# The Stability Derivatives

5.1 General Remarks

We saw in Chap. 4 how the aerodynamic actions on the airplane can be represented approximately by means of stability derivatives (or more exactly by aerodynamic transfer functions). Indeed, all the aerodynamics involved in airplane dynamics is concentrated in this section of the subject: i. e., in the determination of these deriva­tives (or transfer functions). Each of the stability derivatives contained in the equa­tions of motion is discussed in the following sections. Wherever possible, formulas for them are given in terms of the more elementary parameters used in static stability and performance. Where this is not feasible, it is shown in a qualitative way how the particular force or moment is related to the relevant perturbation quantity. No data for estimation are contained in this chapter; these are all in Appendix B.

EXPRESSIONS FOR Cx AND Cz

For convenience, we shall want the derivatives of Cx and Cz expressed in terms of lift, drag, and thrust coefficients. The relevant forces are shown in Fig. 5.1. As shown, the thrust line does not necessarily lie on the x axis. However, the angle between them is generally small, and we shall assume it be zero. With this assumption, and for small ax, we get1 Cx — CT + CLax Cn C – — ~(CL + CDax)

where CT is the coefficient of thrust, T!pV2S.