Motor Across-the-Line Acceleration Time

t = WK^2 x dN / (308 x T_net), the rotational form of F = m x a, where WK^2 is the total inertia (lb-ft^2) reflected to the motor shaft, dN is the speed change (rpm), and T_net is the average net accelerating torque (motor torque minus load torque, lb-ft). A 100 lb-ft^2 inertia reaching 1,750 rpm on 50 lb-ft of net torque takes 100 x 1750 / (308 x 50) = 11.4 s; double the inertia or halve the net torque and the time doubles. A long start heats the rotor -- check it against the motor's thermal-limit (stall-time) curve, or the overload trips. A screen; the motor's speed-torque and thermal-damage curves, the reflected load inertia, and the drive govern.

accel_time_s = WK^2 x dN / (308 x T_net), where WK^2 is the reflected inertia (lb-ft^2), dN the speed change (rpm), and T_net the average net accelerating torque (lb-ft = motor torque - load torque). The 308 folds 2*pi/60 and g.

Motor across-the-line acceleration-time formula (the rotational form of F = m x a; standard motor-engineering references), by name; the motor's speed-torque and thermal-limit curves govern.

The acceleration-time relation is public physics (Newton's second law in rotational form); the reflected inertia, the speed change, and the average net accelerating torque are user-supplied from the motor and load data.

Estimate. AHJ and licensed professional govern.

Field names used by the API: inertia_lbft2, speed_change_rpm, net_accel_torque_lbft, accel_time_s

• Newton's second law (rotational) t = WK^2 x dN / (308 x T_net); 308 folds 2*pi/60 and g = 32.174 ft/s^2first principles / motor-engineering references
• Average net torque T_net = motor torque - load torque averaged over the start; a single average is a screen (the honest method integrates over speed)speed-torque curves