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 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.