FIGURE 11-8. Effect of propellant temperature on burning time and chamber pressure for a particular motor. The integrated areas under the curves are proportional to the total impulse, which is the same for the three curves.
these coefficients are the partial derivative of the natural logarithm of the burning rate r or the chamber pressure p, respectively, with respect to propel-lant temperature T. Values for ap typically range between 0.001 and 0.009 per degree Kelvin or 0.002 to 0.04 per degree F and for nK it is 0.067 to 0.278%/°C or 0.12 to 0.50%/°F. With nK established, the effect of small grain temperature changes on motor chamber pressure is expressed from Eq. 11-5:
where px is the reference chamber pressure and Ap is the pressure rise (psia) for a value of AT or T - T0.
The values of nK and ap depend primarily on the nature of the propellant burning rate, the composition, and the combustion mechanism of the propellant. It is possible to derive a relationship between the two temperature sensitivities, namely
This formula is usually valid when the three variables are constant over the chamber pressure and temperature range. When substituting the value of r from Eq. 11-3 into Eq. 11-5, the temperature sensitivity ap can be also expressed as
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