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HW12solution

# HW12solution - AAE 334 Fall 2011 Homework 12 SOLUTIONS Due...

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AAE 334, Fall 2011, Homework 12 SOLUTIONS Due Wednesday, September 28 at the beginning of class. 1. The first Boeing 787 is delivered to ANA today. It has a maximum takeoff weight of 502,500 pounds and a wing span of 197 feet. If we assume a take-off speed of 140 knots and an elliptical lift loading, then what is the value of the vortex strength distribution at the root of the wing? Density of the air is 0.0024 slugs per cubic foot. Ignore the fuselage. The elliptic lift distribution is 2 2 1 b y V y V y L o o o o . The area of an ellipse is the product of pi and the semi-axes: ab . So the total lift is (remember we have just the “upper half” of an ellipse) is 4 2 1 2 o o bV b V L  . Solving for vortex strength at the root gives us bV L o  4 . Lift equals weight (just before the 787 leaves the runway), so bV W o  4 .

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HW12solution - AAE 334 Fall 2011 Homework 12 SOLUTIONS Due...

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