STABILITY AND CONTROL
STABILITY is a condition whereby an object disturbed has a natural
tendency to return to its first and normal position. Example: a weight
suspended by a cord.
INSTABILITY is a condition whereby an object disturbed has a natural
tendency to move as far as possible away from its first position, with
no tendency to return. Example: a stick balanced vertically upon your
finger.
NEUTRAL INSTABILITY is a condition whereby an object disturbed has no
tendency to move farther than displaced by the force of the disturbance,
and no tendency to return to its first position.
In order that an aeroplane may be reasonably controllable, it is
necessary for it to possess some degree of stability longitudinally,
laterally, and directionally.
LONGITUDINAL STABILITY in an aeroplane is its stability about an axis
transverse to the direction of normal horizontal flight, and without
which it would pitch and toss.
LATERAL STABILITY is its stability about its longitudinal axis, and
without which it would roll sideways.
DIRECTIONAL STABILITY is its stability about its vertical axis, and
without which it would have no tendency to keep its course.
For such directional stability to exist there must be, in effect,[16]
more "keel-surface" behind the vertical axis than there is in front of
it. By keel-surface I mean everything to be seen when looking at an
aeroplane from the side of it--the sides of the body, undercarriage,
struts, wires, etc. The same thing applies to a weathercock. You know
what would happen if there was insufficient keel-surface behind the
vertical axis upon which it is pivoted. It would turn off its proper
course, which is opposite to the direction of the wind. It is very much
the same in the case of an aeroplane.
[Illustration]
The above illustration represents an aeroplane (directionally stable)
flying along the course B. A gust striking it as indicated acts upon the
greater proportion of keel-surface behind the turning axis and throws it
into the new course. It does not, however, travel along the new course,
owing to its momentum in the direction B. It travels, as long as such
momentum lasts, in a direction which is the resultant of the two forces
Thrust and Momentum. But the centre line of the aeroplane is pointing
in the direction of the new course. Therefore its attitude, relative to
the direction of motion, is more or less sideways, and it consequently
receives an air pressure in the direction C. Such pressure, acting upon
the keel-surface, presses the tail back towards its first position in
which the aeroplane is upon its course B.
What I have described is continually going on during flight, but in a
well-designed aeroplane such stabilizing movements are, most of the
time, so slight as to be imperceptible to the pilot.
If an aeroplane was not stabilized in this way, it would not only be
continually trying to leave its course, but it would also possess a
dangerous tendency to "nose away" from the direction of the side gusts.
In such case the gust shown in the above illustration would turn the
aeroplane round the opposite way a very considerable distance; and the
right wing, being on the outside of the turn, would travel with greater
velocity than the left wing. Increased velocity means increased lift;
and so, the right wing lifting, the aeroplane would turn over sideways
very quickly.
LONGITUDINAL STABILITY.--Flat surfaces are longitudinally stable owing
to the fact that with decreasing angles of incidence the centre line of
pressure (C.P.) moves forward.
The C.P. is a line taken across the surface, transverse to the direction
of motion, and about which all the air forces may be said to balance, or
through which they may be said to act.
[Illustration]
Imagine A to be a flat surface, attitude vertical, travelling through
the air in the direction of motion M. Its C.P. is then obviously along
the exact centre line of the surface as illustrated. In B, C, and D the
surfaces are shown with angles of incidence decreasing to nothing, and
you will note that the C.P. moves forward with the decreasing angle.[17]
Now, should some gust or eddy tend to make the surface decrease the
angle, _i.e._, dive, then the C.P. moves forward and pushes the front
of the surface up. Should the surface tend to assume too large an
angle, then the reverse happens--the C.P. moves back and pushes the
rear of the surface up. Flat surfaces are, then, theoretically stable
longitudinally. They are not, however, used, on account of their poor
lift-drift ratio.
As already explained, cambered surfaces are used, and these are
longitudinally unstable at those angles of incidence producing a
reasonable lift-drift ratio, _i.e._, at angles below about 12°.
A is a cambered surface, attitude approximately vertical, moving through
the air in the direction M. Obviously the C.P. coincides with the
transverse centre line of the surface.
With decreasing angles, down to angles of about 30°, the C.P. moves
forward as in the case of flat surfaces (see B); but angles above 30° do
not interest us, since they produce a very low ratio of lift to drift.
[Illustration]
Below angles of about 30° (see C) the dipping front part of the surface
assumes a negative angle of incidence resulting in the _downward_ air
pressure D, and the more the angle of incidence is decreased, the
greater such negative angle and its resultant pressure D. Since the
C.P. is the resultant of all the air forces, its position is naturally
affected by D, which causes it to move backwards. Now, should some gust
or eddy tend to make the surface decrease its angle of incidence,
_i.e._, dive, then the C.P. moves backwards, and, pushing up the rear
of the surface, causes it to dive the more. Should the surface tend to
assume too large an angle, then the reverse happens; the pressure D
decreases, with the result that C.P. moves forward and pushes up the
front of the surface, thus increasing the angle still further, the final
result being a "tail-slide."
It is therefore necessary to find a means of stabilizing the naturally
unstable cambered surface. This is usually secured by means of a
stabilizing surface fixed some distance in the rear of the main surface,
and it is a necessary condition that the neutral lift lines of the two
surfaces, when projected to meet each other, make a dihedral angle. In
other words, the rear stabilizing surface must have a lesser angle of
incidence than the main surface--certainly not more than one-third of
that of the main surface. This is known as the longitudinal dihedral.
[Illustration]
I may add that the tail-plane is sometimes mounted upon the aeroplane at
the same angle as the main surface, but, in such cases, it attacks air
which has received a downward deflection from the main surface, thus:
[Illustration]
The angle at which the tail surface attacks the air (the angle of
incidence) is therefore less than the angle of incidence of the main
surface.
I will now, by means of the following illustration, try to explain how
the longitudinal dihedral secures stability:
[Illustration]
First, imagine the aeroplane travelling in the direction of motion,
which coincides with the direction of thrust T. The weight is, of
course, balanced about a C.P., the resultant of the C.P. of the main
surface and the C.P. of the stabilizing surface. For the sake of
illustration, the stabilizing surface has been given an angle of
incidence, and therefore has a lift and C.P. In practice the stabilizer
is often set at no angle of incidence. In such case the proposition
remains the same, but it is, perhaps, a little easier to illustrate
it as above.
Now, we will suppose that a gust or eddy throws the machine into the
lower position. It no longer travels in the direction of T, since the
momentum in the old direction pulls it off that course. M is now the
resultant of the Thrust and the Momentum, and you will note that this
results in a decrease in the angle our old friend the neutral lift line
makes with M, _i.e._, a decrease in the angle of incidence and therefore
a decrease in lift.
We will suppose that this decrease is 2°. Such decrease applies to
both main surface and stabilizer, since both are fixed rigidly to the
aeroplane.
The main surface, which had 12° angle, has now only 10°, _i.e._, a loss
of _one-sixth_.
The stabilizer, which had 4° angle, has now only 2°, _i.e._, a loss of
_one-half_.
The latter has therefore lost a greater _proportion_ of its angle of
incidence, and consequently its lift, than has the main surface. It must
then fall relative to the main surface. The tail falling, the aeroplane
then assumes its first position, though at a slightly less altitude.
Should a gust throw the nose of the aeroplane up, then the reverse
happens. Both main surface and stabilizer increase their angles of
incidence in the same amount, but the angle, and therefore the lift, of
the stabilizer increases in greater proportion than does the angle and
lift of the main surface, with the result that it lifts the tail. The
aeroplane then assumes its first position, though at a slightly greater
altitude.
Do not fall into the widespread error that the angle of incidence varies
as the angle of the aeroplane to the horizontal. It varies with such
angle, but not as anything approaching it. Remember that the stabilizing
effect of the longitudinal dihedral lasts only as long as there is
momentum in the direction of the first course.
These stabilizing movements are taking place all the time, even though
imperceptible to the pilot.
Aeroplanes have, in the past, been built with a stabilizing surface
in front of the main surface instead of at the rear of it. In such
design the main surface (which is then the tail surface as well as the
principal lifting surface) must be set at a less angle than the forward
stabilizing surface, in order to secure a longitudinal dihedral. The
defect of such design lies in the fact that the main surface must have
a certain angle to lift the weight--say 5°. Then, in order to secure
a sufficiency of longitudinal stability, it is necessary to set the
forward stabilizer at about 15°. Such a large angle of incidence results
in a very poor lift-drift ratio (and consequently great loss of
efficiency), except at very low velocities compared with the speed of
modern aeroplanes. At the time such aeroplanes were built velocities
were comparatively low, and this defect was, for that reason, not
sufficiently appreciated. In the end it killed the "canard" or
"tail-first" design.
Aeroplanes of the Dunne and similar types possess no stabilizing surface
distinct from the main surface, but they have a longitudinal dihedral
which renders them stable.
The main surface towards the wing-tips is given a decreasing angle of
incidence and corresponding camber. The wing-tips then act as
longitudinal stabilizers.
[Illustration]
This design of aeroplane, while very interesting, has not proved very
practicable, owing to the following disadvantages: (1) The plan design
is not, from a mechanical point of view, so sound as that of the
ordinary aeroplane surface, which is, in plan, a parallelogram. It is,
then, necessary to make the strength of construction greater than would
otherwise be the case. That means extra weight. (2) The plan of the
surface area is such that the aspect ratio is not so high as if the
surface was arranged with its leading edges at right angles to the
direction of motion. The lower the aspect ratio, then, the less the
lift. This design, then, produces less lift for weight of surface than
would the same surface if arranged as a parallelogram. (3) In order to
secure the longitudinal dihedral, the angle of incidence has to be very
much decreased towards the wing-tips. Then, in order that the lift-drift
ratio may be preserved, there must be a corresponding decrease in the
camber. That calls for surface ribs of varying cambers, and results in
an expensive and lengthy job for the builder. (4) In order to secure
directional stability, the surface is, in the centre, arranged to dip
down in the form of a V, pointing towards the direction of motion.
Should the aeroplane turn off its course, then its momentum in the
direction of its first course causes it to move in a direction the
resultant of the thrust and the momentum. It then moves in a more or
less sideways attitude, which results in an air pressure upon one side
of the V, and which tends to turn the aeroplane back to its first
course. This arrangement of the surface results in a bad drift. Vertical
surfaces at the wing-tips may also be set at an angle producing the same
stabilizing effect, but they also increase the drift.
The gyroscopic action of a rotary engine will affect the longitudinal
stability when an aeroplane is turned to right or left. In the case of
a Gnome engine, fitted to a "pusher" aeroplane, such gyroscopic action
will tend to depress the nose of the aeroplane when it is turned to the
left, and to elevate it when it is turned to the right. When fitted to a
"tractor" aeroplane, the engine is reversed so that a reverse condition
results. In modern aeroplanes this tendency is not sufficiently
important to bother about, except in the matter of spiral descents
(see section headed "Spinning"). In the old days of crudely designed
and under-powered "pusher" aeroplanes this gyroscopic action was very
marked, and led the majority of pilots to dislike turning an aeroplane
to the right, since, in doing so, there was some danger of "stalling."
LATERAL STABILITY is far more difficult for the designer to secure
than is longitudinal or directional stability. Some degree of lateral
stability may be secured by means of the "lateral dihedral," _i.e._,
the upward inclination of the surface towards its wing-tips thus:
[Illustration]
Imagine the top =V=, illustrated opposite, to be the front view of a
surface flying towards you. The horizontal equivalent (H.E.) of the left
wing is the same as that of the right wing. Therefore, the lift of one
wing is equal to the lift of the other, and the weight, being situated
always in the centre, is balanced.
If some movement of the air causes the surface to tilt sideways, as in
the lower illustration, then you will note that the H.E. of the left
wing increases, and the H.E. of the right wing decreases. The left wing
then, having the greatest lift, rises; and the surface assumes its first
and normal position.
Unfortunately, however, the righting effect is not proportional to the
difference between the right and left H.E.'s.
[Illustration:
R, Direction of reaction of wing indicated.
R R, Resultant direction of reaction of both wings.
M, Horizontal (sideway) component of reaction.
L, Vertical component of reaction (lift).]
In the case of A, the resultant direction of the reaction of both wings
is opposed to the direction of gravity or weight. The two forces R R
and gravity are then evenly balanced, and the surface is in a state of
equilibrium.
In the case of B, you will note that the R R is not directly opposed
to gravity. This results in the appearance of M, and so the resultant
direction of motion of the aeroplane is no longer directly forward,
but is along a line the resultant of the Thrust and M. In other words,
it is, while flying forward, at the same time moving sideways in the
direction M.
In moving sideways, the keel-surface receives, of course, a pressure
from the air equal and opposite to M. Since such surface is greatest
in effect towards the tail, then the latter must be pushed sideways.
That causes the aeroplane to turn; and, the highest wing being on the
outside of the turn, it has a greater velocity than the lower wing. That
produces greater lift, and tends to tilt the aeroplane over still more.
Such tilting tendency is, however, opposed by the difference in the
H.E.'s of the two wings.
It then follows that, for the lateral dihedral angle to be effective,
such angle must be large enough to produce, when the aeroplane tilts,
a difference in the H.E.'s of the two wings, which difference must be
sufficient to not only oppose the tilting tendency due to the aeroplane
turning, but sufficient to also force the aeroplane back to its original
position of equilibrium.
It is now, I hope, clear to the reader that the lateral dihedral is not
quite so effective as would appear at first sight. Some designers,
indeed, prefer not to use it, since its effect is not very great, and
since it must be paid for in loss of H.E. and consequently loss of lift,
thus decreasing the lift-drift ratio, _i.e._, the efficiency. Also, it
is sometimes advanced that the lateral dihedral increases the "spill" of
air from the wing-tips and that this adversely affects the lift-drift
ratio.
_The disposition of the keel-surface_ affects the lateral stability. It
should be, in effect, equally divided by the longitudinal turning axis
of the aeroplane. If there is an excess of keel-surface above or below
such axis, then a side gust striking it will tend to turn the aeroplane
over sideways.
_The position of the centre of gravity_ affects lateral stability. If
too low, it produces a pendulum effect and causes the aeroplane to roll
sideways.
If too high, it acts as a stick balanced vertically would act. If
disturbed, it tends to travel to a position as far as possible from its
original position. It would then tend, when moved, to turn the aeroplane
over sideways and into an upside-down position.
From the point of view of lateral stability, the best position for
the centre of gravity is one a little below the centre of drift. This
produces a little lateral stability without any marked pendulum effect.
_Propeller torque_ affects lateral stability. An aeroplane tends to turn
over sideways in the opposite direction to which the propeller revolves.
[Illustration]
This tendency is offset by increasing the angle of incidence (and
consequently the lift) of the side tending to fall; and it is always
advisable, if practical considerations allow it, to also decrease the
angle upon the other side. In that way it is not necessary to depart so
far from the normal angle of incidence at which the lift-drift ratio is
highest.
_Wash-in_ is the term applied to the increased angle.
_Wash-out_ is the term applied to the decreased angle.
Both lateral and directional stability may be improved by washing out
the angle of incidence on both sides of the surface, thus:
[Illustration]
The decreased angle decreases the drift and therefore the effect of
gusts upon the wing-tips, which is just where they have the most effect
upon the aeroplane, owing to the distance from the turning axis.
The wash-out also renders the ailerons (lateral controlling services)
more effective, as, in order to operate them, it is not then necessary
to give them such a large angle of incidence as would otherwise be
required.
[Illustration: Note: Observe that the inclination of the ailerons to
the surface is the same in each case.]
The less the angle of incidence of the ailerons, the better their
lift-drift ratio, i.e., their efficiency. You will note that, while the
aileron attached to the surface with washed-out angle is operated to the
same extent as the aileron illustrated above it, its angle of incidence
is considerably less. Its efficiency is therefore greater.
The advantages of the wash-in must, of course, be paid for in some loss
of lift, as the lift decreases with the decreased angle.
In order to secure all the above described advantages, a combination is
sometimes effected, thus:
[Illustration: "Wash Out" on both sides relative to the Centre.]
BANKING.--An aeroplane turned off its course to right or left does not
at once proceed along its new course. Its momentum in the direction of
its first course causes it to travel along a line the resultant of such
momentum and the thrust. In other words, it more or less skids sideways
and away from the centre of the turn. Its lifting surfaces do not then
meet the air in their correct attitude, and the lift may fall to such an
extent as to become less than the weight, in which case the aeroplane
must fall. This bad effect is minimized by "banking," _i.e._, tilting
the aeroplane sideways. The bottom of the lifting surface is in that way
opposed to the air through which it is moving in the direction of the
momentum and receives an opposite air pressure. The rarefied area over
the top of the surface is rendered still more rare, and this, of course,
assists the air pressure in opposing the momentum.
The velocity of the "skid," or sideways movement, is then only such
as is necessary to secure an air pressure equal and opposite to the
centrifugal force of the turn.
The sharper the turn, the greater the effect of the centrifugal force,
and therefore the steeper should be the "bank." _Experientia docet_.
_The position of the centre of gravity_ affects banking. A low C.G. will
tend to swing outward from the centre of the turn, and will cause the
aeroplane to bank--perhaps too much, in which case the pilot must remedy
matters by operating the ailerons.
A high C.G. also tends to swing outward from the centre of the turn. It
will tend to make the aeroplane bank the wrong way, and such effect must
be remedied by means of the ailerons.
The pleasantest machine from a banking point of view is one in which
the C.G. is a little below the centre of drift. It tends to bank the
aeroplane the right way for the turn, and the pilot can, if necessary,
perfect the bank by means of the ailerons.
_The disposition of the keel-surface_ affects banking. It should be,
in effect, evenly divided by the longitudinal axis. An excess of
keel-surface above the longitudinal axis will, when banking, receive an
air pressure causing the aeroplane to bank, perhaps too much. An excess
of keel-surface below the axis has the reverse effect.
SIDE-SLIPPING.--This usually occurs as a result of over-banking. It is
always the result of the aeroplane tilting sideways and thus decreasing
the horizontal equivalent, and therefore the lift, of the surface. An
excessive "bank," or sideways tilt, results in the H.E., and therefore
the lift, becoming less than the weight, when, of course, the aeroplane
must fall, _i.e._, side-slip.
[Illustration]
When making a very sharp turn it is necessary to bank very steeply
indeed. If, at the same time, the longitudinal axis of the aeroplane
remains approximately horizontal, then there must be a fall, and the
direction of motion will be the resultant of the thrust and the fall as
illustrated above in sketch A. The lifting surfaces and the controlling
surfaces are not then meeting the air in the correct attitude, with the
result that, in addition to falling, the aeroplane will probably become
quite unmanageable.
The pilot, however, prevents such a state of affairs from happening by
"nosing-down," _i.e._, by operating the rudder to turn the nose of the
aeroplane downward and towards the direction of motion as illustrated in
sketch B. This results in the higher wing, which is on the outside of
the turn, travelling with greater velocity, and therefore securing a
greater reaction than the lower wing, thus tending to tilt the aeroplane
over still more. The aeroplane is now almost upside-down, _but_ its
attitude relative to the direction of motion is correct and the
controlling surfaces are all of them working efficiently. The recovery
of a normal attitude relative to the Earth is then made as illustrated
in sketch C.
The pilot must then learn to know just the angle of bank at which the
margin of lift is lost, and, if a sharp turn necessitates banking beyond
that angle, he must "nose-down."
In this matter of banking and nosing-down, and, indeed, regarding
stability and control generally, the golden rule for all but very
experienced pilots should be: _Keep the aeroplane in such an attitude
that the air pressure is always directly in the pilot's face._ The
aeroplane is then always engaging the air as designed to do so, and both
lifting and controlling surfaces are acting efficiently. The only
exception to this rule is a vertical dive, and I think that is obviously
not an attitude for any but very experienced pilots to hanker after.
SPINNING.--This is the worst of all predicaments the pilot can find
himself in. Fortunately it rarely happens.
It is due to the combination of (1) a very steep spiral descent of small
radius, and (2) insufficiency of keel-surface behind the vertical axis,
or the jamming of the rudder and/or elevator into a position by which
the aeroplane is forced into an increasingly steep and small spiral.
Owing to the small radius of such a spiral, the mass of the aeroplane
may gain a rotary momentum greater, in effect, than the air pressure of
the keel-surface or controlling surfaces opposed to it; and, when once
such a condition occurs, it is difficult to see what can be done by the
pilot to remedy it. The sensible pilot will not go beyond reasonable
limits of steepness and radius when executing spiral descents.
[Illustration: Nose Dive Spin.]
In this connection every pilot of an aeroplane fitted with a rotary
engine should bear in mind the gyroscopic effect of such engine. In the
case of such an engine fitted to a "pusher" aeroplane, its effect when a
left-hand turn is made is to depress the nose of the machine. If fitted
to a "tractor" it is reversed, so the effect is to depress the nose
if a right-hand turn is made. The sharper the turn, the greater such
effect--an effect which may render the aeroplane unmanageable if the
spiral is one of very small radius and the engine is revolving with
sufficient speed to produce a material gyroscopic effect. Such
gyroscopic effect should, however, slightly _assist_ the pilot to
navigate a small spiral if he will remember to (1) make _right-hand_
spirals in the case of a "pusher," (2) make _left-hand_ spirals in the
case of a "tractor." The effect will then be to keep the nose up and
prevent a nose-dive. I say "slightly" assist because the engine is, of
course, throttled down for a spiral descent, and its lesser revolutions
will produce a lesser gyroscopic effect.
On the other hand, it might be argued that if the aeroplane gets into a
"spin," anything tending to depress the nose of the machine is of value,
since it is often claimed that the best way to get out of a spin is
to put the machine into a nose-dive--the great velocity of the dive
rendering the controls more efficient and better enabling the pilot to
regain control. It is, however, a very contentious point, and few are
able to express opinions based on practice, since pilots indulging in
nose-dive spins are either not heard of again or have usually but a hazy
recollection of exactly what happened to them.
GLIDING DESCENT WITHOUT PROPELLER THRUST.--All aeroplanes are, or should
be, designed to assume their correct gliding angle when the power and
thrust is cut off. This relieves the pilot of work, worry, and danger
should he find himself in a fog or cloud. The pilot, although he may not
realize it, maintains the correct attitude of the aeroplane by observing
its position relative to the horizon. Flying into a fog or cloud the
horizon is lost to view, and he must then rely upon his instruments--(1)
the compass for direction; (2) an inclinometer (arched spirit-level)
mounted transversely to the longitudinal axis, for lateral stability;
and (3) an inclinometer mounted parallel to the longitudinal axis, or
the airspeed indicator, which will indicate a nose-down position by
increase in air speed, and a tail-down position by decrease in air
speed.
The pilot is then under the necessity of watching three instruments
and manipulating his three controls to keep the instruments indicating
longitudinal, lateral, and directional stability. That is a feat beyond
the capacity of the ordinary man. If, however, by the simple movement
of throttling down the power and thrust, he can be relieved of looking
after the longitudinal stability, he then has only two instruments to
watch. That is no small job in itself, but it is, at any rate, fairly
practicable.
[Illustration]
Aeroplanes are, then, designed, or should be, so that the centre of
gravity is slightly forward of centre of lift. The aeroplane is then,
as a glider, nose-heavy--and the distance the C.G. is placed in advance
of the C.L. should be such as to ensure a gliding angle producing a
velocity the same as the normal flying speed (for which the strength
of construction has been designed).
In order that this nose-heavy tendency should not exist when the thrust
is working and descent not required, the centre of thrust is placed a
little below the centre of drift or resistance, and thus tends to pull
up the nose of the aeroplane.
The distance the centre of thrust is placed below the centre of drift
should be such as to produce a force equal and opposite to that due to
the C.G. being forward of the C.L. (see illustration above).
LOOPING AND UPSIDE-DOWN FLYING.--If a loop is desired, it is best to
throttle the engine down at point A. The C.G. being forward of the C.P.,
then causes the aeroplane to nose down, and assists the pilot in making
a reasonably small loop along the course C and in securing a quick
recovery. If the engine is not throttled down, then the aeroplane may be
expected to follow the course D, which results in a longer nose dive
than in the case of the course C.
[Illustration: Position A. Path B. Path C. Path D.]
A steady, gentle movement of the elevator is necessary. A jerky movement
may change the direction of motion so suddenly as to produce dangerous
air stresses upon the surfaces, in which case there is a possibility of
collapse.
If an upside-down flight is desired, the engine may, or may not, be
throttled down at point A. If not throttled down, then the elevator must
be operated to secure a course approximately in the direction B. If it
is throttled down, then the course must be one of a steeper angle than
B, or there will be danger of stalling.
[Footnote 16: "In effect" because, although there may be actually the
greatest proportion of keel-surface in front of the vertical axis, such
surface may be much nearer to the axis than is the keel-surface towards
the tail. The latter may then be actually less than the surface in
front, but, being farther from the axis, it has a greater leverage,
and consequently is greater in effect than the surface in front.]
[Footnote 17: The reason the C.P. of an inclined surface is forward of
the centre of the surface is because the front of the surface does most
of the work, as explained on p. 62.]