From Wikipedia, the free encyclopedia
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 .
Definition
Power is the
product of
torque and
angular velocity :
[1]
Let:
P
=
{\displaystyle P=}
Power in
Watt (W)
M
=
{\displaystyle M=}
Torque in
Newton-metre (N·m)
n
=
{\displaystyle n=}
Crankshaft speed per
Second (s−1 )
ω
=
{\displaystyle \omega =}
Angular velocity =
2
π
n
{\displaystyle 2\pi n}
Power is then:
P
=
M
⋅
ω
{\displaystyle P=M\cdot \omega }
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 }
:
[2]
P
=
M
⋅
2
π
⋅
n
{\displaystyle P=M\cdot 2\pi \cdot n}
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
=
M
⋅
2
π
⋅
n
60
{\displaystyle P=M\cdot 2\pi \cdot {n \over 60}}
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
=
{\displaystyle P=}
Power in
Kilowatt (kW)
M
=
{\displaystyle M=}
Torque in Newton-metre (N·m)
n
=
{\displaystyle n=}
Crankshaft speed per Minute (min−1 )
Then:
P
=
M
⋅
n
9550
{\displaystyle P={M\cdot n \over 9550}}
Technical unit system (MKS)
P
=
{\displaystyle P=}
Power in
Pferdestärke (PS)
M
=
{\displaystyle M=}
Torque in
Kilopondmetre (kp·m)
n
=
{\displaystyle n=}
Crankshaft speed per Minute (min−1 )
Then:
P
=
M
⋅
n
716
{\displaystyle P={M\cdot n \over 716}}
Imperial/U.S. Customary unit system
P
=
{\displaystyle P=}
Power in
Horsepower (hp)
M
=
{\displaystyle M=}
Torque in
Pound-force foot (lbf·ft)
n
=
{\displaystyle n=}
Crankshaft speed in Revolutions per Minute (rpm)
Then:
P
=
M
⋅
n
5252
{\displaystyle 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
{\displaystyle M}
of 234 N·m at
n
{\displaystyle n}
4200 min−1 , which is the engine's rated speed.
Let:
M
=
234
N
⋅
m
{\displaystyle M=234\,N\cdot m}
n
=
4200
m
i
n
−
1
=
70
s
−
1
{\displaystyle n=4200\,{min}^{-1}=70\,s^{-1}}
Then:
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}
or using the numerical value equation:
234
⋅
4200
9550
=
102.91
≈
103
{\displaystyle {234\cdot 4200 \over 9550}=102.91\approx 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
Bibliography
Böge, Wolfgang (2017), Alfred Böge (ed.), Handbuch Maschinenbau (in German), Wiesbaden: Springer,
ISBN
978-3-658-12528-8
Böge, Alfred (1972), Mechanik und Festigkeitslehre (in German), Wiesbaden: Vieweg,
ISBN
9783528140106
Kemp, Albert W. (1998), Industrial Mechanics , American Technical Publishers,
ISBN
9780826936905
Fred Schäfer, Richard van Basshuysen, ed. (2017), Handbuch Verbrennungsmotor (in German), Wiesbaden: Springer,
ISBN
978-3-658-10901-1
References