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Assume the motor on the vertical reel is fixed, and the entire base of the reel rotates on the bottom plate. If both of these hose reels weigh the same amount, will the vertical reel require the same amount of force to rotate as the horizontal reel? Or could the vertical reel be rotated using a less powerful motor?

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Unless you're doing something very wrong, the majority of the torque generated by the motor will be used to overcome the force required to pull the hose onto the reel.

So, assuming that the application for both of these reels is the same — i.e., they're reeling up the same kind of hose under the same circumstances — the torque required will be the same.

Any secondary effects related to the reel bearings, etc. should be miniscule relative to that.

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