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© 2009 Mark Kennett 

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Boat design: an introduction to stability

Stability is the element of a boat’s performance that influences its ability to return to an upright position after it has been inclined by some force.

There are two distinct types of stability that influence boat performance: form stability and weight stability.

Form stability

Form stability is gained by the shape of the hull alone. A good way to visualise this is to use the plank of wood analogy.

Imagine a plank of wood floating on the surface of the sea. Let’s give it some dimensions, say 39 inches (1 metre) long, 1 foot (300 mm) wide and 2 inches (50 mm) thick. This plank is obviously going to float flat face down. It is not going to float on its edge.

In flat water this plank would be quite hard (for a plank) to tip over or capsize transversely. This plank has the characteristic known as ‘stiffness’. It resists being rolled about its longitudinal axis.

Now imagine the plank on the face of a steep wave. The ‘stiff’ plank would immediately conform to the new water surface, even if it were 45 degrees.

Even if the water surface were 60 degrees.

It is quite easy to visualise that if the plank were struck by a breaking wave crest while inclined at 60 degrees to the horizontal it could well capsize.

It would then float just as stably upside down and would need a similar breaking wave to turn it ‘right side up’.

So stiffness, or form stability, which resists rolling motion and fights to return the plank (hull) to an upright position in flat or moderate seas actually contributes to the danger of capsize on a steep wave face.

Weight stability

Weight stability is the stability gained by positioning weight in a hull. This can be ballast or structural weight.

To visualise how this works imagine a buoyant cylinder, sealed at each end, floating on the surface of a flat calm sea.

If you give it a spin it will continue to rotate until it is eventually stopped by the friction of water against the cylinder walls. It won’t necessarily stop in the same position that it started from. This hull section (the arc of a circle) has zero form stability.

Now open up the cylinder and pour in a small amount of cement ballast and allow it to settle and harden in the horizontal position (not all poured down to one end) and re-seal the cylinder. Place it back on the water. The cylinder will now float with the weighted side downward.

Rotate (incline) the cylinder to say 90 degrees.

As soon as the ballast (fixed in the cylinder) is rotated out of the vertical position its weight tries to return the cylinder to its original (vertical) position. If the cylinder is rotated to 179 degrees (upside down) the weight will still rotate the cylinder back towards its original position.

This is weight stability.

With this circular hull form, however, the cylinder, when rolled to 90 degrees, will roll back beyond the upright, like a pendulum, to nearly 90 degrees on the other side, slowed only by the friction effect of water on the cylinder walls. This rolling back and forth will continue until all the rolling energy is dissipated by friction. Needless to say this is hardly a desirable state of affairs. By changing the cylindrical shape to one with elements of form stability, the rolling can be damped and a more practical motion achieved.

In reality most hulls show a mixture of weight and form stability and it is the combination of these two elements that give a hull its overall stability characteristics.

Measuring intact statical stability 

The combination of weight and form stability is called static or statical stability because the hull is assumed to be inclined by some force while floating in flat calm (static) water and not moving ahead.

Intact means what it says: there is an assumption that the hull, deck and superstructure remain watertight at all angles of heel.

Real world sailors will see problems with both of these assumptions. Nevertheless statical stability can be one useful indicator of the fundamental ability of a hull to return to upright from various angles of inclination.

There is a number of measures of intact statical stability. Perhaps the most useful for the small boat sailor is the GZ curve (graph).

GZ is the theoretical line of action or force that exists between the forces of buoyancy and gravity operating on the weight of a boat. It is commonly referred to as the GZ arm or lever and can be either positive or negative.

A positive GZ works to twist the inclined hull back to upright. A negative GZ works to twist the inclined hull upside down.

The length of the GZ arm varies with the angle of inclination. The shorter it gets the less twisting force (positive or negative) is available.

Most hulls will increasingly resist heeling up to about 50 degrees, i.e. the positive GZ arm continues to lengthen up to this point. This also means that the force will have to keep increasing up to this point to continue inclining the boat.

As the inclination continues to greater angles, the GZ arm becomes gradually shorter. It is still positive, and if the inclining force is reduced or removed the hull will start to return to upright.

At some angle of heel the GZ can be reduced to zero. The boat is then said to be in unstable equilibrium: it could tip either way. A further increase in the angle of inclination results in a negative GZ. Now the forces of weight and buoyancy actively work to capsize the hull. Even if the inclining force is removed the hull will still capsize.

It will need to be rolled by a wave, back past the point of unstable equilibrium to regain a positive GZ and return to upright.

Presentation of GZ data

GZ arms are plotted on a graph at various angles of heel known as a GZ curve.

If you multiply the GZ arm by the displacement of the boat you get the righting moment, an indication of the force available to right the hull. This can also be expressed in a graph for different angles of heel.

Real world GZ curves

The old rule of thumb for boat designers in the real world was that in order to have basic offshore ability a boat should be able to self-right from 80–90 degrees, i.e. if thrown over onto her beam ends. Most displacement motor boats of traditional form have this ability if top hamper weights are kept down. Some offshore boats, power and sail, show self-righting, i.e. have a positive righting arm up to 180 degrees. 

The limitations of intact statical stability as a predictor of boat safety

As the name suggests intact statical stability is based on a number of assumptions. I touched on the problem of assuming that a boat, with windows, hatches, ventilators, engine air intakes, etc., will be or will remain intact and watertight when upside down.

Perhaps a more significant and problematic assumption is the one that assumes that boat stability is the same in ‘static’ (i.e. flat water ) conditions as it is in dynamic ones (i.e. the sea).

The most serious and dangerous assumption in my opinion is that if a boat has a good positive GZ curve, this alone is enough to assure safety at sea.

Many boat designers and naval architects still make all of these assumptions. However, citing the Fastnet race disaster of 1979 in which a large number of boats with adequate GZ performance were capsized, some free thinking naval architects have raised questions about these assumptions.

C. A. Marchaj, a leading naval architect and hydrodynamic researcher, has explored many of the factors that he thinks contribute to superior performance at sea. Of course, a good range of stability, as defined by GZ criteria, is up there as an important component of the overall safety of a boat at sea. However, factors such as size, displacement, hull section, hull damping, lateral plane area, underwater plan form, underwater aspect ratio, keel configuration, ballast, topside form, freeboard, centres of gravity, are all of significant importance.

One of the most important factors for boat survivability in extreme conditions is the condition of its crew. It is quite possible to produce a boat that can be knocked down by every passing wave yet still be fully self-righting up to 180 degrees of heel. But such a craft would be disastrous to its crew who would be in danger of serious injury, being lost overboard, etc. In constrast, a strongly built boat of proper form and displacement that showed but half the righting angle of the previous boat could well be a substantially safer craft.

It is important to remember that the safe performance of a boat at sea is quintessentially the result of all the elements that make up its design and construction, blended into a harmonious whole. Crew skill, judgement and competence are an integral part of this picture. No one feature can make a safe boat. Only by combining a large number of sometimes contradictory features can a boat designer produce a craft that can perform its designed role safely at sea.

Click on this link to see the GZ curve for the Independence 48, in the boat plans page.