Characteristic velocity explained

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} = (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 ^{*} = (p _{c} A _{t})/(• 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)• m is the mass flow rate of the engine (kg/s, slug/s)c ^{*} = (I _{sp} g _{0})/(C _{F}) = (c)/(= \sqrt{ C _{F}) (RT _{c})/(l ( \gamma) (\gamma +1)/(2) r ) ^{(\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 coefficientc 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)

References

• Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz
• Rocket Propulsion Elements, 9th Edition by George P. Sutton, Oscar Biblarz