Stochastic Theory of Human Slipping

The conventional approach to human slipping is essentially deterministic; it states that no slipping will occur when the average friction coefficient is greater than some critical friction criterion. Under this condition, pedestrians will not slip when they encounter the average friction coefficient. On the other hand, to successfully negotiate a walk of n-steps they must not slip when they encounter the smallest of the n friction coefficients. Consequently, a new slip theory has been formulated as a problem in extreme value statistics. An elegant relationship is obtained among the probability of slipping, the critical friction criterion, the number of steps taken by the walker, and the central measure, scatter, and asymmetry of the distribution of friction coefficients. The new theory reveals the structure of human slipping in a startling way that introduces completely new concepts: the go/no go nature of classical slip predictions is replaced by a probability of slipping; low friction floor/footwear couples may lead to fewer slips than high friction ones; slipping can occur in any case where conventional theory predicts “no slip”; and the number of slips depends on the distance traveled by a pedestrian. Finally, this paper develops the idea that the slipperiness of a real floor must be evaluated for a duty-cycle. Duty-cycles can be represented as frequency histograms when a floor is homogeneous and isotropic.