Fourth power law

The fourth power law (also known as the fourth power rule) states that the greater the axle load of a vehicle, the stress on the road caused by the motor vehicle increases in proportion to the fourth power of the axle load. This law was discovered in the course of a series of scientific experiments in the United States in the late 1950s and was decisive for the development of standard construction methods in road construction.

Background
At the beginning of the 1950s, the American Association of State Highway Officials (AASHO) dealt with the question of how the size of the axle load affects the service life of a road pavement. For this purpose, a test track was built in Ottawa, Illinois, which consisted of six loops, each with two lanes. The lanes were paved with both asphalt and concrete of varying thicknesses. In the two-year test, trucks with different axle loads then drove the roads almost continuously. The test was called the AASHO Road Test. When evaluating the series of tests, it was found that there is a connection between the thickness of the pavement, the number of load transfers and the axle load, and that these have a direct effect on the service life and condition of a road. The service life of the road is thereby reduced with approximately the fourth power of the axle load.

The accuracy of the law of the fourth power is disputed among experts, since the test results depend on many other factors, such as climatic conditions, in addition to the factors mentioned above.

Calculation examples
This example illustrates how a car and a truck affect the surface of a road differently according to the fourth power law.


 * Car (total weight 2 tonnes, 2 axles): load per axle: 1 tonnes
 * Truck (total weight 30 tonnes, 3 axles): load per axle: 10 tonnes

$$10^4=10\cdot10\cdot10\cdot10=10,000$$ times as large

The load on the road from one axle (2 wheels) is 10 times greater for a truck than for a car. However, the fourth power law says that the stress on (damage to) the road is this ratio raised to the fourth power.


 * The road stress ratio of truck to car is 10,000 to 1.