Pseudo-analytic approach to determine optimal conditions for maximizing altitude of sounding rocket

A pseudo-analytic approach is suggested to determine the optimal launching conditions for maximizing the altitude of a sounding rocket flying with a constant mass flow of propellant in a standard atmosphere. The one-dimensional rocket momentum equation including thrust, gravitational force, and aerodynamic drag is considered, for which it is impossible to obtain the analytic solutions since the governing equation is nonlinear. The piecewise pseudo-analytic solutions are obtained with a constant control parameter introduced to make the velocity integral in the governing equation be analytic. The rocket flight in the standard atmosphere is analyzed by dividing the entire range into small intervals where the drag parameter or the gravitational acceleration can be treated as a constant in each interval. The pseudo-analytic approach gives precise predictions of the rocket velocity and the rocket altitude that agree well with the numerical ones. A characteristic equation exists and provides accurate predictions of the optimal mass flow rate for maximizing the altitude at burn-out state or at apogee.