Summary
The induced drag of non-planar wings is compared to that of planar wings which result from unfolding the non-planar ones. It is shown that due to the induced lift, there exist non-planar configurations with positive span camber that have an overall aerodynamic performance increase in comparison to the planar ones. The induced lift and increment of aerodynamic performance increases with decreasing aspect ratio. The effect is opposite for configurations with negative camber. Without the induced lift, the positive non-planar configuration would have more induced drag. Analysis is performed using a lifting line method, which takes into account the induced lift, and using Euler solutions. For the inviscid solutions, the induced drag is obtained with a far-field drag analysis method.
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References
Bourdin, P.: Numerical Predictions of Wing-Tip Effects on Lift Induced Drag, Thermal Control, Design, and Operation. In: ICAS 2002, Congress, pp. 223.1–223.10 (2002)
Büscher, A.: Flügelendformen zur Leistungssteigerung eines Langstrecken-flugzeuges, ZLR, Forschungsbericht 2008-06
Cone, C.D.: The Theory of Induced Lift and Minimum Induced Drag of Nonplanar Lifting Systems, NASA Technical Report R-139 (1962)
Destarac, D.: Far-Field / Near-Field Drag Balance and Applications of Drag Extraction in CFD. In: CFD-based Aircraft Drag Prediction and Reduction, Hampton (VA), November 3-7. VKI Lecture Series (2003)
Eppler, R.: Induced Drag and Winglets. Aerospace Science and Technology (1), 3–15 (1997)
Gold, N., Visser, K.: Aerodynamic Effects of Local Dihedral on Raked Wingtip. In: 40th Aerospace Science Meeting & Exhibit Reno, NV, AIAA-2002-0831
Heinrich, R., Wild, J., Streit T., Nagel, B.: Steady Fluid-Structure Coupling for Transport aircraft, Deutscher Luft- und Raumfahrtkongress 2006, Braunschweig (2006)
Horstmann, K.H.: Ein Mehrfach-Traglinienverfahren und seine Verwendung für Entwurf und Nachrechnung nichtplanarer Flügelanordnungen, DVFLR-FB 87-51 (1987)
Kroll, N., Fassbender, J.K. [Hrsg.]: MEGAFLOW – Numerical Flow Simulation for Aircraft Design. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol. 89. Springer, Heidelberg (2002)
Kroo, I.: Nonplanar Wing Concepts for Increased Aircraft Efficiency. VKI lecture series on Innovative Configurations and Advanced Concepts for Future Civil Aircraft, June 6-10 (2005)
Leyser, J.: Kraftberechnung an der nichtplanaren tragenden Fläche, Dissertation, Universität Stuttgart (1966)
Liersch, C., Streit, T., Visser, K.: Numerical Implications of Spanwise Camber on Minimum Induced Drag Configurations. In: 47th AIAA Aerospace Science Meeting, Orlando FL, AIAA 2009-898
Liersch, C., Wunderlich, T.: A fast aerodynamic tool for Preliminary Aircraft Design. In: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, BC (September 2008) AIAA-2008-95901
Lowson, M.: Minimum Induced Drag for with Spanwise Camber. Journal of Aircraft 27(7), 627–631 (1990)
Lundry, J.L., Lissaman, P.B.S.: Minimum Induced Drag on Non-planar Wings. J. Aircraft 5(1), 17–21 (1968)
Mangler, W.: Die Auftriebsverteilung am Tragflügel mit Endscheiben. Jahrbuch deutsche Luftfahrt-Forschung, S1149–S1157 (1938)
Munk, M.: Isoperimetrische Aufgaben aus der Theorie des Fluges. Inaugural-Dissertation, Göttingen (1919)
Ning, A., Kroo, I.: Tip Extensions, Winglets and C-Wings: Conceptual Design and Optimization. In: 26th AIAA Applied Aerodynamics Conference, Honolulu, Hawai, AIAA 2008-7052
Streit, T., Himisch, J., Heinrich, R., Nagel, B., Horstmann, K.H., Liersch, C.: Design of a Retrofit Winglet with Assessment of Cruise and Ultimate Structural Loads. In: 15th STAB/DGLR Symposium, Darmstadt. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 96 (2006)
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Streit, T., Visser, K., Liersch, C. (2010). Minimal Induced Drag for Non-planar Lifting Surfaces with Moderate and Small Aspect Ratio. In: Dillmann, A., Heller, G., Klaas, M., Kreplin, HP., Nitsche, W., Schröder, W. (eds) New Results in Numerical and Experimental Fluid Mechanics VII. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14243-7_67
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DOI: https://doi.org/10.1007/978-3-642-14243-7_67
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