A physical perturbation based study on the prediction of free-fall disks with chaotic modes in the water

Abstract

We report a phenomenon that physical perturbations sometimes can benefit the certainty of a free-fall motion with chaotic modes, albeit, as commonly believed, they can ruin it. We statistically compare those factors that may lead to uncertainty, by which we find that the growth of the standard deviation of the landing locations is directly determined by the physical perturbations. A significant yardstick is defined in the meantime. This temporal criterion is of big relevance to the replicability of such problems experimentally, although they are inherently chaotic. Our hypothesis is verified by experiments from other literature. This outcome also provides a practical strategy to evaluate the credible prediction time by estimating the disturbances from physical parameters as a priori.