long, and one inch wide.--_Original._]
[Illustration: 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._]
[Illustration: 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._]
[Illustration: 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._]
[Illustration: 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.
[Illustration: 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.
[Illustration: 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._]
[Illustration: 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._]
[Illustration: 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.
[Illustration: FIG. 126.]
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.
[118] The human wrist is so formed that if a wing be held in the
hand at an upward angle of 45°, the hand can apply it to the air in
a vertical or horizontal direction without difficulty. This arises
from the power which the hand has of moving in an upward and downward
direction, and from side to side with equal facility. The hand can
also rotate on its long axis, so that it virtually represents all the
movements of the wing at its root.
_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.