Engine power

<h2 id="definition">Definition</h2>
<p>Power is the <a href="/facts/Product_(mathematics)/aXY11nGS">product</a> of <a href="/facts/Torque/KcrcvNtV">torque</a> and <a href="/facts/Angular_velocity/2n8JljAT">angular velocity</a>:<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p><p>Let:
</p>
<ul><li>
  
    
      
        P
        =
      
    
    {\displaystyle P=}
  
 Power in <a href="/facts/Watt/VK8oqRrm">Watt</a> (W)</li>
<li>
  
    
      
        M
        =
      
    
    {\displaystyle M=}
  
 Torque in <a href="/facts/Newton-metre/1c1LhdB8">Newton-metre</a> (N·m)</li>
<li>
  
    
      
        n
        =
      
    
    {\displaystyle n=}
  
 Crankshaft speed per <a href="/facts/Second/jtFxnJXx">Second</a> (s−1)</li>
<li>
  
    
      
        ω
        =
      
    
    {\displaystyle \omega =}
  
 <a href="/facts/Angular_velocity/2n8JljAT">Angular velocity</a> = 
  
    
      
        2
        π
        n
      
    
    {\displaystyle 2\pi n}
  
</li></ul>
<p>Power is then:
</p>

P
        =
        M
        ⋅
        ω
      
    
    {\displaystyle P=M\cdot \omega }

<p>In internal combustion engines, the crankshaft speed 
  
    
      
        n
      
    
    {\displaystyle n}
  
 is a more common figure than 
  
    
      
        ω
      
    
    {\displaystyle \omega }
  
, so we can use 
  
    
      
        2
        π
        n
      
    
    {\displaystyle 2\pi n}
  
 instead, which is equivalent to 
  
    
      
        ω
      
    
    {\displaystyle \omega }
  
:<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p>

P
        =
        M
        ⋅
        2
        π
        ⋅
        n
      
    
    {\displaystyle P=M\cdot 2\pi \cdot n}

<p>Note that 
  
    
      
        n
      
    
    {\displaystyle n}
  
 is per Second (s−1). If we want to use the common per Minute (min−1) instead, we have to divide 
  
    
      
        n
      
    
    {\displaystyle n}
  
 by 60:
</p>

P
        =
        M
        ⋅
        2
        π
        ⋅
        
          
            n
            60
          
        
      
    
    {\displaystyle P=M\cdot 2\pi \cdot {n \over 60}}

<h2 id="usage">Usage</h2>
<h3>Numerical value equations</h3>
<p>The approximate <a href="/facts/Numerical_value_equation/ChdpNzEx">numerical value equations</a> for engine power from torque and crankshaft speed are:<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p>
<h4>International unit system (SI)</h4>
<p>Let:
</p>
<ul><li>
  
    
      
        P
        =
      
    
    {\displaystyle P=}
  
 Power in <a href="/facts/Kilowatt/VK8oqRrm">Kilowatt</a> (kW)</li>
<li>
  
    
      
        M
        =
      
    
    {\displaystyle M=}
  
 Torque in Newton-metre (N·m)</li>
<li>
  
    
      
        n
        =
      
    
    {\displaystyle n=}
  
 Crankshaft speed per Minute (min−1)</li></ul>
<p>Then:
</p>

P
        =
        
          
            
              M
              ⋅
              n
            
            9550
          
        
      
    
    {\displaystyle P={M\cdot n \over 9550}}

<h4>Technical unit system (MKS)</h4>
<ul><li>
  
    
      
        P
        =
      
    
    {\displaystyle P=}
  
 Power in <a href="/facts/Horsepower/jRMwmIxA">Metric horsepower</a> (hp, PS)</li>
<li>
  
    
      
        M
        =
      
    
    {\displaystyle M=}
  
 Torque in <a href="/facts/Kilopondmetre/qd3bnkED">Kilopondmetre</a> (kp·m)</li>
<li>
  
    
      
        n
        =
      
    
    {\displaystyle n=}
  
 Crankshaft speed per Minute (min−1)</li></ul>
<p>Then:
</p>

P
        =
        
          
            
              M
              ⋅
              n
            
            716
          
        
      
    
    {\displaystyle P={M\cdot n \over 716}}

<h4>Imperial/U.S. Customary unit system</h4>
<ul><li>
  
    
      
        P
        =
      
    
    {\displaystyle P=}
  
 Power in <a href="/facts/Horsepower/jRMwmIxA">Horsepower</a> (hp, bhp)</li>
<li>
  
    
      
        M
        =
      
    
    {\displaystyle M=}
  
 Torque in <a href="/facts/Pound-force_foot/eYQsElep">Pound-force foot</a> (lbf·ft)</li>
<li>
  
    
      
        n
        =
      
    
    {\displaystyle n=}
  
 Crankshaft speed in Revolutions per Minute (rpm)</li></ul>
<p>Then:
</p>

P
        =
        
          
            
              M
              ⋅
              n
            
            5252
          
        
      
    
    {\displaystyle P={M\cdot n \over 5252}}

<h3>Example</h3>
Torque and power diagram of the example diesel engine<i>The power curve (orange) can be derived from the torque curve (blue)by multiplying with the crankshaft speed and dividing by 9550</i>
<p>A diesel engine produces a torque 
  
    
      
        M
      
    
    {\displaystyle M}
  
 of 234 N·m at 
  
    
      
        n
      
    
    {\displaystyle n}
  
 4200 min−1, which is the engine's rated speed.
</p><p>Let:
</p>
<ul><li>
  
    
      
        M
        =
        234
        
        N
        ⋅
        m
      
    
    {\displaystyle M=234\,N\cdot m}
  
</li>
<li>
  
    
      
        n
        =
        4200
        
        
          
            m
            i
            n
          
          
            −
            1
          
        
        =
        70
        
        
          s
          
            −
            1
          
        
      
    
    {\displaystyle n=4200\,{min}^{-1}=70\,s^{-1}}
  
</li></ul>
<p>Then:
</p>

234
        
        N
        ⋅
        m
        ⋅
        2
        π
        ⋅
        70
        
        
          s
          
            −
            1
          
        
        =
        102
        ,
        919
        
        N
        ⋅
        m
        ⋅
        
          s
          
            −
            1
          
        
        ≈
        103
        
        k
        W
      
    
    {\displaystyle 234\,N\cdot m\cdot 2\pi \cdot 70\,s^{-1}=102,919\,N\cdot m\cdot s^{-1}\approx 103\,kW}

<p>or using the numerical value equation:
</p>

234
              ⋅
              4200
            
            9550
          
        
        =
        102.91
        ≈
        103
      
    
    {\displaystyle {234\cdot 4200 \over 9550}=102.91\approx 103}

<p>The engine's rated power output is 103 kW.
</p>
<h2 id="units">Units</h2>
<table><tbody><tr><th></th><th><a href="/facts/Kilowatt/VK8oqRrm">Kilowatt</a></th><th><a href="/facts/Kilopondmetre/qd3bnkED">Kilopondmetre</a> per Second</th><th><a href="/facts/Horsepower/jRMwmIxA">Metric horsepower</a></th><th><a href="/facts/Horsepower/jRMwmIxA">Horsepower</a></th><th><a href="/facts/Pound-foot_(torque)/0tcULQU3">Pound-force foot</a> per minute</th></tr><tr><th>1 kW (= 1000 kg·m2·s−3) =</th><td>1</td><td><i>101.97</i></td><td><i>1.36</i></td><td><i>1.34</i></td><td><i>44,118</i></td></tr><tr><th>1 kp·m·s−1 =</th><td><i>0.00980665</i></td><td>1</td><td><i>0.013</i></td><td><i>0.0132</i></td><td><i>433.981</i></td></tr><tr><th>1 PS =</th><td><i>0.73549875</i></td><td><i>75</i></td><td>1</td><td><i>0.986</i></td><td><i>32,548.56</i></td></tr><tr><th>1 hp =</th><td><i>0.7457</i></td><td><i>76.04</i></td><td><i>1.014</i></td><td>1</td><td><i>33,000</i></td></tr><tr><th>1 lbf·ft·min−1 =</th><td><i>2.26·10−5</i></td><td><i>0.0023</i></td><td><i>2.99·10−5</i></td><td><i>3.03·10−5</i></td><td>1</td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/List_of_production_cars_by_power_output/pIWwdwsF">List of production cars by power output</a></li></ul>
<h2 id="bibliography">Bibliography</h2>
<ul><li>Böge, Wolfgang (2017), Alfred Böge (ed.), <i>Handbuch Maschinenbau</i> (in German), Wiesbaden: Springer, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-658-12528-8</li></ul>
<ul><li>Böge, Alfred (1972), <i>Mechanik und Festigkeitslehre</i> (in German), Wiesbaden: Vieweg, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9783528140106</li></ul>
<ul><li>Kemp, Albert W. (1998), <i>Industrial Mechanics</i>, American Technical Publishers, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780826936905</li></ul>
<ul><li>Fred Schäfer, Richard van Basshuysen, ed. (2017), <i>Handbuch Verbrennungsmotor</i> (in German), Wiesbaden: Springer, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-658-10901-1</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Böge 2017. p 233 - Böge, Wolfgang (2017), Alfred Böge (ed.), Handbuch Maschinenbau (in German), Wiesbaden: Springer, ISBN 978-3-658-12528-8 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Fred Schäfer, Richard van Basshuysen 2017. p. 21 - Fred Schäfer, Richard van Basshuysen, ed. (2017), Handbuch Verbrennungsmotor (in German), Wiesbaden: Springer, ISBN 978-3-658-10901-1 <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Böge 2017. p 233 - Böge, Wolfgang (2017), Alfred Böge (ed.), Handbuch Maschinenbau (in German), Wiesbaden: Springer, ISBN 978-3-658-12528-8 <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Böge 1972. p 154 - Böge, Alfred (1972), Mechanik und Festigkeitslehre (in German), Wiesbaden: Vieweg, ISBN 9783528140106 <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Kemp 1998. p 259 - Kemp, Albert W. (1998), Industrial Mechanics, American Technical Publishers, ISBN 9780826936905 <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
</ol>

Engine power open-in-new

Engine power