When sailing into the wind the lift creates a force on the sail that makes a cross section of the sail look like the Nike swoosh. For a given wind speed, sail size, and angle of attack, the equation of the slope should always look the same. I believe another assumption that needs to be made is the linear density of the sail, but I'm not sure. I looked at the differential equation for a telephone wire hanging between two telephone polls and tried to equate the relationship of the shape of a sail this way. One way I tried to do it was by showing the lift and drag vectors as two different forces acting at different angles. Another way was adding the Lift and Drag vectors and applying them at the combined angle. So far I haven't been able to derive a differential equation that works. What's bothering me is there is clearly a relationship which means there has to be an equation. Even if it's a messy one. I can provide more information if you need it, but any insight with the information that I've already given would probably be the most beneficial. Thanks in advance!