Bryon Anderson’s article on the physics of sailing provides a good introduction to the topic, but his discussion of wind-generated lift in sails, the effect that allows sailing to windward, leaves out the important concept of circulation. Anderson emphasizes the Bernoulli principle by explaining that the pressure difference between the upwind and downwind sail surfaces is due to the higher air speed on the downwind side. Anderson notes that “classic wing theory” ascribes the path length difference to asymmetry in the airfoil; however, the asymmetric airfoil is not a good model for sails because the path lengths along the upwind and downwind sides are almost the same. He points out that there are difficulties with classic wing theory and refers the reader to a NASA website. It is, however, well known by aircraft designers, and more recently by sailmakers, that lift is produced by circulation of air around the airfoil or sail and that viscosity plays a key role in its production. 1
The simplest example of circulation-induced lift is the spinning ball, an effect exploited by baseball pitchers and known as the Magnus effect. Instead of spinning, a sail produces circulation by its shape and angle of attack to the wind. Because of the angle of attack, initially the upwind-side airflow attempts to turn sharply around the sail’s trailing edge to rejoin the downwind flow. That sharp turn is resisted by the air’s viscosity, producing a starting vortex near the trailing edge. By the Helmholtz theorem, a counterrotating, or bound, vortex must be induced around the sail. The strength of the circulation around the sail is such that the air flows smoothly off the trailing edge, an effect known as the Kutta condition. When the Kutta condition is established, the starting vortex disconnects from the sail and is left behind. Circulation causes air that would otherwise flow upwind of the sail to be deflected to the downwind side; this upwash effect results in the longer path length responsible for the higher downwind-side air speed and pressure drop.