Wouldn't it be smarter to design VTOL rotorcraft with many smaller rotors than one big rotor? With more rotors you have more redundancy and smaller blade velocity (and perhaps better stabilisation) thus leading to a safer more reliable system. It seems like the problem with lots of rotors is that you lose all efficiency. I don't get this though. If a rotor prop produces x thrust at y efficiency, couldn't this be simply scaled up to produce the same thrust and efficiency ratio?
Rotors need something to power them and the current generation of aircraft (once you get bigger than model size) burn hydrocarbons to get that power. If you want twelve rotors, then you either need twelve engines or you need a smaller number of engines plus a bunch of heavy driveshafts and gearboxes.
I assume from the fact that most contemporary aircraft designs use a small number of engines (usually one or two; sometimes three or four) that having a few larger engines is generally more efficient than having more smaller engines. This seems to apply equally to jet engines, turboprops and piston engines.
It's possible that the tradeoffs will change if you move to electric motors. However, at the moment, batteries are so heavy that electric motors don't seem to be a practical option.
The problem with many propellers is that more of the propeller slipstream will flow around wings and tail. The higher local flow speed might be beneficial if you want blown flaps, but for regular flight and especially in hover it will increase viscous and pressure drag without any benefit. This will reduce overall efficiency when the number of propellers goes up.
Generally, one single, big item can be made more efficient than many small ones.
