Engine power

Common symbols

| P
SI unit| Kilowatt (kW)
In SI base units| 1000 kg⋅m2⋅s−3

Derivations from
other quantities

| P = M·ω
Dimension| ML2T−3

Engine power is the power that an engine can put out. It can be expressed in power units, most commonly kilowatt, pferdestärke (metric horsepower), or horsepower. In terms of internal combustion engines, the engine power usually describes the rated power, which is a power output that the engine can maintain over a long period of time according to a certain testing method, for example ISO 1585. In general though, an internal combustion engine has a power take-off shaft (the crankshaft), therefore, the rule for shaft power applies to internal combustion engines: Engine power is the product of the engine torque and the crankshaft's angular velocity.

## Contents

* 1 Definition
* 2 Usage
* 2.1 Numerical value equations
* 2.1.1 International unit system (SI)
* 2.1.2 Technical unit system (MKS)
* 2.1.3 Imperial/U.S. Customary unit system
* 2.2 Example
* 3 Units
* 4 See also
* 5 Bibliography
* 6 References

## Definition

Power is the product of torque and angular velocity:[1]

Let:

* P= Power in Watt (W)
* M= Torque in Newton-metre (N·m)
* n= Crankshaft speed per Second (s−1)
* ω= Angular velocity = 2πn

Power is then:

P=M⋅ω

In internal combustion engines, the crankshaft speed n is a more common figure than ω, so we can use 2πn instead, which is equivalent to ω:[2]

P=M⋅2π⋅n

Note that n is per Second (s−1). If we want to use the common per Minute (min−1) instead, we have to divide n by 60:

P=M⋅2π⋅n60

## Usage

### Numerical value equations

The approximate numerical value equations for engine power from torque and crankshaft speed are:[1][3][4]

#### International unit system (SI)

Let:

* P= Power in Kilowatt (kW)
* M= Torque in Newton-metre (N·m)
* n= Crankshaft speed per Minute (min−1)

Then:

P=M⋅n9550

#### Technical unit system (MKS)

* P= Power in Pferdestärke (PS)
* M= Torque in Kilopondmetre (kp·m)
* n= Crankshaft speed per Minute (min−1)

Then:

P=M⋅n716

#### Imperial/U.S. Customary unit system

* P= Power in Horsepower (hp)
* M= Torque in Pound-force foot (lbf·ft)
* n= Crankshaft speed in Revolutions per Minute (rpm)

Then:

P=M⋅n5252

### Example

Torque and power diagram of the example diesel engine
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The power curve (orange) can be derived from the torque curve (blue)
by multiplying with the crankshaft speed and dividing by 9550

A diesel engine produces a torque M of 234 N·m at n 4200 min−1, which is the engine's rated speed.

Let:

* M=234N⋅m
* n=4200min−1=70s−1

Then:

234N⋅m⋅2π⋅70s−1=102,919N⋅m⋅s−1≈103kW

or using the numerical value equation:

234⋅42009550=102.91≈103

The engine's rated power output is 103 kW.

## Units

| Kilowatt | Kilopondmetre per Second  | Pferdestärke | Horsepower | Pound-force foot per minute

|
|
|
|
|

1 kW (= 1000 kg·m2·s−3) =  | 1 | 101.97 | 1.36 | 1.34 | 44,118
1 kp·m·s−1 =  | 0.00980665 | 1 | 0.013 | 0.0132 | 433.981
1 PS =  | 0.73549875 | 75 | 1 | 0.986 | 32,548.56
1 hp =  | 0.7457 | 76.04 | 1.014 | 1 | 33,000
1 lbf·ft·min−1 =  | 2.26·10−5 | 0.0023 | 2.99·10−5 | 3.03·10−5 | 1

## See also

* List of production cars by power output

## Bibliography

* Böge, Wolfgang (2017), Alfred Böge, ed. (in German), Handbuch Maschinenbau, Wiesbaden: Springer, ISBN 978-3-658-12528-8

* Böge, Alfred (1972) (in German), Mechanik und Festigkeitslehre, Wiesbaden: Vieweg, ISBN 9783528140106

* Kemp, Albert W. (1998) (in English), Industrial Mechanics, American Technical Publishers, ISBN 9780826936905

* Fred Schäfer, Richard van Basshuysen, ed. (2017) (in German), Handbuch Verbrennungsmotor, Wiesbaden: Springer, ISBN 978-3-658-10901-1

## References

1. ↑ 1.0 1.1 Böge 2017. p 233
2. ↑ Fred Schäfer, Richard van Basshuysen 2017. p. 21
3. ↑ Böge 1972. p 154
4. ↑ Kemp 1998. p 259

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