Efficiency Map⚠ unverified
Electrical / Motors · Compute a motor efficiency value from a simple parabolic map model
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| T | T | N.m | 1.0 | Operating torque |
| omega | ω | rad/s | 1.0 | Operating angular speed |
| T_max | Tmax | N.m | 1.0 | Maximum (rated) torque |
| omega_max | ωmax | rad/s | 1.0 | Maximum (rated) angular speed |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | η | — | Modelled efficiency as a dimensionless ratio |
The science & history
Understanding the Parameters
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$T/T_{max}$ and $\omega/\omega_{max}$ — the operating point normalised to the machine's limits; the model reduces efficiency as either approaches 1.
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$\eta$ — the modelled efficiency; the constants $0.9$ and $0.1$ merely set the peak height and a floor, and are not physically calibrated.
Derivation / Rationale (a heuristic, not a proof)
A real efficiency map has the qualitative shape of a peak in the middle of the torque–speed plane, because two loss families pull in opposite directions across the operating range: copper loss ($\propto I^2 \propto T^2$) grows with torque, while friction/iron losses matter most (relative to a small output) at low load, and both reduce efficiency near the machine's limits (see Motor Efficiency). The two independent parabolic factors $(1-(T/T_{max})^2)$ and $(1-(\omega/\omega_{max})^2)$ reproduce that "dome" shape cheaply:
$$\eta = 0.9\,\big(1 - (T/T_{max})^2\big)\big(1 - (\omega/\omega_{max})^2\big) + 0.1.$$
It should be read as a curve‑fit surrogate for interpolation and quick estimates — it is not derived from the loss physics and is not accurate near the extremes (e.g. it does not force $\eta\to0$ at zero output). Authoritative maps are measured on a dynamometer or built from a validated loss model.
History
Motor and inverter efficiency maps became standard with electric and hybrid vehicle drivetrains, where operating‑point efficiency over a duty cycle determines range. Simple analytic surrogates like this are used in early system‑level simulation before measured maps are available.
Related Concepts: Motor Efficiency, Motor Power, Motor Torque
Notes: Registry calculator efficiency-map (unverified). A heuristic parabolic model, not a
first‑principles or measured map; use dyno data for real analysis.