Motor RMS Horsepower for a Duty-Cycle Load
The smallest continuous-rated motor that will not overheat on a repeating on/off (duty-cycle) load: the RMS horsepower is the constant HP that heats the motor the same as the varying load. HP_rms = sqrt( (HP_run^2 x t_run + HP_idle^2 x t_idle) / (t_run + t_idle / K) ), where the idle or stopped time is divided by a cooling factor K (~3 stopped, ~2 unloaded) because a self-cooled motor sheds heat less well when it is not turning at speed. A 20 HP load for 10 s then a 20 s rest at K = 3 gives 15.5 HP_rms, so a 15 HP continuous motor is marginal and a 20 HP is safe. This sizes the THERMAL duty only -- the PEAK horsepower must still fall within the motor's breakdown torque, a separate check. A screen; the motor's thermal-damage curve, service factor, and the manufacturer's duty rating govern.
Formula and source
rms_hp = sqrt( (hp_run^2 x run_time_s + hp_idle^2 x idle_time_s) / (run_time_s + idle_time_s / cooling_factor) ). The idle/stopped time is divided by the cooling factor K (~3 stopped, ~2 unloaded).
Motor duty-cycle RMS-horsepower sizing method (NEMA MG-1 duty-cycle practice; standard motor-application references), by name; the motor's thermal-damage curve and duty rating govern.
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