Solutions of the equations of motion of vertically ascending rockets (both in power flight and in free flight) are given in closed form. Atmospheric density is assumed to vary exponentially with altitude, and the variation of the drag coefficient of the rocket with Mach number is assumed to follow a definite pattern. (The validity of the latter assumption is established by its close agreement with measured results.) These solutions, given in terms of special transcendental functions, can be used for the rapid estimation of sounding-rocket performance, eliminating the often-used laborious process of stepwise integration. The general rocket-performance parameters prescribed in the analysis also can be used to advantage in comparing and selecting multistage sounding rockets.

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