Geometry of Sailmaking

The aerodynamic force developed by a sail depends on the sail's shape. The horizontal cross-sectional shape is of particular importance in determining sail performance. Two parameters for describing the shape are presented and three methods of measuring the shape are outlined. The current practice of using edge rounding and broadseaming is de­scribed and four solutions to the problem of creating faster shapes are presented. First, the pragmatic approach which uses an interative search for the fastest edge round and broadseam pattern is examined. Three other approaches that model the sail as a mathematical surface and use geometry to compute the patterns are presented. Here the sail is treated as a stack of horizontal arcs with precisely defined shapes. In one method, a path excess equation is used to calculate the luff round for a mainsail. Another approach plots the geodesic paths on the sail's surface and computes the seam­by-seam broadseaming. Lastly, an integral method is employed to find the broadseaming for a sail based on the Penguin mainsail. Measurements of the sail made by this method are presented and discussed.