The number of cars available on our planet is continuously increasing. But also other factors are important for the emissions and the energy consumption: How efficient is the motor of the car? How much fuel does it consume on a certain distance? How long are the distances the car owner goes per year in average? What driving style does the driver exhibit? What is the average speed?
The energy needed for optimal consumption of a car is not easy to calculate. The most simple physical equation for the description of accelerating a body of the mass m from the velocity v = 0 to the velocity v is the kinetic energy equation:
The energy required to accelerate a body increases with the mass of the body and with the square of the velocity gained. We can deduce this formula from four simple physical expressions:
a) work / energy = force × distance (E = F × s) b) force = mass × acceleration (F = m × a) c) acceleration = change of velocity with time (a = dv/dt) d) velocity = change of distance with time (v = ds/dt)
If we change the velocity from 0 to v the energy invested over the distance s is given according to:
The SI unit of an energy is 1 Joule [J] according to:
If the velocity of a mass is increasing continuously in time, which means 1 m/s after 1 second, 2 m/s after 2 seconds, we have a constant acceleration of 1 meter per second squared. The force needed for this acceleration depends on the mass itself. If the mass is 1 kg the required force is 1 Newton (N) = 1 kg × 1 m/s2. The total energy required or the work we have to carry out depends on over which distance we exacerbate the accelerating force. If it is one meter, the energy is 1 kg m2/s2 = 1 Joule.
1. Illustration of Newton's second law of motion by LEIFI (Ernst Leitner, Uli Finckh)
Resistance
Generally we can say that for low energy consumption a car should be light and the velocity should be low. Since energy needed increases with the square of the velocity more energy is required to bring a car of the same mass to the twofold speed than to bring a car of the double mass to the same speed.
The energy required in reality, however, is more complicated, because processes do not occur in a vacuum under ideal physical conditions. We have two consider friction slowing down the car in two ways:
a) the contact of tyres with the road b) the contact of the auto body with the air
- In order to reduce the friction with the road the correct pressure in the tyres is important, which optimises the contact area of the rolling wheel. The higher the pressure the less the friction. However, if you go to the uppermost limit the wheels becomes very hard. This could damage the under-carriage, since the tyre does not buffer anymore the unevenness of the street. - In order to reduce the aerodynamic resistance two things are important: the drag coefficient Cd of the car, which is given by its shape and the speed with which you go.
Aerodynamic drag increases with the square of speed. You can strongly feel the resistance of the air if you go fast in an open car. This resistance is called drag and has the unit of a force. More than 60% of the power required to cruise at highway speeds is taken up overcoming air drag, and this increases very quickly at high speed, according to the drag equation.
The drag D [Newton] increases with the desity of the medium, the square of the velocity, the frontal area A of the car and the drag coefficient Cd. The drag force can be calculated according to the following equation:
Air drag equation:
A vehicle with substantially better aerodynamics will be much more fuel efficient.
Aerodynamics can be measured in a dimensionless constant, the drag coefficient Cd. This Cd-value is for modern passenger cars in the range of 0.30 to 0.35, for Sport Utility Vehicles (SUVs) with their flat fronts in the range of 0.35 to 0.45. It can go down for sport cars to 0.25.
5. The front area A in the drag equation can be calculated from the shadow a car makes on a projection screen if parallel light is shone perpendicular to its front.
A factor which cannot be influenced by yourself, but only by the developers of cars is the optimisation of the combustion process in the motor. Clear progress has been made in this in the recent years, but often companies follow the clients wish to increase the power in parallel, so that the improvement in fuel consumption is often lost.
Power is work per time or the energy conversion rate. The higher the power (measured in Watt) of a car is, the more energy can be converted per time. This allows for example a higher acceleration but also increases the fuel consumption significantly.
If going on high speed we should consider, that the energy needed to accelerate the car quadruples with a doubling of the velocity and also the air drag quadruples with double velocity. Therefore, a car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). Twice the speed requires eight times the power.
