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I mean that as the boom gets closer and closer to the centerline, the forward drive from the sails does not increase to infinity as your model predicts.

Depending on what you mean by "in line", I'm not sure I agree. But whatever, I agree that there's some point near "in-line" at which the sails luff.

Inline means that if the wind is moving paralel to the sail then the sail must luff and the boat can't accelerate.

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Can you give a formula for the way in which maximum speed you can go is defined by the ratio? And the ratio of what to what? length of boom / distance from boom to centerline?

Just like pitch on a propeller, look more closely at how that's defined and you may understand what I'm saying. Technically it's the Tangent of the angle of the sail given that 90 is close hauled (tan=infinity), and 0 when the sails are let all the way out (hitting the spreaders perpendicular to the centerline).

Perhaps it wasn't useful to bring this up but this forms the upper bound on speed. The point is that only wind coming off the side of the boat can be leveraged in this fashion and on a beam reach (or close to it) the coponenet of wind in this direction is maximized. This is more technical than necessary.

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They absolutely need to be discussed. Here's the limits you've mentioned:

1) Ignoring drag, there's no limit. Put your boom on the centerline; your boat will travel at infinite speed. Maximum of speed is based only on the angle the boom makes with the wind.

2) Obviously we can't ignore drag. So drag puts a limit.

All of your dynamical discussions and your analogies to propellers are only interesting in the discussion of point 1. You don't actually state a speed limit due to drag; you just state that there must be point where drag balances forward drive. Your source for this forward drive is the leverage effect which, according to point 1, can be made arbitrarily large.

If you want to talk about drag, you have to talk about lift as well. Lift and drag are two components of the force that the wind applies to the boat.

I get what you're trying to do; you're trying to talk about the kinematics of sailing without talking about the mechanics. That is, you're trying to describe the motions (wind moves across sails, sails move in relation to the wind) without discussing the underlying mechanism that causes that motion. That's a valid thing to do, but *your kinematics are completely wrong*. Your kinematic statement is "speed is determined by this ratio", which is clearly not true, and then you get around the obvious flaw in the kinematic description by referring to a mechanical one.

My point is not that your understanding of drag is wrong, but that the formula you give for speed in the absence of drag, and the analogy that it's motivates it, are useless. Since the "ratio" rule doesn't describe anything we observe, why use it at all?

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No. I'm trying to describe the simplest way to understand the mechanics for why a boat moves forward when wind hits it (the sail is at an angle to the wind, the wind hits it and deflects backwards, the keel prevents the boat from moving sideways and the boat has to go forward). You ignored my example of the iceboat with the steel sail which strips the mechanics of sailing down to the basics, removes lift (in the sense that there are no foils, perhaps you will still use term), and yet we still have a vessel that we both agree will move (I think).