Air has weight (about 13 cubic feet = 1 lb.), inertia, and momentum. It therefore obeys Newton's laws14and resists movement. It is that resistance or reaction which makes flight possible.
Flight is secured by driving through the air a surface15inclined upwards and towards the direction of motion.
S = Side view of surface.
M = Direction of motion.
CHORD.—The Chord is, for practical purposes, taken to be a straight line from the leading edge of the surface to its trailing edge.
N = A line through the surface starting from its trailing edge. The position of this line, which I call the Neutral Lift Line, is found by means of wind-tunnel research, and it varies with differences in the camber (curvature) of surfaces. In order to secure flight, the inclination of the surface must be such that the neutral lift line makes an angle with and ABOVE the line of motion. If it is coincident with M, there is no lift. If it makes an angle with M and BELOW it, then there is a pressure tending to force the surface down.
I = Angle of Incidence. This angle is generally defined as the angle the chord makes with the direction of motion, but that is a bad definition, as it leads to misconception. The angle of incidence is best described as the angle the neutral lift line makes with the direction of motion relative to the air. You will, however, find that in nearly all rigging specifications the angle of incidence is taken to mean the angle the chord makes with a line parallel to the propeller thrust. This is necessary from the point of view of the practical mechanic who has to rig the aeroplane, for he could not find the neutral lift line, whereas he can easily find the chord. Again, he would certainly be in doubt as to “the direction of motion relative to the air,” whereas he can easily find a line parallel to the propeller thrust. It is a pity, however, that these practical considerations have resulted in a bad definition of the angle of incidence becoming prevalent, a consequence of which has been the widespread fallacy that flight may be secured with a negative inclination of the surface. Flight may conceivably be secured with a negative angle of chord, but never with a negative inclination of the surface. All this is only applicable to cambered surfaces. In the case of flat surfaces the neutral lift line coincides with the chord and the definition I have criticised adversely is then applicable. Flat lifting surfaces are, however, never used.
The surface acts upon the air in the following manner:
As the bottom of the surface meets the air, it compresses it and accelerates it DOWNWARDS. As a result of this definite action there is, of course, an equal and opposite reaction UPWARDS.
The top surface, in moving forward, tends to leave the air behind it, thus creating a semi-vacuum or rarefied area over the top of the surface. Consequently the pressure of air on the top of the surface is decreased, thus assisting the reaction below to lift the surface UPWARDS.
The reaction increases approximately as the square of the velocity. It is the result of (1) the mass of air engaged, and (2) the velocity and consequent force with which the surface engages the air. If the reaction was produced by only one of those factors it would increase in direct proportion to the velocity, but, since it is the product of both factors, it increases as V(2S).
Approximately three-fifths of the reaction is due to the decrease of density (and consequent decrease of downward pressure) on the top of the surface; and only some two-fifths is due to the upward reaction secured by the action of the bottom surface upon the air. A practical point in respect of this is that, in the event of the fabric covering the surface getting into bad condition, it is more likely to strip off the top than off the bottom.
The direction of the reaction is approximately at right-angles to the chord of the surface, as illustrated above; and it is, in considering flight, convenient to divide it into two component parts or values, thus:
1. The vertical component of the reaction, i.e., Lift, which is opposed to Gravity, i.e., the weight of the aeroplane.
2. The horizontal component, i.e., Drift (sometimes called Resistance), to which is opposed the thrust of the propeller.
The direction of the reaction is, of course, the resultant of the forces Lift and Drift.
The Lift is the useful part of the reaction, for it lifts the weight of the aeroplane.
The Drift is the villain of the piece, and must be overcome by the Thrust in order to secure the necessary velocity to produce the requisite Lift for flight.
DRIFT.—The drift of the whole aeroplane (we have considered only the lifting surface heretofore) may be conveniently divided into three parts, as follows:
Active Drift, which is the drift produced by the lifting surfaces.
Passive Drift, which is the drift produced by all the rest of the aeroplane—the struts, wires, fuselage, under-carriage, etc., all of which is known as “detrimental surface.”
Skin Friction, which is the drift produced by the friction of the air with roughnesses of surface. The latter is practically negligible having regard to the smooth surface of the modern aeroplane, and its comparatively slow velocity compared with, for instance, the velocity of a propeller blade.
LIFT-DRIFT RATIO.—The proportion of lift to drift is known as the lift-drift ratio, and is of paramount importance, for it expresses the efficiency of the aeroplane (as distinct from engine and propeller). A knowledge of the factors governing the lift-drift ratio is, as will be seen later, an absolute necessity to anyone responsible for the rigging of an aeroplane, and the maintenance of it in an efficient and safe condition.
Those factors are as follows:
1. Velocity.—The greater the velocity the greater the proportion of drift to lift, and consequently the less the efficiency. Considering the lifting surfaces alone, both the lift and the (active) drift, being component parts of the reaction, increase as the square of the velocity, and the efficiency remains the same at all speeds. But, considering the whole aeroplane, we must remember the passive drift. It also increases as the square of the velocity (with no attendant lift), and, adding itself to the active drift, results in increasing the proportion of total drift (active + passive) to lift.
But for the increase in passive drift the efficiency of the aeroplane would not fall with increasing velocity, and it would be possible, by doubling the thrust, to approximately double the speed or lift—a happy state of affairs which can never be, but which we may, in a measure, approach by doing everything possible to diminish the passive drift.
Every effort is then made to decrease it by “stream-lining,” i.e., by giving all “detrimental” parts of the aeroplane a form by which they will pass through the air with the least possible drift. Even the wires bracing the aeroplane together are, in many cases, stream-lined, and with a markedly good effect upon the lift-drift ratio. In the case of a certain well-known type of aeroplane the replacing of the ordinary wires by stream-lined wires added over five miles an hour to the flight speed.
Head-resistance is a term often applied to passive drift, but it is apt to convey a wrong impression, as the drift is not nearly so much the result of the head or forward part of struts, wires, etc., as it is of the rarefied area behind.
Above is illustrated the flow of air round two objects moving in the direction of the arrow M.
In the case of A, you will note that the rarefied area DD is of very considerable extent; whereas in the case of B, the air flows round it in such a way as to meet very closely to the rear of the object, thus DECREASING DD.
The greater the rarefied area DD. then, the less the density, and, consequently, the less the pressure of air upon the rear of the object. The less such pressure, then, the better is head-resistance D able to get its work in, and the more thrust will be required to overcome it.
The “fineness” of the stream-line shape, i.e., the proportion of length to width, is determined by the velocity—the greater the velocity, the greater the fineness. The best degree of fineness for any given velocity is found by means of wind-tunnel research.
The practical application of all this is, from a rigging point of view, the importance of adjusting all stream-line parts to be dead-on in the line of flight, but more of that later on.
2. Angle of Incidence.—The most efficient angle of incidence varies with the thrust at the disposal of the designer, the weight to be carried, and the climb-velocity ratio desired.
The best angles of incidence for these varying factors are found by means of wind-tunnel research and practical trial and error. Generally speaking, the greater the velocity the smaller should be the angle of incidence, in order to preserve a clean, stream-line shape of rarefied area and freedom from eddies. Should the angle be too great for the velocity, then the rarefied area becomes of irregular shape with attendant turbulent eddies. Such eddies possess no lift value, and since it has taken power to produce them, they represent drift and adversely affect the lift-drift ratio.
From a rigging point of view, one must presume that every standard aeroplane has its lifting surface set at the most efficient angle, and the practical application of all this is in taking the greatest possible care to rig the surface at the correct angle and to maintain it at such angle. Any deviation will adversely affect the lift-drift ratio, i.e., the efficiency.
3. Camber.—(Refer to the second illustration in this chapter.) The lifting surfaces are cambered, i.e., curved, in order to decrease the horizontal component of the reaction, i.e., the drift.
The bottom camber: If the bottom of the surface was flat, every particle of air meeting it would do so with a shock, and such shock would produce a very considerable horizontal reaction or drift. By curving it such shock is diminished, and the curve should be such as to produce a uniform (not necessarily constant) acceleration and compression of the air from the leading edge to the trailing edge. Any unevenness in the acceleration and compression of the air produces drift.
The top camber: If this was flat it would produce a rarefied area of irregular shape. I have already explained the bad effect this has upon the lift-drift ratio. The top surface is then curved to produce a rarefied area the shape of which shall be as stream-line and free from attendant eddies as possible.
The camber varies with the angle of incidence, the velocity, and the thickness of the surface. Generally speaking, the greater the velocity, the less the camber and angle of incidence. With infinite velocity the surface would be set at no angle of incidence (the neutral lift line coincident with the direction of motion relative to the air), and would be, top and bottom, of pure streamline form—i.e., of infinite fineness. This is, of course, carrying theory to absurdity as the surface would then cease to exist.
The best cambers for varying velocities, angles of incidence, and thicknesses of surface, are found by means of wind-tunnel research. The practical application of all this is in taking the greatest care to prevent the surface from becoming distorted and thus spoiling the camber and consequently the lift-drift ratio.
4. Aspect Ratio.—This is the proportion of span to chord. Thus, if the span is, for instance, 50 feet and the chord 5 feet, the surface would be said to have an aspect ratio of 10 to 1.
For A GIVEN VELOCITY and A GIVEN AREA of surface, the greater the aspect ratio, the greater the reaction. It is obvious, I think, that the greater the span, the greater the mass of air engaged, and, as already explained, the reaction is partly the result of the mass of air engaged.
Not only that, but, PROVIDED the chord is not decreased to an extent making it impossible to secure the best camber owing to the thickness of the surface, the greater the aspect ratio, the better the lift-drift ratio. The reason of this is rather obscure. It is sometimes advanced that it is owing to the “spill” of air from under the wing-tips. With a high aspect ratio the chord is less than would otherwise be the case. Less chord results in smaller wing-tips and consequently less “spill.” This, however, appears to be a rather inadequate reason for the high aspect ratio producing the high lift-drift ratio. Other reasons are also advanced, but they are of such a contentious nature I do not think it well to go into them here. They are of interest to designers, but this is written for the practical pilot and rigger.
5. Stagger.—This is the advancement of the top surface relative to the bottom surface, and is not, of course, applicable to a single surface, i.e., a monoplane. In the case of a biplane having no stagger, there will be “interference” and consequent loss of Efficiency unless the gap between the top and bottom surfaces is equal to not less than 1 1/2 times the chord. If less than that, the air engaged by the bottom of the top surface will have a tendency to be drawn into the rarefied area over the top of the bottom surface, with the result that the surfaces will not secure as good a reaction as would otherwise be the case.
It is not practicable to have a gap of much more than a distance equal to the chord, owing to the drift produced by the great length of struts and wires such a large gap would necessitate. By staggering the top surface forward, however, it is removed from the action of the lower surface and engages undisturbed air, with the result that the efficiency can in this way be increased by about 5 per cent. Theoretically the top plane should be staggered forward for a distance equal to about 30 per cent. of the chord, the exact distance depending upon the velocity and angle of incidence; but this is not always possible to arrange in designing an aeroplane, owing to difficulties of balance, desired position, and view of pilot, observer, etc.
6. Horizontal Equivalent.—The vertical component of the reaction, i.e., lift, varies as the horizontal equivalent (H.E.) of the surface, but the drift remains the same. Then it follows that if H.E. grows less, the ratio of lift to drift must do the same.
A, B, and C are front views of three surfaces.
A has its full H.E., and therefore, from the point of view from which we are at the moment considering efficiency, it has its best lift-drift ratio.
B and C both possess the same surface as A, but one is inclined upwards from its centre and the other is straight but tilted. For these reasons their H.E.'s are, as illustrated, less than in the case of A. That means less vertical lift, and, the drift remaining the same (for there is the same amount of surface as in A to produce it), the lift-drift ratio falls.
THE MARGIN OF POWER is the power available above that necessary to maintain horizontal flight.
THE MARGIN OF LIFT is the height an aeroplane can gain in a given time and starting from a given altitude. As an example, thus: 1,000 feet the first minute, and starting from an altitude of 500 feet above sea-level.
The margin of lift decreases with altitude, owing to the decrease in the density of the air, which adversely affects the engine. Provided the engine maintained its impulse with altitude, then, if we ignore the problem of the propeller, which I will go into later on, the margin of lift would not disappear. Moreover, greater velocity for a given power would be secured at a greater altitude, owing to the decreased density of air to be overcome. After reading that, you may like to light your pipe and indulge in dreams of the wonderful possibilities which may become realities if some brilliant genius shows us some day how to secure a constant power with increasing altitude. I am afraid, however, that will always remain impossible; but it is probable that some very interesting steps may be taken in that direction.
THE MINIMUM ANGLE OF INCIDENCE is the smallest angle at which, for a given power, surface (including detrimental surface), and weight, horizontal flight can be maintained.
THE MAXIMUM ANGLE OF INCIDENCE is the greatest angle at which, for a given power, surface (including detrimental surface), and weight, horizontal flight can be maintained.
THE OPTIMUM ANGLE OF INCIDENCE is the angle at which the lift-drift ratio is highest. In modern aeroplanes it is that angle of incidence possessed by the surface when the axis of the propeller is horizontal.
THE BEST CLIMBING ANGLE is approximately half-way between the maximum and the optimum angles.
All present-day aeroplanes are a compromise between Climb and horizontal Velocity. We will compare the essentials for two aeroplanes, one designed for maximum climb, and the other for maximum velocity.
ESSENTIALS FOR MAXIMUM CLIMB:
1. Low velocity, in order to secure the best lift-drift ratio.
2. Having a low velocity, a large surface will be necessary in order to engage the necessary mass of air to secure the requisite lift.
3. Since (1) such a climbing machine will move along an upward sloping path, and (2) will climb with its propeller thrust horizontal, then a large angle relative to the direction of the thrust will be necessary in order to secure the requisite angle relative to the direction of motion.
The propeller thrust should be always horizontal, because the most efficient flying-machine (having regard to climb OR velocity) has, so far, been found to be an arrangement of an inclined surface driven by a HORIZONTAL thrust—the surface lifting the weight, and the thrust overcoming the drift. This is, in practice, a far more efficient arrangement than the helicopter, i.e., the air-screw revolving about a vertical axis and producing a thrust opposed to gravity. If, when climbing, the propeller thrust is at such an angle as to tend to haul the aeroplane upwards, then it is, in a measure, acting as a helicopter, and that means inefficiency. The reason of a helicopter being inefficient in practice is due to the fact that, owing to mechanical difficulties, it is impossible to construct within a reasonable weight an air-screw of the requisite dimensions. That being so, it would be necessary, in order to absorb the power of the engine, to revolve the comparatively small-surfaced air screw at an immensely greater velocity than that of the aeroplane's surface. As already explained, the lift-drift ratio falls with velocity on account of the increase in passive drift. This applies to a blade of a propeller or air-screw, which is nothing but a revolving surface set at angle of incidence, and which it is impossible to construct without a good deal of detrimental surface near the central boss.
4. The velocity being low, then it follows that for that reason also the angle of incidence should be comparatively large.
5. Camber.—Since such an aeroplane would be of low velocity, and therefore possess a large angle of incidence, a large camber would be necessary.
Let us now consider the essentials for an aeroplane of maximum velocity for its power, and possessing merely enough lift to get off the ground, but no margin of lift.
1. Comparatively HIGH VELOCITY.
2. A comparatively SMALL SURFACE, because, being of greater velocity than the maximum climber, a greater mass of air will be engaged for a given surface and time, and therefore a smaller surface will be sufficient to secure the requisit lift.
3. A small angle relative to the propeller thrust, since the latter coincides with the direction of motion.
4. A comparatively small angle of incidence by reason of the high velocity.
5. A comparatively small camber follows as a result of the small angle of incidence.
Essentials for Maximum Essentials for MaximumClimb. Velocity1. Low velocity. High velocity.2. Large surface. Small surface.3. Large angle relative to Small angle relative topropeller thrust. propeller thrust.4. Large angle relative to Small angle relative to directiondirection of motion. of motion.5. Large camber. Small camber.
It is mechanically impossible to construct an aeroplane of reasonable weight of which it would be possible to very the above opposing essentials. Therefore, all aeroplanes are designed as a compromise between Climb and Velocity.
As a rule aeroplanes are designed to have at low altitude a slight margin of lift when the propeller thrust is horizontal.
ANGLES OF INCIDENCE (INDICATED APPROXIMATELY) OF AN AEROPLANE DESIGNED AS A COMPROMISE BETWEEN VELOCITY AND CLIMB, AND POSSESSING A SLIGHT MARGIN OF LIFT AT A LOW ALTITUDE AND WHEN THE THRUST IS HORIZONTAL
MINIMUM ANGLE.
This gives the greatest velocity during horizontal flight at a low altitude. Greater velocity would be secured if the surface, angle, and camber were smaller and designed to just maintain horizontal flight with a horizontal thrust. Also, in such case, the propeller would not be thrusting downwards, but along a horizontal line which is obviously a more efficient arrangement if we regard the aeroplane merely from one point of view, i.e., either with reference to velocity OR climb.
OPTIMUM ANGLE (Thrust horizontal)
The velocity is less than at the smaller minimum angle, and, as aeroplanes are designed to-day, the area and angle of incidence of the surface is such as to secure a slight ascent at a low altitude. The camber of the surface is designed for this angle of incidence and velocity. The lift-drift ratio is best at this angle.
BEST CLIMBING ANGLE
The velocity is now still less by reason of the increased angle producing increase of drift. Less velocity at A GIVEN ANGLE produces less lift, but the increased angle more or less offsets the loss of lift due to the decreased velocity, and in addition, the thrust is now hauling the aeroplane upwards.
MAXIMUM ANGLE
The greater angle has now produced so much drift as to lessen the velocity to a point where the combined lifts from the surface and from the thrust are only just able to maintain horizontal flight. Any greater angle will result in a still lower lift-drift ratio. The lift will then become less than the weight and the aeroplane will consequently fall. Such a fall is known as “stalling” or “pancaking.”
NOTE.—The golden rule for beginners: Never exceed the Best Climbing Angle. Always maintain the flying speed of the aeroplane.
By this means, when the altitude is reached where the margin of lift disappears (on account of loss of engine power), and which is, consequently, the altitude where it is just possible to maintain horizontal flight, the aeroplane is flying with its thrust horizontal and with maximum efficiency (as distinct from engine and propeller efficiency).
The margin of lift at low altitude, and when the thrust is horizontal, should then be such that the higher altitude at which the margin of lift is lost is that altitude at which most of the aeroplane's horizontal flight work is done. That ensures maximum velocity when most required.
Unfortunately, where aeroplanes designed for fighting are concerned, the altitude where most of the work is done is that at which both maximum velocity and maximum margin of lift for power are required.
Perhaps some day a brilliant inventor will design an aeroplane of reasonable weight and drift of which it will be possible for the pilot to vary at will the above-mentioned opposing essentials. Then we shall get maximum velocity, or maximum margin of lift, for power as required. Until then the design of the aeroplane must remain a compromise between Velocity and Climb.
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,16more “keel-surface” behind the vertical axis than there is in front of it. By keel-surface I mean every-thing 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.
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.
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.
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 degrees.
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 degrees, the C.P. moves forward as in the case of flat surfaces (see B), but angles above 30 degrees do not interest us, since they produce a very low ratio of lift to drift.
Below angles of about 30 degrees (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.
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:
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:
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 degrees. Such decrease applies to both main surface and stabilizer, since both are fixed rigidly to the aeroplane.
The main surface, which had 12 degrees angle, has now only 10 degrees, i.e., a loss of ONE-SIXTH.
The stabilizer, which had 4 degrees angle, has now only 2 degrees, 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 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 degrees. Then, in order to secure a sufficiency of longitudinal stability, it is necessary to set the forward stabilizer at about 15 degrees. 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.
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, 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. In modern aeroplanes this tendency is not sufficiently important to bother about. In the old days of crudely designed and under-powered 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:
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.
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.
Propeller torque affects lateral stability. An aeroplane tends to turn over sideways in the opposite direction to which the propeller revolves.
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:
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.
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:
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.” Experentia 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.
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 end 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.
GLIDING DESCENT WITHOUT PROPELLER THRUST.—All aeroplanes are, or should be, designed to assume their 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.
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.
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.
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.
Diagram p. 88.—This is not set at quite the correct angle. Path B should slope slightly downwards from Position A.