Objective  In order to provide a quantitative basis for the layout of buoyant material in a submersible to improve its initial transverse metacentric height, this paper attempts to obtain the critical height equation of buoyant material through analytic derivation, and proposes layout schemes and suggestions on this basis.

  Methods  By deriving the initial transverse metacentric height equation after adding buoyant material in combination with the partial derivatives method, such factors as buoyant material volume and gravity center are analyzed, and the buoyant material critical height equation is obtained through equivalent substitution. To gain a better understanding of the critical height equation and other factors that can affect the results such as displacement and transverse metacentric height before the installation of the buoyant material, an equivalent mathematical model of a typical transverse section of a submersible is constructed, and different numerical examples are studied by comparison.

  Results  It is concluded that the initial transverse metacentric height of a superior scheme can be 1.8% higher compared to pre-installation conditions. It is also likely that much better initial transverse metacentric height could be achieved if the 3D districts were released.

  Conclusions  The results of this study can improve the initial transverse metacentric height of submersibles. The proposed equation is key to a buoyant material layout scheme. In addition, several layout principles are put forward to help designers when incorporating buoyant material into submersible design.