Richard Nakka's Experimental Rocketry Web Site

Example of Chamber Pressure Calculation due to Igniter Charge Combustion

Consider the rocket motor and igniter shown in the figure above (dimensions are inches).

The motor chamber volume is Vc = p/4 (3) ² (12) = 85 in³

And the grain volume is Vg = p/4 (2.75 ² - 1 ² ) 11 = 57 in³

Therefore the free volume is V = 85 - 57 = 28 in³

The igniter volume is Vi = p/4 (0.5) ² (2) = 0.39 in³

The charge material is Black Powder (non-commercial grade) with an impetus of 75000 ft-lb_f / lb_m

and has a mass density of 0.057 lb_m / in³

Charge mass is C = 0.057 (0.39) = 0.022 lb_m

Loading density is D = 0.022 / 28 = 1 / 1273 lb_m / in³

Let G = 1 since we are interested only in the maximum pressure that results from the charge combustion

The ambient pressure is Pa = 14.7 psia

The effective force is l = 75000 (12) = 900 000 in-lb_f / lb_m

This gives the resulting chamber pressure of