# 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 = 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

Engine torque or moment 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.

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