Car - Required Power and Torque
Engine Power
Required power from an engine to keep a car at constant speed can be calculated as
P = FT v / η (1)
where
P = engine power (W)
FT = total forces acting on the car - rolling resistance force, gradient resistance force and aerodynamic drag resistance (N)
v = velocity of the car (m/s)
η = overall efficiency in the transmission, normally ranging 0.85 (low gear) - 0.9 (direct drive)
For a car that accelerates the acceleration force must be added to the total force.
Example - Car and required Engine Power
The required engine power for a car driving on a flat surface with constant speed 90 km/h with an aerodynamic resistance force 250 N and rolling resistance force 400 N and overall efficiency 0.85 - can be calculated as
P = ((250 N) + (400 N)) (90 km/h) (1000 m/km) (1/3600 h/s) / 0.85
= 19118 W
= 19 kW
Engine Torque or Moment
Motor torque vs. power and rpm can be calculated
T = P / (2 π nrps)
= 0.159 P / nrps
= P / (2 π (nrpm / 60))
= 9.55 P / nrpm (2)
where
T = torque or moment (Nm)
nrps = engine speed (rps, rev/sec)
nrpm = engine speed (rpm, rev/min)
Example - Car and required Engine Moment
The moment delivered by the motor in the car above with the engine running at speed 1500 rpm can be calculated as
T = 9.55 (19118 W) / (1500 rpm)
= 121 Nm
Wheel Force
The total force (1) acting on the car is equal to the traction force between the driving wheels and the road surface:
Fw = FT
where
Fw = force acting between driving wheels and road surface (N)
The traction force can be expressed with engine torque and velocity and wheels sizes and velocities:
Fw = FT
= (T η / r) (nrps / nw_rps)
= (T η / r) (nrpm / nw_rpm)
= (2 T η / d) (nrpm / nw_rpm) (3)
r = wheel radius (m)
d = wheel diameter (m)
nw_rps = wheel speed (rps, rev/sec)
nw_rpm = wheel speed (rpm, rev/min)
Note that curved driving adds a centripetal force to the total force acting between the wheels and the road surface.
For power required for inclination - check car example at the end of "Forces Acting on Body Moving on an Inclined Plane".
Related Topics
• Dynamics
Motion - velocity and acceleration, forces and torque.
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