Aviation, theorico-pracitcal text-book for students

Front matter

Class "t" Li 5*4 S "

Book 'C3 .

Copyright^

Preface

In the compilation of this book, the guiding principle has been to use matter of actual theorico-practical value to the aviation students to enable them to work knowingly.

For a given aeroplane part, the most common term has been chosen out of the maze of confusing terminology, which ought to have been relegated into oblivion long ago to facilitate the study of one of the greatest, if not the greatest, products of the human mind. Admittedly, the aeroplane is in its infancy, but an infant that can go at such a high rate of speed and perform such marvelous feats certainly deserves more than passing attention, and it is high time to standardize the names of its parts, at least. Although wrong as any other, the term " plane' ' has been used to designate a wing or a wing-like structure, because it is incorporated in the very word "aeroplane," and to have introduced a new and proper term would have meant the changing of even the name of the machine, thus creating more confusion.

The appendix has been added for the benefit of the students who wish to go deeper into the science of aerodynamics, and to facilitate the task of those who have not the necessary mathematical knowledge, the superficial elements of algebra, trigonometry and the metric system have been given in the definitions.

It is hoped that this treatise will fill the long felt want of a theorico-practical text-book on aviation.

The Author.

Aerodynamical formulae and calculations 133

Aviation glossary, algebra, metric system, trigonometry 147

Index 167

ix

CHAPTER I THEORY OF FLIGHT Planes

Aviation is the branch of aeronautics that treats of the gasless aircraft.

The fundamental law governing aviation is based on the resistance of the air against a body moving through it.

Man's first application of this law to obtain flight is found in the use of the kite, which is in reality the forerunner of the aeroplane.

In analyzing the process of kite flying, we find that, in order to accomplish flight, a natural current of air must blow against the kite or the kite must be dragged through the air generating its own artificial current, and that in either case the kite must be at an angle with the horizon and not in a vertical position. While it is immaterial, therefore, whether the air attacks the kite or the kite attacks the air, it is imperative that the kite be at an angle with the horizon or there will be no flight. From experience, we know this to be so; now let us see why.

Flat Planes. — If we move through the air a normal plane, it simply pushes the air back without accomplishing any work, because the air meets the plane perpendicularly and slips off all around the edges evenly. The air pushed back by the plane will exercise against it a certain resistance with a consequent pressure, whose center will be in the center of figure. If we double the speed of the plane, the plane will displace double the amount of air and the air will strike the 1 plane with double the force, so that the resultant resistance will be the product of two times the mass of air engaged by two times its striking force, that is, four times as great as before or equal to the first amount of resistance multiplied by the square of two. If we treble the speed, the plane will engage three times the amount of air, the air will strike the plane with three times the force and the result will be nine times greater or equal to the first amount of resistance by the product of three times three or the square of three; and so forth. We can say, therefore, that the resistance of the air to a normal plane moving through it is proportional to the surface of the plane and to the square of the velocity. Properly speaking, for very high speeds the resistance increases at a greater rate than the square of the velocity, until we reach the 5th power at about 800 miles per hour, when it begins to diminish until it becomes less than the square, but for all practical purposes, we may say that the square law holds good.

If we now move through the air an inclined plane A B (Fig. 1), the air strikes the under side of the plane and flows

downward perpendicularly. In so doing, while it tries to force the plane backward, in the meantime, forces it upward. In this case, the center of pressure P is toward the g * front, because the

front part of the plane does most of the work, as it engages undisturbed air. We may consider this resultant force P divided in its two components L and D, the first acting in a vertical direction and pushing the plane upward, the second in a horizontal direction and pushing the plane backward. The vertical component is the lift and the horizontal, the drift.

The angle a formed by the plane A B with the horizontal C E is the angle of incidence. If we lower the front edge of the plane still further until it is horizontal, then the angle of incidence will be zero; and if we continue to lower it still more, the angle formed by the plane below the horizontal will be a negative angle of incidence.

The resistance of the air, against an inclined plane moving through it, is proportional to the surface, the square of the velocity and the sine of the angle of incidence.

Flat planes do not give good results, because the air meeting the plane is shot down vertically and the rear part does little work, as it engages air which has already a downward trend, besides the fact that the air rushing past the entering edge of the plane carries away part of the air in the rear of it, causing a partial vacuum, which renders easier the work of the pressure of the air in front of the plane in pushing it back and resulting, therefore, in greater drift. In this connection, the arrangement of planes which deserves special attention is the tandem arrangement, because it explains the increased lift of curved planes.

If we place three planes, equal in shape, dimension and inclination, one after the other in a straight line and drive them through the air, we find that the first plane lifts a great deal more than the second and the third respectively. The reason for this marked falling off in the lift of the rear planes is that they have to engage the air, which was already pushed downward by the preceding ones and therefore caused to meet the rear planes with a different horizontal velocity than it met the forward planes.

It is evident that if we want to use the tandem arrangement, we have to dispose the planes so that the rear ones will be able to engage undisturbed air, and to do this, we have to place the second plane lower than the first, and the third lower than the second; that is, in steps. This difference in level must be proportional to the size of the planes, so that the air moved by the preceding ones will pass above the rear planes. The best disposition will be attained when the sum of all the spaces between the planes is equal to the whole area occupied by the planes. In this way, we will be able to produce a large lift per unit of surface and a relatively low drift.

But we can dispose the same planes in another way, which is just as effective as the step formation and which, incidentally, leads us to the formation of the curved planes. Cambered Planes. — As we have just seen, an inclined plane, moving through the air, leaves it at the rear edge with a downward motion; if we, therefore, want to use two or more planes one after the other, we have to place the rear planes at a greater angle than the preceding ones, so as to engage the air already pushed downward by the latter.

Suppose that A B (Fig. 2) is a plane inclined at an angle of 6°; if we drive it forward, it is clear that the air will flow

_4 away at B with a downward trend; so, if we want to use another plane C D behind it, we will have to put it at a greater angle, say 10°, and if we want to add a third plane E F, we have to set it at a greater angle than the second plane, say 12°. As there is no reason why we should use three planes instead of one, which will answer the same purpose, we can substitute for the three planes A B, C D, E F, the plane A F, which will have the same shape formed by the other three, with the joints rounded off, so as to present a continuously curved stream-lined surface, that is, a surface so shaped as to exactly follow the contour of the line traced by the successive positions of a particle of fluid moving according to a determinate law. A stream -line is a continuous curve, as a fluid can not instantly change its direction of flow without forming a detrimental surface of discontinuity, as is the case with flat planes. This explains partly the reason why curved surfaces give more lift and relatively less drift than flat ones; and it explains it only partly because the planes used to-day have a double curvature, one above and one below, differing in degree and imitating the conformation of a bird's wing. Planes so shaped were at first used in mere imitation of nature, as in trying to realize man's dream of centuries, the conquest of the air, nothing was more natural than to imitate the only real, living flying machine in existence, the bird, but the attempt failed, not because the principle was wrong, but for the great disparity for unit weight between the muscular power of man and bird and for the multiplicity of parts needed, with the consequent friction, which would render uneconomical even the use of motors to accomplish flight through such a mechanism. But although the machine with the flapping wings, or ornithopter, was a failure, it played a very important part in the solution of the problem of aerial navigation, for it revealed to us the mysteries of the conformation of the bird's wing, whose construction we imitate in the design of the successful flying machine of to-day. The revelation of this natural secret, coupled with the knowledge of the laws that govern the flight of the kite, gave us the means to conquer the air.

If we move through the air a plane A B (Fig. 3), having an upper and lower camber as the planes used to-day, the leading edge A splits the air and forms two currents; one follows the lower camber and produces a compression, which resolves itself in lift and drift as in the flat plane, but, in the present case, it flows smoothly along the camber and gives the maximum lift, although the front part has more lift than the rear even in a cambered plane, as it engages always undisturbed air; the other current, striking the front paH of the upper camber, glances upwards and, in rushing to the rear, carries with it the air lying between itself and the upper camber, causing in this way a rarefaction perpendicular to the plane and rendering more effective the pressure on the lower camber, which tries to equalize the difference

Fig. 3

in the density of the air above and below and produces a greatly increased lift. The greater amount of lift is due to the rarefaction on the upper camber, which in some planes is as much as 80 per cent, the balance, or 20 per cent, being given by the pressure on the lower camber, while the drift is simply the horizontal component of this pressure. From this, we see clearly why cambered planes are much better suited than flat ones to accomplish flight.

A very simple experiment will conclusively prove the lift due to the upper camber.

If a sheet of paper A B (Fig. 4) is first folded, then opened, without flattening it out, and one part C is laid flat on a board, the other part D forms a curve behind the line of the fold; if we now hold the flat part and by mouth

Wind

Fig. 4 direct a stream of air parallel to it, the curved part rises and, if the current is strong, it jumps up.

In considering the lift and drift of a plane, we have to take into consideration its horizontal and vertical projections or

Fig. 5 equivalents. The horizontal projection A C of a plane A B (Fig. 5) increases A C with a decrease in the angle of incidence, while its vertical projection A D decreases A D', and vice versa. The lift is proportional to the horizontal equivalent, the drift to the vertical equivalent. This means that the smaller the angle, the greater the lift, and the greater the angle, the greater the drift; but, on the other hand, the increase of the angle causes the plane to engage more air, and as in reality it is the product of the two that must count, that is, the surface of the plane and the mass of air, an increase of angle means an increase of lift besides an increase of drift, so that at a certain angle the two forces will balance. The best proportion of lift to drift, or lift drift ratio, is found for small angles, as, in this case, the proportion of the horizontal equivalent to the vertical equivalent is the highest. In other words, the nearer the plane comes to the vertical, the greater the drift and, consequently, the greater the power needed to overcome it, and vice versa; which means that the theory of the plane set at an angle is the same as the old known theory of the inclined plane.

Let us make this clearer. If the greatest weight that a man can lift in a perpendicular line to a height of two feet is 150 pounds and he has to lift a greater weight, he usually resorts to the use of a plank, by putting one end of it on the point where he wants to raise the weight and the other end on the ground, and rolling on it the given weight to the given height. As weight means gravity, it is clear that in this case the power employed to lift the weight is less than that of gravity, and, consequently, the use of the inclined plane is very economical in the expenditure of power. For this>very reason, the solution of the problem of aerial navigation by means of the helicopter, or machine intended to fly by means of horizontal propellers which would raise it straight up from the ground, has not been possible so far, as such a machine, to leave the ground, must produce first of all a vertical force powerful enough to overcome that of gravity, and this without considering the power lost in consequence of the extreme fluidity of the air. Other considerations are against the use of the helicopter. Even admitting that a motor so light and powerful could be found to accomplish flight by such means, it is necessary to use at least two propellers, because if only one were used, the propeller torque, or rotary force of the propeller, would cause the machine to revolve in an opposite direction. Then again, once the machine is raised from the ground, another propeller would be necessary to make it move in a horizontal direction or the machine should be tilted so that the same propellers that raise it, cause it to move horizontally. And finally, supposing that flight could be accomplished by means of a helicopter, there is to consider the ever present possibility of the stoppage of the motor, in which case the machine would tumble down like a plummet. In opposition to this and in further confirmation of the great superiority of the machine using the inclined plane for its sustentation in the air, we will cite the case of the glider used in the experimental stages of aerial navigation, which was sufficient to raise into the air the weight of a man by means of his muscular power; and the glider was nothing but a flying machine without motor and propeller.

In regard to the shape of the curvature of cambered planes, the best suited is the parabolic curve, with its highest point near the front edge. This parabola, as soon as struck by the air, pushes it downward with a constant vertical velocity, without interference with the following masses of air, in this way increasing the lift and decreasing the drift.

As to the degree of curvature, no definite rule can be given, because it must vary according to the speed of the machine; the curvature being smaller, the speedier the machine, in order to decrease the drift. From this, it follows that the rule set by the great, unlucky pioneer, Lilienthal, that the curvature be 1/12 of the chord of the arc, can not be applied generally. Most likely this conclusion was reached through the study of bird wings, but evidently we could not properly compare them with the planes of a machine, as the birds use their wings both for napping and gliding, while we use the planes for gliding only. That the same curvature would be successful for both cases is, therefore, out of the question.

The angle of incidence of the cambered planes is of the greatest importance ; the plane must be set so that, in splitting the air, it allows the latter to flow above and below without disturbing its continuity. What this angle is to be, it must be arrived at according to the shape of the plane.

From the foregoing, it is clear that nothing is established with certainty as yet in regard to cambered planes, and, therefore, we must be guided by actual experience to find the best angle of incidence and the center of pressure, which differ with the degree of curvature.

Owing to the camber of the planes, it would be impossible to measure the angle of incidence, which would vary at different points, unless some means were found to make it equal throughout and this is accomplished by using the chord or straight line A B (Fig. 6a) drawn from the leading to the trailing edge, but, in this case, when the angle of incidence is zero, that is, when the chord is parallel with the horizontal or line of flight, the plane has still lift, due to the upper camber and, consequently, the real zero angle for cambered planes must be below that given by the chord. This point is found by experiment in the wind tunnel by lowering the leading edge D (Fig. 66) of the plane, until it is in such a position that there is no lift. Then, a line C E drawn from the trailing edge through the width of the plane, parallel to thejine of flight, will be the neutral line.

a

This, therefore, brings us to the consideration of two angles of incidence in a cambered plane; one B A F (Fig. Ga) formed

by the chord A B with the line of flight A F, or rigger's angle of incidence, and the other G A F formed by the neutral line A G with the line of flight A F, or flying angle of incidence.

For practical pur- Fig. 6 , ., . , & poses, only the rigger s

angle of incidence is used, as the neutral line is imaginary and we have no means to find it unless by experiment in the wind tunnel, while the chord can always be found. So, when we say that a plane is set at a zero angle of incidence, we mean that its chord is parallel with the line of flight, and if the plane is said to be at a negative angle of incidence, it means that the chord forms an angle below the line of flight.

The travel of the center of pressure in flat and cambered planes deserves our attention. If the front edge of a flat plane is lowered, the center of pressure moves forward and lifts the plane, and if the edge is raised, the center of pressure moves backward and lowers the plane. Flat planes, therefore, are stable. It is not so with cambered planes, because, on account of the two cambers, the center of pressure is the resultant of two forces and, consequently, it acts differently than in flat planes; that is, when the leading edge of a cambered plane is lowered, the center of pressure moves backward, and if it is raised, it moves forward. From this, it is clear that cambered planes are unstable, because if the leading edge rises, the center of pressure, moving forward, causes it to rise still more, and if it is lowered, the center of pressure moves backward and causes the plane to lower still more;

but although cambered planes are unstable, they are used because they give greater lift and smaller drift than flat planes.

Another factor of great importance entering in the consideration of lift is the proportion of the dimensions of the plane, that is, the ratio of length or span to width or chord, which constitutes its aspect ratio. The greater the proportion of span to chord, the greater the lift of the plane, because, as we know, the greatest part of the work is done by the front of the plane and again because all the air entering at the leading edge does not flow to the rear, but some of it is spilled at the lateral ends of the plane. The area of a plane, found by multiplying its dimensions, is not, therefore, the effective area, and for this reason, the plane must be much longer than it is wide. From this, it follows that the longer the plane, the better it would be in respect to lift, but of course there is a limit. The plane must be light and strong in the meantime, and we could not build a plane immensely long without increasing its weight beyond the limit imposed by the aerodynamical laws, for the reason that the volume, and therefore the weight, of a body increases as the cube of the linear dimensions, and the surface as the square of the dimensions, and, consequently, the relations between weight and surface would be completely disturbed. Therefore, it is better to have several superposed planes of reasonable dimensions, say 6 to 1, rather than one of great length. In regard to width, it is to be observed that while narrow planes give greater lift than wide ones, they do not offer the same safeguard in minimizing the fall of a flying machine in case of a compulsory glide from a height. As we see, therefore, there is a limit for both dimensions, span and chord.

If the span of a plane A (Fig. 7) is 30 feet and the chord is 6 feet, its aspect ratio is 30: 6 = 5. If we cut it in half lengthwise and we put the rear half B alongside the front half, then the aspect ratio would be 60: 3 = 20. The former would be a low aspect ratio and the latter a high aspect ratio. While in both cases we have the same surface, the second plane would be much more efficient than the first,

-50'-

-50^

A

Fig. 7

because in taking the rear part of the plane, where it was doing very little work, and putting it in front, where it will do the greatest work, we have greatly increased the lift. Besides this, there is to consider the spill of air, which is halved, in the former plane taking place along two edges six feet long, and in the second along two edges only three feet long. For the same reason, if we were to turn the plane A so as to offer to the air the smaller side (Fig. 8), the lift would be immensely reduced, because of the great spill of air and the small section of the plane doing effective work ir front. In conclusion, we may say that a high aspect ratio is the best, but, on the other hand, it would be impossible to build a plane with a very high aspect ratio, as it would be necessary to increase the thickness of the frame work used in the construction of planes to such a point, that what we would gain in lift, we would lose in weight. It is for this reason that we resort to the grouping of planes in superposed fashion. By arranging the planes in this way, we get about as much lift as with one long plane equal to the sum of their dimensions, a good saving in weight and great strength of construction.

In the arrangement of superposed planes, care should be taken to make the gap or interplane distance at least equal to their width, otherwise there will be interference and the lift will be diminished. Interference is the detrimental effect

Fig. 8 produced in the gap by the rush of air, or wash, which disturbs both the rarefaction of the top camber of the lower plane and the compression of the lower camber of the upper plane. The greater loss of lift is in the lower plane, because in this case it is the rarefaction which is disturbed and we know that it is from the rarefaction that we get the greater

Fig. 9

amount of lift. For parity of surface, two superposed planes give about 15 per cent less lift than one single plane. The effect of interference could be eliminated by spacing the planes far apart one from the other, but as wooden sticks or struts are used to accomplish this, they should be made so thick that their weight and resistance would cause a loss instead of a gain. The best way to diminish interference as far as possible, without unduly increasing the weight, is to stagger the planes, that is, to dispose them in steps (Fig. 9). If the top plane is forward of the lower plane, the stagger is positive (Fig. 9a); if the position is reversed, it is negative (Fig. 96); and if there is no stagger at all, it is zero (Fig. 9c). Sometimes in superposing planes, the top one is made ___________________________ longer (Fig. 10) as in

this case the extension gives the full amount of

lift, having no plane on

F j g 10 the under side to pro-

duce interference.

Active and Passive Drift. — We have considered so far the best angle and disposition of the planes without mentioning either the means to keep them rigidly in place to maintain the angle and disposition given or those to furnish the motive power. It is evident that a framework, an engine and a propeller are necessary to obtain our object. The embodiment of these different parts in a unit constitutes the aeroplane, which is, therefore, a power driven aircraft sustained in flight by the reaction of the air against planes set at an angle with the line of motion. It is distinguished as monoplane and multiplane, according to the number of superposed planes used; the biplane and triplane being simply particular cases of the multiplane.

The shape of an aeroplane very closely resembles that of a bird, both having a body, legs, wings and a tail, the only difference being that the bird has movable wings, which furnish both motive power and sustentation, while the aeroplane has rigid wings for sustentation only and the power is furnished by a motor, whose rotary motion is transformed into a linear motion by means of a propeller attached to it. As the machine moves through the air, there is resistance against the planes as well as against the framework. The resistance against the planes is active, as it gives lift besides drift, but the resistance against the other parts is all passive drift and must be overcome in order to accomplish flight. To diminish this passive drift as much as possible, the different parts used in a machine are given a special shape, which has been found to be the best suited for the purpose.

If we move through the air a body A B C D (Fig. 11), having right-angled corners, the air, coming in contact with

Fig. 11

the front part of the body, jumps off at the corners and falls toward the rear, until it meets again at a certain point E. Between this point and the rear part of the body a vacuum is formed which retards the forward motion of the body. This is due to the fact that the air meeting the corners can not instantly change its direction of flow and follow the shape of the body. If we round the front corners, the air, instead of jumping off, flows gradually along the curvature and the sides, meeting at a nearer point F in the rear. If we cut the sides tapering down to a point toward the rear, then the air follows exactly the contour of the body, eliminating the formation of the vacuum. The body will then be so shaped as to be blunt at the front part and thin at the rear. This is a stream-lined body and the ratio of length to width is its fineness. The fineness of a stream-lined body is proportional to the velocity, that is, the thinner the body the better suited to move through the air at a high velocity, because the air has less tendency to jump off in meeting the blunt part. If the body, instead of being rounded off at the front, had a sharp end, it would split the air more easily, but this would be a loss instead of a gain, because when the air meets the blunt part and is split, it forms a vacuum C7, which, being in the direction of motion, is beneficial, both because it helps move the body forward and because of the saving in the weight of material by cutting off the sharp edge. This small vacuum in front of a stream-lined body is known as Phillip's coefficient. When a body can not be stream-lined by cutting it into shape, then additional parts of wood, metal or fabric are used, so as to give it the proper form for least resistance.