## Problems

1. Ideally the solid oxidizer particles in a propellant can be considered spheres of uniform size. Three sizes of particles are available: coarse at 500 pm, medium at 50 pm, and fine at 5 pm, all at a specific gravity of 1.95, and a viscoelastic fuel binder at a specific gravity of 1.01. Assume that these materials can be mixed and vibrated so that the solid particles will touch each other, there are no voids in the binder, and the particles occupy a minimum of space similar to the sketch of the cross section shown here. It is desired to put 94 wt % of oxidizer into the propellant mix, for this will give maximum performance, (a) Determine the maximum weight percentage of oxidizer if only coarse crystals are used or if only medium-sized crystals are used, (b) Determine the maximum weight of oxidizer if both coarse and fine crystals are used, with the fine crystals filling the voids between the coarse particles. What is the optimum relative proportion of coarse and fine particles to give a maximum of oxidizer? (c) Same as part (b), but use coarse and medium crystals only. Is this better and, if so, why? (d) Using all three sizes, what is the ideal weight mixture ratio and what is the maximum oxidizer content possible and the theoretical maximum specific gravity of the propellant? (Hint: The centers of four adjacent coarse crystals form a tetrahedron whose side length is equal to the diameter.)

2. Suggest one or two specific applications (intercontinental missile, anti-aircraft, space launch vehicle upper stage, etc.) for each of the propellant categories listed in Table 12-2 and explain why it was selected when compared to other propellants.

4. Determine the longitudinal growth of a 24-in.-long free-standing grain with a linear thermal coefficient of expansion of 7.5 x 10~5/°F for temperature limits of —40 to

5. The following data are given for an internally burning solid propellant grain with inhibited end faces and a small initial port area:

Determine the initial forces on the propellant supports produced by pressure differential and vehicle acceleration. Answers: 19,600 lbf, 5090 lbf.

6. A solid propellant unit with an end-burning grain has a thrust of 4700 N and a duration of 14 sec. Four different burning rate propellants are available, all with approximately the same performance and the same specific gravity, but different AP mix and sizes and different burning rate enhancements. They are 5.0, 7.0, 10, and 13 mm/sec. The preferred L/D is 2.60, but values of 2.2 to 3.5 are acceptable. The impulse-to-initial-weight ratio is 96 at an L/D of 2.5. Assume optimum nozzle expansion. Chamber pressure is 6.894 MPa or 1000 psia and the operating temperature is 20°C or 68°F. Determine grain geometry, propellant mass, hardware mass, and initial mass.

7. For the rocket in Problem 6 determine the approximate chamber pressure, thrust, and duration at 245 and 328 K. Assume the temperature sensitivity (at a constant value of Ab/At) of 0.01%/K does not change with temperature.

8. A fuel-rich solid propellant gas generator propellant is required to drive a turbine of a liquid propellant turbopump. Determine its mass flow rate. The following data are

Length Port area Propellant weight

Initial pressure at front end of chamber Initial pressure at nozzle end of chamber Propellant density Vehicle acceleration

40 in. 27 in.2 240 lb 1608 psi 1412 psi 