Well, I tried to do a search on windmill boats but could find none, Ill have to take your word on how they work until you can provide a link explaining it. I find that to be very neat if it does actually do what you say it does. Power is defined as the amount of work per unit time, so I don't see why you mentioned power from the sail but energy from the river. I am probably not right, but I will give this a shot. The water boat system has energy relative to the observer on the shore. Neglecting the windmill for a moment, the boat would move at the same speed as the river. So it would have the same veloctiy. Its energy would be 1/2 mv^2. Obviously, the river had to loose that same amount of energy to give the boat that additional amount of energy. Note that hull friction is not an issue here because the boat is drifting and not pushing its way through the water. Now put in the windsail. Its going to see drag from the wind resistance, and that in turn is going to turn the sail, which via a shaft and gearing system will turn a propellor. Now that amount of drag to turn the propellor must be overcome by the river too. The river is pushing the boat forwards at at-most a speed equal to the river. And if you consider the drag in turning the windmill as a constant, then that amount of work the river lost in addition would be w=F(drag)*distance. You said it would give you at most 1/2 the speed of the river, I think that would depend on how efficent the windmill is in sending its energy to the propellor. Now I am really not sure what I am talking about and I am just making a lot of simplified guesses. Another thing to consider is that the windmill can't create energy outa no where. So I would think that the boat would speed up, slow down, speed up over and over again, because the river will cause the windmill to turn and create a small amount of thrust for a small peroid of time. But once the boat sails faster than the river, the river can no longer give it any more push that the speed with which the river flows. So now that drag from the windmill can't be compensated by the river, and it will slow down to the rivers speed again, and the process will repeat. Also, once the boats going faster than the river, the water relative to the boat has to be pushed out of the way to go faster than the rivers current, its not drifting along with the same velcoity as the river, so the hull will cause additional drag that the windmill propellor has to overcome to hold its faster than river speed. But I don't think the air can give any energy to the boat, if the air is STILL, then there is no energy in it to give up in the first place, it can only steal energy away when something moving through it creates turbulence. I am done guessing, hopefully someone smart can supply a real anwser now :-)
