To determine this, short of actual experiments with a machine in horizontal translation, is impossible, unless it is done by taking into account the factor due to momentum and the element attributable to the lift of the plane itself due to its impact against the atmosphere.

LANGLEY'S LAW.--The law enunciated by Langley is, that the greater the speed the less the power required to propel it. Water as a propelling medium has over seven hundred times more force than air. A vessel having, for instance, twenty horse power, and a speed of ten miles per hour, would require four times that power to drive it through the water at double the speed. The power is as the square of the speed.

With air the conditions are entirely different.

The boat submergence in the water is practically the same, whether going ten or twenty miles an hour. The head resistance is the same, substantially, at all times in the case of the boat; with the flying machine the resistance of its sustaining surfaces decreases.

Without going into a too technical description of the reasoning which led to the discovery of the law of air pressures, let us try and understand it by examining the diagram, Fig. 7.

A represents a plane at an angle of 45 degrees, moving forwardly into the atmosphere in the direction of the arrows B. The measurement across the plane vertically, along the line B, which is called the sine of the angle, represents the surface impact of air against the plane.

In Fig. 8 the plane is at an angle of 27 degrees, which makes the distance in height across the line C just one-half the length of the line B of Fig. 7, hence the surface impact of the air is one-half that of Fig. 7, and the drift is correspondingly decreased.

_Fig. 7. Equal Lift and Drift in Flight._

_Fig. 8. Unequal Lift and Drift._

MOVING PLANES VS. WINDS.--In this way Boisset, d.u.c.h.emin, Langley, and others, determined the comparative drift, and those results have been largely relied upon by aviators, and a.s.sumed to be correct when applied to flying machines.

That they are not correct has been proven by the Wrights and others, the only explanation being that some errors had been made in the calculations, or that aviators were liable to commit errors in observing the true angle of the planes while in flight.

MOMENTUM NOT CONSIDERED.--The great factor of momentum has been entirely ignored, and it is our desire to press the important point on those who begin to study the question of flying machines.

THE FLIGHT OF BIRDS.--Volumes have been written concerning observations on the flight of birds. The marvel has been why do soaring birds maintain themselves in s.p.a.ce without flapping their wings. In fact, it is a much more remarkable thing to contemplate why birds which depend on flapping wings can fly.

THE DOWNWARD BEAT.--It is argued that the downward beat of the wings is so much more rapid than the upward motion, that it gets an action on the air so as to force the body upwardly.

This is disposed of by the wing motion of many birds, notoriously the crow, whose lazily-flapping wings can be readily followed by the eye, and the difference in movement, if any, is not perceptible.

THE CONCAVED WING.--It is also urged that the concave on the under side of the wing gives the quality of lift. Certain kinds of beetles, and particularly the common house fly, disprove that theory, as their wings are perfectly flat.

FEATHER STRUCTURE CONSIDERED.--Then the feather argument is advanced, which seeks to show that as each wing is made up of a plurality of feathers, overlapping each other, they form a sort of a valved surface, opening so as to permit air to pa.s.s through them during the period of their upward movement, and closing up as the wing descends.

It is difficult to perform this experiment with wings, so as to show such an individual feather movement. It is certain that there is nothing in the structure of the wing bone and the feather connection which points to any individual feather movement, and our observation is, that each feather is entirely too rigid to permit of such an opening up between them.

It is obvious that the wing is built up in that way for an entirely different reason. Soaring birds, which do not depend on the flapping motion, have the same overlapping feather formation.

WEBBED WINGS.--Furthermore, there are numerous flying creatures which do not have feathered wings, but web-like structures, or like the house fly, in one continuous and unbroken plane.

That birds which fly with flapping wings derive their support from the air, is undoubtedly true, and that the lift produced is due, not to the form, or shape, or area of the wing, is also beyond question.

The records show that every conceivable type of outlined structure is used by nature; the material and texture of the wings themselves differ to such a degree that there is absolutely no similarity; some have concaved under surfaces, and others have not; some fly with rapidly beating wings, and others with slow and measured movements; many of them fly with equal facility without flapping movements; and the proportions of weight to wing surface vary to such an extent that it is utterly impossible to use such data as a guide in calculating what the proper surface should be for a correct flying machine.

THE ANGLE OF MOVEMENT.--How, then, it may be asked, do they get their support? There must be something, in all this variety and diversity of form, of motion, and of characteristics, which supplies the true answer. The answer lies in the angle of movement of every wing motion, which is at the control of the bird, and if this is examined it will be found that it supplies the correct answer to every type of wing which nature has made.

AN INITIAL IMPULSE OR MOVEMENT NECESSARY.-- Let A, Fig. 9, represent the section of a bird's wing. All birds, whether of the soaring or the flapping kind, must have an initial forward movement in order to attain flight. This impulse is acquired either by running along the ground, or by a leap, or in dropping from a perch. Soaring birds cannot, by any possibility, begin flight, unless there is such a movement to change from a position of rest to one of motion.

_Fig. 9. Wing Movement in Flight._

In the diagram, therefore, the bird, in moving forwardly, while raising the wing upwardly, depresses the rear edge of the wing, as in position 1, and when the wing beats downwardly the rear margin is raised, in relation to its front margin, as shown in position 2.

A WEDGING MOTION.--Thus the bird, by a wedge-like motion, gives a forwardly-propelling action, and as the rear margin has more or less flexure, its action against the air is less during its upward beat, and this also adds to the upward lift of the body of the bird.

NO MYSTERY IN THE WAVE MOTION.--There is no mystery in the effect of such a wave-like motion, and it must be obvious that the humming bird, and like flyers, which poise at one spot, are able to do so because, instead of moving forwardly, or changing the position of its body horizontally, in performing the undulatory motion of the wing, it causes the body to rock, so that at the point where the wing joins the body, an elliptical motion is produced.

_Fig. 10. Evolution of Humming-Bird's Wing._

HOW BIRDS POISE WITH FLAPPING WINGS.--This is shown in Fig. 10, in which eight successive positions of the wing are shown, and wherein four of the position, namely, 1, 2, 3, and 4, represent the downward movement, and 6, 7, 8, and 9, the upward beat.

All the wing angles are such that whether the suspension point of each wing is moving downwardly, or upwardly, a support is found in some part of the wing.

NARROW-WINGED BIRDS.--Birds with rapid flapping motions have comparatively narrow wings, fore and aft. Those which flap slowly, and are not swift flyers, have correspondingly broader wings. The broad wing is also typical of the soaring birds.

But how do the latter overcome gravitation without exercising some sort of wing movement?

INITIAL MOVEMENT OF SOARING BIRDS.--Acute observations show that during the early stages of flight, before speed is acquired, they depend on the undulating movement of the wings, and some of them acquire the initial motion by flapping.

When speed is finally attained it is difficult for the eye to note the motion of the wings.

SOARING BIRDS MOVE SWIFTLY.--Now, the first observation is, that soaring birds are swiftly- moving creatures. As they sail overhead majestically they seem to be moving slowly. But distance is deceptive. The soaring bird travels at great speeds, and this in itself should be sufficient to enable us to cease wondering, when it is remembered that swift translation decreases weight, so that this factor does not, under those conditions, operate against flight.

MUSCULAR ENERGY EXERTED BY SOARING BIRDS.

--It is not conceivable that the mere will of the bird would impel it forwardly, without it exerted some muscular energy to keep up its speed. The distance at which the bird performs this wonderful evolution is at such heights from the observer that the eye cannot detect a movement.

WINGS NOT MOTIONLESS.--While the wings appear to be absolutely motionless, it is more reasonable to a.s.sume that a slight sinuous movement, or a rocking motion is constantly kept up, which wedges forwardly with sufficient speed to compel momentum to maintain it in flight. To do so requires but a small amount of energy. The head resistance of the bird formation is reduced to a minimum, and at such high speeds the angle of incidence of the wings is very small, requiring but little aid to maintain it in horizontal flight.

CHAPTER II

PRINCIPLES OF AEROPLANE FLIGHT

FROM the foregoing chapter, while it may be rightly inferred that power is the true secret of aeroplane flight, it is desirable to point out certain other things which must be considered.

SPEED AS ONE OF THE ELEMENTS--Every boy, probably, has at some time or other thrown small flat stones, called "skippers." He has noticed that if they are particularly thin, and large in diameter, that there is a peculiar sailing motion, and that they move through the air in an undulating or wave-like path.

Two things contribute to this motion; one is the size of the skipper, relative to its weight, and the other is its speed. If the speed is slow it will quickly wend its way to the earth in a gradual curve. This curved line is called its trajectory.

If it is not very large diametrically, in proportion to its weight, it will also make a gradual curve in descending, without "skimming" up and down in its flight.

SHAPE AND SPEED.--It has been observed, also, that a round ball, or an object not flattened out, will make a regular curved path, whatever the speed may be.

It may be a.s.sumed, therefore, that the shape alone does not account for this sinuous motion; but that speed is the element which accounts for it. Such being the case it may be well to inquire into the peculiar action which causes a skipper to dart up and down, and why the path thus formed grows more and more accentuated as the speed increases.

As will be more fully described in a later chapter, the impact of air against a moving body does not increase in proportion to its speed, but in the ratio of the square of the speed.

WHAT SQUARE OF THE SPEED MEANS.--In mathematics a figure is squared when it is multiplied by itself. Thus, 4 X 4= 16; 5 X 5 = 25; and so on, so that 16 is the square of 4, and 25 the square of 5. It has been found that a wind moving at the speed of 20 miles an hour has a striking or pushing force of 2 pounds on every square foot of surface.

If the wind travels twice as fast, or 40 miles an hour, the pushing force is not 4 pounds, but 8 pounds. If the speed is 60 miles an hour the pushing force increases to 18 pounds.