Anderson replies: I agree with almost everything in these two letters concerning the generation of lift by an airfoil. The fact that lift is described by “circulation” around a foil has been known for almost a century, since the introduction of the Kutta–Joukowski theorem. Reference 2 in my February article discusses circulation in mathematical detail.
The article as originally submitted contained a brief reference to circulation and lift. However, I decided that lift for a foil would need to be presented in detail elsewhere. I used the space available to discuss the application of lift to sails and keels and the concepts of resistance, induced drag, hull speed, and so forth, that determine how a sailboat performs. I did provide a quick review of “classical” lift theory while indicating that the basic physical understanding is hard to arrive at. I refer the reader to Ross Garrett’s attempt to do that in his book The Symmetry of Sailing. 1 In chapter 3 he outlines three ways for understanding lift. First is the “flow line method,” which describes classical lift theory and arrives at Bernoulli’s principle applied to a foil. Garrett’s second way, “momentum change,” emphasizes that macroscopically a foil must have the net effect of deflecting the fluid flow in order to derive lift. That is obvious, but must be appreciated. His third way to understand lift is the “mathematical approach,” which introduces circulation, using several fluid flow theorems leading to the Kutta–Joukowski theorem. That approach is what engineers use to calculate lift, but it does not provide a clear physical description of lift. Several websites discuss lift. 2
I am aware that airflow around a foil is not isochronal. I was careful not to say that it is. The flow over the “top” is faster and arrives at the end of the foil sooner than the flow along the “bottom.” That difference in flow times leads to circulation. Because the flow is faster over the top, the pressure is reduced, as verified by measurement—which I did mention. Whether that is the cause of lift or the consequence of circulation becomes, I think, a matter of semantics.
