PROM v4.3 — Validation Report

Summary prose for PROM v4.3 has not been authored yet.

Validated envelope

Benchmark results

Propeller — held-out

Motor — in-sample

Per-case tables

Known limitations

Every model is wrong somewhere. This section states where PROM v4.3 is wrong, in which direction, and by how much, so that you can judge whether a given prediction is one you should trust.

Shaft speed is the weak channel, and PROM over-predicts it

PROM predicts motor current well and motor speed noticeably less well. At wide-open throttle it over-predicts achievable shaft speed, and 54 of the 95 bench motors still fall outside a ±5% band even after the v4.3 improvement described below. This is the limitation a user is most likely to notice first, because predicted RPM sets predicted thrust.

On the held-out portion of the bench set the speed result is better than the headline — mean absolute error 6.10% with 49% of rows inside ±5% — and against an independent laboratory's motors it is worse, at 14.6%. That spread is itself information: treat ±5% as optimistic for a motor we have never measured.

The cause is structural rather than a missing adjustment. The speed and current channels want different values of motor phase inductance and no single value satisfies both: optimised for speed, the residual current error is 8.2%; optimised for current, the residual speed error is 7.1%; the best joint value still leaves 1.9% and 3.4%. PROM ships a value nearer the current-optimal end, because current is what drives runtime and thermal predictions. The speed residual is the price of that choice, and it is a choice.

What v4.3 changed, and what it did not

Measured on identical rows — 95 motors, 7,416 bench rows — against the version running before it:

Both improvements are real, and they came from two separate pieces of work: the electrical loss model moved the current channel, and a correction to how the back-EMF constant is derived moved the speed channel.

Two honest qualifications. First, the speed work left current and efficiency flat where it landed (6.55% → 6.49%, 5.067 → 5.068 points) — its large gain at wide-open throttle is diluted roughly 13:1 because wide-open throttle is only 558 of 7,416 rows, and it is partly offset by a small under-prediction at part throttle. Second, the inductance change in this version is close to bias-neutral across these motors, so it is not what produced the current gain. Neither change made every channel better, and the table above is the whole picture rather than the flattering half of it.

The thrust channel also moved, and it carries the strongest evidence in this report: it was measured on 25 propellers held out of the model's construction entirely — 3,222 rows, none of which informed it.

Every propeller family improved, which was a condition set before the numbers were known rather than a property discovered afterwards.

The qualification here is the second row. On propellers it had never seen, the previous version's adjustment was slightly worse than applying no adjustment at all — it had been built and evaluated in a way that could not detect this. The v4.3 figure is the first one measured on propellers held out from the start.

Static thrust deserves its own line, because it is where a multirotor spends most of its life and because a pooled number can hide it. Measured across every zero-airspeed row in the propeller set, thrust-coefficient error improved from 0.01076 to 0.00665, and on the held-out propellers specifically from 0.01138 to 0.00802. Every family improved. The hover number moved the same direction as the pooled number, not against it.

Below 30% throttle the motor model is weak

Motor current error rises sharply at low throttle: roughly 21% mean absolute error below 30% throttle, with only about a quarter of rows within ±10%. This is confirmed on an independent laboratory's data rather than inferred from a thin sample, so it is a real limitation and not an artifact.

The 60–99% throttle band, where most hover and cruise operation sits, is the strongest part of the range.

Efficiency is not a second opinion

Motor efficiency error is roughly 5 percentage points, but it should not be read as independent corroboration of the current result — it is the same current residual re-expressed. Additionally, predicted motor efficiency saturates near 84%, so PROM cannot reproduce measured efficiencies above that.

Motor magnetic saturation is not modelled

PROM treats the motor torque constant as independent of current. Real surface-permanent-magnet motors lose torque constant as armature current rises, which means PROM will tend to under-predict current draw for a heavily loaded motor — the error grows with load, and is largest on high-pitch propellers at high cell counts. The term needed to represent this exists in the model but ships disabled, because we do not yet have the measurements to set it honestly.

About one motor in six sits at an inductance bound

PROM estimates phase inductance from published motor specifications, and bounds the result to the range supported by bench data. 357 of 1,984 catalogue motors (18.0%) sit at the upper bound, and the pole-count term saturates outside 14–42 poles, which affects a further 120 catalogue entries. For those motors the inductance is a bounded estimate rather than an interpolation, and predictions should be treated as correspondingly less certain. The bounds exist because extrapolating past the measured range produced unphysical results.

Propeller torque is under-predicted at low advance ratio

The propeller model uses a station-local wake closure that does not capture interaction between blade stations across the helical wake surface. The consequence is systematic under-prediction of thrust at heavy loading and low advance ratio — which is to say, near static thrust, where a multirotor spends most of its life. The per-family tables above quantify how large the effect is on the propellers we measured.

The effect concentrates in the short-pitch, large-diameter regime. If you are simulating a large-diameter, low-pitch propeller near static thrust, expect the widest error there.

Several candidate improvements to this closure were implemented and evaluated against the measured set, and none of them improved accuracy overall; some made it worse. The standard empirical modification for very high disk loading is likewise not part of the shipped model. We mention both because "not implemented" here reflects evidence that it did not help, rather than an oversight.

Edgewise flight: modelled, but the in-plane force is a lower bound

PROM resolves both the axial and the edgewise component of the airflow a rotor sees, including each rotor's own mounting tilt, and reports thrust in both the rotor frame and the ground frame. Tilted and forward-flight operation is a modelled condition, not an approximation of hover.

Two things about it are worth knowing:

• The in-plane (edgewise) force is a deliberate lower bound. It is computed as a first-order estimate from the revolution-averaged blade state rather than by resolving the disk azimuthally. Against a higher-fidelity azimuthally resolved calculation, it recovers roughly 58%, 64% and 81% of the in-plane force at advance ratios of 0.06, 0.13 and 0.25 respectively. It is therefore most conservative exactly where multirotors spend most of their time — low advance ratio. Treat in-plane force as a floor, not an estimate of centre.
• Per-revolution effects are not represented. Because the disk is not resolved by azimuth, the once-per-revolution variation in blade loading and the pitch and yaw hub moments that arise from it are not part of the solution.

Rotor-to-rotor interaction: modelled, but not measured against

Rotors stacked in each other's wake are coupled: PROM applies the upstream rotor's axial and swirl perturbation to the downstream disk, in both steady-state and transient solutions, and the transient case carries the convection delay before an upstream change reaches the rotor below.

The physics is derived from vortex-tube theory with no empirical constants and is verified against closed-form limiting cases. Steady-state stacked-rotor results are the validated path. Transient stacked-rotor results are not: the wake-convection lag that carries an upstream change down to the rotor below ships without verification against measurement, because no such measurement exists in our corpus. Treat coaxial results in dynamic runs as provisional, and stacked-rotor results generally as theory-grade rather than measurement-backed — none of the error bars in this report were measured on a stacked configuration.

Steep descent

In a fast, steep descent a rotor can re-ingest its own wake. PROM detects operating points that enter this regime and flags them; the result is returned but should be read as an approximation. Everything else in the same run is unaffected.

Not attempted at all

• No acoustic prediction. Aerodynamic forces only — no tonal or broadband noise output.
• Propeller geometry uncertainty dominates. For propellers whose geometry is derived rather than supplied by the manufacturer, blade chord is the largest single source of uncertainty — see the user-supplied geometry section below.

Out-of-envelope behaviour

PROM does not refuse to run outside the envelope above, and it does not warn you when you leave it. It will return a number for a propeller half the size of anything we have measured. This section is how you tell whether that number deserves your confidence.

Propellers outside the measured set

The envelope above describes propellers we have compared against wind-tunnel measurement. Outside it, three things degrade at different rates:

• Smaller propellers. Below roughly 12 inches, blade Reynolds numbers drop into a regime where sectional drag rises sharply and is less predictable. Expect efficiency to be optimistic.
• Higher advance ratios. Above the advance-ratio range in the envelope table, we have no measurements to report against.
• Other manufacturers and blade families. Our measured set is dominated by one manufacturer's electric series. Geometry from other families is represented by the same underlying model, but its accuracy on those families is not something this report establishes.

Flight condition, not just propeller

There is a second and less obvious way to leave the envelope. Every measurement behind this report was taken with the airflow arriving along the rotor's spin axis. Edgewise and tilted operation is fully modelled, as described above, but nothing in this report measures it: there is no wind-tunnel data here taken at an angle to the disk. The same is true of stacked rotors and of steep descent.

So the numbers in the tables above quantify the model's accuracy in axial flight. They do not transfer unchanged to a forward-flight multirotor, a tilt-rotor, or a coaxial stack. Those configurations run through additional model paths whose error bars this report does not establish — and for the in-plane force specifically, the shipped value is a known lower bound rather than a best estimate.

The held-out results in this report are a deliberately harder test than the in-sample ones: those propellers are new to the model, and nothing about them informed it. They also sit almost entirely inside the geometric range over which the production configuration is supported, so the held-out numbers are a clean measure of how the model treats an unfamiliar propeller rather than a mixture of that and a fade toward the physics-only prediction.

One asymmetry is worth stating plainly, because it is visible in the tables above: for the power coefficient, the production and physics-only configurations report the same numbers. PROM applies no empirical adjustment to power — that channel is the model's own prediction in both configurations. Where the two columns differ, you are looking at thrust.

User-supplied and custom components

Every number in this report was produced from catalogue components whose geometry we control. Components you supply yourself are outside the validated envelope, and this is the common case rather than an edge case — custom components are available on every tier.

The reason is simply that we have not measured it. Every figure in this report comes from comparing a prediction against a wind-tunnel or dyno measurement of a specific known component. A component you define yourself has no such measurement behind it, so the error bars above do not extend to it — not because we know it to be worse, but because we have not established what it is.

The sensitivity worth understanding is geometric: blade chord and pitch scale thrust and power directly, so small errors in a reconstructed blade shape propagate straight into the result. If you supply geometry, its accuracy is the dominant term, and it is one only you can check.

Results computed with user-supplied components are marked as such in the interface. Treat the error bars in this report as inapplicable to them.

What to do about it

Out-of-envelope predictions are still useful for comparing designs against each other, because the errors described here are largely systematic and move similar configurations in the same direction. They are much weaker as absolute predictions. If you need an absolute number outside the envelope — a flight time you will commit to, a current a component must survive — measure it.

Changes from previous version

PROM v4.3 is the first published validation report; there is no previous published report to diff against.

Data sources

• UIUC Propeller Data Site, Volume 1 — APC Thin Electric / Slow Flyer / Sport — Brandt, J. B. and Selig, M. S., 'Propeller Performance Data at Low Reynolds Numbers', AIAA 2011-1255, January 2011; Brandt 2005 UIUC M.S. thesis. (revision: e60b6ff97f78)
• UIUC Propeller Data Site, Volume 4 — APC Thin Electric — Dantsker, O. D., Caccamo, M., Deters, R. W. and Selig, M. S., 'Performance Testing of APC Electric Fixed-Blade UAV Propellers', AIAA 2022-4020, June 2022. (revision: e4c6b24c399e)
• T-Motor published bench dataset (curated corpus) — Manufacturer-published product-page test tables, curated and energy-consistency filtered. (revision: bcd9bcaba479)
• Independent third-party motor bench — Commercial laboratory dataset; source withheld under its terms of use. Used for aggregate metrics only. (revision: cb506f184793)