Dispersion radius of a magnus rotor

Abstract

A Magnus rotor is a small bomblet designed to have self-induced spin which generates Magnnus-type lift. The bomblet is a sphere, or sometimes an ellipsoid. Ridges are attached on the surface of the bomblet to impart spinning. The spin also arms the fuze so that the bomblet is ready to explode on impact. A large number of such bomblets are deployed at the predetermined altitude to spread over a wide area of the ground. To know the performance of the bomblet, an analysis is required for the dispersion radius of the bomblet. For this analysis, a free spinning wind tunnel model made of wood is tested in the KAIS subsonic wind tunnel. The Magnus force, the drag force, and the spin-rate at various wind speeds are measured. A non-spinning model is also tested to check the spin effect. And this shows that spin does not affect the drag coefficient very much. The obtained wind tunnel test data are compared with the results of a spinning bare sphere. This comparison shows a good qualitative agreement, though the quantitative values are different because of the difference of the shape. The equations of motion describing the flight of the bomblet are set up and non-dimensionalized for a general analysis. These non-dimensional equations of motion are analyzed by means of both the analytic method and the numerical calculations using the measured wind tunnel data. The following cases are studied in detail: (i) Falling in the still atmosphere with zero initial conditions. (ii) Falling with the initial velocity and the path angle. The above studies are concerned with only subsonic flight range. The motion of the bomblet is found to have a unique steady state regardless of the initial conditions.