Rocket Motor Sizing – Example 3

A LoPer class EX rocket is being designed to achieve an apogee of 500 metres. The applicable design parameters are:

· Body diameter 70mm

· Dead mass of rocket 3.27 kg

· Mass ratio target 1.07

· Average drag coefficient 0.55

· Average motor thrust 400 N.

· Propellant KNSB

Figure 1 – Rocket Example 3

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 = 500 m.

g = 9.808 m/sec²

F = 400 N.

a = 1.050

b = 0.00172

m_o = 1.07 ´ 3.27 = 3.5 kg.

The average mass is calculated from eqn.7:

giving:

This represents a 20% I-Class motor.

(2) The propellant (KNSB) has a specific impulse of 125 seconds. The mass of propellant, therefore, required to deliver a total impulse of 384 N-sec. is:
m_p = 384/(125´ 9.808) = 0.313 kg.

The liftoff weight will be slightly greater than projected:

m_o = 3.27 + 0.313 = 3.58 kg

The required rocket mass ratio is somewhat greater than design target:

However, the average mass of the loaded rocket has increased by about 1% (was 3.385 kg):

Will this have much effect upon the impulse prediction? Let’s find out:

The predicted impulse is 1% higher than the original prediction. As such, it is generally not necessary to repeat the impulse calculation if the mass increases as small amount.

(3) RASAero app was used to simulate the flight of the rocket. A rocket motor file was created to produce a total impulse of 388 N-sec. (400 N. thrust over duration of 0.96 seconds). The simulation tool was run and the following result was obtained:

Max. altitude = 497 metres (1629 ft.) which is within 1% of the apogee goal.

References:

1. Rocket Motor Sizing webpage

2. Ex3.CDX1

3. rasp_ex.eng