Thin-ship theory and influence of rake and flare

  • Francis NoblesseEmail author
  • Gerard Delhommeau
  • Hyun Yul Kim
  • Chi Yang


The basic computational task of the thin-ship theory of free-surface potential flow about a ship that advances at constant speed along a straight path in calm water, of large depth and lateral extent, is considered. Specifically, a straightforward method for evaluating the pressure and the wave profile at a ship hull (the wave drag, hydrodynamic lift and pitch moment, and sinkage and trim are also considered) in accordance with Michell’s thin-ship theory is given. A main ingredient of this method is a simple analytical approximation to the local-flow component in the expression for the Green function (associated with the classical Michell–Kelvin linearized free-surface boundary condition) of thin-ship theory. This practical Green function is used to evaluate and analyze steady flow about a four-parameter family of ship bows with rake and flare. In particular, the variations of the bow-wave height and location with respect to the draft-based Froude number, the entrance angles at the top and bottom waterlines, and the rake angle are explored via a systematic parametric study. This parametric study provides estimates—immediately useful for design—of the influence of rake and flare on the height and the location of a ship bow wave, and shows that rake and flare effects can be significant, especially at low Froude numbers.


Bow flare Bow rake Green function Ship bow wave Thin-ship theory 


  1. 1.
    Noblesse F, Delhommeau G, Guilbaud M, Hendrix D, Yang C (2008) Simple analytical relations for ship bow waves. J Fluid Mech 600: 105–132zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Noblesse F, Hendrix D, Faul L, Slutsky J (2006) Simple analytical expressions for the height, location, and steepness of a ship bow wave. J Ship Res 50: 360–370Google Scholar
  3. 3.
    Noblesse F, Delhommeau G, Guilbaud M, Yang C (2008) The rise of water at a ship stem. J Ship Res 52: 89–101Google Scholar
  4. 4.
    Faltinsen OM (2005) Hydrodynamics of high-speed marine vehicles. Cambridge University Press, Cambridge, pp 454Google Scholar
  5. 5.
    Day AH, Doctors LJ (2001) Rapid evaluation of near and far field wave wake from ships and application to hull form design and optimization. J Ship Res 45: 73–84Google Scholar
  6. 6.
    Stoker JJ (1957) Water waves. Interscience, New YorkzbMATHGoogle Scholar
  7. 7.
    Kostyukov AA (1959) Theory of ship waves and wave resistance. English translation 1968, ECI, Iowa City, Sudpromfiz, LeningradGoogle Scholar
  8. 8.
    Wehausen JV, Laitone EV (1960) Surface waves. In: Encyclopedia of Physics, vol 9. Springer-Verlag, BerlinGoogle Scholar
  9. 9.
    Wehausen JV (1973) The wave resistance of ships. Adv Appli Mech 13: 93–245CrossRefGoogle Scholar
  10. 10.
    Standing RG (1974) Phase and amplitude discrepancies in the surface wave due to a wedge-ended hull form. J Fluid Mech 62: 625–642zbMATHCrossRefADSGoogle Scholar
  11. 11.
    Noblesse F (1981) Alternative integral representations for the Green function of the theory of ship wave resistance. J Eng Math 15: 241–265zbMATHCrossRefGoogle Scholar
  12. 12.
    Ponizy B, Noblesse F, Ba M, Guilbaud M (1994) Numerical evaluation of free-surface Green functions. J Ship Res 38: 193–202Google Scholar
  13. 13.
    Noblesse F (1978) On the fundamental function in the theory of steady motion of ships. J Ship Res 22: 212–215Google Scholar
  14. 14.
    Noblesse F (1975) The near-field disturbance in the centerplane Havelock source potential. In: 1st IL conference on numerical ship hydrodynamics, Washington, DC, pp 481–501Google Scholar
  15. 15.
    Telste JG, Noblesse F (1989) The nonoscillatory near-field term in the Green function for steady flow about a ship. In: 17th symposium on naval hydrodynamics, The Hague, pp 39–52Google Scholar
  16. 16.
    Noblesse F (1978) The steady wave potential of a unit source, at the centerplane. J Ship Res 22: 80–88Google Scholar
  17. 17.
    Masson E, DeBayser O, Martin D (1991) Evaluation de la resistance de vagues d’un sous-marin en immersion totale. 3emes Journèes de l’Hydro, Grenoble, FranceGoogle Scholar
  18. 18.
    Newman JN (1987) Evaluation of the wave resistance Green function: part 1—the double integral. J Ship Res 31: 79–90Google Scholar
  19. 19.
    Lyness JN, Jespersen D (1975) Moderate degree symmetric quadrature rules for the triangle. J Inst Math Appl 15: 19–32zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    McCarthy JH (1985) Collected experimental resistance and flow data for three surface ship model hulls. David W Taylor Naval Ship Research and Development Center, report DTNSRDC-85/011Google Scholar
  21. 21.
    Cooperative experiments on Wigley parabolic model in Japan. In: 17th ITTC resistance committee reportGoogle Scholar
  22. 22.
    Noblesse F, Delhommeau G, Yang C (2008) Practical evaluation of steady flow due to a free-surface pressure patch. J Ship Res (submitted)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Francis Noblesse
    • 1
    Email author
  • Gerard Delhommeau
    • 2
  • Hyun Yul Kim
    • 3
  • Chi Yang
    • 3
  1. 1.David Taylor Model BasinNSWCCDWest BethesdaUSA
  2. 2.Laboratoire de Mécanique des Fluides (UMR CNRS no 6598)École CentraleNantesFrance
  3. 3.Department of Computational and Data SciencesGeorge Mason UniversityFairfaxUSA

Personalised recommendations