A wheel or axle load is the instantaneous force applied by a tire or the series of tires of an axle on the road. This force varies along the road and depends on the static load, the pavement evenness, and the vehicle speed and suspension. A WIM sensor measures this force at a given section (abscissa). This force may differ from the static wheel or axle load by 5%, 10%, 25% and up to 100%. The ratio (impact or dynamic force / static load -1) is the dynamic impact factor (DIF). Lighter the static load higher the absolute value of the DIF.
The average impact force along the vehicle path tends to the static load. Therefore, sampling the impact force of a wheel/axle at several road sections and combining these measurements may give a better estimate of the static load, e.g. the simple average or any other estimate. That is the principle of the multiple sensor (MS-)WIM. The number and spacing of the sensors should be adapted to the impact force signal characteristics, above all the eigenfrequencies, but also amplitude and phase.
For a simple sinus model of the impact force, with a mean frequency f, and a mean velocity V, a uniform sensor spacing d was proposed by Cebon and Winkler depending on the number of sensors N:
It was shown in the WAVE project that with 10 to 12 “perfect” sensors and an advanced algorithm (Sainte-Marie), the theoretical accuracy of the static load estimator may be 2%. However, because of the intrinsic errors of any WIM sensor and other external factors, the experimental results showed accuracies between B+(7) and B(10) for 6 to 12 sensors, with individual sensors in the accuracy class C(15) (COST323).
