How High Can The U-CAS Fly?

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 hm–the maximum hovering height of this top. We show that the bounds are of the form al0 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 l0 is a characteristic length, given by l0 ≡ μ0 4π μM0 mg . Here, μ0 is the permeability of the vacuum, μ is the magnetic moment of the top, M0 is the maximum magnetization of the base, m is the mass of the top, and g is the free-fall acceleration. For modern permanent magnets we find that l0 ∼ 1[meter], thus limiting h to about few meters.