Applications of the Ogilvie-Tuck Formulae to Ship Hydrodynamics

The work of Ogilvie and Tuck [1] was critical in extending strip theory to problems with forward speed. Salvesen et al. [2] used some of those findings in their classical work to determine the hydrodynamic coefficients in five degrees-of-freedom. Other methods have also utilized the formulae with success. The original derivation makes several assumptions about the hull shape and the steady flow around it. In practice, these assumptions do not hold exactly. Other simplifications are usually made, i.e. the mean ship speed is used instead of the actual steady flow around the hull. These may violate the original assumptions, but the results are generally satisfactory. The truly elegant aspect of the Ogilvie-Tuck hydrodynamic coefficients is that they can be calculated from zero-speed results. This is a product of the approach, assumptions, and mathematics done in Appendix A of the original work [1] to derive the Ogilvie-Tuck theorem, also called Tuck’s theorem by many authors. The Ogilvie-Tuck formulae include the hydrodynamic coefficients, expressions of the m_j terms, and the Ogilvie-Tuck theorem. This paper discusses the original derivation and several practical applications, including those where the assumptions may be violated. Several qualitative or quantitative statements can be made about the errors introduced by simplifications. Some computational results are presented to emphasize the significance in practical use.