View source for Physics:Engine power

{{ Infobox physical quantity
| name = Engine power
| unit = [[Kilowatt]] (kW)
| symbols = {{mvar|P}}
| baseunits = 1000 kg&sdot;m{{sup|2}}&sdot;[[Second|s]]{{sup|−3}}
| dimension = <math>ML^2T^{-3}</math>
| derivations = {{math|1=''P'' = [[Physics:Torque|''M'']]·[[Physics:Angular velocity|''ω'']] }}
}}

'''Engine power''' is the [[Physics:Power|power]] that an [[Engineering:Engine|engine]] can put out. It can be expressed in power units, most commonly [[Kilowatt|kilowatt]], [[Pferdestärke|pferdestärke]] (metric horsepower), or [[Horsepower|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 (mathematics)|product]] of the engine [[Physics:Torque|torque]] and the crankshaft's [[Physics:Angular velocity|angular velocity]].

== Definition ==

Power is the [[Product (mathematics)|product]] of [[Physics:Torque|torque]] and [[Physics:Angular velocity|angular velocity]]:<ref name="Böge_233">{{Harvnb|Böge|2017}}. p 233</ref>

Let:

*<math>P=</math> Power in [[Watt]] (W)
*<math>M=</math> Torque in [[Newton-metre]] (N·m)
*<math>n=</math> Crankshaft speed per [[Second]] (s<sup>&minus;1</sup>)
*<math>\omega=</math> [[Physics:Angular velocity|Angular velocity]] = <math>2\pi n</math>

Power is then:

:<math>P= M \cdot \omega</math>

In internal combustion engines, the crankshaft speed <math>n</math> is a more common figure than <math>\omega</math>, so we can use <math>2 \pi n</math> instead, which is equivalent to <math>\omega</math>:<ref>{{Harvnb|Fred Schäfer, Richard van Basshuysen|2017}}. p. 21</ref>

:<math>P= M \cdot 2 \pi \cdot n</math>

Note that <math>n</math> is per Second (s<sup>&minus;1</sup>). If we want to use the common per Minute (min<sup>&minus;1</sup>) instead, we have to divide <math>n</math> by 60:

:<math>P= M \cdot 2 \pi \cdot {n \over 60}</math>

== Usage ==

=== Numerical value equations ===

The approximate [[Physics:Numerical value equation|numerical value equation]]s for engine power from torque and crankshaft speed are:<ref name="Böge_233" /><ref name="Böge_154">{{Harvnb|Böge|1972}}. p 154</ref><ref name="Kemp_259">{{Harvnb|Kemp|1998}}. p 259</ref>

==== International unit system (SI) ====

Let:

*<math>P=</math> Power in [[Kilowatt]] (kW)
*<math>M=</math> Torque in Newton-metre (N·m)
*<math>n=</math> Crankshaft speed per Minute (min<sup>&minus;1</sup>)

Then:

:<math>P= {M \cdot n \over 9550}</math>

==== Technical unit system (MKS) ====

*<math>P=</math> Power in [[Pferdestärke]] (PS)
*<math>M=</math> Torque in [[Kilopondmetre]] (kp·m)
*<math>n=</math> Crankshaft speed per Minute (min<sup>&minus;1</sup>)

Then:

:<math>P= {M \cdot n \over 716}</math>

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

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

Then:

:<math>P= {M \cdot n \over 5252}</math>

=== Example ===

{{box
|header=Torque and power diagram of the example diesel engine
|align=right
|{{Graph:Chart|width=300|height=200|type=line|xAxisTitle=Crankshaft speed (1/min)|y1AxisTitle=Torque (N·m)|y2AxisTitle=Power (kW)|legend=|y1Title=Torque (N·m)|y2Title=Power (kW)|x=1250,1750,2000,2500,3000,4000,4500|y1=265, 320, 320, 320, 300, 245, 200|y2=35, 59, 68, 84, 94, 103, 94|interpolate=monotone}}<br />''The power curve (orange) can be derived from the torque curve (blue)<br />by multiplying with the crankshaft speed and dividing by 9550''
|caption =
}}

A diesel engine produces a torque <math>M</math> of 234&nbsp;N·m at <math>n</math> 4200&nbsp;min<sup>&minus;1</sup>, which is the engine's rated speed.

Let:

*<math>M= 234 \, N \cdot m</math>
*<math>n= 4200 \, {min}^{-1} = 70 \, s^{-1}</math>

Then:

:<math>234 \, N \cdot m \cdot 2 \pi \cdot 70 \, s^{-1} = 102,919 \, N \cdot m \cdot s^{-1} \approx 103 \, kW</math>

or using the numerical value equation:

:<math>{234 \cdot 4200 \over 9550} = 102.91 \approx 103</math>

The engine's rated power output is 103&nbsp;kW.

== Units ==

{| class="wikitable" 
! 
! [[Kilowatt]] 
! [[Kilopondmetre]] per Second
! [[Pferdestärke]]
! [[Horsepower]]
! [[Pound-foot (torque)|Pound-force foot]] per minute
|-
! 1 kW (= 1000 kg·m<sup>2</sup>·s<sup>&minus;3</sup>) =
|   1       ||''101.97'' ||''1.36''||  ''1.34'' || ''44,118''
|-
! 1 kp·m·s<sup>&minus;1</sup> =
|  ''0.00980665'' || 1 || ''0.01<span style="text-decoration: overline;">3</span>'' || ''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<sup>&minus;1</sup> =
| ''2.26·10<sup>&minus;5</sup>'' || ''0.0023'' || ''2.99·10<sup>&minus;5</sup>'' || ''3.03·10<sup>&minus;5</sup>'' || 1
|}

== See also ==

* List of production cars by power output

== Bibliography ==

* {{Citation
 | last = Böge
 | first = Wolfgang
 | editor = Alfred Böge
 | year =2017
 | title =Handbuch Maschinenbau
 | publisher = Springer
 | location = Wiesbaden
 | language = German
 | isbn = 978-3-658-12528-8}}

* {{Citation
 | last = Böge
 | first = Alfred
 | year = 1972
 | title = Mechanik und Festigkeitslehre
 | publisher = Vieweg
 | location = Wiesbaden
 | language = German
 | isbn = 9783528140106}}

* {{Citation 
 | last = Kemp
 | first = Albert W.
 | year = 1998
 | title = Industrial Mechanics
 | publisher = American Technical Publishers
 | location = 
 | language = English
 | isbn = 9780826936905}}

* {{Citation 
 | last = 
 | first =
 | editor = Fred Schäfer, Richard van Basshuysen
 | year = 2017
 | title = Handbuch Verbrennungsmotor
 | publisher = Springer
 | location = Wiesbaden
 | language = German
 | isbn = 978-3-658-10901-1}}

==References==
{{reflist|colwidth=30em}}

[[Category:Mechanics]]
[[Category:Power (physics)]]
[[Category:Engines]]

{{Sourceattribution|Engine power}}