Question

What derivatives associated with static stability for airplanes? How these derivatives may affect dynamic rigid body modes?

Answer 1

Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change (parameters such as airspeed, altitude, angle of attack, etc.). For a defined "trim" flight condition, changes and oscillations occur in these parameters. Equations of motion are used to analyze these changes and oscillations. Stability and control derivatives are used to linearize (simplify) these equations of motion so the stability of the vehicle can be more readily analyzed.

Stability and control derivatives change as flight conditions change. The collection of stability and control derivatives as they change over a range of flight conditions is called an aero model. Aero models are used in engineering flight simulators to analyze stability, and in real-time flight simulators for training and entertainment.

CL {\displaystyle \beta }, called dihedral effect, is a stability derivative that measures changes in rolling moment as Angle of sideslip changes. The "L" indicates rolling moment and the {\displaystyle \beta } indicates sideslip angle.

Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change (parameters such as airspeed, altitude, angle of attack, etc.) Stability derivative.