# Conditions For 5000n Thrust

1. What is the ratio of the burning area to the nozzle area for a solid propellant motor with these characteristics?

Propellant specific gravity 1.71

Chamber pressure 14 MPa

Burning rate 38 mm/sec

Temperature sensitivity ap 0.007 (K)"1

Specific heat ratio 1.27

Chamber gas temperature 2220 K

Molecular mass 23 kg/kg-mol

Burning rate exponent n 0.3

2. Plot the burning rate against chamber pressure for the motor in Problem 1 using Eq. 11-3 between chamber pressures of 11 and 20 MPa.

3. What would the area ratio Ab/At in Problem 1 be if the pressure were increased by 10%? (Use curve from Problem 2.)

4. Design a simple rocket motor for the conditions given in Problems 1 and 2 for a thrust of 5000 N and a duration of 15 sec. Determine principal dimensions and approximate weight. FIGURE 11-28. Simplified schematic diagram of two propulsion systems for one type of maneuverable upper stage of an interceptor missile. The side or divert forces are relatively large and go essentially through the center of gravity (CG) of the upper stage vehicle. To minimize the CG travel two grains are above and two grains are below the CG. Each nozzle has its own hot gas valve, which is normally open and can be pulsed. The attitude control system (ACS) is fed from the reaction gas of two grains and has six small nozzles.

FIGURE 11-28. Simplified schematic diagram of two propulsion systems for one type of maneuverable upper stage of an interceptor missile. The side or divert forces are relatively large and go essentially through the center of gravity (CG) of the upper stage vehicle. To minimize the CG travel two grains are above and two grains are below the CG. Each nozzle has its own hot gas valve, which is normally open and can be pulsed. The attitude control system (ACS) is fed from the reaction gas of two grains and has six small nozzles.

5. For the Orbus-6 rocket motor described in Table 11-3 determine the total impulse-to-weight ratio, the thrust-to-weight ratio, and the acceleration at start and burnout if the vehicle inert mass and the payload come to about 6000 lbm. Use burn time from Table 11-3 and assume g 32.2 ft/sec2.

6. For a cylindrical two-dimensional grain with two slots the burning progresses in finite time intervals approximately as shown by the successive burn surface contours in the drawing on the next page. Draw a similar set of progressive burning surfaces for any one configuration shown in Figure 11-16 and one shown in Figure 11-17, and draw an approximate thrust-time curve from these plots, indicating the locations where slivers will remain. Assume the propellant has a low value of n and thus the motor experiences little change in burning rate with chamber pressure.

7. Explain the significance of the web fraction, the volumetric loading ratio, and the L/D ratio in terms of vehicle performance and design influence.

8. The partial differential equations 11-4 and 11-5 express the influence of temperature on the burning of a solid propellant. Explain how a set of tests should be set up and exactly what should be measured in order to determine these coefficients over a range of operating conditions.

9. What would be the likely change in r, Is,pltF, tb, and I, if the three rocket motors described in Table 11-3 were fired with the grain 100°F cooler than the data shown in the table? Assume typical average temperature effects.

10. A newly designed case-bonded rocket motor with a simple end-burning grain failed and exploded on its first test. The motor worked well for about 20% of its burn time, when the record showed a rapid rise in chamber pressure. It was well conditioned at room temperature before firing and the inspection records did not show any flaws or voids in the grain. Make a list of possible causes for this failure and suggestions on what to do in each case to avoid a repetition of the failure.

11. Derive Eq. 11-7. (Hint First derive nK by differentiating Eq. 11-3 with respect to temperature.) Note: This relation does not fit all the experimental data fully because there are other variables besides n that have a mild influence. For a more complex approach, see Ref. 11-32.

12. What will be the percent change in nominal values of A,, r, Is, T0, th, Ab/A, and the nozzle throat heat transfer rate, if the Orbus-6 rocket motor listed in Table 11-3 is to be downgraded in thrust for a particular flight by 15% by substituting a new nozzle with a larger nozzle throat area but the same nozzle exit area? The propel-lants, grain, insulation, and igniter will be the same. Slivers

Initial port area contour

### Slivers

13. What would be the new values of /„ Is, pu F, tb, and r for the first stage of the Minuteman rocket motor described in Table 11-3, if the motor were fired at sea level with the grain temperature 20°F hotter than the data shown. Use only data from this table.

Answers: I, = 10,240,000 lbf-sec, Is = 224 sec, p, = 796 psia, F = 1.99 x 105 lbf, tb = 51.5 sec, r = 0.338 in./sec.

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