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ChapterV.PartI - Chapter V Handout#1 Prandtls Lifting Line...

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Chapter V. Handout #1 Prandtl’s Lifting Line Model In this handout we look at how the forces on a wing of arbitrary shape can be computed. By arbitrary shape we mean that the chord c(y) may have any general function, and that the twist distribution θ (y) may be any general function. We are interested in computing lift force L and the drag force D, the spanwise distribution of lift, and moments. x y C(y) b In the figure above the semispan is given the symbol ‘b’. the total span is, thus, 2b. The wing area is given the symbol S. The ratio (span^2)/wing area = (2b)^2/S is called the aspect ratio. Commercial aircraft have a large span, and high aspect ratio, between 9 and 11. Gliders may have even larger aspect ratio, around 15 or so. Figher aircraft, for agility in roll purposes, have a short span, and a low aspect ratio. The theory we will use is by Prandtl. He assumed that, at each span station, all the vorticity over the wing embedded in the boundary layer may be lumped at a single point, at the quarter chord as a point vortex Γ . Of course, the magnitude of Γ will vary depending on which span station we are talking about, i.e. Γ is a function of y.
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