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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:

  1. 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?

  2. 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.

  3. The central shaft has no given dimensional restriction, what is the optimum length of the core?

Thanks in advance.

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  1. Yes, even through a simple parallelization of a single-rotor design. If there's no other payload than the helicopter itself, and the challenge is for staying airborne, you gain about nothing performance-wise by adding more blades, but hey, +75% score. Go with quadcopter and four bands. Driving four rotors through a single shaft in line would be a hell of mechanics.

  2. Single-bladed airfoil will mean the blade is way off-center, introducing hopeless torque. If your single blade is a full turn of a helix, its center of mass is dead in the axis of rotation. It's not really beneficial aerodynamically but it's a way to cheat center of mass into rotation axis with the contrived "single blade" restriction through making the blade big.

    The airfoil gives a decent lift to mass ratio at higher airspeeds, but you won't get high airspeeds from a rubber band. You must buy your lift with wing surface area - and the helical blade will give you that. The blade doesn't need to be THAT big for that, but that's one way to make center of mass and axis the same.

  3. It will likely be dictated by many factors - keeping the rubber band tension, minimizing mass, keeping center of mass low enough. I don't think you can find a good formula for it. It's something that should be found experimentally.

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