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Variational Analysis and Euler Equation of the Optimum Propeller Problem

In: Variational Analysis and Aerospace Engineering

Author

Listed:
  • Francesco Torrigiani

    (University of Pisa)

  • Aldo Frediani

    (University of Pisa)

  • Antonio Dipace

    (University of Pisa)

Abstract

The problem of the optimum propeller with straight blades was first solved by Goldstein; in this paper, a variational formulation is proposed in order to extend the solution to non-planar blades. First, we find a class of functions (the circulation along the blade axis) for which the thrust and the aerodynamic drag moment are well defined. In this class, the objective functional is proved to be strictly convex and then the global minimum exists and is unique. Then we determine the Euler equation in the case of a general blade and show that the numerical results are consistent with the Goldstein’s solution. Finally, some numerical results with the Ritz method are presented for optimum propeller blades.

Suggested Citation

  • Francesco Torrigiani & Aldo Frediani & Antonio Dipace, 2016. "Variational Analysis and Euler Equation of the Optimum Propeller Problem," Springer Optimization and Its Applications, in: Aldo Frediani & Bijan Mohammadi & Olivier Pironneau & Vittorio Cipolla (ed.), Variational Analysis and Aerospace Engineering, pages 453-488, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-45680-5_18
    DOI: 10.1007/978-3-319-45680-5_18
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