The numerical solution and analysis of airplane spin equations modeled in a fixed coordinate system

Abstract

Three forms of the airplane spin equations of motion, derived by Buehler in Reference [l], form the basis for the development of a computer program designed to seek dynamically stable equilibrium solutions of a spinning aircraft. The program incorporates two solution techniques: one based upon Eule r integration, the other, a version of minimization by gradient search. Secondary programs are developed to (1) generate power-off glide parameters for use in the validation of the equations of motion, and (2) evaluate equation residuals obtained from a grid of initial conditions over the potential solution space. F-lll and F-4 aerodynamic force and moment models were utilized to evaluate the solution methods and equations of motion. The numerical results indicate that the F-lll and F-4 data are not representative of the actual aircraft and, therefore, it is highly unlikely that dynamically stable equilibrium solutions can be achieved from these models. The utility of the two solution methods is evaluated and the numerical results are analyzed in order to gain insight into the optimal application of the three forms of the equations of motion. The paper concludes with a discussion concerning the qualitative validation of the equations of motion.