I am building a free flight helicopter for a Science Olympiad competition, and the general rules are as such: https://www.soinc.org/sites/default/files/uploaded_files/Helicopters_2017_Diagram.pdf
This leaves a lot of opportunity for math that is well beyond my ability, so my questions are as such:
You get scored based on how long the craft stays in the air, but you can get 25% added (up to 75% total) for each single bladed rotor, is a single bladed rotor a worthwhile investment?
I have tried using an airfoil shaped wing at the regional competition, and it failed because of how heavy it was, but people have been suggesting a helical blade shape, what are the mathematical advantages of this over a flat rotor.
The central shaft has no given dimensional restriction, what is the optimum length of the core?
Thanks in advance.