Sail shape and mathematics

If a sail is fastened at its foot and luff, the cut of the sail alone does not determined its shape. For this geometry, an “ideal” sail shape is generally not obtainable.

However, if one could fasten all points of the sail edge to a rigid structure, one could essentially determine the entire sail shape. The only requirement is that the sail must have positive curvature (be cup-shaped, not flat and not saddle-shaped) at each interior point.

Thanks to Warren Smith for pointing out this oversight.  The mathematics of this is based on work by Cauchy, Pogorelov and Alexandrov.

5 Responses to “Sail shape and mathematics”

  1. i am into sailing and i am also a diy fiberglass sailing boat enthusiasts for 5 years now. i really love sailing.:;:

  2. Evan Nelson says:

    i love to sail even if we do not have our own sailboat “*”

  3. sailing is funstuff, i wish i could afford a fast sailing boat,~`

  4. Leon Murray says:

    sailing is just like jogging, it is an addictive sport and hobby at the same time :~’

  5. Mike Casdi says:

    The rigid sail with (positive) airfoil curvature would be more efficient, but it is not necessary for lift. Airplanes with their wings designed for optimum lift fly upside down at airshows every weekend. We can generate lift from a piece of plywood or even a negatively curved sail shape… just not as efficiently. The lift to drag, L/D, ratio goes way down.

Leave a Reply