Ollie:

A lot of times, when you're designing something, someone else has derived the formula and you can look it up. For me, it helps to have done at least some of the calculus, which makes it easier to re-derive when I forget part of the formula. Not that I remember all that much calculus any more. Having derived formulas in the past is probably good for my garbage detector. If you slip a digit when plugging numbers into a formula, it's helpful to recognize when the results are absurd.

The other day a friend of mine called me because he was all excited that he'd figured out how to store useful amounts of electrical power* in flywheel. At reasonable rpms. He was going to power his house that way, I think with charging from solar cells. It turns out almost anything is feasible if you move the decimal point enough places. BTW, I'm not saying it's impossible to store lots of power in flywheel, just that some exotic materials and very sophisticated engineering will be required. I think some utilities use fancy flywheels for evening out short term surges or sags. One constraint is the strength of materials. The stronger the flywheel, the faster you can spin it and the more energy it stores. Or releases if it breaks and causes an explosion.

Anyway, one handy source of these formulas is Machinery's Handbook. The formulas might just lead you down the primrose path, but it may be useful to compare your calculations to the results from FEA.

Anyway, to design an entire ultralight from scratch, backed up with calculations, may be a really large project for high school. It may be better to look at a bunch of designs, pick one, and figure out what needs to be different to suit your purposes. Or you could pick some subset of the design task.

Has anyone mentioned Mike Sandlin's designs in this thread? I don't know if they've been rigorously analyzed, but I think the ones on line have flown. The drawings have lots of info in them and show ways of doing things that have been shown to work.

*Comparable to batteries or better.