Transverse Stability, Part 2: Stability Curve and Knock-Down Energy

Last Updated on 05 August 2016 by

This article follows Transverse Stability Part 1: Fundamentals

The most relevant way of expressing the relation between heel and stability for a given vessel is plotting the GZ-curve or the righting moment curve.

Ships and load-carrying vessels start from KN-curves, because they allow taking into account large variations in trim and loading, but at the expense of added complexity we don’t need for pleasure crafts and the outcome after a lot of work is still a GZ-curve.

GZ is a quantity that was introduced earlier and since the righting moment is simply GZ multiplied by the weight of the vessel, both curves look exactly the same, the only difference being the unit used for expressing them.

There are number of elements of immediate interest in such a stability curve:

• Its initial slope. This highlights how quickly the vessel stiffens up with heel and also relates to another quantity known as metacentric height, or GM, which we won’t develop here because we don’t need it to understand stability. GM is interesting in motor vessel and ship design primarily.
• The maximum value and its position.
• The cross-over point with the horizontal axis, also known as Angle of Vanishing Stability (AVS).
• The balance between the positive and negative areas under the curve highlights the relative difference between upright and inverted stability and the likelihood of the boat to remain inverted if ever rolled and capsized.
• The area under the curve represents the energy required to respectively capsize and then re-right the vessel afterwards if the curve is plotted as righting moment. If it is plotted in terms of GZ instead, it leaves out the differences in inertia between a light and a heavy vessel.

Desirable properties in the stability curve of small ocean-going vessels are:

• A large area of positive stability compared to inverted stability
• Sufficient stability increase at small angles
• Vanishing stability at an angle unlikely to ever be reached

The Effect of VCG Increase on the Stability Curve

The consequence adding weight above the original centre of gravity of a vessel on its stability curve depends on how stability was achieved in the first place.

Shallow, beamier hulls nearly always feel stiff and safe under normal conditions and variations in the height of the centre of gravity are not readily noticeable. The issue is that unless their centre of gravity is kept adequately low, their stability can peak very quickly and then collapse towards the point of capsize. There is little in the way of a gradual warning.

Deep hulls don’t have a great deal of initial stability, but their limit in terms of acceptable vertical centre of gravity only reduces gradually with heel. It is a mixed blessing. Since they are not very stiff in the first place and the change is very gradual, it is difficult to assess the safe zone. By the time they start feeling tender, rolling further and coming back more slowly, they may already be a long way into the danger zone. A tide rip, a steep wave on the beam and they can capsize with little warning.

One should refrain from drawing too many conclusions from a stability curve alone

The stability curve relates to the hydrostatic properties of the hull. Stability at sea is altered in dynamic ways that depend on other design aspects. The stability curve doesn’t show the likelihood of reaching a given heel angle for example.

A frequent requirement for offshore yachts is exhibiting an AVS greater or equal to 120°, but the condition is quite weak. The EU-developed Stability Index (STIX) formula takes into account displacement and requires up to 125° AVS not to penalise small vessels. An 8-tonne yacht requires 120° to achieve a neutral score.

Commercial motor vessels are often required to meet conditions based on a minimum area underneath the GZ curve between given angles of heel: this equates to saying they must be “hard enough” to heel up to a specified point to be acceptable.