(Borcherts and Davis, “Force on a Coil Moving over a Conducting Surface Including Edge and Channel Effects, Journal of Applied Physics (1972))
The complexity of equations (like the one seen above) for the magnetic field produced by a real current-carrying loop with finite dimensions is why the perfect dipole approximation had to be made in the course of my research. Potentially, future work would involve using the equations for the “real” case and attempting to model the motion of trains that use these coils to levitate.
It’s very difficult for me.
What else materials about maglev systems, do you recommend to read?
There is such a clear progression from your proposal, through the problems with complicated equations and how you solved them, to your final model of the forces responsible for maglev train motion. I especially liked the diagram and your subsequent exposition that explained how EDS works. It did a good job of showing how the lift and drag forces relate to how and when the train passes over the coils in the track. Focusing on EDS was a good idea given the inherent instability of an EMS system. Your graphs were easy to read and the assumptions you made to create them were well-justified. It was interesting to see how the performance of the train increased as its speed increased and the drag force was overcome. I also enjoyed seeing the method of images brought back for a real world application because I didn’t know the method (which we now know about from EM 1) could be used to explain how maglev trains work. I think you have good plans for future work, especially the plan to do actual experiments with trains you build yourself and use the results to model the forces more exactly. Good work!
I found your project particularly interesting because, before this, I legitimately knew absolutely nothing about maglev trains. I loved being able to see the evolution of your project as you conducted more research and worked through the kinks in Mathematica. I like that you were able to make references to familiar concepts from previous physics classes like method of images, Faraday’s Law, and Lenz’s law instead of just skipping ahead to the more complicated equations. This helped to ground your math in a simpler reality. At the same time, I appreciate that you commented on these equations as sometimes being too simplified for the real world and that you would like to look into more realistic models for how these systems could potentially function commercially. Since this is still a developing technology, I want to assume that this would be a difficult topic to research, but you seem to have gathered a lot of really great material and I think you explained it in a readable way. In your presentation, you roughly sketched the differences between the main methods of maglev technologies, this really helped me to separate the concepts visually, so if I were to add anything to your blog it would be the diagrams you drew for us. Conclusion: nice project!