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Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Applications

Author

Listed:
  • Luciano Demasi

    (San Diego State University)

  • Giovanni Monegato

    (Politecnico di Torino)

  • Emanuele Rizzo

    (SkyBox Engineering S.r.l.)

  • Rauno Cavallaro

    (San Diego State University
    University of California San Diego)

  • Antonio Dipace

    (Università di Pisa)

Abstract

An invariant procedure for the minimization of induced drag of generic biwings and closed systems (Joined Wings) was presented in the companion paper (minimum induced drag theorems for Joined Wings, closed systems, and generic biwings: theory) and is now adopted to study several theoretical open questions regarding these configurations. It is numerically verified that a quasi-closed C-wing presents the same optimal induced drag and circulation of the corresponding closed system. It is also verified that when the two wings of a biwing are brought close to each other so that the lifting lines identify a closed path, the minimum induced drag of the biwing is identical to the optimal induced drag of the corresponding closed system. The optimal circulation of this case differs from the quasi-closed C-wing one by an additive constant. The non-uniqueness of the optimal circulation for a closed wing system is also addressed, and it is shown that there are an infinite number of equivalent solutions obtained by adding an arbitrary constant to a reference optimal circulation. This property has direct positive impact in the design of Joined Wings as far as the wing load repartition is concerned: The percentage of aerodynamic lift supported by each wing can be modified to satisfy other design constraints, and without induced drag penalty. Finally, the theoretical open question regarding the asymptotic induced drag behavior of Joined Wings, when the vertical aspect ratio approaches infinity, has been resolved. It has been shown that for equally loaded wings indefinitely distant from each other, the boxwing minimum induced drag tends to zero. In that condition, the upper and lower wings present a constant aerodynamic load. Prandtl’s approximated formula for the minimum induced drag of a boxwing (Best Wing System) cannot be used to describe the asymptotic behavior. This work also shows that the optimal distribution over the equally loaded horizontal wings of a boxwing is not the superposition of a constant and an elliptical functions. This is an acceptable approximation only for small vertical aspect ratios (of aeronautical interest).

Suggested Citation

  • Luciano Demasi & Giovanni Monegato & Emanuele Rizzo & Rauno Cavallaro & Antonio Dipace, 2016. "Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Applications," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 236-261, April.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-015-0850-5
    DOI: 10.1007/s10957-015-0850-5
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    References listed on IDEAS

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    1. Emanuele Rizzo & Aldo Frediani, 2009. "Application of Optimisation Algorithms to Aircraft Aerodynamics," Springer Optimization and Its Applications, in: Variational Analysis and Aerospace Engineering, chapter 0, pages 419-446, Springer.
    2. Giuseppe Buttazzo & Aldo Frediani, 2009. "Variational Analysis and Aerospace Engineering," Springer Optimization and Its Applications, Springer, number 978-0-387-95857-6, June.
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    Cited by:

    1. Cezary Galinski & Mateusz Lis & Jaroslaw Hajduk, 2017. "Electric Propulsion Concepts for an Inverted Joined Wing Airplane Demonstrator," Energies, MDPI, vol. 10(6), pages 1-21, May.

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