A Treatise on the Stability of Ships

Reed, Edward James

doi:10.1017/cbo9780511794087

Cited by 2 publications

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“…The problem of the stability of floating bodies, which can be traced back to Archimedes, 1 is of continued interest [2][3][4][5][6][7][8][9][10] and an important part of academic studies. [11][12][13][14][15][16][17][18] In addition to the force of gravity ͑weight͒ F g , a floating body is subject to a force equal to the weight of the displaced fluid and acting in the opposite direction to F g .…”

Section: Introductionmentioning

confidence: 99%

Metacenter and ship stability

Mégel

Kliava

2010

American Journal of Physics

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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.

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Section: Introductionmentioning

confidence: 99%

Metacenter and ship stability

Mégel

Kliava

2010

American Journal of Physics

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“…On the other hand, the question of the location of A is closely related to that of ship stability, which can be traced back to Archimedes himself, see [1, On Floating Bodies, Book I, pp 253-62; Book II, pp 263-300]. The latter problem has never ceased to interest scientists and engineers [8,[12][13][14][15][16][17][18][19] and has become an important part of academic studies [2, 5-7, 10, 20-22]. Meanwhile, the relation between Bouguer's criterion and that given 3 years later by Euler in Scientia Navalis (1749) [12] (the ship remains stable as long as the couple weight and buoyancy force creates a restoring moment), to our knowledge, has not been discussed before.…”

Section: Introductionmentioning

confidence: 99%

Non-uniqueness of the point of application of the buoyancy force

Kliava¹,

Mégel²

2010

Eur. J. Phys.

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Even though the buoyancy force (also known as the Archimedes force) has always been an important topic of academic studies in physics, its point of application has not been explicitly identified yet. We present a quantitative approach to this problem based on the concept of the hydrostatic energy, considered here for a general shape of the cross-section of a floating body and for an arbitrary angle of heel. We show that the location of the point of application of the buoyancy force essentially depends (i) on the type of motion experienced by the floating body and (ii) on the definition of this point. In a rolling/pitching motion, considerations involving the rotational moment lead to a particular dynamical point of application of the buoyancy force, and for some simple shapes of the floating body this point coincides with the well-known metacentre. On the other hand, from the work–energy relation it follows that in the rolling/pitching motion the energetical point of application of this force is rigidly connected to the centre of buoyancy; in contrast, in a vertical translation this point is rigidly connected to the centre of gravity of the body. Finally, we consider the location of the characteristic points of the floating bodies for some particular shapes of immersed cross-sections. The paper is intended for higher education level physics teachers and students.

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A Treatise on the Stability of Ships

Cited by 2 publications

References 0 publications

Metacenter and ship stability

Metacenter and ship stability

Non-uniqueness of the point of application of the buoyancy force

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