Modeling of Dynamics of Land Boat Based on the Magnus Effect

Abstract

The motion of a wind powered land boat is studied. It is supposed that the land boat moves along a straight line in a steady horizontal wind flow. The axis of rotation of the Savonius rotor is vertical. The rotation of the Savonius rotors induces the Magnus force that maintains the motion of the load boat. Such vehicles can be used to perform transportation in large open areas, where there is an access to free wind. In this paper, the mathematical model of the land boat driven by the Savonius rotor is constructed. The quasi-steady approach is used to describe the aerodynamic action upon the system. Corresponding aerodynamic coefficients are approximated basing on experimental data. The angle between the wind velocity and the velocity of the boat is a varied parameter of the model. The equations of the model are presented as a dynamic system of the second order. The conditions of existence and stability of stationary modes of the dynamic system motion are obtained. It is described how the boat speed at steady motion depends upon the angle formed by the velocity of the boat and direction of the wind. In particular, it is shown that the maximum of the boat speed is achieved on the close-hauled course, that corresponds to the recommendations of the sail settings known in sea navigation.