Steady performance prediction of a heeled planing boat in calm water using asymmetric 2D+T model

Abstract

This article presents a simple mathematical model for predicting the running attitude of warped planing boats fixed in a heel angle and free to trim and sinkage. The proposed model is based on asymmetric 2D + T theory utilizing a pressure equation which is previously introduced in the literature to compute the hydrodynamic force acting on a heeled planing hull. Integration of pressure distribution on the asymmetric wedge sections enables the suggested model to compute trim angle, center of gravity rise, resistance, and heeling moment acting on the heeled planing boat in calm water. The hydrostatic force in addition to two drag forces acting on the pressure area and spray area are also taken into account. Finally, a computational algorithm is introduced to find the running attitude of the heeled planing boats. The validity of the proposed model is examined by comparing the obtained running attitudes for two planing hulls series with zero heel angle and computed lift force and heeling moment of a heeled planing boat against available experimental data. Based on the comparisons, favorable accuracy is observed for both symmetrical and asymmetrical conditions. Moreover, it is shown that existence of a heel angle can lead to a decrease in trim angle and resistance, while it intensifies the center of gravity rise of planing boats. It is also observed that as the beam Froude number increases, the heeling moment of the heeled boat reduces.

Experimental and Numerical Investigation of Stepped Planing Hulls in Finding an Optimized Step Location and Analysis of Its Porpoising Phenomenon

“…One of the greatest theories proposed for examining the performance of a high-speed craft is 2D + T. In 2013, Haase et al [6] investigated the behavior of a prismatic planing hull motion in head waves by 2D + T theory. Ghadimi et al [7] studied the running attitude of the warped planing hulls using a simple model based on the 2D + T theory. Morabito [8] used slender body theory and estimated side forces acting on planing hulls and compared the results with the experimental data.…”

Experimental and Numerical Research on the Influence of Stern Flap Mounting Angle on Double-Stepped Planing Hull Hydrodynamic Performance

“…A series of model tests on a double-stepped planing hull were carried out to research the resistance performance influencing factors of the hull. Besides the numerical method, other research has also been conducted focusing on the stepped planing hull [13][14][15].…”

Experimental Study of the Wedge Effects on the Performance of a Hard-chine Planing Craft in Calm Water

“…The sectional forces and the 3D values are again found using the developed program by Ghadimi et al [20]. The estimated wedge lift computed by 2D+T theory and by implementing the measurements are displayed and compared against the results of Savitsky and Brown [6] empirical relation (equation (8)) in Figure 21.…”

“…tr HD f C f  (20) 2D hydrodynamic forces for each test case are computed by implementing the measured trim angle and keel wetted length as inputs. These values are implemented in the above mentioned equations and the 2D forces are determined.…”

“…Performance of the planing hulls with appendages cannot be mathematically modeled easily in both steady and unsteady conditions. For such cases, the previous semi-empirical works [15][16][17] and analytical works [18][19][20] cannot be used directly and the available empirical relations [6,21] might be applicable which are limited to some specified conditions. Therefore, by following the previous works, the best alternatives for studying such phenomena are recommended to be numerical and experimental approaches.…”