## Stability At Small Angles

The concept of the stability of a floating body can be explained by considering it to be inclined from the upright by an external force which is then removed. In Figure 5.6 a ship floats originally at waterline W0L0 and after rotating through a small angle at waterline W1L1.

The inclination does not affect the position of G, the ship's centre of gravity, provided no weights are free to move. The inclination does, however, affect the underwater shape and the centre of buoyancy moves from B0 to B1. This is because a volume, v, represented by W0OW1, has come out of the water and an equal volume, represented by L0OL1, has been immersed.

If ge and gi are the centroids of the emerged and immersed wedges and gegi = h, then:

B0B1

v X h where V is the total volume of the ship.

In general a ship will trim slightly when it is inclined at constant displacement. For the present this is ignored but it means that strictly B0, B1, ge, etc., are the projections of the actual points on to a transverse plane.

The buoyancy acts upwards through B1 and intersects the original vertical at M. This point is termed the metacentre and for small inclinations can be taken as fixed in position. The weight W = mg acting downwards and the buoyancy force, of equal magnitude, acting upwards are not in the same line but form a couple W X GZ, where GZ is the perpendicular on to B1M drawn from G. As shown this couple will restore the body to its original position and in this condition the body is said to be in stable equilibrium. GZ = GM sin <p and is called the righting lever or lever and GM is called the metacentric height. For a given position of G, as M can be taken as fixed for small inclinations, GM will be constant for any particular waterline. More importantly, since G can vary with the loading of the ship even for a given displacement, BM will be constant for a given waterline. In Figure 5.6 M is above G, giving positive stability, and GM is regarded as positive in this case.

If, when inclined, the new position of the centre of buoyancy, B1, is directly under G, the three points M, G and Z are coincident and there is no moment acting on the ship. When the disturbing force is removed the ship will remain in the inclined position. The ship is said to be in neutral equilibrium and both GM and GZ are zero.

A third possibility is that, after inclination, the new centre of buoyancy will lie to the left of G. There is then a moment WX GZ which will take the ship further from the vertical. In this case the ship is said to be unstable and it may heel to a considerable angle or even capsize. For unstable equilibrium M is below G and both GM and GZ are considered negative.

The above considerations apply to what is called the initial stability of the ship, that is when the ship is upright or very nearly so. The criterion of initial stability is the metacentric height. The three conditions can be summarized as:

 M above G

## How To Have A Perfect Boating Experience

Lets start by identifying what exactly certain boats are. Sometimes the terminology can get lost on beginners, so well look at some of the most common boats and what theyre called. These boats are exactly what the name implies. They are meant to be used for fishing. Most fishing boats are powered by outboard motors, and many also have a trolling motor mounted on the bow. Bass boats can be made of aluminium or fibreglass.

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