> road damage scales as the fourth power of the axle weight Is there a theoretical basis for this? It looks like the "fourth power law" comes from an empirical

> road damage scales as the fourth power of the axle weight Is there a theoretical basis for this? It looks like the "fourth power law" comes from an empirical test conducted in the 50s: https://en.wikipedia.org/wiki/AASHO_Road_Test https://en.wikipedia.org/wiki/AASHO_Road_Test However, that article says: > ...critics point out that its data is only valid under the specific conditions of the test with regard to the time, place, environment, and material properties present during the test. Extrapolating the data to different situations has been "problematic".[3] Other studies have attempted to refine the results, either through further empirical studies, or by developing mathematical models, with varying success. I have some intuition for why certain physical systems would scale quadratically or cubically, but where on earth is the quartic scaling coming from here??