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Numerical analysis of multiple, thin-sail geometries based on Prandtl’s lifting-line theory. (English) Zbl 1290.76053
Summary: Solutions obtained from a numerical method based on Prandtl’s lifting-line theory, valid for multiple lifting surfaces with arbitrary sweep, are obtained for a number of rigid wing and sail geometries. The results are compared against solutions obtained using established vortex-lattice methods, and computational fluid dynamics solutions to the Euler equations. For the case of an untwisted, rectangular wing, numerical lifting-line, vortex-lattice, and Euler solutions were all in reasonable agreement. However, the numerical lifting-line method was the only method to predict the constant ratio of induced-drag coefficient to lift coefficient squared, which has been predicted from the analytic solution and confirmed by well established experimental data. Results are also presented for a forward-swept, tapered wing. Additional results are presented in terms of lift and induced-drag coefficients for an isolated mainsail, and mainsail/jib combinations with sails representative of both a standard and tall rig Catalina 27. The influence of the nonlinear terms in the lifting-line solution appears minimal, with the exception of mainsail results when considering jib/mainsail combinations.
##### MSC:
 76G25 General aerodynamics and subsonic flows
##### Keywords:
potential flow; aerodynamics; lifting line theory
##### Software:
Sailcut; STAR-CCM+; AVL
Full Text:
##### References:
 [1] Prandtl L. Tragflügel Theorie. Nachrichten von der Gesellschaft der Wisseschaften zu Göttingen, Geschäeftliche Mitteilungen, Klasse; 1918. [2] Prandtl L. Theory of lifting surfaces. NACA TN 9; July 1920. [3] Prandtl L. Induced drag of multiplanes. NACA TN 182; July 1920. [4] Phillips, W. F.; Snyder, D. O., Modern adaptation of prandtl’s classic lifting-line theory, J Aircraft, 37, 4, 662-670, (2000) [5] Phillips, W. F., Mechanics of flight, 2nd ed., (2010), John Wiley and Sons Inc. [6] Drela M. . [7] Wood, C. J.; Tan, S. H., Towards an optimal yacht sail, J Fluid Mech, 85, 459-477, (1978) · Zbl 0375.76012 [8] Sugimoto, T., A first course in optimum design of yacht sails, Fluid Dyn Res, 11, 153-170, (1993) [9] Jackson, P. S., Modeling the aerodynamics of upwind sails, J Wind Eng Ind Aerodyn, 63, 17-34, (1996) [10] Glauert, H., The elements of airfoil and airscrew theory, (1947), Cambridge Science Classics · JFM 52.0880.03 [11] Milgram, J. H., The analytical design of yacht sails, Trans - Soc Naval Architects Mar Eng, 76, 118-160, (1968) [12] Berbente, C.; Maraloi, C., Theoretical and experimental research regarding the aerodynamics of a ship sail system, UPB Sci Bull Ser D, 68, 17-32, (2006) [13] Bertin, J.; Cummings, R., Aerodynamics for engineers, (2009), Prentice-Hall [14] CD-Adapco. STAR-CCM+ users manual; 2011. [15] Laine R, Laine J. The sailcut CAD handbook. ; 2009. [16] Gentry A. The aerodynamics of sail interaction. In: Proceedings of the third AIAA symposium on aero/hydronautics of sailing, Redondo Beach, CA; November 1971.
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