The energy consumption of a car covering a given distance depends mainly on the speed of the vehicle. The faster a car drives, the more energy is required for propulsion. At higher speed the energy consumption of a car per unit distance increases proportional to the square of the speed. This is caused by the air drag which dominates over the tyre rolling resistance at high speeds.
Driving twice as fast therefore costs approximately four times as much fuel per unit of distance. The required power increases with the cube of the speed, so driving twice as fast costs theoretically eight times as much fuel per unit of time.
Fuel consumption by a traditional car causes air pollution by combustion. This air pollution produced over a given distance likewise increases quadratically with increasing speed. Neglecting details, reducing the speed from 130 to 100 km/hour entails theoretically that only a relative fraction of (100/130)2 = 0.59 = 59% of energy is expended, so that 41% less fuel is consumed over the same distance. This leads to a comparable reduction in air pollution from gasoline combustion.
Calculation
The energy for propulsion supplied by a car's engine is spent on: accelerating the car (abbreviated to ac), overcoming the air resistance (aerodynamic drag, dr), and overcoming the rolling resistance (rr). so that
The energy effects of wind, ascent and descent are not considered here, nor the repeated braking and accelerating when driving in a city.
Acceleration
The kinetic energy of a moving car with mass and speed can be calculated theoretically as
so for a car with a mass of 1,000 kg at a speed of 120 km/h (33.3 m/s)
(One kilowatt hour (kWh) equals 3.6 million joules (J).)
The required kinetic energy is supplied by the motor when the car accelerates starting from rest. It is lost when the driver brakes (unless the available kinetic energy is stored in, for example, a flywheel). Part of this energy can also be recovered from electric cars via recuperative braking and can be stored in a accumulator.
In practice, the real energy consumption of a car depends on many additional factors, including the traffic situation and personal driving style. In order to be able to make comparisons, standardized consumption tests have been devised, driving cycles, such as the New European Driving Cycle (NEDC) and the newer Worldwide harmonized Light vehicles Test Procedures (WLTP).
Without any resistance or friction, by Newton's First Law a car with speed would continue at this speed forever. However, air drag and rolling resistance cause energy losses which must be overcome to drive at a constant speed.
Air drag
Depending on its surface area , streamlining and speed , a car moves a lot of air, which causes energy loss by the aerodynamic drag force. We can imagine the moving air as a tube (trunk) of air behind the car, with a volume of the cross-sectional area of that tube times the length, which equals the distance traveled by the car. This length is then equal to the car speed times the elapsed time. The effective cross-section of the air tube is less than the front surface of the car , for example due to streamlining. This can be taken in account by introducing a drag coefficient for the air resistance of about 1/3. Suppose the surface area of the wind shield of a car is
then the effective volume of that tube of swirling air behind the car, after a period of driving at speed equals
with = the distance traveled. The mass of the displaced air over a journey of meters is equal to the volume of the tube times the specific mass of air, so .
The energy loss due to air resistance is equal to the kinetic energy that the car imparts to the air.Using the value of for the density of air results in
Rolling resistance
The mathematical formula for the force due to the rolling resistance of the car tyres is:
with
the roll coefficient which is around 0.01. the mass of the car, and the gravitational acceleration.
The corresponding energy loss caused by the rolling resistance is (the work done by the rolling resistance)
,
with the distance covered, so the energy spent on overcoming the rolling resistance per unit distance is a constant.
Total energy consumption to overcome friction
Adding up the energy consumption required to overcome both air drag and tyre rolling resistance, we have
From the graphs it is seen that per unit distance the drag resistance dominates over the rolling resistance at higher car speeds.