Structural and Multidisciplinary Optimization

, Volume 41, Issue 4, pp 637–646 | Cite as

Aeroelastic tailoring using lamination parameters

Drag reduction of a Formula One rear wing
  • Glenn A. A. Thuwis
  • Roeland De Breuker
  • Mostafa M. Abdalla
  • Zafer Gürdal
Open Access
Industrial Application


The aim of the present work is to passively reduce the induced drag of the rear wing of a Formula One car at high velocity through aeroelastic tailoring. The angle-of-attack of the rear wing is fixed and is determined by the required downforce needed to get around a turn. As a result, at higher velocity, the amount of downforce and related induced drag increases. The maximum speed on a straight part is thus reduced due to the increase in induced drag. A fibre reinforced composite torsion box with extension-shear coupled upper and lower skins is used leading to bending-torsion coupling. Three-dimensional static aeroelastic analysis is performed loosely coupling the Finite Element code Nastran and the Computational Fluid Dynamics panel code VSAERO using ModelCenter. A wing representative of Formula One rear wings is optimised for minimum induced drag using a response surface methodology. Results indicate that a substantial induced drag reduction is achievable while maintaining the desired downforce during low speed turns.


Aeroelastic tailoring Lamination parameters Drag reduction Automotive 


  1. Abdalla M, De Breuker R, Gürdal Z (2007) Aeroelastic tailoring of variable-stiffness slender wings for minimum compliance. In: IFASD, StockholmGoogle Scholar
  2. Abrate S (1994) Optimal design of laminated plates and shells. Compos Struct 29:269–286CrossRefGoogle Scholar
  3. Beckert A (2000) Coupling fluid (CFD) and structural (FE) models using finite interpolation elements. Aerosp Sci Technol 4:13–22MATHCrossRefGoogle Scholar
  4. Beckert A, Wendland H (2001) Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. Aerosp Sci Technol 5:125–134MATHCrossRefGoogle Scholar
  5. Benzing E (1992) Ali/Wings: studio per tecnici e piloti di auto da corsa/study for racing car engineers and drivers. MilanoGoogle Scholar
  6. Bisplinghoff R, Ashley H, Halfman R (1955) Aeroelasticity. Addison-Wesley, ReadingMATHGoogle Scholar
  7. de Boer A, van Zuijlen A, Bijl H (2007) Review of coupling methods for non-matching meshes. Comput Methods Appl Mech Eng 196:1515–1525MATHCrossRefGoogle Scholar
  8. Bramesfeld G, Ironside D, Schwochow J (2008) Simplified modeling of wing-drag reduction due to structural dynamics and atmospheric gusts. In: 26th AIAA applied aerodynamics conference, HonoluluGoogle Scholar
  9. Cramer E, Gablonsky J (2004) Effective parallel optimization of complex computer simulations. In: 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, AlbanyGoogle Scholar
  10. Diaconu C, Sato M, Sekine H (2002) Feasible region in general design space of lamination parameters for laminated composites. AIAA J 40(3):559–565CrossRefGoogle Scholar
  11. Dowell E (2004) A modern course in aeroelasticity. Kluwer, DordrechtMATHGoogle Scholar
  12. Farhat C, Lesionne M (1998) Higher-order staggered and subiteration free algorithms for coupled dynamic aeroelasticity problems. In: 36th aerospace sciences meeting & exhibit, RenoGoogle Scholar
  13. FIA (2007) 2008 Formula 1 technical regulations. Federation Internationale de l’AutomobileGoogle Scholar
  14. Fukunaga H, Sekine H (1992) Stiffness design method of symmetric laminates using lamination parameters. AIAA J 30(11):2791–2793CrossRefGoogle Scholar
  15. Fukunaga H, Sekine H (1994) A laminate design for elastic properties of symmetric laminates with extension-shear of bending-twist coupling. J Compos Mater 28(8):708–731Google Scholar
  16. Fukunaga H, Vanderplaats G (1991) Stiffness optimization of orthotropic laminated composites using lamination parameters. AIAA J 29(4):641–646CrossRefGoogle Scholar
  17. Guo S, Cheng W, Cui D (2005) Optimization of composite wing structures for maximum flutter speed. In: 46th AIAA/ASME/ ASCE/AHS/ASC structures, structural dynamics & materials conference, AustinGoogle Scholar
  18. Guo S, Cheng W, Cui D (2006) Aeroelastic tailoring of composite wing structures by laminate layup optimization. AIAA J 44(12):3146–3149CrossRefGoogle Scholar
  19. Gürdal Z, Olmedo R (1993) In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA J 31(4):751–758MATHCrossRefGoogle Scholar
  20. Gürdal Z, Haftka R, Hajela P (1999) Design and optimization of laminated composite materials. Wiley, New YorkGoogle Scholar
  21. INTEC GmbH (2004) Simpack user’s guideGoogle Scholar
  22. Kameyama M, Fukunaga H (2007) Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters. Comput Struct 85:213–224CrossRefGoogle Scholar
  23. van Kan J, Segal G, Vermolen F (2005) Numerical methods in scientific computing. VSSDGoogle Scholar
  24. Katz J (1989) Aerodynamics of high-lift, low-aspect-ratio unswept wings. AIAA J 27(8):1123–1124CrossRefGoogle Scholar
  25. Katz J (2006) Aerodynamics of race cars. Annu Rev Fluid Mech 38:27–63CrossRefGoogle Scholar
  26. Liebeck R (1978) Design of subsonic airfoils for high lift. J Aircraft 15(9):547–561CrossRefGoogle Scholar
  27. Liu B, Haftka R (2004) Single-level composite wing optimization based on flexural lamination parameters. Struct Multidiscipl Optim 26:111–120CrossRefGoogle Scholar
  28. Lynch R, Rogers W (1976) Aeroelastic tailoring of composite materials to improve performance. In: 17th AIAA/ASME/ASCE/ AHS/ASC structures, structural dynamics & materials conference, King of Prussia, pp 61–68Google Scholar
  29. MacNeal RH (1972) The Nastran theoretical manual. NASA (SP-221(01))Google Scholar
  30. Maskew B (1982) VSAERO A computer program for calculating the nonlinear aerodynamic characteristics of arbitrary configurations. NASA (CR-166476)Google Scholar
  31. Massegur D, Quaranta G, Cavagna L (2007) Race cars flex their muscle. ANSYS Advantage 1(1):9–11Google Scholar
  32. Miki M, Sugiyama Y (1993) Optimum design of laminated composite plates using lamination parameters. AIAA J 31(5):921–922CrossRefGoogle Scholar
  33. Patil M (1997) Aeroelastic tailoring of composite box beams. In: 35th AIAA aerospace sciences meeting & exhibit, RenoGoogle Scholar
  34. Persson P, Strang G (2004) A simple mesh generator in matlab. SIAM Rev 46(2):329–345MATHCrossRefMathSciNetGoogle Scholar
  35. Phoenix Integration (2003) Improving the engineering process with software integrationGoogle Scholar
  36. Rehfield L, Cheung R (2003) Some basic strategies for aeroelastic tailoring of wings with bend-twist coupling: part one. In: 44th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference, NorfolkGoogle Scholar
  37. Rehfield L, Cheung R (2004) Strategies for aeroelastic tailoring of wings with bend-twist coupling: part two. In: 45th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference, Palm SpringsGoogle Scholar
  38. Rendall T, Allen C (2007) Unified fluid-structure interpolation and mesh motion using radial basis functions. Int J Numer Methods EngGoogle Scholar
  39. Setoodeh S, Abdalla M, Gürdal Z, Tatting B (2005) Design of variable-stiffness composite laminates for maximum in-plane stiffness using lamination parameters. In: 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference, AustinGoogle Scholar
  40. Setoodeh S, Abdalla M, Gürdal Z (2006) Design of variable-stiffness laminates using lamination parameters. Composites: Part B 37:301–309CrossRefGoogle Scholar
  41. Shirk M, Hertz T, Weisshaar T (1986) Aeroelastic tailoring—theory, practise, and promise. J Aircraft 23(1):6–18CrossRefGoogle Scholar
  42. Stanford B, Ifju P (2008) Aeroelastic tailoring of fixed membrane wings for micro air vehicles. In: 49th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Schaumberg, ILGoogle Scholar
  43. Thuwis G, De Breuker R, Abdalla M (2008) Aeroelastic tailoring of a Formula One car rear wing. In: Proceedings of the sixth international conference on engineering computational technology, AthensGoogle Scholar
  44. Török J (2000) Analytical mechanics. Wiley, New YorkGoogle Scholar
  45. Tsai S, Pagano N (1968) Invariant properties of composite materials. In: Composite materials workshop, pp 233–253Google Scholar
  46. Weisshaar T (1981) Aeroelastic tailoring of forward swept composite wings. J Aircraft 18(8):669–676CrossRefGoogle Scholar
  47. Weisshaar T, Duke D (2006) Induced drag reduction using aeroelastic tailoring with adaptive control surfaces. J Aircraft 43(1):157–164CrossRefGoogle Scholar
  48. Weisshaar T, Ryan R (1986) Control of aeroelastic instabilities through stiffness cross-coupling. J Aircraft 23(2):148–155CrossRefGoogle Scholar
  49. Weisshaar T, Nam C, Batista-Rodriguez A (1998) Aeroelastic tailoring for improved UAV performance. In: 47th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference, Long BeachGoogle Scholar
  50. Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math 4:389–396MATHCrossRefMathSciNetGoogle Scholar
  51. Wright P (1974) Aerodynamics for Formula 1. Aeronaut J 78:226–230Google Scholar
  52. Zhang X, Toet W, Zerihan J (2006) Ground effect aerodynamics of race cars. Appl Mech Rev 59:33–49CrossRefGoogle Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Glenn A. A. Thuwis
    • 1
  • Roeland De Breuker
    • 1
  • Mostafa M. Abdalla
    • 1
  • Zafer Gürdal
    • 1
  1. 1.Faculty of Aerospace EngineeringTU DelftHS DelftThe Netherlands

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