Thank you for Bryon Anderson’s interesting and informative article, “The Physics of Sailing” (Physics Today, Physics Today 0031-9228 61 2 2008 38 https://doi.org/10.1063/1.2883908 February 2008, page 38 ). I especially enjoyed learning that the keel, not just the sail, acts to provide lift.
The article appears to adopt the traditional model: “An airplane wing is designed to cause the air moving over its top [the longer path] to move faster than the air moving along its undersurface.” In that model, the “cause” is often based on the assumption that flows over the top and underside of the wing are isochronal. That assumption has been shown to be false; the flow time over the top of the wing is considerably shorter than that predicted by the dictum of equal time. Thus the model does not explain why a longer path should lead to higher flow speed.
Other difficulties arise with the traditional model. It does not explain the vital concave-downward curvature of the flow. It does not accurately predict observed average speeds near asymmetrical, symmetrical, inverted, or thin airfoils. The model does not predict point-to-point speeds—that is, from low speed near the leading edge over the top of the wing, to high speed in the region of maximum airfoil curvature, to free-stream speed near the trailing edge. The possibility of directly measuring the pressures of interest, rather than circuitously using the Bernoulli principle to calculate them from flow speeds, is not addressed. Additionally, the traditional model calculates pressure gradients from the very air speeds that are caused by those pressure gradients. Thus the traditional model seems to suffer from circular reasoning.
The article mentions an alternative model—“turning of the fluid flow.” Indeed, airfoils are designed for establishing pressure gradients, which in turn result in observed changes in flow speed and direction, according to Newton’s second law. Reversing that statement to claim that the changes of flow speed and direction above and below the airfoil result in pressure gradients is simply not correct. Thus the idea that the higher-speed air over the wing causes lower pressure above it by the Bernoulli principle reverses the correct assignment of cause and effect. Likewise with Newton’s second law, net force causes acceleration; it is not correct to say that acceleration causes net force.
The model using Newton’s second law in impulse and momentum form provides a consistent explanation of lift by deflection of the air stream, a fact that is lost with the use of the scalar Bernoulli equation. In addition, when the correct cause and effect are used, the Bernoulli principle becomes irrelevant to the explanation of pressure gradients established by airfoils.
Parenthetically, Anderson’s question “whether the pressure difference arises entirely from the Bernoulli effect or partly from … redirection of the air” seems not to be meaningful. By any model, air must be deflected as a third-law reaction to lift.
