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The real question I have is how does this rotating the mast do anything. The hook is attached to the mast, the sail lot is attached to the mast the sail is attached to the sail lot and the ring is attached to the sail very close to the slot, so how does this rotating change any of the geometry.
Yes, but the mast can rotate independently of the sail, so it's angle can be changed in relation to the angle of the sail - one of the beauties of a rotating rig. So when you rotate the mast during the sail hoisting process, you are able to change the position of the hook (which is fixed to the mast) in relation to the position of the ring (which is fixed to the sail). Rotating the mast gives you the ability to swing the hook under the ring or away from the ring, depending on whether you are trying to raise or lower the sail.
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This same point has me thinking about the comments "dead into wind" what if you are off by 15 degrees do you not just rotate the whole thing those 15 degrees and things are fine?
Up to about 10 or 15 degrees, you may be ok, but the closer to head to wind that you are, the more consistant and more easily the system will work. When we are talking about rotating the mast to hook or un-hook the sail, we are talking about roataing the mast somewhere around 90 degrees relative to the sail. If the sail is blown to one side or the other, then you may not be able to physically rotate the mast far enough to get the hook to do what you want it to.
sm