Aeronautical Engineering
and
Airplane Design
Klemin
Engineering Library
Aeronautical Engineering
and Airplane Design
Aeronautical Engineering
and
Airplane Design
by
LIEUTENANT ALEXANDER KLEMIN
n
Air Service, Aircraft Production, U. S. A., in charge Aeronautical Research Department, Airplane Engineering Department.
Until entering military service, in the Department of Aeronautics, Massa- chusetts Institute of Technology and Technical Editor of Aviation and Aeronautical Engineering.
Based on a series of articles in Aviation and Aeronautical Engineering by Alexander
Klemin and T. H. Huff, S.B., chief aeronautical engineer for the Standard
Aircraft Corporation, formerly instructor in Aeronautics,
Massachusetts Institute of Tecimology.,
Published 1918
Engineering Library
CopyriKlit. in] 7
Alexander Klcniin
All KlKlits 1!.-. r\cii
'J'he (ianlnor-MolTat <'".. Inc. New York
PREFACE
In submitting the series of articles appearing in AVIATION AND AERONAUTICAL ENGINEERING in book form, only minor corrections have been made.
No attempt has been made for obvious reasons to include new material at hand, and under stress of urgent war work no systematic revision has been attempted.
It is felt, nevertheless, that as the articles contained matter mainly regarding fundamental principles, that they will still be of assistance, particularly to younger designers and draftsmen, .while they should be of value as a reference to more experienced men.
The author has, unfortunately, not had the advantage of Mr. Huff's valuable collaboration in this production in book form. He thanks Mr. G. M. Denkinger, instructor in aeronautics at the Massa- chusetts Institute of Technology, and Mr. Clarence D. Hanscom for valuable assistance in corrections.
ALEXANDER KI.EMIN.
Dayton, Ohio, October, 1918.
INTRODUCTION
This work, practically a course in aerodynamics and airplane design, is subdivided into two parts: Part I, Aerodynamical Theory and Data; Part II, Airplane Design.
In PART I it is proposed to deal briefly with the fundamental ideas and theories of aerodynamics in a simple yet comprehensive manner.
It is important for the aeronautical engineer and for every student of aerodynamics to have at his disposal exact definitions of such terms as lift, drag or resistance, center of pressure, wing cord, angle of incidence, and other well known expressions.
Although the exact nature of viscosity, skin friction, eddying or density resistance, stream line flow, turbu- lent flow, the sustaining action of cambered wing surfaces, and the principles of comparison for forces on bodies of varying dimensions still present many difficulties, it is hoped to give a simple and, above all, practical sum- mary of these points. The more difficult theoretical demonstrations will be reserved for special articles.
The authors propose also to give a brief description of the chief aerodynamical laboratories and of experi- mental methods there employed. Without a knowledge of such methods, appreciation, and application of the laboratory data available is certainly not easy.
Considering the comparatively recent growth of aerodynamics, the amount of material now available is extraordinary. It is unfortunately scattered through a variety of publicatons; English, French, German, Rus- sian and Italian, presented in varying ways and in varying systems of units. Nor is all of it entirely wor.thy of credence.
In this course it has been attempted to reduce this material, particularly that of English and French origin, to one system of presentation with forces measured in pounds, areas in square feet and velocities in miles per hour or feet per second, so as to be more readily applicable in American design ; to include all the material which is trustworthy and of immediate and pressing utility to the designer, in carefully classified form.
The Economic Laws of Flight will be fully dealt with, in horizontal and ascensional flight. The consideration of the performance curves of a machine will be particularly useful to those engineers and students to whom the subject is comparatively new.
Throughout, illustrative problems will be worked out on important points, especially to facilitate comparison between wing sections.
PART II will include a discussion of available aeronautical materials, timber, steel, alloys, rubber, etc. — with trustworthy values for stresses; a variety of diagrams and scale drawings representative of modern design, and a classification of the most important modern machines, with their main data.
At this stage of the art, it is impossible to say that any method in design is standard, but a systematic pro- cedure of design will be fully developed.
Particular stress is laid on the evaluation of factors of safety. The dynamic factor of safety, the material factor of safety, the worst loading possible in the air, the worst possible shock on landing; nothing offers so many possibilities of confusion and untrust worthiness ; and nothing is in more need of definite and accurate statement.
Complete strength calculations will be presented for body, chassis, wing girders, and controlling surfaces, and 1he design of a standard machine will be carried through, with consideration of motor and propeller problems, weight distribution and balancing.
Throughout the course, the most elementary mathematics arc employed, and nothing beyond a knowledge of the first mechanical principles is presupposed.
It is hoped, therefore, that the course will be easily understood by any engineer or student approaching the scriuis study of the airplane for the first time. At the s;ime time it is felt that much will be of service even to the expt rt aeronautical engineer.
TABLE OF CONTENTS
PART ONE
Aerodynamical Theory and Data
CHAPTER I
MODERN AERODYNAMICAL LABORATORIES
Early Experimental Aerodynamics — General Requirements in Airplane Design — Difficulties of Full Scale
Experiments — Towing Methods — Wind Tunnel Methods — Laboratories of the Wind Tunnel Type 15
CHAPTER II
ELEMENTS OF AERODYNAMICAL THEORY
Liquid, Fluid and Perfect Fluid — Density of Air — Variation of Density of Air with Height — Principle of Relative Motion — Bernouilli's Theorem for Fluid Motion — Total Energy of a Fluid Applied to the Theory of the Pitot Tube — Definition of Angle of Incidence, Resultant Pressure, Lift, Drag, and Center of Pres- sure in a Plane or Cambered Wing Section — Definition of Lift and Drag Coefficients — Position of Center of Pressure or Resultant Vector of Forces — Forces on a Flat Plate Immersed in a Fluid and Normal to the Direction of Motion — Forces on Flat Plates Inclined to the Wind 23
CHAPTER III
ELEMENTS OF AERODYNAMICAL THEORY — Continued
Skin Friction — Viscosity — Coefficients of Kinematic Viscosity — Reynolds' Number — Prandtl's Theory of the Boundary Layer — Density Resistance to a Plate Moving Edgewise — Total Skin Friction; Dr. Zahm's Experiments — Curves for Computaions with Dr. Zahm's Formula — Turbulent Flow, Eddy, or Density Resistance — Comparison of Forces Acting Upon Similar Bodies; the Importance of Kinematic Viscosity and Reynolds' Number — Stream Line Bodies — Energy Considerations for a Perfect Fluid Flowing Past a Stream Line Body — Stream Line Bodies in a Viscous Fluid — Resistance of Wires, Cables, and Cylin- ders— Fluid Motion Around Wing Surface. . -1
CHAPTER IV
FLAT PLATES. SIMPLE PROBLEMS ON SUSTENTION AND RESISTANCE OF WING SURFACES
Coefficients of Resistance for Circular or Square Plates Normal to the Wind; Varying Sizes — Coefficients for Rectangular Flat Plates Normal to the Wind ; Varying Aspect Ratio — Coefficients for Flat Plates In- clined to the Wind — Preliminary Application of Data for Flat Plates in Rudder and Elevator Design — Problems on Flat Plates — General Considerations of Sustaining Power and Resistance of Wing Sections — Problem of Sustention and Resistance of Wing Surface 32
CHAPTER V
COMPARISON OF STANDARD WING SECTIONS
Representative Wing Sections Selected — Complete Data Presented — Points of Interest in Considering a Wing
Section — Consideration of a Few Sections in Common Use 37
CHAPTER VI EFFECTS OF VARIATIONS IN PROFILE AND PLAN FORM OF WING SECTIONS
Effect of Variation of Position of Maximum Ordinate in a Wing Section of Plane Lower Surface, and Con- stant Camber 0.100 for Upper Surface — Behavior of Wings with Reverse Curvature at the Trailing Edgi — Effect of Thickening the Leading Edge of a Wing — Effects of Thickening Wing Towards the Trailing Edge — " Phillips Entry ' —Effects of Varying Aspect Ratio — Choice of Aspect Ratio — Effects of Raking the Plan Form of a Wing-Swept Back Wings — Negative Wings Tips of Swept Back Wings; Effect on Longitudinal Stability 41
9
10 AERONAUTICAL ENGINE BRING
CHAPTER VII STUDY OP PRESSURE DISTRIBUTION
Methods of Obtaining Pressure Distribution — Comparison of Results from Pressure Distribution and from Force Experiments — Effect of Variation of Speed and Scale on Lift and Drag Coefficients — Distribution of Pressure at Median Cross Section of Various Surfaces — Distribution of Pressure Over the Em in: Surface of a Wing; Lateral Flow, Its Bearing on Aspect Ratio — Distribution of Pressure Over the Entire Surface of Wing and Curves of Equi-Pressure — Relative Importance and Interdependence of Two Surfaces — Distribution of Pressure; the Principle of the Dipping Front Edge; "Why a Wing Sec- tion Is Advantageous as Compared with a Flat Plate 46
CHAPTER VIII BIPLANE COMBINATIONS
< h-tliogonal Biplane Arrangement) with Varying Gap Between Planes — Distribution of Forces Between the Upper and Lower Wings of a Biplane — Distinction Between Static and Dynamic Stability — Stable Biplane Arrangements — Results of Experiments on Biplanes with Staler and Decalage — Comparison of Aerodynamical Losses Involved in Obtaining Stability by Reversed Curvature Wings and by Stag- ger; Decalage Combinations — Aerodynamic Comparison Between the Monoplane and the Biplane' M
CHAPTER IX TKIPLANE COMBIN ATIONS— USES OF NEGATIVE TAIL SURFXCES
Interference in Triplanes — Some Considerations for Tri planes — Triplanes for Fast Speed Scouts — Use of Negative Tail Surfaces— Effect of Influence of the Wash of the Wings on Stabilizer Surface— Problem on the Design of Tail Surfaces to Give Longitudinal Static Stability f>7
CHAPTER X
RESISTANCE OF VARIOUS AIRPI. \.\i-: PAUTS
Airplane Bodies from the Aerodynamical Point of View — Tractor Bodies — Pusher Bodies — Radiator Resist- ance— Resistance of Fittings — Resistance of Airplane Wheels — Resistance of Wires and Methods of Plot- ting — Resistance of Stationary Smooth Wires — Resistance of Vibrating Wires — Resistance of Stranded Wires — Resistance of Wires Placed Behind One Another — Resistance of Inclined Wires — Suggestions for Stream-Lining Wires — Resistance of Miscellaneous Objects 61
CHAPTER XI
RESISTANCE AND COMPARATIVE MERITS OK AIUPI.AM: STRUTS
Considerations of Comparative Merit of Strut Sections — Strut Sections Developed bv Oirilvie — Another Series of Struts Tested at the N. P. L.— Tests on Struts, Length to Width Varied— Two Eiffel Struts— Effect of Length of Struts— Resistance of Inclined Struts— The Effect of Changing the DV Product for Struts 65
CHAPTER XII RESISTANCE AND PERFORM AM i.
Nomenclature — Structural and Wing Resistance for British B.E.2 — Theoretical Laws for Minimum Thrust and Minimum Horsepower — Effective or Propeller Horsepower Available Curve — Minimum and Maximum Sp.-ed; Maximum Excess Power; Best Climb; Descent — The Two Regions of Control; Control by Throt- tling— Variations in Propeller Horsepower Curves — Angle of Glide 69
CHAPTER X11I RESISTANCE COMPUTATIONS — PRELIMINARY WIM; SEI.EITIONS
Example of Estimate for Parasite Resistance for a British Machine — Examples of Parasite Resistance Distri- bution in School Machines — Parasite Resistance Coefficient for a Sturtevant Seaplane — Allowance for Slip Stream — Preliminary Estimates for Parasite Resistance — Preliminary Selection of Wini: Section and Area. . 7-
PART TWO
Airplane Design
OHAPTEB 1
<'I.\.->IFI< \TloN <IK M\IN D\T\ FOR Mol.lUN AlRIM.\MS: I'x MIMED LAND Rl.l nN N MSS \ \ < I .\I\CII1M.S; LAND
TRAIMM; MUIIIM-
The Army < 'lassitieation I'liarnieil Land Reconnaissance Machine Anahsisof Main Data for R pr.-seiita- tive I'narrned Reconnaissance Biplanes Moiv Than L'.'iOO Pounds (iross Weight Average Values for Ma- chines More Than 'J.'iJHi Pounds in Weight Primary and Advanced Training Ail-planes Data for a Typical School Machine Less Than 2(KK) Pounds in Weight- Photographs and Drawings 77
AND AIRPLANE DESIGN H
CHAPTER II LAND PURSUIT MACHINE; LAND GUN-CARRYING MACHINE; TWIN-ENGINED ALL-ROUND MACHINE
The High Speed Scout or Land Pursuit Type — Data for Pursuit Type, 100 Horsepower Engine — Data for More Powerful Pursuit Types — Trend of Design in the Pursuit Type — Guns on the Pursuit Type — Land Gun-Carrying Machines — Twin-Engine Machines 83
CHAPTER III
ESTIMATES OF WEIGHT DISTRIBUTION
Difficulties of the Subject — Weight Schedules for a Machine of the Unarmed Tractor Reconnaissance Type (Two-Seater) More Than 2500 Pounds in Weight — Summary for Weight Distribution for Standard H-3 —Percentage Table for Machines About 2500 Pounds — Weight Distribution for a Typical School Machine — Summary of Weight Distribution for JN-4-B — Empirical Formulas and Values for Weight Estimates — Some General Considerations on Distribution of Weight and Useful Load , 87
CHAPTER IV
ENGINE AND RADIATOR DATA
General Requirements of Aeronautical Engines — Weights for Radiators and Cooling Water — Practical Rules for Cooling Surface for Radiator of Honeycomb Type — Position and Resistance of a Radiator — Prac- tical Construction of Radiators 91
CHAPTER V
MATERIALS IN AIRPLANE CONSTRUCTION
Special Utility of Wood in Airplane Construction — Weight of Wood — Specific Gravity and Weights of Woods — Factors in the Mechanical Properties of Woods — Tensile Strength — Compressive Strength — Crashing Across the Grain — Strength in Bending — Knots — The Effect of Moisture on Strength of Wood —Time Factor in Tests of Timber — Difficulties of Wood Construction in Airplanes — Strength Values for Timber — Wires and Cables — Properties of Metals — Strength and Weights for Wire and Cables — Wire, Strand, or Cord — Turnbuckles — Strength of Steel; Pounds per Square Inch — Strength of Steel Castings; Well Annealed ; Pounds per Square Inch — Strength of Special Steel Alloys ; Pounds per Square Inch — Strength of Copper, Aluminum, and Various Alloys ; Pounds per Square Inch — Strength and Weight of Mild Steel Rivets and Pins — United States Standard Bolts and Nuts — Airplane Fabrics — Some Repre- sentative Specifications; Strength and Weight Figures — Wing Dope and Varnish 95
CHAPTER VI WORST DYNAMIC LOADS; FACTORS OP SAFETY
Conditions Under Which Heavy Loads Come on an Airplane: (1) Flattening Out After a Steep Dive; (2) Loading in Heavy Banking; (3) Loading in Looping; (4) Stresses Due to Gusts — Limiting Velocity for a Sheer Vertical Dive — Worst Loads on Landing 102
CHAPTER VII
PRELIMINARY DESIGN OP SECONDARY TRAINING MACHINE Preliminary Weight Estimates — Choice of Wing and Area — Position of Center of Gravity 106
CHAPTER VIII GENERAL PRINCIPLES OP CHASSIS DESIGN
General Proportions — Chassis Height — Location of Chassis with Respect to C. G. — Stresses and Structural
Considerations — Shock Absorbers — Types of Chassis — Brakes and Braking 109
CHAPTER IX TYPE SKETCHES OF SECONDARY TRAINING MACHINE — GENERAL PRINCIPLES OP BODY DESIGN
General Requirements in Body Design: (1) Stream-Line Form; (2) Fin Area of Body ; (3) Length of Body ; (4) Provision for Pilot and Passenger ; (5) Engine Installation ; (6) Gasoline Tanks; (7) Engine Foun- dation; (8) Engine Must Be Secured Against Weaving; (9) Strength of Body — Formulas for Spruce Compression Members — Body Stress Diagrams — Army Specifications 1000, 1001, and 1002 — Army Speci- fication 1003 — Another Suggested Method — A Detailed Example of Stress Diagram 114
CHAPTER X Computation of Strength Members and General Layout oi Body Cable Terminals 119
CHAPTER XI WING STRUCTURE ANALYSIS FOR BIPLANES
Distribution Between Planes — Spacing of Wing Spars; Limiting Angles of Incidence — Running Loads — Reso- lution of Forces in Planes of Wing Trussing and of Wings, and in Plane of Spar Web — Different Methods Employed in Stress Diagrams for Lift Truss — Bending -Moment Diagrams: Theorem of Three Moments — Working Out, of Bending Moment and Shear Diagrams for Upper Rear at 0 Degree 122
12 AERONAUTICAL ENGINEERING
CHAPTER XII Wis<; STRICTI KK ANALYSIS KOU BUM. AM >
Reactions in Plain- of Lift Truss Due to I'pper Rear Spar at 0 Degree Reactions in Plane of Lift Truss Due to Lower Rear Spar at 0 Degree — Stress Diagram for Rear Lift Truss at 0 Degree— Stress Diagram I'm- Internal l']>per Wing Hraeing at 0 Degree — Computation* for J)imensions of Rear Upper Spar — A Complete Example of Wing Analysis Arrangement — Computations for Shear in Spars.
APPENDIX
NOTES ON AERIAL Pum-Ki.i.Kits
Constant Ineidence Method— Value of Angle of Attack — Efficiency of Elemental Strip, and Curve of Effi- ciencies Propeller Diagrams— Ideal Curves — Determination of Scale*— Computation of Thrust— Load
Grading Curve Pressure per Sq. Ft. Curve — Number of Mlades — Interferenee Construction and
Stivngth of Wade— Materials and Stresses Eiffel's Experiments— Summary of IVoeedure in Design.. l:!l
Part I Aerodynamical Theory and Data
M. KIFKKL1N HISLATKST AERODYNAMICAL LABORATORY
Chapter I
Modern Aeronautical Laboratories
Early Experimental Aerodynamics
Aeronautics as a whole anil aviation, the science of the heavier than air machine, has from its earliest conception, been an experimental art. When Professor Langley in 1887 started his experiments on an extended scale for determining the possibility of, and the conditions for, transporting in the air a body whose specific gravity is greater than that of air,
measuring these forces were designed with the intention of correcting the errors which had rendered so untrustworthy the results of their predecessors.
During the winter of 1901-1902 their investigations included some hundred different surfaces of which about half have been tabulated and the results used in their subsequent work. Experiments were made on the effect of varying aspect ratio, curvature, camber, and the variation of the position of the
Fin. 1. WHIRLING Ami USED BY MESSRS. VICKERS IN TESTING PROPELLERS
he had before him papers by such scientists as Gay-Lussac and Xavicr, proving conclusively that mechanical flight WHS im- possible.
Langley was not easily discouraged and by a carefully conducted series of experiments carried on under very ad- verse conditions, he was able to build a machine which though unsuccessful in its flight in his day. due to faulty mechanism in the launching device, has since been flown under its own power b\ Glenn Curtiss in 1914, at Haininondsport, N. Y., — possibly with some alterations.
At the time the Wrights took up the subject in 189C, there were but few aerodynamical works of interest or value in ex- istence. They were dependent upon the meager experiments and tables of Lilienthal and Duchemin and the work of Lang- ley which seemed to verify Duchemiivs formula. After spend- ing two years experimenting upon these figures of Lilienthal and Dnchemin, the Wrights came to the conclusion that the tables were so much in error as to be of no practical value in airplane design.
In 1901 the Wrights designed and built a small " Wind- Tunnel " in which they could carry on systematic investiga- tions on the pressure produced by various surfaces when pre- sented to the air at different angles. The instruments used in
maximum ordinate of the wing section from the leading edge. Thick and thin surfaces were tested to determine the effect of thickness. The effect of superposing the surfaces, as well as placing one behind the other, were measured and what was of even greater interest, the first measurements of center of pressure motion on curved surfaces at carrying angles were tabulated by them. As a direct result of their laboratory ex- periments and the development of a system of control, worked out in their earlier gliding flights, they were able to build the first power driven airplane.
To demonstrate that the United States deserved a right to leadership in aviation in the earlier years, one need but men- tion other names, such as those of Octave Chanute and Dr. Zalun. The latter, through the efforts of Hugo Matthul- lath, was provided with an aerodynamical laboratory which was in its day the most perfect of its kind: and although the experiments extended over a few years only, the results of Dr. Zahni's labors were exceedingly valuable.
General Requirements in Airplane Design
As is the case in ship building, a suitable machine for every purpose cannot be developed and there must be a special type
15
AERODYNAMICAL THEORY AND DATA
with specific qualities in slow speed, high speed, weight, arma- ment and defense. Some of these factors arc directly opposed to others. For example, the ideal machine for the regulation of artillery fire, would be able to remain immovable or circle about very slowly above one point. The " chaser " or machine used to rid the air of the enemy's planes should be the fastest possible. With the comparatively narrow range of speed pos- Mblc in mi iiirplane one can see the nselessncss of MM Mitrmpt to combine these two types in one machine. On the other hand from the productive side, it is impracticable to increase the number of types indefinitely, for this would call for an enor- mous outlay in machinery and increase in personnel. A com-
K!<;. 2. FIRST PLATFORM EQUIPPED FOR TRIAL AT AEROTECHNIC
IXSTITfTK OF S.UXT-Cvi:
promise has therefore been made, with the selection of some four master types of airplanes which may lie classed accord- ing to their military uses:
1. THE STRATEGIC SCOUT. A slow endurance machine for use on long raids into the enemy's country, for mapping and photographic work.
2. THE HIGH SPEED SCOUT. For tactical re. -om .-n-sanee and use over the lines, and capable of out-climbing and out Hying the enemy.
3. Fniimxc OR BATTLEPLANE. Armed and armored, for driving off the enemy's scouts and protecting the fourth dm.
4. BOMB DKOPPHIS m: WKU;HT CARRIERS. For use in de- -t roving small bridges, railway--, etc.. depending for their protection upon the battleplane.
In order to design and build machines to meet such quali- fications the designer must give up the old hapha/.ard method- of building first, and then determining (lie performance. 11, must go about the design in a thorough and scientific manner in order to hope to come within reasonable limits of his speci- fication.
The most important items in the performance of present ..lay machines are: their weight, their rate of climb, high anil low -peed-, aii'.'le (.1 L'lidc, propeller ctn'ciencv, and endurance at •'meal --peed for various loading. These depend on a il manipulation of aerodynamical data, including the lift ami rcM-tancc of the main plane* and control sin •: the resistance of stnii wheel-, radiators and ap-
pendages, the distribution of loads <>n surfaces, nnd different eiiiiitiiiiHlinii- of surfaces. On the ctlVet- of (be various -up porting, control and (in surface-, and on the summation of all aerodynamical forces depend not onlv the performance, but OntrollabilitV, factor of -aletv. and -lability of the :m
plane. To produce a desired type the designer must bear in mind every factor.
The desired type can be obtained by the "cut and try" process on the full size machine. This experimental flying is. however, a dangerous and costly, method that has led to many an unfortunate accident.
Difficulties of Full Scale Experiments
The real worth of full scale experiments depends on the delicacy and precision of the recording instruments, (!.. pertness of the pilot and the interpreter of the recorded data. The chief objections, other than that of danger to the pilot, are the great variations in atmospheric conditions and therefore the unavoidable delays in tests, the inability to repeat the trials under exactly the same conditions, the necessarily short time allowable for observation and the unavoidable introductions of many variables, when but a slight change is made in one part of the design. It is this inability to discriminate among the possible causes of behavior of the machine that may lead to a ma/e of conllicling results.
There is a place, nevertheless, and a very important one for full si/eil experimental flying — that the machine may be tuned up and minor adjustments mad" for ea-e of control and steadi- under actual llyini.' conditions. Such work, however, -hould not be undertaken until the safety of the pilot is rea -oiiably assured.
Towing Methods
The most natural and logical thing to do with model air planes would be to tow them through s|jl] air and record the forces and moments to which they are subjected. This is not SO simple an arrangement as in marine work. The airplane is free to move along the three axes in space and around an\ of the same, which introduces complications in the recording mechanism that are most dillicult to overcome. Very much higher speeds are rei|uired in aeronautical work nnd this in- creases the length of track for testing prohibitively or de- creases the ti f experimental observation to such an extent
as to spoil the precision of the results.
The principal objection to towed model tli'jht is the inability to obtain still air, as even in a closed room eddies are con- stantly present, which are impossible of measurement: this may be observed by making apparently calm air visible by the introduction of smoke, li'adiation of heat from the walls is apt to cause such eddy making to a verv marked degree.
In a niea-nre the dillicullies of rectilinear-motion are over come by replacing it by rotation about a fixed axis: but here the radius mu-i be relatively large and the building necessarily of similar great dimensions. The rotation is not wholly com parable with translation since along the transverse axes of the body, under test, the different parts have not the same relative velocity and some compromise is necessary due1 to this differ enee in radial length. Centrifugal force is present which must be overcome by the measuring instrument, as well as the dis turbance -el up in the air by so large an object as the whirlim: arm passing the same point a number of t:1
The whirlim: arm used by Mc-si>. Yickers. Ltd.. of F.iiL'hind. in then experimental work is illustrated in Fig. 1.
\\ UK! Tunnel Methodi
If we arc willing to accept the doctrine of relative motioi then the resultant force on a solid with a uniform motion through still air. is the same as that for an immovable solid
AERODYNAMICAL THEORY AND DATA
17
upon which a constant current of air impinges. A " Wind Tunnel " test, where a steady current of air impinges on a model at rest, should therefore give the same results as a tow- ing test. Differences would be due to experimental errors and not to a difference in principle.
In the towing method, the influence of the mounting stage and unsteadiness of the air introduce errors. In the wind tunnel, there may be slightly non-uniform flow, disturbances due to the sides of the tunnel, etc. Wind tunnel work, how- ever, has proved far superior to the towing method, which it has almost entirely replaced and it has now been developed to a high degree of precision and usefulness.
From wind tunnel tests, the engineer may obtain data for the "balancing" up of an airplane — the adjustment of the center of gravity with reference to the air forces, the loading on his wing and control surfaces, the resistance of the body and appendages, and other useful information. It will be scarcely disputed that such tests are of immediate commercial value to the practical designer.
Laboratories of the Wind Tunnel Type
The Institut Aerotechnique de I'Universite de Paris, under the directorship of M. Maurain and M. Toussaint, situated at St. Cyr, some ten miles out of Paris, is devoted, for the most part, to experiments on full size surfaces and aeroplanes. Covering some eighteen acres of land, a splendid opportunity is offered for ample buildings, as well as the seven-eighths of a mile railway track used for experimental work.
The main building with a large central hall is surrounded on three sides with work shops, laboratories and a power station. Within the hall is installed the experimental apparatus directly connected with aviation. Here there are several wind tunnels of different dimensions and wind speed, arranged for the test- ing of scale models and appendages, apparatus similar to Colonel Renard's for the investigation of stability and proper propeller testing apparatus. A motor testing plant for endur- ance and economy of aeronautical motors, instruments for measuring the propeller torque for various rotational speeds at a fixed point and the testing of propellers at rupturing speeds are also included.
In the chemical laboratory investigations on balloon fabrics and gases are undertaken with special reference to their manu- facture and purification. The physical laboratories are de- voted to the production of instruments for aeronautical pur- poses, both experimental and applied. Work shops are at one end and an individual power station supplies energy and light tn the Institute and experimental departments.
In a separate building, covering a quarter of an acre, is housed a " \vhirling-ann " some 50 feet in radius, used prin- cipally for the calibration of instruments. It is, however, not as popular as the track and wind tunnel experimental ap- paratus. The out-door track proper is of standard -rage, seven-eighths of a mile long, level for the part over which ex- perimental data is recorded, but rising slightly for some distance at either end to facilitate the starting and stopping of the five-ton electric car, upon which the surface, full size airplane or propeller is mounted and carried.
Four cars, each rigged for one type of experiment, are con- sidered necessary. Car number one measures the horizontal and vertical components of the resultant air force, as well as the center of pressure for various angles of incidence of the sur- face to the wind : two and three are for large and small pro- pellers in connection with dirigible and airplane work; and number four is especially equipped for the measurement of
the resistance of appendages. The carriages are equipped with appropriate measuring instruments of the recording type, readings being recorded simultaneously as the car moves over the track. The velocity of the air is recorded by means of a calibrated venturi tube anemometer.
The testing apparatus is of such size that a full scale air- plane can be mounted and subjected to test for lift and resistance and static longitudinal stability. In order to accom- modate such large forces as are encountered in full scale work, the instruments are of considerable size; this has the disad- vantage of destroying much of the delicacy of the measure- ment. The results obtained are said to be in error by about five per cent in lift and about ten or fifteen per cent in re-
!
FIG. 3. PLAN OF EIFFEL'S AERODYNAMICAL LABORATORY
sistance. The real value of experimental work of this nature and its comparison with results obtained from model tests is as yet not fully determined.
Eiffel in liis laboratory at Auteuil, in an investigation to ascertain the aerodynamical effect produced by the car, sit- uated as it was directly beneath the surface under test, reports that when correction is made for the presence of the carriage, agreement with wind tunnel results is fairly obtained. He also notes that modification is being made at St. Cyr in the position of the surface as mounted on the car in order to reduce the interference as much as possible. A similar comparative test made at the National Physical Laboratory, England, on wind tunnel models shows good agreement with the lift coefficients, but the resistance coefficient in the full size experiment is still unsatisfactory.
The Laboratoire ASrodynamique Eiffel, supported by the personal means of, and directed by G. Eiffel, is of the most elaborate in design. Devoted entirely to wind tunnel experi- ments, it is completely housed in a beautiful white stone build- ing, fronted by a formal garden. The building proper, two stories in height, is 100 by 40 feet.
As may be seen by the accompanying photographs, the lab- oratory room is rectangular in shape, with a large and small wind tunnel side by side, occupying the central space and suspended mid-way from floor to ceiling. The position of the tunnels permits the free circulation of the air in the room. The wind tunnels are of similar character, one being of smaller working diameter than the other. They each consist of a bell- shaped collector, a large laterally air-tight experimental cham- ber, used for both the large and small tunnel, and independent expanding trunks leading from the experimental chamber to the individual suction blowers. The air is drawn from the large surrounding room or hangar into the bell collector.
AERODYNAMICAL THEORY AND D A T \
through a honey-comb balHe to straighten the tlow, then across the experimental chamber into the expanding trunk where it passes through the suction Mower and is discharged at low velocity, bark into the room.
M. Eiffel's characteristic variant is his hermetic experi- mental chamber. When first interested in experimental aero- nautics, lie experienced dillicnlty, due to interference of How around his models caused by the walls of the closed tunnel. In order to avoid a tunnel of excess size and still not reduce his model dimensions, the walls were removed for some distance and replaced by an air-tight chamber enclosing the stream of air. The pressure in the hermetic room is necessarily that of the air stream it contains, so that a cylinder of air traverses
obstructions 1(1 incteis. 33 lect. in length, -) mclci-. 111.! in width and 5 meters, 16.4 feet, in height. A rail supporting a sliding floor carries the observer anil weighing mechanism above and clear of the air stream. A second observer on the floor is required to regulate the wind and adjust the model during a test. The two tunnels are of course so arranged thai the one not in use may be blocked off with air-tight wall plates so preserving the low pressure in the experimental chamber. In order to avoid the possible physical discomfiture often a.- ciimpanying sudden changes in pressure, an air-lock is pro- vided for passage into or out of the experimental chamln
The models are mounted upon especially designed standards or measuring instruments, such a- a lai'.-e and small ;\> •
FIG. 4. LONGITUDINAL SECTION OF THE LARGK WIND TUNNEL IN Kinn.'s I..U:C>I!.\T<>I:Y
the chamber in parallel stream lines and without showing any appreciable eddy. If a fine silk thread is held in the working stream, a slight play up and down or to the right and left may be noted, showing some variation is present. The velocity of the stream is measured by an alcohol manometer, registering' the difference in pressure in the experimental chamber and the laboratory room outside. This is one method of velocity de- termination and will be explained in detail later. The manometer when left to itself shows a slow variation in velocity with time of some four per cent.
The general dimensions of the installation at Auteuil are as follows: The large channel has a bell collector with end diam- eters of 4 and 2 meters, 13.1 and 6.6 feet, with a length of 3.3 meters, 10.8 feet, and an expanding trunk 9 meters, 29.5 feet, long with end diameters equal to the collector. The expanding; trunk connects with a suction blower, having a sectional an a of 9 square meters, 97 square feet. The small tunnel . prises a bell collector, ends 2 meters and 1 meter in diameter, I.H.'i meter-, in length and an expanding trunk 6 meters long, connected to a Sirocco suction blower.
The above dimensions permit in the larger, n uniform stream t '2 meters, (i.lj I'cet. in diameter to be drawn throuL'h the experimental chamber at a speed varying between '2 and .'!'J "lid, or (i and ]<>"> feet per second; this is accom- plished by a ">O h.p. electric motor driving a .">() per cent efficient blower. In the small tunnel of 1 meter diameter air How. a maximum velocity of t'l meter-, l.'tl feet. ]»< ond, i- obtained bv a .">(» h.p. electric motor driving the Sirocco blower.
TI.e experimental chamber is a rectangular room free from
namical balance — devices for measuring the lateral IV pressure distribution and a very excellent apparatus for test- ing small propellers. All the apparatus is mounted in the most convenient manner and may be used for either the large or small channel as desired. The accuracy of the results oh tained, while possibly not sufficient for exact physical research. are ample, from the practical stand-point.
'///•• Ih'utarhe \'erstichsanstalt fiir Luftfahrt :u Adlershof, superintended by Prof. Dr. Hendemaiin, is of the same order as the experimental grounds at St. Cyr, but on a much h-s elaborate scale. The work is principally on lull scale air- planes and block tests on aeronautic motors. One building is devoted to full scale testing, another to construction and re- pairs and five smaller ones to the housing of motor testing apparatus. The main building has a central tower some inn feet in height from which wind observations may be made and other atmospheric conditions recorded. Cables from the. top of this tower are nseil to support full si/.e airplanes in the determination of their moments of inertia. A track ouKiile of the building is used, as at St. Cvr, for the testing of full si/e airplanes or surlaces. In this instance a locomotive used to pu-h the mounting stage is substituted tor the St. < 'v i trie driven car, a rather doubtful ad.junct.
'It', n .lirdili/niniiiiiil J.nliiiriitnri/, under the super-
vision of Profe-sor Praiidtl. lias little of the ornate as com
pared to the KitTel Instituti housed as it is in a plain one
-lory brick building. 1(0 by -Id feet in si/.e. The building, as nmy lie seen from the drawing, is about equally divided b. tween wind tunnel and office space. Glass doors in the snle next the observation room permit of access to the experimental
AERODYNAMICAL THEORY AND DATA
19
section of the tunnel, while trap doors open here and there to allow entrance into other sections for the adjustment of the honey-combs, baffles, etc.
Unlike the Eiffel tunnel, the air follows a closed circuit necessitating the turning of four corners. The 2 meter diam- eter blower, driven by a 30 h.p. electric motor, forces a steady current of air through the 2 meter, 6.6 foot, square wooden tunnel. At a short distance down stream the air passes through the first honeycomb, 400 large square metal cells, similar to the pigeon holes used for post office boxes. These cells are so constructed with two-ply metal walls that the quantity of air passing through any one may be regulated by partly bending out one thickness wall to obstruct the pas-
passes through the second honeycomb, much finer than the first. This last honeycomb is constituted of about 9,000 cells from which the air, after passing a wire mesh to remove any foreign matter, issues with a maximum velocity of 10 meters or 32.8 feet per second, to act upon the model suspended some distance down stream.
Section Plan
Via. 5. THE GOTTINGEN AERODYNAMICAL LABORATORIES
sage. The cells, in many instances, have been so restricted to regulate the air flow that it might be as uniform as possible. Vanes, similar to those of a turbine, are utilized at the four corners to turn the current through a 90 degree angle, without producing excess eddy-motion. After the second turn, just before the nir enters the experimental part of the tunnel, it
A great deal of the work in the Gottingen Laboratory hfas been devoted to the resistance of airship hulls, etc., for which work a special suspension method of mooring wires, bell cranks and weights, has been adopted with great success. A differential pressure gage, sensitive to pressure changes of one- millionth of an atmosphere is used in the determination of
FIG. 6. ELEVATION AND PLAN or THE WIND TUNNEL OF THE UNITED STATES NAVY DEPARTMENT
AERODYNAMICAL THEORY AND I)V1\
velocity. Many interesting experiments on the distribution of pressure have been conducted upon small propellers, con- structed by electroplating with copper, wax models. A more detailed description of the suspension device and differential ira-je will follow.
The Wind-tunnel of the United States Xavy Department, under Naval Constructor li olden C. Richardson, is at the Washington Navy Yard. Washington, D. C. The tumid is similar to the German liottiiigeii Laboratory in that the air is confined in a closed circuit, in tliis case eight feet s<|iiarc at the -I'ctiun. The cross sectional dimensions vary as may he seen in the accompanying print, hi order to compensate for the curves taken by the stream. Only one set of honeycomh baffles is employed, these being placed just at the entrance of the experimental chamber and 20 feet up stream. These 04 cells.
Fie. 7. EXTERIOR OF THK WIND Tr.\xn. AT TIIK MASSA-
• •Hl SETTS IXSTITITK OK TECH XOI.O<;1 . SlIllXVlM, CKI.I.S
TllROt-(iir Winni An; Is SrcKKi* IN II:<MI Tin: IJoOM
each one foot square and eight feet long, are equipped with individual adjustable dampers used as a control upon the quantity of air passim; and so producing uniform How to within about '2 per rent. The balance ami motor control are mounted on a platform upon the roof of the tunnel. The model is supported in a horizontal position in the wind on ;, balance similar to thai ol Kind's and sen.-itixe to at least J 1000th of a pound. Models up to :t(i-inch span are per- mitted without nutieejihle in1' I mm the walls or chok- ing of the air flow.
The velocity measurement* are unique in tluit in place of a
-itiifle pilot and pics-lire tlllie. placed in I he Mcimtx n!' th"1
model, a series of twelve tubes equally spaced, directly on the di-chiirge side of the Mower icconl on an integrating manometer the xelociix of the stream. The velocity of the -tream from the blower ha- a direct relation to the veloeily of the wind in the experimental chamber, ntrainst which it has ••alibrated tor nil speed-. The pilot tubes u-ed have been themselves checked with the standard tubes of the National Physical Ijihoralorx »: Kiiirland and the Aerodx namical I*ab- • •ral-tiy of the UMHMlnMttl Institute of Technology.
Cower for drivinu the suction blower is -upplied by a 500 h p. J.Vl volt direct current elti-tric motor, operated on
the Ward-Leonard system. A velocity of 75 miles an hour may be obtainable, but due to the heating of the air by friction and other dillieultius in maintaining regular How this high speed is seldom utilized. Generally tests are made at a speed of about to miles an hour.
Fid. 8. (A) 1'HOPELLEl: AND ( I ! I A l.l.'c Hil N A M 1C I'.AI.ANCK IN USE AT TIIK M \SSAl IHJSKTTS IXSTlTfTK OK TECHNOLOGY
The National 1'hiixical Labvrator/i at '/ViWiH'''"" <""' ''"' I\oyal Aircraft l-'actonj at Farnborough, England, constitute the most complete aeronautical experimental combination in the world. The aeronautical portion of the National Physical Laboratory is devoted to experimental investigations of the I'.ritish Advisory Committee for Aeronautics. This committee, with I>r. I!. T. < ila/.chrook as chairman, and such able co-
Kni. !'. KXTUKM i NH//I.I Simxvixi; HIIM-.M o.xtr.
worker- :LS l»r. Stanlon and Mr. I.. I'.airstow. initiale- the investigations at the N. I'. L. and mersi-es the general work in aeronautics throughout the Kinu'dom.
The l»o\al Aircraft Kactorx. superintended by Mervyn
<i'(!orman. work- in close i peiation with the N. I'. I.. It
hius facilities for model experiments, but is more Concerned xvilh tests on lull size airplanes and the application of the iiuesti'.'ation- of the National Phv-ical laboratory. There is
AERODYNAMICAL THEORY AND DATA
21
necessarily some overlapping in the work carried on at the two institutions, but no interference.
The Royal Aircraft Factory before the war. was the largest factory then in existence devoted lo the manufacture of airplanes. All the experiments arc carried on in the large flying field in connection with the factory. Machines equipped with intricate recording instruments are flown under their own power and such important information as: power utilized, angles of pitch, roll and yaw, speed through the air, altitude and control movements are simultaneously recorded. This, in a true sense, is full scale experimental work and the results have been to disclose defects and encourage the improvement and safety of the machines. By the careful application of the model experimental work of the N. P. L. an inherently stable biplane with a speed range of 40 to 80 miles an hour had been produced by the R. A. F. before the war. Improved machines of this type have been of the greatest value to the Royal Fly- ing Corps.
The National Physical Laboratory has turned over ample space for the exclusive use of the Aeronautic Committee, com- prising a large and small wind tunnel house, a whirling table house and ample space for any independent investigations. The small and large wind tunnels are of similar character, one 4 and the other 7 feet square in cross-section. Each is mounted in a separate building, the smaller being included in the engi- neering laboratory building. For details of the small tunnel, reference is made to the description of its duplicate in the Massachusetts Institute of Technology Laboratory. The new 7 foot tunnel only differs from the 4 foot in its dimensions and power. It is 80 feet in length with an air flow of 60 feet a second produced by a low pitched four bladed propeller driven by a 80 horse power electric motor.
A great amount of time was spent in experimenting with this form of tunnel before the committee was satisfied with the results. They have the deep satisfaction of knowing that the artificial wind produced by it, is the most uniform in the world and adaptable to the most scientific research. The cur- rent is uniform in velocity, both in time and space, to within one-half of one per cent. The velocity measurements and aero- dynamical balance will be described in detail later. It suffices here to say that they are as carefully worked out and results obtained as gratifying as the wind tunnel itself. The work of the committee has been extremely broad and the results are of untold value to aeronautics. The whirling-arm and small water channel, the former used in the calibration of velocity instruments, the latter in the study of stream line flow, are both examples of high engineering skill.
The Wind-tunnel of the Massachusetts Institute of Tech- nology was built after a careful study of European Labora- tories, on plans furnished through the courtesy of the National Physical Laboratory. Maintained in connection with the graduate course in aeronautics at the Institute, with the helpful cooperation of Professor Peabody of the Naval Architectural Department, and under the former directorship of Lieutenant J. C. Hunsaker, U. S. N., the work has been of the most com- mendable character.
The tunnel is housed in a temporary building on the new Technology site in Cambridge, with offices in the main Insti- tute building. Enclosed in a 20x25x66 foot shed, the tunnel is suspended in the center of the room. 6 feet from the floor, so that ample space is provided for the free circulation of air. The illustrations indicate the general form of the tunnel which has an overall length of about 56 feet and a working section 4 feet square. The air which is drawn from the room around the cowled entrance end passes through a honeycomb formed from 3-inch metal conduit pipes 2 feet 6 inches in length into the
experimental chamber. This honeycomb helps to straighten out the Mow and prevent eddies in the wind.
The experimental chamber reaches from this honeycomb to the expanding trunk, but only the section midway between these points is utilized. The air after passing the model goes through a series of diagonal vanes and enters the expanding trunk. Here the velocity decreases with an increase of static pressure. The expansion in 11 feet of length is to a cylinder of 7 feet diameter. This cone expansion, in the English tunnel is only 6 feet on the 11 foot length. By expansion the pres- sure difference maintained by the four-bladed propeller is re-
FIG. 10. INTERIOR OP DIFFUSER LOOKING FROM PROPELLER
duced and some turbulence in the wake avoided. The dis- charge from the propeller is received by a large perforated d iff user with the end opposite the propeller a blank wall. The function of this diffuser is to distribute the air into the room at a uniform rate and at a very low velocity. This is indeed accomplished for the area of the perforation in the diffuser is several times that of the tunnel and when a velocity of 30 miles an hour is maintained in the tunnel, the discharge from the diffuser is hardly noticeable.
A four bladed black walnut propeller of low pitch, revolv- ing 600 r.p.m. will produce a wind of 25 miles per hour. The propeller is driven by a 10 h.p. electric motor through a " silent " chain. The motor is mounted on a separate con- crete foundation, as are likewise the aerodynamic balance and the tunnel proper, to avoid any variation in alignment caused by vibration. The sectional area of the tunnel permits of models of 18 inch span and as an extreme 24 inch span, to be tested at speeds from 6 to 40 miles per hour.
The control of the wind is by sentitive rheostats in the motor field and wind speeds may be kept constant as in the English tunnel to within one-half of one per cent. Measure- ment of velocity is by means of a calibrated " side plate " in
22
AERODYNAMICAL THEORY AND DATA
the wall of the tunnel, recording on un alcohol manometer the difference of the pressure in the room and in the experimental part of the tunnel. These manometer readings were calibrated against a standard N. P. L. pilot tube to ascertain the true velocity.
The aerodynamical balance was constructed by the Cam- bridge Scientific Instrument Company, England, and is a counter-part of the English installation. Most model adjust- ments are possible from the outside without stopping the wind, thus greatly facilitating the experimental work. The balance is arranged so that complete data for the calculation of the stability coefficients for airplanes is obtainable.
While the laboratory is primarily for research work, investi- gations are conducted for private individuals or manufacturers at nominal charges.
It is interesting to note that the Curtiss Company has re- cently erected at Buffalo, under the direction of Dr. A. F. Zahm a wind tunnel similar in construction to that of the N. P. L. and the Massachusetts Institute of Technology.
References for Chapter 1
.National 1'liysiral Laboratory. Teddlngtuu, and ICiival Ai lory. Faruborough, England. Publication: Technical AY/»/rl «f tin Adritom Committee /or Aeronautics, for tin- v..n- \'.<i<:< 1<>. T.H'i 11. 1911-12. 1012-13.
• Unltnl States Navy Department Wind Tunnel. Wiishlnirirui. 1>. c
•The Aerodynamical Laboratory of tho UanacnowtU institute of Technology, r.o-ion, .Mass.
The LaUoratolre Aerodynamlque ElftVI. Autenil. Kraneo. I'nlilii-a- tlons : •• ],:i BeaUtance de 1'Alr <-t 1'Avialion." by <;. KIITH. nil'-', trans Intod hy J. C. Hunsnkcr. •• Nonvelles lieeherehes sur la i;i--i>i.-inM' ilc 1'Alr .'i 1'Aviall " l>y <:. Kiffi-l, Diiiuid aud I'lnal. 1'arls. r.H I
Jlillli'tin </c I'lnntilut .!( rui/ifiiumii/ui (/.• Knuli-lniio, Mox-ou.
t UuttiiiKi'ii Acroilvnainiral Laboratory, <:rniini:i>ii, (irrinanv.
t Tin- Dentcche 7enachaanital< fiir i.iifii'aiin /.n Adii'rsin.i. i'..Tiiii. (IcTinany.
" Heport on European Aeronautical Laborati.rirs." i,y A. K X.ahni. Vol. «i, Xo. I! : •• Ki-port on Wind Tunnel Experiment! In Am- djrnainlca." by llunsaki-r and otJbcrs, Vol. ti^. NO. -i. E^ibllihed b\ Snillbsonian Institution, Washington, 1>. ('.. in Smith. Uiscellaneotn
<'i,ll<rli,,M,, Vol. 02.
Itullitin dc I'lnstitut Afrotechniquc dc l'Unlrcr«il, <1< l'nri«. I'.HJ 18-14.
• Work published at Irregular Intervals In standard periodicals ami reports, such as: Aeronautical Journal, England; L'At'rojilani. Paris. France; Smithsonian Institution Keportt, Washington, D. C. ; Hni/lnnr ing, London; Annual Keport of the National Advisory Committee lor Aeronautics, Washington. D. C., "
1915.
t Jahrbueh der Motorluftscliiffstudiengesellachaft, Berlin, years 1908-09, '09-10. '10-11, '11-12. '12-13, and ZcltocMJt fiir l-'hiiitrrl, ml. und tfotorluftschiffahrt (semi-monthly periodical of research work).
Chapter II
Elements of Aerodynamical Theory
Liquid, Fluid, and Perfect Fluid
Both liquids and fluids may be defined as substances which flow or are capable of flowing. A liquid is incompressible and therefore of constant density, a fluid is compressible and of varying density. Thus water is commonly spoken of as a liquid, air as a fluid, yet the hard and fast distinction is un- fair, since water itself is slightly compressible.
In the transportation speeds employed in aeronautics, the variations in pressure of the air, and the consequent varia- tions in density are so slight, that the air may also be regarded as incompressible. Thus for a dirigible at a speed of 100 miles per hour the increase in pressure at the nose is only about one per cent. It is only at the tips of fast moving propeller blades that the compressibility of air assumes any importance.
The motion of fluids is so complex that no complete mathe- matical theory has yet been evolved for it. In hydrodynamics the mathematicians have stipulated a perfect fluid possessing no viscosity. In such a fluid all bodies may move without encountering resistance. Although the conception of a perfect fluid may seem of no practical importance, yet hydrodynamical theory serves as a guide in the theory of aeronautics and we shall have to make occasional reference to this idea.
Density of Air
In setting forth data from the laboratories the air will be assumed as having a temperature of 15° C. and a density of .07608 Ibs. per cubic foot at sea level.
Variation of Density of Air with Height
Height (ft.)
0
500
1,000
2,000
5,000
10,000
20,000
Density (Ibs. per cu. ft.) .0761 .0748 .0734 .0707 .0632 .0523 .0357
Principle of Relative Motion
We shall assume throughout without further reference that the same resistances will be brought into action whether a body- is moving through a fluid or a fluid is streaming past a body, provided the relative motion is the same.
This is an idea which often presents difficulties and is very difficult of theoretical demonstration, yet it is merely a matter of common sense. In La Technique Aeronautique of May 15th, 1913, M. Lecornu has given a very sound discussion of this point. We will venture a rough illustration. Imagine a
boat propelled through a river at rest at a speed of 5 miles per hour. The oars will exert a certain force of propulsion. Now if the river has a contrary current of 5 miles an hour, the boat will remain at rest relative to the banks, yet exactly the same force will be exercised by the oarsman. There is really nothing more to be grasped underlying the principle of relative motion.
Bernouilli's Theorem for Fluid Motion
In the steady flow of a fluid the current at any point is always in the same direction and magnitude and may be rep- resented by a series of stream lines, or by tubes of flow.
The energy of a fluid consists of three parts: (1) The po- tential energy, or the energy due to its position of height through which it may fall, (2) The pressure energy, (3) The kinetic energy due to its motion, neglecting the effects of vis- cosity or friction. Bernouilli's theorem states that along any stream line, the sum of these energies is a constant, and if
y = acceleration due to gravity h = height p = pressure \' = velocity 9 = density*
p V -{- — constant
In considering air flow in aeronautics where we deal with a fluid ocean of immense depth, the variations in height are negligible, and the theorem becomes: —
, +
= constant
The theorem is of fundamental importance in aeronautics; its proof will be found in any text-book on hydrostatics.
This equation may also be written in the following useful form, by multiplying both sides of the equation by p :
fl" p -\- - — = constant
Total Energy of a Fluid Applied to the Theory of the Pitot Tube
The Pitot tube, so frequently employed in aeronautics to measure the speed of a machine in actual flight, furnishes an excellent illustration of the principles just set forth. In Fig. 1 is given a diagram of such a tube.
Its main function is to measure the velocity of flow for e
* (p) is used for Density to prevent confusion with D for l)rag and tu conform with standard usage.
24
AERODYNAMICAL THKORY AND DATA
steady irrotational (low of air, and it is unsuitable for mca.- uring the velocity of turbulent flow, such as that occurring in the vicinity of a fan to give an example.
In practice the Pitot tube is finely rounded so as to give the least possible disturbance to the air How. It consists of two concentric tubes. The inner one is open to the wind, the outer lube is closed to the wind and is only connected to the surrounding air by a .-cries of tine holes. The lubes are con- nected to the two arms of a pressure gauge as shown in the figure, and the gauge measures the difference in pressure U-tween them.
The inner tube, open to the wind, brings the air impinging on it to rest, and the pressure in it is therefore a measure of both the static pressure in the stream and of the kinetic energy- head of the stream. If p is the static pressure of the stream. V the velocity, the total pressure will be given by
9V>
Definition of Angle of Incidence. KeMiltunt Pres>nre.
Lift, Drag and Center of Pressure in a Plane or
Cambered Vi in;; Section
Whether for a plane or a curved wing M-ction. the angle
L int «f mad-
FIG. 2. LIFT, DRA<;, ANIII.K OF |X<-II>K\CK. AM> l-'i.n- 1'i.vn.
of incidence is defined as the angle i expressed in decrees, be- twcen the relative wind and a line in the supporting surface. termed thu chord, lu the case of the tlat plate, this line coin- I-H!C> with the face of the plate and is physically justifiable -ince when the face of the plate coincide- with the relative wind, there is no sustaining force or lift on the plate.
The outer tube, on tlie other hand, being closed to the wind. will, if the holes are small enough to prevent velocity having
2 rifles at front &• boc/r 02 " diam /'// outer tube
.4.4.' JF _»I
FIQ. 1. PITOT TUBE.
any effect on its pressure, read the static pressure of the air flow.
Hence the difference in pressures read on gauge will be
and will therefore be a measure of the velocity.
We shall discuss the methods employed in connection with the Pilot gauge more fully when dealing with laboratory methods, but may state now the results of recent experiments as summarized by Dr. .1. ('. Hunsaker: —
1. The precision is one-tenth of one per cent.
'_'. The open tube correctly transmits the total pr« regardless of size or shape.
.1. The nose of the combination tube must be of easy form.
4. The static openings should be clean holes from 0.01 to 0.04 inches dintm •;•
"i. Slain- opeiiuii;- -lioiild lie well hack troni the no>e ol (lie instrument on a polished cylindrical portion of the tube.
Static opening may In- from 1 to '_' 1 in number ar- ranged in an arbitrary manner.
7. The tube should be pointed into the wind, but an error of two degrees in alignment will cause |e— I ban 1 per cent error on velocity nica»urcm<
Line of ChcrW
ii;. :t. LIFT, DRAG, LINE OF CHORD, ANGLE OF INCIDKM f FOR DOVBLK CAMBKRKI, SK. TIOK.
In the case of cambered surfaces, the posi- tion of the chord has been fixed by conven- tional usage, and is best illustrated by the diagrams in Figs. 2. .'! and 4. With cam- bered surfaces, when the conventional chord coincides with the relative wind there is lift as a rule, although the position of no lift may be only a degree or so removed.
Owing to I he relative motion of the air, the wing experiences a resultant pressure which we will designate as ]{. This resultant is very nenrlv normal to the face of a flat plate, but it is quite wrong to state that it is exactly at right angles to this face. The re- Miltant force H may be generally resolved into two com- ponents; one at right angles to the relative wind, which is termed Resistance or Drag (D). Drag will he used instead of the term drift, which unfortunately is capable of misinter- pretation. The component at right angles to the relative wind. L. may act upwards, giving 1'i^itii; Lift, or downwards
Fie;. 4. LIFT. HUM;, AM.I.K OF Jxrii'i.s. t k\n Cnoui' >«i: ('AMHKKKH SCKKV i
L-uiiig .Wi/n/i'rc Lift, depending on the position of the sur-
• lativc to I be wind.
The hit mi ;iMircs the sustaining power, the drair the n -iRtftnce to forward motion. The tnnirent of the mitrle In
AERODYNAMICAL THEORY AND DATA
25
the R and D gives the ratio L/D, lift over drag. The greater the value of L/D the greater is the path efficiency of the sup- porting surface.
The center of pressure will be arbitrarily defined as the point of application of the resultant force R on the plane of the wing chord. This is by no means a rigid definition.
Definition of Lift and Drag Coefficients
We shall employ throughout the following notation : Lift == L = K,AV. Resistance or Drag = D = K^AV'. Where L and D are in pounds, A = area in square feet of one surface projected on the line of chord, and r = velocity in feet per second, K7 and K* will represent forces for unit areas and unit velocity. We shall see later the justification for these expressions.
Position of Center of Pressure or Resultant Vector of Forces
It has become customary in Aerodynamics to speak of Centers of Pressure, and it is very often convenient to em- ploy this term. But it would be much better to speak of the position of the resultant vector of forces, a vector being a line representing a force in magnitude and direction. For a Hat plate or a cambered wing section, the term center of
FIG. 5. ILLUSTRATING POSITION OF VECTOR OF RESULTANT
FORCES.
pressure might answer fairly well, but for a combination of wing surfaces, as in a biplane, or for any kind of airplane, it is very unsatisfactory. Thus as in Fig. 5 for certain angles the resultant force passes right outside the wing surface, and to speak of a center of pressure in such a case is meaningless. It is also often stated that the stability of a wing depends on the motion of the center of pressure with reference to the center of gravity. The moment about the center of grav- ity can be more correctly stated as depending on the position and direction of the resultant vector of forces. If current practice leads us to speak of center of pressure, the reader will always bear these considerations in mind.
Forces on a Flat Plate Immersed in a Fluid and Normal to the Direction of Motion
Newton was the first to consider the case of a flat plate placed normal to its direction of motion. Ho stipulated a medium composed of an infinite number of small particles, having no
sensible magnitude but possessing mass, and not intercon- nected in any way. A plate of area A, moving with a velocity I* in a medium of density p would meet a quantity of fluid fAV and impart to this quantity a velocity V per unit of time.
From the fundamental equation in mechanics:
Force =
(mass acted upon) X (velocity imparted)
Time
we should derive the equation :
9 9
Similar reasoning from the Principle of Relative Motion would apply were the plate held at rest, and the fluid im-
FIG. 0. MOTION NEAR A FLAT PLATE N
THE WIND
pinging on it. The force as derived from actual experiment is considerably less than this.
But Newton's theorem is obviously incorrect, no account be- ing taken of the action at the back of the plate, or of the com- plicated interaction between the particles, or of the formation of eddies and whirls. The photograph in Fig. 6 gives an idea
FIG. 7 FIG. 8
DIAGRAMS ILLUSTRATING FLUID MOTION AND PRESSURE DIS- TRIBUTION ON PLATES NORMAL TO THE STREAM
of the complicated actions which take place. These are repre- sented diagrammatically in Figs. 7 and 8.
From a consideration of Bernoulli's Theorem it will be seen that the pressure in front of the plate will become greater than the statical pressure of the stream. At the back of the plate, owing to the considerable velocity of the eddies or whirls, we can say again from a consideration of Bernouilli's equations — that the pressure will be less than the statical pressure. It is to the difference in pressures front and back of the plate that the resistance is due. Fig. 8 represents roughly the distribution of pressure on either side of the plate.
20
\KR(» DYNAMICAL THEORY AND DATA
Ni-wton was coned. however. in so far as the resultant force of a plate normal to the wind is proportional to the velocity squared. the area, and the density; and if K denotes the re- sultant foroe we can write:
where K is au experimental coefficient.
We shall show later that a similar law holds for all cases of bodies producing turbulent flow, and discuss fully the re- sistances due to such flow.
Forces on Flat Plate* Inclined to the Wind
Figs 9 and 10 represent diagrammatically the fluid section in the case of an inclined plate, and the distribution of pres- sure, which are further illustrated by the photograph (after Kiabouchinsky) in Fig. 11.
Just as in the ease of the plate normal to the wind, the re- sultant forre will he determined by the difference in pressures
reached. After this, the resultant force slowly diminishes to the value in normal presentation.
At small angles the center of pressure is near the mid posi- tion, and gradually moves forward as the angle of incidence increases. That the center of pressure should be forward of the mid position is fairly obvious from the above mentioned photograph. It is in the forward region of the plate that the air experiences the most abrupt changes of direction, with consequently the greatest variation of pressures. This can be seen also from the diagram of distribution of ; sures.
Numerous efforts have been made to deduce expressions for lift and drag and for the motion of the center of pres- sure from theoretical considerations. But the only trustworthy values are those directly taken from experimental data ob- tained by Eiffel and others which will be dealt with later.
It may be stated here, to remove a somewhat common inis-
Fio. 9. FIG. 10.
DIAGRAMS ILLUSTRATING FLUID MOTION AND PRESSURE DI-TRIIHTION ON INCLINED PLANK.
at the front and back of the plate, and lift and drag will vary as A.V, as in the case of all bodies producing turbulent flow, with a different coellicient for each angle of incidence.
The minimum resultant force of a plate occurs when it is in the line of the wind. As the angle of incidence increases so does the pressure, until a critical angle of some 40 degrees is
FIG. 11. MOTION- XKAU A FLAT PLATE INCLINED TO THE WIND
conception, that the resultant pressure on a flat plate is not perpendicular to the plate except for a certain limited raii'_'«' of angles of incidence. At zero degree of incidence the re- sultant pressure is 90 decree-, behind the normal, rapidly approaches the normal at small angles, and shoots past it at 10 depi
Chapter III
Elements of Aerodynamical Theory — Continued
Skin Friction
Skin friction may be defined as the total resistance of a thin plate moving edgewise through a fluid, and is due to two components:
(1) Viscosity resistance
(2) Density resistance which we shall consider in turn.
In some respects skin friction is a misleading term. We shall see shortly that the skin of a body has nothing to do with the resistance, a moving body being covered with a layer of fluid at rest. Its usage, however, has been sanctioned by time.
Viscosity
Real fluids like air and water offer a resistance to shear, which is a measure of their viscosity.
Let us imagine two horizontal planes, one of which, AB,
\\\\\\
I* /y
Jjf
be AT
Z'y-
T
c
.1
FIG. 12. VISCOSITY ACTION FOR THIN SURFACES.
is at rest, as in Fig. 12, while the other, CD, is dragged past with a velocity V, with the viscous substance intervening, the distance between the two plates being c.
Particles of the substance nearest to CD will adhere to it. < )ther particles will be carried along to the line yyyyy a con- stantly decreasing amount xy. If /•' is the horizontal force per unit area required to drag CD, it is obvious that it will be proportional to some constant dependent on the nature of the substance and on the velocity gradient.
We may then write
F = [A - where JA is some constant, t
c
II' V and c are unity
/•' = [A and [A becomes the coetlicient of viscosity.
The simplest case of viscous drag is that of a thin plate moving edgewise through a fluid. Length is I and breadth b. There will be a thin boundary of fluid of thickness a which connects the particles adhering to the body with the particles at rest in the fluid. This layer will continually lose and gain fluid as it is rubbed off. In unit time a mass of fluid propor- tional to the cross section of the layer, (bn), and to the veloc- ity, will be captured and have its velocity partly destroyed.
t fj. is Greek lottcr mu.
The inertia force required for this change of momentum •will therefore be proportional to
(p ab V) V or p ab V The viscous drag must be equal to this inertia force; and is
V itself proportional to p. (bl) X -- by the definition given
above. And if
V- (bl) -~9ab F2, then, a ~-\l-^. a \ p v
\Jv
The viscous drag therefore is proportional to y. (bl) V -vl
or to I/.'5 6 Z'V5 vl'°
Coefficients of Kinematic Viscosity
To represent the relative importance of density and viscosity a coefficient
is employed, known as the coefficient of kinematic viscosity. Substituting from this equation in the expression for viscous drag we obtain
F~ v5b/-5pV'-5 which may be expressed in the more practical form
fl,. = dv°-M.0-"F1"> where B-, = viscous drag d = constant A, = area in shear A,'n is equivalent to 6Z'° dimensionally.
Reynold's Number
It is interesting to note that the thickness of the boundary layer
The expression
will be of use in comparing resistances for similar bodies in the same fluid.
It is known as Reynold's number and expresses mathe- matically a relationship between velocity linear dimensions and viscosity. We shall have frequent occasion to refer to it in comparing resistances of stream line bodies, rods, wires and so forth.
Prandtl's Theory of the Boundary Layer
The theory of the thin boundary layer is due to Dr. Prandtl of Gb'ttingen, his hypothesis being that the velocity gradient is at first very steep but flattens out quickly, until
27
28
AERODYNAMICAL THEORY AND DATA
in the free stream the velocity gradient between stream lines is negligibly small. Elaborate experiments by Dr. Prandtl bear out this theory, and demonstrate that the viscous drag does indeed vary as V'\
Dr. Zahm's experiments on skin friction on the other hand have shown that for even surfaces, bodies covered with such widely varying substances as dry varnish, wet varnish, water, sheet, zinc, etc., all experience the same frictional resistances. It seems therefore reasonably safe to assume that viscous drag is due to internal fluid friction and not to the sliding of the fluid along the surface of the solid.
Density Resistance to a Plate Moving Edgewise
For exceedingly small velocities, it has been found that re- sistance varies as I'1 indicatin;: purely a drag due to shear (Stokes). For small velocities experiments by Allen have shown a resistance varying as I"1'1 indicating the condition of viscous drag which we have developed in the preceding paragraphs. But for the velocities with which we are con- cerned the resistance of a thin plane surface moving edgewise increases as some higher power of 1". Tliis is probably — although it is impossible to state the exact cause — due to the fact that the viscous drag not only imparts translational velocity to the particles which adhere to it in the boundary" layer but the boundary layer acting as a species of gearing also gives some eddying or rolling velocity to particles adjacent to this boundary layer. It is a commencement of turbulent. eddying motion. As such this extra resistance is proportional to some area A of the body, and to the velocity V, squared. and is termed density resistance and
/,'„ AMI where K is a constant for the fluid.
Total Skin Friction. Dr. Zahm's Experiments
Total skin friction = R, = R, + B«
= viscosity resistance -f- density resistance Strictly speaking if K, — I"'1 and Rj ~ I'3 no one expression with V raised to a power n can satisfy this expression. But
Slut rncfion Resist once of> Ttvi flat
of My Area* Unts Lta p»r Sq rt.
FIG. 13. SKIN FRICTION CHAIJT
for practical purposes the results of Dr. Zahm's valuable ex- periments have been accepted, his formula being:
R = 0.00000778 J" r1 " 6 where I{ = resistance for one side of board
/ = length in direction of wind in feet
6 = width iii
I" = velocity in IK "iid.
In the British Technical Keport of the Advisory Comn for Aeronautics. l!'l 1 -1 !'!•_'. \>. -M. an alternative form of
• •n h:is In-, h siiliinittcil. MI :i- lo iiinkr llir equation con -i-tent with the principle- nt' ilvi.aiiin- -innlant
// o.iMiooOsj I I
MIIC »|ile nt tin hi<:i
Amongst other applications. Dr. Zahm's formula may be used to compute the resistance of flat rudders, elevators, and -taliilizers when neutral to tlit- wind. In Fijr. 13 cum-- for the resistance of plates of various area at varying speeds have been plotted, to facilitate such computations.
Dr. /.a Inn's skin friction experiment- an- doc-rilied in Ilul- letin, Vol. xiv, pages 247-276, of the Philosophical Society of Washington, June, 1904. The plane was suspended in the wind tunnel as shown in sketch in Fig. 14, with wind shields at either end so as to give purely tangential forces.
FIG. 14. ARRANGEMENT OF THIN PLATE IN WIND TUNNEL IN DR. ZAHM'S EXPERIMENTS.
As the wind friction moved the plane edgewise the displace- ment was determined by the motion of a sharp pointer at- tached to one suspension wire and traveling over a fine scale lying on the top of the tunnel, and hence the forces were de- duced. A variety of shapes and surfaces were tried.
Curves for Computations with Dr. Zahm's Formula
TABLE 1.— SKIN FRICTION RESISTANCE
|
Speed |
Ares «q. ft.) |
||||||
|
second) |
1 |
a |
10 |
15 20 |
L>i |
30 |
35 |
|
30 |
.0046 |
.020 |
.039 |
.036 .074 |
.091 |
.108 |
.124 |
|
70 |
|||||||
|
H |
.022 |
.099 |
.189 |
.280 .360 |
.440 |
.520 |
.610 |
|
90 |
.036 |
.159 |
.300 |
.440 .580 |
.710 |
.840 |
.970 |
|
100 |
.043 |
1'iJ |
.370 |
.530 .700 |
.860 |
1.02 |
1.18 |
|
120 |
.060 |
.270 |
.510 |
.740 .970 |
1.19 |
142 |
1.66 |
TABLE 2.— ZAHM'S FORMULA R-O.OQOOW7 A'» l'"». r-milct ptr.kouf
|
Speed |
Are* ( |
HJ. ft.) |
||||||
|
(milraper hour) |
1 |
5 |
10 |
15 |
H |
25 |
30 |
35 |
|
30 |
DOM |
.041 |
.080 |
.114 |
.151 |
.186 |
.220 |
HO |
|
40 |
.0159 |
.071 |
.137 |
.198 |
JM. |
.320 |
.;vi |
.430 |
|
50 |
.024 |
.108 |
.210 |
.300 |
.390 |
.490 |
.570 |
.650 |
|
60 |
.034 |
.151 |
.200 |
.430 |
.550 |
670 |
.800 |
.,_.,, |
|
70 |
.045 |
WO |
.390 |
.570 |
.730 |
,. |
1 06 |
1.24 |
|
80 |
.057 |
.260 |
.490 |
.710 |
.940 |
1.16 |
1.37 |
1.59 |
|
90 |
073 |
.:.'" |
„!,, |
.900 |
1.18 |
1 45 |
1.71 |
1.98 |
|
100 |
188 |
390 |
.760 |
1.08 |
1.43 |
1.76 |
2.06 |
2 41 |
In rY_'. l.i. the skin friction n -Mancc in Ills, per square foot
AERODYNAMICAL THEORY AND DATA
29
is plotted against the speed in miles per hour. Since the re- sistance increases less rapidly than the area, separate curves have been drawn for several different areas, and the force per unit area on any other surface can be found by interpola- tion. The curves were plotted by modifying Zahm's formula:
JB, = 0.0000082. 1 -<«r..»
where F is in feet per second. To throw this into mile hour units it was necessary to multiply by (ff)l'"°, or 2.04, giving
R, = 0.0000167 .-I •T'"
In Tables 1 and 2 similar data has been given for speeds ir feet per second and miles per hour.
Turbulent Flow, Eddy or Density Resistance
We have already seen in the case of a flat plate normal to the wind that the resistance was due to a region of turbulent, eddying, low pressure behind the plate. This resistance varies as o .1 I""
where .1 = area in normal presentation 2 = density V — velocity.
It will be assumed for the time being that wherever there is a region of turbulent, eddying flow, there will be a density resistance
/,- ~ Ml"
A fairly complete demonstration of this has been given by a. French author.
Comparison of Forces Acting Upon Similar Bodies. The
Importance of Kinematic Viscosity and the
Reynold's Number
For the comparison of forces acting on similar bodies, a knowledge of the geometric proportions and of the wind veloc- ities is insufficient. The density of the fluid, the viscosity and hence the coefficient of kinematic viscosity, and the compressi- bility of the fluid all enter into the complete comparisons.
Compressibility, we have seen, may fortunately be neglected in all aerodynamical work.
For bodies in which the resistance is purely of a density or eddy making nature — as in the case of a flat plate normal or inclined to the wind, and as we shall see subsequently in the case of a wing section at large angles — viscosity does not enter into consideration, or is of so small importance that it may be neglected, [n such cases
where .1 is the area of one face of the plate, comparison be- tween two bodies such as a full sized wing and its model be- come extremely simple.
But for stream line bodies such as struts, cables, wires, and cylinders the resistance is compounded of density resistance and viscosity resistance in varying proportions.
Viscosity resistance depends, as we have seen, on velocity, linear dimensions and the coefficient of kinematic viscosity. For such bodies therefore the resistance must be expressed in a form involving these variables, and by the principle of dynamic similarity it can be demonstrated that
R = '-f f"*/
where / is some unknown function and f is of the same di- mensions as A. The 5 I" I'"' brings out the density resistance.
,//l'\ IV
I I - Ithe viseositv resistance: since — = the Reynold's num-
v / v
ber r, we can write
The reader will now appreciate the importance of the Rey- nold's number in comparing the resultant forces on the above mentioned bodies.
It is quite incorrect to compare such bodies, making allow- ance for variation in f and V" only unless the Reynold's num- ber is the same for the two bodies under comparison.
In practice it is very rare that comparisons of forces are made with reference to two different fluids. We are al- most solely concerned with bodies in air. The coefficient of viscosity becomes a constant, and instead of considering the Reynold's number, we can drop the v and compare bodies having the same product IV.
Stream Line Bodies
A stream line body may be defined as one which has a gradual change of curvature along any section, and which when moved through air or water at ordinary speeds makes little disturbance or turbulent wake. Such a body moving in a viscid fluid would experience mostly frictional resistance.
Energy Considerations for a Perfect Fluid Flowing Past a Stream Line Body
It is most useful to have a definite idea of the exchange of energy which occurs in such a case. The first treatment ap- pears to have been given by W. Fronde.
Imagine the fluid in the vicinity of the body to be divided up into a large number of imaginary tubes of flow. Well ahead of the body where the stream is as yet undisturbed the energy of the fluid will be that due to the static pressure pa of the stream and the kinetic energy head of !"„. the undisturbed velocity. In a perfect fluid this will remain a constant along any tube of flow by Bernouilli's theorem, and is equal to
PO TV __ _ '_/< _!" For the portion L. as shown in Fig. 15, of the body, the tubes
FIG. 15. LINKS OK FLOW FOI: A STIJKAM Lixio BODY.
of flow widen out, the velocity and the kinetic energy head diminish and the pressure on the body becomes greater than the static pressure p». The nose of the body therefore does work upon the fluid in contact with it. This is also evident by considering the effect of curvature and the centrifugal force resulting from it. For the portion 31 the tubes crowd together, the velocity increases and the body is under the action of a pressure less than pa — it is really under suction and the fluid does work on the body. By similar reasoning it can be shown that the portion .V the body works upon the fluid, and for the portion P, the fluid works upon the body. The balance of work done on the body is thus found to be zero.
Stream Line Bodies in a Viscous Fluid
At slow speeds in water almost perfect stream line motion has been observed and recorded by Dr. Ahlborn (see Fig. 16). But at ordinary speeds, even with stream line forms, there is
30
AERODYNAMICAL THEORY AND DATA
It is obvious that the resistance will be partly due to viscos- ity over the front part of the cylinder, and partly due to eddy or density resistance. The forces in action will therefore be
Fiu. 1C. MOTION AKOUND A STREAM LINE BODY.
always a region of turbulence and eddying motion such as we have already observed in the case of the flat plate, accom- panied by a surface of discontinuity between the main stream and the turbulent region. The eddying motions are in part due to pressure differences in the undisturbed stream and the region behind the body, in part due to viscosity. The exact theoretical investigations of the causes at play are unimportant from the designer's point of view. It is more important to notice that just as in the case of the flat plate, this turbulent
FIG. 19. FLOW AROUND A CYLINDER.
represented as previously stated by an expression of the form PfFV(r).
And two wires or ruble's will only be comparable when r is the same for both, or simply when the product IV is the same.
Fluid Motion Around Wing Surface
It is to Langley, above all other men, that we owe an appre- ciation of the value of cambered surfaces. A good \\iiu
i-lG. 17. t'LOW FOR A SHORT STRUT.
region will be a region of low pressure and will introduce a density or eddying resistance.
This density resistance for a stream line body may be said to increase with the extent of the turbulent region. Thus in
f lli. 20. t LOW FOR A I'AMIIKKKII WlMi AT - .
tion may give a lit't-drit't ratio of 18 as compared to I lie 6 or 7 of a flat plate, and it is the remarkable efficiency of a wing surface which has largely rendered aviation possible.
In wing surfaces, we recognize two distinct types of flow. For the small angles up to 6° or thereabout-; a sle.ulv flow as shown in Fig. 20 for a typical airplane wing. At this angle —
J'Ki. 18. > l.ow KIR r INK .-MI:
17 and 18 depleting two standard struts, the finer strut has a smaller turbulent region and con>idorahly less resistance. On the other hand, as the fineness ratio, or the ratio of length to maximum thickness, of a stream lino body increases, the •res in shear and the viscosity drag itic-rea.se also: the fineness ratio niu-t l>e kept within reasonable limits even from a purely aerodynamic point of view.
Resistance of Wires, Cables and Cylinders
111 repn-i-nt- diagrimmticiilly the fluid motion round a cylindrical Ixidy, such as a wire or cable, at usual airplane speeds.
I'l.llU KH< A ( .\.\lltKlthll \\INli AT 10"
often termed the first or lower critical angle, turbulence begins. At Id', as shown in Ki-_'. '-'1. this turbulence is (piite consider able. Finally a second critical or " burble point" is reached at 18° for the same wing. Here an extremely turbulent type' of motion, as shown in FJL'. 1'- is found, and the lift of a. wing attains its maximum. Beyond this " burble point " the motion becomes extremely unsteady and the lift decreases.
AERODYNAMICAL THEORY AND DATA
31
The lift of a wing, as experiment shows, varies directly as
p AV, with a different coefficient for everj angle of incidence.
Where turbulent flow is present this is readily explainable,
FKI. 22. FLOW roii A OAMDKRED WING AT 18°.
as in the case of the flat plate, on the hypothesis of low pres- sure region at the back of the wing.
It is the lifting power at small angles and in a condition of steady flow that offers theoretical difficulties. The most likely explanation is offered by Kutta's theory or the vortex theory of sustentation. We shall reserve the full treatment
FIG. 2li. A KiiOPLANE WING WITH TRAILING VORTICES.
of this theory also to a special article, contenting ourselves with the barest outlines:
An airplane wing in steady flow gives off a series of trail- ing vortices as depicted diagrainatically in Fig. 23. These vortices are constantly destroyed and renewed. The circular
motion in these vortices and their interaction is such that — as the hydrodynamical theory demonstrates — they have a downward momentum, and action and reaction being equal, the airplane wing receives an upward momentum.
The drift or drag of a wing is for all practical purposes taken as varying directly with A I'", with a different co- efficient for every angle of incidence.
At high angles of incidence, the drift is almost entirely a component of the density resistance, and we see that what is taken to be the case in practice, is also theoretically correct. But at small angles and steady flow the resistance is more of a viscous nature, more akin to skin friction. And skin friction, as we have already seen, varies as I'1'8", and depends also on the dimensions of the body. This introduces con- siderable difficulties, as we shall see later, in computing re- sistance in actual flight from small model experiments at low speeds.
As to the form of wing giving the best results, no general laws are yet available, and each type of wing must be con- sidered separately.
This section constitutes but a brief introduction to aerodyn- amical theory, but will perhaps assist the reader in the ap- preciation of the extensive aerodynamical data which we shall present later.
References for Chapters 2 and 3
" A Krview of Hydrodynamical Theory as Applied to Experimental Aerodynamics," 3. C. Ilunsaker, International Engineering Congress, San Francisco. Sept., I'.iir,. An authoritative and advanced treatment; containing numerous references for further readine.
" Aerodynamics." F. W. Lanchestcr (Archibald Constable & Co., Ltd., London.) A valuable, classical treatise.
"The Aeroplane," A. Fage (Griffin & Co.. London). A concise scien- tific study, excellent in matter and presentation
•' The Aeroplane," T. O'B. Hubbard, J. H. Ledeboer, and C. C. Turner (Longmans. Green & Co., London). An elementary text book cif the principles of dynamic flight, suitable for beginners.
" Loitfaden der Flugtechnik," S. Huppert (Springer, Berlin).
" Wind Resistance of Some Ae-oplane Struts," Booth and Eden. Technical report of the (British) Advisory Committee for Aeronautics, 1911-1912, No. 49 (Wyinan & Sons, Ltd., London).
" Investigation by Visual and Photographic Methods of the Flow Past Plates and Models," Eden. British report, 1911-1912, No. 58.
•• Photographic Investigation of the Flow Hound a Model Aerofoil," Keif. British report, 1912-1913, No. 76.
These papers in the British report contain some beautiful and In- structive photographs.
Chapter IV
Flat Plates : Simple Problems on Sustention and
Resistance of Wing Surfaces
Coefficients of Resistance for Circular or Square Plates Normal to the Wind. Varying Sizes
Although it would seem that the question of the forces on a flat plate placed normally to the wind would be fundamental in aeronautics, and although it can be shown by the principle of dynamical similarity that similar plates should have the same coefficients no matter what their size, provided that IV remains constant, yet considerable controversy exists as to the variation in the values with the size of plate, and with the velocity of flow. Those who are interested in the controversial aspect of the question are referred to the references at the end of the section. For all practical purposes, the following table may be safely used.
R = KA V where S = resistance in pounds.
A = area of plate in square feet. V = velocity in miles per hour.
TAIU.I. 1. Side of Square or Diameter of Circular Plate,
In Feet. fc-
O % 00269
. .00286
2V! 00814
SO 00.122
50 00.127
10.0 00327
Coefficients for Rectangular Flat Plates Normal to the Wind. Varying Aspect Ratio
The aspect ratio of a flat plate is the ratio of b to a a.< shown in the Fig. 1. With increased aspect ratio the resistance
coefficient increases. A thor- ough theoretical ilisrussion of this invol- • nlou- ilif-
fieillties, but the inere.i probably due to the faet thai with inereaseil aspect ratio the air How i> broken up into a greater number of vortices. with a resultant '.'iratcr tur- bulence. The following table
TIIK Wisi'
These values are plotted in Fig. 2 and are assumed to be true independently of the size of the plate.
-hows the effect of inci • a-peet ratio, accorilini; to e\ penment- by KilTel. The co- efficient tor ;i -i|iiaie plat.- ol the -ame aren i- taken a- unity.
TAB1
Anpect Rjitln
K fur lln-taiiuulnr Plate
ii
1 :. 10.0. .
-.0 O
.10
20
.". i
'.47
|
I; iso \ 4, |
^ |
|||||||||
|
^- |
jr^ |
|||||||||
|
Ratio of pressure to pressure on a si $ * § S 8 |
/ |
s^ |
||||||||
|
/ |
||||||||||
|
/ |
||||||||||
|
/ |
||||||||||
|
/ |
Variation with as- pect ratio of the pressure on a normal flat plate |
|||||||||
|
/ |
||||||||||
|
/ |
||||||||||
|
2 |
1 J |
r — -4 |
0 4 |
T~3 |
||||||
|
r o s - |
>o ^s• J |
Aspect Ratio
FII;. -2. VARIATION WITH AM-NT RATIO OF TIM: PRKSSI-RK ON \ NORMAL FLAT Pi ATI
Coefficients for Flat Plates Inclined to the \\ in.l
Table .'! gives valuer for A\. A',, anil 1. \>. and Table the distance of the center of the pressure from the leading edge of the plate in terms of the chord, for flat plate- of variiiti- Biped ratio.-. The ilra-r al " may lie calculate.! /.ahni's formula for skin friction. TAT, i
|
ratio = 1. |
Asjii-ct ratio |
||||||
|
Angle •» . , 1 n |
K, . .0(M H.j |
A, .in 7 |
LID <•,.:; |
. OOo'., o 1140 |
A Ol ill 11 .00028 |
LID 7.fi |
|
|
1 U . . 20. . |
i !00208 I2M 90207 |
'. 7-1 .00178 00210 |
2> 1.7 |
-in.' : no. |
. .00210 . .001:1:: . .0011" |
.00077 .001 11 |
2.7 1.7 .59 |
|
BO! ! |
. .inii:;:i |
.0021:, |
:,7 |
||||
|
rrltlo 1 |
:, |
: rnti, |
|||||
|
v,.-.. 20 |
.00109 00218 |
A 120 :ir, |
/. H T7 |
Ancl. 20. |
A . .OOlo'i !7:'. 1109 |
.00071 |
7. /) ':','•! 2.7 |
|
10 so. |
"127 |
.00152 .00221! |
1.2 ..",7 |
80. |
. .oirjol . .00141 |
.00120 .00211 |
1.7 |
|
A-IMTI r:iti>, :i |
|||||||
|
Angli 10. 20. to. |
A . . .OoilTI . .OII12.-. 00217 .00178 |
K, 00010 .00021 .OOOOl .0011 I .0014(1 |
/. 1> 7.7, :,.:i 27 17 1.2 |
Ang 10. 20 :io. 60. |
A . .001:17 . .ooisr, .0021 1 . .00210 . .00140 |
K, OO026 .OIHI40 00080 .00127 .00858 |
LID S.2 4.7 2.6 LT |
|
00126 |
.0022:, |
M |
|||||
|
\-|i, it |
n.ti,, 1 ::. |
Aspect ratio = 1/6. |
|||||
|
Ang |
A |
.00007 |
'-M |
Anglt. A 00020 |
.00008 |
Lin 4.0 |
|
|
.ooo.-.'.l |
OOO 1 t |
4.2 |
10 .000111 |
OOO 1 O |
iB |
||
|
001 :is |
"II. "01 t 1 |
||||||
|
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1.7 :,- |
:;o. . . .110171; I , . .00217 |
.00102 00217 IMI2S2 |
1.7 .99 .88 |
AERODYNAMICAL THEORY AND DATA
33
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Left Coefficients for Rectangular Flat Plates of Various Aspect Ratios. Units: Lbs. per Sq. rt.; Miles per Hrr |
Asp RO.-I. 1.5 2 3. 6. |
N |
^S |
s |
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IO' SO" 3O" 4O' SO" 6O' 7O~ 8U~ ai Anff/e of Incidence. |
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Rat/o of £.fft to Drag tn Rectangu- lar Flat P/ates of Various Aspect Ra- tios. |
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? f icy L |
T' Si |
FIG. 3. LIFT COEFFICIENTS FOR RECTANGULAR FLAT PLATES OF VARIOUS
ASPECT RATIOS
Angle of Incidence.
FIG. 4. RATIO OF LIFT TO DRAG IN
RECTANGULAR FLAT PLATES OF
VARIOUS ASPECT RATIOS
TABLE 4.
DISTANCE OP CENTER OF PRESSURE FROM LEADING EDGE, MEASURED IX
TEEMS OF CHORD, FOR RECTANGULAR FLAT PLATES OF VARIOUS
ASPECT RATIOS.
|
A. E. |
= 1. |
A. R. |
= 3. |
A. R |
. = 6. |
A. E. |
= 1/3. |
A. B. |
= 1/6. |
|
Dlst. |
Angle. |
Dist. |
Angle. |
Dlst. |
Angle. |
Dlst. |
Angle. |
Dist. |
Angle. |
|
.12 |
.8 |
.233 |
5.0 |
.267 |
3.0 |
.167 |
3.0 |
.289 |
2.5 |
|
.16 |
1.0 |
.267 |
7.8 |
.300 |
8.0 |
.267 |
5.0 |
.311 |
7.5 |
|
.18 |
2.0 |
.300 |
10.0 |
.333 |
10.0 |
.283 |
6.8 |
.323 |
10.5 |
|
.20 |
2.8 |
.333 |
12.0 |
.367 |
12.2 |
.300 |
10.8 |
.334 |
19.0 |
|
.22 |
3.8 |
.367 |
13.8 |
.400 |
26.0 |
.317 |
17.5 |
.345 |
49.0 |
|
.24 |
6.5 |
.400 |
17.5 |
.433 |
54.0 |
.333 |
30.5 |
.356 |
52.0 |
|
.28 |
13.0 |
.433 |
52.8 |
.467 |
73.7 |
.350 |
45.0 |
.367 |
53.5 |
|
.30 |
15.3 |
.467 |
73.7 |
.500 |
90.0 |
.367 |
47.8 |
.378 |
56.2 |
|
.32 |
18.0 |
.500 |
90.0 |
.383 |
50.2 |
.389 |
58.0 |
||
|
.34 |
21.0 |
.400 |
52.5 |
.400 |
59.5 |
||||
|
.36 |
25.0 |
.417 |
54.3 |
.411 |
60.0 |
||||
|
.38 |
28.0 |
.433 |
56.5 |
.422 |
63.0 |
||||
|
.40 |
33.5 |
.450 |
65.0 |
.433 |
64.0 |
||||
|
.42 |
39.0 |
.467 |
77.8 |
.444 |
68.5 |
||||
|
.44 |
55.2 |
.483 |
85.8 |
.455 |
72.5 |
||||
|
.46 |
73.5 |
.500 |
90.0 |
.466 |
80.0 |
||||
|
.48 |
84.0 |
.477 |
84.0 |
||||||
|
.488 |
87.5 |
||||||||
|
.SCO |
no.o |
] n Fig. 3 are plotted values of Kr against angle of incidence for various aspect ratios. In Fig. 4 the same treatment is applied to the L/D ratio.
In Fig. 5 are indicated the positions of the center of pres- sure for various aspect ratios and angles of incidence. In Fig. 6 the directions and points of application of the resultant forces are indicated for a flat plate of aspect ratio 6 — the value which is usually employed for purposes of comparison — in order to give the reader a more graphic idea of the forces at play.
In all these values it may be noted that no allowance is made for possible variation in the coefficients with size of plates, and this is probably accurate enough for all practical purposes.
Preliminary Application of Data for Flat Plates in Rudder and Elevator Design
These curves and tables give fairly complete data for flat plates and are likely to meet all the requirements of design.
|
Distance of C.Pfrom leading edge. < r« U) -Iv |
_____ |
|
______ _ |
-— -= |
===•= |
sr-=3 |
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/7 |
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Travel of Cet Pressure in |
nter of ffectang- es of it Ratios. 7— |
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1 |
ular Vartc Asp.h |
Flat Plat ius Aspec >a.** / |
|||||||||
|
R |
|||||||||||
|
•J 10' ,SO- 30' 40" SO- -Anyle of Incidence. |
FIG. 5. TRAVEL OF CENTER OF PRESSURE IN RECTANGULAR FLAT PLATES OF VARIOUS ASPECT RATIOS
It may be useful to indicate a few salient points, and to make preliminary reference to the design of flat rudders and eleva- tors.
(1) For plates of all aspect ratios when turned from zero angle, the lift increases until the critical angle or " burble point " is reached. Beyond this angle the lift rapidly de- creases, and no rudder or elevator should be employed beyond this critical angle.
34
AERODYNAMICAL THEORY AND DATA
(2) The lift drag ratio is not much improved, for flat plates at the same angles, by increased aspect ratio. For all plates the ratio reaches its maximum value at small angles, 6* or 7*. At angles still smaller it decreases, due to the predominating
Fio. 6. DIAGRAM SHOWING DIRECTION AND POINT OF APPLI- CATION OF RESULTANT FORCE IN A RECTANGULAR FLAT PLATE OF ASPECT RATIO 6 AT SMALL ANGLES OF INCIDENCE
effect of the skin friction. Plates of large aspect ratio, being more sensitive at small angles, are, on the whole, more efficient in flight.
(3) On the other hand, plates of small aspect ratio have the critical angle much later and give a wider range of action. They also give a much higher lift at the critical angle, which is important in the action of the rudder when " taxying " at low speeds on the ground.
(4) For the elevator, which is more constantly used in the air, and from which great liftine power is not required on the ground, an aspect ratio of three seems a fair compromise.
(5) For the rudder, the above considerations seem to indi- cate an aspect ratio of one or two as advisable.
(6) It should be noted that, as the angle of incidence is in- creased, not only does the force increase, but also that from the point of application of the resultant force to the hinge, giving a greatly increased moment about the hinge. If either the elevator or the rudder is placed too near the wings it
|
D • . XTN ! |
1 J |
E |
|
Rudder, Balance |
||
|
"7 T \ |
)? Aspect Pi Ratio. -g-.
*-El«voior Ploo«»-x
Fio. 7. DIAGRAMS FOR ASPECT RATIO IN RUDDER AND KLKVATUI:
necessitates large nn-.-i- for the controlling .-ur fa <•<•«, and the pilot may have to exert tremendous force at large angles.
(7) To obviate the necessity of exercising large forces on the controls, it is possible to use a balanced rudder; one in which the hinge is placed about in the position of the center of pressure at small angles. The rudder in Fig. 7 is a balanced
rudder. It should be noted that the " balance " is only ap- proximate.
Problems on Flat Plates
A rectangular flat plate 4 feet 9 inches high and 3 feet a inches long is employed as a rudder, and is placed with its leading edge at a distance of 18 feet from the center of grav- ity of the machine. The machine is traveling at CO miles an hour. The rudder is hinged at the leading edge, while the control leads are one foot from the rudder surface. (See Fig. 8.) Find (a) the frictional resistance of the rudder when
FIG. 8. RUDDER FOR PROBLEM ON FLAT PLVTKS. RCDPER is UNBALANCED AND HINGED AT LEADING EDGE
neutral; (b) its turning moment about the center of gravity when set at an angle of 10° and its resistance at that angle; (c) the tension in the control lead under the same conditions as (b).
(a) The area of the rudder = 2 X SVc X 4% = 30 square feet. From Fig. 13 in Chapter 3, we sec that the t'rictinnul re- sistance on a surface of 15 square feet at 60 miles an hour equals .0285 pounds per square foot. Thus tin- total f fictional
= 2X 15 X -0-s:' >i;- rounds.
(b) The aspect ratio of the rudder = 1.5. The distance from the leading edge to the center of pressure is given by Fig.
5. Interpolating between (A. !{. = !) illnl (A.Ii. 3), u
that the center of pressure on a plate of aspect ratio 1.5 at an angle of incidence of 10 deg. is .L'(!S of the chord from tlie leading edge. Thus the desired distance - :!',-, X .268 = .S.". It.
The moment arm about the center of gravity longitudinally (see sketch of machine) = 18 + .85 cos 10° = 18.84 fed.
The moment arm about the center of gravity laterally = .85 sin 10° = .14 feet.
By Figs. 3 and 4, K, = .00109 and L/D = 5.5. Then L, the rone peipcndicular to ilie line of ilighi. i A". I I .nnl09X 15X(60)' = 5S.!I pound,, and 1>. the reM>laiicr,= L^D/L =
58 9
= 10.8 pounds. It will be seen that turning the rudder 5*5
causes a decided increase in the resistance of the machine.
The above work a basis tor rapidlv computing
the turning moment. M = 58.9 X 18.84 + 10.8 X -14 = 1112
pound feet, taking the movements of hotli the lift, and the drag about the center of t;ra\ity.
AERODYNAMICAL THEORY AND DATA
35
(c) The turning moment about the leading edge of the rudder = 58.9 X -85 cos 10° + 10.8 X -85 sin 10° = 51 pound feet.
Moment arm of control lead = cos 10° = .986 foot.
Then, since the stress in the control lead times the moment arm must just balance the turning moment of the rudder about
51
its axis, tension in lead = — — = 52.7 pounds .986
General Considerations of Sustaining Power and Resistance of Wing Sections
We have seen that the equation for lift is
L = K7AV (1)
where Ky is a constant varying with the angle of incidence, A = area in square feet, and F = speed in miles per hour.
In horizontal flight, the lift equals the weight of the ma- chine, W, and the equation becomes
W = K,AV (2)
which can be expressed in the forms W
AV1
(3)
(4)
(5)
as may be convenient. The lift coefficient is small at small angles and increases at larger angles until the " burble " point
W
-f*-. — ^— -r^*
|
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15 14 13 ia II 10 9 ;| 6 5- |
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Characteristic Curves for R.A.F 6 Wing Sec- t/on. Wind Speed- 3O ft per- sec. DV'7.5 Units: Lbs. per Sq. ft; Miles per Hour |
3 r |
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'-• 0- a- 4- B- B' tO- /2' 14' 16- It |
Angle of Incidence. Fin. 9. CHARACTERISTIC CURVES FOR R. A. F. 6 WING SECTION
or critical angle is reached, as can be seen from the curve of a standard wing section (R. A. F. 6) in Fig. 9.
From these considerations may be deduced the following ideas, which should become absolutely familiar to every student of aeronautics:
A machine traveling fast will require, by equation (3), a small value of Ky, and hence a small angle of incidence. Con- versely, flying slowly it will require a large angle of incidence.
Sustaining a given weight, we can vary angle of incidence and either area or speed.
If we give a machine a large wing area, it will fly slowly. With a small area, it will attain a high velocity if sufficient engine power is available.
The drag equation is
D = KfAV (6)
The higher the value of L/D, the smaller will be the drag for a given lift and weight of machine at a given speed, and the less will be the power required. The ratio L/D is therefore a measure of the wing efficiency. For the R. A. F. 6, the maxi- mum value of L/D is at about 4° and at about this angle a machine would fly at its greatest efficiency.
We have here neglected all other resistances than those of the wings. These resistances will modify the drag equation and the best angle of flight. We shall deal with these modifica- tions under the Economic Laws of Flight.
Problem of Sustentation and Resistance of Wing Surface
A monoplane weighing 2000 pounds uses an R. A. F. 6 wing section.
(a) What area will it require so that its lowest speed may be 45 miles an hour?
CO
'GO ~ SS GO 65 .TO 75 SO 35 90
Speed (Miles per Hourj
FIG. 10. RESISTANCE, HORSE-POWER AND SPEED DIAGRAM
(b) What will be the drag of the wing at this speed and what will be the horse-power required for the wing alone?
(c) Assuming that the parasite resistance (resistance of the body, chassis, wires, struts, etc.) is 120 pounds at 60 miles an hour, and that it varies directly as the square of the speed, what will be the total resistance and horse-power required at this speed?
(d) If the power delivered at the propeller is 100 horse- power, what is the maximum speed available?
(a) Let A = wing area
W = weight of machine D = drag of wing P = parasite resistance R = total resistance = D + P.
From Fig. 9 we see that the maximum value of K, is .00309, at 16°. Then, since W = K,AV*, and V — 45 miles per hour,
W 2000
— . = 319 square feet.
A =
.00309 X(45)2
2000
(b) From Fig. 9, L/D at 16° = 6.8. Then D = = 294
6.8 pounds.
Since ~, horse-power is required to overcome a resistance
o / O
of 1 pound at 1 mile per hour, horse-power = —
375 375
= 35.3 horse-power to overcome wing drag at 45 miles per hour.
36
AERODYNAMICAL THEORY AND DATA
The drag of the wings can also be obtained, of course, by substituting the proper value of A", in the equation
The first method described will prove the simpler when a number of cases are to be worked out. but the second is more accurate at very small angles of incidence.
W 9ftf>ft
(c) At 60 miles an hour K, = — = g^SO? = -00174.
Fig. 9 shows us that this value of K, will be attained at an .•iii-;lp of incidence of 5.7°, at which angle L/D = 14.2.
10 = 141 pounds, and R = D + P = 141 + 120
= 14.2 = 261 pounds.
EV 261 x 60 The power required equals — r = — — : —
OYO O/O
: 41.8 horse-
power.
(d) In order to determine accurately the speed obtainable with a given power, it is necessary to plot a curve of power required at various speeds. In computing points on this curve, we assume the parasite resistance proportional to V. This is approximately true, the deviation being due to changes in resistance coefficients of body, struts, etc., as the angle at which they meet the wind changes. Proceeding on this assump- tion, P = KV. since P = 120 pounds when F = 60 miles per
hour, K = -j = .0333, and P = .0333 F1.
In Table 5 are given a few points on such a curve, com-
puted as was that for 60 miles an hour, which we just secured. A student might carry through some of these computations, checking his results against those here given, in order to make sure that the method is perfectly clear to him.
TABLE 5.
|
r |
K, |
Angle of inc. |
/C. |
L/D |
D |
P |
R |
WlM ii. i: |
Para- site II. P. |
Total II. P. |
|
|
U |
.00309 |
16.0 |
.000446 |
6.9 |
289 |
67 |
356 |
34. |
8 |
8.0 |
42.8 |
|
30 |
.00251 |
9.9 |
.0(10218 |
11.5 |
174 |
83 |
257 |
u:: |
11.1 |
34.3 |
|
|
55 |
.00207 |
7.4 |
.000156 |
13.3 |
150 |
101 |
251 |
•-2, |
1 |
14.8 |
36.9 |
|
60 |
.00174 |
5.6 |
.000122 |
14.3 |
140 |
120 |
260 |
L-J |
4 |
19.2 |
41.6 |
|
65 |
.00148 |
4.4 |
.000102 |
14.5 |
138 |
141 |
279 |
LM |
.0 |
24.4 |
48.4 |
|
70 |
.00128 |
3.5 |
.000093 |
13.8 |
145 |
163 |
308 |
•21 |
.1 |
30.4 |
57.5 |
|
75 |
.00111 |
2.8 |
.000087 |
12.8 |
156 |
187 |
34:1 |
31 |
1 |
37.4 |
68.6 |
|
80 |
.00008 |
2.2 |
.000082 |
11.9 |
168 |
213 |
381 |
.'!.-, |
.7 |
45.5 |
81.2 |
|
85 |
.00087 |
1.8 |
.000081 |
10.7 |
187 |
241 |
428 |
42.5 |
H4.6 |
97.1 |
|
|
90 |
.00077 |
1.3 |
.000081 |
9.5 |
211 |
270 |
481 |
50.6 |
64.8 |
11C.4 |
References to Chapter 4
CONTROVERSIAL ASPECTS OF VALVES OF COEFFICIENTS FOR
FLAT PLATES OF VARYING S/ZBX;
Notes on the Dlinenslonril Theory of Wind Tunnel Experiments. E. Buckingham ; Reports ou Wind Tunnel Experiments In Aerodynamic*, Smithsonian Miscellaneous Collections.
" Critical Speeds for Flat Disks in a Normal Wind," J. C. Hunsaker and E. B. Wilson ; loc. cit.
Bulletin de I'lnstitut de. Koutcltino, Moscow, 1912.
DATA FOR FLAT PLATES.
"The Resistance of -\ir and Aviation," G. Eiffel, translated by J. C. Hunsaker.
DATA FOR K. A. F. 6 WIXO SECTION.
Reports on Tests of Four Aerofoils. Report of the British Advisory Committee on Aeronautics. l!H2-1!ii::. Report No. 72.
Chapter V
Comparison of Standard Wing Sections
The National Physical Laboratory has often been criticized in the past for not stating, in spite of its voluminous reports, what the " best " wing section is. There is no such thing as a " best " section. There are very bad wing sections giving abnormally high resistance and low lifting power; there are
oratories. German laboratories have done a great deal of work with reference to propeller sections, and also have car- ried out tests on wing shapes of a great many forms, but the present selection is representative and sufficient for all prac- tical purposes. When a designer wishes to introduce slight
Each Aspect Ratio 6
Eiffel I3
. .
ta
Comber -?|i TyP'Cd Plodn9 °f Win9 S*»ra
Eiffel 37
Eiffel 33 M 3 ?
Eiffel 35 . ?
Eiffel 36 -
.088
= Cambers
0/6
Surface = ooe
FIG. i.
sections giving high lift at big angles of incidence, but too great a resistance at small angles, others giving a low maxi- mum lift, but very suitable for high speeds; others give a very- stable motion of the center of pressure, but sacrifice aerody- namic efficiency. The selection of any particular form depends on the performance required of the machine in view.
As the result of several years' practice, modern machines all tend to a few types of wings, although there are numberless small modifications by individual designers. We shall attempt to classify and give data for what may be called Standard Sec- tions, using the (pounds, per square foot, per miles hour) system of units for force coefficients.
Representative Wing Sections Selected
These have all been taken from the N. P. L. and Eiffel lab-
variations in the standard forms, it will be always necessary for him to submit his variation to a special test, so that a com- plete collection of every form that has ever been submitted to publication would be useless.
The sections we have selected are: R. A. F., No. 3, 4. 5, 6 and Eiffel 13 bis., 32, 33, 35, 36, 37. In Fig. 1 these forms are represented on a uniform plan, with complete dimensions, and values of camber. The camber of the upper surface is defined as ratio of maximum height above chord to chord length, and the saiMu definition holds for the lower surface. The hollowing out of the lower surface, as we shall see later, has little importance — it scarcely affects the Lift/Drag ratio or the angle of inci- dence for the burble point, but it increases the lift about 17 per cent at any angle when a plane lower surface is cambered out to a camber of 0.06. An increase in lift obtained in this
38
AERODYNAMICAL THEORY AND DATA
way involves a dangerous weakening of the wing. In Dr. J. C. Hunsaker's opinion, a decrease of camber below 0.05 or an Increase of camber above 0.08 for the upper surface is dis- advantageous in practice. Broadly speaking for the incidence
LJ ft/ Drag for Wings Tested at the 1(1. PL.
B" 8~ nr t?- Tf
Angle of fnadencf FIG. 2.
/6" 16' Scr
giving maximum Lift/Drag ratio, the lift for upper surface camber of 0.08 may be twice as great as for a camber of 0.05, but the Lift/Drag ratio is diminished by nearly 25 per cent. We shall deal later with the effects of varying the position of the maximum ordinate of the upper surface; the best position for this maximum ordinate is about % of the cord from the leading edge.
Complete Data Presented
In Figs. 2 to 8 are given curves for Lift, Drag, Lift/Drag
so /a te
14
Lft/Drag for Wings Tested by Eiffel
a- icr of Incidence.
Fio. 3.
16- Iff
and Center of Pressure motion for these wings. In Fig. 0 a comparative table has been drawn up giving maximum Lift coefficients and corresponding angles; maximum L/D and cor- responding angles; the angle of incidence and the correspond- ing L/D for a lift coefficient of value .00086, and also the value of V for the tests from which these rr-ulN IKIVC been taken. This is as complete data as the designer can po^-ihly rc<|nin>. The aspect ratio for all these sections is G.
We shall deal later witli the effects of variation of scale and speed. At this point it is sufficient to state that whereas the lift coefficient is unaffected by variation in the product IV- *f>an of wing in feet times velocity of relative wind in feet per
second — the drag coefficient and the L/D ratio are both im- proved by increase in IV. The N. P. L. tests and Eiffel's testa are unfortunately not concordant in this respect. Eiffel's ex- periments were made in a larger wind tunnel and at higher speeds, aud if the same wing were tested at the N. P. L. and Eiffel's laboratory, the latter would give better results for bott drag and L/D. Since in an actual machine the product IV will be very much greater than the values of either laboratory, the full size performance will always be somewhat better than
Travel of Center of Pressure in Wings Tasted at the ft/PL.
4- 6~ 8' IO' !£• 14" 16- IB" SO'
Angle of Incidence
FIG 4.
the one deduced from these experimental results, particularly where an N. P. L. section is used. Employing the exact figures of our curves, the designer will be proceeding on a very con- servative basis. Certain experiments of the X. P. L. — which we shall deal with fully later — permit us to make approxi- mate corrections. These have been made in the last column of Fig. !».
Travel of Center of Pressure in Wings Tfstad Oy Eiffel
sr 4- & er tcr ? w
Angle of Incidence. FIG. 5.
te
^o•
Points of Jiitrrr.«t in Considering a Wing Section
In discussing the merits of a section, there are so many points at issue that it is only in an actual design that it is possible to enter fully into all. Study of the data submitted will be of much more use if the following features are always kept in mind :
(a) The maximum value of L/D, and the corresponding Kr.
AERODYNAMICAL THEORY AND DATA
A macliine in normal horizontal flight will generally be navi- gated at the angle giving the best L/D ratio, which is there- fore most important from an efficiency point of view. The
FIG. 6.
value of the lift coefficient at the best L/D is of importance. The greater the lift at this ratio the smaller the area of the wing surface required for a given load. With a heavy ma- chine, such as a flying boat, or an armored battleplane, a big
.00300 .0006
LIFT & DRAB
COEFFICIENTS FOR
VARIOUS WINGS TESTED
AT THE N. P. L
Units: I bs. per Sq. Ft. Miles per Hour
.00250 .0005
•00200 .0004
.00/50 .0003
4" 6° 8° 70° Angle of Incidence
FIG. 7.
lift coefficient is essential. With a speed scout or a light re- connaissance machine, a small value of K, at best L/D is usual. With a sufficiently powerful motor a small wing surface may be used and a great speed attained.
(b) The maximum KT has a bearing on a number of points.
The greater the maximum Ky the slower is the speed at which a machine may land. If the maximum Kf, or simply large values of Kf, are accompanied by a good L/D ratio, then the machine will be efficient and ready in climbing — though the best angle of climb is by no means the angle of maximum KT, as we shall see later in considering the economic laws of flight.
(c) The maximum Kr should occur at as high an angle as possible, so as to give a big range, and possibility of a large speed variation.
(d) The angle of maximum lift is termed the burble point,
.00350 .0001
1.1 fT ANO OKfAG COEPVICICMTS FOR
VARIOUS VV1MG3 TEST El BV Eifrci_
4° e' a- to- \ef
AHOlf. OF iNCIOeMCE.
FIG. 8.
i*' «r
as we know, and also the " stalling " angle. It is very im- portant to consider what the shape of the lift curve is in the neighborhood of this angle. If the lift past the burble point falls off very rapidly, the pilot may easily stall the machine. He may increase the angle of incidence too far and find his sustaining power fall off dangerously. A wing with a flat lift curve at the burble point will avoid such danger.
(e) The L/D ratio at small angles of incidence and small values of K7 determines whether the machine is really suitable for high speeds. We have arbitrarily chosen K, = 0.00086 as the value of comparison, and it can be seen from the tables how widely L/D varies at this point. A machine with good maximum L/D and a high maximum Kf might be totally in- efficient at high speeds.
(f) The movement of the center of pressure is important at low angles. If at low angles the center of pressure moves steeply back towards the trailing edge, the machine will have a tendency to " dive," provided for, of course, by fixed stabil- izing surfaces on modern machines. If the center of pres- sure remains stationary, on the other hand, as in Eiffel 32, it will maintain its attitude at low angles, and will not tend to dive even with small stabilizing surfaces and inefficient or inoperative elevator. Similar considerations apply to " stall- ing" angles.
(g) In addition to the separate consideration of these points, there yet remains the appraisal of the wing through-
40
AERODYNAMICAL THEORY AND DATA
FIG. 9 COMPARATIVE TABLE OF STANDARD WING SECTIONS LIFT COEFFICIENTS IN LBB. PER Sq. FT.; MILES PEE HK. ASPECT RATIO 6
|
CAMBER |
Wrao |
MAX. Ky |
MAX. LID |
K, -.00086 |
Max. LID |
|||||||
|
— corrected |
||||||||||||
|
Span of |
app. to full |
|||||||||||
|
Wins in |
size mach. |
|||||||||||
|
Feet x |
in actual |
|||||||||||
|
Relatire |
Sight in |
|||||||||||
|
Wind in Ft/Sec. |
Upper |
Lower |
Section |
Angle |
K, |
LID |
Angle |
K, |
LID |
Angle |
LID |
accordance with eip'ts |
|
IV. |
at the |
|||||||||||
|
N. P. L. |
||||||||||||
|
16 |
0.081 |
0.036 |
Eiffel 13 Bis. |
4.3° |
0.00129 |
13.6 |
1.9° |
11.4 |
14.5 |
|||
|
49 0.079 |
0.030 | " 32 |
3.0° |
0.00103 |
18.2 |
2.2° |
18.0 |
18.2 |
|||||
|
30 0.092 |
0.033 |
" 33 |
16.8° |
0.00336 |
7.2 |
3.5° |
0.00152 |
13.4 |
-0.2° |
9.5 |
13.6 |
|
|
37 0.080 |
0.050 |
" 35 |
14.6° |
0.00296 |
5.2 |
4.8° |
0.00165 |
18.7 |
0.5° j 10.6 |
18.9 |
||
|
37 " 088 |
0.022 |
" 36 |
3.1° |
0 00142 |
14 3 |
0.0° |
13.1 |
14.3 |
||||
|
37 | 0.087 |
0.041 |
" 37 |
14.1° |
0.00288 |
4.0 |
-0.8° |
0.00086 |
20.4 |
-0.8° |
20.4 |
20.4 |
|
|
6.3 |
0.088 |
0.032 |
R.A.F. 3 |
15.7° |
0.00347 |
7.8 |
5.0° |
0.00195 |
14.3 |
-0.1° |
7.4 |
18.1 |
|
6.3 |
0.075 |
0.022 " 4 14.0° |
0.00304 |
8.0 |
4.2° |
0.00142 |
13.8 |
1.4° |
10.3 |
19.2 |
||
|
6.3 |
0.075 |
0.022 |
" 5 |
14.2° |
0.00288 |
7.0 |
4.2° |
0.00142 |
13.8 |
1.4° |
11.0 |
19.2 |
|
6.3 |
0.076 |
0.008 |
" 6 |
15.4° |
0.00310 |
7.8 |
4.9° |
0.00157 |
14.6 |
1.9° |
10.4 |
18.5 |
out its performance. The designer must see how far one point of excellency conflicts with other requirements; what the range is. The ideal wing would give great lift and efficient climb, high efficiency in normal flight, and high efficiency at maximum speeds.
(h) A wing may be entirely satisfactory from an aero- dynamic point of view, and yet fail to satisfy as regards structural requirements. In Fig. 1 is shown a typical arrange- ment of the wing spars. It is important that the points where the wing spars are likely to be placed, the wing should have sufficient thickness to permit the use of reasonably deep spars without exaggerated width. A wing may indeed have sufficient thickness at two points for good spars to be placed, yet these points may be totally unsuitable. They may be too near to- gether, so that a weak overhanging construction or excessive spar loading is the result, or too far apart so that too long an unsupported rib section results.
There could be no better plan for the reader to whom the subject is comparatively new than to go through all the wing sections presented with reference to these eight points.
Consideration of a Few Sections in Common Use
We shall consider a few sections in this manner ourselves.
Take Eiffel 37, for instance. Its maximum L/D — the high- est of any section considered here is 20.4, occurring at — 0.8°. which is still a good many degrees from the angle of no lift.
though its center of pressure motion at this point is rapid. Its iiinxinniin AT,, is small (0.00288), with a L/D of only 4.0. Surh a machine would be unsuitable for heavy loading, but would be excellent for a high speed racing machine, in which little vari- ation in speed would be required. It would, however, have to land at comparatively high speed because of the low maximum KT. The structural difficulties would be considerable, because there is insufficient thickness in the wing for the rear spar.
Eiffel 32 is an excellent all-around wing. Its maximum L/D, unconnected for scale, is high 18.7. It has fairly good values of L/D for high lift coefficients. Its center of pressure motion is almost nil.
E. A. T. 3 has the highest value of K}. (0.00195) at maximum L/D. It would be suitable for a heavy flying boat. At small values of K,, on the other hand, its L/D is very small. It would be unsuitable at high speeds. Structurally it is ex col- lent.
R. A. F. 6 would also be a good all-around wing, noi ciipa- ble of sustaining the heavy loads of R. A. F. 3, or given the high speed of Eiffel 37. but compromising usefully.
References for Chapter 5
les Recherches Sur la Resistam v British Report. 1011' nil::. No. TL'. i:<>p<>H ,,n the Results of 'IVsts
"if I'lilM' AiT'il'nils.
Eiffel: " Nouvclles Recherches Sur la Resistance iif 1'Air et 1'Avln- tlon."
Chapter VI
Effects of Variation in Profile and Plan Form of
Wing Sections
As we have seen in Chapter 5, numberless variations are pos- sible in the profile of wing sections. A slight variation in the profile may, however, introduce considerable changes in the aerodynamic properties of a wing, and necessitate a wind tun- nel test. Experiments conducted at the various laboratories on variations of camber, of position of maximum ordinate, on the thickening of leading and trailing edges, and so forth, have therefore rather a qualitative than a quantitative significance. But the results obtained deserve attention, and may serve as a guide to useful modifications. The most important of these ex- periments are summarized here, and a fuller reference list is appended.
Effect of Variation of Position of Maximum Ordiuate in
a Wing Section of Plane Lower Surface, and
Constant Camber 0.100 for Upper Surface
These experiments of the N. P. L. are mainly interesting be- cause they indicate where approximately the maximum ordi-
RATIO .500
B
.163
FIG. 1. SECTION'S USED IN INVESTIGATING VARIATIONS OF POSITION OF MAXIMUM OIJDINATE
uate of a section should be to give the best possible L/D ratio. In Fig. 1 are shown a selection of three of the sections tested. They were all developed from one section by altering. the position of the maximum ordinate and compressing or ex- panding the other ordinates to correspond. The Lift and Lift/Drag curves for these sections show considerable varia- tions in values as can be seen from the following table:
Wixu
TABLE 1.
SECTIONS Pi, AXE LOWER SURFACE. UWEII SURFACE CAMBER 0.100. POSITION OF MAXIMUM ORDINATE VARIED.
Ratio of position of maximum ordinate to . chord length.
500 332
168
Maxi-
mum
L/D.
11.2
13.G
11.0
|
Angle for maxi- mum L/U. 8° 4° 4° |
Maximum K:i in Ibs., sq. ft., miles/ hour, units. .00317 .00338 .00206 |
Angle for maxi- mum K" 18° 16° 8.5° |
We see that the maximum L/D for section B with a ratio .332 is as high as 13.6, while for section C, where the maxi- mum ordinate is well forward, it sinks to 11. Again, the max- imum lift for B is about 50 per cent greater than that for C. The angle of maximum lift also appears much earlier when
the maximum ordinate is nearer the leading edge. A further inspection of the N. P. L. curves also shows that at the point of maximum lift, a slight variation in the ratio changes a smooth burble point into a dangerously steep one.
The main result of the investigation is to show the care re- quired in altering even slightly the position of maximum ordinate for a given section, and also to indicate that the best position is about one-third from the leading edge.
Behavior of Wings with Reverse Curvature at the Trailing Edge
This constitutes a far more important question than that of the preceding paragraph. It would considerably simplify
|
NO. OF TAIL |
1 |
Z. |
3 |
4 |
|
Amount ta.il is r<xiseii 0.3 a- fnxction of chpra( |
DOO |
0.011 |
0.027 |
0.057 |
Fi.;. 2.
MODIFICATIONS OF THE R. A. F. 6 WITH UPTURNED TRAILING EDGES
airplane design, from the point of view of statical and dy- namical stability if the position of the centre of pressure or of the vector of resultant force on the wing did not vary its position so rapidly with change in the angle of incidence. It may be said that as a general rule for the usual angles of flight that when the angle of incidence decreases the centre of pressure on a wing moves far back, and the resultant force tends to dive the machine, decreasing the angle of incidence still further. When the angle of incidence increases, the centre of pressure moves forward and the resultant force tends to stall the machine, increasing the angle of incidence still fur- ther. "We shall deal fully with this important point when con- sidering the general statical equilibrium of the airplane.
Among other means of attaining stability, wings have been designed with a slight reverse curvature at the trailing edge, \\-\ncli have been very successful in keeping the centre of pres- sure motion within narrow limits. It is important to us to see what sacrifice of sustaining power and efficiency reverse curva- ture entails.
At the N. P. L. a section (No. 1) very similar to that of the R. A. F. 6 was employed, and three reversed curvature forms 2, 3, 4 were developed from it by turning up the trailing edges through successively increasing distances while keeping the thickness of section unaltered. The point of inflexion, at which the reflexing began was in each case 0.4 of the chord
41
42
AERODYNAMICAL THEORY AND DATA
from the trailing edge, though this could be varied to 0.2
without much effect. These sections are illustrated in Fig. 2.
The trnvol of the centre of pressure is shown in Fig. 3 for
|
•<* o |
|||||||||||
|
0 f . |
^ |
MOD)FICATtOM60f R.A F. 6 |
|||||||||
|
"^^_ |
I |
||||||||||
|
U a |
--^, |
~-^^. |
'— — |
2 |
|||||||
|
0 -m |
— |
— |
*^ |
XJ |
3 4 |
||||||
|
/ |
"1^ |
*=: |
=rzn |
5^~ |
Eiffel<32 |
||||||
|
K |
^^s* |
c?^ |
|||||||||
|
*- i |
z |
||||||||||
|
o So |
6° 6" 10 Angle of lnciden.ce.
FIG. 3. TRAVEL OF CENTER OP PRESSURE FOR A SERIES OF WINGS WITH UPTURNED TRAILING EDGES
all five sections. The curves for the N. P. L. sections show that as the elevation of the trailing edge increases, the centre of pressure motion becomes less marked in its movement toward the trailing edge, than stationary, and finally moves toward the leading edge. This is certainly satisfactory from the stability point of view, but the questions of efficiency and maximum lift have also to be considered. The following are the values obtained for maximum L/D and maximum K, :
Section.
1
2
3
4
TABLE 2.
Amount tail
Is raised
as fraction
of chord.
0.000
0.011
0.027
0.057
Maxi- mum L/D. 16.1 10.0 14.3 13.0
Maxi- mum K,
.0:!20 .0294 .0282 .0245
It can be seen that as the rear edge is turned up the L/D and the maximum K, both decrease progressively.
The main conclusion of the British investigators was that with an elevation of the rear edge of about .037 of the chord, the centre of pressure can be kept stationary, but with a loss of 12 per cent, of the maximum L/D and 25 per cent, loss of the maximum possible lift. This would be too great a sacrifice for the sake of stability and the designer would find other methods of stabilization such as the use of decalage in biplanes and negative stabilizers far more useful.
Eiffel has, however, investigated a section with a very slightly reversed trailing edge (Eiffel No. 32 Lanier-Law- ranee, details of which have been given in Chapter 5), which is far more satisfactory and in wide use. Its maximum L/D is about 18.2, maximum lift coefficient is about .0033, and it has an excellent working range. The centre of pressure motion is almost nil between 0 degrees and' 10 degrees of incidence, and such a wing would certainly not tend to dive a machine, although it is not very good at stalling angles. Its shape offers certain constructional difficulties in the region of the rear spar.
Effect of Thickening the Leading Edge of a Wing Contrary to a somewhat common conception, the thickening
Fio. 4. SECTIONS EMPLOYED IN INVKSTK;ATIN<; KKKWTS OK Tine KKNIM; I.KADI.VG Ki/«,
of the lending edge as shown in Kig. I \vn< distinctly disac!
vantageous, the decrease in efficiency progressing proportion- ately to the thickening.
Effects of Thickening Wing Towards the Trailing Edge
Thickening towards the trailing edge is sometimes advan- tageous from the point of view of structural strength, and experiments have been conducted to see the loss in aero- dynamic efficiency such thickening involved. The sections em-
FIG. 5. EXPERIMENT OF THICKENING THE TRAILING EDGK OF
WING
ployed are shown in Fig. 5. It appears from these experi- ments that the lift coefficient at a given angle of incidence is not much affected at angles greater than 7 degrees but that at smaller angles of incidence the lift coefficient is actually a little greater for the thickened sections. The maximum Lift/Drag steadily diminishes as the trailing edge is thick- ened:
TABLE 3.
Section.
1
2
3
4
Maximum L/D.
l::.2
. 13.4 . 14.2
14.6
" Phillips Entry "
As shown in Fig. 6, the section R. A. F. 4 was modified into the R. A. F. 5 to give the well-known " Phillips Entry." This
R./VF S, -PHILLIPS CNTRY"
FIG. 6. MODIFICATION OF R. A. F. 4 WING TO GIVE PHILLIPS
ENTRY
modification was found to have no effect on the aerodynamic properties of the wing, an important consideration in view of the fact that numerous attempts have been made to utilize this modification.
Effects of Varying Aspect Ratio
Fbppl's and Eiffel's experiments have dealt with cambered plates; the N. P. L. has investigated the effect of varying aspect ratios on a practical wing section rectangular in plan
FIG. 7. WING SECTION' EMPLOYED AT THE N. P. L. IN INVESTI- GATION OK KKKECTS OF VARYING ASPECT K.vno
similar to the Bleriot XI bis which is shown in Fig. 7. For a more or less accurate understanding of tin- pliei'nmena ac- companying such variation, it is necessary to consider pres- sure distribution, but for design it is more important to bear in mind the simple results of this investigation : As aspect ratio increases
(1) The maximum L/D ratio improves, the corresponding angle of incidence remaining sensibly the same, and the L/D at other angles improves also.
(2) the drag diminishes.
(3) the lift cocflicicnts at all except very small angles and the maximum lift coefficient remain practically constant; the
AERODYNAMICAL THEORY AND DATA
43
maximum lift coefficient occurs at a smaller angle of in- cidence. (4) the angle of no lift occurs at smaller positive angles, or
larger negative angles as the case may be. Although the Bleriot wing tested by the N. P. L. was of practical form, it is not commonly employed in modern con- struction. The correction tables (Tables 4 and 5) are solely based on results derived from it, and it does not at all follow that similar corrections would apply to wings of other form. In default of other experimental work, however, such correc- tions can be applied with probably a fair degree of accuracy. The values for aspect ratio of 6 are taken as a standard of comparison, this being the aspect ratio used for so much ex- perimental work on wing sections.
TABLE 4.
APPROXIMATE CORRECTIONS FOR MAXIMUM L/D WITH VARIATION OF ASPECT RATIO.
Ratio
of maximum L/D
Aspect to maximum L/D
ratio. at aspect ratio 6.
3 .72
4 .82
5 .92
6 1.00
7 1.08
8 1.11
The following table shows the ratio of drag for various as- pect ratios to drag for aspect ratio 6 as unity :
TABLE 5. APPHOXIMATE CORRECTION FOR VALUES OF R r WITH VARIATION OF
ASPECT RATIO.
Angle of Incidence.
0
2
4
6
10.. 12.. 14.. 1C..
18..
|
3 |
4 |
8 |
|
1.12 |
1.05 |
1.00 |
|
1.15 |
1.90 |
1.02 |
|
1.13 |
1.022 |
1.10 |
|
1.11 |
l.O.'il |
1.0:i |
|
1.22 |
1.0-10 |
1.01 |
|
1.04 |
1.047 |
1.06 |
|
l.SO |
l.O.-iG |
1.11 |
|
1.14 |
1.071 |
1.02 |
|
1.17 |
.94 |
l.OD |
|
.876 |
1.130 |
.91 |
Aspect Ratio. 6
1 1 1 1 1 1 1 1 1 1
7 1.10
1.00
1.00
.91
.89
.88
.98
.92
.85
1.05
8
1.00
1.05
1.00
1.14
.91
.91
.99
.89
1.01
1.20
Choice of Aspect Ratio
In selecting ratio for an airplane many other considera- tions enter besides those of aerodynamic efficiency. Thus as aspect ratio and the span of the wings increase, the heavier the structure becomes for the same strength. This involves heavier bracing and more structural head resistance; the in- crease in weight itself reduces the aerodynamic efficiency indi- rectly. Hence if the aspect ratio were increased to an exag- gerated extent, structural difficulties would more than counter- balance the gain due to this increase. The question is too com- plex for theoretical treatment or for definite rules. Later in the design of a standard machine, comparative designs will be made for various values of aspect ratio.
For preliminary design, the best method of fixing aspect ratio is to follow standard practice, and this would indicate:
5 to 1 aspect ratio for monoplanes and small biplanes.
6 to 1 or 7 to 1 for large biplanes.
Effects of Raking the Plan Form of a Wing
Experiments on the effect of raking the plan form of a wing have been conducted by Eiffel in France and FSppl in Ger- many, references to which are given at the end of this section. Unfortunately, their investigations were mostly on circular wings, were somewhat contradictory, and their results varied with different cambers.
In the experiment which Eiffel conducted on a practical wing section, Coanda Wing, Eiffel No. 38, as illustrated in Fig. 8, the raked wing was decidedly superior to the rectangu- lar form into which it was cut down. Nor can this improve- ment be due to variation in aspect ratio which is negligibly small. The ratio of maximum L/D was about 1.2 to 1.
It would seem therefore that experiment is in agreement with practice in imputing certain advantages to raking. But in view of the variation in results with wings of different
|
J.5^ |
_ „ J x-x . |
|
|
-»|,56|— |
. — ~- i — |
|
|
H 0*20 '' n |
in
FIG. 8. SECTIONS EMPLOYED IN EIFFEL'S EXPERIMENTS ON " RAKING "
camber, it would be unsafe to employ a correction ratio of 1.2 in maximum L/D for the raking of any other wing, say an R. A. F. 6 section, until there has been further investigation of this point.
Swept Back Wings
Another variation in the plan form of wing sections, very largely employed on German machines of recent type, and also on one or two American machines, is that of swept back wings. Swept back wings are mainly used to give lateral stability. It has also been thought that their arrow-like form gave them an increased aerodynamic efficiency, and that longitudinal stability was also improved by their employment. We are not at present concerned with lateral stability. Aerodynamically a recent investigation at the Massachusetts Institute of Tech- nology shows a progressive decrease in efficiency with in- creased sweep back. As regards longitudinal stability the ac-
18'
1 — '.— f
4-
V-"
FIG. 9.
WINGS USED IN EXPERIMENTS ON SWEPT BACK WINGS
tion is peculiar and not at all so satisfactory as that of the wings with reversed trailing edges.
An R. A. F. 6 wing, originally of aspect ratio 6 was em- ployed and swept back as shown in Fig. 9. The results of the investigation are summarized in Table 6 :
TABLE 6.
Section.
1
2
3
4. .
Angle of
incidence Maxi-
Sweep for m.ixi- mum
back, mum L/D. L/D.
0 4° 17
10 4° 10.5
20 4° 16.2
30 4" 12.8
|
Ky for maxi- mum L/D. .00143 .001 :!0 .00129 .00120 |
Angle of incidence for maxi- mum Kf. 14° 16° 16° 17° |
Maxi- mum K .00288 .00276 .00276 .00266 |
44
AERODYNAMICAL THEORY AND DATA
Up to 20 degrees sweepback, it can be seen that the loss in efficiency is not so great, but the 30 degree entails a loss for which good lateral stability would scarcely compensate.
TRAILING EDGE
6'
a°
flnylt of If ci<* eni e
Iff
16'
FIG. 10. MOVEMENT OP CENTER OF PRESSURE FOR WINGS WITH VARYING DEGREES OF SWEEP BACK
The centre of pressure motion is illustrated in Fig. 10. It has the same peculiar characteristic for each of the wings. At small angles the centre of pressure moves backward, thus producing diving, but at large angles the centre of pressure moves forward, thus tending to stall the machine. Longi- tudinal stability is thus not secured.
Negative Wings Tips of Swept Back Wings; Effect on Longitudinal Stability
Swept back wings with negative wing tips have been suc- cessfully employed in German machines; and in the Burgess- Dunne, without the use of tail surfaces. Such wings certainly give a great degree both of longitudinal and lateral stability, but at some sacrifice of efficiency. Experimental results, ex- cept for complete airplane models, are not available, but a simple theoretical discussion at this stage is instructive; this involves the application of the first principles of mechanics, yet always presented considerable difficulty. It also gives us the opportunity of considering the stabilizing influence of tail surfaces in an elementary manner.
Consider the two arrangements of Fig. 11, A and B, one
"Ftfrce on Rwitive •Tail Surface-l
B
! Force on < ; ta.il 5urfa.ce' I
r
FIG. 11. DIAGRAM TO ILLUSTRATE VARIATION OF RKM-I.TANT FORCE WITH POSITIVE AND NKGATIVE TAIL SURFACES
with a positive tail surface, the other with a negative tail sur- face. We will assume the forces on the wing and on the tail to be vertical for simplicity's sake, although this would not actually he the ease, with positions of forces and centre of
gravity as in sketch. Assume the force on the wing to be 10 times that on the tail. Then in case A moments about centra of gravity are:
(10Xl)-f-(25Xl)=35 *n a divmg or counter clock- wise direction. The resultant must be aft of the centre of
qc
gravity, and since its value is 10 + 1, it is — = 3.18 feet aft
of the centre of gravity between the two forces on wing and tail.
For ease B moments about centre of gravity are: (10X1)— (25X1)=— 15 in a stalling or clockwise di-
15
rection. The resultant will now be — = 1.67 feet forward of
y
the centre of gravity and forward of the force on the wing.
A negative tail can thus convert a diving moment into a stalling moment at small angles. At large angles of incidence the negative lifting surface will become positive and may be used to convert a stalling moment into a diving moment. A negative tail surface can thus be suitably adjusted to give lon- gitudinal stability at all angles within the flight range.
Similarly for a machine with swept back wings and nega- tive wing tips, as shown in Fig. 12, at an angle of 1 degree incidence for a positive section A-A, the force has a counter-
SECTION KT Force on Negative Clement at B B
A'A\ IrVootuciog Stalling Moment
JAbout t he Center of G
I " of Gi-o-vity ^ B B""
Force on Fbsitive Element at A" A FVoiiucing Divina Moment About the Center of ph>.vity
FIG. 12. DIAGRAM TO ILLUSTRATE STABILIZING EFFECT OF BA< ic WINGS WITH NEGATIVE WING TIPS
clockwise moment about the centre of gravity tending to dive the machine. For a negative section B-B, the force has a stalling moment about the centre of gravity which prevents diving action. Similarly, at large angles of incidence the positive surfaces of the wing may tend to stall the machine, while the negative wing tips then assume a positive action and counteract the tendency to stall. Thus if the wings are sufficiently swept back and the negative surfaces powerful, static longitudinal stability can be secured.
The negative surfaces having so small an arm compared with negative tail surface must have a much larger surface than the latter. Consequently such an arrangement must be aerodynamically inefficient. This may be compensated for by the fact that no structural extensions to tail surfaces are neces- sary in a machine of this type.
AERODYNAMICAL THEORY AND DATA
45
References for Part I, Chapter 6
EFFECT OF VARIATION OF POSITION OF MAXIMUM ORDINATE IN A WING SECTION OF PLANE LOWER SURFACE AND
CONSTANT CAMBER FOR UPPER SURFACE British Report 1912-1913. No. 72. Section (1).
OF WINGS WITH REVERSE CURVATURE AT THE
TRAILING EDGE British Report 1912-1913, page 85.
Supplement to Eiffel's Resistance of Air and Aviation, page 151 " Nouvelles Recherches sur la Resistance de 1'Air et 1'A
Eiffel, page 114.
vlation."
EFFECTS OF THICKENING THE LEADING EDGE OF I WING British Report 1912-1913. No. 72, page 75.
EFFECT OF PHILLIPS ENTRY Loo. Oil., page 70.
page
EFFECTS OF THICKENING TOWARDS THE TRAILING EDGE Loc. Cit., page 77.
EFFECTS OF VARYING ASPECT RATIO
O. Foppl, Zeitschri/t fur Flugtechnik, April 30. 1910.
O. Foppl, Zeitschrift fiir Fluyteclmik, August 13 1910
British Report 1911-1912. No. 62, page 74.
Eiffel (Hunsaker). "The Resistance of Air and Aviation," 143-146.
Eiffel. " Nouvelles Recherches sur la Resistance de 1'Alr et i'Avia- tiou," page 138. EXPERIMENTS ON "RAKING" THE PLAN FORM OF A WING
•' Nouvelles Recherches sur la Resistance de 1'Air et 1'Aviation " Eiffel, page 141.
" Mitteilungen aus der Gb'ttinger Modeiversuchsanstalt." Sonderab- druck, Zeitsclirift Jilr Flugtechnik. 1910, Heft 20 ; 1911, Heft 7, 13, 14. SWEPT BACK WINGS
H. E. Rossell and C. L. Brand.
"Wind Tunnel Experiments in Aerodynamics," Smithsonian Miscel- laneous Collections. Vol. 62, No. 4.
Chapter VII
Study of Pressure Distribution
For general purposes, a knowledge of lift, drag and the position of the vector of resultant force at various angles of incidence is as much aerodynamical data as the designer re- quires with reference to a wing section. But an investigation of pressure distribution bears directly on an understanding of the following important points :
1. The variation of stresses in the covering fabric of a wing,
due to the unequal distribution of pressures.
2. The great efficiency of a cambered surface as compared
with a flat plate.
3. The analysis of the forces at play and their exact bearing
on efficiency, and on the position of the resultant vector.
4. The relative importance and the inter-dependence of the
two surfaces of a wing.
5. The effects of varying aspect ratio.
6. The variation of lift and drift with speed and size of
model.
It is evident, therefore, that the question is not of purely scientific or academic importance. Much useful work has been done in this direction by Eiffel and the N. P. L., and a great deal still remains to be done.
Methods of Obtaining Pressure Distribution
The mapping of pressure distribution is a lengthy process requiring numberless readings. It is fully described in the
Norma.1 Suction Force
tam/sonent Fttrallel to MnA
Ancle of IncideKcc.— Direction
Component* cf Pressure on Upper Surface .
Drtctmrr e/ tvjnit
Mor/nal Preaai/re force,—
IL
"Component PfrfrendKuUrto i Components of Pressure Of Lotvcr Svrfo.ee.
Fro. 1. DIAGRAM TO ILLUSTRATE How THE FORCES ON UPPER AXD LOWER SURFACES ASSIST EACH OTHER.
N. P. L. reports, and we shall only summarize briefly the methods employe'!.
Holes of '/„ inch diameter are drilled in the \\intr where required, normally to its surface, and are rl-.igged with plasti- cine, excei t the one under observation. The hole in use is connected by a length of very tliin hypodermic syringe tubing, too small to cause disturbance, with a three- way cork. A pilot
and static pressure tube is placed in the channel where the flow is undisturbed by the presence of the model. The static pressure tube is permanently connected to one arm of the usual manometer; the other arm can be connected alternately by means of the three-way cock either to the pitot tube or to the hole drilled in the wing section.
The manometer can be thus made to read either the velocity head of the wind, or the difference in pressure between the static pressure of the channel, and the pressure on the wing at the point considered; and a direct comparison between these two quantities is immediately possible. Great care has to be exercised in obtaining values of pressure distribution which correspond to a constant value of the wind velocity, and in maintaining the same direction of the pitot tube relative to the wing.
Over the upper surface of a wing there will be suction, on the lower surface pressure, and we shall indicate the exact distribution in this section. In Fig. 1, the suction force normal to the upper surface, and the pressure force normal to the lower surface, are represented diagrammatically for the same position on the chord. If these forces are resolved along the line of the relative wind and perpendicular to it, we see that they add up to give a force upwind and lift. At other points along the chord these forces may oppose one another or inve a force downwind. An elaborate method of graphical in- tegration for pressure forces has been devised by the X. P. L.. but their integration was normal and perpendicular to the chord. Such summations, if taken as giving lift and drag, involve errors except at very small angles.
Comparison of Results from Pressure Distribution and from Force Experiments
In Chapters 2 and 3 we have divided the forces acting on a wing into two classes: density or turbulence forces, and skin friction forces. A study of pressure diagrams en-
I
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Kii;. 2. COMPARISON OF KK-II.TS FROM PRESSURE DISTRIBUTION AND KOIII-E EXPERIMENTS FOR A R. A. F. fi \\'ING.
46
AERODYNAMICAL THEORY AND DATA
47
ables us to determine the part which these forces play in pro- ducing lift and drag. In Fig. 2, the results of a pressure force integration are shown from experiments on a R. A. F. 6 wing, and compared with the usual force determinations.
The result for the lift values coincides. Now, it is fairly clear that skin friction forces would not impart lift to a wing. We can conclude that lift is solely due to the density or turbu- lence forces, and, further, that lift can be obtained from the integration of the components of the pressure forces per- pendicular to the relative wind.
The drag curves coincide at high angles, while between 0 degree and 8 degrees the drag derived from the pressure in- tegration is less than that obtained from force experiments. The difference is due to the fact that the pressure results give no indication of skin friction forces.
Effect of Variation of Speed and Scale on Lift and Drag Coefficients
These considerations enable us to deal more closely with the question of variation in coefficients with change of speed and scale, the product (IV).
Experiments at the N. P. L. show that lift coefficients are scarcely affected by such change. If, as has been shown, lift is due to pressure forces solely, there is no reason why the lift should be affected.
That portion of the drag due to density resistance and ac- counted for by the pressure integration would vary as AV. But the skin friction, not accounted for by the pressure ex- periments, varies as bl'^V1'". Therefore, with increase in speed and scale, the drag would not vary as AV', but some- what less rapidly, and Kx would not be a constant.
It might be possible for any model wing to find the density component of the drag by allowing for skin friction, step this
FIG. 3. DIAGRAM SHOWIXG VARIATIONS OF LIFT/DRAG WITH IV FOR R. A. F. 6.
up to full size as AV and then to compute the skin friction from the bl '" V1 '" formula. But we are not too sure of this formula, and the process would be very complicated.
Some experiments at the X. P. L. provide, perhaps, the best guide, although they have been carried over too narrow a range. In Fig. 3 are given values L/D for the R. A. F. 6 section, plotted at the same angle of incidence against log (IV), the logarithm being used purely for convenience in plotting. If the designer wishes to correct to the full -sized machine, he must take the value IF which is given in connec- tion with the section he employs and compare values of L/D at any angle of incidence with that corresponding to log H = 2.75 (IT = 560), a good value for a full-sized machine. The X. P. L. also gives corrections for lift, which are to be regarded with doubt, and corrections for drag coefficients. But it would seem safer to employ only the L/D corrections;
and even these should be only used for the designer's personal benefit, or in comparing the merits of two sections, as in the last column of Fig. 9 of Chapter 5. Designing without any corrections would be the most conservative method, and might ensure a pleasant surprise for full-size performance.
Distribution of Pressure at Median Cross Section of Various Surfaces
With the ribs, stringers, fillers and good fabrics employed in modern wing construction, the stresses produced in the fabric are well within the limits of safety, as we shall see later. But it is important to remember that it is not the mean pressure over a wing which gives the maximum stress in the fabric; it is the maximum pressure at one particular point. Also a small hole at one point of the fabric may
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FIG. 4. DISTRIBUTION OF PRESSURE FOR MEDIAN CROSS-SEC- TIONS FOR VARIOUS SURFACES AT 6 DEGREES ANGLE t.
cause it to carry the added effect of the snction at the upper surface and the positive pressure at the lower surface.
Eiffel in his earlier experiments consistently investigated the pressure distribution over both surfaces, and a number of his diagrams are shown in Fig. 4, while the maximum effect of suction on upper surface and pressure on lower face is shown in table in Fig. 4, at the same angle of incidence of 6 degrees in each case. The speed of the test was 32 feet per second. Although these surfaces are not in common use, they serve as a qualitative criterion from this standpoint for more practical wings.
An incidence of 6 degrees may be taken as normal flight, and at a speed of 60 miles per hour it is seen that pres- sures may vary from 13.4 to 8.82 pounds per square foot. This is, however, by no means the worst loading that can occur on a wing fabric. Under abnormal conditions such as flattening out after a steep dive, the maximum load per square foot may be many times greater. This question will be considered in detail in dealing with factors of safety.
Distribution of Pressure Over the Entire Surface of a Wing; Lateral Flow, Its Bearing on Aspect Ratio
The most instructive experiments on the pressure distribu-
AERODYNAMICAL THEORY AND DATA
tion over the entire surface of an aeroplane are those due to Jones and Patterson, at the N. P. L. and to Eiffel.
At the N. P. L. a single wing section has been dealt with in this way, but there has been a close and useful analysis, which is a first step in the investigation of phenomena of lateral flow, and of the underlying causes of the effects of varying aspect ratio.
A section resembling the R. A. F. 6, but with somewhat greater camber, was employed. Rectangular in plan, it had a series of observation points as shown in Fig. 5, on five sec-
3 4-
Profile of Aerofoil
Lead ing
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FIG. 5. SECTION EMPLOYED AT THE N. P. L. IN OBSERVING PRESSURE DISTRIBUTION ON 'AN ENTIRE WING.
tions parallel to the median section. The actual methods were similar to those already described in considering pressure dis- tribution over a median section, and the same remark applies to the resolution of components normal and perpendicular to the chord and their subsequent summation. The centers of pressure for each section were obtained by taking moments by a process of elementary mechanics, a similar process is fully described in the Bulletin de I'Institut Aerotechnique. Normal forces were again taken as a measure of the lift, and forces parellel to the chord as a measure of the drag, skin friction being neglected. The resolution of forces along and perpendicular to the chord, instead of along and per-
Pressure Distr/buioition on an Aerofoil flrea.3 of Ft auras a.re Porp ort/ofJA / to forces Norm A I to Chord.
Lotver f~a.ce
Lower f~a.cs
\rO. O/3O
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Lower fa. ce
Pressure Distribution on a.n /~ero fo// /~rea.s of-f7oures Porportiona.1 to forces Par A I lei to Chor*
FlG. 6.
pendicular to the relative wind, involved the error already mentioned, unimportant, however, except at large angles.
In Fig. 6 are shown the curves of normal and parallel forces at the five sections for various angles of incidence. In 7, the contributory effects of each section of the wini: is clearly illustrated by curves giving lift, L/D and center of pressure for ea<-h section. The following observations can be made from this data :
(a) As each section, beginning with the median, is consid- ered, the distribution on the upper surface from high
^i...
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II- T
ooi at ,00031
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FIG. 7. CONTRIBUTORY EFFECTS ON VARIOUS ELEMENTS OF A
WING AT VARIOUS ANGLES OF INCIDENCE. SECTIONS
LOCATED AS IN FIG. 5.
suction forward and low suction aft alters progressively until when the tip is reached the highest suction occurs in the neighborhood of the trailing edge.
(b) On the lower surface, the positive pressures found over the central portion of the wing fall off, and eventually change sign, so that near the tip almost the whole sec- tion is under suction.
(c) At the same time, the areas of the curves of normal forces c.ii upper and lower surface decrease at first to about */, of their original value, but subsequently in- crease as the tip is readied.
(d) Again as we move from the median section outward, the areas of diagrams proportional to parallel forces change from negative values (which oppose drag) to appreciable positive values, so that drag of the sections increases very rapidly in the neighborhood of the wing tips. Thus maximum L/D at A is 24, at E it is only 5.
(e) It is the variations in pressure distribution as we move out laterally which cause the center of pressure of the whole wing to move back.
This seems to demonstrate clearly that at the sides of the wing section there is a considerable amount of lateral flow, which prevents the establishment of a regime as efficient as at the center, where the air does not escape but follows the contour of the wing.
It is now also clear why increased aspect ratio is advan- tageous: As aspect ratio is increased, the inefficient action of the exterior sections assumes less importance. Without further research it is, however, impossible to say whether increase in aspect ratio leaves the aerodynamical conditions at the median sections unaltered, or whether it improves con- ditions everywhere on the wing except on the lateral tip.
These experiments may not be of immediate application in design, but may serve to give a better conception of what may be expected when a wing is varied in plan form. Be- sides the effects of varying ratio, these considerations would tend to explain the effects of raking.
Distribution of Pressure Over Entire Surface of Wing and Curves of Equi-Pressure
Kill'i'l employs an instructive method of curves of equi- |ii-r-Mire- over the entire surface of the wing, lie has ob- tained such curves for flat plates and for cambered surfaces, but has unfortunately not carried his analysis very far, and gives us nothing beyond a graphical idea of the actual dis- tribution of pressures. In Fig. 8 we find curves of equi- |.nssure and pressures at various sections for the Nieuport which are somewhat more suggestive.
In tlic Viouport wiiiir. the sections, while preserving their
AERODYNAMICAL THEORY AND DATA
49
general character, thin down as we move from the median section outward. This has the effect of maintaining nearly tlie same character of pressure distribution on all sections.
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From these considerations we can apparently conclude :
(a) That it is the upper surface of a wing which is by far the most important.
(b) That hollowing out a section has very little effect either on its lifting power or on its efficiency.
A somewhat similar conclusion was arrived at by Bende-
wing Section A/o /
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FIG. 8. DISTRIBUTION OF PRESSURE ON NIEUPORT WING.
The outer sections have smaller values, it is true, but the maximum suction on them is still not far from the leading edge. This from considerations of preceding paragraphs tends to minimize the aerodynamic inefficiency on the outer section. A wing such as the Nieuport wing might, therefore, be very valuable, but further experiments would be necessary before this point could be definitely settled.
Relative Importance and Interdependence of Two Surfaces
In Fig. 9 are shown curves due to the National Physical Laboratory, which show the distribution of pressures along and normal to the chord on the upper and lower surfaces of two wing sections. The sections are alike in their upper surfaces, but one of them, section 2, is hollowed out, while the other, section 1, has a plane under surface.
As we have already stated, the sum of two forces normal to the chord is scarcely distinguishable from the lift. And it can be readily seen from these curves that in both sections the upper surface contributes all the normal force at 2 de- grees and nearly three-quarters of it at 12 degrees.
Tt can be deduced from this that the lower surface of a wing section provides not more than one-quarter of the total lift. We notice further that the curves for the upper sur- faces in both sections are practically identical.
Section 1 has no components parallel to the chord; in sec- tion 2, as can be seen from the curves, the lower surface contributes very little of such components. Up to 7 degrees, the lower surface gives an upward force which helps to dimin- ish drag ; above this it has down a " downward " and detri- mental effect. It can be seen here that the effect of the upper surface is similar in both sections.
FIG. 9. DIAGRAMS ILLUSTRATING THE INTERDEPENDENCE AND ' RELATIVE IMPORTANCE OF Two SURFACES OF A WING SECTION. COEFFICIENTS ARE IN FOOT POUNDS PER SQUARE FOOT PER MILE HOUR.
mann in examining a heavily cambered almost circular pro- peller section; the camber of the lower surface scarcely af- fected the value of the coefficients.
Distribution of Pressure; the Principle of the Dipping
Front Edge. Why a Wing Section Is Advantageous
as Compared with a Flat Plate
We know from the pressure diagrams that for any wing such as that in Fig. 10, the pressure at A is negative, while
FIG. 10. DIAGRAM ILLUSTRATING THE PRINCIPLE OF THE DIPPING FRONT EDGE.
that at B is positive. This seems paradoxical, since A would appear to be facing the wind, while B is sheltered from it. Fage gives a very good explanation of this phenomenon com- monly known as the "Principles of the Dipping Edge." Photographs, such as we have already given in Chapter 3, show that the wind is deflected upward as it approaches the leading edge of the wing. A, although it faces the general wind direction, is thus screened from it, and becomes a region of low pressure; while on B the relative wind impinges di- rectly and receives a slight downward deflection.
From somewhat similar considerations, we are now in a position to explain roughly why a wing section is so much more advantageous than a flat plate:
(1) The suction on the upper surface of a wing toward the trailing edge is much greater than that for a flat plate, explainable by the principle of the dipping front edge. And a greater suction implies a greater lifting power.
(2) From the pressure distribution curves on the median sec- tion, it can be seen at once that the greater part of the force on the upper surface is due to the suction in the region of the leading edge.
50
AERODYNAMICAL THEORY AND DATA
Hence in summing up components parallel to the chord, for a good wing, the resultant force will tend to be "up- wind," and tend to nullify the skin friction, reducing the total drag. In a flat plate no such advantageous action will be present. A wing will, therefore, give a greater lifting power and a bigger lift to drag ratio.
References for Part I, Chapter 7
INVESTIGATION OP THE PRESSURE IN A MEDIAN SECTION
OVER THE UPPER AND LOWER SURFACES
OF THREE AEROFOILS
British Report, 1911-1012. No. 60. Page 62.
INVESTIGATION OF THE DISTRIBUTION OF PRESSURE OVBK
THE ENTIRE SURFACE OF AN AEROFOIL British Report, 1912-1913. No. 73.
EFFECT OF VARIATION OP SPEED AND SIZE, LIFT AND DRAG
COEFFICIENTS British Report, 1912-1913. No. 72. Page 81.
DISTRIBUTION OF PRESSURE AT MEDIAN CROSS SECTION Of VARIOUS SURFACES
"The Resistance of Air and Aviation," Eiffel (trans. Hunsaker), page 70.
DISTRIBUTION OF PRESSURE
Bulletin de I'lnatitut Atrotechnlque de VUniversiU de Parit 1!U3. Etude des Surface RU Chariot Electrlque.
"Curves of Equl-Pressure for the Nleuport Wing," Eiffel (Hun- saker), page 171.
INTERDEPENDENCE OF THE TWO SURFACES OP A WINO British Report, inil-1912. No. 60. Paev (is.
" Luftschrauhen-Untersuchungen," F. Bendemann. Zeittchritt fir Flugtechnik, 1911-1912.
PRINCIPLE OF THE DIPPING FRONT EDGE A. Page. " The Aeroplane," page 17
Chapter VIII
Biplane Combinations
Monoplane surfaces are aerodynamically the most efficient. Biplane combinations of any kind introduce interference be- tween the planes, a diminution of the suction on the lower plane, with a consequently diminished efficiency. But as air- planes increase in size the difficulties of suitably bracing monoplane surfaces become very great, and their lifting ca- pacity inadequate, and biplane construction must be resorted to.
Another important aspect of biplane construction is the possibility of obtaining longitudinally stable arrangements by staggering or displacing the wings relative to one another, and by introducing small angles between their planes, which is known as decalage.
The effects of staggering the planes for convenience of con- struction or with a view to increasing the range of view are to be considered within the province of practical construction.
Orthogonal Biplane Arrangements with Varying Gap Between Planes
An orthogonal biplane, as shown in Fig. 1, Setting No. 1, is one in which the lines joining the leading and trailing edges of the two wings are both at right angles to the chord.
Experiments to which reference is given at the end of this section to determine the aerodynamic coefficients of such com- binations with varying gap between planes have been carried
SETTING N't. I FORCES ON ORTHOGOHAL I BIPLANE. '
I At, 3CMP.H StandartlAir
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51
52
AERODYNAMICAL THEORY AND DATA
out solely on wings of an antiquated type, and it is by no means certain that similar values would apply exactly to modern wings. In default of further exhaustive experimenta- tion, the N. P. L. values must be taken as a guide, however. The results of the N. P. L. experiments showed that for nor- mal angles of incidence:
(1) Drag per unit area of biplane combination was not appreciably greater than that of a similar monoplane surface.
(2) The lift coefficients as compared with a monoplane sur- face decreased considerably, and that the loss was the greater the smaller the ratio between gap and chord.
(3) Loss in value of lift/drag follows:
On the basis of these experiments the following table can be employed :
TABLE 1. FOB ANGLES or INCIDENCE IN NOIIM.M. FLIGHT
0.80 1.00 1.20 1.60
tribution of lift on the upper and lower wing of a biplane, with ratio gap to chord 1.2:
Ratio of gap to chord 0.40
Factor for K, to reduce biplane lift from coefficients of a monoplane
surface 0.61
Factor for Kj/Ki to reduce from coefficients of a monoplane sur- face 0.75
0.76 0.81 0.86 0.89
0.79 0.81 0.84 0.88
Distribution of Forces Between the Upper and Lower Wings of a Biplane
By an indirect deduction from Dr. Hunsaker*s experiments on the triplane the following figures may be given for the dis-
„ SETTING N'S
FORCES ON STAGGERED BIPLANE MODEL
At 30M.PH Standard, Air Stagycr: 50^. Decalaqe: *4" Scale ofForcea*r025U> Scale- of Drawing 2~
_J
SETTING N-i*. ,
'FORCES OH MODEL BIPLANE
\At 30MP11 StamdanLfar iltoDecalaae /
'. Scale of forces 'j-(j£Olb. I Scale of Drawing 2'fXcnModtL
Angle of Incidence 0 2
8 12
TABLE 2. Percentage Lift DpperVlng
r,4' , 53% 54%
Percentage Lift Lower Wing 38%
45% 46% 47% 46%
It is possible that the upper wing does not only carry a greater proportion of the lift, but that it also has a better L/D ratio and has a proportionately small drag. Still the standard assumption, as used by Dr. Zahm, among other emi- nent authorities, that 55 per cent of all the forces acting on a biplane may be taken as acting on the upper plane is suffi- ciently accurate for all practical purposes. The distribution of forces between the two planes is only useful in stress cal- culations in design, where an error of a few per cent will have little or no importance. In Eiffel's earlier experiments some interesting data for pressure distribution on the upper and lower wings of a biplane are given which bear out the above values.
Distinction Between Static and Dynamic Stability
It is important at this stage of the work to draw a dis- tinction between static and dynamic stability. An airplane with stutic longitudinal stability has a righting moment
SETTING N'IM.
+y— - -J
FORCES ON MODEL BIPLANE At bOMP.H. Standard Air Nopecalajje
ScjUeof Forces •HL
Scble ofDramnff 2-3~imModel / Spout if both, Win,
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Fin. 2. VECTOR DIAGRAMS ton DIFFERENT BIPLANE SETTINGS, USING R. A. F. (i WIN.; SKCTION.
AERODYNAMICAL THEORY AND DATA
53
when displaced from its position of equilibrium, which tends to bring it back to the position of equilibrium. This righting moment may be so violent, however, that the airplane may acquire a considerable rotational velocity (pitching velocity),
-"*' -*' -2' 0' +2 +•;•+<;• £• 70" 7i" w- is' is' 20' 22' Angles of IncicU -'ce.
FIG. 3. LIFT AND DRAG COEFFICIENTS.
overshoot its position of equilibrium, and then, with the inter- vention of a righting moment in the opposite direction, oscil- late back and forth. In fact, the greater the static stability, the more violent may be the longitudinal oscillations.
In addition, therefore, there must be dynamic stability sup- plied by large tail surfaces, with a long arm about the center of gravity to damp out the oscillations which the static sta- bility alone is unable to subdue. A concise but authoritative
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Angles or Incidence. LIFT AND DRAG COEFFICIENTS.
discussion of dynamic stability has appeared in AVIATION AND AERONAUTICAL ENGINEERING (see appended references).
Stable Biplane Arrangements
We have seen that it is possible to secure a large degree of static stability at the expense of some loss in efficiency by the employment of wings with reversed curvature at the trailing
edge. It is possible to insure static stability also by the em- ployment of biplane combinations with stagger and decalage. Dynamic stability without preliminary static stability is im-
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FIG. 5. LIFT AND DRAG COEFFICIENTS.
possible, but if an airplane is statically stable, dynamic sta- bility is certainly possible.
Dr. Hunsaker investigated a great number of biplane ar- rangements at the Massachusetts Institute of Technology, with
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varying degrees of stagger and decalage. and found that witli certain combinations:
(1) Static longitudinal stability could be obtained with but little loss in aerodynamic efficiency.
(2) By suitable arrangements, the lift curve at the burble point can be flattened out and made to maintain its maximum for a wide range. This is particularly valuable, because it
54
AKROUYNAMICAL THKORY AND DATA
eliminate* the danger usually attending stalling altitudes. With a sharp drop in lift at the burble point, the loss in sus- tentation beyond a certain angle may be so great that the ma- chine may drop.
Results of Experiments on Biplanes with Stagger and De'calage
In Table 3 are given the summarized results for a series of tests on such combinations. In Figs. 1 and 2 are shown the corresponding combinations with the vector diagrams ; in Figs. 3, 4, 5 and 6 are shown Ky and Kx curves, and in Fig. 7 are plotted these Kv against K* curves for all the settings.
To judge of the stability of any combination it is necessary to assume a number of positions for the center of gravity, to assume a normal flying angle of incidence, and to see whether displacement from the normal flying position is fol- lowed by the correct righting moment about the center of gravity. If, for instance, the center of gravity for the setting No. 4 of Fig. 1 is placed as shown, between the vectors for 4 degrees and 6 degrees incidence, with normal flying angle 5 degrees, there will be statical stability. If the airplane dives to 2 degrees, the resultant force will have a clockwise mo- ment about the center of gravity and will tend to right the machine. If the airplane stalls to 8 degrees, the resultant force will have a counter-clockwise moment and will again tend to restore the biplane to its normal position.
In Table 3 the various settings are classified as stable and unstable, and it forms a very useful exercise to examine each •ombination from this point of view. The comparative values aerodynamically and the lift at the burble point are Drought out clearly by Table 3 and by the Kv and Kx curves.
Even with these extensive tests it is impossible to draw- definite conclusions as to the selection of any particular type,
and the results should be regarded as more qualitative than quantitive. The qualitative results would prevent any fan- tastic combination being employed.
Some of the main conclusions may be summarized as fol- lows:
(1) Stagger alone improves the aerodynamical qualities of a biplane, and flattens out the burble point, moves the vectors of force forward, but does not increase the stability to any appreciable extent.
(2) Cutting down the lower wing of a biplane does not im- prove the stability, but it lessens interference, improves the aerodynamic efficiency, and flattens out the burble point.
(3) Increasing decalage combined with stagger produces progressive stability, but at the expense of aerodynamic cfli- ciency.
(4) Among the most promising arrangements seem to be: No. 4. Decalage 2% degrees, stagger 50 per cent. The
stability is gained at the expense of but 4 per cent of the maximum lift/drag ratio, while a gain is obtained in all other properties.
No. 3A. Decalage 2.1 degrees, stagger 50 per cent, lower chord 83 per cent of the upper chord. Here the stability is also attained at a loss of but 4 per cent on maximum lift/drag ratio, while the lift curve remains at its maximum over a range of 12 degrees.
Comparison of Aerodynamic Losses Imnlvrd in Obtain- ing Stability by Reversed Curvature \\ iiiys and by Stagger — Decalage Combinations
For reverse curvature wings giving static longitudinal sta- bility the maximum lift is 17 per cent less and the maximum lift/drag ratio is about 14 per cent less than for a simple orthogonal biplane, as seen from the last column of Table 3.
TABLE 3. CHIEF PABTICOT.ABB FOB STABLE BH-UNB ABRANOIIIENT*
|
Rang* |
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K,/K. |
Kf/K, |
of Hat |
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Typ« |
Gap |
Stagger |
Tpper Chord |
Lower Chord |
Deralage 1 :'• ,-r- . - |
MMT. K,/K, |
Max. K, |
w here A'. - 0.0005 |
where K, - 0.0018 |
Hurl. If. Point in I )' ,-M . s |
Remarks on Stability with reference to FipB. 1 and 2 |
|
Monoplane |
C |
1.16 |
1.18 |
0 90 |
1.24 |
2° |
Unstable. |
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Biplane No. 1... |
c |
0. |
C |
C |
0.0 |
1.00 |
1.00 |
1.00 |
1 00 |
2° |
Unstable. |
|
Biplane No. 2. . . |
C |
O.SOC |
c |
C |
0.0 |
1.00 |
1.06 |
1.00 |
1.02 |
2° |
nt forces from 2Vi° to li < t near a |
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Biplane No. 3... |
C |
. ioc |
c |
C |
1.0 |
0.95 |
1.03 |
1.00 |
1.01 |
6° |
The force vector* for ;uu'!es from 0° to 10° intersect |
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point the e<iuilil>rn:ru is ueutT:tl from 0( to 111°. |
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Biplane No. 4... |
C O.SOC |
c |
fj |
2.5 |
0.95 |
1.03 |
1.00 |
1.02 |
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n!n of irra\ ity locntci! nn.VM here in the lower -2C' :inil — 5° |
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Kxreraivc nubility. Mncliim s MiitnMr for amateur*. |
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Biplane No. 1A. |
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0. |
0.83C |
0.0 |
1.04 |
1.04 |
0 90 |
1 05 |
4« |
..iinidly nriMnble. |
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Biplane No. 2A. |
c |
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C |
0.83C |
0 0 |
1 04 |
1 04 |
0 93 |
1 08 |
12" |
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Biplane No. 3A. |
c |
., ,. - |
C 'i HC -' 1 I' '-"< 1.03 |
0.96 |
1.05 |
12° |
Longitudinal Mi.bilit> for nny center of gravity • 1 within tl > n^lc formed bv the |
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ture Winn. . |
c |
0. |
C « |
0.0 |
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0.83 |
1.21 |
2« |
longitudinally stable. |
C <• chord length (upper).
K.JK, and other aerodynamic roeffirienu referred to th« othoffoul itantUrd bipUike M unity.
AERODYNAMICAL THEORY AND DATA
55
With a stagger decalage combination there is an actual in- crease in the maximum lift, while the L/D loss is only 4 per cent. The constructional difficulties in the region of the rear spar are also avoided. On the other hand, stagger involves
the biplane drag was greater than that of the monoplane, while at high angles the biplane gave the better qualities. The later Massachusetts Institute of Technology experiments gave diametrically opposite indications. Since these experiments
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AERODYNAMIC LABORATORY MASS. INSTITUTE TECHr BIPLANE ARRANGEMENTS - Span ofallMo&els: 18 Inches Sap of. all Models: SInches Wmd Velocity: 30 Miles per Hoar Density of Air: 0-07608Lbsper OMcR IOTE:-Resistance. of Struts and Supports has beervSubtracteA WingSection, ofaliModels:JRA.F.{ |
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Lift Coefficient-
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FIG. 7. LIFT COEFFICIENTS PLOTTED AGAINST DRAG FOR VARIOUS SETTINGS.
increased length and resistance of wing struts and increased stresses in the drift bracing of the wings.
The relative merits of the two systems can only be decided upon by a practical comparative experience of the two types. In the authors' opinion, the stagger-decalage system is more likely to give good results than the reversed curvature wing system for ordinary machines. For very high speed machines, flying at a small angle of incidence, however, the reversed curvature biplane offers 20 per cent less resistance than the orthogonal biplane with R. A. F. 6 wing section. In such ma- chines, where a low maximum Kv coefficient and high landing speeds are permissible, the reversed curvature wing might be very advantageous from the point of view of high maximum speeds.
Aerodynamic Comparison Between the Monoplane and the Biplane
In Table 1 are given the correcting factors from monoplane values for biplanes with varying gap/chord ratios from the N. P. L. experiments. These will, although based on a wing section of an antiquated type, as already mentioned, be quite correct enough for angles of normal flight, 4, 6 or 8 degrees incidence. But for very low angles of incidence and for very high angles of incidence there is a discrepancy between the results obtained by the British investigators and by Dr. Ilun- saker. The former concluded that at low angles of incidence
were conducted at a later date, and were carried out with R. A. F. 6 wing sections, they are probably worthy of more credence. The following table has been deduced from the curves of Fig. 7, where Kv is plotted against K x :
TABLE 4.
LIFT/DRAG RATIO AND K, FOR ORTHOGONAL BIPLANE, R. A. F. 6 WING SECTION, GAP/CHORD RATIO 1, GIVEN AS PERCENTAGE OF MONO- PLANE VALUES FOB THE SAME A'y
K?
0.11004 O.H006 0.0008 0.0012 0.0(11 (} 0.0o:>0 0.00^4
KS
110
10T
09
85
85
75
73
K,
90
93
101
115
115
125
127
To consider L/D and Kx for the same values of ~KV for mon- oplane and biplane is really a much fairer comparison than to consider L/D and Kx for the same angles of incidence. It really matters very little what the angles of incidence for biplane and monoplane are, provided we have the same Kv and the same sustaining power at the same speed.
From Table 4 one would conclude that the biplane has a very distinct advantage for a high-speed scout. Apparently at a high speed, and hence a low lift coefficient, the biplane resistance is 10 per cent less than the monoplane resistance. This is an appreciable saving. For a machine which must fly slowly, and consequently with a high lift coefficient, the bi- plane resistance is from 15 to 25 per cent greater than the monoplane resistance.
5(j AERO DYNAMICAL THEORY AND DATA
References for Part I, Chapter 8 ^"jan.^aSS'i^T;.. by J" C" Hunsakcr- in
" Dynamic stnMllt.v of Aeroplanes," by J. C. Hunsaker, In AVIATION
" Chapter on Aeronautics," by J. C. Hunsaker, In The Neic Mechanical AND AERONAUTICAL ENGINEEUIM;. Aug. 1, 1910.
Enpineeri' Handbook. "Determination of the Effect on the Lift and Drift of a Variation in
" The De«lgn of Aeroplane*," by A. W. Judge, page 42. the Spacing In a Biplane." British Report, 1911-2, No. 60.
„ _._ . . " Determination of the Effects of Staggering the Wings of a Biplane."
"The Resistance of Air and Aviation, by G. Eiffel (translated by J. British Beport, 1911-2, No. 60.
C. Hunmker). .. Application of Experimental Results to Practical Problems In Aero-
" La Reslstencc de 1'Alr ct 1'Avlatlon," by G. Eiffel, 1914. Chapter 5. plane Design." British Report, 1911-2, No. 60.
Chapter IX
Triplane Combinations — Uses^of Negative Tail
Surfaces
In an article on " The Aerodynamical Properties of the Tri- plane," by J. C. Hunsaker and T. H. Huff, published in the November 1, 1916, issue of AVIATION AND AERONAUTICAL EN- GINEERING, the reader will find a complete treatment of the aerodynamic properties of the triplane, with a complete record of the experimental results obtained at the Massachusetts In- stitute of Technology. It remains for us only to summarize the main results, and to review recent constructional applica- tions of the triplane principle.
The main conclusions from these experiments are:
(I.) At the stalling angles such as 16 degrees the triplane and biplane give nearly the same maximum lift; the triplane has a materially lower resistance at this angle, giving a much better performance at slow speed. Thus the L/D ratio at 16 degrees is 4.5 for the monoplane, 5.6 for the biplane, and 6.5 for the triplane.
(II.) At angles below 12 degrees the drag coefficient is not greatly different in the three cases, but the lift for the triplane is considerably reduced; it is inferior to that of the biplane which again is inferior to that of the monoplane.
(III.) The best L/D for the triplane combination is only 12.8 as compared with 13.8 for the biplane, and 17 for the monoplane.
(IV.) The center of pressure motion is almost identical with that of the biplane. We have seen previously that the center of pressure motion for the biplane is nearly that of the monoplane. This demonstrates that the commonly made as- sumption of monoplane center of pressure motion for a wing of a biplane also holds for the triplane. This is an important fact in view of the methods employed in stress diagrams.
The experimental results for Kr and L/D for the triplane as compared with the monoplane and biplane are summarized in Table 1 :
TABLE 1
TABLE SUMMAUIZING COMPARATIVE VALUES OK K AND L/D FOR MONO- PLANE, BIPLANE AND TKIPLANE.
|
» 0. |
, — MONO Actual Ky 000486 |
PLANE. — N Per- centage. 100 100 100 100 100 100 L/D 100 100 100 100 100 100 |
, BIPLANE. v , TRIPLANE. , Actual Percent, of Actual Percent, of /Cj, Monoplane. K y Monoplane. .000432 88.8 .000404 83.0 .000864 83.8 .000776 75.4 .00123 85.4 .00109 75.7 .00186 85.2 .00169 77.4 .00244 87.6 .00226 81.2 .00273 98.5 .00267 96.4 L/D L/D L/D L/D 6.3 73.2 6.1 70.8 12.2 74.7 11.4 69.8 13.8 82.0 12.8 76.1 11.3 81.9 11.1 80.4 9.5 95.0 8.9 89.0 5.6 124.0 6.5 145.0 |
|
2 |
. . . 00103 |
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4 |
... 00145 |
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8 |
. . . 00218 |
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12 |
00278 |
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16. |
00277 |
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0 |
L/D 8 6 |
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2 |
16 3 |
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4 |
16.8 |
||
|
8 12 |
. . . 13.8 100 |
||
|
16.. |
4.5 |
Interference in Triplanea
Dr. Hunsaker's paper also deals fully with interference in triplanes. It is important in the structural design of the
wing girder to know what portion of the lift and drag to attribute to each wing. The comparitive efficiency of each wing is also important from the point of view of overhang. It appears from Table 2 that the upper wing is very much the most effective of the three and the middle wing the least effective. The very poor lift of the middle wing is caused by the interference with the free flow of air due to the presence of the upper and lower wings.
One interesting point brought out by Dr. Hunsaker toward the end of his paper was the fact that when the effects of the upper and lower wings were combined, results identical with that of a simple biplane combination were obtained. This would tend to show that the interference in the case of a triplane is similar to interference in the case of a biplane. The upper wing of a triplane would" seem to be influenced by the middle wing in the same way that the upper wing of a biplane is influenced by the lower wing of a biplane. Again the lower wing of a triplane would seem to be influenced by the middle wing in the same way that the lower wing of a biplane is influenced by the upper wing. These are im- portant considerations to be kept in mind when modifications of the triplane are attempted such as stagger, overhang, decalage, etc.
TABLE 2
TABLE OF VALUES FOR LIFT AND L/D FOR EACH WING OF A TRIPLANE
COMBINATION AS RATIOS TO LIFT AND L/D OF MIDDLE WING.
Angle of Lift Lift Lift L/D L/D L/D
Incidence. Upper. Middle. Lower. Upper. Middle. Lower.
0 2.68 1.0 1.82 3.63 1.0 2.30
2 2.14 1.0 1.76 3.18 1.0 2.13
4 1.91 1.0 1.64 2.59 1.0 1.69
8 1.56 1.0 1.36 1.49 1.0 1.37
12 1.56 1.0 1.31 1.30 1.0 1.34
16 1.49 1.0 1.20 1.22 1.0 1.17
Some Considerations for Triplanes
There are two types of airplanes, quite dissimilar, for which triplanes have been employed in this country, the huge Curtiss flying boats, and the recent Curtiss speed scout. It is interesting to consider what the possible advantages of the triplane are at these two extremes of design.
In the heavy types, particularly in seaplanes, the increased size must be developed without increase in landing speed. To insure about the same landing speed, the loading must remain at a figure of about 5 pounds per square foot. And for an aeroplane of four times the ordinary weight the wing area must be increased in like proportion. Monoplane construction is obviously impractical for such great areas of wings, and even with the biplane there is an enormous wing span. Such a span introduces great difficulties from the stress point of view and from the point of view of housing and handling. The employment of a triplane enables the span to be kept within reasonable dimensions and also permits the employment of larger nspect ratios.
57
AERODYNAMICAL THEORY AND DATA
At high angles the lift of a triplane is only 1.1 per cent less than that of a biplane of the same area. At 16 degrees the L/D ratio of a triplane is 16 per cent better than that of a biplane. At stalling attitudes, the triplane has therefore very decided advantages, giving a greater reserve power at low speeds in alighting. At 4 degrees incidence for best L/D the triplane does not show up so well, and requires an increase in power of about 6 per cent. It would seem as if the 6 per cent increase in power can be compensated for by the pos- sibility of a less heavy type of construction with decreased span. Also there is the possibility of employing much greater aspect ratios than in biplane work, and this may compensate to some extent for the losses due to extra interference.
Triplanes for Fast Speed Scouts
From the photographs issued by the Curtiss Company, it seems clear that the original machine (see AVIATION August 15, 1916) was transformed (see AVIATION October 15, 1916) by placing the triplane wing structure on the same body struc- ture as for the biplane. With approximately the same wing area divided between these planes the aspect ratio was in- creased very considerably, without exaggerating the span, giv- ing some aerodynamical advantage. The extremely narrow blade like wing permitted the single plane bracing system to be used with much greater security. The employment of a single plane bracing system cuts down resistance very con- siderably, and if this bracing system is only possible with triplane narrow blade construction, then triplane construction would be a very sound tendency in the design of small fast machines.
Use of Negative Tail Surfaces
In Chapter 6 we saw the possibility of using a negative tail surface so as to give static longitudinal stability, and in the problem which follows a definite case will be taken as an illus- tration of this possibility. In other methods of attaining stability such as employment of the reversed curvature wing or of stagger-decalage combinations, dynamic stability might not follow the static stability unless tail surfaces were em- ployed. In such cases the tail surfaces would probably have to be placed at zero angle to the wings, or even at a small positive angle. It is for this reason that the stable biplane arrangements, apparently so advantageous, are not more fre- quently used in practice.
Effect of Influence of the Wash of the Wings on Stabilizer Surface
Eiffel in his later experiments conducted some tests on tandem wings. One important result of these tests was to prove that an airplane built with tandem wings would be
Fio. 1. DIAGRAM FROM EIFFEL TO SHOW DKVIATION 07 STREAM-LINES BY " DOWN-WASH " OF WINGS.
aerodynamically disadvantageous. Another loult was that the down wash of the trout wing would cliiinye the flow relative to the rear wing so that the angle of incidence of the
latter would be smaller than that of the former. The al- lowances made for the change in the angle of incidence were arrived at indirectly by measuring lift and drag on the sec- ond wing while in the presence of the first, and are not en- tirely reliable. Fig. 1 represents Eiffel's conclusions diagram- atically for a specific case.
The relative wind for the front wing is horizontal; the chord of the front wing is at 10 degrees to the horizontal, the chord of the rear wing is at 4 degrees to the horizontal, with a decalage of 6 degrees. Owing to the downwash of the front wing the stream lines at the rear wing now make a negative angle of 7 degrees with the horizontal, and the rear wing is actually at a negative angle of 3 degrees to the stream.
Owing to the fact that the tail surfaces of a machine are so much further away from the wings, the deviation will be less perceptible and the following practical formula gives satisfactory results:
If t = angle of incidence of the wings,
Deviation of stream = (J/£ » -)- 1)
To take a concrete case, if the wings are at 8 degrees incidence, and the stabilizer is placed at a negative angle of 2 degrees to the chord, then its incidence will be (8 — 2) — (i/2 i + 1) = (8—2) — (8/2 -f 1) = 1
This deviation has an important bearing in the design of stabilizing surfaces on the angle of setting between the chord of the wing and the line of the stabilizing plane.
Problem on the Design of Tail Surfaces to Give Longitudinal Static Stability
The requirements of static longitudinal stability may be briefly stated as follows :
(1) The machine must be in stable equilibrium at some angle of incidence, generally the angle of normal flight, say 6 degrees for purposes of illustration.
(2) If the angle of incidence of the aeroplane is from any cause less than 6 degrees, there should be a positive restoring
^TQ£wt-*~m*K^ K/8 I |
Fio. 2. DIAGRAM ILLUSTRATING STABILIZER PROBLEM.
moment or stalling moment; if for any reason, greater than 6 degrees, there should be a negative or diving moment.
(3) Within a t'ew degrees of the position of equilibrium the ri^hiiujr moments should be comparatively small so as to give iVxibility of control.
(4) As the displacement from the position of equilibrium increases the righting moments should increase also.
(5) The righting moments should never be excessive and should never exceed ' :1 of the possible moment which can be exercised by the elevator.
These results can be readily obtained by the use of a suit- able negative tail. \Vc shall now take a concrete case of an unstable orthogonal biplane with a total wing area of 432 square feet; wing section R. A. F. 6; the center of gravity of
AERODYNAMICAL THEORY AND DATA
59
TABLE 3. TABLE ILLUSTRATING COMPUTATIONS IN STABILUEB DESIGN
|
S |
o |
sH. |
L |
S |
2 |
ij |
0 |
£« |
1 |
I |
C |
1.2 |
||||
|
s« |
•S H |
• |
d"0 |
** a |
J3 |
|||||||||||
|
•gs |
•g.5 |
•"a |
E-3 |
1 * |
3 |
•§ " |
•§~ |
as |
B a |
1 |
•s |
1.9 |
1.2 |
|||
|
Ed •aj JD 3-9 •< t |
1 a a) a.9 |
* |
fa II |
la8? 8.9 « |
«1 5.9 |
Jj" |
1.9 |
Moment drag in 1 |
K S3 |
§J .11 t-i E |
1- 11 $*" |
|1M |
J |
fl . °l 3.9 |
Moment stabilizer |
Resultani about c.g |
|
0 |
.000493 |
.000075 |
110. |
392 |
2560 |
2 |
-1.2 |
+784 |
-3020 |
-2236 |
-3 |
-.00051 |
16 |
-309 |
+4950 |
2614 |
|
2 |
.000882 |
.000072 |
82.5 |
212 |
2560 |
2 |
- .6 |
+424 |
-1500 |
-1076 |
-2 |
-.00035 |
16 |
-119 |
+ 1910 |
834 |
|
4 |
.00121 |
.000093 |
70. |
197 |
2560 |
2 |
- .30 |
+394 |
- 750 |
- 356 |
-1 |
-.00018 |
16 |
-44.1 |
+ 704 |
348 |
|
e |
.00155 |
.000130 |
62. |
216 |
2560 |
2 |
- .24 |
+432 |
- 600 |
- 168 |
0 |
0 |
16 |
0 |
0 |
- 168 |
|
8 |
.00187 |
.000166 |
56.6 |
230 |
2560 |
2 |
- .12 |
+460 |
- 300 |
+ 160 |
1 |
+ .00018 |
16 |
+28.7 |
- 459 |
- 299 |
|
13 |
.00242 |
.000255 |
49.8 |
275 |
2560 |
2 |
0 |
+550 |
0 |
+ 550 |
3 |
+ .00051 |
16 |
+65 |
-1040 |
- 490 |
the machine, as shown in Fig. 2. The loading is such that the machine has an angle of incidence of about 4 degrees at a speed of 70 miles per hour. The gap chord ratio is 1.0. The tail surfaces, stabilizer and elevator are taken together, are placed at a distance of 16 feet from the center of gravity. It is required to design a stabilizer to meet the above require- ments.
We will assume that:
(a) The design of the stabilizing surface is carried out prior to wind tunnel tests.
(b) The center of pressure motion for each wing of the com- bination is precisely similar to that of the wing acting alone, so that L and D forces on each wing may be taken as acting at precisely the same point they would on a monoplane wing ; this assumption is justified by results of both the biplane and tri- plane experiments.
(c) The resultant force on the tail surfaces may be taken as approximately perpendicular to the moment arm and as being equivalent to the lift. This is not far from true for an- gles wilhin normal llight and simplifies our calculations enor- mously. The stabilizer surface is taken as being equivalent to a flat plate.
(d) The displacement of the vertical through the center of gravity for varying angles of incidence is neglected.
The machine selected for this problem is shown in Fig. 2 with the position of the center of gravity as indicated. It has a wing area of 432 square feet. The normal angle of flight being 4 degrees, it must weigh from elementary considerations (introducing .85 as correcting factor for lfy due to biplane effect).
W = KyAT = .0014 X -85 X 432 X 702 = 2560 pounds
Taking moments about the center of gravity the general equation for the pitching moment at any angle is
M = 2La — DC + DC' — 167? (1)
Where a is the distance between the vertical center of grav- ity line and the parallel line of lift on each wing (the wings assumed to carry equal loads), C and Cl are the distances from the horizontal axis through the center of gravity to the point of application of the drag forces. The distance of 16 feet is assumed as the distance from the center of gravity to the point of application of the resultant force R acting on the stabilizer as defined previously.
Since, Fig. 2, the distance C = 4 feet ; 6rl = 2 feet ; the quan- tity (6 — b) =2 and the equation can be simplified to the following form :
2(La — D — 8B)=M (2)
The lift arm a varies of course with the center of pressure motion.
Unfortunately no set method of design exists for this par-
ticular problem. Area of stabilizer and the angle of setting to the wing chord have to be assumed more or less arbitrarily until the right combination is found, although each designer will probably find a short cut method. In two instances after a number of tentative combinations, the following values were found to specify our conditions fairly well.
Stabilizer, aspect ratio 3, area 50 square feet, angle of set- ting to wing chord 2 degrees. The K7 coefficients for the sta- bilizer treated as a flat plate can be taken from the curves given in Chapter 4.
•5000
-«M
^000
yaao zyx
ZOOO
1500
1000
JOO
0
-500
-{0«l
-BOO -tax
*
MC* S
WINGS
EN' T3 ON MACH
Or WING
TO WINO
FIG. 3. LONGITUDINAL PITCHING MOMENTS ON MACHINE.
A careful distinction has to be made between the apparent angle of incidence of the stabilizer to the relative wind and the real angle, taking account of the deviation of the stream in accordance with the formula given. Thus if the wings are at an incidence of 6 degrees to the wind, and the stabilizer is at — 2 degrees to the wing chord, the real angle of incidence becomes
(6 — 2)— (1/2-6 + 1) = 0 degrees
The computations for the setting finally selected are shown in the Table 3. The curves of moments due to the wings, the moments due to the stabilizer, and the resultant moment are shown in Fig. 3. The conventional method of regarding mo-
BO
AERODYNAMICAL THEORY AND DATA
meiits tending to stall the machine as positive, and moments tending to dive the machine as negative is adhered to.
It is seen from the curves of Fig. 3 that the solution is only fairly good. Equilibrium is secured at 6 degrees. Approxi- mately on either side of the equilibrium position, the correct moments are obtained. If the machine goes below 6 degrees the resultant moment tends to stall it bock to 6 degrees. If the machine goes above 6 degrees the resultant moment tends to dive it back to 6 degrees; that is satisfactory so far. But the resultant moment curve is far too steep about the position of equilibrium and the machine is sometimes too stable to be
under perfect control. The problem is left in tlii> t'orui, how- ever, because an improvement of the solution would be an ex- n'llciit exercise for a student. The variations possible are in I Length of stabilizer arm. II Area of stabilizer.
Ill Angle of setting of stabilizer.
It must also be pointed out that the approximations em- ployed, and the factors neglected, such as the effect of the body and other structural parts, are so numerous that in construct- iiii; ;m actual machine a wind tunnel test would be finally necessarv.
Chapter X
Resistance of Various Airplane Parts
N.P.L. Body 5
B.F. 36
One of the most difficult problems in aeronautical design is 40 pounds. A blunt, square form of body such as is often the prediction of the total resistance of the machine. The seen in American practice may increase resistance even more, wind tunnel test is a good check, but it is most important to assign resistance values to various parts and to tabulate them prior even to the construction of the model. In this chapter have been collected as far as possible all the data available for bodies, radiators, fittings, wheels, cables and wires and certain other miscellaneous objects.
Airplane Bodies from the Aerodynamical Point of View
If airplane bodies were designed from a purely aerodynam- ical point of view, they would follow dirigible practice and be of streamline form. There are, however, a number of structural requirements which have to be met, which preclude the employment of such forms. The body must enclose the power plant and the personnel, the length must be long enough to place the rudders well clear of the wash of the planes, the shape of the body must conform to structural requirements such as the use of four longitudinal girders, or a triangular form which has been found to be advantageous in steel con- struction.
No wind tunnel tests on bodies alone can determine exactly their resistance on an airplane, because the question is com- plicated by the position and form of the motor, and the dis- position of the tail surfaces. The propeller in a tractor ma- chine also introduces three possible variations in drag coeffi- cients: (1) when the propeller is pulling and there is a slip stream of velocity greater than the airplane velocity, (2) the resistance on a glide when the engine is shut down, but the propeller is revolving as an air motor; (3) when the propeller is not revolving at all. the engine being held.
Tractor Bodies
In Table 1 is given a comparative table of resistance co- efficients for area in normal presentation of a number of air- plane bodies, and in Fig. 1 are shown sketches of the same bodies. Exact comparisons are impossible because some of the bodies are made for two men and others for one. Still qualitative conclusions can be drawn. The N. P. L. Model 5, more symmetrical than the B. E. 3, shows a distinct improve- ment over the latter which is somewhat discounted by the fact that the B. E. 3 carries two men unshielded. The B. F. 36, an almost perfect dirigible form, is markedly better than either of these two bodies.
The resistance of the body in an airplane is apparently a small quantity, but the figures given below do not represent the resistance of a body in full flight where it is increased by 40 per cent, the propeller slip stream increasing the relative speed of the air by some 25 per cent. Also, it must be re- membered that with a best glide of 1 in 8, a 5-pound increase in resistance is practically equivalent to an added weight of
61
Deperdussin FIG. 1. TRACTOR BODIES.
and better aerodynamical design of bodies seems a feature worth considering.
TABLE 1.
Designation.
COMPARATIVE TABLE FOB TRACTOR BODIES.
Coefficient of resist- ance, K where R — KA7* (A = area
in normal presenta- tion in square feet
7 = miles per hour ; maximum B = drag in Ibs.) depth.
Length
British B. E. 3 (with 2 men) . . .000720 7.35
N. P. L. Model 5 000420 (approx.)5.50
British B. P. 36 (dirigible form) .000258 5.75
Deperdussin (enclosing rotary
motor) 001215 5.6
TABLE 2. COMPARATIVE TABLE FOR PUSHER BODIES.
Resistance
for a body
of 8 square
feet normal
presentation
at a speed
of 60m. p. h.
20.7 12.0
7.4
35.1
Designation.
Coefficient of resistance K where R = KA.V* (A ~ maximum area in normal presenta- tion in square feet ; V = miles per hour ; R = drag in lbs.1
X. P. L. Model Body 3 (fairly symmetrical section) 000271
Farman 3 (body in form of a
boat, two men unshielded).. .OOOS45
Pusher Bodies
Length.
3
3.2
Resistance
for a body
of 8 square
feet normal
presentation, at a speed
of 60 m. p. h.
7.8 24.4
A pusher body such as the Farman 3, illustrated in Fig. 2, gives a not much larger resistance than the tractor
62
AERODYNAMICAL THEORY AND DATA
bodies, bat when the head resistance of the uncovered oat- riggers is taken into account, it will probably HP found that
Farman 8 Fin. 2. A PUSHER BODY.
pusher arrangements offer considerably more resistance than tractor bodies.
Radiator Resistance
The only values available for this are the results of some tests at the Massachusetts Institute of Technology. These were carried out on portions of a radiator of the honeycomb type having sixteen %-inch cells to each square inch of the surface normal to the wind. The tests were repeated on two sizes of radiator section, one 0.25 square feet and the other OJ.11 square feet, and at various wind speeds. No important variation in the resistance coefficient was apparent and the average coefficient may be used for practical calculations. This has a value Kx = .000814 pounds per square foot of pro- jected area per foot per second or .00173 pounds per square foot of projected area per mile per hour.
Resistance of Fittings
Fittings are so variable in design that it is impossible to give definite figures to meet every type of wing strut fitting. Tests were conducted at the Massachusetts Institute of Tech- nology on the fittings of which dimension drawings are given in Fig. 3; the coefficients of resistance are R — .00030 \ B = .00040 1" for the two types which at 60 miles an hour
ranol. R - .OOOrin v:.
Inn. r rand with Wins Illinji'.
BfcB
R = .00040 V1.
.1. FITTINGS EMPI/JYKI. IN TESTS FOR HEAD RESISTANCE AT MASSAI i M -SETTS INSTITKTK OK TECHNOLOGY
CIAIIK HTRIT FITTJNON. Id-«l'.|aii<-1. ln< Imlcii fitting, five turntmrk].^ and nuU but not dotti il portions UK Imllrntnl mi drnuliiKi. ItnUtann* In pound!: Velocity In mil"* J»T h»ur
gives 1.07 and l.H pound-; respectively. Such figures will he •t least apprrmninlcK
\irplaiir \\ lirrU
For a standard airplane wheel of about 26 X 4 inenes in size, the drag found by the X. P. L. is about 1.7 pounds at tiO miles per hour. This again is sufficiently accurate for prac- tical purposes. Eiffel has experimented with a number of wheels and shown that no great variation need be expected from the above value. An important result from the French experiments was the fact that an uncovered wheel had a re- sistance of 50 per cent more than a covered wheel of similar dimensions. This justifies the standard practice of covering the wheel in.
Resistance of Wires ami Methods of Plotting
A certain complication is necessary in the methods of plot- ting the results for the resistance of cables ami wires. As we have seen from the diagram of Kig. 1!'. in Chapter '.'•, of the Course, the resistance of a wire or any cylindrical body is partly due to turbulence, partly due to skin friction. It cannot therefore be represented by such a simple expression as R = KAV* as for a wing, but by an expression involving
v Kevnolds' number, R = KA\"~ f ( - ), or if we replace th«
DV area of a wire by LD where I) = diameter and L is length
v in feet, then E — KLD T" / ( - - ). Since v, th.- coefficient
DV
of kinematic viscosity is constant for air, we can simplify this expression by writing:
R = KLD V- F(VD).
We do not know what the function F(V'D) is exactly, nor how it varies with size and scale except from experimental re- sults, and comparisons of resistance varxing as l.l> I" can only be made between two cables if VI) \< a constant. If K is taken as a function of VD, then E may be written R — KLD P but then A' must be plotted against \T> in analyzing experimental results. This is the only rational and scientific method.
An empirical method, however, is sometimes employed with fair accuracy of plotting the resistance of a wire whose length is equal to its diameter against T5 Tf. This has the advantaire that the graph approximates very closely to a straight line, the slope of which is equal to K, thus giving an easy means of determining a mean value of A".
Resistance of Stationary Smooth Win--
The most accurate researches have been carried out nl the
X. 1'. L. and their results are shown in Kig. I plotted against
B
V'D. In the expression A" . /.' is in pounds, /. in
r. in"
feet, 1) in feet, and 1" in miles per hour. Hut in the values of \ '!>, V is in feet per second, and l> in feet, so as to give the correct scale and speed relationships which must he in the same units.
The accuracy of the curve at its |owi-i portion is doubtful. -nice (he (low is apparently jiisl changing its nature at that point, and successive observations under the same conditions may i_'ive quite different results. On modern machines of fairly high speed, however, the value's of \"D nearly always • I II. .'i5 and consequently, do not he on (his section of the curve'.
Similar tests were made by Mr. Tlmrston and M. KifTel, and the values obtained by the Conner are plotted in the same fiinire. ThnrslonV experiment*, however, were very nnn-h
AERODYNAMICAL THEORY AND DATA
63
earlier, and Eiffel's covered a less range and were performed
VD IM
;c. or
SMOOTH WIRES OMITS: LBS. FT. MILES
o .3 10 i.sr £o e.5 3a
FIG. 4. RESISTANCE OF SMOOTH WIRES PER FOOT RUN.
with less sensitive apparatus, so it is advisable to use the N.P.L. results.
Resistance of Vibrating Wires
When the question of resistance first began to arouse in- terest, it was popularly supposed that a vibrating wire had jnuch greater resistance than a stationary one. This, however, is not the case. Research on this point at the N.P.L. failed to disclose any difference whatever, although the balance would have shown deviations as small as 3 per cent, even for the extremely small forces under consideration. Mr. Thurs- ton, on the other hand, concluded that vibration at the rate of 15 per second increased the resistance by about 5 per cent for small wires and by a somewhat smaller percentage for those of larger diameter. In any case, the effect is unim- portant.
Resistance of Stranded Wires
The air resistance of stranded wires was also investigated at the N.P.L., and was found to be about 20 per cent greater
r
FIG. 5.
RESISTANCE OP WIRES IN TANDEM AS A RATIO OF THE RESISTANCE OF A SINGLE WIRE.
than that for a smooth wire of the some diameter. This is only approximate, as the coefficient depends on the number of strands, type of lay, etc. It is also impossible to plot the values of K against VD for wire rope, as the VD law holds good only for objects which possess strict geometrical simi- larity, a thing which stranded wires of different sizes never do.
Resistance of Wires Placed Behind One Another
The manner in which resistance is affected by the close juxta- position of two wires, one behind the other, is a point of great interest. Here, too, it is at present necessary to rely on Mr. Thurston, although we hope to be able soon to present the results of some more extensive and accurate tests on this matter.
Fig. 5 gives, in terms of the resistance of a single bar, the resistance of two bars or wires separated by various dis- tances. It will be seen that two wires placed one behind the other and spaced from 5 to 9 diameters apart, as is usual in double-wiring a biplane cellule, have from 60 per cent to 75 per cent more resistance than a single wire. The force is,
K for LIMITS
pounds per V D in
OBJECT square foot foot second ATTITUDE
per mile units hour units
phere 0.000445 V D > 32 »•
Hemispherical Shell 0.003840 V D > 11
Hemispherical Shell 0.008100 V D > 22
Circular Disk 0.002820 V D > 22
Cone Closed Base. .[.0. 001300
Cone Closed Base.. 0.000850
Cone Hemispherical End.. . 0.000406
Cone Hemispherical
End.. . 0.000222
FIG. 6. RESISTANCE OF MISCELLANEOUS OBJECTS (AFTER EIFFEL)
however, materially less than for the two wires placed side by side.
Resistance of Inclined Wires
Eiffel has experimented on the resistance of inclined wires. As would be expected the resistance of a wire progressively decreases as its angle with the wind diminishes. Table 3 gives correcting values.
TABLE 3.
Ratio of resistance to that of a
Angle of a wire to the wind. wire at 90 degrees to the wind.
90 degrees. 1.00
75 degrees. 0.92
60 degrees. 0.70
45 degrees. 0.46
30 degrees. 0.20
AERODYNAMICAL THEORY A IS D DATA
Suggestions for Stream-lining Wires
It has been suggested from time to time that wire resist- ance should be decreased by "stream-lining" or adding a triangular portion in back of the wire. From experiments by Ogilvie, however, it appears that a section made up of a semi-circle and a triangle has a decidedly high resistance, and the gain from such a procedure would be small.
Wires placed behind one another have also been covered in. The British Royal Aircraft Factory produces a very heavy R.A.F. wire in use on big machines which is stream-line in form. But the direction in which progress manifests itself at present is in the elimination of wires by certain modern trussing such as used in the recent Curtiss biplane.
Resistance of Miscellaneous Objects
The resistance of certain miscellaneous objects as deduced by Eiffel may sometimes be useful. The values for such objects within certain limits are illustrated in Fig. 6.
References for Part I, Chapter 10
AIRPLANE BODIEH
British Ucport 1911-1012, page 52.
British Report 1012-1913, page lie,.
" La Resistance de 1'Alr et r Aviation," Eiffel, 1914, page 250.
AIRPLAXE WUEE1*.-
Britlsh Report I'.H- l!'i::. I«'K" T--
"La Resistance de 1'Alr ••< 1'Avlatlon," Eiffel, page 250.
\\1I1K AND CABLES
" Aerodynamic Resistance of Struts, Bars and Wires," by A. P. Thurston, Aeronautical Journal, April and July, 1912.
British Report 1010-1911.
" La Resistance de 1'Alr et 1'Avlatlon," Eiffel, page 97. "New Mechanical Engineers' Handbook," Section on Aeronautics, by J. C. Hunsaker.
Chapter XI
Resistance and Comparative Merits of
Airplane Struts
Considerations of Comparative Merit of Strut Sections
It is naturally desirable that some single expression be found which will give the general efficiency and theoretical desirability of any strut section under consideration. This was first done by the staff of the National Physical Labora- tory, who devised what they called the " equivalent weight," ami
we have here employed an adaptation of this quantity under the name of the " merit factor." In deriving this, we start with the basic- as- sumptions that the speed of the machine is 60 miles per hour, the gliding angle 1 in 7, and the average width of the struts about 1 inch (the exact breadth assumed depending on the form and strength of the section).
Then, since gliding
W angle = ^- , every /
pounds of strut \vright will give rise to 1 pound of resistance, in addition to the aerodynamic resistance of the struts.f We can, therefore,
W write T = — 1- R, where T = thrust due to the struts, and
It is their aerodynamic resistance. Simplifying, we have G = W + 7R, but, since this expression has a maximum value for the least efficient strut, the reciprocal is here employed,
14300 and multiplied by the constant 14300, giving C = = jp i 7^
The best strut under the conditions above specified is then the one showing the highest value for C. The reason for choosing this particular value for the multiplier is that it makes C = 100 for the best strut of the first and largest series which we shall consider.
If the speed of the machine for which the struts are being selected is greater than 60 miles an hour, the resistance be- comes of greater importance as compared with the weight, and the merit factors for those sections which, although heavy, offer very low resistances are relatively improved. If the glid- ing angle is flatter than 1 in 7, a similar effect ensues.
On the other hand, if it becomes necessary to use struts having a diameter of more than 1 inch or thereabouts, the ad-
OGILVIE'S SECTIONS
vantage inclines toward the sections which have the greatest strength for their weight, and the relative importance of re- sistance is diminished, since, in similar sections, weight varies as the square of the breadth and resistance only as the first power. These effects are, however, of slight importance, and would not be likely to change the merit factors enough to have serious influence on the choice of a section in any given case.
The question of strength will be taken up more fully in another section of the course. It will suffice to say here that the strengths of two struts have been considered to be equal when their moments of inertia about their longitudinal axes are equal.
Strut Sections Developed by Ogilvie
We may now proceed to the examination of definite data for a number of series of struts, tested at various times and places. The following figures are the result of experiments performed at the N. P. L. at the suggestion of Alec Ogilvie, the sections being illustrated in Fig. 1.
/ = moment of inertia for the section in question about its longitudinal axis (inches* for a strut 1 inch wide).
R = resistance in pounds of 100 feet of strut 1 inch wide at 60 miles per hour.
W = weight in pounds of 100 feet of spruce strut 1 inch wide.
b = width of strut whose strength will be equal to that of a strut of section a, and 1 inch wide.
W = weight of 100 feet of spruce strut of width b.
CM = merit factor at 60 miles per hour.
No.
W
W
|
a |
.167 |
104.4 |
41.6 |
1.00 |
41.8 |
19 |
|
b |
.049 |
81.9 |
16.4 |
1.36 |
30.3 |
18 |
|
c |
.090 |
59.2 |
30.4 |
1.17 |
41.6 |
27 |
|
d |
.124 |
36.9 |
34.8 |
1.08 |
40.6 |
45 |
|
e |
.074 |
63.0 |
33.4 |
1.23 |
50.6 |
24 |
|
1 |
.134 |
28.6 |
37.7 |
1.06 |
42.4 |
56 |
|
0 |
.094 |
54.9 |
30.0 |
1.15 |
39.7 |
30 |
|
h |
.119 |
12.8 |
39.7 |
1.09 |
47.1 |
99 |
|
i |
427 |
12.8 |
41.0 |
1.07 |
47.0 |
100 |
|
; |
.119 |
13.5 |
39.7 |
1.09 |
47.1 |
96 |
|
i |
.111 |
13.5 |
38.0 |
1.11 |
46.8 |
94 |
|
I |
.106 |
29.9 |
36.4 |
1.12 |
45.6 |
51 |
|
m |
.106 |
45.9 |
36.6 |
1.12 |
45.9 |
35 |
|
n |
.171 |
14.2 |
51.9 |
0.99 |
509 |
97 |
|
o |
.146 |
13.5 |
47.0 |
1.03 |
49.9 |
97 |
|
p |
.128 |
18.7 |
44.1 |
1.07 |
50.5 |
75 |
|
q |
.245 |
15.1 |
71.0 |
0.91 |
58.9 |
93 |
|
r |
.227 |
16.4 |
67.2 |
0.93 |
58.1 |
87 |
|
s |
.194 |
13.5 |
62.0 |
0.96 |
57.2 |
97 |
|
t |
.209 |
13.5 |
66.1 |
0.95 |
59.7 |
95 |
|
.115 |
24.6 |
42.5 |
1.10 |
51.4 |
59 |
t Relationships between weight and resistance on a glide will be fully considered in Section 12.
Many very interesting conclusions can be drawn from this table. In the first place, it is evidently of the utmost im- portance to avoid rapid changes in curvature. Several sec- tions, notably, e and I, although they appear to have a very smooth outline, oppose a large resistance simply because the transition from the entrance to the run is so abrupt that the air-flow cannot follow its contour, and violent eddy-making ensues.
8fi
AERODYNAMICAL THEORY AND DATA
The good performance of several sections so formed indi- cates that it may be wise actually to run the sides of the strut parallel for some little distance, as illustrated by q and t. This is counteracted, however, by the fact that skin-friction increases in proportion to the " wetted surface " of the strut. It is for this reason that the very longest sections did not give such low resistances as those of more moderate form. This matter of the ratio of length of section to width will be dis- cussed more fully somewhat later, in connection with another series of tests.
It will be seen, too, that the resistance is little affected by the chopping off of a portion of the tail in such a manner as to leave it straight across. Examples of this are furnished by n, ( and i. This is due to the fact that it has not been pos- sible in any strut yet designed to totally eliminate the region of deadwater behind the strut. As will be evident from any section of air-flow about a fair-shaped section, the lines of flow always leave the contour of the strut some distance short of the extreme rear. Since no changes made in the contour within this region will have any decided effect on the re- sistance, it avails nothing to go to the trouble and expense involved in the attempt to construct a wooden strut running out to a sharp point at the back.
Another Series of Struts Tested at the N. P. L.
At about this same time another series of struts was tested at the same laboratory, the sections being those actually em-
Dt Haulllant
Beta
B.F.34
c
Baby
FIG. 2. STRUT SECTIONS TESTED AT N. P. L.
G>
PIG. 3. N. P. L. STRUTS
ployed in machines then existing. The outlines of the sections tested are shown in Fig. 2, and the characteristics are given below.
Blerlot A 070
Bleriot B 107
Fmrma n 074
De Harilland. .052
Baby 110
B.F. 34 279
B.F. 35 238
188
K
51.0 52.7 49.3 54.9 17.0 i: -..r. 13.5 14.8
34.9 25.2 20.5 41.6 93.2
si! 7
61.7
b 1.24
1.11: 1.22 1 .:;•» 1.11
0 -v
0.92 0.97
40.0 43.8
36.8
r,i.:.
n.9
70.0 58.0
Om 80
31
26
7K
90
of the symbols being the same as in the tables already given, except that n = the ratio of the length to width of section.
n 2. 2.5 3. 3.5 4. 4.5 5.
.094 .117 .141 .104
.iss .211 .235
R
24.8 13.7 13.4 11.4 11.2 11.7 12.1
W
32.0 40.0 48.1 50.1 04.1 72.1 80.1
b
1.15 1.0!) 1.04 1.00 0.97 O.94 0.92
W
42.3
47.5
52.1
M.1
)i'J.'J
67.8
73.7
59 94
9(i
in:,
LOS
99 94
Tims it is apparent that the best of these sections are inatc- rinlly superior to the best of the sections tested by Ogilvie. both in resistance and in merit factor. In Fig. 4 resistance of
RESISTANCE
OP R.A.K STRUTS
FIG. 4.
UESISTAVCE AND FACTORS OP MEKIT FOR R. A. STRUTS
100 feet of strut at 60 miles per hour, and merit factor at 60 miles per hour, are plotted against ratio of length to width. As this ratio diminishes, the air-flow about the strut takes on a very uncertain character, and the values when n is less than 2 are rather doubtful. Such extremely short sections as this are also undesirable from the standpoint of lateral stability. as will be shown in another section of the Course. On the other hand, n may be considerably pi-eater than the absolute optimum value without any great disadvantage, so it will be well in general to employ a ratio of four, or even a slightly higher figure. The photographs of Mow aliout strut sections. reproduced in Fig. ~>. show clearly why such a procedure c-.-m be safely adopted.
It will be seen that these figures simply supplement and confirm the conclusions already deduced from the more exten- sive and systematic investigations directed by Mr. Ogilvie.
Te»U on Struts, Length to Width Varied
As a result of these and other tests. » series of struts em- bodying the best features of those already tried, and varying only in the ratio of length of section to width, was made and tested at the National Physical laboratory. Three rep re live members of tin- series are shown in Fig. .'!. The table below gives the characteristics of these struts, the meaning
Two Kiffcl Struts
Two struts of somewhat the same section as those just di- eiisscd have recently l.een I, '-led by Kifl'el. and show remark- ably low resistances. Their outlines arc uivcn in Fiir. (i. For Xo. 1, having n equal to :!.L'.'I, If equals !i.7 pounds, while for No. 2. with a somewhat sharper entry, »i is L'.lKi and R is only 8.7 pounds. I'arl of this improvement oxer the best of the Knglish tests, hoxvexei. i- undoubtedly due to the higher wind speed which is secured in Kiffel's laboratory, the resistance coefficient having a tendency to rise as the speed of test i^. decreased.
AERODYNAMICAL THEORY AND DATA
67
Effect of Length of Struts
We now turn our attention to the effect of the length of the strut. While this point is less important than was gen- erally supposed a few years ago, and while its effects are largely determined by the nature of the surfaces in which the strut terminates, the experimental results bearing on the mat- ter should nevertheless be studied. For this data we are indebted to Mr. Thurston, who has described his results in the series of articles already cited. As the result of a great
nel would be exceedingly difficult to devise. The matter might well be investigated in an outdoor, full-scale plant such as that at St. Cyr.
Resistance of Inclined Struts
The only point which remains to be studied is the resistance of struts which are not normal to the line of flight. Some much more recent tests by Mr. Thurston have covered this point, and show very surprising results. Struts of square, rectangular, circular, and stream-line section were tested at angles from 0 to 90 degrees, and the effects of the ends of the strut offering a direct resistance when inclined were overcome by the use of the method of differences: that is, tests were made first on a strut 34 inches long, and then on one 16 inches long, the difference of the figures obtained being equal to the resistance of an 18-inch section of an infinite strut.
The ratio of the resistance of a strut inclined at various
BETA
FIG. 5.
DE HAVILLAND ILLUSTRATING FLOW AROUND STRUTS
many experiments on manifold different types of strut, he came to the conclusion that resistance for a strut with free ends could best be expressed by the formula B = KltV1- .0073fF2, where R is the resistance in pounds, I and *, re- spectively, the length and thickness of the strut in feet, K a constant, and V the speed in miles per hour.
It is evident from this equation that, even with the lowest values of K yet obtained, the effects of length will be prac-
Fio. 6. Two EIFFEL STRUTS
tically negligible when the length is more than 50 times the thickness, as it generally is. Since, in addition, the case of a strut with free ends is one which never occurs in practise, resistance may be considered as independent of length-thick- ness ratio for all the purposes of design.
The form of air-flow about the wing may have very decided effects on the resistance of interplane struts, but we have no means of knowing how great these aro. and experiments cover- ing this point and susceptible of performance in a wind tun-
INCMMATIOM Of BAH TO WIMO
FIG. 7. DATA FOR INCLINED STRUTS
angles to the resistance of a normal strut of like section and equal projected length is plotted in Fig. 7. It will be seen that the resistance at 30 degrees to the wind is less than one- third of that at 90 degrees, and this large difference is by no means accounted for by the difference in length of section parallel to the wind. When a circular strut is placed at an angle of 30 degrees to the wind, the section parallel thereto is an ellipse having a length of twice its width, and the resist- ance of an elliptical strut such as this, when placed normal. is only 36 per cent less than that for a circular section. About 45 per cent of the reduction due to inclination thus remains unaccounted for.
Since, however, the curve of reduction is substantially a sine curve, and is therefore very flat at the ends, there is very little advantage to be gained from inclining a stream- line strut unless it is inclined at least 30 degrees to the nor- mal. This reduced resistance should, however, be kept in mind as a point in favor of the staggered biplane. Eiffel also made a few tests on struts inclined 30 degrees from the normal, the results cheeking very well with Mr. Thurston's.
The Effect of Changing the DV Product for Struts
As was shown in Chapter 10, the resistance coefficient is not an absolute constant, but is a function of VI), when- V Is the speed and I) the diameter of the strut. The coeffi- cient tends to decrease as VI) increases, but the change for values of I'D (in foot/second units) above 6 is extremely small, as Eiffel lias demonstrated. The tests made at thp National Physical Laboratory have been made with a value of VD equal to only 2.5. whereas, in an actual machine, this quantity would never be likely to fall below 5, and is generally from 7 to 10.
i is AERODYNAMICAL THEORY AND DATA
We can therefore deduce from Kitlel's experiments that it References for Part I. Chapter 11 is safe to reduce the values for resistance here given (for the
N. P. L. tests) by about 25 per cent in applying them to a " strut*." FHoht. June is. 1012.
design. This indicates that, as was hinted above, the superior- -Aerodynamic RMMUM of struts. Bare, and wires." by A. v.
ity of Eiffel's strut sections is more apparent than real, and Thurston ; Aeronautical Journal, April and July, 191::.
that the best sections yet available are the N. P. L. sections Technical Reports of the British Advisory Committee on Aeronautics.
having fineness ratios of from 3.5 to 4.5. The correction 1911-12. 1912-13.
given here should be applied only to Struts of fairly good "The Resistance of Inclined Struts In a Uniform Air Curri'iit," by A.
section, as the value of VD has much less effect on those sec- i^1"1""0" "Dd "' Tonnsteln' Aeron<""lcal •""•"•«'• Janu"5'-
tions for which the resistance is relativelv IUL-II. and in which
" Nouvelles Recbercues sur In Resistance de 1'Alr et 1'Avlatlon." by G.
there is more effect due to turbulence than to skin friction. Eiffel. (1914 edition.)
Chapter XII
Resistance and Performance
Nomenclature
It may be useful to restate the symbols which we employ in considering performance curves, ascent and descent.
IT" = weight of the machine;
A = area of the wings.
i = angle of incidence of the wings.
L = lift.
Ku = lift coefficient.
D = drag of wings.
K., = drag coefficient.
11 = resultant of lift and drag on the wings.
P = parasite or structural resistance of a machine.
Dt = total resistance or drag = T) -\- P.
Rt = total resultant air force on a machine. // = -propeller thrust.
6 = angle of flight path with the horizontal.
Structural and Wing Resistance for the British B.E.2
In Chapter 4, a problem was worked out on the sustentation and resistance of wing surfaces, which in spite of some rough
50 00
MILES PER HOUR
FIG. 1. PERFORMANCE CURVES FOR THE B.E.2
assumptions, illustrated the main performance curves and cal- culations employed. In Fig. 1 are shown curves for the Brit- ish B. E. 2. It is not a particularly modern machine, but has been worked out so thoroughly that it deserves particularly careful study.
The body or parasite resistance which includes the resis- tance of the wing bracing, chassis, etc.. as well as the resistance of the body proper, is taken as varying as T'"2 and allowance has been made for propeller slip stream velocity. The body resistance is seen to play an unimportant part at low speeds. But at about 53 miles per hour it becomes greater than the plane or wing resistance, and at high speeds it. is almost twice
as great as the wing resistance. This emphasizes the imppr- tance of minimizing the resistance for a high-speed machine. However good a wing section itself may be, high structural resistance will make high speeds impossible.
The plane resistance curve has a minimum value at about 65 miles per hour and increases on either side of this speed. It is interesting to follow out how this increase in resist- ance on either side occurs. At high speeds, the angles of incidence and the drift coefficients are small but the speeds are very great, and the increase in wing resistance is obvious. At small speeds on the other hand the airplane is flying at large angles of incidence to give the necessary sustentation and the drift coefficients are large. The shape of the total re- sistance curve follows from the summation of the two.
Theoretical Laws for Minimum Thrust and Minimum Horsepower
From a theoretical treatment of the question, the following interesting law has been derived :
Minimum thrust is required to overcome the resistance of an airplane when Hie parasite resistance is equal to the drag of the wings.
For a proof of this law, reference to Chasseriaud and Espitallier is appended. In the case we have selected, illus- trated in Fig. 1, the structural air resistance and the wing drag are equal at a speed of 53 miles an hour, while the minimum resistance is at 49 miles per hour. The law does not seem to be borne out by practice, though it may be occasion- ally useful as a rough check.
The minimum horsepower required generally occurs at a low speed, but not at the minimum speed; and its position will vary for every machine. Another theoretically deduced law states that:
Minimum horsepower is required irln'ii Hie machine is mov- ing at a speed at which the wing resistance is three times the body resistance. "• This law is often highly inaccurate, but may be useful.
Effective or Propeller Horsepower Available Curve
Typical curves for these are also illustrated in Fig. 1, and are of the greatest interest to the designer. In establishing such curves it is generally assumed that the engine is running at the rated revolutions per minute and that in designing the propeller the efficiency for this revolution per minute at every airplane speed is known. Thus assuming an engine which delivers 140 horsepower at an ail-plane speed of 80 miles an hour, the propeller having an efficiency of 75 per cent at this speed, the available horsepower will be 140 X 75
100
= 105 horsepower.
69
70
AERODYNAMICAL THEORY AND DATA
Since the power of a propeller is given by the product of us thrust into the speed and the speed of the propeller is the speed of the airplane, it follows that when the propeller is delivering sufficient power, it is also delivering sufficient thrust. Hence propeller horsepower available is sufficient for all practical consideration, and propeller thrust curves need not be included in a performance chart.
Minimum and Maximum Speed; Maximum Excess Power; Best Climb; Descent
The maximum and minimum speeds of an airplane are gen- erally given by the two points of intersection of the propeller horsepower available and the total horsepower required. If the machine is highly- powered, and the propeller efficient, the two curves may not intersect at the speed at which the lift becomes insufficient, and the airplane would climb at stalling angle, unless the engine is considerably throttled down. The climb decreases the angle of incidence, and checks stalling. It is thus a decided advantage to have excess available power at high angles.
It is a simple matter to deduce the speed of climb from the excess power. This is absorbed in raising the machine.
Ex
power
Total weight X climb per second
551)
The maximum excess power does not occur at the lowest speed. To find it, we must measure the maximum ordinate between the available propeller horsepower and the total re- quired horsepower. In Fig. 1 this is to be found at 48 miles per hour. The excess is 21 horsepower and the weight of the machine is 1650 pounds.
Climb =
21 X 550
= 7 feet per second or 420 feet per min-
ute. This is, however, only the initial rate of climb. As the machine rises, the density of the air, the power of the engine, and the climb gradually diminish.
In practice, the pilot need not know the change of in- cidence that he produces to climb, although for a given ma- chine it is an easy matter to calculate the correct angle from the performance curves. In Dr. Hunsaker's words, " a care- ful man moves his elevator slowly until he has placed him- self on the desired trajectory." Part of the art of aviation is to do this without exceeding safe limits, for obviously there is a limit to the rate of climb the engine can handle. If the machine is put on a climb too steep for the power of the ma- chine, the speed is suddenly lost, the controls become ineffec- tive, and the machine has stalled.
In descent, very analogous considerations obtain. The pilot decreases his angle of incidence to a negative value. At this angle the speed required for sustentation is beyond that of the maximum, and the propeller horsepower is insufficient. If D = deficiency in horsepower,
n Total weight X velocity of descent. Mt
The machine descends and gains the required speed under tin- action of gravity.
The Two Regions of Control. Control by I limiilin-
Consider the performance curves of the same machine, the Hnti-h I'..K.'_' shown in Fig. 1. Suppose the machine to be flown iit in degrees at the point J/ with the engine throttled. so that there is equilibrium, and the power curve is as shown. 26 horsepower. The pilot wishing t<> rise will naturally in crease his angle of incidence to say 12 degrees. He will thru require 30 horsepower while the throttled engine will deliver
even less than the 2(j horsepower through the propeller. In- stead of rising the machine will fall.
Suppose now that flying at the same point and under the same conditions he wishes to descend, and decreases his angle to 8 degrees. He will now have an excess of power of 3 horsepower as can be seen from the curves and will ascend instead of descend. There is therefore a region of reverse controls, known to French authors as the regime lent.
At the point M . when the pilot wishes to rise and in- creases his angle of incidence, he does indeed obtain excess power and rises. Here the controls are normal and the region is known as regime rapide. For an inexperienced pilot the regime lent is dangerous. Even if he knows the angle of in- cidence at which he is working, he is likely to get into diffi- culties.
With a flexible engine, an expert pilot can operate an air- plane in the slow speed region by manipulation of the throttle
40 M 60 TO SO 90 100
MILES PEU HOUR
Fiu. 2. VARYING SPEED RANGE WITH ENGINE THROTTLED
alone. In Fig. 2 the propeller horsepower available is shown with the engine throttled down to various speeds for a design taken i'rom Dr. Hunsaker's pamphlet, to which reference is appended. For each speed of the engine there is a different maximum and minimum speed of the airplane, and a different speed range. If the airplane is living at the minimum speed in the regime lent region at a certain revolution per minute, the pilot can by unthrottling his engine pass to a larger speed !.-iii'_re, obtain excess power and climb without changing his forward speed or angle of incidence. When an engine is throttled the danger of reversed controls is still greater, lie- cause the speed range becomes so very small. Kven the best of pilots may mistake his position on the curve.
In French airplane contests, a premium has been placed on low speeds, and the regime lent with throttling has been largely and successfully used. Such operation does not seem advisable for ordinary flying.
Variations in PropHIrr Horsepower (lunr-
We will now consider the possible variations in performance by changing the design of the propeller from a high speed to a climbing propeller. In Fig. 3 the B.E.2 is again illustrated. The power required curve remains the same. By suitable design the propeller ellicicncy curve can be changed so as to give maximum etlicieney at varying speeds. The design of a suitable propeller cannot unfortunately be detailed here.
For the propeller with Kllieicncy Curve 1, the maximum ellieiency is at high speed, and the Horsepower Available Curve 1 shows that such a propeller will give a high maxi-
AERODYNAMICAL THEORY AND DATA
71
mum speed. It is a high speed propeller when applied to this particular airplane.
For the propeller with Efficiency Curve 2, the maximum efficiency occurs at a lower speed. Such a propeller will give
100*
70
MILES PER HOUR
FIG. 3. VARIATION OF PERFORMANCE WITH CHANGE IN PRO- PELLER DESIGN
a smaller maximum speed, as can be seen from Horsepower Available Curve 2, but a greater excess power. It will be a climbing propeller. There are many such variations pos- sible for any machine.
Angle of Glide
The best L/D for a wing section may be in the neighbor- hood of 14 or 15. But the parasite resistance of a machine, i. e., the resistance of the body, wing bracing, etc., increases the drag to such an extent that the L/Dt of the whole machine may be reduced to 7 or 8. It is this value of L/Dt which de- termines the angle of glide of a machine.
In Fig. 4 is shown a machine which is gliding with the engine shut down so that the propeller exerts no thrust, i be- ing the angle of incidence, and 0, the angle which the machine makes with the horizontal line, being the angle of glide. Re-
solving forces perpendicular to and along the line of motion, the equations of equilibrium for steady glide are:
L (1)
= Dt = D + P (2) The angle of glide is therefore given by the equation
tan
=- (3) L
and has its maximum value when Dt is a maximum.
The minimum angle of glide is also termed the " best " angle of glide. At a given height above the ground, the
WSinff= D+P
FIG. 4. FORCES ON AN AIRPLANE IN A GLIDE
forward displacement of the machine before landing varies as cos 6 and will be a maximum for the smallest value of 6. The pilot has at this angle the greatest radius of action when de- scending from a height with his engine shut off.
The angle of glide for any machine at any speed can be at once obtained from the total resistance curve for Dt and the weight of the machine, assuming L = W which makes a com- paratively small error. In Fig. 1, the angle of glide is shown for all speeds of the machine in question.
References for Part I, Chapter 12
Barnwell's " Aeroplane Design."
" Aeroplane Design," by J. C. Hunsaker, United States Naval In- stitute Proceedings, November-December, 1914. Itrttish Uep.)rt. 1912-1013. No. SB. Chasseriaud et Espltalller, " Conrs d'Aviatlon."
Chapter XIII
Resistance Computations — Preliminary Wing
Selections
Example of Estimate for Parasite Resistance for a British Machine
The B.E.2, mentioned in Chapter 1:2, will serve as an ex- ample of the estimate of the total parasite resistance of a machine. The estimate was arrived at by the Royal Aircraft Factory after the most careful tests, both at the N. P. L. laboratory and in full flight, and is given in Table 1.
TABLE 1.
B.E.2; WEIGHT. 1650 POUNDS; 372 SQUARE FEET BIPLANE ScKrACE, 70 HORSE- POWER ENGINE.
Estimated parasite resistance at 60 miles per hour.
|
Value in pound.* per ««uar« foot of Resistance Part. Whence obtained. projected area. in pound*. Strut* 8.6'0"X1«" N.P.L.Teet . 4.2 4. 4'0" X IJi"... " 1 * |
||
|
6, 3'0" X 1M" |
*» |
1 6 |
|
Wings 2. 2O" cable. |
7.2 29 5 |
|
|
70, 12G.H.T. wire |
M |
5 6 |
|
Estimated |
3 0 |
|
|
Rudder and elevators |
38.1 20 |
|
|
Body with passenger and pilot. Axle |
N.P.L. Teet |
40.0 2 0 |
|
Main skids and axle mounting Rear skid... |
1.0 |
|
|
5 |
||
|
Wheels |
N P L. Test |
3 5 |
|
Wing, skids, wiring, plates, •ten. silencers, etc. . . |
Estimated . |
. 10.0 |
59.0
Szpoted to a tlip stream of IS feet per second, for an airplane speed of SO miles per hour. i. e., SS feet per second.
Bodv 40.
4. 4'0" strata 1.4
2/3 of 3'0" strut*.
50" cable
30'H.TwJre
Rudder and clerator . .
Rear skid
Fittings
.8 6.7 2.4 2.0
.5 2.0
55^8 91.5
In slip stream resistance increased to
Increase 35.7
Total 140.0
One of the most interesting features of this resistance esti- mate is the allowance for slip stream. The parts of the air- plane included in the slip stream are, of course, taken within the area swept out by the propeller. The speed of the machine is 60 miles per hour, i.e., 88 feet per second, and the slip stream is 25 feet per second, i.e., 28.4 per cent, increasing the resistance of the parts involved by some i>5 per •
I \.llllple- ill I'.IIM-itl- l!r-i-t;UHT I )\-\ T\ Illlt i< III ill •"rhiMil M.leliine-
Tahle J furni-he- useful estimates of parasite resistance distribution tor a number ol -tandard school machines. The -lip stream velocity ha« been taken as 15 per cent of (lie air- plane speed, givintr an im-na-e in re.«i» lance of .TJ per Cent for the parts exposed to it.
Uiscrejmncies in these values arise from a number • The Martin has interplane ailerons, and the other machines have wing flaps. The Curtiss has a water-cooled motor with radiator in front. The machine designed at M. I. T. has a radiator above the upper wing. The Curtiss has a two-wheeled landing gear, while the Martin has a third wheel in front.
TABLE 2. Percentage of Parasite Resistance.
|
Zgi |
j |
S |
Z: |
i |
. 3 |
*• |
|
IP |
ii |
i |
C |
^ « |
C T. |
c |
|
llli |
"t i. C |
5 • |
!< |
u C j: — |
5 $ |
|
|
o |
- c |
-^- j= |
• |
|||
|
fo ** |
M fi |
M |
H™ |
2 * |
™ |
|
|
S'l a. |
= ' |
M C |
- 5 |
d / |
'| £ ? |
^ i |
|
1 ifel |
ll |
yg £'£ |
E| §1 |
tfc |
N £3 |
Curtis 90 h.p.. two place, 1893 Ibs. tractor 39.5%
Martin, 1800 lb».,
70 h.p. Renault. . 28.8%
P-.
10.5% 17.5% 28.5% 4.0% 18.7% 14.1% 14.7% 22.7% P
.Q3SW .042V"
126lb». 151 Ibs.
90 h.p. biplane, 1850 Ibs., tractor, designedatM.I.T. 36.0% 15.1%
.'•'• :).5% P-.OMV* ll.Ml.i.
Two tractor machines, carefully designed by students at the Massachusetts Institute of Technology, gave the following figures :
Paras:- Allnuint:
Tractor Biplane Reconnaissance.
Tractor Biplane Reconnaissance ,
WVicht in Ibs.
2300
iirionl. In Engine. I'inm.p.h. for t*lip stream.
2885
120 h.p. 125 h.p.
P-.040 V P-.04.S.-, I'
.011 V«
Resistance at
00 m.p.h.
158 ll.s.
Parasite Resistance Coefficient for a Stnrtevant Seaplane
For a Sturtevant seaplane, weighing 2650 pounds, with a 140 horsepower engine, and where para-iie iv.-isiance. 01 count of the floats, is higher than for a land machine of the same weight, the structural n-i-tance i| e.-timated as being given by the formula P= .()".:;_' I . and 10 per cent increase on all the parasite resistance is allowed for. hrin<_rin<r up the Value to 7' • .0.")7fiT/;. or 212 pounds approximately, at tin null - per hour.
Mlowanrc for Slip Stream
The i|ue-iimi ni -]i|i •,11-rani \elm-itv i< mn- of plexily, ami. in the present stair ol knowledge, it docs not -•.•in advisable to enter into very eomplinitcd calcuhilions when working out perfuniianee eiirves. The estimated liirure- triven tor the various American ma<-hine~ ^enu to he very well liorne out by tests in tile field. The Hrilish allowance for slip
-•1
AERODYNAMICAL THEORY AND DATA
73
stream increase was 28.4 per cent, and the one given by American practice is 15 per cent. It would be safe to say that if for the parts of the machine, within the area swept out by the propeller, the speed is increased by some 20 per cent, and resistance of those parts increased by some 44 per cent, a sufficiently accurate estimate will be made.
The other method adopted of increasing the total structural resistance by some 10 per cent to allow for slip resistance, though not so rational, has the advantage of being simpler, and is still in accordance with tests in the field. For a mono- plane, where the parts exposed to the slip stream bear a larger ratio to the rest of the machine, an increase of 15 per cent on the total structural resistance is probably advisable.
Preliminary Estimates for Parasite Resistance
In making preliminary estimates for a machine, a really difficult point is the allowance to be made for parasite re- sistance. Some authorities allow for the parasite resistance by finding the resistance of the body and multiplying it by four for a biplane and by three for a monoplane. Such rules can only be roughly correct, and it is best to refer to data for standard machines and select parasite resistance coefficients of a machine of similar type and weight. The figures given in this section will be sufficiently accurate for a preliminary design.
Preliminary Selection of Wing Section and Area
A great many ingenious methods have been devised for the selection of correct wing sections and areas for the preliminary
design of a machine whose engine-power and specification are given. Eiffel, among others, has developed a very complete system. It seems best, however, to employ the simplest and most straightforward trial and error methods, based on the following rules :
(1) From a consideration of standard practice, select the loading per horsepower and hence weight of the machine.
(2) From a consideration of standard practice, select the ap- proximate loading per square foot.
(3) From some such considerations as those given in Chapter IV select two or three wings which are likely to give the qualities desired.
(4) Assume a parasite resistance coefficient which from a standard practice is likely to apply to a machine of the type and weight in question.
(5) Draw up a number of performance curves varying:
(a) Wing sections
(b) Area for each wing section
(c) Assumed propeller efficiency curves.
Some data on standard practice will be given in the Second Part of the book, and the above rules will be applied to the design of a standard machine.
References for Part I, Chapter 13
Barnwell's " Aeroplane Design." British Report, 1912-1913. No. 86.
Part II Airplane Design
Chapter I
Classification of Main Data for Modern Airplanes
Unarmed Land Reconnaissance Machines
Land Training Machines
The Army Classification
Constructors in America have hitherto mainly developed one type of airplane, the tractor biplane reconnaissance ma- chine. But with the rapid development of military aeronau- tics, airplanes are evolving into distinct classes, just as the component vessels of a fleet. The memorandum on " Military Airplanes," prepared by the office of the Aviation Section of the Signal Corps, offers the most authoritative classification, and one which constructors must of necessity follow very closely. It suggests six distinct types, which we shall study as closely as possible, within the limits of data held confidential by manufacturers. (I) Land Reconnaissance Machine, used when there are no enemy airplanes; (II) Land Primary School Machine; (III) Land Advanced School Machine; (IV) Land Gun Carrying Machine, (V) All-round Twin-engined, Land or Water, (VI) Land Pursuit Type.
Unarmed Land Reconnaissance Machine
For tliis machine, the memorandum gives the following figures :
and the empirical rules to be derived from it are invaluable in the preliminary stages of a design, and enable the designer to avoid misleading rough estimates of weights and dimen- sions.
TABLE 2.
MAIN DATA FOR TWO-SEATER TRACTOR BIPLANES op THE UNAH.MKU
RECONNAISSANCE TYPE OVER 2,500 POUNDS IN WEIGHT. RECENT
EXAMPLES op CONSTRUCTION.
TAnr.K i.
Unarmed Land Reconnaissance
Machine.
130
Tractor
Horsepower
Puslipr or trac'tor
Number of men
Military load, pounds 475
Fuel load, pounds 450
Miles radius of action, full power 41 ."
Climb In 10 nn'imtes. feet 3,400
High speed, miles per hour 82
Low speed, miles per hour 4ti
Factor of safety 7
Percentage made in war 2
(Gross load is well over 2,500 pounds for this type.)
The memorandum deals very unfavorably with this type of machine, which forms, as we have said, an important part of American construction. It is said to be a false development, suitable only for use against an enemy who has no airplanes. Possibly useful for long-range reconnaissance, it will be out- matched in warfare by the armed " pursuit " type and the large armed twin-engine machine. For short ranges the pur- suit type will surpass it, for long ranges the larger machine may be not quite so rapid, but will have a greater radius of action. A careful study of these views would lead one to believe them correct and in accordance with developments abroad.
Analysis of Main Data for Representative Unarmed Reconnaissance Biplanes More Than 2500
Pounds Gross Weight
This group is composed of excellent, controllable machines
In Table 2 are given the main dimensions and perform- very similar in character. It is therefore possible to drnw ances of a number of representative machines. Such analysis some fairly definite conclusions.
77
|
Machine Standard |
Curtiss Wright- Sturtevant Wright-) |
|
H-3 |
R-4 Martin V S Martin R j |
|
Engine Hall-Scott |
Curtiss Hispano- Sturtevant Hall-Scott 1 |
|
A-5 |
Suiza A5a J |
|
Horsepower 135 |
200 150 140 150 |
|
Number of cylinders. 6 |
8886 |
|
Revolutions per min.. 1,250 |
1,400 1,450 2,000 1,375 |
|
Gasoline tank capac- 68 |
100 ... ... 70 ) |
|
ity gallons |
gallons gallons ) |
|
Endurance in hours.. 6 Maximum speed, miles |
5.42apiir. 6 4.5 4.84 |
|
per hour 84 |
90 ... 86 Sfi |
|
Minimum speed, miles |
|
|
per hour 40 |
4S ... 42 47 |
|
Climb in 10 minutes, |
|
|
feet 3,400 |
4,000 . . . 3,500 3,500 |
|
Propeller diameter(two blades) 9' |
8' 4" S' f." |
|
Weight loaded, pounds 2,700 |
3,245 2,310 2,550 2,880 |
|
Weight bare, pounds. 1,900 |
2,225 1,725 1,850 1,905 |
|
Useful load, pounds. 800 |
1,020 90f> 700 ns:« |
|
Percent useful load.. 29.6 |
31.4 34.2 27.4 34.2 |
|
Weight per horsepow- |
|
|
er in pounds 20.0 |
16.21 16.86 18.2 19.1 |
|
Weight per square foot |
|
|
wing area in pounds. 5.08 |
6.42 5.86 4.64 6.25 |
|
Overall length 27' 0" |
29' 0" 27' 2" 27' 0" 26' 8" |
|
Mean span of wing/ |
|
|
length 1.41 |
1.49 1.37 1.65 1.64 |
|
Wing section R. A. F. 6 |
R. A. F. 6 Vought 4 R. A. F. 6 . . . |
|
Upper span 407 1' |
48'4VS" 39' S%" 49' 6" 50' 8" |
|
Upper chord 6' 6' |
' 6' 3" 5' 9" 6' 3" 5' 6" |
|
Upper aspect ratio.. 6.2 |
7.7"> 0.95 7.95 9,25 |
|
Lower span 40' 1" |
38' 5(4" 39' 81/-" 39' 6" 36' 10" |
|
Lower chord 6' 6" |
6' 3" 5' 9" 6' 3" 5' 6" |
|
Lower aspect ratio.. 6.2 |
6 15 0.95 6.32 6.6 |
|
Gap 6' 6" |
6' 2" 5' 7" 6' 3" 6' 0" |
|
Gap, lower chord.... 1.00 |
0.9S 0.98 1.00 1.09 |
|
Total area of wings. |
|
|
including ailerons, |
|
|
in square feet 532 |
505 430 540 458 |
|
Area of rudder in |
|
|
square feet 10 |
16.5 12.37appr. 15 8.7 |
|
Area of vertical fln |
|
|
in square feet. ... 5 |
7 5 appr. . . . 7.3 |
|
Area of elevator in |
|
|
square feet 23 |
27.5 ... 24 ... |
|
Area of stabilizer in |
|
|
square feet 32 |
40.5 51.2 (ele- 28 53.21 |
|
vator and sta- (elevator and V |
|
|
bilizer) stabilizer) 1 |
|
|
Ailerons upper wing. 31 |
33.S 32.3 39 48 |
|
Ailerons lower wing. 31 |
20.5 32.3 3fi |
|
Type of fuselage Rectan- |
Rectan- Rectan- Trian- ... \ |
|
gular |
anlar gular aular ) |
|
Dihedral 3° |
3° " 1° 15' 2° 1" |
|
Stagger 10° |
5° appr. 1 ft. None 20.4% ) |
|
chord length ( |
|
|
Sweephack 10° |
Xone None None None |
Average \' allies for Machines Over 2500 Pounds in Weight
78
AIRPLANE DESIGN
(a) Average gross weight, 2737 pounds.
(b) Average wing area, 493 square feet.
(c) Average horsepower, 155. The latter figure is consider- ably increased by the inclusion of the Curtiss R-4 with its 200 horsepower engine. There is a tendency to give higher power to this class, with correspondingly better performances.
(d) Average endurance, 5.65 hours. This figure is probably a very fair value of the endurance possible if good climb is to be maintained. It should be noted that it would be possible to take up much more fuel, and not decrease the speed ; in fact, to increase it slightly. At the same time, minimum speed would be increased.
(c) Average weight per horsepower, 18.1 pounds. The Curtiss lowers this average value, and is an indication of what will follow when lighter new engines, such as the new Thomas and Sturtevant, enter into construction.
(f) Average weight per square foot of wing area, 5.65 pounds.
(g) Average maximum speed, 86.50 miles per hour. Average minimum speed, 45.75 miles per hour. Average climb in 10 minutes, 3666 feet.
The number of machines considered is too small for curves to be plotted, but it is interesting to see how in diminishing the weight per horsepower from 24.2 pounds to 16.21 pounds the maximum speed increases from 84 to 90 miles per hour, while the low Sturtevant wing loading gives a landing speed of 42 miles per hour as compared with the Curtiss of 50 miles
per hour.
mean span
(h) Average of ratios of — - =1.51.
overall length
This is an important point to be considered in the design of a machine. As we shall see later in considering longi- tudinal stability, it is quite possible to secure adequate static stability by using a short body with a large tail surface placed at a negative angle. But an excessively short body, although it means saving in weight,, may fail to give dynamic stability, due to lack of damping. At this stage of the science, we can only fix on a length for the body by taking average values such as the above.
(i) Average aspect ratio upper wing, 7.60. Average aspect ratio lower wing, 6.76.
There seems in the light of these figures no reason why an aspect ratio of 7.5 for the upper span, and 7.0 for the lower should not be successfully employed.
(j) Gap/chord ratio is practically 1.00 in every case. Without undue conservatism, it would appear that for ma- chines of this size, the increased structural weight of a larger gap/chord ratio is prohibitive, whereas in smaller machines with smaller chord, much greater values might be employed to advantage.
The dimensions of control and stabilizing surfaces present an exceedingly complex problem, so many factors brinj; in- volved. They will be carefully studied in our design, but in the preliminary stages some of the following empirical rela- tionships may be useful :
(k) Aileron or wing flap area: The dimensions of these will depend on the area of the wings whose rolling moment it may be necessary to overcome, on tlie weight and lateral radius of gyration of the machine and on the span of the wings which gives the moment arm of the ailerons. These factors are too complex, however, and at present the following fonnula offers a fairly satislactnry standard of comparison:
'i, -}-S,a,) = CA, where A — area nf wings, S, and S, = spans of upper and lower wings, o, and a, = aileron areas on upper and lower wings. (' = a constant. Where (' is large there is powerful lateral cmtrol, where (' is small there i-
weak lateral control, are as follows :
The values for the above live machines
Standard H :s 4.65
Curtiss R-4 4.50
Wright-Martin 5.95
Sturtevaut
S 6.50
Wright-Martin It
Too powerful lateral controls present difficulties in handling just as too weak controls. The average value of C = 5.38 might be at least some guide.
(1) For the horizontal elevator and stabilizer, the following very rough formula is sometimes employed in preliminary work, based on ideas similar to those enunciated in the pre- vious paragraph:
QL
d = *TJ, where d = some constant, Q = area of elevator and .1C
stabilizer, L = overall length, A = area of wings and C = mean chord.
The following constants hold for our five well controlled machines :
Standard
ri-3
.429
Curtiss R-4 .625
Wright-Martin .607
Sturtevant
S .416
\Vriclit-Mnriin
i: .661
These constants are fairly close together, with an average value of .507. A big value of d means powerful control. Without further analysis, it is seen from Table 1 that the stabilizer is made between 20 to 50 per cent larger than the elevator.
(m) Similarly for vertical surfaces, if / =-r^» where f =
A&
constant, V — vertical area of rudder and fin, L = length, A = area of wings and s = mean span of wings, we find
standard H-3 .019
Curtiss H-4 .031
Wright-Martin V
sturtcvaiit
S
.01.-, Average value, .023.
Wright-Martin .082
We shall discuss the problem of vertical fin and rudder area more closely later.
Primary ami Advanced Training Airplanes
In the training of military pilots similar methods are now employed in the majority of schools, and there are two distinct stages, " primary " and " advanced " training.
On the primary machine, the aviator obtains his first certifi- c.-ite. and the requirements of this type tend toward a steady, slow type of machine, in which it is easy to acquire confidence. The advanced training machine is scarcely distinguishable from the land reconnaissance machine, although it is somewhat slower. In the memorandum on Military Airplanes, the fol- lowing suggestions arc made for these two types, which are of obvious and permanent utility.
TAl'.u: :;.
Land Adviitu . <1 S,-lnr>l, may l/iinil Primary School, can possibly be used for
also he used for tielii artillery flre control
Horsepower M»
I'u-li. r or tractor Trie tor
Number of riH'ii '2
Military loail, pnun.ls :IT".
Fuel load, pounds 150
Miles radius (f netinn. full power.. l:i.~>
Climb, foet in in minutes 2.000
llitfli speed, miles per hour Ort
l/ow speed, miles per hour 37
r (if safety T.'i
Pcrcentace mnde In war 2.1
mountain and forest tactical recomiai
100 Tra< tor
•-•
40(1
240
:too
8,000
Tl
43
7.5 M
In dcsignm-: training machines, tin- constructor has the ad- \. -intake of complete specifications issued by the Signal Corps I Aeronautical Specifications. Nos. 1001 and 1002). These specifications are readily obtainable, but some of the main points are set forth here, as they will he applicable to our design of a standard machine, and must lie constantly kept in mind by the designer.
AIRPLANE DESIGN
MODERN AMERICAN TWO-PLACE TRACTORS
These Photographs Show Representative Two-Seater Tractor Biplanes of the Unarmed Reconnaissance Type, Weighing Over 2,500 Pounds
THK WRIGHT-MARTIN. MODEL R. TRACTOR
STURTEVANT S TRACTOR
MODEL V. WRIGHT-MARTIN TRACTOR
THE STANDARD. MODEL H-S. TRACTOR
THE CURTISS R-4 MILITARY TRACTOR
80
AIRPLANE DESIGN
IMPORTANT POINTS IN SPECIFICATIONS NOS. 1001 AND 1002 FOR MILITARY TRAINING AIRPLANES
I
Advanced
Primary 1. Tractor biplane, useful load
(a) Pilot nud passenger. 330 pounds. Three hours
(b) Gasolene, oil an •; water.
1>. Curtiss eight-cylinder, OX-2, 90 horsepower at 1400 revo- lutions per minute, or an approved American made engine be- tween 70 and 90 horsepower, for the primary, and between 00 and 110 horsepower for the advanced.
(a) Pilot mid passenger. 330 pounds.
Four hours
(b) Gasolene, oil and water.
.".. Minimum speed, 37 miles
I>er hour.
Maximum speed, not less than 66 miles per hour.
Minimum speed, 43 miles per
hour. Maximum speed, not less than
75 miles per hour.
4. Fully loaded machine must attain an altitude of 10.000 feet in 1
Two hours. To minutes.
5. Climb in 10 minutes shall be not less than
2600 feet. | 3000 feet.
6. Celerity of response to control, the proper degree of sym- metric and assymmetric stability (static and dynamic) ; steadi- ness in disturbed air, etc. Satisfactory inanoeuvering on the ground.
7. Both the dual Curtiss (shoulder or chest yoke) and dual Deperdussln types of control ready for installation in cockpits.
8. Factors of safety.
(a) Main plane structure. Conditions assumed :
(1) Load as above.
(2) Angle of incidence of mean chord of main planes : that of maximum lift coefficient.
(3) Air speed : that normally corresponding to the above load, and angle of incidence for the net effective surface area.
Factor of safety not less than 7.5. (It) Body and tail structure.
(1) Air speed, 100 miles per hour.
(2) Angle of incidence of fixed horizontal tail sur- face, minus 0 degrees; elevator surface minus 20 degrees.
Factor of safety not less than 2.5.
9. A complete outfit of instruments, tools, pressure gauges. etc., is specified.
Lauding gear of two-wheel type. Wheels, 26 x 4 inch tires, and 6 x I1/!) inch hubs.
10. Three-wheel type land- ing gear, the third wheel be- ing 20 x 4 inches, just in rear of the plane of rotation of the propeller; normally not touching the ground, but de- signed to touch the ground when the mean chord of the main planes is horizontal. Mil in wheels, 26 x 4 inch tires, and 6x1% Inch hubs. with spokes.
11. Hody shall be of one part, not the jointed tail type. All nirnbuckles in the body wiring to be readily accessible. In ihr •-i'le wiring they should be near the upper longerons. The wini: spar fittings on the body to which the lower planes are attached shall be tied together across through Hie body by M'-el tubing. The interior of the body shall bo so constructed n- in permit thorough inspection of :iil wiring, control lend-.. .•tc. As far as praelieable .-ill leads shall be direct.
]•_'. The design and monnliiiL' of the tail skid and vertical rudder sbiill be such us to prevent injury to Hie verlicjil rudder in case of failure of the tall skid.
I."?. The number of different sixes of tiirnbuckles shall be n- di|ee,| to the minimum. Pulleys, pins, bolls, ninibin-kles. Bt<
drilled for safety ing. Safety wire shall be of No. is gage cop per wire.
14. Satisfactory fields of vision.
15. Seats in tandem, padded cockpits, safety belts.
16. Housing around power plant readily detachable. Con- venient access to all parts of the engine which may require ad- justment or inspection.
17. Radiator proof against vibration.
IS. Gravity feed throughout preferred. A positive and reli- able system of pumping may be used; in which case a gravity feed tank holding at least forty minutes supply to be embodied.
19. Upper plane to extend beyond the lower plane laterally by an amount approximately equal to the chord. Lateral con- trol to be by means of trailing edge flaps on the upper plane only.
20. Stranded steel cable shall be used for all tension mem- bers which are readily accessible for adjustment and for all control leads. Structural tension members shall be of hard cable, and control leads shall be used for terminals of hard, single-strand wire. No spliced terminals in hard cable will be accepted. All cables which are members of the wing struc- ture and normally under tensile load in flight shall be in du- plicate and made independent between fittings. Satisfactory provision for convenient and thorough inspection of control cables and pulleys and vital structural members. In the in- ternal wing bracing, the compression members carrying the drag of the wings shall be separate wooden struts and not wing ribs. Rib webs shall be reinforced between lightening holes to strengthen them in longitudinal shear.
The above specification not only provides an excellent guide for the design of the school machine, but is also a guide to the . performance which may be expected of this type. A machine might be perfectly acceptable, however, even if it did not adhere rigidly to the above specification, provided its main requirements were successfully carried out. Particularly is this true as regards the engine power.
Data for a Typical School Machine Less Than 2000 Pounds in Weight
The Curtiss JN4-B, for which full data is supplied by the manufacturer is a good example of this type, and in default of a classification such as that of Table '_'. should prove a reli- able guide in preliminary design.
CURTISS .IN 1 i:
Engine, Curtiss OX; horsepower. '.MI; cylinders. S; revolu- tions per minutes, 1400; weight per rated horsepower. 4.02 pounds: bore and stroke, 4x5 inches; fuel consumption per hour, '.) gallons; fuel tank capacity, 20 gallons; oil capacity, 4 gallons; fuel consumption per brake horsepower per hour. 0.60 pounds: oil consumption per brake horsepower per hour. 0.030 pounds.
Maximum speed, 75 miles per hour: minimum speed. 4.'! miles per hour; climbing speed, 3000 feet in 10 minutes.
Net weight, machine, empty, 1320 pounds: gross weight of machine and useful load (fuel for 4.16 hours), 1905 pounds; distributed us follows: 225 pounds fuel. 30 pounds oil. 1(15 pounds pilot. 165 pounds passenger. Total. 5*5 pounds. Per- centage useful load, 30.7 per cent.
Total support ing surface. :;:.i;.7 square feet : loading per brake horsepower. 21.16 pounds: loading per square foot of support- ing surface. ."..". pounds.
Win- section. Eiffel. ::ii: upper span. I.", feet 7% inches; upper chord. 4 feel II'... indies: lower span. 33 feet 11% inches: lower chord. I feet 11 'j inches; gap. 5 feet 2 3-16 inches: o\crall length of machine. 'J7 feet 3 inches; overall height. '.» feet lo'.. inches; ratio of mean span to overall lenu'ih. l.t::.
liihcdral. 2'L- degrees; swcepback. .(I degrees; stagger, 12 5-16 inches.
Control surfaces.— Ailerons (upper wingl. 35.2s square led
AIRPLANE DESIGN
81
Constant in formula (S, a, + S. a.) = CA. C = 4.3. Horizon- developed in our design in subsequent sections, and drawings tal stabilizer 28.7 square feet ; elevator 22.0 square feet. Con- of one or two representative machines will precede this design.
In the ensuing chapter, we shall study the pursuit type, the Twin Engine Machine, and the armed reconnaissance type.
QL
stant in formula, d=^-d = .766. Rudder 12.00 square feet; Vertical fin 3.80 square feet. Constant in formula, /= -|g-, / = .029.
References for Part II, Chapter 1
Photographs and Drawings
Considerations of space do not permit inclusions of draw- "Memorandum on Military Airplanes," Prepared" in the office of tbe
f ,v mi u i Officer in Charge of the Aviation Section. Signal Corns. U. S A AVIA-
mgs ot these types, ihe accompanying photographs are rep- TION AND AERONAUTICAL ENGINEERING, September lo 1910
resentative. Details of construction and drawings will be fully 6.Jo^er0naUtiCR'" by J' ' ' I1IinHttker- in the *«*««<«" Engineer Han,,-
83
AIRPLANE DESIGN
EXAMPLES OF PURSUIT TYPE AIRPLANES
GERMAN AI.HATHOSS OK UMIi
Tin: Cri;Ti« TIMIM. \\ :i
Photo. Irum I'mlrrtrimtl ami I'mli nr<,<«l
\ N'iKi IMIKT FrHsriT MAI HINK
EXAMPLES OF GERMAN ARMED BIPLANES
Aw L. V. 0. OP 1916
AN AVIATIK GUN-CARRIEK
Chapter II
Land Pursuit Machine
Land Gun Carrying Machine
Twin Engined All 'Round Machine
The High Speed Scout or Land Pursuit Type
The high speed scout or pursuit type has in the present war assumed a very great importance. In the War Department memorandum on " Military Airplanes," its functions are well defined :
" By virtue of its tremendous speed and climbing ability, it can dodge and outmaneuver its larger enemy, maintaining an effective fire with its machine gun, at the same time pre- senting a small and bewildering target. This is an ideal ma- chine for tactical reconnaissance. It can even drop a few bombs where they will do most good."
The United States Army memorandum gives the following figures pertaining to this type:
TABLE 1. LAND PURSUIT TYPE.
Horsepower 110
Type '. Tractor
Number of men 1
Military load, pounds 200
Fuel load, pounds 1 f>i i
Miles, radius of action, full power
Climb, feot in 10 minutes
High speed, miles per hour
Low speed, miles per hour
Factor of safety
Percentage demand in war
Sir, 3000 116 43
7.5 21.0
Very few machines of this type have been built in America. Abroad such machines have been used in great numbers, but little information is available for recent French and English types, such as the Nieuport, Morane, Vickers, Bristol, Sop- with, etc., with light rotary engines of between 80 and 130 horsepower. Lately very light and more powerful 150 horse- power V-type Hispano-Suiza engines have been employed in great numbers.
We may say that an average of 120 horsepower is used in this type, that it is a single seater machine, almost always a biplane with the smallest possible wing spread, a tractor with a light machine gun firing either through the propeller or above the wings.
English opinion based on experience in the war supports an inherently stable machine which the pilot can leave uncon- trolled for a short period while engaged in combat or other functions. To obtain inherent stability in this type is a diffi- cult problem. The high loading per square foot of area is not conducive to , stability, and the employment of correct fin areas and dihedrals is still a problem. The high loading also introduces difficulties from the point of view of stresses in the wing structure. Nothing lower than 7 pounds per square foot of wing area seems possible.
With the production in the United States of such engines as the General Vehicle Company's Gnome and the Hispano- Suiza, there is to be expected a very rapid increase in the
number of American speed scouts. These light and powerful engines will enable the weight per horsepower to be diminished and the speed and climb to be increased until European prac- tice is equaled.
Data for Pursuit Type, 100 Horsepower Engine
In Table 2 some data has been collected bearing upon some ol: these types. Little detailed information is available, but these figures and illustrations should be sufficient to give a general idea of present development.
TABLE 2. DATA FOR HIOH-SPEED PURSUIT MACHINKS.
|
Model |
Nieuport |
S.P.A.D. |
Bleriot |
Curt IMS |
|
150 h.p. |
150 h.p. |
triplane |
||
|
Kn^ine |
80 h.p. |
Hispano- |
Hispano- |
OXX-2 |
|
Le Rhone |
Suiza |
Suiza |
100 h.p. |
|
|
Xuinber of men |
1 |
1 |
1 |
|
|
Endurance at full speed (hours. |
2'A to 3 |
214 to 3 |
||
|
Maximum speed (miles per |
||||
|
hour) |
125 |
125 |
120 |
|
|
Minimum speed (miles per |
||||
|
hour) . . |
56 |
|||
|
Climb in 10 minutes (feet) .... Climb to 3,200 feet (minutes) Climb to 6,400 feet (minutes) |
6,000-7,000 |
9,200 3 6 |
9,200 3 6 |
10,000 |
|
( 'limb to 9,600 feet (minutes) |
10)4 |
W% |
||
|
Total weight (pounds) |
1,218 |
|||
|
Useful load |
460 |
460 |
||
|
I'ounds per horsepower. . . . |
12.18 |
|||
|
Area wings (square feet).. . . |
185 |
185 |
143 |
|
|
Wing loading (pounds per |
||||
|
square foot) . . . |
8.5 |
|||
|
Wing area per brake horse- |
||||
|
power (square feeO |
1.23 |
1.23 |
1.43 |
|
|
Span top plane |
24' 6" |
25' 20" |
||
|
all three planes |
||||
|
Chord top plane |
:f 11" |
2'0" |
||
|
Aspect 'Ratio top pi-mo |
6.15 |
all three planes 125 |
||
|
Span bottom plane' |
23' 0" |
all three planes |
||
|
Chord bottom plane |
2' 4" |
|||
|
Aspect ratio bottom plane. . . |
9.9 |
Data for More Powerful Pursuit Types
So rapid is the deye'ppment of the foreign military air- planes that it would seem as if the speed scout fitted with a rotary engine of about 100 horsepower, is now being displaced by a more powerful type.
It is interesting to note that in the S. P. A. D. and Bleriot type* the climb does not apparently fall off with altitude, showing probably that the difficulties of maintaining the power of the engine at high altitudes have been successfully met.
Trend of Design in the Pursuit Type
Among the salient features of this type is the very small weight per horsepower, 12 pounds or thereabouts, as compared
M
AIRPLANE DESIGN
with tin- 18 or 20 of the large reconnaissance type. There is a tendency t<> employ large aspect ratios— the small weight per horsepower and small wing surface permitting the chord r., he cut down considerably. Thus we find in the Nieuport aspect ratios of 6.15 and 9.9; in the Curtiss triplane 12.5 on nil the planes. In the triplane the extraordinary aspect ratio • •I1 1 •_'.."> is rendered possible by the distribution of the carry- ing Mirface among three planes instead of two. Stream-lining to the very limit is another feature.
Hitherto (ierman constructors do not appear to have sought the reduction of head resistance to any great extent, but the new AII.Mli-o-- shows a beautiful body, struts reduced to a minimum, and the stream-lining carried to the extent of a hemispherical nose-pieee over the propeller boss. In the Nieu- |iort scout the Y strut system "jives both lightness of construc- tion ami aerodynamic efficiency. The wonderful improvement of the Curtiss triplane with no larger power, as compared with its predecessor, the " Baby" scout, is due in part to the large aspect ratio which counterbalances the inefficiency of the tri- pliine. lint more to the clever K strut construction with the two tubular struts stream-lined in, and the stream-lined chassis construction. Such valuable yet simple ideas in the design of this type are well worth attention.
German practice in every respect seems to be following I'Yench practice very closely tor this type. Recent information at hand shows that the small biplane, such as the Albatross just mentioned and the new Fokker biplane are being built in great numbers. The Fokker biplane has apparently super- seded the monoplane.
Guns on the Pursuit Type
However stable a machine may be, and even if it is equipped with a stabilizer or automatic pilot, it seems impossible that a pilot should at the same time be a gunner capable of firing in all directions. The light machine guns which are employed, are probably fired straight ahead towards the enemy machine which the pilot is approaching. They may be
(1) fired thromjh the propeller, which is suitably protected
for rtrlleetinji stray bullets.
CM tired through the propeller with a suitable synchroniz- ing mechanism as on the Fokker (see appended refer once i .
C'.p placed al.ove (lie wing within reach of the pilot as on the \ieii|Mirl.
Land Gun Carrying Machines
l-'..r the land gun-carrying type of airplane the War De- partmeni memorandum specifies:
TABL
i
Number or ni'-n
Military liu.il. |i"
Km I l< ..
Th n. full •
I.IT liour
Kn-tor of Mnfr-ty
I In war. .
180
Tractor
BOO
1-j:.
77
I .
ntured with regard to the menu.
randum. it is on tli- :•"> implicit faith in the all round
Iwin-ciiL'ined machine, and iieiMc.-t ..I the importance of the Riin-carryin"; machine of thi- type. Most of our information as tn tin- t\pi- c..iiie- from the splendid description- of cap lured (termini machines in /.'.!»' r»/<//i'/' . The Hermans have .•led in providing this t\pc with one or two marhine
guns, with a good range of fire and arrangements for throw- ing bombs, and yet with excellent performance.
TABLE 4.
DATA FOR GERMAN TWO-SEATER GCM-CAHRTINI; MVHIM (From L' Atraphilt).
|
Rumpler 1916 |
Aviatik 1'Mi. |
1916 |
|
|
'.: • - . I7ii |
Mrrrpili';* 165- |
||
|
horsepower |
horsepower |
170 hors«i> |
|
|
Maximum speed on ground. |
92 |
93 |
• :. |
|
Minimum speed on ground. |
49.5 |
||
|
Speed at 1,000 meters, |
84 |
87 |
|
|
Speed at 2,000 meters. |
85 |
82 |
81 |
|
at 3,000 meters, |
81.5 |
u |
|
|
dim!., in feet per minute.. . |
3,200 in 10 6.400 in 16 9,600 in '.".I |
1,600 io r :!,i;iHiin •..-.. 6,400 in '2 1 ' -j 9,600 i |
3.201! |
|
Maximum altitude fully loaded, feet |
14,800 |
11,200 |
10,000 |
|
Endurance, fully loaded, hours |
4 |
4M |
4H |
|
2,780 |
1340 |
! MO |
|
|
1,830 |
1,860 |
||
|
HO |
980 |
980 |
|
|
Percentage useful load |
:>!.•_", |
34.4% |
34 |
|
580 |
:,.-,ii |
-, -.. i |
|
|
Loading per brake horse- power, pounds |
16.8 |
lli.7 |
|
|
Loading per square foot of |
7.35 |
6.6 |
7.1 |
|
25.2 |
|||
|
Total wine area, square feet |
378 |
||
|
39.2 |
40.68 |
1 |
|
|
Chord feet |
5.4 |
6.1 |
|
|
35.4 |
35.4 |
36.4 |
|
|
5.4 |
6.1 |
||
|
Gap feet |
G.H |
||
|
27.8 |
22 |
||
|
.SIM! ili/cr-iicii, square feet. |
35.4 |
35.2 |
|
|
— 1.36° |
— 1° |
||
|
>r area, square feet |
18.2 |
I |
|
|
..1 fin, square |
4> |
||
|
7.25 |
i |
||
|
DiliKlr.il (if willyy |
2' |
||
|
• :' wings to l» |
&• |
4.5' |
|
|
Ala |
|||
|
- • • |
None |
||
|
Pilot t i r i n t h i • • - LMT i rear ^ <lr..|i|.in« '!' |
In i, ttir. •-• in 1 hin all <ir culnr i |
for Her, UK |
In Table 4 some useful data has been collected, and photo- graphs of (he Aviatik and L. V. (!. shown herewith, are good examples of this type. lieeent development in America has sho«n the necessity of slandardi/.cd te.-ts al \ai'i..us altitude- nnd it is interestinc to note that Inures are Ki\,-,\ for spe. d
AIRPLANE DESIGN
85
the ground and at various standard altitudes; while maximum altitude, or " plafond," as the French term it, is also specified.
These German machines, as regards climb, are on a par with the American unarmed reconnaissance machines. They appear to be much superior in maximum speed. Their per- centage of useful load is greater. By careful construction and probably with a lower factor of safety, they actually have a lower loading per brake-horsepower, even when carrying two machine guns, the ammunition required, and bombs and bomb- ing devices. This indicates how much room there still is for improvement in American machines as regards weight saving.
They are short machines, with large stabilizing planes, but comparatively small control surfaces. The wings are very
FIG. 1. AVIATIK WING SECTION
heavily cambered, as shown in Fig. 1, yet look as if they were efficient, and deserve careful study. They appear to be an improvement on the wing sections commonly employed. The wings also appear to be set at large angles to the body, so that the propeller axis is coincident with the line of flight at nor- mal angle of incidence, and at a small angle to the line of flight in climb.
Their design is characterized by a robust lightness due to careful utilization of material throughout, and probably a uni- form factor of safety.
The Mercedes engine so largely employed on German air- planes has the reputation of being extremely reliable and effi- cient, but is considerably heavier per brake-horsepower than American engines of about the same power, an important fact to be considered when the American designer sets out to equal the German machine.
Twiii-Engined Machines
The memorandum prepared in the office of the officer in cliarge of the Aviation Section, Signal Corps, U. S. A., gives very interesting data on twin-engined seaplanes, reproduced in Table 5 herewith. It lays strong stress on the advantages of this type, partly on the ground that a thoroughly developed engine of over 200 horsepower had not yet been constructed; but since that time progress has been made and the 300 horse- power engine is becoming a practical possibility. Stress is laid on the versatility of the twin-engined machine. In a land twin-engined machine, with the engines supported on the wings, and a central body, it is suggested that the pilot with his controls could be placed in the rear cockpit in rear of the propellers ; the observer with his machine gun, in the forward cockpit forward of the propellers ; and the bombs and gasoline between the pilot and observer, near the center of gravity of the complete system. With such an arrangement, the observer would have an ideal field for observation and for gun fire; with a stabilizer the pilot could fight the machine to the rear, and the machine would be an excellent fighting airplane as well as a bomber. By decreasing the bomb weight, the radius could be increased to a very long range. A third man could be in- stalled in between the front and rear cockpits by making slight alterations in the construction of the body. If the third man had charge of the controls, there would be an even better fight- ing machine. If neither bombs nor a third man were carried, the landing wheels could be replaced by two or three pontoons, giving a military seaplane.
TABLE 5.
Horsepower 260
Type Pusher or tractor
Number of men 2
Military load, pounds n50 to 1100
Fuel load, pounds 600 to 1150
Miles radius of action, full power 450 to 600
Climb, feet in 10 minutes 3400
High speed, miles per bour 90
F»\v speed, miles per hour 47
Factor of safety 7.0
Percentage made in war 4
A further evident advantage of this type is that it could be flown with one engine out of commission. The propeller would not be required to take the great power of a 300 horse- power engine. Although the support of the engine on the wing presents considerable difficulties, yet this arrangement might react favorably on the weight of the wing structure by distributing the load, and therefore giving less bending moment to the inner wing panels.
If a single engine of 250 or 300 horsepower were used, the same military and useful loads would be available. With a single body the parasite resistance would probably be dimin- ished. But the difficulties of constructing such a machine for fighting as well as bombing purposes would be very consid- erable. With the engine in front, it might be possible for the pilot to sit in the forward cockpit and shoot through the pro- peller, while in the rear the observer could operate a machine gun in all directions. If bombs and bombing apparatus were included in the single body, there would be an extremely diffi- cult construction problem. If the high-powered machine were made a pusher, the rear occupant would be under difficulties as a machine-gun operator. The other possible alternative would be to place the observer in a cockpit forward of the propeller — which would revolve round the body — the engine behind the propeller, then the pilot in the rear seat. None of these arrangements seem to have the straight forwardness and simplicity of the twin engined type.
It would seem, therefore, that in spite of the development of a reliable 300 horsepower engine, the twin-engined machine would have much to recommend it.
The following points may be disadvantages of the twin- engined machine, or merely problems which careful design can overcome :
(1) There are difficulties in preliminary design. In the school machines, the armed and unarmed reconnaissance types, and in the speed scout, we have data to draw upon from which loading per square foot of wing area, loading per brake-horse- power, useful load, etc., can be at once fixed within certain limits. Here we have an entirely new problem. Theoretical considerations show that with increased span, the bending moment and other stress producing forces for geometrically similar machines vary as the cube of the span. The resistance of bracing wires would vary as the square of tlie span. The section modulus of the wing spars would vary as the span cubed, but their area, resisting direct tension or compression would only vary as the square of the span. Similar considera- tions would follow for other strength members. Even if we allow the structural weight advantage of engines on the winsis MS previously mentioned, the conservative designer would still I'xptrt weights to go against him. If the twin seaplane that he is designing follows the same outlines of construction that In- hiis been accustomed to in a single-engined type, he should allow for a slightly heavier loading per horsepower and a slightly smaller loading per square foot of wing area, i. e., a larger wing area than he would, in the light of past experience, expect to employ. Such a conservative outlook — well founded in the author's opinion, particularly for experimental machines — would lead again to less favorable estimates of performance, and avoid the ridiculously optimistic estimates for these large machines in the recent bids. It is interesting, in the light of these remarks, to study the performances submitted in these
X,,
AIRPLANE DESIGN
lii«U for seaplanes. (AVIATION AMI AEKU.NAUTICAX, ENGINEKK- i\t.. December 1. 1916.) The Curtiss Company, with its past 1-Mx-rienee in the building of twin-engined machines (Twin JN), specified n climb of 2.000 feet and a speed of 65 mil» per hour, although probably equipped with two 200 horsepower engines. The Wright-Martin Corporation was so conservative as to specify no performance. A great many optimistic bids were submitted. The average climb sent in appears to be 3,580 feet, the average maximum speed 77 miles i>er hour. One would be inclined to think that with present American methods of construction, a climb of 2,800 feet, and a maximum speed of about 6S mile* IMT hour would be as much as could possibly be expected.
(2) Control surfaces ;md stability furnish interesting prob- lems. The effect of placing the engines out on the winsrs is to increase the moment of inertia in roll, and it is very difficult to say what effect this will have on inherent lateral stability. It is certain that the aileron area required will be somewhat greater than that in a machine where the engine is at the cen- ter of gravity and that the machine will be slow to respond to lateral controls. The moment of inertia in yaws will simi- larly be increased so that rudder and vertical fin surfaces may- have to be larger proportionately than on the usual machine. These are points requiring the most careful attention in design
(3) Another problem in connection with the twin-engined machine is that of propeller slip from the two screws, both turning inwards. This symmetrical arrangement is prescribed by the Army specifications as avoiding torque and gyroscopic effects. The down stream from the propellers impinging on the stabilizer is said to increase the safety from the point of view of longitudinal balance, giving tail heaviness with power.
and nose heaviness without power. The exact effects are, how- ever, still open to experimentation.
Space forbids a discussion of numerous other points which this type presents. The appended references will give the reader some information. The German twin-hydro reproduced iii AVIATION AND AERONAUTICAL ENGINEERING. September lf>. 1916, is of particularly neat construction, the specification No. 1002 is almost a text-book on design, and the S. A. E. pa- per on twin-engined machines read by Lieut. Col. V. K. (lark. U. S. A., touches on a greater number of points than we are in a position to deal with. Anyone setting out to construct such a type would do well to devote considerable time to wind tunnel experimentation, computation of moments of inertia. etc.
References for Part II, Chapter 2
"OUlf-CARRYlXG TWO-SEATER MACHINES."
• Itumpler," L'AfropMle, Dcccuilier. t!U6.
". \\ialik." L'AfropMle, October, liilii
" L. V. O.," L'Afrophilr. Nnveml . r. ]:>:>;
" Other German liaehii"1*." /." \nophile, March. I'.HI.
PROPELLER AND MACHINE QUX SYNCHRO M/.l \ f/ UACUIKES.
" Fokker Firing Mechanism." L'Afrophilf. .linn-, I'.ni,
" Twin-Kngined Machines."
L'AfropMle, July, lalO (abstract in AVIATION AM* .Si.i!<>~ . >
ENGIKKEBINO, Sept. 15, I'.H-: "Some Problems in Airplane Construction " (S. A. K. llullrtin,
December, 1916).
"Army Aeronautical Specification No. 1002." "The Development of the Milii.-irv Aeroplane," by !'. W. I-anches-
ti-r. Knyineerina. March ::. 191G.
Chapter III
Estimates of Weight Distribution
of flip Siihiprt Details tor upper wings:
Front spar, total span 18' 5%" ; 18' 8%" length 25.0 Ib.
Hear spar, total span 18' 9%" ; 19' 0 length 23.5 "
Hardly any branch of practical airplane design offers such Compression posts or solid ribs (7) . 16.2 "
Lightened ribs and straps (10 long, 7 short), total 18.4 "
difficulties as the estimate of weights. A manufacturer who Entering edge, 4 pieces 8.0 "
, . „ , . , , Trailing edge, 4 pieces 3.9 "
has built a number of machines and has kept careful weight Edge pieces and cross battens 5.5 '
schedules has valuable data in his possession, but is, as a rule, Wire°BcSiip's and 'turnbuckie's.'.'. ll's "
chary of making such data public. Even an experienced manu- Donpen'anddvSrnishnd .tape and taeks. ^ 'tap'°g; : ! "I »
fWtilvor hnwpTTPT- rnnv \\o nt a Incc wVlon VmilHintr art anti-rolv Flaps Uncovered, total . 20.0 "
er, However, may C ling an entirely Flap ninges and'hlnge flttlngs> complete 1.1 ••
new type, particularly if the new type is of a very different Om?ccoSntisdBforOpe and varnlsb ' ' ' 2oo '"' size from that to which he has been accustomed.
Theoretical considerations apply only to a limited extent.
n • • , j, , , , . .. . . . Kody wing section . 16.5 Ih.
Empirical formulas have ')een suggested by several authorities,
but are only partly satisfactory. The authors' thanks are due Details for lower wings :
to manufacturers and others for such data as they have per- Front gpari total span 18, 5%,, . 18, s%,, len^n 25-OUj.
mission to publish. ^gSt^^ £f^£j (189,'.0. .lengt": '. \ Hi '•'•
Lightened ribs and straps (7 short, 9 long) 19.5
Weight Shedules for a Machine of the Unarmed Tractor Trailing edge,' 4 pieces! '.'. '. '. \\ .'.'..]'.'.'.'.'.'.'. '.'.'.'.'.'. '.'.'.'.'.'. 3.9
m ,m ci \ HT rni Edge pieces and cross battens, hinge, block braces, etc. . 5.5 "
Reconnaissance lype (iwo beater) More Lhan Fittings ...... 1.3 "
.-\re\i\ TI i • wr • i Wire, clips and turnbuckles 11.8 "
2.->(>(j bounds 111 Weight Linen, undoped, and tape and tacks for taping 15.9 '•
Dope and varnish 6.3 "
Flaps uncovered, total 20.0 "
Full weight data can be published for one of the tive ma- F'ap binges and hinge flttngs, complete 1.1 '•
Flap yokes and yoke fittings 3.8 "
chines which have been examined in Part 2, Section 1 — the Flap coverings, dope and varnish 1.2 '•
oi, , -. TT „ „,, , , . ,, ... , . . Unaccounted for 2."i.:; "
Standard H-3. Ihe schedule for this machine is very com- plete, and is almost exactly in the form specified by the Avia- tion Section of the Signal Corps.
Weight Weight Area per sq. ft.
TABLE '• Upper wings 178.0 Ib. 262 sq. ft. .680 Ib.
Standard H-3, Hall-Scott A-5, 135 h.p. Maximum speed S4 m.p.h. Body section
Minimum speed 46 m.p.h. Climb 3400 ft. Total wing area, 532 sq. ft. Lower wings 190.0 262 .720
Weight loaded, 2651.9 Ib. (6 hours). Weight bare, 1908 Ib. Tota, wing w(;.ght g^^
Body structure : Percentage of total weight, 14.52%.
Details :
Longeron, forward upper right 9.0 Ib.
Longeron, rear upper right . . 9.0 Interplane struts, fittings, and wiring: 107.6 Ib.
LoSIcron' re™ uppTleft ' "90 Weight per square foot of wiDS arwl 203 '
Longeron| forward lower right! ...!.!!....!!..! 9.0 Percentage of total weight, 4.06%.
Longeron, rear lower right 9.0
; r'e^owerTf't . ^ * ! ! ! ! ! ! ! ! ! ! ' I '. "i ! ! !! ! ! ! ! ! S3 •'•»» ^rfaces : Weigh,
PPo°sSttS' t0tal" l!i Vertical fin complete, covered We'8ht ^ ^ ^ "'
Horiontal nostV'to't'a'l' ' 135 and varnished 3.0 Ib. 5 sq. ft. .600 Ib.
Fneine beds (two) 19 0 Vertical rudder 9.0 " 10 •• " .900 "
Enfinl bldf s'upportin-g poVts : : : ! : ! ! : ! : : : : ••:. ::::::::::: Jlo E^^to^'20111211 ta" : : ' iii •• 5? « "•
Engine plates, total 19.0 Elevators ^l.o
Kadiator supports 27.5 „ . .
Fittings, total 27.5 Total 53-3 "'•
Kivets, bolts, nuts, screws, total 7.1 Percentage of total, 2.0%.
Wire and cable, total with terminal clips and thimbles, etc. 21.1
Turnbuckles 10.0
Floor of cockpits 18.0 Control system :
Tail skids 6.0
Body cover strips 7.0 Combined Curtiss and Dep. control, with I o« 9 u
Front and rear seats and supports 31.5 Control operators in rear cockpit only /
Cowling and body cover 59.5 Control wires, wiring and switches 4.4 "
Total 302.0 Ib. Total 30.6 Ib.
I'ercentacr of total weight, 11 f, Percentage of total weight, 1.15%.
Chassis : Details :
Wheels and tires, 2 at 26" x 5" 57.0 Ib.
Axles (1) 22.0
Struts (2) 25.0
Axle braces 8.5
Axle mounting and guides 12.0
Rubber shock absorber 2.5
Fittings 7.5
Wiring and turnbuckles 2.5
Fairing 1.5
Total 138.5 Ib.
Percentage of total weight, 5.23%.
Gasoline and oil :
Gasoline for 6 hours 396.00 Ib.
Oil for 6 hours 33.5 ••
Total 429.50 Ib.
Percentage of total, 16.2%.
Tanks :
Tanks and connections and supports (68 gallons fuel) . Percentage of total, 2.95%.
78.5 Ib.
87
88
AIRPLANE DESIGN
Engine group :
Kadlator, complete* and con- nections without watrr.. 40.0 Ib.
Engine, complete without propeller, radiator or any water, any oil, long ex- haust tube or self-starter.558.5 "
Water for radiator piping and jackets (30 Ih. car- ried in raillntnr alone) . . . 911.8 "
Propeller complete and bolts 27.5 "
Long exhaust pipe 13.0 "
Weight of radiator
per hp .". 1 Ib.
Engine weight per
up 4.15 "
Water weight per
hp 095 "
Propeller weight per
hp 2IC- "
Total 738.8 Ib.
r.-rrcntago of total weight. 27 ,
I'.i -~cnger and equipment :
IMlot
Passenger
Total
Percentage of total, 1 -
1 r,.-..i> Ih. H-..VO ••
330.0 Ib.
Equipment :
Instruments iMid Instrument liuard. nnd accessories com- piled for rear cockpit 22.7 Ib.
Same for front cockpit.
Side pockets, both sides
Cnmsfiaft oiler
Speaking tutio
Pyrene and brackets complete, Oil pressure line and sight oil. Tool kit and case complete. . . .
9.2 3.0 4.1
2.8
c-,.7 1.8
7.::
Total
Percentage of total weight, 2.20%.
OS.G Ib.
Summary of Weight Distribution for Standard H-3
(irnup Weight
lv assembly and equipment 370.5 Ib.
Chassis 138.5
Wing group 384.5
Interplane bracing 107.6
Tail surfaces 53.3
Control system 30.6
Gasoline and oil 429.5
Casollne taaks and piping 78.5
Knsine group 738.8
Passengers and equipment 330.0
Percentage of
1'scful Load
18.60%
6Jtt
14.:
4.i»
s.ou
1 1 :/ : 10.20%
2.9.1% 27.70% 12.50%
Totals 2651.9 Ib. 100.00%
The Standard figures are fairly representative for this type of niaohim-.
Percentage Table for Machines About 2500 Pounds
In Table 2 are given figures compiled by Dr. J. C. Hunsaker for a number of typical machines. The percentage values seem to hold very closely for machines of the large tractor type.
TABLE 2 Useful load :
Personnel and equipment
Gasoline and oil, 6 hours
Engine weight :
Tanks and pipes
Engine and accessories,
Radiator (empty)
Cooling water
Propeller and bub
Structural weights :
Body
Landing carriage
Directive surface* .
Wing bracing
useful load. . . . • nginc weight . . structural weight
Per cent 13.1 19.8
3.3 17.9 2.2 1.7 1.0
8.2
ij
4.1
lft.8
4.M
82 :> M.1 41.0
100
Weight Distribution for a Typical School Machine
Figures can be published for the Curtiss JN-4. Data was given in Section 1 for the JN-4B, but the difference between the two types is very slight.
CurtlM JN-4. OX 90 hp engine. Maximum speed 75 inph. Mini- mum speed 43 mph. Climbing speed :t<>OO ft. In 10 min. Total wing area. Including wing flaps, 367.0 iq. ft. Weight lond-l. l!i"i!.35 Ib.
Weight bare, 12M.:,
4.4 hours fuel.
Part :
: v assembly
Tall skid with rubber ela»tlc cor.l .:: ft i . Cushions
Welglit
linn ciOlb.
2 7.-. "
3.50 "
Total
of total load. 15.60%.
290.25 Ib.
Chassis : Details :
Landing gear braces with fittings ..................
Axle ......................................
2 Aluminum hearings for sbock absorbers and straps. 2 Itubbcr shock absorbers (elastic cord 37 ft.) ........
2 Wheels 26" x 3" tire and IV," hub ...............
Total chassis group ...........................
Percentage of total weight, 4.03%. Wiug group:
. 28.5 Ib.
1.V7.-, " •J.( ii i •' .-...-,n "
•J7.0II ••
7f,.7." Hi.
Part Weight Upper wings without flaps or
fittings ................ 120.00 Ib.
Upper center section without
fittings ................. 13.00 "
Lower wings without fittings. 112.00 "
2 wing flaps with fittings ---- 2 I .:.«
Total for wing group. . . 269.50 Ib. Percentage of total weight, 14.1
Wing bracing and fittings :
1'etails :
Area 172.2 sq. ft.
152.2 40.8
Weight PIT
SM. fl
Slll'i
.772 Hi.
.7.".n
Upper wing fittings, 8 strut fittings, 4 fittings to center
section ......................................... lii..-,ii Hi.
Lower wins fittings. 8 strut fittings, 4 fittings to body. . . '.i.."i"i " 2 Win;; skids .................. ........ ...... 2 -
4 (Inter section struts (length of staggered struts = lil" •. i:;..".n ••
4 Intermediate se< ti.ni struts ...................... IT.. MI ••
4 Drift wires i ..... ise from upper anil lower planes ...... 3.OO "
Klylng landing and outer strut wires (not in. -111(11111:
.......................... 21 mi ••
4 Aileron wires with littings .......... ......... .Vim ••
4 Short uprights for bracing overhang ..... l.im "
Center section struts .................. I ."in "
Center section brace wire ...............
Total
Percentage of total load, -4
Tall surfaces :
Weight Vertical tall fin and fittings. 14.00 Ib.
Kudder and fittings 10.00 "
Fixed liori/oiitnl tall with
hinge lit tines only 14.00 "
2 Elevator Maps with wires
and pnMs 14.50 "
111.2.-, Hi.
'-'.."l Sl|. ft.
10.2 " "
22.7 " " 17.r. " -
\V,
per sq. ft.
ii 112 III. 1.09 "
n.r,2 - 0.88 "
Total 52.50 Ib.
•Mtage of total, 2
Control system :
Steering post. nnMer wheels with rudder wires
littings
4 Elevator wires
Total
Percentage of total weigh t.
Gasoline and oil :
4.4 hours
Percentage of total load, i
Tanks :
me tank with capneit> of ."." gall.. Percentage of total weight, 1
Weight
2V 1 Hi.
Engine group :
Propeller nnd hub ....... :;4.75 Ib.
;ie nnd accessories
(including 2 hot air
stoves. :;.,ri HI., top of
enu-inc Tilates and side
plate. 20.1.-, ib.) ...... ::ii::.7r, "
Radiator .............. ri.V7.-. "
Water ................ 39.00 "
1 Water pl|B- and fit-
tings ............... :i.OO "
Total .............. 496.25 Ib.
IVr, enlace of total weight. 2i;.Hf;.
Passengers :
I'ilot ................
t per hp
Wright per lip. Weight per hp. Weight per hp.
12.25 Ib.
1.V7.-I Ib.
C.-.2 Hi.
WciuM of
tank per galli>n
::M; |l>.
. . . 4.0.-.H -
. . . u.i;2n "
. 0.4:!0 "
ir.f, ib. in:, ••
Totnl .......................
Percentage of total weight, lti.95%.
Ih
Summary of Weight Distribution for J!ST-4-B
.-igbt
.25 Ib.
assembly and equipment ..... 200.
ill ......................... 070.7.-.
Wings .......................... 2'-.'.i.:.i>
Inl.-rplane bracing. n'.i I 2".
urfaces ................... 052.50
I'onlrol system ................. 015.75
in- and oil .................. 252.00
liasi.line tnnk and piping .......... 028.10
Kiiglne i: "up .................... (:ii;.'J-i
Passengers ...................... .",21 nn
IVrcclltace nf total 16.50% i 0
14 1 al Q
II2.7I-. "
Illl -
i :; 20 " in r,:t "
in - n.'.ir, ••
1902.r.5lb.
ion mi';
AIRPLANE DESIGN
89
Empirical Formulae and Values for Weight Estimates
Some empirical formulae and values are given here. Such empirical formulas can never be entirely trustworthy, since so much depends on the type of machine to be constructed, the type of construction to be employed for any particular part of the machine, and the factor of safety desired. Much greater reliance is to be placed on direct comparisons from actual machines and on actual computations from drawings. Still, they may serve a useful purpose in the preliminary stages of design, when a rapid estimate is needed.
(1) Body
Bare rectangular wooden longeron body, with fabric cover- ing for small monoplane and biplane scouts about 1200 Ib. total weight, 70 Ib. is a good average figure. For large biplanes about 2500 Ib. total weight, 150 Ib. is a liberal allowance.
(2) Seating
About 10-12 Ib. per person is sufficient.
(3) Single control system 30 Ib. Double control system 50 Ib.
(4) Landing Gear
A landing gear of about V16 the loaded weight of the machine can be easily designed.
(5) Tail skid
Is roughly V,0th the weight of the landing gear.
(6) Main plane weights (surface alone)
A fair average figure is 0.75 Ib. per square foot of wing area, although wing weights will vary with size of machine, section employed, aspect ratio, strut spacing and numerous other features in design.
(7) Weiyltt of control surface
Control surfaces with fittings and hinges may, with careful design, not exceed 0.5 or 0.6 Ib. per square foot. .(8) Tanks
About 0.75 Ib. to 1.00 Ib. per gallon.
(9) Engine weights, fuel consumption
Full values for these are available and will be given in a subsequent section.
(10) Engine mounting
One-eighth of the engine weight for a rotary type and one- twelfth the engine weight for a fixed type engine.
(11) Propellers
A good rule is weight = 2.5 Vhp.
(12) Radiators
For radiators, manufacturers' figures will be given later, and empirical formulas are not necessary.
(13) Passengers
Some 10 Ib. should be added for aviation dress.
(14) Miscellaneous
An allowance of 10 Ib. is sufficient for instruments, such as compass, altimeters, etc. Fire extinguisher, 8 Ib. Tool kit, 5 Ib. First-aid kit, 5 Ib. (15)
In a subsequent section we shall deal with weights of such parts of the machine as cables, wires, turn-buckles, fabrics, dopes, wheels, etc., etc.
Some General Considerations on Distribution of Weight and Useful Load
F. W. Lanchester has approached the question of weight distribution for various sizes of machines in a very interesting article. The subject offers many difficulties, and the following notes, mainly based on Mr. Lanchester's article, are merely an introduction.
When estimating the structural weight of a new machine
from data available on one constructed, certain theoretical con- siderations are available.
Simple and reasonable assumptions in dealing with the main planes are that the wing section remains geometrically similar, and the velocity constant. On such a basis from ordinary con- siderations of aerodynamics, the span must vary as the square root of the gross weight, and conversely the loading on the wing will vary as the square of the span. The direct forces of tension and compression on the spars will vary directly as the loading and square of the span, but the cross-sectional
500 7000 1500 2000 2500 3000 3500 4000 4500 5000 5500 3000
Pounds FIG. 1.
areas of the spars will also vary as the square of the span ; geometrically similar wings will, therefore, be equally strong as regards direct forces. The bending moments will vary as the gross weight or loading multiplied by the span, i.e. as the cube of the span. But the resisting moment of the spars will vary as the section modulus or cube of the linear dimensions; geometrically similar wings will, therefore, be equally strong as regards bending moments. It follows that with constant velocities geometrically similar wings will be equally strong for both direct and bending stresses. From the weight of aerofoil point of view, the position is unfavorable, since the weight will vary as the cube of the linear dimensions or cube of the span.
It follows that the weight of the wings will vary as W*/* where W is the gross weight.
In the interplane bracing, the wires, which only take direct stresses, will be equally strong when geometric similarity is maintained. For the struts just as for the spars, the same will apply. Therefore, the interplane bracing will also vary as W3/1.
For the body it is possible to make the somewhat more favorable assumption that its weight is directly proportional to the gross weight. With increase in span, it is by no means necessary to increase the arm of the tail surfaces proportion- ately, while the resisting moment of a body cross-section varies as the depth squared and the breadth. Current practice also seems to bear out the above assumption. It might even prove to be true that on large machines a slight saving on weight of body would be possible.
The shock of landing to be taken up by the chassis depends, for the same landing speed, on the gross weight.
If a chassis for a large machine were geometrically similar to that of a smaller machine, it would probably show greater strength in the struts, and equal strength in the shock absorber. The question is very complex. Mr. Lanchester insists on the analogy of the greater relative diameter of the legs of such a large animal as an elephant as compared with the legs of a flamingo. But with very big landing gear so much becomes
AIRPLANE DESIGN
possible in the way of shock absorption that keeping the weight of the chassis a constant proportion of the gross weight seems feasible.
For -the power installation, no general discussion seems
1000 1200 1400
POUNDS Fir.. 2.
its ordinatcs represent il» u'ro>- wciL-iii. juM MS the abscissae for the same point represent the gross weight. In accordance with the above considerations, the total structural weight i- taken as a constant proportion of the gross weight, namely. 25 per cent. The power installation weight is taken a.- 25 pel- cent, as previously mentioned. The weight of aerofoil curve. \arying as W'/', is obtained i'roui present-day English prac- tice in biplane construction, with a factor of safety of 6 — somewhat lower than American practice. The military load is kept at 500 Ib. in one case, at 150 Ib. in the other, and the remainder is allotted to the supply of petrol.
The above remarks, the distribution of weights, and these two curves arc open to criticism. However, they are the con- clusions of a most eminent authority, and may serve as a use- ful guide in the preliminary design oi a machine, particularly as regards possible endurance, which can at once be derived from the petrol capacity. They also give an idea of the lim- itations of the airplane. Thus the curves of Fig. 1 show the lowest possible weight level, with a big load of 500 Ib., and if extended to greater gross weights would show where, witli in- creased size, the petrol capacity begins to diminish. Fit:. - would be particularly useful in considering the |"issihilit: a speed scout with a single passenger.
possible, and Mr. Lanchester has assumed this to be 25 per cent of the gross weight in the graphs of Fig. 1 and Fig. 2.
The construction of these is easily followed. The bounding line of these curves is drawn at 45r to the Case line, so that
References, for Part 11. Chapter ,'i
The Development of tbe Military Aeroplane." l>v K \v ].:in Miirdi ::. "
Chapter IV
Engine and Radiator Data
General Requirements of Aeronautical Engines
The main requirements of an airplane engine are light weight, low fuel and oil consumption, reliability, accessibility, and a form suitable for installation in an airplane. The general form, apart from its weight, is important because of the question of mounting in the body, and the problem of engine cooling and body stream-lining. Selecting an engine for an airplane means unfortunately buying the engine most nearly suitable which is purchasable at the moment, and the choice is none too great. Nevertheless it is part of a designer's training to consider the comparative merits of every engine available, mainly with reference to the above points.
As regards reliability, no rules can be laid down. Satis- factory tests in Government or college laboratories are good guides. The reputation which an engine has earned among pilots under the more trying conditions of actual flying is even more important. Accessibility depends not only on the design of the engine itself, but on its careful mounting in the body. Fuel and oil consumption, weight and suitability of form are best studied by the compilation of such a table as Table 1. Such a table will require constant revision.
In considering weights of two engines of like power but of different type, such as a stationary air-cooled and a water- cooled engine, or a rotary air-cooled engine and a stationary water-cooled engine, radiator and cooling water should not be neglected. In dealing with rotary engines, fuel and oil consumption tend to make comparisons with stationary engines less favorable to the former type than is at first apparent. Particularly is this the case when a flight of more than 2\» or 3 hours duration is contemplated. The extra weight ol gasoline and oil to be carried for the rotary may actually make it the heavier engine at the beginning of a fairly long flight.
The form of an engine, from the points of view of mount- ing and projected area, are best studied from drawings appearing in technical magazines and makers' catalogs. The dimensions given in the table serve as a preliminary guide in narrowing down selection.
For a general study of the subject of aeronautical engines reference is appended to one or two excellent books — in which, however, no information as to recent developments is available.
The question of revolutions per minute apart from the question of power and efficiency in the engine itself has an important bearing on propeller design. Wooden propellers of large diameter seem to reach their maximum permissible safe speed at about 1300 r.p.m. Beyond this figure, it is hard to keep stresses down. Questions of direct drive and geared-down drives must be considered from this point of view.
Acknowledgment is made to Lieutenant H. C. Child, and to Mr. Lee S. Wallace for valuable data.
Weights for Radiators and Cooling Water
The following are good preliminary figures for design in accordance with general data:
Bare radiator 55 Ib. per blip.
Water in radiator 13 Ib. per bhp.
The Ajax radiator employed in conjunction with a 130-hp. Hall-Scott engine weighs 45 Ib. bare and carries 30 Ib. of water. On a school Curtiss of the JN type with n 90 hp. Curtiss engine, the figures for a Rome-Turney radiator are
Weight of empty radiator 58% Ib.
Weight of water contents 24% Ib.
Thickness of core 2% in.
Active front area 400 sq. in.
Total radiating surface 15,360 sq. in.
For the Livingston Radiator, the following information is available:
"For a 120 h.p. engine, from 16,000 to 18,000 sq. in. of radiator surface is required. Each square inch of projected area of 4 in. section contains 50 sq. in. of cooling surface. A 5 in. section contains 60 sq. in., and a 3 in. section contains 40 sq. in. Therefore, a radiator for a 125 h.p. engine will have between 320 sq. in. (2.2 sq. ft.) and 360 sq. in. (2.5 sq. ft.) projected area of 4 in. section. A radiator for such an engine contains approximately 4 gallons of water. Of this, 1 gallon is contained in the cells, the other 3 gallons in the headers. The headers should be of such proportions that the lower has about two-thirds the capacity of the upper."
Practical Rules for Cooling Surface for Radiator of Honeycomb Type
From Dr. Hunsaker's experiments at the Massachu- setts Institute of Technology, and certain theoretical con- siderations, a surface of .83 sq. ft. per bhp. has been found necessary for the honeycomb type. C. Sage recommends 1.08 sq. ft. per bhp. for an airplane of an average speed of 60 m.p.h., and presumably a minimum speed of 45 m.p.h. An allowance of 1 sq. ft. per bhp. seems very fair for machines of medium speed. In fast machines of the pursuit type, it would be possible to go considerably below this figure; even if a fast machine makes a prolonged climb, it will never do so at its slowest speed. Dr. Hunsaker has shown that an empirical formula may be established of this type:
C X blip.
—?-
where a = area of cooling surface, C is some constant and V is the speed in miles per hour. A designer, who has satis-
91
92
DATA FOR AMI
Subject
|
Maker and Model |
No. Cylinders. |
1 |
0j H T3 1 |
SB CH rt |
R.P.M. of Propeller. |
£J _c 4 Pu a a 1 o |
_i ^C u •? fc m I 0 |
.6 ** '1 a E° "1 _ - 1.8 >* f a |
Weight Cooling Water in Radiator and Engine, Ib. |
•o V "E a • OC II |
Weight Cooling Water in Radiator, Ib. |
•o • "3. L 0~" si tm ^ |
^ 1 ( 1 *, 1 'J \ \ 9 |
|
Aeromarine |
6 |
Vert. |
85 |
1400 |
1150 |
.7 |
.069 |
440 |
37.5 |
31 |
8.12 |
||
|
Aeromarine D-12 |
12 |
V. |
160 |
1400 |
750 |
• |
|||||||
|
Aeromarine |
8 |
V. |
100 |
410 |
• |
||||||||
|
Atwocxl C-12 |
12 |
V. |
150 |
2500 |
1250 |
.64 |
.V.I2 |
63 |
13.25 |
||||
|
Christofferson |
6 |
Vert. |
113 |
1450 |
1450 |
.665 |
.0266 |
510 |
67.5 |
8.7 |
4i |
||
|
ii |
8 |
V. |
160 |
2500 |
630 |
65 |
85 |
15 |
17 |
||||
|
Curtiss-Ox 2 |
8 |
V. |
90 |
1400 |
1400 |
375 |
58>i |
24^ |
|||||
|
" -OXX 2 |
8 |
V. |
100 |
1400 |
1400 |
.59 |
.035 |
423 |
44 |
76 |
12.26 |
1 |
|
|
" -VX |
8 |
V. |
160 |
1400 |
1400 |
.575 |
.0328 |
04.-> |
62 |
86 |
16 |
7 |
|
|
" -VX 3 |
8 |
V. |
200 |
.73 |
.031 |
667 |
70 |
94 |
Iti |
6 |
|||
|
" -V-4 |
12 |
V. |
250 |
.612 |
1125 |
100 |
120 |
2rl |
|||||
|
Duesenberg |
4 |
Vert. |
140 |
2100 |
455 |
7.21 |
|||||||
|
ii |
12 |
V. |
250 |
1800 |
425 |
15.5 |
|||||||
|
Genl. Ordnance Co. |
8 |
V. |
230 |
1800 |
867 |
||||||||
|
Genl. Vehicle Gnome |
9 |
Roty. |
100 |
1200 |
.72 |
272 |
|||||||
|
Gyro K |
7 |
Roty. |
90 |
1250 |
.VI.-, |
. 100 |
^!L> |
||||||
|
" L |
9 |
Roty. |
100 |
1200 |
Oil |
.180 |
285 |
||||||
|
Hall-Scott A-7 |
4 |
Vert. |
80-90 |
1370 |
1370 |
.47 |
.037 |
410 |
34* |
40 |
|||
|
A-5 |
6 |
Vert. |
125 |
1300 |
1300 |
.507 |
Ol'S |
592 |
52* |
45 |
30 |
4 |
|
|
A-5at |
6 |
Vert. |
162 |
1325 |
14. 7J |
•4t |
562 |
||||||
|
IH-pano-Suiza |
8 |
V. |
154 |
1500 |
455 |
48.3 |
10 |
||||||
|
Knox |
12 |
V. |
300 |
1800 |
1425 |
19.4 |
7 |
||||||
|
Packard |
12 |
V. |
225 |
2100 |
800 |
||||||||
|
Rausenberger C-12 |
12 |
V. |
150 |
1300 |
570 |
||||||||
|
Sturtevant 5 |
8 |
V. |
140 |
2000 |
.54 |
IMS |
600 |
70 |
60 |
40 |
5 |
||
|
5-A |
8 |
V. |
lio |
2000 |
1200 |
514 |
66 |
54 |
10 |
• |
|||
|
tt |
12 |
V. |
276 |
2000 |
9 |
||||||||
|
Thomas 8 |
8 |
V. |
i:<r> |
2000 |
1200 |
59 |
.053 |
572 |
so |
LOO |
16.3 |
6 |
|
|
" 88 |
8 |
V. |
160 |
2000 |
.59 |
485 |
|||||||
|
Wisconsin |
6 |
Vert. |
110 |
1380 |
1380 |
.550 |
027 |
637 |
38* |
50 |
26 |
||
|
ii |
12 |
V. |
260 |
1200 |
1200 |
liO'J |
.029 |
1000 |
142 |
18.1 |
t |
||
|
Wright |
6 |
Vert. |
60 |
1400 |
.-,!.-, |
39 |
6.28 |
* Kngine only.
t Figures obtained from test run.
t Gallons per hour.
RICAN ENGINES
ication
|
"o CD "a, B It o tT s= la 0> O s£ |
Weight of Example of Mounting, Ib. |
"S CD "E S $ w . «4-( -^ o~ •w h/D |l ^j O 5^U |
m <D J3 O _C ^g £ 1 |
GQ 5 1 a | 1 |
Piston Displacement, cu. in. |
.0 1 J 1 1 O |
_g ^a M 43 73 ^ 1 | O |
,c .a ^ f 3 1 O |
60 a 1 |d = 1 wi 0 g 2;« |
S § . f.3 3J £§ 2^ - a *S II |
Athwartship distance between Brackets. |
Athwartship distance between Bolt Holes. |
Maker and Model |
|
29. 8 |
28.2 |
5.5 |
4A |
5% |
449 |
58 |
30 |
36?4 |
Aeromarine |
||||
|
67 |
24 |
30 |
3 |
Aeromarine D-12 |
|||||||||
|
Aeromarine |
|||||||||||||
|
58 |
55 |
40.9 |
3% |
4Ji |
519.5 |
48 |
27 |
26 |
Atwood C-12 |
||||
|
!6.5 |
34 |
6.5 |
4% |
6 |
Christofferson |
||||||||
|
40 |
41 |
17.5 |
•• |
||||||||||
|
4 |
5 |
502 |
50 |
30 |
27 |
3 |
9 |
12% |
Curtiss-Ox 2 |
||||
|
!2.5 |
23.2 |
10.6 |
4M |
5 |
567.5 |
50 |
30 |
29 |
3 |
9 |
12% |
" -OXX 2 |
|
|
64 |
45 |
12.2 |
5 |
7 |
1100 |
67 */8 |
35 |
34 |
5 |
9 |
14 |
16 |
•• -vx |
|
64 |
14.7 |
12.2 |
5 |
7 |
" -VX 3 |
||||||||
|
95 |
60.1 |
19.6 |
5 |
7 |
84^ |
34^ |
40 |
" -V-4 |
|||||
|
29.5 |
4.8 |
4% |
7 |
496 |
43% |
15J^ |
37% |
4 |
13% |
13% |
14M |
Duesenberg |
|
|
49.2 |
18 |
4% |
7 |
1488 |
68 |
31M |
39% |
4 |
15% |
14 |
15^ |
tt |
|
|
4% |
6H |
920 |
Genl. Ordnance Co. |
||||||||||
|
4.33 |
6M |
920 |
Genl. Vehicle Gnome |
||||||||||
|
23.2 |
22.7 |
12.4 |
4^ |
6 |
Gyro K. |
||||||||
|
27.6 |
24.4 |
13.2 |
4K |
6 |
859 |
24.7 |
37^ |
371A |
'• L |
||||
|
37 |
28.9 |
4.5 |
5 |
7 |
550 |
57 |
18^ |
39^ |
4 |
16M |
14 |
16 |
Hall-Scott A-7 |
|
42.5 |
39.6 |
6.8 |
5 |
7 |
825 |
63 ?s |
18H |
41^ |
3 |
35^ |
14 |
16 |
A-5 |
|
A-5af |
|||||||||||||
|
17 |
13.5 |
28.3 |
4% |
5 |
672 |
52^ |
32H |
35M |
12^ |
14% |
Hispano-Suiza |
||
|
56.8 |
21 |
4% |
7 |
1555 |
" " |
Knox |
|||||||
|
4 |
6 |
905 |
62^ |
23 A |
41 J^ |
3 |
16M |
18M |
Packard |
||||
|
4% |
6 |
900 |
42 |
24 |
Rausenberger C-12 |
||||||||
|
40 |
30 |
30 |
4 |
5J--2 |
522 |
59A |
23 |
29^ |
3 |
14A |
13% |
Sturt.evant 5 |
|
|
4 |
5J^ |
522 |
59 A |
34 |
34^ |
3 |
14A |
5-A |
|||||
|
24 |
4 |
5K |
|||||||||||
|
49.8 |
40.1 |
13.6 |
4 |
5^ |
552.9 |
60 |
28 |
37% |
3 |
ISA |
13^' |
Thomas 8 |
|
|
3 |
13A |
l:!:i-, |
88 |
||||||||||
|
42 |
5 |
5K |
765.7 |
17M |
24 |
«A |
4 |
14H |
13M |
16^ |
\\ iscuiism |
||
|
54.2 |
10.8 |
5 |
6J^ |
1532 |
76^ |
wys |
37 A |
4 |
14?i |
15H |
IS', |
" |
|
|
19 |
25.9 |
6.4 |
4% |
4^ |
Wright |
AIRPLANE DESIGN
factory data on a machine of a certain speed, cau employ this rule for machines of a different speed.
Position and Resistance of a Radiator
Tests at the Massachusetts Institute of Technology show that the resistance of a radiator may be represented by the
equation
R = KTAV'-
where R = resistance in pounds
A = area of radiator face in square feet F = speed in miles per hour.
and Kf= .00175
While these tests were conducted on very small sections, the results are safely applicable to full-size radiators.
Figures on the resistance of a given section of radiator in a current of air do not by any means settle the problem of the best position for the radiator. Manufacturers have placed radiators in various positions, claiming minimum re- sistance for each position. If a radiator is placed behind the propeller where the slip stream increases the velocity by some 25 per cent, the cooling surface may be decreased by 25 per cent with a consequent reduction of resistance pro- ducing area, but since the resistance varies as the square of the velocity, there is finally an increase of 25 per cent. These or similar considerations have led designers to place radiators underneath the wings. But it is forgotten that when a radiator is placed underneath the wings, it is no longer a shelter for the body. There is also the question of extra length of piping. For radiators placed at the sides, Dr. Hunsaker's opinion is that a more generous allowance is necessary. Dr. Zahm's skin friction formula is of the form E = 0.0000158 1*" Vlfe b. as we saw in Part 1, Section 3, AVIATION AND AERONAUTICAL as we saw in Part 1, Chapter 3, where I is the length of sur- face parallel to the wind. Owing to the greater length of side radiators in the direction of motion, they are therefore probably less effective.
The authors' opinion is that the best and most natural posi- tion of the radiator is behind the propeller, but the question is hardly capable of a decision so far.
Practical Construction of Radiators
C. Sage, engineer of the Rome-Turney Radiator Company, has submitted the following authoritative views:
" As to the construction of radiators, we may say that the simpler the outline the more durable will be the radiator — and the cheaper. The cooling section of honeycomb radiators ought to have outlines composed entirely of straight lines —
curves in the honeycomb are expensive and are weak points for the reason that all honeycomb cooling sections are at the start made of rectangular blocks and then sawed to shape on a band saw like a board. The sawed-off waterways have then to be patched up again with solder and their ends are naturally not as strong as before. Then this section has to be fitted to the case and the more curves there are the more difficult and costly the fitting will be. Concerning the case of the radiator the same principle holds good — the simpler the design the better and cheaper the product. All curved surfaces are costly if they have to be produced by hand work and pressed eases must be made in large quantities in order to pay for the necessary punches and dies and it takes a long time until production can be started on them.
" As for water connections between engine to radiator and pump to radiator, it is very important that they be large enough to convey the large bulk of water with the least possible pressure. If the connections are too small a considerable vacuum will be set up in the suction line from the radiator to the pump and consequently air will be drawn into this line at all leaky points, prominent among these being the stu fling box and the grease cups of the pump. This air will be mixed with the water forming a milky liquid like charged water, increasing its volume, and consequently a considerable loss through the vent pipe will take place.
" As to support of a radiator, the most satisfactory method is the use of a cradle or cross piece at the front of the body, in the case of a tractor, on which the radiator is placed and fastened by studs in the bottom tank. In the case of pushers, many different suspension methods are used, none of which can be called standard, and the same is true for side radiators."
An excellent point made by the manufacturers of the Ajax radiator is the reinforcement of the fins rear and front by soldering on 1/16 in. wires. Dividing a radiator into two parts by a small % in. deep water tank to permit settling of the water, is another good point in this type.
As a general rule, the sub-division of a radiator into a number of sections is advantageous. In the present ill-defined position of radiator design, it is an advantage to be able to increase or diminish the radiator surface of a given machine.
References for Part II, Chapter 4
•• Surface Cooling and Skin Friction." by F. W. Lancbester. British Iteporta, No. 94, 1912-1913.
" Notes on Radiator Design," by J. C. Hunsaker, Aerial Age, May 29. 1916.
" Aeronautical Engines." by Francis J. Kean, 1916.
" Aero Engines." by G. A. Burls.
" Entwerfen von leichten Benzlnmotoren." by 0. Winkler.
" Report on Aeronautical Engines." by Charles E. Locke. First An- nual Report of the National Advisory Committee for Aeronautics.
Chapter V
Materials in Airplane Construction
Within the limits of one chapter it is impossible to treat adequately all the data on materials required for airplane construction. The data included here will be sufficient for the purpose of our design, however, and a number of refer- ences are appended. For practical work, the designer must procure all necessary handbooks, make tests of his own special fittings, and generally collect his own data.
Special Utility of Wood in Airplane Construction
It is the remarkable strength for its weight which makes wood so useful in airplane construction. If we compare spruce, weight per cubic foot 26 lb., tensile strength 9000 lb., with mild steel weighing 490 lb. per cubic foot with a tensile
strength of 60,000 lb., the spruce will be-^ ^X^- = 2.9
oO,000 26
times as strong for the same weight.
The selection, mechanical properties and correct structural employment of timber are, however, inexhaustible subjects, and the following notes are the barest summary of the factors the designer must have in mind.
Weight of Wood
The weight of wood varies greatly for the same species and for portions of the same tree. Sapwood is heavier than heart- wood, summerwood than springwood. Green timber naturally weighs more than dry timber, due to the presence of sap and moisture. The ultimate wood fiber of all species has a specific gravity of 1.6, so that no wood would float in water were it not for the buoyancy of the air present in the cells and walls.
TABLE 1 Specific Gravity and Weights of Woods
Dry woods Wt. per cu. ft. lb.
Ash, American white 38.
Balsa 6.5
Boxwood 60.
Cherry 42.
Chestnut 41.
Cork 15.
Elm 35.
Ebony 76.1
Hemlock 25.
Hickory 53.
Lignum-vitjB 83 .
Mahogany, Spanish .... . 53 .
Mahogany, Honduras 35.
Maple. . .' - 49.
Oak, live 59.3
Oak, white 48.
Oak, red 40.
Pine, white 25.
Pine, yellow 34.3
Pine, southern 45 .
Sycamore 37.
Spruce 25.
Walnut 38.
Specific gravity .610 .104 .960 .672 .660 .250 .560 1.220 .400 .850 1.330 .850 .560 .790
950
770 .640 •400 .550 .720 .590 .400 .610
The weight of wood is experimentally determined by sub- jecting thin discs to an oven temperature of 100° Cent, until they cease to lose weight by evaporation of moisture. But even with this provision, the results will be extre-nely variable,
and the value usually assigned to a given species is simply the average of a large number of tests. Table 1, taken from a Bulletin of the Forestry Division, United States Department of Agriculture, will give values sufficiently accurate for design. Weight is a good indication of the strength of wood, pro- vided the amount of moisture contained is known. As a gen- eral rule, we may say that a comparison of two woods, each containing the same percentage of moisture, will show the heavier to be the stronger; in fact, the strength will be very nearly proportional to the weight.
Factors in the Mechanical Properties of Woods
The strength properties of wood depend on (1) correct identification of species and variety; (2) age and rate of growth; (3) position of test specimens in the tree; (4) mois- ture content; (5) relative freedom from defects, such as knots, etc.
Tensile Strength
Tensile tests are difficult because tests cannot be devised that do not involve either shear along the grain or compression across the grain. It is for the same reasons that wood may be unsuitable in tension, though it is apparently strong under such a stress.
Failure in tension along the grain involves principally the resistance offered by the wood elements to being torn apart transversely or obliquely. The strands of wood elements are practically never pulled apart by failure of the union between adjacent strands or fibers.
Cross grain is prejudicial to tensile strength and rays, ow- ing to their transverse position with respect to a load applied along the grain, and small resistance to tension in a direction normal to the direction of their fibers greatly weaken the timber. Knots weaken wood subjected to longitudinal tension.
Conipressive Strength
Individual fibers act as so many hollow columns bound firmly together, and failure involves either buckling or bend- ing of the individual fibers or bundles of elements which finally come to act almost independently.
Conipressive strength depends on a number of factors: (1) density; (2) strength of union between individual fibers as affected by moisture content; (3) stiffness of wood fibers (again largely a matter of moisture content) ; (4) continuity of the course of longitudinal strands in a direction parallel to axis of the piece. Woods in which separate elements are closely interlaced and bound together will be stronger than woods of opposite character.
The strongest woods in compression with the grain are, roughly, in the following classes :
95
!X5
AIRPLANE DESIGN
(1) The dense and tough hickory, birch, hard maple, etc.; (2) oak, elm, ash; (3) spruce, pine and fir.
Crushing Across the Grain
Crushing strength across the grain is dependent practically entirely upon the density of the wood. Crushing strength across the grain is, therefore, least for the lightest, most porous woods, and greatest for heaviest and densest woods.
Compressive strength across the grain is to compressive strength along the grain as 13 to 14 per cent for white pine, cedar, cypress and spruce, 15 to 16 per cent for the various grades of hard pine, 18 to 26 per cent for elms, 21 to 26 per rent for ash, 22 to 26 per cent for oaks, 23 to 31 per cent for hirkuries.
Strength in Bending
In considering the strength of a wooden beam in bending, several difficulties occur. Longitudinal shear is very important. A wing spar may be amply strong in bending, and yet if highly channeled out fail by longitudinal shear. The tensile fiber strength of wood is much ia excess of the compressive stress, but even if the compressive fiber stress of wood is em- ployed in the formula / = — — , it is no true criterion. If this
formula is employed for strength computations in bending, it is assumed that the material is still behaving elastically up to actual failure, and therefore that the fiber stress is still di- rectly proportional to the distance of the fiber from the neutral axis. As a matter of fact, the elastic limit of the material may have long been passed when the breaking load is reached, the neutral axis may have shifted, and the extreme fiber may be no longer proportional to the bending. Therefore, in stress calculations for wing spars, these considerations should be applied, making use of the modulus of rupture — for which values are given in Table 2 — deduced from actual bending tests, which are far more trustworthy guides.
Knots
Knots originate in the timber cut from the stem or branches of a tree because of the encasement of a limb, either living or dead, by the successive animal layers of wood. Most limbs originate at the pith of the stem, and the knots found deep in a log are therefore small, increasing in size toward the bark. So long as the limb is growing, its layers of wood are a con- tinuation of those of the stem. But a majority of the limbs die after a time, and if a portion of a dead limb is subse- quently encased by the growing stem, there will be no intimate connection between the new stem wood and the dead wood of the limb, and a board so cut as to intercept this portion of the log will contain a loose knot. A board cut from the log at such a depth that the limb is intercepted at a point where it was encased while still living will contain a sound knot, unless the knot has rotted, become badly checked, or contains a large pith cavity.
A sound knot is usually harder than the surrounding wood, and in coniferous woods is apt to be very resinous. On this account it may constitute a defect because of its non-retentiv- ity of paint or varnish. Otherwise it constitutes a defect only on account of the disturbance to the grain and difliculty caused in working, or in the event of its occurrence on the under side of a timber used as a beam, a weak point exists, owing to its small resistance to tensile stress. A knot constitutes an im-
pediment to the splitting of timber, since the fibers of the stem wood above a limb bend aside and pass around the limb, while the fibers below run continuously into the limb. Thus it often happens that a cleft started above a limb will never run into a knot, but one started below- is very apt to do so.
The Effect of Moisture on Strength of Wood
Loss of moisture does not affect the strength of wood in any way, until the total moisture content has been reduced below the critical percentage, which represents the fiber-sat- uration period. Beyond this point, progressive loss of mois- ture affects the strength very considerably. Thus the strength of green wood is only 50 to 60 per cent of normal air-dry conditions (12 per cent moisture), while the strength of kiln- dry wood exceeds the strength of air-dry woods by some 50 to 70 per cent.
Time Factor in Tests of Timber
Timber differs from most other materials in that small variations in the rate of application of load have a more pronounced effect upon the strength and stiffness shown by a specimen under test. If a timber-compression block or beam is loaded rapidly, it will appear to have a higher elastic limit and ultimate strength, and will also appear to be stiffer, than it will if loaded less rapidly. This is due to the fact that the deformation lags far behind the load, and if any load is permitted to remain upon a specimen for a time the deformation increases, the amount of increase becoming greater for heavier loads. Actual failure appears to be consequent upon the attainment of a certain limiting amount of deforma- tion or strain, rather than a limiting load or stress.
Difficulties of Wood Construction in Airplanes
The comparative values of Table 2 demand the most care- ful study. A certain type of timber may be most suitable for the direct stress to which it is subjected, yet fail completely under certain indirect stresses, either inherent in the construc- tion or due to faulty design. For example, at the hinging of a wing spar to the body, if the bolts are not correctly placed, they may shear out the wood. These points will be considered in detail in the design, but enough has been said to show the value of studying not only the direct stresses on a piece of timber in a machine, but also the indirect stresses producing crushing across the grain, shear, etc.
Strength Values for Timber
In no material are such conflicting values given by various authorities as for timber. The size of the specimen under test, the dryness, the method of applying the load, and its previous history, all tend to introduce discrepancies. Until the Bureau of Standards, or some other testing laboratory, lias gone thor- oughly into the question, all the values employed by airplane constructors will be open to suspicion. Table 2 is a summary of information taken from various sources. This table is not unimpeachable, but it approximates closely values used in current practice. In airplane design, fiber stress is still taken as a criterion, without due consideration of the modulus of rupture.
Acknowledgement is due Prof. W. H. Keith for collabora- tion on brief notes on timber.
AIRPLANE DESIGN
97
TABLE 2
|
x |
ifeX |
'a! |
ss |
a |
||||
|
- |
1 |
1 |
j?sf |
•ffl 3 |
II |
£ |
||
|
1 |
i |
a1 |
i-Ii |
a £ |
fa-- |
3 i |
||
|
| ! |
i |
£ 1 |
|| |
u a • |
£— 5j |
t£ °l |
||
|
3 |
01 |
i |
3*3 -^ |
c? ^ |
a> ^ m |
3.S |
||
|
OTJ.^ |
||||||||
|
•i |
i-i |
'55 e |
s.s |
g-3 OT |
SJ <• |
1-3 |
||
|
S |
hfi |
Is H no |
61 |
6 II |
M§J |
Si |
||
|
Ash |
12,000 |
1,600 |
9,000 |
1 300 |
1,500 |
56 5 |
15,660 |
|
|
11,000 |
1,600 |
1,200 |
60-70 |
|||||
|
Beech |
11,000 |
1,600 |
8,600 |
1,200 |
10,000 |
|||
|
Birch |
15000 |
1 800 |
3 500 |
1,050 |
11,700 |
|||
|
Cedar |
10800 |
700 |
5700 |
7,400 |
||||
|
Elm |
10000 |
7000 |
8,800 |
|||||
|
Hickory. . . |
15,000 |
2,200 |
11,000 |
944 |
1,500 |
15,000 |
||
|
Mahogany. |
16,000 |
8,200 |
11,000 |
|||||
|
Maple |
11,150 |
1,500 |
7,150 |
606 |
1,130 |
12,000 |
||
|
Oak |
15 000 |
2000 |
7000 |
1,215 |
1,139 |
10,600 |
||
|
Pine.yellow |
13,000 |
1,100 |
5,400 |
342 |
640 |
310 |
•4,760 |
|
|
Pine, white |
10,000 |
1,100 |
5,000 |
314 |
640 |
304 |
5,000 |
|
|
Spruce |
9,000 |
600 |
6,500 |
400 |
500 |
272 |
9,200 |
Wires and Cables
The following terms are in common use: (1) " Solid wire stay " or " aviation wire " of one wire of suitable diameter ; (2) " strand stay," consisting of either 7 or 14 wires stranded together and known to the trade as "aviation strand"; (3) " cord " or " rope stay," consisting of 7 strands twisted to- gether, forming a rope, the strands being either 7 wires or 19 wires; (4) "flexible cord," composed of six strands of seven wires, with a center of either cotton or wire, as ordered. The cord with the cotton center is considerably more pliable than that with the wire center.
Vanadium steels and other special steels have uot as yet become established as desirable wire steels, and carefully made high-grade carbon steel is at present most largely employed in the manufacture of wires and cables.
Properties of Metals
Strength and Weights for Wire and Cables TABLE 3
Diameter of cord, Inches 1/16 5/69 3/32 7/64 1/8 5/32 3/16 7/32 1/4 5/16
ROEBLING SOLID WIRE
Breaking strength
of cord,
Pounds
400
480
780
830
1,150
2,200
2,750
4,000
5,000
7,900
Approximate weight per 100 ft., Pounds .73 .83 1.30 1.50 2.20 4.20 5.30 7.43 4.50 15.00
ROEBLING'S 19 WIRE GALVANIZED — AVIATOR WIRE STRAND
1/32 (7 wire) 1/16 5/64 3/32 7/64 1/18 5/32 3/16 7/32 1/4 9/32 5/16 11/32 3/8
AMERICAN STEEL AND WIRE
1/32 (7 wires)
1/16
3/32
1/8
5/32
185
500
780
1,100
1,600
2,000
2,800
4,200
5,600
7,000
8,000
9,800
12,500
14,400
Co. GALVANIZED STRAND
125
500 1,100 2,000 3,000
0.30
0.78
1.21
1.75
2.60
2.88
4.44
6.47
9.50 12.00 14.56 17.71 22.53 26.45
(19 WIRE) AIRPLANE
.23 .89
1.70
3.3
5.1
ROEBLING'S 7 BY 19 HEAVILY TINNED — AVIATOR CORD
1/8 5/32 3/16 7/32 1/4 9/32 5/16 11/32 3/8
2,000 2,800 4,200 5,600 7,000 8,000 9,800 12,500 14,400
2.88
4.44
6.47
9.50
12.00
14.56
17.71
22.53
26.45
ROEBLING EXTRA FLEXIBLE AVIATOR CORD, 6x7 COTTON CENTER
5/16
1/4
7/32
3/16
5/32
1/8
7/64
3/32
5.64
1/16
9,200
5,800
4,600
3,200
2,600
1,350
970
920
550
485
16.70
10.50
8.30
5.80
4.67
2.45
1.75
1.45
.93
.81
AMERICAN STEEL AND WIRE Co. GALVANIZED OR TURNED FLEXIBLE CORD
3/16 (19 x 7)
5/12 (19 x 7)
1/8 (19x3)
3/32 (12 x 3)
2,600
1,800
1,150
725
5.52 3.85 2.45 1.55
The figures given above have been revised, and the following
|
Only the briefest outline can be given of the metals that are commonly employed in airplane construction. To enter into any adequate discussion of this branch of the work would require a book in itself. The constructor must keep constantly before him some standard book on this subject and at the same time resort to strength of material and part tests whenever new combinations are to be employed in his design. The following table of weight and melting points for various metals may be of service : |
ROEBLING TINNED AIRCRAFT WIRE American Minimum gauge breaking Weight (B&S) Diameter, strength, Ib. per Number in. Ib. 100ft. 8 .128 3000 4.40 9 .114 2500 3.50 10 .102 2000 2.77 11 .091 1620 2.20 12 .081 1300 1.744 13 .072 1040 1.383 14 .064 830 1.097 15 .057 660 .870 16 .051 540 .690 17 .045 425 .547 |
||||||
|
18 |
.040 |
340 .434 |
|||||
|
Weight per |
Weight per |
Specific |
Melting point |
19 |
.036 |
280 .344 |
|
|
Metal. |
cu. in. |
cu. ft. |
Gravity |
Fahr. °. |
20 |
.032 |
225 .273 |
|
Aluminum . |
096 |
166 |
2.66" |
1,215 |
21 |
.028 |
175 .216 |
|
Antimony .... |
.242 |
418 |
6.70 |
786 |
|||
|
Bismuth |
.350 |
607 |
9.74 |
516 |
ROEBLING |
19-WiRE GALVANIZED |
AIRCRAFT STRAND |
|
Brass ca^t |
.292 |
504 |
8.10 |
1,635 |
|||
|
Bra^s rolled |
.303 |
524 |
8.40 |
Diameter |
Breaking |
Approximate |
|
|
Bronze, gunrnetal... |
. . .305 |
529 |
8.50 |
1,866 |
of strand, |
strength of |
weight, |
|
Copper cast .... |
.314 |
542 |
8.70 |
1,980 |
in. |
strand, Ib. |
Ib. per 100 ft. |
|
Copper cold |
321 |
555 |
8.90 |
5/16 |
12,500 |
20.65 |
|
|
Duralumin . . . |
.103 |
178 |
2.85 |
(approx.) 1,300 |
1/4 |
8,000 |
13.50 |
|
Gold 24 carat |
694 |
1,204 |
19 26 |
1,950 |
7/32 |
6,100 |
10 00 |
|
Iron cast . . |
260 |
450 |
7.21 |
2,012 |
3/16 |
4,600 |
7.70 |
|
Iron, wrought |
.. .278 |
480 |
7.70 |
2,912 |
5/32 |
3,200 |
5.50 |
|
Lead cast |
410 |
710 |
11.38 |
621 |
1/8 |
2,100 |
3.50 |
|
Mercury 60" Fahr.. |
... .489 |
846 |
13.58 |
7/64 |
1,600 |
2.60 |
|
|
Monel metal |
.. .320 |
553 |
8.85 |
2,486 |
3/32 |
1,100 |
1.75 |
|
Platinum . . . |
.779 |
1,342 |
21.50 |
3,236 |
5/64 |
780 |
1.21 |
|
Silver |
.378 |
655 |
10.50 |
1,762 |
1/16 |
500 |
.78 |
|
Steel rolled |
.283 |
490 |
7.85 |
2,552 |
1/32 7 wire |
185 |
.30 |
|
Tin cast |
.266 |
459 |
7.35 |
450 |
|||
|
Zinc. cast... |
.248 |
429 |
6.88 |
786 |
98
AIRPLANE DESIGN
ROEBLINO 6x7 (COTTON CENTER) GALVANIZED AIRCRAFT COKD
|
Diameter of cord. |
Breaking strength of |
Approximate weight, |
|
in. |
cord, Ib. |
Ib. per 100 ft. |
|
5/16 |
7,900 |
15.00 |
|
1/4 |
5.000 |
9.50 |
|
7/32 |
4.0()0 |
7.43 |
|
3/18 |
2,750 |
5.30 |
|
5/32 |
2,200 |
4.20 |
|
1/8 |
1,150 |
2.20 |
|
7/64 |
830 |
1.50 |
|
3/32 |
780 |
1.30 |
|
5/64 |
480 |
.83 |
|
1/16 |
400 |
.73 |
|
ROEBLINO |
7x7 (Wine CENTER) GALVANIIED AIRCRAFT |
CORD |
|
Diameter of cord, |
Breaking strength of |
Approximate weight, |
|
in. |
cord, Ib. |
Ib. per 100 ft |
|
5/16 |
9,200 |
16.70 |
|
1/4 |
.-,.NK> |
10.50 |
|
7/32 |
•1,600 |
8.30 |
|
3/16 |
3,200 |
5.80 |
|
5/32 |
2.0011 |
4.67 |
|
1/8 |
1.350 |
2.45 |
|
7/64 |
970 |
1.75 |
|
3/32 |
920 |
1.45 |
|
3/64 |
550 |
.93 |
|
1/16 |
485 |
.81 |
|
ROEBLINO 7x19 TINNED AIRCRAFT CORD |
||
|
Diameter |
Breaking |
Approximate |
|
of cord, in. |
strength of cord, Ib. |
weight, Ib. per 100 ft. |
|
3/8 |
14,400 |
26.45 |
|
11/32 |
12,500 |
22.53 |
|
5/16 |
9,800 |
17.71 |
|
9/32 |
8.000 |
14.56 |
|
1/4 |
7,000 |
12.00 |
|
7/32 |
5,600 |
9.50 |
|
3/16 |
4,200 |
6.47 |
|
5/32 |
2,800 |
4.44 |
|
1/8 |
2,000 |
2.88 |
Wire, Strand or Cord
Roebling's report does not settle the question as to which is a correct selection. A comparative table shows the progressive decrease in strength.
Material. Wire Strand 7 by 19 cord
Diameter. 3/16 3/16 3/16
Strength of material. 5,500 4,600 4,200
Strength of stay 5,100 4,100 3,500
A stranded or cord stay has about 20 per cent more aero- dynamical resistance than a solid wire of about the same diameter. There appears to be a slight advantage in favor of solid wire as regards strength of stay. On the other hand, the strand stay is one and a third times more elastic, the cord one and three-quarter times more elastic than the solid wire. In American practice all three types of stays appear. No doubt the use of strand or cord is justified by the extra elastic stretch and flexibility.
Exact data on the fatigue values of the three materials is not available, but it is well known that strand or cord will stand up much better to vibration than a wire. Also in a continuous beam structure such as that of a wing, there may be deflections of unknown magnitude, in which case the more elastic cable will be somewhat safer. On the other hand an exposed cable is liable to damage. A single small wire of one strand may be damaged and lead to the eventual destruction of the whole cable. In the covered in body a cable is not likely to be damaged. The problem is by no means settled yet, and only comparative experience in actual flight and further experi- mentation can give a definite solution.
Tnrnbuckles
The breaking strength of turnbuckles made of precisely the same material will vary enormously with every type of con- struction, and the makers' catalog or data sheet has to be con- sulted for every special case. In Figs. 1 and 2 are shown two representative types, the Curtiss and the National, Burgess, Meyer, Binet types. The weights and strength values are I'iiirly representative of what can be obtained from this impor-
tant brand of airplane material. In Table 4 are given results of tests on some specimens of the Standard Screw Co. of Pennsylvania :
TABLE 4 STANDARD SCREW Co. TURNBUCKLES
Manufacturer Mean break- Mean break- Initial shank Weight in Ib
number. ing load. ing load from test, area per s<*. in. Long,barrel male
326 2,150 2,432 .01864 .122
327 2,850 3,490 .0260 .167
328 3,500 4,605 .0350 .232
329 5,000 6,545 .0515 .275
330 840 9,530 .0794 .411
Mean tensile strength of shank, 128.610 Ib. per s<<. in. Material — shank, 3>£ per cent, nickel steel, heat treated; barrel, robin bronze. Turnbuckles are madejin short and long male and female ends.
Strength of Steel — Pounds per Sq. Inch
|
0.05 %C for rivets... 0.10% C boiler plate. 0.25% C structural. . 040% C rails . |
Tension Ultimate yield point. . 45,000 22,000 . 55.000 30.000 . 65,000 34,000 70 000 45 000 |
Compression Ultimate yield point. 70,000 40,000 95,000 65.000 110,000 85,000 120000 90000 |
Shearing Ultimate vield point. 45,000 22,000 50,000 28,000 55,000 32,000 60000 35000 |
|
0.90% C machinery. 1.00 to 2.00% tool... |
. 90,000 70,000* . 150,000 none |
140,000 110,000* 200,000 none |
70,000 «45,000 120,000 none |
•When well annealed.
Modulus of elasticity.
|
Direct |
Shearing |
||
|
0.05% C... |
. . . . 26,000,000 |
13,000,000 |
|
|
0.10% C |
. . . . 28,000,000 |
13,500,000 |
|
|
0.25% C |
30,000,000 |
14,000,000 |
|
|
0.40% C |
30,000,000 |
14,000,000 |
|
|
0.90%C |
32,000,000 |
14,500,000 |
When well annealed. |
|
1.00 to 2.00% C |
. . . . 35,000,000 |
16,000,000 |
When hardened. |
|
Modulus of Kupture |
|||
|
For flat plates |
1.0 (t. s.) |
||
|
For squares |
1.2 (t. s.) |
||
|
For high rectangles |
1.5 (t. s.) |
||
|
For rounds and diamonds. . . . |
1.8 (t. s.) |
Strength of Steel Castings — Well Annealed —
SMALL CASTINGS
Shearing ld
Tension Compression
Ultimate yield point Ultimate yield point Ultimate yield point
60,000 30,000 80,000 45,000 45,000 25,000 *
Modulus of elasticity (direct) ....... .............................. 29,000,000
Modulus of elasticity (shearing) ................................... 13,000,000
Modulus of rupture in same ratios as above.
LAKGE CASTINGS
Tension Compression Shearing
Ultimate yield point Ultimate yield point Ultimate yield point
40,000 20,000 70,000 40,000 40,000 20,000
Modulus of elasticity (direct) ..................................... 28,000,000
Modulus of elasticity (shearing). .................................. 13,000,000
Modulus of rupture in same ratios as above.
Steel Castings with Vanadium show about 20 per cent increase over the above values.
Special Steel Alloys — Pounds per Square Inch
Tensile strength.
Manganese Up to 140,000
Nickel HO.mn
Chrome Vanadium 200,000
Chrome Nickel 140,000
Tungsten 170,000
Chrome Tungsten 185,000
up to
Yield point
90,000
90,000 175,000 100,000 150,000 160,000
Strength of Copper, Aluminum and Various Alloys Pounds per Square Inch
CAST
Tension ........................................... 22.000
Compression ....................................... 45,000
Shearing .......................................... 18,000
Modulus of elasticity (direct) ..................................... 12,000,000
Modulus of elasticity (shearing) ................................... 8,000,000
Modulus of rupture (rectangular sections) .......................... 35,000
COLD ROLLED OR HAMMKKKD PI.ATKS
Tension ........................................... 32,000
Compression ....................................... 60,000
Shearing ........................................... 28,000
COLD DRAWN \ViKK
Tension .................................... 50,000 to 60,000
Shearing ................................... 40,000
Modulus of elasticity of cold worked cupper 17,000,000. Copper has no well defimd > ield point.
AIRPLANE DESIGN
99
L
|
Cur- |
Th'ds |
||||||||||||||||||||||||||||
|
tiss |
No. |
A |
H |
C |
L) |
E |
F |
G |
H |
I |
j |
K |
L |
M |
N |
0 |
P |
Q |
R |
S |
T |
u |
V |
\v |
X |
Per |
Br'k'g |
Cable |
Weight |
|
No. |
Inch |
Stress |
|||||||||||||||||||||||||||
|
M iQ- |
|||||||||||||||||||||||||||||
|
Spec |
ial |
7?4 |
4 |
X |
K |
X |
A |
H |
.320 |
A |
% |
% |
14 |
A |
H |
H |
A |
1A |
A |
H |
X |
H |
A |
IX |
IX |
24 |
8846 |
^able |
|
|
3 |
326 |
8 |
4 |
A |
A |
% |
ft |
A |
.159 |
X |
.203 |
H |
% |
M |
.110 |
A |
A |
ft |
A |
1A |
A |
,".. |
,:!,, |
IX |
lij |
30 |
2183 |
h |
|
|
4 |
327 |
7H |
4 |
M |
H |
15 |
H |
A |
.187 |
A |
.234 |
A |
tt |
X |
H |
A |
M |
H |
A |
K |
X |
ft |
M |
IX |
LM |
28 |
3037 |
% in. Cable |
|
|
5 |
328 |
T:,: |
4 |
H |
H |
H |
A |
% |
.215 |
A |
.265 |
A |
H |
A |
H |
A |
K |
H |
M |
H |
H |
'4 |
k |
i A |
1« |
26 |
3993 |
A |
|
|
6 |
329 |
~\':, |
4 |
H |
'A |
H |
tt |
A |
.258 |
A |
A |
% |
K |
% |
H |
A |
A |
H |
A |
K |
A |
A |
A |
14 |
i,s« |
24 |
5750 |
A |
|
|
10GA |
|||||||||||||||||||||||||||||
|
326-S |
'•'•I':. |
2 |
A |
A |
X |
ft |
A |
.159 |
X |
.203 |
X |
H |
34 |
.110 |
A |
A |
ft |
A |
J4 |
A |
A |
A |
A |
H |
30 |
2183 |
Wire |
||
|
8GA |
|||||||||||||||||||||||||||||
|
327-S |
4A |
2H |
H |
H |
H |
J5 |
A |
.187 |
A |
.234 |
A |
H |
X |
.110 |
H |
M |
H |
A |
H |
Yt |
A |
K |
A |
H |
28 |
3037 |
Wire |
Material: — Mang. Bronze and 55-Ton Steel
FlO. 1. CUHTISS TURNBUCKLES.
|
i ! |
|
|
30 |
|
L
-L--
!
|
SPECIMEN |
L |
H |
d, |
d, |
da |
di |
d, |
1 |
Weight Ibs. |
Estimated Load. Pounds |
Remarks |
|
2 35 |
1 30 |
28 |
23 |
11 |
15 |
20 |
45 |
039 |
1250 |
||
|
National No 327 |
2 50 |
2 50 |
40 |
32 |
19 |
23 |
35 |
60 |
161 |
2200 |
|
|
National No. 328 |
5.00 |
2.75 |
48 |
37 |
20 |
27 |
.40 |
.65 |
.''29 |
2800 |
Yield in barrel. |
|
National No 328 |
5 00 |
2 80 |
46 |
38 |
22 |
27 |
40 |
70 |
.242 |
2200 |
|
|
National No 329 |
6 00 |
3 25 |
54 |
44 |
23 |
31 |
47 |
85 |
361 |
4000 |
|
|
A J Meyer No. 3 |
2.35 |
1.30 |
.28 |
.21 |
.11 |
.15 |
.19 |
.45 |
.037 |
1200 |
Yield in barrel. |
|
Above average. |
|||||||||||
|
A J Meyer No 4 |
3 00 |
1 75 |
32 |
20 |
14 |
18 |
28 |
45 |
0682 |
1500 |
|
|
A J Meyer No. 6. |
4 50 |
2.5ID |
42 |
32 |
19 |
23 |
35 |
.55 |
.161 |
2200 |
Yield in barrel. |
|
6 00 |
20 |
.172 |
"SOU |
||||||||
|
4.80 |
2.70 |
.62 |
.51 |
.30 |
.33 |
.57 |
.80 |
.506 |
7000 |
Yield in barrel. |
|
Estimated load based upon average strength at yield point of barrel 41,000 Ib. per sq. in. Average tensile strength barrel, 69,033 Ib. per s<j. in. Average tensile strength of shank 130,000 Ib. per sq. in.
FIG. 2: — MEYER. NATIONAL. BURGESS AND BINET TURXBUCKLES.
100
AIRPLANE DESIGN
CAST AI.UMI.NCH
Tension 14,000
Compression 25,000
Shearing 10,000
COLD WOBKED ALUMINUM PLATE AND WIRE
Tension.. . 24,000 (Plate)
Tension 40,000 (Wire)
Modulus of elasticity (direct) 8,000,000
Aluminum has no well defined yield point.
DUEALUMIN
Tension. 33,000; Compression, 68,000; Modulus elasticity, 10,000,000. High brass Tension 35,000
Low brass
Composition
Bronze
Phosphor bronze. . . .
Tobin bronze
Tobin bronze
Delta metal
Manganese bronze. . .
28.000 30,000
30,000 to 75,000 varying with composition. 40,000 to 130,000, varying with form. 80,000, yield point 50,000 hot rolled. 100,000, vield point, 70,000 cold rolled. 45,000 Cast. Tension, 70,000 cold rolled. 70,000 Ibs./sg. in. Compression, 120,000 Ibs./sq. in.
Monel metal (hot rolled) Tension (ultimate) 88,150 Ibs./sq. in.
(yield. 58,000 Ibs./sq. in. elongation in 2 inch, 38 per cent.
The steel at present in common use among manufacturers is the mild sheet steel generally designated as cold rolled steel (C.R.S.). Whether its easy working qualities or its cheap- ness and easy supply has brought about this poor choice, is hard to judge. It is a relief to find that the constructors and the Government are endeavoring to do away with this most unreliable and inefficient of materials. Instances have only too often been brought to our attention when upon the com- pletion of some small stamped fitting, the apparently solid metal is found to be of two distinct layers of thinner metal held together only at a few points. It is not well, however, to jump too quickly to the other extreme and attempt to use the very high strength alloys — requiring expert working and heat treatment. Companies to-day are, with a few exceptions, not in a position to undertake this added responsibility and the forcing of such delicate work upon inexperienced hands would be as dangerous as the present methods.
The following table outlines the general influence of chemical composition of the physical properties of steel:
|
i |
E |
i |
||||||
|
J- c |
8 |
0 |
S£ |
01 |
||||
|
£ 1 |
w |
H C |
a g |
SCO r- ^ |
£•»! |
s |
||
|
V o |
1 |
1 |
g I . |
11 |
S"l |
.0 |
||
|
B 'S |
8 |
•D |
9 |
3 -2-3 |
.2« |
SS » |
T3 |
|
|
g % H K |
Q |
i |
a |
£ 11 |
ll |
6»« fi-S? |
^ |
|
|
(1) + |
• |
(2) |
+ (12) |
I |
||||
|
Phosphorus . . |
(13) . . . |
(3) |
0 |
(4) — |
— |
0 |
||
|
.1. |
_L_ |
(5) |
||||||
|
0 |
||||||||
|
(6) |
0 |
(7) |
||||||
|
(8) |
0 |
|||||||
|
Vanadium. . . |
+ + |
(9) |
+ |
4_ |
||||
|
Chromium.. . |
+ + |
_l_ |
•L |
,1. |
||||
|
4- |
||||||||
|
4- 4- |
||||||||
|
Nickel |
i i |
(9) |
1 |
t |
-f. |
|||
|
0 |
00) |
|||||||
|
_l_ |
(11) |
|||||||
|
_L |
The above table, while very comprehensive, should not be considered as final.
The matter of weldability of the chrome vanadium and nickel steel is indefinite, very reliable information showing that 3a/4 per cent, nickel steels give better welds than the chro- mium steel.
The S.A.E. Specification No. 3130 for a low carbon chrome- nickel steel, or Specification No. 2330 for 3l/2 nickel steel would seem to meet the requirements of the manufacturers as well as the Army Specifications of the S.A.K. No. 6130
chrome-vanadium, eliminating at the same time, the great danger of segregation due to faulty heat-treatment.
Heat treatment and its influence cannot be gone into; it requires very careful study and infinite care in application.
Strength and Weight of Mild Steel Rivets and Pins
Diameter, inches. Strength in Pounds
"d." Single Shear. Double Shear. Crushing + (.
1/8 1,000 1,600 1,200
3/16 1,600 3,000 1,800
1/4 2,750 4,500 2,400
5/16 3,900 7,000 2,800
3/8 5,000 9,800 3,600
1/2 9.000 17,800 4,800
3/4 20,000 40,000 7,200
1 35,500 71,000 9,600
The above values are based upon a shearing strength in pounds per square inch fs = 45,000 and a crushing strength, fc = 96,000.
Ps = ff—~ for single shear.
pc = fcdxt, for crushing, where t, the thickness of the plate or other piece held by the rivet or pin.
The values for crushing have been worked out for a plate 1 inch thick, therefore the crushing strength for various thick- nesses of plate may be computed by multiplying the above values by " t " in inches.
If the crushing strength of the rivet is greater than its shearing strength the design should be based upon the smaller result.
In case the bolt is subjected to a load other than tension, the strength should be based upon the corresponding form of loading. When bolts and pins are used in turnbuckle fittings and wire connections they arc usually subjected to a form of bending and should be calculated as a beam round cross section loaded at the center.
/ = — , where / = modulus of rupture, M = bending mo- ment due to load generally considered concentrated at the center, Y = distance from neutral axis to most strained fiber, in this case */2 D ; I = moment of inertia of cross section.
In figuring bolts that pierce wooded members the failure of the wood should be considered first, since in this type of con- nection rupture is most often caused by the fastening pulling out or loosening due to the wood crushing in front of the P = fc X L X D. Where P = crushing load, /c = crushing strength of wood, L = length of bolt in wood, D = normal bolt diameter.
United States Standard Bolts and Nuts
|
X |
*~ |
*o - |
j |
>< c |
S |
V) W |
|
|
5 — |
o |
o ii |
|||||
|
1 |
|.s |
i |
I? |
S |
If |
S . "g |
. a |
|
1 |
.213" |
41 |
T) |
a c ^ a |
.S-°a WB1" |
.2 * |
|
|
i |
"° a |
C-- |
™ S |
g |
b |
. Ol - C. G « |
dc |
|
h |
§5 |
1* |
^^ |
i H |
« M |
<8c |
§8.S |
|
1/4 |
0.185 |
0.049 |
0.027 |
20 |
1/4 |
0.578 |
0.707 |
|
5/16 |
0.240 |
0.077 |
0.045 |
18 |
19/32 |
0.686 |
0.840 |
|
3/8 |
0.294 |
0.110 |
0.068 |
16 |
11/16 |
0.794 |
0.972 |
|
7/16 |
0.345 |
0.150 |
0.093 |
14 |
25/32 |
0.902 |
1 . 105 |
|
1/2 |
0.400 |
0.196 |
0.126 |
13 |
7/8 |
1.010 |
1.237 |
|
9/16 |
0.454 |
0.249 |
0.161 |
12 |
31/32 |
1.119 |
1.371 |
|
5/8 |
0.507 |
0.307 |
0.202 |
11 |
1- 1/16 |
1.227 |
1 503 |
|
3/4 |
0.620 |
0.442 |
0.302 |
10 |
1- 1/4 |
1.443 |
1.768 |
|
7/8 |
0.731 |
0.601 |
0.420 |
9 |
1- 7/16 |
1.661 |
2.033 |
|
1 |
0.837 |
0.785 |
0.550 |
8 |
1- 5/8 |
1.876 |
2.298 |
|
1-1/8 |
0.940 |
0.994 |
0.694 |
7 |
1-13/16 |
2.093 |
2.564 |
|
1-1/4 |
1.065 |
1.227 |
0,891 |
7 |
o |
2.310 |
2.828 |
|
1-3/8 |
1.160 |
1.485 |
1.057 |
6 |
2- 3/16 |
2.527 |
3.094 |
|
1-1/2 |
1.284 |
1.767 |
1.295 |
6 |
2- 3/8 |
2.743 |
3.358 |
|
1-5/8 |
1.383 |
2.074 |
1.515 |
5-1/2 |
2- 9/16 |
2.959 |
3.624 |
|
1-3/4 |
1.431 |
2.405 |
1.746 |
5 |
2- 3/4 |
3.176 |
3.889 |
|
1-7/8 |
1.616 |
2.761 |
2.051 |
5 |
2-15/16 |
3.393 |
4.156 |
|
NOTE: — Depth of |
nut = |
nominal |
diameter. |
||||
|
Depth of |
head •- |
one-half |
short diam. |
of hex. and |
su. nuts. |
AIRPLANE DESIGN
101
The strength of United States standard bolts may be based upon the formula P = A X ft- Where P = the strength of the bolt, ft = tensile fiber stress per square inch = 65,000, A = effective area at root of thread. Solving for D the nom-
inal diameter Z> = 1.24 -» —
.088.
Quality
Width
TABLE 6.
Approximate breaking strength per inch.
|
A24 . . . |
inches. 36 |
Warp 72 Ib 90.5 108.5 114.7 112 129.4 |
Weft. 78 Ib 101.9 94.6 103.6 115.6 123.4 |
Weight per 4.00 o 4.00 ' 4.00 ' 4.00 ' 4.12 ' 3.75 ' |
an. yd. ,. |
|
A29 . |
36 |
||||
|
A31 |
36 |
||||
|
A33 |
36 |
||||
|
*A37. |
36 |
||||
|
*A40... |
. 36 |
*British Government Standard qualities.
Airplane Fabrics
The general requirements and tests for airplane fabrics are well summarized by the following table:
(1) Fabric should present reasonably great resistance to flame.
(2) It should be proof against the action of salt water, moist air, extreme dryness
quick changes of temperature.
(3) It should not stretch in any direction.
(4) It should have a tensile strength of at least 75 !b. per inch width in any,
direction.
(5) The tendency to tear and split because of tacks, bullets, etc., should be
almost nil.
(6) The weight should be taken in an atmosphere of 65 per cent relative hu-
midity at 70° Fahr.
(7) The weight, yarn number and tensile strength of the fabric should be ob-
tained when it is in a bone dry condition, i. e. after it has been subjected to
a temperature of 221V Fahr. for two hours. Identity and average length of fibers should be ascertained. Determination should be made of the percentage moisture "regain" under
the available range of temperature and humidity. A shrinkage determination should be made.
(8) (9)
(10)
Some Representative Specifications, Strength and Weight Figures
In Table 4 are given some representative specifications which represent the average values of current practice.
TABLE 5.
|
Specifications Curtiss No 66 |
Weight per square yard ounces 4 |
Threads Threads per .per inch inch warp weft 96 100 92 95 94 100 95 99 275 threads per sq. in. |
Strength per inch width (warp) 91 92 75 87 |
Strength per inch width weft (Ib.) 102 95 85 (minimum) 108 96 |
|
Oct. 26, 1916 R. A. F. No. 17-C.... U. S. Army No. 1002 . McBratney tests |
4 .3.75-4.4 4 |
|||
|
Clarence Whitman (cotton)... |
4 |
Messrs. Lamb, Finlay and Co. have kindly communicated the average values of tests extending over a number of ship- ments, in accordance with British Government specifications:
"Three pieces are cut from the length and three pieces from the width of the goods. These samples must be long enough to leave 6 in. clear between the grips and sufficiently wide to leave the test pieces 2 in. wide after trimming. The test pieces are soaked in water for two hours. They are then taken out and the excess water ia removed and the goods put in an Avery machine, the load being applied at the rate of 50 Ib. per inch width per minute."
This method of testing, while apparently arbitrary, is con- venient and avoids errors due to humidity changes, and is preferable to a test on dry material.
In the National Advisory Report the following figures are given for fabrics of difrYient weights:
|
I |
Weight in ozs. per sq. vd. 3.67 |
Strength Warp Filler 65.0 54.4 69.5 49.2 80.7 79.0 86.9 74.0 90.2 82.7 82.9 100.1 95.0 60.0 90.4 102.5 |
|
II |
3.78 |
|
|
III |
3.87 |
|
|
IV |
4.04 |
|
|
V |
4.09 |
|
|
VI |
4.48 |
|
|
VII |
4.60 |
|
|
VIII. |
....4.86 |
Wing Dope and Varnish
The following notes on dope and varnish may be of interest to the manufacturer:
Dope alone on Irish linen surfaces has proven very satis- factory. Four to five coats, allowing about one-half hour for drying between each coat are ample protection for the most severe conditions. Very rigorous tests on samples exposed to the weather during the month of February resulted in no ill effects, the cloth remaining tight, glossy and without spots, cracks or tears. The weight of the covering is increased about .66 oz. per square yard per coat, with an application of ap- proximately one gallon to ten square yards.
Varnish finish is recommended in many cases as more permanent and, being less effected by salt water, has some ad- vantages on water machines. When repairing is to be done it is first necessary to remove the varnish before the patch is applied with dope, as a glue, causing some inconvenience.
Doped surfaces have about 8 per cent to 10 per cent more strength and more resistance to tearing. It is necessary to redope all surfaces every three to five months.
Cotton and silk fabrics have a tendency to rot when covered with dope or varnish and such surfaces are not recommended.
References, Part II, Chapter 5
AIRPLANE FABRICS
"First Annual Report of the National Advisory Committee on Aeronautics." "Balloon and Aeroplane Fabrics," by Willis A. Gibbons and Omar H. Smith. "Circular No. 41." Bureau of Standards.
TIMBER
Judge's "Aeroplane Design."
"Material of Construction," Adelbert P. Mills.
"Mechanical Engineers' Handbook," Lionel S. Marks.
"Lanza's Applied Mechanics."
"The Mechanical Properties of Wood," by Samuel J. Record (containing numerous references.)
"Reports of Tests on the Strength of Structural Material," Made at the Watertown Arsenal, Mass.
Publications of the U. S. Forest Sertice on "The Mechanical Properties of Wood and Timber Testing."
METALS "Materials of Construction," Prof. Upton, of Cornell University.
WIRES AND CABLES
First Annual Report of the National Advisory Committee on Aeronautics, Avia- tion Wires and Cables."
(This also contains much valuable information on fastenings.)
TURNBUCKLES Arthur Orr, AVAITION AND AERONAUTICAL ENGINEERIEG, December 1, 1915.
Chapter VI
Worst Dynamic Loads; Factors of Safety
One of the most difficult problems in aeronautics is the estimate of the worst loads likely to come on under unusual circumstances, on which alone correct allowances for factors of safety can be based. In speaking of factors of safety, a distinction must be made between the load factor of safety and the gross factor of safety. Thus, if the load factor of safety
levotot-
FlG.l
for a certain part of the machine is four, the material employed may be so untrustworthy that an allowance for it, of say one and a half, may have to be made, bringing up the gross factor of safety to six. It is the gross factor of safety which is commonly spoken of as the factor of safety.
Conditions Under Which Heavy Loads Come
Heavy loads come on an airplane under so many conditions, that the following classification is probably incomplete. It is, however, all that is possible in the present stage of the art.
(A) In the air:
(1) in flattening out of a steep dive
(2) in heavy banking
(3) in looping
(4) in sudden gusts.
(B) On the ground: (1) on landing
We shall consider these conditions one by one as far as possible.
The wing structure will meet with the greatest loads in the air. On landing, the wing structure has to meet only the shock resulting from the decceleration of its own weight which may be some 12-15 per cent of the weight of the machine, while in the air, it has to support the whole weight of the airplane and under certain conditions five or six times the whole weight. It is in the air, therefore, that the wings meet the worst condi- tions. The body may carry severe stresses in the air when powerful forces come into play on the rudder and elevator, but it may also be powerfully stressed on landing. For chassis design, it is only landing and taxi-ing stresses that need be considered.
(1) Flattening Out After a Steep Dive
The exact mathematical computation of stresses in such a case is not yet possible; it is, however, interesting to see how such stresses arise, and how they are limited.
In order to have a concrete case, we will consider the Clark model tested at the Massachusetts Institute of Technology, and described in Hunsaker's " Dynamical Stability." This had the following estimated characteristics:
Wing area including ailerons 404 sq. ft.
Span 4O.2 ft. mean
Area, stabilizer 10 1 sq. ft.
Area, elevators 10.0 sq. ft.
Area, rudder "J. .';.") sq. ft.
Length, body £4,5 ft.
Weight (tanks half full) 1000 II).
(5.2 ft. in roll Kadii of gyration •{ 4.05 ft. In pitch
U).!>75 ft. in yaw
lirake horse-power 110
Maximum speed N7 in.p.h.
-Minimum speed 35 m p.li.
Best glide 1 in 9
For a tail setting of — 5 deg. to the wings, the model (l/26th full size) had the following forces acting on it at a speed of 30 m.p.h., which we shall use without correction for Iranst'erring to the full size machine:
Lift on model at Drift on model at
Angle 30 m.p.h. :;o ni.p.h.
— 1 —.ll.-> +.12S
— 2 +.112 +.M8
—1 -f.240 +.104
0 +.::oo +.lol
+1 +.41KI +.102
+2 +.025 +.105
+4 +.872 +.115
+8 +1.305 +.1.13
+12 4-1.BA8 +.213
+ 10 4-1,640 +.:t70
+ 18 4-1.680 +.498
102
AIRPLANE DESIGN
103
In the U. S. Army Specifications 1002 (reprinted in AVIA- TION AND AERONAUTICAL ENGINEERING of November 1, 1916), one of the stipulations for airworthiness is that the pilot may be required to dive at an angle of 50 deg. to the horizontal, to maintain such a dive for one or two seconds, and then to pull out reasonably quickly. We will assume that the dive is continued for even a longer period so that the limiting velocity is reached, and then try to see what will happen on flattening out sharply.
The propeller thrust on the dive may be neglected whether the engine is cut off or not, the slip being so enormous as to reduce it to a negligible quantity.
Considering the sketch of Fig. 1, the equations of motion evidently are
D = W sin 6 L = W cos 6
The most straightforward way of finding at what incidence to the flight path the machine is under steady limiting condi- tions, is one of trial and error. After one or two trials, we find that the angle of incidence, 2% deg. will satisfy condi- tions.
The drag on the model at this angle is 0.111 lb., and the lift 0.094 lb. at 30 m.p.h. The two equations are very nearly satisfied. Thus converting to full size conditions:
(1) TF sin 50 deg.-= (1600) (0.7660) = 0.1235 =
0 111 X 26"
-~ 7'and F= = 14,850, V = 122 m.p.h.
(2) TF cos 50 deg. = (1660) (0.06428) = 1030 while 0.094 X26*
302
• X 0.14850 = Lift = 1040 lb.
the difference of 10 lb. in the lift being negligible.
If, at this point, the pilot throws his elevator hard up, he will increase his angle of incidence rapidly, and move his path more and more to the horizontal. . The rapidity with which he can come out of the dive depends on the force which he can bring to bear on the elevator, and is resisted by the inertia of the machine, and the damping against angular rotation. There is reason to believe that during this process he loses very little speed. The equations of motion during this process are some- what complicated and cannot be solved directly. But if we assume that for a machine of this type, the pilot can change his angle of incidence to say 8 deg. without losing speed, the lift on the model at this speed being 1.305, the lift on the machine becomes
-X26'X1222 = 14,400 lb.
or a load of nine times the weight of the machine. It is commonly accepted that the actual load is not quite so great, being between 5 and 6. The pilot could not easily wreck a machine with moderately strong controls, and weights dis- tributed far from the center of gravity giving a large moment of inertia. But with a light machine, with weights close to the center of gravity and a powerful elevator, a reckless recovery would be highly dangerous.
It should be pointed out that the uncertainty as to the exact movements a machine goes through on flattening out, makes the question of the angles of incidence at which loads on front and rear spars should be distributed and computed a very con- troversial one. The latest U. S. Army specifications call for a stress diagram at 15 deg., which throws the greater load on the front spar. If, as is quite possible, a machine flattening out after a steep dive does not reach such a high angle of incidence, but arrives at some intermediate angle such as the 8 deg. mentioned above, then it would be fairer to draw a
stress diagram at this angle of incidence, with a more equal distribution between the two spars.
(2) Loading in Heavy Banking
The loading on a steep bank is dependent on the speed, radius of turn, and angle of bank.
In the sketch, Fig. 2, the machine is moving out of the plane of the paper and turning at an angle of bank 6. The three forces acting in the vertical plane of the machine are the lift, the weight and the centrifugal force, which may be assumed as acting at the center of gravity of the machine. Resolving L along the lines of these two forces, we have as equations of equilibrium
TF F2
L sin 6 = KT AV* sin 6 =— -^~
g K
L cos 6 = K* AV cos 6 = TF
where F = speed in feet per second, and R = radius in feet. From these equations, one important fact appears, that on a
FIG. 2
steep bank where cos 6 is small, the lift of normal flight is insufficient, and that before banking a pilot must increase his power and speed, otherwise his machine may drop on the bank.
The load on the machine in banking will increase with the centrifugal force to be overcome in addition to the weight, and is, therefore, greatest when the velocity has increased beyond the maximum in normal flight and when the radius of turn is very small.
For the Clark model previously considered, we will assume that the machine has attained a speed of 120 m.p.h. or 176 ft. per second, after a dive and that the pilot goes into a sharp turn of 400 feet radius.
From the equations of equilibrium we have W F|
g JR_ _ V^ _ 30.500 gE
tan 6 =
= 2.37
TF gE 32.2 X 400
6 = 67 deg. and sec 6 = 2.559, which is certainly a fairly steep angle of bank. Since L cos 6, L = sec TF = 2.559 TF.
It is possible to consider a case where the velocity would be still greater than the 120 miles per hour, and the radius still smaller, in which case the loading might still be heavier. It does not seem probable, however, that the worst possible loading on a bank would exceed 3 or 4 TF.
The angle of incidence on a bank interests us again from the point of center of pressure and distribution of pressure
104
AIRPLANE DESIGN
between the two spars. Considering the Clark model of the previous paragraph, IF = 1600 and L = 2.559 TT = 4100 = K, X 464 X1201 from which K, = * = 0.000615
4,400
and the angle of incidence is not much above 0 deg. for the Clark machine on such a bank.
(3) Loading in Looping
In looping similar methods would be employed as in con- sidering flattening out after a dive. The probable maximum loading is estimated to be 4.
(4) Stresses Due to Gusts
Another cause of violent stresses is in the action of sudden gusts on a machine, where the inertia tends to maintain the same speed for a different angle of incidence, or the same incidence for a different speed.
The machine may encounter:
(a) a head-on gust
(b) a following gust
(c) an up-gust
(d) a down-gust.
Granted a sufficiently violent gust, there is no possible limit to the stresses which may come on a machine in such cases, and a hurricane might wreck a machine for whatever factor of safety it was designed. It is necessary to investigate, how- ever, whether the gusts, as we may expect to occur in ordinary practice from our metereological data, are well within safe limits.
(a) Head-on Gusts
Imagine the Clark machine to be moving at 59 m.p.h. at an angle of incidence 2 deg. against a head-on wind of 20 m.p.h. so that its absolute velocity relative to the earth is 39 m.p.h. If the head-on wind increases to 30 m.p.h., the absolute velocity relative to the earth will still remain at 39 miles for a second or two. During this period, the velocity to the air will increase to 69 miles per hour, with the angle of incidence unchanged. The lift on the machine will, there-
69* fore, be momentarily increased in the ratio of -rrj *= 1.36.
Elevator
(c) Up-gusts; (d) Down-gusts
Without going into numerical examples, we can see easily from Fig. 3, the effect of an up-gust in increasing the load. The up-gust both increases the velocity of the relative wind and its angle of incidence, with a corre- sponding increase in lift, except at very high angles where a reverse effect is possible. For a down-gust the con- verse would hold true.
With normal l:ying weather, the ef- fect of gust should never increase the load to more than two or three times the weight of the machine.
Limiting Velocity for a Sheer Vertical Dive
A sheer vertical dive is unlikely to occur and is not required for stress calculations in practice, but it is inter- esting to note the extreme limiting velocity in such a case. A sheer ver- tical dive is only possible if the ma- chine is at the angle to the vertical which gives no lift, and the elevator is set only at such an angle that the moment of the total drag about the center of gravity is neutralized.
For the machine in question the angle of no lift is — 3 deg.
The drag on the model at this angle is 0.118 Ib. To find the limiting veloc- ity, we can write
0.118 = 26'
FIG. 4
W = 1600 = -
30'
from which V = 134 m.p.h., which is not so very much greater than the limiting speed on the 50 deg. drive.
Worst Loads on Landing
The computation of such loads is connected with chassis design, and we shall deal more fully with it later. Some calcu- lations taken from " Notes on Aeroplane Shock Absorbers of Rubber" are an interesting introduction to the subject:
An airplane weighing W pounds striking the ground at I" feet per second on a glide of 1 in 7 has kinetic energy to be absorbed by the landing gear of — ( "7 ) If the machine comes to rest after a motion of z feet, the work done by gravity on it is Wx, and the tot al stored in the shock absorber is W li + o~ (y ) * } • Tne average force in the springs is half the maximum /•', given by the equality:
FIG. 3
There will be au acceleration upwards and an increased load on the machine = 1.36 W.
(b) Following Gusts
If the machine were traveling in a following wind, which suddenly diminished, a similar action would ensue, since the relative velocity to the air would here also increase.
If, on the other hand, in the case considered above the head- on gust suddenly diminished to 10 miles an hour, the relative velocity to the air would be decreased to 4!) miles per hour, and
49s Ihc- lift w.nild he diminished in the ratio of cgT = 0.6!) and the
lift on the wings would, in this case, be actually less than in norniiil tli'_rht. MI that the machine would drop.
It i- al-n clear from (lie above tlint the gust effects are nn»t important, when the speed of the machine is lowest.
If we take ordinary conditions as
2.77
'66 ft. per sec. (45 m. p. b.)
(2 77\ 2 + — ; — 1, from which we get the following table for use in design:
i
1 in.
2 "
3 "
4
8 10
ia
F
:t.-».o W
19.0 W
13.0 W
10.. -i W
8.6 W
7.r. If
ii.1 H
5.:i w
4 X li-
lt appears that the load on the landing gear is nearly 14 times the weight of the airplane, if a motion of only 5 in. is allowed. This requires an excessive factor of safety and makes a very heavy construction. Of course, no allowance has been made for the collapse of pneumatic tires which may add 2 in. to the motion of the recoil mechanism.
AIRPLANE DESIGN l()o
P-irt TT Chanter f\ Volume (Oldenbury. Mime-hen).
rart 11, Chapter t untish Report Xo. 96. (not yet published)
•• Dynamical Stability of Airplanes." J. C. Hunsaker, Smithsonian, " The Flying Machine from an Engineering Standpoint," F. W. Lan- Vol. 62, No. 5.
Chester. " Notes on Airplane Shock Absorbers of Rubber," J. C. Hunsaker,
" Mechanische Grundlagen des Flugzeugbaues," A. Baumann. 2nd AVIATION AND AERONAUTICAL ENGINEERING, Sept. 1, 1916.
Chapter VII
Preliminary Design of Secondary Training Machine
Preliminary Weight Estimates
Every designer will approach the design of a new machine in a different manner, and no definite rules can be laid down. In the design of a standard secondary training machine, we have the advantage of following well-known lines, with such excellent examples of machines tried out in practice as, for example, the Curtiss JN. Following such practice we can make very close estimates of possible weights and performances, and easily determine possible wing and control surfaces. A new and difficult type, such as a military twin-hydro, would require long preliminary study.
Recalling Army Specification No. 1001 — detailed in Part '2, Chapter 1 — we have to meet the following requirements :
Pilot and passenger, 330 Ibs.
Gasoline and oil for 4 hours' flight
Kneinc between 00 and 110 h.p.
Maximum speed, 75 ui.p.h.
Minimum speed, 43 m.p.h.
Climbing speed. 3000 ft. in 10 min.
Two wheel landing gear
From the engine data of Chapter 5 we could select a number of suitable engines. We shall select the Curtiss 90 h.p. OX. It is with this engine that a student has designed a similar machine, the salient features of which we shall embody in the post-graduate course at the Massachusetts Institute of Technology.
Practice shows that the above performances can be achieved with a weight of about 1850 lb., i.e., 20.4 Ib. per horsepower, and we shall make this our preliminary estimate. This figure is slightly less than that of the JN-4, but is probably very near to the JN-4B.
The first step is to set down all weights of which we can be fairly certain, and on which no improvement is possible, thus:
lb.
A B Pilot and passenger in aviation dress 330
C Engine and accessories 360
D Radiator 50
K Water )n engine and radiator and piping 40
F Propeller and hub 35
G Gasoline tank of 40 gallons capacity '•'•"
II Gasoline and oil for 4 hours' flight 220
I J 2 Instrument boards, with a set of barograph, tachometer.
nlr-speed Indicator and clock on each 40
K L 2 Dep controls 25
1130
This leaves us with some 720 lb. available for the purely structural parts of the machine : chassis, complete body assem- bly, wings, interplane bracing, and tail surfaces. On the Cur- tiss JN-4 (Part 2, Chapter 3) we have the following per- centages for these groups :
Chauls 4.03% equivalent In our machine to 74.5 lb.
Wings 14.13% " " 201.0"
Inu-rplane bracing •( :iv; " " " " " 91.5 ••
Tall surface* 2.70% " " " " " 61.0 "
Body assembly 15.55%
equivalent to 286.0 lb., from which must be de- ducted 40 lb. for ItiKrru in' ni boards and Instru- ments, leaving 240.0 "
724.0
Since we are following standard practice very closely we can take the above figures to hold fairly well for various parts of the machine.
Choice of Wing and Area
For a machine of this type it is not necessary to have a wing of extreme characteristics. It is more practical to select a good all-round wing, with fair structural characteristics, than to choose a wing with high efficiency at low speeds, but a low lift coefficient at maximum angles, and the R.A.F.6 can be adopted without much chance of mishap.
In a machine of the pursuit type, it would be worth while trying a number of different wing areas, but in a training machine it is, in the first place, essential to secure the necessary landing speed, and then to attain as high a speed and climb as possible with careful design. It only remains for us to find the maximum Kv of the R.A.F.6 and the necessary correcting factor for biplane effects.
There is, first of all, the question of stagger to be consid- ered. The increased efficiency due to staggering is offset by questions of weight and head resistance, while the increase in efficiency is not so very important. Stagger is, therefore, mainly determined by considerations of the view obtainable by pilot or passenger. On this particular machine we shall employ a very slight stagger of about 5 per cent, giving a good overhead view for the pilot.
Overhang is likely to improve efficiency, but no aerodynam- ical data is available. It must be remembered that a large overhang, together with the aileron loads, imposes a very serious load on the rear spar of the wing. If any unsupported overhang is employed, it should be less in length than the gap. We should, in the present state of the art, make no improve- ment in the K,,. correction for biplanes on account of overhang.
We must also settle on gap/chord ratio. We have seen in our aerodynamical work the improvement consequent on great gap/chord ratio. But to offset this, we have the question of increased weight and resistance of struts and wires. For tri- planes with their blade-like wings, a very high gap/chord ratio is, no doubt, permissible, but for biplanes the permissible lim- its are 0.9 to 1.2. We shall assume a value of 1.0 as a good conservative figure.
Under these circumstances, we need only correct our maxi- mum Ky as for an orthogonal biplane with gap/chord ratio of 1. The correcting figure for this as given in Part 1, Chap- ter 8 is 0.81, but Dr. Jlunsaker's experiments have shown that at maximum lift a better factor of 0.86 may be employed.
Since at high angles the tail surfaces will also be providing some lift, we may safely use this figure. Any obstruction be- tween the wings, such as the body, will diminish the Kv, and in a twin-engined machine this effect would become quite seri-
IMI,
AIRPLANE DESIGN
107
ous, but it need not be considered for a single-engine type. Constructors, in fact, using a correcting factor of 0.81 or 0.82 and neglecting the lifting effect of the tail surfaces have found their landing speeds surprisingly low.
The maximum Ky for the R.A.F.6 is 0.00310. Extending the equation W = KVAV to include the correcting factor of 0.86, we have when F = 43 m.p.h.
1850 =(0.0031) (0.86)4 (43)' 1850
' = 376
= (0.0031) (0.86)43 clnde the ailerons.
ft" which » taken to in~
lateral stability. For longitudinal stability to place the sta- bilizer at 3 deg. to the wings is a good setting prior to a wind tunnel test.
Position of Center of Gravity
In order to fix the position of the center of gravity, a vector diagram for the whole machine is necessary. But to draw a vector diagram, a wind tunnel model test is necessary, and in the model we have already fixed the positions of the various parts of the machine. To draw a probable vector diagram
Fio. 1
The questions of aspect ratio is again only partially de- pendent on efficiency, and a large aspect ratio introduces structural difficulties and tends to lateral instability. We shall assume an aspect ratio of 7 to 1 on both planes. If the planes are slightly raked, the aspect ratio will be 7 for the mid-line of the wings.
If x = chord in feet, Ix = span, and we have 14x2 = 376 and chord = o ft. 2 in. and span = 36 ft. 5 in.
We shall now fix purely on empirical grounds the length of the machine and the size of the control and fixed surfaces.
The designer is always tempted to shorten the length of the machine and to rely on a large stabilizer placed at a big nega- tive angle, to secure static longitudinal stability. But in dynam- ical stability, it cannot be too strongly emphasized that damp- ing is also essential, and damping improves rapidly with the length of the stabilizing arm. Too short a length would give rapid, undamped oscillations. The overall length of the Cur- tiss JN-4, 27 ft. 3 in., is the outcome of several years' practical experience, and is probably a most suitable figure.
By empirical rules, such as outlined in Part 2, Chapter I, the control surfaces may be fixed approximately at
Ailerons 35 sq. ft.
Horizontal stabilizer. ... 28 sq. ft. (atau angle of 3 deg. to the wings)
Elevator 22.0 sq. ft.
Rudder 12.0sq. ft,
Vertical fln 4 sq. f t.
The question of lateral stability is one which still requires much investigation. Purely on empirical grounds, we can say that with no sweepback, but a fin of the above size with a dihedral between the wings of 2 deg. will secure a moderate
without a model test is a most difficult matter. We have ex- periments to show the vectors for an orthogonal biplane alone, but with every different tail setting, body, shape and landing gear, we have a different vector diagram.
The best that can be done in preliminary design is, therefore, to make as shrewd a guess as possible, and to draw compari-
FIG. 2
sons from as many model tests as possible. We have fortu- nately at our disposal the results of the tests on the Curtiss JN-2, which is almost identical with the design we are fol- lowing. The vector diagram of this machine is shown in Fig. 2. Eiffel 36 wings are used, but in general arrangement
108
AIRPLANE DESIGN
the machine is almost identical with ours. In Fig. 1 is shown a side view of this machine, with the vector diagram of a wind tunnel test.
The center of gravity is indicated in the sketch, and lies on the 4 deg. vector. Such an arrangement will give an adequate amount of longitudinal static stability. The propeller thrust passes through the center of gravity and does not, therefore, affect the stability in normal flight. Let us suppose that 4 deg. is the normal angle in flight, as it very probably would be. Then if the machine dives to 2 deg., the 2 deg. vector passing in front of the center of gravity will tend to pitch the airplane back to 4 deg. If the machine goes to a higher angle, say 8 deg., the vector will be behind the center of gravity and will give a counter clockwise moment about the center of grav- ity tending to restore it to 4 deg. again.
The next step is to see whether we can balance our machine about this point both in a vertical and in a horizontal plane. Before drawing up our three general arrangement views, we must go into a number of points connected with chassis de- sign, but we can use the side view of Fig. 1 with slight modi- fications for our balancing up.
We shall employ the usual method for finding the center of gravity of a system consisting of a number of small bodies. That is, we choose a plane somewhere in the system as an axis and take moments about it, finally dividing the sum of the moments by the total weight of the members to find the equiva- lent moment arm, or distance of the center of gravity from the axial plane. In this case we shall take the axis at the rear propeller flange, that being the usual practice.
The following table illustrates the method in detail. The designations refer to Fig. 1, where the positions of the centers of gravity of the various elements are indicated.
Designation A B C D E P G B I J K L M N O P Q
|
\ Name of Element Pilot |
height, Ib. 165 165 360 50 40 35 30 220 20 20 12 12 74.5 2G1 91.5 51 246 |
J )ist. from Moment about propeller propeller flange flange (ft.) (ft. Ibs.) 10.57 1745 6.67 1100 2.59 932 0.77 39 2.36 • 94 —0.17 —6 6.44 193 6.44 1417 9.46 189 5.90 118 10.57 127 6.67 80 4.59 342 6.32 1649 6.32 578 24.75 1262 9.11 2241 |
|
Hadiator |
||
|
Water |
||
|
Propeller |
||
|
Rear Instrument board.. . . Forward Instrument board |
||
|
Wings |
||
|
Tall |
||
|
Body |
||
Totals 1853
12,100
Dividing the moment by the total weight of the machine, we see that the center of gravity of the machine is 6.53 ft. back of the moment axis. This brings it to a position virtually coincident with the tanks, and about one-third of the chord from the leading edges of the wings, which is virtually the position chosen from the vector diagram. If the center of gravity does not come to the desired position at the first trial, it may be forced to do so by manipulation of the weights, shifting the engines, pilot, etc., slightly forward or backward, as the need may be.
A similar method, with moments taken about the ground line, is used to give the vertical position of the center of grav- ity. The actual work for this computation is omitted in order to avoid confusing the figure.
References for Part II, Chapter 7
Barnwell's "Airplane Design."
" Experimental Analysis of Inherent Longitudinal Stability for a Typical Biplane."
National Advisory Report, 1915.
Chapter VIII
General Principles of Chassis Design
The design of landing gears is among the most complex of the problems which confront the aeronautical engineer, due to the many conflicting factors which must be taken into consideration and. so far as possible, reconciled.
General Proportions
The height of the chassis is dictated by the necessity of providing ground clearance for the propeller and by the
allowing a total displacement of five or six inches, the pro- peller clearance with the machine stationary should be not less than twelve inches, thereby insuring a minimum clearance of six inches when the shock absorber has its maximum displacement.
Under some circumstances, the governing condition may be the angle of incidence to which it is desired to pitch the machine. The greatest possible angle should, in general, be at least as great as that which corresponds to the burble
FIG. 1.
angle of attack which is desired in starting and in pulling up after touching the ground. The track must be sufficient to insure against overturning when making a landing on rough ground, yet not so great that the striking of a soft spot by one wheel will give rise to an excessive moment tending to spin the machine around. The fore-and-aft location of the wheels is determined by the requirements of longitudinal stability on landing. The structure must be strong enough 'to withstand side thrusts and twisting moments due to alight- ing on one wheel, as well as the large direct dynamic stresses which are set up when an airplane lands without sufficient flattening out of the angle of descent. Lastly, the means of shock absorption must be of such quality and number that they will permit of high speed along the ground and of heavy landings without breakage of the shock absorption means itself and without danger of the " bottoming " of the axle in its guides. The play of the absorbers should also be large enough so that the dynamic landing and taxying loads pre- viously alluded to will not reach excessive values. Each of these conditions will now be taken up in turn, and discussed in detail.
Chassis Height
Ordinarily, the most important factor here is the protec- tion of the propeller. With a conventional shock absorber.
point, and it may be advisable, if a very short run after landing is required and brakes are not desired, to make it somewhat larger than this. The following example will illus- trate the use of this condition :
A two-seat tractor biplane is 26 feet long, and the hori- zontal distance between the axle and the point of contact of the tail skid is 20 feet. In normal flight, when the line of thrust is horizontal, the wings are set at an angle of incidence of 4 deg., and the point of contact of the tail skid is 2 ft. vertically below the line of thrust. It is desired to find the least distance of the lower rim of the tire below the thrust line which will permit the assumption of an angle of 18 deg. Since the wings are at an angle of 4 deg. in normal flight, the maximum angle between the thrust line and the ground must be 18 deg. — 4 deg., or 14 deg. Tan 14 deg. = .249, and the difference in heights of the wheels and tail skid is therefore 20 X -249, or 4.98 ft. It is then evident that the required height is 4.98 -(- 2, or virtually 7 ft, a much greater height than would be necessitated by propeller clearance alone. If such large angles must be attained it is worth while to sacri- fice something from the perfect symmetry of the body by putting most of the longitudinal curvature on the lower surface of the body, thereby bringing the tail skid more nearly into the line of thrust and decreasing the height, and consequently the weight and resistance, of the body, to an
1(19
110
AIRPLANE DESIGN
extent which more than compensates for any loss of aero- dynamic efficiency of the body.
The tread, or track, is, on airplanes of conventional size, from 5 to 7 ft., except on slow pusher biplanes with long skids, where it may reach values as high as 13 ft.
Location of Chassis with Respect to C. C.
In Fig. 1 are shown the forces which come into play while the machine is running along the ground. It is evident that, if we assume the thrust line to pass through the c. g., and the machine to be in equilibrium with the elevator either in neutral or diving position, so that the resultant air pressure with the body horizontal passes through or slightly behind the c. g., the moment P X a> due to the upward reaction of the ground, must be at least equal to the moment R X &> due to the tractive resistance. We then have, since we may write
E = fP, P X a = >vP X b, or ^ — tan 6 = f, where
Y is the coefficient of tractive resistance. If we assume Y = 1/10, which is perhaps a fair value for a vehicle with large and flabby pneumatic tires running over smooth grass, we have 8 = 5 deg. 44 min. Since, however, it is necessary to allow for soft ground, where the coefficient of tractive resistance will be much increased, as well as for ruts and changes of slope, which introduce a backward component in P itself, it is obvious that 6 will have to be considerably larger than the value given above. Lieut. Col. B. Q. Jones, U. S. A., states that the best practise indicates a value of 13 deg. 10 min. for 0.
Stresses and Structural Considerations
An unequal distribution of stress between the wheels, due to landing on one wheel before the other or to a difference in ground conditions between the two tracks, produces a moment tending to twist the axle about a vertical axis. This moment is carried to the struts or skids by means of axle guides or radius rods, and thence to the body. A landing on one wheel generally involves a sideways motion, and the resulting side- ways blow is usually carried by the cross-wires, although some landing gears, particularly on speed scouts, have in- clined struts which, acting either in tension or compression.
take the place of the wires in this respect. In order to resist side blows, too, a special wheel construction is neces- sary, as an ordinary wire wheel, such as is used on motor- cycles, will be completely wrecked by a relatively small side blow against the rim. It may be laid down as a rule that the length of hub should be at least twice the diametei of the tire, and three times is preferable. The obliquity ol the spokes is thus greatly increased.
Direct dynamic loads in landing have already been dis- cussed in this course (see Part II, Chapter 6).
Shock Absorbers
Rubber and steel springs are the only substances which have been widely used as shock absorbers. Of these, rubber has proved by far the more satisfactory, due to its easy fabrication and replacement, its greater energy-storing capac- ity (500 to 1,000 ft. Ibs. per lb., as against 10 to 20 ft. Ibs. per lb. for steel), and, most of all, the fact that it actually absorbs and dissipates the energy, instead of merely storing it and giving it out again. If steel springs are used, some auxiliary device must be employed to dissipate the energy in the form of heat. In the case of leaf springs, this is done in a fairly satisfactory degree by friction between the leaves, and such springs have been used on light machines built for smooth fields, but they do not afford sufficient give for heavy work. Where helical springs are used, as on many large pusher biplanes with four-wheeled landing gears, they are usually in combination with a hydraulic or pneumatic shock absorber. As an illustrative problem, we shall give the complete calculation of a rubber shock absorber for a two- seator tractor biplane weighing 2000 Ibs.. having a gliding angle of 1 in 7, and a speed range of from 45 to 90 miles an hour. We shall start with the assumption that the heaviest landing shock which needs to be provided against is that due to landing at 45 m.p.h. on a slope of 1 in 6 without any attempt at flattening out.
The shock absorbers will be made up of rubber rings '2 in. in diameter, and 2 in X T5ff i'1- in section. We shall use a two-wheeled landing gear, so that each wheel will have an initial load of 1000 Ibs. The initial stretch will then be
' . E, the modulus of elasticity, may be taken equal * X -A- X n
to 300 Ibs. per sq. in. for rubber of good quality. A, the total cross-section area of one ring, is 2 X 2 X T\H or I1/^ sq. in. I, the length, may be taken equal to one-half the
perimeter of the rings, or Z= — ^ — = 3.14 ins. »? is the num-
2
number of rings employed.
We then have the initial stretch = S = •
1000X3.14
300 X IVi X a
o •)(! -| rj r-y i •
— , and s, the deflection under any load, = — rr; — , /•' IMMIII;
the total load.
On landing on a slope of 1 in 6 at a speed of 66 ft. per see., the vertical speed is 11 ft. per sec., and the kinetic energy is
( 11 ) * X W
- — -^-± — , or 1.8817 ft. Ibs. The potential energy possessed
II" s /
on touching the ground is— ^-, making a total of W { 1.88 +
— I, or 17 I .04 + — I on each wheel.
The enei'uy absorbed bv the shock absorber is — V — = II W . ,.9 - • Equating this to the energy possesed by the machine,
3§'= "(« + £} *
shall assume a deflection of
AIRPLANE DESIGN
111
,r, 402.7 (.94 + 5/24)
0 in. Then n = - v ' ' — = 18.54. We shall use
00
18 rings and recalculate. Then „ = .94 -|- -j-, and 18 s = 378 + 16.78 s. s = 5.05 in.
„
C AC
The stress in the rubber is ^^ X 300 = 482 Ib. per sq. in.,
as against a breaking strength of 800 Ibs. per sq. in., and the
(s \ 1.88 + -[I, ) 4000 x 2 30
load on the chassis
s_ 12
.42
21,900 Ibs. At the instant of greatest displacement, then.
FIG. 3. ARRANGEMENTS OF RUBBER CORD AND RINGS USED ON VARIOUS FRENCH MONOPLANES.
every part of the machine has on it a downward load of eleven times its own weight.
We have so far assumed the most unfavorable condition with respect to the tires: that is, that they do not deflect at all. We shall now work the same problem on the assump- tion of the most favorable conditions reasonably to be ex- pected, that 26 X 4 tires are used, and that they are pumped to such pressure that they collapse 2 in. under the same force which causes the shock absorbers to yield 5 in. The effect of this is equivalent to increasing the length of the
shock absorbers by 40 per cent. We then have F =— — — , and
s now equals 7 in., and n is there-
isl= w (M +>:
563.8 (.94+-^)
49
= 14.28. Only 14 rings will be needed
under this assumption.
Actually, a 2500-lb. airplane usually employs about 12 rings on each bridge, and is therefore unable to sustain conditions as severe as those which we have assumed. In order to provide the desired shock absorption capacity, machines of the size which we are considering use 26 X 4 or 26 X 5 wheels. These wheels weigh, complete with tire, from 17 to 25 Ibs. each, and the manufacturers recommend that they be pumped to 60 Ib. pressure.
In place of rubber rings, as specified above, rubber cord woven from manv strands mav be used. Some recent tests
on % in. cord, made up of 180 strands ^ in. square, showed a modulus of elasticity of 434 Ib. per sq. in. The breaking load was not determined. During these tests, it was discov- ered that of the " permanent " set which rubber cord takes after being stretched, 40 per cent of its original length almost
FIG. 4
entirely disappears after 17 hours of rest, the rubber regaining ;ill its original pi'operties.
Types of Chassis
We may, in general, divide chassis into three classes: self- contained chassis with wheels alone, chassis with two principal wheels and a tail skid, and chassis built up around one or two long skids as a basis. There are also numerous compromise designs, which it is difficult to assign to any one class. Nearly all the land machines now built in the United States come into the second of these classes, although all three types had some vogue here at one time.
Chassis with wheels alone were first used by Curtiss. Due
FIG. 5
to their complexity and considerable weight and resistance, they are now seldom employed except on heavy machines, par- ticularly pusher biplanes designed for gun-carrying, where they are generally combined with helical steel springs and hydraulic shock absorbers. Such a chassis may have either three or four wheels, four being the more common. The fore- and-aft distance between the two pairs of wheels must be con- siderable, in order to insure against the machines falling over on its tail as it is brought to rest.
Chassis with two principal wheels and a tail skid, either with or without one or two subsidiary, and usually unsprung, wheels in front, are nearly universally employed on machines of me- dium and light weight, except on the very slow and lightly- loaded pusher biplanes. The framework of such a landing •rear is reduced to its lowest terms, consisting, in its conven- tional form, merely of two Vs, closed at the top by the lower body longerons, and separated at the top by a distance equal
112
AIRPLANE DESIGN
to the width of the body, and at their lower vertices by a little less than the track of the wheels. The bottoms of the Vs are connected by a strut. The two wheels are mounted just outside the Vs, either on a single axle or on separate axles hinged at the center, usually the former. The present practice is to in- cline the axle guides HO that the wheels travel backward some- what as they rise in the guide slots, but this causes excessive wear on the front of the slots, and experiments at the Signal Corps school indicate that no harmful results follow the elim- ination of the backward slope. Fig. 2 gives a diagrammatic view of a typical chassis of this class.
On speed scouts, where the reduction of resistance is of the
FIG. 6. SOPWITH CHASSIS, SHOWING COMBINATION OF Two WHEELS WITH SHORT SKIDS
utmost importance, the chassis is sometimes so built that it forms a unit with the wings. This makes possible the elimina- tion of all wiring from the chassis, and in a few cases from the wing panel as well. Fig. 4 represents a machine so braced. Chassis based on long skids are used on Farman. Caudron. and Wright biplanes. They generally embody four compara- tively small and light wheels arranged in a straight line, one pair of wheels, about 18 inches apart, being attached to each skid. Each pair of wheels has its own axle, and radius rods are used to prevent the axle twisting with respect to the skid. Rubber shock absorbers are used. In some cases the skids are carried up in front to a forward elevator, as in the Maurice Farman, or in the rear to the tail, as in the Caudron. Such a chassis is illustrated in Fig. 5.
.Among the hybrid types, involving some of the features of all three classes, one of the most interesting is the old Nieuport. In this there were 2 pairs of struts, each pair forming a V with the vertex downward. At the bottom of these was mounted a comparatively short skid. Below the skid a leaf spring, of semi-elliptic form, was clamped, and the wheels were at the extremities of this spring. The rear of the skid acted as a tail skid, and, in addition, made a very effective brake, as it was close to the c. g., and consequently carried a considerable portion of the weight.
Brakes and Braking
All the devices which have been brought forward for check- ing the speed of airplanes after touching the ground fall natu- rally into one of two divisions: depending either on air re-
sistance or ground resistance. The best example of a brake depending on air resistance is the airplane itself. We have already mentioned the desirability of being able to depress the tail to such a degree as to secure a very large angle of incidence, not only so that we may land at low speed, but also so that the drag may be increased, and thus aid in checking the speed after landing.
It has often been proposed that air brakes, consisting of sur- faces normally lying parallel to the line of flight, but capable of being pulled around approximately normal to that line, should be provided. If two such surfaces, one on either side of the body and at a considerable distance from the longi- tudinal axis, are furnished, one at a time may be pulled out lo act as a drag and assist in turning the machine in a small circle while taxi-ing, or both may be used at once as a brake. The trouble with all air brakes is that they rapidly lose their effectiveness as the airplane begins to slow up. They have, on (he other hand, the advantage that their force is exerted well above the c. g., so that there is no tendency to stand the machine on its nose.
Brakes depending either directly or indirectly on friction, with the ground for their retarding power, may be subdivided into wheel brakes and sprag or claw brakes. Wheel brakes, although they can be made very powerful, are hardly ever used, due to their danger, which lies in the difficulty in releas- ing them quickly, and in the fact that they have no tendency to release themselves automatically as the machine starts to pitch over on its nose.
Claw brakes are more used than any other type. Thev :ire usually attached to the strut, which lies just below the axle in a V-type landing gear, and are hinged to that strut. The claw on the end can be brought to bear against the ground by a lever within reach of the pilot. The advantage of such a brake is that, being in back of the forward point of suspen- sion, the claw tends to release itself as the machine starts to dive, pivoting about the point of contact of the wheels with the ground. From this point of view, the brake should be as far back as possible, but the available retarding force is greater and the construction is simpler when it is kept near the chassis proper. The tail skid itself acts as a very ellicient claw brake if it is so arranged as to carry a considerable por- tion of the load. If extra quick stops are desired from a machine, whatever type of brake is used, the wheels should be placed farther forward of the c. g. than usual, thus permit- ting a larger moment to be applied at the ground level without upsetting the machine, making it easier to get the tail skid down in contact with the ground immediately after landing, and throwing a larger portion of the weight on the tail skid or sprag brake, if one is used.
It is of interest to determine the retarding force required to bring a machine to rest in a given distance. If, for exam- ple, we wish to land a 2oOO-lb. machine at 45 m.p.h. and bring it to rest in 200 ft. after touching the ground, we have
s = — , or a = ' = 7.20 ft. per see. where a is the nec- 2a GOO
essary deceleration. F, the average retarding force, = —
9
50.") II)., a force whieji might easily be secured without the u><- of any brake save that afforded by the wings themselves.
NOTE — The vector diagram for the JN-2, to which- reference was made in discussing the design of a secondary training airplane in the last installment of the course, is reproduced
herewith. The weights are omitted in order not to confuse the diagram, but the position of the c. g. is that indicated pre vioiislv.
AIRPLANE DESIGN
113
References for Part II, Chapter 8
('!. de Havilland in flight, March 9, 1912. F. W. Lanchester in Engineering, May 22. 1914.
" The Flying Machine from an Engineering Standpoint," by F. W. Lanchester ; p. 80.
" Itelativo Positions of Propeller Axis, Center of Gravity and
Wheels," by Capt. B. Q. Jones ; AVIATION AND AERONAUTICAL ENGINEERING, Nov. 1, 191G.
" L'Essor et 1'Atterissage," by Maurice Percheron.
" La Construction des Organes de Contact avec le Sol," by P. James ; Revue Generate de I'Aeronautique, Jan., 1914.
" Notes on Aeroplane Shock Absorbers of Rubber," by J C Hun- saker ; AVIATION AND AERONAUTICAL ENGINEERING, Sept. 1, 1916.
Chapter IX
Type Sketches of Secondary Training Machine General Principles of Body Design
In Fig. 1 are shown three views of a secondary training machine, very similar to the JN-2, and in accordance with our figures of Chapter 7.
A few modifications have been made in the process of draw- ing up the machine from the figures given in Chapter 7. The figures there were derived from empirical formulas, but in the present stage of the art it cannot be too strongly insisted that no empirical formulas hold with absolute rigidity, and that " eyeability " is almost as important — except in the case of the stabilizer and elevator, on which more data is available. Thus the rudder lias been reduced in area from 12 to 10 sq. ft., and the vertical fin from 4 to 3.5 sq. ft.
The stabilizer and elevator have been left unchanged. In drawing the plan view of the machine, modifications were also found necessary in the ailerons. The original scheme was to place the ailerons on the top plane only. But in order to secure the necessary area it was necessary, with the spar posi- tion selected, to make the ailerons very long and bring them in comparatively close to the body (with an overhang on the top plane this difficulty would not have occurred), and ailerons brought in close to the body have an insufficient leverage for part of their surface. The better plan seemed to be, there- fore, to place the ailerons on both surfaces. Their area was also slightly increased, from 38 to 42 sq. ft. total area.
It must be insisted upon again that this machine is not a perfect specimen of its type. For instance, had an overhang been employed as on the JN-4, the aileron area of 35 sq. ft., with its greater lever arm, would have been amply sufficient. Also the outer strut would have been almost at the mid point of the aileron, thus permitting the use of a single aileron post ; whereas in the present case we are obliged to use two aileron posts.
Another poor point is that the tail skid abuts directly on the rudder post. The control surfaces should never be so placed as to sustain injury by an abrupt landing, as might be the case in this arrangement.
A drag wire is shown carried from the top of the inner strut to the engine. This helps to keep the body from twisting under the effect of gyroscopic forces on the engine, and also to relieve the drag bracing. Nevertheless, in computing the drag bracing the effects of such a wire are totally neglected.
General Requirements in Body Design
These may be very briefly summarized : (1) Stream-Line Form
The power plant and personnel must be enclosed in a form approximately stream-lined. The general shape of the bodi- es largely determined by the size and shape of the engine selected. For the vertical six-cylinder engine the body may
be narrow and deep. For a V cylinder engine, a wider but shallower body is advisable, and with a rotary engine a body of very large maximum diameter. But consistent with struc- tural and other considerations, a body should be selected which gives minimum aerodynamic resistance. The best form of body would, of course, be symmetrical about an axis. Some data for the resistance of airplane bodies has been given in the first part of the Course, but there is no doubt that con- siderable improvement is possible in this direction, possibly by employment of monocoque construction. Where a four girder body is used, and attempts are made to secure stream- line form, the designer must guard against excess weight.
(2) Fin Area of Body
A flat bottomed body may be very helpful in securing longi- tudinal dynamic stability. A body with flat sides has to be handled carefully. It is equivalent to a long fin, with most of the fin area aft of the center of gravity, and this tends to head a machine into the wind — an advantage if the effect is not excessive. Such fin area is, however, best secured by the use of a vertical fixed fin. With a large flat sided body, it is as well to investigate yawing moments in the wind tunnel. One of the reasons why totally enclosed bodies have not come into use is that with their large fin areas, they have a tendency to spinning.
(3) Length of Body
Apart from the necessary length of body to give sufficient arm to the tail surfaces, it is important that the tail surfaces should be far enough away from the wing so that the wash of the wings should not affect them too much.
(4) Provision for Pilot and Passenger
The necessary requirements are obvious. To protect the face of the passenger, a transparent lip is generally fitted on the front edge to deflect the air upwards. The back of the pilot's head may be stream-lined with a suitable projection. Specifi- cation 1002 gives standard arrangements for pilot's and pas- senger's seats.
(5) Engine Installation
Should be readily accessible and cowling easily removable. (6) Gasoline Tanks
Should be near the center of gravity of the whole machine, so as to disturb balance as liltle as possible as fuel is con- sumed. Where it is impossible to place the fuel supply directly over the center of gravity, the gasoline and oil may be made to balance one another approximately.
(7) Engine Foundation
Must be- rugged to prevent loosening up of the bolts by vibration, transmission of the torque of the engine to the body,
114
AIRPLANE DESIGN
115
FIG. 1
AIRPLANE DESIGN
and breaking loose in a bad landing. Nevertheless, the foundation should be flexible enough so that slight engine vibration is easily taken up. The following example will illus- trate the forces on the foundation bolts due to engine torque:
Six cylinder 120 h.p. 1200 r.p.m. Torque = ^ ° ^S^.° = 525,
JrcX £v
then if /•' is force on either side, 2F X -575 = 525. where .575 is half the distance between engine bed bolts, and the force on either side is 457 Ib.
(8) Engine Must Be Secured Against Weaving
When the airplane pitches, there is a tendennj owing to gyroscopic action of the propeller, for the engine to " weave " either to right or left. Diagonal members in the plane of the engine bearers as well as wires are often used. The ideal engine foundation would seem to be of pyramidal form.
(9) Strength of Body
The body must be strong enough to withstand (a) air loads due to tail surfaces, (b) dynamic loads in the air, (c) loads on landing.
These are but a few of the requirements in body design. Numberless points arise in detail work, in which experience and care, and not general roles, are necessary.
Formulas for Spruce Compression Members
The most reliable data on spruce struts — the material in which we are most interested — is given in Dr. Hunsaker's note to which reference is appended. Experiments were car- ried out on Maine white spruce, West Virginia white spruce, and Oregon red spruce. Values varied so much for each specimen that it would be unsafe to use them definitely for wood of varied origin, of varied position in the log, and de- gree of seasoning, and in actual construction tests on speci- mens are always necessary.
In these experiments, the modulus of elasticity found by observing deflection under loading was found to be 1,825,000 pounds per square inch. Two formulas for crippling stress, defined as the crippling load divided by the area of cross sec- tion in square inches, were deduced.
8.72 E
(1) For long struts, L >70, •- = K A.
2 where 7> =
crippling load A = area in square inches L = length in inches K -= least radius of gyration in inches E = modulus of elas- ticity in pounds per square inch. (Some designers employ
using n value
WJ
the ordinary Euler's formula. — =
A
of £ = 1,600,000.)
(2) For short struts, ^ < 70, — = 6500 — 46.5 — . ( Some **- A K
designers employ a modification of Rankine's formula: where fe = 8,000 Ibs. for spruce, E =
1.HOO.OOO. 4> =
-—
It C,
By careful selection of spruce the crippling loads given by the above formulas can be easily secured. It was formerly customary to use a material factor of safety of 2 for the wing struts, and IVz for body struts.
There arises a further difficulty in connection with the above formulas, in determining whether a strut is fixed or hinged at the ends. It is usually assumed that
(1) wiug struts with pin joint fastcuiugs are hinged at either cml
(2) wing struts with socket fastenings of usual type are consid- ered as being fixed at one end. and round at the other.
(3) body longitudinals, continuous over Joints, are taken as flxeil at cuds.
(4) body horizontal and upright struts arc taken as fixed at one end and hinged at the other.
For a strut fixed at one end, and hinged at the other, the
L
equivalent length becomes -=, for a strut fixed at both ends.
v -
the equivalent length becomes — . Thus the above formulas lie- come:
p 8.7-J /•: P r.
£. = 6500 — 46.5 ^
A'.
(1) Ends hinged — = L 2
(2) One end fixed = one hinged
(|)
2
= 6500
(3) Both ends -= , "" . ~ . fixed 1 (I)
""' ''
Z-6BOO- 2K
Body .Stress Diagrams
Body stress diagrams are still on a somewhat unsatisfactory basis, and a number of different methods are adopted. Al- though the longerons of a body are continuous, and the cross bracing members more or less fixed, stress diagrams are always drawn as if it were entirely a pin-jointed structure. Subse- quently, compression members are treated as either wholly or partly fixed at the ends. This is inconsistent but probably all that can be done, without very lengthy refinements.
Factors of safety have been specified in a number of way*, of which we have noted some already.
Army Specifications 1000, 1001 and 1002
Air speed, 100 miles an hour. Angles of incidence of fixed horizontal tail surface, minus 6 deg. ; elevator surface, minus 20 deg. Factor of safety not less than 2.5. This is based on the forces met with when the machine is violently righted after a rapid dive. It takes care solely of the air loads due to tail surfaces. When in the air the body is supported at the hinges of the wings, and the air loads are not transmitted to the part of the body forward of the hinge pins. It can be seen that this is by no means an ideal specification. It has also been criticized on the ground that no pilot can, under ordinary conditions, exert sufficient force to move the elevator to such a position.
Army Specification 1003
Body forward of the cockpit shall be designed for a factor of safety of ten (10) over static loading conditions with the propeller axis horizontal. Body in the rear of cockpit shall be designed to fail under loads not less than those imposed under the following conditions :
(a) Dynamic loading of "> as the result of quick turns in [Hilling out of a dive; (b) superposed on the above dynamic loading shall be the load which it is possible to impose upon the elevators, computed by the following formulas : L = .(»»."). I I"3 where A is the total area of the stabilizing sur- faces, i.e. elevators and fixed horizontal surface, and I is the horizontal high speed of the airplane. The units are kilo- grams. s<|u:uv meters, kilometers per hour; (<•) superposed on this loading shall be the force in the control cables producing compression in the longerons.
AIRPLANE DESIGN
117
This specification is sounder than the previous one. It im- poses the air load on the rear part of the body, which is as it should be, and provides a sufficient dynamic loading for the forward part of the machine.
Another Suggested Method
In the author's opinion, the stress diagrams should be even more complete. They should include calculations (a) carried through on the air loads, (b) calculations carried through on the landing loads, specifying some landing speed, a gliding angle, and travel of shock absorber.
A Detailed Example of Stress Diagram
In Fig. 2, is shown the skeleton framework of a JN-2 body, which fits in with our design of a standard airplane body.
Pio. 2
lu accordance with the preceding paragraph, we should draw two diagrams for it:
(1) With the body and tail surfaces in position shown in Fig. 2, horizontal tail surface at minus 6 deg., elevator sur-
Kl
<L
face at minus 20 deg. The air loads on these surfaces can be computed as follows: Lacking precise experimental data, we may assume that in the worst possible case, the pressure on the tail = .00264 V area of stabilizer and elevator = 50 sq. ft. V , the highest speed attainable during a dive, may be taken as 100 m.p.h. F, the tail load, then equals .0026 X 50 X (100)2 = 1300 Ib.
With these air loads computed, a stress diagram can be easily drawn as for a simple cantilever with supports at the rear body hinges. As an article in AVIATION and AERO- NAUTICAL ENGINEERING for March 1, 1917, shows, the stresses obtained in this way are in certain members smaller, in other members larger, than those obtained from the landing diagram.
(2) The stress diagram on the assumption of the landing shock leaves room for much discussion. The difficulty arises primarily from the fact that it is difficult to say what the worst landing conditions before breaking are for which a machine should be designed. Also it is extremely difficult to include all the forces in play, which may include (a) lift on the wings, (b) drag on wings and body, (c) lift and drag on the tail surfaces, (d) the reaction perpendicular to the ground, (e) tractive resistance on the wheels.
Further difficulties arise from the fact that the center of the wheels does not lie under the center of gravity of the whole machine, so that if a dynamic load is applied vertically at the wheels, the weight applied at the center of gravity gives a turning moment which must be balanced in some way or another. Two methods are suggested which seem fairly reasonable, and provide a rational method of computation. In the first method, it is assumed that the machine is gliding on a path of say 1 in 7, and hits the ground nose heavy. In
\ ' L '
FIG. 4
118
AIRPLANE DESIGN
such a case as can be seen from Fig. 3 the reaction of the ground may be assumed to pass through the center of gravity of the machine, and a balance of forces is obtained. The
FIG. 3
dynamic load in such a case may be obtained on lines indi- cated in a previous section on chassis design.
In the second method, the pilot is assumed to flatten out from the glide, and then turn up to a big angle and pancake down, with the wheels and skid striking the ground simul- taneously. In such a case, it is very difficult to compute the dynamic load, but a balanced system of forces is readily ob- tained, distributing the load between the wheels and the skids as shown in Fig. 4. The dynamic load factor there is taken
as 8. In Table 1 are tabulated the stresses in various mem- bers. In the ensuing sections, dimensions will be allotted to such members.
TABLE I
BODY STRESSED
av bx ci ca' cc' ce'
c< ci
ck'
PR ra
tu
gr at uv wx
y» at)'
0
460 T. 490 C. 1680 C.
aoro c.
2070 C. 1990 C. 1910 C. 1770 C. 1540 C. 1170 C.
560 C.
330 C. 3900 C. 1410 C.
470 C. 0
570 T. 1200 T. 3400 T. 1910 T.
590 T.
100 T.
Pl- ot mu Iw
hd' fi
*
Longerons
490 C. 1250 C.
260 C. 1200 T. 1600 T. 2000 T. 1920 T. 1780 T. 1550 T. 1180 T.
b'c' d'e' fV h'i' i'k'
StrutsO
70 C.
90 C. 140 C. 210 C. : 10 C. 9 . C.
c'd' e'f
c
Wires
120 T. 210 T. 300 T. 480 T. 1470 T.
References for Part II, Chapter 9
"Notes sur la Construction des Aeroplanes," by P. James; Recite Gentrale dt I'Aeronn'i'itj'.'f Mili'-i-r, \faroh, 19M.
"Sprure Aeroplane struts under Compression," by J. C. Hunsaker; Aerial Ag August 13, 1910.
Chapter X
Computation of Strength Members and General
Layout of Body
In designing tension members for the body, no feature is of greater importance than the choice of terminal fastenings which will permit the development of as large a percentage as possible of the true strength of the wire or other tension member.
The main points to be considered in dealing with terminal connections are :
(1) The efficiency, as mentioned above.
(2) Quickness and ease of manufacture.
(3) The possibility of easy and efficient repair or replace- ment in the field.
(4) Reliability, i.e., the difference in efficiency between the
FIGS. 1-15. TERMINAL FITTINGS FOR SOLID WIRE, TESTED BY JOHN A. ROERI.ING'S SONS Co.
best and poorest terminals of a series all made up in the same way should be as small as possible.
(5) The possibilities of defects due to the use of acid and solder, overheating, imperfect bends, flattening of wire on bends, or unskillful handling of the material in the field. This requirement is obviously closely allied to that of reliability.
Extended tests on terminal connections of all types have been made by John A. Roebling's Sons Co. A summary of the most important results is given herewith, and reference to the original report is appended.
The first series of tests related to hard-drawn aviator wire. The form of terminal which was most common up to a few years ago, consisting of a ferrule made from a coil of wire, through which the wire is passed and then doubled back on itself (Figs. 2 and 3), gave very poor and uneven results, the efficiency varying from 60 to 75 per cent, with an average of
65 per cent. These efficiencies were improved by about 5 per cent when the free end of the wire, instead of being doubled back outside the ferrule, was wound three times around the standing portion of the stay.
The next type of terminal tested was similar to the last, but was dipped in solder after being made up (Fig. 1). The fer- rule for such a connection may be made of a coil of wire, as previously, or of a strip of thin sheet metal, wrapped around both portions of the wire. The efficiencies obtained ran from 60 to 90 per cent, with an average of 80 per cent. These values are surprisingly low, and indicate probable damage of the wire by overheating in the process of soldering, as a connection such as this, absolutely preventing any slippage of the wire through the ferrule, should always show 100 per cent efficiency if properly made up. Tests on similar terminal fittings at the Massachusetts Institute of Technology have nearly always de- veloped the full strength of the wire, the stay breaking near the center on every test. The soldered joints have, however, the disadvantage that they cannot readily be replaced in the field, and they are peculiarly susceptible to poor workmanship, the effects of which cannot be determined in any way until the break actually comes.
In the Roebling tests, the best results were secured by the use of tapered ferrules, winding a coil of wire into the form of a slightly flattened cone instead of a flattened cylinder, in conjunction with wedges designed to increase the friction be- tween the stay and the ferrule as the pull increased. Such
FIG. 16.
SERVED AND UN SERVED SPLICED JOINTS AND TYPICAL FRACTURE IN AVIATOR CORD.
wedges may be separate members, fitted between the eye and the ferrule, in which case the wire is looped completely around to make a double eye, or they may be embodied as a part of the thimble, which is interposed between the fittings and the eye to prevent any change in shape or size of the eye under strain. No solder whatever is used (Figs. 13-15). The effi-
119
120
AIRPLANE DESIGN
,-iencies obtained with such terminals were very uniform, rang- ing only t'rnin i>- to 96 j>er cent, with an average of 94 per cent. Such a terminal, although necessarily somewhat complex, has marked advantages. It can readily be made up in the
may ail\ antageously be used ( Fig. 1!) ) . They give 100 per rent ellieiency. or very nearly; they require no high degree of skill to apply, and the fitting is neat and simple in appearance. The common type consists of a conical shell, the hole in the small end being just large enough to admit the strand. The strand is passed through this hole for a short distance, unravelled, and the ends spread out as much as possible. The conical shell is then poured full of solder, and the ends of the component wires cut off flush with the large end of the shell. The only danger in the use of such a fitting arises from the liability to deterioration of the solder.
As we mentioned in the preceding chapter of the course, the stress diagram which was then drawn does not form a complete
l-'n:. 17. SERVED AND UNSERVED SPLICED JOINTS AND TYPICAL FRACTURE IN AVIATOR STRAND.
field, and there are unlikely to be hidden defects, any slipshod workmanship being instantly apparent on inspection.
The British standard, which has recently been adopted by the Society of Automotive Engineers, calls for the use of the plain wire coil ferrule with solder. A device which has been considerably used in England, although not yet employed in this country, is the streamline wire with swaged and threaded ends, thus doing away with the necessity for turnbuckles. Such wires are very expensive and difficult to make, but have decided advantages in prac- tice. They are unlikely to come into use except for fighting machines, where cost is of no importance.
Cable Terminals
Both strand and cord can be spliced with excellent results if the work is done by an expert rigger. Roebling's. tests indicated an efficiency of from 80 to 85 per cent for aviator cord with spliced and served terminals (Fig. 16), and from 90 to 100 per cent, the highest values corresponding to the smallest wire sizes, for 19-wire aviator strand (Fig. 17). The break always occurred at the last tuck in the splice, which would suggest the advisability of taper- ing the splice to a greater extent.
For Held connections, fittings similar to those recommended for solid wire. consisting of a thimble embodying a wedge and a ferrule of soft wire ( Fig. 18), gave excellent results, showing an efficiency of 90 per cent.
The status of solder is the same a- in llie case of solid wire. 100 per cent cffi- eiencie- c.in lie secured by the use of thimble, ferrule, and solder with either -tiand or cord, but there is the same
risk of injury to the material through improper manipulation. In connection with tin- larger diameters of strand,
I'n, l*. UKSOL-
1 1 I i: 1 . 1 1 F I E I. II
TERMINAL FOR AVIATOR STRAND.
FIG. 19. SOCKET TERMINALS FOH AVIATOR STRAND.
basis for the choice of members, but should lie supplemented by various other diagrams corresponding to different condi- tions of loading. We shall, therefore, confine ourselves to fig- uring, for purposes of illustration, a few of those members which are most heavily stressed under the conditions which we have already considered.
Since a dynamic load factor of 8 has already been allowed tor, we shall use a factor of safety above this of only one and a half. This is equivalent to an overall factor of safely, rela- tive to tbe static load, of t \vel\e, a value which is fairly rep- resentative of modern practice in the design of bodies for training machines. The latest specification issued by the (iovernment calls for an overall factor of ten, but tins relates to pnr.Miit machines, which are to be flown by skilled pilots oni\. and in which the factor of safety is purposely kept low in order to make possible a belter performance, and hence a higher decree of military safety. In tbe case of those por- tions of the longerons which are curved to a considerable extent
AIRPLANE DESIGN
121
Steel Mr*
I <
GALVANIZED NON- FLEXIBLE CABLE ENDS
^' [
••-•A -••"P--~S erring • ^.-^o/dered under serving
S fan ijard Thimbl f
'--ShcllaKfd Harness ™'wo' 0,28'WIREK LARGO
OlOlwiRE
,- p Splice! j ----- 1
FIGS. 20, 21, 22. S. A. E. STANDARD TEBMINALS FOR SOLID WIRE, STRAND, AND CORD.
0.080 WIRE
FIG. 23. LAYOUT OF BODY FOR STANDARD TRAINING MACHINE.
between struts, th • factors of safety should lie1 considerably in- creased, as a strut which has even the slightest sign of initial curvature will support much less load than one which is per- fectly straight.
The members I'm- which we shall compute the required size include a longeron section, a strut, and a wire, and they are marked with numbers on the layout drawing. We shall con- sider all compression members as perfectly square, although channeling is commonly employed, especially in struts and the rear portions of the longerons.
(1) The length of the section is 40 in. We shall try, as a lirst assumption, a section l1/^ in. square. The crippling load
i hen 17.44 X 1,825,000 Xl 4U
> or 4,050 Ib. This corre- -
sounds t<» a factor of safety of 9 nr-.y or 1.95, above the dynamic
_,.u i i *
loading. We shall, therefore, use this section. It is well to have the factor in the longerons slightly greater than in the struts. since their end conditions approach less closely to fixa- tion.
(2) The length of the strut is 31 in., and the com- pressive load is 3,900 Ibs. Here, again, a section IVi in. square will be tentatively chosen. The crippling load equals
(I1/.
17.44 X 1,825,000 X -371
safety is then 1.72.
X 12'
or (i,740
The factor of
(3) The tensile load is 3,400 Ibs. We shall select for this stay 10-wire strand & in. in diameter. The breaking load of such strand is 6,100 Ib., and the factor of safety, allowing for 90 per cent efficiency of the terminal connections, is 1.61.
The struts which carry the weight of the engine should be materially heavier than would be indicated by considerations of dead loading alone, since they are constantly submitted to a live, vibrative load, and, in addition, are subjected to bending forces because of the gyroscopic action hi diving. These forces are calculable, but such an analysis is beyond the scope of this pa | er.
In Fig. 23 is shown the layout of the body. The only points at which channeled struts are used are the forward panels, which have the duty of transmitting the propeller thrust to the longerons, and thence to the wings. The other struts are made octagonal by chambering off the corners slightly. The longerons are channeled everywhere in back of the forward chassis strut, except that they are left solid for a few inches adjacent to every strut.
References for Part II, Chapter 10
First Annual Hcport of the National Advisory Committee on Aero- nautlos, Report No. 2; Government Printing Office,' 1916.
Chapter XI
Wing Structure Analysis for Biplanes
There are many difficulties in the analysis of a biplane struc- ture: the distribution of loading between upper and lower planes; the resolution of loading in the planes of the lift truss and the internal bracing; the resolution of loading to give bending moments on the spars, and the alternative methods which may be employed in drawing up the stress diagrams. But in the following notes is developed a system which is now generally employed, and which although it is not rigidly exact, gives sufficiently accurate results for practical needs, and as a system of comparison for machines which have been successful in flight.
Distribution Between Planes
The information available regarding distribution of loads
FIG. 1
between planes is scanty and contradictory. In practice it is sufficient to follow this equation :
(1) W = (Avx)-£j -\-Aix, where W = gross loading of the machine, Au = area of upper wing, AI = area of lower wing,
x = gross loading per square foot on lower wing, -p-x = gross
y
loading per square foot on upper wing.
Unless the biplane truss falls away very much indeed from the conventional form, this will be a fair approximation.
Spacing of Wing Spars — Limiting Angles of Incidence
As the angle of incidence of a wing changes its center of pressure moves, and accordingly varying loads are placed on the rear and front spars (the center of pressure motion in a biplane is assumed to be identical with that of a monoplane). The spar spacing lias to be so arranged that too great a pro- portion of the load is not thrown on either of the spars within the range of the usual angle of, flight. This would be the case were the spars too close together or placed so that one of them would be quite close to one center of pressure. At the same time, the spars must not be placed too near either the front or the rear edge, so that there is always sufficient depth of spar. Thus in t he machine the design of which we are carrying through, the spars are placed as shown in Fig. 1, about 10 per cent from leading edge and about 30 per cent from trailing edge, where the centers of pressure at 0 deg. and at 16 deg. are indicated. The loading is in this case
Front spar Hear spar
At 0° 29.8% 70.2%
At 16° 06.6% 33.3%
0 deg. and 16 deg. are taken in our design as the limiting angles of incidence, although very possibly the machine might fly both at some negative angle, and at some angle above 16 deg.
Running Loads
Applying equation (1) where W = 1793 Ib. and Au = 188 sq. ft., A i = 175 sq. ft. for our machine, we find that the gross loading per square foot on the upper wing is 5.4 Ib./sq. ft. and on the lower wing it is 4.43 Ib./sq. foot. In the same manner the total gross weight supported by the upper wing is 1020 Ib. and the total gross weight supported by the lower wing is 773 Ib.
For simplicity, the running load is assumed to be uniform from tip to tip of the wings, and hence the gross running lifts are for a span of 36 ft. 6 in., 28.0 Ib./foot on upper wing and 22.8 Ib./foot on lower wing.
It is from the gross running lifts per foot that we obtain the running drifts per foot run, by dividing by the L/D ratio.
Thus we have
Lower wing running drift in Ib. /ft. run
At 0° At 10°
L/D
7.2
6.92
Upper wing running drift in Ib. /ft. run
3.90
4.05
3. IS 3.30
Next it is necessary to determine the net running lift. To do this it is necessary to make assumptions for the weight of the wings and the weight of the interplane bracing.
Thus for the upper wing, assuming a weight of .73 Ib./sq.
ft., and half the weight of the interplane bracing of 91.5 Ib.
to be carried by it, we have a net lift of 1020 — 137 — 45.7 =
837.3 Ib. or 22.9 Ib./ft. run, and for the lower wing 773 — 128
- 45.7 = 599.3 Ib. or 17.7 Ib./ft. run.
We can now tabulate our results in such form that they can be used in resolving forces in planes of lift trussing and of the wings.
Percentage front spar _'.!> At 0° Percentage rear spar till. 2
Upper wing
Gross loading per foot run. . 28 Ib. Drift per ft. run front spar. 1.16 Ib. Drift per ft. run rear spar. . 2.74 Ib. Net lift per ft. run front spar 6.85 Ib. Net lift per ft. run rear spar 16.05 Ib.
At 10° Upper wing
Drift per ft. run front spar. . 2.7O Drift per ft. run rear spar. . 1.35 Net lift per ft. run front spar in. 20 Net lift per ft. run rear spur 7.65
Lower wing
22. 8 Hi.
.95 Ib.
2.23 Ib.
5.27 Ib.
12.43 Ib.
Percentage front spar ii(i.(> Percentage rear spur :;."...".
Ixwer wing
2.17
1.09
11.80
5.90
Resolution of Forces in Planes of Wing Trussing and of Wings, and in Plane of Spar Web
In Figs. 2 and 3 are shown the resolutions of forces at 0 deg. and 16 deg. respectively. It will be noticed that the resultant force in the plane of the lift truss is decomposed in plane of the spar web. It is this component in the plane of spar web
122
AIRPLANE DESIGN
123
RESOLUTION OF' FORCES IN PLANES OF LIFT TRUSS & WINGS NET LIFT is ALSO COMPONENT IN PLANC or SPAR
RESOLUTION or FORCES IN PLANES or LIFT TRUSS t Wwcs AT /6"
NET Lirr I6.0S '
TOTAL Fo«c« m PLANE or Wine 56"
TOTAL Fence IN PLANE ^ OF Wine 1, 9*
Fence 11
OF
LIFT TRUSS 5.34*
O/MC .95
FIG. 2
Z.S3
TOTAL FOHCS IN PLANE or *,~o 4.4S"
which is subsequently used to draw the bending moment dia- unnns for the spurs. This is u slightly arbitrary procedure. It would be more accurate to take the force in the plane of the lift truss as producing bending, but there would then he the <-i>iii|>liciitiiiii of computing moments of inertia about an axis not perpendicular to the web.
From these resolutions it is now possible to tabulate figures which can be employed in the lift truss stress diagram, the drift bracing stress diagram, etc.
At 0°
L'ppor wing. Front spar. Hoar spar.
Force In plane of lift truss run- ning foot.
7 Ib. 16.3 Ib.
Force in plane of wiag/nmnlng
foot.
2.4 Ib. 5.6 Ib.
Force in plane of spar web/run- ning foot. 6.85 Ib. 16.05 Ib.
Lower \\ IML Front spar. Hear spar.
Force in piano of lift truss/run- ning foot
5.34 Ib. 12.67 Ib.
Force in plane of wing/running
foot
1.9 Ib. 4.45 Ib.
Force in piano of spar wob/run-
nliiK foot 5.27 Ib. 12.43 Ib.
Upper wing.
Front spar. Hoar spar.
Force in plane of lift truss/run- ning foot.
15.5 Ib. 7.8 Ib.
Foive in plane of wing/rumiiug
foot.
1.18 Ib. 0.48 Ib.
Force in plane of spar web/run- ning foot. 15.2 Ib. 7.75 Ib.
At 16°
Lower wing.
Front spar. Hoar spar.
Force in plane of lift truss/run- ning foot
12.1 Ib. 6.0 Ib.
Force in plane of wing/running
foot.
0.90 Ib. 0.40 Ib. -
Force in plane of spar wob/run-
ning foot. 11.9 Ib. 5.9 Ib.
Figs. 2 and 3 indicate some peculiar results. Thus at 0 deg., part of the net lift is resolved into the plane of the wing, greatly increasing the. demands on the internal wing bracing. Were the stagger of the biplane more pronounced, this effect would be still greater, and that is one of the disadvantages of excessive stagger. But at 16 deg., in this particular case, the component of the net lift along the plane of the wing relieves the internal wing bracing.
LIFT-
TOTAL foflc/r IN PLANE, of LIFT TRUSS IS. ^
COMPONENT IN PLANS of
TOTAL. Fence IN PLANE of LIFT THUSS 7.6* DP/IS 2.7*
1 ,FT 7.65
TOTAL Fo/tcf IN
PLANE OF WINS
//a*
TOTAL Foncf IN PLANE OF WING .-fa*
COMPONENT PLANS of 11.9*
TOTAL
of LIFT Ttrvss 6
TOTAL
N PLANE of .9or
COMPOHCNT
IN PLANE or SPAR WEB 77
DRAG 1. 35
COMPONENT IN PLANE or SPAR wee f.S*
DPAS /.OS*
TOTAL Fopce IN PLANE or WING
.40'
Kin. 3
Different Methods Employed in Stress Diagrams for Lift Truss
Two distinct methods have been adopted in getting out stress diagrams for the lift truss.
(1) The trussing is treated as if pin jointed throughout by the ordinary bridge truss method, and the bending moments for the spars found as if they were freely supported at the ends, with uniformly distributed loads.
(2) The spars are treated as if continuous, so that bending moments in them and reactions at their supports are found by theorem of three moments. Then the reactions having been found, the stress diagram is drawn with such reactions as a basis.
The first method has the advantage of simplicity and of giv- ing a very large factor of safety. The second method is much more difficult, but probably is nearer the mark, and we shall employ it accordingly.
Bending Moment Diagrams: Theorem of Three Moments
Any good text book on applied mechanics treats fully of the theorem of three moments, so that the following notes will be of the briefest :
In Fig. 4 is shown a beam loaded with unequal distributed loads over the two spans. At the three supports, 0, 1, 2 M0, Ma M2 are corresponding bending moments; Ba Ba R, are corresponding reactions; S +„, £-„; S +0, S-l; S +,, S — are shears on either side of the supports.
124
AIRPLANE DESIGN
Jf the beam is continuous over tlie three supports and has
|
1 |
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|
i |
1 |
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i |
J |
1 J) |
1 |
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o Z |
5 |
b O t — o |
**- 1 |
R |
5n |
t o
FIG. 4
I lie same cross-section throughout, the bending moments at the supports and the loads are.connected by the following formula:
All difficulties in working the theory of three moments are due to mistakes in the conventional signs.
TfrNS
NEGATIVE
&ENDING- MoMfcNT
Fio. 5
The convention for bending moments is shown in Fig. 5. From this follows the rule:
Forces lo left of a point must tend to turn a beam clockwise 'tbout that point in order to give a positive bending moment fit that point — anti-clockwise to give a negative bending mo- ment.
Forces to the right of a point must turn the beam anti-clock- wise about that point in order to give a positive bending moment at that point — clockwise to give a negative bending moment.
If these rules are observed, the effect of the fixing moments is also automatically deter- mined. Thus if a fixing mo- ment is found to be negative at
a support, and the above rules are followed, its effect will be negative on either side of that support.
The convention for shear is shown in Fig. 6. If forces to
BENDING noMENT.S SHEflR DlflGPflMS FO)? REflR UPPER SPflf? flT O°
_ LonpmG 1fc.05* PE(? FOOT Pun . W ENS, MI Pw.r._
Tbsmvt SHEAR
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--2 |
•** |
STRUT PO.NT |
• (• |
STRUT Poif |
' 6-3" , |
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, |
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f |
\ |
SH |
* ., |
... |
.,:•' |
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• |
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, |
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,.' |
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. m |
r - |
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Fio. n
the left of a point tend to shear the beam upward, the shear at this point is positive. As a result of this arbitrary rule, when finding the shear by means of bending moments, the sign as found must be reversed if the origin chosen is to the left of the line of action of the shearing force.
Observance of this rule is not so important as the observance of the rule for bending moments. Tt is generally easier to see what happ ons physically.
Working Out of Bending Moment and Shear Diagrams for Upper Rear at 0 Deg.
The principles of the preceding paragraph will be best illustrated by working out the above case fully. In Fig. 7 is shown the disposition of the wing. With a total span of 36 ft. 6 in. and an engine panel of 2 ft. 6 in., we allow an over- hang of 2 ft. 6 in., 7 ft. 9 in. for outer span between struts. and a smaller inner span of 6 ft. 9 in., which seems a reason- able spacing. The loading in plane of spar web as previously found is 16.05 Ib./ft. run. . For simplicity's sake, we neglect the engine panel.
To get bending moments at supports :
(a) M, = 0, since wing is hinged at engine panel;
(b)Jfi=1606X(2.5)' =50.21b,.ft..
(c) to find Mn we write
MA + 2(1, + L)M. + MJ, = - %!!../, — %!«•/: and by substituting in this equation,
M0 = 03.7 Ibs.-ft. To get shears at supports:
(a) S_, = 2.5 X 16.05 = 40.1 Ibs.
(b) Taking moments about support 0 we have
therefore S +, = —56.7 Ibs. (c) Taking moments about support 2 we have
therefore (reversing signs),
S_0 = 68.0 Ibs. (d) Taking moments about support 1 we have
therefore S+,, = — 68.3 Ibs.
(e) Taking moments about support 0 we have
^"i "7 "I *J 1^1 ~~ «*ni
therefore (reversing signs)
6'_, = 40.4 Ibs.
To find the total reactions (the absolute sum of tlie shears)., we have
£_,- + *>'+« = K.. = 96.8 Ibs. tf_. + -V = «." = 136.3 Ibs. S_t = It, = 40.4 Ibs.
After having found the bending moments, shears, and re- actions at the supports, it is very easy to draw the entire bend- ing moment diagram by finding points of zero shear and maximum bending moment.
Thus in the outer span, if x is the distance to the light of support 2 of the point of zero shear, S+! = a •«•.. and .c = 56.7
16.05
= 3.53 ft.
The bending moment at this point is (taking forces to the left)
+
,x = - 49.8 Ibs.-ft.
Similarly in the inner span, if x = distance to the righl of support 0 of the point of zero shear,
and x = 4.26 ft.
The bending moment at this point is (taking forces to the left)
,., wx'.
M „ = -p-1 +S+ .r = — ol.3
References for Part II, Chapter 11
"Wins Data and Analysis for a Staggered Biplano," by Dr. A. F. Kahm, Franklin Institute, December 1914.
British Ueport 1912-l!tl.",. .No. s:s. A pivlimiiiary note on methods <>f calculation whicli may he employed in the determination of the sinssrs in the spars of airplane wings l;y Itairsimv niul MacLachlan.
Chapter XII
Wing Structure Analysis for Biplanes
Reactions in Plane of Lift Truss Due to Upper Rear Spar at 0 Degree
At tlic conclusion of the previous chapter, we drew the bend- ing moment diagram for the upper rear spar as a continuous beam, and found the appropriate reactions. But since the bending moment diagram was drawn for that component of the force in the plane of the lift truss which was in the plane of the spar web, allowance has to be made for it on "reverting in the lift truss. The running loads were in the ration of 16.3 tn 10.05. Hence rca'-limis arc
10.3
R,= 96.8 X K0 = 136.3 X fl, = 34.0 X
16.05 16.3
16.05 16.3
10.05
= 98.311).
= 138.4 Ib.
= 41.011).
Reactions in Plane of Lift Truss Due to Lower Rear Spar at 0 Degree
Since the spacing of the supporting points on the lower wing is identical with that of the upper wing, and the slight overhang is the same, the bending moment diagram and the shears and reactions will be in direct ratio to the loads. The ratio of loads on upper plane to lower plane is 14 to 11.5. 1 ICMCC reactions are
/•'. = 98.3
= 75.4 Ib.
«„ = 138.4 X r = 107.5 Ib. 10.3
/.', = 41.0
~
=: 31.4 Ib.
Stress Diagram for Rear Lift Truss at 0 Degree
We are now in a position to draw the stress diagram for the lift truss as shown in Fig. 1. The only other loud to be added is 20.3 Ib., which is allowance for half the air force din- to the engine panel acting on the rear spar.
In drawing this stress diagram, the strut K L is assumed as taking no tensile load, and the lift load at F G is transmitted by the cross wire L M to the body.
Stress Diagram for Internal Upper Wing Bracing at 0 Degree
In Fig. 2 is drawn the stress diagram for the internal brac- ing of the upper wing at 0 deg. incidence.
The spars have so much less resisting moment in the plane of the wing that it is perfectly justifiable to treat the inter-
plane wing bracing as a pin-jointed structure and neglect all consideration of bending moments.
The running loads per foot run are taken from the preced-
FIG. 1 STRESS DIAGRAM OK REAR LIFT TRUSS AT 0 DEG. INCIDENCE
ing sections, with the addition of J/2 Ib. drift at each external bracing point.
Computations for Dimensions of Rear Upper Spar
Having drawn the bending moment diagram, the lift truss stress diagram and the internal wing bracing stress diagram,
FOR EXTERNAL DRIFT AT EACH EXTERNAL CONNECTION
FIG. 2 STRESS DIAGRAM OF UPPER WING INTERNAL DRAG BRACING AT 0 DEG. INCIDENCE
all at 0 deg. incidence, we are in position to determine the dimensions of the rear upper spar. Since the worst loads
125
AIRPLANE DESIGN
come on the rear spar at this angle of incidence, it is not neces- sary to recompute it at 16 deg. also.
The worst loads it has to meet occur in the inner span, 3 feet from the wing hinge:
Compression from the lift diagram of 675 Ib.
Compression from the drag diagram of 330 Ib.
Bending moment of 44 ft. Ib.
It is first of all necessary to fix the effective deptli of spar for the wing section employed, namely, the R.A.F.6. The spar is placed at 30 per cent from the rear edge, where the thickness of the wing is .054 of the chord. For a 62-in. chord, this gives a thickness of 3.34 in., or 3 21/64 in. very nearly.
From this must be deducted the thickness of the two rib caps or flanges. The construction and dimensioning of 'ribs is a matter of some uncertainty and controversy, and will be dealt with fully in a later article.
moment that a thickness of rib flanges, so that the effective depth of the flanges will be re- duced tx) 3 5/64 in. The actual drawing up of the beams is largely a matter of trial and error. That is to say, an appar- ently suitable section has to be drawn in its area, and moments of inertia, etc., have to be computed together with the factor of safety consequent thereon.
in.
We will assume will be sufficient
for for
the the
NLUTRRL
FIG. 3
— 1.75
REAR UPPER SECTION
After ;i number of trials, the spar section of Fig. 3 is found to be satisfactory.
The upper surface of the spar follows the outline of the R.A.F.6 wing section at this point, but in making computations the slight slope may be neglected.
To compute the moment of inertia, the quickest way is to compute for the solid section and deduct the moment of inertia of the material channeled out. The moment of inertia of a
rectangle being given by the formula -rj
1.75 X 3.083 1.125 X 1.7:'
= 4.27 — (1.46 = 3.81
12 12
A = 1.75 X (3.08)— 1.125 X 1-7 = 5.39 — 1.91 = 3.48 The stress in the outermost fibers will now be given by the formula
P My / = — - —f— where P = direct load, y = distance of outer
A. I
fibers from the neutral axis and / = stress. Since P = 1120 Ib., M = 93.7 ft, Ib. = 1125 inch. Ib. and maximum / =; 1125X1-54
3.48
3.81
= 777 Ib.
Allowing a maximum fiber stress for spruce of 6500 Ib., we get a factor of safety of 8.35, which is in excess of the 7.5 specified by the Army.
Similar computations can be carried out for the upper front spar at 16 deg. — since the biggest 'oad is carried at this angle.
It must be pointed out, however, that although the formula
/ =— -(--^-y-is largely used, and is, therefore, perfectly sound A. i
on a comparative basis, the factor of safety given by it is not exactly true. Tests on breaking beams by bending show great variations from the above formula, depending largely on sec- tions employed, but special values for moduli of rupture by bending are not available.
For the lower wing, if the same chord is employed as in the upper wing, and the spars have the same dimensions, no com- putations need be made, since the loads on the lower wing will always be considerably less. Whether with the same chord the lower spars should be smaller than the upper ones is a matter to be determined largely from the manufacturing point of view.
A Complete Example of Wing Analysis Arrangement
In Fig. 4 is shown the complete analysis for the wing structure of a Curtiss biplane. The methods employed in get- ting out this analysis are substantially the same as indicated above, and the method of presentation is an excellent model.
Computations for Shear in Spars
Wood is so much weaker in shear than in either tension or compression, that it is somewhat surprising that designers do not make computation for shear in the spar web — although spars are always made solid for 2 in. or 3 in. on either side of a supporting point, to allow for the maximum shear occurring at such points.
The maximum longitudinal shear for a beam which is sub- jected to vertical shear occurs at the neutral axis, and its value is determined by the formula
F .
where /'' = vertical shear at the point due to external loads, I = moment of inertia of whole section, b = breadth of web at neutral axis, .4, = area of section above neutral axis, y = dis- tance of ccntroid of this area from the neutral axis.
Thus consider the same upper rear spar 6 inches from support 0. The shear at this point, as given by the shear force diagram of Fig. 7 of the preceding chapter, is 60 11). Considering the section of spar shown in Fig. 3:
/ = 3.81 in.4 Al = 1.76 in/ b = 0.625 in. ,/ = 093 in.
«= 3^V625 X 1-76 = 0.93 = 41.2 II,
Allowing shearing value of spruce to be 400 Ib./sq. inch, we have a factor of safety of 9.7, which is amply sufficient. But cases might occur where the shear near supports is very large, and resistance to shear being largely due to the web, it is al- ways advisable to make such computations.
Fie. 4
A.I) POUND*
I Itl P«»NOS
not* Lir-rm* P»M«D»
007«P»UNO»
MET D»irri« POUNDS
enessl, T IOJI POUHOS
P*WND«.
AND 0»<FT WMP.NINTS
«.I«»TI»U«»I"«
6°. POUNDS.
<SROS» Linr AND NIT DRIFT
ON SUPPOHTIH* PLANES
ff*N*>M»lirr22
P»u*e>t f»» LWU
ITONT STRUTS IMCI.UD1N* CF'ttT i
•Y«o". i'.™.VT"AN'iwI7«»T" OF STRUTS A-ND »TAV».
c 9 >«
3>' in 75 i7« •«' ziz /a '
ere
BlNOIN* M«MtNT« 0»»R«NT,TOP»ND LOWER «PAR« IN PLAN* or XBKkPlWM.
POUNDS P
PE» ANO L*Wt*
BB.rr i.«AO% A NO »T»e»a«» IMTMC PLANKS Of TN« - . - — -
^jy^^^F^^s^sr^^^s:-
• 003Z
.0024 oozo .00 i«
.0012 .0000 000*
AritLc Or INC
ii To 12 14- i« CHXITACTEITiaTIC OATA r
AN4UE Or INCIDENCE
-IFT TO DRIFT RATIO
roT
t IN F-mtnK,'
CHORD DCPTM
|
srnsoL |
K1CMBIK |
MCTISHM. MOMENT AWI A -r KUTtRiAU SQOARC 1 incurs )H*wriA |
St«tic« XOOU.U1 |
Fa |
||
|
Fiotfi : |
||||||
|
hLl.uil |
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|
A |
FRONT t>HAR |
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3.8 |
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H |
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M3- |
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C |
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143 |
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3.54 |
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117: |
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1) |
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4.0 |
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3.C |
Me |
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- |
- |
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RtAR SPAR |
- |
4.73 |
5.4-8 |
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ti7 |
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J |
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„ '1 |
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- |
te» |
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LIFT STRUT |
!^r.88 |
0.7^ |
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768 |
2.07 |
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M |
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4. 1C |
0.5-7 |
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f |
e.5 |
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4« * i WOKB4.IMC ixiu |
NC O I CAMtJS |
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2 |
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6400 |
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w |
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7/32 |
11200 |
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5/3Z |
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TACTORS OF 8AFETY AUt «|WFN TOR STRtSS >N DRirT WIRES AN& |
FIG. 4
A SSCMBLE D DATA AN
I «8 P.I/NB.
|
m. — ~-^ |
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i |
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j |
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1 CUWK «R |
r« |
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1 |
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e* cN«ifb |
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0 VOC |
CO la 16 H- 12 0 a e * 2 |
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2 |
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fe |
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/ |
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J |
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/ |
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f |
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2 |
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An |
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>NOPLANE WINS SHAPE -AIR At Iff'tENT. CT RATIO ^, |
|||||||||
|
0' |
Z' |
4^' |
6* |
«9* |
10' |
12° |
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is- |
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00 Z4 |
|
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|
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42J |
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3IZ |
302 |
21Z |
t«» |
?q« |
33» |
|
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TOR HIGH SPEED |
|||||
|
& iNUB3./<,'0.m. |
FACTOR OF SAriry |
: (SRE 3TIT»sr l X UB5/I*. 1 N- |
FACTOR Of SAFETY |
|||
|
.IfT • |
bRirT |
9END1H<* |
LIFT |
DRIFT |
||
|
37 |
O |
20 |
- 161 |
-22 |
O |
33 |
|
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|
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16 |
|
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|
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13 |
|
115 |
-55 |
iq |
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|
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23 |
|
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+ 15 |
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|
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16 |
|
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26 |
|
296 |
6 |
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1 4 • |
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If |
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ioq |
17 |
-224 |
6 |
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|
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1 0 |
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zq |
+ 134- |
4-7 |
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|
715 |
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14- |
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40 |
q |
tcqe |
\e |
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|
61 |
7S |
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36 |
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|
zes |
^4 |
+ J42 |
il |
|||
|
4&\ |
^e |
tees |
13 |
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|
Ft POINTS OF GREATEST STffESS PRUTS SEE DRIFT PUGRAMS. |
NET RwNNir.ii LIFT AND ORIPr COMPONENTS IN FIANEC or WIN* TRUSSING
SROSS LIFT Awo D»irr
LirrLo»D» »NB »Tt»ts»t*iNPL*Mt or »i»« STRUTS IMCLUOIX
OPBCNDrN* MOMENT AND WEIGHT OF STRUTS AND STAYS
POUNDS
3000 ESOo loo o 15 e « i«e o
50"
O
500
i o 0 e
ISO O
Zoo e tsoo
* 4-tlHEOIUI.
ON FRONT, TOP AND LOWCBSPAKS OF IBCAM WEB.
t DRIFT C.IZ4 Pen TNC.H
j n n
17 i is in 11 j
PUAN OF UPPER SPARS
;OMPUTEP VALUES
Appendix
Notes of Aerial Propellers
By H. Bolas
Presented by Mervyn O'Gorman, Superintendent of the Royal Aircraft Factory Reports and Memoranda, No. 65. March, 1912
The object dl' the present notes is to give an account of a met IKK! which has been employed in propeller design at the lioyal Aivcrai't Factory, with some particulars as to the theo- retical assumptions on which it is based. In principle the met hud is essentially the same as that which has been described by M. Dr/ewiecki,* and is commonly referred to as the con- stant incidence method.
Ciiiixtinit Influence Method. — In this method the propeller blade is regarded as an aerofoil, each element of which makes a constant angle with its path in space. In other words, the lihnle is treated exactly as though it were an airplane, except that the path of the blade is a helix instead of a straight line.
The path in space of any point of a propeller moving for- ward with constant velocity is a helix, the advance of the screw per revolution being called the pitch. If the angle of the Made at any point corresponds with that of the effective helix, the only resistance to motion is head resistance and skin fric- tion, and no thrust is obtained. If, however, any element is gel at some angle of incidence to the effective helix it becomes an aerofoil possessing lift and drift, and a propeller so de- signed will give a definite thrust.
In this method, then, the angles of the effective helix are first calculated for various fixed points of the blade for a given velocity of advance and a given propeller speed. Each of these angles is then augmented by the angle of attack.
Value of Angle of Attack. — The value of the angle of attack to be used depends chiefly on the form of blade profile adopted.
FIG. 1
Consider Fig. 1, which is intended to represent a section of an aerofoil, or of a propeller blade, in motion. D = drift or re- \jstance to motion; L = lift (not to be confused with thrust of element ) ; B = angle of attack; G = gliding angle, or ratio 1> I. nearly. As the angle of attack U is varied the ratio II I. will also vary, and for some particular value of B this ratio will be a minimum. It is this value of H which, on this method, is employed, so far as possible, in practice. As already stated, this best value depends on the form of blade profile; it is usually found to be in the neighborhood of 4° f for good
* See Abstracts No. 4r>. Report for 1909-10. Theorie Generate dee Propvlsewi IleHcoiclnuj- ct Mi-tlnnlc dc Caicul dc ces prouuUcurs pour I' Air. Paris, F. Louis Vivien. I'.m'.i.
forms. It is well to note, however, that in some cases it is impossible to use this best value, as the width of blade required may be too great. In such a case a compromise must be made and the angle of attack increased. This only happens, how- ever, when the primary conditions are bad.
Efficiency of Eli-mcnlal XtripA and Curve of Efficiencies
I
FlG. 2
(see Fig. '2). — Let -1 denote the angle the effective helix makes with the line at right angles to the axis, B the angle of attack. Also as above, let D/L = K = tan G. Then the efficiency E of- the element is readily shown to be given by ,, _ tan A
~ tan (.4 -\-G)
and for variation of G, K is a maximum when G is a minimum.
From this a curve of efficiencies for different values of the
angle A can be plotted (Fig. 3). The curve in Fig. 3 has been
7CC
|
•~40- |
§ |
|
|
20- |
Radius JL |
|
|
Scale of Effect Pitch A/e |
||
|
4 . |
. |
|
|
0 .2 |
.4 .6 .8 7.0 7.7 |
|
|
Scn/e .>/ ^;;s//e ^ |
||
|
60° 43° 30' |
78' 72° 9° 8' |
FIG. 3
drawn for G = 4° 35'. In propeller diagrams it is more con- venient to employ r/pe as abscissa instead of the angle ,-i
i Si'c Notes added June, 1912, p. 136.
j Di-iiiH-il as the ptliciency of a strip of blade at radius r and of width dr this strip being supposed not isolated from thc> neighboring elements.
12!)
NOTES ON AERIAL PROPELLERS
when? /i is the clTi-ctive pilch, I he relation between them being
r/pt = — . volA. alt
One other point may !«• inentioiieil — tile <|Ueslion of variation til' efficiency a- we I ravel out along tile Made. It will be >cen from the cun-e, that as we inerea.-e r ji, the elliciency increases very rapidly at first, and reaches a maximum at the point where r/pt = 0.17 (or A = about 43°). From the formula given ab.i\e for K it is readily shown that /•.' heeomes a maximum when- -I =45° — (G/2). Thus in the particular case given. G = 4° 35,' and the angle for max. efliciency = 42° 43'. As r/pe increases still further, it will lie noticed that, the efficiency decreases and continues to do so. Hence, beyond a certain radius on the blade the elements get less and less efficient towards the tip. This is an unfortunate point in the design of actual propellers.
1'riifirlli'r I Hiii/ nuns. Supposing the velocity of advance, the revs, per minute of the propeller, and the horse-power of the engine are known, we can now proceed to set out our
1.0
I.I
FIG. 4
2'8"
3-4"
4'0" 4'3"
diagrams. The scales of these are in the first place immaterial. (flee Fig. 4.) It will be best to explain first the meaning of the various curves, and afterwards to devote some attention to the ideals to lie aimed at and the determination of scale.
' 'irre 1. — This is termed the Linear Gradimi Ciiri-e, and its ordinates are everywhere proportional to the blade widths, these l>eing supposed to be developed on to the plane of the paper.
Curve 2. Pressure per sq. ft. curre. — The pressure upon the blade per unit area of surface at any point depends principally upon (i) the form of section, (ii) the angle of attack, (iii) the velocity of that particular point relative to the air. Let C be a constant depending upon the form of section. Let B as before be the angle of attack, and I', the velocity of a particular element relative to the air. Then we may write with sufficient truth —
I 're-sure per >«,. ft. I It I , and since i and II are constants along the blade we can write
I 're-sure per sq. ft. a 1 . Now if K be the axial velocity of translation
Vt'= V/sin-.\. But V also in constant along the blade. We may therefore put
Vt' a 1/sinM,
and it is now only necessary to plot a curve, the ordinates of which are proportional In 1 -in I, in order to obtain the pres- sure per sq. ft. diagram. The scale i- for the present imma- terial.
< iirf .','. I.fiiil i,rii>iinii ( itrve. — Consider any value of r/p, represented by 0-r. Then at lhi> point the width of blade is icprc-cnicd by Hi. Kvidcntlv then the quantity f.ri/ will He a measure .,1 the load |>er tool run on the blade, and
if we perform this operation for a number ol points at dif- ferent radii we can draw a curve, the ordinates of which will represent the loading per foot run. (,'urve :i ( Fig. 4l has been obtained in this way.
Cun-f I. Thrust (irinliii<i Caret'. -The thrust grading curve is such that the ordinate at any point repre-ents the thrust per unit length (per foot I of blade, and is obtained from the load grading curve in the following manner.
Consider the sketch shown in Fig. ~>, which represent* .1 MC
Fi.i. 5
tion of the blade at any radius. The line KO, which rcpu- sents the pressure per unit length upon the element, makes with the axis (or direction of thrust) an angle (A -\ i. . where as before A is the angle the effective helix makes with OM, and (i is the gliding angle. Both A and (1 are known for any point of the blade. Now we have: —
Thrust per foot run = load per foot run X ('os ( -1 -\- (!1.
The ordinates of the thrust grading curve are thus obtained from those of the load grading curve by multiplying by eot
(.1 + '•'•
Curve :'>. Efficiency Curve. — The values of the angle .1 and gliding angle G being known, the efficiency at any point is given by
tan .1
tan (A + G) and an efficiency curve can be plotted a> described earlier.
It should be explained that the order in which we set out the diagrams will depend upon our initial data. For instance, if we are given the shape of the thrust grading diagram, we may first lay down the load grading diagram, then the pressure per si|uaie foot curve, and finally, from the pivviou- two, the • linear grading curve, vi/... the plan form of the blade. On the other hand, if we start with the plan form curve, we may.
FIG. 6
by rcvcr-ing the above process, finally ain\e at the thrust grading curve. In practice the latter method is always adopled for reason- which we are now in a position to explain.
lilnil ('tin-,'-. 1 1 we a— lime as an ideal condition that the velocity in the slip -liea'ii i- e\ cry where parallel lo the axis
NOTES ON AERIAL PROPELLERS
131
and uniform, then the momentum per second imparted, and hence I he thrust at any radius, will be proportional to that radius. In other words, the ideal thrust grading diagram is a straight line passing through the origin, as shown in Fig. G — M I)B. In practice, however, such a form of diagram would be undesirable, even if attainable, and some compromise as that sketched in Fig. 6 — AEB — would have to be adopted. Accord- ing to Mr. Lanchester, the best practical shape of thrust grad- ing curve is that shown in the next figure, in which " con-
jugate " ' points on the diagram have ei|iial efficiencies (Fi". 7).
If, however, we started out with a diagram of this type, and from it constructed a linear grading curve, our final plan form would take the shape shown in Fig. 8. Such a Wade could
Linear Orat//,,
FIG. 8
never be employed in practice, since under existing conditions we should require an immense blade width and a very large diameter in order to obtain the needed thrust. It is useful, however, inasmuch as we know the direction in which to work when given good conditions at the start.
When designing then, as I have already stated, we invariably begin with our plan form, and finish up by obtaining a thrust grading diagram, which will usually differ considerably in shape from the ideal diagram first described.
The propeller curves being laid down, it only remains now to give them their proper scales in order that we may satisfy the initial requirements.
Determination of Scales. — Since the ordinates of the thrust finding diagram are measures of the thrust per foot run along tua blade, and the abscissae represent the radii in feet (pt- the effective pitch being constant), it will be evident that the area of the thrust grading diagram represents to some scale the total thrust on the blade.
T
Now thrust per blade I = — ,
.\ci. of blades
» here T is the total thrust of the propeller.
Let p = horizontal scale (known), viz., 1 inch on diagram = f> ft. of radius.
Let q = vertical square (required), viz., 1 inch on diagram = </ Ibs. per ft.
Then jiq X area of diagram in square inches = Thrust per blade.
Hence
Thrust per blade area of diagram . p'
In this equation the horizontal scale p is known, the area of the diagram may easily be computed by means of a planimcter,
•Conjugate points are dcfliuMl as the points in which a straight line through tho origin cuts the thrust grading diagram.
and it is then only necessary to tind t, the thrust per blade, in order to determine completely the vertical scale.
Before t can be calculated, however, the total efficiency of the propeller must be found (see Fig. 9). To do this we divide up our thrust grading diagram into a number of parts and
FIG. 9
then compute the area of each. The mean efficiency of each part is now read off on the efficiency curve, then divided into its corresponding area, and all the quotients so obtained are summed up. The sum arrived at in this way, divided into the area of the thrust grading diagram, will give the total efficiency of the blade.
Computation of Thrust. — Let H = H.P. of engine, Et = total efficiency of propeller, V = velocity of advance in ft. per SIM-., 7' = thrust of propeller. Then rr/550 = 11. F
We then have
Thrust per blade = 7'/No. of blades.
The thrust per blade having been thus ascertained, the vertical scale of the thrust grading diagram is calculated as before explained, from
Thrust per blade
q = — .
area of diagram X P
Thus in a given case H = 58, E = .67, T" = 73 ft./sec. Therefore
T = 58 X 07 X 550 = .,,,._, ^
No. of blades = 4.
Therefore, thrust per blade = 73 Ibs.
Further, area of thrust grading diagram = 40 sq. ins.
p = 0.381 ft, Therefore
Load (iratlhiy Curve. — Since this was obtained by dividing the ordinates of the thrust grading curve by cos (A-\-G), wliich is itself a mere ratio (and has therefore no dimensions), the scales, both thrust and load grading curves, will evidently be identical.
Pressure per sq. ft. Curve. — The determination of the in- tensity of pressure on the blade at any point is of course a matter for experiment, and the data at present available are somewhat scanty. In an account of the recent experiments of M. Eiffel, however, a curve will be found which gives the lift and drift for a particular form of section, and this form of section is the one we have adopted. A rough* reproduction of M. Eiffel's curve is shown in Fig. 10. some explantion of which is perhaps necessary.
The angles of incidence (viz., angles of chord UV) are marked along the curve itself. Consider the point where the
* NOTE. -This curve is to be taken .-is diagrammatic only.
132
NOTKS (IN \KKI\I. I'KOI'I I I I li-
angle is 4J (I'\ and lot the ordinal <• then- be denoted by A"v and the abscissa by A".r. Then wo have for this particular angle of attack
I.it't per unit area of surface • K'II \ (velocity)'. Drift " = K'x X
Further, if the point /' l>e joine<l to (>. the alible /'") i- the
»
0.005 0.004 0.003
0.00.
0.001 K' x
0.05
0.04
0.03
0.02
0.01
0.00
t—1-
Form of Sec'/nn
h'Ki. 10
•rlidinj; an^le of the aerofoil, since ratio ot drift to lift of the plane, that the best an^le of incidence tangent from n to the curve, since drill lift, and what is more, it will for this particular section is 4°. planalion we can now proceed to choose some point on the blade, -ay 0.9.
Then a> before explainol.
the tangent oi' I'O ) is the It will therefore be evident \s obtained by drawing a this gives the least value of be seen that the best angle With this preliminary cx- the scale of our diagram: the point A" wh-T- r
eol.-l = - •-; whence .1 = 10° ^, /'•
and sin A = 0.17*1'.
Hut we have prc\ ioiisU -how n that
Ab-olnte velocity of point Velocity of advance sin .1.
I'Jii ft. per sec.
Now from KilTel'.- curve, lor aiiL'le of attack 1 . A',r H.iMiori' in, English iin
Therefore, lift in Ibs. |>er sq. ft. — A',, (velocity in ft. per
= .( 5 U'JOi
_;!-li iii.il-i \<. .
"l«l<-il .Inn-.
KlITi-
In :..• |> !
:i - im
, we have from the pressure per s<|. ft. curve
= 88 Ibs. per sq. ft. Therefore 1" = 25.7 Ibs. per sq. ft.,
thus fixing the scale of our pressure per sq. ft. eur\c.
It will be noticed in the above that I have taken actual lift* on blade instead of total pressure, vi/... \/ ( A'//' -f- A'.r"). I'', but the difference is usually so small as to be negligible.
Liin'iir (Inidiiifi 1'iin-i-. Again consider the point \ of this. where r/p, — .9 We have
Ordinate of blade f ^ f pn-sure per in feet at point \ ' sq. ft. in Ibs. Ma le.
Ordina.e ot blade in fl. a. point = 'Oa(1 **T. "
preesnre per s<). ft. \ M X 4.79 =
' X 25.7 = 7".33
„. per it. run
V - 1".7 = (!'.4 of Made width. 1" . ll'.L'.'l.-) Of Made wi Illi We lliive :llso
Max. blade width •= 0'..'>f>7 (i".H. say 7" wide.
The scale tit the lirear eradiuy rune belli*: known, we are now in :i posi'ion In set out our propeller,., -moo (lie blade angles at the \arions radii have lieen previously deterinined.
.\nmber of lilades. — At the present lime, the majority of propellers in use are of wood, and hence two or four lilades are employed, three blade* lieiny excluded for eiiiislnictional reasons.
It is difficult at present, until further experimental data are available, to decide as to the relative, merit- of two- and four- bhided pro]iellers. The four-bhided. propeller is possibly better ae:-odynamically and from the point of view of balance, but the two-bladed propcll'T involves much |(.Ss work in cons' ruc- tion and is stronger at the buss.
Kl(i. 11
////. erence, or the disturbinj; actio'i which
any one blade e\ert> upon the air dealt with by any olhev. i> a matter abotii which little is yet known. The following siiir- L;c-tion is put forward merely as afl'ordini; a rou.irh yuidc in design.
Kc\(i'iini: |i> comparison with the airplane. IIIO\I.IL; in a continuous -' rai^lit line, we may look upon the blade- of a propeller a.- -upcrpo.-ed aerofoils which travel in a helical path. Assume that the- thickness of air -iralum affected by the blade is a constant proportion of the blade width at any point. Then we may write (Kin. Ill
NOTES ON AERIAL PROPELLERS
133
EO = PO cos A = ^ cos A. n
(n = No. of blades). Let blade width at point = b, and put, according to above
SO
assumption, — j^- = m.
Then l> must lie less than
m X '•'
cos .A.
If we now plot a curve where abscissa represent radii, or /• /i, . and whose ordinates are the calculated values o;
m X '
cos A, we shall arrive at what we call the limit curve, and the linear curve should at all points lie within this if there is to be no interference. Such a curve has been plotted for the case ni l he propeller already mentioned, and is shown in Fig. 12.
15-
|
- |
^^ |
Eforfej |
Limit |
Curve |
\ |
|
|
. — • — • ( :- ear |
Grading |
-C«rve |
^ |
|||
|
I.- , _," ji'0" f-u" 3 |
4" 4'U"f>'ldnis |
FIG. 12
N//VJ////;/ of Blade. — Having now indicated l he method of fixing the sizes of a propeller in order to satisfy •riven mechanical and aerodynamical conditions, it would ap- pear desirable to devote a little attention to the actual con- structional design. The following remarks are made with ivt'ei-enre io ilie usual type of wood propeller, though the man- ner ol procedure is quite general whatever the material iidopte:!. The process is essentially one of trial and error. The extreme radius of the Made beiiij;' known, a number of sections are decided upon, say (j or 8 inches apart, and the blade angles at these points computed. The linear grading curve will now provide us with the necessary blade widths, anil it is only I'r-sary to set these down at their proper projection in order to determine the true plan form. The di -intuition of the width, however, about a line lluough the centre of the blade root has yet to lie discussed. It is usual in deMun so to shape the blade that twisting ac- tion is either greatly minimized, or eliminated altogether, and for this reason a symmetrical plan form is undesirable. Fig. 13 will explain this point.
A number of preliminary liial blade.' sec- tions must now be sketched out, and previous examples ol similar design will act as a good guide as to the thicknesses required. The next point is to estimate the strength of the blade, and the stresses to which this is subjected must be divided into (1) Centrifugal, (2) Bending. These are to be treated separately and then added together.
(1) Cent :•/ f>ii/nl Stresses. — It has been found convenient lo write out the calculations in column form as follows :
13
|
c |
c |
8 |
g |
I |
I |
|||||
|
section. |
>f clt-iw |
1 |
section |
"o "3 |
i |
"S |
§ |
•2 II |
|J |
E en |
|
<M |
. |
« |
0 |
-~ |
- |
0 |
x -? |
'E - |
01 |
~ " |
|
. |
s |
t |
A |
1 |
r- |
•*~T |
1 |
^ 7 |
||
|
E |
B |
[c |
v c |
" - |
||||||
|
7. |
z |
< |
Z-. |
* = |
O o |
O o |
O e |
|||
|
lb». sq. |
||||||||||
|
feet. |
sq.cm. |
cm. |
sq. c-m. |
cu.cm. |
Ibs. |
Ibs. |
if,, |
inch. |
||
|
1 |
A |
1.0 |
44 |
20.3 |
44 |
893 |
1.1 |
635 |
424S |
620 |
|
2 |
B |
1.67 |
44 |
20.3 |
40.5 |
822 |
1.01 |
970 |
3610 |
530 |
|
3 |
C |
2.33 |
37 |
20.3 |
31.5 |
640 |
0.79 |
1060 |
2640 |
460 |
|
4 |
D |
3.00 |
26 |
20.3 |
21 |
426 |
0.52 |
895 |
1580 |
390 |
|
5 |
E |
3.67 |
16 |
20.3 |
11 |
223 |
0.28 |
590 |
685 |
275 |
|
6 |
K |
4 . 1 1'.", |
6 |
7.6 |
4 |
31 |
0.04 |
95 |
95 |
102 |
3.74 4245
NOTE. — In CDrupJtin; weignt of eleaunts, cm, (cm)?, and (cm)3 were em- ployed. This is m^rsly a matter of convenienc3, the weights being obtained in In. nnd streams calculated in Ibs. per square inch.
Bending Stresses. — (See Figs. 14, 15, 16.-)
In order to determine the bending stress, a bending moment
FIG. 14
Load Grading Diagram
FIG. 15
3 4
FIG. 16
diagram for the blade is first drawn, and it will usually be found good enough to assume all the loading uniplannr. Ta:; ing each of the elements A, B, C, D, E and F, estimate the lo id on each from the load grading diagram thus :
|
~ |
- '" •; |
= 0 |
i |
|||||
|
D |
""•c |
I |
||||||
|
.£ |
i « |
c "-^ It-1 |
~ - 7.2 1 •-- |
.-; = "t |
= '-_ |
i |
||
|
». J |
||||||||
|
* |
D |
<- ^ i" |
t l_ |
'"c-— |
'~ i |
n |
!* ; |
|
|
Y. |
^ E - |
jl r. |
u |
i ~ ^r |
|| |
= ,~ |
^ ~ Z-- |
if |
|
1 |
A |
1.40 |
2.56 |
0 275 |
12 5 |
4 5 |
12 |
1150 |
|
2 |
B |
4 . 34 |
7 '!") |
0.45 |
ao.s |
99 |
1«X> |
|
|
S |
C |
8.06 |
14.75 |
L'T L1 |
313 |
|||
|
4 |
D |
11.78 |
21 55 |
0.79 |
36.0 |
604 |
1080 |
|
|
." |
I |
11.78 |
•J.\ 55 |
0 <»7 |
44.3 |
783 |
1000 |
|
|
— |
F |
•2 ill |
5 38 |
1.07 |
48.8 |
48.8 |
220 |
|
|
T t:.l 40. .'i |
7;; 7t |
2031 |
— |
m
NOTES ON AERIAL PROPELLERS
bending moments MI each of the sections 1, 2, 3, 4, 5 im<l
Btnd/ng Moment L B. Inohia 2031 —
FIG. 17
6 are now known, and the moduli of the sections are to be computed either graphically or by dividing up into parts and estimating for each part.
Then
Bending moment on section
= Stress due to bending.
Modulus of section The sum of centrifugal and bending stresses at each section will then be the maximum skin stress to which the section is subjected. (See table.)
|
Section |
. |
2 |
3 |
4 |
5 |
|
Centrifugal strcso. llw. s<|. inch. . Bending strew. the. sq. inch |
620 1150 |
530 1000 |
460 1050 |
390 1080 |
275 1000 |
|
Total stress . |
1770 |
1330 |
1510 |
1470 |
IL'7.-, |
Materials and Stresses.— Walnut, Honduras, mahogany and spruce are the best materials for a wood propeller, and wal- nut, though the heaviest, is probably the best of the three, since mahogany is more inclined to warp, and spruce is rather weak in tension. The ultimate tensile strength of walnut and ma- hogany is about 4 tons per sq. in. (though, of course, it varies considerably), so that a working load of 2,000 Ib. pur sq. in. may be considered fairly safe. As a matter of fact, in order to insure good jointing and provide the required stiffness when in action, the best working figures are found to be l,(iOO to 1,800 Ib. per sq. in. for walnut and mahogany, and 800 Ib. per sq. in. for spruce. These figures arc for the root where the materials are most highly stressed.
Having strengthened up the sections satisfactorily, the next process is to arrange the lamination and "fair up" the eon- tours. For glueing purposes the thickness of the laminas should be in the neighborhood of 1 inch (except in very small propellers). It will usually be found on setting out the con- tours that it is impossible to draw a fair eurve through the series of point* obtained primarily- -the blade sect mns must he
revised until tliis can be done. Probably the best method is first to draw a smooth curve to lie evenly between the contour points and then reset out the sections to suit.
Before leaving the discussion of blade strength, it may be advisable to say a word or two as to the conditions governing the employment of thick and thin blades. In the case of a very fast running propeller in which the thrust is comparatively small, the stress produced by centrifugal action alone is a large proportion of the total, and no advantage is gained by unduly thickening up the sections. This will be evident where we con- sider that an increase in sectional area means a proportional increase in weight, and therefore in centrifugal force, the centrifugal stress remaining constant. On the other hand, a slow-moving propeller with a big thrust requires the reverse treatment. A large proportion of the total stress is now due to bending action, while the centrifugal stress is of minor im- portance. Hence a fairly thick blade section now becomes advantageous.
NOTES ADDED JUNE, 1912. — More recent experiments have afforded us the following additional data:
Eiffel's Experiments show — (1) that for different shapes of section the best angle of attack remains constant. (In the par- ticular case given it was 5°.) This would indicate the inad- visability of employing a variable angle of attack, unless it be found that very high velocity has a big effect.
(2) That the best gliding angle varies a little. For the effective portion of the blade this variation is not great. The mean value was 6°.
(3) That the lift constant varies somewhat (as one would expect) for the different sections.
The yatintidl Phj/sical Laboratory Experiments are valuable so far as ordinary aerofoil experiments can be applied to propeller design (and these are practically all we have to go upon at present). They indicate the advantage of employing a thin section. Strength considerations, however, forbid this in the case of wood, and we are thus led to the serious considera- tion of metal construction.
Effect of Plan Form ii/mn Kflici<-m->i. — Purely mathematical treatment has led to the conclusion that very little is to be ex- pected in the direction of effect of plan form upon efficiency. The two cases which have been treated are —
(a) Triangular developed plan form with apex at blade tip.
(b) Triangular developed plan form with base as tip.
The integration is cumbersome and is not given here. It was found that the total efficiency of the propeller could be repre- sented very approximately by the expression
1
where
1 -f- A' tan (i cot 0
K = a constant depending upon plan form.
ti = gliding angle of section adopted.
8 = angle of effective helix at tip of blade.
an I cot 0 =
Kit
where l> =- diameter, and //, cfl'ectivc pitch.
K was found to be about 0.6 in case (a) and 0.8 in case (b).
Thus as a first approximation for the efficiency of a propel- ler we may use the formula
1
1 -(- 0.7 tan (1 cot 0
The results given by this will be found to agree, very well with those obtained from the diagrams.
Addenda
Summary of Procedure in Design
Data initially required: —
Horse Power and r.p.m. of engine. Estimated speed of aeroplane or dirigible. Number of blades required.
1. Fix diameter of propeller. This should usually be as large as the general design will allow. It is here assumed that the propeller is direct driven from the engine. If geared down, the speed of rotation will first have to be decided upon. Experience is the only guide as to what this can conveniently be for the weight at our disposal.
2. Calculate effective pitch (pe) and angles of effective helix (A) at suitably chosen radii. Tabulate these and augment each by angle of attack (say 4 degrees).
3. Decide upon the general developed plan form of blade. Here again experience will help us. A blade which tapers towards the tip has greater efficiency and has its material better distributed to withstand stresses than one with full tip. Plot linear grading curve.
4. Plot pressure (Ibs. per sq. ft.) curve, remembering that this is proportional to l/sin2^ (Scale at first quite immaterial).
5. Lay out load grading curve by multiplying ordinates of (3) and (4).
6. Lay out thrust grading curve. This is obtained by multi- plying ordinates of (5) by cos (A -(- G) where G = gliding angle for particular section to be adopted.
7. Calculate values of tan A/tim. (A -\- G) for various radii and plot efficiency curve.
8. Compute total efficiency of blade from above curve and Ilirust grading diagram.
t). Calculate total thrust and then thrust per blade, knowing horsepower of engine, total efficiency, and velocity of advance.
10. Obtain scales of diagrams and thus true blade widths at various radii.
11. Plot " limit " curve for blade width to ensure no inter- ference.
12. Lay out preliminary blade sections at correct angles and subsequently projected plan form of blade, having regard to
Flat Working Space
FIG. 18
elimination of " twist." A good form of section is shown in Fig. 18.
13. Investigate strength of various sections, finding first centrifugal, and then bending stresses, afterwards summing to obtain total. Do not exceed stress at root of about 1,800 Ibs. per sq. in. in case of walnut or mahogany, "and 800 Ibs. per sq. in. for spruce.
14. Set down blade laminations and plot contours. The thickness of laminations should be about %" to 1" in ordinary propellers (say about 8 to 9 ft. diameter) and the contours should be smooth continuous curves. Adjust sections judici- ously until correct.
15. Design boss and run blade root into boss by suitable curves. It is advisable also to lay out a blade section quite close to the boss. In this part of the blade the chosen form of section will usually have to be departed from, but this is not a serious matter. The angles of such sections, however, should not be less than the corresponding effective helix angles.
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29 1949 /'
MAR311950\ 1950
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