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)


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.


Vortex Line Wake Vortex Circulation Function Lift System Lateral Wing 
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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.


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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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