I think sailing into the wind works because you divide the force of the wind into components twice. Dividing into components first one way and then another lets

I think sailing into the wind works because you divide the force of the wind into components twice. Dividing into components first one way and then another lets you pull some tricks. The first time comes from the sail, you divide the wind into a component flowing along the sail (doing nothing), and one that is perpendicular to it (pushing it) Then you take the perpendicular-to-the-sail part and divide that into a side-ways (drift) and a forwards component (propulsive). The side ways one is neutralized by the keel. Btw I kinda wonder if a rotatable keel tuned just right would allow sailing right into the wind...