Aerodynamic Derivatives in Body Fixed Axes
In Chapter 14, the idea of aerodynamic stability derivatives was introduced for a body fixed (or wind) axes system; these allow the effect on aerodynamic forces and moments, for a small perturbation about the equilibrium condition, to be defined. In this appendix, an example of calculating three such derivatives will be shown. Other references should be consulted for more detail and additional derivative examples (Cook, 1997; ESDU Data Sheets).
E.1 LONGITUDINAL DERIVATIVE ZW
In this section, the longitudinal derivative Zw will be obtained for use in Chapter 15, along with many other derivatives that are not derived here.
E.1.1 Perturbed state
The aircraft is in steady level flight at velocity V0 (equilibrium value) and experiences a small perturbation as shown in Figure E.1; wind axes are used and the lift, drag, pitching moment and thrust are all perturbed quantities. In the perturbed condition, the total velocity is V with components U, W along the oxz axes. Then
For wind axes, the pitch attitude perturbation θ is equal to the incidence perturbation α and so for small angles
The lift and drag forces produced in the perturbation ...