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Check the math yourself

Every equation behind RotorLab's hover, endurance, range and radio-link numbers is written out with its derivation and its reference. Your browser re-evaluates each one and checks it against what the engine returned for three worked examples, badge by badge.

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Signed in, the same page runs every check on your own build, with your own inputs.

The RotorLab Builder: all-up weight, hover thrust-to-weight, hover endurance and power loading for a quad, the figures these equations produce
 equations re-evaluated in your browser for the example shown
 the most a card may differ from the engine and still read matches engine
 worked examples: a multirotor, a VTOL transition and a fixed wing
 references cited, listed at the foot of the page

Switching the example re-runs every card on the page and re-checks each one against the engine.

The equations, topic by topic

Open a topic to read each equation, how it is derived, the worked line for this example and whether the engine agrees. The first is open; the rest show their card count and their result.

References

The sources the cards cite, and where a fit of RotorLab's own stands in for a published one.

  1. Leishman, J. G. Principles of Helicopter Aerodynamics, 2nd ed. Cambridge University Press, 2006. Actuator-disc / momentum theory for hover and forward flight.
  2. U.S. Standard Atmosphere, 1976. NOAA/NASA/USAF. Pressure and density lapse used for density altitude.
  3. Anderson, J. D. Fundamentals of Aerodynamics. McGraw-Hill. Lift, the drag polar, stall, and the power-required / rate-of-climb relations for the wing-borne model.
  4. McCormick, B. W. Aerodynamics, Aeronautics, and Flight Mechanics. Propeller thrust and power coefficient forms T = CT ρ n2 D4 and P = CP ρ n3 D5. The scaling of CT with pitch and blade count, are RotorLab’s own first-order fits.
  5. Brandt, J. B. and Selig, M. S. UIUC Propeller Data Site, volume 1. Static and advance-ratio tests of APC Thin Electric and Slow Flyer propellers, the data the high-pitch figure of merit and the thrust lapse are fitted to, and one of the three sources of the static thrust coefficient.
  6. DJI, E800 tuned propulsion system specifications (dji.com): the DJI 3510 motor at 350 rpm/V on the 13x4.5 propeller, 2,100 g of thrust a rotor at 25 V, the third source of the static thrust coefficient.
  7. T-Motor published bench tests (store.tmotor.com, uav-en.tmotor.com, ligpower.com): full-throttle RPM of 67 propeller and motor pairs from 5 in to 40 in, the data the assumed loaded RPM fraction is the median of and, with their thrust, two of the three sources the static thrust coefficient and its carbon-propeller term are fitted to.
  8. Cameron et al., Journal of Aircraft, DOI 10.2514/1.C033442. Measured interference between the two rotors of a coaxial pair, the effect the coaxial hover penalty and thrust share stand for.

This page computes a first-order, sizing-grade model. It is a transparent statement of what the software does, not a claim that the model captures every real-world effect. Measured thrust-stand and flight data remain definitive. Model limits are listed in the documentation.

Put the numbers to work on your own aircraft.

Talk to us about your program, or start a trial and run these checks on your own build.

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