Aerodynamics & Engineering
Wow, I'm impressed. I used to work for Columbia helicopters as a design engineer. We flew Boeing model 107 and 234 (civilian versions of the Sea Knight and Chinook) helicopters for logging, fire fighting, construction, etc. I got a supplemental type certificate to convert the 234 bladder tanks to wet-cell type. I was also exposed to airframe, engines, transmission, flight controls, electrical, hydraulics, and avionics. I've taken more helicopter rides than I care for.
You should make this a research project. Start with the original Igor Sikorsky technical papers and work your way through to modern technology. The flight controls on a tandem rotor, for example, are very interesting. The whole discovery of gyroscopic precession as it relates to helicopter control is also interesting. I think Igor discovered/invented the lead-lag and flapping hinge and subsequent dampers. Then there is the engineering behind power, gearing, rotor diameter, rotor speed, tail rotor speed, and on and on.
Good luck.