The perturbations u, w (or a), q and are independent of each other. Body-axis derivative calculations: i) Partial derivative of dynamic pressure (switching between w and a in the linearized model) q=pV;;V =U +V +W; For the disturbed airplane (w only, symmetric flight), V = U+(W+w) U BV, av 2W ow Ow pW aw U=V, cos cos W-V, sin cos tan = W U Wo W Holding U constant, a small change in W produces cos as U (for small ) aw U % q a 1 OF X m m pvtan -(2q_tan aS_Cx, +q_S_Cx) 1 OF X 4 m ow 1 (2q_tan S_C+q_S_C) m V Note also that in a Taylor expansion, X=x_w