CJ: In your book and talk you refer to classical wing theory including Bernouilli's principle, downwash and wing tip vortices, as the explanation of the generation of lift of a sail. Is this correct?
BDA: The physical origin of lift for an airplane wing or a sail or a keel has been discussed for about 100 years now. What I presented in my short book on the physics of sailing is "classical" lift theory. The basic physical understanding is hard to arrive at. I refer people to the excellent book by Ross Garrett entitled, "The Symmetry of Sailing" for a detailed attempt to do this. In Chapter 3 Garrett 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 it 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. This approach is what engineers use to calculate lift; but it does not provide a clear physical description of lift. A good website discussing lift for a wing (or sail or keel) is provided by A. Gentry, The Origins of Lift.
CJ: I get your point. But isn't it difficult to explain the Physics of Sailing, when "the basic physical understanding is hard to arrive at"?
BDA: What I tried to do in my book entitled "The Physics of Sailing Explained" was to talk about how sailboats work including the limitation of hull speed, the basic kinds of resistance, the basic principles of how sails and keels work, and how all this comes together to enable a sailboat to move through water, including moving up to within 30 to 45 degrees off the direction of the wind. The detailed description of lift is both beyond what I was trying to do there and is something many existent books already discuss in more appropriate detail. This is also a topic of research and discussion in great detail for airplane wings of course, and even more attention has been applied to this question in that context. See, for example, the text "Foundations of Aerodynamics," by Kuethe and Chow. I believe my book works well at pointing out and explaining a number of important physical considerations for sailing and seems to have been well received in that way.
I have found that a number of persons have very strong opinions on how sails work, including those who feel that it is all "Newtonian Mechanics" and is just due to air molecules bouncing off the sails. This effect is certainly involved, but saying that it is only this ignores the fact that air is a fluid with interactions between the molecules (called Van der Waals forces). If one can reduce the pressure on one side of the sail, the higher pressure on the other side, without any wind needed, will cause there to be a force exerted on the sail toward the low pressure side. Because a moving fluid produces a drop in pressure, as measured experimentally and explained by Bernoulli, causing the air to move faster over one side of the sail will produce this kind of difference in pressure.
For a sailboat moving directly downwind, the Bernoulli effect is small and most of the driving force comes simply from air molecules hitting the back of the sail. As the direction of sail moves more into the wind, the Bernoulli effect becomes larger and eventually dominates. As Fig. 3.2 in my book shows, for moving at an angle forward of 90 degrees into the wind direction, the drop in pressure on the leeward (downwind) side of the sail is much greater than the rise in pressure on the windward side of the sail.
Persons advocating the "Newtonian" approach will note that airplanes can sail upside down, even with asymmetrical wing shapes; however, they do this by flying at a bit of an angle, called the angle of attack, which has the effect of still producing a longer path over the "up" side of the wing and leading to the Bernoulli effect again. (See my description of how this works for symmetrical keels in water flow.) Clearly, as speed increases, say to jet plane speeds, it does not need much of an angle of attack and the wings become more symmetrical in cross section (just as keels are). Early descriptions of air flow around a wing assumed that the flow over the curved top, with the longer path had to arrive at the back of the wing at the same time as the flow under the bottom of the wing, with a shorter path. Since it is a longer path over the top, the air flow had to be faster to arrive at the same time as the flow beneath the wing. Wind tunnel demonstrations with "smoke" in the air clearly shows that the air flow over the top is faster, but that it still does not arrive at the back of the wing at the same time as the air flow under the bottom; in fact the difference in time leads to the idea of "circulation" of air flow around the wing.
Putting all of this together, in order for a wing (or sail or keel) to provide lift, there must be a net deflection of the air downward behind the wing; it is then the reaction force to this downward deflection of the air that is the lift provided to the wing. This downwash is seen in the photo of Fig. 2.8 in my book. The reaction force is applied to the wing through the pressure increase on the bottom and the pressure decrease on the top. The downward deflection of the air and the reaction force on the wing is a "macroscopic" description, while the pressure differentials on the wing is a more "microscopic" description of how the reaction force is applied.
CJ: Thanks for detailed account of your standpoint. You connect lift to reaction from downwash, which is obvious, but you don't explain why there is downwash, right?
BDA: Downwash occurs from the redirection of the air flow past the wing (or sail or keel). In usual wing theory (see again the text by (Kuethe and Chow, Chaps 4-6) this is explained in terms of the circulation of fluid flow around the wing. Because the air flows faster over the top and slower past the bottom, there is a net circulation of air around the wing. This is called the "bound vortex." (Bound in the sense that it stays with the wing. When the wing starts moving, a reverse vortex is formed called the Starting vortex.) The circulation of the bound vortex provides the net downward flow of air from the wing which we call the downwash.
Now again, those who advocate the Newtonian approach will say this is just due to the air molecules bouncing off the bottom of the wing; however, a downwash occurs even if the wing is moving through the air with the flat bottom exactly parallel to the oncoming air. The air moving over the curved top will move faster and create the circulation to provide the downwash. Now, at the same time, one can talk about the air following the shape of the wing because it is a viscous fluid, with interactions between the air and the wing and between the air molecules themselves. These forces (the Van der Waals forces again) will cause the air to follow the shape of the wing, resulting in a downward flow from the back of the wing, all in a way consistent with the circulation theory. If the angle of attack is made too steep, or there are too many obstructions on the wing surface, the flow will leave the surface of the wing (it is said to "separate") and the circulation pattern, and hence the downwash, will be reduced and the lift will decrease. The overall downwash pattern is affected also by the tip vortices at the end of the wing (or sail or keel) reducing the lift and this is called "induced drag," and is discussed also in my book.
CJ: OK, so you say that lift comes from downwash, which comes from circulation, right? From where does then circulation come? Compare with Why It Is Possible to Sail.
BDA: I indicated in my last response how circulation arises. Your website shows that you have thought a lot about how wings actually work. It will take me awhile to digest all that you present there.
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