Characteristic velocity

Short description: Measure of rocket performance

This page is about rocketry. For the algebraic structure in mathematics, see C* algebra.

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. It is independent of the nozzle, making it a useful metric for evaluating propellant combustion alone. c* should not be confused with c, which is the effective exhaust velocity related to the specific impulse by: Is=cg0. 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, or the combustion efficiency. This is known as c*-efficiency, or nv, and is calculated by dividing cActual* with cTheoretical*. Standard values for nv range from 0.85 to 1.03.

## Formula

cActual*=pcAtm˙

* c* is the characteristic velocity (m/s, ft/s)
* pc is the chamber pressure (Pa, psi)
* At is the area of the throat (m2, in2)
* m˙ is the mass flow rate of the engine (kg/s, slug/s)

cTheoretical*=Ispg0CF=cCF=RTcγ(γ+12)γ+1γ−1

Alternative Imperial Form:

cTheoretical*=Ispg0CF=cCF=g0γRTcγ2γ+1γ+1γ−1

* Isp is the specific impulse (s)
* g0 is the gravitational acceleration at sea-level (m/s2)
* CF is the thrust coefficient
* c is the effective exhaust velocity (m/s)
* γ is the specific heat ratio for the exhaust gases
* R is the gas constant per unit weight (J/kg-K)
* Tc is the chamber temperature (K)

## See also

* Characteristic Length (L*)

## References

* Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz
* Rocket Propulsion Elements, 9th Edition by George P. Sutton, Oscar Biblarz
* Modern Engineering for Design of Liquid-Propellant Rocket Engines, Volume 147 by Dieter K. Huzel, David H. Huang

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