Question

A solid motor has an average thrust of 67,000 N, a specific impulse of 285 sec, and a propellant mass fraction of 0.92. Calculate the total mass of the vehicle for a 42 sec burn time.

Answer 1

The equation for the specific impulse of a propeller motor is:

where, I_sp is the specific impulse, F is the average thrust m dot is the mass flow rate of the propellent, and g is the acceleration due to gravity.

rearranging the above equation to obtain mas s flow rate:

Now, the burn time (t_b) is 42 seconds. In this time all of the propellent is burnt.

so, multiplying the mass flow rate by the burn time, we get the mass of the propellent (m_p):

Now, the propellent mass fraction is 0.92. So, if the total mass of the vehicle is M, m_p = 0.92 X M

therefore, the total mass of the vehicle is:

puttiing F = 67000 N, I_sp = 285 sec, t_b = 42 sec and g = 9.8 m/s², we get:

M = 1095.13 kg

thus, the total mass of the vehicle is 1095.13 kg.

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