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solution3 - 650:460 Aerodynamics Homework Assignment No. 3...

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Unformatted text preview: 650:460 Aerodynamics Homework Assignment No. 3 Prof. Doyle Knight Tel: 732 445 4464, Email: doyleknight@gmail.com Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1 Problem 5.3 Using Eq (5.46) and treating C D o and k as constants, show that the lift coefficient for maximum lift/drag ratio and the maximum lift/drag ratio for an incompressible flow are given by C L | max L / D = radicalbigg C D o k L D vextendsingle vextendsingle vextendsingle vextendsingle max L / D = 1 2 radicalbig kC D o 2 Problem 5.3 Solution The drag coefficient of a finite wing is C D = C D o + kC 2 L and thus the lift/drag ratio is L D = C L C D = C L C D o + kC 2 L Differentiating with respect to C L and setting to zero d ( L / D ) dC L = 1 C D o + kC 2 L + C L (- 2 kC L ) ( C D o + kC 2 L ) 2 = 0 Solving C D o = kC 2 L 3 Problem 5.3 Thus C L = radicalbigg C D o k To confirm that this corresponds to a maximum, d 2 ( L / D ) dC 2 L =- 4 k 2 C 3 L ( C D o + kC 2 L ) 3 using C D o = kC 2 L Since this is negative, the value of C L corresponds to a maximum of L / D ....
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solution3 - 650:460 Aerodynamics Homework Assignment No. 3...

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