engine power

Power is the product of torque and angular velocity:{{Harvnb|Böge|2017}}. p 233

Let:

• $P=$ Power in Watt (W)
• $M=$ Torque in Newton-metre (N·m)
• $n=$ Crankshaft speed per Second (s⁻¹)
• $\backslash omega=$ Angular velocity = $2\backslash pi\; n$

Power is then:

:$P=\; M\; \backslash cdot\; \backslash omega$

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

:$P=\; M\; \backslash cdot\; 2\; \backslash pi\; \backslash cdot\; n$

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:

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

The approximate numerical value equations for engine power from torque and crankshaft speed are:{{Harvnb|Böge|1972}}. p 154{{Harvnb|Kemp|1998}}. p 259

Let:

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

Then:

:$P=\; \{M\; \backslash cdot\; n\; \backslash over\; 9550\}$

• $P=$ Power in Metric horsepower (hp, PS)
• $M=$ Torque in Kilopondmetre (kp·m)
• $n=$ Crankshaft speed per Minute (min⁻¹)

Then:

:$P=\; \{M\; \backslash cdot\; n\; \backslash over\; 716\}$

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

Then:

:$P=\; \{M\; \backslash cdot\; n\; \backslash over\; 5252\}$

{{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}}
The power curve (orange) can be derived from the torque curve (blue)
by multiplying with the crankshaft speed and dividing by 9550

|caption =

}}

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

Let:

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

Then:

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

or using the numerical value equation:

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

The engine's rated power output is 103 kW.

• List of production cars by power output

• {{Citation

| author-link =

| 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

| author-link =

| 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}}

{{reflist|colwidth=30em}}

Category:Mechanics

Category:Power (physics)

Category:Engines