PRINCIPLES OF FLIGHT
=Support of an Airplane by Its Wings.=—An airplane is supported just
as definitely as though on top of a post, and by the same law, namely
reaction. If you try to sweep the air downward with a wing held at a
slight angle, the air just before it consents to be pushed downward,
delivers a momentary reaction which is upward. If you have a bag of
air in your hand it exerts no push upward of course; but the minute
you give it a quick push downward it resists, due to its inertia, thus
delivering an upward “reaction” against your hand.
Whenever you move anything, it reacts an amount just equal to the force
that is moving it; if you move a bullet out of a gun, just before
starting the bullet reacts and you have “kick.” If you should shoot a
thousand guns downward, the reaction would be considerable, and for the
instant might be sufficient to support heavy weight.
The airplane is a device for pushing downward millions of little
bullets, made out of air and exceedingly small and light. The wing of
an airplane sweeps through these bullets, or molecules, of air like a
horizontal plow, wedges the particles downward in vast numbers and in
a continual stream, making up in amount what is lacking in weight, so
that as long as the airplane rushes along, there are many thousands
of cubic feet of air forced down beneath its wings, delivering up
a reaction that results in complete support for the machine. This
reaction is just as definite and secure as though the machine were
supported from the ground on wheels, but it disappears entirely when
the airplane is at rest. Part of the whir of a training machine as it
glides back to earth is made by the air driven downward from the wings;
the same phenomenon may be noticed when a bat flies close to your ears
at night, and if you were a few feet below the airplane as it flew, you
would feel the rush of air driven downward from its wings (see Fig. 16).
The net result of all the reactive pushes from this air is =lift=. It
may amount to several pounds for every square foot of the wing surface.
This is all that need be said about why the air supports an airplane;
all you have to remember is that as long as you have the forward
sweeping movement, you will have the lift.
The forward movement is absolutely essential, however, and to maintain
it requires a lot of horsepower and gasoline. For it is by means of
the engine and propeller that this forward movement is maintained. The
engine is a device for creating forward movement—the propeller drives
the machine ahead in exactly the same way as is the case in a torpedo,
or steamboat.
[Illustration: FIG. 16.—Relative path of air particles past an airplane.
This diagram illustrates the general downward trend of the stratum of
air met by the wings.]
=Lift.=—Assuming that we have all the forward motion needed, let
us now investigate the lift that results. Experimenters such as
the Wrights and others have found out how to get this lift most
conveniently. Lift depends upon the four following factors:
1. Area. 2. Density of air. 3. Angle of incidence. 4. Speed of motion.
1. _Relation of Area of Wings to Support._—Consider a small wing;
suppose it to be held by hand outside a train window in a given
attitude, its area being 1 sq. ft. It tends to lift a certain amount,
say 5 lb. Now increase its size to 2 sq. ft. and it will lift with
10-lb. force, tending to get away from your grasp. Rule: When only the
area of a wing is changed, its lift varies with the area. If, as above
mentioned, you can get 5 lb. of lift from each square foot of wing
surface, you can by the same sign get 10-lb. of lift from 2 sq. ft. And
if you have 500 sq. ft. of surface you can get 2500 lb. of lift.
[Illustration: FIG. 17.—Diagram showing that in fast airplanes wings
are small; in slow airplanes wings are large.
(Above) Small wings; speed 115 mi. per hr.; for fighting. One seat.
(Below) Large wings; speed 80 mi. per hr.; for reconnaissance. Two
seats.]
Regarding =area= of wing surface, the pilot does not have to worry in
a flight since he can do nothing to change it anyway. All he needs to
know is that in different airplanes small wing area accompanies high
speed and small weight-carrying capacity, as in the case of the Fokker
and Sopwith speed scouts (see Fig. 17). Conversely, large wing areas
are used for heavy load carrying and slow speed (see Fig. 18). Speed
and weight-carrying capacity thus appear to be antagonistic and can not
both be attained with efficiency, but only at the expense of enormous
power. The incompatibility between high speed and weight carrying keeps
the designer busy in efforts toward a reconciliation.
[Illustration: FIG. 18.—Diagram showing use of large wings for heavy
airplanes, and small wings for light airplanes.]
2. _Density._—The second factor affecting the lift is the character of
the air itself. I refer to the density of the air. The heavier each
particle of air becomes, the more reaction it can furnish to the wing
that drives it downward; so on days when the barometer is high the wing
will lift more than on other days. Now the air is heaviest, or most
dense, right near the ground; because in supporting the 50 miles or so
of air above it, it becomes compressed and has more weight per cubic
foot. Therefore, the wing gets more lift at a low altitude than at a
high. Some airplanes will fly when low down but won’t fly at all high
up. In Mexico, for instance, when the punitive expedition started out
they were already at an altitude of several thousand feet above sea
level. The airplanes had been built for use at places like New York and
England, close to sea level, and when our army officers tried to fly
with them in Mexico, they would not fly properly, and the factory had
to redesign them.
Regarding _density_, the pilot should know that for a low density he
should theoretically get a high speed. As density decreases, high up in
the air, the speed tends to increase, and moreover he gets more speed
for the same amount of gasoline. Unfortunately, at an altitude the
motor power falls off, so that nowadays the speed is not faster high up
than low down; but when the motor builders succeed in designing their
motors to give the same horsepower at 20,000 ft. as they do on the
ground, airplanes will be able to reach terrific speed by doing their
work above the clouds.
It is found desirable to give large wings to airplanes which are going
to fly at high altitudes, so as to offset the lack of density by an
increase in area, thus leaving the angle range—that is, the speed
range—as large as possible. The army airplanes in Mexico mentioned
above were simply given a new set of larger wings to offset the lower
air density in Mexico, and thereafter flew better.
3. _Angle of Incidence._—The angle of incidence is defined as the
_angle between the wing-chord and the line of flight_. The line of
flight is the direction of motion of the airplane, and is distinct from
the axis of the airplane which corresponds with the line of flight only
for a single angle of incidence. If the line of flight is horizontal,
the airplane may be flying tail-high, tail-level, or tail-low; that is,
its axis may have varying positions for a given line of flight. This
is true, if the line of flight is inclined, as in climbing. It is a
mistake to confuse the line of flight with the axis of the machine.
The angle of incidence of the wings of the U. S. training machine
may have any value from 15° down. When the angle is smaller the lift
of the wings is smaller. Consider the model wing held out of a train
window; if its front edge is tilted up to an angle of 15° with the line
of motion it will lift say 1 lb.; if reduced to a 10° angle, it will
lift less, say ⅔ lb. A model of the training-machine wing could be
tilted down to an angle several degrees less than zero before its lift
disappeared, because it is a curved, not a flat wing; this angle would
be the “neutral-lift” angle; notice then that O° is not a neutral-lift
angle, and therefore may be used in flight.
If the model wing were tilted up to an angle greater than 15°, the lift
would not increase any more, but would be found to decrease. For this
wing, 15° is called the critical, or “Stalling” angle, beyond which it
is unwise to go.
4. _Velocity._—If the model wing which is imagined to be held out of
the car window, is held now in a fixed position at a given angle of
incidence, any change of the train’s speed will result in a change
of lift; should the speed rise from 30 miles per hour to double this
value, the lift would increase enormously, fourfold in fact.
Lift varies as the square of the speed. Thus any increase or decrease
of speed results in a great increase or decrease of lift.
=Interdependence of Angle of Incidence and Velocity.=—The four factors
above mentioned all contribute to the lift; if in an airplane wing each
factor be given a definite value, the resulting lift is determined
according to the formula:
_L = KrAV^2_
where _L_ is lift.
_K_ is a coefficient referring to the angle.
_A_ is the area.
_V_ is the velocity.
_r_ is the density.
Two only of these quantities change materially in flight, the angle
and the velocity; the lift itself remains substantially the same under
most normal circumstances. The angle always changes simultaneously with
the velocity, increasing when the velocity decreases. Thus the drop of
lift due to velocity decrease is balanced by gain of lift due to angle
increase, and the lift remains unchanged when speed changes.
Speed change then requires that the pilot alter the angle of incidence
simultaneously with the throttle; so there are two things to do, unlike
the case of the automobile where only the throttle is altered.
=Minimum Speed.=—When, in slowing up an airplane, the angle of
incidence reaches the 15° limit, no further decrease of speed is
allowable; therefore, the critical angle determines the minimum limit
of speed. If for any reason the machine exceeds the 15° limit, it must
speed up to gain support; that is, the pilot has to increase angle and
speed simultaneously instead of oppositely.
=Efficiency of Airplane Wings.=—I said at the beginning of this chapter
that the airplane was a device for pushing down an enormous quantity
of air. A certain amount of force has to be furnished in order to
keep the airplane moving, and this force is furnished by the engine
and propeller. The propeller by giving a certain amount of push in a
horizontal direction to the airplane wing enables this wing to extract
from the air ten or twenty times this amount of push in a vertical
direction; that is, the airplane wing will give you 10 lb. or more of
lifting in exchange for 1 lb. of push.
[Illustration: FIG. 19.
Lift and Drift.—Lift is perpendicular to line of flight, drift is
parallel.
Angle of Incidence.—Wing in position shown has angle of 5° if moving
in direction “A,” 10° if in direction “B;” and a negative angle of 4°
if moving in direction “C.” In the last case it is moving along its
neutral-lift-line, lift becomes zero. ]
The propeller push is necessary to overcome the drift or resistance of
the wings to forward motion. It appears then that the airplane wing as
it moves through the air has two forces on it, one acting straight up
and called “lift,” the other acting straight back and called “drift”
(see Fig. 19). The lift is several times greater than the drift, and
the situation is quite analogous to that of a kite, which rises upward
in the air due to its lift but at the same time drifts backward with
the wind due to its drift. In the case of the kite the string takes up
an angle which just balances the joint effect of the lift and drift.
The efficiency of an airplane wing is indicated by the ratio of lift
to drift, and for a given lift, the efficiency is best, therefore, for
small drift. If the lift is 1900 lb. and the wing drift 190 lb.,
Wing efficiency = Lift or weight/Wing drift = 1900/190 = 10
=Factors Determining Best Efficiency.=—It goes without saying that an
airplane wing should attain the best efficiency it can, and there are
several ways of doing this.
The first relates to the question of angle of incidence; we have
already discussed the effect of angle on lift, but when we come to
discuss its effect on efficiency we find that there is only one angle
at which we can get the best efficiency. This is a small angle, about
3° to 6°; at this angle the lift is nowhere near as much as it would be
at 10° or 15°, but the drift is so small compared to the lift that it
is found desirable in airplanes to employ these small angles for normal
flight. As the angle increases above this value of maximum efficiency,
the efficiency drops off, and when you get up to the stalling angle,
the efficiency becomes very low indeed (see Fig. 20).
[Illustration: FIG. 20.—Wing characteristics.
Curves showing lift, drift, efficiency, and center of pressure travel
of typical training-airplane wing, as determined in Aerodynamical
Laboratory.]
The second way to get good efficiency is to choose the shape of the
wings properly. For instance, early experimenters tried to get results
with flat wings, and failed completely, for the flat wing proved to be
very inefficient. When it was observed that birds had curved wings,
this principle was applied to early experiments and then for the
first time man was able to obtain support in a flying machine. The
fundamental principle of efficiency in wings is that they must be
curved, or cambered, as it is sometimes called. This is because as the
wing rushes onward it wants to sweep the air downward smoothly and
without shock, as can be done only when the wing is curved (see air
flow, Fig. 21).
[Illustration: FIG. 21.—Efficiency of curved and flat wing.
(_a_) Air flow past curved wing is smooth without much eddying; (_b_)
air flow past flat wing produces eddies above it.]
The question of wing curvature is exceedingly important then; we find
that the curvature of its upper surface is particularly so. We notice
that airplane wings all have a certain thickness in order to enclose
the spars and ribs; it is not necessarily a disadvantage for them to
be thick, due to the fact that the upper curve of the wing does most
of the lifting anyway, and the lower side is relatively unimportant.
You can make the lower surface almost flat, without much hurting the
effect of the wing, so long as the upper surface remains properly
curved. However, the upper surface must be accurately shaped, and is
so important that in some machines we find cloth is not relied on to
maintain this delicate shape, but thin wood veneer is used (I refer to
the front upper part of the wing). In general, then, wings are thick
toward the front and taper down to a thin trailing edge.
[Illustration: FIG. 22.—Diagram of vacuum and pressure on airplane
wings.
Note in biplane reduced vacuum on bottom wing.]
You may wonder how it was found that the upper surface of the wing was
the most important; and I will say that this was one of the interesting
discoveries of the early history of aerodynamics. People at first
thought that a wing sweeping through the air derived its support
entirely from the air which struck the bottom of the wing, and they
assumed that if the bottom of the wing were properly shaped, the top
did not matter; that is, all the pressure in the air was delivered
up against the bottom surface. But a French experimenter conceived
the idea of inserting little pressure gages at various points around
the wing. He found, it is true, that there was considerable pressure
exerted in the air against the bottom of the wing; but he found a more
surprising fact when he measured the condition above the wing. When he
applied his gage to the upper surface of the wing, it read backward,
that is, showed a vacuum, and a very pronounced one. He found that
there was a vacuum sucking the top part of the wing upward twice as
hard as the pressure underneath was pushing; so that two-thirds of the
total lift on this wing was due to vacuum above it (see Fig. 22).
In the diagram the shaded area on top of the wing represents vacuum
above, that below the wing represents pressure beneath.
[Illustration: FIG. 23.—Wings of small and large aspect ratio]
=Aspect Ratio.=—The third factor in wing efficiency has to do with
the plan shape. It was early found that square wings were not much
good, and that if you made them wide in span like those of a bird, the
efficiency was best (see Fig. 23). Aspect ratio is the term which gives
the relation of the span to the fore and aft dimension of the wing,
and this relation is usually equal to six or so. The reason why large
aspect ratios are advantageous is as follows:
The tips of all wings are inefficient, because they allow the air
to slip sideways around the ends, and there is all the trouble of
disturbing this air without extracting any considerable lift from
it. In a wide-span wing these inefficient wing tips are only a small
percentage of the total area, but in a small-span wing they may be an
important consideration (see Fig. 24).
[Illustration: FIG. 24.—Diagram illustrating aspect-ratio effect.
Arrows show direction of air flow past plate; note that air escapes
sideways around sides of plate. This phenomenon occurs at the tips of
all airplane wings and accounts for small efficiency of narrow-span
wings. ]
=Wing Arrangements.=—All the foregoing remarks in this chapter have
applied only to a single wing. They apply in general to double or
triple wings (biplanes and triplanes), but the matter of arranging
multiple wings affects the efficiency.
The monoplane with its single layer of wings is the most efficient type
of flying machine. We find if we arrange wings into the biplane shape
that the presence of the upper wing interferes with the vacuum formed
above the lower wing, and the efficiency decreases (see Fig. 22). The
same is true of the triplane and the quadruplane arrangement. If all we
wanted in airplanes was efficiency, we would use monoplanes, but the
biplane is pretty popular now in spite of its low efficiency; this is
because it can be much more strongly trussed than the monoplane, and
also because of the fact that sufficient area may be secured with less
span of wings.
It may be said that the low efficiency of the biplane can be somewhat
relieved by spacing the upper and lower wings at a considerable
distance apart; but if they are spaced at a distance much greater than
the chord, it requires extra long struts and wires, and the resistance
and weight of these will offset the advantage of wider spacing; so that
practically biplane-wing efficiency may be taken as 85 per cent. of
monoplane efficiency.
It remains to mention the tandem arrangement, used in all airplanes,
where the tail is a tandem surface in conjunction with the wings.
A surface located in the position of an airplane tail is at a
disadvantage and shows low efficiency for flight purposes. This is
because the main wings deflect the air downward and when the tail comes
along it meets air which has a more or less downward trend, instead of
encountering fresh, undisturbed air (see Fig. 16).
=Resistance of an Airplane to Motion.=—Earlier in this chapter the
support of an airplane was explained and it was seen that the weight
was exactly equalled by the lift or support; it was also explained that
the production of this lift required considerable force in moving the
wings rapidly through the air. It is not only the wings, however, which
require force to overcome the resistance to motion. In order to have
any wings at all it is unfortunately necessary to supply also struts,
wires, etc., for bracing these wings, also a motor and seat for the
passenger, which are usually included inside a fuselage, also wheels
for landing and various control surfaces. None of these accessories to
the wings contribute material lift, but they involve a large amount of
resistance which is therefore a dead loss. Note carefully that there
are two distinct sorts of resistance: (1) that of the wings, which is
the necessary price paid for securing lift; (2) that of all the rest
of the machine, in return for which nothing beneficial is received,
and which therefore has sometimes been called “parasite” or “deadhead”
resistance.
In a typical training machine the total resistance to be overcome if
forward motion is maintained is as follows: (See Fig. 26.)
_At 72 miles per hour_:
Wings 160 lb.
Deadhead {Fuselage 75}
resistance {Wiring 70}
{Struts 20} 195
{Miscellaneous}
{ Balance 30}
———
Total 355 lb.
_At a speed of 57 miles per hour_:
Wings 158 lb.
Deadhead resistance 130
———
Total 288 lb.
_At a speed of 43 miles per hour_:
Wings 350 lb.
Deadhead resistance 125
———
Total 475 lb.
It is seen that the above resistance values total to the highest figure
at the lowest speed, and that the lowest value of resistance occurs at
an intermediate speed; the resistance decreases as the speed decreases
from 73 to 57 miles per hour; but a further decrease in speed finds the
resistance running up rapidly so that at minimum speed the resistance
is very great again. This is due to the fact that at high speeds the
deadhead resistance exceeds that of the wings but at slow speeds
although the deadhead resistance is very small, the wings being turned
up to a large angle within the air, have a resistance which is at its
maximum. This seems clear enough when we remember that the lift of the
wings remains the same as the angle decreases (and speed goes up) but
that the efficiency of the wings increases so that the wing resistance
is a smaller fraction of the lift at high speed than at low speed.
=Cause of Resistance.=—Wing resistance, which is affected, as mentioned
previously, by the wing curvature, can not be decreased unless new and
improved sorts of wings are invented. As to deadhead resistance, it
may be decreased in future by methods of construction which eliminate
unessential parts. In a high-speed airplane in this country an attempt
was made to eliminate the wires altogether and most of the struts
(because the wiring is one of the largest single items of deadhead
resistance); so far the attempt has failed for structural reasons. In
the monoplane type of airplane of course the struts are eliminated,
which is an advantage from the standpoint of resistance.
[Illustration: FIG. 25.—Diagram illustrating advantage of stream-line
shape.
Note large eddy disturbance and vacuum behind round shape, causing high
resistance.]
As long as struts, wires, etc., are used at all, the minimum resistance
can be secured by giving them a proper “stream-line” shape. The
stream-line shape is one in which the thickest part is in front and
tapers off to a point in the rear, like a fish. If, for instance, we
take round rods instead of the struts of the training machine above
mentioned and having the same thickness, the resistance might be 80
lb. instead of 20 lb.; and if we take a rod whose shape is elliptical
with its axes in a ratio of 1 to 5 the resistance might be 40 lb.
instead of 20 lb.; and if we took the stream-line struts out of the
training machine and put them back sharp edge foremost, the resistance
would be increased. The advantage of the stream-line shape is that it
provides smooth lines of flow for the air which has been thrust aside
at the front to flow back again without eddies to the rear. This is not
possible in the case of the round strut, behind which will be found a
whirl of eddies resulting in a vacuum that tends to suck it backward.
By fastening a stream-line tail behind the round rod the eddies are
greatly reduced, as is the vacuum. The wires of the airplane are
subject to the same law and if the training machine above mentioned had
stream-line wires instead of round wires we might expect them to have
less than 70 lb. resistance. The fuselage should always be given as
nearly a stream-line shape as the presence of the motor and tanks will
permit; and it must all be inclosed smoothly in “doped” fabric in order
that the air-flow phenomena may operate. As for the wheels, they must
of necessity be round, but by enclosing them with fabric the air flow
past them is more easy and the resistance may be halved.
=Total Resistance.=—The necessity has been explained of discriminating
between wing and deadhead resistance; if we are talking about wings
we may ignore everything except the wing resistance (commonly called
“wing drift”), but if we are talking about the whole airplane, we then
must refer to the total resistance, which includes all the others and
is overcome by the propeller thrust. “Skin-friction” resistance has not
been mentioned nor need it be more than to say that any surface moving
through air attributes part of its resistance to the actual friction of
the air against it, and therefore should be as smooth as possible.
=Motor Power Required for Flying.=—The reason resistance interests us
is that motor power is required to propel the airplane against it; more
and more power as the resistance and speed increase. Obviously, the
power required is least when the resistance is small, _i.e._, when the
speed is intermediate between minimum and maximum. It takes more power
to fly at minimum speed than at this intermediate speed. Of course
it also takes more power to fly at maximum speed, where again the
resistance is high.
=Maximum Speed.=—Ordinarily, for moderate speeds, airplanes have a
margin of power at which the throttle need not be opened wide; should
speed be increased the resistance and horsepower required will increase
steadily until the throttle is wide open and motor “full out;” this
establishes the maximum speed of an airplane; there is no margin of
power, no climb is possible. The only way to increase speed is to
use the force of gravity in addition to the motor force. It may be
interesting to know what is the maximum possible speed in the case
of a vertical dive with the motor shut off; it will be about double
the maximum horizontal speed as may be readily seen from the fact that
the thrust in the direction of motion is now no longer horizontal and
equal to the resistance but is vertical and equal to the weight of the
machine; that is, the thrust may be increased fivefold, and the speed
resulting will be increased correspondingly, if the motor be running in
such a vertical dive the velocity may be slightly increased though at
this speed of motion the propeller would not have much efficiency.
There is danger in such high speeds; the stresses in the machine are
increased several times merely by the increased resistance, and if the
angle of incidence should be suddenly brought up to a large value at
this high speed the stress would again be increased so that the total
stress increase theoretically might be as high as fourteen times the
normal value, thus exceeding the factor of safety. It is for such
reasons that the maximum strength is desirable in airplanes; holes
must not be carelessly drilled in the beams but should be located if
anywhere midway between the top and bottom edges, where the stress will
be least; initial stresses, due to tightness of the wires, should not
be too great.
=Climbing Ability.=—Climbing ability refers to the number of feet of
rise per minute or per 10 min. In order to climb, extra horsepower
is required beyond that necessary for more horizontal flight. The
machine can, for instance, fly at 56 miles per hour at which speed
it requires 43 hp. If now the throttle is opened up so as to increase
the horsepower by 22, making a total of 65 hp., the machine will climb
at the rate of 380 ft. per minute, maintaining approximately the same
flight speed. If instead of 65 hp., it were 54 hp. the speed of climb
would be about one-half of the 380, or 190 ft. per minute; the flight
speed again remaining approximately as before; that is, any margin
of horsepower beyond the particular value of horsepower required may
be used for climbing without material change of the flight speed. It
is necessary here to state that lift does not increase during climb;
and while for the instant that a climb commences there may be, due
to acceleration, more lift on the wings than balances the weight,
this does not remain true after a steady rate of climb is reached.
To illustrate, in a wagon drawn uphill by horses the wheels which
support the wagon do not exert any more support than on the level, and
the entire force to make the wagon ascend is supplied through extra
hard pulling by the horses. Thus in a climbing airplane the propeller
furnishes all the climbing force and lift is no greater than in
horizontal flight. In fact, the actual lift force may be even less, as
the weight of the airplane is partly supported by the propeller thrust
which is now inclined upward slightly.
To secure maximum climbing ability, we must determine at what velocity
the margin of motor power is the greatest. In the above-mentioned
machine we know that the horsepower required for support is least for
a speed of near 55 miles per hour, and it is near speed where therefore
the excess margin of power is greatest and at which climbing is best
done. An airplane designed chiefly for climbing must have low values of
motor power necessary for support, namely, must have small resistance,
therefore small size, therefore small weight.
[Illustration: FIG. 26.—Performance curves for typical training
airplane.]
=Gliding Angle.=—Gliding angle denotes the angle at which the airplane
will glide downward with the motor shut off and is spoken of as 1 in 5,
1 in 6, etc., according as it brings the airplane 1 mile down for each
5, 6, etc., miles of travel in the line of flight. The gliding angle of
a machine may be found by dividing the total resistance into the weight:
Gliding angle = Weight/Total resistance.
In the above-mentioned airplane it is one in 6.6 when the resistance
is 288 lb., that is, when the speed is 57 miles per hour. At any other
speed the resistance increases and hence the gliding angle decreases.
Hence the importance of putting the airplane into its proper speed in
order to secure the best gliding angle.
=The Propeller.=—The propeller or “screw,” by screwing its way forward
through the air, is able to propel the airplane at the desired
velocity. Regarding principles of propeller action the matter can be
hastily summarized in the following brief lines. The propeller blades
may be regarded as little wings moving in a circular path about the
shaft; and they have a lift and drift as do the regular wings. The lift
is analogous to the thrust; to secure this thrust with least torque
(drift) the blades are set at their most efficient angle of incidence,
and while the blade appears to have a steep angle near the hub, it
actually meets the air in flight at the same angle of incidence from
hub to tip.
=Propeller Pitch.=—Pitch is best defined by analogy to an ordinary
wood-screw; if the screw is turned one revolution it advances into
the wood by an amount equal to its pitch. If the air were solid, a
propeller would do the same, and the distance might be 8 ft., say.
Actually the air yields, and slips backward, and the propeller advances
only 6 ft. Its “slip” is then 8 minus 6, equals 2 ft., or 25 per cent.
Such a propeller has an 8-ft. pitch, and a 25 per cent. slip.
This “slip stream” blows backward in a flight so that the tail of an
airplane has air slipping past it faster than do the wings. Hence the
air forces at the tail are greater than might be expected. The rudder
and elevators therefore give a quicker action when the propeller is
rotating than when, as in the case of a glide, it is not.
[Illustration: FIG. 27.—Washout in left-wing tips.]
=Washout.=—Due to torque of the motor, the airplane tends to rotate
in the opposite direction to the propeller. This tendency may be
neutralized by giving one wing tip a smaller angle of incidence,
called “washout,” so that the machine normally tends to neutralize the
torque-effect.
PRINCIPLES OF AIRPLANE EQUILIBRIUM
[Illustration: FIG. 28.—Balances of forces in an airplane.
Weight forward of lift, thrust below resistance. Thrust equals
resistance, weight equals lift.]
=Introductory.=—Under this head will be discussed: (_a_) features of
airplane design which tend to maintain equilibrium irrespective of the
pilot; (_b_) matters of voluntary controlling operations by the pilot.
As regards (_a_) the tendency of the airplane toward inherent stability
acts to oppose any deviation from its course whether the pilot so
desires or not. The more stable is a machine, the less delicately is it
controlled, and the present consensus of opinion among pilots is that
a 50-50 compromise between stability and controllability is the best
thing.
In questions of airplane equilibrium the starting point is the center
of gravity; obviously, if the center of gravity were back at the tail
or up at the nose there would be no balance; the proper place for
it is the same spot where all the other forces such as thrust, lift
and resistance act; there it is easy to balance them all up. But it
is not always easy to bring the line of thrust and the line of total
resistance into coincidence, because the line of thrust is the line
of the propeller shaft and when this is high up as in the case of
some pushers it may be several inches above the line of resistance.
And as the thrust is above the resistance there is a tendency to nose
the machine down; to balance which the designer deliberately locates
the center of gravity sufficiently far behind the center of lift so
that there is an equal tendency to tip the nose upward; and all four
forces mentioned completely balance each other. But things may happen
to change the amount or position of these forces during flight, and if
this does happen the first thing to do is to restore the balance by
bringing in a small new force somewhere. In an actual airplane this
small restoring force is supplied at each critical moment first, by
the tail, etc., of the airplane and second, by voluntary actions of
the pilot. The center of gravity of any airplane may be determined
easily by putting a roller under it and seeing where it will balance,
or by getting the amount of weight supported at the wheels and tail,
according to the method of moments.
=Longitudinal Stability.=—Longitudinal stability has to do with the
tendency of an airplane to maintain its proper pitching angle. It was
said above that the four forces of lift, resistance, thrust and weight
always exactly balanced due to their size and their position. Now the
first consideration about longitudinal stability is that while the
centers of gravity and other forces remain in a fixed position, the
center of lift changes its position whenever the angle of incidence
(that is the speed) is changed. The phenomenon of shift of center of
pressure applies only to the wings and to the lift (the position of
center of resistance remains practically fixed at all angles).
Note the effect on center of pressure position of a change of wing
angle (see Fig. 20). The wing used on the U. S. training machine has a
center of lift which is about in the middle of the wing when flying at
a small angle of maximum speed; but if the angle is increased to the
stalling angle of 15°, the center of pressure moves from midway of the
wing to a point which is about one-third the chord distance of the wing
from the front edge. The lift may travel about ½ foot, and it is equal
in amount to the weight of the machine (that is, nearly a ton), and
the mere effect of changing the angle from its minimum to its maximum
value therefore tends to disturb the longitudinal equilibrium with a
force which may be represented as 1 ton acting on a lever arm of ½ ft.
Suppose that the airplane is balancing at an angle of 2° so that the
center of gravity coincides with the center of lift for this angle; now
if a gust of wind causes the angle to increase for an instant to 2¼°,
the center of lift will move forward and tend to push the front edge of
the wing up, thus increasing the angle further to 2½°. Then the center
of lift, of course, moves further forward to accommodate the increase
of angle, and in a fraction of a second the wing would rear up unless
it were firmly attached to the airplane body and held in its proper
position by the tail. Similarly if for any reason the proper angle of
2° were decreased, the same upset would follow, only this time tending
to dive the wing violently to earth. This tendency is neutralized in an
airplane by the “Penaud Tail Principle.”
There are certain shapes of wings in which the center of pressure
travels in the reverse direction; a flat plate, for example; or a wing
having its rear edge turned up so that the general wing shape is like
a thin letter “S.” Such wings as these would not tend to lose their
proper angle, because when the angle is changed for any reason the
center or pressure in these wings moves in just the manner necessary to
restore them to their proper position; but these wings are inefficient
and are not in present use on airplanes.
[Illustration: FIG. 29.—Diagrams illustrating theory and application
of longitudinal dihedral angle.]
=The Penaud Tail Principle.=—_Rule._—The horizontal tail must have a
smaller angle of incidence than the wings. The upsetting force above
mentioned must be met by a strong opposite righting force, and this
latter is furnished by the horizontal tail surface. In the angle of
equilibrium of 2° above mentioned, the flat horizontal stabilizer will
perhaps have no force acting on it at all because it is edgewise to
the air and its angle of incidence is zero. When the angle of the wing
increases to 2¼° and the lift moves forward tending to rear it up,
the wing being rigidly fastened to the body pushes the tail downward
so that the tail now begins to have a small lift force upon it due to
its angle of ¼°; and this newly created force, though small, acts at
such a long lever arm that it exceeds the rearing force of the wing
and will quickly restore the airplane to 2°. This action depends upon
the principle of the Penaud Tail or longitudinal “Dihedral” which
requires that the front wings of an airplane make a larger angle with
the wind than the rear surface. This principle holds good even when
we have rear surfaces which actually are lifting surfaces in normal
flight, the requisite being that the wings themselves shall in such
cases be at an even greater angle than the tail. No mention has been
made of the elevator control, because its action is additional to the
above-mentioned stability. The elevator is able to alter the lift on
the tail; such alteration requires, of course, immediate change of
angle of the wings so that equilibrium shall again follow; and this
equilibrium will be maintained until the lift at the tail is again
altered by some movement of the elevator control. Thus the elevator may
be considered as a device for adjusting the angle of incidence of the
wings.
The air through which the wings have passed receives downward motion,
and therefore a tail which is poised at zero angle with the line of
flight may actually receive air at an angle of -2° or -3°. In the above
case we would expect an actual downward force on the tail, unless this
tail is given a slight arch on its top surface (for it is known that
arched surfaces have an angle of zero lift which is negative angle).
=Longitudinal Control.=—Steering up or down is done by the elevator,
which as explained above is merely a device for adjusting the angle
of incidence of the wings. The elevator controls like all the other
controls of an airplane depend for their quick efficient action upon
generous speed; they can not be expected to give good response when the
machine is near its stalling speed. The elevators like the rudder are
located directly in the blast of the propeller and in case the speed
of motion should become very slow, the elevators may be made to exert
considerable controlling force if the motor is opened up to blow a
strong blast against them. This is good to bear in mind when taxying
on the ground because if the motor is shut off at the slow speed of
motion the elevator and rudder will lose their efficacy. The propeller
blast, due to a 25 per cent. slip, adds 25 per cent. of apparent speed
to those parts which are in its way, and therefore the tail forces are
affected as the square of this increase, that is, the forces may be 50
per cent. greater with the propeller on than off.
=Lateral Stability.=—This depends upon the keel surface or total side
area of an airplane. The keel surface includes all the struts, wires,
wheels, wings, as well as body, against which a side wind can blow.
Skidding and side-slipping have the same effect as a side wind, and
the resulting forces acting against the side of the machine should be
made useful instead of harmful. This is done by properly proportioning
the keel or side surface. If keel surface is low, the side force will
rotate the airplane about its axis so that the windward wing sinks; if
high, so that it rises. But if the keel surface is at just the right
height (_i.e._, level with the center of gravity) the side forces will
not rotate the machine at all and will simply oppose the skidding
without upsetting equilibrium.
[Illustration: FIG. 30.—Diagram showing effect on lateral stability of
dihedral angle and non-skid fins.
(_a_) Machine flying level. (_b_) Machine tips and side-slips: excess
pressure is created on windward wing and fins, (_c_) Machine has
side-slipped and rotated back to level. ]
=Lateral Dihedral.=—Now when an airplane appears to have its
keel-surface center too low, the easiest way to raise it level with the
center of gravity is to give the wings a dihedral angle, that is make
them point upward and outward from the body. Thus their projection, as
seen in a side view, is increased, and the effect is to add some keel
surface above the center of gravity, thus raising the center of total
keel surface.
A further advantage of the lateral dihedral is that any list of the
airplane sideways is automatically corrected (see Fig. 30). The low
wing supports better than the high wing, because a side slip sets in,
hence will restore the airplane to level position.
=Non-Skid-Fins.=—Where for the above-mentioned purposes an excessive
dihedral would be needed, resort may be had to non-skid-fins erected
vertically edgewise to the line of flight above or beneath the topwing.
These are used in marine machines to balance the abnormally large keel
surface of the boat or pontoon below.
=Lateral Control.=—By means of ailerons, lateral control is maintained
voluntarily by the pilot; the aileron on the low tip is given a greater
angle of incidence while on the high tip a less angle of incidence
thus restoring the proper level of the machine. Notice that the
efficacy of the ailerons depends upon speed of motion of the airplane,
irrespective of propeller slip because the propeller slip does not
reach the ailerons. Therefore, at stalling speeds the ailerons may not
be expected to work at their best, and when lateral balance is upset at
slow speeds it is necessary to dive the machine before enough lateral
control can be secured to restore the balance.
[Illustration: FIG. 31.—Deperdussin control.
System used in U. S. training airplanes.]
=Directional Stability.=—Directional stability has to do with the
tendency of an airplane to swerve to the right or left of its proper
course. To maintain directional stability the “vertical stabilizer” is
used, which acts in a manner analogous to the feather on an arrow. Thus
in case of a side slip the tail will swing and force the airplane nose
around into the direction of the side slip so that the airplane tends
to meet the relative side wind “nose-on” as it should. The vertical
stabilizer should not be too large, however, as then any side pressure
due to deviation from a rectilinear course will cause the machine to
swerve violently; the wing which is outermost in the turn will have
preponderance of lift due to its higher speed; that is, the airplane
will get into a turn where there is too much bank and a spiral dive may
result.
=Directional Control.=—The rudder gives directional control in
exactly the same way that it does on a boat; it should be said,
however, that the rudder is sometimes used without any intention
of changing the direction, that is, it is used simultaneously with
the ailerons as a means of neutralizing their swerving tendency.
The ailerons, of course, at the same time that they restore lateral
balance create a disadvantageous tendency to swerve the machine away
from its directional course; that is what the rudder must neutralize.
Moreover, the rudder is frequently used against side winds to maintain
rectilinear motion.
=Banking.=—Banking combines the lateral and directional control, which
should be operated simultaneously so as to tilt the machine and at the
same time maintain the radius of turn. The wings are tilted in a bank
because in going around a curve of a certain radius the weight of the
machine creates a centrifugal force in a horizontal direction and if
the curved path is to be maintained this centrifugal force must be
neutralized; and this is done by inclining the force of lift inward
until it has a horizontal component equal to the centrifugal force.
That is why the angle of bank must be rigidly observed, or else the
inward component of the lift will change. Now as soon as the wings bank
up, the lift force is no longer all vertical and therefore may not be
enough to support the weight of the machine. To offset this have plenty
of motor power for speed in a bank; and do not try to climb while
banking.
It is better to bank too little than too much; too little results in
skidding which may be easily cured; too much results in side slipping
inward and if the tail surface is too great in this latter case, a
spiral dive may result—so look out for over banking.
It is better for the beginner in banking to move his ailerons first and
then move the rudder; for if he moves the rudder first there will be
skidding outward, forward speed will drop and a stall may result. On
high angles of banking, over 45°, it should be noted that the elevators
are now more nearly vertical than horizontal and operate as a rudder;
similarly the rudder’s function is reversed, and to turn down the
rudder will be used.
=Damping in an Airplane.=—Above have been mentioned the restoring
forces which tend toward airplane equilibrium. Now these restoring
forces tend to push the machine back to equilibrium and even beyond
in exactly the same way that gravity causes a pendulum to swing about
its point of equilibrium. This can sometimes be noticed in the case
of an automobile when travelling at high speed along country roads
where a sort of slow oscillation from side to side may be noticed due
to the forceful maintenance of equilibrium of the body in its forward
motion. This oscillation in an airplane would be serious unless there
were means of damping it out and these means are: first, the wings;
second, the tail surfaces; third, the weight and inertia of the machine
itself. Regarding inertia it should be said that a machine with weight
distributed far from the center of gravity, such as the double-motor
airplane has a large tendency to resist the rolling motions associated
with lateral stability. But from the same sign airplanes with large
moment of inertia are difficult to deviate from any given attitude, and
therefore have the name of being “logy.” The proper proportioning of
an airplane’s parts to secure first, the restoring forces; second, the
proper damping force; third, the proper amount of moment of inertia, is
a very delicate matter and beyond the scope of the present chapter.