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As you can see in the video in the imgur link below i recorded a video of the Alouette 2 rear tail rotor and as you can see it moves freely in that direction. Why does it freely move in that direction, what is the purpose? Also just to clarify this is a different movement than when you press the pedals in the cockpit. when i used the pedals in the cockpit it moved the rear rotor in a different way than this, this is different than that. Is the purpose of this movement so that when there is an unexpected load on the rear rotor it can freely move and decrease the total amount of load absorbed by the rotor and lengthen the life of the rotor?

https://imgur.com/a/T26K5aE

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Those are flapping hinges that give the blade some freedom of movement in the flapping axis, to accommodate the variations in lift of the blade as it moves around while the machine is moving forward. It's the same function as the flapping hinges in the main rotor, but without the disc tilting function provided by the swashplate (as if the swashplate was fixed at neutral).

Having no swash plate, the geometric angle commanded by the input linkage of the blade is constant going around. The advancing blade that gets increased lift wants to flap "out", and the retreating blade that gets decreased lift wants to flap "in" to accommodate the increase and decrease of blade tip speed through the air while moving forward. The hinge accommodates that flapping motion.

There's also usually a geometric relationship built into blade's pitch change horn and the flapping axis itself that causes blade angle to decrease slightly when the blade flaps out from increased lift, and increase slightly when the blade flaps in from decreased lift. This reduces the amount of actual flapping movement required because the slight blade angle change induced by the flapping movement partially cancels out some of the lift change caused by the velocity change.

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