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What is the distance between the tip of a fan blade and the inside of the nacelle for a turbofan like the Rolls Royce Trent 900? Does this distance change significantly during cruise due to thermal expansion?

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Can't say for sure without specific information from the manufacturer, which would be proprietary, but it's probably somewhere between 0.010" and 0.100". As you make the clearance tighter, you run the risk of a heavy rub between the blades and the case. But as you make the clearance more open, you lose efficiency. Somewhere in between there is a sweet spot where efficiency is fairly good and risk of a rub is low enough. The exact clearance may vary significantly between different manufacturers and models, depending on what type of blades they have.

And yes, this distances changes significantly as you go from idle to takeoff to cruise. Thermal expansion is a player, but most of it is mechanical loads (i.e. centrifugal force).

also, very minor point, but the clearance you are looking for is between the fan blades and the fan case. The nacelle is a separate structure that is outside of the case.

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