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 of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.
Related Documents
Bodies Moving on Inclined Planes - Acting Forces
Required forces to move bodies up inclined planes.
Car - Traction Force
Adhesion and tractive force between car wheel and surface.
Car Acceleration
Car acceleration calculator.
Car Fuel Consumption - liter/100 km
Calculate fuel consumption in liter per km - consumption chart and calculator.
Centripetal and Centrifugal Acceleration Force
Forces due to circular motion and centripetal / centrifugal acceleration.
Drag Coefficient
The drag coefficient quantifies the drag or resistance of an object in a fluid environment.
Driving Distances between European Cities
Driving distance between some major European cities.
Electrical Vehicle Charging - Power vs. Voltage and Amps
EV Charging - AC vs. DC, single phase vs. three phase and power vs. voltage and amps.
Formulas of Motion - Linear and Circular
Linear and angular (rotation) acceleration, velocity, speed and distance.
Fuel Consumption - mpg
Calculate fuel consumption in miles per gallon - mpg - calculator and consumption charts.
Impact Force
Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.
Improvised Torque Wrench
Improvise a torque wrench with a luggage scale.
Impulse and Impulse Force
Forces acting a very short time are called impulse forces.
New vs. Old Car Costs: A Comprehensive Cost Comparison
Compare the total cost of owning a new car versus an old car, including purchase price, maintenance, fuel efficiency, insurance, and depreciation. Use our detailed breakdown to make an informed financial decision before buying the next vehicle.
Piston Engines - Compression Ratios
Cylinder volume and compression ratios in piston engines.
Piston Engines - Displacement
Calculate piston engine displacement.
Rolling Resistance
Rolling friction and rolling resistance.
Toggle Joint
A toggle joint mechanism can be used to multiply force.
Vehicle - Distance Traveled vs. Velcocity and Time Used (mph)
Speed (mph) and time (hours) and distance traveled (miles) chart.
Vehicle - Distance Traveled vs. Velocity and Time (km/h)
Speed (km/h) vs. time (hours) and distance traveled (km).
Vehicles Traffic Flow and Density
Traffic flow and density as used in highway design.