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Is a longer, two-bladed propeller more efficient than a three-bladed propeller with a smaller diameter?

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As Troy E and Dave said, most of this question is already answered here.

In addition to this previous answer, just remember that a propeller is a technological solution to a simple question: how do we make the aircraft fly ? Therefore, there is no single solution, but multiple compromises that can be found depending on various parameters, mostly based on the type of operations the aircraft should take part in :

  • Speed
  • Altitude
  • Mass of the aircraft
  • FOD / injestion risks and tolerance
  • ...

Since your question only states the efficiency of the propeller, you actually miss at least part of the real problem. Let's say you manage to make a propeller with an efficiency of 1, but that it weighs 1 ton or is impossible to manufacture, you won't get far.

In that sense, only considering the efficiency to say what is the best solution is not good enough. The best solution is the best compromise between all of your requirements, that's why it is so difficult to find ;) !

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I don't have a definitive source, but I read this recently: "The rule of thumb is that you need 100 HP to justify each blade. Two blades are considered adequate through 200 HP. Three-bladed props seem to come into their own on efficiency at or above 300 HP. "

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