NapkinCalc

AC Motors

Induction motors: synchronous speed, slip, full-load current, shaft torque, and power-factor correction.

The three-phase induction motor runs most of the industrial world — pumps, fans, conveyors, compressors. Three windings make a magnetic field that rotates at a speed fixed by the line frequency; the rotor chases it, always lagging just behind — and that lag is exactly what makes the torque.

  1. 01 Synchronous speed ELI5: the rotating field spins at n_sync = 120·f / p, where p is the number of magnetic poles. More poles → a slower field. At 60 Hz: 2 poles → 3600 rpm, 4 →…
  2. 02 Slip — why the rotor lags ELI5: if the rotor ever caught the field, it would cut no field lines, induce no current, and make no torque — so it can never quite catch up. It settles just…
  3. 03 Power, efficiency & full-load current ELI5: the nameplate lists shaft power (what the load actually gets). The line has to supply more, to cover losses (efficiency η) and the magnetizing current…
  4. 04 Shaft torque ELI5: power is torque × spin rate: P = T·ω. So the same power at half the speed means twice the torque — which is exactly why low-rpm motors (and gearboxes)…
  5. 05 Power-factor correction ELI5: that 0.86 power factor means the line carries extra current that does no useful work (it just sloshes back and forth magnetizing the motor). A capacitor…

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