Analytical solution of the inverse problem of the interior ballistics of a controlled solid rocket motor

The inverse problem concerning the interior ballistics of a solid rocket motor is considered for the case where the pressure in the motor is a given time function. Given the pressure, the problem reduces to calculation of the temperature and cross-sectional area of the nozzle. An analytical solution of the inverse problem is obtained. It is shown that as the pressure changes, the combustion temperature also changes. It is found that the increase in the combustion temperature with an intense increase in pressure is greater than that under constant-volume conditions.