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Optimum velocity for a person moving under rain

The total rain received by a moving body has previously been modelled by defining a wetness function. Several cases such as one-dimensional motion of an inclined plane, two-dimensional motion of an inclined plane, motion with time-varying velocity, inclined rain for an inclined plane, rain on a cylindrical surface and three-dimensional motion of a convex body were treated in detail. One of the major conclusions was that for a fixed distance, assuming vertical rain, the body should travel as fast as possible since the total wetness decreases with increasing velocity. The wetness function was shown to decrease asymptotically to a constant value as the velocity increases and in the high-speed range, increasing the velocity does not decrease the wetness substantially. One might think that the excess amount of energy required for a higher speed does not compensate for the small fraction of decrease in wetness. In this work, criteria are developed for a critical speed (optimum speed), for which the wetness is small enough for a reasonable energy consumption. Three cases are investigated: (1) vertical rain; (2) rain inclined towards the body; (3) rain inclined away from the body. In the first two cases, there is no absolute minimum for the wetness function and the optimum velocity is determined by special criteria. The third case is somewhat different, however, and if the inclination angle is higher than a critical value, an absolute minimum for wetness is obtained and the optimum velocity for this case is defined to be the velocity corresponding to this absolute minimum. Therefore the definition of optimum velocity is qualitatively different from the first two cases.