A nonlinear mathematical model for coupled heave, pitch, and roll motions of a high-speed planing hull

Tavakoli, Sasan; Ghadimi, Parviz; Dashtimanesh, Abbas

doi:10.1007/s10665-016-9878-2

Cited by 32 publications

(9 citation statements)

References 26 publications

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“…Further extensions of 2D+ T theory for different purposes have been seen and highly accelerated in the past decade in comparison with 1990s and 2000s. Furthermore, Ghadimi and colleagues, [13][14][15] Tavakoli and colleagues, [16][17][18][19] developed several mathematical models for motions in waves, roll motion, asymmetric and yawed condition motions. From these research works, it can be inferred that if 2D+ T theory is developed for performance prediction of a double-stepped planing boat.…”

Section: Motivationmentioning

confidence: 99%

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

Bilandi

Dashtimanesh

Tavakoli

2018

Proceedings of the Institution of Mechanical Engineers, Part M:

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In this article, a mathematical model based on the 2D+T theory has been developed to predict the performance of two-stepped planing hulls in calm water. It has been attempted to develop a mathematical model without using regression formulas. It leads to development of a computational model with no common limitations related to empirical models which have an individual range of applicability. For this purpose, theoretical solution of water entry of a two-dimensional wedge section has been implemented to compute the pressure distribution over wedge section entering water, and then normal forces acting on the two-dimensional sections are computed. Bottom of the boat has been divided into three different planing surfaces including fore, middle and aft bodies. Computations are performed for each of these surfaces. By integrating the two-dimensional sectional normal forces over the entire wetted length of the vessel, the trim angle, wetted surface and resistance have been obtained. To evaluate the accuracy of the presented method, the obtained results are compared against experimental data and a previous empirical-based method developed by authors. The comparison suggests that the proposed method predicted dynamic trim angle, wetted surface and resistance of double stepped boats with reasonable accuracy. The mean errors in prediction of trim angle, wetted surface and resistance are, respectively, 13%, 16% and 8%. It should also be noted that although computation of running attitudes and resistance of double-stepped planing boats are targeted in this article, the mathematical model has been developed in such a way that it has the potential to model transverse and vertical motions of two-stepped planing hulls in future studies.

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Section: Motivationmentioning

confidence: 99%

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

Bilandi

Dashtimanesh

Tavakoli

2018

Proceedings of the Institution of Mechanical Engineers, Part M:

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“…If the forces and moments are determined, they can be used to find the hydrodynamic coefficient of the vessel in horizontal plane, providing us with necessary data for determining the detection of stability of the vessel. Different methods such as analytical, [38][39][40][41] semi-empirical [42][43][44] and experimental approaches [45][46][47] can be used for finding these forces and moments. However, in this article, a numerical method is used.…”

Section: Description Of the Problemmentioning

confidence: 99%

Numerical investigation of hydrodynamic forces acting on the non-stepped and double-stepped planing hulls during yawed steady motion

Ghadimi

Panahi

2018

Proceedings of the Institution of Mechanical Engineers, Part M:

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This article focuses on the steady motion of yawed planing hulls with emphasis on the effects of adding steps to the bottom of these vessels on the hydrodynamic forces and moments acting on the boat. To analyze the problem, the Ansys-CFX software is used and three different planing hulls are investigated in steady yawed condition. The main targeted results include hydrodynamic forces and moments acting on the boat at different yaw angles and beam Froude numbers which provide important insights regarding the effects of loading and adding step on these forces and moments. The numerically predicted sway forces are compared against experimental data, suggesting that the current numerical model predicts sway and surge forces with reasonable accuracy. Moreover, it is observed that surge force coefficient of the investigated prismatic planing hull with light loading condition does not change significantly when the hull is relocated in a yaw angle, while it is remarkably affected when the boat is heavy. Furthermore, it is observed that this prismatic planing hull has smaller rolling moment in a steady yawed motion, when it moves at larger beam Froude number. Meanwhile, the computed yawing moments of this hull indicate that an increase in speed does not change this moment notably, while an increase in its weight yields larger yawing moment. Comparison of the results of stepped and non-stepped planing hulls indicates that surge force coefficient of the stepped hull is larger, while its sway force and rolling moment are smaller. This is mainly caused by the shape of the interrupted wetted surface and larger number of maximum pressure area in the stepped planing hull. Finally, it is concluded that there is no significant difference between the yawing moment of the investigated stepped and non-stepped planing hulls.

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“…One of the achievements in providing relationships for discrete motions is to make it possible to obtain relationships for the coupled motions. So far, some relationships have been provided by researchers to consider coupled heave and pitch motions (Ghadimi, Tavakoli, Dashtimanesh et al, 2016b) as well as coupled heave, pitch, and roll motions (Tavakoli et al, 2017). However, these investigations may be conducted in calm water or in the presence of waves, depending on the purpose of the researcher.…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of the effect of two steps on the performance and longitudinal stability of a mono-hull high-speed craft

Sajedi

Ghadimi

2020

Cogent Engineering

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Transverse steps in modern high-speed craft can increase the longitudinal stability in addition to reducing frictional resistance. The porpoising instability can also be avoided by selecting the appropriate location and height of the transverse step. In the current paper, a non-step and a double-step model are investigated. The primary purpose of the present study is to examine the impact of second step on the stability and performance of the craft. Both models are generally identical. They are prismatic with a deadrise angle of 24 degrees, made of fiberglass, and are 2.64 meters long and 0.55 meters wide. The only difference between the two models is the bottom shape. One has two transverse steps, and the other has no step. These models are tested in a towing tank within a range of beam Froude numbers of 0.43 to 3.87. Measured parameters include rise-up of the bow and aft as well as center of gravity, trim, and resistance of the models. The obtained results indicate that through creating the second step, the longitudinal stability of the model increases, and the trim decreases. On the other hand, the double-step model has lower resistance in the pre-planing state.

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A nonlinear mathematical model for coupled heave, pitch, and roll motions of a high-speed planing hull

Cited by 32 publications

References 26 publications

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

Numerical investigation of hydrodynamic forces acting on the non-stepped and double-stepped planing hulls during yawed steady motion

Experimental investigation of the effect of two steps on the performance and longitudinal stability of a mono-hull high-speed craft

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