APPROXIMATE SOLUTIONS FOR REENTRY TRAJECTORIES WITH AERODYNAMIC FORCES
POLYTECHNIC INST OF BROOKLYN NY
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When the motion of the reentry vehicle is expressed in two equations for the components in the instantaneous trajectory plane, and one for the component normal to the plane, the former equations are uncoupled from the latter. Thus, the problem of a nonplanar trajectory is reduced to an equivalent planar trajectory. Approximate analytic solutions for planar trajectories with constant lift and drag coefficients are obtained by improving and extending existing analytic solutions. The present solutions are not subjected to the restrictions which are valid for drag-only vehicles at large entry angle, nor for lifting vehicle entering the atmosphere at near circular orbit velocity and shallow angles. They are derived in a closed form of simple functions expressing the relations between the velocity, the angle of inclination and the density, or elevation. Using these relations, the acceleration experienced by the pilot can be calculated and the peak value determined. The numerical results calculated for these cases, where the above restrictions are violated, show good agreement with the machine results by direct integration of the equations of motion.
- Spacecraft Trajectories and Reentry