Calculating fractal parameters from low-resolution terrain profiles

Driver comfort on rough terrain is an important factor in the off-road performance of wheeled and tracked ground vehicles. The roughness of a terrain has typically been quantified by the U.S. Army as the root-mean-square elevation deviation (RMS) of the terrain profile. Although RMS is an important input into many mobility calculations, it is not scale invariant, making it difficult to estimate RMS from low resolution terrain profiles. Fractal parameters are another measure of roughness that are scale invariant, making them a convenient proxy for RMS. While previous work found an empirical relationship between fractal dimension and RMS, this work will show that, by including the cutoff length, an analytic relationship between fractal properties and RMS can be employed. The relationship has no free parameters and agrees very well with experimental data - thus providing a powerful predictive tool for future analyses and a reliable way to calculate surface roughness from low-resolution terrain data in a way that is scale invariant. In addition, we show that this method applies to both man-made ride courses and natural terrain profiles.