Abstract
In the current article, the hydrodynamic forces of single-stepped planing hulls were evaluated by an analytical method and compared against towing tank tests. Using the 2D + T theory, the pressure distribution over the wedge section entering the water and the normal forces acting on the 2D sections have been computed. By integrating the 2D sectional normal forces over the entire wetted length of the vessel, the lift force acting on it has been obtained. Using lift forces as well as the consequence pitch moment, the equilibrium condition for the single-stepped planing hull is found and then resistance, dynamic trim, and the wetted surface are computed. The obtained hydrodynamic results have been compared against the experimental data and it has been observed that the presented mathematical model has reasonable accuracy, in particular, up to Froude number 2.0. Furthermore, this mathematical model can be a useful and fast tool for the stepped hull designers in the early design stage in order to compare the different hull configurations. It should also be noted that the mathematical model has been developed in such a way that it has the potential to model the sweep-back step and transverse the vertical motions of single-stepped planing hulls in future studies.
Highlights
Over time, researchers in naval architecture developed different methods to reduce the frictional resistance of planing hulls
Savitsky [4] developed a mathematical model for the performance prediction of planing hulls
A 2D + T analytical method has been developed for the performance evaluation of stepped hulls
Summary
Researchers in naval architecture developed different methods to reduce the frictional resistance of planing hulls. The application of 2D + T theory dates back to the end of the 1970s, where Zarnick [14] utilized Wagner [10] and von Karman [9] theoretical equations and developed a mathematical model based for computation of planing hull behavior in waves This method could be used for the performance prediction if the water surface is set to be at rest. Ghadimi et al [17,18,19] and Tavakoli et al [20,21,22,23], developed several mathematical models for computation of roll motions in waves, roll motion, asymmetric, and yawed condition motions All of these studies are performed using 2D + T theory and relate to non-stepped planing hulls.
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