Algebraic ship hull surfaces with a main frame from three plane curves in coordinate planes

Cover Page

Cite item


One of the important problems of naval architects and designers is a choice of rational ship hull shape. A choice of ship hull form is based often on empirical formulae or on designers’ intuition. In the study, a method of determination of generalized explicit algebraic equations of theoretical ship hull configuration with three main cross sections given in advance and coinciding with waterline, main buttock (keel line), and midship section that are taken in the form of superellipses or in the form of any algebraic curve. Presented three of algebraic equations of surfaces with the same frame from three plane curves describes infinite number of ship hull surfaces. Having the same three plane curves one can get three algebraic surfaces of different order. The optimal shape, including cylindrical fragment or the ship hull shape containing two different - stern and bow - parts, joining along midship section, can be chosen with the help of methods of computer modelling with the application of artificial intellect using the materials of the paper. One can apply given results for the design of underwater apparatus on the early stage of the design.

About the authors

Sergey N. Krivoshapko

Peoples’ Friendship University of Russia (RUDN University)

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

DSc, Professor of the Department of Civil Engineering, Academy of Engineering

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


  1. Avdonev EYa. Analytical description of the ship hull surfaces. Prikladnaya Geometriya i Inzhenernaya Grafika (issue 15). Kiev; 1972. p. 156–160. (In Russ.)
  2. Janson C, Larsson L. A method for the optimization of ship hulls from a resistance point of view. National Research Council. Twenty-First Symposium on Naval Hydrodynamic. Washington: The National Academies Press; 1997. p. 680–696.
  3. Oliveira MC, Fernandes José V. modelling and simulation of sheet metal forming processes. Metals. 2019;9(12):1356.
  4. Oetter R, Barry CD, Duffty B, Welter J. Block construction of small ships and boats through use of developable panels. Journal of Ship Production. 2002;18(2): 65–72.
  5. Krivoshapko SN. Hydrodynamic surfaces. Shipbuilding. 2021;(3):64–67. (In Russ.)
  6. Krivoshapko SN, Ivanov VN. Algebraic surfaces for rational ship hulls. Tekhnologiya Mashinostroeniya. 2022;(3):17–24.
  7. Karnevich VV. Generating hydrodynamic surfaces by families of Lame curves for modelling submarine hulls. RUDN Journal of Engineering Research. 2022;23(1):30–37.
  8. Karnevich VV. Hydrodynamic surfaces with midship section in the form of the Lame curves. RUDN Journal of Engineering Research. 2021;22(4):323–328.
  9. Krivoshapko SN. Tangential developable and hydrodynamic surfaces for early stage of ship shape design. Ships and Offshore Structures. 2022:1–9.
  10. Morozov BN, Tzvetkov VV. On the question of choice of scheme of making bottom section of hulls. Vesnik RAEN (issue 7). Kaliningrad: KGTU Publ.; 2013. p. 80–85. (In Russ.)
  11. Rozinov AYa. Technological improvement of the hull boats design and the process of their assembly. Tekhnologiya Mashinostroeniya. 2020;(5):15–23. (In Russ.)
  12. Bronskiy AI, Glozman MK, Kozlyakov VV. The basis of choice of structures of ship hull. Leningrad: Sudustroeniye Publ.; 1974. (In Russ.)
  13. Kwang Hee Ko. A survey: application of geometric modeling techniques to ship modeling and design. International Journal of Naval Architecture and Ocean Engineering. 2010;2:177–184.
  14. Zhang Sh, Tezdogan T, Zhang B, Lin L. Research on the hull form optimization using the surrogate models. Engineering Applications of Computational Mechanics. 2021; 15(1):747–761.
  15. Bajoria GCh. On one method of the development of a torse surface. Shipbuilding. 1984;(9):37–38.

Copyright (c) 2022 Krivoshapko S.N.

License URL:

This website uses cookies

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

About Cookies