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 ".