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Fluid Statics
Published in Ahlam I. Shalaby, Fluid Mechanics for Civil and Environmental Engineers, 2018
For the case of a top-heavy floating body that is streamlined/average-height body, as illustrated in Figure 2.42c, for a larger-than-designed rotational disturbance, θ the resulting metacenter, M is located below G and thus the metacentric height, GM is negative (overturning moment). Thus, the resulting distance BM is less than the distance GB (remains the same prior to and after the rotational disturbance) due to the larger than design rotational disturbance, θ. One may note that because a larger than design rotational disturbance, θ has been applied, Equations 2.261 and 2.263 for GM and BM, respectively, are no longer valid; instead, an experimental/empirical approach may be used to compute GM and BM.
Offshore Drilling and Production Platforms/Units
Published in Sukumar Laik, Offshore Petroleum Drilling and Production, 2018
The distance GM, that is, the distance between the centre of gravity and the metacentre of a floating body, is called the ‘metacentric height,’ and the distance BM, that is, the distance between the centre of buoyancy and the metacentre of the floating body, is called the ‘metacentric radius.’ Referring to Figure 3.52(a) and 3.52(b), a relationship between metacentric height and metacentric radius can be established as follows:
Substructures of Major Overwater Bridges
Published in Wai-Fah Chen, Lian Duan, Bridge Engineering, 2003
As with all prismatic floating structures, stability requires that a positive metacentric height be maintained. The formula for metacentric height, GM¯, is
Operability analysis of traditional small fishing boats in Indonesia with different loading conditions
Published in Ships and Offshore Structures, 2023
Muhammad Iqbal, Momchil Terziev, Tahsin Tezdogan, Atilla Incecik
One of the ship motion responses obtained from the seakeeping analysis is roll. This response is related to ship stability, defined as the ship's ability to keep returning to its original position due to roll motion caused by external disturbances. Ship accidents, such as capsizing, mostly occur due to stability failures. One of the reasons for capsizing is that ship operators are not given sufficient training regarding ship stability, so there are decision-making mistakes (Davis et al. 2019). To solve this problem, Caamaño et al. (2018) proposed a methodology to automatically assess the ship's stability to minimise the interaction between the crew and the system. This method can estimate the natural frequency of roll motion and the metacentric height throughout the vessel’s voyage. Later, Caamaño et al. (2019) proposed real-time detection of ship stability changes. The system lets the crew know how far the current situation is from the safety limit.
Dynamics of a Y-shaped semi-submersible floating wind turbine: a comparison of concrete and steel support structures
Published in Ships and Offshore Structures, 2022
Chao Li, Shengtao Zhou, Baohua Shan, Gang Hu, Xiaoping Song, Yongqing Liu, Yimin Hu, Xiao Yiqing
The free decay test results listed in Table 6 show a good agreement between the numerical simulations and the model tests, which indicates that the centre of mass, moment of inertia and mooring stiffness of the numerical models are properly modeled. The main differences between the LCP3 and HSP3 model lie in the roll and pitch DOFs. The natural period of HSP3 is nearly 1.6 s smaller than that of the LCP3 model. This can be explained by the formula T = 2π(I/DhT)0.5, where T is the roll/pitch natural period of a platform; I is the rolling/pitching moment of inertia; D is the platform displacement; hT is the metacentric height. As Table 1 shows, the steel platform has a lower CoG (larger metacentric height) and smaller rolling/pitching moment of inertia than the concrete platform, hence shorter roll/pitch natural period is seen.
Parametric study of seakeeping of a trimaran in regular oblique waves
Published in Ships and Offshore Structures, 2020
Leo Nowruzi, Hossein Enshaei, Jason Lavroff, Michael R. Davis
In Figure 10, there is a considerable difference between the maximum and minimum roll response peaks for different configurations that varies between 0.17 and 0.71. In other words, with variation in outriggers’ positions (longitudinally, transversely and vertically), the roll response increased by a factor of five. This highlights the necessity to select the outriggers positions to optimise the design of trimarans based on the motion responses. The formula for the natural roll period, is as follows (Bhattacharyya 1978; Lloyd 1989; Molland 2011):where K is the roll radius of gyration (RoG roll), GM is metacentric height and g is the acceleration of gravity. The roll period is dependent on the ship’s roll radius of gyration and the dynamic metacentric height. Having GM and K for all configurations, the roll natural period is estimated using Equation (2). As shown in Table 6, the calculated value and the measured response from oscillation tests matched very well. Variation in the waterplane area can affect the dynamic metacentric height, while weight distribution is the contributing factor in determining RoGRoll. Added mass moment of inertia also affects the roll damping (Yun et al. 2018).