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EXPERIMENTS
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AHRODYNAMICs.

Ss P. LANGLEY.

SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE.

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HXPERIMENTS

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CITY OF WASHINGTON :
PUBLISHED BY THE SMITHSONIAN INSTITUTION.
1891.

COMMISSION TO WHOM THIS MEMOIR HAS BEEN REFERRED.

Professor Simon Newcoms, U.S. N. .
Professor Henry A. Rowianp.

Professor CLrevELAND ABBE.

PRINTED BY
JUDD & DETWEILER.

;
CONTENTS.
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(111)

PREFACE.

If there prove to be anything of permanent value in these investigations, I
desire that they may be remembered in connection with the name of the late
William Thaw, whose generosity provided the principal means for them.

I have to thank the board of direction of the Bache fund of the National
Academy of Sciences for their aid, and also the trustees of the Western Uni-
versity of Pennsylvania for their permission to use the means of the observatory
under their charge in contributing to the same end, and I desire to acknowledge
especially the constant and valued help of Mr. Frank W. Very, who has assisted
me in all these experiments, and my further obligation to Mr. George E. Curtis,

who has most efficiently aided me in the final computations and reductions.

CHAPTER I.
LIN 10183) 1D) WW) CHAO) YE

Schemes for mechanical flight have been so generally associated in the past
with other methods than those of science, that it is commonly supposed the
_long record of failures has left such practical demonstration of the futility of all
such hopes for the future that no one of scientific training will be found to give
them countenance. While recognizing that this view is a natural one, I have,
however, during some years, devoted nearly all the time at my command for
research, if not directly to this purpose, yet to one cognate to it, with a result
which I feel ought now to be made public.

To prevent misapprehension, let me state at the outset that I do not undertake
to explain any art of mechanical flight, but to demonstrate experimentally certain
propositions in aerodynamics which prove that such flight under proper direction
is practicable. This being understood, I may state that these researches have
led to the result that mechanical sustentation of heavy bodies in the air, com-
bined with very great speeds, is not only possible, but within the reach of mechan-
ical means we actually possess, and that while these researches are, as I have said,
not meant to demonstrate the art of guiding such heavy bodies in flight, they do
show that we now have the power to sustain and propel them.

Further than this, these new experiments, (and theory also when reviewed
in their light,) show that if in such aerial motion, there be given a plane of fixed
size and weight, inclined at such an angle, and moved forward at such a speed,
that it shall be sustained in horizontal flight, then the more rapid the motion is,
the less will be the power required to support and advance it. This statement
may, I am aware, present an appearance so paradoxical that the reader may ask
himself if he has rightly understood it. To make the meaning quite indubitable,
let me repeat it in another form, and say that these experiments show that a
definite amount of power so expended at any constant rate, will attain more
economical results at high speeds than at low ones—e. g., one horse-power thus
employed, will transport a larger weight at 20 miles an hour than at 10, a still
larger at 40 miles than at 20, and so on, with an increasing economy of power
with each higher speed, up to some remote limit not yet attained in experiment,
but probably represented by higher speeds than have as yet been reached in
any other mode of transport—a statement which demands and will receive the

amplest confirmation later in these pages.
(3)

4 EXPERIMENTS IN AERODYNAMICS.

I have now been engaged since the beginning of the year 1887 in 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 the
air, and I desire to repeat my conviction that the obstacles in its way are not
such as have been thought; that they lie more in such apparently secondary
difficulties as those of guiding the body so that it may move in the direction
desired, and ascend or descend with safety, than in what may appear to be the
primary difficulties due to the nature of the air itself, and that in my opinion
the evidence for this is now sufficiently complete to engage the serious attention
of engineers to the practical solution of these secondary difficulties, and to the
development of an art of mechanical flight which will bring with it a change in
many of the conditions of individual and national existence whose importance can
hardly be estimated.

The way to this has not been pointed out by established treatises on aero-
dynamics, whose fundamental postulates, like those of any other established
science, may be held to contain implicitly all truths deducible from them, but
which are so far from being of practical help here, that from these postulates
previous writers of the highest repute have deduced the directly opposite con-
clusion, that mechanical flight is practically impossible.* Reason unaided by
new experiment, then, has done little or nothing in favor of the view now taken.

It may be asked whether it is not otherwise with statements which are
authorized by such names as that of Newton, and whether a knowledge of truths
mathematically deducible from them, would not at any rate furnish a test to
distinguish the probably true from the probably false; but here it is important
to remember that the mathematical method as applied to physics, must always
be trustworthy or untrustworthy, according to the trustworthiness of the data
which are employed; that the most complete presentation of symbols and pro-
cesses will only serve to enlarge the consequence of error hidden in the original
premises, if such there be, and that here, as will be shown, the error as to fact
begins with the great name of Newton himself.

In this untrodden field of research, which looks to mechanical flight, not by
means of balloons, but by bodies specifically heavier than the air in which they
move, I think it safe to say that we are still, at the time this is written, in a
relatively less advanced condition than the study of steam was before the time
of Newcomen; and if we remember that such statements as have been com-
monly made with reference to this, till lately are, with rare exceptions, the product
of conjecture rather than of study and experiment, we may better see that there
is here as yet, no rule to distinguish the probably important from the probably
unimportant, such as we command in publications devoted to the progress of
already established sciences.

*See paper by Guy-Lussac and Navier, cited later.

INTRODUCTORY. oD

There is an excellent custom among scientific investigators, of prefacing the
account of each new research with an abstract of the work of those who have
already presumably advanced knowledge in the science in question; but in this
case, where almost nothing is established, I have found hardly any test but that
of experiment to distinguish between those suggestions presumably worth citation
and attention and those which are not. Since, then, it is usually only after
the experiments which are later to be described have been made, that we can
distinguish in retrospective examination what would have been useful to the
investigator if he could have appreciated its true character without this test, I
have deferred the task of giving a résumé of the literature of the subject until it
could be done in the light of acquired knowledge.

TU have thus been led to give the time which I could dispose of, so exclusively
to experiment, that it may well be that I have missed the knowledge of some
recent researches of value; and if this be so, I desire that the absence of mention
of them in the present publication, may be taken as the result, not of design, but
of an ignorance, which I shall hope, in such case, to repair in a later publication ;
while, among the few earlier memoirs that I am conscious of owing much useful
suggestion to, it is just that I should mention a remarkable one by Mr. Wenham,
which appeared in the first number of the London Aeronautical Society’s report,
24 years ago, and some by Penaud in L’ Aeronaute.

The reader, especially if he be himself skilled in observation, may perhaps
be willing to agree that since there is here so little yet established, so great a
variety of tentative experiments must be made, that it is impossible to give each
of them at the outset all the degree of accuracy which is ultimately desirable, and
that he may yet find all trustworthy within the limits of their present application.

I do not, then, offer here a treatise on aerodynamics, but an experimental
demonstration that we already possess in the steam-engine as now constructed, or
in other heat engines, more than the requisite power to urge a system of rigid
planes through the air at a great velocity, making them not only self-sustaining,
but capable of carrying other. than their own weight. This is not asserting
that they can be steadily and securely guided through the air, or safely brought
to the ground without shock, or even that the plane itself is the best form
of surface for support; all these are practical considerations of quite another
order, belonging to the yet inchoate art of constructing suitable mechanisms
for guiding heavy bodies tirough the air on the principles indicated, and
which art (to refer to it by some title distinct from any associated with bal-
looning) I will provisionally call aerodromics.* With respect to this inchoate
art, I desire to be understood as not here offering any direct evidence, or

¥ > - L : Seen Na = :
* From dzpodpopew, to traverse the air; dspo0por0g, an air-runner.

6 EXPERIMENTS IN AERODYNAMICS.

expressing any opinion other than may be implied in the very description of
these experiments themselves.

It is just to say, finally, in regard to the extreme length of time (four years)
which these experiments may appear to have taken, that, beyond the fact of their
being in an entirely new field, nearly all imply a great amount of previous trial
and failure, which has not been obtruded on the reader, except to point out
sources of wasted effort which future investigators may thus be spared, and that
they have been made in the intervals of quite other occupations, connected with
administrative duties in another city.

CHAPTER II.
CHARACTER AND METHOD OF EXPERIMENTS.

The experiments which I have devised and here describe, are made with one
specific object, namely, to elucidate the dynamic principles lying at the basis of
the aerial mechanical flight of bodies denser than the air in which they move, and
I have refrained as a rule from all collateral investigations, hewever important,
not contributing to this end. These experiments, then, are in no way concerned
with ordinary aeronautics, or the use of balloons, or objects lighter than the air,
but solely with the mechanical sustentation of bodies denser than the air, and the
reader will please note that only the latter are referred to throughout this
memoir when such expressions as “planes,” “models,” “mechanical flight,”
and the like, are used.

The experiments in question, for obtaining first approximations to the power
and velocities needed to sustain in the air such heavy inclined planes or other
models in rapid movement, have been principally made with a very large
whirling table, located on the grounds of the Allegheny Observatory, Allegheny,
Pa. (lat. 40° 27’ 41.6”; long. 5° 20" 2.93°; height above the sea-level, 1,145 feet).

The site is a hill on the north of the valley of the Ohio and rising about 400
feet above it. At the time of these observations the hill-top was bare of trees
and of buildings, except those of the observatory itself. This hill-top is a plane
of about three acres, of which the observatory occupies the south side. The
ground slopes rapidly both toward the east and west, the latter being the quarter
from which come the prevailing winds.

The general disposition of the grounds of the observatory buildings, of the
engine, and of the whirling table is shown in plate I. The whirling table is
shown in plate II, in elevation and in plan, and with details on an enlarged scale.
It has been constructed especially in view of the need of getting the greatest
continuous speed thus attainable, under circumstances which should render
corrections for the effects of circular motion negligible, in relation to the degree
of accuracy aimed at.

The first disturbing effect of circular motion to present itself to the mind of
the reader will probably be centrifugal force; but in regard to this he may observe
that in all the pieces of apparatus hereafter to be described, the various parts are
so disposed that the centrifugal force proper, viz., the outward thrust of the plane

(7)

8 EXPERIMENTS IN AERODYNAMICS.

or model which is the subject of experiment, shall not disturb or vitiate the
quantitative data which are sought to be obtained.

On the other hand, the effects of circular motion, as regards the behavior of
the air in its enforced circulation, are only to be obtained, as I believe, empir-
ically, and by very elaborate experiments; the formule that are likely to
present themselves to the reader’s mind for this computation, largely involving
the very errors of fact which the experiments here described are meant to
correct. This class of corrections is, then, only approximately calculable, and
we have to diminish their importance by the use of so large a circle that the
motion can be treated as (for our purpose) linear. To show that these corrections
are negligible in relation to such degree of accuracy as we seek, we may advan-
tageously consider such a numerical example as will present the maximum error
of this sort that obtains under the most unfavorable circumstances.

Let this example be the use of a plane of the greatest length hereafter
described in these experiments, viz., 30 inches, and let us suppose its center to be
at the end of a revolving arm 30 feet in length, which was that employed.

Let us suppose the plane to be so disposed as to cause the effect of the
inequality of air resistance arising from the circular motion to be a maximum,
which will presumably be the case if it is placed parallel to the arm of the whirling
table, so that there is also presumably the greatest possible difference between the
pressure on the outer and the inner half. Under these circumstances it is assumed
in the experiments detailed in the following chapters, that the whole plane may
be treated as moving with the linear velocity of its center, and it will be now
shown that this assumption is permissible. The portions of the plane as we pro-
ceed outward from the center, are exposed, on the whole, to a greater pressure,
and as we proceed inward to the center to a less. Using, in the absence of
any wholly satisfactory assumption, the well-known one implicitly given by New-
ton in the Principia, that the pressure of the air at every point of the plane is
strictly proportional to the square of the velocity with which it is moving (thereby
neglecting the secondary effect of the mutual action of the stream lines on each
other), the pressure at the inner end of the plane is proportional to (282)°= 826.6 ;
at the outer end to (314)*= 976.6, and at the center to (30)*=900. The mean of
these pressures at the inner and outer ends, viz., 901.6, differs from the pressure
at the center by 1.6, or less than one-fifth of one per cent., and a@ fortiori the inte-
grated pressure over the whole area in this and still smaller planes, differs from
the pressure computed with the velocity at the center, by less than the same amount.
The example will, it is hoped, make it sufficiently clear that such disturbing
effects of air-pressure arising from circular motion, are for our purposes negligible,
and the precautions taken against other detrimental effects, will be evident from a
consideration of the disposition of the apparatus employed in each case.

CHARACTER AND METHOD OF EXPERIMENTS. 9

Most of the various experiments which I have executed involve measure-
ments of the pressure of air on moving planes,* and the quantitative pressures
obtaining in all of these experiments are of such magnitude that the friction of
the air is inappreciable in comparison. This fact may be stated as the result,
both of my own experiments (which are here only indirectly presented) and of
well-known experiments of others.+ It will be seen that my experiments implicitly
show that the effect of friction on the surfaces and at the specds considered is negli-
gible, and that in them I have treated the actual air-pressure as being for practical
purposes normal to the surface, as in the case of an ideal fluid.

The whirling table consists essentially of two symmetrical wooden arms, each
30 feet (9.15 meters) long, revolving in a plane eight feet above the ground. Each
arm is formed of two continuous parallel strips united by struts as shown in the
plate, and is made at once broad and thin, so as to possess the requisite lateral
strength, while opposing as little resistance to the air as possible, its vertical
rigidity being increased by guys. The arms are accordingly supported by iron
wires extending from a point in the axis about 8 feet (2.5 meters) above the table.
An enlarged section of the lower end of the axis is given in the plate, showing the
lower bearing and the position of the bevel-wheels connected with the shaft, which
is driven by the engine. A lever is also shown, by means of which the table may
be lifted out of its gearing and revolved by hand. The gearing is so disposed
that the direction of rotation is always positive—i. e., clockwise to one looking
down on it. The whirling table was driven first by a gas-engine of about 14 horse-
power, but it was found inadequate to do the work required, and, after October
20, 1888, a steam-engine giving 10 horse-power was used in its stead. This
was a portable engine of 10-inch stroke, having a fly-wheel giving from 60 to
150 revolutions per minute, but ordinarily run at about 120 revolutions, with 90
pounds of steam. The belt of either engine communicates its motion to a set of
step-pulleys, by means of which four different velocity-ratios can be obtained.
These pulleys turn a horizontal shaft running underground to the axis of the
turn-table, as indicated on the ground plan of the engine-house at A, and also

* Since it is impossible to construct absolutely plane surfaces at once very thin and very rigid, those “ planes ”
in actual use have been modified as hereafter described. They have all, howeyer, it will be observed, square and
not rounded edges, and it should be likewise observed that the values thus obtained, while more exactly
calculable, give less favorable results than if the edges were rounded, or than if the section of the plane were
such as to give “stream lines.”

{ There is now, I believe, substantial agreement in the view that ordinarily there is no slipping of a fluid
past the surface of a solid, but that a film of air adheres to the surface, and that the friction experienced is
largely the internal friction of the fluid—i. e., the viscosity. Perhaps the best formula embodying the latter is
given by Clerk Maxwell in his investigation on the coéfficient of the viscosity of the air. This is » =0.0001878
(1 + .€027 0), » and @ being taken as defined in his paper on the dynamical theory of gases in Phil. Trans., Vol.
civu. By this formula the actual tangential force on a one-foot-square plane moying parallel to itself through
the air at the rate of 100 feet a second is 1,095 dynes (0.08 poundals), or less than =; of 1 per cent. of the pressure
on the same plane moving normally at this speed, and hence theory as well as observation shows its negligibility.
2

10 EXPERIMENTS IN AERODYNAMICS.

on the elevation at A’, where it is shown as geared to this vertical axis by a pair
of bevel-wheels, that of the shaft having 15 teeth and that of the turn-table axis
having 75 teeth, or 1 to 5. The cone-pulleys used from the beginning of the
experiments up to September, 1890, have four steps with diameters of 214, 18+,
118, and 8 inches. The speeds given by these pulleys in terms of whirling-table
revolutions for 1,000 revolutions of the gas-engine are approximately—

MOwestiSpeedstc.yerateiveracit chek ciate MOE ae 25
SECOmds’ AS | see sissay recsyet lose vaste tore er ansneas erecta ee 50
SPIT Pye Sx Secasceme et otere ec roye sven ateaeyee area eee tee 100
1 hited o¥ers| Neetemm Peet crcer ocr ater coke camrerar cers er 200

The gas-engine speed varied from 180 to 190 revolutions per minute.

In September, 1890, the above-described pulleys were replaced by a larger
set of three steps, having diameters of 36, 252 and 18 inches, respectively, which
give speeds in the ratio of 4, 2, and 1, and the gear, which had broken, was
replaced by a new one of 1 to 4.

This system gives for 120 revolutions of the steam-engine per minute,
driving—

18 in. pulley, 48 revolutions of turn-table per minute = 100 + miles per hour at end of arm.
BBN Ha : 4 8 =50 + « « eee
26 gion er ato g : g = fo eae

By regulating the speed of the engine any intermediate velocities can be
obtained, and thus the equipment should be susceptible of furnishing speeds
from 10 to 100 miles per hour (4.5 to 45 meters per second); but owing to the
slipping of belts the number of turn-table revolutions was less than this for
the higher velocities, so that the highest attained in the experiments did not
reach this upper limit, but was a little over 100 feet (30 meters) per second, or
about seventy miles per hour. The precise velocity actually attained by the
turn-table is determined, quite independently of the speed of the engine, by an
electrical registration on the standard chronograph in the observatory. The
electrical current passes into four fixed contact-pieces (shown at O-P, plate II,
and on large scale in plate III) fastened to a fixed block placed around the
axis of the whirling table, these fixed pieces being placed symmetrically around
the axis, while another platinum contact-piece is fastened to a horizontal arm
screwed into the axis of the turn-table and revolving with it, thus “ making
circuit ” every quarter revolution of the table. The current passes out of the axis
through a brush contact, shown in plate III, and thence to the chronograph in the
observatory. C designates the fixed contact pieces, and P the platinum piece
revolving with the axis. Sand L are adjusting screws. Turning again to plate
II, an additional brush contact, shown at B, and again at BY’, serves to transmit

CHARACTER AND METHOD OF EXPERIMENTS. 11

a current to wires running out to the end of the whirling arm, so that seconds
from the mean time clock and other phenomena can be registered on the recording
cylinder of the dynamometer chronograph at the end of the arm; and also
phenomena taking place at the end of the arm can be registered on the chrono-
graph in the observatory. By these means the experiments are put under
electric control and perfect knowledge is obtained of the velocity of the turn-
table at the moment when any phenomenon occurs. This brush contact was
made sufficiently large and heavy to transmit a current from a dynamo to an
electric motor placed on the whirling arm, and, having this electric equipment
extending to the outer end of the whirling arm, different pieces of apparatus
were devised for registering pressure and other phenomena there.

The whirling table was thus established and the experiments conducted in
the open air, not through choice, but because the erection of a large building
specially designed for them was too expensive to be practicable. It was hoped
to take advantage of calm days for the performance of experiments, as in a calm,
a whirling table in the open air is under the best possible conditions, for in a
confined building the rotating arm itself sets all the air of the room into slow
movement, besides creating eddies which do not promptly dissipate. Practically,
however, these calm days almost never came, and the presence of wind currents
continued from the beginning to the end of the experiments, to be a source of
delay beyond all anticipation, as well as of frequent failure.

In the latter part of April, 1889, an octagon fence 20 feet high (shown on
plate I) was erected around the whirling table with the object of cutting off, to
some extent, the access of the wind. This, however, proved to be ineffectual, and
the difficulty experienced from the wind continued nearly unabated.

If any one should propose to repeat or extend these experiments, I would
advise him, first of all, and at all costs, to establish his whirling table in a large,
completely inclosed building.

CHAPTER III.

THE SUSPENDED PLANE.

The first instrument, called the Suspended Plane, was devised to illustrate
an unfamiliar application of a known principle. I call the application “ un-
familiar”? because distinguished physicists have held, for instance, that a bird
(which obviously expends a certain amount of muscular effort in simply hovering
in the air) must expend in flight all the effort required for hovering, together
with so much additional energy as is required to overcome the resistance of
the air to its horizontal motion, so that the energy expended increases with the
velocity attained,* while the consideration of the action of the suspended plane
indicates, if it do not demonstrate, that the opposite view is the true one, and
thus serves as a useful introduction to the demonstrative experiments I have
spoken of as coming later.

* This view of flight received indorsement from a source of the highest authority in a report by Gay-Lussac,
Flourens, and Navier, accepted and published by the Institute of France in 1830. [Navier, C. L. M. H.—Rapport
sur un Mémoire de M. Chabrier concernant les moyens de yoyager dans l’air et de s’y diriger, contenent une
nouvelle théorie des mouvements progressifs. (Commissaires, MM. Gay-Lussac, Flourens, et Navier, rapporteur.)
Paris, Mém. Acad. Sci. x1, 1832 (Hist.), pp. 61-118.] The report is drawn up by Navier, to whom the mathe-
matical investigation is due. He formulates the differential equations of motion for the two cases of hovering
and horizontal flight, integrates them in the customary way, assumes approximate values for the constants of
the equations, and computes the work expended by an ordinary swallow with the following results: For
hovering, the work done per second by the swallow is approximately equal to the work required to raise its own
weight eight meters. While in horizontal flight the work done varies as the cube of the velocity, and for 15
meters per second is equal to 5.95 kilogrammeters per second, or enough to raise its weight 390 meters. This
is fifty times as much as that expended in hovering, or in English measures, over 2,500 foot-pounds per minute,
which is a rate of working greater than a man has when lifting earth with a spade.

The same computation applies to any larger bird whose weight bears the same ratio to the extent of its
wings. In view of these figures Nayier suggests that there exists the same ratio between the efforts necesssary for simple
suspension and for rapid flight as exists for terrestrial animals between the effort required for standing upright and that
required for running. [Nous remarquerons la grande différence qui existe entre la force nécessaire pour que l’oiseau
se soutienne simplement dans lair, et celle qu’exige un mouvement rapide. Lorsque la vitesse de ce mouvement
est de 15™ par seconde, on trouve que cette derniére force est environ cinquante fois plus grande que la premiere.
Ainsi l’effort qu’exerce l’oiseau pour se soutenir dans lair est fort petit comparativement 4 effort qu’il exerce
dans le vol. Il en coute peut-étre moins de fatigue 4 l’oiseau pour se soutenir simplement dans l’air, eu égard a
la fatigue qu’il est capable de supporter, qu’il ne’en cofite 4 Yyhomme et aux quadrupédes pour se soutenir debout
sur leurs jambes.”—Paris, Mém. Acad. Sci. x1, 1832 (Hist.), p.71.] The supposed elegance and validity of
Nayier’s mathematical processes, and especially the elaboration with which they were carried out, appears to
have obscured the absolutely inadmissible character of these results, and they received the unqualified adherence
of the remainder of the committee. This report thereupon became a standard authority upon the theory of

flight, and continued to be so accepted for many years.
(12)

THE SUSPENDED PLANE. 13

The suspended plane (plate IV) consists of a thin brass plane one foot square,
weighing two pounds, hung vertically by a spring from a surrounding frame.
Eight delicate friction rollers AA’, BB’ enable the plane to move freely along
the frame, but prevent any twisting or lateral motion, the use of the guide-frame
being to prevent the plane from so “ flouncing ” under irregular air currents that
its pull cannot be measured. The guide-frame carrying the plane turns symmet-
rically about an axis, CC’, so that the gravity-moment about the axis is simply
the weight of the plane on a lever arm measured from its center. The axis
CC’ rests upon a standard which is placed upon the whirling arm. A pencil, P,
attached to the plane is pressed by a spring against a registering card at the side
of the plane and perpendicular to it. The card contains a graduated are whose
center is at C and whose zero angle is under the pencil point at the vertical
position of the plane. The distance of the trace froin the center C registers
the extension of the spring.

When the plane is at rest the extension of the spring measures the weight
of the plane. When the plane is driven forward horizontally the pressure of
the wind on the plane inclines it to an angle with the vertical, and the higher
the speed the more it is inclined. [or any position of equilibrium there is
neither upward nor downward pressure on the guide-frame, and the whole
resulting force acting on the plane, both that of gravity and that arising from the
wind of advance, is borne by the spring.

The apparatus being mounted at the end of the arm of the large whirling
table and being still, the weight of the plane is registered by an extension of
the suspending spring corresponding to two pounds. Next, lateral motion being
given (from the whirling table) and the plane being not only suspended but
dragged forward, the spring is seen not to be extended further, but to contract,
and to contract the more as the speed increases. The drawing contains a copy
of the trace made by the pencil upon the recording sheet, showing how the
spring contracts with the increasing angles of the plane with the vertical, where
these angles correspond to increasing velocities of translation, or, we may almost
say, to increasing speeds of flight. The experiment also calls attention to the
fundamental circumstance that in the horizontal flight of an aeroplane increasing
speeds are necessarily accompanied by diminishing angles of the plane with the
horizontal.

The experiment may perhaps be held to be superfluous, since the principle
involved, that the pressure of a fluid is always normal to a surface moving in it,
is already well known; but we must distinguish between the principle and its
application. Though when attention is called to it, the latter is seen to be so
immediate a consequence of the principle as to appear almost self-evident, I must
still call the application “ unfamiliar” since, as will be seen, it indicates the way

14 EXPERIMENTS IN AERODYNAMICS.

to consequences Which may appear almost paradoxical, such as that in horizontal
frictionless flight, the greater the speed, the Jess the power required to maintain it.
I do not mean that this illustration as here given, offers a satisfactory demonstration
of this last consequence, but that any one who has really always possessed the
idea that the experiment suggests, in its full import, must have been inclined to
admit the possibility that machine flight grows more and more economical of
power as higher speeds are attained—and this is not self-evident.

‘This preliminary apparatus can indeed, with little modification, be used to
demonstrate this fact, but it is actually presented here, it will be noticed, not as
demonstrative, but as illustrative, of the possibility suggested ; a possibility whose
fundamental importance justifies, and indeed demands, the fullest demonstration,
which can be better supplied by apparatus designed to give data of precision for
computing the actual work done in flight at different speeds; data which will be
furnished here subsequently from quite other experiments.

CHAPTER IV.
THE RESULTANT PRESSURE RECORDER.

As preliminary to obtaining the data mentioned at the close of the last
chapter, it is desirable to determine experimentally the direction of pressure of
the air, (since the air is not an ideal fluid such as the theory contemplates,) on an
inclined plane, and to investigate the assumption made by Newton that the
pressure on the plane varies as the square of the sine of its inclination.

The second instrument constructed was, then, for the purpose of obtaining
graphically, the direction of the total resultant pressure on an inclined plane
(in practice a square plane) and roughly measuring its amount.* For this reason
it will be called here the Resultant Pressure Recorder.

DESCRIPTION.

Plate V contains drawings of the instrument. Upon a base-board, BB’, is a
standard, E, carrying an arm, AA’, hung symmetrically in gimbal joints. On
the outer end of the arm a one-foot-square plane (called here the wind plane) is
fastened with a clamp, and a graduated circle assists in setting the plane at
different angles of inclination to the horizon. The extremity of the inner end of
the arm carries a pencil, P, which registers on the surface of a vertical plane, which
is in practice a sheet of diagram paper clamped on the surface FE” of an upright
circular board fixed by a standard to the base-board BB’. The pencil-holder H
fits closely into a ring at the center of a system of four equal radial springs attached
to a circular frame, MM’, projecting immediately in front of the registering
board and concentric with it. This frame MM’ is connected by supports to a
close-fitting ring, which closes around the registering board and serves as a holder
for the diagram sheets which are, as stated, clamped on the face FI” of the cir-
cular board. The radial-spring system and its frame may be rotated about the
registering board, so that the diagram sheet may be rotated in its own plane.
The inner or recording end of the arm is weighted so as exactly to counterpoise
the outer end carrying the wind plane. Hence this plane is virtually weightless,

* Observations of the pressure on inclined planes haye been made by previous experimenters, the first being
by Hutton in the summer of 1788, just 100 years before those about to be recorded. But in the experiments of
Hutton, as well as in most of the later ones, the horizontal component of the pressure on the inclined plane has
been the subject of measurement, while the apparatus about to be described affords a measurement of the total

normal pressure on the plane.
(15)

16 EXPERIMENTS IN AERODYNAMICS.

and when the apparatus is at rest the pencil-point rests in the center of the
radial springs without pressure upon them, but when any force changes this
position of equilibrium it is resisted and measured by the resultant extension of
the four radial springs, shown by a definite departure of the pencil from the
center in a definite direction.

The tension of these springs is determined before the apparatus is mounted
for trial, by rotating the frame MM’ about a longitudinal (imaginary) axis passing
through the centers of the wind plane and registry plane. If the pencil end of
the arm be weighted with (for instance) one pound, it traces out a curve on the
paper corresponding to aone-pound tension in every direction. With two pounds
another and larger curve is described, and so on till the resultant pressure of the
four radial springs are then tabulated for every direction and every pressure
which the wind of advance may later be expected to exercise. These curves are
in practice very nearly circles.

The distance from the pencil to the gimbals is the same as that from the
gimbals to the center of the wind plane, so that the wind pressure, considered as
acting at the center of the plane, has the same lever arm as the pressure
imposed by the extended springs. It should be particularly noted as a con-
sequence of the above-described conditions that, although the wind plane is
perfectly free to move in every direction, it is not free to rotate—i. @., it is
always during this motion parallel to itself.

The only other feature of the construction to be noted is the combination of a
spring and an electro-magnet connected with the recording pencil. The pencil is
held away from the paper by means of the spring until a desired velocity
of rotation of the turn-table is attained, when by means of the electro-magnet the
pencil is released and allowed to record.

The method of using the apparatus is as follows: The wind plane is set at
an angle of elevation a; a disk of paper is placed upon the recording board and
oriented so that a line drawn through its center to serve as a reference line is
exactly vertical. The whirling table is then set in motion, and when a uniform
velocity has been attained a current is passed through the electro-magnet and
the pencil records its position on the registering sheet. Since gravity is virtually
inoperative on the counterpoised plane, the position of this trace is affected by
wind pressure alone and is experimentally shown to be diametrically opposite to
its direction, while the radial distance of the trace from the center is evidently a
measure of: the pressure on the plane. Thus the instrument shows at the same
time the direction and magnitude of the resultant wind pressure on the plane for
each inclination of the plane and for different velocities of the whirling table.
Since the arms of the apparatus are exposed to the wind of rotation, the outer
end, moving with greater velocity than the inner end, will be subject to a slightly

THE RESULTANT PRESSURE RECORDER. 17

greater pressure. Preliminary experiments were therefore made without the wind
plane for detecting this effect, with the result that no sensible difference was
apparent between the pressure on the inner and outer arm, even at the highest
speeds.

On August 25, 1888, the spiral springs were calibrated by hanging weights
of 1, 2, and 3 pounds to the center of the springs and marking the displaced
position of the center when the system was rotated through successive octants in
the manner already described. Experimental circles were drawn through the
system of points, and, the departures of the individval points being very small,
the circles were adopted as the curves giving the relation between pencil excursions
and pressures. From these curves the following table has been constructed :

TaBieE I.
Excursion of trace. Pressure. Excursion of trace. Pressure.
|
Centimeters. Lhs. \Grammes.+ Centimeters. Lbs. \Grammes.
0.28 0.1 45 | 4.45 deGe| 726
0.55 0.2 91 4.73 le | 771
0.82 0.3 136 5.03 1.8 | 816
1.10 OA 181 || 5.33 leo) $62
les 0.5 227 || 5.65 2.0 907
1.64 0.6 PP, 5.98 alll 953
1.92 0.7 318 | 6.29 29) 998
2.20 0.8 | 363. | 6.60 23 | 1043 |
2.47 0.9 408 | 6.91 94 | 1089 |
2.73 1.0 454 TQ, 25 | i134
3.02 net 499 || 7.60 2.6 1179
3.30 if 545 || 7.93 ei 1225
3.59 es 590 8.28 2.8 1270
3.89 1.4 635 8.63 29) 138d5
4.17 ED 680 || 9.00 3.0 1361

After many days of preliminary experimentation, in which the instrument
was gradually perfected by trial in successive forms before being brought to the
condition to which the foregoing description applies, two days’ experiments were
made on August 27 and 28, and a final series on October 4, 1888. These
are presented in detail in the accompanying tables, and consist of sixty-four
separate experiments made with the plane set vertical and at angles varying
between 5° and 45° with the horizon. The mean temperature is obtained from
thermometer readings at the beginning and end of each set of experiments, which
usually continued from one to two hours. The mean wind velocity is obtained
from the readings of a Casella air meter. The apparatus is so placed upon the
whirling arm that the center of the wind plane is nine meters from the axis of
rotation. One registering sheet serves for a group of observations, consisting in

9
o

18 EXPERIMENTS IN AERODYNAMICS.

general of a succession of settings of the wind plane beginning with a setting at
90° and followed by diminishing angles of elevation. At each setting two obser-
vations are usually obtained by turning the register sheet through an angle of
180°. Thus the two traces made at the same setting should lie in a straight
line passing through the center.

The method adopted in reading the traces is as follows: Straight lines are
drawn through the center and the two traces made at each setting of the plane.
The angle is then measured between the trace of the plane at 90° and the traces
corresponding to other settings. The pressure being normal to the plane, these
measured values should be the complement of the angles of elevation at which
the plane is set. It will be seen by inspection of the accompanying tables that
this relation approximately obtains.

Tables I, II], and IV contain all the original data of the experiments and
their reduction. The first columns require no explanation. The fifth column
(Tables II and III) gives the angle measured on the register-sheet between the
radial direction of each trace and the direction of the trace made when the plane
was set vertical. The sixth column gives the measured distance of the trace from
the center, and the seventh gives the results of these extensions converted into

: iP .
pressure on the plane by means of Table I. The column headed £,, — + contains

V,
the results of measurements of pressure on the normal plane expressed in terms
of the coefficient *,, of the equation P—*,, V’, in which V is the velocity of the
plane in meters per second and P the pressure on the plane in grammes per square
centimeter, the subscript m being used to designate units of the metric system.

THE RESULTANT PRESSURE RECORDER.

Experiments with the Resultant Pressure Recorder to determine the resultant pressure, on a square

plane moved through the air with different velocities and different inclinations.

Taste IIl.—Avausr 27, 1888.

S. P. Lanetry, Conducting experiments; F. W. Very, Assisting.

Wind plane, 1 foot square (929 square centimeters) ; center of wind plane, 9 m. from axis of
rotation; barometer, 736 mm.; temperature at 6 p. m., 21°.0 C.; mean wind velocity, 0.52 meters
per second.

Seka eee secrees eS litaae
So eee Ser aell sey ol aoe Meee Bos) =
3 fea See satel! eCennoa| ons gig a Po= P.
2 |$es| e2 | 258 | 852) 28. | (88 P| omy) 2
eee cn ere te ewe | ee)
© ore aS S,7|/ on S| B50 aes
Earn lbeews SS | gSS |esh| Baa | sak
Be |< oS <° A Ay
(p. m.)
5:45 Oe 26h. | a eae eee 110} 0.195 | 0.0097
Ope) 12GA AAAs oes. 1.05 | 0.185 | 0.0092
Bn jee 58a) tan 57: LOO | ONG tpanoneens 0.156 | 1.13
15 | 1267| 446) 75 8 OO) OO ete gee 0.153 | 0.58
6:06 90 G58 PR BGOi ees os 2.80 | 0.495 | 0.0066
90 BiGOMl) MASI ale Sains: 2.80 | 0.495 | 0.0067
3 655| 864] 54.5 BIGON|s MOAGS Icons 0.575 | 0.80
15 644| 878) + 735 WWG@pily <ODORi ears nen 0.594 | 0.49
m5 | 644i) (8'78'| 92:0 OisOnammOnta ee mere e 0.594] 0.24
75| 643| 879| 88.0 (fe) OMAR Se ee. 0.595 | 0.24
6:29 90 Sita eeeeog eee ee 410| 0.722) 0.0075
90 Fgh OBO eo ae ae 440| 0.771 |. 0.0070
30 4.87 | 11.61) 60.3 ANG5 ms OS 20" pee ens 1.088 | 0.79

20 EXPERIMENTS IN AERODYNAMICS.

TaBLE IIJ.—Auveusr 28, 1888.
S. P. Laneiry, Conducting experiments; F. W. Very, Assisting.

Wind plane, 1 foot square (929 square centimeters) ; center of wind plane, 9 m. from axis of
rotation; barometer, 756.6 mm.; temperature, 19°.4 C.; mean wind velocity, 0.37 meters per

second.
x 1 Sie wee : a. c |
3 ate Bore ese ee Gael see ERA |
S ao oer il scae. (Neos LY a3 8
a oS aa a 8, 2S | en So kn= |
gee Bae) ge) | See) See i oe cee ie) ee ti emralee
S PS | ele, ieee | eres ran i|) Gongs a8 77 72 P.
ig ee | go |e oealee | see eG se aes
2 O'S a S,0] on & | 225 ae
eB |< eels eee! ca
|
(p. m.) |
2:26 90° 12.62 VASA Crchelstelbers 1.03 0.180 | 0.0090
90 12.62 A ASW cictelolelobt 1.00 0176 | 0.0088
30 12.62 448 | 65°.8 0.70 OE 27a eyarevereteks rere 0.155 0.79
15 12.57 450 | 78 .8 0.65 OsIeh a earteroreyar 0.156 0.72
2:52 90 6.45 Swit llbooosoor 0.25 0.576 0.0075
90 6.52 SOW loogeness 3.15 0.561 0.0075
45 6.48 8.738 | 48 5 3.30 OSD a reerinener 0.587 1,00
45 6.51 8.69 46 .0 3.10 OUSSIE secon noe 0.581 0.95
30 6.45 8.77 61 5 | 3.00 MIDS 2 |eeeenenctenciers 0.592 0.90
30 6.45 8.77 60 .5 3.20 OIG M Nase ster 0.592 0.96
15 6.45 8.79 | 75 6 2.05 OBS OG3Rerreeterier 0.595 0.61
15 6.40 8.84 76 5 1.90 (SANE | trsnctene vena: 0.602 0.57
7.5 6.44 8.78 86.0 1.45 OD Ol eer ier rere 0.594 0.44
7.9 6.45 8.77 80 5 1.15 O20 om ereretetetentet: 0.592 0.385
3:40 90 5.05 note Oa eee aers a 5.40 0.9380 0.0074
90 5.3 O15 OM Excestevenetct= 4.50 0.786 0.0070
45 5.19 10.90 | 48 .0 4.00 Osi O2M eeeretntorcest: 0.915 0.77
45 5.29 10.69 48 .0 4.10 OF Ipebos oo c0 0.880 0.82
3 5.26 10.75 | 60.5 4.40 OW ((ale tern tetret 0.890 0.87
30 5.44] 1040] 59 .0 3.90 (UGH) ooo 00096 0.853 0.82
15 5,09 11.11 $1 .0 2.35 QUAM oil eeecetorenerenets 0.950 0.44
15 5.18 10.92 75 5 2.20 Naty onooc006 0.918 0.42
7.5 4.95 11.42 84 5 1.80 2810) lis accc0500 1.004 0.23
7.9 5.83 10.61 85 .5 1.45 OD Oil reerememeneie rere 0.867 0.80
4:30 90 5.79 sili | Mecetoretetere 3.90 0.683 0.0072
90 5.78 OriSal merece 3.85 0.673 0.0070
30 5.53 10.23 59 .O 3.85 OlGiS i | brrercnerererce 0.806 0.84
30 5.56 10.17 58 .8 3.60 OMGSAG errr 0.796 0.80
7.5 5A 10.45 85 .0 1.20 EDA ereroetster 0.841 0.26
7.5 5.09 lait 75 .0 1.75 S12 ererteioetet: 0.950 0.33
|

Remarxks.—During these experiments the slight breeze has almost died away ; angle of mean
trace made by plane set at 90° with vertical plumb line drawn on rezister sheet = 95°.

THE RESULTANT PRESSURE RECORDER 21

Taste IV.—Ocroper 4, 1888.
F. W. Very, Conducting experiments ; JosepH LupEwie, Assisting.

Wind plane, 1 foot square (929 square centimeters); center of wind plane, 9 m. from axis of
rotation; barometer, 732.3 mm.; temperature 10:15 a. m., 48° F.; 2:30 p- m., 56° F.; mean
temperature, 52° F. = 11°.1 C.; mean wind velocity, 0.85 meters per second.

During these experiments both the velocity of the wind and its direction were quite variable.

Bi Zs S2 282 Se Sia a |
= ad EES oO & es SES) ane
S Jk oa eee eae “zs kim=
5 cen 5H Sea o =o m »
2 Ae os 3.4m SS Bag Po= IP,
S PaaS | sa | SES | e82 | “as ta 0076 v2? | P,
3 ¢ o> 26 OR |
Si = wm 4 A ay |
(a. m.)
11:40 15 12.50 4,52 0.5 OlOSSets ear 0.155 0.57
10 12.60 4.49 05 OLOSS A 0 Be ae 0.154 0.57
10 12.50 4.52 0.5 OSS ans ete 0.155 0.57
(p. m.) 20 12.50 4,52 0.7 CIE le ee eee 0.155 0.79
1:07 20 12.55 4.51 0.6 OMO4Y Wee acsene. 0.154 0.68
90 6.60 8.57 3.0 0.532 0.0073 0.558
90 6.53 8.66 3.0 0.532 | 0.0071 0.57
1:13 20 6.39 8.85 2.6 OG Se ree 0.595 0.78
20 6.43 8.79 nS OOS oocdsessec 0.587 0.70
90 6.48 8.73 3.0 0.532 0.0070 0.579
90 6.45 8.77 3.0 0.532 0.0069 0.584
1:30 10 6.43 8.79 1.3 O55 il bein. 0.587 0.40
10 6.43 8.79 C7 S030 ies eee 0.587 0.52
90 6.50 8.70 3.0 0.532 0.0070 0.575
90 6.45 8.77 3.2 0.566 0.0074 0.584
15 6.47 8.74 1.5 O68 yee ae = 058i 0.46
15 6.47 8.74 1.9 OSA He an eee 0.581 0.59
90 6.45 8.77 3.8 0.664 0.0086 0.584
90 6.57 8.61 3.8 0.664 0.0090 | - 0.563
5 6.43 8.79 1.0 ONUAGia ee een 0.587 0.30
1:52 5 6.45 8.77 il Oulghe dss ae 0.584 0.33

bo
bo

EXPERIMENTS IN AERODYNAMICS.

Collecting the values of &,, from the several days’ observations and reducing
them to acommon mean temperature of 10° C. and pressure of 735 mm., we
have the following summary of results:

coe
August 27, 1888s 2 5c en sede lente come 0.00810
“ DT Re ee ets ETA eS ee ee 0.00794
October 4 eee eee eee ee ee 0.00757

The observations of October 4 being of inferior accuracy to the others on
account of the wind, which blew in sudden gusts, the mean of the first two days’
experiments, viz., k,,= 0.0080, may be considered as the final value for the
coefficient of normal pressure resulting from the experiments with this instrument.

The columns headed P,,= 0.0077 V* in the experiments of August 27 and
28, and P,,=0.0076 V* in the experiments of October 4, give for each obser-
vation of the inclined plane the computed pressure which the plane would
sustain if moving normally with its velocity V. The coéfficient adopted for the
computation is the mean value of £,,, resulting from the experiments of the day.
The last column of the tables contains the ratio of the actual pressure on the
inclined plane to the computed pressure on the normal plane given in the
preceding column.

These ratios from the several days’ experiments are collected in the following
summary, and mean values are taken for the different angles of experiment.
These mean ratios are plotted in Fig. 1,and a smooth curve is drawn to represent
them.

TasLe V.—Summary of ratios of pressure on inclined plane to pressure on normal plane.

; ; Angles of inclination.
Linear velocity of o

plane (meters | Remarks.
per sec.). 45° 30° 20° 15° | 10° 74° 5° |
|
45 1AsE | 79) 58 SDT filececete lomsessrac *< Omit.
|e OA oereceee lexoke eres siayaerere 7 Give one-quarter weight.
0.79 | .68 2 TT |
8.7 1.00 | 0.80 | .78 | 49 | 40 | .24 | 30
0.95 | 0.90 | .70 | 62 | .52 | .24 | -.33 |
0957 lena Thi tig eee | 44
I} oz opel enaipee | 35
| 09 |
11.2 Osi ae O on Peer {tA S Soke | .23
HOSZ OST a eer EA epee 80
OS ZR eer Heneeoe vs | even cies | 26
OBA epecemeberel teustetarayclllaeeaeatens OF
0.80 |
Mean....... 0.89 | 0.84 74 dO | 48 | 20; 231 |

THE RESULTANT PRESSURE RECORDER. 23

Bie. 1.

See
pot ee

bate

[ol pt ee ee

Ratio of the total normal pressure (P,) on an inclined square plane to the pressure (P,,) on
a normal plane, the planes moying in the air with the same velocity.
Abscissze. Angles of inclination (4) of plane to horizon.
. IR
Ordinates. po (a) (expressed as a percentage).
90

24: EXPERIMENTS IN AERODYNAMICS.

The values in the tables are subject to a correction resulting from a flexure
in the balance-arm and its support. It was observed (see note in Table III)
that the trace of the plane set at 96° did not coincide with the horizontal (7. e.,
the perpendicular to the vertical) line marked on the trace, but was uniformly 4°
or 5° below it; so that the angle between the vertical and the trace of the plane
did not measure 90°, as had been assumed, but uniformly 94° or 95°, the average
being 94°.6. This result was found to be due to the bending backward of the
balance-arm and its support by the pressure of the wind, while the recording
board and plumb-line presented only a thin edge to the wind, and consequently
remained relatively fixed. During motion, therefore, the plane actually had an
inclination to the horizon about 5° greater than the angle at which it was set when
at rest. This flexure seemed to obtain for all angles of experiment, but with
indications of a slightly diminishing effect for the smaller ones; consequently
the pressure ratios above given for angles of 45°, 30°, 20°, ete., really apply to
angles of about 50°, 35°, 25°, ete. After making this correction the final result of
the experiments is embodied in the line of Fig. 1 designated “ corrected curve.” *

At the inception of the experiments with this apparatus it was recognized
that the Newtonian law,+ which made the pressure of a moving fluid on an
inclined surface proportional to the square of the sine of the angle between the
surface and the current, is widely erroneous, though it is still met in articles
relating to fluid pressures, and vitiates the results of many investigations that

;

* The ratios given by the “corrected curve” of the diagram have been tabulated for angles of every 5° and
then compared with all the experiments and formulze with which I am acquainted. Only since making these
experiments my attention has been called to a close agreement of my curve with the formula of Duchemin,
whose valuable memoir published by the French War Department, Mémorial de I’ Artillerie No. V,1 regret not
knowing earlier. The following table presents my values, the values given by Duchemin’s formula, and a column
of differences :

Ratio of the total pressure (Pa) on an inclined square plane to the pressure (Py) on a normal
plane moved in the air with the same velocity.

| | Ja .
| | > as given by—
| | Pe |
| Aneles of inclination = ;
of plane to direc- | | i Difference: Duche-
tion of motion. | Experiments with Duchemin’sformula:| — min—Langley.
| (@) | Resultant Pres- | 2 sina ,
| sure Recorder. | 1 + sin®a
| —
| ye 5 | LZ | + .02
10 30 5S 04
| 15 AG AS 02
| 20 60 61 01
25 71 72 OL
| 30 18 50 02
39 S4 86 02
40 89 01 02
45 93 4 OL

+ Implicitly contained in the Principia, Prop. XX XIV, Book II.

THE RESULTANT PRESSURE RECORDER. 25

would otherwise be valuable. Occasional experiments have been made since the
time of Newton to ascertain the ratio of the pressure upon a plane inclined at
various angles to that upon a normal plane, but the published results exhibit
extremely wide discordance, and a series of experiments upon this problem
seemed, therefore, to be necessary before taking up some newer lines of inquiry.

The apparatus with which the present experiments were made, was designed
to give approximations to the quantitative pressures, rather than as an instru-
ment of precision, and its results are not expected to afford a very accurate
determination of the law according to which the pressure varies with the angle
of inclination of the surface to the current, but incidentally the experiments
furnish data for discriminating between the conflicting figures and formulze that
now comprise the literature of the subject. We may remark that they incident-
ally show that the effect of the air friction is wholly insensible in such experi-
ments as these; but the principal deduction from them is that the sustaining
pressure of the air on a plane 1 foot square, moving at a small angle of inclina-
tion to a horizontal path, is many times greater than would result from the
formula implicitly given by Newton. Thus for an angle of 5° this theoretical
vertical pressure would be sin’ 5°cos 5° = 0.0076 of the pressure on a normal
plane moving with the same velocity, while according to these experiments it is
in reality 0.15 of that pressure, or twenty times as great as the theoretical amount.

CHAPTER V.
THE PLANE-DROPPER.

It is so natural to suppose that to a body falling in the air under the
influence of gravity, it is indifferent whether a lateral motion is impressed upon
it or not, as regards the time of its fall, that we may sometimes find in elemen-
tary text-books the statement that if a ball be shot from a cannon horizontally,
at any given height above the ground, and if a ball be dropped vertically at the
same instant with the discharge, the two projectiles will reach the ground at the
same time, and like illustrations of a supposed fact which has in reality no
justification in experience. According to the experiments I am about to describe,
this cannot be the case, although it requires another form of projectile to make
the difference in the time of fall obvious.

It is shown by the following experiments that if a thin material plane be
projected in its own plane horizontally, it will have a most conspicuously different
time of falling according to the velocity of its lateral translation; and this time
may be so great that it will appear to settle slowly down through the air, as it
might do if almost deprived of weight, or as if the air were a highly viscous
medium, the time of fall being (it will be observed) thus prolonged, when there
is no inclination of the plane to the horizon—a noteworthy and unfamiliar fact,*
which is stated here on the ground of demonstrative experiment. ‘The experi-
mental quantitative demonstration of this important fact, is the primary object
of the instrument I am about to describe, used with the horizontal plane. It is,
of course, an entirely familiar observation that we can support an inclined plane
by moving it laterally deriving our support in this case from the upward com-

* An analogous phenomenon concerning the movement of one solid over another yielding one, such as whem
“Swift Camilla scours the plain,
“Flies o’er the unbending corn, and skims along the main ;”
or in the familiar illustration of the skater on thin ice, or in the behavior of missiles like the boomerang, has
long been observed; and yet, remarkable as its consequences may be, these seem to have attracted but little
attention. Neither has the analogy which it is at least possible may exist between this familiar action of the skater
upon the ice and of the potential flying-machine in the air been generally observed till lately, if at all—at least,
so far as I know, the first person who has seemed to observe the pregnant importance of the illustration is
Mr. Wenham, whom I have already alluded to. I do not, then, present the statement in the text as a fact in
itself unpredictable from experience, for it is a familiar fact that the air, like every material body, must possess
inertia in some degree. It is the quantitative demonstration of the extraordinary result of this inertia which
ean be obtained with simple means in causing the thin air to support objects a thousand times denser than
itself, which I understand to be at the time I write, both unfamiliar in itself, and novel in its here shown con-

sequences,

(26)

THE PLANE-DROPPER. 27

ponent of pressure derived from the wind of advance; but, so far as I am now
aware, this problem of the velocity of fall of a horizontal plane moving hori-
zontally in the air has never been worked out theoretically or determined experi-
mentally, and I believe that the experimental investigation whose results I am
now to present is new.

With all the considerations above noted in view, I have devised a piece of
apparatus which, for distinction, I will here call the Plane-Dropper, intended, in
the first place, to show that a horizontal plane in lateral motion requires an
increased time for its descent ; second, to make actual measurement of the time
of fall of variously shaped planes and to give at least the first approach to the
procuring of the quantitative data; third, to connect these experiments with those
immediately allied to them, where the plane has an inclination to the horizon ;
and, fourth, to make experiments to show the depth of the air strata disturbed by
the moving plane during the time of its passage.

Drawings of the Plane- Dropper are given in plate VI. F is a vertical iron
frame with a wooden back WW, which is shown fastened by bolts B to the
end of the arm of the turn-table. The fourth side of the rectangle is a planed
brass frame on which an aluminum falling-piece runs up and down on friction
rollers. The plate contains enlarged front and side views of the falling-piece,
and a section of the brass frame and falling-piece, showing the arrangement of
the ebonite friction rollers. By means of the clamps CC’ the falling-piece carries
two wooden planes, which may be set by the clamps DD’ horizontal, or at any
angle with the horizon up to 45°. Guy lines extend from the top and bottom of
the falling-piece to the outer edges of the planes and keep them from bending.
A detent at the top of the frame holds the falling-piece until released at any
desired instant by the action of an electro-magnet, M. A spring cushion, 8, at
the bottom of the frame, breaks the force of the fall.

Provision is made for setting the brass frame vertical, and by means of the
handle H the frame can be revolved 180° about its vertical axis, so as to present
successively one side or the other side to the wind of advance, and thus to eliminate
any defect in setting the wings absolutely horizontal, or any inequality in the
instrument not otherwise suspected.

The total fall is four feet, and the total time of fall is registered electrically
by means of contact-pieces a and e, near the top and bottom of the frame. As
soon as released, the aluminum falling-piece presses the contact-piece @ against
the frame and completes the circuit. While falling, the circuit is open, and at
the distance of four feet the contact-piece ¢ is pressed against the frame and the
circuit is again closed. In November, 1890, three additional contact-pieces,
b, c, d, were added, so as to measure the time of fall through each successive foot.
The registration is made on the stationary chronograph, together with that of

28 EXPERIMENTS IN AERODYNAMICS.

the quadrant contacts of the turn-table, the currents for the moment being cut
off from the quadrant contacts and sent through the Plane- Dropper.

The dimensions and weight of the principal parts of the apparatus are as
follows :

Then ethvote brass uty Cire o,< cc oorars sage Rcronctenctoveienctapenietkestelalers are 160 centimeters.
Length of aluminum fallimp-piece <2. 2... snes ss ee sees 25 fs
Leen Oh lI o cop ooadcovaDooUDOoDDODODOOoDODSOwOODDUOODE 5 a
Actual distance of fall (between contacts)................++.0+- 122 ct
Distance of center of brass frame and falling-piece from center of
iuen=talbleuwhenumountediemcrmcrmiiatierseericce secret 981 é
\Weichtrofetallime-piecerritita-t leer ares 300 grammes.

The planes are made of varnished pine about 23mm. thick, and stiffened on
one edge with an aluminum strip.

Five different pairs were used, having the following dimensions and
weights :

(1) Two planes, each *6 x 12 in. (15.2 x 30.5 em.); weight of pair, 123 grammes.
Cres ee a 8x 9in. 22.9 x 20.3 cm.); sé bey uw
@) * a * 12x 61in. (80:5 x 15.2 cm.) as Sop lia eS
(0 “2 ff Ska Anima G4oyi x 10 iem*)) a a ell: Se
ye es a exe eam (GS alexel'0!2 em) Saal S

Each pair of planes, therefore, except the last, has an area of one square
foot, and weighs, with the aluminum falling-piece, approximately one pound.

It may be desirable to add that this instrument was constructed with special
pains in all the circumstances of its mechanical execution, the very light falling-
piece, for instance, moving on its friction wheels so readily that it was not
possible to hold the rod in the hands sufficiently horizontal to keep the “ falling-
piece”? from moving to one end or the other, like the bubble of a level held in
the same manner.

Preliminary experiments were made to determine the effects of friction on
the time of fall, when the Plane- Dropper is in rapid horizontal motion, by drop-
ping the aluminum falling-piece without planes attached, and it was found that
under these circumstances the time of fall is not sensibly greater when in rapid
motion than when at rest. Asa further test, the planes were then attached to
the falling-piece in a vertical position, that is, so as to present their entire surface
to the wind of rotation, and thus to produce a friction very much greater than any
occurring in the subsequent experiments; but the time of fall was not increased
to any notable degree. The effect of friction and other instrumental errors are
shown thus, and by considerations already presented, to be negligible in com-
parison with the irregularities inevitably introduced by irregular air currents

* First measurement refers to advancing edge.

ES ee

THE PLANE-DROPPER. 29

when the whirling table is in motion, which appear in the observations, The
probable error of the measured time of falling in still air, when only instrumental
errors are present, 1s within 74,5 of a second.

The first series of experiments with horizontal planes was made May 25
and June 10 to June 14, 1889, and was devoted to the first two objects already
set forth, namely:

Ist. To show by the increased time of fall that the supporting power of the
ar increases with the horizontal velocity cf the body; and,

2d. To get first approximations to the times of falling of rectangular planes of
different shapes and aspects, the latter condition having reference to whether the
long or the short side of the rectangle is perpendicular to the direction of advance.

An abstract of the note book for June 11, 1889, is given here as an example
of the detailed records made in these experiments.

JuNE 11, 1889.—S. P. Lanciry, Conducting experiments and recording; F. W. Very, Assisting.
’ ‘} ) ; Y

Notes: “A” and “ B” designate the direct and reversed positions of the brass frame and falling
piece; belt on third pulley.
To determine time of falling.

' falling

Size and attitude of planes.

table (seconds).
of
(seconds).

Time of 1 reyvo-
lution of turn-

Time

18 x 4-inch planes, horizontal.....

fora)
bh
ee

pene ey pee
OS oe

bd
Hi bo

12 x G-inch planes, horizontal :
AGrest| GmlOpen ain) eee ersleeencre aa: 0.52
ue ” 0 sic cio.cb allo. wonbopaos 0.52
A ee ye. Sentral at | 052
re e So Sania osha cette | 0.54
5.0) | BO.71
2 | B0O.80
6.1 | A 0.76
On |e) 50)
5 A 1.00

The detailed observations with the five different planes already described
are contained in Tables VI and VII, and the results are presented graphically
in figure 2, where the times of fall are plotted as ordinates, and abscissze are
horizontal velocities of translation,

30 EXPERIMENTS IN AERODYNAMICS.
Tasie VI—May 25, 1889.
To find the time of fall of different planes ; plane-dropper statioua;y.
S. P. Lanatey, Conducting experiments; F. W. Very, Assisting.

Barometer, 731.5 mm.; temperature, 17°.5 C.; wind, light.

Weight (with dropping piece). Time of fall of

Go, Angle with | 4 feet (1.22
Size of planes. horizon. meters).

(Grammes.) (Pounds.) (Seconds. )

One pair 12 x 6 inches (50.5 x 15.2 | 464 1.02 0° 0.58
cm.). 0 0.58
412 TB | O 0.52
Ho") | i 034
i z2 | 45 0.55
One pair 18 x 4 inches (45.7 x 10.2 | 464 1.02 0 0.54
cm.). ' 0 0.55
45 0.55

Result: The time of fall of both planes, at angles both of 0° and 45°, is, approximately, 0.55

seconds.
Taste VII—June 10, 11, 12, anp 14, 1889.

S. P. Lanerry, Conducting experiments; F. W. Very, Assisting.

Mean barometer, 734.0 mm.; mean temperature, June 10, 26.6° C.; June 11, 17.8° C.; June 12,
21.1° C.; June 14, 26.1° C.

To determine the times of fall of horizontal planes endowed with See edocs
horizontal velocity. pee aoe eee
’ ported by the air.
| ea |e b ea Sees cones
| seg lee |e | F | BES | 8s
| se =) q ae Ney, 1 ae 2 Pa "Oo
o a, O° - 2 eo e o oO es 3 i Zz
: a et) o ton . +O aa MO
Dimensions and aspect | BO as ales Sap Peon Ola as Gee
3 Date 7 etcetera Date ono 2 Sn
of plane. Se seseom Renee ec al Bie | See
cecal eee ou lge 2 ons |S.
SSS oa he moe Se es ees
a a Sr sce Bet
1889. 1889.
18 18 June 10 0.00 0.0 0.53 | June 10} 16° oul toe
* x te 5.70 10.8 0.70 s 5 3.4 18.1
78 18 “ 5.90 10.4 0.65
c R a 3.385 18.4 1.62
18x 4 inches (45.7 x 10.2 | = 3.45 L793 1.65
cm.). | fe 5.80 10.6 0.85
Weight, 1.02 lbs. (464 | fe 4.35 14.2 0.90 ||
erammes). & 3.79 16.4 1.08
Radius of rotation to cen- | June 11 3.80 16.2 1.50 || June 11 20° 6.0 10.8
ter of planes, 9.81 m. | « 3.80 16.2 1.15 | s 15 6.2 9.9

THE PLANE-DROPPER.

Taste VII—Continued.

1 1 : reer 1
SES /Sa | 8
eS eb) Sa =
258|/28.|/3<
Dimensions and aspect Cie eo Sea ae
of plane. ie 8s | fea | ea ere
ofa | Ns 5 oe
g28/628/ 8
~ se} eS |
{
1889. 1889.
18 18 June 11 3.75 16.4 1.20 || June 11
* * fe 4.25 14.5 1.15
18 78 June 12 3.00 20.5 1.95 || June 12
q 3.60 s/eil 1.50 2
18 x 4 inches (45.7 x 10.2 i 3.00 20.5 2.55
em.). ie 3.05 20.2 2.68
Weight, 1.02 lbs. (464 ge 3.10 19:9 | 2:75 ||
erammes). 3.15 19.6 2.05
a 3.70 16.8 | 1.65 |
12 12 - 0.00 0.0 | 0.56 || June 11
(+E e 615 W100 | O80 |)“
Iz Z2 " 6.05 10.2 | 0.74 || June 12
June 11 3.50 17.6 1.00
12x 6 inches (80.5 x 15.2 * 3.40 18.1 1.16
em. June 12 2.87 21.4 1e29
Weight, 464 grammes. rf 2.82 21.9 1.59
soe tla ecesemtrge 0.0 | 0.57 if
: TB ye Z| OG s
sf 3.50 | Gm Osa y
se 2.85 21.6 | 0.82 e
2.65 | 23:3 | 0.86
Co Mel lPrstoezern cs 0.0 | 0.57 ue
io 11.65 5.8 | 0.58 .
us 4.10 15.0 | 0.65 i
s 5.10 ial 0.70 is
s 2.78 22:2 | O72) | :
6 x 12 inches.
Weight, 473 grammes.
15 15 June 14} 5.65 10.9 | 0.76 | June 14 |
“ane | 310 | 199 | 128] «
1s 15 a 3.00 20.5 1:28) | -
15 x 4 inches (88.1 x 10.2 |
cm.).
Weight, 468 grammes. |

Angle of eleva-
tion

bo
Svcd. o1

Time of one revo-
lution of turn-
table (seconds).

mo CO
Orr

Roles COOK Now cw
woNwoo 9 60 Op

bo Co OU
Comnmocd

99 29 CO OT

HO ode bo
OO O1or1or1© Or

ity (meters per

Horizontal veloc-
second),

18.7

18.4
21.6

32 EXPERIMENTS IN AERODYNAMICS.

Fia. 2.

Times of falling 4 feet of horizontal planes on the Plane-Dropper.

Average weight of planes = 465 grammes.
Abscissee : = Horizontal velocities of translation in meters per second.

Ordinates : = Times of fall in seconds.

THE PLANE-DROPPER. 33

Perhaps the most important primary fact exhibited by these experiments
is that the time of fall for horizontal planes of all shapes is greater as tho
horizontal velocity increases, and also (as the form of the curves shows) that this
retardation in the velocity of falling goes on at an increasing rate with
increasing velocities of translation.

Secondly, we see that those planes whose width from front to back is small
in comparison with the length of the advancing edge have a greater time of
fall than others. This difference is uniform and progressive from the 6 x 12
inch planes to the 18 x 4inch planes. Expressing this advantage quantitatively,
the curves show that the planes having an advancing edge of 6 inches and
a width of 12 inches from front to back, when they have a horizontal velocity
of 20 meters per second, fall the distance of 4 feet in 0.7 second, while planes
of the same area and weight having the advancing edge 18 inches and 4 inches
from front to back, when moving with the same velocity, are upheld to such an
extent that their time of fall is 2 seconds. This interesting comparative result is
also indirectly valuable in giving additional evidence that the largely increased
time of fall of the better-shaped planes at the high speeds is not due to the lateral
friction of the falling-piece against the frame. The friction with the 6 x 12 inch
planes is as great as with any of the others, yet their time of falling is only
slightly greater at high speeds than at rest. Attention is called to the fact that
at the highest velocity attained in the present series of experiments, 20 meters
per second, the curve shows that the time of falling of the 18 x 4 inch planes was
increasing very rapidly, so much so as to make it a subject of regret that the
slipping of belts prevented experiments at still higher speeds. We may, however,
reasonably infer that with a sufficient horizontal velocity, the time of fall may be
prolonged to any assigned extent, and that for an infinite velocity of translation,
the time of fall will be infinite, or, in other words, that the air will act as a solid
support.

In may be of interest to connect these observations with some partly analogous
facts which are more familiar.

It is frequently observed that a sheet of very thin ice will bear up a skater
if he is in rapid motion which would not sustain his weight if he were still; and
even if we neglect the slight difference of specific gravity between water and
ice, and suppose the latter to have no differential buoyancy, the rapid skater
will still be able to pass safely over ice that would not bear his weight if he
were at rest; for while his mass is the same in both cases, that of the ice called
into play in sustaining him is only that corresponding to one unit of area when
he is at rest, but to many when he is moving.

In this form of explanation and illustration the attention is directed only to
the action of the air beneath the plane, but in fact the behavior of the air above

34. EXPERIMENTS IN AERODYNAMICS.

the plane is of perhaps equal importance, and its action has been present to my
mind throughout these experiments, although for the purpose of concise exposition
only the former is here referred to. By analogous reasoning in the case of a
heavy body immersed in any continuous fluid, even gaseous, while the mass
of air or gas whose inertia is called into action is small and affords a slight
sustaining power when the body is at rest, it becomes greatly multiplied with
lateral motion, and the more rapid this lateral motion, the greater will be the
sustaining action of the fluid. So, then, in the case of any heavy body which
will fall rapidly in the air if it fall from rest, the velocity of fall will be more
and more slow if the body be given successively increasing velocities of lateral
translation and caused to run (so to speak) upon fresh masses of air, resting but
a moment upon each.

The above analogy, in spite of its insufficiency as regards the effect of elas-
ticity, is useful, and may be further extended to illustrate the relative results
obtained with the differently shaped planes and with the same plane under
different “aspects ;”’ thus the action on the air of a plane whose advancing edge
is twice its lateral edge—e. g., the 12x 6 inch plane, with 12-inch side foremost—
may be compared to that of two skaters side by side, each advancing over his own
lines of undisturbed ice; but the same plane with the 6-inch side foremost, to the
same skaters, when one is behind the other, so that the second is passing over ice
which has already yielded to the first and is partly sinking.

The second series of experiments, made on the same dates as the first, was to
cover the third object of experiment—that is, to determine for different angles of
inclination what speed is necessary in order to derive an upward thrust just
sufficient for sustaining the planes.

The results of these two series of experiments furnish all that is needed to
completely elucidate the proposition that I first illustrated by the suspended
plane, namely, that the effort required to support a bird or flying machine in the
air is greatest when it is at rest relatively to the air, and diminishes with the
horizontal speed which it attains, and to demonstrate and illustrate the truth of
the important statement that in actual horizontal flight it costs absolutely less
power to maintain a high velocity than a lowone. It has already been explained
that when the planes have such an angle of elevation and such a horizontal
velocity that they first rise from their support and are then with a slightly
diminished velocity just sustained without falling, they are said to “soar,” and
the corresponding horizontal velocity is called “soaring speed.” Attention has
already been called to the importance thus attachable to the word “horizontal”
as qualifying flight, and implying its most economic conditions, when no useless
work is expended.

THE PLANE-DROPPER. 35

The actual mode of experiment with the inclined planes was to set the plane
at a given angle of elevation, for example 5°, and. approximate to the critical
soaring speed by gradual variations of velocity, both above and below it. The
following extract from the note book shows the character of the record made in
executing this experiment :

12x 6 inch planes, inclined.

Time of 1 revolution

Angle of inclination. of turn-table Attitude of plane.
(seconds).
25° 5.6 Soaring.
- 6 3.8

18 x 4 inch planes, inclined.

' Hea
o a4
= BES
a Peon
3 3
a ral ce
“sa oo 6 f
=e ee Attitude of plane. Estimated result.
i So
oun ie
= eee
Es aS
< a
4° 3.4 More than soaring............. { For angle 33°, soaring speed = 1 rey-
3 3.2 Not quite Soaring..-.......... {olution in 3.3 seconds.
20 6.0 Soaring.
15 5.) More'than soaring............-. { For angle 15°, soaring speed = 1 rey-
15 6.8 Not quite’soarme-.-.......--- /{ olution in 6.2 seconds.

The detailed observations have already been given in Tables VI and VII
and the results are plotted in Figure 3, in which the ordinates are soaring speeds
and the abscissze are the corresponding angles of inclination of the planes to the
horizon. This diagram shows that when set at an angle of 9° the 6 x 12 inch
plane requires a horizontal velocity of 21.2 meters per second to sustain it in the
air, while the 18 x 4 inch plane, set at the same angles, is supported by the air
when it is driven at a velocity of only 14 meters per second. The work to be
done in maintaining the flight at 14 meters per second is less than one-half that
for 21.2 meters per second, the angle remaining the same.

‘These experiments enable us to make a first computation of the work expended
in horizontal flight. Let us, then, determine the horse-power required to drive
the two 18 x 4 inch planes horizontally in the air, when the planes are inclined
successively at 9° and at 5°. The work done per second is given by the product
RX V, & being the horizontal component of pressure on the plane, and V the

36 EXPERIMENTS IN AERODYNAMICS.

Velocities of soaring of inclined planes on the Plane-Dropper.
Average weight of plane = 465 crammes.

Abscissee : = Angles of inclination (2) of plane to horizon.
Ordinates : = Velocities in meters per second.

THE PLANE-DROPPER. 37

soaring speed. From Fig. 3 we find that the soaring velocities corresponding
to these angles are respectively 14 and 17.2 meters per second.
Taking the vertical component of pressure as equal to the weight of the plane,

464 grammes, which relation obtains at soaring speed, the horizontal component
of pressure, or the resistance to advance, is given by the formula:

R = 464 tan 9° = 73.3 grammes, for 9°;

R = 464 tan 5° = 40.6 grammes, for 5°,
a formula which is immediately derived from the fundamental principles of
mechanics and appears to involve no assumption whatever. The work done per
minute, RX V, is 62 kilogrammeters (450 foot-pounds) for 9°, and 43 kilogram-
meters (312 foot-pounds) for 5°. For the former case this is 0.0156 horse-power,
and for the latter case, approximately 0.0095 horse-power ; that is, less power is

Bie. 4:

Abscissse: Horizontal velocities of translation in meters per second.
Ordinates: Time of fall in seconds.

required to maintain a horizontal velocity of 17 meters per second than of 14; a
conclusion which is in accordance with all the other observations and the general
fact deducible from them, that it costs less power in this case to maintain a high
speed than a low one—a conclusion, it need hardly be said, of the very highest
importance, and which will receive later independent confirmation.

Of subordinate, but still of very great, interest is the fact that if a larger
plane have the supporting properties of this model, or if we use a system of
planes like the model, less than one-horse power is required both to support in
the air a plane or system of planes weighing 109 pounds, and at the same time
to propel it horizontally at a velocity of nearly 40 miles an hour.

38 EXPERIMENTS IN AERODYNAMICS.

The third series of experiments made with the plane-dropper is designed
to investigate the effect of two sets of planes, one above the other. For this
purpose the planes and falling piece are so weighted that the previous ratio of
weight to surface is retained; that is, in the previous case the weight is 1 pound
to 1 square foot of surface, and with the double set of planes the weight is

Experiments with two sets of planes, one above the other.

Taste VIII.—June 14, 1889.

To determine the horizontal velocities at
which a system of inclined planes will
be supported by the air.

To determine the times of fall of a system of horizontal planes
endowed with horizontal velocity.

S4am| O58 } & a a : :
Sees By 2 2 ££ | Horizontal velocity.
os ~ ON
Ea 2 m 2 CS =
° a 4 a o ° nH ca
aesS|q8.|aa| 2 gol) 25 ®
Dimensions and aspect of plane.| 9 (@/ S8S8Q |)" 3 | 2o8y |] oOo 1@ me ae
I Sage a ° 1 a n =
009 Owe 9°90 COR RS ee
onsen ES So eo os ose] £8 oS
SS HS? oO Ss 60 a Sicss ood ood
a+ On n a o aa Ss 2 cE, @
is = a < a cS S
45 __t 18 3 19.9 | 0.90'/ 10° | 433 | 149 46.7
oO. . . 00 4 D./
y Q OF 2 Ap) is
st 3 | ses | to | see
| 6 3.48 fem 58.1
15 x 4 inches (88.1 x 10.2 em.). 6 38.35 18.4 60.3
Double pair of planes, 2 inches 5 Did not! rise.
(5.1 em.) apart.
Total weight of planes and falling- | |
piece, 942 grammes.
Same planes, 4 inches (10.2 em.) 7.80 8.4 | 0.73 | 15 5.80 11.6 38.1
apart. 3.13 ONG 1.36 | 10 4.65 13.3 45.5
10 | 465 | 13.8 43.5
7 3.38 18.2 59.8
5 3.33 18.5 60.7
4 3.38 18.5 60.7
| 4 3.27 18.9 61.8
| |
Same planes, 6 inches (15.2 cm.) | 5.88 10.5 | 0.73 | 20(?)| 5.60 11.0 36.1
apart. | 2.78 22.2 1.34 | 15 5.40 114 ov
0.00 0.0 | 0.55 | 10 4.55 13.5 44.4
2.65 23.3 CON ei 3.95 15.6 51.2
5 3.45 We 58.6
5 B45 Wie 58.6
| 4 2.98 21.0 69.0
4 2.95 20.9 68.5
23 2.85 21.6 71.0

made 2 pounds to 2 square feet. The preceding experiments, made with the
single pair of 15 x 4 inch planes, were then repeated on June 14, with a double
5 ) ’
pair of planes placed at distances of 2, 4, and 6 inches apart. The detailed
observations are given in Table VIII. The times of falling are plotted in Fig. 4.
5 5 5
The soaring speeds are plotted in Fig. 5, without attempting to smooth out the

THE PLANE-DROPPER,

lave, 45),

Second.

per

2 Leet

Velocities of soaring of single and double pairs of 15 x 4 inch inclined
planes on the Plane-Dropper.

Abscissze : = Angles of inclination (2) of plane to horizon.

Ordinates : = Velocities in meters per second and feet per second.

40 EXPERIMENTS IN AERODYNAMICS.

inaccuracies Of observation. The general result presented by both the falling
and soaring planes is that when the double pairs of planes are placed 4 inches
apart, or more, they do not interfere with each other, and the sustaining power
is, therefore, sensibly double that of the single pair of planes; but when placed
2 inches apart, there is a very perceptible diminution of sustaining power shown
in the higher velocity required for support and in the greater rapidity of fall.
Manifestly, however, this result can hold good only above some minimum
velocity of translation, and, in general, we may say that the closeness with
which the planes can be set without producing any diminution of sustaining
efficiency is a function of the velocity of translation, so that the higher the velocity,
the greater the proximity. It was desired, therefore, to ascertain the minimum
velocity for which the preceding conclusion holds good, namely, that planes 4
inches wide do not suffer any loss of sustaining power if placed one above the
otler and 4 inches apart. Experiments with these double pairs of planes were,
therefore, continued on August 22, 23, and 24 for the purpose of getting these
data. The same planes were used and were placed at the same distance apart,
viz., 2, 4, and 6 inches, and a set of experiments was also made with the single
pair. Previous to these experiments at high speeds the Plane- Dropper was
stiffened in order better to preserve its verticality under strong wind pressures,
and precaution was taken to observe how closely this condition was maintained.
The new observations were somewhat different from the early ones, and consisted
in measuring the time of fall of the double planes—7. ¢., one over the other when
set at different angles ranging from — 7° to + 7° at three different velocities, viz.,
23.5, 13.0, and 6.5 meters per second. For every setting the brass frame was
turned on its pivot through an angle of 180°, so as to present first one side then
the opposite as the advancing face. The two positions are designated by A and
B in the accompanying Tables, IX, X, and XI, which contain 125 separate
observations at the above-named different velocities, angles, and settings.

THE PLANE-DROPPER. A}

Experiments to determine the time of falling of two sets of planes, one above the other (second series).
Taste [X.—Avcusr 22, 1889.

F. W. Very, Conducting experiments.

Barometer, 731.8 mm.; mean temperature, 23°.9 C.; wind, light.
Bai oe ees ese eve? tS
Dimensions and aspect of | 3S |u| $58 | 38/82
planes. a, og - ae | 2 eS “ = Remarks.
Zs a aii aa ae gerne ca (eet
a < a (x a
fs re A OP ee eeeeals <OO) I OIRS
a | Be GOpa les oo 0.0 | 062
15 15 A 0 2.60 23.7 1.68
| 18 0 2.65 23.3 1.70
15 x 4 inches (88.1 x 10.2 B Q) || 2430 23.7 1.70
cm.). | B |—2 2.65 23.3 | 0.70
Double pair of planes. 4 B |—2 2.65 23.3 | 1.00
inches apart. eee ro 2.60 23.7 0.75
Total weight, 942 grammes. | A | —5 2.50 24.6 | 0.50 |
[le AC te 2.50 24.6 2.20 | Fell, then soared.
A {+1 2.65 23.3 6.15 | Fell slowly.
B |—1 2.65 23.3 | 0.90
B |—1 2.65 23.3 1.20
Same planes, 2 inches apart. A 0° 2.35 26.2 1.60
B 0 2.45 25.1 1.20
A 0 2.60 23.7 1.90
B 0 2.60 23.7 1.30 |
A 2 2.95 20.9 | 4.15 | Soared, then fell.
B |-2 2.75 22.4 | 0.70
A | +2 2.70 22.8 | 5.80 | Gradual fall, but very slow.
B |—2 2.65 arom OTe)
A 3 2.60 Su Tiam | ere Stayed at top.
B |—3 2.65 23.3 | 0.70
B 3 2.75 22.4 | 0.50
Same planes, 6inchesapart. | A 0° | 3.80 1837 ||) 100)
B 0 3.80 18.7 || 1.20 |
A 0 3.35 184 | 1.50 |
B OP ees380) 18.7 1.30 |
A |j|+1 | 3.00 20.5 | 14.80 | Fell very slowly.
B |—1 2.95 20.9 1.00 |
A {+1 3.00 20.5 |14.20 | Fell very slowly.
B |—1 3.00 20.5 1.10
B |}—83 3.15 19.6 0.75
Bis 38.20 19.2 | 0.75 |
|

Result: It is certain that any angle greater than + 1° (with planes 6 inches apart) would
produce soaring, and as the error of verticality in this day’s observations probably does not
exceed 1° during motion, we may take about 2° as the soaring angle for the speeds used.

42 EXPERIMENTS IN AERODYNAMICS.

Taste X.—Aveust 23, 1889.

Barometer, 752.5 mm.; mean temperature, 22°.8 C.; wind, light.

= | 2 Diseases
SG sah Gano eee ueleses
Dimensions and aspect of S83 else ce e Be a3 Renae
planes. Se | Ooo! acs o6
xs eo ofS |. 8.8 | o
Z ea Be) Sess) ee
a < & a &
15 15 A 0°; 7.80 7.9 | 0.80
‘he B | o| 930 | 66 |. 070
1S is A 0} 9.10 6.8 | 0.70
B 0} 8.45 7.3 | 0.65
15x 4 inches (88.1x102} A 0} 4.80 12:8 | 1.08
cm.). B 0 4.80 12.8 1.02
Double pair of planes, 6 A O} 4.85 12.7 0.90
inches apart. B 0 5:00 12.3 1.20
Total weight, 942 grammes.| A |+ 5] 4.95 12.4 | 1.55
A |+ 65, 10.05 6.1 | 0.70
Bonen o:3 6.6 | 0.60
By one 70 13.1 | 0.64
B |-+ 5 | 475 SOs 2a)
Bat oul 9:00 6.8 | 0.78
A |= & |) eel 7.6 | 0.69
A |— 5 | 4.75 13.0 | 0.70
Aaa sta 4.85 SLE em oLaLea
A |+ 7] 8.20 7.5 | 0:90
13 jp |) Shs 6.6 | 0.62
By We | 2b7@ 13.1 | 0.58
B |+ 7} 4.70 ales 3) I 3)
Bead 9.10 6.8 0.80
LS | 9.50 6.5 0.60
A |—7 4.75 13.0 0.57
A |+10 4.65 tes Ome eee Soars.
A 10 | 7.90 (eOmn eeleat(()
B 10 | 10.25 6.0 | O75
Same planes, 4inchesapart. | <A O°} 11.55 5.3 | 0.62
B 0 8.60 7.2 0.60
A 0 4.60 13.4 0.95
B 0 4.70 13.1 0.89
B |+ 5] 10.10 6.1 0.69
BS eb) 4270 131 i) 2:30
A |— 5| 4.70 13.1 | 0.70
A |— 5] 10.20 6.0 0.65
A |+ 5| 7.65 8.1 | 0.63
A |+ 5 4.70 13.1 2.90
B |}— 5 4.80 12.8 0.59
B |— 5} 10.50 5.9 0.59
A |+ 7) 13.70 4.5 | 0.59
A |+ 7] 4.85 Te ao
B |—7| 4.87 12.7 | 0.58

THE PLANE-DROPPER. 43

Taste X.—Aususr 23, 1889—Continued.

eee ese alcs &
| & 3 o De, So > x =e
Dimensions and aspect of | S38 |u| S58 |S8n)/S4 es
planes. I a. CB ly as | eee |e Remarks.
a S S55 Om n S
ae |<4 |e se B
ca is 1 = ae bid) | 0158
a B |+ 7] 1140 | 54 | 069
ae Beier || 4.85 |) toi, 2:80
15x4 inches (881x102); A |— 7 4.90 12.6 0.58
cm.). |} A |— 7] 11.40 5.4 | 0.58
Double pair of planes, 4 A |+10] 8.60 U2 || 0830
inches apart. | 2X feoal@y| Zero) 13.1 |...--- Soars.
Total weight, 942 grammes. B |+10)] 11.00 5.6 | 0.60
Same planes, 2 inchesapart.| A O°; 11.40 5.4 | 0.58
3 0 | 11.00 5.6 | 0.56
| A O 4.90 12.6 0.69
B 0} 4.80 12.8 | 0.68
A |}+ 5} 4.50 13.7 1.13
A |+ 51 10.30 6.0 | 0.60
B |1— 5] 9.20 6.7 | 0.55
B |— 5| 4.80 12.8 | 0.55
B |+ 5] 4.90 12.6 | 0.74
Bo -Pe 5 | 3970 6.4 | 0.60
A |— 5} 9.90 6.2 | 0.56
A |— 5| 4.95 12.4 | 0.60
A |+ 7] 4.95 12.4 | 1.50
BO a eb O0) 5.6 | 0.50
B |— 7] 10.60 5.8 | 0.52
B |— 7| 4.80 12.8 | 0.50
Bec ee-b0 134 L3
13 Se eg || Galo) 6.8 | 0.60
USS (al OSE) 7.0 | 0.54
A |— 7} 4.90 12.6 | 0.58
A |+10} 4.80 12.8 | 3.45
A |+10] 10.60 5.8 | 0.60
B |}+10)] 10.20 6.0 | 0.61
B |}+10) 4.90 LGM EO
NGS | foe leln ee teoO) 12.6 | 11.30 | Falls slowly.
A |+12} 4.90 12.6 |27.50 | Falls very slowly.
A |}+14] 4.95 12.4 | 27.65 | Falls very slowly.
A |+14 4.70 ASST i eeeersceze Soars.
Single pair of planes, 15x4 | A 0°| 4.60 13.4 | 0.90
inches (38.1 x 10.2 em.). B O| 4.60 13.4 0.99
B 0} 8.45 7.3 | 0.64
A 0} 840 7.3 | 0.65
A |+ 5} 845 7.3 | 0.69
A |}+ 5] 5.00 LSet
A |+ 7] 5.00 12.38 | 2.50
A |+ 7} 840 7.3 | 0.68
A |}+10} 7.90 (eSa Oto [soar.
Ae eh 5.00 12.3 | 11.20 | Falls slowly, but does not

44 EXPERIMENTS IN AERODYNAMICS.

Taste XI.—<Auveust 24, 1889.

Barometer, 734.3 mm.; mean temperature, 25°.0 C.; wind, light.

Zt 3 Sap | 28 b
| 3 o Paes lps 02 ae nell
Dimensions and aapect of |SSlud| fos |eea las |
gmc ae aspect o 8 3 = z a g ES ae Rermarka:
| ES; a o me = = | S i 9 ra 7 |
~~ cml OrFHe | -sa Be o
a el SSS) Sirs ale
a |=a |& ss &
| | | |
Single pair of planes, 15 x 4 A |— 5° 9.50 6.5 0.60
inches. B |}+ 5 9.50 6.5 0.65
B |-+ 5 5.00 ES 1.30
qs 1s A 5 4.95 12.4 0.60
“he 2 Ales Algs, | isiron Role
15 75 N |= 7 9 eal 0.60
Bsi+7 ).A0 6.6 0.70
B | +10 8.75 7.0 0.70
B |+10] 4.95 12.4 1.85
B |+12 5.00 12.3 2.70
B |}+14 5.10 IAL 1.60
B |+14] 450 Ser |
A 0 2.63 23.4 2.60 |
B 0 2.64 23.3 1.07
A 0 2.60 23.7 1.80 |
B 0 2.60 23.7 1.00 |
A |+ 1 2.60 Duan arte | Fell after soaring about 20
B |— 1 2.65 23.3 1.00 | seconds.
B |+ 1 2.60 23.7 4.30 |
A ;|— 1 2.58 23.9 1.10 |
A |— 5 2.60 23.7 0.70 |
a CO PE | ISD |
|

The actual velocities obtaining in the individual observations varied some-
what; for the lowest velocity ranging between 5 and 8; for the second velocity
ranging between 12.5 and 13.5, and for the highest velocity ranging in gen-
eral between 22.5 and 24.0, except for the planes 6 inches apart, for which the
velocities were about 19 meters per second. The numerical results for the
lowest and the highest speed will be found plotted in Figs. 6 and 7, respectively.
In these diagrams the abscissze are angles of inclination of the planes to the
horizon, and the ordinates are times of falling. For the highest velocity, the
times of falling of the single pair of planes and of the double pair, both, 4 inches
and 6 inches apart, are alike, while for the planes 2 inches apart, the time of falling
is shorter. For the lowest velocity, viz., 6.5 meters per second, the planes 4 inches
apart as well as those 2 inches apart fall a little faster than the single plane,
and are therefore not quite so well sustained by the air.

This result confirms the statement above made, that for double sets of planes,
one above the other, the maximum supporting effect relatively to the single

THE PLANE-DROPPER. 45

planes is obtained only above a certain minimum velocity of translation. For
the present planes, of size 15 x 4 inches set 4 inches apart, this minimum velocity
is shown by the curves to be higher than 6.5 and less than 23.5 meters per
second, and, from comparison of all the data, apparently lies at about 13 meters
per second. These results substantially confirm those obtained from the experi-
ments of June 14, with this additional information as to the minimum velocity
at which the maximum sustaining power can be obtained for a distance apart
of 4 inches. For a distance of 2 inches apart even the highest velocities show a
serious diminution of efficiency.

The results of these observations with two sets of planes, one above the
other, give us a first conception of the form and initial vertical amplitude of the
wave that is set in motion in the air by a plane passing horizontally through it
in the manner of these planes.

KiGaNG:

1.25

0.75

Times of falling 4 feet of single and double pairs of 15 x 4 inch planes set at different angles of
elevation and haying a horizontal velocity of 6.5 meters per second.

Abscisse : = Angles of inclination of plane to horizon.

Ordinates : = Time of fall in seconds.

These later observations also incidentally furnish additional data as to the
velocity of soaring. When inclined at an angle of 10° the single planes and
the double planes, at a distance of 4 inches apart and upward, are sustained in
the air if they have a horizontal velocity of about 13.2 meters per second.
When set at 1°, soaring took place at velocities from 21 to 23 meters per second.
Close observation also indicated that the error of verticality of the plane-dropper
during motion did not exceed 1°; hence for these velocities the soaring angle
may be taken at about 2°. This is a fraction of a degree less than that given by
the observations of June 14, as plotted on Fig. 3.

‘The most general and perhaps the most important conclusion to be drawn from
them appears to be that the air is sensibly disturbed under the advancing plane

46 EXPERIMENTS IN AERODYNAMICS.

Fie. 7.

Dizgram of Planes _|

SS
=e

Times of falling 4 feet of single and double pairs of 15 x 4 inch planes set at different angles of
elevation and having a horizontal velocity of 23.5 meters per second.
Abscissee : = Angles of inclination (2) of plane to horizon.

Ordinates : = Time of fall in seconds.

THE PLANE-DROPPER. 47

for only a very slight depth ; so that for the planes 4 inches apart, at the average
speeds, the stratum of air disturbed during its passage over it, is, at any rate, less
than 4 inches thick. In other words, the plane is sustained by the compression
and elasticity of an air layer not deeper than this, which we may treat, for all our
present purposes, as resting on a solid support less than four inches below the
plane. (The reader is again reminded that this sustenance is also partly due to
the action of the air above the plane.)

Summing up the results obtained with the plane-dropper, we have determined:

1. The relative times of falling a distance of 4 feet (1".22) that obtain for
differently shaped but horizontally disposed planes moving with different hori-
zontal velocities, showing quantitatively the primary fact that the time of fall is
an increasing function of the velocity of lateral movement.

2. The varying velocities of translation at which planes of given size and
weight, but of different shapes, will be sustained by the air when inclined at
different angles.

3. The maximum proximity at which successive planes can be set one above
the other in order to give a supporting power proportional to their surface.

4. A first approximation to the initial amplitude of the wave motion origi-
nated by a plane passing horizontally or at a small angle through the air with a
considerable velocity.

5. The approximate resistance to advance of a wind-plane at soaring speeds,
and (by computation) the work necessary to be expended in overcoming this

resistance.

These experimentally show that the higher horizontal speeds are maintained
with less expenditure of power than lower ones, and the quantitative experiments
by which these results are established are, so far as I am aware, new, and I
believe have a most immediate bearing on the solution of the problem of artificial
flight.

I may add that these experiments with the horizontal plane, when properly
executed, give results of a character to forcibly impress the spectator; for, since
there is no inclination, there is no visible component of pressure to prolong the
fall, yet the plane nevertheless visibly behaves as if nearly deprived of its weight.
The pair of 18 x 4 inch planes, for instance, ji, of an inch thick and weighing
464 grammes, has a specific gravity of about 1,660 times that of air; vet while the
retardation due to the still air in the direct fall is but 20°.03, that due to the same
air in strictly lateral motion is 1*°.50—a most noteworthy result in its bearing on
the use in mechanical flight that may be derived from a property of the air much
utilized by nature, but hitherto almost wholly neglected in this connection by

man—its inertia.

CHAPTER VI.

THE COMPONENT PRESSURE RECORDER.

The experiments with the Plane-Dropper in the preceding chapter give the
soaring speeds of wind-planes of different shapes set at varying angles, and enable
us by the use of a fundamental formula of mechanics to make a provisional com-
putation of the work expended per minute in their uniform horizontal flight,
neglecting frictional resistances.

Among several conclusions, one of prime importance, namely, that in such
aerial motion of heavy inclined planes the higher speeds are maintained with less
expenditure of power than the lower ones, presents an appearance so paradoxical
that, in view of its obviously extraordinary importance, I have endeavored to
establish it independently wholly by experiment, without the use of any formula
whatever. For this purpose it is desirable to measure by means of a suitable
dynamometer the number of foot-pounds of work done in overcoming the resist-
ance to advance when a wind-plane is driven at soaring speeds (i. e., speeds at
which it maintains a horizontal course by virtue of the vertical component of
pressure, which in this case is just equal to the weight), by means of the whirling
table, yet under conditions strictly assimilable to those of free flight, in the case
of an actual aerodrome propelled by its own motor.

After much study and much experiment, I gradually perfected an instru-
ment (that described here as the Component Pressure Recorder), to be used in
connection with the Dynamometer-Chronograph in recording the speed, the resist-
ance to forward motion at the instant of soaring, and other attendant phenomena.
Its use in connection with the Dynamometer-Chronograph will also be further
described in chapter VII.

In the present chapter, I shall not consider further the action of the self-
propelling model, but treat of it as reduced to its simplest type of an inclined
plane, the “ wind-plane,” or system of planes driven forward by the turn-table
arm until they are raised from it by the wind of rotation and soar. The imme-
diate objects of experiment are, therefore, to determine soaring speeds and the

’

horizontal resistances corresponding thereto.
DESCRIPTION.

The Component Pressure Recorder (or Component Recorder), plate VII, may
be compared to a balance which rocks on a knife-edge bearing, in the ordinary
way, but which also oscillates horizontally about a vertical axis. With respect

(48)

THE COMPONENT PRESSURE RECORDER. 49

to its vertical oscillations about the knife-edge bearing, it is a true balance, whose
arms, each one meter long, are in delicate equilibrium, and I will call this part
of the instrument distinctively “ the balance.”

If an actual working aerodrome model with its motor be not Teed upon
the outer arm (outer, that is, as reckoned from the center of the turn-table), a
plane of given weight (the “ wind-plane”’) is clamped there, so as to make any
desired angle of inclination with the horizon. The horizontal oscillation about
the vertical axis provides for the measurement of the horizontal component of
pressure on this plane; the vertical oscillation on the knife-edge provides for
measuring the vertical component. The horizontal pressure is measured by the
extension of a spring fastened to an arm moving around the axis with the
horizontal oscillation of the balance, and to the surrounding fixed frame. The
vertical component of pressure is measuredgonly when it is equal to the weight
of the plane—i. e., by the fact that the plane is actually just lifted by the wind
of rotation, or, in the technical term previously used, when it soars. The requisite
registration of this fact is automatically accomplished by making an electric
contact. As the wind-plane is raised, the inner end of the balance descends, until
it strikes a stop through which electric connection is established, and the
“making” of the current is registered on the stationary chronograph, which
at the same time records the speed of the whirling table four times in each
revolution, and thus the horizontal velocity which produces a vertical pressure
sufficient to lift or sustain the wind-plane is determined.

The detailed manner in which these objects are attained by the apparatus
is described later in the text, and is shown by the drawings of plate VII. The
letters S designate the iron supports by means of which the frame of the recorder
rests upon the arm of the whirling table in such a manner that the instrument
is half above and half below it. The knife-edge and the wind-plane are brought
thereby into the plane of rotation, and equal surfaces above and below the
supporting arm of the whirling table are exposed to the wind pressure.

The details of the knife-edge bearings are shown on the plate in enlarged
scale. It is evident that when the balance resting on its knife-edge is in motion
on the whirling table, there will be an outward thrust on the instrument tending
to throw the knife-edge off from its bearing. In order to take up this thrust,

‘and yet in no way impair the action of that portion of the instrument which
acts the part of a balance, a pair of cylindrical pivots exactly concentric with the
prolongation of the knife-edge are made to extend out beyond the knife-blade
and rest in a suitable bearing. The pivots thus arranged take up the outward
thrust arising from centrifugal force, while the freedom of motion of the balance
on the knife-edge is not at all impaired.

=
‘

50 EXPERIMENTS IN AERODYNAMICS.

The wind-plane is fastened to a brass tube on the outer end of the instrument,
and set to any angle of inclination by means of the graduated circle G. This
tube is adjustable in position so that the center of the wind-plane, whatever be
its size, is at a constant distance of 1.25 meters from the center of the balance
and of the whole instrument. A similar adjustable tube on the inner arm
serves to adjust the balance to equipoise for any position of the outer tube.
Beneath the inner arm of the balance a registering arm is rigidly fastened to
the vertical axis, and partakes of the horizontal oscillation of the balance, but
not of its vertical motion. Near its extremity is attached the horizontal spring
already referred to, and at the end it carries a pencil, which registers on a
revolving chronograph cylinder below the extension of the spring produced by
the horizontal pressure on the wind-plane.

The length of the record arm from center of balance to spring is 28.5 inches,
(72.4 cm.)

The length of the record arm from center of balance to pencil is 31.5 inches,
(80.0 em.)

The pencil departures are therefore longer than the true spring extension,
and the latter are obtained from the former by multiplying by the factor
28.5 _ 0905,

31.5

To reduce the pull on the spring to what it would be if the spring had the
same lever arm as the center of the plane, we must multiply it by the factor
ae 0579,

Within the limits of attainable precision, we observe the spring calibration
to be linear, and the two factors may be multiplied together, giving the single
factor 0.524, by which the pressure corresponding to pencil departures, as taken
from the calibration curves, must be multiplied in order to get the pressures on
the plane. The horizontal springs used in these experiments are those hereafter
more fully described in connection with the Rolling Carriage.

The uniform distance from the center of rotation of the turn-table to the
center of wind plane is 9.55 meters. The balance arms are protected from wind
by covering the sides of the surrounding frame with cloth and paper and placing
over the top an adjustable lid of veneer. An experimental test of the Recorder
without wind-plane was first made, to discover the effect of any residual wind
pressure on the arms. The instrument was carefully adjusted on the turn-table,
and then set in rapid, uniform motion without exhibiting any tension of the
horizontal spring. The result indicates that whatever wind pressure still
remains is equal on both arms. It is to be noted that a theoretically perfect
measurement of horizontal wind pressure by this instrument requires a uniform

expressing the ratio of the lengths of the arms, viz.

THE COMPONENT PRESSURE RECORDER. 51

velocity of the turn-table at the instant for which the reading is made. The
oecasion for this condition arises in the circumstance that with a varying
velocity the inertia of the inner arm of the balance produces a different effect on
the instrument from the inertia of the outer arm; thus with increasing velocities
the outer arm tends to go slower than the inner arm, and with decreasing veloci-
ties tends to go faster. This differential effect of inertia is taken up by the spring
and is combined with the wind pressure until a uniform velocity is attained, and
then the wind pressure alone remains to extend the spring.

Each arm of the balance carries a brass friction wheel, R, which is intended
to rest upon a track, P P’, thereby limiting the vertical motion of the balance
arms. When the wind-plane is vertical, and horizontal wind pressure is being
measured, the outer arm carrying the plane rests continuously on the track and
the friction wheel affords perfect freedom of horizontal motion of the balance,
which fulfills its proper function at the same time that it turns about the vertical
axis; so that when the plane is inclined and is raised by the vertical component
of the wind—. e., when the wind-plane soars—the inner arm is brought down
to the stop P and the friction wheel insures free motion of the balance about the
vertical axis. An electric wire connects with P, and a second wire earries a
current through the knife-edges into the balance, and thence to the friction wheel,
where the electric current is completed at the moment of contact between the
friction wheel and the stop. After leaving the whirling table the current passes
through an electric bell, which serves to inform the experimenter of the fact of
soaring (though this is independently recognizable by the motion of the arm),
and thence to the observatory chronograph, where the contacts are registered.
On this chronograph, then, are registered (1) the second-beats of the mean time
standard clock of the observatory ; (2) the contacts, which are made four times
in every revolution of the turn-table and show its speed, and (3) the electric
current which registers soaring; the two latter records being clearly distin-
guishable.

The actual method of experiment employed to determine the velocity at
which soaring is just attained is as follows: The velocity of the whirling table
is increased to the point at which soaring almost begins to take place—that is,
when the plane begins to flutter. This velocity is then still further, but very
slowly, increased and adjusted until the electric bell rings as nearly as possible
half the time. The velocity at which this occurs represents that of soaring.
This method is based on the following considerations: If the precise velocity be
attained at which the plane would be just sustained in quiet air, not resting on
the stop at either end, the actual wind which prevails to a greater or less extent
in the open air disturbs this equilibrium and causes the plane to be more than
sustained during the half revolution of the turn-table which carries it against

52 EXPERIMENTS IN AERODYNAMICS.

the wind, and less than sustained during the remaining half. Consequently,
this condition of electric contact half the time is taken to be the one desired, and
the velocity corresponding to it is taken from the chronograph and ealled the
soaring velocity for the plane and angle obtaining in the experiment. When
the electric bell indicates to the observer an exact soaring, the speed is main-
tained uniformly for a few revolutions, as required by the theory of the Recorder
already alluded to, as a requisite for the proper measurement of the wind pressure
on the plane. A brush H is attached to the inner arm of the balance for the
purpose of producing a regulated friction, and thereby diminishing somewhat
the fluctuations of the apparatus, which was found to be too sensitive to currents
to do work of all the accuracy it is capable of, except in calm weather.

Some preliminary experiments were made in August, 1889, to determine the
relative velocities of soaring of different planes. But the first Component- Recorder
was shortly afterwards destroyed in an accident, and the observations were inter-
rupted until September, 1890, when they were resumed with the newly constructed
and improved Component-Recorder figured in the plate. Nine new planes were
made of light pine, and backed with lead so as to have the following sizes and

weights :

| |
30 x 4.8 |76.2 x 12.2 250 | 24x6 |61.0x 15.2 250
50 x 4.8 | 76.2 x 12.2 500 | 9x6 |61.0x 15.2
30x 4.8/76.2x122} 1,000 | 24x6 |610x ve
| | |

| 12x 12 |30.5 x 30.5) 250
500 || 12x12 |30.5 500
1,000 | 12x12 |30.5x 80.5 1,000

It was found that the heavier planes, and especially the longer ones, required
light trussing in order to prevent them from bending when in rapid motion.
This was effected by inserting a transverse arm of round brass in the end of the
brass tube where the planes are attached, and carrying fine steel wire out to the
extremity of the plane. The 30-inch plane was further trussed by a post at its
center carrying wires to the four corners.

Inasmuch as the center of pressure on an inclined plane is in front of the
center of figure (as will be shown in connection with the Counterpoised Eccentric
Plane), the lead backing was inserted to one side of the center, so as to bring the
center of gravity into approximate coincidence with the center of pressure when
the plane is inclined at low angles, and the plane was grasped at a similar
distance in front of the center. These provisions contributed to diminish the
twisting of the planes. These planes were used until November 25, when they

THE COMPONENT PRESSURE RECORDER. 53

were replaced by others backed with strips of brass, which gave the planes the
desired weight, and also contributed the necessary stiffness. The latter planes
are made of pine ¢ of an inch thick, with square-cut edges. The brass strip
is a piece of hard-rolled brass running the whole length of the plane, and about
2 inches wide. In the 24 and 30 inch planes the middle of the strips was bent
slightly outward—. e., “corrugated ”

The experiments were made in two series. The first series was made on
eight days, from September 29 to October 9, inclusive, and consisted in deter-
mining the soaring speeds and corresponding resistances of the above-described
planes set at angles from 2° to 30°, and the horizontal pressure on the planes
when set at 90°—that is, normal to the line of advance. In all, 95 complete

—for greater stiffness.

observations were taken.
The following is an example of the original record made in these observa-
tions, extracted from the note book for October 8 :
Experiments with Component Pressure Recorder to determine horizontal pressures at soaring speeds.
OcroBER 8, 1890.
F. W. Very, Conducting experiments ; JosepH Luprwic, Regulating engine.

Barometer, 736.6; temperature, 15° C.; air meter at 10:30 a. m., 1,509,500; air meter at
3:20 p. m., 1,500,400; 30 x 4.8 inch plane; weight, 500 grammes; spring No. 2.

| Velocity of plane |

Seconds in one revo- | Extension of spring) Pull of spring

Angle. lution of turn-table. ae per Sec- (inches).** (grammes).
| 5
90° 12.10 | 4.96 | 1.40 45
10.05 | 5.97 | 2.20 472,
9.60 | 6.25 2.45 526
|

* The use of an English scale instead of a metric one in measuring the spring extensions introduces a lack
of harmony in the system of units employed that is not to be recommended; but since this is a record of the
original observations, the measurements as actually made are faithfully presented.

54 EXPERIMENTS IN AERODYNAMICS.

A | Dstimated soaring | Spring
Angle, Seconds Tone Exe speed (meters per | extension Remarks.
ee second), (inches). |
30° | 55 >
6.3 <
5.5 > +5.65 sees. 10.6 2.3
5.75 <<
Oo) 4)
15° 48 a
5.4 >
ances ae < d J
pee right 5.79 10.4 0.8 Plane quivers at tip with
Gipm—e .
BQ < highest speed.
Rh
5.85 right J
10° 0) SS)
5.4 right
5.85 S \ 5 OD eo 0.75 | Plane somewhat bowed.
00
0:0) <<
5.3 right
Plane stiffened by thin iron plate at both ends and at middle, and experiment
repeated with same setting.
| |
10° «=| 49 > |
5.0 <
4.75 > 7-495 12.1 0.9
(Repeated) Bee
5.0 <

The extensions of the spring corresponding to the horizontal component of pressure
on the plane, and caused by the movement of the Recorder about the vertical
axis, are taken from the sheet of the recording cylinder carried on the turn-table
arm, as already described and as shown on plate 7. The records of velocities
are found on the stationary chronograph registering the quadrant contacts of
the turn-table, and on the same sheet with the electric contacts made at soaring
speeds. Thus, when the latter sheet has been taken off its chronograph barrel,
the observer has before him a permanent record of the velocity of the turn-table
measured four times in every revolution, and together with it the trace of the
irregular contacts made by the vertical rocking of the balance arm which takes
place at soaring speed. Now, since the criterion of exact soaring is that these
signals shall appear on the trace half the time of each revolution, an inequality
mark is added to the record of the measured velocities, which indicates how
nearly this condition is attained. If the chronograph sheet for any complete
revolution of the turn-table is more than half filled with the signals, the velocity

THE COMPONENT PRESSURE RECORDER. D9

is too great; if less than half filled, the velocity is too small, etc. Two or more
inequality marks are used to indicate a wide difference from the mean condition.
By putting down a series of such readings measured at a number of revolutions
of the turn-table and taking a mean estimate, a very close approximation to the
soaring speed may be made, and the result has the weight of a very considerable
number of single readings.

After completing the experiments of September 29 to October 9 according
to the plan laid out, the observations were reduced, and their discussion served
to show that additional experiments were needed to supplement them. There-
upon a second series was instituted for the purpose of obtaining additional data.
In this series the following five planes were used :

Size. Weight.

|
(Inches.) | (Centimeters.) | (Grammes.)

80x 48 76.2 x 12.2 500
24x 6 61.0 x 15.2 500
12 x 12 80.5 x 380.5 500
Zien 30.5 x 15.2 250

G6 15.2 x 15.2 125

The principal further objects to be attained were to determine with greater
precision the soaring speeds of the 24 x 6 and 30 x 4.8 inch planes at small angles
and the horizontal pressure at those speeds; to determine the soaring speed for
angles of the plane above 30°, so as to get the minimum point in the soaring
speed curve—that is, to determine the angle at which soaring takes place with
minimum velocity ; and to ascertain the effect of size of plane on soaring speed
by adding to the planes previously used two of smaller size, viz., 12 x 6 inches
and 6 x 6 inches, having a corresponding diminution of weight. The five planes,
therefore, all have sizes and weights in the proportion of 500 grammes to the
square foot * (or 5,382 grammes to the square meter), and their soaring speeds are
entirely comparable for indicating the relative effect of shape and size. The new
observations were carried out on November 25, 26, December 5 and 11, and com-
prised over 80 individual experiments. The detailed observations of both series
are presented in Tables XIV and XV, placed at the end of this chapter.

The column headed “ description of planes” gives the dimensions and weight
of the planes. The aspect of the plane—i. ¢., its position with respect to the

*The square foot was adopted as a unit in the earliest experiments, and its use has been continued as a
matter of experimental convenience, owing to considerations bearing upon the uniformity of apparatus. Were
these experiments to be recommenced, IL should prefer to use C. G.S. (or at least metric) units throughout.

56 EXPERIMENTS IN AERODYNAMICS.

direction of advance—is indicated by the order in which the dimensions are
stated, the first dimension being always the horizontal edge parallel to the
whirling arm. Thus the 24 x 6 inch plane is placed with its 24-inch edge hori-
zontal and parallel to the whirling arm, and the 6 x 24 inch plane is the same
plane placed with its 6-inch edge horizontal and parallel to the whirling arm.
This difference of position, then, will be uniformly spoken of as the aspect of the
plane. The column “ pull of spring” contains the spring extensions converted
into pressures by means of the calibration curves, and the column “ horizontal
pressure on plane” (é. ¢., the horizontal component of pressure) is obtained by
multiplying the spring pressure by the factor 0.524, which arises from the unequal
lengths of the arms of the instrument. The next column, headed Coane
for the observations with normal planes the computed value of the coefficient in
the equation P=k,, V*, where V is expressed in meters per second, and P is the
pressure on the plane in grammes per square centimeter. The column ‘“%” gives
the corresponding value of this coéfficient in English measures, the velocity being

gives

expressed in feet per second and the pressure in pounds per square foot.
SOARING SPEEDS.

The soaring speeds determined in these two series of experiments are plotted
in Figs. 8 and 9, in which the abscissze are angles of inclination of the planes to
the horizon, and the ordinates are the soaring speeds which correspond to them.
Figure 8 contains the observations made with the planes that weigh 250 and 1,000
grammes to the square foot, and Fig. 9 those made with the planes that weigh
500 grammes to the square foot (5,382 grammes to the square meter). The
experiments with the first two of these classes of planes, plotted in Fig. 8, were
not repeated, and consequently the curves do not possess so high a quantitative
value as obtains in the case of most of the planes weighing 500 grammes to the
square foot, but they serve to present several fundamental relations :

First, they show quantitatively, when taken together with the curves of Fig.
9, the increase of velocity necessary to sustain the heavier planes (per unit area)
over that which will sustain the lighter ones, at the same angle of inclination.

Second, the curves both of the 250 and the 1,000 gramme planes show the
difference due to shape and aspect, the soaring speeds, for small angles of inclina-
tion, being much less for those planes whose extension from front to back is small,
than for those in which this dimension is large, so that, in general, the planes
having this dimension smaller, for small angles of inclination, soar at lower
speeds. This result entirely accords in character with that already obtained with
the Plane- Dropper; and, when freed from accidental errors, the present data are
of higher quantitative value, because in this apparatus there are no guides, and
the plane has practically perfect freedom.

THE COMPONENT PRESSURE RECORDER.

ee nc et fo) .
||P aeed LAincha We horiz 0. pie.
B.Ox24 inch plage, wi 1009 gramiméas,
D inch side horizoraal.)

Ou
~I

IBTGanoe

28
27
(30 ich azde\h Z
Cd

‘

ate 26

etree eee ee
25 | ¢

ae Ce ee ae a

(Ottech side \horizontal. 24
eo eee ee a eae
scale aoe a a

)

‘ iE oul ae

Lote coo ee
dad Glee

C oD .
30 Wech wide horizonitat.)

\ tO inch plane, weight 240 gra
t (2Hinch side| hoizonital.)

Velocities of soaring of inclined planes obtained with the Component Pressure Recorder.
Abscissz : = Angles of inclination (2) of plane to horizon.

Ordinates : = Velocities in meters per second.

58 EXPERIMENTS IN AERODYNAMICS,

Third, many of the curves show a tendency to reach a minimum point for
an inclination of the planes of about 30°, the highest angle at which these planes
were used. It was, therefore, seen to be desirable to extend the angles of inclina-
tion far enough to include the minimum point of the curve within the range of
observation. This was done in the case of four of the planes whose results are
plotted in Fig. 9. In examining these curves, it will be seen that the minimum
point falls between 25° and 35°. It should also be noted that the change in the
soaring speed is quite small for settings between 25° and 40°, and that in a
number of individual observations the real character of the curve over this range
was masked by the errors introduced by wind and weather.

Since the planes whose results are plotted in Fig. 9 all have the same
weight per unit area, the difference in their soaring speeds arises solely from their
difference of size, shape, or aspect. The effect of shape and aspect indicated in
Fig. 8 is beautifully exhibited and amply confirmed in the six comparable curves
of Fig. 9. For low angles, viz., below 15° or 20°, the curves of soaring speed
for the different planes oceupy the following relative positions from below
upward: 30 x 4.8 inches, 24 x 6 inches, 12 x 6 inches, 6 x 6 and 12 x 12,6 x 24
inches. It will be observed that the planes placed in the above order are
symmetrically arranged. Remembering that the first written dimension is the
horizontal edge, perpendicular to the line of motion, which may be called the
spread, and that the second written dimension is the inclined edge, or the distance
from front to back, it will be seen that, in the above order, the ratio of the spread
to the extent from front to back is uniformly diminishing. In other words, the
planes whose spread is largest in comparison with their extent from front to back
have the smallest soaring speed, and these planes are therefore to be considered
as being, in shape and aspect, the most favorable for mechanical flight. Thus the
30 x 4.8 inch and the 24 x 6 inch planes are favorable forms and aspects, while
the 12 x 12 inch plane and, to a greater degree, the 6 x 24 inch plane are
unfavorable forms and aspects.

Between 15° and 30°, and in general at about 30°, a reversal takes place,
and for higher angles the curves are all found from below upward in the reverse
order. Thus the 30 x 4.8 inch plane, which for low angles soars at the lowest
speed, for settings above 30° requires the highest speed. This relative efficiency
for low angles was manifested in the experiments with the Plane-Dropper, but
the reversal in the position of the curves for higher angles is a relation which
those observations were not sufficiently extended to present. The interpretation
of this reversal will be developed by a consideration of the general relations
existing between these results and the total normal pressure on the planes, and
will also be found to be connected with corresponding changes in the relative
positions of the center of pressure.

THE COMPONENT PRESSURE RECORDER. 59

Hire. 9:

Me | ld
Hi tee
AW Lees

Velocities of soaring of inclined planes obtained with the Component Pressure Recorder,
Abscissee : = Angles of inclination (2) of plane to horizon.
Ordinates : = Velocities in meters per second.

60 EXPERIMENTS IN AERODYNAMICS,

The pressure on a plane moving normally in the air is usually represented
by the equation
EeAWG B

where Vis the velocity of the plane; A is its area, B the atmospheric pressure
in millimeters, ¢ the temperature in centigrade degrees, and & a coéfficient whose
value for a standard temperature of 10° C. is determined by experiment. If the
pressure per unit area is different for planes of different sizes and shapes, it will
be manifested by differences in the resulting values of #. Then, if & be given
its value for a plane of some fixed size and shape, one or more additional factors
must be inserted in order that the formula shall give the pressure on a plane of
any other size and shape. Experiments show that the variations in & for planes
of different shapes and, within the range of experiment, for planes of different
sizes, are very small.

Proceeding now to the case of inclined planes, and for our present purpose
neglecting the pressure and temperature, we may represent the resultant pressure
P, on an inclined plane moved horizontally in the air at an angle a with the
horizon by the equation

P,=P, F(a) =k AV? F(a),

where F (a) is a function to be determined by experiment. From this equation
also we obtain directly the vertical component of pressure

W=P,cosa=k A V? F(a) cosa
and the horizontal component of pressure
R=P,sina=k A V* F(a) sina.

The point to which I wish now to direct especial attention is that, although shape
and aspect of plane have but slight effect on the pressure on normal planes, they
have a most important influence in determining the pressure on inclined planes.
Consequently, / (a) must be determined separately for planes of different size,
shape, and aspect. An empirical curve (Tig. 1) representing F (a) for a square
plane has been obtained from the experiments with the Resultant-Recorder.

It is obvious that the above equation for W furnishes the basis for determin-
ing F(a) for variously shaped rectangles from the observations of soaring speed
obtained with the Component-Recorder, together with experiments on normal
planes. The vertical component of pressure at soaring speed is the weight of
the plane, # is the fundamental constant of normal pressure derived from
experiments on the normal plane, and V is the soaring speed for the angle a.

THE COMPONENT PRESSURE RECORDER. 61

For the 12x 12 inch square plane, and for the 30x 4.8 inch and the 6 x 24
inch planes, which last two are the planes having the extremes of aspect, F (a)
has been computed from the above equation for W, and the results are plotted in
Fig. 10. In this computation W is 500 grammes; V is taken from the soaring
speed curves for successive values of a, and the adopted value of &,,, viz., 0.0080,
in metric units, is the mean value given by the normal planes in these experi-
ments. Comparing the resulting curve for the 12-inch square plane with the
curve derived from the experiments with the Resultant Pressure Recorder, we
find the following values:

TABLE XII.

F' (2), or the ratio of the pressure on an inclined plane one foot square,
to the pressure on the same normal plane.

y oe eens

a Soe sy

Ss Sore | eee

= eee | S285

= mews | 59.45

= et ow aa oes a Difference:
4 as Kh CS KA

oe ~~ O a3 o oO

2 Seen ee src=

2 SES cal asesne

<q Ey ey

45 93 91 + .02
40 89 88 + 01
35 84 S4 OO
30 78 78 00
25 71 69 + .02
20 60 oT + .03
15 46 44 + .02
10 3 30 OO
5 15 16 = {Oil

The agreement between these values of F («) derived from these two entirely
dissimilar methods of observation (dependent also, as it is, on the experimental
value of *,,) bespeaks the essential harmony of the entire system of results. If,
now, the curves of soaring speed have been determined for the 30 x 4.8 inch
and 6 x 24 inch planes with the same degree of accuracy as for the 12-inch square
plane, the computed values of / (a) for these planes has the same precision as
that for the 12-inch square plane.

Looking at the curves, we find that for small angles the resultant normal
pressure is greatest in the 30 x 4.8 inch plane and least on the 6 x 24 inch plane;
but for angles above 30° this relation is reversed.

The reversal in the relative positions of the curves of soaring speed at an
angle of inclination of about 30°, for differently shaped. planes, is now seen to

62 EXPERIMENTS IN AERODYNAMICS.

Hie. 10:

6X241NCH PLANE

9 BX 12 INCH. PLANE.
eee, if ae
ot

PLANE.
® | 0x 481NCH

[RA | |
P| ee

Ratio of the resultant normal pressure (P,) on an inclined rectangle to the pressure (P,,) on

a normal rectangle, computed from experiments with the Component Pressure Recorder.
Abscissee: = Angles of inclination («) of plane to horizon.
ea 7 W Realy. a
Ordinates: = /'(a) = —_______ = _—* (expressed as a percentage).
kA V? cos a pp |

THE COMPONENT PRESSURE RECORDER. 63

be due to a reversal in the total normal pressure on the planes.* Thus, shape
and aspect of plane, while having but slight influence in modifying the pressure
when the plane itself is normal to the wind, are most important factors when the
plane is inclined. This predominating influence of aspect is, so far as I am
aware, now for the first time clearly set forth with quantitative data.

HORIZONTAL PRESSURES.

With every observation of soaring speed, the horizontal pressure on the
plane has been measured by means of a horizontal spring. The detailed obser-
vations in Tables XIV and XV contain the number of the spring used, the
extension of the spring as measured on the trace in inches, the corresponding
pull of the spring, measured in grammes, as taken from the calibration curves,
and, lastly, the computed pressure on the plane, obtained by multiplying the pull
of the spring by the factor 0.524, which reduces the effect of the actually unequal
arms of the instrument to what it would have been were the arms equal. For
angles of 90° the instrument affords an additional method of determining the
constant of normal pressure, and for all these observations the resulting values
of &, and & have been computed. As previously used, the numerical value of &
relates to velocities expressed in feet per second and pressure in pounds per
square foot, and £,, relates to velocities expressed in meters per second and
pressures expressed in grammes per square centimeter.

The horizontal pressures on the inclined planes diminish with decreasing
angles of elevation, and for angles of 5° and under are less than 100 grammes.
Now, for a pressure less than 100 grammes, or even (except in very favorable
circumstances) under 200 grammes, the various errors to which the observations
are subject become large in comparison with the pressure that is being measured,
and the resulting values exhibit wide ranges. In such cases, therefore, the
measured pressures are regarded as trustworthy only when many times repeated.
On the 30x 4.8 inch plane, weight 500 grammes, fifteen observations of horizontal
pressure have been obtained at soaring speeds. These values have been plotted
in Fig. 11, and a smooth curve has been drawn to represent them as a whole.
For angles below 10° the curve, however, instead of following the measured
pressure, is directed to the origin, so that the results will show a zero horizontal

* For a further analogy with a corresponding reversal in the position of the center pressure, see Appendix C.

+ Only after completing these experiments has my attention been called to those of Hutton, who appears to
have been the first to make experiments in this field, in 1787, and who, it is interesting to see, appreciated the
necessity of examining this question of aspect. He tried a plane $ x 4 inches with both the long edge and the
short edge in the direction of the arms of his whirling machine, but failed to obtain any sensible difference in
his resulting horizontal pressure, probably because the friction of his apparatus swallowed up the small differ-
ences that exist in the horizontal component of the pressure at small angles. If he had measured the total
pressure or the vertical component, he would probably haye discovered a difference in the two cases. I also
find that while my experiments have been in progress, Mr. W. H. Dines has likewise been investigating the

effect of aspect, at Hersham, England, with results similar to my own.

64 EXPERIMENTS IN AERODYNAMICS.

Ercan il

500

400

300

200

100

ie
is
aged
Bak.
AE
a!
Saeed
a
a
a

0 5 10 | 20 25 30 35 40 45
Horizontal pressure (or resistance to advance) on 30x 4.8 inch plane at soaring speeds
obtained with the Component Pressure Recorder.
Abscissee : = Angles of inclination (4) of plane to horizon.
Ordinates : = Horizontal pressure (/2) in grammes.

THE COMPONENT PRESSURE RECORDER 65

pressure for a zero angle of inclination. This, of course, must be the case for a
plane of no thickness, and cannot be true for any planes of finite thickness with
square edges, though it may be and is sensibly so with those whose edges are
rounded to a so-called “fair” form. Now, the actual planes of the experiments
presented a squarely-cut end-surface one-eighth of an inch (3™™.2) thick, and
for low angles of inclination this end-surface is practically normal to the wind.
Both the computed pressures for such an area and the actually measured
pressures, when the plane is set at 0, indicate conclusively that a large por-
tion of the pressures measured at the soaring speeds of 2°, 3°, and 5° is end
pressure, and if this be deducted, the remaining pressure agrees well with the
position of the curve. The observed pressures, therefore, when these features
are understood, become quite consistent. The curve represents the result obtained
from these observations for the horizontal pressure on a plane with “fair ”-shaped
edges at soaring speeds.

A comparison of this experimental result can now be made with the formula,
which appears to be nothing else than an expression for a simple resolution of
forces. I say “appears,” since error is so subtle in its intrusion in these cases
that I have preferred to give the matter, even here, experimental confirmation.

From the analysis above given we have the equation R= W tan a, W being
the vertical component of pressure which, at the instant of soaring, is the weight
of the plane. For the purpose of comparing the points given by this equation
with the curve deduced from the observed pressures, the former are shown by
crosses on the diagram with the curve. The agreement between the two is
remarkably close, and, according to the standpoint from which the subject is
viewed, we may say that the formula is actually identifiable, as it appears to be,
with a simple case of the resolution of forces, or that the accuracy of the har-
monized experiments is established by their accordance with an unquestioned
law of mechanics.

WORK NECESSARY TO BE EXPENDED IN FLIGHT.

Having now obtained final values for the horizontal pressure, or the resist-
ance to the horizontal advance of inclined planes, and having determined their
soaring speeds at different angles of inclination, the work necessary to be expended
per minute in propelling such planes through the air is given in kilogrammeters
by the expression 60RV, 2 being the horizontal pressure in grammes, and
the soaring speed expressed in meters per second.

The following table, XIII, contains a computation, for the case of the 30 x 4.8
inch plane weighing 500 grammes, of the work necessary to be expended per
minute, the values of & being taken from the curve of figure 11:

66 EXPERIMENTS IN AERODYNAMICS

TABLE XIII.

ae ‘| Horizontal) Work expended per y gen a pian ee 2
Soaring speec pressure mite orm that 1 horse-power
ems ean R 6ORV. will drive through the
c Ratinon i | ie air at velocity V.
a. | es ae
Meters Feet “I Kilogram-| Foot- Kilo- F
Decne per second. Grornmnes. | meters. | pounds. | grammes. Pounds:
45° 11.2 36.7 500 | 33 2,43 6.8 15
380 10.6 34.8 275 175 1,268 3.0 29
15 ial 36.7 128 86 623 26.5 58
10 12.4 40.7 88 65 474 34.8 77
5 15.2 49.8 45 41 297 59.5 122
2 20.0 65.6 20 24 174 95.0 209
|

This table shows that for an inclination of 2° the velocity of flight which
suffices for soaring is 20.0 meters per second, and that the work expended per
minute to support the plane (weighing 500 grammes) is 24 kilogrammeters, or 174
foot-pounds. The last two columns contain the weight with planes of like form
that one horse-power will drive through the air at velocity V. At 2° this is 95
kilogrammes, or 209 pounds. This, strictly speaking, holds good only for a system
of planes whose weight, inclusive of any actual motor or other attached weight, is
500 grammes per square foot of inclined plane surface, and which is made up of
30 x 4.8 inch planes. The experiments with the Plane-Dropper show that in
horizontal flight at attainable speeds, a system of such planes can be made by
placing one above the other at a distance of about 4 inches without any sensible
diminution of relative efficiency. Whether these relations of power, area, weight,
and speed, experimentally established for small planes, will hold good in the
same ratios for indefinitely large ones, Iam not prepared to say; but from all
the circumstances of experiment, I can entertain no doubt that they do so hold,
far enough to afford entire assurance that we can thus transport (with fuel for a
considerable journey) weights many times greater than that of a man.

The preceding investigation, which results in an expression for the varying
amounts of work done by an elementary aerodrome driven at the various soaring
speeds corresponding to the various angles given, has been derived for the ease in
which the direction of propulsion of the aerostat is horizontal and in which its
plane makes an angle @ with the horizon. In the case of an actual aerodrome,
however, it will very probably be found advantageous to propel it in the line of
its plane at such an angle (in practice a very small angle) that the resultant
forward motion due to this elevation and to the simultaneous action of gravity
will be exactly horizontal. If in this case its horizontal velocity be represented
by V, the work done per unit of time will be expressed by the product of the

THE COMPONENT PRESSURE RECORDER. 67

weight multiplied by V tan a, the latter factor being the height H to which the
plane is virtually lifted against gravity.

It will be seen, now, that this expression is the same as that derived for the
former case, V being the horizontal forward velocity, and « the inclination of the
plane to the horizon. In order to prove the perfect identity of significance of
the two expressions it, would, however, remain to show experimentally that the
relation of V to a in this new case is the same as that experimentally derived for
the first case. I have made no experiments with which to determine this relation,
but I may say that, since all the circumstances of the resulting motion seem the
same in the one case as in the other, the relation between V and « is presumably
the same, and consequently the amount of work done in the second case is
presumably the same as that done in the first case; it is certainly so nearly so
that whenever a is small (and it always is so in such economic or horizontal flight),
we may, for all practical purposes, assume an identity of the two cases. It fol-
lows that, in soaring with (horizontal) velocity V, the direction of propulsion can
vary between 0° and «° at will, without sensibly changing the amount of work
that is expended, so long as the plane remains at the angle a with the horizon.

The reader who has followed the description of this instrument will see that
the experiments have consisted in measuring with a dynamometer the actual
resistance to motion experienced by planes when just “soaring” or supporting
themselves under all the circumstances of flight in free air, except that the plane
is restricted from the ‘“ flouncing ” caused by irregular currents, etc., and made
to hold a steady flight.

The most important conclusion may be said to be the confirmation of the
statement that to maintain such planes in horizontal flight at high speeds, less power
is needed than for low ones.

In this connection I may state the fact, surely of extreme interest in its
bearing on the possibility of mechanical flight, that while an engine developing
one horse-power can, as has been shown, transport over 200 pounds at the rate
of 20 meters per second (45 miles an hour), such an engine (?. é., engine and
boiler) can be actually built to weigh less than one-tenth of this amount.

68 EXPERIMENTS IN

AERODYNAMICS.

Experiments with the Component Pressure Recorder to measure the horizontal pressure on normal and inclined planes

and to determine their soaring speeds.

TABLE XIV—FIRST SERIES.

F. W. Very, Conducting experiments ; JosepH LupEwic, Regulating engine.

mare Mean barometer Mean temperature | Mean wind velocity
wat Qnillimeters). (centigrade). (meters per second).
|
1890. |
Sian oee PN) oe cousensouotecndsouseande | 741.0 14° 0.80
October te erent Sa te eco oe ce Noe ore 738.6 HT | 1.20
se Dapp oesyshe Reser sro yke ST uaa RRO 736.6 18 | 0.50
« Cena tie rae eee aa | 735.8 15 | 0.55
af Ae Seca retake jolene one 734.5 19 0.60
; OSs ee Deracateiettetueaies 727.7 15 0.60
af SUP cham cia orci eleg ea crear 736.6 15 0.80
& DP Seen eiabhs Merle Daten tiiek 740.1 17 0.50
5 coer alte ey. | See | eee
is €E5/5 | 23) e8| 8S
= Mccann feces cals
Date. Deseription of planes. = | Attitude of plane. => E I) oe as og | a | bm. k.
S bo 2 m | oS) of | 22
See eee ep | ous
S | Sesh eles =~ | Be
| =p eee es nee = a
S | @ - A bes Os
| < > 424|e a mo
1890. | em. cm.
Sept. 29 | 24 x 6 inches (61.0 15.2) | 30°.-................ AO e20 8 2088 et
| Weight, 500 grammes. UD) SOATIME Ty -1-t le -1- 4} 0.80 | 294 | 154
a 10 CO Siem ie piste AN O20 0229959120
cm. cm, F
Oct) i) 24 s<Gimchesi(G1Os15!2)) 1-90) Sears sei 4} 2.80 |1,858 | 712 | .0083 | .00158
rs Weight, 250 grammes. | 0) |) Srormabners condo ces 4
ss | 30 SO arias eens 2} 1381) 294) 154
G | 15 Shy eeesysietere “1 0.64 | 164 86
Oct. 2 | | 30 Bee) Peseckis tee 25 | 284] 149
i. | 15 SO Mey eas deanysrote
she | 10 Le Oe aiciereSotetetl 0.50) 184) 70
s | 9 CC Gia excheentere 0.45 | 121) 68
af 3 | Not quite soaring | 0.35 | 101] 58
nMOS OAT oye tet 0.39 | 107 | 56
Rs 2 were cen tr: OAL 113 59
x | O| Not soaring. 0.50 | 134 70 |
cm. em.
Oct. 3 | 24x 6 inches (61.0 x 15.2) | QO a sfires cheyvwhcset-Woesvers 6.7 0.88 | 567 | 297 | .0071 | .00135
- Weight, 1,000 grammes. | 90).......-.5.-4.... 7.2 1.21 | 708 | 871 |.0077 | .00146
‘a WOO) brrrererratererser ae 9.8 2.80 |1,858 | 712 | .0079 | .00151
‘ | | BON MS oamin oro 15.2 1.60 | 867 | 454
Ee 15 OS bee aes 16.2 0.95 | 594} 311
| | 10 saseaicncr ener agaiev<he 19.4 0.68 480 | 252
i | | 5 | Notsoaring......| 25.0 0.50 | 397 | 208 |

THE COMPONENT PRESSURE RECORDER. 69

Taste XT V—Continued.

| “Sm a an oie
= ieee | 2 2 | A i= |
g a Spe cremall erecta!
= Bes Gee ee aren ere
Date. Description of planes. = | Attitude of plane. => 2 Ses tah An k.
= | hs ll aa monet tones tee
I See een a m | o8
|} 2 6 8 ra Ss aS | nx
| "ap omasa,| 8) 3 ral ees
| A | Sn oat al senna E Ss |
< | |= 4 8 mo ao |
| | | |
1890. cm. em. | | | |
Dein Sale xo2/imehes) (30/5 x 30.5) | 90 |... 22 ee ee 9.5 | 4) 2.70 |1,325 | 694 |.0083 | .00157
s Weight, 500 grammes. WOON Eeteerncteerseias stare | 838 | “| 1.84} 970 508 |.0079 | .00150
a | 30 | Soaring........ | Oo Olas so10) | 22675
ee | 15 OF at Seah act. Wioeeele 222 Oi ieesco| OS /an sali eA
f 10 SO eerie tes ane 15.0 | CO als8) S83
os | 10 ee en career 14.6 2) 0.80} 197 103
7 | 5 He Peete ) ONO) |) Pa) LAO) alae 92
cm. em,
ia 1D sxe UF reves (OVD s* GUY) || GIO |osounscovessoooe 6.2 “) 2.20) 471 | 247 | .0069 | .00132
£ Weight, 250 grammes. SON FSoarine yl: 6.6 Sa OZ 2428 7
“ 15 ee it ul can) 130 68
“e 10 Pee Meyers 10.6 | “| 045} 120 63
a 5 ioe od ertearon | 14.6 “7 0.35 | 100 52
s 3 Sonate Sate eal 16.7 Hs) OZ) || able 59
se 2 CO sean: 18.8 “1 0.55} 145 76
nf 0 | Not soaring....| 23.1 “1 0.80 | 199 | 104
em. cm. | | |
Oe, Gb |) Tse 1 shovel ness (ROY) Se GLO) |W 5 poe acaoaenanece lee) 4} 1.25 | 726) 380 | .0084 | .00160
Weight, 1,000 grammes. DOW ersrcister Beare eee EL “| 2.48 |1,2385 | 647 | .0079 | .00150
Ne | 20) || Stommmines oooocsc PHS) || HT als || Bie) |) BOs
= 30 Soe) atetcscseusiehs 12.8 Se eSON On SnmAg9
15 Sr Sa cisarien stone 17.4 OO a Asal 228 |
Oct. 3 15 See tt tae AGT) | P20 LTS) S88il 2203
oi 10 pam Tete cuncostst 20.0 COO E2oN 285) 49 |
- 5 Sa eras teen ner: 95.5 | “; O80] 199 |. 104 |
cm. em. reall
Ogi, 7 || G sx Vb stadags (Gj2 se GLO) || MO) ||-scccccccesences 6.2 «| 2.65 | 563 | 295 | 0081 | .00155
i Weight, 250 grammes. 30 | Soaring........ 7.6 eon eo OSe peel
se 15 Sle eas arene 11.8 SI OLSO] 2165 | eats
is 10 Soares Ne serie 14.1 “| 0.60 | 155 81
ss 5 Oak Pile a O2O ee Gm elas,
a 3 | Nearly soaring..| 25.0 SO OON | 28am 128
em. em.
is Gexe Aime esi lS 22x G20) GON Fe ttarcter yet erenet stern 6.8 ) 2.70% 571% 299%) .0081%*| .00154**
ce Weight, 500 grammes. [POO eiterak siesta ete « 54 “1 2.08 458 | 287 | .0089 | .00169
S QOD | iets ssterscorrmaxcterer scetete 41 “! 110} 256) 134 | .0085 | .00161
* 30 | Soaring........ 10.5 “| 2:30 | 492) 258 |
15 | So nme eis 15.2 1.00 | 235) 128 |
a 10 ee ome any: 20.7 S 1 0.85 206 108
8 5 | SOP bRaesave eet 27.3 42 |! (ONG}5) 166 | 8&7 |
cm. cm. +4 |
9 6 x 24 inches (15.2 x 61.0) | 90 | Beis ae 1.3 4/ 1.70) 909] 476 | .0096 |.00182
. Weight, 1,000 prammes. | 90 |................ 5.7 “1! 0.95 | 597 | 3818 |.0103 | .00197
ie3OR |e Soanine seer set 14.6 «| 1-80) || 953) || 499 |
| 15 AEN eA ee 91.4 | “| 0.60| 450] 286 |
a 10 SE ere cayee 27.3 “1 0.80 | 294) 154

*Tyrace was at limit of admissible extension, and hence the correct results are greater than these values.

70 EXPERIMENTS IN AERODYNAMICS.

Taste XI V—Continued.

é Se | PIS || Be
~ : oral mM - fay
S SWS |Eloe| o8 | be
Date. Description of planes. @ | Attitude of plane.) %S Calneaeet cm locn Selec = Km k
re moe] s | -a cae Caan gees
© 3 Bee ee Bea ene 8 4
< > Zale ieee eee
2 Ee [eae ee eee SS
1890. cm. em.

Oct. 8 | 6 x 24 inches (15.2 x 61.0) | 15 | Soaring......... 21.8 2
e Weight, 1,000 grammes. 10 Pigeibeuctetanssisicne 28.6 - |
- 5 | Not soaring..... 380.0 O08 ells 59

cm. cm.
2 SUpeA Sam ches\((/ 6:25 122) 190) Same aeeeeeceeieee 5.0 “1 140 | 317] 166 | .0073 | .00138
f Weight, 500 grammes. DON rcsetsyecavsve eerste toe avers 6.0 “1 2.20; 471] 247 | .0075 | .00142
7 QO ey coy cveteloevete crete a cerece 6.2 “| 2.45 | 527 | 276 | .0076 | .00145
« 310) || Sophatole, ooaa0 cnc 10.6 “| 2.30'| 492 | 258
= 10 cahumieeher tyes te Weg ) 0.75 | 183 96
Se 10 abe mack eee ae 12.1 Soe ODOT ea Gs | eas
a Dillltaty ton piace eee 15.2 SN O4d a 22 64
e 3 | Not soaring..... 21.1 SS) O50) || BA 70
= ON Bscrarisctometee craart 25.0 SE LOLQON e2N Gis eels
cm, em.
e SU a4. Sun ch es\(7G-2exall 2!2)il (OOM hear eee else 5.8 “1 2.60 | 554} 290 | .0091 | .00173
i. Weight, 250 grammes. OO UR e tne eet a coe 4.3 “1 1.20] 277] 145 | .0086 | .00163
5 30) Searinesneesee 8.1 “1 1.80] 294] 154
is 15 SOR Soa cern 8.3 4 || (Oss0) | al) 70
ss 10 SOON Uke nee are 9.3 “1 0.35 | 100 52
3 5 SOD er cioraskatotete 13.5 OKO) |] alls} 59
# 3 SED Apkoisne an eenyee ule “1 0.55 | 145 76
ef Oe emer oteees 26.1 “1 0.50) 134 70
: DWEtactaemacsator ne 22.2 ae) ri | ales
u: ON edge dete ciekeee 27.9 fa leo ON oom meali6
| cm. cm.

Octo SOE<4s Snchiesi(7G:2exal 2°) O(n Renee ere a 5.8 AS OZ 490 | 257 |.0082 | .00157
. \iVesralonr, 1000 rerementaaes, © | C0) |lbecbcuscaccoocacr 8.3 rN Le 909 | 476 | 0074 | 00141
ce 30)|| Sarin es... are) 15.2 Salle (cle Si
i 15 SOM aren cere ete 17.1 “9 Pel 659 | 345
: 15 pe Nita cexete tac hers 17.4 2) 2.3 492 | 258
Ss 10 OT teyenierexegsrne 17.9 4
: 10 fey gers ee tten 18.2 Dales) 416 | 218
i 5 SOIT Bethe arlee 22.6 amelie 855 | 186

Average of 22 determinations of k» (at mean temperature, 16° C.) = .00816.

THE COMPONENT PRESSURE RECORDER.

TABLE XV—SECOND SERIES.

NovemMBer 25, 1890.—F. W. Very, Conductor of experiments.

Barometer, 730 mm.; temperature, 10°.0 C.; wind velocity, 2.4 meters per second.

Description of planes.

24 x 6 in. (24 in. side
horizontal).
Weight, 500 grammes.

oon Se | Angle of elevation 4.
°

HH
oe
oS
Attitude of plane. |35 §
Bed
388
oO eH

>
SOs oeeerertererster: 10.9
Sie OUD ce archist shen 11.2
Cot arapehtal sats 16.9
fy Moi acesk avs 17.2
Not quite soaring | 19.4
SLO aI Oy eerete errs 10.6
LO Decree 13.3

So EOS | Number of spring.

Extension of spring
(inches).

Pull of spring
(grammes).

on plane FR (gram’s).

Horizontal pressure

Remarks.

Adopt 19.6 for soaring speed.

Too small extension of spring
to give reliable pressure.

Novemser 26, 1890.—F. W. Very, Conductor of experiments.

Barometer, 736 mm.; temperature, 0°.0 C.; wind velocity, 0.3 meters per second.

Description of planes.

24x 6 in. (24 in. side
horizontal).

Weight, 500 grammes.

Same plane (6 in. side
horizontal).

6 x 6 inches.

Weight, 125 grammes.

: ee oleae cee
6 roe rer aublliey alla
art a Si se aes Se ecoited
SN a BG) alae | ae | ke
9 | Attitude of}. 8] 2 | 8 = | _e
o plane. ° e ° ¢ "OS State St s oO
a Sol! |. 68 | OS laa
© BAe) Slac| Hlésa
© Oo 3 = Sq aT ING
"eb rere et ie nee
q 2 5 nA 5 aS
OF ceoonbooees 16.6 3 | 0.10 2 14
Da Pity sveetoaeFos 18.5 3 | 0.40 82 3
3 | Soaring 16.2 3 | 0.45 86 | 45
5 e 14.4 3} 0.57 | 100} 52
Oe ereierershsrerecra 9.08 | 4 | 2.50 |1,068 | 558
DO Rlneeyrarkatr.c; 741 | 4] 1.70 | 749 | 392
DOM etacasraercc.s 7.99} 4] 1.85 | 803 | 421
QO Miers aioe avers 5.86 | 4] 0.97 | 404 | 238
|

OO gercesectses aces | 17.96 | 4] 2.40 |1,021 | 534
SOR emia revere 16.74 | 4] 2.05 | 885 | 464
| 3) Soaring...| 20.1 SOO! |” BOia ess
5 emer elon sy 3 | 0.60] 100) 52
10 seers LOO) 3 | 073 | 113) 59

0074
0077
0071
0075
0071
0071

00141
00146

00136
00142

00136
00136

Remarks.

~I
1)

EXPERIMENTS IN AERODYNAMICS.

Tabte XV—Continued.

= | oH) Bl a@ | SS | Be
ra i SHO ial ear ee g " & ;
Description of planes. = | naciruge OF) a els ue ae |S | Km. es Remarks.
es p ane. = - S = a & S = = 2
le Se 2S a Sa ieconl ones
| | See) reales Nase
a Sae| Ele |e |8a
=< | [= 4|e ay =e
| !
12 x 12 inches. HO’; Conese ee 167 | 3| 035| 77 | 40
Weight, 500 crammes.; @|........... elie 3 | O40 84 | 44
21) Not soar-| 20.7 | 3] 0.70} 109] 57
2\) ine. 16.7 3 || (OLSi3) 95 | 450
3) | Nieanliy, 1) e209 in| ele OO) amete llega (oO) eetepet eee Adopt 21.4 m. per see.
soaring. | | as probable soaring
5 | Soaring. ..| 201 3 speed.
OMe CoP esieeiot ane) gS
| 20 | SO eee mlah SLY MIN MBA eters. alle meters (Orage eer ekarees eae Spring extended to
| 0) Soh alaleil Gi a limit.
(PSO) fr. Reel eS OPN ean
VIO Oey F_UN aes
IOI tee crac Suen 0078 | 00148
SOM ease aah 8.45 | 4) 0077 | .00146
DOM epwepicty ta ers Ona a 2e70 995 | 0077 | .00146
| QO hese, eo cern: 8.11] 4] 2.00 | 863 | 452 | 0074 | .00141
12x 6in. (12in.side| 0 | Meo etek 18.6 3 | 0.55 95 | 50
horizontal). es | Searcely | 18.8 | 3] 0.67] 107| 56]...... Ifoencneees Probable soaring speed,
Weight, 250 grammes. | soaring. | 19.2 m. per sec.
| 5 | Soaring...) 175 | 3| 0.78| 115 | 60
10 | sf Seales 3 | 1.00 13 69
(| ns eee rE 3) ale Se | 85) |
20 | eres ON oa R03 30] Mason ese
30 ee Os a Olga |) Bea || ns!
45 Sa eee LOL 4) tld | 522) | 273
DOG aise 7.78 | 4} 0.83 | 899 | 209 | 0074 | .00141
EGON eee eee 9.09 | 4] 1.21 | 549 | 288 | .0075 | .00142)
QO iiareaeiareoaccsaa che | 10.89 | 4] 1.98] 862 | 452 | .0082 | .00156
G08 | Setecseete eons tete 12.50 | 4} 2.55 |1,089 | 571 | .0079 | .00150
AOU Nees gee ec saacee 11.19 | 4) 2.02] 871 | 456 | .0079 | .00149,
nt aes he 10.00 | 4] 1.60] 704 | 869 |.0079 | .00151!
QD |ccm coer. 8.14} 4) 1.00 | 463 | 248 | 0079 | 00150)
30x 4.8in.(30in.side| 0 |........... 1798 oS hMO30) |) teaalness
horizontal). 2) soamime se 20 eee OO ON lee 65
Weight,500grammes.| 3) “ ...| 17.8 | 3) 1.04] 184] 70
5 | eal) ala) 3 | 1.12 etsy || 2
|10} “ ...| 126 | 3| 1.92) 197 | 103
DON leictxere helene re | alate 3 3.34 | 300 | 157
UN peek eee be AG |) 4) O70) 2950) 155
30 | Soaring...) 10.8 4 | 1.21 | 550} 288
Aba © 6 etal D | ae os19) CON ear
SUB soe eeeeer| 8.39 | 4] 2.20) 935 | 490 | .0075 | .00143
Dear eevee eee 10.26 | 4 | 3.30 |1,380 | 723 | .0074 | .00141
Ray aaa 8.00 | 4| 205 | 885 | 464 |.0078 | 00148

THE COMPONENT PRESSURE RECORDER.

TaBLE XV—Continued.

December 5, 1890.—F. W. Very, Conductor of experiments.

Barometer, 732 mm.; temperature, -+ 1°.0 C.

; wind velocity, light.

v | Sz Soe et Ree
o st Pres Sans
8 BS | S| | | 88
ae Papeete: RAIS
Ss NeZans B Mian ees ee
5 Oe | es ||) oo 4) eh ee
. . - = | - is
Description of plane. | 3 | Attitude of plane. |S) 4% | 2S [4g leas Remarks.
SI ce Os OPS Ons | aq
= Stee ee [neues t| oS
© SCS a an a aV7/Ne
"bp oes 2 | 2 Ea | Bic)
a "oO S| kK Bay its
< = 4 |e a =
12 x 12 inches. 10°, More than soaring.| 15.8
Weight, 500 grammes. | 10 | Soaring..........| 15.0 | 3] 1.80} 191 | 100
|
Flange of cone-pulley broke and stopped observations for the day.
DrcempBer 6, 1890.
Barometer, 730 mm.; temperature, + 2°.5 C.; wind velocity, calm.
; sae 5) 9) oA |
8 On Bn
g AS ey S| a 5 a
9 Qo eas als
6 cq g : “a wm . 2 aN 2 a
3 Owns a = “a ep
al CRS rae an ae
Sr a 5 Cet - & = nizq
Description of planes. s | Attitude of plane. |= SS |g 3 = 5 Ee S Nemarks.
oa 3 =
° eee sf rsei lees a
2 SOaGH| Oo] a a=
Tap | eae! | 2 x peta
S ces eae 3 o8
<i | > 24/2 Ay q
|
12 x 12 inches. 20° Soaring ......-.. 12.8] 3] 2.60 | 245 | 128 | Velocity of soaring not so well
Weight, 500 grammes. determined as on Noyem-
ber 26.
20 | SO tee ye aha: LO earn regents |heeeeiel | etexct Velocity of soaring not so well
| : : determined as on Novem-
30 | Mee ie intesehehcshsh 10.3 | 4] 1.10 | 500 | 262 ber 26.
45 | OS naseGeterers 11.4 | 4] 2.20 | 939 | 492 | Velocity of soaring not so ac-
45 | Not soaring......| 10.0 | 4] 1.82 | 794 | 416 curately determined as on
30 | Ea ae pce 10.0 | 4 | 0.85 | 408 | 214) November 26.
30 | “ NF Nascar 10.0 | 4] 0.75 | 340 | 178
20) “ Aes 10.0} 3] 1.00} 15 69
80 x 4.8 inches. 5 | Not quite soaring TAT Bel yatetal ie ceroeet cl] encresciltenenevete 14.9 meters per second assumed
|

Weight, 500 grammes.

as soaring speed.

Fine mist throughout the observations.

74 EXPERIMENTS IN AERODYNAMICS.

Taste XV—Continued.

December 11, 1890.—F. W. Very, Conductor of experiments.

Barometer, 724 mm.; temperature, + 5° C.; wind velocity, 0.8 meters per second.

S| ne oo |e =a ae
S | oe ./4/8 |salés
g Atiinae one = e\se| og |aS
enith _| 5 | Attitude o S| os Sel Seow
Description of planes. 3 mince = S 3 es <5 ge Kae
"Sb cS ieyee aie ne ieee
a S| Hw = 5
< > Z2\|e ae
30 x4:81n. (0im. side | 90°)... 552.-...- 8.30 | 1} 1.80 | 930 | 487 | .0076
horizontal). 9O |... . sees eee | 9.15 | 1} 2.20 |1,098 | 576 | .0074
Weight, 500 grammes. | 45 | Soaring....| 11.38 1} 2.10 | 1,057 | 553
380 ss eee |toceieres 1| 0.91 | 557 | 292
20 ws peer LOL 1 | O47 | 350 | 183
15 « eee | elidel 3
Ose woosoracds 20.7 3 | 0.20 59 | 381
Dae Opt (AAI SIC Onl NON cpersretcdeeererectele 20.7 3 | 0.20 59 | 31
horizontal). 10 | Soaring....} 18.0
Weight, 500 grammes.

0.00144
0.00140

Remarks.

Mean of 22 determinations of i, (at temperature 0° C.) = 0.0076.

CHAPTER VII.

THE DYNAMOMETER-CHRONOGRAPH.

Having determined by means of the Component- Recorder the resistance that
must be overcome in moving a material plane horizontally through the air at
different speeds, the next step of my investigation has consisted in devising means
for measuring the power that must be put out by a motor in doing this useful
work; for, by any form of aerial propulsion, the useful work that can be derived
from the motor is only a percentage, either large or small, of that which is
expended. It becomes important, therefore, to determine the ratio between the
propelling force obtained, and the amount of power that must be expended in any
given case.

In devising the following apparatus I have confined my attention to aerial
propellers for reasons of present convenience, and not because I think them the
only practicable method of propulsion, although they are undoubtedly a most
important one.

If we consider the actual circumstances of such experiments, where the motor
under investigation is mounted at the extremity of the large turn-table arm and
is in motion, frequently at a rate of over a mile a minute, and that the end of
this slender arm is 30 feet from any solid support where an observer might be
stationed, it will be seen that the need of noting at every moment the action of
apparatus, which under such circumstances is inaccessible, imposes a difficult
mechanical problem. After trying and dismissing other plans, it became evident
that a purely automatic registry must be devised which would do nearly all that
could be supposed to be done in the actually impracticable case of an observer
who should be stationed at the outer end of the whirling arm beside the apparatus,
which we may suppose for illustration to be an aerodrome moved by a propeller.
The registering instrument for the purposes desired must indicate at every
moment both the power expended on the supposed aerodrome to make it sustain
itself in flight, and also the portion of that power which is utilized in end-thrust
on the propeller shaft, driving the model forward at such a rate as to maintain
soaring flight, under the same circumstances as if it were relieved from all
constraint and actually flying free in a horizontal course in the air. For this
purpose a peculiar kind of dynamometer had to be devised, which, after much
labor over mechanical difficulties, finally became completely efficient in the form

(75)

76 EXPERIMENTS IN AERODYNAMICS.

I proceed to describe and which I have called the Dynamometer-Chronograph.
A plan of the instrument is given in plate VIII. Its method of operation in
measuring and registering (1) the power expended in producing rotation and (2)
the useful result obtained in end-thrust is here separately described.

(1) MEASUREMENT OF THE POWER EXPENDED.

The propeller wheel L, which is to be investigated, is fastened to the shaft
SS’, which becomes its axis, and is driven by a belt running from the pulley.

When the pulley is driven from any source of power, the resistance offered
by the air to the rotation of the propeller develops a torsional force on the shaft
SS’. This shaft is divided into two portions at the clock-spring in the upper end
of the cylinder D, so that the torsional force set up by the pulley is transmitted
to the rest of the axis and to the propeller through the spring in question. This
torsional force can and does cause the cylinder E, which turns with the propeller
end of the shaft, to be twisted with respect to D, which rotates with the pulley,
until the force is balanced by the winding tension of the clock-spring. The rela-
tive angular motion between the pulley and the shaft S causes a longitudinal
motion of the cylinder E into the cylinder D, by means of a spiral groove cut in
the cylinder D, in a manner which is sufficiently shown in the drawing, so that
there can be no angular movement of the pulley C relative to the shaft and to
the cylinder E, without a corresponding longitudinal motion of the cylinder E
and of the pencil P’, which registers the amount of this longitudinal motion
on the recording cylinder; and it will be observed that there will be no angular
motion and no linear motion, unless work is being done by the pulley ; for, if the
propeller wheel were removed, or if its blades were set with their planes in the
planes of its rotation, however fast the pulley may be driven, there will be no
record. The linear motion of the pen P” is, then, caused by, and is proportional
to, the torsional force exerted by the pulley, and to this only. It is obvious that
if the recording cylinder revolve at a known rate, the pencil trace will give a
complete record of the two necessary and sufficient factors in estimating the total
power put out, namely, the amount of this power from instant to instant (how-
ever it vary) and the time during which it is exerted; the former being given by
the “departure” of the pen from its normal position, the latter by the length of
the trace, so that a complete indicator-diagram showing the power expended is
found on the sheet when it is unrolled from the cylinder. The abscissa of any
point in the developed curve is proportional to the time; its ordinate, which
represents the departure of the pencil parallel to the axis of the cylinder, is pro-
portional to the tension of the clock-spring. The value of this departure, or the
actual stress it represents, after allowing for all circumstances of friction, is
obtained by calibrating the spring by hanging weights on the circumference of

THE DYNAMOMETER-CHRONOGRAPH. i

the pulley. This departure, then, corresponds to the effect of a definite and
constant weight so applied, so long as we use the same spring under the same
adjustment. When widely different ranges of power are to be measured, the
additional range of tension required is obtained with the same spring by insert-
ing a set-screw in successive holes, numbered 0 to 15, around the end of the
cylinder D, so as virtually to shorten or lengthen the clock-spring. A separate
calibration is, of course, required for each setting.

(2) MEASUREMENT OF THE END-THRUST.

I have thus far spoken of the shaft or axis as if it were in one piece between
the clock-spring and the pulley, but for the purpose of measuring the end-thrust
the shaft is also cut in two within the cylinder F. The two pieces are maintained
in line by suitable guides, and forced to rotate together by a fork within I’, but
the propeller end of the shaft is given freedom of longitudinal motion. Any end-
thrust on the axis, whether received from the propeller or otherwise, causes, then,
this portion carrying the pencil P to slide up within the other toward the pulley,
telescoping the part of the shaft next the propeller within that next the clock-
spring, and causing the longitudinal compression of the spiral spring in cylinder
F, as shown in the drawing. All the parts of the axis, then, between the
clock-spring and the propeller must rotate together when the latter is revolved,
but the end of the axis nearest the propeller, and this end only, has the
capacity not only of rotatory but of a longitudinal motion, which latter is per-
mitted by this portion of the axis telescoping into the other, as above described.
The force of the end-thrust is recorded by the “departure” of the pencil P, which
bears a definite relation to its own spring, determined by independent calibration.
The record made by P on the recording cylinder is a curve whose abscissze are
proportional to time and whose ordinates are proportional to end-thrust. This
curve cannot by itself properly be called an indicator-diagram, since, taken
alone, it records a static pressure only, but when the experiments are adjusted
in a manner later described in this chapter the record of the speed of the turn-
table (on which it will be remembered this apparatus is being carried forward)
supplies the requisite additional data that an indicator-diagram demands. Hence,
while the pencil P” actually traces an indicator-diagram giving the expenditure
of power at every moment, the pencil P traces in part a second indicator-diagram
giving synchronously the useful result attained.

A third pencil, P’, records the seconds of a mean time-clock through the
action of an electro-magnet, M, and obviously gives the means of determining
with all needful precision the time corresponding to each element of angular
rotation of the cylinder, even should this vary. ‘This time record, then, serves
two purposes: (1) it gives the speed of rotation of the cylinder, and (2) permits

78 EXPERIMENTS IN AERODYNAMICS.

the traces to be synchronized with the speed of the whirling table registered on
the stationary chronograph.

The cylinder is rotated in either of two ways: (first) by the driving pulley,
through a system of gearing, which gives the cylinder rates of rotation equal to
L000; F000; OF ry ve that of the driving pulley according as desired, so that the speed
of the pulley is thus measured by the rate of rotation of the cylinder; or (second)
the cylinder may be independently rotated by an attached clock when it is desired
to give it a uniform motion rather than to record the speed of the pulleys. In
practice the clock and recording cylinder have been used as the registering appa-
ratus in most of the experiments already described with other instruments.

The drawing shows a portion of an actual dynamometer trace which was
obtained with the instrument when set in motion by a foot-lathe, the power
supplied by the foot through the fly-wheel of the lathe being transferred by a
belt to the pulley and thence to a propeller wheel carried at the end of the shaft
S. The pencil P”, it will be remembered, is connected with the clock-spring, its
“departure,” or motion parallel to the axis, being in this case at every instant
proportional to the tension at the same instant at the circumference of the pulley.
P’ is the pencil, which records every beat of the mean time-clock, while the trace
made by the third pencil, P (in the case actually under consideration, in which
the dynamometer is at rest), measures the static end-thrust obtained from the
propeller blades for the amount of power put out. I may ask attention to the
comparability of these two absolutely independent traces, and invite the reader
to note how perfectly the relation of end-thrust obtained responds to the power
expended. The person turning the lathe did so with the greatest uniformity
attainable by the use of a heavy fly-wheel, but every motion of the foot is, never-
theless, as will be seen, most conspicuously registered. Every change in the
amount of power finds also its counterpart in a variation of end-thrust, and the
inequalities in the application of the power during a single revolution of the fly-
wheel of the lathe may be distinctly traced not only in the first of the two curves
but in the second. (It is interesting to note that in each stroke the power pen P”
starts up sharply and then comes nearly or quite back to the zero line, although
we see from the pen P that work is being done all the time. This is repeated
substantially at every stroke of the foot, in spite of the inertia of the lathe fly-
wheel, and is an indication of the extreme sensitiveness of the apparatus.)

Preliminary to the use of the dynamometer it was necessary, as has been
explained, to calibrate the clock-spring and the end-thrust spring and prepare
curves or tables for evaluating the readings of the traces.

The clock-spring was calibrated in the following manner: The propeller
end of the axle being held fast, weights were applied at the circumference of the
large pulley, 10 centimeters diameter, by means ofa cord. The torsional force

THE DYNAMOMETER-CHRONOGRAPH. 79

of these weights at a lever-arm of 5 centimeters (the effective radius of the pulley)
is balanced by the tension of the clock-spring and is measured by the longitudinal
motion of the pencil P’. On account of the appreciable friction of the guide-
wheel in the helical groove, two measures are desirable for exact calibration in
each case at an upper and lower limit of repose. The mean of these is taken as
the true extension for the given weight, and the observation is repeated three
times with each weight to eliminate errors of observation. This series of observa-
tions was made with the set-screw in the “0” hole, the 5th hole, and the 10th
hole, in order to get a sufficiently wide range of action for the instrument.

The following table, XVI, gives the system of calibration obtained from
experiments made November 14, 1890—F. W. Very, observer:

TaBLe XVI.
Calibration of Clock-Spring of Dynamometer.

Weight applied at circumference of large pulley, effective radius 5
centimeters, by cord passing over a small pulley at edge of table.

Weight. Extension of trace.
BES C(O S C00
Pounds. |Grammes.| Inches. | Centimeters.
lOthyholesseeeeceeres 4.32 1,960 1.84 4.67
4.10 1,860 1.70 4.32
3.88 1,760 1.49 3.77
3.44 1,560 1.02 2.59
3.22 1,460 0.86 2.18
3.00 1,360 0.60 1.52
2.78 1,260 0.37 0.94.
EXGME Ol Geese sitar 3.00 1.860 1.82 4.62
2.78 1,260 1.60 4.06
2.56 1,160 1.35 3.43
2.34 1,060 | Isls} 2.92
Delo, 960 | 0.88 2.24
1.90 860 0.66 1.68
1.68 760) | 0.41 1.04
}
BOP Iivalle\6 asanesoode | 1.83 830 | 1.86 473
1.61 730 1.64 4.17
| 1.30 630 1.39 3:53
1.17 530 1.18 3.01
0.95 430 O.91 Deol
0.73 330 0.71 179
0.51 230 0.49 1.24
0.29 150 0.25 0.63 |
0.07 BOM Ons 0.38
1

80 EXPERIMENTS IN AERODYNAMICS.

The end-thrust spring was calibrated by suspension of weights in a similar
way. The following calibration was obtained from experiments made March 8,
1888 :

Calibration of End-Thrust Spring.

Weight. Extension of |

trace.
(Grammes). (Centimeters).
100 0.43
200 1.07 |
300 1.75
400 221

The method of computing the horse-power expended, and the return in end-
thrust obtained, may now be illustrated in the reduction of the following observa-
tions taken without change from the original notes:

OcroBEeR 380, 1888.

Six-bladed propeller, with blades set at 45° with axis. Dynamometer driven by belt from a
small dynamo. Belt driving 2.1 inch pulley. Dynamometer geared so as to give one revolution
of cylinder for 2,000 revolutions of pulley. Time of one revolution of cylinder, 295 seconds.
Departure of pencil of clock-spring (set-screw in “0” hole), 1.48 inches.

60 x 2000

39, revolutions per minute. Circumference of

2.1 1416 , z , 2000 x 2.1 x 3.1416
pulley equals oe feet. Velocity of belt equals ee feet

Driving pulley makes

per minute. From calibration of March 8, 1888, an extension or departure of
1.43 inches of the pencil of the clock-spring, with the set-screw in “0” hole,
is equivalent to a weight of 1.35 pounds on a 3.9-inch pulley. The tension on
the present 2.1-inch driving pulley is therefore 1.35 x = pounds. Multiplying

tension of belt by velocity of belt and dividing by 33,000, we have the work
expended per minute expressed in horse-power, viz:

60 x 2000 135 x 3.9 1.85
295 x 12 :

It will be noticed that in this expression the factor 2.1 has dropped out, and the
only variables are the time of one revolution of cylinder and the tension on the
spiral spring taken from the calibration curve. If the former be represented by
a and the latter by 6, and the gearing remain unchanged, the horse-power in any

experiment will be given by the formula 3.713 x ’.

THE DYNAMOMETER-CHRONOGRAPH. 81

I lave now to ask attention to a condition of vital importance in the experi-
ments, and yet one which may, perhaps, not appear obvious. It is, that it is
indispensable that the power expended on, and obtained from, the propeller shall,
for its economical use, be expended on fresh and undisturbed masses of air. To
make my meaning clearer, I will suppose that the Dynamometer-Chronograph is
mounted on a fixed support in the open air, with the axis pointing east and west,
and that in a perfect calm a certain amount of power (let us suppose 2 horse-
power) is put out on a pulley and through it on the propeller, giving a certain
return in end-thrust. Under these circumstances, let the wind blow either from
north to south or from south to north; that is, directly at right angles with the
axle, so that it might at first sight appear that nothing is done to increase or
diminish the amount of end-thrust to be obtained. The amount of end-thrust
under these circumstances will, in fact, be very greatly increased (even though
the constant expenditure of m horse-power be maintained)—so greatly increased,
that a neglect of such considerations would completely vitiate the results of
experiment, the great difference being due to the fact that the propeller-wheel is
now operating from moment to moment on fresh masses of air whose inertia has
been undisturbed.

This being understood, it is not desirable for our purpose to experiment
upon the case where the air is carried at right angles or at any very considerable
angle to the propeller shaft—a case which is used here only for illustration of a
principle. The circumstances of actual motion cause the wind of advance to be
always nearly in the line of the shaft itself; and this condition is obtained by
moving the instrument so that the wind of advance caused by the motion of the
turn-table is in this direction. It is this supply of fresh material (so to speak)
for the propeller to work upon, which causes the need of noting minutely the
speed of advance, as affecting the result, so that for a given constant quantity of
power expended, the percentage of return in end-thrust depends upon the rate
of supply of fresh and undisturbed masses of air. These considerations very
intimately connect themselves with the theory of the marine screw-propeller, and
the related questions of slip and rate of advance, but I have preferred to approach
them from this somewhat less familiar point of view.

The dynamometer and propeller were therefore mounted, as has been said,
on the end of the whirling-table. The propeller was driven by means of its
pulley C by a belt from a small electro-motor also on the turn-table, the motor
being actuated by a current from a stationary dynamo, shown on plate II. This
dynamo sent a current through the brush contact B of the whirling-table to the
small electric motor mounted on the arm. The whirling-table was then raised

82 EXPERIMENTS IN AERODYNAMICS.

out of its gearings by the means shown in plate IT, and with full current from
the dynamo the little propeller blades proved capable of rotating the great turn-
table, though slowly, for manifestly the work to be done in moving this great
mass was quite incommensurate with the eapacity of a small propeller of 15 or 20
inches radius. Some special means must therefore be devised for utilizing the
advantages given by the attainable speed, steadiness, and size of so large a
whirling-table, without encountering the disadvantages of friction, resistance of
the air to the exposed surface, and similar sources of difficulty. To place the
propeller wheels, either actually driving inclined planes or models, or otherwise,
so far as possible under the conditions they would have in actual free flight, and
to measure the power put out in actuating them, the resistance experienced, ete.,
under these conditions, is evidently an object to be sought, but it is equally
evident that it is difficult of attainment in practice. Much study and much
experiment were given to this part of the problem, with the result of the inven-
tion, or rather the gradual evolution through successive forms, of the auxiliary
instrument described in the last chapter as the Component Pressure Recorder.
This conception of a method by which the Dynamometer could be effectively
used was reached in February, 1889, and, together with its final mechanical
embodiment, was the outcome of much more thought than the invention of the
Dynamometer itself.

As already stated, one of the objects of the Dynamometer is to determine the
power necessary to be expended in mechanical flight; but manifestly this must be
done indirectly, for we have to experiment with a model or an inclined plane so
small as to be incapable of soaring while supporting the relatively great weight of
the Dynamometer-Chronograph, even if it had an internal source of power capable
of giving independent flight (which the simple inclined plane has not). If such
a working model were placed upon the end of the turn-table arm, with the
Dynamometer supported on this arm behind or beneath it, and if the arm of the
turn-table were without inertia and offered no resistance to the air, the whole
might be driven forward by the reaction of the propeller of the model, actuated
by a motor, until the latter actually soars, and the Dynamometer supported on
such an imaginary arm might note the work done when the soaring takes place.
This conception is, of course, impossible of realization, but it suggests a method
by which the actual massive turn-table can be used so as to accomplish the same
result. Suppose the model with attached propeller and Dynamometer to be placed
on the end of the whirling arm, and the latter rotated by its engine. Further,
suppose the model aerodrome be also independently driven forward by its pro-
peller, actuated by an independent motor, at the same speed as that of the table;
then, if both speeds are gradually increased until actual soaring takes place, it is

THE DYNAMOMETER-CHRONOGRAPH. $3

evident that we reach the desired result of correct dynamometric measures taken
under all the essential circumstances of free flight, for in this case the propeller is
driving the model independently of any help from the turn-table, which latter
serves 1ts purpose in carrying the attached Dynamometer.

As a means of determining when the propeller is driving the model at a
speed just equal to that of the turn-table, let the whole apparatus on the end of
the arm be placed on a car which rolls on a nearly frictionless track at right
angles to the turn-table arm. Then, when the turn-table is in rotation, let the
propeller of the model be driven by its motor with increasing speed until it
begins to move the model forward on the track. At this moment, that is, just
as the aerodrome begins to move forward relatively to the moving turn-table,
it is behaving in every respect with regard to the horizontal resistance (é. @.,
the resistance to advance), as if it were entirely free from the table, since it is
not moved by it, but is actually advancing faster than it, and it is subject in this
respect to no disturbing condition except the resistance of the air to the bulk of
the attached Dynamometer. In another respect, however, it is far from being
free from the table, so long as this helps to take part in the vertical resistance
which should be borne wholly by the air; the aerodrome, in other words, will
not be behaving in every respect as if in free air, if it rests with any weight on
the track. The second necessary and sufficient condition is, then, that at the
same moment that the model begins to run forward with the car it should alse
begin to rise from it. This condition can be directly obtained by rotating the
turn-table at the soaring speed (previously determined) corresponding to any
given angle of the inclined plane.

This conception of a method for attaining the manifold objects that I have
outlined was not carried out in the form of the track, which, although constructed,
was soon abandoned on account of the errors introduced by friction, ete., but in
the Component Recorder, whose freedom of motion about the vertical axis provides
the same opportunity for the propeller-driven model to run ahead of the turn-
table as is offered by the track. This instrument, therefore, a part of whose
functions have been described in the preceding chapter, has been used as a neces-
sary auxiliary apparatus to the Dynamometer-Chronograph, and this is an essential
part of the purpose for which it was originally devised. In naming the instru-
ment, however, only a part of its purpose and service could be included, or of
the mechanical difficulties that it surmounts indicated.

The investigation of the velocity at which an inclined plane will sustain its
own weight in the air, and the determination of the end-thrust, or horizontal
resistance, that is experienced at this velocity, were made with the Recorder
independently of the Dynamometer, and have been presented in detail in chapter

84 EXPERIMENTS IN AERODYNAMICS.

VI. The investigation of the power that must be expended to furnish this end-
thrust, and the determination of the best form and size of propeller for the pur-
pose, combines the use of the two instruments.

In the center of the Recorder is provided a place (see plate VII) for the
electric motor already referred to, whose power is transmitted by a belt to the
pulley of the Dynamometer-Chronograph, which is mounted on the end of the rigid
arms. It may be observed that, in this manner of establishing the motor, the
tension of the pulley, however great, in no way interferes with the freedom of
motion of the arms of the Recorder—a very essential mechanical condition, and
one not otherwise easily attainable. With the various pieces of apparatus thus
disposed, and with the propeller to be tested fastened to the shaft of the Dyna-
mometer, the whirling table is rotated at any desired speed. The propeller is then
driven by the motor with increasing amounts of power until the forward motion
of the Recorder arm about its vertical axis indicates that the propeller is driving
the Dynamometer ahead at a velocity just exceeding the velocity of the whirling-
table. ‘This is the moment at which all the records admit of interpretation. The
work that is being done by the propeller is that of overcoming the resistance of
the air to the bulk of the Dynamometer, and in place of this we may substitute,
in thought, the resistance that would be caused by an aerodrome of such a size
as to produce the same effect. The power put out and the resistance to advance
are both registered on the cylinder of the Dynamometer. The result realized is
found by multiplying the static pressure indicated by the pencil which registers
the end-thrust by the velocity of the turn-table at the moment when the pro-
peller’s independently acquired velocity is just about to exceed it. The static
pressure represents the resistance overcome, and the velocity of advance gives
the distance through which it is overcome per unit of time. The product there-
fore represents the effective work done per unit of time. If the adopted velocity
of the whirling-table be the soaring velocity of an aerodrome which would have
the actually observed resistance, the experiment will virtually be made under all
the conditions of actual horizontal flight. In practice, the experiments were
made at a series of velocities, and the results obtained—power expended and
useful work done—ean be interpolated for any desired speed.

Preliminary experiments were made with wooden propellers having four,
six, and eight blades set at different angles with the axis. Lastly, two aluminum
propellers were used having only two blades each, extending 24 and 30 inches,
respectively, from tip to tip.

In order that the reader may follow the method of experiment in detail, the
following description of experiments made November 4, 1890, is here given,
together with abstracts from the original record of observations for that date :

THE DYNAMOMETER-CHRONOGRAPH. 85

Novemser 4, 1890.

Continuation of experiments with 30-inch (diameter) two-bladed aluminum propeller to determine ratio
of power put out to return in end-thrust obtained.

Dynamometer-Chronograph with attached propeller is placed on outer arm of the Component-
Recorder and driven by an electric motor placed in the center of the Recorder. The electric motor
is run by a dynamo, the current from which is carried to the heavy brush contact B (plate IL) of
the turn-table, and thence along the arm to the electric motor, and the dynamo itself is ran by
the steam-engine which drives the turn-table.

Tn the manner already described, the pencil P” of the Dynamometer-Chronograph registers the
power put out; P’ registers seconds from the mean time-clock, and P registers the end-thrust of
the propeller. A fourth pencil is fixed to the frame of the Recorder and registers on the dyna-
mometer cylinder the forward motion of the Recorder arm about its vertical axis against the ten-
sion of a horizontal spring, the spring being disposed so as to be extended by the forward motion
of the outer arm. Thus, when the propeller is driven at such a velocity as just to exceed the
velocity of the turn-table, the outer arm bearing the Dynamometer moves forward, the horizontal
spring begins to extend, and its extension is recorded on the Dynamometer sheet, together with the
power put out, the amount of end-thrust obtained, and the time trace from the mean time-clock.

Preliminary to the experiments the surface of the inner arm of the balance was increased so
that the resistance of the Dynamometer on the outer arm to the wind of advance should be largely
counterbalanced. This was accomplished by adding a surface of 17 square inches at a distance
of 4 inches (104 centimeters) from the axis of rotation.

h. om.
At 2 12 Casella air-meter reads 1,779,600.
At 5 39 2 ss “1,881,900.

Toward end of experiments, wind almost entirely died away.

Dynamometer-Chronograph sheet No. 8—notes and measurements :

Propeller blades set at angle of 75° with axis. Horizontal spring No. 3.
Pulley cord of Dynamometer running on 4-inch pulley.
Chronograph cylinder geared so as to make 1 revolution to 2,000 revolutions of propeller.
Set screw of Dynamometer in “0” hole.
Turn-table driven so as to give linear speed of approximately 2,000 feet per minute.
(a) Dynamo = 1,170 revolutions per minute.
5.52 x 2000

(6) Propeller = =a
(c) Extension of power pencil P” = 0.65 inches.
(d) Extension of end-thrust pencil P = 0.20 inches (varying).
(e) Horizontal spring: no appreciable extension, except occasional jumps produced by wind.
(f) Speed of turn-table (from sheet of stationary chronograph in office) = 5.41 seconds in one

revolution = 1,865 feet per minute.

1,032 revolutions per minute.

The above entries, taken from the original note-book, will be readily under-
‘stood in connection with the following explanations :

(a) The 1,170 revolutions of dynamo refer to the revolutions of the dynamo-
electric machine, and are read off by means of a Buss-Sombart Tachometer.

86 EXPERIMENTS IN AERODYNAMICS.

(b) 5.52 is the number of inches of the Dynamometer-Chronograph barrel
revolved in a minute, as determined by measuring the time trace. An entire
revolution corresponds to the entire circumference of the barrel, 10.7 inches, and
(with the gearing used in this experiment) to 2,000 revolutions of the Dynamometer
pulley shaft.

Hence

5.52 x 2000 _

1,032
10.7 yt

is the number of revolutions of the Dynamometer pulley per minute at the time
of this experiment. The effective diameter of the pulley being 4 inches, this
gives for the velocity of the cerd 1,063 feet per minute.

(c) The extension of the power pencil P’ = 0.65 inches. From the calibra-
tion tables we find that this corresponds to a tension of 0.67 pounds on the pulley
cord. The product of this tension by the pulley speed gives the power put out,
viz., 712 foot-pounds per minute.

(d) The extension of the end-thrust trace, 0.20 inch, corresponds to a
pressure of 0 20 pound.

(e) The horizontal spring has no appreciable extension, except as caused by
puffs of wind. This indicates that the propeller is not driving quite fast enough
to equal or exceed the velocity of the turn-table; but the deficiency of velocity is
so small that we shall not discard the experiment, but compute the record as if
the requisite velocity were just attained.

(f) The speed of turn-table multiplied by the end-thrust gives the work
done per minute by propeller, viz., 373 foot-pounds per minute.

We have, then, as a result of the experiment, that the ratio of work done
by the propeller to the power put out is 52 per cent., the form of the propeller
blades not being a very good one.

The whole series of experiments is not given here in detail, but their prin-
cipal results will be communicated in general terms. The first result is that the
maximum efficiency of a propeller in air, as well as in water, is obtained with a
small number of blades. A propeller with two blades gave nearly or quite as
good results as one with a greater number. This is strikingly different from the
form of the most efficient wind-mill, and it may be well to call attention to the
essential difference in the character of the two instruments, and to the fact that
the wind-mill and the movable propeller are not reversible engines, as they might
at first sight seem to be. It is the stationary propeller—i. ¢., the fan-blower—
which is in reality the reversed wind-mill; and of these two, the most efficient
form for one is essentially the most efficient form for the other. The efficiency
of a fan-blower of given radius is expressed in terms of the quantity of air
delivered in a unit of time for one unit of power put out; that of the wind-mill

THE DYNAMOMETER-CHRONOGRAPH. 87

may be expressed in terms of the amount of work done per unit quantity of air
passing within the radius of the arms. If any air passes within the perimeter
which does not strike the arms and do its work, it is so much loss of an attainable
efficiency. This practical conclusion is confirmed by experience, since modern
American wind-mills, in which practically the entire projection area is covered
with the blades, are well known to be more efficient than the old wind-mills of
four arms.

Turning now to the propeller, it will be seen that the expression for its
efficiency, viz., the ratio of useful work done to power expended, involves quite
different elements. Here the useful work done (in a unit of time) is the product
of the resistance encountered by the distance advanced, which is entirely different
in character from that in the fan-blower, and almost opposite conditions conduce
to efficiency. Instead of aiming to set in motion the greatest amount of air, as
in the case of the fan-blower, the most efficient propeller is that which sets in
motion the least. The difference represents the difference between the screw
working in the fluid without moving it at all, as in a solid nut, and actually
setting it in motion and driving it backward—a difference analogous to that which
in marine practice is technically called ‘ slip,” and which is a part of the total
loss of efficiency, since the object of the propeller is to drive itself forward and
not to drive the air backward. It may now be seen why the propeller with few
blades is more efficient than one with many. The numerous blades, following
after each other quickly, meet air whose inertia has already yielded to the blades
in advance, and hence that does not offer the same resistance as undisturbed air
or afford the same forward thrust. In the case of the propeller with two blades,
each blade constantly glides upon new strata of air and derives from the inertia
of this fresh air the maximum forward thrust. The reader will observe the
analogy here to the primary illustration of the single rapid skater upon thin ice,
who advances in safety where a line of skaters, one behind the other, would
altogether sink, because he utilizes all the sustaining power to be derived from
the inertia of the ice and leaves only a sinking foothold for his successors. The
analogy is not complete, owing to the actual elasticity of air and for other reasons,
but the principle is the same. A second observation relating to aerial propellers,
and one nearly related to the first, is that the higher the velocity of advance
attained, the less is the percentage of “slip,” and hence the higher the efficiency
of the propeller. The propeller of maximum efficiency is in theory one that
glides through the air like a screw in an unyielding frictionless bearing, and
obtains a reaction without setting the air in motion at all. Now, a reaction from
the air arising from its inertia increases, in some ratio as yet undetermined, with
the velocity with which it is struck, and if the velocity is high enough it is
rendered probable, by facts not here recorded, that the reaction of this ordinarily

88 EXPERIMENTS IN AERODYNAMICS.

most mobile gas may be practically as great as we please and, with explosive
velocities, for instance, may be as great as would be the reaction of a mass of iron.

The theory of aerial propellers being that for a maximum efficiency, the
higher the velocity, the sharper should be the pitch of the blades, it has been the
object of the complete series of experiments with the Dynamometer-Chronograph
to determine by actual trial the velocity of advance at which the maximum
efficiency is attained when the blades are set at different angles, and the best
forms and dimensions of the blades. The details of these are reserved for future
publication, but, very generally speaking, it may be said that notwithstanding
the great difference between the character of the media, one being a light and
very compressible, the other a dense and very incompressible fluid, these observa-
tions have indicated that there is a very considerable analogy between the best
form of aerial and of marine propeller.

CHAPTER VIII.

THE COUNTERPOISED ECCENTRIC PLANE.

If a rectangular plane be made to move through the air at an angle of
inclination with the direction of advance, it was implicitly assumed by Newton
that the center of pressure would coincide with the center of figure. Such, how-
ever, is not the case, the pressure being always greater on the forward portion,
and the center of pressure varying with the angle of inclination.

The object of the present chapter is to present the results of experiments
made to determine the varying positions of the center of pressure for varying
angles of inclination of a plane moved in a horizontal course through the air.
Drawings of the apparatus devised for this purpose are given on plate V. AA’
represents the eccentric wind-plane one foot square held in a brass frame about
8 of an inch wide and 2 of an inch thick. Two sliding pieces, SY, move in a
groove in the edge of the brass frame, and may be clamped in any position by
screws. Each sliding piece has a small central hole, in which fits a pivot, V.
The wind-plane (eccentric plane) is suspended by these pivots and swings about
the axis passing through them, so that by moving the plane in the sliding
pieces this axis of rotation can be moved to any distance up to two inches. A
flat lead weight, which also slides along the back of the plane, can be adjusted
so as to counterpoise it in any position. When the weight is adjusted, therefore,
the plane is in neutral equilibrium about its axis of rotation. A pencil, P, is
fixed on the lower part of the plane and records against a tracing board perpen-
dicular to it. In order to leave the position of the plane entirely uncontrolled
by the friction of the pencil, the registering board is held away from the plane
by spring hinges HH’, and caused to vibrate by an electro-magnet so as to touch
the pencil point many times in a second.

In the experiments the sliding pieces were set so that the axis of rotation
was successively 0 inch, 0.25 inch, 0.75 inch, etc., from the center, and the
plane was counterpoised about this axis. When placed in rotation upon the arm
of the whirling-table, the moment of rotation of the plane about the axis is pro-
portional to the resultant wind pressure multiplied by the distance of the center
of pressure from the axis of rotation, and it will reach its position of equilibrium
when the plane has taken up such an angle of inclination that the center of

12 (89)

90 EXPERIMENTS IN AERODYNAMICS.

pressure is at the axis of rotation. The measurement of this angle is, therefore,
the object of observation.

In actual experiment the exact angle of equilibrium of the plane is masked
by slight inequalities of speed and by fluctuation of the wind, and there is oscil-
lation about a mean position. In measuring the trace, the extreme angles of this
oscillation were read, as well as the mean position of equilibrium.

The following transcript from the note-book for September 22, 1888, will
afford an illustration of the detailed records made in connection with each series
of experiments. The column headed “range” gives the range of oscillation of
the plane, and shows that the plane is far more unsteady when the axis of oscil-
lation and center of pressure is very eccentric than when it is nearer the center.

SEPTEMBER 22, 1888.

| Aq nq - | a Es
| Air tempera-| Wind direc-

Time. Barometer. ture. re Air meter.
(Inches.) (Fahr.) :
10.20 a. m. 29.080 58.9 N. N. E. 183380
12.20 a. m. 29.069 61.2 N.N. E. 224065

Meteorological conditions not so favorable as yesterday, the wind being rather strong.
Engine run by Eisler; J. Ludewig sets wind-plane; F. W. Very attends to chronograph and records.

Two complete sets of observations were made, both on September 21 and
September 22, 1888, making in all 31 separate readings, which are given in detail
at the close of the chapter.

The mean of these observations is presented in the following table XVII:

THE COUNTERPOISED ECCENTRIC PLANE. om

TaBLE XVII.

Summary of Experiments giving position of center of pressure on a plane one foot square (30.5 x 30.5
centimeters) for different angles of inclination.

Distance from center of press- | Distance as a Maelo of tn Angle of plane | Angle of plane
ure to center of plane d. percentage of | "5 th i itial with with
the side of the lit Pe vertical horizontal
(Inches.) (Centimeters.) plane. a S0Soe a.
a = “ ° ° a
0.00 0.00 0.000 5 0.0 90.0
0.25 0.64 0.021 17.4 12.0 78.0
0.50 1.27 0.042 28.2 22. 67.5
0.75 1.90 0.063 39.7 34.2 55.8
1.00 2.54 0.083 50.6 45.0 45.0
1.25 317 0.104 59.7 54.2 85.8
1.50 3.81 0.125 67.5 62.0 28.0
1.75 4.44 0.146 75.0 69.5 20.5

The first two columns give the distance from the center of pressure to the center
of the plane in centimeters and inches, and the third column gives it as a per-
centage of the length of the plane. The fourth column gives the angle of trace
with the initial vertical line drawn through the position of the pencil at rest. It
will be noticed that this angle is 5°.5 for the case when the axis of rotation passes
through the center of the plane—a setting for which the plane must be vertical.
This observed angle of 5°.5 is to be explained, not by a tipping of the plane,
but by a tipping of the line of reference due to a yielding of the supports, etc., to
the wind of rotation. This angular deflection, therefore, becomes a correction to
be applied to all the observations, and the fifth column, headed “angle of plane
with vertical,” contains the corrected values for the inclination of the plane.

The resulting relations here established between the angle of inclination of
the plane and the position of the center of pressure are of importance, but their
application is not made in the present memoir.*

* References to the results of Joéssel and of Kummer will be found in Appendix C.

92 EXPERIMENTS IN AERODYNAMICS.

Experiments to determine the position of the center of pressure on an inclined square plane.
SEPTEMBER 21, 1888.
F. W. Very, Conducting experiments ; JoserpH LupEwia, Assisting.

Barometer, 737.06 mm.; temperature, 18° C.; wind velocity, 0.006 meter per second ; length
of side of wind-plane, 12 inches (80.5 centimeters).

Sn gq SH

SS Distance of axis of oscil- S 2

2H lation from center of os aS

eas plane. Sa 2g
Time. < é = = < é E Range.

Bao or 3

33 S (Inches.) | (Centimeters. ) "eb 5

4 < e
p. M. ° ° ° °
3.17 4.49 1.75 4.44 76.0 65-88 23
3.23 4.49 1.50 3.81 67.5 60-75 15
3.28 4.49 1.25 3.17 60.0 57-63 6
3.83 4.51 1.00 2.54 50.4 47-54 U
3.387 447 0.75 1.90 39.0 37-41 4
3.41 4.51 0.50 127, 29.5 29-380, i
3.45 4.46 0.25 0.64 20.9 19-23 4
3.48 4.49 0.00 0.00 6.4 2-11 9
3.58 8.47 1.75 4.44 73.0 61-91 30
4.02 8.57 1.50 3.81 67.0 50-80 30
4.06 8.70 1.25 3.17 60.0 58-63 5
4.09 8.56 1.00 2.54 50.5 47-55 8
4.25 7.92 0.75 1.90 40.1 37-48 6
4.34 8.47 0.50 1.27 28.5 28-31 2
4.41 7.81 0.25 0.64 16.8 15-17 2
4.44 7.63 0.00 0.00 5.0 4-7 3

THE COUNTERPOISED ECCENTRIC PLANE. 93

SEPTEMBER 22, 1888.
F. W. Very, Conducting experiments; JoserpH LuDEWIG, Assisting.
Barometer, 738.4 mm.; temperature, 15.°5 C.; wind velocity, 2.06 meters per second.

Meteorological conditions not so favorable as on the 21st, the wind being rather strong. The
effect is to produce a much wider oscillation of the trace.

o 8 z (oa

> Distance of axis of oscil- 9 R

ae lation from center of ae =

S A plane. S'S ag
Time. 2 A 5:8 pee Range.

Hod 6S ae

3 = © or a

33 5 (Inches.) | (Centimeters. ) "eb 5

ae 4 A
a. M. e Aa S
10.3 12.8 2.00 5.08 82.0 64-98 3
10.42 12.8 1.75 4.44 76.0 58-98 40
10.46 12.8 1.75 4.44 76.0
10.50 12:9 1.50 3.81 68.0 48-84 36
10.55 10.4 1.25 3.17 59.0 35-76 A}
11.26 13.6 1.00 2.54 51.0 37-59 22
11.29 13.6 0.75 1.90 40.0 37-43 6
11.32 14.3 0.50 1.27 26.5 25-28 3
11.3 13.4 0.25 0.64 15.0 11-19 8
11.41 13.8 0.00 0.00 5.0 3-7 4
11.58 14.5 2.00 5.08 79.0 58-96 38

mM.

15.03 14.7 1.50 3.81 66.0 50-80 30
12.06 14.0 1.00 2.54 49.0 45-52 7
12.09 13.8 0.50 1.27 27.0 26-28 2
12.12 3.3 0.00 0.00 6.0 Q-12 12

CHAPTER IX.

THE ROLLING CARRIAGE.

The Rolling Carriage was constructed for the purpose of determining the
pressure of the air on a plane moving normal to its direction of advance.* What-
ever be the importance of this subject to aerodynamics or engineering, we are
here interested in it only in its direct bearing on the aerodromic problem, and
carry these observations only as far as this special object demands. Before this
instrument was constructed, a few results had already been obtained with the
Resultant Pressure Recorder (chapter TV), but additional observations were desired
with an instrument that would be susceptible of greater precision. The state-
ment has frequently been made that the law that the pressure is proportional to
the square of the velocity fails for low velocities as well as for very high ones.
As it appears to me that this conclusion was probably based on imperfect instru-
mental conditions due to the relatively excessive influence of the friction of the
apparatus at low velocities, particular pains were taken in the present experi-
ments to get as frictionless an action as possible. Plates IX and X contain
drawings in elevation and plan of the apparatus devised for this purpose.

A metal carriage 83 inches long is suspended on a set of delicately con-
structed brass wheels 5 inches in diameter, which roll on planed ways. Friction
wheels bearing against the sides and bottom of the planed ways serve as guides
to keep the carriage on its track. Cushions of rubber at each end break the
force of any end-thrust. Through the center of this carriage passes a hollow
brass rod 273 inches long, on the forward end of which is set the wind-plane by
means of a socket at its center. On the other end is attached a spiral spring,
which is also fastened by a hook to the rear of the carriage-track in a manner
illustrated in the drawing. The rod is of such length that the wind-plane may
be removed from the disturbing influence on the air of the mass of the registering
apparatus, and the center of gravity of wind-plane and rod falls under the center
of gravity of the carriage. The pressure of the wind on the wind-plane is bal-

*These measurements of pressure on the normal plane are not presented as new. They were made as a
necessary part of an experimental investigation which aimed to take nothing on trust, or on authority however
respectable, without verification. They are in one sense supplementary to the others, and although made early
in the course of the investigations presented in this memoir, are here placed last, so as not to interrupt the
presentation of the newer experiments, which are related to each other by a consecutive development.

(94)

THE ROLLING CARRIAGE. 95

anced by the extension of the spiral spring, while the Rolling Carriage bears an
arm, F’, carrying a pencil which rests upon a chronograph cylinder to automat-
ically record this pressure, the axis of the cylinder being parallel to the track of
the carriage and the chronograph rotated by clock-work. The position of the
pencil for zero pressure on the spring is marked on the chronograph sheet, and
a reference line is drawn through this point, so that distances of the pencil point
from this reference line are measures of the extension of the spring, while a second
pencil, being placed on the opposite side of the chronograph barrel, and operated
by an electro-magnet in electrical connection with the mean time clock, registers
seconds on the chronograph barrel, and thereby every point of the pressure trace
made by the first pencil can be identified with the synchronous points in the
trace on the stationary chronograph on which is registered the velocity of the
whirling-table.

Much care was bestowed upon the manufacture and calibration of the spiral
springs. The following is a list of the springs, giving their size, length, and
weight :

q SS —
. n
ES pie 3 OniG |

H of mn S

as = SN g

‘> 80 S oe s

4 oe pac 5p

o Ss - 3 a 5 ~

3 5 S e = a7 "sp

The method of calibration adopted is as follows:

The spring to be calibrated is fastened at one end to the brass tube of the
Rolling Carriage and at the other to a fixed support. A string fastened to the end
of the shaft passes over a light, almost frictionless pulley, and carries a bag, in
which the weights are placed. The extensions of the spring are registered by
the pencil on the chronograph barrel. Settings are made on opposite sides of a
mean position, first, by letting the weight fall gradually to its lowest position ;
and, second, by extending it beyond its normal position and allowing the tension
of the spring to draw it back. In both cases a series of vibrations are sent
through the apparatus by the jar set up on the table, by means of a large tuning-
fork, so as to overcome the friction of the moving parts. In a portion of the
calibration experiments, these vibrations were produced by an electro-magnet.

96 EXPERIMENTS IN AERODYNAMICS.

The results of the calibration were plotted in curves, and these curves have
been used for translating all the spring extensions of the experiments into
pressures.

Three square planes were used, 6, 8, and 12 inches on a side, and in every
case the center of the plane was placed nine meters from the center of the
whirling-table. The air temperature was recorded at the beginning and end
of each series of observations. The average wind velocity was obtained from a
Casella air meter, which was read each day at the beginning and end of the
experiments. It should be noted that these wind velocities are valuable as indi-
cating the conditions of experiment, but do not afford any basis of correction to
the observations, since the method adopted in reading the trace eliminates the
effect of wind currents, so far as it is possible to do so. In a complete revolution
of the turn-table the arm during half of the revolution moves with the wind, and
during the other half moves against the wind; consequently the pressure will
be too great during the latter half and too small during the former half of the
revolution. Thus, if the velocity at the end of the arm be V, and the wind
velocity be v, the wind pressure at one point of the revolution will be propor-
tional to (V+ v)%, and at the opposite point will be proportional to(V—v)*. The
resulting trace, therefore, vibrates on either side of a mean position, and a line
drawn through the trace to represent this mean position gives a numerical value
that is larger than the pressure due to the velocity V in the ratio of V* + v* to V’.
But, in general, this error in reading the traces is quite negligible, and the average
mean position may be taken as reliable within the limits of accuracy imposed
onus. The spring extension adopted always refers to this mean position, and no
further correction is admissible. A specimen of the records of a series of experi-
ments is here given in detail, taken from the note book for October 25, 1888:

OctoBER 25, 1888.
Barometer, 738 mm.; mean temperature, 16°C. At 4.53 p. m., air meter, 416,445; at 5.25
p. m., air meter, 419,130. Eight-inch square wind-plane. Spring No. 1. Distance of center of

plane from axis of rotation, 9 meters.

First registering sheet. Four records at about 44 revolutions per minute. Ended at 4.05.
Almost a perfect calm. Velocity too small to get reliable spring extensions.

Second sheet started at 4.24 p.m. Two records at 10 revolutions per minute. Ended at
4.28 p.m. Pencil failed to make satisfactory record.

THE ROLLING CARRIAGE. 97

Third sheet started at 4.34 p.m. at nearly 14 revolutions per minute. Four records obtained.
Ended at 4.44 p. m.

Reading of traces.

Number of seconds |} Velocity of center of

i : axtensi spring | Pressur :
in one revolution plane (meters per Extension of spring) Pressure on plane

ap rieneanlel second). No. 1 (inches). (pounds).
4.29 13.14 0.97 1.30
4.29 13.14 0.75 1.10
4.38 12.93 0.82 1.15
4.38 12.93 0.78 1.12

Fourth sheet. Velocity about 20 revolutions per minute. Two records obtained. Ended
at 4.57 p.m.

Reading of traces.

| Number of seconds | Velocity of center of

extensi ing | Pressure
plane (meters per Extension of spring | Pressure on plane

in one revolution

of turn-table. | second). No. 1 (inches). (pounds).
2.88 19.60 2.33 2.55
| 2.90 19.50 2.28 2.51

Fifth sheet. Velocity about 25 revolutions per minute. Two records obtained. The first
record is good. The second record cannot be interpreted. Ended at at 5.15 p. m.

Reading of traces.

Number of seconds | Velocity of center of
in one revolution | plane (meters per
of turn-table. second).

Extension of spring | Pressure on plane
No. 1 (inches). (pounds).

2.45 23.10

oo
~I
o>
co
oO
o

The experiments were made from October 24 to November 2, 1888, with a
short series on November 28, 1890, and embrace observations with 6, 8, and 12
inch square planes, those with the 6-inch plane extending over velocities from 7
to 30 meters per second. They are presented in extenso at the end of the present
chapter The extension of the spring is given in inches, as originally measured
from the trace, and the corresponding pressures are given in pounds and
erammes. The next succeeding column gives the pressure P in grammes per
square centimeter of the wind-plane surface. The last column gives the value of
the coéfficient #,, in the equation P= %,, V*, where P is the pressure in grammes
on a square centimeter of surface, and V the velocity expressed in meters per
second. The subscript m is used here, as in previous chapters, to designate these
metric units.

One of the objects of the experiments was to test the generally accepted law,
that the pressure varies as the square of the velocity, and for this purpose

98 EXPERIMENTS IN AERODYNAMICS.

velocities were used ranging from 7 to 30 meters per second (11 to 67 miles per
hour). The mean of 10 observations with the 6-inch plane, at velocities between
25 and 30 meters per second, gave #,, = 0.0081; and the mean of 12 observations,
at velocities between 7.1 and 14.3 meters per second, gave the same value.
Therefore the departure from the law of the squares, if there be any between
these limits of velocity, is not sufficiently large to be detected by this apparatus.

If variations in the density of the air produced by changes of temperature
be considered in their effect upon the relation between pressure and velocity, the
preceding formula may be expressed in the form

‘ae Im V?
1 + .00366 (¢ — 10°)’

where .00366 is the coéfficient of expansion of air per centigrade degree; ¢ is the
temperature of the air expressed in centigrade degrees, and &,, is the value of
the coefficient for a standard temperature of 10°C. In the following summary,
all the values of %,, are collected and reduced by aid of this formula to a common
mean temperature of 10° C.; the values refer, also, toa mean barometric pressure
of 736 mm. An additional column is added, giving the corresponding value of
x in English measures for velocities expressed in feet per second and pressures in
pounds per square foot.

TABLE XVIII.

Summary of values of km obtained with the Rolling Carriage.

Number T :
: empera- ; :
Size of plane Date a ture k , bm; Ih
; pane. aah observa- ce ao TORE — OIC tong —n Ocxc
tions. ;
|
1888.
12 inches square. | Oct. 24 9 10.0 0.01027 0.01027
od) il 7.8 0.00913 0.00906
Nov. 2 4 19.0 0.00830 0.00859
1890.
Nov. 28 3 — 2.0 0,00990 0.00948
Weighted mean........ 0.00944 0.00180
1888. ae re
6 inches square. | Oct. 24 3 10.0 0.00760 0.00760
Wass 29 6 12.0 0.00785 0.00790
| Nov. 1 12 20.0 0.00810 0.00840
oe 2 13 19.0 0.00840 0.00867
| Weighted mean........ 0.00833 0.00159
fh oe ; q
8 inches square. | Oct. 25 7 16.0 0.00754 0.00770 0.00147
General weighted mean. 0.0087 0.00166

THE ROLLING CARRIAGE. 99

The resulting values of #,, for the 6, 8, and 12 inch square planes are not
entirely accordant, as the successive sets of observations with the 12-inch plane
all give considerably larger values than those obtained with the smaller planes,
I am not disposed, however, to consider this as a real effect due to an actual
difference in the pressure per unit area on these planes. Such a difference, if one
exists, is in all probability quite small, and much within the degree of accuracy
possessed by these experiments. The resulting differences in the mean values of
k,, I consider, therefore, as discrepancies in the observations, the cause of which
has not become apparent. In recognition, however, of the fact that other experi-
menters have claimed to discover a difference in the pressure per unit area on
planes of different sizes, I have, in general, in the preceding chapters, taken pains
to specify the area of the plane to which all my experimental results apply.
That there should be a real, though perhaps a small, difference between the
pressure per unit area on planes of different sizes seems in fact quite probable,
when we consider that the ratio of perimeter to area varies for similar shaped
planes of different sizes. If the side of a square plane be a and that of another

: : - 4. 4.
be na, the ratio of perimeter to surface is ;, in the one case and ~~ in the other,

which is not merely an expression of a mathematical relation, but calls attention
to a possibly important physical fact, for it seems probable that this relation
between perimeter and area has a considerable influence in determining the
pressure on the plane, especially that part of it produced by the diminution of
pressure on its posterior face.

The general weighted mean of all the values of #,, is .0087, or, in English
measures, 4 = .00166, and I believe this result is within 10 per cent. of the true
value. These experiments lead me to place the limits of the value of #,, for a
1-foot square plane between 00078 (4 = .0015) and 0.0095 (4 = .0018) for the
assumed temperature of 10° C., and pressure 736 mm., and, made as they were
in the open air and subject to wind currents, they are not sufficiently precise to
give more contracted limits. It may be noted that the value of /,, obtained from
the experiments with the Resultant Pressure Recorder, viz., k,,= .OO80, falls
between the probable limits above assigned, and is within the probable uncertainty
(10 per cent.) of the mean of the results with the Rolling Carriage. 'The Rolling
Carriage, therefore, although a very sensitive and delicate piece of apparatus, has
not been able under the conditions of experiment to yield a sensibly better
result than the rougher instrument.

100 EXPERIMENTS IN AERODYNAMICS.

Measurement of wind pressure on normal planes by means of the Rolling Carriage.
OcroBer 24, 1888.
PRESSURE ON ONE-FOOT SQUARE PLANE (929 square centimeters).

Barometer, 735 mm.; mean temperature, 10°.0 C.; wind velocity, 2.8 meters per second.

| 3 e8 eo ;
3 ao ae ei Pressure cn wind-plane.
Ss | S Ss oo a i |
5 | 28 3 q = > a 2 | |
3 | ae Se o's iP
é hens z eS ga | (grammes | km = ca
oI 3 ea Bog Ht (Pounds.) | (Grammes. ) per Ys
2 ‘a58 BiG} 8S square
2 BES | Gee Ko centimeter).
eH Za > a
1.20p.m.} 14.00 13.18 3.39 3.55 1,610 1.78 0.0100
| 14.00 13.18 3.62 3.84 1,740 1.87 0.0108
1.40 p.m. | 9.49 8.92 1.42 1.71 776 0.83 0.0105
9.49 8.92 1.42 alta 776 0.83 0.0105
2.00 p.m. 5.50 5.15 0.32 0.58 263 0.28 0.0107
5.60 5.28 0.30 0.53 240 0.26 0.0093
2.15 p.m. 14.90 14.03 3.90 3.99 1,810 1.95 0.0099
15,00 14.09 4.10 4.19 1,900 2.04 0.0104
14.80 13.91 4.00 4,08 1,850 egg 0.0103
Mean =| 0.01027

PRESSURE ON SIX-INCH SQUARE PLANE (232 square centimeters).

d Os come Py ;
3 Se Pa aS Pressure on wind-plane.
oe Onsite RS) aN
3 5 2 Pra Cy 2
a Co Crewe GH
o >a o > 5°5S P
R wos S q
Ss One 3= S at > (grammes | km Sa
o as Bog ao (Pounds.) | (Grammes.) per
: mee | Saa |) Be square
3 2 Se ra 28 we centimeter).
a A S S
4.00 p.m. Doe 24.3 1.98 DAIS 990 4.26 0.0072
2.52 23.8 1.97 2.22 1,008 4.34 0.0077
2.52 23.8 2.05 2.29 1,040 4.48 0.0079
Mean=| 0.0076

THE ROLLING CARRIAGE. 101
OcroBeR 25, 1888.
PRESSURE ON EIGHT-INCH SQUARE PLANE (413 square centimeters).

Barometer, 738 mm.; mean temperature, 16°.0 C.; wind velocity, 0.6 meter per second.

RD 2 on
& = 8 1 ee Pressure on wind-plane.
3 Semis o Le
> OSa 5 BA Rn 2 |
Z Boe) ea ||) oe IE P
3 enn S= 9 ace (grammes | kn =—,
<= HOR > 5 Sg Q 14, avi 3 VY?
3 Sas Son Bo (Pounds.) | (Grammes.) per
2 Rees Sask a6 square
= BAO To Ae Ke centimeter).
a A = —
4.30 p.m. 4.29 13.14 0.97 1.30 590 1.43 0.0083
4.29 13.14 0.75 1.10 499 1.21 0.0070
4.3 12.93 0.82 1.15 522 1.26 0.0075
4.38 12.93 0.78 1.12 508 1.23 0.0074
2.88 19.60 2.88 2.55 1,157 2.80 0.0073
2.90 19.50 2.28 2.51 1,139 2.76 0.0073
5.15 p. m. 2.45 23.10 3.76 3.90 1,770 4.29 0.0080
Mean=| 0.00754

OcroBER 29, 1888.
PRESSURE ON SIX-INCH SQUARE PLANE (232 square centimeters).

Barometer, 735 mm.: mean temperature, 12°.0 C.; wind velocity at 1 p.m., 3.3 meters per second.
’ d ? ? r)

qa gs 62 oo :

5 eee 2 ce Pressure on wind-plane.

£ on oo aD

3 oF db ssc 4 R

> oSa aa a n 2

3 oa oS aS | P

L Hos eines! q | IP

6 Siete or aS | (grammes km =

oI S e S 228 ‘ao (Pounds.) | (Grammes.) per

® jatonen oak 3.9 square

& ERetS ay aes centimeter).

= A = |
4.24 p.m. 2.15 26.30 3.00 3.20 1,450 6.25 0.0090
4.28 p. m. 2.03 27.85 3.08 3.26 1,480 6.38 0.0082
4.33 p.m. 1.88 80.15 3.41 3.57 1,620 6.98 0.0077
4.37 p.m. 1.93 29.20 3.19 3.35 1,520 6.55 0.0077
5.29 p. m. 4.29 13.20 0.36 0.61 207 | lel 0.0068
5.33 p.m. 3.99 14.30 0.50 0.80 363 1.57 0.0077

Mean =| 0.00785

102 EXPERIMENTS IN AERODYNAMICS.

OcroserR 30, 1888.
PRESSURE ON ONE-FOOT SQUARE PLANE (929 square centimeters).

Barometer, 739 mm.; mean temperature, 7°.8 C.; wind velocity, —.

ne Sn @ 50 .
= LS m E ie a Pressure on wind-plane.
nos SoS S
98 ec Se P Pp
Saas Oke 2 ac Z grammes | kn = —
Sak Bon “i (Pounds.) | (Grammes.) per V
gos S84 Bs square
Bn Oo = a a ail centimeter).
Za = |
7.23 7.84 0.88 1.20 O44 0.586 0.0095
10.14 5.58 0.25 0.50 227 0.244 0.0079
7.89 lel 0.69 1.01 458 0.493 0.0096
10.86 5.22 0.27 0.51 231 0.249 0.0092
11.32 5,00 0.28 0.52 236 0.254 0.0102
8.56 6.62 OAT 0.75 340 866 0.0084
6.64 8.51 1.00 1.30 589 0.634 0.0088
6.74 8.39 1.00 1.30 589 0.6384 0.0090
6.80 8.98 1.33 1.62 73 0.790 0.0098
6.20 Oey eles: 1.63 739 0.796 0.0096
5.93 954) 1.27 1.56 707 0.761 0.0084
Mean =| 0.00918
NovemsBer 1, 1888.
PRESSURE ON SIX-INCH SQUARE PLANE (232 square centimeters).
Barometer, 741 mm.; mean temperature, 20°.0 C.; wind velocity, 1.5 meters per second.
c oe Ee of : a
2 eS = S ae Pressure on wind-plane.
+e ree = 9 ey (grammes) | km = —
3 Sas Bog ie (Pounds.) | (Grammes.) | per J
© cies S25 5,2 square
s 5-4 Oo 3 Be aa centimeter).
a A = &
3.30 p.m. 4.35 13.00 | 1.60 0.78 356 53 0.0091
4.32 15.10 1.48 0.70 20 1.38 0.0080
3.99 14.20 2.19 1.04 472 2.08 0.0100
4.00 14.14 2.07 0.99 449 1.93 0.0096
4.00 14.14 1.60 0.78 396 1.53 0.0077
3.96 14.30 1.58 0.78 854 1.58 0.0075
5.64 10.00 0.64 0.36 163 0.70 0.0070
5.67 JO 0.61 0.85 159 0.69 0.0069
5.A0 10.47 0.80 0.48 197 0.85 0.0077
5.51 10.26 0.69 0.38 174 0.75 0.0071
7.93 7.13 0.30 0.20 91 0.39 0.0077
5.25 p.m. 7.60 7.44 0.40 0.25 113 0.49 0.0089
Mean=| 0.00810

THE ROLLING CARRIAGE. 103
NovEeMBeER 2, 1888.
PRESSURE ON SIX-INCH SQUARE PLANE (232 square centimeters).

Barometer, 735.6 mm.; mean temperature, 19°.0 C.; wind velocity, 1.5 meters per second.

qi Zea 6B op :
et 5-8 no oe Pressure on wind-plane.
3 SEs 22 ae s
5 Boal soe 2
3 ee OS aes (grammes | km = =
a Re A >o O S : Gi a ; We
3 aes Bea “at (Pounds.) | (Grammes. ) per
2 scien Sak Bo square
5 BAO DHS uo centimeter).
B A > ea)
11.00 a. m. 2.14 26.40 2.92 3.11 1,411 6.08 0.0087
2.13 26.55 2.62 2.85 1,294 5.56 0.0079
2.43 23.30 2.27 2.52 1,143 4.92 0.0091
2.73 20.70 1.80 2.10 953 4.10 0.0096
2.91 19.40 1.32 1.67 758 3.26 0.0087
5.66 10.00 0.16 0.45 204 0.88 0.0088
8.72 15.20 0.52 0.90 408 1.76 0.0076
3.62 15.60 0.53 0.91 413 1.78 0.0078
3.10 18.20 aS) 1.54 699 3.01 0.0091
2.03 27.85 3.49 3.63 1,646 7.09 0.0091
2.03 27.80 3.08 3.27 1,484 6.38 0.0083
1.99 28.40 3.00 3.19 1,448 6.22 0.0077
1.94 29.10 2.84 8.04 1,380 5.95 0.0070
Mean =| 0.0084
PRESSURE ON ONE-FOOT SQUARE PLANE (929 square centimeters).
Note: Wind too high for best results.
a nD SS
2 = 3 = 8 a Pressure on wind-plane.
a n> 2 Sy wo
a nm OS ee os P P
= Cs Ciao go (grammes | km = Pp
se @ a8 og “i (Pounds.) | (Grammes.) per
2 Teas Say 8S square
5 B-n oO. Bae mo centimeter).
a A Se |
1.50 p.m. 2.27 24.9 2.28 10.60 4,810 5.18 0.0084
2.34 24.1 1.92 9.05 4,105 4,42 0.0076
2.90 19.5 1.28 6.25 2,835 3.05 0.0080
3.10 18.2 1.27 6.20 2,310 3.03 0.0092
| Mean=)| 0.0083

104

EXPERIMENTS IN AERODYNAMICS.

NoveMBER 28, 1890.

PRESSURE ON ONE-FOOT SQUARE PLANE (929 square centimeters).

Barometer, 737 mm.; mean temperature, — 2°.0 C.; wind velocity, 1.2 meters per second.
< 2d one of ; |
oS aoe = 6 ae Pressure on wind-plane.
= See ae
5 oa 8 a a a =
= cru Sel aa
z ie Ses cs E P
= Sees oS go (grammes | km = Ti
= B88 One, Gam (Pounds.) | (Grammes.) per
2 2os one ac
° Sones £28 BS square
ie aa SSeS iz centimeter).
aS a = =
4.8 11.8 2.60 2.80 1,270 1.37 0.0099
5.0 11.3 2.40 2.60 Dei 1.27 0.0099
9 11.5 2.48 2.68 1,216 1.51 0.0099

CHAPTER X.

SUMMARY.

The essential feature of the present work has been the insistance on the
importance of a somewhat unfamiliar idea—that rapid aerial locomotion can be
effected by taking advantage of the inertia of the air and its elasticity. Though
the fact that the air has inertia is a familiar one, and though the flight of certain
missiles has indicated that this inertia may be utilized to support bodies in rapid
motion, the importance of the deductions to be made has not been recognized.
This work makes the importance of some of these deductions evident by experi-
ment, and perhaps for the first time exhibits them in their true import.

This memoir is essentially a presentation of experiments alone, without
hypotheses, and with only such indispensable formulze as are needed to link the
observations together. These experiments furnish results which may be suc-
cinctly summarized as follows:

The primary experiment with the Suspended Plane is not intended per se
to establish a new fact, but to enforce attention to the neglected consequences of
the fundamental principle that the pressure of a fluid is always normal to a
surface moving in it, some of these consequences being (1) that the stress neces-
sary to sustain a body in the air is less when this is in horizontal motion than
when at rest; (2) that this stress instead of increasing, diminishes with the
increase of the horizontal velocity (a fact at variance with the conclusions of
some physicists of repute and with ideas still popularly held); (8) that it is at
least probable that in such horizontal flight up to great velocities the greater the
speed the less the power required to maintain it, this probability being already
indicated by this illustrative experiment, whi'e demonstrative evidence follows
later.

The experiments which are presented in Chapter IV result in an empirical
curve, giving the ratio between the pressure on an inclined square plane and
on a normal plane moving in the air with the same velocity. Incidentally it
is shown that the pressure is normal to the inclined surface, and hence that the
effects of skin-friction, viscosity, and the like are negligible in such experiments.
It is also shown that for the small angles most used in actual trial of the plane, the
pressure on it is about 20 times greater than that assignable from the theoretical
formula derived from Newton’s discussion of this subject in the Principia. This

14 (105)

106 EXPERIMENTS IN AERODYNAMICS.

last experimental result is not presented as a new contribution to knowledge,
since it had previously been obtained by experimenters in the early part of this
century; but as their results appear not to have met with the general attention or
acceptance they deserve, it is not superfluous either to produce this independent
experimental evidence or to urge its importance.

The experiments with the Plane- Dropper introduce matter believed to be
novel as well as important. They show (1) that the time of falling of a hori-
zontal plane is greater when moving horizontally than when at rest, and (2) that
this time of falling most notably increases with the velocity of lateral translation ;
(3) experiments with different horizontal planes show that this increase in the time
of falling is greater for those planes whose extension from front to back is small
compared with their length measured perpendicular to the line of advance ,
(4) the horizontal velocities are determined at which variously shaped inclined
planes set at varying angles can soar—that is, just sustain their own weight in
the air under such circumstances—and these data afford the numerical basis
for the important proposition that the power required to maintain the horizontal!
motion of an inclined aeroplane is less for high speeds than for low ones ; (5) by
experiments with double planes, one above the other, it is shown that planes of
the advantageous shape mentioned above, do not interfere with each other at.
specified speeds, if so placed at an interval not less than their length from front
to back ; and it is pointed out that an extension of this method enables us to
determine the extent to which any underlying air stratum is disturbed during
the plane’s passage.

Chapter VI contains further data, which confirm the important conclusions
derived from the experiments with the Plane- Dropper, already cited, and some
results on the pressures on inclined planes having different “aspects”? with refer-
ence to the direction of motion are also presented, which are believed to be new
and of importance. Further chapters present experiments with a special instru-
ment called the Dynamometer-Chronograph and with other apparatus, which
give data regarding aerial propellers, a series of experiments on the center of
pressure of moving planes, and another series upon the pressure on a normal
plane.

The conclusions as to the weights which can be transported in horizontal
flight have included the experimental demonstration that the air friction is
negligible within the limits of experiment. It has not been thought necessary
to present any evidence that an engine or other adjunct which might be applied
to give these planes motion, need itself oppose no other than frictional resist-
ance, i enclosed in a stream-line form, since the fact that such forms oppose
no other resistance whatever to fluid motion, has been abundantly demonstrated
by Froude, Rankine, and others.

SUMMARY. 107

The most important general inference from these experiments, as a whole,
is that, so far as the mere power to sustain heavy bodies in the air by mechanical
flight goes, such mechanical flight is possible with engines we now possess, since
effective steam-engines have lately been built weighing less than 10 pounds to
one horse-power, and the experiments show that if we multiply the small planes
which have been actually used, or assume a larger plane to have approximately
the properties of similar small ones, one horse-power rightly applied, can sustain
over 200 pounds in the air at a horizontal velocity of over 20 meters per second
(about 45 miles an hour), and still more at still higher velocities. These numer-
ical values are contained in the following table, repeated from p. 66. It is searcely
necessary to observe that the planes have been designedly loaded, till they weighed
500 grammes each, and that such a system, if used for actual flight, need weigh
but a small fraction of this amount, leaving the rest of the sustainable weight
indicated, disposable for engines and other purposes. I have found in experiment
that surfaces approximately plane and of +5 this weight are sufficiently strong for
all necessary purposes of support.

Data for soaring of 30 x 4.8 inch planes ; weight, 500 grammes.

Weight with planes of like

Soaring speed V. Work expended per min- a ve : Boe Tee
Auslowaith ute. wil drive through the
nek air at velocity V.
horizon a. ;
Teaters ay Nee AY cac- re ye B ilo-
Meters per Feet per sec Kilogram Foot-pounds. _Kilo ; Pawns:
second. ond. meters. | grammes.
45 11.2 26.7 336 2,434 6.8 15
3 10.6 3438 175 1,268 15.0 29
15 hee 36.7 86 623 26.5 58
10 12.4 40.7 65 474. 34.8 77
5 15.2 49.8 41 297 59.5 122
2 20.0 65.6 24 174 95.0 209

I am not prepared to say that the relations of power, area, weight, and
speed, here experimentally established for planes of small area, will hold for
indefinitely large ones; but from all the circumstances of experiment, I can
entertain no doubt that they do so hold far enough to afford assurance that we
can transport, (with fuel for a considerable journey and at speeds high enough to
make us independent of ordinary winds,) weights many times greater than that
of a man.

In this mode of supporting a body in the air, its specific gravity, instead of
being as heretofore a matter of primary importance, is a matter of indifference,
the support being derived essentially from the inertia and elasticity of the air on
which the body is made to rapidly run. The most important and it is believed

108 EXPERIMENTS IN AERODYNAMICS.

novel truth, already announced, immediately follows from what has been shown,
that whereas in land or marine transport increased speed is maintained only by
a disproportionate expenditure of power, within the limits of experiment in such
aeria! horizontal transport, the higher speeds are more economical of power than the
lower ones.

While calling attention to these important and as yet little known truths, I
desire to add as a final caution, that I have not asserted that planes such as are
here employed in experiment, or even that planes of any kind, are the best forms
to use in mechanical flight, and that T have also not asserted, without qualification,
that mechanical flight is practically possible, since this involves questions as to
the method of constructing the mechanism, of securing its safe ascent and descent,
and also of securing the indispensable condition for the economic use of the power
I have shown to be at our disposal—the condition, I mean, of our ability to guide
it in the desired horizontal direction during transport,—questions which, in my
opinion, are only to be answered by further experiment, and which belong to the
inchoate art or science of aerodromics, on which I do not enter.

I wish, however, to put on record my belief that the time has come for
these questions to engage the serious attention, not only of engineers, but of
all interested in the possibly near practical solution of a problem, one of the
most important in its consequences, of any which has ever presented itself in
mechanics ; for this solution, itis here shown, cannot longer be considered beyond
our capacity to reach.

APPENDIX A.

I append here the results of some additional experiments made with the Plane- Dropper
to determine the law of falling of a horizontal plane having a horizontal velocity of transla-
tion. It will be recalled that the preceding data given in the chapter on the Plane-Dropper
show only the total time of falling a distance of four feet, and that we cannot determine
from it the law of fall, unless we know, in addition, the relative diminution in the accelera-
tion during the descent, and whether at the end of the fall the plane has attained an
approximately constant velocity. For high horizontal velocities and for the most advan-
tageous planes, it is not impossible that an approximately constant velocity is reached within
the four-foot fall of the Plane-Dropper. In order to obtain these additional data, I placed
electric contacts upon the Plane-Dropper at intervals of every foot, and introduced other
modifications into the method of experiment. The accuracy with which it was necessary
to measure the relative times of fall through successive feet precluded the further use of the
stationary chronograph for the registration, and I adapted a Konig chronoscope to this
purpose.

This chronoscope consists of a tuning-fork of low pitch, which is made to vibrate by
the action of an electro-magnet. The vibrations are registered by a pen-point on a strip of
paper covered with lamp-black, which is passed over a roller during the time of fall. A
second pen-point worked by an electro-magnet records the passage of the falling-piece over
the five successive contact-pieces of the Plane-Dropper., On the same strip, therefore, we
have the relative intervals between the successive contacts, and a time-scale for their
evaluation. Although not essential for the evaluation of the intervals, approximate
uniformity in the motion of the strip of paper was obtained by fastening to the ends brass
clips differing suitably in weight, and converting this part of the apparatus into an Atwood’s
machine.

Two separate batteries were used, an electropoion battery of four cells, equivalent to
thirty or forty Daniel’s cells, for vibrating the tuning-fork, and an ordinary battery of eight
cells for the Plane-Dropper and the quadrant contacts of the turn-table. The current from
this battery is forked into two branches, one branch running to the quadrant contacts of the
turn-table and to the observatory chronograph on which they register; the other branch,
going to the Plane-Dropper, actuates the release magnet, passes through the five electric
contacts, and thence goes to the electro-magnet on the Kénig chronoscope, where these
contacts are registered, and finally back to the battery. This circuit is closed by a make-
key in the hands of the operator at the chronoscope.

A preliminary calibration of the tuning-fork was made by connecting one pen of the
chronoscope with the mean time-clock, and obtaining a number of strips containing both
second intervals and tuning-fork vibrations.

(109)

110 EXPERIMENTS IN AERODYNAMICS.

Calibration of tuning-fork.
DecemBer 12, 1890.—G. E. Curtis, Observer.

Temperature of tuning-fork, 18° C.

Number of vibrations of fork per second.
_ Number of

strip. 9
Ist second. 2d second. pe at
| reece eee eet ee 49.9
3 48,
4 48.2 51.9
47.8
5 48.8 51.0
48.6 50.8
48.8

Mean, 49.9 vibrations per second.

The measurement of the strips showed that the clock was not “on beat,” and that two
successive seconds must be taken in order to get the true interval. The mean of the
measurements gave 49.9 vibrations per second. The tuning-fork was evidently constructed
to give 50.0 vibrations per second, and this value was therefore adopted. The fraction of
a vibration can be accurately estimated to tenths; hence the instrument, as used in these
observations, gave time intervals to =, part of a second, which is sufficiently accurate for
the purpose.

Preliminary experiments were made with the Plane-Dropper at rest indoors for the
purpose of testing the new contacts and the Konig registration apparatus. The pair of
12 x 6 inch planes were fastened horizontally to the falling piece. Then the observer, with
one hand, sets in motion the blackened strip on the Kénig, and with the other, immediately
thereafter, presses the make-key, which operates the release magnet of the Plane-Dropper.
The blackened strip containing the-registration is then passed through a solution of shellac
and ammonia, by which the trace is permanently set.

The result of these preliminary experiments is as follows:

Time of fall of pair of 12 x 6 inch planes, horizontal.

DercemBer 10, 1890.—G. E. Curtis, Observer.

)bserved time of | Theoretical time

Total) 4 feet==—-=5<-- =

| fall (seconds). | (in vacuo). Difference.
Net afcbsca = ote ee 0.220 | 0.250
A footee <2 SRR ee eee 0.110 0.104 +- .006
BOifoot ===. 52 see ee 0.090 0.080 LO
4th fo0t Sosa asene2 ee see 0.080 0.066 + O14

APPENDIX A. Wali

The first contact is not at absolute rest, but a fraction (0.4 or 0.5) of an inch below the
position of rest; hence, when it records, the plane has already attained a small velocity.
To this is due the fact that the time of falling the first foot, which is registered by the first,
and second contacts, is less than the computed time in vacuo by .03 second. At least this
amount should therefore be added to the observed time for the first foot, and the total time
will be 0.53 seconds. This gives a total retardation of 0.03 seconds, due to the resistance of
the air. Attention is called to the symmetrical character of the differences between the
observed and the computed time in vacuo, showing the increasing retardation corresponding
to increasing velocities of fall. Being assured by these results of the perfect adaptation of
the apparatus to secure the desired data, the Plane-Dropper was placed upon the whirling-
table December 13, 1890.

When the whirling-table has attained uniform motion at the speed desired, a signal is
given to the observer seated at the Konig chronoscope to proceed with the experiment.
First, by a break-key he cuts out for a moment the quadrant contacts as an evidence on
the chronograph sheet of the time of the experiment. Second, the chronoscope strip, which
has previously been prepared and placed upon the roller, is set in motion by the release of
a detent, and an instant later, when the strip has gotten fully into motion, the make-key of
the Plane-Dropper circuit is pressed, releasing the falling plane. As the falling plane passes
each of the five contact pieces the circuit is completed, and registration is made upon the
Konig strip. In two seconds after setting in motion the Konig strip the experiment is at
anend. The strip containing the record is then passed through the solution of shellac and
alcohol for setting the trace, after which it is measured at leisure. Meanwhile a new strip
is placed upon the chronoscope, and the apparatus is in readiness for another trial.

The results of the observations covering a range of horizontal velocity from 6 to 26
meters per second (13.5 to 58.5 miles per hour) are contained in the accompanying table.

To find the times of falling successive feet of planes having a horizontal velocity.
DEcEMBER 13, 1890.

F. W. Very, G. E. Curtis, Observers.

One pair 12 x 6 inch planes horizontal; weight, 464 grammes (1.02 lbs.); mean temperature, 0° C.; wind
velocity, 1.85 meters per second.

TIMES OF FALL AT DIFFERENT HORIZONTAL VELOCITIES.

Horizontal

velocity | > Fp ; aD nto
(meters per At rest. 6.0 TAO 12.0 1221 14.6 144 18.0 22.1 26.2

second). |
ishiootes: = —=- 0.218 | 0.314 | 0.284 | 0.889 | 0.429 | 0.83 OA48 | 0.678 | 0.930 | 0.600 | 1440 | 0.962
2d foot-..--- ----] 0.112 | 0.120) 0.111 ; 0.125 | 0.257 | 0.205 0.147 | 0.202 | 0.450 | 0.220 | 0.285 | 0.303
SOOO tesa aae= 0.089 | 0.094 | 0.088 | 0.105 |------- 0.213 0.166 | 0.360 | 0.306 | 0.340 | 0.280 | 0.399
4th) foot-——— ==—= 0.079 | 0.082 | OO iia) O1098) |S====e= 0.235 QHSO | -=S==== | Saaneae 0.180 |-------]} 0.487
Total, 4 feet--| 0498 | 0.610 0.560 | OF 7s | ee lS 755 OLObIs Baan [eat 1.340 | 2.005 | 2.151

| |

* Seriously affected by wind.

112 EXPERIMENTS IN AERODYNAMICS.

SUMMARY.

| Velocity (meters | Time of falling | Increase over time

per second). 4 feet. in vacuo.
0.0 0.55 0.05
| 6.0 0.72 0.22
12.0 0.95 0.45
18.0 1.34 0.84
22.0 2.00 1.50
| 26.0 2.15 1.65

The time of falling the total 4 feet increases from 0.55 second, when the plane is at
rest, to 2.15 seconds, when the plane has a horizontal velocity of 26 meters per second.
Examining the time of falling the several successive feet, it will be seen that there is no
uniformity in the relative times in which the several distances were passed over. Only the
first experiment at 6 meters per second shows a velocity of fall continually increasing at a
diminishing rate as the circumstances require. The remaining four experiments, for which
a complete record was obtained, show decreasing velocities of fallin a part or all of the
distance after the first foot. These anomalous and discordant results are in all probability
due to wind currents having a vertical component, which vitiated the observations. Thus
the completeness of the apparatus and the perfection of the details of operations, whereby
an accuracy of <4, of a second was secured, were all rendered futile by the uncontrolled
conditions under which the experiment was unavoidably conducted, and no decisive result
was added to those already summarized.

APPENDIX B.

Mr. G. E. Curtis calls my attention to the fact that the conclusion that the power
required to maintain the horizontal flight of an aeroplane diminishes with the increasing
speeds that it attains, may be deductively shown by the following analysis:

Representing the work to be done per second by 7, the resistance to horizontal motion
by &, and the horizontal velocity by V, we have by definition

T= RV.

Substituting for A its value, W tana (see p. 65), W being the weight of the plane, we
have the equation
T=VW tana,

in which «and V are dependent variables. The curves of soaring speed (Fig. 9) enable

us, in the case of a few planes, to express « in terms of V, but, for any plane and without

actually obtaining an analytical relation between V and 2, we may determine the character

of the function T, 7. e., whether it increases or decreases with V, in the following manner:
Differentiating with respect to V, we obtain

dl
ra =W (tan a +-V sec? a oe

Now, since in flight « is a very small angle, tan « will be small as compared with the

term V sec? a ae Hence the sign of the latter factor a will control the sign of a
ae da
7d V avi
negative, and therefore, in general, T is a decreasing function of V. In other words,
neglecting the skin friction and also any end pressure that there may be on the plane, the

work to be done against resistance in the horizontal flight of an inclined plane must

Now, since V increases as « diminishes is negative, which makes the term V sec? a

diminish as the velocity increases.

15 (113)

APPENDIX C.,

At the time of my experiments to determine the varying position of the center of
pressure on an inclined plane moving in the air, I was unacquainted with the similar
experimental work of Joéssel* and of Kummer? in the same field. Joéssel, who appears
to be the first experimenter on the subject, found for a square plane of length L that, as
the angle between the plane and the current is diminished, the center of pressure approaches
a point + Z from the forward edge, and that its position for any angle « between the plane
and the current may be represented by the formula

d = (0.8 — 0.8 sin a) L,

d being the distance of the center of pressure from the center of plane.

The method of experiment adopted by Kummer is essentially similar to the one pur-
sued by me in the use of the Counterpoised Eccentric Plane. The object is to determine the
position of the center of pressure corresponding to different angles of inclination of a plane
to the current. The method pursued both by Kummer and myself has been the one which
most naturally suggests itself to find the angle of inclination « of the plane corresponding
to a series of fixed distances d of the center of pressure from the center of figure. Thus in
the experiments, d has been the independent variable, while in the use of the results, @ is
in general the independent variable.

For a square plane 90 mm. (3.54 inches) on the side, Kummer obtained the following
results, which may be compared with the results given here in chapter VIII and with the
formula of Joéssel :

Distance of center | Distance as a per- aati oe
of pressure from centage of side of | Angle of plane with
center of plane. plane. eon

|
|
| mm B
0 0.000 90
1 0.011 S4
2 0.022 77
| 9 0.033 70
| 4 0.044 62
| 5 0.056 52
| 6 0.067 41
7 0.078 3]
8 0.089 28
9 0.100 25
10 | 0.111 25
3 0.144 21
4 0.156 19
15 0.167 18
|

* Mémorial du Génie Maritime, 1870.

} Berlin Akad-Abhandlungen, 1875, 1876.
(114)

APPENDIX C. aS

In addition to determining the position of the center of pressure for a square plane,
Kummer extended his experiments to the case of differently shaped rectangles, and his
results with these are strikingly suggestive. It has been pointed out in chapter VI that
above and below an angle of about 30° there is a reversal in the relative amounts of the
pressure on inclined rectanglar planes of different shapes; the tabulated results of Kummer
exhibit a similar reversal in the position of the center of pressure, of which the following
may be given as an example:

Distance of center of pressure from center of plane.

Angles between plane and current. |

Size of plane.

45°. LOZ

mm. mm. mm.
180 x 180 11 40
90 x 180 14 36

For small angles the position of the center of pressure is further from the center of
figure in the 180 x 180 mm. plane than in the 90 x 180 mm. plane, while for 45° this
relation is reversed. It appears, therefore, that the reversal in the amount of pressure,
brought out in the experiments presented in this memoir, finds its counterpart in a corre-
sponding reversal in the position of the center of pressure exhibited in the work of Kummer.
It is believed that in this striking analogy may be found a key to the more complete
rational and deductive treatment of these inseparably related problems.

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bom) “OR P/ VOT.

CoUNTERPOISED Eccentric PLANE.

SGAME:

1 e 4 6 8 10 2
— —— =e Lp ——

9 INCHES

My -----F---4

SORDER.

p Foor.

See ed

=P wea as :
aaa 5 PP eehesegh Seey a:

(e0as.4 ¢2.2004 2 4a 2260.4 (Per
?

Sipe View.

Scace.

FRONT VIEW.

Prane Dropper.
Designed by S.P. LANGLEY.

PL.VI

Plane

ELEVATION

ScCALe
‘

COMPONENT PRESé&f

HoRIZONTAL
SECTION ON LINE G-H.
VLE te

}
tS)
AovyusTaB_Lele

SECTIONAL VIEW OF BEARING.

SipeView of KniFe Epce ANd PivorT.

|
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OUTLINE OF KNIFE-EDGE, :
PivOT AND BEARINGS.
|

mn Zen

PL.VII.

RE RECORDER.

4ANGLEY.

12 INCHES

10 i

‘ION.

hw aw \ \Ww
|

Plane

re)

ae
> 7
7
5
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nt
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Leros

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ge iam CC

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Designed b
S.P. LAnNGr

PLVIII.

AB.

SECTION ON LINE

f INCHES.

TRONOGRAPH.

Pfs

SIDE ELEVATI|

Rotuine Carriage & UY

SCAL}

INCHES.

RIS

N OF

RoNoGRAPH BARREL.

LANGLEY.

) Bilis 5: STi

watt

RECORDING ¥

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8 01421 0462

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