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Introduction to Transonic Aerodynamics pp 427–511Cite as

Aerodynamics of Swept Wings

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 110))

Abstract

In this chapter we discuss the aerodynamics of swept wings in transonic flow. To demonstrate the merits of swept-back wings, simple sweep theory is presented. It is shown why a swept wing can experience local supersonic flow while still being in subcritical conditions, thereby postponing the onset of strong shock waves and drag divergence. It is also shown how the wave drag coefficient of a swept wing can be estimated based on the wave drag coefficient of an unswept wing. This method can be used to show the favorable effect of wing sweep on the wave drag coefficient over the transonic Mach number range. Apart from these advantages the chapter also presents the adverse effects of wing sweep. It is shown how the chordwise pressure distribution changes over the center section and tip section of a swept wing of finite span. It is explained what shape modifications (both in airfoil and in planform) can be applied to reduce the form drag of the center section of an aft-swept wing. In addition, viscous effects on swept wings are detailed. In particular, the transition mechanisms of attachment-line instabilities and crossflow vortices are explained. It is also shown why aft-swept wings are susceptible to tip stall and how a controlled form of stall can lead to a stable leading-edge vortex. Finally, the aeroelastic implications of (aft-)swept wings are detailed: a change in aerodynamic twist due to wing bending and a resulting reduction in control surface effectiveness. This chapter contains 7 examples and closes with 24 practice problems.

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Notes

  1. 1.

    The Oswald factor, \(e\), of a full airplane is not the same as the span efficiency factor. However, the two are related according to \(\frac{1}{e}=X\pi A +\frac{1}{\phi }\). \(X\) is the coefficient that relates the profile and parasite drag to \(C_L^2\). For more information on this relation, the reader is referred to Ref. [53].

  2. 2.

    The solver that is used is MSES. See Refs. [21, 26] for details on this viscous-inviscid solver.

  3. 3.

    A negative incidence angle of the wing is often termed “washout”. This wing would therefore have \(+3^\circ \) of washout at the tip.

  4. 4.

    The dihedral angle is the upward angle of the wing measured with respect to the horizontal.

  5. 5.

    For more information on Fourier transformations, the reader is referred to [61].

References

  1. Abbott, I.H., von Doenhoff, A.E.: Theory of Wing Sections. Dover Publications, New York (1959)

    Google Scholar 

  2. Adler, A.: Effects of Combinations of Aspect Ratio and Sweepback at High Subsonic Mach Numbers. NACA RM L7C24, Langley Field (1947)

    Google Scholar 

  3. Aly, S., Ogot, M., Pelz, R., Siclari, M.: Jig-shape static aeroelastic wing design problem: a decoupled approach. J. Aircr. 39(6), 1061–1066 (2002). doi:10.2514/2.3035

    Article  Google Scholar 

  4. Anderson, J.: Fundamentals of Aerodynamics, 5th edn. McGraw Hill, New York (2010)

    Google Scholar 

  5. Anderson, J.D.: Introduction to Flight. McGraw Hill, New York (2000)

    Google Scholar 

  6. Anon.: Transonic data memorandum; method for predicting the pressure distribution on swept wings with subsonic attached flow. ESDU TM 73012, London (1973)

    Google Scholar 

  7. Anon.: Airbus Industrie A 310. L’Aeronautique et L’Astronautique 6(91), 15 (1981)

    Google Scholar 

  8. Anon.: Fact Sheets: X29. www.nasa.gov/centers/dryden (2008)

  9. Arnal, D., Casalis, G.: Laminar-turbulent transition prediction in three-dimensional flows. Prog. Aerosp. Sci. 36, 173–191 (2000)

    Article  Google Scholar 

  10. Bendiksen, O.O.: Transonic limit cycle flutter of high-aspect-ratio swept wings. J. Aircr. 45(5), 1522–1533 (2008). doi:10.2514/1.29547

    Article  Google Scholar 

  11. Bendiksen, O.O.: Influence of shocks on transonic flutter of flexible wings. In: Proceedings of the 50th AIAA/ASME/AHS/ACS Structures, Structural Dynamics, and Materials Conference, AIAA 2009-2313, pp. 1–29. Palm Springs, CA, May 2009. doi:10.2514/6.2009-2313

  12. Bergrun, N.R.: An Empirically Derived Basis for Calculating the Area, Rate, and Distribution of Water-Drop Impingement on Airfoils. NACA TR 1107 (1952)

    Google Scholar 

  13. Biao, Z., Zhide, Q., Chao, G.: Transonic flutter analysis of an airfoil with approximate boundary method. In: Grant, I. (ed.) Proceedings of the 26th Congress of the International Council of the Aeronautical Sciences. ICAS 2008-7.10.5 (2008)

    Google Scholar 

  14. Bisplinghof, R.L., Ashley, H., Halfman, R.: Aeroelasticity. Dover Publications, Mineola, New York (1996)

    Google Scholar 

  15. Boyne, W.J.: Boeing B-52: A Documentary History. Smithsonian Institution Press, Washington (1981)

    Google Scholar 

  16. Broadbent, E.G., Mansfield, O.: Aileron Reversal and Wing Divergence of Swept Wings, ARC Technical Report R&M 2817, London (1954)

    Google Scholar 

  17. Chambers, J.R.: Concept to Reality: Contributions of the NASA Langley Research Center to U.S. Civil Aircraft of the 1990s. SP 2003-4529, NASA (2003)

    Google Scholar 

  18. Collar, A.R.: The first fifty years of aeroelasticity. Aerospace 5(2), 12–20 (1978)

    Google Scholar 

  19. Deyhle, H., Bippes, H.: Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions. J. Fluid Mech. 316(1), 73–113 (1996). doi:10.1017/S0022112096000456

    Article  Google Scholar 

  20. Dowell, E.H., Hall, K.C., Thomas, J.P., Kielb, R.E., Spiker, M.A., Li, A., Charles, M., Denegri, J.: Reduced order models in unsteady aerodynamic models, aeroelasticity and molecular dynamics. In: Grant, I. (ed.) Proceedings of the 26th International Congress of the Aeronautical Sciences. ICAS 2008-0.1 (2008)

    Google Scholar 

  21. Drela, M., Giles, M.B.: Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25(10), 1347–1355 (1987). doi:10.2514/3.9789

    Article  MATH  Google Scholar 

  22. Dusto, A.R.: An analytical method for predicting the stability and control characteristics of large elastic airplanes at subsonic and supersonic speeds, part I—analysis. In: Aeroelastic Effects from a Flight Mechanics Standpoint, vol. 46. AGARD (1970)

    Google Scholar 

  23. Dykins, D.H., Jupp, J.A., McRae, D.M.: Esso energy award lecture, 1987. Application of aerodynamic research and development to civil aircraft wing design. Proc. R. Soc. Ser. A. Math. Phys. Sci. 416(1850), 43–62 (1988)

    Google Scholar 

  24. Garrick, I.E., Rubinov, S.I.: Flutter and Oscillating Air-Force Calculations for an Airfoil in a Two-Dimensional Supersonic Flow. NACA Report No. 846, Langley Research Center, Hampton Virginia (1946)

    Google Scholar 

  25. Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, 4th edn. Stanley Thornes Ltd, Cheltenham (1972)

    Google Scholar 

  26. Giles, M.B., Drela, M.: Two-dimensional transonic aerodynamic design method. AIAA J. 25(9), 1199–1206 (1987). doi:10.2514/3.9768

    Article  Google Scholar 

  27. Görtler, H.: Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden. Ges. d. Wiss. Göttingen, Nachr. a. d. Math. 2(1) (1940)

    Google Scholar 

  28. Hadcock, R.: X-29 composite wing. In: Presented at the American Institute of Aeronautics and Astronautics Symposium on the Evaluation of Aircraft/Aerospace Structures and Materials. Air Force Museum, Dayton, Ohio (1985)

    Google Scholar 

  29. Hall, M.G.: Transonic flows. In: Proceedings of IMA Conference on Numerical Methods and Problems in Aeronautical Fluid Mechanics. Academic Press (1975)

    Google Scholar 

  30. Harper, C.W., Maki, R.L.: A Review of the Stall Characteristics of Swept Wings. NACA TN D-2373 (1964)

    Google Scholar 

  31. Hoak, D.E., Anderson, R., Goss, C.R.: USAF Stability and Control Datcom. Air Force Wright Aeronautical Laboratories, Wright Patterson Air Force Base, Ohio (1978)

    Google Scholar 

  32. Hunton, L.W.: A study of the application of airfoil section data to the estimation of the high-subsonic-speed characteristics of swept wings. NACA-RM-A55C23 (1955)

    Google Scholar 

  33. Jenkinson, L.R., Simpkin, P., Rhodes, D.: Civil Jet Aircraft Design. American Institute of Aeronautics and Astronautics, Reston, VA (1999)

    Google Scholar 

  34. Jenks, M.: The Boeing 787 dreamliner programme. In: Grant, I. (ed.) Proceedings of the 26th Congress of the International Council of the Aeronautical Sciences. ICAS 2008-0.8 (2008)

    Google Scholar 

  35. Johnson, R.: Minimum Drag Coefficient of Wings. RAND RM-604, Santa Monica (1951)

    Google Scholar 

  36. Kehoe, M.W., Freudinger, L.C.: Aircraft Ground Vibration Testing at the NASA Dryden Flight Research Facility. Technical Memorandum 104275, NASA (1993)

    Google Scholar 

  37. Kuechemann, D.: The distribution of lift over the surface of swept wings. Aeronaut. Q. 4, 261–278 (1953)

    Google Scholar 

  38. Kuechemann, D.: The Aerodynamic Design of Aircraft. Pergamon Press, Oxford (1978)

    Google Scholar 

  39. Kuechemann, D., Weber, J.: The Subsonic Flow Past Swept Wings at Zero Lift Without and With Body. Aeronautical Research Council Reports and Memoranda 2908, London (1956)

    Google Scholar 

  40. Kuzmina, S., Karas, O., Ishmuratov, F., Zichenkov, M., Chedrik, V.: Analysis of static and dynamic aeroelastic characteristics of airplane in transonic flow. In: Grant, I. (ed.) Proceedings of ICAS 2012, pp. 1–10. Brisbane, Australia (2012)

    Google Scholar 

  41. Livne, E.: Future of airplane aeroelasticity. J. Aircr. 40(6), 1066–1092 (2003). doi:10.2514/2.7218

    Article  Google Scholar 

  42. Meier, G.E.A.: Unsteady phenomena. In: Zierep, J., Oertel, H. (eds.) Symposium Transsonicum III, IUTAM, pp. 441–464. Springer, Berlin (1988)

    Google Scholar 

  43. Nelson, H.C., Berman, J.H.: Calculations on the Forces and Moments for an Oscillating Wing-Aileron combination in Two-Dimensional Potential Flow at Sonic Speed. NACA TN 2590. Langley Research Center, Hampton (1952)

    Google Scholar 

  44. Newberry, C.F.: Consideration of stability augmentation systems for large elastic aircraft. In: Aeroelastic Effects from a Flight Mechanics Standpoint, vol. 46. AGARD (1970)

    Google Scholar 

  45. Obert, E.: Aerodynamic Design and Aircraft Operation, Part III. Aerodynamics of Combat Aircraft. Delft University of Technology, Delft (1996)

    Google Scholar 

  46. Obert, E.: Aerodynamic Design of Transport Aircraft. IOS Press, Delft (2009)

    Google Scholar 

  47. Pfenniger, W.: Laminar flow control - laminarization. In: Special Course on Concepts for Drag Reduction, AGARD R-654, pp. 3.1–3.75 (1977)

    Google Scholar 

  48. Poll, D.I.A.: On the generation and subsequent development of spiral vortex flow over a swept-back wing. In: AGARD-CP-342, pp. 6.1–6.14 (1983)

    Google Scholar 

  49. Poll, D.I.A.: Some observations of the transition process on the windward face of a long yawed cylinder. J. Fluid Mech. 150, 329–356 (1985). doi:10.1017/S0022112085000155

    Article  Google Scholar 

  50. Reed, H., Saric, W.: Stability of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 21, 235–284 (1989)

    Article  MathSciNet  Google Scholar 

  51. Ringleb, F.: Some Aerodynamic Relations for an Airfoil in Oblique Flow. NACA TM 1158 (1947)

    Google Scholar 

  52. Roskam, J.: Airplane Design, Part 6: Preliminary Calculation of Aerodynamic, Thrust and Power Characteristics. DARcorporation, Lawrence, KS (2006)

    Google Scholar 

  53. Ruijgrok, G.J.J.: Elements of Airplane Performance. Delft University Press, Delft, the Netherlands (1989)

    Google Scholar 

  54. Saric, W., Reed, H.: Crossflow instabilities—theory & technology. In: 41st Aerospace Sciences Meeting & Exhibit. AIAA 2003-0771, Reno, NV (2003)

    Google Scholar 

  55. Saric, W.S.: Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409 (1994)

    Article  MathSciNet  Google Scholar 

  56. Saric, W.S., Reed, H.L., White, E.B.: Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35(1), 413–440 (2003). doi:10.1146/annurev.fluid.35.101101.161045

    Article  MathSciNet  Google Scholar 

  57. Schlichting, H., Truckenbrot, E.: Aerodynamik des Flugzeuges. Springer, Heidelberg (1960)

    Book  MATH  Google Scholar 

  58. Schoernack, W., Hässler, E.: Theoretical investigation of aeroelastic influences on the lift distribution and the aerodynamic derivatives of swept wings at symmetric and antisymmetric stationary flight conditions. In: Aeroelastic Effects from a Flight Mechanics Standpoint, vol. 46. AGARD (1970)

    Google Scholar 

  59. Shevell, R.S., Kroo, I.: Compressibility drag: 3D effects and sweep. In: Aircraft Design: Synthesis and Analysis. Department of Aeronautics and Astronautics, Stanford University, CA (1992)

    Google Scholar 

  60. Stack, J., Lindsey, W.: Characteristics of Low Aspect Ratio Wings at Supercritical Mach Numbers. NACA TN 1665. Langley Air Force Base (1948)

    Google Scholar 

  61. Strauss, W.A.: Partial Differential Equations, An Introduction. Wiley, Chichester, UK (1992)

    Google Scholar 

  62. Sturdza, P.: An Aerodynamic Design Method for Supersonic Natural Laminar Flow Aircraft. Ph.D. thesis, Stanford University (2003)

    Google Scholar 

  63. Tempelmann, D.: Stability and Receptivity of Three-Dimensional Boundary Layers. Dissertation, Royal Institute of Technology, Sweden (2009)

    Google Scholar 

  64. Tijdeman, H.: Investigations of the Transonic Flow Around Oscillating Airfoils. Ph.D. thesis, Delft University of Technology, the Netherlands (1977)

    Google Scholar 

  65. Timmons, L.M.: Improving Business Jet Performance: The Mark Five Sabreliner. SAE Paper 790582 (1979)

    Google Scholar 

  66. Torenbeek, E.: Synthesis of Subsonic Airplane Design. Delft University Press, Delft (1976)

    Google Scholar 

  67. Van der Wees, A.: A Nonlinear Multigrid Method for Three-Dimensional Transonic Potential Flow. Ph.D. thesis, Delft University of Technology, the Netherlands (1988)

    Google Scholar 

  68. Van Muijden, J., Broekhuizen, A.J., Van der Wees, A.J., Van der Vooren, J.: Flow analysis and drag prediction for transonic transport wing/body configurations using a viscous-inviscid interaction type method. In: Proceedings of the 19th ICAS Congress. Anaheim, California (1994)

    Google Scholar 

  69. Weaver, J.H.: A method of wind tunnel testing through the transonic range. J. Aeronaut. Sci. 15(1) (1948)

    Google Scholar 

  70. Weber, J.: The Calculation of the Pressure Distribution over the Surface of Two-Dimensional and Swept Wings with Symmetrical Aerofoil Sections. Aeronautical Research Council Reports and Memoranda No. 2918 (1953)

    Google Scholar 

  71. Weber, J., Kuechemann, D., Brebner, G.: 2882 Low-Speed Tests on 45-deg Swept-Back Wings, Aeronautical Research Council Reports and Memoranda No. 2882 (1958)

    Google Scholar 

  72. Weisshaar, T.A.: Aircraft Aeroelastic Design and Analysis. Purdue University, West Lafayette (2009)

    Google Scholar 

  73. Wright, J., Cooper, J.: Introduction to Aeroelasticity and Loads. Wiley, Chichester, UK (2007)

    Google Scholar 

  74. Yates, E.C.: 765 AGARD Standard Aeroelastic Configurations for Dynamic Response I- Wing 445.6, AGARD Report 765 (1985)

    Google Scholar 

  75. Young, A.D., Booth, T.B.: The Profile Drag of Yawed Wings of Inifinite Span, Cranfield College of Aeronautics Report No. 38 (1950)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands

    Roelof Vos

  2. Department of Aerospace Engineering, The University of Kansas, Lawrence, KS, USA

    Saeed Farokhi

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  1. Roelof Vos
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Vos, R., Farokhi, S. (2015). Aerodynamics of Swept Wings. In: Introduction to Transonic Aerodynamics. Fluid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9747-4_8

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