CHAPTER XV. BALANCE AND STABILITY.

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

Elements of Stability. When we balance a board on a fulcrum so that it stands in a perfectly horizontal position, the board is said to be "In equilibrium," or is supported at its "Center of gravity." There is only one point at which a body will balance, and this point is at the center of gravity or "C. G." In an aeroplane, the combined mass of the body, motor, wings, fuel, chassis, tail and live load has a center of gravity or a balancing point at which the lift must be applied if the machine is to rest in equilibrium. When the center of lift (or center of pressure) does not pass through the center of gravity of the aeroplane, some other force must be applied to overcome the unbalanced condition. When the machine is unbalanced in a fore and aft direction with the tail low, a force must be applied by the elevator flaps that is opposite and equal to the moment of the unbalanced forces. An aeroplane is stable when it is balanced in such a way that it returns to a state of equilibrium after meeting with a disturbance.

When disturbed, a stable body does not usually return instantly to its position of equilibrium, but reaches it after a series of decreasing oscillations. The heavier the body, and the more compact its form, the longer will it oscillate about its fulcrum before coming to rest. By arranging broad surfaces at the ends of the oscillating body, a portion of the energy will be expended in creating air currents, and the motion will be readily "damped out." If the damping effect is so great that the body does not swing back after once reaching the position of equilibrium, the body is said to be "dead beat," or "dynamically stable." There is a great difference between the static forces that tend to return the body to a position of equilibrium and the dynamic retarding forces that tend to damp out the oscillations. Usually, a body with excessive static stability is far from being stable in a true sense, since such a body tends to oscillate longer, and more violently, than one in which the static restoring forces are not so strongly marked. A body may be statically but not dynamically stable, but a dynamically stable body must of necessity be statically stable.

Static stability in calm air is determined by the location of the center of gravity, the center of lift, the center of propeller thrust, the center of area of the surfaces, and the center of the forward resistance. The forces acting through these centers are: (1) The weight; (2) The lifting force; (3) The propeller thrust; (4) The resistance. The weight and lift are vertical forces equal and opposite in direction. The thrust and resistance are horizontal forces, also equal and opposite in direction. When all of these forces intersect at a common point, they will completely neutralize one another and the body will be in equilibrium.

Dynamic stability is attained by the use of large damping surfaces such as the stabilizer surface, fins, and the elevator. These act to kill the oscillations set up by the static righting couples or forces. Without suitable damping surfaces the machine would soon be out of control in gusty weather since successive wind gusts will act to increase the oscillations of the righting forces until the machine will turn completely over. On the other hand, an aeroplane can be too stable and therefore difficult to steer or control in gusts because of its tendency toward changing its attitude with every gust in order to restore its equilibrium. A machine should only be partially stable, and the majority of pilots are firmly set against any form of mechanical or inherent control. No matter how simple the method, mechanical control always introduces a certain amount of mechanism that may go wrong. The question of stability has already been solved to a sufficient extent.

A disturbance that simply changes the direction of travel is not considered an unstable force since it normally does not tend to endanger the machine. Nearly any machine, equipped with any possible form of control apparatus, tends to change its direction when being righted.

Axes of Stability. An aeroplane has six degrees of freedom or motion. Three are of translation or straight line motion, and three are of rotation about rectangular axes. It can travel forward in a straight line, rise and fall in a vertical plane, or skid sidewise. When it rolls from side to side about the fore and aft axis (X axis) it is laterally unstable. When pitching up and down in a fore and aft direction, and around an axis parallel with the length of the wings (Y axis), the machine is said to be longitudinally unstable. When swinging or "Yawing" from right to left about a vertical axis (Z axis) it is unstable in "Yaw."

Rolling is resisted by the ailerons, pitching by the elevators and stabilizer, and yawing by the vertical directional rudder. Lateral oscillation are damped out by the wing surfaces and by vertical surfaces or "Fins." Longitudinal oscillations are damped mostly by the stabilizer and elevator surfaces. Directional or yawing vibrations are corrected by the damping action of the vertical tail fin, vertical rudder and the sides of the body, the latter also serving to damp out longitudinal vibrations. On an absolutely calm day, the pilot can shut off the motor and glide down without touching the controls if the machine is longitudinally stable. The glide generally starts with a few pitching oscillations, but these gradually are damped out by the tail as soon as the machine picks up its natural gliding angle and speed, and from this point it will continue without oscillating.

The Spiral and Nose Dive. There are two forms of instability that have not yet been fully corrected, and both are highly dangerous. One of these is known as the "spiral dive" or nose spin, and the other as the straight nose dive. The aeroplane in a spiral nose dive rotates rapidly about a vertical axis during the dive. Spiral instability resulting from lateral instability, can be minimized by decreasing the area of the vertical rudder and by the proper placing of fins so that there is not so great an excess of vertical area to the rear of the C. G.

The covered-in body acts as a fin and will be productive of spiral instability if the area is not properly distributed. In the majority of cases the rear of the body is equivalent to a large fin placed to the rear of the C. G. A fin above the G. G. tends to reduce all spiralling.

Stability and Speed. An aeroplane in straight horizontal flight must be driven at such an angle, and such a speed, that the weight is just sustained. To be inherently stable the machine must always tend to increase its speed by diving should the power be cut off in any way. An aeroplane that does not tend to increase its speed in this way, "Stalls" or becomes out of control. Any machine that will automatically pick up its gliding angle after the propeller thrust has ceased is at least partially inherently stable, and if it does not possess this degree of stability, other forms of stability are practically worthless. The machine having the smallest, flattest gliding angle is naturally safest in cases of power failure, and hence the gliding angle is somewhat related to the subject of stability.

A Spanish Aeroplane Using a Peculiar Form of Upper Fin.A Spanish Aeroplane Using a Peculiar Form of Upper Fin. These Fins Also Perform the Duty of Vertical Rudders as Well as Acting as Stabilizers.

A Spanish Aeroplane Using a Peculiar Form of Upper Fin. These Fins Also Perform the Duty of Vertical Rudders as Well as Acting as Stabilizers.

The longitudinal stability decreases with a decrease in the speed, the fore and aft vibrations becoming more rapid due to the decreased effect of the tail surfaces, and to the reduction of wing lift. Instability at low speeds is common to all aeroplanes, whether inherently stable or not, and at a certain critical speed the machine becomes absolutely unstable in a dynamic sense. If a machine is to be stable at low speeds, it must not fly at too great an angle of incidence at these speeds, and it should have a very large tail surface acting at a considerable distance from the wings. Hunsaker states that the lowest speed should not require more than 80 per cent of the total lift possible.

Inertia or Flywheel Effect. The principal weights should be concentrated as nearly as possible at the center of gravity. Weights placed at extreme outer positions, as at the wing tips, or far ahead of the wings, tend to maintain oscillations by virtue of their flywheel effect. The measure of this inertia or flywheelage is known as the "Moment of Inertia" and is the sum of the products of all the masses by the squares of their distances from the center of gravity. A great amount of inertia must be met by a large damping surface or control area if the vibrations are to be damped out in a given time. In twin-motored aeroplanes the motors should be kept as close to the body as the propellers will permit.

Wind Gusts and Speed. A machine flying at high speed is less affected by wind gusts or variations in density than a slow machine, since the disturbing currents are a smaller percentage of the total speed. In addition, a high speed results in smaller stresses due to the gusts.

Gyroscopic Instability. The motor gyroscopic forces do not affect the stability of a machine to any great extent, and in twin motored aeroplanes the gyroscopic action of the propellers is almost entirely neutralized. At one time the gyroscopic torque was blamed for every form of instability, but on investigation it was found that the practical effect was negligible.

Instability Due Power Plant. The power plant affects stability in a number of ways. The thrust of the propeller may cause a fore and aft moment if the center line of thrust does not pass through the center of resistance. This causes the machine to be held head up, or head down, according to whether the line of thrust is below or above the C. G. If the propeller thrust tends to hold the head up in normal flight, the machine will tend to dive, and assume its normal gliding velocity with the power off, hence this is a condition of stability. With the effect of the thrust neutral, or with the thrust passing through the center of resistance, the machine will not tend to maintain the speed, and hence it is likely to stall unless immediately corrected by the pilot. With the line of thrust above the C. G., the stall effect is still further increased since with this arrangement there is a very decided tendency for the machine to nose up and increase the angle of incidence when the power is cut off.

Steel Elevator and Rudder Construction Used on a European Machine. The Elevators Also Act as Stabilizers, the Entire Surface Turning About the Tube Spar.Steel Elevator and Rudder Construction Used on a European Machine. The Elevators Also Act as Stabilizers, the Entire Surface Turning About the Tube Spar.

Steel Elevator and Rudder Construction Used on a European Machine. The Elevators Also Act as Stabilizers, the Entire Surface Turning About the Tube Spar.

The slip stream of the propeller has a very decided effect on the tail surfaces, these being much more effective when the propeller slip stream passes over them. With lifting tails, or tails that normally carry a part of the load, the stoppage of the slip stream decreases the lift of the tail and consequently tends to stall the machine. Non-lifting tails should be arranged so that the slip stream strikes down on the upper surface. This tends to force the tail down, and the head up in normal flight, and when the power ceases the tail will be relieved and there will be an automatic tendency toward diving and increase in speed. On a twin aeroplane, a similar effect is obtained by making the upper tips of both propellers turn inwardly. The air is thus thrown down on the tail.

With a single motor, the torque tends to turn the aeroplane in a direction opposite to the rotation of the propeller. Lateral stability is thus interfered with when the motor is cut off or reduced in speed. With right-hand propeller rotation, for example, the machine will be turned toward the left, forcing the left tip down. To maintain a horizontal attitude, the left aileron must be held down by an amount just sufficient to overcome the torque. In some machines one wing tip is given a permanent increase in incidence so that the down seeking tip is given permanent additional lift.

Lateral Stability. When an aeroplane is turned sharply in a horizontal plane, or "Yaws," the outer and faster moving wing tip receives the greater lift, and a lateral rolling moment is produced about the fore and aft axis. In the opposite condition, a lateral rolling moment tends to yaw or to throw the aeroplane off a straight course. Below a certain critical speed, the lateral or rolling oscillations increase in amplitude, with a strong tendency to side slip, skid or spiral. The tail fin or rudder retards the tail velocity in a side slip, and thus turns the slipping or skidding machine into a vertical spiral or spinning nose dive. This spin increases the angle of bank and hence the side slip. This in turn increases the turning or yawing velocity, and the spiral starts. This tendency toward a spiral dive can be corrected by a vertical fin placed forward, and above the center of gravity, or by raising the wing tips. An upper fin of this type will give a force that tends to break up the bank when side slip starts and thus will prevent spinning.

Sperry Gyroscopic Control System for Automatic Stability.Sperry Gyroscopic Control System for Automatic Stability. The Gyroscopic Control at the Left Controls the Movements of the Electric Servo-Motor at the Extreme Right. This Motor Operates the Control Surfaces Through the Pulley Shown. A Small Electric Generator Between the Servo-Motor and Gyroscope Provides the Current and Is Driven by a Small Wind Propeller.

Sperry Gyroscopic Control System for Automatic Stability. The Gyroscopic Control at the Left Controls the Movements of the Electric Servo-Motor at the Extreme Right. This Motor Operates the Control Surfaces Through the Pulley Shown. A Small Electric Generator Between the Servo-Motor and Gyroscope Provides the Current and Is Driven by a Small Wind Propeller.

At normal speeds the rolling is damped down by the wing surfaces, and can be further controlled by the application of the ailerons. At the lower critical speed when the machine is stalled, one wing tip has no more lift than the other, and hence the damping effect of the wings and the action of the ailerons becomes negligible.

Dutch Roll. In "Dutch Roll," the rolling is accompanied by an alternate yawing from right to left. This is aggravated by a fin placed high above the C. G., and hence corrections for spiral dive conflict with corrections for Dutch roll. The rolling is accompanied by some side slip, and the motion is stable providing that there is sufficient fin in the rear and not an excessive amount above the C. G.

Degree of Stability. Excessive stability is dangerous unless the control surfaces are powerful enough to overcome the stable tendency. Since a stable machine always seeks to face the relative wind, it becomes difficult to handle in gusty weather, as it is continually changing its course to meet periodic disturbances. This is aggravated by a high degree of static stability, and may be positively dangerous when landing in windy weather.

Control Surfaces. A non-lifting tail must give no lift when at a zero angle of incidence. It must be symmetrical in section so that equal values of lift are given by equal positive and negative angles of incidence. Square edged, flat surfaces are not desirable because of their great resistance. A double cambered surface is suitable for such controls as the stabilizer, elevator and rudder. It has a low resistance, permits of strong internal spars, and is symmetrical about the line of the chord. Some tails are provided with a cambered top and a flat bottom surface so that the down wash of the wings is neutralized. Under ordinary conditions this would be an unsymmetrical lifting surface, but when properly adapted to the wings the lifting effect is completely neutralized by the down wash.

The curvature of the section should be such that the movement of the center of pressure is as small as possible. With a small movement of the center of pressure, the surface can be accurately balanced and hinged on the center of pressure line. It is desirable to have the maximum thickness of section at, or near to the C. P., so that a deep spar can be used for the support of the hinge system. Usually the movement of the control surfaces is limited to an angle of 30 degrees on either side of the center line, as the lift of all surfaces start to decrease after this point is reached. The surface movement should be limited by the maximum lift angle of the section in any case, since an accident will be bound to occur if they are allowed movement beyond the angle of maximum lift.

In locating the control surfaces, careful attention should be paid to the surrounding air conditions so that they will not be unduly affected by the wash-down of the wings or body. The effectiveness of the tail surfaces is very much reduced by bringing them close to the wings, and the lift is always reduced by the wash of a covered fuselage.

The wash-down effect of the wings on the tail is proportional to the chord and not to the span, and for this reason an increase in span does not always necessitate an increase in the length of the body. An adequate damping effect requires a large surface at the end of a long lever arm.

Balancing the Aeroplane. Figs. 1 to 6 show the principles involved in the balancing of the aeroplane. In Fig. 1 a number of weights 1'-2'-3' and 5M are supported on a beam, the load being balanced on the fulcrum point M. The load 2' being directly over the fulcrum, has no influence on the balance, but load 1’ at the left tends to turn the mass in a left-hand direction, while 3' and 5M tend to give it a right-hand rotation. This turning tendency depends upon the weights of the bodies and their distance from the fulcrum. The turning tendency or "Moment" is measured by the product of the weight and the distance from the fulcrum. If weight 1' should be 10 pounds, and its distance A' from the fulcrum should be 20 inches, then it would cause a left-hand moment of 10 x 20 = 200 inch pounds. If the system is to be in balance, then the left-hand moment of 1’ should be equal to the sum of the moments of 3’ and 5M. Thus: 1’ x A = (3' x B) + (5M x C').

Figs. 1-6. Methods of Balancing an Aeroplane About Center of Lift.Figs. 1-6. Methods of Balancing an Aeroplane About Center of Lift.

Figs. 1-6. Methods of Balancing an Aeroplane About Center of Lift.

The application of this principle as applied to a monoplane is shown by Fig. 4, in which X-X is the center of pressure or lift. The center of lift corresponds to the fulcrum in Fig. 1, and the weights of the aeroplane masses and their distance from the center of lift are shown by the same letter as in Fig. 1. The engine 1' is at the right of the C. P. by the distance A, while the fuel tank 2 is placed on the C. P. in the same way that the weight 2' in Fig. 1 is placed directly over the fulcrum. By placing the tank in this position, the balance is not affected by the emptying of the fuel since it exerts no moment. The chassis G acting through the distance E is in the same direction as the engine load. The body 5 with its center of gravity at M acts through the distance C, while the weight of the pilot 3 exerts a right-hand moment with the lever arm length B. If the moments of all these weights are not in equilibrium, an additional force must be exerted by the tail V.

Fig. 2 shows an additional weight 4' that corresponds to the weight of the passenger 4 in Fig. 5. This tends to increase the right turning moment unless the fulcrum is moved toward the new load. In Fig. 2 the fulcrum M remains at the same point as in Fig. 1, hence the system requires a new force P’ acting up at the end of the beam. If the load was in equilibrium before the addition of 4', then the force P’ must be such that P’ x T’ = 4" x D’. In the equivalent Fig. 5, the center of gravity has moved from its former position at S to the new position at R, the extent of the motion being indicated by U. To hold this in equilibrium, an upward force P must be exerted by the elevator at Y, the lever arm being equal to (T + U).

Fig. 6 shows the single-seater, but under a new condition, the center of pressure having moved back from X-X to Z. To hold the aeroplane in equilibrium, a downward force must be provided by the tail V which will cause a right-hand moment equal to the product of the entire weight and the distance U. For every shift in the center of pressure, there must be a corresponding moment provided by the elevator surface. The condition is shown by the simple loaded beam of Fig. 3. In this case the fulcrum has been moved from M to N, a distance equal to the center of pressure movement in Fig. 6. This requires a downward force P' to maintain equilibrium.

Center of Pressure Calculation. Fig. 7 is a diagram showing the method of calculating the center of gravity. The reference line R is shown below the elevators and is drawn parallel to the center of pressure line W-W, the latter line being assumed to pass through the center of gravity. The line R may be located at any convenient point, as at the propeller flange or elsewhere, but for clearness in illustration it is located to the rear of the aeroplane. The weight of each item is multiplied by the distance of its center of gravity from the line R, these products are added, and the sum is then divided by the total weight of the machine. The result of this division gives the distance of the center of gravity from the line R. Thus, if the center of gravity of the body (11) is located at (10), then the product of the body weight multiplied by the distance B will give the moment of the body about the line R. The weight of the motor (2) multiplied by the distance F gives the moment of the motor about R, and so on through the list of items.

Center Of Gravity TableCenter Of Gravity Table

Center Of Gravity Table

The distance of the center of gravity (or center of pressure) from the reference line R is given by H + K. This gives the numerical value 219350/1375 = 1596 inches. Thus if we measure 159.6 inches from R toward the wings we will have located the center of gravity. The location of the C. G. can be changed by shifting the weights of the motor, passenger, or other easily moved items. In any case, the C. G. should lie near the center of pressure.

Tail Lever Arms. The effective damping moment exerted by the fixed stabilizer surface (12) will be the product of its area by the distance (I), measured from the center of pressure of the wing to the center of pressure of the stabilizer. The lever arm of the elevator is the distance (H) measured from the centers of pressure as before.

Fig. 7. Method of Determining the Center of Gravity of an Aeroplane.Fig. 7. Method of Determining the Center of Gravity of an Aeroplane.

Fig. 7. Method of Determining the Center of Gravity of an Aeroplane.

Resultant Forces and Moments in Flight. The aeroplane is in equilibrium when all of the forces pass through a common center, as shown by Fig. 8. In this figure the lift (L), the weight (W), the line of propeller thrust (T), and the resistance (R) all pass through the center of gravity shown by the black dot C. G. There are no moments and hence no correction is needed from the elevator (T). In Fig. 9, the thrust and resistance pass through the center of gravity as before, but the center of lift (L) does not pass through the center of gravity, the distance between the two being indicated by (n). This causes a moment, the length of the lever arm (n) being effective in giving a right-hand rotation to the body. If horizontal flight is to be had this must be resisted by the upward elevator force (E).

In Fig. 10, the lift passes through the center of gravity, but the line of resistance lies below it by the amount (m). The thrust (T) tends to rotate the machine in a left-handed direction. The elevator must exert a downward force (e) to resist the moment caused by (m). This is a bad disposition of forces, as the machine would tend to stall or tail-dive should the propeller thrust cease for even an instant. The stability of Figs. 8 and 9 would not be affected by the propeller thrust, as it passes through the C. G. in both cases. In Fig. 11, the center line of thrust is below the line of resistance (R), so that the thrust tends to hold the nose up. Should the motor fail in this case, the nose would drop and the machine would start on its gliding angle and pick up speed.

In Fig. 12 none of the forces intersect at a common point, the lift and weight forming a right-handed couple, while the thrust (T) and the resistance (R) form a left-handed couple that opposes the couple set up by the weight and lift forces. If the thrust-resistance couple can be made equal to the lift-weight couple, the aeroplane will be in equilibrium and will need no assistance from the elevator. As the weights in the aeroplane are all located at different heights, it is necessary to obtain the center of gravity of all the loads in a vertical plane as well as horizontally. Thus in Fig. 13 the line C. G. is the center of gravity of the engine weight (1), the wing weight (2), the pilot's weight (3), the chassis weight (4), the fuselage weight (5), and the fuel tank weight (6). The line C. G. is the effective center of all these loads, and is calculated by taking the products of the weights by the distance from a reference line such as R-R. The center of resistance is the effective center of all the resistance producing items such as the wings, body, struts, chassis, etc.

Figs. 8-15. Forces Affecting the Longitudinal Stability of an Aeroplane.Figs. 8-15. Forces Affecting the Longitudinal Stability of an Aeroplane.

Figs. 8-15. Forces Affecting the Longitudinal Stability of an Aeroplane.

A suggestion of the method employed in obtaining the center of resistance is shown by Fig. 14, the center line of resistance R-R being the resultant of the wing resistance (D), the body resistance (B), and the chassis resistance (C). It will be noted that the wing resistance of biplane wings (W-W') does not lay midway between the wings but rather closer to the upper wing, as shown by (E). This is due to the upper wing performing the greater part of the lift. In locating the center of resistance, the resistance forces are treated exactly like the weights in the C. G. determination. Each force is multiplied by its distance from a horizontal reference line, and the sum of the products is divided by the total resistance. As shown, the center of resistance R-R passes through the center of gravity C. G. The center of pressure line X-X also contains the center of resistance.

A staggered biplane cell is shown by Fig. 15, the center of pressure of the upper and lower wings being connected by the line X-X as before. The center of resistance of the pair is shown at (D), where it is closer to the upper wing than to the lower. A vertical line Y-Y dropped through the center of resistance gives the location of the center of lift. As shown, the center of lift is brought forward by the stagger until it is a distance (g) in front of the leading edge of the lower wing. The center of lift and the center of resistance both lie on a line connecting the center of pressure of the upper and lower wings.

Calculation of Control Surfaces. It is almost impossible to give a hard and fast rule for the calculation of the control surfaces. The area of the ailerons and tail surfaces depends upon the degree of stability of the main wings, upon the moment of inertia of the complete machine, and upon the turning moments. If the wings are swept back or set with a stagger-decalage arrangement, they will require less tail than an orthogonal cell. All of these quantities have to be worked out differently for every individual case.

Aileron Calculations. The ailerons may be used only on the upper wing (2 ailerons), or they may be used on both the upper and lower wings. When only two are used on the upper wing it is usually the practice to have considerable overhang. When the wings are of equal length either two or four ailerons may be used. Roughly, the ailerons are about one-quarter of the wing span in length. With a long span, a given aileron area will be more effective because of its greater lever arm.

If a = area of ailerons, and A = total wing area in square feet, with S = wing span in feet, the aileron area becomes: a = 3.2A/S. It should be borne in mind that this applies only to an aeroplane having two ailerons on the upper wing, since a four-aileron type usually has about 50 per cent more aileron area for the same wing area and wing span. For, example, let the wing span be 40 feet and the area of the wings be 440 square feet, then the aileron area will be: a = 3.2A/S = 3.2 x 440/40 = 35.2 square feet. If four ailerons were employed, two on the upper and two on the lower wing, the area would be increased to 1.5 x 35.2 = 52.8 square feet. As an example in the sizes of ailerons, the following table will be of interest:

Aileron Sizes TableAileron Sizes Table

Aileron Sizes Table

In cases where the upper and lower spans are not equal, take the average span—that is, one-half the sum of the two spans.

Stabilizer and Elevator Calculations. These surfaces should properly be calculated from the values of the upsetting couples and moments of inertia, but a rough rule can be given that will approximate the area. If a' = combined area of stabilizer and elevator in square feet; L = distance from C. P. of wings to the C. P. of tail surface; A = Area of wings in square feet, and C = chord of wings in feet, then:

a’ = 0.51AC/L. Assuming our area as 430 square feet, the chord as 5.7 feet, and the lever arm as 20 feet, then:

a’ = 0.51AC/L = 0.51 x 430 x 5.7/20 = 62.5 square feet, the combined area of the elevators and stabilizer. The relation between the elevator and stabilizer areas is not a fixed quantity, but machines having a stabilizer about 20 per cent greater than the elevator give good results. In the example just given, the elevator area will be: 62.5/22 = 28.41 square feet, where 2.2 is the constant obtained from the ratio of sizes. The area of the stabilizer is obtained from: 28.41 x 1.2 = 34.1 square feet.

Negative Stabilizers. A considerable amount of inherent longitudinal stability is obtained by placing the stabilizing surface at a slight negative angle with the wings. This angle generally varies from -2° to -6°. At small angles of wing incidence the negative angle of the tail will be at a maximum, and acting down will oppose further diving and tend to head the machine up. At large wing angles, the tail will be depressed so far that the tail angle will become positive instead of negative, and thus the lift on the tail will oppose the wings and will force the machine to a smaller angle of incidence. The negative angle can thus be adjusted to give longitudinal stability within the ordinary range of flight angles.

Stabilizer Shapes and Aspect Ratio. Stabilizers have been built in a great number of different shapes, semicircular, triangular, elliptical, and of rectangular wing form. Measured at the rear hinged joint, the span or width of the stabilizer is about 1/3 the wing span for speed scouts, and about 1/4 the wing span for the larger machines. Nearly all modern machines have non-lifting tails, or tails so modified that they are nearly non-lifting. Since flat plates give the greatest lift with a small aspect ratio, and hence are most effective when running over the ground at low speeds, the stabilizers and elevators are of comparatively low aspect. In general, an aspect ratio of 3 is a good value for the stabilizer. Vertical rudders generally have an aspect ratio of 1, and hence are even more effective per unit area than the stabilizers. This is particularly necessary in ground running.

Aileron Control Diagram of Curtiss JN4-B.Aileron Control Diagram of Curtiss JN4-B.

Aileron Control Diagram of Curtiss JN4-B.

Elevator Control Diagram of Curtiss JN4-B.Elevator Control Diagram of Curtiss JN4-B.

Elevator Control Diagram of Curtiss JN4-B.

Vertical Rudders. The calculation of the vertical rudders must take the moment of inertia and yawing moments into effect, and this is rather a complicated calculation for the beginner. As an approximation, the area of the rudder can be taken from 9 to 12 square feet for machines of about 40 feet span, and from 5 to 8 square feet for speed scouts.

Stick Control Used on the Caudron Biplane. Wing Warp Is Used Instead of Ailerons. Back and Forth Movement Actuates Elevator.Stick Control Used on the Caudron Biplane. Wing Warp Is Used Instead of Ailerons. Back and Forth Movement Actuates Elevator.

Stick Control Used on the Caudron Biplane. Wing Warp Is Used Instead of Ailerons. Back and Forth Movement Actuates Elevator.

German Stick Control With Double Grips.German Stick Control With Double Grips. A. Latch on the Side of the Stick Acts on a Sector So That the Lever Can Be Held at Any Point. It Is Released by the Pressure of the Knees.

German Stick Control With Double Grips. A. Latch on the Side of the Stick Acts on a Sector So That the Lever Can Be Held at Any Point. It Is Released by the Pressure of the Knees.

Wing Stability. Under wing sections, the subject of the center of pressure movement has already been dealt with. The variation of the center of pressure with the angle of incidence tends to destroy longitudinal stability since the center of pressure does not at all times pass through the center of gravity. On some wings, the camber is such that the variation in the position of the center of pressure is very little, and hence these are known as stable wings. A reflex curve in the trailing edge of a wing reduces the center of pressure movement, and swept back wings are also used as an aid in securing longitudinal stability. Introducing stagger and decalage into a biplane pair can be made to produce almost perfect static longitudinal stability. It should be noted that stability obtained by wing and camber arrangements is static only, and requires damping surfaces to obtain dynamic stability.

Form of Control Used on the Nieuport Monoplane.Form of Control Used on the Nieuport Monoplane.

Form of Control Used on the Nieuport Monoplane.

Manual Controls. In flight, the aviator has three control surfaces to operate, the ailerons, elevator, and rudder. In the usual form of machine the ailerons and elevator are operated by a single lever or control column, while the rudder is connected with a foot bar. In the smaller machines "Stick Control" is generally used, the ailerons and elevator being moved through a simple lever or "Joy Stick" which is pivoted at its lower end to the floor. The Deperdussin or "Dep" control is standard with the larger machines and consists of an inverted "U" form yoke on which is mounted the wheel for operating the ailerons.

Stick Control. With the stick pivoted at the bottom, a forward movement of the lever causes the machine to descend while a backward movement or pull toward the pilot causes the aeroplane to head up or ascend. The stick is connected with the elevators with crossed wires, so that the flaps move in an opposite direction to the "Stick." Moving the stick from side to side operates the ailerons.

Standard Stick Control and Movements Used in the U.S.A.Standard Stick Control and Movements Used in the U.S.A.

Standard Stick Control and Movements Used in the U.S.A.

Deperdussin Control. A "U" shaped yoke, either of bent wood or steel tube, is pivoted the bearers at the sides of the fuselage. Wires are attached to the bottom of the yoke so that its back and forth movement is communicated to the elevator flaps. On the top, and in the center of the yoke, is pivoted a hand wheel of the automobile steering type. This is provided with a pulley and is connected with the aileron flaps in such a way that turning the wheel toward the high wing tip causes it to descend. Pushing the yoke forward and away from the aviator causes the machine to descend, while a reverse movement raises the nose. The "Dep" control is reliable and powerful but is bulky and heavy, and requires a wide body in order to allow room for the pilot.

Foot Rudder Bar Used in the Standard H-3. Courtesy "Aerial Age."Foot Rudder Bar Used in the Standard H-3. Courtesy "Aerial Age."

Foot Rudder Bar Used in the Standard H-3. Courtesy "Aerial Age."

Rudder Control. Foot bar control for the rudder is standard with both the stick and Dep controls. The foot bar is connected with the rudder in such a way that the aeroplane turns opposite to the movement of the foot bar in the manner of a boat. That is, pushing the right end of the bar forward causes the machine to turn toward the right.

Automatic Control System (Sperry) Installed in Fuselage of Curtiss Tractor Biplane.Automatic Control System (Sperry) Installed in Fuselage of Curtiss Tractor Biplane.

Automatic Control System (Sperry) Installed in Fuselage of Curtiss Tractor Biplane.

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