By A. W. Babister (Auth.)
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Additional resources for Aircraft Dynamic Stability and Response
The line of action of the thrust is the aircraft (along Ox). Resolving these forces into components X and Z and Oz respectively, we find (from Fig. 3 . 11) C sinA). D are functions of wing incidence a and velocity V (due to compressibil- ity e f f e c t s ) . FORWARD SPEED V Fig. 2 Differentiating Eq. 10) with respect to U, and then using Eq. )V) 2ee ( 3 . 8 ) , we find D + dT/dV , where the incidence A, the density p and the speed V have been given their constant datum values (for the given state of steady flight) after the differentiation.
Z and 0 z Thus a (assumed small) is the angle between 0 x and 0 x . x xx 0x xx a r e in the plane of symmetry, perpendicular to 0 x and 0 x y is to starx xx respectively, and 0x board. W e suppose that the wing has a dihedral angle T, where V is small. Thus, if w e consider the projection of the wing in the plane O yz S to x x and take POx represent the mean of the projection of the upper and lower surfaces of the wing in that plane, then Y is the angle between 0 S (the starboard projection) and 0 y; X x similarly the angle between 0 P (the port projection) and 0 y' (the negative y axis) X x is also T.
E. from Eqs. 1) to ( 4 . 4) where Q is the local chord length and dCjj/dCLfa is the local value of the lift curve Fig. 2 Velocity components RT, slope. and forces on a chordwise strip As shown in Fig. 2, dL will have components dL sin (a^ - a ) parallel to 0 x and x Thus, neglecting small quantities of the third -dL cos (a/z - a) parallel to 0 z. x order and the component of the drag, and taking moments about the axis 0 x, we see x that the rolling moment due to the starboard wing is where s is the semi-span (= \b).