Rocket Motor Efficiency

If we look closer at the rocket equation

\Delta V = v_e \ln \left( \frac{M_i}{M_f} \right),

we see that \Delta V is proportional to v_e. This means that if the motor is throwing out gas molecules faster, the force per unit mass of propellant is higher. v_e is then a measure of how efficient the rocket motor is. The exhaust velocity parameter is very important when designing a rocket motor, and we can actually calculate it since we know that it is the same as dividing the total impulse by the propellant mass m_{p}. Since it is specific to propellant mass we often call it specific impulse, and are thus given as

I_{SP} = v_e = \frac{I_t}{m_p} = \frac{\int_0^{t_b} F \, dt}{m_p} = \frac{\bar{F} \, t_b}{m_p}.

Since I_{SP} is the same as the exhaust velocity, the unit is, in fact, m/s. We have here described I_{SP} as being the same as the exhaust velocity. In some cases the specific impulse is defined differently, as

I_{SP, *} = \frac{I_t}{m_p g_0} \neq v_e,

where g_{0}=9.81 m/s^2. This definition is often used in USA, and the unit is seconds.

Common values of the specific impulse on expensive rocket motors is 2500-4500 m/s. The most efficient motor to date (2016) is the RL10 motor, an upper stage on the American Delta IV rocket. It has a specific impulse in vacuum of 4 567 m/s.

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This article is a part of a pre-course program, used by NAROM in different courses, for example Fly a Rocket!