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HW14 - downwash is computed at the point(x 2 y j in the...

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AAE 334, Fall 2011, Homework 14 Due Monday, October 3 at the beginning of class. Building on homework 11: Consider a single horseshoe vortex of span i b centered on the origin of the coordinate system, 0 , 0 , y x , in the z=0 plane as shown below in a view from above the wing. The strength of the vortex is i . We wish to formulate a solution to be computed for the induced drag on a wing of span i b b that is created by the downwash of the upwind wing. That is, the downwash of the second wing on itself is covered in the text we will add that in for a computer project. For this assignment, compute the induced drag assuming: Density is constant and is called Flight velocity is constant and is called V Both wings are in the z=0 plane The second wing is centered at the point (x 2 , y 2 ) and has circulation distribution j y The second wing is divided into N equal-length segments along the span and the
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Unformatted text preview: downwash is computed at the point (x 2 , y j ) in the center of each of these segments. For this assignment, assume the values of y j are known (you will derive the y j values in the first part of your computer project). So, 1. find the downwash at y j , written as a function of x i , y i , i , x 2 , y j , and j (applying the result of the first part of HW 11 might be a good start) 2. then find the induced drag per span at y j , (note the sign correction from the lecture of 9/30) 3. multiply by the length of the spanwise segment to get a drag force on that segment, 4. add up all the induced drags on the segments to get total drag. Steps 1, 2, and 3 can be solved analytically, assuming that i , j , and y j are known. Step 4 is a summation over N segments. (see figure on next page) x y A i y=b i /2 y=-b i /2 B i (x j , y j ) (x 2 , y 2 ) j...
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