• #### Archimedean screws and systems for raising water, from Leonardo da Vinci, Codex Atlanticus, f. 26 v. Milan, Biblioteca Ambrosiana.

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# Flow around airfoils

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Lifting bodies (airfoils, hydrofoils, or vanes) are intended to provide a large force normal to the free stream and as little drag as possible.

If the chord line between the leading and trailing edge is not a line of symmetry, the airfoil is said to be cambered. The camber line is the line midway between the upper and lower surfaces of the vane. The angle between the free stream and the chord line is called the angle of attack. The lift L and the drag D vary with this angle. The rounded leading edge of airfoils prevents flow separation there, but the sharp trailing edge causes a separation which generates the lift. At a low angle of attack, the rear surfaces have an adverse pressure gradient but not enough to cause significant boundary-layer separation.

As the angle of attack is increased, the upper-surface adverse gradient becomes stronger, and generally a separation bubble begins to creep forward on the upper surface. At a certain angle of attack, 15 to 20°, the flow is separated completely from the upper surface. The airfoil is said to be stalled: Lift drops off markedly, drag increases markedly, and the foil is no longer flyable.

Early airfoils were thin, modeled after birds’ wings. The German engineer Otto Lilienthal (1848–1896) experimented with flat and cambered plates on a rotating arm. He and his brother Gustav flew the world’s first glider in 1891. Horatio Frederick Phillips (1845–1912) built the first wind tunnel in 1884 and measured the lift and drag of cambered vanes. The first theory of lift was proposed by Frederick W. Lanchester shortly afterward. Modern airfoil theory dates from 1905, when the Russian hydrodynamicist N. E. Joukowsky (1847–1921) developed a circulation theorem for computing airfoil lift for arbitrary camber and thickness. With this basic theory, as extended and developed by Prandtl and Kármán and their students, it is now possible to design a low-speed airfoil to satisfy particular surface-pressure distributions and boundary-layer characteristics. There are whole families of airfoil designs, notably those developed in the United States under the sponsorship of the NACA (now NASA).

Prof.
Michele Mossa
PhD
Professor of Hydraulics at the
Polytechnic University of Bari
POLYTECHNIC UNIVERSITY OF BARI
DICATECh
Department of Civil, Environmental, Land, Building Engineering and Chemistry
Via E. Orabona, 4 - 70125 Bari - ITALY

www.dicatech.poliba.it

LIC
Coastal Engineering Laboratory
Area Universitaria di Valenzano