The ice skating analogy makes a lot of sense. But to me that’s more like how a propeller moves a motor boat with stored energy. A sailboat passes energy between the wind and water.
Another way to think about it (at the risk of being more confusing): the boat is capturing energy from the difference in momentum between the wind and the water. Imagine the water and wind flowing in the same direction, at the same speed. From the boats frame of reference that is equivalent to being in still water with no wind. No sailing going to happen. Only a motor boat with stored energy could move.
Think of a windmill facing upwind. The windmill is on little wheels connected to the windmill drive shaft by a chain or belt. You can imagine that you could drive the windmill slowly upwind. From the frame of reference of the windmill that’s the same as going downwind faster than the wind.
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