Power Spectral Density of Road Profiles

The road profile is usually considered to be a random process x (d), where x is the road height and d is the distance along the road. As the vehicle travels along the road with velocity v, the random process x (d) is converted to a random process x (t) which is input to the vehicle suspension via the tyre. The random process x (d) is usually described in terms of its power spectral density as a function of frequency in either radians or cycles per unit distance. However, there are several different ways of defining power spectral density, and this makes it difficult to compare published data without knowing how the power spectral density has been defined. The proper calculation of RMS values of vehicle response for an assumed road power spectral density is explained by an example.