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.
[Illustration: FIG. 127.
FIG. 127.--Path described by artificial wave wing from right to left.
_x_, _x´_, Horizon. _m_, _n_, _o_, Wave track traversed by wing
from right to left. _p_, Angle made by the wing with the horizon
at beginning of stroke. _q_, Ditto, made at middle of stroke. _b_,
Ditto, towards end of stroke. _c_, Wing in the act of reversing;
at this stage the wing makes an angle of 90° with the horizon, and
its speed is less than at any other part of its course. _d_, Wing
reversed, and in the act of darting up to _u_, to begin the stroke
from left to right (_vide u_ of fig. 128).--_Original._]
[Illustration: FIG. 128.
FIG. 128.--Path described by artificial wave wing from left to right.
_x_, _x´_, Horizon. _u_, _v_, _w_, Wave track traversed by wing from
left to right. _t_, Angle made by the wing with horizon at beginning
of stroke. _y_, Ditto, at middle of stroke. _z_, Ditto, towards end
of stroke. _r_, Wing in the act of reversing; at this stage the wing
makes an angle of 90° with the horizon, and its speed is less that at
any other part of its course. _s_, Wing reversed, and in the act of
darting up to _m_, to begin the stroke from right to left (_vide m_
of fig. 127).--_Original._]
If the piston, which in the experiment described has been working
_vertically_, be made to work _horizontally_, a series of essentially
similar results are obtained. When the piston is worked horizontally,
the anterior and posterior elastic bands require to be of nearly
the same strength, whereas the inferior elastic band requires to be
much stronger than the superior one, to counteract the very decided
tendency the wing has to fly upwards. The power also requires to be
somewhat differently applied. Thus the wing must have a violent impulse
communicated to it when it begins the stroke from right to left, and
also when it begins the stroke from left to right (the _heavy parts_
of the spiral line represented at fig. 71, p. 144, indicate the points
where the impulse is communicated). The wing is then left to itself,
the elastic bands and the reaction of the air doing the remainder of
the work. When the wing is forced by the piston from right to left,
it darts forward in double curve, as shown at fig. 127; the various
inclined surfaces made by the wing with the horizon changing at every
stage of the stroke.
At the beginning of the stroke from right to left, the angle made by
the under surface of the wing with the horizon (_x x´_) is something
like 45° (_p_), whereas at the middle of the stroke it is reduced
to 20° or 25° (_q_). At the end of the stroke the angle gradually
increases to 45° (_b_), then to 90° (c), after which the wing suddenly
turns a somersault (_d_), and reverses precisely as the natural wing
does at _e_, _f_, _g_ of figs. 67 and 69, p. 141. The artificial
wing reverses with amazing facility, and in the most natural manner
possible. The angles made by its under surface with the horizon depend
chiefly upon the speed with which the wing is urged at different stages
of the stroke; the angle always decreasing as the speed increases, and
_vice versâ_. As a consequence, the angle is greatest when the speed is
least.
When the wing reaches the point _b_ its speed is much less than it was
at _q_. The wing is, in fact, preparing to reverse. At _c_ the wing is
in the act of reversing (compare _c_ of figs. 84 and 85, p. 160), and,
as a consequence, its speed is at a minimum, and the angle which it
makes with the horizon at a maximum. At _d_ the wing is reversed, its
speed being increased, and the angle which it makes with the horizon
diminished. Between the letters _d_ and _u_ the wing darts suddenly
up like a kite, and at _u_ it is in a position to commence the stroke
from left to right, as indicated at _u_ of fig. 128, p. 250. The course
described and the angles made by the wing with the horizon during the
stroke from left to right are represented at fig. 128 (compare with
figs. 68 and 70, p. 141). The stroke from left to right is in every
respect the converse of the stroke from right to left, so that a
separate description is unnecessary.
_The Artificial Wave Wing can be driven at any speed--it can make its
own currents, or utilize existing ones._--The remarkable feature in
the artificial wave wing is its adaptability. It can be driven slowly,
or with astonishing rapidity. It has no dead points. It reverses
instantly, and in such a manner as to dissipate neither time nor
power. It alternately seizes and evades the air so as to extract the
maximum of support with the minimum of slip, and the minimum of force.
It supplies a degree of buoying and propelling power which is truly
remarkable. Its buoying area is nearly equal to half a circle. It can
act upon still air, and it can create and utilize its own currents.
I proved this in the following manner. I caused the wing to make a
horizontal sweep from right to left over a candle; the wing rose
steadily as a kite would, and after a brief interval, the flame of the
candle was persistently blown from right to left. I then waited until
the flame of the candle assumed its normal perpendicular position,
after which I caused the wing to make another and opposite sweep from
left to right. The wing again rose kite fashion, and the flame was a
second time affected, being blown in this case from left to right. I
now caused the wing to vibrate steadily and rapidly above the candle,
with this curious result, that the flame did not incline alternately
from right to left and from left to right. On the contrary, it was
blown steadily away from me, _i.e._ in the direction of the tip of the
wing, thus showing that the artificial currents made by the wing, met
and neutralized each other always at mid stroke. I also found that
under these circumstances the buoying power of the wing was remarkably
increased.
_Compound rotation of the Artificial Wave Wing: the different parts of
the Wing travel at different speeds._--The artificial wave wing, like
the natural wing, revolves upon two centres (_a b_, _c d_ of fig. 80,
p. 149; fig. 83, p. 158, and fig. 122, p. 239), and owes much of its
elevating and propelling, seizing, and disentangling power to its
different portions travelling at different rates of speed (see fig. 56,
p. 120), and to its storing up and giving off energy as it hastens to
and fro. Thus the tip of the wing moves through a very much greater
space in a given time than the root, and so also of the posterior
margin as compared with the anterior. This is readily understood by
bearing in mind that the root of the wing forms the centre or axis of
rotation for the tip, while the anterior margin is the centre or axis
of rotation for the posterior margin. The momentum, moreover, acquired
by the wing during the stroke from right to left _is expended in_
_reversing the wing_, and in preparing it for the stroke from left to
right, and _vice versâ_; a continuous to-and-fro movement devoid of
dead points being thus established. If the artificial wave wing be
taken in the hand and suddenly depressed _in a more or less vertical
direction_, it immediately springs up again, and carries the hand
with it. It, in fact, describes a curve whose convexity is directed
downwards, and in doing so, carries the hand upwards and forwards. If
a second down stroke be added, a second curve is formed; the curves
running into each other, and producing a progressive waved track
similar to what is represented at _a_, _c_, _e_, _g_, _i_, of fig. 81,
p. 157. This result is favoured if the operator runs forward so as not
to impede or limit the action of the wing.
[Illustration: FIG. 129.]
_How the Wave Wing creates currents, and rises upon them, and how the
Air assists in elevating the Wing._--In order to ascertain in what
way the air contributes to the elevation of the wing, I made a series
of experiments with natural and artificial wings. These experiments
led me to conclude that when the wing descends, as in the bat and
bird, it compresses and pushes before it, in a downward and forward
direction, a column of air represented by _a_, _b_, _c_ of fig. 129,
p. 253.[119] The air rushes in from all sides to replace the displaced
air, as shown at _d_, _e_, _f_, _g_, _h_, _i_, and so produces a circle
of motion indicated by the dotted line _s_, _t_, _v_, _w_. The wing
rises upon the outside of the circle referred to, as more particularly
seen at _d_, _e_, _v_, _w_. The arrows, it will be observed, are all
pointing upwards, and as these arrows indicate the direction of the
reflex or back current, it is not difficult to comprehend how the air
comes indirectly to assist in elevating the wing. A similar current is
produced to the right of the figure, as indicated by _l_, _m_, _o_,
_p_, _q_, _r_, but seeing the wing is always advancing, this need not
be taken into account.
[119] The artificial currents produced by the wing during its descent
may be readily seen by partially filling a chamber with steam, smoke,
or some impalpable white powder, and causing the wing to descend in
its midst. By a little practice, the eye will not fail to detect the
currents represented at _d_, _e_, _f_, _g_, _h_, _i_, _l_, _m_, _o_,
_p_, _q_, _r_ of fig. 129, p. 253.
If fig. 129 be made to assume a horizontal position, instead of the
oblique position which it at present occupies, the manner in which
_an artificial current_ is produced by one sweep of the wing from
right to left, and utilized by it in a subsequent sweep from left to
right, will be readily understood. The artificial wave wing makes a
horizontal sweep from right to left, _i.e._ it passes from the point
_a_ to the point _c_ of fig. 129. During its passage it has displaced
a column of air. To fill the void so created, the air rushes in from
all sides, viz. from _d_, _e_, _f_, _g_, _h_, _i_; _l_, _m_, _o_, _p_,
_q_, _r_. The currents marked _g_, _h_, _i_; _p_, _q_, _r_, represent
the reflex or _artificial currents_. These are the currents which,
after a brief interval, force the flame of the candle from right to
left. It is those same currents which the wing encounters, and which
contribute so powerfully to its elevation, when it sweeps from left
to right. The wing, when it rushes from left to right, produces a new
series of artificial currents, which are equally powerful in elevating
the wing when it passes a second time from right to left, and thus
the process of making and utilizing currents goes on so long as the
wing is made to oscillate. In waving the artificial wing to and fro, I
found the best results were obtained when the range of the wing and
the speed with which it was urged were so regulated as to produce a
perfect reciprocation. Thus, if the range of the wing be great, the
speed should also be high, otherwise the air set in motion by the right
stroke will not be utilized by the left stroke, and _vice versâ_. If,
on the other hand, the range of the wing be small, the speed should
also be low, as the short stroke will enable the wing to reciprocate
as perfectly as when the stroke is longer and the speed quicker. When
the speed attained is high, the angles made by the under surface
of the wing with the horizon are diminished; when it is low, the
angles are increased. From these remarks it will be evident that the
artificial wave wing reciprocates in the same way that the natural wing
reciprocates; the reciprocation being most perfect when the wing is
vibrating in a given spot, and least perfect when it is travelling at a
high horizontal speed.
_The Artificial Wing propelled at various degrees of speed during the
Down and Up Strokes._--The tendency which the artificial wave wing has
to rise again when suddenly and vigorously depressed, explains why the
_elevator_ muscles of the wing should be so small when compared with
the _depressor_ muscles--the latter being something like seven times
larger than the former. That the contraction of the elevator muscles is
necessary to the elevation of the wing, is abundantly proved by their
presence, and that there should be so great a difference between the
volume of the elevator and depressor muscles is not to be wondered at,
when we remember that the whole weight of the body is to be elevated by
the rapid descent of the wings--the descent of the wing being entirely
due to the vigorous contraction of the powerful pectoral muscles.
If, however, the wing was elevated with as great a force as it was
depressed, no advantage would be gained, as the wing, during its ascent
(it acts against gravity) would experience a much greater resistance
from the air than it did during its descent. The wing is consequently
elevated more slowly than it is depressed; the elevator muscles
exercising a controlling and restraining influence. By slowing the wing
during the up stroke, the air has an opportunity of reacting on its
under surface.
_The Artificial Wave Wing as a Propeller._--The wave wing makes an
admirable propeller if its tip be directed _vertically downwards_,
and the wing lashed from side to side with a sculling figure-of-8
motion, similar to that executed by the tail of the fish. Three wave
wings may be made to act in concert, and with a very good result; two
of them being made to vibrate figure-of-8 fashion in a more or less
horizontal direction with a view to elevating; the third being turned
in a downward direction, and made to act vertically for the purpose of
propelling.
[Illustration:
FIG. 130.--Aërial wave screw, whose blades are slightly twisted (_a
b_, _c d_; _e f_, _g h_), so that those portions nearest the root (_d
h_) make a greater angle with the horizon than those parts nearer
the tip (_b f_). The angle is thus adjusted to the speed attained
by the different portions of the screw. The angle admits of further
adjustment by means of the steel springs _z_, _s_, these exercising
a restraining, and to a certain extent a regulating, influence which
effectually prevents shock.
It will be at once perceived from this figure that the portions of
the screw marked _m_ and _n_ travel at a much lower speed than those
portions marked _o_ and _p_, and these again more slowly than those
marked _q_ and _r_ (compare with fig. 56, p. 120). As, however, the
angle which a wing or a portion of a wing, as I have pointed out,
varies to accommodate itself to the speed attained by the wing, or a
portion thereof, it follows, that to make the wave screw mechanically
perfect, the angles made by its several portions must be accurately
adapted to the travel of its several parts as indicated above.
_x_, Vertical tube for receiving driving shaft. _v_, _w_, Sockets
in which the roots of the blades of the screw rotate, the degree of
rotation being limited by the steel springs _z_, _s_. _a b_, _e f_,
Tapering elastic reeds forming anterior or thick margins of blades of
screw. _d c_, _h g_, Posterior or thin elastic margins of blades of
screw. _m n_, _o p_, _q r_, Radii formed by the different portions of
the blades of the screw when in operation. The arrows indicate the
direction of travel.--_Original._]
_A New Form of Aërial Screw._--If two of the wave wings represented
at fig. 122, p. 239, be placed end to end, and united to a vertical
portion of tube to form a two-bladed screw, similar to that employed in
navigation, a most powerful elastic aërial screw is at once produced,
as seen at fig. 130.
This screw, which for the sake of uniformity I denominate _the aërial
wave screw_, possesses advantages for aërial purposes to which no
form of _rigid_ screw yet devised can lay claim. The way in which it
clings to the air during its revolution, and the degree of buoying
power it possesses, are quite astonishing. It is a self-adjusting,
self-regulating screw, and as its component parts are flexible and
elastic, it accommodates itself to the speed at which it is driven, and
gives a uniform buoyancy. The slip, I may add, is nominal in amount.
This screw is exceedingly light, and owes its efficacy to its shape and
the graduated nature of its blades; the anterior margin of each blade
being comparatively rigid, the posterior margin being comparatively
flexible and more or less elastic. The blades are kites in the same
sense that natural wings are kites. They are flown as such when the
screw revolves. I find that the aërial wave screw flies best and
elevates most when its blades are inclined at a certain upward angle
as indicated in the figure (130). The aërial wave screw may have the
number of its blades increased by placing the one above the other; and
two or more screws may be combined and made to revolve in opposite
directions so as to make them reciprocate; the one screw producing the
current on which the other rises, as happens in natural wings.
_The Aërial Wave Screw operates also upon Water._--The form of screw
just described is adapted in a marked manner for water, if the blades
be reduced in size and composed of some elastic substance, which will
resist the action of fluids, as gutta-percha, carefully tempered
finely graduated steel plates, etc. It bears the same relation to, and
produces the same results upon, water, as the tail and fin of the fish.
It throws its blades during its action into double figure-of-8 curves,
similar in all respects to those produced on the anterior and posterior
margins of the natural and artificial flying wing. As the speed
attained by the several portions of each blade varies, so the angle at
which each part of the blade strikes varies; the angles being always
greatest towards the root of the blade and least towards the tip. The
angles made by the different portions of the blades are diminished in
proportion as the speed, with which the screw is driven, is increased.
The screw in this manner is self-adjusting, and extracts a large
percentage of propelling power, with very little force and surprisingly
little slip.
A similar result is obtained if two finely graduated angular-shaped
gutta-percha or steel plates be placed end to end and applied to the
water (vertically or horizontally matters little), with a slight
sculling figure-of-8 motion, analogous to that performed by the tail
of the fish, porpoise, or whale. If the thick margin of the plates be
directed forwards, and the thin ones backwards, an unusually effective
propeller is produced. This form of propeller is likewise very
effective in air.
CONCLUDING REMARKS.