Rocket Motor Sizing Example 6

A HiPer class EX rocket is being designed to achieve an apogee of 3000 metres. The applicable design parameters are:

Body diameter 89mm

Dead mass of rocket 5 kg.

Average drag coefficient 0.4

Average motor thrust 600 N.

Propellant Isp = 205 sec.

Figure 1 Example 6 rocket

Problem Statement:

1. Determine total impulse of motor to achieve target apogee using Isp method

2. Determine propellant mass required, propellant mass fraction and rocket mass ratio

3. Verify apogee prediction using RASAero sim tool

Solution:

(1) Using the Isp method, the total impulse (I ) needed to achieve an apogee goal (Z_ap) may be determined from the following equation:

Z_ap = 3000 m.

g = 9.808 m/sec²

F = 600 N.

a = 1.050

b = 0.00172

m_d = 5 kg.

The average mass is calculated using eqn.9:

Equation 9 is used together with equation 10 to solve for impulse using the Goal Seek function of MS Excel (Impulse_(Isp)_Ex6.xlsx). A screenshot of the worksheet is shown below.

The Goal Seek function iteratively solves the equation by incrementally adjusting the value for I until I ² - term = 0.

(2) The propellant specific impulse is 205 seconds. The mass of propellant, therefore, required to deliver a total impulse of 2244 N-sec. is:
m_p = 2244/205/9.808 = 1.11 kg.
The liftoff mass and resulting propellant mass fraction is:
m_o = 1.11 + 5.0 = 6.11 kg
The mass ratio of the rocket is
M_R = 6.11/5.0 = 1.22

(3) RASAero app was used to simulate the flight of the rocket. A rocket motor file was created to produce a total impulse of 2244 N-sec. (600 N. thrust over duration of 3.74 seconds). The simulation tool was run and the following result was obtained:

Max. altitude = 3063 m. (10,049 ft.) which is within 2% of the apogee goal.

References:

1. Rocket Motor Sizing webpage

2. Impulse_(Isp)_Ex6.xlsx

3. Ex6.CDX1

4. rasp_ex.eng