Lighter than Air
Fixed balloon,
Drifting balloon,
Sailing balloon,
Dirigible balloon
rigid (Zeppelin),
ballonetted.
Heavier than Air
Orthopter,
Helicopter,
Aeroplane
monoplane,
multiplane.
We will fall in with the present current of popular interest and
consider the aeroplane--that mechanical grasshopper--first.
What Holds It Up?
[Illustration: OCTAVE CHANUTE (DIED 1910)]
To the researches of Chanute and Langley must be ascribed much of
American progress in aviation.
When a flat surface like the side of a house is exposed to the breeze,
the velocity of the wind exerts a force or pressure directly against
the surface. This principle is taken into account in the design of
buildings, bridges, and other structures. The pressure exerted per
square foot of surface is equal (approximately) to the square of the
wind velocity in miles per hour, divided by 300. Thus, if the wind
velocity is thirty miles, the pressure against a house wall on which it
acts directly is 30 × 30 ÷ 300 = 3 pounds per square foot: if the wind
velocity is sixty miles, the pressure is 60 × 60 ÷ 300 = 12 pounds:
if the velocity is ninety miles, the pressure is 90 × 90 ÷ 300 = 27
pounds, and so on.
[Illustration: PRESSURE OF THE WIND]
If the wind blows obliquely toward the surface, instead of directly,
the pressure at any given velocity is reduced, but may still be
considerable. Thus, in the sketch, let _ab_ represent a wall, toward
which we are looking downward, and let the arrow _V_ represent the
direction of the wind. The air particles will follow some such paths
as those indicated, being deflected so as to finally escape around
the ends of the wall. The result is that a pressure is produced which
may be considered to act along the dotted line _P_, perpendicular to
the wall. This is the invariable law: that no matter how oblique the
surface may be, with reference to the direction of the wind, there is
always a pressure produced against the surface by the wind, and this
pressure always acts _in a direction perpendicular to the surface_. The
amount of pressure will depend upon the wind velocity and the obliquity
or inclination of the surface (_ab_) with the wind (_V_).
Now let us consider a kite--the "immediate ancestor" of the aeroplane.
The surface _ab_ is that of the kite itself, held by its string _cd_.
We are standing at one side and looking at the _edge_ of the kite. The
wind is moving horizontally against the face of the kite, and produces
a pressure _P_ directly against the latter. The pressure tends both to
move it toward the left and to lift it. If the tendency to move toward
the left be overcome by the string, then the tendency toward lifting
may be offset--and in practice _is_ offset--by the weight of the kite
and tail.
[Illustration: FORCES ACTING ON A KITE]
We may represent the two tendencies to movement produced by the force
_P_, by drawing additional dotted lines, one horizontally to the left
(_R_) and the other vertically (_L_); and it is known that if we let
the length of the line _P_ represent to some convenient scale the
amount of direct pressure, then the lengths of _R_ and _L_ will also
represent to the same scale the amounts of horizontal and vertical
force due to the pressure. If the weight of kite and tail exceeds the
vertical force _L_, the kite will descend: if these weights are less
than that force, the kite will ascend. If they are precisely equal to
it, the kite will neither ascend nor descend. The ratio of _L_ to _R_
is determined by the slope of _P_; and this is fixed by the slope of
_ab_; so that we have the most important conclusion: _not only does
the amount of direct pressure (P) depend upon the obliquity of the
surface with the breeze (as has already been shown), but the relation
of vertical force (which sustains the kite) to horizontal force also
depends on the same obliquity_. For example, if the kite were flying
almost directly above the boy who held the string, so that _ab_ became
almost horizontal, _P_ would be nearly vertical and _L_ would be much
greater than _R_. On the other hand, if _ab_ were nearly vertical, the
kite flying at low elevation, the string and the direct pressure would
be nearly horizontal and _L_ would be much less than _R_. The force _L_
which lifts the kite seems to increase while _R_ decreases, as the kite
ascends: but _L_ may not actually increase, because it depends upon the
amount of direct pressure, _P_, as well as upon the direction of this
pressure; and the amount of direct pressure steadily decreases during
ascent, on account of the increasing obliquity of _ab_ with _V_. All of
this is of course dependent on the assumption that the kite always has
the same inclination to the string, and the described resolution of the
forces, although answering for illustrative purposes, is technically
incorrect.
It seems to be the wind velocity, then, which holds up the kite: but
in reality the string is just as necessary as the wind. If there is
no string, and the wind blows the kite with it, the kite comes down,
because the pressure is wholly due to a relative velocity as between
kite and wind. The wind exerts a pressure against the rear of a railway
train, if it happens to be blowing in that direction, and if we
stood on the rear platform of a stationary train we should feel that
pressure: but if the train is started up and caused to move at the same
speed as the wind there would be no pressure whatever.
One of the very first heavier-than-air flights ever recorded is said
to have been made by a Japanese who dropped bombs from an immense
man-carrying kite during the Satsuma rebellion of 1869. The kite as
a flying machine has, however, two drawbacks: it needs the wind--it
cannot fly in a calm--and it stands still. One early effort to improve
on this situation was made in 1856, when a man was towed in a sort of
kite which was hauled by a vehicle moving on the ground. In February
of the present year, Lieut. John Rodgers, U.S.N., was lifted 400 feet
from the deck of the cruiser _Pennsylvania_ by a train of eleven large
kites, the vessel steaming at twelve knots against an eight-knot
breeze. The aviator made observations and took photographs for about
fifteen minutes, while suspended from a tail cable about 100 feet
astern. In the absence of a sufficient natural breeze, an artificial
wind was thus produced by the motion imparted to the kite; and the
device permitted of reaching some destination. The next step was
obviously to get rid of the tractive vehicle and tow rope by carrying
propelling machinery on the kite. This had been accomplished by Langley
in 1896, who flew a thirty-pound model nearly a mile, using a steam
engine for power. The gasoline engine, first employed by Santos-Dumont
(in a dirigible balloon) in 1901, has made possible the present day
_aeroplane_.
[Illustration: SUSTAINING FORCE IN THE AEROPLANE]
What "keeps it up", in the case of this device, is likewise its
velocity. Looking from the side, _ab_ is the sail of the aeroplane,
which is moving toward the right at such speed as to produce the
equivalent of an air velocity _V_ to the left. This velocity causes the
direct pressure _P_, equivalent to a lifting force _L_ and a retarding
force _R_. The latter is the force which must be overcome by the motor:
the former must suffice to overcome the whole weight of the apparatus.
Travel in an aeroplane is like skating rapidly over very thin ice: the
air literally "doesn't have time to get away from underneath."
[Illustration: DIRECT, LIFTING, AND RESISTING FORCES
If the pressure is 10 lbs. when the wind blows directly toward the
surface (at an angle of 90 degrees), then the forces for other angles
of direction are as shown on the diagram. The _amounts_ of all forces
depend upon the wind velocity: that assumed in drawing the diagram
was about 55 miles per hour. But the _relations_ of the forces are
the same for the various angles, no matter what the velocity.]
If we designate the angle made by the wings (_ab_) with the horizontal
(_V_) as _B_, then _P_ increases as _B_ increases, while (as has been
stated) the ratio of _L_ to _R_ decreases. When the angle _B_ is a
right angle, the wings being in the position _a´b´_, _P_ has its
maximum value for direct wind--1/300 of the square of the velocity,
in pounds per square foot; but _L_ is zero and _R_ is equal to _P_.
The plane would have no lifting power. When the angle _B_ becomes
zero, position _a´´b´´_, wings being horizontal, _P_ becomes zero
and (so far as we can now judge) the plane has neither lifting power
nor retarding force. At some intermediate position, like _ab_, there
will be appreciable lifting and retarding forces. The chart shows the
approximate lifting force, in pounds per square foot, for various
angles. This force becomes a maximum at an angle of 45° (half a
right angle). We are not yet prepared to consider why in all actual
aeroplanes the angle of inclination is much less than this. The reason
will be shown presently. At this stage of the discussion we may note
that the lifting power per square foot of sail area varies with
the square of the velocity, _and_
the angle of inclination.
The total lifting power of the whole plane will also vary with its
area. As we do not wish this whole lifting power to be consumed in
overcoming the dead weight of the machine itself, we must keep the
parts light, and in particular must use for the wings a fabric of light
weight per unit of surface. These fabrics are frequently the same as
those used for the envelopes of balloons.
Since the total supporting power varies both with the sail area and
with the velocity, we may attain a given capacity either by employing
large sails or by using high speed. The size of sails for a given
machine varies inversely as the square of the speed. The original
Wright machine had 500 square feet of wings and a speed of forty
miles per hour. At eighty miles per hour the necessary sail area for
this machine would be only 125 square feet; and at 160 miles per hour
it would be only 31-1/4 square feet: while if we attempted to run the
machine at ten miles per hour we should need a sail area of 8000 square
feet. This explains why the aeroplane cannot go slowly.
It would seem as if when two or more superposed sails were used, as in
biplanes, the full effect of the air would not be realized, one sail
becalming the other. Experiments have shown this to be the case; but
there is no great reduction in lifting power unless the distance apart
is considerably less than the width of the planes.
In all present aeroplanes the sails are concaved on the under side.
This serves to keep the air from escaping from underneath as rapidly
as it otherwise would, and increases the lifting power from one-fourth
to one-half over that given by our 1/300 rule: the divisor becoming
roughly about 230 instead of 300.
[Illustration: SHAPES OF PLANES]
Why are the wings placed crosswise of the machine, when the other
arrangement--the greatest dimension in the line of flight--would seem
to be stronger? This is also done in order to "keep the air from
escaping from underneath." The sketch shows how much less easily the
air will get away from below a wing of the bird-like spread-out form
than from one relatively long and narrow but of the same area.
A sustaining force of two pounds per square foot of area has been
common in ordinary aeroplanes and is perhaps comparable with the
results of bird studies: but this figure is steadily increasing as
velocities increase.
Why so Many Sails?
Thus far a single wing or pair of wings would seem to fully answer
for practicable flight: yet every actual aeroplane has several small
wings at various points. The necessity for one of these had already
been discovered in the kite, which is built with a balancing tail. In
the sketch on page 18 it appears that the particles of air which are
near the upper edge of the surface are more obstructed in their effort
to get around and past than those near the lower edge. They have to
turn almost completely about, while the others are merely deflected.
This means that on the whole the upper air particles will exert more
pressure than the lower particles and that the "center of pressure"
(the point where the entire force of the wind may be assumed to act)
will be, not at the center of the surface, but at a point some distance
_above_ this center. This action is described as the "displacement of
the center of pressure." It is known that the displacement is greatest
for least inclinations of surface (as might be surmised from the
sketch already referred to), and that it is always proportional to the
dimension of the surface in the direction of movement; _i.e._, to the
length of the line _ab_.
[Illustration: BALANCING SAIL]
If the weight _W_ of the aeroplane acts downward at the center of the
wing (at _o_ in the accompanying sketch), while the direct pressure
_P_ acts at some point _c_ farther along toward the upper edge of
the wing, the two forces _W_ and _P_ tend to revolve the whole wing
in the direction indicated by the curved arrow. This rotation, in an
aeroplane, is resisted by the use of a tail plane or planes, such as
_mn_. The velocity produces a direct pressure _P´_ on the tail plane,
which opposes, like a lever, any rotation due to the action of _P_.
It may be considered a matter of rather nice calculation to get the
area and location of the tail plane just right: but we must remember
that the amount of pressure _P´_ can be greatly varied by changing
the inclination of the surface _mn_. This change of inclination is
effected by the operator, who has access to wires which are attached to
the pivoted tail plane. It is of course permissible to place the tail
plane _in front_ of the main planes--as in the original Wright machine
illustrated: but in this case, with the relative positions of _W_ and
_P_ already shown, the forward edge of the tail plane would have to be
depressed instead of elevated. The illustration shows the tail built as
a biplane, just as are the principal wings (page 141).
Suppose the machine to be started with the tail plane in a horizontal
position. As its speed increases, it rises and at the same time (if
the weight is suspended from the center of the main planes) tilts
backward. The tilting can be stopped by swinging the tail plane on its
pivot so as to oppose the rotative tendency. If this control is not
carried too far, the main planes will be allowed to maintain some of
their excessive inclination and ascent will continue. When the desired
altitude has been attained, the inclination of the main planes will, by
further swinging of the tail plane, be reduced to the normal amount,
at which the supporting power is precisely equal to the load; and the
machine will be in vertical equilibrium: an equilibrium which demands
at every moment, however, the attention of the operator.
In many machines, ascent and tilting are separately controlled by using
two sets of transverse planes, one set placed forward, and the other
set aft, of the main planes. In any case, quick ascent can be produced
only by an increase in the lifting force _L_ (see sketch, page 24) of
the main planes: and this force is increased by enlarging the angle of
inclination of the main planes, that is, by a controlled and partial
tilting. The forward transverse wing which produces this tilting is
therefore called the _elevating rudder_ or elevating plane. The rear
transverse plane which checks the tilting and steadies the machine is
often described as the _stabilizing plane_. _Descent_ is of course
produced by _decreasing_ the angle of inclination of the main planes.
[Illustration: ROE'S TRIPLANE AT WEMBLEY
(From Brewer's _Art of Aviation_)]