How would you design an electromagnet for maximum force when you have a fixed power available?

Question

There are number of variables like current, wire dia, number of turns, dia and length of electromagnet. The distance at which force is applied is constant

The distance is nearly 12 inches. Power is nearly 88.4 KW. The electromagnet should be not more than a few meters at max. Weight is not much of an issue. Calculation is not needed just need an idea on how to select the optimum values of variables. The formula I am using is F=(mu)(n*I)^2/2g^2 mu= permeability

The project is about use of regenerative braking to charge electomagnets to attract the rails. This force is being utilised to avoid derailment during train emergency braking. Just a college project in analysis not any research.

Answer 1

First, identify your magnetic circuit. Is that 12" distance air? Or perhaps it's 2x12" for out and return. If it's air, then that will be a key limiting factor in how much H field you get for your Ampere.Turns (AT).

Next, can you use an iron core for the magnet? If so, that limits the air gap to the 12" necessary for the geometry of your situation, gives you complete freedom for the form factor of the coil, and makes it (relatively) easy to calculate the coil H field. If not, your AT are going to be diluted over a larger distance through the coil as well, the coil geometry (short&fat or long&thin) must be optimised as well, and the H field must be approximated or got through integration.

Next, how long must the magnet operate for? Short enough that the 88kW can be absorbed in heating the coil, or longer, so you must consider cooling?

Finally, set up a spreadsheet. Create cells for wire size, coil length, I/D, O/D, and from those compute copper mass, length, resistance, AT, thermal capacity and so operating time without cooling. Then depending on whether you have an iron core or not, use a very simple approximation, or a more complicated approximation, for the field due to the magnet. And start playing with the variables.