Propeller Efficiency

Inputs

Choose what to solve for, then fill in the other three. Scientific notation such as 2.5e5 is accepted. Units convert automatically.

Results

Propeller energy flow

Shaft power P_shaft enters from the engine; the useful power T·V leaves as thrust times airspeed; the difference is lost to slipstream kinetic energy, swirl and profile drag. The engine supplies P_shaft; the airframe receives T·V.

Efficiency vs airspeed

At fixed thrust and shaft power, η_p rises linearly with airspeed (the useful power T·V grows while P_shaft stays constant). The dashed curve is the ideal actuator-disk efficiency at the same disk loading. The shaded region above 100 % is physically impossible — if your point lies there, one of the inputs needs revisiting.

What is being calculated

Common examples

Computed by the same engine. Illustrative values, not manufacturer data.

Typical propeller efficiencies

Propeller efficiency is defined only in forward flight — at V = 0 the useful power T·V vanishes, so η_p is identically zero even though the rotor may still be producing thrust.

Key relations and unit conversions

Formula

• η_p: propeller (propulsive) efficiency, dimensionless or %
• T: thrust (N, lbf, kgf)
• V: true airspeed (m/s, kt, km/h, mph)
• P_shaft: shaft power delivered to the propeller (W, kW, hp, shp)
• T · V is the useful power delivered to the airframe

Example — a light aircraft at cruise. T = 1500 N, V = 70 m/s (≈136 kt), P_shaft = 130 kW. Then T·V = 105 000 W and η_p = 105 000 / 130 000 = 0.808, or 80.8 %. That is a typical figure for a constant-speed propeller on a light twin at normal cruise.

The propeller is an energy converter. It accepts shaft power from the engine and delivers thrust to the airframe. The useful power is the thrust times the forward speed — this is the mechanical work done on the aircraft per unit time. The difference P_shaft − T·V is lost: it goes into the kinetic energy of the slipstream, into swirl that the propeller imparts to the air, and into the drag of the blades themselves. Efficiency is the ratio of what the airframe gets to what the engine supplies.

Because useful power is T·V, efficiency must go to zero at V = 0. A propeller generating static thrust is doing no useful work in this sense — the airframe is not moving, so T·V = 0. This is why the efficiency definition only applies in forward flight; for a hovering helicopter it is meaningless, and rotor performance is instead characterised by the figure of merit.

Real propellers peak around 85 % efficiency and are usually designed to operate near their peak over the cruise portion of the flight. The shape of the efficiency curve is set by two competing effects. At low airspeed (low advance ratio J = V/(nD)), the blades are at high angle of attack and the profile drag is high — efficiency falls. At high J, the blades are nearly feathered and lose lift — efficiency also falls. In between there is a broad optimum. The advance ratio also explains why a fixed-pitch propeller cannot be optimal over a wide speed range: the blade angle is fixed, so J drifts away from its design value as speed changes. Constant-speed propellers vary the blade pitch to hold J near the optimum across the flight envelope, which is why they cost more and deliver more.

The theoretical upper bound comes from actuator-disk momentum theory. Even an ideal, frictionless propeller must accelerate the air to produce thrust, and the kinetic energy that goes into that slipstream is a loss. The ideal efficiency is η_i = 2 / (1 + √(1 + T/(qA))), which depends only on the thrust, the disk area and the free-stream dynamic pressure. Bigger disks and higher speeds push η_i closer to 1. The figure of merit is the ratio η_p/η_i and typically lands around 0.7–0.8 for real propellers — that is, real propellers recover about three-quarters of the ideal.

Advanced mode adds the disk loading T/A, the ideal actuator-disk efficiency, the figure of merit, the advance ratio J, the thrust and power coefficients C_T and C_P, and the useful and loss powers.

References

• Wikipedia, Propulsive efficiency: definition of η_p = T·V/P
• Wikipedia, Propeller (aeronautics): thrust, advance ratio, efficiency curve
• Wikipedia, Momentum theory: the actuator-disk model and ideal efficiency
• Wikipedia, Advance ratio: J = V/(nD) and its role in propeller performance
• Wikipedia, Figure of merit (rotorcraft): comparing real and ideal performance
• NIST SP 811, Guide for the Use of the SI: unit conversion factors

How to Use This Tool

1. Choose what to solve for: η_p, T, V, or P_shaft.
2. Pick a preset, or type the three known values and choose their units.
3. In Advanced, add density and diameter to see the ideal efficiency and figure of merit; add rotational speed for the advance ratio and thrust/power coefficients.
4. Click Calculate.
5. Read the highlighted answer, then check the energy-flow diagram and the efficiency chart.

What This Tool Offers

• Solves η_p = T·V/P_shaft for any of the four variables
• Automatic unit conversion for thrust, speed and power
• Useful power and loss power breakdown
• Ideal actuator-disk efficiency, figure of merit and disk loading (Advanced)
• Advance ratio J and thrust/power coefficients (Advanced)
• Dynamic energy-flow diagram and an efficiency-vs-airspeed chart
• Reference tables of typical propeller efficiencies and unit relations
• Ready-made presets and a mobile-friendly layout