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by O. Chanute

 

Part I

November 1891.

THE earlier adventurers upon aerial enterprises possessed little accurate knowledge of the properties of air. They had only their observations of the birds as a guide, and knew of no motive power save that derived from muscular energy; hence their thoughts first turned to flapping wings, to be propelled by their own exertions. Some few, as we shall see, have considered the force of the wind, but it is only since the age of steam that artificial motors of any kind have been proposed for flying machines.

The well worn legends of antiquity, concerning Dedalus, Abaris, Archytas, etc., may be passed over without comment. They merely indicate how the problem of artificial flight appealed to the imagination of men from the earliest periods, but some curious traditions will be mentioned, indicating partial successes in soaring flight, when we come to treat of aeroplanes.

About the first authentic account which we have of a proposal to provide man with flapping wings seems to be due to Leonardo da Vinci the painter, sculptor, architect. and engineer. He is said not only to have experimented with aerial screws made of paper, and to have designed a parachute, but also to have seriously contemplated building an apparatus to propel a pair of wings, of which several sketches have been found in his note-books.

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FIG. 2. -- LEONARDO DA VINCI -- 1500

The first sketch shows a wing, actuated by the arms, but Da Vinci, becoming aware, upon reflection, that all possible muscles of man must be brought into play to act effectually upon the air, designs in the second and third sketches an apparatus in which the wings are to be waved downward by the legs and lifted up by the arms. The third sketch is represented in fig. 2. In this Da Vinci only shows the legs in place, so as not to obscure the construction of the parts. The date is probably about the year 1500. The construction is simple, and might not prove altogether inefficient did the muscles of man possess the same energy and rapidity of action as do those of birds in proportion to their respective weights. lt is not known just how far Da Vinci elaborated his idea, but he never put it to practical test, and it is chiefly mentioned here as a curious forerunner of actual experiments.

The first wing experiment reported by tradition seems to be that of a French tight-rope dancer named Allard who, under the reign of Louis XIV., announced that he would fly from the terrace at Saint Germain toward the woods of Vesinet in presence of the king. It is probable that he had previously succeeded in gliding short distances, but upon trial before the court his strength failed him; he fell near the foot of the terrace, and he was grievously hurt.

This probably occurred about the year 1660, and in 1678 a French locksmith named Besnier constructed a pair of oscillating wings, approximately represented in fig. 3.

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FIG. 3. -- BESNIER -- 1678.

The apparatus consisted of two bars of wood hinged over the shoulders, and carrying wings of muslin, arranged like folding shutters, so as to open flat on the down stroke and fold up edgewise on the up stroke. They were alternately pulled down by the feet and by the arms, in such wise, that when the right hand pulled down the right wing, the left leg pulled down the left wing, and so on, thus imitating the ordinary movements in walking.

Besnier did not pretend that he could rise from the ground or fly horizontally through the air. He only tried short distances; having begun by jumping off from a chair, then from a table, then from a window-sill, and next from a second story, and finally from the garret, on which occasion he sailed over the roof of an adjoining cottage. He gradually grew more expert, sold his first pair of wings to a mountebank, who performed with them at the fairs, and he expected with his second pair to fly across moderately wide rivers by starting from a height, but it is not known whether he ever performed this feat.

The illustration is evidently an imperfect sketch made from a description; for the hinging at the shoulder is not shown, the attachment for pulling down the wings with the legs is evidently inefficient, and the supporting surfaces are entirely inadequate. The four wings are apparently each 3 ft. by 2 ft, say, an aggregate of 24 sq. ft. in area, while in the table of birds, to be given hereafter, it will be seen that the duck, which has the smallest bearing surface in proportion to its weight, measures 0.44 sq. ft. to the pound, and at this rate a man, weighing, say, 150 Ibs., would require wings aggregating 66 sq. ft. in area. It is probable that Besnier had even more than this, that he took short downward flights aided by gravity, but that he utterly failed when he undertook to go considerable distances

It is not stated whether the Marquis de Bacqueville had engaged in similar preliminary practice when he announced, in 1742 that he would, on a certain day, fly across the river Seine from his mansion, situated in Paris on the quay at the corner of the Rue des Saints Peres, and alight in the Tuilleries, a distance of 500 or 600 ft. A large crowd having assembled on the appointed day, the marquis, with large wings attached to his hands and to his feet, launched himself into space from the summit of a terrace jutting out from one side of the mansion.

For a space he seemed to get along well. but soon his movements became uncertain, he faltered, and then he fell, alighting upon the deck of a washerwomen's barge a short distance out into the stream. He broke his leg in the fall, and never attempted the feat again.

The Marquis de Bacqueville was judicious in trying the experiment over a water-bed, for could he have held out but a few feet further he would probably have escaped with a mere ducking. He probably glided about 120 ft. with most violent exertions, and fell when his strength became exhausted. Fig. 4, which is probably incorrect, represents the traditional apparatus with which this feat was attempted. The surfaces measure about 24 ft. in area, and are quite insufficient to sustain the weight of a man.

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FIG. 4. -- DE BACQUEVILLE -- 1742.

Aware of this experiment of De Bacqueville and of its consequences, the Abbé Desforges, a canon of the church at Sainte-Croix at Etampes, invented, in 1772 a flying chariot, with two wings and a small horizontal sail or aeroplane attached, which from contemporary descriptions seem to have measured about 145 sq. ft. in aggregate area. He expected to rise from a height of a few feet above the ground, and to fly horizontally by rapidly beating his wings. Upon actual trial, the machine being held aloft by four men, the Abbé flapped violently, but utterly failed to start off. Indeed, some of the accounts say that the action of the wings pulled him down instead of up, so that he got a harmless tumble when the men let go.

In 1781 Blanchard, who subsequently became a fervent aeronaut, and who was the first to cross the British Channel in a balloon, constructed near Paris a flying chariot with four wings, measuring in the aggregate some zoo sq. ft. in area. He never exhibited the apparatus in public, having probably ascertained by private experiment that he was unable to move the wings rapidly enough to produce any useful effect.

These last two experiments, taken in connection with those previously mentioned, exhibit fairly well the two horns of the dilemma that confront inventors who endeavor to provide man with wings to be worked by his own muscular power. Either those wings have to be relatively small, in order to permit their being waved rapidly--and then they do not afford sufficient supporting area--or if they are made to approximate to the proportion which generally obtains with birds, or about one square foot to the pound, they become so large that the man does not possess the muscular power to wave them at any adequate speed.

Ideas, however, die hard, and we may disregard somewhat the chronological order of date, in order to follow the evolution of the small- wing idea, which each fresh inventor fancies has been incorrectly worked out by his predecessors.

Of these was Bourcart, who in 1866 experimented with the apparatus shown in fig. 5, It consisted of four wings with a feathering action, so that it presented the edge to the air upon the up stroke and the broad side upon the down stroke, but the results were insignificant, and the experiment was abandoned. The supporting areas measure approximately some 36 sq. it., but are only effective upon the down stroke.

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FIG. 5. -- BOURCART -- 1866.

In 1873 Professor Pettigrew published his work on "Animal Locomotion," in which he called attention to the fact that birds in flapping flight, flex their wings so as to resemble a screw propeller, and that the tips describe a figure of 8 motion. This led to the inference that man had not succeeded in raising himself with wings because he had not hit upon the right motion, and in 1879 Dandrieux constructed an apparatus in which the wings were attached to an oblique axle, so as to describe a figure of 8 movement. This is represented in fig. 6, and there being but two wings in place of four, the supporting surfaces measure about 32 sq. ft. in area. The result was not satisfactory; a partial alleviation of the weight was obtained, but nothing like human flight or the hope of it.

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FIG. 6. -- DANDRIEUX -- 1879.

Charles Spencer exhibited an apparatus consisting of a pair of wings measuring each 15 sq. ft. in area, to which was attached an aeroplane measuring 110 ft. more, and also a tail like a boy's dart, and a longitudinal keel-cloth to preserve the equilibrium, the whole weighing 24 lbs. and giving a sustaining surface of 140 sq.. ft. As Mr. Spencer was an athlete, he was enabled, by taking a preliminary run down a little hill, to accomplish short horizontal flights of 120 to 130 ft., in which he was wholly sustained by the air. He weighed 140 lbs., and his apparatus, which, it will be noted from the description, differed from those which propose "wings for man" by the addition of an aeroplane, measured 0.85 sq. ft. to the pound, or about the proportion of the larger soaring birds. The experiments attracted great attention at the time, but were not sufficiently encouraging to warrant pursuing the matter further.

At the same exhibition Mr. W. Gibson showed a machine consisting of two pairs of wings, worked by the hands and feet together, so as to impart a feathering movement similar to that of birds. He stated that In a former machine, having only one pair of wings of lighter construction, their action upon the air during a vigorous down. stroke was sufficient to raise the man and machine; but no practical demonstration was given, and although the inventor stated that he was then engaged in constructing a more perfect machine, nothing more has been heard of it.

Notwithstanding these many failures, the idea does not seem to be dead yet, for in September, 1890, Mr. W. Quartermain, who exhibited an explosion engine for aerial purposes in 1868, in which the motive power was derived from the gases generated from a species of rocket composition. wrote a letter to the London Engineer, in which he stated that he had abandoned his attempts to procure a light and energetic motor from hydrocarbonous matter, in favor of man's weight and muscular power, which he considers preferable, and was then engaged in experimenting with an apparatus consisting of four wings, formed after the stag beetle type, each 10 1/2 ft. long by 2 1/4 ft. wide, opposing go sq. ft. of expanse of surface to the air. This arrangement weighed 350 lbs., including 212 lbs. for the weight of the operator, who by working both handles and treadles, thus bringing all his muscles into action as well as his weight, was enabled to wave the wings, which are 25 ft. from tip to tip, so as to produce a double stroke for every single stroke of his body on the motive shaft. He describes the result as resembling that of domestic fowls flapping their wings without lifting themselves from the ground, but is of opinion that the uplifting force was greater than his weight of 212 lbs., and believes that further improvements in the mechanism, with more skilful workmanship, might produce an ascensive force greater than the whole weight of 350 lbs. This may well be doubted, for not only will it be shown hereafter that the energy of man must be less than that of birds, but none of the latter fly with so small a bearing surface in proportion to the weight-0.26 square foot to the pound-as in Quartermain's apparatus.

It has been suggested, however, that umbrella-like surfaces might prove more effective than wings, and increase the uplift to be derived from the air. Such contrivances were experimented upon by Sir George Cayley, who constructed, about 1808, a pair of wings which appear from the drawings to have been a fabric stretched tightly over a dished frame, this framework consisting of two ribs at right angles to each other, bent and tied across so as to secure rigidity. This double umbrella contained 54 sq. ft. and weighed only 11 lbs., and the inventor says: "Although both these wings together did not compose more than half the surface necessary for the support of a man in the air, yet during their waft they lifted the weight of 9 stone" (126 lbs.). It is not stated with what speed they were wafted nor with what power, but that the result did not promise to provide "wings for man" may be inferred from the fact that Sir George Cayley, in a very valuable series of articles in Nicholson's Journal for 1809 and 1810, starts out with the assertion that, in order to accomplish aerial navigation, "it is only necessary to have a first mover which will generate more power in a given time, in proportion to its weight, than the animal system of muscles."

The next experiments with umbrella wings attracted attention all over Europe. They were carried on by J. Degen, a clockmaker of Vienna, from 1809 to 1812 with the apparatus shown in fig. 7. It consisted of two wings 8 1/2 ft. wide and 22 ft. across in the aggregate, each being shaped somewhat like a poplar or an aspen leaf. They were stretched upon an umbrella-like frame and thoroughly braced back, both above and below, to a central stick by a number of small cords. The supporting surfaces consisted of bands of taffeta so attached as to have a valvular action, in order to imitate the supposed action of the feathers of birds, and the total supporting surface was 130 sq. ft., while the weight, without the operator, was stated at 20 lbs.

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FIG 7. -- DEGEN -- 1812

With this apparatus Degen, was stated, in 1809, to have risen to a height of 54 ft., by beating his wings rapidly, in presence of a numerous assembly m Vienna, and all the newspapers began to publish accounts of the performance.

These descriptions failed to mention one important addition. Degen was also attached to a small balloon capable of raising 70 lbs., so that the uplift exerted by the wings was only 70 lbs. of the 160 lbs. weight of the operator and his apparatus.

In 1812 Degen; went to Paris to exhibit his invention. He then stated that the balloon was of no sort of utility in obtaining headway, but that it was necessary as a counterpoise to maintain his equilibrium and to lighten his muscular efforts. He evidently expected by the action of his wings to drag the balloon along in still air while it lifted part of his weight

He gave three public exhibitions in Paris, but unfortunately for him, as there was wind upon each occasion, he was blown away, and on the third attempt he was attacked by the disappointed spectators, beaten unmercifully, and laughed at afterward as an impostor.

The umbrella idea had, however previously proved to be of value for parachutes, and in 1852 Letur devised the apparatus shown in fig. 8. with which he expected to direct himself through the air. by means of the wings and tail, first starting from an elevation.

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FIG. 8. -- LETUR -- 1852.

In 1854 he ascended from Cremorne Gardens in London suspended about 80 ft. below a balloon manoeuvred by Mr. Adam, the areonaut, who was assisted by a friend. Letur performed several evolutions in the air by means of his wings, none of them apparently very conclusive, but in coming down near Tottenham, the wind carried the apparatus violently against some trees, and poor Letur received injuries which resulted in his death.

His apparatus measured about 660 sq. ft. in bearing surface, and had he been entirely detached from the balloon, it is possible that he might have reached the ground in safety; but it is evident that his wings would have been as of little service in enabling him to obtain more than a slight horizontal direction.

Undeterred by this sad fate, a Belgian shoemaker named De Groof designed, in 1864, an apparatus which was a sort of cross between beating wings and a parachute. His plan was to cut loose with it from a balloon, and to glide down in a predetermined direction by maneuvering the supporting surfaces. He endeavored to make a practical experiment, both in Paris and in Brussels, but it was only in 1874 that he succeeded in doing so in London.

The apparatus is shown in fig. 9. It consisted of two wings, each 24 ft. long, moved by the arms and the weight of the operator, and of a tail 20 ft. long, which could be adjusted by the feet.

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FIG. 9. -- DE GROOF -- 1864.

De Groof first went up on June 29, 1874, from Cremorne Gardens, London, attached to the balloon of Mr. Simmons. He came down safely, and claimed to have cut loose at a height of 1,000 ft., but it was subsequently stated by others that in point of fact he had not, upon this occasion, cut loose at all, but had descended still attached to the balloon. In any event, he went up again on July 5 following, with the same aeronaut, and on this occasion he really did cut loose.

The result was disastrous. As soon as, in the descent pressure gathered under the moving wings, they were seen to collapse together overhead and to assume a vertical position, when De Groof came down like a stone, and was killed on the spot.

Had the wings been prevented from folding quite back, by means of suitable stops, the descent might not have proved fatal. The area of the wings and tail, as extended horizontally, is said to have amounted to 220 sq. ft., while the weight of the man and machine was 350 lbs., or at the rate of 0.65 square foot to the pound. This corresponds to a pressure of 1.54 lbs. to the square foot, which would be generated by a velocity of 25.7 ft. per second, or a free fall from a height of 10.3 ft.; an unsafe distance for an ordinary person, but not for a trained acrobat.

Ordinary parachute practice is said to allow from 2 to 3 sq. ft. per pound, corresponding to velocities in falling of 14.7 to 12 ft. per second.

It was the most egregious folly for Letur and De Groof as well as for Cocking, who was killed in 1836 in an experiment with a parachute shaped like an inverted umbrella, to attempt a descent with an apparatus previously untried to test its strength and behavior. A few prior experiments, with a bag of sand, instead of the man, would have exhibited the action that was to be expected.

Another class of inventors of "wings for man" have endeavored to secure safety by the use of large bearing surfaces. The first of these was probably, Meerwein, architect to the Prince of Wales, in 1784 who an apparatus shaped like the longitudinal section of a spindle, separated into two wings, by a hinge at the center. It measured nearly 200 sq. ft. in area, and probably was never tried, but if it had been, it is quite certain that a man could never have imparted to the wings sufficient velocity to perform any useful effect.

The next proposal of this class was that of Bréant, who designed in 1854 the apparatus shown in fig. 10. It consisted of two wings, each measuring about 54 sq. ft. in area, and provided with three valves to relieve pressure on the up stroke. The down stroke was to be produced by the joint action of the feet and hands, and the wings were to be drawn back by elastic cords. It is not known whether it was ever tried, but it would have proved ineffective if it had been.

 

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FIG. 10. -- BRÉANT -- 1854.

The next design was that of Le Bris in 1857, which is exhibited by fig. 11. By noting the little man working the levers in the center, the proportions of the apparatus, which seems to have measured some 550 sq. ft. in area, will be appreciated. It is said to have been experimented with in a small model, in which levers pulled down the wings which were then drawn back by springs, but it did not succeed in rising into the air, as was hoped by the inventor.

 

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FIG 11. -- LE BRIS -- 1857.

Before proceeding to describe other designs for winged machines, to be driven by artificial motors instead of muscular power, it may be well to call attention to the fact that not only has every attempt of man to raise himself on the air by his own muscular efforts proved a complete failure, but that there seems to be no hope that any amount of ingenuity or skill can enable him to accomplish this feat.

It has been argued that there is no proof that, weight for weight, a man is comparatively weaker than a bird, and that, inasmuch as he can raise his weight in walking up a stairway, he should be able to raise it by acting upon the air with a suitable apparatus, The weak point about this argument is not only that the weight and bulk of such an apparatus become a surcharge on the muscular power of the man, as would be, for instance, the case were an artificial pair of wings applied to an ostrich, but that among the birds themselves the power to rise vertically unaided does not exist for the larger species. These have to resort to various artifices, such as running against the wind or dropping from a perch, in order to gain that initial velocity which enables their surfaces to derive support from the air, and this probably furnishes a good reason why no flying birds exceed some 50 lbs. in weight; for small animals must possess more energy in proportion to their size than large ones.

Assuming that the speed of contraction in the muscles of two similar birds of different sizes is the same, it is evident that the work done per unit of time will be in ratio to the sectional area, or as the square of the dimensions, while the weight to be moved will vary as the cube of the dimensions; hence the rate of increase between the energy and the weight will be:

square root Energy) varies as cubed root weight),

or to put it in the shape of formulas which shall express the relative energy of animals of the same class:

 

These being all merely different ways of writing it. Hence we see that the energy of birds will only increase as the 2/3 power of their weight, and that there will be an increase of size beyond which they will not be able to develop the work required for a start.³

But man is also at a further disadvantage. Not only do birds have an enormous muscular development, but their muscles contract at a much more rapid rate than those of other animals. Were men, therefore, not already relatively weaker than smaller animals, in consequence of the physical law which has been stated, they would still be unable to develop energy fast enough to rise on the air with a pair of wings. They can raise their weight, it is true, but not as quickly as the birds. They can run up a stairway at the rate of about 3 ft. per second, while the sparrows rise up vertically at thrice that speed, and fly horizontally at 22 ft. per second.

³ Thus a bird of 50 lbs. weight can do no more work in a given time than 50^2/3 = 13.57 similar birds each weighing 1 lb., or a bird of 1,000 lbs., did such one exist, could only develop the same foot-pounds per minute as the aggregate of 100 analogous birds, each of 1 lb. weight.

 

Part II

December 1891.

While the inventors who experimented with flapping wings, with which they tried to raise themselves on the air by muscular effort, doubtless had it in mind eventually to substitute artificial motors, if only they could catch the trick by which the bird flies, there have been a few others who have at the outset designed flapping wings, to be moved by some primary artificial motor. As they generally knew of no such motor, within admissible limits of weight in proportion to its energy, such designs have remained mere projects, and but few experiments have been made

The proposal of Gérard, in 1784, shown in fig. 12, seems to have been among the first. It apparently provides, in addition to the body and wings, for a steering arrangement in front, and for feet with springs to land upon. The inventor omitted to state in his printed description what motive power he intended to use, but an inspection of the drawing suggests the conjecture that the apparatus was to be propelled in part by escaping gases, like a rocket, and in part by flapping the wings through the medium of a gunpowder engine; proposals and experiments with such motors antedating, as is well known, those with the steam-engine. Be this as it may, soon after the success of the locomotive engine on the Liverpool & Manchester Railroad, Mr. F. D. Artingstall endeavored to compass an aerial locomotive. He constructed a very light steam-engine, suspended it by a cord from the ceiling, and to the piston-rod he attached wings, which were so constructed that they opened somewhat like a Venetian blind on the up stroke and closed during the down stroke, moving through an arc of 80°. When steam was turned on the wings worked vigorously, but the machine jerked up and down, rushed from side to side, and, in fact, performed all kinds of gymnastic movements except flight. This experiment was terminated by the explosion of the boiler, and a second attempt, in which it was intended to use four wings instead of two, in order to keep up a continuous buoyancy, resulted in a second explosion; after which the experiments were abandoned. In 1868 Mr. Artingstall, in a communication to the Aeronautical Society of Great Britain, stated the weak point in his various experiments to have been the lack of suitable equilibrium.

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FIG. 12. -- GÉRARD -- 1784.

Every experimenter with aerial apparatus has doubtless encountered the difficulty of obtaining in a machine that equilibrium which the bird maintains by instinct, and also of deriving continuous support from the flapping of one pair of wings. These are probably the reasons which led Struvé and Telescheff to design, in 1864, the apparatus shown in fig. 13, in which five pairs of wings are attached to a central plane. The only description accessible to the writer states that the wings were moved by human force acting upon a spring, but it is evident that the apparatus was intended to be driven by artificial power, if the designers could only find one sufficiently light for that purpose. That they did not succeed in this seems to be a fair inference from the fact that the machine was not tested by experiment.

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FIG. 13. -- STRUVÉ & TELESCHEFF -- 1864.

At the Exhibition of 1868. of the Aeronautical Society of Great Britain. Mr. I. Palmer exhibited a pair of wings (to be driven by power) attached to a rotating axle, and so arranged that they expanded in the descent and closed in the ascent, like the action of a duck's foot in swimming; this motion being obtained in a remarkably simple manner by a roller running on an eccentric cam, which could be instantaneously changed in position, so as to convert the vertical lifting power into one of horizontal force. It does not seem to have been applied to any flying machine.

At the same exhibition Mr. I. M. Kaufmann, engineer of Glasgow, exhibited the working model represented in fig. 14, which was intended as the precursor of an aerial steam machine weighing 7,000 or 8,000 lbs. The apparatus consisted of a steam boiler and engine, mounted upon wheels, and propelled by two long wings, which. during the down stroke, were set at an inclined direction backward, and were caused to turn at a forward angle during the up stroke. The main portion of the weight was to be sustained by superposed aeroplanes, and hence the machine should perhaps be described under that head, but it is here included under the head of wings, because of the mode of propulsion. The model weighed 42 lbs., and during the experiments with it its boiler, owing to its small size, was not fired, steam being supplied from an independent boiler. With steam pressure at 150 lbs. to the inch, the wings made a short series of furious flaps, and one of them suddenly gave way about 2 ft. from its base, upon which the other one failed also. The inventor stated that he was then engaged in the construction of a larger machine on the same principle, but since then nothing more has been heard of it. He proposed to secure stability by letting down or raising up a long "pendule" with telescopic joints, so as to adjust the center of gravity and keep the machine in a horizontal position, but it may well be doubted whether this would have proved effective.

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FIG. 14. -- KAUFMANN -- 1867.

At a meeting of the British Aeronautical Society, in 1871, Mr. R. C. Jay exhibited a model to illustrate a method which he proposed in order to use wings of any length and weight without loss of power. This consisted of two pairs of oscillating wings moving on the same shaft. It was expected that the forces generated by their motion would hold the machine is equilibrium, and that one pair of wings would be aided by the current of air, or whirlpool, produced by the movement of the other pair. This does not seem to have answered, for in 1877 the same inventor presented a model to the same society, illustrating a method of obtaining a figure of 8 or sculling action with one pair of wings, but at the same time Mr. Jay candidly stated that "a though he had made a great many experiments, he had not yet succeeded in making a propeller (wings) sufficiently simple and effective for practical purposes."

It is said that about the same time an optician of Leipsic made a small steam bird, mounted on a globular steam boiler and actuated by a cylinder of 2 in. stroke, working wings 32 in. long. This machine would rise vertically 3 ft., the wings making about three beats during the flight, but the boiler limited the performance. It contained spirits of wine only sufficient for 38 seconds, and the apparatus was but a toy.

In 1871 Prigent designed the apparatus shown in fig. 15, which was evidently suggested by the dragon-fly; this is a favorite idea with aviators, who, as we have seen already, have proposed the combination of two pairs of wings over and over again. It was intended to be driven by steam, but although in that same year Moy had produced a steam-engine and boiler weighing but 27 lbs. per horse power, and Stringfellow, in 1868, has shown one claimed to weigh but 13 lbs. per horse power (both applied to aeroplanes), no attempt seems to have been made to experiment with Prigent's device. The fact is, that even the weight of the engines mentioned was too great, for it did not include the fuel and water, which for a noncondensing steam-engine would amount to about 26 lbs. more horse power per hour, and this did not compare favorably with the motive power of birds. The pigeon, for instance, is known, both by dynamometric experiment and computation, to develop in ordinary flight from 160 to 425 foot-pounds of energy per minute for each pound of his weight, and as his pectoral muscles, which constitute his engine, generally compose 10/43 of his weight, we have for the weight of his motor from

(33.000 * 10)/(425 * 43) = 18 lbs. to (33.000 * 10)/(160*43) = 48 lbs.

per horse power developed, including the fuel which enables him to fly for 10 to 12 hours at a stretch.

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FIG. 15. -- PRIGENT -- 1871.

Hopeless, therefore, of accomplishing anything practical with steam-engines, experimenters with wings next turned their attention to springs or reservoirs of energy of various kinds, and with these they have succeeded in devising a number of toys which fly creditably for a few seconds. Clock springs were first tried, but they were found to be unduly heavy, and in 1871 Jobert brought out his first mechanical bird, shown in fig. 16, driven by indiarubber in tension. The wings were arranged so as to change their plane automatically while flapping, in order to imitate the flexions of the natural wings, and the equilibrium was secured by adjusting the center of gravily so as to correspond with the center of pressure due to the angle of flight.

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FIG. 16. -- JOBERT-- 1871.

In 1872 Pénaud who had already succeeded (1870 and 1871) in compassing flight with the superposed screws and with the aeroplane, which will be noticed hereafter, by the force of twisted rubber, applied the same motor to a mechanical bird, which is shown in fig. 17. The wings beat straight down, and the propulsion is obtained from the flexion of their outer edges produced by the reaction of the air. The bird is unable to rise from the ground, but upon being thrown off the hand it first descends some 2 ft., and then, having acquired the initial velocity needed for support, it flies for a distance of 50 ft. in 7 seconds, rising at the same time about 8 or 9 ft. above the point of departure, the equilibrium being perfectly maintained by the tail.

Simultaneously with this M. Hureau de Villeneuve, the permanent Secretary of the French Aeronautical Society, brought out his mechanical bird, which is shown in fig. 18. In this the plane of the wings is inclined at an angle of 45°, and the power is obtained from twisted rubber. In consequence of the peculiar motion of the wings, this model was able to start direct from the ground, but owing to the limited power of the rubber spring it only rose to the height of 4 ft., and then descended, forming a parachute. It was subsequently modified so that it would fly horizontally for a distance of 24 ft., at a velocity of 20 miles per hour.

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FIG. 17. -- PÉNAUD -- 1872.

FIG. 18. -- HUREAU DE VILLENEUVE -- 1872.

M. De Villeneuve has been promoting aviation by flapping wings for the past 25 years. He has, first and last, designed something like 300 experimental models, so that his garret is a complete aviary of artificial birds. He built, some years ago, a huge steam bird on the model of a bat. Being aware that there was at that time no sufficiently light and reliable steam-engine with its boiler to furnish the power required, he placed only the engine on the bird, and connected it by a hose with a boiler on the ground. Upon trial, as soon as the steam was turned on the wings beat violently, and the apparatus rose with the inventor aboard. He grew nervous for for fear that he would get beyond the length of his hose, and shut off steam suddenly, upon which the bird fell and smashed one of its wings. It is still in existence, and the inventor is awaiting the development of a very light motor in order to resume his experiments with this great bird, which is some 50 ft. across.

In 1872 M. Jobert brought out his second mechanical bird, shown in fig. 19. This is driven by twisted rubber, as being more manageable than rubber in tension, and consists of four wings beating alternately in pairs-as a horse trots--in order to produce continuous and uniform support and equilibrium, instead of the jerking motion observable in other apparatus. This flew fairly well, but a measurement of the foot-pounds developed and of the results obtained, in this as well as in the three other mechanical birds previously described, led to the inference that there was great waste of power, as compared with that of birds. This was attributed to the rigidity of the front edge of the wings in all these models, and accordingly in 1876 Tatin took the problem up again and succeeded, by a double eccentric working two levers connected to the front edge of the wing, in giving it a twisting motion similar to that of the bird. His apparatus flew some 65 ft., with rather less weight of rubber.

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FIG. 19. -- JOBERT-- 1872.

In 1889 Pichancourt carried the matter still further in the mechanical bird shown in fig. 20, in which there is a triple eccentric, each one actuating a lever fastened to a different point in the wings. His larger models, measuring 171 in. from tip to tip of wings, and weighing 1 1/2 oz., are said to have flown up to a height of 25 ft. and to a distance of 70 ft. against a slightly adverse wind.

Click on Picture to enlarge

FIG. 20. -- PICHANCOURT-- 1889.

Now here are no less than six artifical birds, each with a somewhat different wing- motion, and they all fly, when urged by the energy stored in twisted rubber. The question, therefore, occurs why practicable machines, to carry passengers, cannot be built by substituting some prime mover for the rubber; and the answer is that all these models are so wasteful of power that there is no motor known sufficiently light, in proportion to its energy, to take the place of the rubber. The best that seems to have been done with the latter was to obtain a flight of 7 seconds with flapping wings, and with the expenditure of energy at the rate of 600 foot-pounds per pound of twisted rubber. As there are 550 foot-pounds per second in a horse power, a primary motor, with its supplies, should in the same proportion weigh no more than:

600/(7x550) =6.4 lbs. per horse power,

and there are none such known in practical operation.

Click on Picture to enlarge

FIG. 21. -- DE LOUVRIÉ -- 1877.

Undeterred by this disheartening fact, M. De Louvrié designed, in 1877, the apparatus shown in fig. 21, which he calls the "Anthropornis," and which consists of a pair of wings, resembling those of the swallow, fastened to a hull mounted upon wheels, and intended to be actuated by a steam-engine or a petroleum motor. A spring is to contribute to the downward stroke, and is to be raised by the motor on the up stroke. M. De Louvrié is a veteran in promoting aviation, and his writings show a better understanding and firmer grasp of the question than most of those which nave been published on this intricate subject. He had proposed, in 1863, a sort of kite-like flying machine, which will be noticed under the head of Aeroplanes, and it is said that, in 1888, he presented his latest views before a commission of the French Academy of Sciences, supplementing them with certain experiments, from which he drew the conclusion that an apparatus capable of carrying four passengers needed no more than 3 horse power to drive it at the rate of 67 miles per hour. It may be inferred that the French Commission was not convinced, from the fact that no action has been taken upon the proposal.

 

 

Part III

January 1892.

 

In the United States very few experiments seem to have been made with flapping wings, and no records of them are attainable. Investigation is, therefore, limited to such proposals as have been patented, and it is found that, aside from balloons, less than 30 flying machine patents have been taken out, of which four are for flapping wings.

The first of these, in order of date, seems to have been the proposal of Mr. W. E Quinby, who patented, in 1869, an apparatus to be operated by man power, consisting of a pair of side wings and a tail, all to be flapped by a series of cords attached to the operator, who is encased in a cuirass which maintains the wings at about the height of his waist. The surfaces shown in the drawings are quite insufficient to sustain the weight, and in 1872 Mr. Quinby took out another patent for a modification of his apparatus, in which he added dorsal surfaces, so that the wings and the tail were continuous and resembled the supporting surfaces of a bat. The arrangement for imparting motion was ingenious but futile, because of the inefficiency of muscular power, which has already been stated.

In 1876 Mr. F. X. Lamboley patented a framework shaped like the wings of a bird, and covered with a wire netting to which birds' feathers were fastened so as to give a valvular action. Human power as relied upon to impart motion through a trapeze-bar and platform, and of course it would prove inadequate.

In 1877 Mr. M. H. Murrell patented an apparatus consisting of a pair of pivoted side wings and a tail, to be also operated by man power. The wings were furnished with slats similar to those of a Venetian blind to close on the down stroke, and open when going up. An investigation of what others had attempted would probably have saved the inventor some misspent time and ingenuity.

So little has been effected with flapping wings that a number of American inventors seem to have turned their attention to various arrangements of revolving vanes. Of these A. P. Keith patented, in 1870, an aerial car with paddle-wheels revolving in a transverse plane, for the purpose of lifting and propelling. Thomas Green patented, in 1873, an apparatus with two wheels, each with four revolving blades passing through the air flatwise on the down stroke and edgewise on the up, and M. H. Baldwin patented. In 1890, an aerial vessel in which weight is to be supported by a set of wheels containing feathering vanes; the wheels revolving in opposite directions on longitudinal shafts. All of these are worthless, as is also the patent of I. M. Wheeler of 1887, which covers the arrangement of a number of oscillating frames superposed to each other on a mast, and carrying slats similar to those of a Venetian blind; these various devices only being mentioned to illustrate how ingenuity has been wasted upon mechanical details, while scarcely any attention seems to have been given to the devising of the lightest possible motive power. Each fresh inventor of winged machines is apt to imagine that his predecessors did not succeed because they did not hit upon the right method of imitating the complicated and swift motions of the birds. Thus Mr. H. Sutton, of Australia, communicated to the British Aeronautical Society, in 1888, that experiment and observation had convinced him that the tips of the bird's wings describe, when viewed from the side, the outline of an inverted cone with rounded base, instead of the figure of 8 motion described by Dr. Pettigrew and Professor Marcy. He had accordingly made a model, driven by clockwork, to test the truth of his theory. This model was not capable of free flight (steel springs and clockwork being much heavier than rubber, in proportion to their stored energy), but when suspended at the end of a counterweighted lever, resting upon an upright support with a ball-and-socket joint, it flew in a circumference of about 12 ft. by the flapping action of the wings. By slightly modifying the stroke of either wing it was made to fly from right to left or from left to right. By altering the guide-rods, which governed the direction of the stroke it could be made to fly upward at any desired angle, but the important, the vital question of an efficient motor was left untouched by the inventor.

Still, earnest attempts are occasionally made in the direction of light motors. At the meeting of the British Aeronautical Society, in 1890, a photograph was shown of a steam- bird machine, designed and built by Mr. E. P. Frost, which is represented in fig. 22. The wings, which are 30 ft. from tip to tip, are in exact imitation of those of the crow, and the various positions which they assume during a stroke are shown in the picture. The weight of the machine, including engine and boiler, is about 650 lbs. It was expected to carry m addition the weight of a man in the air, but it was said that the maker of the engine failed in his contract to secure the necessary power, and the apparatus did not fly.

Click on Picture to enlarge

FIG. 22. -- FROST-- 1890.

At the same meeting Mr. H. Middleton, who has been advocating for several years winged apparatus as superior, in his judgment, to aeroplanes, exhibited two bird machines, one weighing 20 lbs., with a wing-spread of nearly 12 ft., and the other of between 10 and 12 lbs. weight with a wingspread of some 9 ft. He also showed an aeroplane weighing somewhat over 20 lbs., with sustaining planes of 14 ft. across and a screw of 4 ft. diameter, in order to compare its performance with those of the bird machines. Only the smaller of these latter was shown in action, but its balance was not properly adjusted, and although it raised itself from the sustaining horizontal rope during the first few strokes, it soon rested again upon the rope, and on the pressure being raised during a subsequent run, the right wing broke and terminated the experiment.

The aeroplane, being similarly suspended, moved along the rope at a moderately good pace, but without raising itself on the air, and that experiment was brought to an untimely end by the rupture of a joint on the propeller shaft.

Probably the most original conception ever presented for a flying machine is that of M. G. Trouvé, who has just revived (1891) the proposal for his mechanical bird, which was first presented to the French Academy of Sciences in 1870. This is shown in fig. 23, and consists of two wings, A and B, connected together by a "Bourdon" bent tube, such as is used in steam gauges. The peculiarity of this tube, as is well known, is that as pressure increases within it the outer ends move apart, and as pressure diminishes they return toward each other. M. Trouvé increases the efficiency of this action by placing a second tube within the first, and in the experimental model he produces a series of alternate compressions and expansions by exploding 12 cartridges contained in the revolver barrel D, which communicates with the tube. This produces a series of energetic wing strokes which propel and sustain the bird in the air in connection with a silk sustaining plane indicated at C.

Click on Picture to enlarge

FIG. 23. -- TROUVÉ-- 1870.

The manner of starting the bird is equally ingenious and peculiar, and is shown in fig. 24. The bird is suspended from a frame by a thread, which, being attached to the hammer, keeps the latter off the cap. A second thread holds the bird back from the perpendicular, while a common candle A and a blow-pipe flame B complete the preparations. Upon the thread being burned at A the bird swings forward from position 1 to position 2, where the suspending thread is burned by the blow-pipe B, the hammer falls on the cap, an explosion ensues, the wings strike downward violently, and the bird flies on an upward course, as shown in position 3. Then the gases escape from the Bourdon tube, this recovers its shape, raises the wings and actuates two pawls which rotate the revolver barrel and work the hammer, so that a fresh explosion occurs and the bird continues to fly. When the 12 cartridges are exhausted the bird glides gently to the ground, being sustained by its wings and aeroplane as by a parachute. It has thus flown 75 to 80 yards.

Click on Picture to enlarge

FIG. 24. -- STARTING TROUVÉ'S BIRD-- 1890.

This motor is evidently very simple and very light, and for a practical flying machine M. Trouvé proposes to substitute for the cartridges a supply of compressed hydrogen gas, which, when mixed with about three parts of air, becomes an explosive mixture to be fired by the electric spark. Thus the motor would derive the greater portion of its power direct from the atmosphere as wanted, there would be no danger of premature explosion as with fulminates, and, hydrogen being only of the weight of air the weight and the equilibrium of the apparatus would vary but little when supplies became exhausted. Moreover, it is probable that no cooling agent would be required , as in ordinary gas engines, because the tube exposes so great a surface that it is to be expected that the heat would pass into the air while under motion, and that, as there is no piston to be lubricated, a moderate heating would not prove objectionable.

M. Trouvé started out with the assumption that a motor for aerial navigation should not weigh over 8 lbs. to the horse power. He presented to the French Academy of Sciences, in 1886, an electric motor, weighing but 7.7 lbs. per horse power, working an aerial screw, which will be more fully noticed when that subject is treated, and on August 24 last (1891) he deposited with the same body a sealed letter containing the drawings and description of an aeroplane and screws, which, he confidently believes, provide a final solution for the problem of aerial navigation, and which will also be noticed under the head of Aeroplanes.

Meanwhile other inventors are also working in the same field, and the English papers have contained sundry paragraphs, within the last few months, concerning a flying machine some 45 ft. across, in the form of a bat, which is being built in Coventry for Major Moore, of India. It is to be driven by an electric motor, but the descriptions do not make it clear whether this is to be by beating wings or with fixed wings, as in an aeroplane. The cost incurred is stated at over $5000, and the trial is to take place at the Crystal Palace. Should this take place in time, it will be noticed, as well as the great apparatus now being completed by Mr. Maxim, when we come to discuss aeroplanes.

 

Part IV

February 1892.

 

It will be seen from the foregoing statements of what has been accomplished with beating wings, that the principal questions are those of motive power and of proportion of surfaces to weight, and the reader will probably first inquire as to what is really the power developed by birds in their flight. The answer must unfortunately be, that it is not accurately known. A great many computations have been made, based upon more or less plausible assumptions, but none of these computations can be absolutely accepted as correctly based upon indisputably measured data.

This ceases to be surprising when we consider that there is no creature so willful, so swift, and so easily affrighted as the bird, and that once in the air, he will not lend himself to be measured experimentally. Mathematicians have, therefore, partly resorted to conjectures for their data. Thus Napier assumed that a swallow weighing 0.58 oz. must beat his wings 2,100 times per minute while going 33 1/2 miles per hour, in order to progress and sustain his weight, and that it therefore expended 1/13 of a horse power. In point of fact, the bird only beats about 360 times a minute, and is chiefly sustained by the vertical component of the air pressure on the under side of the wings and body, due to the speed, instead of by the direct blow of the wings downward, as supposed in the orthogonal theory already alluded to.

Other mathematicians, starting from the fact that a weight falls about 16 ft. during the first second, and in so dropping does work, have assumed that a bird in horizontal flight, being then sustained, performs a certain fraction of this work. It is evident, however, that if the bird does not drop, the fraction assumed is purely arbitrary, and that such calculations must be quite worthless.

Experiments to measure directly the power expended have proved failures, and resort has been had to indirect measurements.

Thus Dr. W. Smyth, of Edinburgh, succeeded in measuring with a dynamometer the strain exerted by a 12-oz. pigeon while flexing its wings, when excited by a current of electricity, and found it capable of raising 120 lbs. one foot high in a minute, or at the rate of 160 foot-pounds per pound of bird. Professor Marey performed the same experiment on the buzzard and on the pigeon, and ascertained the contractile strength of their muscles to be 18.46 and 19.91 lbs. to the square inch respectively;⁴ but as he was unable to measure satisfactorily the rapidity with which the muscles contracted, he did not calculate the foot-pounds.

Mr. Alexander, starting with the assumption that a 2-lb. pigeon makes 180 completed strokes per minute, each stroke with an amplitude of 1.5 ft. at the center of pressure, calculates the power exerted as being 2 X 180 X 1.5 = 540 foot-pounds per minute, or at the rate of 270 foot-pounds per pound of bird. This is plausible; but the most satisfactory computations are those made by Pénaud from observations of the direct velocity of ascent of various birds. From these he concludes that the pigeon, for instance, expends for rising 579 foot-pounds per minute, and that the proportion of horse power to weight is as follows:

• For the peacock, one horse power for every 66 lbs.

• For the pigeon, one horse power for every 57 lbs.

• For the sparrow, one horse power for every 48 1/2 lbs.

• For the sea pie, one horse power for every 26 lbs.

This, however, is merely the work of elevation, such as would be performed upon a solid support, in addition to which the bird has to overcome the resistance of the air to his motion and to derive support from this mobile fluid. Pénaud calculates that this additional work amounts to over 1,000 foot-pounds per minute, so that the total work done by the pigeon in rising to a perch 35 ft. above the ground amounts to 1,650 foot-pounds per minute, or 1 horse power for every 20 lbs. Moreover, it must be remembered that the pectoral muscles of birds, which constitute their motor, comprise but one-quarter to one- sixth of their total weight, so that in this particular case the relative weight of the motor is only about 5 lbs. per horse power for the force exerted in rising.

These are formidable figures, but they cease to be discouraging when we reflect that the effort of rising is evidently a maximum, and that birds seldom perform it in a nearly vertical direction except for short distances, and that the exertion is clearly so severe that the feat is usually performed only by the smaller birds, which, as previously explained, must possess greater energy in proportion to their weight than those exceeding a few ounces. Heavy birds can only rise at angles less than 45°, and even then they exert for a short time far more than their mean strength, the latter being, for all animals, only a fraction of the maximum possible effort. Thus man, who is usually estimated as capable of exerting 0.13 horse power for 10 hours, can develop 0.55 horse power for 2 1/2 minutes, and nearly a full horse power for 3 or 4 seconds; and it seems probable that similar proportions obtain for birds, the emergency effort being three or four times the average performance, and the possible maximum about twice as great as the emergency effort.

Pénaud states that the ring-dove dispenses in full flight 217 foot-pounds per minute; but he does not give figures for this, so that they can be checked. Goupil estimates the work done by a pigeon weighing 0 .925 lbs. at 1,085 foot-pounds per minute in hovering and 119 foot-pounds per minute in flight; but the latter is arrived at by reasoning from analogy. It is evident that the power exerted in horizontal flight is much less than that required for rising or for hovering; but until a bird is taught to tow behind him some dynamometric arrangement at a regular rate of speed, and on a level course, it will be difficult to settle exactly what are the feet-pounds expended in ordinary performance.

In 1889 Captain de Labouret, an expert in the solution of balistic problems, analyzed mathematically two series of photographs of a gull weighing 1.37 lbs., and just starting out in flight with 5 wing beats per second, as obtained by by Professor Marey with the chrono- photographic process. The calculations showed that the bird expended in this act an average of 3,152 foot-pounds per minute. or 2 .303 foot-pounds per pound of his weight; and as Professor Marey shows that from his other observations of the reduced amplitude and rapidity of the wing beats, the same bird does only expend in full flight 6 of the effort required at starting, the conclusion may be drawn that the gull in full flight expends some 460 foot-pounds per minute for each pound of his weight.

This estimate seems plausible to me, and agrees with my own figures, but it is not accepted by all aviators. The Revue Scientifique of November 28, 1891, contains two articles disputing the conclusions -- one by Mr. V. Tatin, an expert aviator, who claims that the accelerations of the bird have been erroneously calculated; that the center of pressure under the wing is 4/9 of the distance from its root instead of 2/3, as usually assumed, and who figures out from the velocity of this new center of pressure, and from the known trajectory that the bird in full flight only expends from 33 to 197 foot-pounds per minute for each pound of his weight.

The second article is by Mr. C. Richet, the editor of the Revue Scientifique, who, having ascertained the volume of carbonic acid exhaled by a bird at rest, assumes, from experiments on other animals, that in full flight he will give out three times as much, and that the difference represents an effort of 105 foot-pounds per minute per pound of bird.

These two articles, being the most recent computations by earnest students of the subject, are here mentioned chiefly to illustrate how greatly aviators vary in estimates of the power expended, and how many elements have to be assumed in making such computations.

In the absence of direct measurements, and of positively satisfactory computation by others, of the feet-pounds expended in horizontal flight, I believe that an approximation may be obtained by analyzing and calculating the various elements which combine to make up the aggregate of the resistance to forward motion in horizontal progression and as this method promises to be useful in computing the power required by artificial flying machines, I venture to set it out at some length, applying it to the domestic pigeon as being more convenient to compare with the results of the calculations of others. For this purpose two dead pigeons were selected, weighing as near as practicable 1 lb. each. and their dimensions were accurately measured as follows:

 

Cross Section and Horizontal Projection of Pigeons.

 

	Piegon No. 1.	Pigeon No. 2.
Largest cross section of body	4.9 sq. in.	5.3 sq. in.
Largest cross section of edge of wings	5.02 sq. in.	4.88 sq. in.
Weight of bird, freshly killed	1 lb.	0.969 lb.
Horizontal area of both spread wings	90.35 sq. in.	99.86 sq. in.
Horizontal area of body projected	22.49 sq. in.	24.01 sq. in.
Horizontal area of tail spread	19.72 sq. in.	27.17 sq. in.
	132.56 sq. in.	151.04 sq. in.

 

These dimensions all require the application of coefficients in calculating their action upon the air. Thus the wings are concave, and give a greater sustaining power per square foot than a flat plane; the body is convex, and affords less than a plane, while the tail is slightly concave, but partly ineffective from its position. Previous experiments have indicated that, in the aggregate, the supporting power is about 30 per cent. more than that of a flat plane of equal area, so that in the calculations which follow the supporting surfaces will be assumed at 1.3 Sq. ft. to the pound instead of the 1 square foot to the pound which the average of the measurements seems to indicate.

It will be remembered that experiments with parachutes indicate a coefficient of resistance of 0.768 for the convex side and of 1.936 for the concave side, as compared with the plane of greatest cross section.

The cross sectional area of the body is assumed at 5 square inches or 0.03472 of a square foot. and to this a coefficient is applied of one-twentieth of a flat plane, or 0.05, in consequence of its elongated, fusiform shape. This agrees well with experiments on the hulls of ships of "fair" shape.

The cross sectional area of the wings is also taken at 5 square inches, or 0.03472 of a square foot; but the coefficient here assumed is about one-seventh, or 0.15, in consequence of its shape, which is ogival, or rather something like only half of a Gothic arch.

The friction of the air is omitted. as being entirely too small to affect the results in a case where so many coefficients have to be approximated.

The angle of flight is ascertained by selecting from the table previously given of air reactions, the coefficient which will give the nearest approximation to a sustaining "lift" to support the weight, and from this angle the "drift" is obtained to calculate the resistance of the surface.

The velocity Y is in feet per minute, and the pressure P on a plane at right angles to the current by the Smeaton formula is in pounds per square foot. The following are the calculations:

20 miles per hour--V=1760 ft. P = 2 lbs.

Lift, 12°, 1.3 x 2 x 0.39 = 1.014 lbs. sustained.

 

	Resistance.	Power
Drift, 12°	1.3 x 2 x 0.0828 = 0.21520 lb.	x 1760 = 378.7 ft. lbs.
Body resistance,	0.03472 x 2 x 0.05 = 0.00347 lb.	x 1760 = 6.1 ft. lbs.
Edge wings,	0.03472 x 2 x 0.15 = 0.01040 lb.	x 1760 = 18.3 ft. lbs.
	0.22907 lb.	403.1 ft. lbs.

30 miles per hour--V=2640 ft. P = 4.5 lbs.

Lift, 5°, 1.3 x 4.5 x 0.173 = 1.012 lbs. sustained.

 

	Resistance.	Power
Drift, 5°	1.3 x 4.5 x 0.0152 = 0.08892 lb.	x 2640 = 234.7 ft. lbs.
Body resistance,	0.03472 x 4.5 x 0.05 = 0.00781 lb.	x 2640 = 20.6 ft. lbs.
Edge wings,	0.03472 x 4.5 x 0.15 = 0.02343 lb.	x 2640 = 61.9 ft. lbs.
	0.12016 lb.	317.2 ft. lbs.

40 miles per hour--V=3520 ft. P = 8 lbs.

Lift, 3°, 1.3 x 8 x 0.104 = 1.082 lbs. sustained.

 

	Resistance.	Power
Drift, 3°	1.3 x 8 x 0.005343 = 0.05647 lb.	x 3520 = 198.7 ft. lbs.
Body resistance,	0.03472 x 8 x 0.05 = 0.01389 lb.	x 3520= 48.9 ft. lbs.
Edge wings,	0.03472 x 8 x 0.15 = 0.04166 lb.	x 3520= 146.6 ft. lbs.
	0.11202 lb.	394.2 ft. lbs.

50 miles per hour--V=4400 ft. P = 12.5 lbs.

Lift, 2°, 1.3 x 12.5 x 0.07 = 1.137 lbs. sustained.

 

	Resistance.	Power
Drift, 2°	1.3 x 12.5 x 0.00244 = 0.03965 lb.	x 4400 = 174.5 ft. lbs.
Body resistance,	0.03472 x 12.5 x 0.05 = 0.02170 lb.	x 4400= 95.5 ft. lbs.
Edge wings,	0.03472 x 12.5 x 0.15 = 0.06510 lb.	x 4400= 286.5 ft. lbs.
	0.12645 lb.	556.5 ft. lbs.

60 miles per hour--V=5280 ft. P = 18 lbs.

Lift, 1 1/2°, 1.3 x 18 x 0.052 = 1.217 lbs. sustained.

 

	Resistance.	Power
Drift, 1 1/2°	1.32 x 18 x 0.00136 = 0.0318 lb.	x 5280 = 167.9 ft. lbs.
Body resistance,	0.03472 x 18 x 0.05 = 0.0312 lb.	x 5280 = 164.7 ft. lbs.
Edge wings,	0.03472 x 18 x 0.15 = 0.0937 lb.	x 5280 = 494.7 ft. lbs.
	0.1567 lb.	827.3 ft. lbs.

These figures are probably somewhat in excess of the real facts in consequence of the adoption of slightly excessive coefficients for the resistance of the body and wing edges, which coefficients in full flight may be as much as one-third less than those which have been estimated.

It will be noticed that, as the velocity and the consequent air pressures increase, the angle of incidence required to obtain a sustaining reaction or "lift" diminishes, and so does, therefore, the "drift" or horizontal component of the normal pressure, while the "hull resistance," consisting of that of the body and edges of the wings, is at the same time increasing. There will therefore be some angle at which these various factors will so combine as to give a minimum of resistance, and this is probably for most birds at an angle of about 3°, which in the case of our calculated pigeon requires a speed of 40 miles per hour in order to sustain the weight.

This angle of minimum resistance depends upon the relative proportions of the bird -- i.e., upon the ratio between his surface in square feet per pound of weight, and the cross section of his body and wings, as well as their coefficient of resistance; and so, while the angle may not vary greatly, it needs to be ascertained for each case. Mr. Drzewiecki has calculated that for an aeroplane exposing a cross sectional area of 1 per cent. of its sustaining area (instead of the 7 per cent. which the measurements show for the pigeon), the angle of minimum resistance would be 1° 50' 45", and that it would be the same for all velocities. It does not follow, however, that the minimum of power required will coincide with the minimum of resistance, for the latter increases as the square, while the power grows as the cube of the speed. The calculations, therefore, show that the minimum of resistance occurs at 40 miles per hour, while the minimum of work done in foot-pounds is found at 30 miles per hour, and these two favorable speeds are about those observed from railway trains, as habitually practiced by the domestic pigeon.

The estimates of the feet-pounds per minute indicate that the bird finds it less fatiguing to fly at 30 miles per hour than at 20; that his exertions are not much greater at 40 miles per hour, but that at 50 miles per hour he is expending rather more than his mean strength-the latter being probably about 425 foot-pounds per minute, nearly an average of the first four calculations, or about one-quarter of the maximum work done in rising, as estimated by Pénaud.

A flight of 60 miles within the hour is probably a severe exertion for the domestic pigeon, while the finer lines and greater endurance of the carrier pigeon enable him to maintain this speed for hours at a time; but there is reason to believe that this must be nearly the limit of his strength, and that homing birds who have made records of 70 and 75 miles per hour were materially aided by the wind.

The calculations therefore appear plausible, and to agree fairly well with the estimates arrived at with different methods by others. They indicate that if a flying machine can be built to be as efficient as the domestic pigeon its motor should develop one horse power for each 18 lbs. of its weight, provided it can give out momentarily about four times its normal energy, or that special devices, such as that of running down an incline or utilizing the wind, or some other contrivance are adopted to give it as tart and to enable it to rise upon the air.

The next question which the reader will probably want to ask, is as to the amount of supporting surfaces possessed by birds in proportion to their weight. Upon this point a good deal of information has been published; and in 1865 Mr. De Lucy greatly cheered aviators by publishing a paper in which he showed that the wing areas of flying animals diminish as the weight increases, from some 49 square feet to the pound in the gnat to 0.44 square feet to the pound in the Australian crane, and from which tables he inferred the broad law that the greater the weight and size of the Volant animal. the less relative wing surface it required red.

As thus stated, the assertion is misleading. For inasmuch as the supporting surfaces will increase as the square, and the weight will grow as the cube of the homologous dimensions, It was to be expected that wing surfaces would not increase in the same ratio as the weight if the strength of the parts remained the same; and in 1869 Hartings published some tables of birds, in which he compared the square root of the wing surface with the cube root of the weight, and showed that their ratio became what he considered a somewhat irregular constant. Subsequent measurements and tables by Professor Marey have shown that this statement of Hartings is also slightly misleading, inasmuch as the so-called constant varies from 1.69 to 3.13, so that no broad law can be laid down as to any fixed relation between the surfaces and weight of birds of various sizes. The fact seems to be that while their structures are governed by the laws which limit the strength of materials (bones, muscles, feathers, etc.), yet there are differences in the resulting stresses, and in the consequent efficiency of the birds themselves, who are thereby led to adopt slightly different modes of flight; and in 1884 Müllenhoff published an able paper, in which he divided flying animals into six series, in accordance with the ratio between their weight and their wing surface, as well as their methods of flight. As the tables of De Lucy, Hartings Marey and Müllenhoff are all easily accessible in print they will not be repeated here; but the following table is considered more valuable than any of them. It has been compiled from "L'Empire de l'air" of Mr. Mouillard, a very remarkable book, published in 1881, which contains descriptions of the flight of many birds and accurate measurements of their surfaces and weights.

 

TABLE OF SUPPORTING AREAS OF BIRDS.
Measured by L. P. Mouillard.
Compiled by S. Drzewiecki.

Scientific Name.	Common Name.	Sq. Ft. per Lb.	Lbs. per Sq. Ft.	Corresponding speed for a plane at 30 Miles per hr
Nyctinomous aegypticus	Bat	.64	0.131	15.9
Upupa epops	Peewit	3.62	0.276	23.1
Cotile rupestris	Swallow	3.62	0.276	23.1
Budytes flava	Wagtail	3.49	0.286	23.5
Galerita cristata I	Lark	3.18	0.315	24.6
Caprimulgus	Goatsucker	3.17	0.314	24.6
Galerita cristala II	Lark	3.06	0.327	25.1
Accipter nisus	Sparrow-hawk	3.00	0.333	25.3
Pteropus Geoflroyi	Bat	2.79	0.362	26.2
Coracias garrulus	Roller	2.76	0.363	26.5
Tringa canutus	Knot	2.64	0.380	27.0
Falco tinnunculus	Falcon	2.48	0.403	27.9
Passer domesticus I	Sparrow	2.42	0.414	28.2
Vanellus cristatus	Lapwing	2.40	0.417	28.3
Passer domesticus II	Sparrow	2.36	0.424	28.6
Cypselus apus	Martinet	2.35	0.426	28.6
Larus rnelanocephalus I	Gull	2.35	0.426	28.6
Glareola torquata	Glareola	2.32	0.431	28.8
Larus melanocephalus II	Gull	2.30	0.435	28.9
Turtur ægypticus	Egyptian Dove	2.27	0.441	29.2
Otus brachyotus	Owl	2.26	0.443	29.2
Strix flammea	Owl	2.26	0.443	29.2
Milvus ægypticus	Kite	2.19	0.457	29.7
Petrocincla cyanea	Blackbird	2.18	0.460	29.7
Alcedo hispada I	Kingfisher	2.11	0.475	30.3
Alcedo hispada II	Kingfisher	2.11	0.475	30.3
Buphus minutus	Crane	2.02	0.495	30.9
Scolopax gallinula I	Snipe	1.96	0.510	31.4
Ephialtes zorca	Scops	1.90	0.526	31.8
Alcedo hispida III	Kingfisher	1.87	0.535	32.1
Corvus ægypticus	Rook	1.74	0.575	33.3
Astur palumbarius	Goss-hawk	1.73	0.579	33.4
Ibis falcinellus	Ibis	1.66	0.603	34.1
Sturnus vulgaris	Starling	1.65	0.606	34.2
Scolopax capiensis	Snipe	1.65	0.606	34.2
Corvus corax	Raven	1.62	0.614	34.5
Scolopax gallinula II	Snipe	1.60	0.625	34.7
Philomachus pugnax	Water-fowl	1.48	0.634	36.1
Ardea nycticorax	Night Heron	1.43	0.700	36.7
Ciconia alba	Stork	1.40	0.715	37.1
Charadrius pluvialis	Plover	1.38	0.725	27.4
Columbia ægyptica I	Egyptian pigeon	1.37	0.730	37.5
Falco peregrinus	Falcon	1.29	0.775	38.6
Rallus aquaticus	Rail	1.28	0.781	38.8
Pandion fluvialis	Balbuzzard	1.26	0.795	39.2
Neophron percnopterus	Egyptian vulture	1.18	0.848	40.4
Columbia ægyptica II	Egyptian pigeon	1.13	0.885	41.3
Numenius arquatus	Cculis	1.11	0.901	41.7
Ortyx coturnix	Quail	1.08	0.927	42.3
Recurvirostra avocetta	Avocetta	1.05	0.954	42.8
OEdicnomus crepitans	Plover	0.926	1.079	43.6
Anas querquedula	Duck	0.864	1.158	44.2
Puffinus Kulhi	Shearwater	0.853	1.170	44.5
Gallinula chloropus	Water-hen	0.765	1.307	50.3
Numenius arquatus	Curlew	0.761	1.312	50.3
Pelecanus anocrotales	Gray Pelican	0.732	1.365	51.3
Gyps fulvus	Tawny Vulture	0.679	1.473	53.3
Otogyps auricularis	Oricou	0.664	1.473	53.9
Pterocles exustus	Running Pigeon	0.664	1.508	53.9
Procellaria gigantea	Giant Petrel	0.640	1.561	54.9
Anser sylvestris	Wild Goose	0.586	1.708	57.4
Anas clypeata, female	Duck	0.498	2.008	62.2
Anas clypeata, male	Duck	0.439	2.280	66.2

Mr. Mouillard adopted a more rational method than other observers. Instead of merely measuring the surface of the wings, he laid the bird upon its back on a sheet of paper, projected the entire outline, and then measured the total area from which it gains support. The compilation has been made by Mr. Drzeweickt for a paper presented to the lnternational Aeronautical Congress at Paris in 1889, in which he states the general law more accurately than his predecessors, by calling attention to the fact that the ratio of weight to surface will vary somewhat with the structure of the bird, and that the result will be that those possessing the lesser proportionate surface must fly faster in order to obtain an adequate support at the same angle of incidence.

I have added the last column in the table, showing the speed required to sustain the weight of a flat plane loaded to the same proportion of weight to surface as the bird, at an angle of incidence of 3°. This speed merely approximates to the real flight of the bird, because it takes no account of the concavity of the wings, which, as previously explained, increases the effective bearing surface of the animal; but it would require experimenting with each and every bird tabulated in order to give the true and varying coefficients.