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To design a quadcopter there are 4 main types you can decide to implement

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What are the advantages and disadvantages of each of these types?

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'H' gives you the shortest arms, minimum drag, and the lightest frame if all parts of the frame were the same strength. However a strong X frame with a lighter frame for the camera and other light component means that forces are transmitted directly between the motors with the minimum weight.

'+' is rarely used, as it puts a motor directly in front of the camera

'V' (and 'squashed X', 'dead cat' and other variants) are compromises that reduce the separation of the motors to save weight and drag. Their pitch and roll rates and response can be slightly different but the flight controller generally compensates very well. The general aim is shorter arms, while keeping the props clear of the camera view.

The first two also demonstrate 'props in' or normal rotation, and 'props out' or reversed rotation. The first used to be common, but reverse is now common as it can push leaves and small twigs, race gates, etc, out of the way if you just clip them, rather than pulling them in towards the quad. This gives you slightly less chance of crashing in these environments. It can also changes whether the props throw grass cuttings onto your camera lens or flight controller. The first can obscure your view, the second is harder to clean.

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