DEFINITIONS

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.

CHAPTER I - THEORY OF FLIGHT

Planes

Aviation is the branch of aëronautics 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 oft 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 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.

Fig. 1

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 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.

Fig. 2

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 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.

Fig. 3

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 part 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 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.

Fig. 4

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

Fig. 5

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