The initiation of rotational motion of a lying object caused by wind gusts

Abstract

In this paper, the initiation of motion of an object lying on a horizontal floor due to the aerodynamic force produced by a time-dependent wind is considered. It is assumed in this paper that when the aerodynamic force is large enough, the body starts to rotate around the most rearward supporting contact point, or pivoting point. This motion is analyzed by studying the dynamics of the rotation of the body around a pivoting point fixed to the floor, and placed in a gravity field under time-dependent aerodynamic loads produced by a non-steady incoming flow. This rotation initiation phase, which is relevant in the case of a time-varying gusty flow, is an intermediate phase between the two stages generally considered, namely, the initial static equilibrium without motion, and the final flight. In this intermediate phase, which is studied here, the rotational dynamics of the body should be taken into account and the gust characteristics as well, in order to determine whether once initiated the motion it leads to either a frustrated motion or to a successful one. A non-linear mathematical model has been developed, and a linear approximation is deduced, which allows us to obtain the condition for a successful flight. This condition shows two limits, valid for either long or short duration gusts, respectively. Some experiments have been performed in a gust wind tunnel, and results show a satisfactory agreement. To take into account the intrinsic random character of the phenomena in practical situations, expressions for the probability of exceeding the condition for successful flight under short duration gusts are obtained, assuming common probability density functions for the random parameters involved.