On the physics and mechanics of a medieval trebuchet, a type of catapult, its design, working and optimization through improved simulation and mathematical analysis.
Building a trebuchet from scratch and finding the best proportions, weights, angles etc by trial and error certainly works ..well, that's how the Grey Co's first machines were done... but if you could model the rock-throwing beasts mathematically then think of the work and possibly wasted effort you could save.
Besides giving away to charity, most rich people waste their money on boring, frivolous things such as yachts, diamonds, and mansions.
Here's a rich English guy that knows how to have fun. I hope he does build a bigger one. I would like to see a flying double-decker bus.