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4 4 ) , we see that the equations of motion for small disturbances can be split up into two groups. 47) = M(t) q = 0 . 48) These equations involve only symmetric disturbances (u the increment in the velocity of 0 along Ox, w the increment in the velocity of 0 along Oz, 0 the angle of pitch, and their derivatives with respect to t ) . 52) . 53) These equations involve only asymmetric disturbances (V the velocity of sideslip, cj) the angle of bank, ij; the angle of yaw, and their derivatives with respect to t).

Fuselage-tailplane e f f e c t s ) . As pointed out in Chapter 2, the present notation differs from that used before 1970; a table of conversion factors when using the old symbols is given in reference 1. We refer all the derivatives to wind axes. FORCE VELOCITY DERIVATIVES X, u X, w Z, u Z w These derivatives depend upon the lift and drag coefficients for the whole and upon their rates of change with incidence and speed. g. of the aircraft in the motion following a symmetric disturbance (note that this should not be confused with V, the sideslipping velocity, which is zero in longitudinal symmetric m o t i o n ) .

Using potential flow theory, it can be shown that the velocity at the point (x,0) on a flat plate (chord 2a) lying along Ox and rotating with angular velocity q about its mid-point 0 is where x = a cos ri and U, V are the components of the two-dimensional stream in the negative directions of Ox, Oy. external Use this result to find the normal force and pitching moment about the origin per unit span for a flat plate in translation and rotation about its mid-point. z z results for rotation about a general point in the plate.