[Illustration: FIG. 15.--Right Wing of the Red-legged Partridge
(_Perdix rubra_). Dorsal aspect as seen from above.]
[Illustration: FIG. 16.--Right Wing of the Red-legged Partridge
(_Perdix rubra_). Dorsal and ventral aspects as seen from behind;
showing auger-like conformation of wing. Compare with figs. 11 and
18.]
"The wing of the bird, like that of the insect, is concavo-convex, and
_more or less twisted upon itself_ when extended, so that the anterior
or thick margin of the pinion presents a different degree of curvature
to that of the posterior or thin margin. This twisting is in a great
measure owing to the manner in which the bones of the wing are twisted
upon themselves, and the spiral nature of their articular
surfaces--the long axes of the joints always intersecting each other
at right angles, and the bones of the elbow and wrist making a quarter
of a turn or so during extension and the same amount during flexion.
As a result of this disposition of the articular surfaces, the wing
may be shot out or extended, and retracted or flexed in nearly the
same plane, the bones composing the wing rotating on their axes during
either movement (fig. 14). The secondary action, or the revolving of
the component bones on their own axes, is of the greatest importance
in the movements of the wing, as it communicates to the hand and
forearm, and consequently to the primary and secondary feathers which
they bear, the precise angles necessary for flight. It in fact ensures
that the wing, and the curtain or fringe of the wing which the primary
and secondary feathers form, shall be screwed into and down upon the
wind in extension, and unscrewed or withdrawn from the wind during
flexion. The wing of the bird may therefore be compared to a huge
gimlet or auger, the axis of the gimlet representing the bones of the
wing, the flanges or spiral thread of the gimlet the primary and
secondary feathers" (figs. 15 and 16).... "From this description it
will be evident that by the mere rotation of the bones of the forearm
and hand the maximum and minimum of resistance is secured much in the
same way that this object is attained by the alternate dipping and
feathering of an oar."... "The wing, both when at rest and when in
motion, may not inaptly be compared to the blade of an ordinary screw
propeller as employed in navigation. Thus the general outline of the
wing corresponds closely with the outline of the propeller (figs. 11,
16 and 18), and the track described by the wing in space _is twisted
upon itself_ propeller fashion[7] (figs. 12, 20, 21, 22, 23). The
great velocity with which the wing is driven converts the impression
or blur made by it into what is equivalent to a solid for the time
being, in the same way that the spokes of a wheel in violent motion,
as is well understood, more or less completely occupy the space
contained within the rim or circumference of the wheel" (figs. 9, 20
and 21).
[Illustration: FIG. 17.--Right Wing of the Bat (_Phyllocina
gracilis_). Dorsal aspect as seen from above.]
... "The wing of the bat bears a considerable resemblance to that of
the insect, inasmuch as it consists of a delicate, semi-transparent,
continuous membrane, supported in divers directions, particularly
towards its anterior margin, by a system of osseous stays or
stretchers which confer upon it the degree of rigidity requisite for
flight. It is, as a rule, deeply concave on its under or ventral
surface, and in this respect resembles the wing of the heavy-bodied
birds. The movement of the bat's wing in extension is a _spiral_ one,
the spiral running alternately from below upwards and forwards and
from above downwards and backwards. The action of the wing of the bat,
and the movements of its component bones, are essentially the same as
in the bird" (figs. 17 and 18).
[Illustration: FIG. 18.--Right Wing of the Bat (_Phyllocina
gracilis_). Dorsal and ventral aspects, as seen from behind. These
show the screw-like configuration of the wing, and also how the wing
twists and untwists during its action.]
... "The wing strikes the air precisely as a boy's kite would if it
were jerked by its string, the only difference being that the kite is
_pulled forwards_ upon the wind by the string and the hand, whereas in
the insect, bird and bat the wing is _pushed forwards_ on the wind by
the weight of the body and the power residing in the pinion itself"
(fig. 19).[8]
[Illustration: FIG. 19.--The Cape Barn-owl (_Strix capensis_), showing
the kite-like surfaces presented by the ventral aspect of the wings and
body in flight.]
The figure-of-8 and kite-like action of the wing referred to lead us to
explain how it happens that the wing, which in many instances is a
comparatively small and delicate organ, can yet attack the air with such
vigour as to extract from it the recoil necessary to elevate and propel
the flying creature. The accompanying figures from one of Pettigrew's
later memoirs[9] will serve to explain the _rationale_ (figs. 20, 21, 22
and 23).
As will be seen from these figures, the wing during its vibration sweeps
through a comparatively very large space. This space, as already
explained, is practically a solid basis of support for the wing and for
the flying animal. The wing attacks the air in such a manner as
virtually to have no slip--this for two reasons. The wing reverses
instantly and acts as a kite during nearly the entire down and up
strokes. The angles, moreover, made by the wing with the horizon during
the down and up strokes are at no two intervals the same, but (and this
is a remarkable circumstance) they are always adapted to the speed at
which the wing is travelling for the time being. The increase and
decrease in the angles made by the wing as it hastens to and fro are due
partly to the resistance offered by the air, and partly to the mechanism
and mode of application of the wing to the air. The wing, during its
vibrations, rotates upon two separate centres, the tip rotating round
the root of the wing as an axis (short axis of wing), the posterior
margin rotating around the anterior margin (long axis of wing). The wing
is really eccentric in its nature, a remark which applies also to the
rowing feathers of the bird's wing. The compound rotation goes on
throughout the entire down and up strokes, and is intimately associated
with the power which the wing enjoys of alternately seizing and evading
the air.
[Illustration: FIGS. 20, 21, 22 and 23 show the area mapped out by the
left wing of the Wasp when the insect is fixed and the wing made to
vibrate. These figures illustrate the various angles made by the wing
with the horizon as it hastens to and fro, and show how the wing
reverses and reciprocates, and how it twists upon itself in opposite
directions, and describes a figure-of-8 track in space. Figs. 20 and 22
represent the forward or down stroke (a b c d e f g), figs. 21 and 23
the backward or up stroke (g h i j k l a). The terms forward and back
strokes are here employed with reference to the head of the insect, x,
x', line to represent the horizon. If fig. 22, representing the down or
forward stroke, be placed upon fig. 23, representing the up or backward
stroke, it will be seen that _the wing crosses its own track_ more or
less completely at every stage of the down and up strokes.]
The compound rotation of the wing is greatly facilitated by the wing
being elastic and flexible. It is this which causes the wing to twist
and untwist diagonally on its long axis when it is made to vibrate. The
twisting referred to is partly a vital and partly a mechanical
act;--that is, it is occasioned in part by the action of the muscles and
in part by the greater resistance experienced from the air by the tip
and posterior margin of the wing as compared with the root and anterior
margin,--the resistance experienced by the tip and posterior margin
causing them to reverse always subsequently to the root and anterior
margin, which has the effect of throwing the anterior and posterior
margins of the wing into figure-of-8 curves, as shown at figs. 9, 11,
12, 16, 18, 20, 21, 22 and 23.
The compound rotation of the wing, as seen in the bird, is represented
in fig. 24.
Not the least curious feature of the wing movements is the remarkable
power which the wing possesses of making and utilizing its own currents.
Thus, when the wing descends it draws after it a strong current, which,
being met by the wing during its ascent, greatly increases the efficacy
of the up stroke. Similarly and conversely, when the wing ascends, it
creates an upward current, which, being met by the wing when it
descends, powerfully contributes to the efficiency of the down stroke.
This statement can be readily verified by experiment both with natural
and artificial wings. Neither the up nor the down strokes are complete
in themselves.
The wing to act efficiently must be driven at a certain speed, and in
such a manner that the down and up strokes shall glide into each other.
It is only in this way that the air can be made to pulsate, and that the
rhythm of the wing and the air waves can be made to correspond. The air
must be seized and let go in a certain order and at a certain speed to
extract a maximum recoil. The rapidity of the wing movements is
regulated by the size of the wing, small wings being driven at a very
much higher speed than larger ones. The different parts of the wing,
moreover, travel at different degrees of velocity--the tip and posterior
margin of the wing always rushing through a much greater space, in a
given time, than the root and anterior margin.
[Illustration: FIG. 24.--Wing of the Bird with its root (a, b) cranked
forwards.
a, b, Short axis of the wing (axis for tip of wing, h).
c, d, Long axis (axis for posterior margin of wing, h, i, j, k, l).
m, n, Short axis of rowing feathers of wing.
r, s, Long axis of rowing feathers of wing. The rotation of the rowing
feathers on their long axis (they are eccentrics) enables them to open
or separate during the up, and close or come together during the down
strokes.
e f, g p, concave shape presented by the under surface of the wing.]
The rapidity of travel of the insect wing is in some cases enormous. The
wasp, for instance, is said to ply its wings at the rate of 110, and the
common house-fly at the rate of 330 beats per second. Quick as are the
vibrations of natural wings, the speed of certain parts of the wing is
amazingly increased. Wings as a rule are long and narrow. As a
consequence, a comparatively slow and very limited movement at the root
confers great range and immense speed at the tip, the speed of each
portion of the wing increasing as the root of the wing is receded from.
This is explained on a principle well understood in mechanics, viz. that
when a wing or rod hinged at one end is made to move in a circle, the
tip or free end of the wing or rod describes a much wider circle in a
given time than a portion of the wing or rod nearer the hinge (fig. 25).
[Illustration: FIG. 25 shows how different portions of the wing travel
at different degrees of speed. In this figure the rod a, b, hinged at x,
represents the wing. When the wing is made to vibrate, its several
portions travel through the spaces d b f, j k l, g h i, and e a c in
exactly the same interval of time. The part of the wing marked b, which
corresponds with the tip, consequently travels very much more rapidly
than the part marked a, which corresponds with the root. m n, o p,
curves made by the wing at the end of the up and down strokes; r,
position of the wing at the middle of the stroke.]
One naturally inquires why the high speed of wings, and why the
progressive increase of speed at their tips and posterior margins? The
answer is not far to seek. If the wings were not driven at a high speed,
and if they were not eccentrics made to revolve upon two separate axes,
they would of necessity be large cumbrous structures; but large heavy
wings would be difficult to work, and what is worse, they would (if too
large), instead of controlling the air, be controlled by it, and so
cease to be flying organs.
There is, however, another reason why wings should be made to vibrate at
high speeds. The air, as explained, is a very light, thin, elastic
medium, which yields on the slightest pressure, and unless the wings
attacked it with great violence the necessary recoil or resistance could
not be obtained. The atmosphere, because of its great tenuity, mobility
and comparative imponderability, presents little resistance to bodies
passing through it at low velocities. If, however, the speed be greatly
accelerated, the action of even an ordinary cane is sufficient to
elicit a recoil. This comes of the action and reaction of matter, the
resistance experienced varying according to the density of the
atmosphere and the shape, extent and velocity of the body acting upon
it. While, therefore, scarcely any impediment is offered to the progress
of an animal in motion in the air, it is often exceedingly difficult to
compress the air with sufficient rapidity and energy to convert it into
a suitable fulcrum for securing the necessary support and forward
impetus. This arises from the fact that bodies moving in air experience
a _minimum of resistance_ and occasion a _maximum of displacement_.
Another and very obvious difficulty is traceable to the great disparity
in the weight of air as compared with any known solid, and the
consequent want of buoying or sustaining power which that disparity
involves. If we compare air with water we find it is nearly 1000 times
lighter. To meet these peculiarities the insect, bird and bat are
furnished with extensive flying surfaces in the shape of wings, which
they apply with singular velocity and power to the air, as levers of the
third order. In this form of lever the power is applied between the
fulcrum and the weight to be raised. The power is represented by the
wing, the fulcrum by the air, and the weight by the body of the flying
animal. Although the third order of lever is particularly inefficient
when the fulcrum is rigid and immobile, it possesses singular advantages
when these conditions are reversed, that is, when the fulcrum, as
happens with the air, is _elastic_ and _yielding_. In this instance a
very slight movement at the root of the pinion, or that end of the lever
directed towards the body, is followed by an immense sweep of the
extremity of the wing, where its elevating and propelling power is
greatest--this arrangement ensuring that the large quantity of air
necessary for support and propulsion shall be compressed under the most
favourable conditions.
[Illustration: FIG. 26.--In this figure f, f' represent the movable
fulcra furnished by the air, p p' the power residing in the wing, and b
the body to be moved. In order to make the problem of flight more
intelligible, the lever formed by the wing is prolonged beyond the body
(b), and to the root of the wing so extended the weight (w, w') is
attached; x represents the universal joint by which the wing is attached
to the body. When the wing ascends as shown at p, the air (fulcrum f)
resists its upward passage, and forces the body (b) or its
representative (w) slightly downwards. When the wing descends as shown
at p', the air (fulcrum f') resists its downward passage, and forces the
body (b) or its representative (w') slightly upwards. From this it
follows that when the wing rises the body falls, and vice versa--the
wing describing the arc of a large circle (f f'), the body (b), or the
weights (w, w') representing it, describing the arc of a small circle.]
In this process the weight of the body performs an important part, by
acting upon the inclined planes formed by the wings in the plane of
progression. The power and the weight may thus be said to reciprocate,
the two sitting as it were side by side and blending their peculiar
influences to produce a common result, as indicated at fig. 26.
When the wings descend they elevate the body, the wings being active and
the body passive; when the body descends it contributes to the elevation
of the wings,[10] the body being active and the wings more or less
passive. It is in this way that weight forms a factor in flight, the
wings and the weight of the body reciprocating and mutually assisting
and relieving each other. This is an argument for employing four wings
in artificial flight,--the wings being so arranged that the two which
are up shall always by their fall mechanically elevate the two which are
down. Such an arrangement is calculated greatly to conserve the driving
power, and as a consequence, to reduce the weight.
That the weight of the body plays an important part in the production of
flight may be proved by a very simple experiment. If two quill feathers
are fixed in an ordinary cork, and so arranged that they expand and arch
above it (fig. 27), it is found that if the apparatus be dropped from a
vertical height of 3 yds. it does not fall vertically downwards, but
downwards and _forwards_ in a curve, the forward travel amounting in
some instances to a yard and a half. Here the cork, in falling, acts
upon the feathers (which are to all intents and purposes wings), and
these in turn act upon the air, in such a manner as to produce a
horizontal transference.
[Illustration: FIG. 27.--a, b, quill feathers; c, cork; d, e, f, g,
downward and _forward_ curved trajectory made by the feathers and cork
before reaching the ground (h, i).]
In order to utilize the air as a means of transit, the body in motion,
whether it moves in virtue of the life it possesses, or because of a
force super-added, must be heavier than air. It must tread with its
wings and rise upon the air as a swimmer upon the water, or as a kite
upon the wind. This is necessary for the simple reason that the body
must be active, the air passive. The flying body must act against
gravitation, and elevate and carry itself forward at the expense of the
air and of the force which resides in it, whatever that may be. If it
were otherwise--if it were rescued from the law of gravitation on the
one hand, and bereft of independent movement on the other, it would
float about uncontrolled and uncontrollable like an ordinary balloon.
In flight one of two things is necessary. Either the wings must attack
the air with great violence, or the air in rapid motion must attack the
wings: either suffices. If a bird attempts to fly in a calm, the wings
must be made to smite the air after the manner of a boy's kite with
great vigour and at a high speed. In this case the wings fly the bird.
If, however, the bird is fairly launched in space and a stiff breeze is
blowing, all that is required in many instances is to extend the wings
at a slight upward angle to the horizon so that the under parts of the
wings present kite-like surfaces. In these circumstances the rapidly
moving air flies the bird. The flight of the albatross supplies the
necessary illustration. If by any chance this magnificent bird alights
upon the sea he must flap and beat the water and air with his wings with
tremendous energy until he gets fairly launched. This done he extends
his enormous pinions[11] and sails majestically along, seldom deigning
to flap his wings, the breeze doing the work for him. A familiar
illustration of the same principle may be witnessed any day when
children are engaged in the pastime of kite-flying. If two boys attempt
to fly a kite in a calm, the one must hold up the kite and let go when
the other runs. In this case the under surface of the kite is made to
strike the still air. If, however, a stiff autumn breeze be blowing, it
suffices if the boy who formerly ran when the kite was let go stands
still. In this case the air in rapid motion strikes the under surface of
the kite and forces it up. The string and the hand are to the kite what
the weight of the flying creature is to the inclined planes formed by
its wings.
The area of the insect, bird and bat, when the wings are fully expanded,
is greater than that of any other class of animal, their weight being
proportionally less. As already stated, however, it ought never to be
forgotten that even the lightest insect, bird or bat is vastly heavier
than the air, and that no fixed relation exists between the weight of
body and expanse of wing in any of the orders. We have thus light-bodied
and large-winged insects and birds, as the butterfly and heron; and
others with heavy bodies and small wings, as the beetle and partridge.
Similar remarks are to be made of bats. Those apparent inconsistencies
in the dimensions of the body and wings are readily explained by the
greater muscular development of the heavy-bodied, small-winged insects,
birds and bats, and the increased power and rapidity with which the
wings in them are made to oscillate. This is of the utmost importance in
the science of aviation, as showing that flight may be attained by a
heavy powerful animal with comparatively small wings, as well as by a
lighter one with greatly enlarged wings. While, therefore, there is
apparently no correspondence between the area of the wing and the animal
to be raised, there is, except in the case of sailing insects, birds and
bats, an unvarying relation as to the weight and number of oscillations;
so that the problem of flight would seem to resolve itself into one of
weight, power, velocity and small surfaces, _versus_ buoyancy, debility,
diminished speed and extensive surfaces--weight in either case being a
_sine qua non_.
[Illustration: FIG. 28.--Hawk and Pigeon.]
That no fixed relation exists between the area of the wings and the size
and weight of the body to be elevated is evident on comparing the
dimensions of the wings and bodies of the several orders of insects,
bats and birds. If such comparison be made, it will be found that the
pinions in some instances diminish while the bodies increase, and the
converse. No practical good can therefore accrue to aviation from
elaborate measurements of the wings and body of any flying thing;
neither can any rule be laid down as to the extent of surface required
for sustaining a given weight in the air. The statements here advanced
are borne out by the fact that the wings of insects, bats and birds may
be materially reduced without impairing their powers of flight. In such
cases the speed with which the wings are driven is increased in the
direct ratio of the mutilation. The inference to be deduced from the
foregoing is plainly this, that even in large-bodied, small-winged
insects and birds the wing-surface is greatly in excess, the surplus
wing area supplying that degree of elevating and sustaining power which
is necessary to prevent undue exertion on the part of the volant animal.
In this we have a partial explanation of the buoyancy of insects, and
the great lifting power possessed by birds and bats,--the bats carrying
their young without inconvenience, the birds elevating surprising
quantities of fish, game, carrion, &c. (fig. 28).
While as explained, no definite relation exists between the weight of a
flying animal and the size of its flying surfaces, there being, as
stated, heavy-bodied and small-winged insects, birds and bats, and the
converse, and while, as has been shown, flight is possible within a wide
range, the wings being, as a rule, in excess of what are required for
the purposes of flight,--still it appears from the researches of L. de
Lucy that there is a general law, to the effect that the larger the
volant animal, the smaller, by comparison, are its flying surfaces. The
existence of such a law is very encouraging so far as artificial flight
is concerned, for it shows that the flying surfaces of a large, heavy,
powerful flying machine will be comparatively small, and consequently
comparatively compact and strong. This is a point of very considerable
importance, as the object desiderated in a flying machine is elevating
capacity.