The physics model

RotorLab estimates performance from physics rather than rules of thumb. Most quick calculators multiply a fixed grams-per-watt figure by weight, which hides the two variables that actually drive efficiency: disc area and air density. RotorLab derives hover power from actuator-disc (momentum) theory instead, so the result responds correctly to a larger prop, a denser or thinner atmosphere, or a heavier payload.

Treat the output as a strong first-order engineering estimate, then calibrate against bench and flight data for numbers you can fly on.

Hover: momentum theory#

Hover power comes from actuator-disc theory:

induced power per disc = T^1.5 / sqrt(2 * rho * A)

where T is the thrust each disc carries, rho is air density, and A is disc area. The ideal figure is summed across all discs, then divided by the rotor figure of merit to get real power, with an optional penalty applied for coaxial layouts. Coaxial types (Y6, Octo X8) stack two motors over one disc location, so they count as half the discs. This is why prop diameter and density move the numbers strongly: both change disc loading.

Density altitude#

Air density comes from the ISA standard-atmosphere model for the altitude you enter, with density then computed from the real temperature you give it. Hot air at altitude is the worst case for any rotorcraft, and the tool shows the endurance and thrust penalty directly. Set a high altitude and a high temperature to see the effect for a demo or deployment site.

Forward flight: the power-required curve#

Set a flat-plate drag area f (Cd times frontal area, in m2) and RotorLab computes a power-required curve across airspeed instead of scaling hover power by a flat factor. The curve is the sum of three terms:

• Induced power: momentum theory in forward flight, falling as the aircraft speeds up.
• Profile power: a roughly constant term.
• Parasite power: 0.5 * rho * V^3 * f, rising as the cube of speed.

Thrust grows with speed because the disc tilts to beat body drag. From the curve the tool reports the best-endurance speed (minimum power), the best-range speed (maximum distance per unit energy, used as the default cruise speed), cruise endurance and range at that speed, and a top speed limited by the smaller of available thrust and available power. The top-speed sweep derives its ceiling from the build's own thrust and power limits and reports what binds the result.

Leave f at 0 and the tool falls back to the legacy flat cruise factor and pitch-slip top speed. See Forward flight and VTOL for the inputs.

The VTOL wing model#

For the VTOL transition airframe type, the craft takes off vertically on its props (the hover analysis is unchanged), then transitions to horizontal flight where the wing carries the weight and the props become pure forward pushers. Because the props no longer hold the aircraft up, they fight only drag, which is how this regime reaches far higher cruise speeds than a weight-carrying multirotor.

The wing is the airfoil arms: total area is arms times arm length times arm chord. Cruise drag is the wing profile drag plus induced drag (from aspect ratio and span efficiency) plus the body parasite drag (the same flat-plate area f). Power required is drag times speed divided by the cruise propulsive efficiency. The tool reports the stall speed (the transition speed the craft must exceed before the wing flies), wing area and loading, best-range and best-endurance cruise speeds, cruise endurance and range, a thrust- or power-limited top speed, and a transition-feasibility check: whether the thrust-borne phase can accelerate the craft past its stall speed. This is a first-order model; the multirotor forward-flight path adds no wing drag, since in that mode the props carry the weight.

Thrust estimation, and the input that matters most#

max_thrust_per_motor_g is the one input that matters most. Enter a measured or datasheet value and thrust-to-weight, hover throttle, and the WOT current checks become trustworthy. Leave it at 0 and the tool estimates thrust from a coarse static thrust coefficient (T = Ct * rho * n^2 * D^4) and flags every dependent figure [est].

The static estimate is pitch- and blade-aware but still coarse: it is a geometric model, not a datasheet. Prefer a measured thrust-stand value. Loaded RPM is likewise estimated from KV and a loaded-RPM fraction unless you supply a measured WOT RPM.

Anything in the output tagged [est] or [rough] is a model estimate, not a measured value.

Model factor defaults#

The model factors are advanced inputs, grouped at the bottom of the console, meant to be tuned to your own bench data:

Calibrating the model to your aircraft#

The defaults give sensible ballpark numbers. To make them yours:

1. Build the profile and leave the model factors at defaults.
2. Hover the real aircraft and read pack current from telemetry.
3. Adjust figure_of_merit until predicted hover current matches measured.
4. Enter measured max thrust per motor from a thrust stand.

After that, endurance and TWR are specific to your hardware, not generic. The Calibration page automates this from a live flight controller: a steady hover capture yields the measured figure of merit and max thrust, and an optional bench WOT burst cross-checks the thrust figure.

Limitations#

• Static max-thrust estimation is coarse. Prefer a measured thrust-stand value.
• Loaded RPM is estimated from KV unless you supply a measured WOT RPM. Pitch speed remains geometric.
• The forward-flight curve uses a constant profile-power term and a single flat-plate drag area rather than a full blade-element model. It is solid for sizing and planning, not a substitute for flight test.
• Each load carries a single power figure; idle versus peak draw is not modeled separately, so the regulator headroom check uses that one number.
• Catalog mass and power figures are nominal starting points, not guaranteed specs. Edit them to match your exact hardware.
• The model assumes an even, symmetric rotor layout for prop-clearance geometry. Stretched-X, deadcat, H, and non-uniform arm frames are not modeled for clearance.

The Math and validation page#

The Math and validation page at https://rotorlab.app/validate (also in the Menu dropdown) writes out every governing equation the tool uses, derived and referenced: the standard-atmosphere density, momentum-theory hover, the forward-flight power curve, the VTOL wing model, energy and endurance, thrust and RPM, and the regulated rails.

It is more than documentation: each equation is re-evaluated independently in your browser from a set of editable inputs and checked against what the engine returns from its own code path. A green badge means the printed equation and the software agree to within 0.1%; a red badge would mean they diverge. Change any input and every number, and every check, recomputes. The page needs no internet and uses no external math library.

Related#

• The Builder
• Forward flight and VTOL
• Calibration
• Trade study