Characteristic velocity

Characteristic velocity or $$c^*$$, or C-star is a measure of the combustion performance of a rocket engine independent of nozzle performance, and is used to compare different propellants and propulsion systems. c* should not be confused with c, which is the effective exhaust velocity related to the specific impulse by: $$I_s = \frac{c}{g_0}$$. Specific impulse and effective exhaust velocity are dependent on the nozzle design unlike the characteristic velocity, explaining why C-star is an important value when comparing different propulsion system efficiencies. c* can be useful when comparing actual combustion performance to theoretical performance in order to determine how completely chemical energy release occurred. This is known as c*-efficiency.

Formula
$$c^* = \frac{p_c A_t }{\dot{m}}$$
 * $$c^*$$ is the characteristic velocity (m/s, ft/s)
 * $$p_c$$ is the chamber pressure (Pa, psi)
 * $$A_t$$ is the area of the throat (m2, in2)
 * $$\dot{m}$$ is the mass flow rate of the engine (kg/s, slug/s)

$$c^* = \frac{I_{sp} g_0}{C_F} = \frac{c}{C_F} =\sqrt{\frac{RT_c}{\gamma} \Bigl(\frac{\gamma+1}{2}\Bigr)^{\frac{\gamma+1}{\gamma-1}}}$$


 * $$I_s$$ is the specific impulse (s)
 * $$g_0$$ is the gravitational acceleration at sea-level (m/s2)
 * $$C_F$$ is the thrust coefficient
 * $$c$$ is the effective exhaust velocity (m/s)
 * $$\gamma$$ is the specific heat ratio for the exhaust gases
 * $$R$$ is the gas constant per unit weight (J/kg-K)
 * $$T_c$$ is the chamber temperature (K)