PRACTICAL AERODYNAMICS AND THE THEORY OF THE AEROPLANE. PRACTICAL AERODYNAMICS AND THE THEORY OF THE AEROPLANE. A RESUME OF THE PRINCIPLES EVOLVED BY PAST EXPERIMENTS. BY Major B. BADEN-POWELL (Late Scots Guards), F.R.A.S., F.R.Met.S., &c. Vice-President Aeronautical Society of Great Britain. PART I. AERONAUTICS OFFICE: 27, CHANCERY LANE, LONDON, W.C. PREFACE. It was my original intention to compile a complete book dealing- in concise and simple manner with such of the principles of Aerodynamics as are applicable to the practical construction of flying machines. The sub- ject, however, is one which calls for a great deal of time and attention, and, so far, I have not been able to devote sufficient of these to the matter so as to complete the work. But having published some portions as articles in " KNOWLEDGE," I find numerous applicants asking for copies of what has appeared, and craving for further information. I think, therefore, that it may be of some assistance to those now working on the subject to bring out the first portion as a complete (if small) volume, and, following the good example of Mr. Lanchester, leave the second part to be published at some future time when I am able to complete it. This second part will deal with such matters as the behaviour of models in the air; details of actual flying machines; propellers; and natural bird flight. Since most of this book had actually been written, Mr. Lanchester's two great volumes have been pub- lished. While his copious comments and arguments are of the greatest value to the student, they need, as a rule, hardly be referred to in this book, wherein theory is gone into as little as possible. B. B.-P. Ml 80559 CONTENTS. PAGE GENERAL PRINCIPLES ... ... ... ... ... i RESISTANCE TO A PLANE SURFACE MOVING THROUGH THE Am 7 VARIATION OF PRESSURE DUE TO SIZE AND SHAPE OF PLANE 18 THE PRESSURE OF THE AIR ON INCLINED PLANES ... 22 LANGLEY'S LAW 33 THE LEE SIDE OF A PLANE 39^ SUPERPOSED PLANES , 42 COMPOUND PLANES AND AEROCURVES 44 FRICTION OF THE AIR 47 THE RESISTANCE OF VARIOUS SHAPED BODIES ... 51 PRACTICAL AERODYNAMICS AND THE THEORY OF THE AEROPLANE. GENERAL PRINCIPLES. THE subject of aerial navigation has recently been prominently brought before the public. A wide interest has been aroused, and people generally are beginning to see what a vast future there is open to a machine able to traverse, surely and safely, the realms of blue. Although I am one of those who always prefer fact to theory, and though most of the important inventions which have aided human progress have not sprung from the mathematician's brain, I quite realise that a certain amount of study of the principles underlying any such subject is most necessary to one who would add any important work towards the conquest of the atmo- sphere. The air, then, and the effects of its pressure on bodies moving through it, demands our earnest attention. Air may seem a light, subtle fluid. If we pass our hand through it we notice very little resistance to the motion, and we may wonder how it is possible to utilise this very yielding medium to support the heavy weight of a human body or metal machinery against the force of gravity. From a mechanical point of 2 PRACTICAL AERODYNAMICS. view it is just the same whether a body be pushed against the air, or the air blows against a stationary body. Yet we all know what air, when in motion at a great speed, may effect. We know that if the wind be blowing with the force of a gale perhaps 60 or 80 miles an hour it is capable of exerting a very great pressure, especially on .suitably disposed surfaces. We know well enough that when out on a windy day, an umbrella held, even with its convex side to the wind, is sometimes most difficult to hold, and that directly it is turned so as to present a concave surface it is immedi- ately blown inside out, or if made strong enough to resist this action, would pull with such force as to be almost impossible to hold. This enables one to realise what may be effected by making an apparatus to travel very rapidly through the air. It seems probable that an ordinary umbrella (suitably strengthened) held so as to let a very strong wind strike underneath it, would pull so hard as to be almost capable of lifting a man off his legs, momentarily at least. This fact hardly seems extraordinary, yet if we imagine a flying apparatus only as big as an umbrella progressing at 40 or 50 miles an hour through the air, it would surprise most of us to think that it was capable of raising a man. This enables one to realise that if only we can get the power, properly applied, a very small apparatus may be sufficient for our purpose and, if a very largfc aeroplane be used, what great lifting 1 power is to be derived from it. This subject, though likely, as already intimated, to become one of very great importance, yet is one that has received but comparatively little attention among scientific experimentalists. Langley, in the introduction to his book, " Experj- GENERAL PRINCIPLES. 3 ments in Aerodynamics," published in 1891, says : " In this untrodden field of research ... 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." No complete treatise on the subject exists.* All the information that is available has to be extracted from works dealing with aeronautics (mostly historical), hydrostatics, and pneumatics, and from the various technical papers which have been compiled on certain definite branches and on results of particular series of experiments. The following is a general review of the whole subject gathered from these sources. It does not pretend to be complete or exhaustive, but it is hoped that it may be of assistance to those anxious to get an idea of the science, and who are unable to wade through the various sources of information enumerated. I propose treating of the subject in the following order. It will be necessary first to briefly refer to* the theory of the balloon, and ascent by reaction of a fluid, and then to get on to the main subject of aeroplanes and apparatus working on kindred principles. This latter subject must again be subdivided into air pressures acting perpendicularly on a plane surface, air pressures on inclined plane surfaces, the effect on the back of such planes, and pressures on curved sur- faces moving through the air. Finally, to consider the combined effects on various shaped bodies in practice, the flight of birds, and the action of aerial screw propellers. In considering the different methods possible for the attainment of artificial flight which is practically synonymous with means of overcoming the force of * Since this was written (in Feb., 1907) several works have been published, notably those by Lanchester, Maxim, Moedebeck, and Chatley. 4 PRACTICAL AERODYNAMICS. gravity there are three principles to be taken into account : (1) Displacement. By displacing- a bulk of air by a body of less total weight than that air. Under this head would be included hot-air balloons, gas balloons, and the thepretical, if impracticable, vacuum balloon. (2) Downward Reaction. By the reaction of a fluid driven forcibly downwards. Such is the principle of the rocket. (3) Sub-Pressure. Deriving support from the pressure of the air on the under surface of a body driven through it. This would include not only what is understood by the term " Aeroplane," but also revolving aeroplanes or lifting screws, and wings and paddles striking the air downwards. Under this heading, too, must come the wind-borne soaring birds and thistledown. As regards the first of these methods we need but briefly go into it, since the subject of ballooning is rather beyond our present scope. If a given volume of air be displaced and the space filled by a vessel inflated with some substance lighter than air, such as hydrogen, coal gas, steam, or air rendered less dense by being heated, then, if the con- taining vessel is not too heavy the whole will rise in the air. This is in obedience to well-known laws. The heavier particles of air will slip under the lighter body and buoy it up, just as water when poured into a basin would slip under and buoy up a cork lying in the basin. That air has definite weight can easily be proved by carefully weighing a bottle which has been exhausted of air, and weighing it again when air is admitted to it. In this way air is found to weigh .076 Ib. per cubic foot, or 1,000 cubic feet will weigh 76 Ibs. (at 60 F. Bar. 30 in.). Hydrogen gas can be weighed in the same manner, GENERAL PRINCIPLES. 5 and is found to be .005 Ib. per cubic foot, or 5 Ibs. for 1,000 cubic feet. Coal gas varies, but may average about 35 to 40 Ibs. per 1,000 cubic feet. Steam, which has actually been applied to ballooning, varies accord- ing to its temperature. As regards heated air, what is known as Charles's law shows that a given volume, under constant pressure, increases with temperature .00367 times its bulk per degree Centigrade, or .002 (5^0) P er degree Fahrenheit. If, then, the air in a balloon can be raised by 100 F., one-fifth of its weight will be expelled; that is, each cubic foot will then weigh f of .076, or .06 Ib., or 1,000 cubic feet will weigh 64 Ibs. instead of 76. These principles are often overlooked by unscientific inventors, who suggest adding a small balloon to aid in lifting their apparatus, or who> anticipate a hope of finding a gas lighter than hydrogen. One Francis Lana, in 1670, was probably the first to suggest the idea of a machine on this principle, but his suggestion was to exhaust the air from large copper globes, ignoring the practical fact that the pressure of the atmosphere would crush in any such vessel as soon as a very small quantity of air had been extracted from it. The second method, though interesting as a specula- tive suggestion, seems hardly likely to> prove of prac- tical utility, for a man-carrying machine. Rockets are well known. They are practically useful for many special purposes, but are extremely wasteful of fuel, and, therefore, short-lived. Steam jets striking downwards have been suggested. Mr. H. Wilde, F.R.S., conducted a number of ex- periments at one time* in order to ascertain what force * " On Aerial Locomotion," by Henry Wilde, F.R.S. Vol. xliv No. II. of the " Memoirs of the Manchester Literary and Philosophical Society." 1900. 6 PRACTICAL AERODYNAMICS. could be practically applied with this idea. He tried high pressure steam and compressed air discharged through orifices of many various forms, also explosions of gas mixed with air and ignited by electric sparks. He, however, sums up the matter by saying 1 : "The results of all these experiments on the discharge of elastic fluids, made with a view to the possibilities of aerial locomotion, were purely negative, and proved decisively that the solution of the problem was not to be found in that direction." It occurs to me, though I have not actually tried the experiment, that liquid air might be used in this connection. A vessel of liquid air in ordinary atmospheric circumstances is practically equivalent to a vessel of water placed in the middle of a furnace. The liquid air in the one case and the water in the other are boiling hard and rapidly evaporating into air or steam respectively. So that by employing this method we practically have a steam boiler exposed to a comparatively very high temperature (that is the difference between that of the liquid and that of the surrounding atmosphere), yet without any fuel or apparatus for burning fuel. A great pressure may thus be obtained with but little weight, and it could, therefore, be made to ascend. It is true that this action may be very wasteful and would not last long. Still, as an experiment, it might be interesting to see a vessel rise in the air by this novel means. It may be added that though a continuous stream issuing from a jet may, theoretically, be wasteful of power, it would probably not be difficult to make the jet intermittent, or, by progressing rapidly in a hori- zontal direction, to cause it to act continually on fresh air. The third principle, which promises the most practi- cal results, and is a much larger subject, is treated of in the following chapters. RESISTANCE TO A PLANE SURFACE. RESISTANCE TO A PLANE SURFACE MOVING THROUGH THE AIR. ANY body which is being rapidly driven through the air, whether it be the main body or structural parts of the apparatus or the blades of the screws, wings, or other propelling appliances, is acted upon by three different forces (in addition to gravity), which tend to retard its speed. These are : First, the head resistance, caused by the inertia of the particles of air which have to be displaced in order to make way for the body. Second, the negative pressure o>r suction due to the partial vacuum which is usually formed behind the body, and the air which has been displaced taking time to flow back to fill the space which it originally occupied. Third, the side pressure or skin friction, sometimes re- ferred to as tangential force. As Lord Kelvin has said, " In Nature every fluid has some degree of viscous resistance to change of shape," which also accounts for these opposing forces. It will readily be understood that the pressure on a body being pushed against the air, or falling vertically through it, is exactly the same as if the body Were held stationary and a steady current of air be driven against it. It must, however, be noted that wind is not always steady. In considering head resistance we will first take the case of a plane surface propelled perpendicularly to the line of advance. The problem to be decided is, what is the force opposing the progress of the plane as com- pared to the speed and area? This is a most important consideration, as it is on this that all our calcula- 8 PRACTICAL AERODYNAMICS. tions must be based. When we come to investigate the pressure developed on inclined or curved surfaces, it will be seen that these are but a certain definite proportion of the pressure that would be imparted to a plane sur- face of similar area moving" at right angles. Supposing- we find that to propel a given mass at a certain speed it is necessary to apply a steady push of one pound, it is evident that in order to increase that speed it will be necessary to apply more force. But the question is, how much more force must be applied in order to develop, say, double the speed. Newton, by noting the time taken by spheres in fall- ing from the dome of St. Paul's Cathedral, concluded that the resistance of the air on the body is proportional to the square of the velocity. All later experiments have shown this law to be approximately true. This is to be expected, since if we imagine a plane moving against the air at a given rate, if its speed be doubled it will strike the air twice as hard, but it will also pass over double the distance in the time, and will, therefore, strike twice as many particles of air, hence the pressure or force required will be four times as great. There is, however, still some doubt as to whether this law applies when the body is travelling at com- paratively high velocities. Experiments made on the resistance offered by the air to projectiles moving at speeds of 2,000 or 3,000 feet per second tend to prove that the resistance increases in a greater ratio than at rates below a hundred miles an hour (146 feet per second).* But it is only the latter that we need now be concerned with. To get at a proper working formula for computing the resistance of the air, we put P = Kv 2 ; that is, the pressure in pounds per square foot equals the square * Prof. Greenhill, Britt. Ass. 1883. RESISTANCE TO A PLANE SURFACE. 9 of the velocity in miles per hour multiplied by a certain constant K, which has not yet been very exactly deter- mined. A number of separate experiments have been made to solve this point, but the results have not been in per- fect agreement. It may be desirable, considering- how important the results are to the subject, briefly to re- capitulate what has been done in this line, and the con- clusions come to, since, as far as I know, no connected account of these has hitherto been published. The resistance of the air was first carefully investi- gated by Robins* in 1742. His experiments were chiefly directed on the investigation of the resistance offered to bullets fired from a musket, which at that time was a matter almost entirely ignored. Later on he constructed a " whirling machine," consisting of a light arm rotated by means of a weight unwinding" a cord wound round its support. On the end of the arm was mounted a sphere to represent a cannon ball. But, before considering the effect of air pressure on bodies of varying forms, such as spheres, etc., we may take the case of a plane surface at right angles to the motion. Smeaton, who had been investigating the force ob- tainable by means of windmills, shortly afterwards pub- lished a table of wind pressures! which had been communicated to him by Rouse. This was compiled on the supposition that K = .oo5. The table, though pro- duced in so uncertain a way over 150 years ago, never- theless was accepted as authoritative, and is often quoted intact to this day in books dealing with engineer- ing and wind effects. Subsequent investigations, how- ever, show that these deductions were altogether misleading. * " New Principles of Gunnery," by Benjamin Robins, F.R.S., new edition, to which is added " Subsequent Tracts." 1805. | " Philosophical Transactions " for 1759, p, 165. fo PRACTICAL AERODYNAMICS. Nor does there seem to be any record of exactly how the figures were arrived at. Smeaton, in his paper on 1 'The Natural Powers of Water and Wind" (Phil. Trans. Vol. LI., 1759), merely says : " Some years ago Mr. Rouse, an ingenious gentle- man of Harborough, in Leicestershire, set about trying experiments on the velocity of the wind and force thereof upon plane surfaces and windmill sails; and much about the same time Mr. Ellicott contrived a machine for the use of the late celebrated Mr. B. Robins for trying the resistance of plane surfaces moving through the air. The machines of both these gentle- men were much alike, though at that time totally un- acquainted with each other's inquiries." And later in the same paper he quotes the table, prefacing it with these remarks : " The following table, which was com- municated to me by my friend, Mr. Rouse, and which appears to have been constructed with great care from a considerable number of facts and experiments." As almost all the more recent practical tests, which have been made with all care and with the best ap- pliances of modern science, have shown pressures con- siderably less than those in this table, it is not unreason- able to assume that Rouse's figures are incorrect. But now another fact must be referred to. A number of writers o sin Gerlach 4 -f TT sm a Duchemin ...... 2 sp a I -\- Sin- 4 a Renard ....... sin a [2 (a i) sin 2 a] Soreau ....... sin a ( i -f * \ ' I + tg 2 * Manchester Lit. and Phil. Soc., 1899-1900. INCLINED PLANES. 25 \ \ O O" 26 PRACTICAL AERODYNAMICS. Eiffel, in his experiments of 1907 investigated the pressure on inclined planes. In order to carry out such tests with his system of letting the planes slide down a vertical wire, it was necessary to test two similar plates at one time, so as to balance the horizontal components of the pressures, which would otherwise have intro- duced fractional resistance. The mutual influence of them was found to be practically nil at small angles of inclination from the vertical, and they could be fixed apart at an interval of as much as 5 feet. From these tests a new rule was formulated, very simple, yet agree- ing closely with the actual results. This was p p o = for inclinations up to 30, above which the pressure was practically equal to that on the normal surface. The curve obtained closely approaches that of Dines. (It may be represented o-n the chart as a straight line from the point o to the top of the 30 vertical.) Chanute, in his " Progress in Flying Machines " (1894), states that he had a chart plotted "on which was delineated all the experiments on inclined surfaces which I could learn about those of Huttom, Vince, Thibault, Duchemin, de Louvrie, Skye, the British Aeronautical Society, and W. H. Dines; and on this chart I had also> plotted the curves of the various formulas." But he adds : " The whole exhibited great discrepancies, yet by patient analysis various probable sources of error were eliminated, and the conclusion was reached that the formula attributed to Duchemin was probably correct." The following table is extracted from Chanute 's more complete one, based on Duchemin 's formula. The total force acting normally to> the plane, according to INCLINED PLANES. 27 this, may be split up into the vertical force acting in opposition to gravity, or " lift," and the horizontal force which has to be overcome by the propelling agent in order to obtain that buoyancy, called " drift " : Angle of Inclination. Degrees. Normal Pressure. Lift. Drift. I 035 035 0006 2 070 070 0024 3 104 104 0054 4 139 139 0097 5 174 173 0152 6 207 206 0217 7 240 2 3 8 .. 0293 8 273 2 7 0381 9 305 300 0477 10 .. "337 332 0585 ii 369 .. 362 0702 12 398 .. 390 083 !3 431 419 097 14 '457 '443 'US 15 486 468 124 20 613 .. '575 210 25 718 650 304 30 800 693 .. 400 35 '867 708 498 36 '878 709 516 40 900 697 .. 586 45 '945 666 666 28 PRACTICAL AERODYNAMICS. It may be noted that the greatest actual lift occurs when the angle is 36, and that at greater angles the lift decreases again. To give a practical example of the use of this table, let us suppose we have a plane of 500 square feet sur- face propelled by mechanism giving it a speed of 30 miles an hour. This rate would cause a pressure of 2.7 Ibs. per square foot if the surface were perpendicular to the line of advance (according to the table of wind pressures already given). This would equal a total force of 1,350 Ibs. But, now, suppose the plane to be inclined to 5 to the horizontal. The lift would then be .173 of 1,350, or 433 Ibs. The drift or necessary thrust of the propeller would be .0152 of 1,350, or 20.5 Ibs. It must be remembered that this is only taking into account the theoretical resistance of the inclined plane, and does not include the resistance offered by the body or mechanical structure of the apparatus, nor does it include other issues such as skin friction. The foregoing remarks apply to square planes. Rather different results have been obtained with other shapes, such as long oblongs. Langley investigated the subject of inclined planes with two different forms of apparatus. The " Plane Dropper " has already been referred to. The " Com- ponent Pressure Recorder ' ' consisted of a plane surface fixed at any desired angle of inclination on the arm of the whirling table. When given a rapid velocity the plane rose and became supported on the air, and directly this occurred the speed of translation was noted. This is known as the " soaring speed " of the plane. The planes tested were of different shapes, but all weighed just over i Ib. per square foot; 30 to 35 was found to be the angle at which most of the planes soared with INCLINED PLANES. 29 the least speed (about 33 feet per second), but with very small angles far higher speeds were necessary to obtain a lift. With an inclination of only 2 the velocity re- quired was over 65 feet per second. As regards the form of plane, it was found that at angles less than 20 a lower speed sufficed to lift an oblong plane having its longer side foremost than one end on, at greater angles the reverse occurred. The lowest soaring speed for the former shaped plane was obtained when the inclination was 25, but for the latter, 35. This is an important fact to note in the design of aeroplanes. A wide and short one soars when at a flatter inclination than a narrow and long one. Later on we will consider the requisite amount of thrust to drive the planes when inclined at various angles. In the experiments on inclined planes conducted for the Aeronautical Society in 1870* it was found that at 45 inclination " whether the exposed surface was a circle, a square, or a parallelogram, providing the area was the same, the results were identical to the degree of accuracy to which the readings could be determined." Here also an oblong plane 4! by 18 ins. with edge to the wind current gave a greater vertical force than when end on. One of the chief peculiarities noticeable with regard to the action of the air on inclined planes is that the centre of pressure, which when the surface is perpen- dicular is in the centre of area, is now advanced towards the front edge. At first sight this may appear peculiar, but it is easily accounted for. The air which first strikes against the surface will be deflected off at an angle. And this current of air deflects the lower strata and prevents them striking the surface with their * 7th Report of the Aeronautical Society, p. 8. 30 PRACTICAL AERODYNAMICS. original force. This may be better explained with the aid of a diagram. If the top stream A strikes the inclined plane and is deflected at an angle equal to that of impact, it will be evident that the stream B, meeting this deflection, will be diverted and caused to act in a direction nearly parallel with the plane. So a stream of air runs down the front of the plane acting as a cushion to detract from the effect of the lower currents. * This shifting forward of the centre of pressure, noted by Cayley in 1809, was investigated in turn by Joessel in 1870, by Kumrner in 1875, an( ^ ^Y Langley in 1888. Joessel instituted the law that the distance of the centre of pressure from the centre of area = (0.3-0.3 sin a ) L L being 1 the length of side of a square plane. It is also expressed as the distance from the front edge of the plane (0.2 + 0.3 sina) L. Kummer found that much depended upon the shape of the plane, an oblong giving different results to a square. The displacement is greater with oblongs with short side forward at small angles, but a reversal takes place at greater angles. * It seems, probably, moreover, when the velocity is great and the angle small, that this glancing off of the air is so great that the air adjacent to the surface at the back end is actually rarefied. This is a point which has not been much investigated, but which may prove to be of considerable importance. INCLINED PLANES. It is well known that an oblong- plane is differently affected according- to whether the front edge presented to the air be the longer or the shorter one. This may be explained by the same arguments which apply to the shifting forward of the centre of pressure. 8 With the two planes A and B it is easy to see that if the rear part of a plane is comparatively useless, and all the effort exerted towards the front edge, then the centre of effort will come about where the dots are, and all the immense length of the afterpart of B is compara- tively useless. So that we might expect that with a long plane the centre of pressure would advance con- siderably, at low angles. Then there is a further reason for loss of efficiency in a short frontaged plane like B. The air being com- pressed against the face of the plane forms a cushion, which, if visible from the front, would appear somewhat thus being dense in the centre, but towards the K;- ',''1 edges the air can escape away at the sides, giv- vX ing a more or less triangular section to the cushion of air, and therefore a large portion of the air pressure is lost over the sides. When the longer edge is presented the section would be ./ The shifting forward of the centre of pressure is one of the most important factors in considering the design of an aeroplane. Hitherto there has been too much said about the area of any apparatus. Writers have 32 PRACTICAL AERODYNAMICS. gone carefully into the relative area of the wings of birds and so on, and continually talk about aeroplanes having so many pounds per square foot. But there is all the difference between the area along the front edge of the aeroplane and the surface behind. Span must always be taken into consideration as well as area. A glance at the diagram, p. 31, B, enables one to realise how unimportant is the after portion of an inclined plane as compared to the leading" edge. A fairly ap- plicable method is to consider the surface as being equal to S 2 / where S = the span and / the length fore and aft. LANGLEY'S LAW. 33 LANGLEY'S LAW. I have already referred to the fact that if a plane while falling be driven at the same time in a horizontal direction, it will fall more slowly than if simply descend- ing vertically. Also that this action is equivalent to a plane progressing through the air at a slight inclination. This effect, although easily accounted for when known, was never quite understood until investigated by Langley, and it forms the basis of what is now known as " Langley's law." This is defined by Chanute as follows : " The weight remaining the same, the force requisite to sustain inclined planes in horizontal motion diminishes instead of increasing when the velocity is augmented.*' This law has often been misconstrued, and may not at first be easy to comprehend. Even the originator himself states that it has a " paradoxical " appear- ance. When he says that " the power required to maintain the horizontal motion of an inclined aeroplane is less for high speeds than for low ones," it must be remembered that this refers to soaring speeds the speed at which the weight of the apparatus will be borne on the air. If a plane of given weight and area be set at a fixed angle of inclination and driven hori- zontally at such a rate that it is supported, it will absorb a certain force. If the speed be increased, of course, the force will also have to be increased; this, however, gives a greater lift; but a greater lift is not required, and, therefore, either the area presented or the angle D 34 ' PRACTICAL AERODYNAMICS. of inclination can be reduced, and yet the weight of the apparatus be upheld. By reducing- either of these the forward resistance is reduced, hence also the requisite power. Therefore, with less expenditure of power the aeroplane is upheld at a greater speed. Or, to put it another way, if two planes, A and B, of the same area, weight, and shape, be taken, but A is inclined at a greater angle than B, it is evident that, if both be propelled at the same speed, A will require a greater force; or, on the other hand, if equal forces be applied to drive the planes horizontally, B will progress much the faster, since it has less resist- ance to overcome. The dotted lines of air strata show that with A a larger volume of air has to be displaced. The same force, then, being applied, B will travel the faster. But at the smaller angle of inclination the up- ward thrust, or lift, will be greater in proportion to the drift (even at the same speed). Therefore, by de- creasing the inclination and increasing the speed the same lift can be obtained with less power expended. The "Plane-Dropper" consists of a vertical frame mounted on the arm of the whirling table. Two hori- zontal planes are fixed to a falling piece which slides down one of the uprights of the frame and is released electrically. The planes, which may be set to a given angle, are thus free to fall vertically while the arm is travelling rapidly. The actual results obtained by Langley with his LANGLEY 's LAW. 35 " Plane-Dropper " are really important. Not only do they show that the time of fall is greater as the hori- zontal velocity increases, but also " that this retarda- tion goes on at an increasing rate with increasing velocities." Then he proves that with " planes whose width from front to back is small in comparison with the length of the advancing edge " this effect is the more pronounced. It seems a pity that he could not have tested this apparatus at greater speeds, for it looks as if we should then have obtained some very astonishing facts. Take the results obtained with the widest plane shaped thus : /8 * M ' *'l NjH I* The rate of fall at various speeds of translation is shown in the diagram, p. 36; that is, the time in seconds which it took to fall through a height of four feet. Langley only tested this up to a rate of 20.5 metres per second (about 45 miles an hour). By increasing the size of the diagram (as dotted lines) up to double the speed (and 90 miles an hour will probably not be an excessive speed for an aeroplane), we may realise the curious state of affairs probably resulting. Pre- suming the curve to be correctly plotted, it is very evident that at a speed of even 25 or 30 metres per second the rate of fall of such a plane will be almost indefinitely prolonged. "We may reasonably infer," says Langley, "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." This means that a flat plane, weighing a PRACTICAL AERODYNAMICS. pound per square foot, propelled horizontally at say 60 miles an hour, will continue in a horizontal course with- out falling ! 4 sees. SPD 5 ...J +oMertt(3ftiistc. One is inclined at first to consider that in this experi- ment the friction of the falling" piece against the frame might, to so-rne extent, account for the slowness of fall at the higher speeds. But, the experimenter points LANGLEY'S LAW. 37 out, with planes of other shapes, which should offer the same amount of friction, we do not get the same retardation of fall. It may be seen that with a horizontal falling plane the increase of speed of progression is equivalent to diminution of angle of inclination in an inclined plane. This may be made clearer by diagrams. We may, therefore, turn to Langley's experiments with his " Component Pressure Recorder " which gave the soaring- speeds of planes at various angles of in- clination. The accompanying diagram, p. 38, shows the curves of the soaring speeds of three typical planes, each of them being one square foot in area, and weighing 500 grammes. A is moved with its long side foremost, and F with its short side. Here we have a corrobo ration, to some extent, of the former results, for, with plane A (not quite so wide and short as that tested in the former experiment), we find that, as the angle of inclination is diminished, the soar- ing speed is very greatly increased. This would imply that with much greater speeds soaring would be ob- tained with hardly any inclination. If the trace of E is more curved than that of F, and A still more curved than E, we must presume that the curve obtained by a plane 36 ins. by 4 ins. would be more pronounced still than the plane A, 30 ins. by 4.8 ins. Therefore, the curve of such a plane would tend to meet the vertical line of OP much higher up if at all. 38 PRACTICAL AERODYNAMICS. Whilst we have this diagram before us several inter- esting" facts may be pointed out. A wide plane like A does not soar at speeds under icj metres per second, while a square E soars at under 10, and the narrow plane F would apparently soar at a much lower speed. 10* 5* 10" 2.5* "30 5 iS= 40 5 #5^ 50 It is noticeable how, with a plane like A, at inclina- tions between 15 and 45, there is very little difference in the speed necessary to cause it to soar; that is to say, at speeds of about 10^ to 1 1 metres per sec. it will soar whether the angle be 15 or 40. With the long and narrow F, on the other hand, each degree of inclination calls for a different speed. THE LEE SIDE OF A PLANE. 39 THE LEE SIDE OF A PLANE. In considering the theoretical principles of the pressure of air on a plane, it has been usual to> consider only the pressure on the exposed side of the plane," the re-action that takes place on the lee side is often for- gotten. With a thin, rigid plane, it is evident that when driven vertically against the air there will be a negative pressure or partial vacuum at the back. This opens up a most difficult and complex problem. Dr. Stanton has investigated this, and found that the negative pressure was greatest just behind the edges of the planes. The ratio of maximum pressure on the windward side to the pressure on the leeward side of a circular plate was found to be 2.1 to i, whereas the ratio for a rectangular plate was 1.5 to i. That is, the intensity of pressure on the leeward side of a rectangular plate is greater than that on circular or square plates. This ratio, as determined by Dr. Stanton, for discs of 2 inches diameter, was precisely the same as that found by Mr. Dines in his experiments with a plate one foot square iri a whirling table. As regards inclined planes, especially when the angle with the line of progression is small, the case is some- what different. If a thin lamina or plane without ap- preciable thickness be experimented upon, the resulting pressure may be very different to that affecting a solid body with an inclined face. As an instance, if a disc such as a penny be fixed to incline at an angle of 45 40 PRACTICAL AERODYNAMICS. and is exposed to a horizontal current of air, the pressure will be greater than is experienced on the end of a pole sawn through at the same angle and exposing an equal area. As we have already seen (p. 16), the current of air flowing horizontally all round the peri- phery sucks away the air from behind the thin plane, and this suction or lack of pressure has to be added to the force of the air impinging" on the exposed surface. This effect may easily be shown experimentally by the following apparatus : AD is a rigid plane, such as a stiff piece of cardboard. B is a light sheet of light paper, slightly curved, affixed to the back of the plane at its front edge. When a current of air, C, is directed against this, the paper rises up into the position AB 7 . This action is the more pronounced as the angle with the current is increased. In fact, the direction of AB' remains about horizontal, whatever the inclination of AD may be. Dr. Stanton found that with such inclined planes there was a very considerable lack of pressure im- mediately behind the leading edge, but he also found that this pressure fluctuated very greatly, the variation amounting to as much as 50 per cent, above or below the mean value, when the inclination was about 10. Another curious result is, that the air drawn in to fill the partial vacuum flows up the back of the plane towards the front edge. This may be demonstrated by pasting the ends of a number of small strips of tissue paper on the back of the plane, the other ends being THE LEE SIDE OF A PLANE. free to be blown by the wind in whichever direction it may be moving-. Then, at all events when the in- clination is over 30, the papers will turn upwards and Pff $$ equal- sized planes mounted 0*1 the same spindle, when very close together the total pressure was slightly greater than on the single plane. But when the back plane was moved away at a distance equal to about half its dia- meter, the pressure lessened, and continued to decrease as the plates were moved further apart, reaching- a minimum when at about i^ diameters. The value of the total pressure when at that distance apart being " less than 75 per cent, of the resistance of a single plane." This result is probably caused by the pressure on the back plane nullifying the effect of negative pressure on the back of the front plane. As the planes were put still further apart the total pressure steadily increased, so that at a distance of 2.15 diameters the pressure was again equal to that on a single plane. But, though the pressure increased on further separating the planes, the shielding effect was well maintained up to a distance of five diameters, where the total pressure was only 1.78 times that on a single plane. Precisely similar results were got with other shaped planes. This is an important fact to take into con- sideration when designing apparatus with superposed surfaces. According to this theory, if two parachutes were attached one above the other at a distance equal to i^ times their diameter, the whole would fall much faster than a single parachute. Canovetti also made tests, finding that the skidding effect diminished to 3 diameters away, when it ceased. Langley made experiments with superposed planes, but these were practically all made with the apparatus SUPERPOSED PLANES. 43 in horizontal motion, which gave rather different re- sults. In one instance, to be found among" his tables, a pair of planes 15 inches by 4 inches, fixed 6 inches apart, fell vertically at a speed practically the same as a single plane of the same area. When at 4 inches apart they fell slower. When the arrangement of superposed planes is moving horizontally the air between them is less affected, being continually renewed. Langley's conclusions were that, with planes 15 inches wide by 4 inches front to back, when 4 inches or more apart they do not interfere with one another, and the sustaining power is, therefore, double that of single planes. But when placed only 2 inches apart there is a very perceptible diminution of sustaining power, and a greater rapidity of fall. The amount to which the distance apart of the planes affects their action is, of course, dependent upon the rate of transla- tion, and the higher the velocity, the greater may be the proximity of the planes. The general conclusion is that superposed planes, in order to be efficient, that is, to give the effect of the total area of the surfaces, should be at a distance apart at least equal to their width from front to rear. It will be remembered that Wenham many years ago (Aeronautical Soc. Report, 1866) constructed an ap- paratus with several superposed planes, which were placed at a distance apart equal to their widths (3 inches). It is worth mentioning here that the brothers Wright, as a result of their experiments with full-sized machines, have declared* that a pair of superposed, or tandem, surfaces, has less lift in proportion to drift than either surface separately, even after making allowance for weight and head resistance of the connections. * Wilbur Wright, Jl. of the Western Soc. of Engineers, Dec., 1901. 44 PRACTICAL AERODYNAMICS. COMPOUND PLANES AND AEROCURVES. When two planes are placed at an angle, effects are produced that are of a rather complicated nature. Let two Oppositely inclined planes, AB and BC, be joined, and exposed to a horizontal air current. We know that the air flowing up a slope like AB will have a tendency to continue to flow in the same direction after it has left the surface. We also know that the current on the under-surface will eddy round and flow forwards. We may assume, therefore, that the stream lines would prove to be somewhat as in the diagram. The resultant effect would be that AB is pressed down on the upper side, and driven forward and downward on the under side. BC has a partial vacuum created above it, with a normal upward pressure, at all events on the back end of its under side. The general tendency would then be for the plane to turn over forwards. And this is just what happens in practice. If a horizontal plane be interposed between the two, the result is less pronounced. But the combination of planes at varying angles of inclination is nearly equivalent to a curved surface. AEROCURVES. 45 The reactions of air pressures on curved surfaces have been but little studied. It is well known that a surface with a concavity below will fall slower throug-h the air than a flat of a 16 feet by 4 feet board amounted to .0026 Ib. per square foot, while at 37 feet per second it was .005, and the formula deduced was / - 0.00000778 / 9 ' 3 v r85 / being- the average friction in pounds per square foot, / the length in feet, and v the velocity in feet per second. This equation applied to all the velocities and lengths of surface employed. It is very similar to that obtained by Froude for water, allowingf for the relative densities. Trials were also made with various materials to observe the effect of quality of surface on the tangential resistance. Various varnishes and different kinds of paper and zinc, all gave the same result, but with coarse buckram the friction at 10 feet a second was 10 to 15 per cent, greater and increased approximately as the square of the speed. Glazed cambric has about the E fo PRACTICAL AERODYNAMICS. same friction as a varnished surface, but if the cambric is roughened, so as to expose a fine down, the friction is very much increased. Hence he concludes, " All even surfaces have approximately the same coefficient of skin friction. Unev r en surfaces have a greater co- efficient." Though, in these experiments, no determination was made as regards the barometric density of the atmo- sphere, doubtless the friction would increase with the density. VARIOUS SHAPED BODIES. THE RESISTANCE OF VARIOUS SHAPED BODIES. SOLID BODIES. Comparatively few actual experiments seem to have been made on solid bodies driven through the air. It is doubtful to what extent the data gained by experi- ments on bodies immersed in water apply. Colonel Beaufoy's investigations should be of value. Scott Russell demonstrated that with vessels in water there is a corresponding form and dimension suited to each velocity, and this seems likely to be true as regards air. A fish-shaped body is usually considered as that presenting the least resistance to forward pro- gression. As Lanchester puts it, "we may expect that the lines of entrance can with impunity be made less fine than the lines of the run." In the early days of dirigible balloons the French authorities advocated a shape in which the largest diameter was two-fifths of the length from the front. Fish vary, but usually the greatest diameter is not far in front of the centre, though in the mackerel it is about | of the length. Robins, as has been said, experimented with spheres, and decided that such bodies offer one-half the resist- ance of that of a circular plane of equal diameter. Hutton continued the experiments, trying also hemi- spheres and cones. Mr. V. E. Johnson,* in 1894, made a series of com- parative tests with different solid models, all 4 inches in * Invention. February 22, 1896. 52 PRACTICAL AERODYNAMICS. diameter, on a whirling machine about 40 feet diameter at speeds up to 45 miles per hour. He obtained the following results : A spheroid and a cone, no matter which way the vertex pointed, offered less resistance than a disc of the same cross section. A sphere less resistance than a semi-sphere. A cone height 8 inches less than one of 4 inches. A cone 12 inches high less than one 8 inches, and one 16 inches less than one 12 inches. A cylinder offered less resistance than a disc. A cylinder with semi-spherical ends less than one with plane ends. The cylinder with semi-spherical ends considerably less than a sphere of equal diameter. The body having least resistance was thus the greatest diameter being at f the length from the front. " It was not the sharpest pointed head, but the most pointed tail that offered the minimum of resistance," and this statement is well corroborated by the experi- ments of others. But much evidently depends upon the speed with which the model is driven. This has been found to be the case with projectiles; the advantage of an ogival head over a hemispherical one is greater at 1,870 feet per second than at 1,640. Dines, in the course of his investigations on wind pressures, made some tests with solid bodies. For instance, he found that a sphere 6 inches diameter re- ceived a pressure of .13 pounds, while a circular plate of the same diameter and at the same speed (20.86 miles per hour) showed .29 Ibs., or a little more than double. Hemisphere joined to base of cone 3 and 5 diameters long, \ the resistance VARIOUS SHAPED BODIES. 53 He also tried two cones 6 inches in diameter at the base. One of them had an angle of 90, showing a pressure of .29 Ibs. where its base was presented (the same amount as the circular disc) and .19 when its point was towards the current. The other had an angle of 30, and, base first, received a pressure of .3 Ibs. (or greater than the disc) and only .12 on its point. Canovetti* made a series of tests with various models running down the wire at Brescia. Cones of i, i^, 2, and 3 times the length of diameter of base was tried, and the speed of travel varied fro'in the cone of i diameter long with base in front (143 fifths of a sec.) to that i^ diameter long with point in front (98 fifths sec.). A cone i^ diameter long, base in front, had about f the resistance of a disc of equal diameter. A hemisphere, round in front, ^ the resistance. Two cones, base to base, J- the resistance. Hemisphere joined to base of cone 3 and 5 dia- meters long, ^ the resistance. This shape, a hemisphere with a conical tail, was shown to be the best form for cleaving the air (which is in agreement with Renard's trials), and this has been adopted in the design of the latest Italian dirigible balloon. RODS. In any apparatus designed for flight there are likely to be parts such as struts and stays that consist of a length with a given pattern of cross section. Here, once again, but few reliable facts have been ascertained. *" Rapport sur les Experiences de M. Canovetti," par M. Barbet. Soci6t6 d" Encouragement pour 1'Industrie Nationale. Paris, 1903. 54 PRACTICAL AERODYNAMICS. Maxim made a number of tests by exposing 1 various bars of wood to a strong air current. The following gives some of the results : Air Current. Section. Pressure in Ibs. at 40 m, p. h. at 49 m. p. h. 5-47 2.8 ... 2.97 .28 .19 Dines found a f-inch circular-sectioned rod to show a pressure at the rate of 1.71 Ibs. per sq. foot (at 20.86 m.p.h.). VARIOUS SHAPED BODIES. 55 SUSTAINING SURFACES. The sustaining surfaces of most large aeroplane machines, like the wings of birds, are composed of what may be called a concavo-convex body. This often has a comparatively blunt entrance or cutting edge, which may affect both the resistance to forward motion or " drift," and the lift derived from the pressure on the under surface. Some comparative tests were made by Mr. Merrill, of Boston, U.S.A., 51 ' on a small kind of whirling table. He tried seven varieties of the shape recommended by Hargrave, but six of them having a piece added in front with the idea of diminishing the resistance. The shape which he found to give the best resistance is that illustrated below. " In this the distance from the extreme front edge to the point where the under surface proper begins is 20 per cent, of the whole distance to the rear edge." Sir Hiram Maxim made a great many tests both with a large whirling table and with forced air currents. The tests described in his book on sustaining surfaces may be tabulated thus : i. Plano-convex, 12 inches wide, w r ind velocity 40 miles per hour. Angle of incidence. Lift. Drift. Ibs Ibs. Horizontal ... o ... o 1:20 3.98 ... .3 1 : l6 4-59 -53 * Aeronautical Journal. July, 1899. PRACTICAL AERODYNAMICS. 2. Concavo-convex, 16 inches wide, very thin, very slight curves, wind 41 miles per hour. Angle of incidence. i : 10 slightly changed Lift. Ibs. 9-94 10.34 Drift. Ibs. 1. 12 1.23 3. Concavo-convex 12 inches wide. Angle of incidence. Lift. Ibs I H 5.28 I 12 5.82 I 10 6.75 I 8 7-75 I 7 8-5 I 6 9.87 Drift. Ibs. 44 5 73 I.O 1.25 1.71 4. Concavo-convex 12 inches wide, more curved, 41 miles per hour. Drift. Ibs, 37 54 56 7 i. 08 .21 O Angle of incidence. Lift. Ibs. I 16 5-47 J 12 6.12 , ... 6.41 I 10 6.97 I 8 8.22 I 7 9.94 I 6 10.34 horizc ntal 2.O9 i 18 negative O 5. Concavo-convex, upper side about i : 13, lower i : 36, 8 inches wide, more curved, wind 40 miles per hour. VARIOUS SHAPED BODIES. 57 Angle of incidence. Lift. Ibs. horizontal ... 1.56 Driff. Ibs. .08 i 20 3. 62 .21 i 16 4- 09 .26 i J 4 4- 5 33 i 12 5. 43 i 10 5. 75 .60 i 8 6. 75 .86 I .' 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. 9MAY 59VF API? 30 1959 n i r> >Y 1 5 REC'D ,Pf? ir67..-B. - - - ^ : ~ k< 8EC. cut APR 8 LD 21A-50w-9,'58 (6889slO)476B General Library University of California Berkeley U) / U I M180559 THE UNIVERSITY OF CALIFORNIA LIBRARY