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.
Example
You enter
- Working (run) load (HP) 20
- Run time (s) 10
- Idle / rest time (s) 20
- Standstill cooling factor (3 open drip-proof, 2 totally enclosed) 3
You get
- RMS horsepower 15.49
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeThe 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 only STOPPED time is divided by a standstill cooling factor K (3 open drip-proof, 2 totally enclosed) because a self-cooled motor loses its fan at standstill; a light-load segment that still runs counts at full time. 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 or tablerms_hp = sqrt( (hp_run^2 x run_time_s + hp_idle^2 x idle_time_s) / (run_time_s + idle_time_s / cooling_factor) ). Only stopped time (hp_idle = 0) is divided by the standstill cooling factor K (3 open drip-proof, 2 totally enclosed); a segment that still runs counts at full time.
Source and editionMotor 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.
Free accessThe RMS-horsepower relation is public engineering practice (the root-mean-square heating equivalent); the load horsepowers, the run and idle times, and the cooling factor come from the driven-load duty cycle and the motor's cooling type.
What governsEstimate. AHJ and licensed professional govern.
API field nameshp_run, run_time_s, idle_time_s, cooling_factor, rms_hp
- RMS heating equivalent HP_rms = sqrt(sum(HP^2 t) / effective_time); heating goes as HP^2, so the equivalent is a root-mean-squaremotor-application practice
- Standstill cooling factor stopped time divided by C = 3 (open drip-proof) or 2 (totally enclosed) because a self-cooled motor at standstill loses its fan; running time counts in full; peak-vs-breakdown-torque is a separate checkE. Cowern (Baldor), Economical motor sizing for peak loads, Machine Design, 2001