Mathematical Analysis
The major forces involved with levitation are gravity and the magnetic force needed to oppose gravity in order to keep the train above the track.
There are several factors that contribute to the amount of magnetic force that will be felt by the train. They are current through the solenoid, the amount of turns, and the length of the wire. These terms are related by the following equation:
The approximate mass of a train is 50 tons which is 45,000 kilograms (1 ton = 2000 lbs.; 1 lb. = 0.45 kg). The magnetic force induced by the current flowing through the wire would have to oppose this force.
The other forces that need to be taken into account are the changing forces experienced by the train while going around curves and up or down hills. Maglev trains use the equilibrium between the like and unlike poles of the magnet in order to maintain the appropriate orientation with the track, even around sharp curves and on inclines.