Engine power

Engine power
Common symbols	P
SI unit	Kilowatt(kW)
InSI base units	1000kg⋅m2⋅s−3
Derivations from other quantities	P=M·ω
Dimension	$ML^{2}T^{-3}$

Engine poweris thepowerthat anenginecan put out. It can be expressed in power units, most commonlykilowatt,pferdestärke(metric horsepower), orhorsepower.In terms of internal combustion engines, the engine power usually describes therated 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 theproductof the enginetorqueand the crankshaft'sangular velocity.

Definition

Power is theproductoftorqueandangular velocity:

Let:

• $P=$Power inWatt(W)
• $M=$Torque inNewton-metre(N·m)
• $n=$Crankshaft speed perSecond(s⁻¹)
• $\ Omega =$Angular velocity=$2\pi n$

Power is then:

$P=M\cdot \ Omega$

In internal combustion engines, the crankshaft speed$n$is a more common figure than$\ Omega$,so we can use$2\pi n$instead, which is equivalent to$\ Omega$:

$P=M\cdot 2\pi \cdot n$

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:

$P=M\cdot 2\pi \cdot {n \over 60}$

Usage

Numerical value equations

The approximatenumerical value equationsfor engine power from torque and crankshaft speed are:

International unit system (SI)

Let:

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

Then:

$P={M\cdot n \over 9550}$

Technical unit system (MKS)

• $P=$Power inPferdestärke(PS)
• $M=$Torque inKilopondmetre(kp·m)
• $n=$Crankshaft speed per Minute (min⁻¹)

Then:

$P={M\cdot n \over 716}$

Imperial/U.S. Customary unit system

• $P=$Power inHorsepower(hp)
• $M=$Torque inPound-force foot(lbf·ft)
• $n=$Crankshaft speed in Revolutions per Minute (rpm)

Then:

$P={M\cdot n \over 5252}$

Example

Torque and power diagram of the example diesel engine

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:

• $M=234\,N\cdot m$
• $n=4200\,{min}^{-1}=70\,s^{-1}$

Then:

$234\,N\cdot m\cdot 2\pi \cdot 70\,s^{-1}=102,919\,N\cdot m\cdot s^{-1}\approx 103\,kW$

or using the numerical value equation:

${234\cdot 4200 \over 9550}=102.91\approx 103$

The engine's rated power output is 103 kW.

Units

	Kilowatt	Kilopondmetreper Second	Pferdestärke	Horsepower	Pound-force footper 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.),Handbuch Maschinenbau(in German), Wiesbaden: Springer,ISBN978-3-658-12528-8

• Böge, Alfred (1972),Mechanik und Festigkeitslehre(in German), Wiesbaden: Vieweg,ISBN9783528140106

• Kemp, Albert W. (1998),Industrial Mechanics,American Technical Publishers,ISBN9780826936905

• Fred Schäfer, Richard van Basshuysen, ed. (2017),Handbuch Verbrennungsmotor(in German), Wiesbaden: Springer,ISBN978-3-658-10901-1