$7\mathrm{.}7$ The solid rocket shown in Figure $7\mathrm{.}25$ utilizes a cylindrical$-$shaped grain which is inhibited on the forward end. The propellant characteristics are:

$=1\mathrm{.}2,c^{**}=5000f\frac{t}{s},{}_p=0\mathrm{.}063l\frac{b}{i}{n}^3$

$r_b=0\mathrm{.}03p_c^{0\mathrm{.}35}(r_{b}in$ inches $\frac{?}{s},p_{c}in)$

We want to develop a vacuum thrust of $3000$ lbf at a chamber pressure of $500$ psi just after ignition of the motor.

$($a$)$ Under these constraints, determine the dimensions $L$ and $R_t$ as shown in Figure $7\mathrm{.}25.$

$268$

Solid Rocket Motors

Figure $7\mathrm{.}27$ Diagram for Problem $7\mathrm{.}9.$

$($b$)$ Determine the chamber pressure and thrust of the motor just prior to burnout.

$($c$)$ Estimate the overall burn time of the rocket using data developed in parts $($a$)$ and $($b$).$