What are R4's and how do they work?

How do I work out how many/what kind of magnets I need over a certain area to repel a certain weight?

• Im going to design and build a small scale levitating board for a university project. Basically like the hover board from back to the future but using magnets. The scale floor area of my model will be lined with magnets, then the board itself would be lined with magnets set at the opposite polarity so it would effectively float across the floor area without friction. I need to know how to work out how many/what size/what pull/what kind of magnets I need to use in the scale model to repel a certain weight a certain height above the floor. I then need to give some real life values to these calculations to state what magnets I would use if I were to make the board on a life sized scale. For example, if I had a board 500mm x 250mm and wanted it to repel 250mm above the floor with a weight of 100kg on it, how do I work out what pull I need, therefore how many of what size magnets I need across the area given?

• Answer:

  The magnetic field strength between two magnets is the same attracting as repelling. So... you can measure the repelling force of one magnet against another very easily (if you have an appropriate scale). Put a piece of wood or plastic on the scale with the magnet on top. You want the wood/plastic spacer thick enough so the magnet is not "stuck" to the scale. Then tare the scale (so it reads zero). Take the second magnet, hold it so it opposes the magnet that is already on the scale (like you want it to when it is on the board), than force the magnet down until the the scale starts to read a "weight". This is the repelling force you are seeing. If you hold the magnet closer, the force goes up. So, you have to pick a "flying height", a distance you want the board to be above the floor. If the magnet on the scale keeps flipping upside down, use some tape to stick it to the spacer. One of your problems will be because the field strength drops very quickly with distance (if you double the distance, the strength drops by a factor of 4). In practice this means that, as one magnet moves off the top of the other, the magnetic field strength drops off very quickly. Suppose that when you hold the magnets 1 mm apart, the repelling force is 100 grams. If you want to keep the "flying height" at 1 mm and you want to float 1000 grams, you need 20 magnets (10 opposing pairs) but ONLY if all 10 pairs are immediately above each other. As soon as they move off the magnets below, the repelling force drops off. You can minimize this problem if your magnets are as close to each other as you can get them (a close packed array). Another practical problem will be the tendancey for the floating magnets to want to flip upside down. This can be counteracted by have a large board. Sounds like a very interesting project but I suspect you will find that levitating anything 25 cm off the floor is a tall order (pun intended). Good luck