Calibrate hover power from a test flight

Back-solve a multirotor's real figure of merit × efficiency from a measured hover: the energy it drew and for how long, so the hover-power and flight-time tools match your aircraft.

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Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

0.48

Your flight shows a figure of merit × efficiency of 0.48.

Figure of merit
Measured hover power
Ideal induced power

Provenance

Computed by: drone.power.calibrate-hover 1.0.0, core 0.1.0
Model: Measured power = energy used / hover time; lift power = measured − avionics; FM·η = (m·g0)^1.5 / √(2ρA) / lift power; FM = FM·η / η
Accuracy: As good as the measurement: use a steady hover in calm air, and the energy the log or charger reports for that hover alone, not the whole flight.
Notes: 1 shown with the answer
Cites: Leishman, J. G., Cambridge University Press, Principles of Helicopter Aerodynamics

Something look off?

Your values

Showing an example. Change anything.

Takeoff mass Everything on board, like 1.4 kg · plain numbers mean kg Rotors Like 4 Rotor diameter Like 9.4 in · plain numbers mean in Energy used Drawn during the steady hover, from the flight log or recharge, like 40 Wh · plain numbers mean Wh Hover time How long the steady hover lasted, like 15 min · plain numbers mean min

More options 5

Avionics and payload poweroptional Drawn apart from the motors, like 10 W; default 0 · plain numbers mean W Motor and speed-controller efficiencyoptional To split out the figure of merit, 0.5 to 1, default 0.85 Altitudeoptional Pressure altitude of the site, like 5000 ft; default sea level · plain numbers mean ft Air temperatureoptional Like 30 °C; default ISA for the altitude · plain numbers mean °C Density altitudeoptional Instead of altitude and temperature, like 8000 ft · plain numbers mean ft

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How we got thisFormula, worked example, sources, and proof

Model: Measured power = energy used / hover time; lift power = measured − avionics; FM·η = (m·g0)^1.5 / √(2ρA) / lift power; FM = FM·η / η

Show your work

Measured power
energy used / hover time
40 Wh / 15 min = 160 W
Figure of merit × efficiency
ideal power / (measured − avionics)
76.8 W / 160 W = 0.48

The same steps an agent gets from the MCP server with explain: true.

Accuracy: As good as the measurement: use a steady hover in calm air, and the energy the log or charger reports for that hover alone, not the whole flight.

Worked example: The 1.4 kg quad drew 40 Wh in a 15-minute hover. Source: Momentum theory (Leishman 2006, chapter 2) solved for the figure of merit. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Energy used: 40 Wh
Hover time: 15 min
Takeoff mass: 1.4 kg
Rotor diameter: 9.4 in
Rotors: 4

You get

Figure of merit × efficiency: 0.48
Figure of merit: 0.565
Measured hover power: 160 W
Ideal induced power: 76.8 W

Review: Not yet independently reviewed by a Part 107 remote pilot.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Principles of Helicopter Aerodynamics, Leishman, J. G., Cambridge University Press, 2nd edition. Chapter 2 (momentum theory: ideal hover power T^1.5/√(2ρA), figure of merit).

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.

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Sources

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