Stability

So why should a boat stay upright anyway? It’s stranger than it may first appear.

The gravity pulls the boat down, but water pushes the boat up, simple, no? Where it gets surprising is when you realise the ‘up’ force is below the ‘down’ force - like trying to balance a broom upright on your hand. How does that stay upright??

To get a handle on how stability works, it’s helpful to think about the balance of forces on the hull. Normally there’s buoyancy loads from the water, inertial effects from manoeuvring, weight loads from the stuff on the boat (and from the boat itself), wind loads etc, but for now we’ll just look at the forces from the water (buoyancy forces) and forces from the total weight of the boat and all the things in it.

First of all, gravity.

For the sake of stability we can assume that all the weight of the boat and the things in it is acting through a single point - the centre of gravity - also known as the CG. (you can’t make this assumption when looking at the strength of a hull, but that’s for another day…)

As a starting point, assume that the center of gravity is slightly below the main deck.

Second, buoyancy.

The total force of the water pushing back up on the hull is equal to the volume of the hull, times the density of the water. If the boat is afloat, this force will be equal and opposite to the weight force.

This force can also be assumed to be acting through the ‘middle’ of the underwater volume (or the ‘centroid’ of the displaced volume if you want to sound like a pirate) - this point referred to (unsurprisingly) as the centre of buoyancy, or CB for short.

So you can see that the CG is above the CB - how then to boats not just tip over? Wouldn’t they be more stable if the ‘up’ force was above the ‘down’ force? All else being equal yes, but there’s another thing you need to know.

The centre of gravity stays in one place*, but the centre of buoyancy moves!

Recall that the CB is the ‘middle’ of the volume of the boat under water? Well as the boat heels, this middle, moves. This is illustrated in the picture to the right. See that as the boat has heeled, the CG has not moved*, but the CB has!

*[Actually the CG does move as the fluids in tanks move, and sometimes you need to account for the potential of cargo to shift as well - in bulk carriers this is called fluidisation.]

Now that the the CB has moved, the buoyant force is no longer in line with the gravity force, creating what’s called a ‘righting moment’ (‘righting’ = turning the boat upright, ‘moment’ = a force that applies a twisting load. Think of opening a door: you need a force to push it, but you need a twisting force to turn the handle).

This righting moment is equal to the weight of the boat, times the distance between the center of gravity ‘G’ and the line of action of the buoyancy force ‘Z’, (this distance is called ‘GZ’ for short).

So what happens if you roll the boat further until the CG passes over the CB?

Looking at the picture to the right, and recalling the force balance approach from above, you can see that our boat is in trouble.

Our distance from ‘G’ to ‘Z’ is now negative, and the 'moment on the boat will now turn the boat over. This ‘point of vanishing stability’ is the point at which the boat can no longer self-right.

The other, more subtle problem that the boat on the right has is that it’s deck edge is now underwater.

Another strange aspect of stability is that for small angles of roll, the stability depends almost entirely on the shape formed by the intersection of the surface of the water with the hull - the waterplane.

Stranger still is that the stability of the boat is a function of the width of the waterplane cubed.

This means that if the shape of the waterplane suddenly changes (say of the boat has rolled so far that the deck edge is immersed), then the stability will decrease extremely suddenly. not good.

The wrap

This is a high-level view of the basics of stability. There’s all sorts of fun things to consider such as the movement of fluids in tanks (nastier than you might think - check out the free surface effect if you can’t sleep well tonight), and how the boat handles heavy weather (rules like the IMO weather criterion). Also the stability of the boat will change as fuel is burned during a journey, as cargo gets loaded and removed, as tenders are loaded and unloaded and so on and so on!

Nonetheless, I hope you’ve found this helpful.

With kind regards,

Nick.