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# 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 ρ V 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 ρ V 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 + S c d ) which is a suitable alternative objective function.
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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 eﬀect 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 stiﬀness-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 δ/ = 0.2 δ/ = 0.05 δ/ = 0.01 V max = 16 Figure 1: Objective function contours (isolines) in design space of a rectangular wing. Dot shows the stiﬀness-constrained optimum point. 1...
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