spl4a - + S c d ) which is a suitable alternative objective...

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± Design Variable Concepts 4 Mar 06 Lab 4 Lecture Notes Addendum Alternative Objectives Frequently, an engineering design problem will involve competing objectives. For example, an alternative objective to minimize flight power (or maximize duration), is to maximize the maximum-attainable flight speed. The level-flight power relations still apply to this flight con- dition, but now the power is a known quantity, and equal to the maximum available power onboard. C 2 CDA 0 η p η m P max = 1 ρV 3 S + c d ( C L min ; Re max ) + L min (1) 2 max S π eAR 2 W/S where C L min = 2 ρV max This can be solved for V max , or equivalently C L min , by numerical means if necessary. If one can assume that at V max the induced drag is negligible, and c d is some constant, then we have 2 η p η m P max ± 1 / 3 V max ( AR, S ) (2) ρ ( CDA 0
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Unformatted text preview: + S c d ) which is a suitable alternative objective function. The gure shows the isolines of V max versus the design variables, calculated using (1). The slight upturn in the isolines for decreasing AR is the Re eect in c d . The sharp downturn near AR = 0 is due to the induced drag term. Isolines computed using the approximation (2) would be level. Now the stiness-constrained optimum results in an unreasonably small wing, which means that other more practical constraints are likely to come into play. AR S 8 16 24 6 12 18 V max V max = 10 V max = 14 = 12 b b b / = 0.2 / = 0.05 / = 0.01 V max = 16 Figure 1: Objective function contours (isolines) in design space of a rectangular wing. Dot shows the stiness-constrained optimum point. 1...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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