The influence of variable air density and of nonlinear aerodynamic characteristics on dynamic behavior at supersonic speeds

Abstract

The effect of the variable density of the Standard Atmosphere on the dynamic stability of a missile in vertical flight is considered. The analysis is restricted to small disturbances from steady rectilinear flight. The exponential decrease of density with altitude characteristic of the Standard Stratosphere is introduced into the equations of motion and a stability criterion for the dynamic behavior immediately following a small disturbance is found. Alternatively, a hyperbolic variation of density with altitude is used to approximate the Standard Atmosphere and the identical stability criterion is obtained. The effect of non-linear pitching moment and lift variations with angle of attack on the dynamic response to a sudden change in angle of attack is considered. An approximate solution to the non-linear equation of motion is developed. Several numerical examples are considered, and the results of the approximate solution are compared with the very accurate results of numerical integration as well as the classical linearized solution. The effect of a non-linear moment curve on the determination of stability derivatives from flight test data is discussed in the light of these examples.