# Car - Required Power and Torque

### Engine Power

Required power from an engine to keep a car at constant speed can be calculated as

* P = F _{ T } v / η (1) *

* where *

* P = engine power (W) *

* F _{ T } = 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 n _{ rps } ) *

* = 0.159 P / n _{ rps } *

* = P / ( 2 π (n _{ rpm } / 60)) *

* = 9.55 P / n _{ rpm } (2) *

* where *

* T = torque or moment (Nm) *

* n _{ rps } = engine speed (rps, rev/sec) *

* n _{ rpm } = 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:

* F _{ w } = F _{ T } *

* where *

* F _{ w } = 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:

* F _{ w } = F _{ T } *

* = (T η / r) (n _{ rps } / n _{ w_rps } ) *

* = ( T η / r) (n _{ rpm } / n _{ w_rpm } ) *

* = (2 T η / d) (n _{ rpm } / n _{ w_rpm } ) (3) *

* r = wheel radius (m) *

* d = wheel diameter (m) *

* n _{ w_rps } = wheel speed (rps, rev/sec) *

* n _{ w_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

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