Aeroplane Construction and Operation

by John B. Rathbun

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.

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.

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.