Rocket Motor Sizing – Example 4

A MiPer class EX rocket is being designed to achieve an apogee of 6500 feet. The applicable design parameters are:

· Body diameter 3 inches

· Dead mass of rocket 5.9 lbs

· Mass ratio target 1.18

· Average drag coefficient 0.425

· Average motor thrust 110 pound-force

· Propellant Isp = 200 sec.

Figure 1 – Example 4 rocket

Problem Statement:

1. Determine total impulse of motor to achieve target apogee

2. Determine propellant mass required

3. Verify apogee prediction using RASAero sim tool

Solution:

(1) The total impulse (I ) needed to achieve an apogee goal (Z_ap) is given by:

Z_ap = 6500 ft.

g = 32.18 ft/sec²

F = 110 lbf.

a = 1.050

b = 0.00172

m_d = 5.9/32.18 = 0.183 slugs

m_o = 1.18 ´ 5.9/32.18 = 0.216 slugs

The average mass is calculated from eqn.7:

giving:

An impulse of 211 lbf-sec, or 939 N-sec. represents a 47% J-Class motor.

(2) The propellant specific impulse is 200 seconds. The mass of propellant, therefore, required to deliver a total impulse of 211 lbf-sec. is:
m_p = 211/200 = 1.06 lbm.

(3) RASAero app was used to simulate the flight of the rocket. A rocket motor file was created to produce a total impulse of 211 lbf-sec. (110 lbf. thrust over duration of 1.92 seconds). The simulation tool was run and the following result was obtained:

Max. altitude = 6550 ft. which is within 1% of the apogee goal.

References:

1. Rocket Motor Sizing webpage

2. Ex4.CDX1

3. rasp_ex.eng