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account, not only always looks forwards, but it forms a true kite with the horizon, the angles made by the kite varying at every part of the down stroke, as shown more particularly at d, e, f, g ; j, k, l, m of fig. 88, p. 166. I am therefore opposed to Borelli, Macgillivray, Owen, Bishop, M. Liais, the Duke of Argyll, and Marey as to the direction and nature of the down stroke. I differ also as to the direction and nature of the up stroke.

Professor Marey states that not only does the posterior margin of the wing yield in an upward direction during the down stroke until the under surface of the pinion makes a backward angle of 45° with the horizon, but that during the up stroke it yields to the same extent in an opposite direction. The posterior flexible margin of the wing, according to Marey, passes through a space of 90° every time the wing reverses its course, this space being dedicated to the mere adjusting of the planes of the wing for the purposes of flight. The planes, moreover, he asserts, are adjusted not by vital and vito-mechanical acts but by the action of the air alone ; this operating on the under surface of the wing and forcing its posterior margin upwards during the down stroke ; the air during the up stroke acting upon the posterior margin of the upper surface of the wing, and forcing it downwards. This is a mere repetition of Borelli's view. Marey delegates to the air the difficult and delicate task of arranging the details of flight. The time, power, and space occupied in reversing the wing alone, according to this theory, are such as to render flight impossible. That the wing does not act as stated by Borelli, Marey, and others may be readily proved by experiment. It may also be demonstrated mathematically, as a reference to figs. 114 and 115, p. 228, will show.

Let ab of fig. 114 represent the horizon; mn the line of vibration; wc the wing inclined at an upward backward angle of 45° in the act of making the down stroke, and x d the wing inclined at a downward backward angle of 45° and in the act of making the up stroke. When the wing xc descends it will tend to dive downwards in the direction f giving very little of any horizontal support (a b); when the wing wd ascends it will endeavour to rise in the direction g, as it darts up like a kite (the body bearing it being in motion). If we take the resultant of these two forces, we have at most propulsion in the direction ab. This, moreover, would only hold true if the bird was as light as air. As, however, gravity tends to pull the bird downwards as it advances, the real flight of the bird, according to this theory, would fall in a line between b and f, probably in sh. It could not possibly be otherwise ; the wing described and figured by Borelli and Marey is in one piece, and made to vibrate vertically on either side of a given line. If, however, a wing in one piece is elevated and depressed in a strictly perpendicular direction, it is evident that the wing will experience a greater resistance during the up stroke, when it is acting against gravity, than during the down stroke, when it is acting with gravity.

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FIG. 114.

Fig. 115. As a consequence, the bird will be more vigorously depressed during the ascent of the wing than it will be elevated during its descent. That the mechanical wing referred to by Borelli and Marey is not a flying wing, but a mere propelling apparatus, seems evident to the latter, for he states that the winged machine designed by him has unquestionably not motor power enough to support its own weight.

The manner in which the natural wing (and the artificial wing properly constructed and propelled) evades the resistance of the air during the up stroke, and gives continuous support and propulsion, is very remarkable. Fig. 115 illustrates the true principle. Let a b represent the horizon; mn the direction of vibration; as the wing ready to make the down stroke, and at the wing ready to make the up stroke. When the wing us descends, the posterior margin (s) is screwed

1 Revue des Cours Scientifiques de la France et de l'Etranger. 8vo. March 20, 1869.

downwards and forwards in the direction syt; the forward angle which it makes with the horizon increasing as the wing descends (compare with fig. 85 (abc), p. 160, and fig. 88 (c def), p. 166). The air is thus seized by a great variety of inclined surfaces, and as the under surface of the wing, which is a true kite, looks upwards and forwards, it tends to carry the body of the bird upwards and forwards in the direction x W. When the wing at makes the up stroke, it rotates in the direction is to prepare for the second down stroke. It does not, however, ascend in the direction ts. On the contrary, it darts up like a true kite, which it is, in the direction xv, in virtue of the reaction of the air, and because the body of the bird, to which it is attached, has a forward motion communicated to it by the wing during the down stroke (compare with ghi of fig. 88, p. 166). The resultant of the forces acting in the directions xv and xb, is one acting in the direction x w, and if allowance be made for the operation of gravity, the flight of the bird will correspond to a line somewhere between w and b, probably the line r. This result is produced by the wing acting as an eccentric—by the upper concave surface of the pinion being always directed upwards, the under concave surface downwards—by the under surface, which is a true kite, darting forward in wave curves both during the down and up strokes, and never making a backward angle with the horizon (fig. 88, p. 166); and lastly, by the wing employing the air under it as a fülcrum during the down stroke, the air, on its own part, reacting on the under surface of the pinion, and when the proper time arrives, contributing to the elevation of the wing.

If, as Borelli and his successors believe, the posterior margin of the wing yielded to a marked extent in an upward direction during the down stroke, and more especially if it yielded to such an extent as to cause the under surface of the wing to make a backward angle with the horizon of 45°, one of two things would inevitably follow—either the air on which the wing depends for support and propulsion would be permitted to escape before it was utilized; or the wing would dart rapidly downward, and carry the body of the bird with it. If the posterior margin of the wing yielded in an upward direction to the extent described by Marey during the down

stroke, it would be tantamount to removing the fulcrum (the air) on which the lever formed by the wing operates.

If a bird flies in a horizontal direction the angles made by the under surface of the wing with the horizon are very slight, but they always look forwards (fig. 60, p. 126). If a bird flies upwards the angles in question are increased (fig. 59, p. 126). In no instance, however, unless when the bird is everted and flying downwards, is the posterior margin of the wing on a higher level than the anterior one (fig. 106, p. 203). This holds true of natural flight, and consequently also of artificial flight.

These remarks are more especially applicable to the flight of the bat and bird where the wing is made to vibrate more or less perpendicularly (fig. 17, p. 36; figs. 82 and 83, p. 158. Compare with fig. 85, p. 160, and fig. 88, p. 166). If a bird or a bat wishes to fly upwards, its flying surfaces must always be inclined upwards. It is the same with the fish. A fish can only swim upwards if its body is directed upwards. In the insect, as has been explained, the wing is made to vibrate in a more or less horizontal direction. In this case the wing has not to contend directly against gravity (a wing which flaps vertically must). As a consequence it is made to tack upon the air obliquely zigzag fashion as horse and carriage would ascend a steep hill (vide figs. 67 to 70, p. 141. Compare with figs. 71 and 72, p. 144). In this arrangement gravity is overcome by the wing reversing its planes and acting as a kite which flies alternately forwards and backwards. The kites formed by the wings of the bat and bird always fly forward (fig. 88, p. 166). In the insect, as in the bat and bird, the posterior margin of the wing never rises above the horizon so as to make an upward and backward angle with it, as stated by Borelli, Marey, and others (cx a of fig. 114, p. 228).

While Borelli and his successors are correct as to the wedgeaction of the wing, they have given an erroneous interpretation of the manner in which the wedge is produced. Thus Borelli states that when the wings descend their posterior margins ascend, the two wings forming a cone whose base is represented by cbe of fig. 113, p. 220); its apex being represented by a f of the same figure. The base of Borelli's cone. it will be observed, is inclined forwards in the direction of the head of the bird. Now this is just the opposite of what ought to be. Instead of the two wings forming one cone, the base of which is directed forwards, each wing of itself forms two cones, the bases of which are directed backwards and outwards, as shown at fig. 116.

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Fig. 116. In this figure the action of the wing is compared to the sculling of an oar, to which it bears a considerable resemblance. The one cone, viz., that with its base directed outwards, is represented at a b d. This cone corresponds to the area inapped 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 pn. 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 befghd ijkl; the posterior margin describing the figure-of-8 indicated at prn. 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, xs, cd) must have a small scull (m n, qr,op) working at right angles to it. This follows because

1 In sculling strictly speaking, it is the upper surface of the oar which is most effective; whereas in flying it is the under.

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