Analytical surfaces for ship hulls

Cover Page

Cite item


The choice of optimal shape of ship hull surface is one of the main problems of ship architects and designs. A choice of the form is based on empirical formulae or on intuition of designers. In the article a method of determination of explicit algebraic equations of theoretical shape of ship hull with three main cross-sections given in advance and coinciding with the design waterline, the midship section, and with the main buttock line is given. The forms of the lines in the main cross-sections are chosen from conditions taken in advance. These surfaces are called hydrodynamic. A method is illustrated for three threes of main cross-sections of the ship hulls, i.e. nine hydrodynamic surfaces were constructed. All algebraic equations were converted to parametrical form for comfort of computer modelling. With their help, all nine ship surfaces proposed for the introduction were visualized. Having changed constants containing in the surface equations, i.e. correcting the forms of three main geometric parameters of ship hull, one can select the most rational shape of hull surface for the first approach. Further, it is possible to begin planning parallel middle bodies or to combine bow and stern extremities of a ship from different fragments of algebraic surfaces but with the same midship sections. In a paper, only geometrical problems of design of theoretical hull shape are described.

About the authors

Sergey N. Krivoshapko

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
ORCID iD: 0000-0002-9385-3699

Doctor of Technical Sciences, Professor of the Department of Civil Engineering, Academy of Engineering

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Vyacheslav N. Ivanov

Peoples’ Friendship University of Russia (RUDN University)

ORCID iD: 0000-0003-4023-156X

Doctor of Technical Sciences, Professor of the Department of Civil Engineering, Academy of Engineering

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation


  1. Morozov BN, Tzvetkov VV. On the question of choice of scheme of making bottom section of hulls. Vestnik RAEN. 2013;(7):80–85. (In Russ.)
  2. Rozinov AYa. Technological improvement of the hull boats design and the process of their assembly. Tekhnologiya Mashinostroeniya. 2020;(5):15–23. (In Russ.)
  3. Bronskiy AI, Glozman MK, Kozlyakov VV. The basis of choice of structures of ship hull. Leningrad: Sudustroeniye Publ.; 1974. (In Russ.)
  4. Doctors LJ. Optimization of marine vessels on the basis of tests on model series. J. Mar. Sci Technol. 2020; (25):887–900.
  5. Avdonev EYa. Analytical description of the ship hull surfaces. Prikladnaya Geometriya i Inzhenernaya Grafika. 1972;(15):156–160. (In Russ.)
  6. Avdonev EYa. Mathematical model of hull surface. Prikladnaya Geometriya i Inzhenernaya Grafika. 1979; (28):46–49. (In Russ.)
  7. Avdonev EYa, Protodyakonov SM. Research of geometry of some surfaces of the highest orders. Prikladnaya Geometriya i Inzhenernaya Grafika. 1975;(20):138–142. (In Russ.)
  8. Krivoshapko SN. On aero-hydro-dynamical surfaces given by algebraic plane curves. Structural Mechanics of Engineering Constructions and Buildings. 2010;(2):3–4. (In Russ.)
  9. Krivoshapko SN. Hydrodynamic surfaces. Sudostroeniye. 2021;(3):64–67. (In Russ.)
  10. Loginov AYu. Graphical-and-analytical solution on transformation of plane ship curves. Trudy VGAVT (issue 276). Nizhny Novgorod: VGAVT Publ.; 1997. (In Russ.)
  11. Kwang HK. A survey: application of geometric modeling techniques to ship modeling and design. Inter. J. Nav. Archit. Oc. Engng. 2010;2:177–184.
  12. Janson C, Larsson L. A method for the optimization of ship hulls from a resistance point of view. Twenty-First Symposium on Naval Hydrodynamic. Washington: The National Academies Press; 1997. p. 680–696.
  13. Krivoshapko SN. Application of tangential developable surfaces in shipbuilding. Sudostroeniye. 1983; (7):5–7. (In Russ.)
  14. Pyatetzkiy VYu. Ships of simplified forms for river deep stream. Kiev: AN URSR Publ.; 1962. (In Ukr.)
  15. Krivoshapko SN. About parabolic bending of a flat metal sheet into a torso structure. Tekhnologiya Mashinostroeniya. 2020;(11(229)):14–24. (In Russ.)
  16. Ivanov VN, Romanova VA. Constructive forms of spatial structures (visualization of surfaces in MathCad, AutoCad). Moscow: ASV Publ.; 2016. (In Russ.)
  17. Tober H. Evaluation of drag estimation methods for ship hulls. Stockholm: KTH Royal Institute of Technology, School of Engineering Sciences; 2020.
  18. Dambrine J, Pierre M, Rousseaux G. A theoretical and numerical determination of optimal ship forms based on Michell’s wave resistance. ESAIM Control Optimisation and Calculus of Variations. 2016;22(1):88–111.
  19. Alborova LA. Opportunities of velaroidal shells. Engineering Systems – 2020: Proceedings of the Scientific and Practical Conference with International Participation Dedicated to the 60th Anniversary of the RUDN University. 2020;1:59–65. (In Russ.)

Copyright (c) 2021 Krivoshapko S.N., Ivanov V.N.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies