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How to tailor an anti-roll U-tube tank design for a ship

The New Caledonian crow may look like every one you’ve ever seen in your life. However, they’re different in a fundamental way: they make tools. The challenge for this unique species of crow is that it’s on a very isolated island in the South Pacific Ocean. While they rely on grubs and insects for food, they don’t have any natural adaptations to help, like a sharp beak or hardened skull. A woodpecker would find this task easy, but the crow has to somehow get more specialized. This is why they spend their time making tools to help them out. But why are these tools so special?

These crows exhibit a delicate selection process, seeking out sticks with suitable branches. With precision, they carefully remove the branch near its joint, resulting in a flawlessly shaped hook at the end. These hooked tools are ideal for searching crevices and holes to nip out grubs and other bugs for a quick meal. It’s clear these crows create remarkably intricate tools. These are tools specifically tailored to a specific need.

Similarly, on a boat, we have specific needs. Take, for example, the issue of ship motion control. In bad weather, ship motion in roll can get out of control. To keep the ship stable, you can explore stabilizing technologies like anti-roll tanks. But for anti-roll tanks, you need to go through a deliberate process of tailoring them for the specific needs of a ship. In this article, we’re going to talk about how to go through the process of tuning a U-tube tank for a boat and optimizing its performance for a specific vessel.

1. Constraints: use an overall system width as wide as possible, as tall of reservoir tanks as possible, and pick max roll before saturation, shown in green in the image below
2. Pick duct-to-wing tank area section ratio such that it matches the ship’s roll natural period, shown in purple in the image below
3. Pick a reservoir tank width, and finalize remaining tank dimensions to match 1-5% of displacement mass, shown in red in the image below.

U-tube tanks have quite a lot of parameters. The goal is to highlight a process that you can follow to set up the best possible U-tube tank for your vessel. Typical U-tube tank geometry is shown below. The critical factors in the design are the reservoir tanks, spaced apart and connected by a cross duct. So, how do you establish the dimensions of a system like this that will help reduce ship roll motion? The first step is in setting some constraints.

More water in the right places improves performance

In this case, the most effective U-tube tanks will have the most water mass away from the vessel’s center line. The bulk of the system water mass is in the tank reservoirs. So, the starting point for sizing a U-tube tank has three constraints you need to establish: the overall system width, reservoir tank height, and reservoir fluid level.

The general idea is that the farther apart the reservoir tanks can be, the greater the water mass’s leverage in influencing ship roll. So, the greater the system width, the better. On top of this, a greater reservoir tank height also helps because each reservoir can hold more water that is farther from the centerline.

Of course, there are many competing requirements in vessel design or refit, and space is often a significant constraint to work around. But the idea is that as a starting point, see what you can establish as a realistic value for the overall system width and the tank height based on what you have to work with. The larger the width and reservoir tank height, the more ship motion will be improved. On the other hand, constraining the reservoir fluid height has a separate consideration.

We want to avoid tank saturation as much as possible

Tank saturation is when the dynamically changing water height hits the roof. There are many good reasons to avoid this, but an important one is that the U-tube tank won’t work the way you want if the water constantly hits the top of the tank. But how can you set this constraint without any idea of ship motion?

One way to establish this constraint is from the allowable roll angle of saturation. From a static consideration and the system’s geometry, you can see what roll angle would result in saturation. The limit will be related to the needs of each vessel design. But for a large open ocean capable vessel with stringent performance requirements, you could use something like 25-30 degrees.

With these constraints in place, you can tune your vessel’s U-tube tank. This brings us to the next step on sizing the cross duct and tank reservoir width.

The natural period of a U-tube tank needs to line up with the ship’s natural roll period

The effect we are looking for is water moving from one tank to another via the cross duct. If we design the tank such that the natural sloshing period lines up with the ship’s natural roll period, we’ll get the maximum amount of energy and momentum redirected from ship motion into water flow in the tank, reducing ship motion.

Now, the cross duct limits how much flow can move back and forth. The smaller the cross duct width, the less water will flow. In addition, the size of the reservoir tanks dictates how much pressure there is to drive the mass of water back and forth through the cross duct as the tank system moves in roll with the ship. The result is that the natural U-tube sloshing period is generally related to the ratio of the reservoir tank and duct cross-section areas. Once you know the initial ship’s natural roll period, you can establish the target ratio of the reservoir tank area to the cross duct area.

What about vessels with a range of roll natural periods?

Generally, vessels with changes in displacement through their operational life can dramatically change the roll natural period. For example, bulk carriers or container vessels regularly have significant changes in displacement and roll natural period. U-tube tanks can be a challenge to adjust based, especially when compared to anti-roll slosh tanks, that just need an adjustment of water height. However, U-tube tanks can be fitted with valves that allow some control in delaying water transfer from each tank. But there isn’t a way to make the water transfer faster! This means that if you expect some variation, try to tune the tank to the lower end of roll natural period expected for the vessel.

Once you have this ratio of the reservoir tank and cross duct, the rest of the dimensions fall into place. This brings us to the final point of finalizing the tank dimensions.

For any anti-roll tank to work, you need a lot of water

You can have a perfectly tuned U-tube tank, but if there isn’t enough water, it won’t significantly impact ship motion. The mass of water must be large enough to redirect energy and momentum from the ship’s motion in roll into the movement of water in the tank. A rule of thumb for U-tube tank sizing is that you will need a mass of water on the order of 1-5% of vessel displacement for an effective design.

You can establish the system dimensions with the constraints in place and the target tank/duct area ratio. Start with picking a reservoir tank width. With this number in place, you then have the cross duct width from the target tank/duct area ratio. With the overall system width constraint, this gives you the overall tank spacing. The fluid height falls out of these system dimensions in combination with the allowable roll angle before saturation. You then know the water mass per unit length of U-tube tank. The final dimension of the tank length should produce enough water mass to reach a target of 1-5% of vessel displacement.

But how do you verify the designed tank performance?

This process produces an initial estimate at the tank dimensions, giving some fundamental constraints. But the process is often be iterative. As you add mass to the vessel and position the tank on the vessel, the resulting natural period in roll can be affected, as with any anti-roll tank system. Having a method to verify tank performance is crucial.

Seakeeping analysis software tools have numerical models of anti-roll tanks, including U-tube systems. These tools often make it easy to quickly verify performance or adjust the system as needed. For example, the ProteusDS ShipMo3D toolset includes U-tube tank functionality that you can use to rapidly verify the change in vessel RAO and motion performance in a seaway.

Though seakeeping models of anti-roll tanks are sophisticated, they don’t always account for all possible factors, and one area of uncertainty can be viscous dissipation in the tank. The later stages of U-tube tank design can involve scale model testing of the tank to verify the expected system performance and account for complex flow effects beyond the scope of

seakeeping model performance. Scale model testing is crucial to verify the performance of the system using the real structure that is inside the tank.

Example time

We covered a few details on U-tube tank design and now it’s time for an example. We set up several U-tube tank designs with the Generic Frigate to highlight how they change the resulting ship motion. The test scenario includes a beam sea configuration with short-crested JONSWAP sea state with 3m significant wave height and 9.7 second peak period. Note that the Generic Frigate natural roll period without any tanks is close to this at 9 seconds.

With a maximum beam of 16m, a 12 m overall system width and tank height of 6m was used as reasonable limits to start with. In addition, the maximum ship roll before saturation was set at 28 degrees.

From the overall constraints and the maximum roll angle before saturation, the nominal fluid height is 2.8m. With the natural period at 9 seconds, the resulting estimated area ratio of the wing tank and cross duct to match the natural period is 0.35.

Finally, we pick a reservoir tank width of 2m. This allows us to resolve the rest of the tank dimensions. To clarify the impact on performance, we tried several tank lengths to highlight the impact on ship motion performance using the ProteusDS ShipMo3D toolset.

Much like the anti-roll slosh tank design with the Generic Frigate, there is a significant improvement in ship motion performance with greater water mass in the system. While the system will respond with improved roll between 1-2% vessel displacement, there’s marked improvement above 3% and that may be a better threshold to aim for to get the most benefit from the investment of a U-tube tank system. Of course, since each ship design project is unique, the most important thing is that you consider a way to systematically evaluate what a particular anti-roll tank will do for your design.

Table 1: Change in Generic Frigate roll motion with different anti-roll slosh tank length in 3m 9.7s JONSWAP beam sea

Tank length	Tank fluid mass (tonnes)	% ship displacement	Generic Frigate roll RMS (deg)	% improvement
–	–	–	6.4	–
1m	18	0.5	5.7	12
2m	36	1	5.1	21
3m	54	1.5	4.7	27
7m	126	3.4	3.6	44

It’s summary time

We covered several essential facets of sizing a U-tube tank for a ship, and it’s time to summarize. The process of sizing a U-tube tank starts with establishing constraints. Often, you only have so much space on a ship to fit something like this. That said, you should try to get as wide and tall a system as you safely can, as that will drastically improve performance. You can also establish a constraint based on the maximum ship roll angle that would produce saturation of the reservoir tanks, or, in static conditions, when the fluid reaches the top of the tank. This should be high enough that it doesn’t happen often – if the fluid is always hitting the top of the tanks, performance won’t meet expectations.

The next step is resolving the reservoir tank to duct width ratio. This controls the U-tube tank’s natural period, which must line up with the vessel’s roll natural period. The final step is to confirm the tank dimensions so that you produce an overall water mass of 1-5% of vessel displacement. Pick the tank reservoir width, and the other values will fall into place.

Follow this process to get a U-tube tank specifically tailored for a particular vessel. Much like a New Caledonian crow, carefully selecting and shaping a tool for their next meal.

Next step

The ProteusDS ShipMo3D toolset includes an integrated anti-roll U-tube tank model. Check out this video tutorial that shows how to show how different sizes of U-tube tanks change ship roll motion.

Thanks

A very special thank you to Mona Wilhelm, Christian Voosen, and Aaqib Khan from Hoppe-Marine for their insight and feedback on anti-roll U-tube tank dynamics and design.