Let me try to explain myself this way
Sorry David, I didn't see the above post when I responded to Jon's post. I'm not trying to belittle or trivialize your points.
I'll try to address these points, because I too am having fun.
There is no problem with sailing across the river in 10 knots of current generating 10 knots apparent wind. When the boat is being controlled by the water movement, it can use the wind to sail at a right angle to the apparent wind. Let's say the river is very wide so we can set the boat on a broad reach across the river and agree that the boat is efficient enough to achieve 3 times the wind speed in VMG. So now, the boat is sailing perpendicular to the current at about 28.3 knots while also moving down stream at 10 knots so that the vector sum across the river bottom equal 30 knots. We can, at this point, agree to this dynamic. I don't think anyone has argued against this part.
To break out the components of the wind we can take the overall velocity as the hypotenuse of a right triangle with heading (the direction the bow is pointing) as one leg, and river generated wind as the other leg.
900 (30kt^2)-100(10kt^2)=800(28.3kt^2).
This moves the angle of the apparent wind ahead of the beam and apparent wind speed is (800+100)^(1/2)=30 knots. Exactly the same as the velocity because there is 0 true wind. (Note: we are also treating this problem as if there is 0 leeward movement from the wind of 10 knots with perfect lateral resistance).
Now, if the boat changes course to fall off the wind (begin a turn up stream), the 10 knot vector moves aft of the beam, assuming the river movement still has influence on the heading and movement of the boat that has come up onto her foils.
This has the effect of reducing the apparent wind because some component of it now gets subtracted from the apparent wind total. This means that our boat can't sail 30 knots any more. She loses some headway. Her new heading vector constantly gets reduced and apparent wind falls with it.
Now look at the vector components of the wind. The more you turn away from the apparent wind to turn upstream, the farther the component vectors diverge from each other and there is no longer a lateral component to resist. Forward movement stops. Even if the boat were to remain efficient enough to travel at 3 times the wind speed for most of her points of sail, she can't do it going with the wind, which is what sailing upstream is effectively doing. Her only wind component becomes the 10 knot current driven breeze that will fill her spinnaker, but not move her upstream.
-Will (Dragonfly)