Luff curve is basically the feature that makes your downhaul effective. Take a curved edge of a piece of fabric and fix it to a straight mast, the mast is going to force belly/shape into that fabric. The more you tension the downhaul, the more bend is induced into the mast. As the mast bends, it more closely matches the curve of the fabric (luff curve) and so shape/belly is reduced. That is the basic concept, anyway.

If you want to see an extreme example of luff curve, look at any modern windsurfing sail, they have a huge amount of luff curve. Loosen the downhaul and the amount of draft gets huge. Tighten the downhaul/bend the mast and the sail becomes lean and fast.

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