Characteristic velocity or

c^*

, or C-star is a measure of the

combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combusti ...

performance of a

rocket engine A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordanc ...

independent of

nozzle A nozzle is a device designed to control the direction or characteristics of a fluid flow (specially to increase velocity) as it exits (or enters) an enclosed chamber or pipe. A nozzle is often a pipe or tube of varying cross sectional area, a ...

performance, and is used to compare different

propellants A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or other motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicles, the e ...

and

propulsion systems Propulsion is the generation of force by any combination of pushing or pulling to modify the translational motion of an object, which is typically a rigid body (or an articulated rigid body) but may also concern a fluid. The term is derived from ...

. c* should not be confused with ''c'', which is the effective exhaust velocity related to the specific impulse by:

I_s = \frac

. 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

c^*

is the characteristic velocity (e.g. m/s, ft/s) *

p_1

is the chamber

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

(e.g. Pa, psi) *

A_t

is the

area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an obje ...

of the throat (e.g. m², in²) *

\dot

is the

mass flow rate In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is \dot (''ṁ ...

of the engine (e.g. kg/s, slug/s)

c^* = \frac = \frac = \frac

I_s

is the specific impulse (e.g. sec) *

g_0

is the gravitational acceleration at sea-level (e.g. m/sec^2) *

C_F

is the thrust coefficient *

c

is the effective exhaust velocity (e.g. m/sec) *

k

is the specific heat ratio for the exhaust gases *

R

is the gas constant per unit weight (e.g. J/kg-K) *

T_1

is the chamber temperature (e.g. K)

References

* ''Rocket Propulsion Elements,'' 7th Edition by George P. Sutton, Oscar Biblarz * ''Rocket Propulsion Elements,'' 9th Edition by George P. Sutton, Oscar Biblarz Rocketry Rocket propulsion Aerospace engineering {{rocket-stub