jfm
Well-Known Member
Not sure I buy the curved fins concept despite JFMs very thorough and initially convincing explanation. I can believe the side effects bit, but not the getting the better axis bit.
One way I like to test any theories I have is to extrapolate and see where that takes me. In this case I would extrapolate the curvature to 90 degrees and in that case the end of the fin would sweep through the water longitudinally and therefore provide no benefit at all. From that I would reason that even if you could argue that the angle of the vector is better, it would lose its intensity at a similar rate therefore undermining that overall benefit. I suspect that the net effect would therefore considerably less than you might expect with the logic that I think I understand from JFM.
I like your thinking in your second para, the extrapolation approach. (I'm not sure what to say about your first paragraph, as this is Newtonian physics not religion, so "believing" doesn't come into it!
So if you extrapolate as you say, to the point where you have a flat fin whose face is angled 90deg to the shaft, then yes you have zero effective surface area, and the things would indeed be useless as you say. 100% agreed.
But your words following "From that" do not follow from the words that precede them. The reduction in effective surface area of the fin caused by angling it follows a cosine curve (Cosine of 0 degrees is 1; cosine of 90 degrees is zero, but the points in between are not a straight line). At a modest angle you have made a big change to the direction of the antiroll vector (because that IS a linear relationship) but you've made only a small reduction in the effective surface area of the fin (because it is in the first half of the cosine curve). In other words, I'm very much disagreeing with your "at a similar rate" , but agreeing everything else that you wrote.
Once you jettison the flawed (imho) "at a similar rate", you can easily see, by intuition or maths, that the interaction between (a) the positive thing namely the improvement in the direction of the anti roll vector and (b) the negative thing namely the effectively reduced surface area of the fin, results in a humped graph. As you move from the current world of fins that are parallel to their shaft, to our imagined useless fins that are at 90 degrees to their shaft, antiroll torque rises, then peaks, then falls to zero, AOTBE. These new Sleipner fins are of course close to that peak
That is I believe firmly based on your approach to how to think about this (though feel free to disagree if I've misunderstood you) and it is exactly what happens in practice.
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