OK, I have been thinking about this, and can offer some arguments.
Thesis: sailing dynamics cannot possibly be affected by any constant current. (We're talking about constant, not changing currents so far because it's simpler. I think actually that everything we have been talking about is the same with changing currents, but we'll get to that later if we need to.)
Here's one vivid way to visualize it:
A current is relative
motion of water and land. We obviously don't care about the earth's spinning on its axis, or passing around the sun, or the universe expanding, now do we? Did anyone claim we get a lift from sailing towards the direction of the sun? Of course not.
OK, so once we are clear that we're talking about relative motion, then we can conceptualize this motion in either a geocentric or hydrocentric way, right? That is, we can conceptualize the land being still and the water moving, or we conceptualize the water being still and the land moving, although nothing is actually still, of course -- the "stilness" of the land is purely conceptualization, as the earth is spinning, etc.
So let's try thinking hydrocentrically for a change, which as I argued above is going to make more sense mathematically and probably conceptually for this problem. That is because for purposes of how our boats sail, the water IS still. We move in water; everything we do except running aground and laying marks is relative to the water, and it is not so hard to imagine the shoals moving towards us and the marks moving around out there. In particular -- crucially, for this discussion -- when we sail, using the wind, we are sailing in the relative motion
between wind and water. We simply cannot understand the sailing part if we conceptualize both water and wind moving at the same time -- we get an idiotic confusion. This confusion disappears when we make the water hold still in our minds.
OK, so now we have rounded some mark, and are heading towards the windward mark, and the tide is running. What does this look like?
The windward mark is moving relative to us, and so in order to work out how to lay it, we can't just head
straight towards it, or tack towards it, we have to calculate the expected vectors of the mark's motion, so we know which way to go. That's an ordinary Course to Steer calculation. Without this, we don't even know where we're going, and we're screwed before we start.
Now that we have a Course to Steer, we know where we're going. That is to say -- we have Point "B" in the water
, which we have to lay in order to lay the windward mark. We must have some point in the water
to sail towards, because we can't sail towards a point fixed to the land -- we're sailing through water, after all. The Course to Steer calculation does the translation from a land coordinate to a water coordinate, if you like.
OK, so Point "B" in the water is that place where the windward mark will be when we get there (by the way, this definitely works with a changing current as well as a constant one).
Now!!! Delete the windward mark from your mind. It is no longer relevant. We are at Point A in the water -- in water which we conceptualize as being still. We have Point B in the water. We have wind, which is constant in speed and direction in relation to the water (true speed and direction, which is what we sail in).
How do you get from Point A to Point B? Sail as usual -- it's a straight line in our hydrocentric world. All tacks relative to this straight line work just like any tacks anywhere. That is to say -- if we can't lay Point B on one tack, then the fastest way to get there will be by maintaining the highest VMG to windward at all times and on both tacks which means, for God's sake, no pinching, what a perversion.
So we sail, ignoring the mark itself, which we have deleted from our minds. If our Course to Steer calculation was perfect, then the mark (which is moving
relative to the water, which we conceptualize to be still!) will arrive at Point B simultaneously with us. In reality, the CTS calculation will not be perfect, so we will have to correct, but that does not detract from the point.
The motion of the seabed relative to our boat cannot
affect sailing dynamics. It is utterly and categorically impossible. Sailing dynamics are purely and solely determined by the relative motion between air and water.
This is not the only way to conceptualize the problem, but I suggest it is the easiest. You cannot conceptualize sailing dynamics at all if you can't conceptualize the relative motion between air and water. You can't conceptualize this -- and can't do any math with regard to it -- without conceptualizing one or the other of the media to be holding still. So it can't be the land!
I think we just can't work the problem conceptualizing the land to be still.