Formula & Calculator
Characteristic Velocity
Measure of combustion efficiency in a rocket engine, independent of nozzle expansion characteristics.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| c* | Characteristic velocity | m/s |
| p_c | Chamber pressure | Pa |
| A_t | Throat area | m2 |
| mdot | Propellant mass flow rate | kg/s |
What it means
Characteristic velocity (c*) is a parameter that indicates how effectively the combustion process converts chemical energy into kinetic energy, independent of nozzle expansion. It is defined as the chamber pressure times the throat area divided by the mass flow rate. A higher c* means more efficient combustion or a higher heat release. It is used to evaluate rocket engine performance and to compare propellant combinations. c* is also used in the thrust coefficient equation to compute thrust: F = c* C_F ṁ. Understanding c* is important for propulsion engineers to optimise engine design and to select propellants.
Worked example
Characteristic Velocity – Two Examples
Real‑World| Parameter | Value |
|---|---|
| p_c | 7×10⁶ Pa |
| A_t | 0.05 m² |
| ṁ | 220 kg/s |
| Parameter | Value |
|---|---|
| p_c | 1×10⁷ |
| A_t | 0.06 |
| ṁ | 300 |
Common mistakes
- Characteristic velocity c*: c* = (p_c·A_t) / ṁ – in m/s.
- ṁ: Mass flow rate (kg/s).
- Measures combustion efficiency – independent of nozzle.
- Units: Pa·m² / (kg/s) = N·m / (kg/s) = (kg·m/s²)·m / (kg/s) = m²/s²? Actually, compute: p_c (N/m²) * A_t (m²) = N, divide by ṁ (kg/s) gives (N·s)/kg = (kg·m/s²·s)/kg = m/s. So c* in m/s.
Applications
Characteristic velocity, c* = p_c·A_t / ṁ, is a measure of rocket engine efficiency based on the combustion chamber conditions and mass flow. It depends only on the propellant and combustion efficiency, not on the nozzle. c* is used to assess the quality of combustion and to compare propellant combinations. Engineers use it in engine design, to evaluate injector and combustion chamber performance, and to compute the required throat area for a given mass flow. By understanding c*, aerospace engineers can optimise the combustion process and ensure that the engine delivers the expected performance.
- Propellant performance evaluation and ranking
- Combustion chamber design and injector optimisation
- Throat area sizing for a given mass flow and chamber pressure
- Engine performance modelling and test data reduction
- Trade‑off studies between propellant types and engine cycles