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Car - Required Power and Torque

Power, torque, efficiency and wheel force

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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

Engine torque or moment 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.

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