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I am planning on creating a quad-copter with my Arduino that I have. I have created a few land robots before but no aerial vehicles, so this is all new to me. I was looking on the Internet for different models, and I see that most robots have 4 propellers. I have also seen a few hexacopters (?) and octocopters but that many propellers can't get a but out of hand. Does having 4 propellers the best and most efficient thrust to weight ratio, or will 3 propellers/arms work better?

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    $\begingroup$ Don't know about exact "efficient thrust to weight ratio", but the control system for tricopter will be a bit more complicated than quadcopters. If you can afford the extra battery power, hex or oct copters will give you more lifting capacity and better control over external disturbance. Usually, even number of propellors are easier to control than odd numbered arms. However, there are good many tri-copters out there. I've never heard of penta or hepta copters though! $\endgroup$ – metsburg Feb 15 '14 at 4:58
  • $\begingroup$ The smaller the prop the better controllability due to having less inertia. That is one reason for preferring more props. If you can't control the propeller’s pitch like a helicopter you won't be able to fly a 2 prop machine and 4 has a nice symmetry. $\endgroup$ – Guy Sirton Feb 17 '14 at 5:00
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Four fixed pitch propellers is one of the simplest configurations. The motors are mounted rigidly and the control of the vehicle is 100% electronic through controlling the speed of the propellers ( http://en.wikipedia.org/wiki/Quadcopter#Flight_control ).

With the classical two prop helicopter configuration you need pitch control for the main rotor. Let's say you have two blades on the main rotor you would need two additional actuators and you end up with a more complex and expensive design. I think you could get by without pitch control of the tail rotor but I'm not sure. ( http://en.wikipedia.org/wiki/Helicopter_flight_controls#Flight_conditions )

A tri-copter would typically need tilt control of the rear motor. ( http://en.wikipedia.org/wiki/Multirotor )

The basic physics of the situation is that in order to move freely around in 3d space you require certain degrees of freedom. A quadcopter is arguably the simplest mechanical design that provides those degrees of freedom. It's a trade-off.

In terms of additional propellers, the trade-off is often the inertia of a single propeller. Higher inertia means it's harder to change the speed of the propeller and so the vehicle is less agile and less controllable. Therefore to generate more lift more propellers are often a better choice than a larger propellers (if you stick with the premise of fixed pitch, fixed mount). Since adding one prop doesn't really make much sense you mostly see an even number of propellers.

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