Numerical analysis of multiple, thin-sail geometries based on Prandtl’s lifting-line theory.

*(English)*Zbl 1290.76053Summary: 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 |

Full Text:
DOI

##### 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. <http://web.mit.edu/drela/Public/web/avl>. |

[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. <http://sailcut.sourceforge.net/docs/en>; 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. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.