How High Can The U-CAS Fly?

Abstract

The U-CAS is a spinning magnetized top that is levitated in a static magnetic field. The field is produced by a permanent magnet base, positioned below the hovering top. In this paper we derive upper and lower bounds for h - the maximum hovering height of this top. We show that the bounds are of the form a*L where a is a dimensionless number ranging from about 1 to 12, depending on the constraints on the shape of the base and on stability considerations, and L is a characteristic length for the problem. For modern permanent magnets we find that L=~1[meter], thus limiting h to about few meters.