET
DISTRTBirnON_gOX'
BUOYANT MINES. A modern buoyant mine is shown in Fig.
303. The spherical case of steel contains the explosive and the
circuit-closing and firing devices, with sufficient air space for
flotation. A continuous insulated cable extends from the mining
casemate in the fortification to the mine in position. The firing
circuit is broken at the mine, and the electrical arrangements are
such that the mine may be fired by the operation of the circuit-
closer when the mine is struck by a vessel, or at any time at the
will of the operator in the mining casemate. Or the striking of a
582 ORDNANCE AND GUNNERY.
mine may be automatically signaled to the operator, who may
then fire it at once, or after a few moments delay, in order to allow
a ship to get well over it, or not fire it at all.
Buoyant mines are moored at a submergence of about 5 feet
at low water, so that they may be near enough to the surface to be
struck by passing vessels and yet not near enough to be readily
seen. They are not in general used in water less than 20 feet
deep. They may be operated successfully in water 150 feet deep.
In order to obtain the necessary buoyancy the mines used in
waters of the greatest depths are cylindrical in shape with hemi-
spherical ends.
GROUND MINES. Ground mines are used when the depth of the
water does not exceed 35 feet. They rest on the Dottom. A
heavy mushroom-shaped case contains the charge of explosive and
the ebctric firing device. The circuit- closing device is carried by
a buoyant case similar in shape to the buoyant mine. The buoy is
moored, with proper submergence, to the ground mine. When
the buoy is struck by a passing vessel the circuit-closer within it
acts in precisely the same manner as the circuit-closer in the
buoyant mine, and, if desired, completes the firing circuit that
.fires the charge in the mine resting on the bottom.
330. The Explosive. Dynamite and guncotton are the prin-
cipal explosives used in submarine warfare.
Dynamite has been used in the mines of the United States
service. It has the advantages of cheapness and ease of ignition.
Its disadvantages are danger in handling, liability to explosion
when a derelict mine is struck by a vessel, and changing sensibility
to the action of the detonator when freezing and thawing. If the
dynamite becomes wet, through a leak in the mine case, the nitro-
glycerine separates from the absorbent.
Guncotton has the advantage of being perfectly safe in storage
and in handling, and of detonating when wet if a small amount
'Of dry guncotton be present. The dry cotton must be in close
contact with the wet. Too much water will make the detonation
uncertain. The explosive force of guncotton is less than that of
dynamite.
Excellent results have recently been obtained in submarine
work with the explosive tri-nitro-toluol.
SUBMARINE MINES AND TORPEDOES. 583
The Charge. Charges varying from 100 to 1000 pounds of ex-
plosive have been used in mines. A charge of 100 pounds ex-
ploded In contact with, a warship's bottom will disable and prob-
ably sink the ship.
In recent experiments with a submerged target built in exact
representation of the bottom of a battleship, the explosion of a
12-inch mortar shell containing 63 pounds of high explosive, at a
distance of 20 feet from the target and at a depth of 15 feet,
produced serious injury to the target; 64 pounds at a distance of
15 feet nearly disrupted the target and caused bad leakage, pro-
ducing dangerous injury; while 130 pounds at a distance of 15
feet disrupted the double bottom and caused the target to sink
immediately. The results showed the utility of this method of
attack on vessels, and the desirability of using as large an explo-
sive charge as possible in the projectiles for the seacoast mortars.
General Henry L. Abbott, Corps of Engineers, U. S. Army,
conducted a very extensive series of subaqueous experiments with
different explosives. He deduced the following formulas for the
energy and pressure delivered at a distance by a subaqueous ex-
plosion.
/
\
(D+O.Ol) 2 ' 1
1,832,000(7 \
in which W represents the energy per square inch,
P the pressure in pounds per square inch,
C the weight of charge, in pounds,
D the distance in feet.
Applying the pressure formula to the explosions of the three
mortar shell in the vicinity of the battleship target, we find that
the pressures on the target were, in order, 3574, 5401, and 8662
pounds per square inch.
331. Defensive Mine Systems. The submarine mine system
is used as an auxiliary in the defense of a river or harbor in
connection with the land fortifications, and its chief purpose is
to so limit and obstruct the approach of the enemy's vessels that
584
ORDNANCE AND GUNNERY.
they will be compelled to make frontal attack on the fortifications
and be held exposed to the fire of the heaviest guns.
In order that the most effective fire may be employed the outer
lines of mines are .planted at a distance from the fortifications, not
exceeding the most effective range of the guns.
The usual mine system for the defense of a harbor is illustrated
in Fig. 304. Concealed and protected in a fortification is the
FIG. 304.
mining casemate C which contains the electric generators, bat-
teries, and instruments needed in the service of the mines. From
this point the mines are controlled.
The mines are planted, in the waterways to be defended, in
groups, for convenience of service.
Multiple conductor cables, one for each group, lead from the
mining casemate to junction or distribution boxes similar to that
SUBMARINE MINES AND TORPEDOES. 585
shown in Fig. 303. In the junction box the conductors of the
multiple cable are separated and joined to the conductors of single
conductor cables which lead to the individual mines of the group.
Thus each mine has its own cable and may be operated inde-
pendently of all the other mines.
The course of a hostile vessel approaching or moving through
the mine fields is observed by means of the range and position
finding system of the fortification, and the operator in the mining
casemate is apprised of the proximity of the vessel to any mine.
In addition to the groups of mines, other mines, called skirmish
mines, s Fig. 304, may be laid on single cables in irregular lines
about the groups. The skirmish mines may be made active or
safe at the will of .the operator, but cannot, on account of their
arrangement on a single cable, be fired singly by judgment.
The arrangement of all the mines is such that a vessel can
follow no reasonable course into the harbor without encountering
several mines. Gaps, left between the groups in the various lines,
form a more or less tortuous channel which allows passage to
friendly vessels. Guide boats are employed to conduct friendly
vessels through the safe passages.
Subsidiary waterways not of service to the defense may be
closed to the enemy by mechanical mines, which contain within
themselves the electric batteries that provide the firing current.
In the fortifications, gun batteries, usually of 3-inch guns, cover
the mine fields, and protect them against attempts of the enemy
to clear the fields by countermining from boats.
Search lights are provided to illuminate the mine fields at
night.
332. Countermining. Countermining consists in exploding
and cutting adrift the fixed mines of the enemy and destroying
their cable connections by the explosion of other mines distributed
among them. The purpose of countermining is to make a safe
channel through the mines of the defense. Countermining is
usually done at night from small boats.
The Removal of Mines. The experience had in clearing the
harbors of the United States of mines after the Spanish War in-
dicates that the safest way to remove the mines is to explode them
in place.
586 ORDNANCE AND GUNNERY.
Mobile and Automobile Torpedoes. The mobile torpedo con-
veys the explosive charge under the water and explodes the charge
against the bottom of the enemy's ship. Mobile torpedoes are now
used exclusively by navies, and all such torpedoes are self-propelling
or automobile. The necessity of erecting on shore, at the water's
edge, special plants for the service of the torpedoes, and the necessity
of protecting such plants, are considerations that militate against
the use of mobile torpedoes for harbor defense.
The Sims-Edison Torpedo. A long series of experiments were
made a number of years ago with the Sims-Edison torpedo, Fig.
305, to determine whether this torpedo was adapted for harbor
defense.
The torpedo consists of a cylindrical hull with conical ends. It
is 28 feet long, 21 inches in diameter, and is supported at a depth
CABLE TO SHORE STATION. -~ <<
FIG. 305.
of 5 feet under the water by a float, to which it is connected by steel
rods. Two balls carried above the float enable the operator on
shore to observe the position of the torpedo and to direct its move-
ment. The torpedo is propelled, steered, and exploded by elec-
tricity. The power is generated at a station on shore and is com-
municated to the torpedo through a cable which is carried coiled
in a central chamber and is paid out as the torpedo moves.
A charge of 300 pounds of explosive is carried in the head of the
torpedo.
The results obtained in the experiments were *not sufficiently
satisfactory to warrant the adoption of this torpedo for the harbor
defense service.
333. The Whitehead Torpedo. The Whitehead torpedo, Fig.
306, is now used by all the navies of the world. Its motive power
is furnished by compressed air which is stored, at a pressure of
about 1100 pounds per square inch, in a tank carried by the torpedo.
SUBMARINE MINES AND TORPEDOES. 587
The torpedo is fired, by compressed air or by gunpowder, from
launching tubes that are mounted on the ship's deck or built into
the ship below the water line. A torpedo tube arranged for firing
with compressed air is shown mounted on the deck of a torpedo
boat, in Fig. 307.
The explosive charge, carried in the head of the torpedo, is fired
by percussion when the torpedo strikes.
SUBMERSION MECHANISM. In a chamber in rear of the air tank
is the mechanism for regulating the depth of tne torpedo. The
head of a piston, actsd on oy springs, protrudes through a central
hols In the rear wall of the chamber into another narrow chamber
to which the water has access through the holes in the walls of the
torpedo. The water pressure thus acts on one side of the piston
FIG. 306.
and the springs on the other. The springs may be regulated to
exert a pressure on the piston equal to the pressure of the water
at any desired depth. At that depth the piston will be stationary,
while at any other depth it will be moved forward or backward.
The piston is connected with horizontal diving rudders at the tail
of the torpedo, one on each side. Any movement of the piston
caused by the departure of the torpedo from the depth for which it
is adjusted is communicated to these rudders, which act to return
the torpedo to the desired depth.
The piston ceases to act when the torpedo is at the fixed depth,
whatever may be the position of the longitudinal axis of the torpedo.
As the axis will not be horizontal when the depth is reached the
torpedo, if controlled by the piston alone, will overrun the depth
and then return again to it, and will continue in this way rising and
descending. To prevent this action a heavy pendulum, in the
chamber with the piston, is also connected with the diving rudders.
The pendulum remains vertical, and at any departure of the axis
of the torpedo from the horizontal, the diving rudders are turned
to correct the departure. The piston and pendulum together thus
588 ORDNANCE AND GUNNERY.
serve to keep the torpedo on an even keel at the desired sub-
mergence.
THE MOTIVE ENGINES. The motive engines in the next com-
partment are supplied with compressed air through pipes that lead
from the tank forward. The engines actuate two shafts, one
within the other, that carry the propellers. The propellers turn
in opposite directions. This arrangement of the propellers serves
better than any other arrangement to prevent rolling of the
torpedo.
DIRECTING MECHANISM. The compartment in rear of the en-
gine contains the device for correcting any deviation of the torpedo
from a straight course. A small gyroscope, with wheel about 3
inches in diameter, is mounted under the propeller shaft with its
axis parallel to the axis of the torpedo. The gyroscope is set in
motion by a spring-actuated mechanism at the launching of the
torpedo. The axis of the gyroscope tends always to remain
parallel to its original direction, and at any departure of the axis
of the torpedo from its original direction the gyroscope actuates
the valve of a small air steering-engine which moves the vertical
rudders of the torpedo in such manner as to bring the torpedo back
to its course.
SINKING MECHANISM. In order to sink the torpedo at the
end of its course, if it does not strike its target, and thus to pre-
vent its falling into the hands of the enemy or doing injury to
friends, a mechanism is provided which opens a sea-valve into the
comparatively empty chamber that contains the gyroscope. The
water fills the chamber and sinks the torpedo.
DATA. The Whitehead torpedo has a diameter of 18 inches,
and a length of about 16 feet. It has a mean velocity of 28 knots
an hour over a range of 2200 yards. The charge of explosive
weighs 60 pounds.
The Schwarzkopf torpedo differs from the Whitehead only in
that the body of the torpedo is made of bronze instead of steel.
334. The Bliss-Leavitt Torpedo. The Bliss-Leavitt torpedo, a
recent American construction, and in use in the United States
Navy, is of the same general construction as the Whitehead tor-
pedo. Improvements in the mechanisms give to this torpedo
greater range and greater accuracy.
SUBMARINE MINES AND TORPEDOES. 589
The air tank is charged to a pressure of 2225 pounds per square
inch. The motor engine is of the Curtis turbine type and makes
10,000 revolutions a minute, operating the two propellers at the
rate of 900 turns a minute. A large gain in power is obtained by a
superheating process applied to the compressed air. An alcohol
flame, automatically ignited when the torpedo is launched, greatly
increases the expansive power of the compressed air as it enters
the engine. The expansion is so great that trouble has been en-
countered from the freezing of the mechanism. Temperatures of
40 below zero have been registered in some runs.
The gyroscope controlling the vertical rudders is also of a tur-
bine construction, and is rotated by compressed air at the rate of
18,000 revolutions a minute. It is much more effective in main-
taining the torpedo in a fixed course than the spring-actuated
gyroscope in the Whitehead torpedo. The accuracy of the tor-
pedo is therefore greatly increased.
The Bliss-Leavitt torpedo is made in two sizes, 18 and 21
inches in diameter. The 21-inch torpedo is about 16J feet long.
It has an extreme range of 3500 yards and a mean speed over that
range of 28 knots an hour. Over a range of 1200 yards its mean
speed is 36 knots.
The explosive charge consists of 132 pounds of wet guncotton
containing 25 per cent of water.
The firing mechanism in the point is the same as in the Howell
torpedo described below.
The Howell Torpedo. The Howell torpedo was invented by
Admiral John A. Howell, United States Navy. The motive power
of the Howell torpedo is a solid flywheel, w Fig. 308, which is
FIG. 308.
caused to revolve at a rate of 10,000 revolutions a minute, before
the torpedo is launched, by a small turbine engine located in the
launching tube. The rotation of the flywheel is communicated to
two propellers, one on each side, through the bevel gears e and
shafts s
590 ORDNANCE AND GUNNERY.
A device applied to the propellers increases the pitch of the
blades as their velocity of rotation diminishes, thus better main-
taining the speed of the torpedo at the latter end of its course.
The gyroscopic power of the rotating flywheel gives to the
torpedo great rigidity of direction in the horizontal plane.
The submergence is regulated by a hydrostatic piston and
pendulum that act on the horizontal rudders at the tail, the
mechanism being similar to that described in the Whitehead
torpedo.
The small screw at the nose of the torpedo locks the firing
mechanism in the safety position until the torpedo has traveled
30 or 40 yards through the water. The rotation of the screw
during this travel arms the firing mechanism.
The Howell torpedo carried a charge of 174 pounds of gun-
cotton. It was fired by gunpowder from the launching tube. Its
extreme effective range, 1000 yards, was so limited that the tor-
pedo never came into general use.
Towing Torpedoes. Towing torpedoes are so arranged that
they may be made to diverge to a considerable extent on either
side of the wake of the towing vessel, so that this vessel may pass
clear of the ship attacked and yet cause the torpedo to strike.
Towing torpedoes were used by the Russians in their war with
Turkey, 1877, but in no case with success.
335. Submarine Torpedo Boats. While submarine torpedo
boats are new used only by the navy, it has been recommended
that they be used by the Coast Artillery as adjuncts to the sub-
marine mine systems. They will perform a twofold function in
the mine fields ; first, in the inspection and repair of the mines and
cables and other subaqueous material, to which access will be
gained through a diving compartment or caisson provided in the
boat, and second, in supplementing the fixed mines by defending
with the torpedo those channels or passages that by reason of the
great depth or the strength of the current cannot be closed by
fixed mines.
Submarine boats are of two general classes, the diving boat and
the submersible boat. The diving boat submerges by inclination
of its longitudinal axis effected through horizontal rudders. It
rises by the same means. The submersible boat sinks and rises
SUBMARINE MINES AND TORPEDOES.
bodily with even keel, the movements being effected by the ver-
tical component of the water pressure against inclined hydro-
planes projecting from both sides of the boat and symmetrically
disposed with respect to the center of gravity.
Both classes of boats are provided with gasoline engines for
propulsion on the surface, and with electric motors for use when
submerged. When on the surface the motors may be used as
dynamos to charge the storage batteries, the power being supplied
by the gasoline engines.
To adjust the buoyancy, water is pumped into or out of the
ballast tanks by pumps actuated by the engines or motors.
Air compressors, and tanks are also provided. The com-
pressed air is used for the discharge of the torpedoes, and to sup-
plement the pumps in the discharge of water ballast.
The compressed air may also be used to renew the air supply
in the vessel when submerged. The renewal of the air supply is,
however, usually not necessary. Tests have shown that the crew
does not suffer from bad air when the boat is hermetically sealed
for long periods. In one test 7 men remained under water for
15 hours without change of air and without discomfort. In an-
other test the boat, fully manned, remained totally submerged
for 12 hours without change of air. In a recent test the boat,
with 13 men aboard, remained submerged at a depth of about 40
feet for a period of 24 hours. During the last hours air was
drawn from the compressed air supply. The test showed that
the boat could remain under water for three days before exhaust-
ing the supply of air.
The Holland Submarine Boat. The Holland submarine boat
is the latest and most successful boat of the diving type of sub-
marine.
The boat, Fig. 309, is spindle-shaped, circular in cross-section,
with its greatest diameter about one third of its length from
the bow. The single propeller is actuated by gasoline engines
when the boat is on the surface, and by electric engines when the
boat is awash or submerged.
Submergence is effected by means of horizontal diving rudders
at the tail, arranged similarly to the diving rudders of the White-
head torpedo.
592
ORDNANCE AND GUNNERY.
The internal arrangements of the craft do not differ materially
from those of the Lake submarine boat illustrated in Fig. 311,
except that the Holland boat contains no diving caisson. The
conning tower projects very slightly above the general outline of
the boat.
At a recent government test of the Holland boat Octopus an
average speed of 11 knots an hour was maintained by the boat
in cruising condition on the surface, and 10 knots an hour when
awash and submerged.
336. The Lake Submarine Boat. The Lake submarine boat
is of the submersible type. An exterior view of the Protector, the
first torpedo boat of this type, is shown in Fig. 310, and an in-
terior view of the boat submerged is shown in Fig. 311.
TIG. 310.
The hull is spindle-shaped, 67J feet long with 14 feet beam.
The draught, in cruising condition on the surface, is 12 feet. The
displacement is 136 tons in cruising trim and 175 tons when sub-
merged. A superstructure is erected on the hull, the top of the
superstructure forming the deck of the boat. The space between
the superstructure and the hull is occupied by the air, oil, and
ballast tanks, and by the tanks for the gasoline used in the en-
gines. The storage of the gasoline outside the hull greatly dimin-
ishes the chances of explosion from leaking gasoline, or of the
asphyxiation of the crew from the same cause.
A conning tower rises from the hull. A sighting hood projects
above the conning tower, and the omniscope, through which
vision is obtained in all directions, rises 3 or 4 feet above the
sighting hood.
SUBMARINE MINES AND TORPEDOES. 503
The boat is built to withstand an exterior pressure of 75 pounds
to the square inch, which corresponds to a depth of about 150
feet.
The boat is provided with twin screws.
SUBMERSION. Submergence is effected on an even keel; when
under way, by inclining the four hydroplanes, s Fig. 310, down-
ward and forward; and when the boat is stationary by dropping
the anchors at each end, reducing the buoyancy to less than the
combined weight of the anchors, and then pulling the boat down-
ward by the anchor chains. All these operations are simply
effected from the conning tower.
The horizontal rudder, R Fig. 311, is used only to counteract
the pressure of the water on the front of the conning tower when
the boat is running submerged.
The buoyancy of the boat is increased or diminished by pump-
ing water out of or into the ballast tanks. A reserve of about
300 pounds of buoyancy is always maintained except when run-
ning on the bottom, and the boat is held submerged either by the
anchors or, when moving, by the water pressure on the hydro-
planes. It may be kept at any desired submergence, whether
moving or at rest.
For running on the bottom, wheels are provided which are
ordinarily carried in pockets in the keel and which are brought
into position under the keel by hydraulic mechanism. The
wheels are simple rollers and the propellers move the boat, the
chief function of the wheels being to protect the bottom of the
boat against injury from obstacles on the bottom.
When the buoyancy has been destroyed and when, through any
accident to the pumps, it cannot be regained by discharging
ballast, two sections of the keel, N Fig. 311, weighing together
5 tons, may be dropped from the boat by the turn of a wrench.
Should this not be sufficient to cause the boat to rise, the two
anchors, weighing half a ton each, may be let go. As a last re-
source the crew may escape through the diving chamber.
THE DIVING CHAMBER. The diving chamber in the forward
compartment is a feature of this boat that makes the boat espe-
cially valuable for submarine mine work. An air lock affords
access to the chamber from the interior, and a downwardly-open-
594 ORDNANCE AND GUNNERY.
ing watertight door in the hull affords egress to the bottom. The
diving chamber has telephonic communication with the conning
tower.
ARMAMENT AND SPEED. The boat carries three torpedoes, two
in the tubes in the bow and one in the stern tube. The torpedoes
are discharged from the tubes by compressed air. Extra tor-
pedoes may be carried in the living room.
The first boat of this type made, in the official trials by the
Russian Government, a speed of 9.3 knots an hour on the surface,
under engines and motors combined, and 8.5 knots under engines
alone. With conning tower awash and under engines alone the
speed was 7.4 knots; and totally submerged, under electric motors
alone, the speed was 5.4 knots. The cruising radius on the surface
at full speed is about 350 knots. The submerged cruising radius,
with motors, is about 20 knots at full speed and 30 knots at eco-
nomical speed.
A Lake boat, with a displacement of 235 tons, is now (May,
1907) undergoing test by the United States Government, and
boats with 500 tons displacement are projected.
TABLES.
TABLE I. LOGARITHMS OF THE X FUNCTIONS.
TABLE II. HEATS OF FORMATION OF SUBSTANCES.
TABLE III. SPECIFIC HEATS OF SUBSTANCES.
TABLE IV. DENSITIES AND MOLECULAR VOLUMES OF SUBSTANCES.
TABLE V. ATOMIC WEIGHTS.
TABLE VI. CONVERSION; METRIC AND ENGLISH UNITS, TEMPERATURES.,
595
,596
ORDNANCE AND GUNNERY.
TABLE I.
LOGARITHMS OF THE X FUNCTIONS.
Subtract 10 from each characteristic greater than 2.
X
logXo
log*!
log* 2
log ^ 3
logX 4
log X 6
0.001
9.03899
5.56162
6.52263
8.73764
9.16405
8.30001
0.010
9.53911
7.05911
7.52000
9.23296
9.66437
9.30059
0.05
9.88671
8.09440
8.20769
9.56059
0.01322
9.99778
0.10
0.03494
8.53009
8.49515
9.68493
0.16295
0.29663
0.15
0.12078
8.77897
8.65819
9.74798
0.25023
0.47060
0.20
0.18111
8.95170
8.77059
9.78653
0.31194
0.59347
0.25
0.22750
9.08291
8.88541
9.81206
0.35965
0.68834
0.30
0.26509
9.18802
8.92293
9.82962
0.39851
0.76552
0.35
0.29661
9.27522
8.97861
9.84191
0.43127
0.83052
0.40
0.32372
9.34942
9.02570
9.85051
0.45956
0.88660
0.45
0.34746
9.41375
9.06630
9.85640
0.48444
0.93587
0.50
0.36855
9.47036
9.10181
9.86028
0.50663
0.97980
0.55
0.38750
9.52077
9.13327
9.86260
0.52665
1.01937
0.60
0.40469
9.56610
9.16141
9.86371
0.54488
1.05539
0.65
0.42041
9.60719
9.18678
9.86386
0.56161
1.08840
0.70
0.43489
9.64471
9.20982
9.86325
0.57705
1.11887
0.75
0.44829
9.67918
9.23089
9.86201
0.59140
1.14715
0.80
0.46075
9.71100
9.25025
9.86027
0.60479
1.17352
0.85
0.47241
9.74052
9.26812
9.85811
0.61733
1.19821
0.90
0.48334
9.76802
9.28468
9.85562
0.62913
1.22143
0.95
0.49363
9.79373
9.30010
9.85284
0.64027
1.24332
1.00
0.50334
9.81784
9.31450
9.84984
0.65081
1.26404
1.05
0.51255
9.84053
9.32798
9.84664
0.66082
1.28369
1.10
0.52128
9.86193
9.34065
9.84329
0.67034
1.30239
.15
0.52960
9.88217
9.35258
9.83981
0.67942
1.32020
.20
0.53752
9.90136
9.36384
9.83623
0.68809
1.33721
.25
0.54508
9.91958
9.37449
9.83256
0.69640
.35348
.30
0.55234
9.93693
9.38459
9.82882
0.70436
.36908
.35
0.55929
9.95346
9.39417
9.82503
0.71201
.38406
.40
0.56597
9.96926
9.40329
9.82119
0.71936
.39846
.45
0.57238
9.98436
9.41198
9.81732
0.72644
.41230
1.50
0.57856
9.99884
9.42028
9.81343
0.73328
1.42569
1.55
0.58452
0.01272
9.42820
9.80953
0.73988
1.43858
1.60
0.59026
0.02605
9.43579
9.80561
0.74625
1.45104
1.65
0.59582
0.03887
9.44305
9.80169
0.75242
1.46310
1.70
0.60119
0.05122
9.45003
9.79777
0.75840
1.47478
1.75
0.60639
0.06311
9.45672
9.79386
0.76419
1.48608
1.80
0.61143
0.07459
9.46316
9.78996
0.76981
1.49705
1.85
0.61632
0.08567
9.46935
9.78607
0.77527
1.50770
1.90
0.62106
0.09638
9.47532
9.78219
0.78057
1.51803
1.95
0.62567
0.10675
9.48108
9.77833
0.78573
1.52808
2.0
0.63015
0.11678
9.48663
9.77449
0.79075
1.53788
2.1
0.63875
0.13591
9.49717
9.76687
0.80040
1.55668
2.2
0.64691
0.15395
9.50704
9.75939
0.80958
1.57456
2.3
0.65467
0.17097
9.51630
9.75193
0.81833
1.59158
2.4
0.66207
0.18708
9.52501
9.74461
0.82668
1.60783
TABLES.
507
LOGARITHMS OF THE X FUNCTIONS Continued.
Subtract 10 from each characteristic greater than 2.
*
log JT
logXi
log X 2
log ^3
log* 4
log*.
2.5
0.66914
0.20236
9.53322
9.73740
0.83467
.62338
2.6
0.67589
0.21687
9.54098
9.73031
0.84232
.63824
2.7
0.68237
0.23070
9.54833
9.72333
0.84966
.65250
2.8
0.68859
0.24389
9.55531
9.71645
0.85673
.66623
2.9
0.69457
0.25650
9.56194
9.70969
0.86353
.67945
3.0
0.70032
0.26858
9.56826
9.70304
0.87009
.69216
3.1
0.70587
0.28014
9.57427
9.69650
0.87642
.70442
3.2
0.71122
0.29124
9.58001
9.69007
0.88252
.71627
3.3
0.71639
0.30190
9.58551
9.68374
0.88842
.72773
3.4
0.72140
0.31217
9.59077
9.67752
0.89416
1.73882
3.5
0.72624
0.32205
9.59582
9.67140
0.89970
1.74956
3.6
0.73093
0.33159
9.60066
9.66538
0.90508
1.75997
3.7
0.73548
0.34079
9.60532
9.6594G
0.91027
1.77004
3.8
0.73990
0.34969
9.60979
9.65363
0.91537
1.77989
3.9
0.74419
0.35829
9.61410
9.64790
0.92037
1.78955
4.0
0.74836
0.36662
9.61825
9.64225
0.92510
1.79872
4.2
0.75637
0.38250
9.62613
9.63122
0.93432
1.81656
4.4
0.76398
0.39745
9.63348
9.62053
0.94308
1.83349 .
4.6
0.77121
0.41157
9.64036
9.61015
0.95143
1.84962
4.8
0.77810
0.42492
9.64682
9.60008
0.95939
1.86500
5.0
0.78469
0.43759
9.65290
9.59029
0.96700
.87971
5.2
0.79099
0.44963
9.65864
9.58079
0.97430
.89379
5.4
0.79703
0.46110
9.66407
9.57153
0.98130
.90730
5.6
0.80284
0.47205
9.66921
9.56252
0.98803
.92028
5.8
0.80842
0.48251
9.67409
9.55375
0.99450
.93277
6.0
0.81379
0.49253
9.67874
9.54521
1.00074
.94470
6.2
0.81897
0.50213
9.68316
9.53687
1.00676
.95640
6.4
0.82397
0.51136
9.68738
9.52874
.01257
.96760
6.6
0.82881
0.52022
9.G9142
9.52081
.01819
.97844
6.8
0.83349
0.52875
9.69528
9.51303
.02363
.98891
7.0
0.83801
0.53698
9.69897
9.50549
.02890
1.99905
7.2
084241
0.54492
9.70252
9.49809
.03402
2.00892
7.4
0.84G67
0.55259
9.70592
9.49085
.03898
2.01847
7.6
0.85081
0.56000
9.70919
9.48377
.04379
2.02776
7.8
0.85483
0.56717
9.71234
9.47683
.04848
2.03677
8.0
0.85873
0.57411
9.71538
9.47004
1.05304
2.04552
8.2
0.86254
0.58084
9.71830
9.46341
1.05748
2.05408
8.4
0.86625
0.58737
9.72112
9.45689
1.06180
2.06240
8.6
0.86986
0.59371
9.72385
9.45050
1.06601
2.07050
8.8
0.87338
0.59986
9.72648
9.44424
1.07012
2.07841
9.0
0.87682
0.60585
9.72903
9.43809
1.07413
2.08612
9.2
0.88017
0.61167
9.73150
9.43206
1.07804
2.09345
9.4
0.88345
0.61734
9.73390
9.42614
1.08187
2.10100
9.6
0.88665
0.62286
9.73621
9.42033
1.08560
2.10819
9.8
0.88978
0.62824
9.73846
9.41462
1.08926
2.11502
10.0
0.89284
0.63349
9.74065
9.40901
1.09283
2.12209
10.2
0.89584
0.63860
9.74276
9.40349
1.09633
2.12882
10.4
0.89877
0.64360
9.74482
9.39807
1.09976
2.13540
10.6
0.90165
0.6484S
9.74683
9.39274
1.10312
2.14186
10.8
0.90447
0.65324
9.74877
9.38749
1.10640
2.14818
598 ORDNANCE AND GUNNERY.
LOGARITHMS OF THE X FUNCTIONS Continued.
Subtract 10 from each characteristic greater than 2.
X
log^o
log Xi
log.a: 2
logX s
logX,
log JT 6
11.0
0.90723
0.65790
9.75067
9.38233
1.10963
2.15437
11.2
0.90993
0.66245
9.75252
9.37725
1.11279
2.16045
11.4
0.91259
0.66691
9.75432
9.37225
1.11589
2.16642
11.6
0.91520
0.67127
9.75607
9.36732
1.11893
2.17227
11.8
0.91776
0.67554
9.75778
9.36247
1.12192
2.17801
12.0
0.92027
0.67972
9.75945
9.35770
1.12485
2.18364
12.2
0.92274
0.68381
9.76108
9.35301
1.12772
2.18916
12.4
0.92516
0.68783
9.76267
9.34836
1.13057
2.19462
12.6
0.92754
0.69176
9.76422
9.34379
1.13335
2.19996
12.8
0.92989
0.69562
9.76574
9.33928
1.13609
2.20522
13.0
0.93219
0.69941
9.76722
9.33484
1.13877
2.21039
13.2
0.93446
0.70313
9.76867
9.33045
1.14142
2.21547
13.4
0.93669
0.70678
9.77009
9.32613
1.14402
2.22047
13.6
0.93888
0.71036
9.77148
9.32186
1.14659
2.22539
13.8
0.94104
0.71388
9.77284
9.31766
1.14911
2.23023
14.0
0.94317
0.71734
9.77417
9.31350
1.15159
2.23400
14.2
0.94527
0.72074
9.77547
9.30940
1.15403
2.23970
14.4
0.94733
0.72408
9.77675
9.30535
1.15644
2.24433
14.6
0.94936
0.72736
9.77800
9.30136
1.15882
2.24888
14.8
0.95137
0.73059
9.77922
9.29741
1.16115
2.25337
15.0
0.95334
0.73377
9.78043
9.29351
1.16346
2.25780
15.2
0.95529
0.73689
9.78160
9.28966
1.16573
2.26216
15.4
0.95721
0.73997
9.78276
9.28585
1.16797
2.26647
15.6
0.95910
0.74301
9.78391
9.28208
1.17018
2.27073
15.8
0.96097
0.74599
9.78501
9.27837
1.17236
2.27495
16.0
0.96282
0.74892
9.78610
9.27470
1.17450
2.27912
16.2
0.96463
0.75181
9.78718
9.27107
1.17663
2.28309
16.4
0.96643
0.75466
9.78823
9.26748
1.17872
2.28711
16.6
0.96820
0.75747
9.78927
9.26393
1.18078
2.29108
16.8
0.96995
0.76024
9.79029
9.26042
1.18282
2.29500
17.0
0.97168
0.76297
9.79129
9.25695
1.18483
2.29886
17.2
0.97338
0.76566
9.79227
9.25352
1.18682
2.30268
17.4
0.97507
0.76831
9.79324
9.25012
1.18879
2.30645
17.6
0.97673
0.77093
9.79419
9.24676
1.19072
2.31017
17.8
0.97838
0.77351
9.79513
9.24344
1.19264
2.31385
18.0
0.98001
0.77606
9.79605
9.24015
1.19454
2.31750
18.2
0.98161
0.77856
9.79696
9.23689
1.19640
2.32108
18.4
0.98320
0.78104
9.79785
9.23367
1.19825
2.32463
18.6
0.98477
0.78349
9.79872
9.23048
1.20008
2.32814
18.8
0.98632
0.78591
9.79959
9.22732
1.20188
2.33161
19.0
0.98785
0.78829
9.80044
9.22419
1.20367
2.33504
19.2
0.98937
0.79065
9.80128
9.22109
1 .20543
2.33843
19.4
0.99086
0.79296
9.80210
9.21803
1.20717
2.34177
19.6
0.99235
0.79527
9.80292
9.21499
1.20891
2.34510
19.8
0.99382
0.79754
9.80372
9.21198
1.21062
2.34838
20.0
0.99527
0.79978
9.80451
9.20900
1.21230
2.35162
TABLES.
599
TABLE II.
HEATS OF FORMATION, AT 15 C. AND NORMAL ATMOSPHERIC
PRESSURE (760 MM). LARGE CALORIES.
Name.
Formula.
Molec-
ular
Weight.
Heat given off, the product being
Gaseous
Liquid.
Solid.
Dis-
solved.
39.3
29.5
48.8
67.2
141.
-5.8
28.6
164.6
145.2
100.8
96.2
72.7
187.
112.4
103.2
56.8
*
-33.9
23.4
27.4
Hydrochloric acid ....
Hydrobromic acid
Water
HCL
HBr
H 2 O
H^S
HNO 3
H&O.
SO,
SO 3
H0
C1 2
HC1O 4
CO 2
CO
N 2 O
NO
N 2 3
N0 2
NA
K 2 O
Na 2 O
Sb 2 3
Sb 2 5
KCI
NaCl
NH 4 C1
CaCl 2
K 2 S
Na^S
SbJSa
NaNoa
NH 4 NO 3
K 2 S0 4
NaJSO 4
K.(X>a
Na 2 CO 3
C 10 H 7 N0 2
C 10 H 6 (N0 2 ) 2
C (0 H 5 (N0 2 ) 3
KClOa
NH,
NS
CN
HCN
KCN
C 2 H 2
36.5
81.
18.
34.
63.
114.
64.
80.
98.
86.
100.5
44.
28.
44.
30.
76.
46.
108.
94.
62.
287.
329.
74.
58.
53.
110.
110.
78.
335.
68.
101.1
85.
80.
174.
142.
138.
106.
173.
218.
263.
122.5
17.
46.
26.
27.
65.
26.
22.
9.5
58.2
4.8
34.4
69.2
91.8
-15.2
94.3
25.8
-20.6
-21.6
-22.2
-2.6
-1.2
12.2
-19.
-37.3
-29.
-61.4
69.
41.6
124.
-30. 8
-16.2
1.8
3.6
-25.4
-23.8
70.4
42.2
103.6
124.8
11.8
97.2
100.2
167.4
228.8
105.
97.3
76.7
170.
102.2
88.4
34.
118.7
110.6
87.9
342.2
326.4
278.8
274.8
-14.7
-5.7
3.3
94.6
-31.9
30.3
Hydrogen sulphide. . . .
Nitric acid
Hyposulphurous acid. .
Sulphur dioxide
Sulphur trioxide
Sulphuric acid.
Hypochlorous acid an-
hydride
Perchloric acid
Carbon dioxide ....
Carbon monoxide
Nitrous oxide
Nitrogen dioxide ....
Nitrous anhydride
Nitrogen peroxide
Nitric anhydride
Potassium oxide
Sodium oxide
Antimonous oxide ....
Antimonic oxide
Potassium chloride. . . .
Sodium chloride
Ammonium chloride . .
Calcium chloride
Potassium sulphide . . .
Sodium sulphide
Antimony sulphide. . .
Ammonium sulphide . .
Potassium nitrate
Sodium nitrate
Ammonium nitrate . . .
Potassium sulphate . . .
Sodium sulphate . .
Potassium carbonate . .
Sodium carbonate. . . .
Nitronaphthalene
Binitronaphthalene. . .
Trinitronaphthalene . .
Potassium chlorate . . .
Ammonia
Nitrogen sulphide
Cyanogen . .
Hydrocyanic acid
Potassium cyanide.. . .
Acetylene
600
ORDNANCE AND GUNNERY.
HEATS OF FORMATION Continued.
Name.
Formula.
Molec-
ular
Weight.
Heat given off, the product being
Gaseous
Liquid.
Solid.
Dis-
solved.
Ethylene
C 2 H 4
CH 4
C 6 H 6
C 10 H 16
C 10 H 8
CuH 10
CH 3 OH
C 2 H 5 OH
C 3 H 7 OH
C 6 H 5 OH
C 3 H 5 (OH) 3
C 6 H U 6
C 6 H 12 6
n(C 6 H 12 6 )
&
C 2 H 5 NO 3
C 3 H P ,(N0 2 ) 3 3
C 6 H 8 (N0 3 ) 6
C 2 N 2 2 Hg
C^H^A,
C 6 H 5 N0 2
C 6 H 4 (N0 2 ) 2
C 6 H 2 (N0 2 ) 3 OH
C e H 2 (NO,).OK
C H 2 (NO 2 ) 3 ONH 4
C 6 H 2 (NO 2 ) 3 ONa
CH 5 N 3 3
(C 2 H) 2
CH 3 NO 3
SK*
&
CCE^NOa
C fi H 6 2
(C0 2 Na) 2
28.
16.
78.
136.
128.
178.
32.
46.
60.
94.
92.
172.
180.
n(180.)
162.
44.
91.
227.
452.
284.
1143.
123.
168.
229.
267.
246.
251.
167.
74.
77.
152.
76.
1008.
88.
133.
62.
134.
-15.4
18.5
-10.2
8.6
53.6
60.7
50.5
65.3
82.3
7.
-3.2
-17.
62.
70.5
67.
34.5
165.5
56.5
49.3
98.
4.2
72.
39.9
66.9
127.
93.
71.
-0.9
-23.7
-42.4
36.8
169.4
320.
306.
n(269.)
227.
149.
-62.9
624.
6.9
12.7
49.1
117.5
80.1
105.3
-47.4
706.
111.7
313.8
64.
73.
70.
32.
164.
315.
303.
60.1
50.3
41.
107.5
71.4
98.9
78.
95.8
113.4
Methane
Benzene
Terebenthene
Methyl alcohol
Ethyl alcohol
Propyl alcohol
Phenol
Glycerine
Mennite dulcite
Glucoses and isomers. .
Saccharose and isomers
Cellulose (cotton) ....
Aldehyde
Ethyl nitrate
Nitroglycerine
Nitromannite
Mercury fulminate. . . .
Nitrocellulose (N n ) . . .
Nitrobenzene
Dinitrobenzene
Picric acid
Potassium picrate
Ammonium picrate . . .
Sodium picrate
Ether
Methyl nitrate
Dinitroglycol
Propyl glycol
N itrocellulose (N 8 ) ....
Amyl alcohol
Giycol
Sodium oxalate
TABLES.
TABLE III.
SPECIFIC HEATS.
601
Name.
Formula.
Molecular
Weight.
Specific heats referred to
One Gram.
Molecular
Weight.
ft
As 2
Sb 2
C 2
Hg
Pb 2
M|O
Cr.Oa
A1 3
NH 4 C1
KC1
NaCl
Bad,
CaCl 2
AgCl
K,S
Na^S
FeS
I&f N) <
NaNO 3
Ba(N0 3 ) 2
Sr(NO 3 ) 2
Pb(N0 3 ) 2
AgN0 3
NH 4 NO 3
K 2 SO 4
Na 2 SO 4
CaSO 4
SrSO 4
CuSO 4
K 2 Cr 2 O 7
K 2 C0 3
Na 2 CO 3
CaCOa
BaCO 3
PbCO 3
KC10 3
KC1O 4
H 2 O
HNO 3
H 2 S0 4
C 6 H fl 4
C 2 H,OH
C 3 H;(OH) 3
sbA
Si0 2
64.
124.
150.
244.
24.
200.
414.
216.
40.
152.8
103.
53.
74.6
58.5
207.
111.
143.
110.
78.
88.
430.
101.1
85.
261.
211.
330.
170.
80.
174.
142.
136.
183.5
159.5
294.
138.
106.
100.
197.
26C.
122.5
138.5
18.
63.
98.
78.
46.
92.
287.2
60.3
0.203
0.190
0.081
0.051
0.202
0.033
0.031
0.057
0.244
0.190
0.217
0.373
0.173
0.214
0.090
0.104
0.091
0.091
0.091
0.136
0.280
0.239
0.278
0.150
0.180
0.110
0.143
0.455
0.190
0.229
0.180
0.140
0.134
0.187
0.210
0.270
0.200
0.110
0.141
0.210
0.190
1.000
0.445
0.340
0.440
0.595
0.591
0.090
0.195
12.8
11.8
12.1
12.4
4.8
32.56
13.2
12.4
9.76
29.00
22 .40
20.00
12.89
12.5
18.6
18.4
13.1
19.00
19.00
11.94
118.00
24.20
23.70
38.00
38.00
36.4
24.4
36.4
33.2
32.4
25.4
24.8
21.4
36.4
30.0
29.0
21.0
21.4
39.4
25.7
26.3
18.0
28.0
33.4
34.0
27.3
54.4
25.85
11.76
Lead
Silver
Magnesia
Chromic oxide
Aluminum, oxide
Ammonium chloride
Potassium chloride
Calcium chloride
Silver chloride
Potassium sulphide
Sodium sulphide
Iron sulphide
Potassium ferro cyanide .
Potassium nitrate
Sodium nitrate
Barium nitrate
Sodium sulphate
Calcium sulphate
Strontium sulphate
Potassium carbonate
Sodium carbonate
Calcium carbonate
Barium carbonate
Lead carbonate . . .
Potassium chlorate ....
Potassium perchlorate
Water
Nitric acid
Sulphuric acid
Alcohol
Glycerine
Silica
602
ORDNANCE AND GUNNERY.
TABLE IV.
DENSITIES AND MOLECULAR VOLUMES.
Name.
Formula.
Molecular
"Weights,
Density.
D
Molecular
Volume
M
rnc.c./)
a,
64.
2 04
31 36
C 9
24.
(2 . 50 diamond
2 27 graphite
6.85
10 66
Potassium chloride
KGl
74.6
1 . 67 amorph.
1 94
15.28
38 70
Sodium chloride
NaCl
58 5
2 10
97 20
Barium chloride
BaCL
207
3 70
56
Strontium chloride
SrCL
158 5
2 80
59
Ammonium chloride
NH 4 C1
53
1 53
35
Potassium nitrate
KNO 3
101
2 06
49
Sodium nitrate
NaNO 3
85
2 24
QQ f\
Barium nitrate
Ba(NO 3 ),
261
3 25
QO O
Lead nitrate
Pb(NO 3 ) 2
330
4 40
7fi O
Silver nitrate
AgNO 3
170
4 35
QQ O
Ammonium nitrate
NH 4 NO 3
80
1 71
41
Strontium nitrate ....
Sr(NO 3 ) 2
211
2 93
71 ^0
Potassium carbonate
Sodium carbonate
K 2 CO 3
Na 2 CO 3
138.
107
2.26
2 47
62.0
43
Barium carbonate
Ba 2 CO 3
197
4 30
46
Strontium carbonate
SrCO 3
147 5
3 62
40 ft
Calcium carbonate
CaCO 3
100
2 71
Q ft
Potassium sulphate
K2SO 4
174.
2 66
66
Sodium sulphate
Na 2 SO 4
142
2 63
54
Barium sulphate
BaSO 4
233
2 45
52
Strontium sulphate
SrSO 4
183 5
3 59
52
Calcium sulphate
CaSO 4
136
2 93
46
Potassium chlorate . . .
KC1O 3
122 5
2 33
' 52 6
Potassium bichromate
Antimony oxide
K 2 Cr O 7
ShoOa
294.
292.
2.69
5 53
110.0
53
Antimony sulphide
Calcium oxide
Sb a
CaO
334.
56.
4.42
3.15
75.0
18
Ammonium sulphate
(NH 4 ) 2 SO
132.
1.76
75
Copper nitrate
Cu(NO 3 ) 2
192
2 03
94 5
Mercuric oxide
HffO
216
11 14
19 38
Potassium sulphide
Sodium sulphide
KaS
Na S
110.
78.
2.97
2 17
37.0
36
Silica
SKX
60
2 65
23
Potassium cyanide
KCN
65.0
1.52
43.0
TABLES.
603
TABLE V.
ATOMIC WEIGHTS.
The atomic weights in this table are the International Atomic Weights (1906)
modified to make the atomic weight of hydrogen unity.
Element.
Symbol
Atomic
Weight.
Element.
Symbol
Atomic
Weight.
Aluminum .
Al
Sb
A
As
Ba
Be
Bi
B
Br
Cd
Cs
Ca
C
Ce
Cl
Cr
Co
Cu
E
F
Gd
Ga
Ge
Au
He
H
In
I
Ir
Fe
Kr
La
Pb
L
Mg
Mn
Hg
Mo
Nd
26.9
119.3
39.6
74.4
136.4
9.
206.9
10.9
79.4
111.6
132.
39.8
11.9
139.
35.2
51.7
58.5
63.1
164.8
18.9
155.
69.5
71.9
195.7
4.
1.
113.1
125.9
191.5
55.5
81.2
137.9
205.4
7.
24.2
54.6
198.5
95.3
142.5
Ne
Ni
Nb
N
Os
Pd
P
Pt
K
Pr
Ra
Ro
Rb
Ru
Sm
Sc
Se
Si
Ag
Na
Sr
S
Ta
Te
Tb
Tl
Th
Tm
Sn
Ti
W
U
V
Xe
Yb
Y
Zn
Zr
19.9
58.3
93.3
13.9
189.6
15.9
105.7
30.8
193.3
38.9
139.4
223.3
102.2
84.8
100.9
148.9
43.8
78.6
28.2
107.1
22.9
87.
31.8
181.6
126.6
158.8
202.6
230.8
169.7
118.1
47.7
182.6
236.7
50.8
127.
171.7
88.3
64.9
89.9
Antimony
Nickel
\rgon . . . . . .
Barium
Osmium
Oxvsen
Palladium . . .
Phosphorus
Bromine
Platinum . . .
Cadmium
Potassium . .
CsB^ium
P ra se od y mium . .
Calcium .
Radium
Carbon .
Rhodium
Cerium
Rubidium
Chromium . .
Sama rium
Cobalt
Selenium
Erbium
Silicon
Fluorine
Silver
Gadolinium
Sodium . .
Gallium
Strontium . .
Germanium . .
Sulphur
Gold
Tantalum
Tellurium
Hyd ro^en
Terbium
Thallium
Iodine
Thorium
Iridium
Thulium
Iron
Tin
Krypton
Titanium
Lanthanum
Tungsten
Lead
UYanium
Vanad ium
Xenon
Manganese
Ytterbium
Mercury
Yttrium
Molybdenum
Neodymium
Zinc
Zirconium
604
ORDNANCE AND GUNNERY.
TABLE VI.
CONVERSION: METRIC AND ENGLISH UNITS, TEMPERATURES.
ENGLISH TO METRIC.
METRIC TO ENGLISH.
To Convert
Multiply by
To Convert
Multiply by
Inches to centimeters ....
Inches to meters . .
2.539978
0.02539978
0.3047973
0.9143918
1.609329
6.451484
0.09290138
0.8361126
16.38663
0.02831609
0.7645345
0.9463279
0.3785311
0.06479887
28.34951
0.4535922
0.1382537
0.0703082
7 . 03082
Centimeters to inches ....
Meters to inches
0.39370428
39 370428
Feet to meters
Yards to meters
Meters to feet
3 . 280869
1.093623
0.6213769
0.155003
10.76410
1.196011
0.06102537
35.31561
1.307985
1.056716
2 641791
15.43236376
. 03527398
2 . 20462339
7.233080
14.22309
0.1422309
Meters to yards
Miles to kilometers
Square inches to square
cent imeters
Kilometers to miles
Square centimeters to
square inches
Square meters to square
feet
Square feet to square me-
ters
Square yards to square
meters
Square meters to square
yards
Cubic inches to cubic cen-
Cubic centimeters to cubic
inches
Cubic feet to cubic meters
Cubic yards to cubic me-
tere
Cubic meters to cubic feet.
Cubic meters to cubic
yards
Quarts, liquid, to liters ....
Gallons (231 cu. in.) to
Liters to quarts (liq.)
Dekaliters to gallons
Grains to Tarns
Grams to grains
Ounces (avoir.) to grams. .
Pounds (av.) to kilograms.
Foot-pounds to kilogram-
meters
Grams to ounces (avoir.). .
Kilograms to pounds (av.)
Kilogrammeters to foot-
pounds
Pounds per sq. in. to kilo-
grams per sq. cent
Pounds per sq. in. to kilo-
grams per sq. decimeter
Kilograms per sq. cent, to
pounds per sq in
Kilograms per sq. deci-
meter to pounds per
sq . in
TEMPERATURES. T/= temperature Fahrenheit- T c = temperature centi-
grade.
Fahrenheit to centigrade, T =g (7>-32).
Centigrade to Fahrenheit, T f =-T +32.
14 DAY USE
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or on the date to which renewed. Renewals only:
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Renewals may be made 4 days prior to date due.
Renewed books are subject to immediate recall.
4QAM
or
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O
CD
UJ
>
21
HD21A-10m-8,'73
(R1902S! 0)476 A-31
General Library
University of California
Berkeley
f / -
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&
UNIVERSITY OF CALIFORNIA LIBRARY
