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hw12 EMA521

# hw12 EMA521 - of w d What is the advantage of Fying in...

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November 8, 2011 1 EMA521, Fall 2011, Assignment 12, Due 12/1/2011 1. The simplest description of a bird of mass m flying in air at V is given by a single horseshoe vortex, with a bound vortex of length b equal to the bird’s wingspan and two semi-infinite trailing vortices (see sketches in the back). a) Calculate the downwash w 0 induced by the trailing vortices alone at the midpoint of the bird’s wingspan. Now consider three identical birds, all of mass m and wingspan b , flying side by side, with negligible space between the wingtips of two adjacent birds. b)If each bird is still described by a single horseshoe vortex, what is the simplest description of the three birds flying in formation? Draw a sketch of your model. c) Calculate the downwash induced at the midpoint of each bird’s wingspan and express it in terms of w 0 . d) What is the advantage of flying in such fomation?

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Unformatted text preview: of w . d) What is the advantage of Fying in such fomation? Now let the middle bird move ahead of the other two by a distance d and model the three-bird system with a single vortex line (made up of straight segments with a few right angles between them). ²or convenience de±ne r ≡ d/b . e) Sketch the new vortex line. f) Show that the downwash at the midspan of the middle bird is w M = p 1 3 + 1 2 √ 4 + r-2-1 6 √ 4 + 9 r-2 P w and that the downwash at the midspan of the left and right birds is w L = w R = p 3 5-1 4 √ 4 + r-2 + 1 12 √ 4 + 9 r-2 P w g) Using a computer, ON THE SAME PAGE, plot w M /w vs. r and w L /w vs. r . h) What is the advantage of this formation with respect to the previous one? November 8, 2011 2 Figure 1: Bird models...
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hw12 EMA521 - of w d What is the advantage of Fying in...

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