In this figure the action of the wing is compared to the sculling of an oar, to which it bears a considerable resemblance.116 The one cone, viz., that with its base directed outwards, is represented at x b d. This cone corresponds to the area mapped out by the tip of the wing in the process of elevating. The second cone, viz., that with its base directed backwards, is represented at q p n. This cone corresponds to the area mapped out by the posterior margin of the wing in the process of propelling. The two cones are produced in virtue of the wing rotating on its root and along its anterior margin as it ascends and descends (fig. 80, p. 149; fig. 83, p. 158). The present figure (116) shows the double twisting action of the wing, the tip describing the figure-of-8 indicated at b e f g h d i j k l; the posterior margin describing the figure-of-8 indicated at p r n. It is in this manner the cross pulsation or wave referred to at p. 148 is produced. To represent the action of the wing the sculling oar (a b, x s, c d) must have a small scull (m n, q r, o p) working at right angles to it. This follows because the wing has to elevate as well as propel; the oar of a boat when employed as a scull only propelling. In order to elevate more effectually, the oars formed by the wings are made to oscillate on a level with and under the volant animal rather than above it; the posterior margins of the wings being made to oscillate on a level with and below the anterior margins (pp. 150, 151).
Borelli, and all who have written since his time, are unanimous in affirming that the horizontal transference of the body of the bird is due to the perpendicular vibration of the wings, and to the yielding of the posterior or flexible margins of the wings in an upward direction as the wings descend. I am, however, as already stated, disposed to attribute the transference, 1st, to the fact that the wings, both when elevated and depressed, leap forwards in curves, those curves uniting to form a continuous waved track; 2d, to the tendency which the body of the bird has to swing forwards, in a more or less horizontal direction, when once set in motion; 3d, to the construction of the wings (they are elastic helices or screws, which twist and untwist when they are made to vibrate, and tend to bear upwards and onwards any weight suspended from them); 4th, to the reaction of the air on the under surfaces of the wings, which always act as kites; 5th, to the ever-varying power with which the wings are urged, this being greatest at the beginning of the down stroke, and least at the end of the up one; 6th, to the contraction of the voluntary muscles and elastic ligaments; 7th, to the effect produced by the various inclined surfaces formed by the wings during their oscillations; 8th, to the weight of the bird—weight itself, when acting upon inclined planes (wings), becoming a propelling power, and so contributing to horizontal motion. This is proved by the fact that if a sea bird launches itself from a cliff with expanded motionless wings, it sails along for an incredible distance before it reaches the water (fig. 103, p. 186).
The authors who have adopted Borelli’s plan of artificial wing, and who have indorsed his mechanical views of the action of the wing most fully, are Chabrier, Straus-Durckheim, Girard, and Marey. Borelli’s artificial wing, as already explained (p. 220, fig. 113), consists of a rigid rod (e, r) in front, and a flexible sail (a, o) composed of feathers, behind. It acts upon the air, and the air acts upon it, as occasion demands.
Chabrier’s Views.—Chabrier states that the wing has only one period of activity—that, in fact, if the wing be suddenly lowered by the depressor muscles, it is elevated solely by the reaction of the air. There is one unanswerable objection to this theory—the bats and birds, and some, if not all the insects, have distinct elevator muscles. The presence of well-developed elevator muscles implies an elevating function, and, besides, we know that the insect, bat, and bird can elevate their wings when they are not flying, and when, consequently, no reaction of the air is induced.
Straus-Durckheim’s Views.—Durckheim believes the insect abstracts from the air by means of the inclined plane a component force (composant) which it employs to support and direct itself. In his Theology of Nature he describes a schematic wing as follows:—It consists of a rigid ribbing in front, and a flexible sail behind. A membrane so constructed will, according to him, be fit for flight. It will suffice if such a sail elevates and lowers itself successively. It will, of its own accord, dispose itself as an inclined plane, and receiving obliquely the reaction of the air, it transfers into tractile force a part of the vertical impulsion it has received. These two parts of the wing are, moreover, equally indispensable to each other. If we compare the schematic wing of Durckheim with that of Borelli they will be found to be identical, both as regards their construction and the manner of their application.
Professor Marey, so late as 1869, repeats the arguments and views of Borelli and Durckheim, with very trifling alterations. Marey describes two artificial wings, the one composed of a rigid rod and sail—the rod representing the stiff anterior margin of the wing; the sail, which is made of paper bordered with card-board, the flexible posterior portion. The other wing consists of a rigid nervure in front and behind of thin parchment which supports fine rods of steel. He states, that if the wing only elevates and depresses itself, “the resistance of the air is sufficient to produce all the other movements. In effect the wing of an insect has not the power of equal resistance in every part. On the anterior margin the extended nervures make it rigid, while behind it is fine and flexible. During the vigorous depression of the wing the nervure has the power of remaining rigid, whereas the flexible portion, being pushed in an upward direction on account of the resistance it experiences from the air, assumes an oblique position, which causes the upper surface of the wing to look forwards.” . . . “At first the plane of the wing is parallel with the body of the animal. It lowers itself—the front part of the wing strongly resists, the sail which follows it being flexible yields. Carried by the ribbing (the anterior margin of the wing) which lowers itself, the sail or posterior margin of the wing being raised meanwhile by the air, which sets it straight again, the sail will take an intermediate position, and incline itself about 45° plus or minus according to circumstances. The wing continues its movements of depression inclined to the horizon, but the impulse of the air which continues its effect, and naturally acts upon the surface which it strikes, has the power of resolving itself into two forces, a vertical and a horizontal force, the first suffices to raise the animal, the second to move it along.”117 The reverse of this, Marey states, takes place during the elevation of the wing—the resistance of the air from above causing the upper surface of the wing to look backwards. The fallaciousness of this reasoning has been already pointed out, and need not be again referred to. It is not a little curious that Borelli’s artificial wing should have been reproduced in its integrity at a distance of nearly two centuries.
The Author’s Views:—his Method of constructing and applying Artificial Wings as contra-distinguished from that of Borelli, Chabrier, Durckheim, Marey, etc.—The artificial wings which I have been in the habit of making for several years differ from those recommended by Borelli, Durckheim, and Marey in four essential points:—
1st, The mode of construction.
2d, The manner in which they are applied to the air.
3d, The nature of the powder employed.
4th, The necessity for adapting certain elastic substances to the root of the wing if in one piece, and to the root and the body of the wing if in several pieces.
And, first, as to the manner of construction.
Borelli, Durckheim, and Marey maintain that the anterior margin of the wing should be rigid; I, on the other hand, believe that no part of the wing whatever should be rigid, not even the anterior margin, and that the pinion should be flexible and elastic throughout.
That the anterior margin of the wing should not be composed of a rigid rod may, I think, be demonstrated in a variety of ways. If a rigid rod be made to vibrate by the hand the vibration is not smooth and continuous; on the contrary, it is irregular and jerky, and characterized by two halts or pauses (dead points), the one occurring at the end of the up stroke, the other at the end of the down stroke. This mechanical impediment is followed by serious consequences as far as power and speed are concerned—the slowing of the wing at the end of the down and up strokes involving a great expenditure of power and a disastrous waste of time. The wing, to be effective as an elevating and propelling organ, should have no dead points, and should be characterized by a rapid winnowing or fanning motion. It should reverse and reciprocate with the utmost steadiness and smoothness—in fact, the motions should appear as continuous as those of a fly-wheel in rapid motion: they are so in the insect (figs. 64, 65, and 66, p. 139).
To obviate the difficulty in question, it is necessary, in my opinion, to employ a tapering elastic rod or series of rods bound together for the anterior margin of the wing.
If a longitudinal section of bamboo cane, ten feet in length, and one inch in breadth (fig. 117), be taken by the extremity and made to vibrate, it will be found that a wavy serpentine motion is produced, the waves being greatest when the vibration is slowest (fig. 118), and least when it is most rapid (fig. 119). It will further be found that at the extremity of the cane where the impulse is communicated there is a steady reciprocating movement devoid of dead points. The continuous movement in question is no doubt due to the fact that the different portions of the cane reverse at different periods—the undulations induced being to an interrupted or vibratory movement very much what the continuous play of a fly-wheel is to a rotatory motion.
The Wave Wing of the Author.—If a similar cane has added to it, tapering rods of whalebone, which radiate in an outward direction to the extent of a foot or so, and the whalebones be covered by a thin sheet of india-rubber, an artificial wing, resembling the natural one in all its essential points, is at once produced (fig. 120). I propose to designate this wing, from the peculiarities of its movements, the wave wing (fig. 121). If the wing referred to (fig. 121) be made to vibrate at its root, a series of longitudinal (c d e) and transverse (f g h) waves are at once produced; the one series running in the direction of the length of the wing, the other in the direction of its breadth (vide p. 148). This wing further twists and untwists, figure-of-8 fashion, during the up and down strokes, as shown at fig. 122, p. 239 (compare with figs. 82 and 83, p. 158; fig. 86, p. 161; and fig. 103, p. 186). There is, moreover, a continuous play of the wing; the down stroke gliding into the up one, and vice versâ, which clearly shows that the down and up strokes are parts of one whole, and that neither is perfect without the other.
Fig. 117.
Fig. 117.—Represents a longitudinal section of bamboo cane ten feet long, and one inch wide.—Original.
Fig. 118.
Fig. 118.—The appearance presented by the same cane when made to vibrate by the hand. The cane vibrates on either side of a given line (x x), and appears as if it were in two places at the same time, viz., c and f, g and d, e and h. It is thus during its vibration thrown into figures-of-8 or opposite curves.—Original.
Fig. 119.
Fig. 119.—The same cane when made to vibrate more rapidly. In this case the waves made by the cane are less in size, but more numerous. The cane is seen alternately on either side of the line x x, being now at i now at m, now at n now at j, now at k now at o, now at p now at l. The cane, when made to vibrate, has no dead points, a circumstance due to the fact that no two parts of it reverse or change their curves at precisely the same instant. This curious reciprocating motion enables the wing to seize and disengage itself from the air with astonishing rapidity.—Original.
Fig. 120.
Fig. 120.—The same cane with a flexible elastic curtain or fringe added to it. The curtain consists of tapering whalebone rods covered with a thin layer of india-rubber. a b anterior margin of wing, c d posterior ditto.—Original.
Fig. 121.
Fig. 121.—Gives the appearance presented by the artificial wing (fig. 120) when made to vibrate by the hand. It is thrown into longitudinal and transverse waves. The longitudinal waves are represented by the arrows c d e, and the transverse waves by the arrows f g h. A wing constructed on this principle gives a continuous elevating and propelling power. It develops figure-of-8 curves during its action in longitudinal, transverse, and oblique directions. It literally floats upon the air. It has no dead points—is vibrated with amazingly little power, and has apparently no slip. It can fly in an upward, downward, or horizontal direction by merely altering its angle of inclination to the horizon. It is applied to the air by an irregular motion—the movement being most sudden and vigorous always at the beginning of the down stroke.—Original.
The wave wing is endowed with the very remarkable property that it will fly in any direction, demonstrating more or less clearly that flight is essentially a progressive movement, i.e. a horizontal rather than a vertical movement. Thus, if the anterior or thick margin of the wing be directed upwards, so that the under surface of the wing makes a forward angle with the horizon of 45°, the wing will, when made to vibrate by the hand, fly with an undulating motion in an upward direction, like a pigeon to its dovecot. If the under surface of the wing makes no angle, or a very small forward angle, with the horizon, it will dart forward in a series of curves in a horizontal direction, like a crow in rapid horizontal flight. If the anterior or thick margin of the wing be directed downwards, so that the under surface of the wing makes a backward angle of 45° with the horizon, the wing will describe a waved track, and fly downwards, as a sparrow from a house-top or from a tree (p. 230). In all those movements progression is a necessity. The movements are continuous gliding forward movements. There is no halt or pause between the strokes, and if the angle which the under surface of the wing makes with the horizon be properly regulated, the amount of steady tractile and buoying power developed is truly astonishing. This form of wing, which may be regarded as the realization of the figure-of-8 theory of flight, elevates and propels both during the down and up strokes, and its working is accompanied with almost no slip. It seems literally to float upon the air. No wing that is rigid in the anterior margin can twist and untwist during its action, and produce the figure-of-8 curves generated by the living wing. To produce the curves in question, the wing must be flexible, elastic, and capable of change of form in all its parts. The curves made by the artificial wing, as has been stated, are largest when the vibration is slow, and least when it is quick. In like manner, the air is thrown into large waves by the slow movement of a large wing, and into small waves by the rapid movement of a smaller wing. The size of the wing curves and air waves bear a fixed relation to each other, and both are dependent on the rapidity with which the wing is made to vibrate. This is proved by the fact that insects, in order to fly, require, as a rule, to drive their small wings with immense velocity. It is further proved by the fact that the small humming-bird, in order to keep itself stationary before a flower, requires to oscillate its tiny wings with great rapidity, whereas the large humming-bird (Patagona gigas), as was pointed out by Darwin, can attain the same object by flapping its large wings with a very slow and powerful movement. In the larger birds the movements are slowed in proportion to the size, and more especially in proportion to the length of the wing; the cranes and vultures moving the wings very leisurely, and the large oceanic birds dispensing in a great measure with the flapping of the wings, and trusting for progression and support to the wings in the expanded position.
Fig. 122.
Fig. 122.—Elastic spiral wing, which twists and untwists during its action, to form a mobile helix or screw. This wing is made to vibrate by steam by a direct piston action, and by a slight adjustment can be propelled vertically, horizontally, or at any degree of obliquity.
a, b, Anterior margin of wing, to which the neuræ or ribs are affixed. c, d, Posterior margin of wing crossing anterior one. x, Ball-and-socket joint at root of wing; the wing being attached to the side of the cylinder by the socket. t, Cylinder. r, r, Piston, with cross heads (w, w) and piston head (s). o, o, Stuffing boxes. e, f, Driving chains. m, Superior elastic band, which assists in elevating the wing. n, Inferior elastic band, which antagonizes m. The alternate stretching of the superior and inferior elastic bands contributes to the continuous play of the wing, by preventing dead points at the end of the down and up strokes. The wing is free to move in a vertical and horizontal direction and at any degree of obliquity.—Original.
This leads me to conclude that very large wings may be driven with a comparatively slow motion, a matter of great importance in artificial flight secured by the flapping of wings.
How to construct an artificial Wave Wing on the Insect type.—The following appear to me to be essential features in the construction of an artificial wing:—
The wing should be of a generally triangular shape.
It should taper from the root towards the tip, and from the anterior margin in the direction of the posterior margin.
It should be convex above and concave below, and slightly twisted upon itself.
It should be flexible and elastic throughout, and should twist and untwist during its vibration, to produce figure-of-8 curves along its margins and throughout its substance.
Such a wing is represented at fig. 122, p. 239.
If the wing is in more than one piece, joints and springs require to be added to the body of the pinion.
In making a wing in one piece on the model of the insect wing, such as that shown at fig. 122 (p. 239), I employ one or more tapering elastic reeds, which arch from above downwards (a b) for the anterior margin. To this I add tapering elastic reeds, which radiate towards the tip of the wing, and which also arch from above downwards (g, h, i). These latter are so arranged that they confer a certain amount of spirality upon the wing; the anterior (a b) and posterior (c d) margins being arranged in different planes, so that they appear to cross each other. I then add the covering of the wing, which may consist of india-rubber, silk, tracing cloth, linen, or any similar substance.
If the wing is large, I employ steel tubes, bent to the proper shape. In some cases I secure additional strength by adding to the oblique ribs or stays (g h i of fig. 122) a series of very oblique stays, and another series of cross stays, as shown at m and a, n, o, p, q of fig. 123, p. 241.
This form of wing is made to oscillate upon two centres viz. the root and anterior margin, to bring out the peculiar eccentric action of the pinion.
If I wish to produce a very delicate light wing, I do so by selecting a fine tapering elastic reed, as represented at a b of fig. 124.
To this I add successive layers (i, h, g, f, e) of some flexible material, such as parchment, buckram, tracing cloth, or even paper. As the layers overlap each other, it follows that there are five layers at the anterior margin (a b), and only one at the posterior (c d). This form of wing is not twisted upon itself structurally, but it twists and untwists, and becomes a true screw during its action.
Fig. 123.
Fig. 123.—Artificial Wing with Perpendicular (r s) and Horizontal (t u) Elastic Bands attached to ferrule (w).
a, b, Strong elastic reed, which tapers towards the tip of the wing.
d, e, f, h, i, j, k, Tapering curved reeds, which run obliquely from the anterior to the posterior margin of the wing, and which radiate towards the tip.
m, Similar curved reeds, which run still more obliquely.
a, n, o, p, q, Tapering curved reeds, which run from the anterior margin of the wing, and at right angles to it. These support the two sets of oblique reeds, and give additional strength to the anterior margin.
x, Ball-and-socket joint, by which the root of the wing is attached to the cylinder, as in fig. 122, p. 239.—Original.
Fig. 124.
Fig. 124.—Flexible elastic wing with tapering elastic reed (a b) running along anterior margin.
c, d, Posterior margin of wing. i, Portion of wing composed of one layer of flexible material. h, Portion of wing composed of two layers. g, Portion of wing composed of three layers. f, Portion of wing composed of four layers. e, Portion of wing composed of five layers. x, Ball-and-socket joint at root of wing.—Original.
Fig. 125.
Fig. 125.—Flexible valvular wing with india-rubber springs attached to its root.
a, b, Anterior margin of wing, tapering and elastic. c, d, Posterior margin of wing, elastic. f, f, f, Segments which open during the up stroke and close during the down, after the manner of valves. These are very narrow, and open and close instantly. x, Universal joint. m, Superior elastic band. n, Ditto inferior. o, Ditto anterior. p, q, Ditto oblique. r, Ring into which the elastic bands are fixed.—Original.
How to construct a Wave Wing which shall evade the superimposed Air during the Up Stroke.—To construct a wing which shall elude the air during the up stroke, it is necessary to make it valvular, as shown at fig. 125, p. 241.
This wing, as the figure indicates, is composed of numerous narrow segments (f f f), so arranged that the air, when the wing is made to vibrate, opens or separates them at the beginning of the up stroke, and closes or brings them together at the beginning of the down stroke.
The time and power required for opening and closing the segments is comparatively trifling, owing to their extreme narrowness and extreme lightness. The space, moreover, through which they pass in performing their valvular action is exceedingly small. The wing under observation is flexible and elastic throughout, and resembles in its general features the other wings described.
I have also constructed a wing which is self-acting in another sense. This consists of two parts—the one part being made of an elastic reed, which tapers towards the extremity; the other of a flexible sail. To the reed, which corresponds to the anterior margin of the wing, delicate tapering reeds are fixed at right angles; the principal and subordinate reeds being arranged on the same plane. The flexible sail is attached to the under surface of the principal reed, and is stiffer at its insertion than towards its free margin. When the wing is made to ascend, the sail, because of the pressure exercised upon its upper surface by the air, assumes a very oblique position, so that the resistance experienced by it during the up stroke is very slight. When, however, the wing descends, the sail instantly flaps in an upward direction, the subordinate reeds never permitting its posterior or free margin to rise above its anterior or fixed margin. The under surface of the wing consequently descends in such a manner as to present a nearly flat surface to the earth. It experiences much resistance from the air during the down stroke, the amount of buoyancy thus furnished being very considerable. The above form of wing is more effective during the down stroke than during the up one. It, however, elevates and propels during both, the forward travel being greatest during the down stroke.
Compound Wave Wing of the Author.—In order to render the movements of the wing as simple as possible, I was induced to devise a form of pinion, which for the sake of distinction I shall designate the Compound Wave Wing. This wing consists of two wave wings united at the roots, as represented at fig. 126. It is impelled by steam, its centre being fixed to the head of the piston by a compound joint (x), which enables it to move in a circle, and to rotate along its anterior margin (a b c d; A, A´) in the direction of its length. The circular motion is for steering purposes only. The wing rises and falls with every stroke of the piston, and the movements of the piston are quickened during the down stroke, and slowed during the up one.
During the up stroke of the piston the wing is very decidedly convex on its upper surface (a b c d; A, A´), its under surface being deeply concave and inclined obliquely upwards and forwards. It thus evades the air during the up stroke. During the down stroke of the piston the wing is flattened out in every direction, and its extremities twisted in such a manner as to form two screws, as shown at a´ b´ c´ d´; e´ f´ g´ h´; B, B´ of figure. The active area of the wing is by this means augmented, the wing seizing the air with great avidity during the down stroke. The area of the wing may be still further increased and diminished during the down and up strokes by adding joints to the body of the wing. The degree of convexity given to the upper surface of the wing can be increased or diminished at pleasure by causing a cord (i j; A, A´) and elastic band (k) to extend between two points, which may vary according to circumstances. The wing is supplied with vertical springs, which assist in slowing and reversing it towards the end of the down and up strokes, and these, in conjunction with the elastic properties of the wing itself, contribute powerfully to its continued play. The compound wave wing produces the currents on which it rises. Thus during the up stroke it draws after it a current, which being met by the wing during its descent, confers additional elevating and propelling power. During the down stroke the wing in like manner draws after it a current which forms an eddy, and on this eddy the wing rises, as explained at p. 253, fig. 129. The ascent of the wing is favoured by the superimposed air playing on the upper surface of the posterior margin of the organ, in such a manner as to cause the wing to assume a more and more oblique position with reference to the horizon. This change in the plane of the wing enables its upper surface to avoid the superincumbent air during the up stroke, while it confers upon its under surface a combined kite and parachute action. The compound wave wing leaps forward in a curve both during the down and up strokes, so that the wing during its vibration describes a waved track, as shown at a, c, e, g, i of fig. 81, p. 157. The compound wave wing possesses most of the peculiarities of single wings when made to vibrate separately. It forms a most admirable elevator and propeller, and has this advantage over ordinary wings, that it can be worked without injury to itself, when the machine which it is intended to elevate is resting on the ground. Two or more compound wave wings may be arranged on the same plane, or superimposed, and made to act in concert. They may also by a slight modification be made to act horizontally instead of vertically. The length of the stroke of the compound wave wing is determined in part, though not entirely by the stroke of the piston—the extremities of the wing, because of their elasticity, moving through a greater space than the centre of the wing. By fixing the wing to the head of the piston all gearing apparatus is avoided, and the number of joints and working points reduced—a matter of no small importance when it is desirable to conserve the motor power and keep down the weight.
How to apply Artificial Wings to the Air.—Borelli, Durckheim, Marey, and all the writers with whom I am acquainted, assert that the wing should be made to vibrate vertically. I believe that if the wing be in one piece it should be made to vibrate obliquely and more or less horizontally. If, however, the wing be made to vibrate vertically, it is necessary to supply it with a ball-and-socket joint, and with springs at its root (m n of fig. 125, p. 241), to enable it to leap forward in a curve when it descends, and in another and opposite curve when it ascends (vide a, c, e, g, i of fig. 81, p. 157). This arrangement practically converts the vertical vibration into an oblique one. If this plan be not adopted, the wing is apt to foul at its tip. In applying the wing to the air it ought to have a figure-of-8 movement communicated to it either directly or indirectly. It is a peculiarity of the artificial wing properly constructed (as it is of the natural wing), that it twists and untwists and makes figure-of-8 curves during its action (see a b, c d of fig. 122, p. 239), this enabling it to seize and let go the air with wonderful rapidity, and in such a manner as to avoid dead points. If the wing be in several pieces, it may be made to vibrate more vertically than a wing in one piece, from the fact that the outer half of the pinion moves forwards and backwards when the wing ascends and descends so as alternately to become a short and a long lever; this arrangement permitting the wing to avoid the resistance experienced from the air during the up stroke, while it vigorously seizes the air during the down stroke.
If the body of a flying animal be in a horizontal position, a wing attached to it in such a manner that its under surface shall look forwards, and make an upward angle of 45° with the horizon is in a position to be applied either vertically (figs. 82 and 83, p. 158), or horizontally (figs. 67, 68, 69, and 70, p. 141). Such, moreover, is the conformation of the shoulder-joint in insects, bats, and birds, that the wing can be applied vertically, horizontally, or at any degree of obliquity without inconvenience.118 It is in this way that an insect which may begin its flight by causing its wings to make figure-of-8 horizontal loops (fig. 71, p. 144), may gradually change the direction of the loops, and make them more and more oblique until they are nearly vertical (fig. 73, p. 144). In the beginning of such flight the insect is screwed nearly vertically upwards; in the middle of it, it is screwed upwards and forwards; whereas, towards the end of it, the insect advances in a waved line almost horizontally (see q´, r´, s´, t´ of fig. 72, p. 144). The muscles of the wing are so arranged that they can propel it in a horizontal, vertical, or oblique direction. It is a matter of the utmost importance that the direction of the stroke and the nature of the angles made by the surface of the wing during its vibration with the horizon be distinctly understood; as it is on these that all flying creatures depend when they seek to elude the upward resistance of the air, and secure a maximum of elevating and propelling power with a minimum of slip.
As to the nature of the Forces required for propelling Artificial Wings.—Borelli, Durckheim, and Marey affirm that it suffices if the wing merely elevates and depresses itself by a rhythmical movement in a perpendicular direction; while Chabrier is of opinion that a movement of depression only is required. All those observers agree in believing that the details of flight are due to the reaction of the air on the surface of the wing. Repeated experiment has, however, convinced me that the artificial wing must be thoroughly under control, both during the down and up strokes—the details of flight being in a great measure due to the movements communicated to the wing by an intelligent agent. In order to reproduce flight by the aid of artificial wings, I find it necessary to employ a power which varies in intensity at every stage of the down and up strokes. The power which suits best is one which is made to act very suddenly and forcibly at the beginning of the down stroke, and which gradually abates in intensity until the end of the down stroke, where it ceases to act in a downward direction. The power is then made to act in an upward direction, and gradually to decrease until the end of the up stroke. The force is thus applied more or less continuously; its energy being increased and diminished according to the position of the wing, and the amount of resistance which it experiences from the air. The flexible and elastic nature of the wave wing, assisted by certain springs to be presently explained, insure a continuous vibration where neither halts nor dead points are observable. I obtain the varying power required by a direct piston action, and by working the steam expansively. The power employed is materially assisted, particularly during the up stroke, by the reaction of the air and the elastic structures about to be described. An artificial wing, propelled and regulated by the forces recommended, is in some respects as completely under control as the wing of the insect, bat, or bird.
Necessity for supplying the Root of Artificial Wings with Elastic Structures in imitation of the Muscles and Elastic Ligaments of Flying Animals.—Borelli, Durckheim, and Marey, who advocate the perpendicular vibration of the wing, make no allowance, so far as I am aware, for the wing leaping forward in curves during the down and up strokes. As a consequence, the wing is jointed in their models to the frame by a simple joint which moves only in one direction, viz., from above downwards, and vice versâ. Observation and experiment have fully satisfied me that an artificial wing, to be effective as an elevator and propeller, ought to be able to move not only in an upward and downward direction, but also in a forward, backward, and oblique direction; nay, more, that it should be free to rotate along its anterior margin in the direction of its length; in fact, that its movements should be universal. Thus it should be able to rise or fall, to advance or retire, to move at any degree of obliquity, and to rotate along its anterior margin. To secure the several movements referred to I furnish the root of the wing with a ball-and-socket joint, i.e., a universal joint (see x of fig. 122, p. 239). To regulate the several movements when the wing is vibrating, and to confer on the wing the various inclined surfaces requisite for flight, as well as to delegate as little as possible to the air, I employ a cross system of elastic bands. These bands vary in length, strength, and direction, and are attached to the anterior margin of the wing (near its root), and to the cylinder (or a rod extending from the cylinder) of the model (vide m, n of fig. 122, p. 239). The principal bands are four in number—a superior, inferior, anterior, and posterior. The superior band (m) extends between the upper part of the cylinder of the model, and the upper surface of the anterior margin of the wing; the inferior band (n) extending between the under part of the cylinder or the boiler and the inferior surface of the anterior margin of the pinion. The anterior and posterior bands are attached to the anterior and posterior portions of the wing and to rods extending from the centre of the anterior and posterior portions of the cylinder. Oblique bands are added, and these are so arranged that they give to the wing during its descent and ascent the precise angles made by the wing with the horizon in natural flight. The superior bands are stronger than the inferior ones, and are put upon the stretch during the down stroke. Thus they help the wing over the dead point at the end of the down stroke, and assist, in conjunction with the reaction obtained from the air, in elevating it. The posterior bands are stronger than the anterior ones to restrain within certain limits the great tendency which the wing has to leap forward in curves towards the end of the down and up strokes. The oblique bands, aided by the air, give the necessary degree of rotation to the wing in the direction of its length. This effect can, however, also be produced independently by the four principal bands. From what has been stated it will be evident that the elastic bands exercise a restraining influence, and that they act in unison with the driving power and with the reaction supplied by the air. They powerfully contribute to the continuous vibration of the wing, the vibration being peculiar in this that it varies in rapidity at every stage of the down and up strokes. I derive the motor power, as has been stated, from a direct piston action, the piston being urged either by steam worked expansively or by the hand, if it is merely a question of illustration. In the hand models the “muscular sense” at once informs the operator as to what is being done. Thus if one of the wave wings supplied with a ball-and-socket joint, and a cross system of elastic bands as explained, has a sudden vertical impulse communicated to it at the beginning of the down stroke, the wing darts downwards and forwards in a curve (vide a c, of fig. 81, p. 157), and in doing so it elevates and carries the piston and cylinder forwards. The force employed in depressing the wing is partly expended in stretching the superior elastic band, the wing being slowed towards the end of the down stroke. The instant the depressing force ceases to act, the superior elastic band contracts and the air reacts; the two together, coupled with the tendency which the model has to fall downwards and forwards during the up stroke, elevating the wing. The wing when it ascends describes an upward and forward curve as shown at c e of fig. 81, p. 157. The ascent of the wing stretches the inferior elastic band in the same way that the descent of the wing stretched the superior band. The superior and inferior elastic bands antagonize each other and reciprocate with vivacity. While those changes are occurring the wing is twisting and untwisting in the direction of its length and developing figure-of-8 curves along its margins (p. 239, fig. 122, a b, c d), and throughout its substance similar to what are observed under like circumstances in the natural wing (vide fig. 86, p. 161; fig. 103, p. 186). The angles, moreover, made by the under surface of the wing with the horizon during the down and up strokes are continually varying—the wing all the while acting as a kite, which flies steadily upwards and forwards (fig. 88, p. 166). As the elastic bands, as has been partly explained, are antagonistic in their action, the wing is constantly oscillating in some direction; there being no dead point either at the end of the down or up strokes. As a consequence, the curves made by the wing during the down and up strokes respectively, run into each other to form a continuous waved track, as represented at fig. 81, p. 157, and fig. 88, p. 166. A continuous movement begets a continuous buoyancy; and it is quite remarkable to what an extent, wings constructed and applied to the air on the principles explained, elevate and propel—how little power is required, and how little of that power is wasted in slip.