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Best wing system: an exact solution of the Prandtl’s problem

  • Aldo Frediani
  • Guido Montanari
Conference paper
Part of the Springer Optimization and Its Applications book series (SOIA, volume 33)

Abstract

In 1924, Ludwig Prandtl published a fundamental paper in which he showed that the lifting system with minimum induced drag is a box wing. The results were obtained through an approximate procedure. In the present paper we obtain an exact solution of Prandtl’s problem. In particular, we prove that the lift on the horizontal wings results of the superposition of a constant and an elliptical distributions and, on the vertical wings, it is butterfly shaped, as already shown by Prandtl. The discrepancies between the two solutions are discussed.

Keywords

Vortex Line Wake Vortex Circulation Function Lift System Lateral Wing 
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Notes

Acknowledgments

The authors gratefully acknowledge the contributions of Alberto Longhi in the formulation of the problem, Massimo Pappalardo of the Department of Applied Mathematics of Pisa, Piero Villaggio of the Department of Structural Engineering of Pisa, Luigi Polito and Emanuele Rizzo of the Department of Aerospace Engineering of Pisa.

References

  1. 1.
    Prandtl L.: Induced Drag of Multiplanes, NACA TN 182 (1924).Google Scholar
  2. 2.
    Pistolesi E.: Aerodinamica, ETS Editrice, Pisa.Google Scholar
  3. 3.
    Munk M.: Isoperimetrische Aufgaben aus der Theorie des Fluges, Inaugural Dissertation 1919, Gottinga (1919).Google Scholar
  4. 4.
    Munk M.: The minimum induced drag in airfoils, NACA 121(1924).Google Scholar
  5. 5.
    Montanari G.: Problemi di minimo della resistenza indotta in sistemi portanti, Graduating Thesis in Mathematics, Università di Pisa, 1998.Google Scholar

Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Aerospaziale“L. Lazzarino”, Università di PisaPisaItaly
  2. 2.Graduating Student in Mathematics, Dipartimento di Matematica“L. Tonelli”, Università di PisaPisaItaly

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