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How to tune an anti-roll slosh tank design for a ship
Some plants consistently attract animal pollinators in the pitch-black darkness of night. But how can this be so when the brightly coloured flowers need daylight to be seen? The key is through senses other than sight. For instance, sound comes into play perfectly when no light is around.
For instance, bats rely entirely on sound at night to find their way around. Several species of bats are nectar lovers and go out to feed when it’s dark out. But how do they find food? Their chirping sounds reflect on the surroundings, and the echoes they hear give them a highly detailed sense of their environment in spite of the complete darkness.
But the jungle can be acoustically noisy, with leaves, branches, and trees everywhere, each reflecting different amounts of sound from the bat’s call. What’s crucial is that some plants have specially shaped parabolic flowers. The shape of the petals is perfect for reflecting the sounds made by bats. For a hungry bat looking for a quick sugar fix at night, these plants stand out like a beacon. But it only works because the flowers are so specially tuned.
Often, you need tuning to get two systems in alignment. In the world of ship motion, tuning is something that comes up in anti-roll slosh tank design, too. A slosh tank system has many parameters, and you need to get a handle on how it behaves and interacts with the ship that it will be used on. In this article, we’re going to cover a way to tune an anti-roll slosh tank as part of a preliminary design process.
The ultimate goal is to make sure the slosh natural frequency lines up with the ship roll natural frequency, and you’re good to go. But untangling the tank details from these requirements is obvious once you take a closer look.
What we’re going to cover is:
- constrain tank width
- set slosh tank wave speed
- finalize tank volume
Let’s start with constraining tank width.
The wider the tank, the more effective it is
You should look for the widest tank you can fit on your ship. For a slosh tank to work, you need a lot of water. This makes sense because momentum is directed from vessel roll into the sloshing water. A ballpark range for an effective tank is 1-5% of the vessel displacement. That’s a lot!
On top of this, the tank’s stabilizing moment grows rapidly with tank width. This makes sense because of the leverage the water will have away from the midline.
This starting constraint also serves as an easy starting point because it will be some factor of the overall beam of the vessel. Structurally speaking, having a tank wider than your ship won’t be easy! You can adjust it later, but a smidge less than the vessel beam is a good starting point.
So, once you have a starting tank width in mind, the next step is to figure out the natural sloshing frequency. This brings us to the next point on establishing the fluid height from the slosh tank wave speed.
Sloshing is the same thing as a reflecting shallow water wave
A shallow water wave bouncing back and forth is all that is really happening in these tanks. This means that the sloshing natural frequency is the same thing as the rate at which a shallow water wave passes from one end of the tank and back again. The trick is then backing out the fluid height such that this rate matches up with the natural roll frequency of the ship itself. When these are equal, rolling ship motion automatically triggers fluid motion resonance. You get the maximum fluid motion in the tank possible. This also means the maximum amount of momentum is directed from ship motion into the fluid motion in the tank, keeping roll motions low.
Fortunately, the wave speed of shallow water waves is a function of the fluid height only. So, the fluid height is directly related to the tank width and the ship’s natural roll frequency. This leads us to the third and final step of the design process: establishing the tank volume.
The tank volume must reach a certain threshold to be an effective anti-roll system
As we mentioned before, experience shows that anti-roll tanks need enough water to match 1-5% of ship displacement to significantly influence ship roll motions. As we already established tank width and fluid height, the two remaining parameters are tank length and overall height. The tank length is straightforward: it needs to be long enough such that the resulting volume given tank width and fluid height matches 1-5% of ship displacement. But what about the overall tank height?
A slosh tank filled to the brim won’t slosh at all
If the tank is full, it’s impossible to get any fluid motion and energy absorption. But you need more than a minimum air gap between the water and the top of the tank. You want to avoid saturation, or, in other words, when the water is hitting the roof of the tank. So how can you figure out what will work?
Seakeeping software can help with initial tank sizing
With the correct dimensions, a seakeeping software tool can do the calculations behind the physics of slosh tanks and ship motion. It will verify the resulting ship motion and give you an idea of the fluid motion in the tank, too. This is one low-cost way to verify the tank dimensions and fluid height before any additional detailed design.
However, the ultimate verification is through scale model testing of the tank itself. Scale modelling of the tank with an appropriate test rig shows a lot of accurate detail in what happens to the tank in a range of motion frequencies and also helps verify when saturation occurs.
What about the tank location on the ship itself?
A fantastic aspect of slosh tanks is that they can be placed anywhere on the ship in the midplane with minor sensitivity to the expected anti-roll performance. However, there are many essential and practical structural and safety limitations. The higher the tank is on a vessel, the more the free surface effect can reduce the vessel’s static stability. Yet, it is a trade-off because a higher tank position can help improve the roll-damping effect. On top of this, the tank mass and dynamic sloshing forces involved can create immense static and dynamic pressures that create important structural design considerations that need careful consideration in the vessel design.
Example time
We covered a few details on slosh tank design and now it’s time for an example. We set up several box slosh tank designs with the Generic Frigate to highlight how the resulting ship motion is affected. 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. 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 constrained tank width is a reasonable tank width limit to start with. The resulting fluid height then needs to be 0.7m so the slosh wave period matches with the roll natural period. While there are multiple sloshing frequencies, the most important one is the largest and lowest frequency which you can see estimated in the slosh wave radiation damping calculated by the ProteusDS ShipMo3D toolset. The first peak is at 0.7rad/s or 9 sec which is good to confirm in the analysis process.
We tried several tank lengths to highlight the effect on ship motion in the test scenario. Generally, the trend of a larger properly tuned tank shows an increasing impact on reducing roll motions. If you can spare the space and handle the eye-watering static weight of 100 tonnes of water you can get some interesting roll reduction! Of course, each ship design project is unique. What’s crucial is having a way to systematically evaluate performance of different tank configurations in a variety of sea states to build confidence you can meet project requirements.
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 | – |
| 2m | 17 | 0.5 | 6.4 | 0 |
| 5m | 42 | 1.1 | 4.8 | 25 |
| 12m | 100 | 2.7 | 2.1 | 67 |
Summary time
We covered several details on the initial sizing of an anti-roll box slosh tank, and now it’s time to review. A slosh tank works by directing momentum from ship roll into fluid motion in a tank. To make it all work, the tank sloshing natural frequency must be tuned to the ship’s natural roll frequency. The sloshing effect is from a shallow water wave bouncing back and forth in the tank. This means it is easy to resolve by finding the fluid height that works for a given tank width. The tank length then needs to be long enough to have fluid mass 1-5% of the vessel displacement – it’s a lot, but the minimum you need for a tank that will affect ship motion. Verify the tank height with a seakeeping tool and finalize the design with sophisticated scale model tests.
Tuning a slosh tank might seem intimidating because of the complex effects involved. But you won’t be stumbling around in the dark if you follow the steps we covered – just like bats zeroing in on a tasty snack in the darkness!
Next step
The ProteusDS ShipMo3D toolset includes an integrated anti-roll slosh tank model. Check out this video tutorial that shows how to show how different sizes of tanks change ship roll motion.
Thanks
A big thank you to Mona Wilhelm, Christian Voosen, and Aaqib Khan from Hoppe-Marine for their insight and feedback on anti-roll slosh tank dynamics and design.
