# Critically damped vessel motion

In the early 1980s I designed a small research and utility vessel for the Shoals Marine Laboratory, operated by Cornell University and the University of New Hampshire, that needed to be wide and shallow because of her docking situation and capacity requirements. Seakeeping and motion were given very little consideration during the design process so it was a surprise when the vessel turned out to be legendary for its comfort in rough water. The seas of a Buzzards Bay southwester were nearly abeam on the delivery trip and I was able to walk around the aft deck with my hands in my pockets. I knew I was onto something. The lessons of that little boat were a foundation for a quarter century of designing small research vessels.
Vessel motion and stability is a subject rife with misconceptions. A large part of my business for several years was performing stability tests on fishing boats when insurance companies began requiring them. Sometimes a fisherman would say to me that he knew that his boat couldn’t have a stability problem because it hardly rolled at all. I would then know that I probably was going to have some bad news for him when the calculations were completed.

The more stability a vessel has, in terms of being able to resist the heeling forces of wind or weights being moved around the deck, the faster it will roll. Every vessel has a natural rolling period, much as the pendulum of a clock does, and will roll at that rate. Adding more weight, such as net reels and new fishing gear, decreases the stability. Roll period slows as stability decreases so the boat becomes more comfortable. The slowest roll of all is one where the boat just lies over and doesn’t come back. Maximum comfort is thus achieved just about at the same point as maximum danger.

Naval architects have traditionally viewed motion comfort primarily in terms of aiming for the least amount of stability necessary for safe operation. This was not just to achieve the slowest roll period. Stability is developed by the change in shape of the vessel’s hull as it is heeled and the resulting shift in center of buoyancy. The reverse happens when waves pass and change the shape of the immersed portion of the hull. The shift in center of buoyancy causes the hull to roll. Less stability not only means slower roll period, but also less response by the hull to passing waves.

My little 47-foot vessel has enough stability that she has been able to safely carry a small dump truck on deck. What then makes her so comfortable in a seaway?
The motion experienced by people on a vessel is a function not only of the speed of the rolling cycle but its amplitude or angle. If you only travel three feet up and down during a six-second roll, you will be more comfortable than if you traveled five in the same time. Amplitude, or roll angle, is primarily a function of hydrodynamic damping, the amount of water that is moved as the hull rolls.
Add fins like keels and bilge keels to a hull and the angle of roll will be reduced although the time to roll from one side to the other will be unchanged. The lower accelerations of rolling through a shorter distance will make it seem that the vessel is rolling less.

Beam and hull shape contribute to damping. Wide hulls with flat shallow sections have greater inherent damping than the narrow, rounded hulls often associated with seaworthiness. They also tend to have greater stability and to be more reactive to the effects of waves. This has historically led naval architects to look in the other direction for comfort.

The fact that every vessel has a natural rolling period (modified somewhat as different cargo and liquid loading alter the stability) makes motion in waves a resonant phenomena. A child in a swing is a pendulum. The time it takes for them to go all the way forward and back will be the same regardless of how large an arc they are swinging through. Push in time with this period and you will soon have them giggling and saying, “High enough.” Try and push them so that they take a different amount of time to go from front to back and they shortly won’t be swinging at all but just jerking around near the bottom and asking for someone else to push them.

Waves have an exact relationship between their length and the speed they travel through the water. This means that shorter, and generally smaller, waves will encounter a hull more frequently than larger ones. Think of a rolling hull as an upside down swing. Every hull has a wave length which will match its rolling period. The motion excitation of waves with this period will then be like the proper pushing of a child in a swing and the vessel will roll most heavily.

My research vessel has a roll period of just over four seconds. Waves with this period predominantly occur in fair weather conditions when the waves are not very large. The high hydrodynamic damping of her hull keeps the angle of the rolling modest. The accelerations felt by people on board are therefore not as great as they would be in a traditional hull rolling farther at the same rate. When the wind pipes up into a fresh breeze, the boat is out of tune with the seas usually encountered.

The traditional, rounder, hull form will need to have a roll period in the six to eight-second range in order for distance moved in the larger roll angles not to create uncomfortable acceleration. This will put the hull in resonance with waves of a size and period typically encountered in stronger winds when the waves are larger and have more energy. The result will be heavy rolling about the time small craft warnings begin to be issued.

Walking around on the deck of the research vessel, I realized that another factor was at work. Objects rotate around their center of gravity unless influenced by other forces. In a vessel, the interaction of the hull with the water moves the center of rotation closer to the waterline. A traditional hull will have its center of gravity fairly near the waterline so its rolling center will be close to it as well. The center of gravity of a wide hull like the research vessel will be very close to the main deck so the rolling center will be higher. Rolling is thus experienced more as the deck simply changes angle underfoot which is easier to compensate for than being bodily moved from side to side a large amount at the same time. This is also convenient for carrying stuff on deck. Unsecured items placed on the deck tend to stay there without being sent sliding from one side to the other.

The motion characteristics of such hulls, called “critically damped” in a Society of Naval Architects and Marine Engineers (SNAME) paper that came out in the late 1980s, does have a downside. They develop their high-roll damping by moving a larger amount of water when rolling. The reverse also happens. When the water moves, it grabs the same appendages and hull corners and the vessel responds. Although they do not develop deep rhythmic rolling motions, critically damped hulls are more reactive to the effects of waves. This gives them a rougher and less predictable motion and this is where human factors come into the picture.
The experienced seafarer, who has learned to anticipate and move with the more predictable rolling of a traditional hull form, will usually prefer a longer and slower roll period. My distinct impression, from listening to comments and observing aboard vessels, is that people new to being on the water will generally prefer the shorter motion, even though it is less predictable.

The area in which experience is less likely to influence a preference for one type of motion over the other is on the working deck of a vessel, handling gear over the side with cranes or an A-frame. I have a letter from a scientist who deployed the buoys and anchors from two vessels. One of them was a 50-foot, critically-damped research vessel I designed and the other an 80-foot traditional research vessel of four times the displacement. He found the smaller craft to be a better working platform.

The smaller rolling angle of the critically damped hull makes it easier to handle gear hanging from cranes or A-frames. The reduced side-to-side movement of the deck lets crewmembers, whose hands are occupied with handling lines to control the loads, stand more easily. Less rhythmic and slightly irregular motion is not as likely to excite rhythmic swinging of hanging gear.

So from the above discussion, there are some things to keep in mind. All else being equal, a chine hull will have more damping than a round bottom hull as the chines act somewhat like bilge keels. All else not being equal, the round bottom hull could be more comfortable. The higher above the main deck you are, the longer the arc you will travel through in rolling. Higher and larger superstructures increase roll amplitude through their inertia. Marketing pressures which make the sales of a vessel design its primary mission requirement are not conducive to producing hulls optimized for comfort.

The potential of a critically-damped hull form will best be realized in a custom design. Roll damping and low, modest superstructures will contribute to the comfort of both hull types. Looking for these characteristics may help narrow down the search for an existing vessel if comfort underway is an important consideration.

Roger Long, based in Maine, primarily designs educational and research vessels. Seven current Atlantic oceanographic vessels are of his design. He also cruises aboard his Endeavour 32 sailboat.

Evaluating an existing vessel

So, you show up for sea trials to evaluate a potential vessel purchase and it’s dead flat calm. There are still things you can learn, at least to help you decide if you should try coming back another time.

Loosen the dock lines and put one foot on the rail and one on the dock or stand where you can push on a piling. If you look closely, you will be able to see even quite a large vessel respond to your weight or pushing. By pushing or leaning as you see the vessel move, you will be able to set up a good roll. I’ve gotten vessels as large as 100 feet rolling all by myself enough that people started looking around to see what was going on.

Once the boat is rolling, stop pushing and use a stopwatch to time the roll all the way from one side, over to the other, and back. Look for the point where the rail or some other reference point moving against the background stops and changes direction.

A roll period around four seconds indicates a vessel that will be resonant in waves usually found in winds of 10 to 15 knots. Roll periods six seconds or greater mean that maximum rolling will generally occur with winds in the 20- to 25-knot range. Roll periods more than eight seconds indicate a vessel for which stability should be fully evaluated from the safety standpoint.

The behavior of the boat as you let the boat roll on its own will tell you the degree of damping. A hull with low damping will continue rolling for a considerable number of rolls after you let it go. The highly-damped hull will be hard to get rolling and will settle down quickly.

Knowing the roll period is also useful on sea trials since it will generally be easier in relatively calm conditions to determine the vessel’s pitching period as it goes through the wakes of other vessels. If the vessel’s pitching and rolling periods are very close, there is the potential for rolling motions to become coupled to pitching motions in rough water. This will produce increased rolling and an uncomfortable corkscrewing motion. Vessels with closely matched pitching and rolling periods should be carefully evaluated in rough water before committing to purchase.
Roger Long