Hoist and Lift Power Formulas
Hoist formulas: the motor power to raise a load at a speed, the energy to lift it a height and the lifting time, with the drive efficiency.
The formulas
| To find | Formula |
|---|---|
| Motor power (kW) | P = m × g × v / (η × 1000) |
| Energy to lift (J) | E = m × g × h |
| Electrical energy (kWh) | E / (3.6e6 × η) |
| Lifting time | t = h / v |
m is the mass in kilograms (the load and any part of the car or hook that is not balanced), g = 9.81 m/s², v the lifting speed in m/s, h the height in metres and η the efficiency of the gear, rope and motor as a fraction. A counterweight reduces the net mass. The power during acceleration is higher by the force needed to accelerate the mass, which this page does not include. The efficiency of 0.8 and the other values are examples. A hoist is also rated for duty and starts per hour, which this page does not cover.
Worked example: 2,000 kg at 0.5 m/s, efficiency 0.8
- P = 2000 × 9.81 × 0.5 / (0.8 × 1000) = 12.26 kW
- Lifting 15 m takes 15 / 0.5 = 30 s
- E = 2000 × 9.81 × 15 = 294.3 kJ at the load, which is 0.1022 kWh from the supply
Motor power by speed (2,000 kg, η = 0.8)
| Speed | Motor power |
|---|---|
| 0.25 m/s | 6.131 kW |
| 0.5 m/s | 12.26 kW |
| 1 m/s | 24.52 kW |
| 2 m/s | 49.05 kW |
Frequently asked questions
Why divide by the efficiency?
The gearbox, the ropes and the motor waste some power, so the motor must supply more than the power at the load.
Does the motor take power when lowering?
A load being lowered gives energy back. A drive can return it to the supply or burn it in a braking resistor.
Does this include the acceleration?
No. Extra power is needed to speed up the mass, and the motor must be checked for the peak.
What does a counterweight do?
It balances part of the weight, so the motor lifts only the difference and the power is much lower.
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