Basic stability theory
This is based on two concepts. The first is the ‘centre of gravity’ or CG, which is the effective centre of the weight of all the elements comprising the boat and the point through which the total weight effectively acts. It does not change unless weight is changed or moved. Then there is the centre of buoyancy’ or CB, which is the geometric centre of the immersed part of the hull of the boat, and through which the buoyancy force effectively acts. It is continually moving as the boat heels or trims. A boat is stable if, as the boat moves, the CB generates a moment sufficient to return the boat to the upright.
Figure 1 shows that when the boat is upright, the CG is directly above the CB, and so it will remain stationary. If however the boat is heeled by some external influence (eg: wind or waves) the CB moves to one side, thus generating a restoring moment about the CG – see Figure 2. The further the CB moves for a given heel angle, the greater the tendency to return to the upright. The size of the ‘righting moment’ is the weight of the boat multiplied by the distance GZ as shown in Figure 2, which is sometimes known as the ‘righting lever’.
If weights are moved to one side, so that the CG is no longer on the centreline, the boat will adopt a steady angle of heel so that the CG and CB are once again in the same vertical line – see Figure 3.
One can also see from Figure 2 that the size of the righting moment crucially depends on the CG height. Raising the CG inevitably reduces the stability. Conversely lowering the CG improves the stability. But if this is achieved by adding ballast rather than lowering existing weights, it reduces freeboard and may cause down-flooding through openings at lesser angles of heel.
It is clear, therefore, that the stability of a particular boat is dependent on both the hull shape and the amount and position of its component weights. Changes to either will also change the stability characteristics. For this reason the basic design of the boat dictates its stability properties. The hull shape determines the way the CB will move. The layout, which determines the position of most of the heavy components, limits to a large degree the extent to which the overall CG can be controlled. The stability can then only be adjusted by carefully locating the remaining components or adding ballast.
The value of the righting moment varies with the angle of heel, and is normally plotted on a graph as shown in Figure 4. This curve is often used to define minimum static stability properties for boats that may encounter substantial waves.
Note that it is not only the shape of the hull below the gunwale that is significant. The stability at large angles of heel, which governs behaviour in the event of a near-inversion, is greatly affected by the deckhouse and superstructure design.
Boats don’t sink unless they get water inside them! If they have swamped flotation even then they will not do so. The Stability Standard addresses this by setting the following requirements:
◦ minimum height from the waterline to any potential down-flooding aperture, measured when the boat is upright;
◦ minimum heel angle before potential down-flooding openings become submerged;
◦ the size, watertightness and draining ability of all recesses including cockpits;
◦ the watertightness of all closures such as windows, hatches and doors;
◦ the integrity of through-hull fittings.
Traditionally the term ‘freeboard’ is the height from the waterline to the deck, but in stability and buoyancy terms it is the height to potential down-flooding apertures and openings that is important. ISO 12217 uses the more specific term ‘down-flooding height’ rather than freeboard, to avoid confusion.
This maybe necessary for one of two reasons:
◦ showing that a swamped boat will support the required weight;
◦ demonstrating theoretically that a boat will float after being completely inverted or swamped.
The first approach is used for smaller boats where a practical test is most convenient. The most difficult aspect is finding a suitable depth of water in which to conduct the test. If the boat should accidentally sink in deep water, it creates problems!
The second approach requires that the weights of all the components built into the boat are known, together with the density of the material of which they are made. This enables the buoyant volume of each component to be calculated. If the total buoyant volume has a sufficient margin over the loaded weight the boat will float even if swamped or holed.
Clearly stability is not a parameter that can be directly measured such as the length. Neither is there one measure of all aspects of the stability of a boat.
We can measure the amount of stability when the boat is nearly upright by a practical test. To get the stability at large angles of heel (such as might occur in waves) not only practical tests are involve, but also calculations are involved — nowadays most conveniently done by computer.
If a very careful ‘inclining experiment’ is conducted, then the CG position can be calculated, after which the stability at a whole range of heel angles and weights can be calculated. This process requires specialist knowledge, and for many boatyards the most sensible approach may be to involve a consultant naval architect. One needs to know with as much accuracy as possible:
◦ the weight of the boat, by direct weighing or calculation from the drafts measured forward and aft;
◦ the size of the heeling weights and the distance through which they are moved;
◦ the hull shape — from the lines plan;
◦ the precise heel angle for a known weight shifted through a known transverse distance.
Usually a series of angles are measured for a series of heeling moments applied to both port and starboard. The heel angle is traditionally measured by a pendulum, with the plumb bob submerged in a tank of oil or water to dampen any movement. However, a water tube can be used, in which the upright legs of the tube are as widely spaced as possible. A constriction can be introduced to help damp out fluctuations in the water level. An electronic level or inclinometer is also a useful solution.
Tremendous care is needed if an inclining experiment is to yield accurate results. The only boats for which an inclining experiment is not practical are very small boats, which are too sensitive to the wind and small wavelets, and catamarans, because their initial stability is so great in relation to the CG height.