SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE 801 EXPERIMENTS IN AEPxODYNAMICS BY S. P. LANGLEY. CITY OF WASHINGTON : PUBLISHED BY THE SMITHSONIAN INSTITUTION. 1891. SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE 801 EXPERIMENTS IN AERODYNAMICS S. P. LANGLET. CITY OF WASHINGTON : PUBLISHED BY THE SMITHSONIAN INSTITUTION. 1891. COMMISSION TO WHOM THIS MEMOIR HAS BEEN REFERRED. Professor SIMON NEWCOMB, U. S. N. Professor HENRY A. ROWLAND. Professor CLEVELAND ABBE. PRINTED BY JUDD & DETWEILER. CONTENTS. PREFACE 1 CHAPTER I. Introductory 3 II. Character and Method of Experiments 7 III. The Suspended Plane "12 IV. The Resultant Pressure Recorder 15 V. The Plane-Dropper 26 VI. The Component Pressure Recorder. . . .- 48 VII. The Dynamometer-Chronograph 75 VIII. The Counterpoised Eccentric Plane 89 IX. The Rolling Carriage 94 X. Summary 105 Appendix A 109 Appendix B 113 Appendix C * 114 (m) 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. (i) CHAPTER I. INTRODUCTORY. 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 fgct 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. 5 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 prcotimably 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 resume of the literature of the subject until it could be done in the light of acquired knowledge. I 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, amono; the few earlier memoirs that I am conscious of owing much useful O * ' 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 UAeronaute. 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 through 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 *From &spodpoft&i to traverse the air; depodpopof, 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, however 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.4027'41.6"; long. 5 h 20 m 2.93 8 ; 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, antl by very elaborate experiments ; the formulae 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 (28I) 3 = 826.6 ; at the outer end to (31i) 2 = 976.6, and at the center to (30) 2 = 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 w r hole 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 arc here only indirectly presented) and of well-known experiments of others.f It will be seen that my experiments implicitly show that the effect of friction on the surfaces and at the speeds 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 clown on it. The whirling table was driven first by a gas-engine of about 1 J 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, however, 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." t 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 coefficient of the viscosity of the air. This is /JL = 0.0001878 (1 +.C027 ()}, ;JL and being taken as defined in his paper on the dynamical theory of gases in Phil. Trans., Vol. CLVII. By this formula the actual tangential force on a one-foot-square plane moving 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 21 i, 18 i, lit, 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 Lowest speed 25 Second " 50 Third " 100 Highest " 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, 25 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 -f- miles per hour at end of arm. 25} " " 24 " " " = 50 + " " " " 36 " " 12 " " = 25 + " " " " 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 0-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. S and L are adjusting screws. Turning again to plate II, an additional brush contact, shown at B, and again at B', 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 Memoire de M. Chabrier concernant les moyens de voyager dans 1'air et de s'y diriger, contenent une nouvelle theorie des mouvements progressifs. (Commissaires, MM. Gay-Lussac, Flourens, et Navier, rapporteur.) Paris, Mem. Acad. Sci. xi, 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 ffty 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 Navier suggests that there exists the same ratio between the efforts necessmry 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 difference qui existe entre la force uecessaire pour que 1'oiseau se soutienne simplement dans Fair, et celle qu'exige un mouvement rapide. Lorsque la vitesse de ce mouvement est de 15 m par seconde, on trouve que cette derniere force est environ cinquante fois plus grande que la premiere. Ainsi 1'effort qu'exerce 1'oiseau pour se soutenir dans 1'air est fort petit comparativement a 1'effort qu'il exerce dans le vol. II en coute peut-etre moins de iatigue a 1'oiseau pour se soutenir simplement dans 1'air, eu egard ii la fatigue qu'il est capable de supporter, qu'il ne'en coute i 1'homme et aux quadrupedes pour se soutenir debout sur leurs jambes." Paris, Mem. Acad. Sci. xi, 1832 (Hist.), p. 71.] The supposed elegance and validity of Navier'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 CO 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 arc 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 from 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. For 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 less 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 FF' 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 FF' 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 have 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 b3 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 a one-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 sarna 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. e., 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 individual 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 : TABLE I. Excursion of trace. Pressure. Excursion of trace. Pressure. Centimeters, Us. Grammes. Centimeters. Lbs. Grammes. 0.28 0.1 45 4.45 1.6 726 0.55 0.2 91 4.73 1.7 771 0.82 0.3 136 5.03 1.8 816 1.10 0.4 181 5.33 1.9 862 1.37 0.5 227 5.65 2.0 907 1.64 0.6 272 5.98 2.1 953 1.92 0.7 318 6.29 2.2 998 2.20 0.8 363 6.60 2.3 1043 2.47 0.9 408 6.91 2.4 1089 2.73 1.0 454 7.25 2.5 1134 3.02 1.1 499 7.60 2.6 1179 3.30 1.2 545 7.93 2.7 1225 3.59 1.3 590 8.28 2.8 1270 3.89 1.4 635 8.63 2.9 1315 4.17 1.5 680 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 3 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 II, III, arid 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 p pressure on the plane by means of Table I. The column headed k m = -== contains '2 the results of measurements of pressure on the normal plane expressed in terms of the coefficient k m of the equation P = k m F 2 , 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. 19 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. TABLE II. AUGUST 27, 1888. S. P. LANGLEY, 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. p o fl 9 o d ^ O i r-H ^^ 03 O c3 gj d ft 1 1 . 2^ ^M ^ QQ 6 S^ 03 ^ a 1 1 ^H AH '^ O "S \5^/ ft^ ^ of observ "d N S'B f, [ e c5 -rH X -t-5 O2 g M ssi QrS <-! L, o 53 -t-2 *i O 02 P 7- d S " oS . cj ^j gdl 3 o P 'V* .0077 F 2 Pa Ao o fa. d O '^ Pn e3 S a? 02 j jjj d | g^^ Teg > G r! g^^ 2 03 d H g^ 02 s ^ C/2 1 " 1 h-3 ^ ft (p. m.) 5-45 90 12.65 447 1 10 0195 00097 90 12.64 447 105 0.185 0.0092 30 1258 449 57 8 100 0176 0156 1 13 15 1267 446 75 8 050 0088 0153 058 6:06 90 6.53 8.66 280 0.495 0.0066 90 6.60 8.57 2.80 0.495 0.0067 30 655 864 54 5 260 0.463 0575 080 15 6.44 878 73 5 165 0.293 0594 049 7.5 644 878 92 080 0.141 0594 024 7.5 6.43 879 83 080 0.141 0595 024 6:29 90 5.74 9.85 410 0.722 0.0075 90 5.39 10.50 4.40 0.771 0.0070 30 487 11 61 60 3 465 0.820 1038 079 20 EXPERIMENTS IN AERODYNAMICS. TABLE III. AUGUST 28, 1888. S. P. LANGLEY, 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, 736.6 mm. ; temperature, 19.4 C. ; mean wind velocity, 0.37 meters per second. Time of observation. 9 d 1 H . ~3 ^S g*S *J a o o "1 Seconds in one revo- lution of turn-table. Linear velocity of cen- ter of wind plane. F(meters per sec.). Angle of trace with di- rection of trace made by plane set at 90. Departure of trace from center (centi- meters). Pressure on plane. P a (grammes per sq. centimeter). Km P V* -*90 .0077 V 1 Pa -* 90 (p. m.) 2-26 90 1262 448 103 0180 00090 90 12.62 4.48 1.00 0.176 0.0088 30 1262 448 65 8 070 0122 0155 0.79 15 1257 450 78 8 065 0112 0156 0.72 2-52 90 645 877 325 0576 0075 90 6.52 867 3.15 0.561 0.0075 45 648 873 48 5 330 0585 0.587 1.00 45 30 6.51 645 8.69 877 46 .0 61 5 3.10 300 0.551 0532 0.581 0.592 0.95 0.90 30 645 877 60 5 320 0566 0.592 0.96 15 643 879 75 6 205 0366 0.595 0.61 15 640 884 76 5 1 90 0341 0.602 0.57 75 644 878 86 1 45 0259 0.594 0.44 75 645 877 80 5 1 15 0205 0.592 0.35 3-40 90 505 11 20 5.40 0.930 0.0074 90 534 1059 4.50 0.786 0.0070 45 5 19 1090 48 400 0702 0.915 0.77 45 529 1069 48 410 0722 0.880 0.82 30 5 26 1075 60 '5 440 0771 0.890 0.87 30 15 5.44 509 10.40 11 11 59 .0 81 3.90 235 0.683 0415 0.833 0.950 0.82 0.44 15 5 18 1092 75 5 220 0387 0.918 0.42 75 495 11 42 84 5 1 30 0230 1.004 0.23 7 5 533 1061 85 5 145 0259 0.867 0.30 4-30 90 579 977 390 0683 0.0072 90 578 978 385 0673 0.0070 30 553 1023 59 385 0673 0.806 0.84 30 556 1017 58 8 360 0634 0.796 0.80 75 541 1045 85 'o 1 20 0215 0.841 0.26 7 5 509 11 11 75 1 75 0312 0.950 0.33 REMARKS. 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 register sheet = 95. THE RESULTANT PRESSURE RECORDER 21 TABLE IV. OCTOBER 4, 1888. F. W. VERY, Conducting experiments ; JOSEPH LUDEWIG, 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. Time of observation. o a o ^ *3 rt ^ i SO O '-3 Linear velocity of cen- ter of wind plane. F (meters per sec.). ' -3 C3 d 'o _o gl^s Q Pressure on plane. P a (grammes per sq. centimeter). P V* -* 90 .0076 F 2 p w (a. m.) 11:40 15 12.50 4.52 0.5 0.088 0.155 057 10 12.60 4.49 0.5 0.088 0.154 057 10 12.50 4,52 0.5 0.088 0155 057 (n in ") 20 12.50 4.52 0.7 0.122 0155 079 \r i "*y 1-07 20 12.55 4,51 0.6 0.104 0154 068 1:13 90 90 20 6.60 6,53 6.39 8.57 8.66 8.85 3.0 3.0 2.6 0.532 0.532 0463 0.0073 0.0071 0.558 0.570 0595 078 20 6.43 8.79 2.3 0408 0587 070 1-30 90 90 10 6.48 6.45 6.43 8.73 8.77 8.79 3.0 3.0 1.3 0.532 0,532 0.233 0.0070 0.0069 0.579 0.584 0587 040 10 6.43 8.79 1.7 0.303 0587 052 90 90 15 6,50 6.45 6.47 8.70 8.77 8.74 3.0 3.2 1,5 0,532 0,566 0.268 0.0070 0.0074 0.575 0.584 0581 046 15 6.47 8.74 1.9 0.342 0581 059 90 90 5 6.45 6.57 6.43 8.77 8.61 8.79 3.8 3.8 1.0 0.664 0.664 0176 0.0086 0.0090 0.584 0,563 0587 030 1:52 5 6.45 8.77 1.1 0195 0584 033 22 EXPERIMENTS IN AERODYNAMICS. Collecting the values of k m from the several days' observations and reducing them to a common mean temperature of 10 C. and pressure of 735 mm., we have the following summary of results : lc ""m, August 27, 1888 0.00810 " 28, " 0.00794 October 4. " 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., Jc m = 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 90 = 0.0077 V 2 in the experiments of August 27 and 28, and P 90 = 0.0076 F 2 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 F. The coefficient adopted for the computation is the mean value of k m , 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. TABLE V. Summary of ratios of pressure on inclined plane to pressure on normal plane. Linear velocity of plane (meters per sec.). Angles of inclination. Remarks. 45 30 20 15 10 7i 5 4.5 8.7 11.2 1.00 0.95 0.77 0.82 1.13* 0.79 0.80 0.90 0.95 0.79 0.87 0.82 0.84 0.80 .79 .68 .78 .70 .58 .57 .72 .49 .62 .57 .46 .59 .44 .57f * Omit. fGive one-quarter weight. .57f .40 .52 .24 .24 .44 .35 .23 .30 .26 .33 .30 .33 .42 Mean 0.89 0.84 .74 .55 .48 .30 .31 THE RESULTANT PRESSURE RECORDER. FIG. 1. 23 ICO 9( 7[ 6C 5C 4( 3C 21 1C 10 30' 40* 45 Ratio of the total normal pressure (P a ) on an inclined square plane to the pressure (P^) on a normal plane, the planes moving in the air with the same velocity. Absciss. Angles of inclination () of plane to horizon. p Ordinates. ^=F (a) (expressed as a percentage). -* 90 O Represents the mean of observed points for each angle of experiment. 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 90 did not coincide with the horizontal (i. 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, etc., really apply to angles of about 50, 35, 25, etc. 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,f 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 formulae 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, Memorial de VArtitterie No. V, I 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 (P a ) on an.inclined square plane to tlie pressure (Pgo) on a normal plane moved in the air tvith the same velocity. Pa -n- as given by -M:O Angles of inclination of plane to direc- tion of motion. Experiments with Duchemin's formula : Difference: Duche- m in Langley . (01 Resultant Pres- 2 sin a sure Recorder. 1 + siri'a 5 .15 .17 + .02 10 .30 .34 .04 15 .46 .48 .02 20 .60 .61 .01 25 .71 .72 .01 30 .78 .80 .02 35 .84 .86 .02 40 .89 .91 .02 45 .93 .94 .01 f Implicitly contained in the Principia, Prop. XXXIV, 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 formulae 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 z 5cos 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 a%when " 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 can 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 CO' 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, S, 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 a against the frame and completes the circuit. While falling, the circuit is open, and at the distance of four feet the contact-piece e 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 : Length of brass tube 160 centimeters. Length of aluminum falling-piece 25 Length of buffers 5 Actual distance of fall (between contacts) 122 Distance of center of brass frame and falling-piece from center of turn-table, when mounted 981 Weight of falling-piece 350 grammes. The planes are made of varnished pine about 2Jmm. 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 cm.) ; weight of pair, 123 grammes. (2) " " " 8x 9 in. (22.9 x 20.3 cm.) ; " " 115 " (3) " " " 12 x 6 in. (30.5 x 15.2 cm.) ; " 114 (4) " " " 18 x 4 in. (45.7 x 10.2 cm.) ; " " 114 " (5) " " " 15 x 4 in. (38.1 x 10.2 cm.) ; " 118 " 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 djop- 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. As a 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. 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, is within T iff 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 : 1st. To show by the increased time of fall that the supporting power of the air 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. LANGLEY, Conducting experiments and recording ; F. W. VERY, Assisting. 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. O<~* '"^ *"-< GO P o S'g 3 8 o3 02 ^""* r r^ Size and attitude of planes. 11 "o O ^ o fl ^ u a o o '-+3 3 } GO . ~ I~H "*^ S^ H H 18 x 4-inch planes horizontal 38 A 1.30 3.8 A 1.15 3.75 B1.20 4.25 B1.15 12 x 6-inch planes, horizontal : A.t rest (in open air) 0.52 a tt tt 0.52 tt tt tt 0.52 tt tt tt 0^54 In motion on turn-table . . . 6.0 B 0.71 tt tt tt 6.2 B0.80 n tt tt 6.1 A 0.76 it tt it 6.1 A 0.80 It U tt 3.5 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 ordi nates, and abscissae are horizontal velocities of translation. 30 EXPERIMENTS IN AERODYNAMICS. TABLE VI MAY 25, 1889. To find the time of fall of different planes; plane-dropper statiouajy. S. P. LANGLEY, Conducting experiments; F. W. VERY, Assisting. Barometer, 731.5 mm.; temperature, 17.5 C. ; wind, light. Weight (with dropping piece). Time of fall of Size of planes. Angle with horizon. 4 feet (1.22 meters). (Grammes.) (Pounds.) (Seconds.) One pair 12 x 6 inches (30.5 x 15.2 464 1.02 0.58 cm.). 0.58 12 12 0,52 % Dimensions and aspect of plane. Date. O f 1 . rj) Coo O 02 O O ^ lit o Date. C o C "o O 02 r H r^ , Ifi^ o^g *"' ^"T'o S^o o g C c3 'C ^o C i ( -+-3 O -pH co H 3 O -"S 02 H W H < H i 1 (-H 1889. 1889. JA j JS June 10 0.00 0.0 0.53 June 10 16 5.1 12.1 * -m- \* " 5.70 10.8 0.70 " 5 3.4 18.1 JS IS " 5.90 10.4 0.65 u 3.35 18.4 1.62 18 x 4 inches (45.7 x 10.2 u 3.45 17.9 1.65 cm.). " 5.80 10.6 0.85 Weight, 1.02 Ibs. (464 4,35 14.2 0.90 grammes). It 3.75 16.4 1.08 Radius of rotation to cen- June 11 3.80 16.2 1.30 June 11 20 6.0 10.3 ter of planes, 9.81 in. u 3.80 16.2 1.15 1 15 6.2 9.9 THE PLANE-DROPPER. TABLE VII Continued. 1 1 i SH i i i i 1 _i O "^""^ o O c3 ^~^ o S r> t-i r r2 ^ a> > > *-l r SB g * | i i r o3 K &..& -- O > O3 Dimensions and aspect of plane. Date. Goo O 03 o o |lf o . Date. *O '& rH O f, , Jj goo O 03 11? .s ^ 8 Sr3 +1 O " M | Sr3 -^ O -~S 02 H H H 53 g W 1889. 1889. 18 f 18 June 11 3.75 16.4 1.20 June 11 3i 3.3 18.7 * -m- 1* u 4.25 14.5 1.15 IS 18 June 12 3.00 20.5 1.95 June 12 3 3.35 18.4 " 3.60 17.1 1.50 a 2 2.85 21.6 18x4 inches (45.7x10.2 u 3.00 20.5 2.55 cm.). a 3.05 20.2 2.68 Weight, 1.02 Ibs. (464 a 3.10 19.9 2.75 grammes). " 3.15 19.6 2.05 a 3.70 16.8 1.65 12 . J2 tt 0.00 0.0 0.56 June 11 25 5.6 11.0 to ~ffl~ | it 6.15 10.0 0.80 u 6 3.8 16.2 jj> T 1 22 tt 6.05 10.2 0.74 June 12 5 3.3 18.7 June 11 3.50 17.6 1.00 12x6 inches (30.5 x 15.2 n 3.40 18.1 1.16 cm.) June 12 2.87 21.4 1.29 Weight, 464 grammes. " 2.82 21.9 1.59 8 | 8 tt 0.0 0.57 it 25 6.0 10.3 tt 13.15 4.7 0.62 u 15 4.9 12.6 < -[}- 05 u 3.50 17.6 0.72 u 12 4.2 14.7 5 6 tl 2.85 21.6 0.82 tl 6 2.9 21.2 it 2.65 23.3 0.86 Weight, 465 grammes. 6 A /J tl 0.0 0.57 tt 30 5.9 10.5 /l O u 11.65 5.3 0.58 It 20 5.0 12.3 Sj []- ^ tl 4.10 15.0 0.65 11 15 4.2 14.7 11 5.10 12.1 0.70 it 13 3.8 16.2 6 G 11 2.78 22.2 0.72 9 2.9 21.2 6x12 inches. Weight, 473 grammes. IS 15 June 14 5.65 10.9 0.76 June 14 20 5.25 11.7 <$\ -tojf- 1* u 3.10 19.9 1.28 " 15 5.10 12.1 .Zo J5 u 3.00 20.5 1.28 " 15 4.65 13.3 15x4 inches (38.1x10.2 N " 10 7 4.55 3.85 13.6 16.0 cm.). Weight, 468 grammes. 5 4 3.30 3.10 18.7 19.9 32 EXPERIMENTS IN AERODYNAMICS. FIG. 2. 75 l^iagram tfPlane^ ** 250 225 00 1.75- 1.50 1.25 1.00 0.75 0.50 15 150 125 1.00 0.75 0.50 1.75 1.50 1.25 1.00 0.75 0.50 B 10 15 IS" 10 15 Times of falling 4 feet of horizontal planes on the Plane-Dropper. Average weight of planes = 465 grammes. Abscissas : = Horizontal velocities of translation in meters per second. Ordinates : = Times of fall in seconds. 25 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 tha 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 4 inch 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 5 34 EXPERIN KNTS IN AERODYNAMICS. the plane is of perhaps equal importance, and its action has been present to my nrind 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 12x6 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 low one. 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 : 12 x 6 inch planes, inclined. Angle of inclination. Time of 1 revolution of turn-table (seconds). Attitude of plane. 25 6 5.6 3.8 Soaring. u 18-X.4 inch planes, inclined. ( ( G OQ 13 *" ~^ O *4l O 0-43 11 o O Attitude of plane. Estimated result. 1" Hl3 s 4 34 More than soarino p ( For angle 3J soarin^ speed 1 rev- 3 32 Not ouite soarin or 1 olution in 3 3 seconds 20 6.0 Soaring. 15 55 More than soaring f For an"le 15 soarino 1 speed = 1 rev- 15 68 Not quite soarin " 1 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 abscissse 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 E X Vj R being the horizontal component of pressure on the plane, and V the 36 EXPERIMENTS IN AERODYNAMICS. FlG. 3. Velocities of soaring of inclined planes on the Plane-Dropper. Average weight of plane = 465 grammes. Abscissas : = Angles of inclination () 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, E X F, 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 FIG. 4. A. B. Reference. air of plane* 1, n/ apart. c. D. I.O 50 (00 I5C 200 Times of falling 4 feet of single and double pairs of 15 x 4 inch planes. 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 100 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. TABLE VIII. JUNE 14 3 1889. To determine the times of fall of a system of horizontal planes endowed with horizontal velocity. To determine the horizontal velocities at which a system of inclined planes will be supported by the air. M! ii* 6 O PH i o 02 d .2 i i N .2 C3 Horizontal velocity. o > ^2 i 1 . > *o.S -H> o "tf) a Time of one revo- lution of turn- table (seconds). Horizontal veloc- ity (meters per second). 6 no O 1 Remarks. A 0.0 0.69 *l " ZlffiC 1st B 0.0 062 J5 T 13 A 2.60 23.7 1.68 B 2.65 23.3 1.70 15 x 4 inches (38.1 x 10.2 B 2.60 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. A 5 2.60 23.7 0.75 Total weight, 942 grammes. A 5 2,50 24.6 0.50 A -j- 1 2.50 24.6 2.20 Fell, then Soared. A 4- 1 2.65 23.3 6.15 Fell' slowly. B -i 2.65 23.3 0.90 B -i 2.65 23.3 1.20 Same planes, 2 inches apart. A 2.35 26.2 1.60 B 2.45 25.1 1.20 A 2.60 23.7 1.90 B 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 23.3 0.72 A + 3 2.60 23.7 Stayed at top. B 1 3 2.65 23.3 0.70 B 3 2.75 22.4 0.50 Same planes, 6 inches apart. A 3.30 18.7 1.70 B 3.30 18.7 1.20 A 3.35 18.4 1.50 B 3.30 18.7 1.30 A + 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 3 3.15 19.6 0.75 B 3 3.20 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. TABLE X. AUGUST 23, 1889. Barometer, 732.3 mm. ; mean temperature, 22. 8 C. ; wind, light. tJD o c '""^ 6 3 B ^ t> H ^ O o. 03 ^H 03 03 S "35 i H """^ f C3 ""03 03 **" s4 i i Dimensions and aspect of planes. |.| sj 8*8 O 03 *0 03 Is "o ^ i ( ^ ^ o Remarks. " o> r-H 03 '- 3 _N 03 '55 bC 5 ^ c3 M i 1 -M O -r-t GO a O PH S H w H 15 A JS A 7.80 7.9 0.80 rn| -fw" r* B 9.30 6.6 0.70 15 T js A 9.10 6.8 0.70 B 8.45 7.3 0.65 15 x 4 inches (38.1 x 10.2 A 4.80 12.8 1.08 cm.). B 4.80 12.8 1.02 Double pair of planes, 6 A 4.85 12.7 0.90 inches apart. B 5:00 12.3 1.20 Total weight, 942 grammes. A + 5 4.95 12.4 1.55 A + 5 10.05 6.1 0.70 B 5 9.35 6.6 0.60 B - 5 4.70 13.1 0.64 B + 5 4.75 13.0 2.10 B + 5 9.00 6.8 0.78 A 5 8.10 7.6 0.69 A 5 4.75 13.0 0.70 A + 7 4.85 12.7 11.15 A + 7 8.20 7.5 0.90 B - 7 9.35 6.6 0.62 B 7 4.70 13.1 0.58 B 4- 7 4.70 13.1 7.25 B + 7 9.10 6.8 0.80 A 7 9.50 6.5 0.60 A 7 4.75 13.0 0.57 A + 10 4.65 133 Soars. A 1 J - vy 10 7.90 7.8 1.10 B 10 10.25 6.0 0.75 Same planes, 4 inches apart. A 11.55 5.3 0.62 B 8.60 7.2 0.60 A 4.60 13.4 0.95 * B 4.70 13.1 0.89 B + 5 10.10 6.1 0.69 B + 5 4.70 13.1 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 12.7 3.07 B 7 4.87 12.7 0.58 THE PLANE-DROPPER. 43 TABLE X. AUSUST 23, 1889 Continued. tc rt p? f-H -4-3 R 6 c3 i O DO v / Dimensions and aspect of planes. 4-l O it O "1 sl gJ *O O o lit o 3 Remarks. -2 O r-H '-+3 3 N K. O > S^ O ^ O pi. 05 3D 2o5 ij ?H T^ H 2*H 8 > 1 5 '^ Dimensions and .aspect of planes. 8 'i. <4H 0.2 43 g^l 'o o ^ "S S 1 ^ gy o **-< r ( "o o Remarks. j ~> ,_^ O '-+3 ^Q o rH 00 Q tc d Sr2 J 'S ^ o O TH OQ 1 PH H K H 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 12.3 1.30 25 A 15 A 5 4.95 12.4 0.60 rfr[ -KPf- 1^ A 7 4.85 12.7 0.50 23 i 25 A - 7 8.65 7.1 0.60 B + 7 9.40 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 12.1 1.60 . B + 14 4.50 13.7 A 2.63 23.4 2.60 B 2.64 23.3 1.07 A 2.60 23.7 1.80 B 2.60 23.7 1.00 A 4- l 2.60 23.7 Fell after soaring about 20 I -L 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 B 5 2.60 23.7 0.60 - 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 abscissae 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. FIG. 6. 1.25 1,00 075 0.50 1- Single p(( ir cfplana + ttf -5 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 6.5 meters per second. Abscissae : = Angles of inclination of plane to horizon. Ordiiiates : = 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 vertically 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. FIG. 7. 4 4 -i -! i .1 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. Abscissae : = Angles of inclination () 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 (l m .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, T V of an inch thick and weighing 464 grammes, has a specific gravity of about 1,660 times that of air ; yet while the retardation due to the still air in the direct fall is but 20 S .03, that due to the same air in strictly lateral motion is l s .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 used 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 measured only 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 arid 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. 7 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 cm.) The pencil departures are therefore longer than the true spring extension, and the latter are obtained from the former by multiplying by the factor 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 724 expressing the ratio of the lengths of the arms, viz., , ' = 0.579. l^o.U 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 Soiling 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 THE COMPONENT PRESSURE RECORDER. 51 velocity of the turn-table at the instant for which the reading is made. The occasion 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 i. 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 carries 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. Cjnsequently, 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 called 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 : Size. Weight. Size. Weight. Size. Weight. Inches. Cm. Grammes. Inches. Cm. Grammes. Inches. Cm. Grammes. 30 x 4.8 SO x 4.8 30 x 4.8 76.2 x 12.2 76.2x12.2 76.2 x 12.2 250 500 1,000 24x6 24x6 24x6 61.0 x 15.2 61.0 x 15.2 61.0x15.2 250 500 1,000 12x12 12x12 12x12 30,5 x 30.5 30.5 x 30.5 30.5 x 30.5 250 500 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 4 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 i. e., " corrugated " for greater stiffness. 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 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. OCTOBER 8, 1890. F. W. VERY, Conducting experiments ; JOSEPH LUDEWIG, 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. Angle. Seconds in one revo- lution of turn-table. Velocity of plane (meters per sec- ond). Extension of spring (inches).* Pull of spring (grammes). 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. EXPERIMENTS IN AERODYNAMICS. Angle. Seconds in one revo- lution of turn-table. Estimated soaring speed (meters per second). Spring extension (inches). Remarks. 30 5.5 > ^ 6.3 < 5.5 > } 5.65 sees. 10.6 2.3 5.75 < 5.55 > J 15 4.8 1 5.4 > 5.65 right 1 K K /"* o ^-- ^- f O./O 0.0 5.9 < 10.4 0.8 Plane quivers at tip with highest speed. 5.85 right , 10 5.0 > ' 5.4 right 5.85 < U QK 5.5 < f &td5 17.9 0.75 Plane somewhat bowed. 5.3 < 5.3 right. Plane stiffened by thin iron plate at both ends and at middle, and experiment repeated with same setting. 10 4.9 > -) 5.0 < (Repeated) 4.75 > U.95 5.1 < 12.1 0.9 5.0 < J 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. 55 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.) 30 x 4.8 76.2 x 12.2 500 24 x 6 61.0 x 15.2 500 12x12 30.5 x 30.5 500 12 x 6 30.5 x 15.2 250 6x 6 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 6x6 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. inchplcL w, ivtlOf, Qqramm w. C Z4 >> HO '"^ ^> g lit l^td 53 1 59 | rS 4 !? 'o K & a ft| Difference. r-t ^3 S X 2 ^ ft VH O O ill liil <3 s 45 93 91 + .02 40 89 88 + .01 35 84 84 .00 30 78 78 .00 25 71 69 + .02 20 60 57 + .03 15 46 44 + .02 10 30 30 .00 5 15 16 -.01 The agreement between these values of F (a) derived from these two entirely dissimilar methods of observation (dependent also, as it is, on the experimental value of Jc m ) 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 F (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. FIG. 10. 10 10 15 Ratio of the resultant normal pressure (P a ) on an inclined rectangle to the pressure (P 90 ) on a normal rectangle, computed from experiments with the Component Pressure Recorder. Abscissae : = Angles of inclination (a) of plane to horizon. W P Ordinates: = F(a) = _ = ~ (expressed as a percentage). rC jCi V COS O. -t on 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.f 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- vation s 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 k m and k have been computed. As previously used, the numerical value of k relates to velocities expressed in feet per second and pressure in pounds per square foot, and k m 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 30 x 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. t 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 8x4 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 have 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. FIG. 11. 500 400 300 200 100 t /< / / / / / < / I/ > / / *< A 7 i < > / 7 \. < ; / f 5 10 1 5 20 25 30 35 40 4 Horizontal pressure (or resistance to advance) on 30 x 4.8 inch plane at soaring speeds obtained with the Component Pressure Recorder. Abscirisae : = Angles of inclination () of plane to horizon. Ordinates : = Horizontal pressure (R) in grammes. O Represents points observed. X v Represents points given by equation, R = weight X tangent a. 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 mm .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"-skaped 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 E = 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 60 R V, E being the horizontal pressure in grammes, and V 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 E being taken from the curve of figure 11 : 9 66 EXPERIMENTS IN AERODYNAMICS TABLE XIII. Angle with horizon Soaring speed V. Horizontal pressure R. Work expended per minute 6(XR7. Weight with planes of like form that 1 horse-power will drive through the air at velocity V. . Meters per second. Feet per second. Grammes. Kilogram- meters. Foot- pounds. Kilo- grammes. Pounds. 45 11.2 36.7 500 336 2,434 6.8 15 30 10.6 34.8 275 175 1,268 13.0 29 15 11.2 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 55.5 122 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, I am 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 case in which the direction of propulsion of the aerostat is horizontal and in which its plane makes an angle a 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 tliis elevation and to the simultaneous action of gravity will be exactly horizontal. If in this case its horizontal velocity be represented by Vj 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 a 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 F 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 F and a 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 F, the direction of propulsion can vary between and a 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 (i. e., 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 LUDEWIG, Regulating engine. Date. Mean barometer (millimeters). Mean temperature (centigrade). Mean wind velocity (meters per second). 1890. September 29 7410 14 030 October 1 7386 17 1 20 " 9 736.6 18 0.50 " 3 735.8 15 0,55 4 734.5 19 0.60 7 727.7 15 0.60 " 8 7366 15 030 " 9 740.1 17 0.50 Date. Description of planes. Angle of elevation a. Attitude of plane. *s e n o> - '42 % -** > Number of spring. Extension of spring (inches). Pull of spring (grammes). Horizontal pressure on plane R (gram's). Km. L 1890. Sept 29 cm. cm. 24 x 6 inches (61 0x152) 30 120 4 1 20 708 371 u Weight 500 grammes 15 Soaring 122 4 0.30 294 154 a 10 u 136 4 0.20 229 120 Oct. 1 cm. cm. 24 x 6 inches (61.0 x 15.2) 90 9.6 4 2.80 1,358 712 .0083 .00158 u Weight, 250 grammes. 30 Soaring 7.8 4 u 30 K 7.8 2 1.31 294 154 % u 15 U 8.3 u 0.64 164 86 Oct. 2 30 it 7.9 u 1.25 284 149 u 15 U 80 u u 10 U 86 u 050 134 70 u 5 u 118 li 045 121 63 u a 3 8 Not quite soaring Soaring 13.3 154 (I u 0,35 0.39 101 107 53 56 n 9, u 176 u 0.41 113 59 u Not soarin^ 25.0 (( 0,50 134 70 Oct. 3 em. cm. 24 x 6 inches (61.0 x 15.2) 90 67 4 0.88 567 297 .0071 .00135 i Weight, 1,000 grammes* 90 7.2 u 1.21 708 371 .0077 .00146 i 90 98 u 280 1 358 712 0079 00151 i 30 Soarin " 152 u 1.60 867 454 i 15 u 162 u 0.95 594 311 i 10 u 19.4 u 0.68 480 252 . " 5 Not soaring 25.0 a 0.50 397 208 THE COMPONENT PRESSURE RECORDER. 69 TABLE XIV Continued. Date. Description of planes. e a 'i > o -3 IM O O -a B < Attitude of plane. *S E 5-1 o> o 1JU o ""O ^o o b^ Number of spring. Extension of spring (inches). Pull of spring (grammes). Horisorital pressure on plane R (gram's). Km. L 1890. Oct 3 cm. cm. 12 x 12 inches (30 5 x 30.5) 90 9.5 4 2.70 1.325 694 0083 00157 u Weight 500 grammes. 90 8.3 tt 1.84 '970 508 0079 .00150 u 30 Soaring 9.5 n 0.75 510 267 li 15 u 12.0 tt 0.27 271 142 u 10 it 150 it 0.12 159 83 a 10 It 146 9, 0.80 197 103 it 5 tt 200 it 0.70 176 92 U cm. cm. 12 x 12 inches (30 5 x 30 5) 90 62 tt 2.20 471 247 0069 00132 it Weight. 250 grammes. 30 Soaring 66 tt 1.02 242 127 tt 15 u 91 it 0.49 130 68 u 10 u 106 tt 0.45 120 63 it 5 11 146 it 0.35 100 52 n 3 it 167 it 0.40 113 59 a 9, tt 188 tt 0.55 145 76 tt Oct. 4 cm. cm. 12x12 inches (30.5 x 30.5) 90 Not soaring .... 23.1 70 tt 4 0.80 1.25 199 726 104 380 0084 .00160 tt Weight, 1,000 grammes. 90 94 u 2.48 1 235 647 0079 .00150 a 30 Soaring 128 It 1.85 970 508 it 30 u 128 tt 1.80 953 499 u 15 n 174 tt 0.57 435 228 Oct. 3 15 a 167 ^ 1.75 388 203 u 10 tt 200 tt 1.25 285 149 1C 5 it 255 It 0.80 199 104 Oct. 7 cm. cm. 6 x 24 inches (15.2 x 61.0) 90 62 tt 2.65 563 295 0081 .00155 u Weight, 250 grammes. 30 Soaring 76 tt 1.35 308 161 It 15 a 118 tt 0.90 216 113 it 10 tt 141 it 0.60 155 81 tt. 5 it 21 1 a 0.90 216 113 u u cm. cm. 6 x 24 inches (15.2 x 61.0) 3 90 Nearly soaring . . 25.0 63 u tt 1.00 2.70* 235 571* 123 299* 0081* .00154* it Weight, 500 grammes. 90 54 it 2.08 453 237 0089 00169 u 90 41 it 110 256 134 0085 .00161 30 Soaring 105 it 230 492 258 u 15 a 152 tt 1.00 235 123 10 tt 207 tt 0.85 206 108 u 5 it 273 tt 065 166 87 u cm. cm. 6 x 24 inches (15.2 x 61.0) 90 73 4 170 909 476 0096 001 8 9 u Weight, 1,000 grammes. 90 57 tt 095 597 313 0103 00197 u 30 Soarino 1 146 tt 180 953 499 u 15 a 21 4 tt 060 450 236 u 10 u 27.3 it 0.30 294 154 * Trace was at limit of admissible extension, and hence the correct results are greater than these values. 70 EXPERIMENTS IN AERODYNAMICS. TABLE XIV Continued. Date. Description of planes. Angle of elevation . Attitude of plane. o o |Ii Number of spring. Extension of spring (inches). - tsC. . _, QQ r* 1 S O c3 SH Horizontal pressure on plane R (gram's). "-'TO- k. 1890. Oct. 8 cm. cm. 6 x 24 inches (15.2 x 61.0) 15 Soaring 21.8 9 u Weight, 1,000 grammes. 10 t. 28.6 u tt 5 Not soaring 30.0 It 0.40 113 59 it cm. cm. 30x4.8 inches (76.2 x 12.2) 90 50 a 1.40 317 166 .0073 .00138 tt Weight, 500 grammes. 90 60 tt 2.20 471 247 .0075 .00142 tt 90 62 2.45 527 276 .0076 .00145 u 30 Soaring 10.6 n 2.30 492 258 it 10 tt 179 tt 0.75 183 96 u 10 tt 121 a 0.90 216 113 u 5 152 it 0.45 122 64 a 3 Not soarin 01 21 1 u 0.50 134 70 u 250 u 0.90 216 113 tt cm. cm. 30 x 4.8 inches (76.2 x 12.2) 90 58 u 260 554 290 .0091 .00173 u Weight, 250 grammes. 90 43 it 1 20 277 145 .0086 .00163 a 30 Soariiif 81 a 1.30 294 154 u 15 83 it 0.50 134 70 u 10 it 93 a 0.35 100 52 (I 5 it 133 a 0.40 113 59 (l 3 it 171 tt 0.55 145 76 a 9, 261 tt 0.50 134 70 u 9 222 tt 1 20 Til 145 u 27.9 it 1.50 336 176 Oct. 9 cm. cm. 30 x 4.8 inches (76.2 x 12.2) 90 58 4 0.7 490 257 .0082 .00157 a Weight, 1,000 grammes. 90 83 tt 1.7 909 476 .0074 .00141 u 30 Soaring 152 n 2.2 1110 581 15 u 17 1 tt 1 1 659 345 a 15 it 174 9 23 492 258 tt 10 u 179 4 u 10 tt 182 19 416 218 a 5 (t 226 u 1.6 355 186 Average of 22 determinations of km (at mean temperature. 16 C.) = .00816. THE COMPONENT PRESSURE RECORDER. 71 TABLE XV SECOND SERIES. NOVEMBER 25, 1890. F. W. VERY, Conductor of experiments. Barometer, 730 mm. ; temperature, 10.0 C. ; wind velocity, 2.4 meters per second. ^M 02 bJD bC O xA d .2 i-H II &$ "a rH P 3 a Remarks. o -* ^ 1 .2-9 '02 ^ ' O c3 SJ3 a o ^ o '3 C3 Jr! r^ d 2 P-i o i O a o i i 'C - C 'o M d O H HH O "^ ^ " HH PH HH 24 x 6 in. (24 in. side 45 Soaring 10.9 4 2.10 907 476 horizontal). 50 u 11.2 4 2.50 1,070 560 "Weight, 500 grammes. 5 u 16.9 4 5 u 17.2 3 0.38 82 43 3 Not quite soarin " 19.4 Adopt 19.6 for soaring speed. 30 Soarin " .". 10.6 4 1.10 499 261 10 u 13.3 4 0.21 91 48 Too small extension of sprina to give reliable pressure. NOVEMBER 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. d o '-^ CM O Attitude of plane. o 2 O fclS -^ < i ofi^ O T3 ^8 >g 1,1 n -I ^ & > Number of spring. Extension of spring (inches). Pull of spring (grammes). Horizontol pressure on plane R (gram's). Km- L Remarks. 12 x 12 inches. 167 3 0.35 77 40 Weight, 500 grammes. 17.8 3 0.40 84 44 2 2 3 ) Not soar- i ing- Nearly 20.7 16.7 209 3 3 ,3 0.70 0.55 100 109 95 131 57 50 69 Adopt 21.4 m. per sec. 5 10 20 soaring. Soaring . . . a a 20.1 15.8 11 1 3 3 3 1.30 1.70 152 180 80 94 as probable soaring speed. Spring extended to 20 30 45 90 a u u 11.1 8.9 10.2 823 4 4 4 4 0.75 1.20 2.31 220 340 345 985 939 178 285 516 492 .0078 .00148 limit. 90 845 4 2.28 976 511 .0077 .00146 90 915 4 2.70 1,135 595 .0077 .00146 90 811 4 200 863 452 .0074 .00141 12 x 6 in (12 in side 18.6 3 055 95 50 horizontal) 3 S carcely 188 3 067 107 56 Probable soaring speed, Weight, 250 grammes. 5 10 20 20 30 45 90 soaring. Soaring. . . a a a (I a 17.5 13.3 10.8 11.0 10.5 10.9 778 3 3 3 4 4 4 4 0.78 1.00 1.75 0.33 0.77 1.14 083 115 131 182 159 347 522 399 60 69 95 83 182 273 209 .0074 .00141 19.2 m. per sec. 90 909 4 1 21 549 288 .0075 .00142 90 1089 4 1.98 862 452 .0082 .00156 90 1250 4 2.55 1,089 571 .0079 .00150 90 11.19 4 2.02 871 456 .0079 .00149 90 1000 4 1 60 704 369 .0079 .00151 % 90 814 4 100 463 243 .0079 .00150 30 x 4.8 in. (30 in side 179 3 0.30 72 38 horizontal). Weight, 500 grammes. 2 3 5 10 20 Soaring. . . (i u a 20.1 17.8 15.2 12.6 11 7 3 3 3 3 3 0.90 1.04 1.12 1.92 334 125 134 138 197 300 65 70 72 103 157 *O2 ^ ' ^ jl o ^ Tc rS'ftft 1 -2 l-H 'C ^ Q 3 K P v2 o ^ > 5 pq Pi W 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. DECEMBER 6, 1890. Barometer, 730 mm. ; temperature, + 2.5 C. ; wind velocity, calm. Description of planes. Angle of elevation a. Attitude of plane. o r C '^r3 ""a; 1 02 O |U 2 Extension of spring (inches). Pull of spring (grammes). Horizontal pressure on plane R (gram's). Remarks. 12 x 12 inches 90 Soarin " 128 260 245 128 Velocity of soaring not so well Weight, 500 grammes. 9,0 u 12.6 4 determined as on Novem- ber 26. Velocity of soarin<* not so well 30 n 10.3 4 1 10 500 262 determined as on Novem- ber 26. 45 a 114 4 220 939 492 Velocity of soaring not so ac- 45 Not soaring 100 4 1 82 794 416 curately determined as on 30 u u 100 4 085 408 214 November 26. 30 (I U 100 4 075 340 178 90 it a 100 100 131 69 30 x 4.8 inches. 5 Not quite soaring . 143 14.9 meters per second assumed Weight, 500 grammes. as soaring speed. Fine mist throughout the observations. 10 74 EXPERIMENTS IN AERODYNAMICS. TABLE XV Continued. DECEMBER 11, 1890. F. W. VERY, Conductor of experiments. Barometer, 724 mm. ; temperature, -f 5 C. ; wind velocity, 0.8 meters per second. s - *8 S to bC f-( ^OQ * d f-> + bb ' d o CD o Attitude of plane. it! CO CM O h "o? f-j O o3 E ll Km- ft. Remarks. ."tn S o GO ^ ^ 39 O s3 5^ M PH h~j 30 x 4.8 in. (30 in. side 90 8.30 1 1.80 930 487 .0076 0.00144 horizontal). 90 9.15 1 2.20 1,098 576 .0074 0.00140 Weight, 500 grammes. 45 Soaring. . . . 11.3 1 2.10 1,057 553 30 u 1 0.91 557 292 20 a 10.9 1 0.47 350 183 15 tt 11.1 3 20.7 3 0.20 59 31 24 x 6 in. (24 in. side 20.7 3 0.20 59 31 horizontal). 10 Soaring. . . . 13.0 Weight, 500 grammes. Mean of 22 determinations of k m (at temperature 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. 77 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 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 F, 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 abscissae 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 TTtru-j TflWi or YsVir 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 of a 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. Position of set-screw. Weight. Extension of trace. Pounds. Grammes. Inches. Centimeters. 10th hole 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 5th hole 300 1360 1.82 4.62 2.78 1,260 1.60 4.06 2.56 1,160 1.35 3.43 2.34 1,060 1.15 2.92 2.12 960 0.88 2.24 1.90 860 0.66 1.68 1.68 760 0.41 1.04 "0"hole 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 0.91 2.31 0.73 330 0.71 1.79 0.51 230 0.49 1.24 0.29 130 0.25 0.63 0.07 30 0.15 0.38 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 2.21 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 : OCTOBER 30, 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), 1.43 inches. Driving pulley makes Q r revolutions per minute. Circumference of , pulley equals 2.1 x 3.1416 - , r , ., , , . , feet. Velocity 01 belt equals 60 x 2000 x 2.1 x 3.1416 - 295 x 12 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 U 0" hole, is equivalent to a weight of 1.35 pounds on a 3.9-inch pulley. The tension on q Q the present 2.1 -inch driving pulley is therefore 1.35 x ~ pounds. Multiplying Zi.L 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 295 x 12 x 8.1416 X 33000 = 3.713 x 295 = 0.017. 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 #, 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 n 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 n 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 11 82 EXPERIMENTS IN AERODYNAMICS. out of its gearings by the means shown in plate II, 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 capacity 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, etc., 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. 83 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 its 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 (i. e., 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, etc., 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 Dynamo meter- 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 underbill 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 can 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 NOVEMBER 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 II) of the turn-table, and thence along the arm to the electric motor, and the dynamo itself is run by the steam-engine which drives the turn-table. In the manner already described, the pencil P" of the Dynamometer-Chronograph registers the power p ut 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- m ometer 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. m. At 2 12 Casella air-meter reads 1,779,600. At 5 39 " " " 1,881,900. Toward end of experiments, wind almost entirely died away. Dynamometer- Chronograph sheet No. 3 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 " " hole. Turn-table driven so as to give linear speed of approximately 2,000 feet per minute. (a) Dynamo = 1,170 revolutions per minute. (6) Propeller = 5 ' 52 * 2Q( - = 1,032 revolutions per minute. (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. (/) Speed of turn-table (from sheet of stationary chronograph in office) = 5.41 seconds in one revolution = 1,865 feet 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 10.7 = 1,032 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 cord 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 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. e., 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 b3 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 ^j o / 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 of an inch wide and t of an inch thick. Two sliding pieces, SS', 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 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. Time. Barometer. (Inches.) Air tempera- ture. (Fahr.) Wind direc- tion. Air meter. 10.20 a. m. 12.20 a. m. 29.080 29.069 589 61.2 N. N. E. N. N. E. 183380 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. VH OQ <<-l g O> S IH o >f .S 8 ** 1 o> '3 S^ c3 m & S'S tc Time. 1^8 lltei I'l cj o 0} c5 Range. &-I 2 02 ^ ^-j O -C! o g S "^ 8,3 | -2 O3 S 3 r2 a _C PH CH G x H ft H o o o o 10.38 a. m. 12.8 2.00 82.0 64-98 34 10.42 a. m. 12.8 1.75 76.0 58-98 40 10.46 a. m. 12.8 1.75 76.0 10.50 a. m. 12.9 1.50 68.0 48-84 36 12.12 p. in. 13.3 0.00 6.0 0.12 12 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. 91 TABLE XVII. Summary of Experiments giving position of center of pressure on a plane one foot square (80.5 x 80.5 centimeters) for different angles of inclination. Distance from center of press- ure to center of plane d. Distance as a percentage of the side of the Angle of trace with initial Angle of plane with vertical Angle of plane with horizontal (Inches.) (Centimeters.) plane. line. 90 - . o. o 0.00 0.00 0.000 5,5 0.0 90.0 0.25 0.64 0.021 17.4 12.0 78.0 0.50 1.27 0.042 28.2 22.7 67.3 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 3.17 0.104 59.7 54.2 35.8 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 Joessel 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; JOSEPH LUDEWIG, Assisting. Barometer, 737.06 mm. ; temperature, 18 C. ; wind velocity, 0.006 meter per second ; length of side of wind-plane, 12 inches (30.5 centimeters). 'o Distance of axis of oscil- s IM O .1*1 lation from center of G i i o "S plane. o i ' c?o5 Time. l^^ i o3 o C2 ^ Kange. ulTS H O S o . c^ ^ . Time. ] S^ * 2 c3 o o ^ Range. c3 * O |1 |- CD c3 o rj '""' O (Inches.) (Centimeters.) a C -4-3 M a. m. o o o o 10.38 12.8 2.00 5.08 82.0 64-98 34 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 41 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 11.36 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 p. m. 12.03 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 13.3 0.00 0.00 6.0 0-12 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 IV), 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 81 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 27 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 qn 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 ancecl 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 : o ^ *o o 03 0) 2 bJD 1 S ^ & m centimeter). 1.20 p. m. 14.00 13.18 3.39 3.55 1,610 1.73 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 1.71 776 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 1.99 0.0103 Mean = 0.01027 PRESSURE ON SIX-INCH SQUARE PLANE (232 square centimeters). rt tn - +-! 02 bC o s| O fH .a Pressure on wind-plane. ' Q"g CD "g o ^ N g ~s a ^ 02 CD 02 2 02 ^ rO fl 5^ *0 g P (grammes k - P o c1S ^ Sa O (Pounds.) (Grammes.) per * CD i-Q O -t- 3 "o S JH O r-H CD QJ O square ^ J .s*s "H^ centimeter). H ^ > H 4.00 p. m. 2.32 24.3 1.93 2.18 990 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. OCTOBER 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. 101 d .2 oa n! w r^ 11 bo .2 Pressure on wind-plane. 1 II. &1T 02 1 o g[ ._i O J*^ Jii o *"^ ^o ^ o o ~rH C ^ o v ~~'' (Pounds.) (Grammes.) P (grammes per p o C 4n O o square J .2 ^ &PH ~x^ centimeter). EH t? ^ W 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 4.38 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 2.33 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 OCTOBER 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 .2 || S-S to .3 Pressure on wind-plane. 4j o t , S O / "r/T N > ^ . i G Jssl o (Pounds.) (Grammes.) per F 2 O . ^i O o square J |.s*s 5^^ I 12 centimeter). 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 30.15 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 0.61 277 1.19 0.0068 5.33 p. m. 3.95 14.30 0.50 0.80 363 1,57 0.0077 Mean = 0.00785 102 EXPERIMENTS IN AERODYNAMICS. OCTOBER 30, 1888. PRESSURE ON ONE-FOOT SQUARE PLANE (929 square centimeters). Barometer, 739 mm. ; mean temperature, 7.8 C. ; wind velocity, . GO H ^^ CO fcC 11 11 O H rv 02 Pressure on wind-plane. 11,3 "c ^ & l 00 > r^ O ^ i _ rj in o| P (grammes p h 0* C -> 02 "GO 1 ~ (Pounds.) (Grammes.) per V~ r 3 P _, P. . 'o c3 square rj.S o ^lELft "^^ centimeter). fe > H 7.23 7.84 0.88 1.20 544 0.586 0.0095 10.14 5.58 0.25 0.50 227 0.244 0.0079 7.89 7.17 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 0.47 0.75 340 0.366 0.0084 6.64 8.51 1.00 1.30 589 0.634 0.0088 6.74 8.39 1.00 1.30 589 0.634 0.0090 6.30 8.98 1.33 1.62 734 0.790 0.0098 6.20 9.12 1.34 1.63 739 0.796 0.0096 5.93 9.54 1.27 1.56 707 0.761 0.0084 Mean = 0.00913 NOVEMBER 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. . CO rt *g m 1 bn c5 |.J _ .S Pressure on wind-plane. c3 o JE2 d o o ; "S S Xs CO J> o 02 2 (> -^ ^L.^ II P (grammes) m T?2 eg o ^>o g |CN (Pounds.) (Grammes.) per F 2 O rQ O -^ '3 53 f* square .9 |.S*S ^'aa n^* centimeter). * H J5 ^ m 3.30 p. m. 4.35 13.00 1.60 0.78 356 1.53 0.0091 4.32 13.10 . 1.43 0.70 320 1.38 0.0080 3.99 14.20 2.19 1.04 472 2.03 0.0100 4.00 14.14 2.07 0.99 449 1.93 0.0096 4.00 14.14 1.60 0.78 356 1.53 0.0077 3.96 14.30 1.58 0.78 354 1.53 0.0075 5.64 10.00 0.64 0.36 163 0.70 0.0070 5.67 9.97 - 0.61 0.35 159 0.69 0.0069 5.40 10.47 0.80 0.43 197 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 NOVEMBER 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. d o || o| to .9 Pressure on wind-plane. 'a O "^ 1 -i O o ' N 03 CD 7^ r2 CH 02 CD CD J o *s 2! "o^ o o J P (grammes k m - P n>m T/2 o CD p O (Pounds.) (Grammes.) per V o r& O -^ O i CD 1 6 square a .S O ~K^ centimeter). E" 1 fc ^ H 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 3.72 15.20 0.52 0.90 408 1.76 0.0076 3.62 15.60 0.53 0.91 413 1.78 0.0073 3.10 18.20 1.19 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 3.04 1,380 5.93 0.0070 Mean = 0.0084 PRESSURE ON ONE-FOOT SQUARE PLANE (929 square centimeters). Note : Wind too high for best results. d .2 O2 r* T5 o ' . O f-t ,_, O C, SQ Pressure on wind-plane. > O ^ CD g s^ ^2 C 'd O '"O ^M O P 02 CM o> .9 , rH ~ j. p 1 O w T O^O O PvH' (grammes Km == 172 ~o 1 1-2 >> 0) CD ^t P " i 1 ^ (Pounds.) (Grammes.) per V o F^ CD g *-> square I g.tt ^ PnA W centimeter). 1.50p.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 2,810 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. d l| ^ ? i /"" N Pressure on wind-plane. ' I |^ il- &J t> ^ O ^ O g P ro | *S 8-? 'o^ 8 ^ .1-1 . (grammes m f7~2 *s _i O _| O C r-j ,Q g Ja .-* s^ (Pounds.) (Grammes.) per v O O r^ O Q LU s: v- ^ Z 2 ** ^ j FORM NO DD 6 40m 10 '77 UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY, CA 94720 i RETURN CIRCULATION DEPARTMENT TO"-** 202 Main Library LOAN PERIOD 1 HOME USE 2 3 4 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 1 -month loans may be renewed by calling 642-3405 6-month loans may be recharged by bringing books to Circulation Desk Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW RFC, C1R. crp 1 '78 *r\C\\\ O O i < *1 pinFCO?'90 UNIVERSITY OF CALIFORNIA, BERKELEY FORM NO. DD6, 40m, 3/78 BERKELEY, CA 94720