• Journal of computational fluids engineering
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• v.18 no.3
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• pp.42-50
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• 2013

The supersonic airplane with flapped biplane, Busemann biplane equipped flap, is superior to drag and noise reduction due to wave cancelation effect between upper and lower airfoils. In this study, it is numerically calculated and analyzed the lift, drag and lift to drag ratio of flapped biplane with respect to various the length and angle of the flap. Euler solver of EDISON CFD, web based computational fluid dynamic solver for the purpose of education, is employed. Depending on the length of the flap, lift and drag increase linearly, and there exists the optimum flap angle which maximize the lift-to-drag ratio at the freestream mach 2.0 on-design condition. The predictable relational expression is driven as liner equation. As a results of comparison with drag of flapped biplane, Busemann biplane, and diamond airfoil with the same lift, the drag of flapped biplane is 88.76% lower than that of the Busemann biplane and 70.67% lower than that of the diamond airfoil. In addition, the change of pressure is compared to confirm the noise reduction effect of flapped biplane at h/c=5 of lower airfoil. The shock strength of flapped biplane is smaller than that of other airfoils.

• Journal for History of Mathematics
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• v.28 no.3
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• pp.133-149
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• 2015

Arrivals of Hilbert and Minkowski at $G\ddot{o}ttingen$ put mathematical science there in full flourish. They further extended its strong mathematical tradition of Gauss and Riemann. Though Riemann envisioned Finsler metric and gave an example of it in his inaugural lecture of 1854, Finsler geometry was officially named after Minkowski's academic grandson Finsler. His tool to generalize Riemannian geometry was the calculus of variations of which his advisor $Carath\acute{e}odory$ was a master. Another $G\ddot{o}ttingen$ graduate Busemann regraded Finsler geometry as a special case of geometry of metric spaces. He was a student of Courant who was a student of Hilbert. These figures all at $G\ddot{o}ttingen$ created and developed Finsler geometry in its early stages. In this paper, we investigate history of works on Finsler geometry contributed by these frontiers.