HAVING in a previous volume treated the general subject of "Aerial Navigation," in which a sketch was given of what has been accomplished with balloons, I propose in the following chapters to treat of Flying Machines proper --that is to say, of forms of apparatus heavier than the air which they displace; deriving their support from and progressing through the air, like the birds, by purely dynamical means.

It is intended to give sketches of many machines, and to attempt to criticise them.

We know comparatively so little of the laws and principles which govern air resistances and reactions, and the subject will be so novel to most readers, that it would be difficult to follow the more rational plan of first laying down the general principles, to serve as a basis for discussing past attempts to effect artificial flight. The course will therefore be adopted of first stating a few general considerations and laws, and of postponing the statement of others until the discussion of some machines and past failures permits of showing at once the application of the principles.

The first inquiry in the mind of the reader will probably be as to whether we know just how birds fly and what power they consume. The answer must, unfortunately, be that we as yet know very little about it. Here is a phenomenon going on daily under our eyes, and it has not been reduced to the sway of mathematical law.

There has been controversy not only about the power required, but about the principle or method in which support is derived. The earlier idea, now abandoned, so far as large birds are concerned, was that when they flapped their wings downward they produced thereby a reacting air pressure wholly equal to their weight, and so obtained their support. This is known as the "orthogonal theory," and has been disproved by calculations of the velocity and resulting pressures of the wing beats of large birds, and by the more recent labors of Professor Marey. It seems likely that the smaller birds, who, as will be explained hereafter, are probably stronger in proportion to their weight than the larger birds, possess the power of delivering blows upon the air equal to a supporting reaction. Such may be the case in the hovering of the hummingbird and the rising vertically of the sparrow; but the latter exertion is evidently severe, and cannot be long continued.

Mr. Drzeweicki has shown that a buzzard, beating his wings 2 1/2 times a second, with an amplitude of 120°, could only obtain, according to accepted formulæ of air pressures, a sustaining orthogonal reaction of 0.40 pounds or about 1/10 of his weight, while if his wings are considered as inclined planes, progressing horizontally at a speed of 45 miles per hour, a sustaining reaction is easily figured out.

It seems quite certain that large birds cannot practice orthogonal flight, and that they derive their support mainly if not wholly from the upward reaction or vertical component of the normal air pressure due to their speed. That they are living Aeroplanes, under whose inclined wings their velocity creates a pressure which is normal to the surface. This is confirmed by the great difficulty which they experience in getting under way. They run against the wind before springing into the air, or preferably drop down from a perch in order to gain that velocity without which they cannot obtain support from the air. Thus the surfaces of their wings act as aeroplanes as well as propellers, the latter action being produced by the direction of the stroke and the bending upward of the rear flexible portion of the feathers.

Bird flight may be considered as comprising three phases:

  1. Starting, during which great exertion must be made, unless gravity can be utilized.
  2. Sailing, or flight proper, during which the bird exerts his normal force, or makes use of that of the wind, as will be more particularly explained hereafter.
  3. Stopping, in which great exertion may again be required, if the headway is to be rapidly stopped, or in which the retarding force of gravity may be brought to do the work by simply rising to a perch.

Artificial flying machines will certainly have to conform to these three phases of flight, by providing methods of starting and stopping in addition to the means for performing the act of flight proper.

Birds perform all their manoeuvers by regulating the intensity of their action, and by changing the angles at which they attack the air. Hence the important thing for us to know is to ascertain what pressure exists under a wing or, to simplify the question, under a plane surface, when it meets the air at a certain velocity and with a certain angle of incidence.

This has been, until the recent publication of Professor Langley's most important labors, a subject of uncertainty, which uncertainty he has done much to remove. We had had glimpses of the law; but notwithstanding very many experiments by physicists, its numerical values were a subject of doubt and controversy among the few who gave any attention to the subject. It was the missing link, which rendered nearly unavailable the little that was known in other directions.

By the law of fluid reactions all air pressures are "normal," or exerted perpendicularly to the surfaces against which they bear; now the question was: What is the relation between the pressure of a current of air of known velocity against a thin plane surface placed at right angles thereto, and the normal pressure of that same current against the same plane, if the latter be inclined to the current at an angle of incidence less than 90 degrees?

Newton impliedly gave a solution; but experiments long ago proved it to be wrong, although it is still taught in the schools and given in formulas in engineering reference books. He assumed, plausibly enough, that the proportional normal pressure was in the ratio of the sine of the angle of incidence, and when experiment showed this to be erroneous, other formulas were proposed, the following being a few of those which have been wrangled over:

Calling a the angle, and P the pressure on the inclined surface, while P' is that upon the right-angled surface, the following were assumed to represent the relation:

P = P' sin aP = P' sin2 a
P = P' sin3 a P = P' (sin a)1.84 cos a
P = P' (2 * sin a)/(1 + sin2 a) P = 2 P' sin a

Indeed, the field seemed so open in this direction that only two years ago I ventured to propose a formula of my own, which I subsequently concluded to be erroneous; but the question seems now to be set at rest for the present by the experiments of Professor Langley, who proposes no formula of his own, but who shows that his results approximate very closely to the formula of Duchemin:

Approximate Percentages of Normal Pressure. Derived from Chart of Experiments and Theories. Calculated by Bossut's or Duchemin's Formula.

P = P' (2 * sin a)/(1 + sin2 a)
Deg. of
Results of
S.P. Langley's
10.035 0.0350.000611
1 1/20.520.520.00136

I had already independently reached a conclusion quite similar. Finding that my formula was incorrect, I had a chart plotted, on which were delineated all the experiments on inclined surfaces which I could learn about--those of Hutton, Vince, Thibault, Duchemin, De Louvrié, Skye, the British Aeronautical Society, and W. H. Dines; and on this chart I also had plotted the curves of the various formulas. The whole exhibited great discrepancies, yet by patient analysis various probable sources of error were eliminated, and the conclusion was reached that the formula last given, which I have seen variously attributed to Bossut or to Duchemin, was probably correct.

From this formula I had computed for my own use the accompanying table of normal pressures; and as it seems to be quite confirmed by Professor Langley's experiments, and seems to promise to be of great use, I now venture to publish it.

Once the normal pressure is known at a particular angle of incidence, its static components in different directions can be obtained by the laws governing the resolutions of forces. This was shown, as early as 1809, by Sir George Cayley, in the following demonstration, in which he ingeniously evades the then prevailing confusion about the "law of the angle" by starting with the weight of the bird instead of its wing surface and velocity. He says:

When large birds, that have a considerable extent of wing compared with their weight, have acquired their full velocity, it may frequently be observed that they extend their wings, and, without waving them, continue to skim for some time in a horizontal path.

Fig. 1 represents a bird in this act. Let A B be a section of the plane of both wings. opposing the horizontal current of air (created by its own motion), which may be represented by the line C D, and is the measure of the velocity of the bird. The angle B D C can be increased at the will of the bird, and to preserve a perfectly horizontal path, without the wing being waved, must continually be increased in a complete ratio (useless at present to enter into), till the motion is stopped altogether; but at one given time the position of the wings may be truly represented by the angle B D C. Draw D E perpendicular to the plane of the wings. Produce the line C D as far as required, and from the point E, assumed at pleasure in the line D E; let fall E perpendicular to D F; then D E will represent the whole force of the air under the wing--i.e., normal pressure, which being resolved into the two forces E F and F D, the former represents the force that sustains the weight of the bird, and the latter the retarding force by which the velocity of the motion producing the current C D will be continually diminished; E F is always a known quantity, being equal to the weight of the bird, and hence if D is also known, as it will bear the same proportion to the weight of the bird as the sine of the angle B D C bears to its cosine, the angles D E F and B D C being equal.

FIG. 1.

In the table, pages 4 and 5, the first column shows the degree of the angle of incidence; the second the result of Professor Langley's experiments; the third the proportion or percentage which the normal pressure at that angle bears to the pressure at the same velocity of the same plane at right angles to the current; while the fifth and sixth columns show the resolutions of this normal pressure being the force which sustains the weight of the bird vertically as against gravity, which is here termed the "Lift," and the retarding force against horizontal motion, which is here termed the "Drift." They are calculated by multiplying the normal pressure by the sine and by the cosine of the angle.

In order to obtain the aggregate normal pressure, or the lift and the drift, upon any thin plane surface, it is simply necessary to multiply its area by the pressures per square foot, which are given (approximately) in the ordinary tables of wind velocities, and this again by the percentages given in the table.

The angles are only given up to 45°, as more than this would be useless to the general reader; and it will be noted that there is an angle of maximum uplift at about 36°. This results from the fact that the normal pressure is continually increasing while the cosine of the angle is continually diminishing but not equally. so that their product reaches a maximum, as stated. This is confirmed by the results of Professor Langley's experiments, as recorded on page 58 of his "Experiments in Aerodynamics."

It should be borne in mind that the table only purports to apply to thin planes one foot square, and hence is given as containing only approximate percentages of normal pressures. For other shaped planes, for curved surfaces, and for solids the percentages may be different, because a great many anomalies have been found in experimenting upon air resistances, and we yet know painfully little about them.

For instance, the following may be mentioned:

  1. For high velocities, such as those of projectiles, the resistances do not vary as the square of the speed, as assumed in ordinary tables; they more nearly approach the cube of the velocity.
  2. If a thin plane be exposed to a current of air, at right angles thereto, the pressure on the plane is not uniform over all its surface, but is greatest at the center.
  3. Plane surfaces of equal areas but of different shapes (square, oblong, triangular, etc.) are found to receive slightly different pressures at the same speed. Moreover, the average pressure per square foot varies with mere variation of size on the same shaped planes.
  4. The pressure upon an inclined elongated surface will vary for the same speed, whether it be exposed longitudinally or transversely to the current.
  5. Holes may be cut in thin planes without reducing the aggregate pressure in proportion to the surface cut away. Moreover, the aggregate pressure may be made to vary by simply changing the position of the holes.
  6. Inclined planes may be superposed without diminishing the sum of their separate individual pressures, provided they are properly spaced with regard to the angle of incidence. If too close, they will interfere with each other, but the amount of such interference will vary with the speed.
  7. Perfectly horizontal planes, free to fall, have their time of falling much retarded if in rapid horizontal translation.
  8. The weight remaining the same, the force requisite to sustain inclined planes in horizontal motion diminishes instead of increasing, when the velocity is augmented.
  9. If the plane be gradually inclined to the current, the point of maximum pressure will move forward toward the front edge as the angle of incidence diminishes. The position as given by Joëssel's law is shown by the formula:
    C = (0.2 + 0.3 sin a) L,

    in which C represents the position of the center of pressure, L the length, and a the angle of incidence the formula indicating that the position of the center of pressure varies from 0.5 to 0.2 of the distance from the front to the center of the plane.

Of these anomalies, the 6th, 7th and 8th were experimentally determined by Professor Langley; and he partly confirmed the 9th, as well as giving strong confirmation to the results of Duchemin on the "law of the angle" previously mentioned. The 8th is especially important, and its consequences are pointed out by Mr. Langley in the following words:

The most important general inference from these experiments, as a whole, is that, so far as the mere power to sustain heavy bodies in the air by mechanical flight goes, such mechanical flight is possible with engines we now possess, since effective steam-engines have lately been built weighing less than 10 1bs. to 1 H.P., and the experiments show that if we multiply the small planes which have been actually used, or assume a larger plane to have approximately the properties of similar small ones, 1 H.P., rightly applied, can sustain over 200 lbs. in the air, at a horizontal velocity of over 20 meters per second (about 45 miles an hour), and still more at still higher velocities.

These general remarks chiefly apply to thin plane surfaces, such as might be used in flying machines, but mere thickness plays an important part; for in a solid body, with the same area of exposed head surface, the pressure will be varied by the depth, and especially by the form of the body in the rear. Thus curved surfaces and solids have quite different coefficients of pressure from thin flat planes, and theoretical estimates of their resistances have hitherto proved to be quite wrong.

Indeed, it may be said with respect to curved surfaces and solids, that a glimpse has been caught of a still more mysterious phenomenon. It is known that certain shapes, when exposed to currents of air under certain ill-under stood circumstances, actually move toward that current instead of away from it. Thus a hollow sphere impinged upon by an air jet will move up toward It instead of away. The lower disk in Professor Willis's apparatus, when blown upon, moves against the current toward the upper disk. Dr. Thomas Young proved, in 1800, that a certain curved surface suspended by a thread approached an impinging air current, Instead of receding from it. M. Goupil found, in experimenting, that a suspended hollow shape was first blown out to a horizontal position by a wind of sufficient velocity, and then, when that velocity increased, actually drew into the wind for an instant and slackened the tension on the cord. It is also said that certain forms of windmills wear more on the front stop than on the back stop of their axle of rotation; so that there seems to be a mysterious action, which some French observers, who have been watching birds soar, have, for want of a better term, called their "Aspiration," by which a body acted upon by a current may actually draw forward into that current against its direction of motion.

Thus it is seen that in such complicated matters theory cannot progress in advance of experiment, and the extreme importance of those experiments hitherto tried, or hereafter to be tried by a physicist possessing the ability of Professor Langley, will in part be appreciated.

Science has been awaiting the great physicist, who, like Galileo or Newton, should bring order out of chaos in aerodynamics, and reduce its many anomalies to the rule of harmonious law. It is not impossible that when that law is formulated all the discrepancies and apparent anomalies which now appear, will be found easily explained and accounted for by one simple general cause, which has been hitherto overlooked.

Thus far, Professor Langley seems to have experimented upon plane surfaces only, and to have measured chiefly what has been termed in the table here given the "lift" and the "drift" at various angles. His conclusions therefrom are very important; but the "drift" will not be the sole resistance to be encountered, for the sustaining surfaces of a flying machine must not only have a certain thickness, to give them the necessary strength and rigidity, but there will be friction of air upon them, and there must be a solid body or hull to contain the machinery and the cargo.

Thus the elements of resistance are three in number:

  1. The hull resistance.
  2. The drift.
  3. The skin friction.

Of the skin friction Professor Langley says that it is apparently so small that it may be neglected without material error; and he has given the measure of the "drift" as the result of his experiments.

The head or hull resistance will probably be found to be the chief element which will limit the possible speed of flying machines. It will probably grow as the square of the velocity, thus requiring the power exerted to vary as the cube of the speed, but will be modified by a series of coefficients, due to the shape of the solid body, just as some birds are swifter flyers than others of the same weight, in consequence of their difference in shape.

Hence the power required to drive such a machine can only be approximated at present; but this will be more particularly discussed when treating of the areas of supporting surfaces and speed of birds, for the reader may be impatient to be told something of what has been attempted by man.

Inventors, in their ignorance of the laws of air reactions and resistances, have proposed all sorts of devices for compassing artificial flight and experimented with not a few; so that Mr. E. Dieuaide, of Paris, upon making a study of the subject, published in 1880 an illustrated chart, 1 in which he delineated the more remarkable machines which had been proposed for aerial navigation without the use of balloons. This chart contains some 53 figures; and from this, as well as from the book of M. Gaston Tissandier on Aerial Navigation, 2 which contains much accurate information, the following has been chiefly compiled, in which it will be attempted not only to give an account of what has been proposed, so far as the meager data will permit, but also to critcise, the machines with the light of our present knowledge, and to endeavor to point out why they failed. Failures, it is said, are more instructive than successes; and thus far in flying machines there have been nothing but failures.

These various machines, diverse as they are, may roughly be classed under the three following heads, according to the intentions and theories which were held by their authors, as to the most efficacious way of deriving support from the air.

  1. Wings and parachutes.
  2. Screws to lift and propel.
  3. Aeroplanes.


1 Tableau d'Aviation. Représentant tout ce qui a été fait de remarquable sur la navigation Aérienne sans Ballons. Published by the author.
2 La Navigation Aérienne. Par Gaston Tissandier. Hachette et Cie; octavo, 334 pp.
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