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Aerospace
Propeller efficiency from test coefficients
Propulsive efficiency from the advance ratio J = V/(nD), thrust coefficient CT = T/(ρn²D⁴) and power coefficient CP = P/(ρn³D⁵), with n in revolutions per second.
- Ref
- AER-57
- Rev
- v1
- Field
- Aerospace
- Result
- ηp
Propeller tests report non-dimensional coefficients: advance ratio J = V/(nD), thrust coefficient CT = T/(ρn²D⁴) and power coefficient CP = P/(ρn³D⁵), with n in revolutions per second. The efficiency is useful power over shaft power: ηp = TV/P = J CT/CP. If the data give a torque coefficient CQ, convert with CP = 2πCQ before use. The shaft power must be positive.
Propulsive efficiency from the advance ratio J = V/(nD), thrust coefficient CT = T/(ρn²D⁴) and power coefficient CP = P/(ρn³D⁵), with n in revolutions per second. If a torque coefficient CQ is used, convert with CP = 2πCQ first. The shaft power must be positive.
Calculator
- Thrust power coefficient, J·CT0.08
- Torque coefficient, CP/(2π)0.01592
- Power lost, 1 − ηp0.2
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The propeller converts 80 % of the shaft power to thrust power, and loses 20 % to the wake, swirl and blade drag.
- Efficiency is usually highest at an advance ratio near the design value and drops sharply at high J as the blades unload.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| CP Power coefficient | 0.02 to 0.4 | 0.2 | 4 | 3.8 | +10% | −9.09 % |
| CT Thrust coefficient | 0.01 to 0.3 | 0.08 | 2.4 | 2.32 | +10% | +10 % |
| J Advance ratio | 0.1 to 2 | 0.1 | 2 | 1.9 | +10% | +10 % |
Sweep of Advance ratio
| Advance ratio | Propeller efficiency |
|---|---|
| 0.1 | 0.1 |
| 0.3375 | 0.3375 |
| 0.575 | 0.575 |
| 0.8125 | 0.8125 |
| 1.05 | 1.05 |
| 1.288 | 1.287 |
| 1.525 | 1.525 |
| 1.762 | 1.763 |
| 2 | 2 |
Sweep one variable
Variables and how each one contributes
Propeller efficiency
What the equation gives you. Everything else feeds it.
Advance ratio
The advance ratio V/(nD). Raises the efficiency in direct proportion at fixed coefficients. Raising it by 10 % (to 0.88) moves the result by +10 %, from 0.8 to 0.88.
Thrust coefficient
The thrust coefficient. Raises the efficiency in direct proportion. Raising it by 10 % (to 0.11) moves the result by +10 %, from 0.8 to 0.88.
Power coefficient
The power coefficient, positive. Lowers the efficiency in inverse proportion. Raising it by 10 % (to 0.11) moves the result by −9.09 %, from 0.8 to 0.7273.
Worked example with the values above
- Useful power coefficient: J CT = 0.8 × 0.1 = 0.08.
- Shaft power coefficient: CP = 0.1.
- ηp = 0.08 / 0.1 = 0.8.
Assumptions and limits
- An ideal actuator disk with uniform loading and steady incompressible flow, with no swirl.
- Rotor in hover or propeller in axial flight, with consistent revolutions-per-second definitions.
Common mistakes
- Using revolutions per minute where the formula needs revolutions per second.
- Using the disk area of one rotor for a multi-rotor system.
- Treating the ideal power as the shaft power, which ignores the losses.
Statistics and uncertainty
Momentum theory sets a lower bound on power: real propellers need 10 % to 30 % more than the ideal figure for blade profile drag, swirl and tip losses. Figure of merit of good rotors is 0.7 to 0.8, and propeller efficiency peaks around 0.85 to 0.88.
Where it is used
- Estimating the power needed for propellers, helicopters and drones.
- Reducing test data to coefficients and efficiency.
Maths you need
- Momentum theory: thrust equals mass flow times velocity change
- Advance ratio: J = V/(nD)
- Disk loading: thrust per unit disk area