Stability and rolling explained
By Lou Codega
I donít think any subject leads to more arguments in yacht club bars and in letters to popular boating magazines than that of roll motion and stability in general. Can you have too much? Whatís enough? Is more better, or less? What is the difference between initial and ultimate stability? How does stability affect rolling? And what exactly is GM, and what does it have to do with my life?
Youíve heard them all, too. Let me try to confuse the issue a bit more.
Generally defined, stability is the ability of a system that is in a state of equilibrium to return to the same state after it is disturbed. I like to use the analogy of a marble, a steel mixing bowl and a table.
If we put the bowl on the table with the marble inside, weíve made a stable equilibrium. Push the marble a bit to one side, and it rolls back and forth a bit and finally ends up where it started. Push it too far and it overshoots the bowl and ends up on the table. Now letís do some notional experiments. Push the marble harder and it travels further up the side; make the marble heavier and for a given push, it wonít go as high; make the bowl shallower and the marble travels further, though not higher; a marble in a steeper bowl travels less distance, but to the same height.
The shape of the hull is analogous to the shape of the bowl; the weight of the boat is analogous to the weight of the marble. The height to which the marble travels in analogous to the roll angle, and the height of the bowl corresponds to the boats range of positive stability: the point where it will no longer return to equilibrium. The analogy breaks down with the center of gravity, because itís always at the center of the marble, but no matter.
It canít be that simple, you say. Well itís not, exactly, but it is a very good approximation that will illustrate a lot of points.
The angle to which a boat rolls in response to an upsetting force is a function of the shape of the watertight boundary of the hull, deck and topsides, the weight, and the center of gravity. On our trawlers, we have maximized stability by many design characteristics. These include a wide beam, not just in the hull but in the deckhouse; hard chines, a low center of gravity resulting from the heavily laid up solid hull construction combined with a light weight, high strength cored construction for the topsides, liquids located low in hull through the use of narrow, integral tanks, and location of all auxiliary machinery in the engine room. Finally, and often overlooked, we have the weight of the boat itself. The result is a trawler with superb stability characteristics, as measured by both righting arms at low angles of heel as well a large range of stability.
I guess that this is as good a time as any to pull a couple of thorns. First, I donít think it useful to talk about initial stability and range of stability as though they were separate characteristics. The same phenomena affect the stability of the boat at 1 degree of roll as they do at 30 degrees or at 90. And I certainly do not agree with those who advocate applying large ship design guidelines to boats. This shows a lack of understanding of stability criteria, and it is fundamentally unsound, and perhaps even dangerous to apply this guideline to boats.
With all respect for Beebeís pioneering work, there has probably never been such an overused and so fundamentally useless a term as the A/B ratio (See Lesson Seven). The ratio is not now, and so far as Iím aware, has never been used by naval architects. Recall that Beebe used it only when comparing similarly proportioned and sized boats, and it had a bit of utility then. But it neglects almost everything that is important to stability. The height of the center of gravity is accounted for in a roundabout way, but beam, weight, hull form, and watertight integrity are completely ignored. Take any boat that you want as an example. It has the same A/B ratio whether it is 10 feet wide or 25, whether hard chine or round bilge, if it has engine room air inlets on the side of the hull or amidships, or if it weights 100,000 pounds or 10,000.
Which brings us to rolling in waves. The rolling response of a boat in waves is a function of many things, but the most important factor, without a doubt, is the calm water, so-called natural, roll period of the boat compared to the primary period of the wave train.
An absolutely key point is that a boat in a seaway does not roll at its natural roll period at all, but instead rolls at the predominant period of the waves that it is encountering. In every case, a boatís roll response reaches its maximum when the natural roll period of the boat is equal to the period of waves.
Understanding this is critical, so let me go back to the marble in a bowl analogy. Flick the marble, and it will return pendulum-like and roll side to side. This is equivalent to a boat being rocked in calm water and demonstrates the natural roll period. But now leave the marble alone and instead rock the bowl. The motion of the marble is now governed by gravity and the shape of the bowl, and its period is determined by the rolling of the bowl, without regard to its own natural roll period. The marble may lag behind, or even lead, the motion of the bowl, but the period is always the same. A boat behaves in exactly the same way.
The maximum roll angle is proportional to the wave slope, and has no direct relationship to the wave height. When a boatís roll period is much lower than the predominant period of the waves that it is traveling in, a very important behavior occurs. The boat tends to platform the waves and the maximum roll angle is the maximum wave slope, which seldom exceeds nine degrees in open water waves. On the other hand, when a boat is in waves that have a period that is about equal to the natural roll period, the boatís roll angle tends to magnify the wave slope, in some cases by a factor of ten. This fact applies to all craft and, among many other phenomena, explains why paravanes become ineffective in large rolling seas. With some patience, you can also demonstrate this with the bowl and marble by varying the period with which you rock the bowl. Slowly and the marble stays in the lowest part of the bowl. Faster, to match the natural period of the marble, and you can see the magnification that takes place as the marble overshoots from side to side.
We have taken this fact and used it to our advantage. We have designed a boat with a comparatively short roll period, matching with the period of very short, in length, waves. Under most circumstances, these waves are also small in height, have small wave slopes, and most importantly, have very little energy to transfer to the boat to impart rolling. Larger waves carry significant energy but have periods that are very much greater than the natural roll period of the Mirage trawler hull; the boat platforms the wave and does not magnify the wave slope. It is worth repeating again that a boat, any boat, does not roll at its natural roll period in waves, but instead rolls at the forced period that results from the wave train.
Now, a boat that has a comparatively longer natural roll period behaves differently. These vessels are characterized by narrower beams. As wave periods increase with wave size, the roll magnification increases until the wave period corresponds with the natural roll period of the boat and the roll angle becomes many times greater than the wave slope. Unfortunately, these longer period waves are considerably longer and higher, and most importantly, carry much more energy to impart rolling, than those in the short roll period case that I just described. Ballasted trawlers will also see their natural roll exaggerated because of the momentum imparted by the ballast.
The absolute key point, now for the third time, is that the boat rolls at the frequency imparted by the waves regardless of its natural frequency.
We at Mirage have taken this short-roll-period advantage even further by increasing the inherent damping of the hull though the use of hard chines and skegs. These features function in the same way as do bilge keels, which is to say they absorb energy imparted by the waves and dissipate it into the water, rather than into the boat as rolling motion. They are admittedly not so effective as are true bilge keels, but they are far less prone to damage, which is a significant advantage given the large amount of time that a typical boat spends around docks and floating debris. And they do not have the resistance penalty that bilge keels do.