Alternative approach to explore the stability of floating bodies


  • Manuel Alejandro Segura Delgado Universidad de los Andes



Floating bodies, Metacentric height, rotational stability


We present a simplified model of a boat to study its rotational dynamics, which is a significant criterion for the development of navigation systems. The stability of a floating body can be examined by means of rotational potential energy, which depends solely on the boat’s gravity center and a point called the metacentric height. Typically, this geometric point is a function of the body’s orientation in relation to the fluid surface, and the estimation of its value can often be ambiguous. This paper presents an alternative method for calculating the metacentric height using a vectorial approach, as well as a general definition of rotational potential energy applicable to this type of problem. The potential energy facilitates the determination of stable and unstable equilibrium directions as a function of the boat’s relative density and orientation.


H. Shames Irving, Mecánica de fluidos, (Colombia: Mc Graw Hill 1995).

V. L. Streeter et al., Mecánica de los fluidos, (vol. 7 McGraw- Hill Colombia, 1988).

Y. Feigel and N. Fuzailov, Floating of a long square bar: experiment vs theory, European Journal of Physics 42 (2021) 035011.

E. Gilbert, How things float, The American mathematical monthly 98 (1991) 201,

M. A. S. Delgado, Modelo energético sobre la estabilidad estática de un cuerpo flotante en 2D, LatinAmerican Journal of Physics Education 5 (2011) 23,

P. L. Varkonyi, Floating body problems in two dimensions, Studies in Applied Mathematics 122 (2009) 195,

K. J. Spyrou, The stability of floating regular solids, Ocean Engineering 257 (2022) 111615,




How to Cite

M. A. Segura Delgado, “Alternative approach to explore the stability of floating bodies”, Rev. Mex. Fís., vol. 69, no. 5 Sep-Oct, pp. 050601 1–, Sep. 2023.