Library / Fundamentals / FUN-03
Fundamentals
Mechanical power
Power delivered by a force acting on a moving point.
- Ref
- FUN-03
- Rev
- v1
- Field
- Fundamentals
- Result
- P [kW]
P in watts (J/s), F in newtons, v in metres per second. Use the velocity of the point where the force acts, along the direction of the force.
Power is how fast work is done. A force pushing something along at a given speed delivers power equal to the force times the speed.
Calculator
- Power in horsepower (metric)8.158 PS
- Work done in one minute0.36 MJ
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At a fixed power, force and speed trade off: the same engine can pull hard slowly or lightly quickly.
- Power is the rate of doing work, so the energy delivered in time t is P × t.
- Real machines lose power in the drive train; the power at the engine is the useful power divided by the efficiency.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kW) | Local step | Change in result |
|---|---|---|---|---|---|---|
| v Speed | 0.1 to 300 m/s | 0.2 | 600 | 599.8 | +10% | +10 % |
| F Force | 0.1 to 100 kN | 0.3 | 300 | 299.7 | +10% | +10 % |
Sweep of Speed
| Speed (m/s) | Power (kW) |
|---|---|
| 0.1 | 0.2 |
| 0.272 | 0.5441 |
| 0.7401 | 1.48 |
| 2.013 | 4.027 |
| 5.477 | 10.95 |
| 14.9 | 29.8 |
| 40.54 | 81.07 |
| 110.3 | 220.6 |
| 300 | 600 |
Sweep one variable
Variables and how each one contributes
Power
What the equation gives you. Everything else feeds it.
Force
Force acting along the direction of motion. Directly proportional: double the force at the same speed, double the power.
Speed
Speed of the point where the force acts. Directly proportional at constant force. Drag forces grow with v², so the power needed grows roughly with v³.
Worked example with the values above
- Convert the force: 2 kN = 2,000 N.
- P = Fv = 2,000 N × 3 m/s = 6,000 W.
- That is 6 kW.
Assumptions and limits
- Force and velocity along the same line (otherwise P = F v cos θ).
- Steady values over the interval.
- Power at the point of application, before drive-train losses.
Common mistakes
- Using kN with m/s and calling the answer watts: kN × m/s gives kW.
- Using the vehicle speed rather than the speed at the point where the force acts.
- Mixing power (kW) with energy (kWh).
Statistics and uncertainty
Independent errors combine as δP/P ≈ √[(δF/F)² + (δv/v)²]. Force measured by a load cell and speed from a tachometer are typically accurate to a few per cent each.
Where it is used
- Sizing a motor or engine for a towing or lifting job.
- Propulsive power of a vehicle from thrust and speed.
- Checking a winch or conveyor drive.
Maths you need
- Work and energy: power is work per unit time
- Unit prefixes: kN × m/s = kW