Metacenter and ship stability

Abstract

Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.We address the location of the metacenter M of a floating body such as a ship. Previous studies of M in relation to the stability of a ship have mainly used geometrical approaches and were limited to near equilibrium. We develop a quantitative approach to the location of M for a general shape of the cross-section of a floating body in a rolling/pitching motion and for an arbitrary heel angle. We show that different definitions of M refer to one and the same special point of the floating body. We discuss the relation between the height of M with respect to the line of flotation and the contribution of the buoyancy force to ship stability. We provide expressions and graphs of the buoyancy, flotation, and metacentric curves for some simple shapes of floating bodies.

Simulation of a ship’s roll under different loading conditions

“…Авторами [14][15][16] рассматривается поведение судна на тихой воде без сопротивления и указывается, что проведение исследований такой качки позволяет получить ряд важных выводов. Предполагается, что амплитуда качки невелика и судно имеет положительную начальную метацентрическую высоту.…”

Conditions of using floating cranes for lifting sunken objects on inland waterways

“…teretnom uređaju plovne dizalice, smanjiće se stabilitet, a plovna dizalica će se nagnuti u uzdužnom smeru za ugao ψ i u poprečnom za ugao φ (slika 3). Prema tome, za teret poznate mase p koji visi na teretnom uređaju plovne dizalice treba proračunati smanjenje početne metacentarske visine, zatim ugao uzdužnog nagiba ψ, ukupnu promenu trima u, i ugao poprečnog nagiba φ [9]. M G posmatra se kao pri dodavanju tereta p na određenu visinu.…”

Rolling the Black Pearl Over: Analyzing the Physics of a Movie Clip

“…2, the only way that M could remain fixed in location for arbitrary f is if the hull of the ship were exactly cylindrical in shape (and no cargo-including hanging loads such as booms and "free" surfaces of liquids such as drinking water 5 -shifted during rolling), in which case the metacenter would coincide with the hull's center of curvature. 6 In practical terms, if h were constant then r would be linearly proportional to sin f and hence there would be a restoring torque even if the ship were nearly completely inverted (since sin f > 0 for 0 o < f <180 o , cf. the red curve in Fig.…”

“…(6), and where the ship's moment of inertia is I s = m s R 2 . The torque due to the lateral displacement of the runners is t r = -m r gx cos f (since x cos f is the component of the crew members' displacement parallel to the waterline, and where the minus sign indicates that a rightward x would produce a clockwise torque, as one can see fromFig.…”

“…Rotational drag should be most pronounced at the keel, which resists lateral displacements. The distance from the keel K to the flotation point O (which specifies the ship's rotational axis6 ) is equal to the draft, d = 3.8 m. The kinematic viscosity of seawater 8 at 15 o C is v = 1.16 310 -6 m 2 /s. Galleons have a small keel9 with a height of only about D = 8 in = 0.2 m. In the simulations inFigs.…”