*Elements of Stability*. When we balance a board on a fulcrum so that it
stands in a perfectly horizontal position, the board is said to be "In
equilibrium," or is supported at its "Center of gravity." There is only
one point at which a body will balance, and this point is at the center
of gravity or "C. G." In an aeroplane, the combined mass of the body,
motor, wings, fuel, chassis, tail and live load has a center of gravity
or a balancing point at which the lift must be applied if the machine is
to rest in equilibrium. When the center of lift (or center of pressure)
does not pass through the center of gravity of the aeroplane, some other
force must be applied to overcome the unbalanced condition. When the
machine is unbalanced in a fore and aft direction with the tail low, a
force must be applied by the elevator flaps that is opposite and equal
to the moment of the unbalanced forces. An aeroplane is stable when it
is balanced in such a way that it returns to a state of equilibrium
after meeting with a disturbance.
When disturbed, a stable body does not usually return instantly to its
position of equilibrium, but reaches it after a series of decreasing
oscillations. The heavier the body, and the more compact its form, the
longer will it oscillate about its fulcrum before coming to rest. By
arranging broad surfaces at the ends of the oscillating body, a portion
of the energy will be expended in creating air currents, and the motion
will be readily "damped out." If the damping effect is so great that the
body does not swing back after once reaching the position of
equilibrium, the body is said to be "dead beat," or "dynamically
stable." There is a great difference between the static forces that tend
to return the body to a position of equilibrium and the dynamic
retarding forces that tend to damp out the oscillations. Usually, a body
with excessive static stability is far from being stable in a true
sense, since such a body tends to oscillate longer, and more violently,
than one in which the static restoring forces are not so strongly
marked. A body may be statically but not dynamically stable, but a
dynamically stable body must of necessity be statically stable.
Static stability in calm air is determined by the location of the center
of gravity, the center of lift, the center of propeller thrust, the
center of area of the surfaces, and the center of the forward
resistance. The forces acting through these centers are: (1) The weight;
(2) The lifting force; (3) The propeller thrust; (4) The resistance. The
weight and lift are vertical forces equal and opposite in direction. The
thrust and resistance are horizontal forces, also equal and opposite in
direction. When all of these forces intersect at a common point, they
will completely neutralize one another and the body will be in
equilibrium.
Dynamic stability is attained by the use of large damping surfaces such
as the stabilizer surface, fins, and the elevator. These act to kill the
oscillations set up by the static righting couples or forces. Without
suitable damping surfaces the machine would soon be out of control in
gusty weather since successive wind gusts will act to increase the
oscillations of the righting forces until the machine will turn
completely over. On the other hand, an aeroplane can be too stable and
therefore difficult to steer or control in gusts because of its tendency
toward changing its attitude with every gust in order to restore its
equilibrium. A machine should only be partially stable, and the majority
of pilots are firmly set against any form of mechanical or inherent
control. No matter how simple the method, mechanical control always
introduces a certain amount of mechanism that may go wrong. The question
of stability has already been solved to a sufficient extent.
A disturbance that simply changes the direction of travel is not
considered an unstable force since it normally does not tend to endanger
the machine. Nearly any machine, equipped with any possible form of
control apparatus, tends to change its direction when being righted.
*Axes of Stability*. An aeroplane has six degrees of freedom or motion.
Three are of translation or straight line motion, and three are of
rotation about rectangular axes. It can travel forward in a straight
line, rise and fall in a vertical plane, or skid sidewise. When it rolls
from side to side about the fore and aft axis (X axis) it is laterally
unstable. When pitching up and down in a fore and aft direction, and
around an axis parallel with the length of the wings (Y axis), the
machine is said to be longitudinally unstable. When swinging or "Yawing"
from right to left about a vertical axis (Z axis) it is unstable in
"Yaw."
Rolling is resisted by the ailerons, pitching by the elevators and
stabilizer, and yawing by the vertical directional rudder. Lateral
oscillation are damped out by the wing surfaces and by vertical surfaces
or "Fins." Longitudinal oscillations are damped mostly by the stabilizer
and elevator surfaces. Directional or yawing vibrations are corrected by
the damping action of the vertical tail fin, vertical rudder and the
sides of the body, the latter also serving to damp out longitudinal
vibrations. On an absolutely calm day, the pilot can shut off the motor
and glide down without touching the controls if the machine is
longitudinally stable. The glide generally starts with a few pitching
oscillations, but these gradually are damped out by the tail as soon as
the machine picks up its natural gliding angle and speed, and from this
point it will continue without oscillating.
*The Spiral and Nose Dive*. There are two forms of instability that have
not yet been fully corrected, and both are highly dangerous. One of
these is known as the "spiral dive" or nose spin, and the other as the
straight nose dive. The aeroplane in a spiral nose dive rotates rapidly
about a vertical axis during the dive. Spiral instability resulting from
lateral instability, can be minimized by decreasing the area of the
vertical rudder and by the proper placing of fins so that there is not
so great an excess of vertical area to the rear of the C. G.
The covered-in body acts as a fin and will be productive of spiral
instability if the area is not properly distributed. In the majority of
cases the rear of the body is equivalent to a large fin placed to the
rear of the C. G. A fin above the G. G. tends to reduce all spiralling.
*Stability and Speed*. An aeroplane in straight horizontal flight must
be driven at such an angle, and such a speed, that the weight is just
sustained. To be inherently stable the machine must always tend to
increase its speed by diving should the power be cut off in any way. An
aeroplane that does not tend to increase its speed in this way, "Stalls"
or becomes out of control. Any machine that will automatically pick up
its gliding angle after the propeller thrust has ceased is at least
partially inherently stable, and if it does not possess this degree of
stability, other forms of stability are practically worthless. The
machine having the smallest, flattest gliding angle is naturally safest
in cases of power failure, and hence the gliding angle is somewhat
related to the subject of stability.
[Illustration: A Spanish Aeroplane Using a Peculiar Form of Upper Fin.
These Fins Also Perform the Duty of Vertical Rudders as Well as Acting
as Stabilizers.]
The longitudinal stability decreases with a decrease in the speed, the
fore and aft vibrations becoming more rapid due to the decreased effect
of the tail surfaces, and to the reduction of wing lift. Instability at
low speeds is common to all aeroplanes, whether inherently stable or
not, and at a certain critical speed the machine becomes absolutely
unstable in a dynamic sense. If a machine is to be stable at low speeds,
it must not fly at too great an angle of incidence at these speeds, and
it should have a very large tail surface acting at a considerable
distance from the wings. Hunsaker states that the lowest speed should
not require more than 80 per cent of the total lift possible.
*Inertia or Flywheel Effect*. The principal weights should be
concentrated as nearly as possible at the center of gravity. Weights
placed at extreme outer positions, as at the wing tips, or far ahead of
the wings, tend to maintain oscillations by virtue of their flywheel
effect. The measure of this inertia or flywheelage is known as the
"Moment of Inertia" and is the sum of the products of all the masses by
the squares of their distances from the center of gravity. A great
amount of inertia must be met by a large damping surface or control area
if the vibrations are to be damped out in a given time. In twin-motored
aeroplanes the motors should be kept as close to the body as the
propellers will permit.
*Wind Gusts and Speed*. A machine flying at high speed is less affected
by wind gusts or variations in density than a slow machine, since the
disturbing currents are a smaller percentage of the total speed. In
addition, a high speed results in smaller stresses due to the gusts.
*Gyroscopic Instability*. The motor gyroscopic forces do not affect the
stability of a machine to any great extent, and in twin motored
aeroplanes the gyroscopic action of the propellers is almost entirely
neutralized. At one time the gyroscopic torque was blamed for every form
of instability, but on investigation it was found that the practical
effect was negligible.
*Instability Due Power Plant*. The power plant affects stability in a
number of ways. The thrust of the propeller may cause a fore and aft
moment if the center line of thrust does not pass through the center of
resistance. This causes the machine to be held head up, or head down,
according to whether the line of thrust is below or above the C. G. If
the propeller thrust tends to hold the head up in normal flight, the
machine will tend to dive, and assume its normal gliding velocity with
the power off, hence this is a condition of stability. With the effect
of the thrust neutral, or with the thrust passing through the center of
resistance, the machine will not tend to maintain the speed, and hence
it is likely to stall unless immediately corrected by the pilot. With
the line of thrust above the C. G., the stall effect is still further
increased since with this arrangement there is a very decided tendency
for the machine to nose up and increase the angle of incidence when the
power is cut off.
[Illustration: Steel Elevator and Rudder Construction Used on a European
Machine. The Elevators Also Act as Stabilizers, the Entire Surface
Turning About the Tube Spar.]
The slip stream of the propeller has a very decided effect on the tail
surfaces, these being much more effective when the propeller slip stream
passes over them. With lifting tails, or tails that normally carry a
part of the load, the stoppage of the slip stream decreases the lift of
the tail and consequently tends to stall the machine. Non-lifting tails
should be arranged so that the slip stream strikes down on the upper
surface. This tends to force the tail down, and the head up in normal
flight, and when the power ceases the tail will be relieved and there
will be an automatic tendency toward diving and increase in speed. On a
twin aeroplane, a similar effect is obtained by making the upper tips of
both propellers turn inwardly. The air is thus thrown down on the tail.
With a single motor, the torque tends to turn the aeroplane in a
direction opposite to the rotation of the propeller. Lateral stability
is thus interfered with when the motor is cut off or reduced in speed.
With right-hand propeller rotation, for example, the machine will be
turned toward the left, forcing the left tip down. To maintain a
horizontal attitude, the left aileron must be held down by an amount
just sufficient to overcome the torque. In some machines one wing tip is
given a permanent increase in incidence so that the down seeking tip is
given permanent additional lift.
*Lateral Stability*. When an aeroplane is turned sharply in a horizontal
plane, or "Yaws," the outer and faster moving wing tip receives the
greater lift, and a lateral rolling moment is produced about the fore
and aft axis. In the opposite condition, a lateral rolling moment tends
to yaw or to throw the aeroplane off a straight course. Below a certain
critical speed, the lateral or rolling oscillations increase in
amplitude, with a strong tendency to side slip, skid or spiral. The tail
fin or rudder retards the tail velocity in a side slip, and thus turns
the slipping or skidding machine into a vertical spiral or spinning nose
dive. This spin increases the angle of bank and hence the side slip.
This in turn increases the turning or yawing velocity, and the spiral
starts. This tendency toward a spiral dive can be corrected by a
vertical fin placed forward, and above the center of gravity, or by
raising the wing tips. An upper fin of this type will give a force that
tends to break up the bank when side slip starts and thus will prevent
spinning.
[Illustration: Sperry Gyroscopic Control System for Automatic Stability.
The Gyroscopic Control at the Left Controls the Movements of the
Electric Servo-Motor at the Extreme Right. This Motor Operates the
Control Surfaces Through the Pulley Shown. A Small Electric Generator
Between the Servo-Motor and Gyroscope Provides the Current and Is Driven
by a Small Wind Propeller.]
At normal speeds the rolling is damped down by the wing surfaces, and
can be further controlled by the application of the ailerons. At the
lower critical speed when the machine is stalled, one wing tip has no
more lift than the other, and hence the damping effect of the wings and
the action of the ailerons becomes negligible.
*Dutch Roll*. In "Dutch Roll," the rolling is accompanied by an
alternate yawing from right to left. This is aggravated by a fin placed
high above the C. G., and hence corrections for spiral dive conflict
with corrections for Dutch roll. The rolling is accompanied by some side
slip, and the motion is stable providing that there is sufficient fin in
the rear and not an excessive amount above the C. G.
*Degree of Stability*. Excessive stability is dangerous unless the
control surfaces are powerful enough to overcome the stable tendency.
Since a stable machine always seeks to face the relative wind, it
becomes difficult to handle in gusty weather, as it is continually
changing its course to meet periodic disturbances. This is aggravated by
a high degree of static stability, and may be positively dangerous when
landing in windy weather.
*Control Surfaces*. A non-lifting tail must give no lift when at a zero
angle of incidence. It must be symmetrical in section so that equal
values of lift are given by equal positive and negative angles of
incidence. Square edged, flat surfaces are not desirable because of
their great resistance. A double cambered surface is suitable for such
controls as the stabilizer, elevator and rudder. It has a low
resistance, permits of strong internal spars, and is symmetrical about
the line of the chord. Some tails are provided with a cambered top and a
flat bottom surface so that the down wash of the wings is neutralized.
Under ordinary conditions this would be an unsymmetrical lifting
surface, but when properly adapted to the wings the lifting effect is
completely neutralized by the down wash.
The curvature of the section should be such that the movement of the
center of pressure is as small as possible. With a small movement of the
center of pressure, the surface can be accurately balanced and hinged on
the center of pressure line. It is desirable to have the maximum
thickness of section at, or near to the C. P., so that a deep spar can
be used for the support of the hinge system. Usually the movement of the
control surfaces is limited to an angle of 30 degrees on either side of
the center line, as the lift of all surfaces start to decrease after
this point is reached. The surface movement should be limited by the
maximum lift angle of the section in any case, since an accident will be
bound to occur if they are allowed movement beyond the angle of maximum
lift.
In locating the control surfaces, careful attention should be paid to
the surrounding air conditions so that they will not be unduly affected
by the wash-down of the wings or body. The effectiveness of the tail
surfaces is very much reduced by bringing them close to the wings, and
the lift is always reduced by the wash of a covered fuselage.
The wash-down effect of the wings on the tail is proportional to the
chord and not to the span, and for this reason an increase in span does
not always necessitate an increase in the length of the body. An
adequate damping effect requires a large surface at the end of a long
lever arm.
*Balancing the Aeroplane*. Figs. 1 to 6 show the principles involved in
the balancing of the aeroplane. In Fig. 1 a number of weights 1’-2’-3’
and 5M are supported on a beam, the load being balanced on the fulcrum
point M. The load 2’ being directly over the fulcrum, has no influence
on the balance, but load 1’ at the left tends to turn the mass in a
left-hand direction, while 3’ and 5M tend to give it a right-hand
rotation. This turning tendency depends upon the weights of the bodies
and their distance from the fulcrum. The turning tendency or "Moment" is
measured by the product of the weight and the distance from the fulcrum.
If weight 1’ should be 10 pounds, and its distance A’ from the fulcrum
should be 20 inches, then it would cause a left-hand moment of 10 x 20 =
200 inch pounds. If the system is to be in balance, then the left-hand
moment of 1’ should be equal to the sum of the moments of 3’ and 5M.
Thus: 1’ x A = (3’ x B) + (5M x C’).
[Illustration: Figs. 1-6. Methods of Balancing an Aeroplane About Center
of Lift.]
The application of this principle as applied to a monoplane is shown by
Fig. 4, in which X-X is the center of pressure or lift. The center of
lift corresponds to the fulcrum in Fig. 1, and the weights of the
aeroplane masses and their distance from the center of lift are shown by
the same letter as in Fig. 1. The engine 1’ is at the right of the C. P.
by the distance A, while the fuel tank 2 is placed on the C. P. in the
same way that the weight 2’ in Fig. 1 is placed directly over the
fulcrum. By placing the tank in this position, the balance is not
affected by the emptying of the fuel since it exerts no moment. The
chassis G acting through the distance E is in the same direction as the
engine load. The body 5 with its center of gravity at M acts through the
distance C, while the weight of the pilot 3 exerts a right-hand moment
with the lever arm length B. If the moments of all these weights are not
in equilibrium, an additional force must be exerted by the tail V.
Fig. 2 shows an additional weight 4’ that corresponds to the weight of
the passenger 4 in Fig. 5. This tends to increase the right turning
moment unless the fulcrum is moved toward the new load. In Fig. 2 the
fulcrum M remains at the same point as in Fig. 1, hence the system
requires a new force P’ acting up at the end of the beam. If the load
was in equilibrium before the addition of 4’, then the force P’ must be
such that P’ x T’ = 4" x D’. In the equivalent Fig. 5, the center of
gravity has moved from its former position at S to the new position at
R, the extent of the motion being indicated by U. To hold this in
equilibrium, an upward force P must be exerted by the elevator at Y, the
lever arm being equal to (T + U).
Fig. 6 shows the single-seater, but under a new condition, the center of
pressure having moved back from X-X to Z. To hold the aeroplane in
equilibrium, a downward force must be provided by the tail V which will
cause a right-hand moment equal to the product of the entire weight and
the distance U. For every shift in the center of pressure, there must be
a corresponding moment provided by the elevator surface. The condition
is shown by the simple loaded beam of Fig. 3. In this case the fulcrum
has been moved from M to N, a distance equal to the center of pressure
movement in Fig. 6. This requires a downward force P’ to maintain
equilibrium.
*Center of Pressure Calculation*. Fig. 7 is a diagram showing the method
of calculating the center of gravity. The reference line R is shown
below the elevators and is drawn parallel to the center of pressure line
W-W, the latter line being assumed to pass through the center of
gravity. The line R may be located at any convenient point, as at the
propeller flange or elsewhere, but for clearness in illustration it is
located to the rear of the aeroplane. The weight of each item is
multiplied by the distance of its center of gravity from the line R,
these products are added, and the sum is then divided by the total
weight of the machine. The result of this division gives the distance of
the center of gravity from the line R. Thus, if the center of gravity of
the body (11) is located at (10), then the product of the body weight
multiplied by the distance B will give the moment of the body about the
line R. The weight of the motor (2) multiplied by the distance F gives
the moment of the motor about R, and so on through the list of items.
[Illustration: Center Of Gravity Table]
The distance of the center of gravity (or center of pressure) from the
reference line R is given by H + K. This gives the numerical value
219350/1375 = 1596 inches. Thus if we measure 159.6 inches from R toward
the wings we will have located the center of gravity. The location of
the C. G. can be changed by shifting the weights of the motor,
passenger, or other easily moved items. In any case, the C. G. should
lie near the center of pressure.
*Tail Lever Arms*. The effective damping moment exerted by the fixed
stabilizer surface (12) will be the product of its area by the distance
(I), measured from the center of pressure of the wing to the center of
pressure of the stabilizer. The lever arm of the elevator is the
distance (H) measured from the centers of pressure as before.
[Illustration: Fig. 7. Method of Determining the Center of Gravity of an
Aeroplane.]
*Resultant Forces and Moments in Flight*. The aeroplane is in
equilibrium when all of the forces pass through a common center, as
shown by Fig. 8. In this figure the lift (L), the weight (W), the line
of propeller thrust (T), and the resistance (R) all pass through the
center of gravity shown by the black dot C. G. There are no moments and
hence no correction is needed from the elevator (T). In Fig. 9, the
thrust and resistance pass through the center of gravity as before, but
the center of lift (L) does not pass through the center of gravity, the
distance between the two being indicated by (n). This causes a moment,
the length of the lever arm (n) being effective in giving a right-hand
rotation to the body. If horizontal flight is to be had this must be
resisted by the upward elevator force (E).
In Fig. 10, the lift passes through the center of gravity, but the line
of resistance lies below it by the amount (m). The thrust (T) tends to
rotate the machine in a left-handed direction. The elevator must exert a
downward force (e) to resist the moment caused by (m). This is a bad
disposition of forces, as the machine would tend to stall or tail-dive
should the propeller thrust cease for even an instant. The stability of
Figs. 8 and 9 would not be affected by the propeller thrust, as it
passes through the C. G. in both cases. In Fig. 11, the center line of
thrust is below the line of resistance (R), so that the thrust tends to
hold the nose up. Should the motor fail in this case, the nose would
drop and the machine would start on its gliding angle and pick up speed.
In Fig. 12 none of the forces intersect at a common point, the lift and
weight forming a right-handed couple, while the thrust (T) and the
resistance (R) form a left-handed couple that opposes the couple set up
by the weight and lift forces. If the thrust-resistance couple can be
made equal to the lift-weight couple, the aeroplane will be in
equilibrium and will need no assistance from the elevator. As the
weights in the aeroplane are all located at different heights, it is
necessary to obtain the center of gravity of all the loads in a vertical
plane as well as horizontally. Thus in Fig. 13 the line C. G. is the
center of gravity of the engine weight (1), the wing weight (2), the
pilot’s weight (3), the chassis weight (4), the fuselage weight (5), and
the fuel tank weight (6). The line C. G. is the effective center of all
these loads, and is calculated by taking the products of the weights by
the distance from a reference line such as R-R. The center of resistance
is the effective center of all the resistance producing items such as
the wings, body, struts, chassis, etc.
[Illustration: Figs. 8-15. Forces Affecting the Longitudinal Stability
of an Aeroplane.]
A suggestion of the method employed in obtaining the center of
resistance is shown by Fig. 14, the center line of resistance R-R being
the resultant of the wing resistance (D), the body resistance (B), and
the chassis resistance (C). It will be noted that the wing resistance of
biplane wings (W-W’) does not lay midway between the wings but rather
closer to the upper wing, as shown by (E). This is due to the upper wing
performing the greater part of the lift. In locating the center of
resistance, the resistance forces are treated exactly like the weights
in the C. G. determination. Each force is multiplied by its distance
from a horizontal reference line, and the sum of the products is divided
by the total resistance. As shown, the center of resistance R-R passes
through the center of gravity C. G. The center of pressure line X-X also
contains the center of resistance.
A staggered biplane cell is shown by Fig. 15, the center of pressure of
the upper and lower wings being connected by the line X-X as before. The
center of resistance of the pair is shown at (D), where it is closer to
the upper wing than to the lower. A vertical line Y-Y dropped through
the center of resistance gives the location of the center of lift. As
shown, the center of lift is brought forward by the stagger until it is
a distance (g) in front of the leading edge of the lower wing. The
center of lift and the center of resistance both lie on a line
connecting the center of pressure of the upper and lower wings.
*Calculation of Control Surfaces*. It is almost impossible to give a
hard and fast rule for the calculation of the control surfaces. The area
of the ailerons and tail surfaces depends upon the degree of stability
of the main wings, upon the moment of inertia of the complete machine,
and upon the turning moments. If the wings are swept back or set with a
stagger-decalage arrangement, they will require less tail than an
orthogonal cell. All of these quantities have to be worked out
differently for every individual case.
*Aileron Calculations*. The ailerons may be used only on the upper wing
(2 ailerons), or they may be used on both the upper and lower wings.
When only two are used on the upper wing it is usually the practice to
have considerable overhang. When the wings are of equal length either
two or four ailerons may be used. Roughly, the ailerons are about
one-quarter of the wing span in length. With a long span, a given
aileron area will be more effective because of its greater lever arm.
If a = area of ailerons, and A = total wing area in square feet, with S
= wing span in feet, the aileron area becomes: a = 3.2A/S. It should be
borne in mind that this applies only to an aeroplane having two ailerons
on the upper wing, since a four-aileron type usually has about 50 per
cent more aileron area for the same wing area and wing span. For,
example, let the wing span be 40 feet and the area of the wings be 440
square feet, then the aileron area will be: a = 3.2A/S = 3.2 x 440/40 =
35.2 square feet. If four ailerons were employed, two on the upper and
two on the lower wing, the area would be increased to 1.5 x 35.2 = 52.8
square feet. As an example in the sizes of ailerons, the following table
will be of interest:
[Illustration: Aileron Sizes Table]
In cases where the upper and lower spans are not equal, take the average
span—that is, one-half the sum of the two spans.
*Stabilizer and Elevator Calculations*. These surfaces should properly
be calculated from the values of the upsetting couples and moments of
inertia, but a rough rule can be given that will approximate the area.
If a’ = combined area of stabilizer and elevator in square feet; L =
distance from C. P. of wings to the C. P. of tail surface; A = Area of
wings in square feet, and C = chord of wings in feet, then:
a’ = 0.51AC/L. Assuming our area as 430 square feet, the chord as 5.7
feet, and the lever arm as 20 feet, then:
a’ = 0.51AC/L = 0.51 x 430 x 5.7/20 = 62.5 square feet, the combined
area of the elevators and stabilizer. The relation between the elevator
and stabilizer areas is not a fixed quantity, but machines having a
stabilizer about 20 per cent greater than the elevator give good
results. In the example just given, the elevator area will be: 62.5/22 =
28.41 square feet, where 2.2 is the constant obtained from the ratio of
sizes. The area of the stabilizer is obtained from: 28.41 x 1.2 = 34.1
square feet.
*Negative Stabilizers*. A considerable amount of inherent longitudinal
stability is obtained by placing the stabilizing surface at a slight
negative angle with the wings. This angle generally varies from -2° to
-6°. At small angles of wing incidence the negative angle of the tail
will be at a maximum, and acting down will oppose further diving and
tend to head the machine up. At large wing angles, the tail will be
depressed so far that the tail angle will become positive instead of
negative, and thus the lift on the tail will oppose the wings and will
force the machine to a smaller angle of incidence. The negative angle
can thus be adjusted to give longitudinal stability within the ordinary
range of flight angles.
*Stabilizer Shapes and Aspect Ratio*. Stabilizers have been built in a
great number of different shapes, semicircular, triangular, elliptical,
and of rectangular wing form. Measured at the rear hinged joint, the
span or width of the stabilizer is about 1/3 the wing span for speed
scouts, and about 1/4 the wing span for the larger machines. Nearly all
modern machines have non-lifting tails, or tails so modified that they
are nearly non-lifting. Since flat plates give the greatest lift with a
small aspect ratio, and hence are most effective when running over the
ground at low speeds, the stabilizers and elevators are of comparatively
low aspect. In general, an aspect ratio of 3 is a good value for the
stabilizer. Vertical rudders generally have an aspect ratio of 1, and
hence are even more effective per unit area than the stabilizers. This
is particularly necessary in ground running.
[Illustration: Aileron Control Diagram of Curtiss JN4-B.]
[Illustration: Elevator Control Diagram of Curtiss JN4-B.]
*Vertical Rudders*. The calculation of the vertical rudders must take
the moment of inertia and yawing moments into effect, and this is rather
a complicated calculation for the beginner. As an approximation, the
area of the rudder can be taken from 9 to 12 square feet for machines of
about 40 feet span, and from 5 to 8 square feet for speed scouts.
[Illustration: Stick Control Used on the Caudron Biplane. Wing Warp Is
Used Instead of Ailerons. Back and Forth Movement Actuates Elevator.]
[Illustration: German Stick Control With Double Grips. A. Latch on the
Side of the Stick Acts on a Sector So That the Lever Can Be Held at Any
Point. It Is Released by the Pressure of the Knees.]
*Wing Stability*. Under wing sections, the subject of the center of
pressure movement has already been dealt with. The variation of the
center of pressure with the angle of incidence tends to destroy
longitudinal stability since the center of pressure does not at all
times pass through the center of gravity. On some wings, the camber is
such that the variation in the position of the center of pressure is
very little, and hence these are known as stable wings. A reflex curve
in the trailing edge of a wing reduces the center of pressure movement,
and swept back wings are also used as an aid in securing longitudinal
stability. Introducing stagger and decalage into a biplane pair can be
made to produce almost perfect static longitudinal stability. It should
be noted that stability obtained by wing and camber arrangements is
static only, and requires damping surfaces to obtain dynamic stability.
[Illustration: Form of Control Used on the Nieuport Monoplane.]
*Manual Controls*. In flight, the aviator has three control surfaces to
operate, the ailerons, elevator, and rudder. In the usual form of
machine the ailerons and elevator are operated by a single lever or
control column, while the rudder is connected with a foot bar. In the
smaller machines "Stick Control" is generally used, the ailerons and
elevator being moved through a simple lever or "Joy Stick" which is
pivoted at its lower end to the floor. The Deperdussin or "Dep" control
is standard with the larger machines and consists of an inverted "U"
form yoke on which is mounted the wheel for operating the ailerons.
*Stick Control*. With the stick pivoted at the bottom, a forward
movement of the lever causes the machine to descend while a backward
movement or pull toward the pilot causes the aeroplane to head up or
ascend. The stick is connected with the elevators with crossed wires, so
that the flaps move in an opposite direction to the "Stick." Moving the
stick from side to side operates the ailerons.
[Illustration: Standard Stick Control and Movements Used in the U.S.A.]
*Deperdussin Control*. A "U" shaped yoke, either of bent wood or steel
tube, is pivoted the bearers at the sides of the fuselage. Wires are
attached to the bottom of the yoke so that its back and forth movement
is communicated to the elevator flaps. On the top, and in the center of
the yoke, is pivoted a hand wheel of the automobile steering type. This
is provided with a pulley and is connected with the aileron flaps in
such a way that turning the wheel toward the high wing tip causes it to
descend. Pushing the yoke forward and away from the aviator causes the
machine to descend, while a reverse movement raises the nose. The "Dep"
control is reliable and powerful but is bulky and heavy, and requires a
wide body in order to allow room for the pilot.
[Illustration: Foot Rudder Bar Used in the Standard H-3. Courtesy
"Aerial Age."]
*Rudder Control*. Foot bar control for the rudder is standard with both
the stick and Dep controls. The foot bar is connected with the rudder in
such a way that the aeroplane turns opposite to the movement of the foot
bar in the manner of a boat. That is, pushing the right end of the bar
forward causes the machine to turn toward the right.
[Illustration: Automatic Control System (Sperry) Installed in Fuselage
of Curtiss Tractor Biplane.]