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.
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