Upper bounds on the height of levitation by permanent magnets

The limitations on the levitation height obtainable using permanent magnets are studied. We find that with mechanical transverse stabilization and optimal distribution of magnetization of the (infinite) base a maximum height of 12l/sub 0/ is achievable for ideal magnets. Here, l/sub 0/=M/sub 0//sup 2///spl rho/g where g is the free fall acceleration, /spl rho/ the mass density of the levitated magnet and M/sub 0/ is the magnetization of the supporting base plate and levitated magnet. For uniform magnetization this height is only 3.5l/sub 0/. With levitation based on spin transverse stabilization mechanism an additional constraint enters into the problem and we find that the maximum achievable height is only 4.7l/sub 0/. The value of l/sub 0/ for the best magnet known to us is about 1.5 meters. Note, however, that because real permanent magnets are not ideal the above results are only upper bounds on the levitation height by permanent magnets.