Part 15

The loops made by the wing of the insect, owing to the more oblique stroke, are more horizontal than those made by the wing of the bat and bird. The principle is, however, in both cases the same, the loops ultimately terminating in a waved track. The impulse is communicated to the insect wing at the heavy parts of the loops _a b c d e f g h i j k l m n_ of fig. 71; the waved tracks being indicated at _p q r s t_ of the same figure. The recoil obtained from the air is represented at corresponding letters of fig. 72, the body of the insect being carried along the curve indicated by the dotted line. The impulse is communicated to the wing of the bat and bird at the heavy part of the loops _a b c d e f g h i j k l m n o_ of fig. 73, the waved track being indicated at _p s t u v w_ of this figure. When the horizontal speed attained is high, the wing is successively and rapidly brought into contact with innumerable columns of undisturbed air. It, consequently, is a matter of indifference whether the wing is carried at a high speed against undisturbed air, or whether it operates upon air travelling at a high speed (as, _e.g._ the artificial currents produced by the rapidly reciprocating action of the wing). The result is the same in both cases, inasmuch as a certain quantity of air is worked up under the wing, and the necessary degree of support and progression extracted from it. It is, therefore, quite correct to state, that as the horizontal speed of the body increases, the reciprocating action of the wing decreases; and _vice versâ_. In fact the reciprocating and non-reciprocating action of the wing in such cases is purely a matter of speed. If the travel of the wing is greater than the horizontal travel of the body, then the figure-of-8 and the reciprocating power of the wing will be more or less perfectly developed, according to circumstances. If, however, the horizontal travel of the body is greater than that of the wing, then it follows that no figure-of-8 will be described by the wing; that the wing will not reciprocate to any marked extent; and that the organ will describe a waved track, the curves of which will become less and less abrupt, _i.e._ longer and longer in proportion to the speed attained. The more vertical direction of the loops formed by the wing of the bat and bird will readily be understood by referring to figs. 74 and 75 (p. 145), which represent the wing of the bird making the down and up strokes, and in the act of being extended and flexed. (Compare with figs. 64, 65, and 66, p. 139; and figs. 67, 68, 69, and 70, p. 141.)

The down and up strokes are compound movements,--the termination of the down stroke embracing the beginning of the up stroke; the termination of the up stroke including the beginning of the down stroke. This is necessary in order that the down and up strokes may glide into each other in such a manner as to prevent jerking and unnecessary retardation.

_The Margins of the Wing thrown into opposite Curves during Extension and Flexion._--The anterior or thick margin of the wing, and the posterior or thin one, form different curves, similar in all respects to those made by the body of the fish in swimming (see fig. 32, p. 68). These curves may, for the sake of clearness, be divided into axillary and distal curves, the former occurring towards the root of the wing, the latter towards its extremity. The curves (axillary and distal) found on the anterior margin of the wing are always the converse of those met with on the posterior margin, _i.e._ if the convexity of the anterior axillary curve be directed downwards, that of the posterior axillary curve is directed upwards, and so of the anterior and posterior distal curves. The two curves (axillary and distal), occurring on the anterior margin of the wing, are likewise antagonistic, the convexity of the axillary curve being always directed downwards, when the convexity of the distal one is directed upwards, and _vice versâ_. The same holds true of the axillary and distal curves occurring on the posterior margin of the wing. The anterior axillary and distal curves completely reverse themselves during the acts of extension and flexion, and so of the posterior axillary and distal curves (figs. 76, 77, and 78). This antagonism in the axillary and distal curves found on the anterior and posterior margins of the wing is referable in the bat and bird to changes induced in the bones of the wing in the acts of flexion and extension. In the insect it is due to a twisting which occurs at the root of the wing and to the reaction of the air.

_The Tip of the Bat and Bird’s Wing describes an Ellipse._--The movements of the wrist are always the converse of those occurring at the elbow-joint. Thus in the bird, during extension, the elbow and bones of the forearm are elevated, and describe one side of an ellipse, while the wrist and bones of the hand are depressed, and describe the side of another and opposite ellipse. These movements are reversed during flexion, the elbow being depressed and carried backwards, while the wrist is elevated and carried forwards (fig. 79).

_The Wing capable of Change of Form in all its Parts._--From this description it follows that when the different portions of the anterior margin are elevated, corresponding portions of the posterior margin are depressed; the different parts of the wing moving in opposite directions, and playing, as it were, at cross purposes for a common good; the object being to rotate or screw the wing down upon the wind at a gradually increasing angle during extension, and to rotate it in an opposite direction and withdraw it at a gradually decreasing angle during flexion. It also happens that the axillary and distal curves co-ordinate each other and bite alternately, the distal curve posteriorly seizing the air in extreme extension with its concave surface (while the axillary curve relieves itself by presenting its convex surface); the axillary curve, on the other hand, biting during flexion with its concave surface (while the distal one relieves itself by presenting its convex one). The wing may therefore be regarded as exercising a fourfold function, the pinion in the bat and bird being made to move from within outwards, and from above downwards in the down stroke, during extension; and from without inwards, and from below upwards, in the up stroke, during flexion.

_The Wing during its Vibration produces a Cross Pulsation._--The oscillation of the wing on two separate axes--the one running parallel with the body of the bird, the other at right angles to it (fig. 80, _a b_, _c d_)--is well worthy of attention, as showing that the wing attacks the air, on which it operates in every direction, and at almost the same moment, viz. from within outwards, and from above downwards, during the down stroke; and from without inwards, and from below upwards, during the up stroke. As a corollary to the foregoing, the wing may be said to agitate the air in two principal directions, viz. from within outwards and downwards, or the converse; and from behind forwards, or the converse; the agitation in question producing two powerful pulsations, a vertical and a horizontal. The wing when it ascends and descends produces artificial currents which increase its elevating and propelling power. The power of the wing is further augmented by similar currents developed during its extension and flexion. The movement of one part of the wing contributes to the movement of every other part in continuous and uninterrupted succession. As the curves of the wing glide into each other when the wing is in motion, so the one pulsation merges into the other by a series of intermediate and lesser pulsations.

The vertical and horizontal pulsations occasioned by the wing in action may be fitly represented by wave-tracks running at right angles to each other, the vertical wave-track being the more distinct.

_Compound Rotation of the Wing._--To work the tip and posterior margin of the wing independently and yet simultaneously, two axes are necessary, one axis (the short axis) corresponding to the root of the wing and running across it; the second (the long axis) corresponding to the anterior margin of the wing, and running in the direction of its length. The long and short axes render the movements of the wing eccentric in character. In the wing of the bird the movements of the primary or rowing feathers are also eccentric, the shaft of each feather being placed nearer the anterior than the posterior margin; an arrangement which enables the feathers to open up and separate during flexion and the up stroke, and approximate and close during extension and the down one.

These points are illustrated at fig. 80, where _a b_ represents the short axis (root of wing) with a radius _e f_; _c d_ representing the long axis (anterior margin of wing) with a radius _g p_.

Fig. 80 also shows that, in the wing of the bird, the individual, primary, secondary, and tertiary feathers have each what is equivalent to a long and a short axis. Thus the primary, secondary, and tertiary feathers marked _h_, _i_, _j_, _k_, _l_ are capable of rotating on their long axes (_r s_), and upon their short axes (_m n_). The feathers rotate upon their long axes in a direction from below upwards during the down stroke, to make the wing impervious to air; and from above downwards during the up stroke, to enable the air to pass through it. The primary, secondary, and tertiary feathers have thus a distinctly valvular action.[76] The feathers rotate upon their short axes (_m n_) during the descent and ascent of the wing, the tip of the feathers rising slightly during the descent of the pinion, and falling during its ascent. The same movement virtually takes place in the posterior margin of the wing of the insect and bat.

[76] The degree of valvular action varies according to circumstances.

_The Wing vibrates unequally with reference to a given Line._--The wing, during its vibration, descends further below the body than it rises above it. This is necessary for _elevating purposes_. In like manner the posterior margin of the wing (whatever the position of the organ) descends further below the anterior margin than it ascends above it. This is requisite for _elevating and propelling purposes_; the under surface of the wing being always presented at a certain upward angle to the horizon, and acting as a true kite (figs. 82 and 83, p. 158. Compare with fig. 116, p. 231). If the wing oscillated equally above and beneath the body, and if the posterior margin of the wing vibrated equally above and below the line formed by the anterior margin, much of its elevating and propelling power would be sacrificed. The tail of the fish oscillates on either side of a given line, but it is otherwise with the wing of a flying animal. The fish is of nearly the same specific gravity as the water, so that the tail may be said only to propel. The flying animal, on the other hand, is very much heavier than the air, so that the wing requires both to propel and _elevate_. The wing, to be effective as an _elevating organ_, must consequently be vibrated rather below than above the centre of gravity; at all events, the intensity of the vibration should occur rather below that point. In making this statement, it is necessary to bear in mind that the centre of gravity is _ever varying_, the body rising and falling in a series of curves as the wings ascend and descend.

To _elevate_ and _propel_, the posterior margin of the wing must rotate round the anterior one; the posterior margin being, as a rule, always on a lower level than the anterior one. By the oblique and more vigorous play of the wings _under_ rather than _above_ the body, each wing expends its entire energy in pushing the body _upwards_ and _forwards_. It is necessary that the wings descend further than they ascend; that the wings be _convex_ on their upper surfaces, and _concave_ on their under ones; and that the concave or biting surfaces be brought more violently in contact with the air during the down stroke than the convex ones during the up stroke. The greater range of the wing below than above the body, and of the posterior margin below than above a given line, may be readily made out by watching the flight of the larger birds. It is well seen in the upward flight of the lark. In the hovering of the kestrel over its quarry, and the hovering of the gull over garbage which it is about to pick up, the wings play above and on a level with the body rather than below it; but these are exceptional movements for special purposes, and as they are only continued for a few seconds at a time, do not affect the accuracy of the general statement.

_Points wherein the Screws formed by the Wings differ from those employed in navigation._--1. In the blade of the ordinary screw the integral parts are rigid and unyielding, whereas, in the blade of the screw formed by the wing, they are mobile and plastic (figs. 93, 95, 97, pp. 174, 175, 176). This is a curious and interesting point, the more especially as it does not seem to be either appreciated or understood. The mobility and plasticity of the wing is necessary, because of the tenuity of the air, and because the pinion is an _elevating_ and _sustaining organ_, as well as a _propelling_ one.

2. The vanes of the ordinary two-bladed screw are short, and have a comparatively limited range, the range corresponding to their area of revolution. The wings, on the other hand, are long, and have a comparatively wide range; and during their elevation and depression rush through an extensive space, the slightest movement at the root or short axis of the wing being followed by a gigantic up or down stroke at the other (fig. 56, p. 120; figs. 64, 65, and 66, p. 139; figs. 82 and 83, p. 158). As a consequence, the wings as a rule act upon successive and undisturbed strata of air. The advantage gained by this arrangement in a thin medium like the air, where the quantity of air to be compressed is necessarily great, is simply incalculable.

3. In the ordinary screw the blades follow each other in rapid succession, so that they travel over nearly the same space, and operate upon nearly the same particles (whether water or air), in nearly the same interval of time. The limited range at their disposal is consequently not utilized, the action of the two blades being confined, as it were, to the same plane, and the blades being made to precede or follow each other in such a manner as necessitates the work being virtually performed only by one of them. This is particularly the case when the motion of the screw is rapid and the mass propelled is in the act of being set in motion, _i.e._ before it has acquired momentum. In this instance a large percentage of the moving or driving power is inevitably consumed in slip, from the fact of the blades of the screw operating on nearly the same particles of matter. The wings, on the other hand, do not follow each other, but have a distinct reciprocating motion, _i.e._ they dart first in one direction, and then in another and opposite direction, in such a manner that they make during the one stroke the current on which they rise and progress the next. The blades formed by the wings and the blur or impression produced on the eye by the blades when made to vibrate rapidly are widely separated,--the one blade and its blur being situated on the right side of the body and corresponding to the right wing, the other on the left and corresponding to the left wing. The right wing traverses and completely occupies the right half of a circle, and compresses all the air contained within this space; the left wing occupying and working up all the air in the left and remaining half. The range or sweep of the two wings, when urged to their extreme limits, corresponds as nearly as may be to one entire circle[77] (fig. 56, p. 120). By separating the blades of the screw, and causing them to reciprocate, a double result is produced, since the blades always act upon independent columns of air, and in no instance overlap or double upon each other. The advantages possessed by this arrangement are particularly evident when the motion is rapid. If the screw employed in navigation be driven beyond a certain speed, it cuts out the water contained within its blades; the blades and the water revolving as a solid mass. Under these circumstances, the propelling power of the screw is diminished rather than increased. It is quite otherwise with the screws formed by the wings; these, because of their reciprocating movements, becoming more and more effective in proportion as the speed is increased. As there seems to be no limit to the velocity with which the wings may be driven, and as increased velocity necessarily results in increased elevating, propelling, and sustaining power, we have here a striking example of the manner in which nature triumphs over art even in her most ingenious, skilful, and successful creations.

[77] Of this circle, the thorax may be regarded as forming the centre, the abdomen, which is always heavier than the head, tilting the body slightly in an upward direction. This tilting of the trunk favours flight by causing the body to act after the manner of a kite.

4. The vanes or blades of the screw, as commonly constructed, are fixed at a given angle, and consequently always strike at the same degree of obliquity. The speed, moreover, with which the blades are driven, is, as nearly as may be, uniform. In this arrangement power is lost, the two vanes striking after each other in the same manner, in the same direction, and almost at precisely the same moment,--no provision being made for increasing the angle, and the propelling power, at one stage of the stroke, and reducing it at another, to diminish the amount of slip incidental to the arrangement. The wings, on the other hand, are driven at a varying speed, and made to attack the air at a great variety of angles; the angles which the pinions make with the horizon being gradually increased by the wings being made to rotate on their long axes during the down stroke, to increase the _elevating_ and _propelling_ power, and gradually decreased during the up stroke, to reduce the resistance occasioned by the wings during their ascent. The latter movement increases the _sustaining_ area by placing the wings in a more horizontal position. It follows from this arrangement that every particle of air within the wide range of the wings is separately influenced by them, both during their ascent and descent,--the elevating, propelling, and sustaining power being by this means increased to a maximum, while the slip or waftage is reduced to a minimum. These results are further secured by the undulatory or waved track described by the wing during the down and up strokes. It is a somewhat remarkable circumstance that the wing, when not actually engaged as a propeller and elevator, acts as a _sustainer_ after the manner of a parachute. This it can readily do, alike from its form and the mode of its application, the double curve or spiral into which it is thrown in action enabling it to lay hold of the air with avidity, in whatever direction it is urged. I say “in whatever direction,” because, even when it is being recovered or drawn off the wind during the back stroke, it is climbing a gradient which arches above the body to be elevated, and so prevents it from falling. It is difficult to conceive a more admirable, simple, or effective arrangement, or one which would more thoroughly economize power. Indeed, a study of the spiral configuration of the wing, and its spiral, flail-like, lashing movements, involves some of the most profound problems in mathematics,--the curves formed by the pinion as a pinion anatomically, and by the pinion in action, or physiologically, being exceedingly elegant and infinitely varied; these running into each other, and merging and blending, to consummate the triple function of _elevating_, _propelling_, and _sustaining_.

Other differences might be pointed out; but the foregoing embrace the more fundamental and striking. Enough, moreover, has probably been said to show that it is to wing-structures and wing-movements the aëronaut must direct his attention, if he would learn “the way of an eagle in the air,” and if he would rise upon the whirlwind in accordance with natural laws.