Mathematical Model of the Manoeuvring Motion of a Ship

  • Yassen Adnan Ahmed
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 85)


There are many kinds of mathematical models that have been proposed to simulate the ship manoeuvring characteristics. The total force model or the simple rudder to yaw response model are useful to do real-time simulation and control. However, each of these models has some limitations. The total force model combined the hull, propeller and rudder forces together. Therefore, if the propeller or rudder is changed in the model, the whole force model needs to be modified. Moreover, the hydrodynamic derivatives for the force terms have less physical meaning to compare. On the other hand, using the rudder to yaw response model, the change in ship velocity or speed drop during manoeuvring cannot be predicted. Considering these facts, this paper describes a widely used mathematical model known as the manoeuvring mathematical group (MMG) or modular model. This model considers not only the hull, rudder and propeller forces separately but also the interactions among them. Each term used in this model has a physical meaning and is constructed as simple as possible. The given model is also verified by the turning tests and speed tests results.


Mathematical models Ship manoeuvring Manoeuvring mathematical group 


  1. 1.
    Ogawa, A., Koyama, T., Kijima, K.: MMG report-I, on the mathematical model of ship manoeuvring (in Japanese). Bull Soc. Naval Archit. Jpn. 575, 22–28 (1977)Google Scholar
  2. 2.
    Ogawa, A., Kasai, H.: On the mathematical method of manoeuvring motion of ships. Int. Shipbuild. Prog. 25(292), 306–319 (1978)Google Scholar
  3. 3.
    Matsumoto, K., Suemitsu, K.: The prediction of manoeuvring performances by captive model tests (in Japanese). J. Kansai Soc. Naval Archit. Jpn. 176, 11–22 (1980)Google Scholar
  4. 4.
    Inoue, S., et al.: A practical calculation method of ship manoeuvring motion. Int. Shipbuild. Prog. 28(325), 207–222 (1981)MathSciNetGoogle Scholar
  5. 5.
    Hirano, M.: Prediction of manoeuvring in shallow water (in Japanese). J. Soc. Naval Archit. Jpn. 69, (1985) Google Scholar
  6. 6.
    Kose, K., Yumuro, A., Yoshimura, Y.:. Concrete of Mathematical Model for Ship Manoeuvrability (in Japanese). In: 3rd Symposium on Ship Manoeuvrability, SNAJ, pp. 27–80 (1981)Google Scholar
  7. 7.
    Yoshimura, Y., et al.: Coasting manoeuvrability of single CPP equipped ship and the application of a new CPP controller. In: Proceedings of MARSIM’93, pp. 651–660 (1993)Google Scholar
  8. 8.
    Ueda, N., Ueno, M.A.: A comparative study on experimental results for manoeuvring hydrodynamic coefficients (in Japanese). Bachelor Thesis paper, Osaka University (1982)Google Scholar
  9. 9.
    Fujiwara, T., et al.: Estimation of wind forces and moment acting on ships. J. Soc. Naval Archit. Jpn. 183, 77–90 (1998)CrossRefGoogle Scholar
  10. 10.
    Davenport, A.G.: The dependence wind loads on meteorological parameters. In: Proceedings of Conference on Wind Effects on Buildings and Structures (1967) Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Malaysian Institute of Marine Engineering TechnologyUniversiti Kuala Lumpur, Dataran Teknologi Kejuruteraan Marin, Bandar Teknologi MaritimLumutMalaysia

Personalised recommendations