Professional athletes make artistic synchronized swimming look effortless. Yet it is an incredibly demanding sport: it requires tremendous muscle power, endurance, and control to tread water and perform an elaborate dance simultaneously. On top of that, swimmers need to simultaneously keep in perfect sequence with a group in the water. So how do they keep synchronized while many of them are entirely underwater?
It’s essential to use special underwater speakers. The swimmers can each hear the music used for their performance loud and clear both above and below the water at the same time. Without this, there’s no way to keep the routine synchronized. Underwater speakers are crucial to fine tune the details.
Sometimes you have no choice but to fine tune the details to succeed in what you are doing. But sometimes a quick approximation might be all you need to get to the next step. This is certainly the case in surface buoy hydrodynamic damping: you can spend a lot of time and energy fine tuning hydrodynamic details, but there are workarounds. What we’re going to cover is:
- Ignoring buoy damping altogether
- Using a simple approximation when buoy motion may be important
- Dialing in the details when buoy motion is crucial
First, we will cover the first point on ignoring damping altogether.
When can you ignore damping altogether?
Buoy damping comes into play when there is lots of relative motion between the buoy relative to the water surface. Suppose a surface buoy is light enough and has enough flotation to track the water surface, even in extreme storm conditions. In that case, buoy damping won’t have much of an effect on the system response. This kind of scenario often happens in deepwater oceanographic moorings.
In many deepwater oceanographic systems, the surface buoy may have a primary role in supporting the weight of the mooring itself. Full ocean depth moorings may have 5 kilometers of mooring line or more, bristling with dozens of instruments along most of the span. Surface buoys of a mooring like this are often very light, with a lot of extra flotation to support the weight of the mooring line and instruments. These buoys may be so large and light in the water they need a substantial mooring weight to stay stable and upright in the water!
In deepwater mooring, buoy heaving, or up and down motion, drives the dynamic mooring loads. Many surface buoys closely follow the water surface in moderate and extreme storm conditions. In this case, there isn’t much need to resolve the damping effects of the buoy itself when computing mooring loads. But not all surface buoys follow the wave surface perfectly, which can affect dynamic mooring loads. Also, buoy motion and acceleration may introduce constraints and limits on equipment and needs to be better understood. In these cases, ignoring buoy damping may not be good enough. This brings us to the second point about approximating buoy damping.
Some moored systems have instrumentation only in the buoy
The surface buoy may also be much larger and heavier to accommodate an extensive suite of devices to measure waves, wind, and current conditions. If the buoy is larger and heavier, it is less likely to merely follow the water surface in heave in most sea states. On top of this, if the system is in moderate or shallow depth water, the more detailed motion of the buoy – beyond only heave motion – may significantly influence the dynamic mooring loads. In these cases, it may be good to look into more detailed buoy motion, which means you need a rough approximation of buoy damping. But how can you make this rough approximation?
It doesn’t take much to make a rough approximation of buoy damping
It takes relevant experience or knowledge of the particular buoy you’re using. The main idea is you need to know roughly how the buoy responds in calm water to heave and tilt. This is sometimes referred to as the decay response. After a slight disturbance in heave or tilt, are there many motion oscillations before it calms down, or does the motion damp out and settle down right away?
You don’t need to be exact. Nevertheless, the expected decay response combined with the hull geometry, mass, and inertia defines the linear buoy damping. The buoy damping becomes an additional input into a dynamic analysis tool to resolve the mooring loads and buoy motion in various sea states.
While it’s a rough approximation, it’s still an excellent way to make progress on a mooring design problem. It’s an improvement on ignoring damping completely, too. However, more detail in buoy damping is warranted when accurate buoy motion is crucial. This brings us to the third point on dialing in the details on buoy damping.
In some cases, buoy motion has a critical impact on sensors or safety systems
Buoys using current or LIDAR wind profilers are particularly sensitive to surface buoy tilt motion. Visibility of Aid to Navigation buoys, and therefore safety at sea, is directly affected by the amount of tilt. If you’re uncertain about buoy damping, this directly translates into uncertainty about the buoy’s motion affecting data quality and equipment performance. So how do you dial in the detail of buoy damping?
The source of linear damping for floating systems is wave radiation
Wave radiation effects are often solved using potential flow software tools. These hydrodynamic software tools resolve how a moving hull shape creates radiating wave patterns at a range of motion frequencies. Dynamic analysis tools can then use the resulting forces to refine buoy motion.
An example of a potential flow software tool like this is ShipMo3D. The wave radiation forces are computed for a range of motion frequencies and all degrees of motion for a particular surface buoy hull shape. The dynamic analysis tool ProteusDS uses hydrodynamic data from ShipMo3D. Using these tools, mooring designers working with ProteusDS can incorporate more detailed buoy damping effects.
Do all buoys need to resolve wave radiation forces?
Not necessarily. Wave radiation effects are often only significant in larger and heavier buoy hulls that tend to displace a lot of water. These larger and heavier buoys may not simply follow the water surface in most conditions, and a more detailed look is warranted. Experience with a particular buoy form factor may provide the data and expertise to work with a rough approximation only without the need to get into the details of a tool like ShipMo3D. But the decision to use a tool like ShipMo3D should not be taken lightly: it takes time to collect necessary information, set up and compute the system hydrodynamics and validate it. A simple approximation may take a small fraction of the time and still get reasonable results.
Let’s look at an example
In this example, we are going to illustrate what happens to buoy motion when linear damping is ignored altogether. In a partnership between Nortek, AXYS Technologies, Caribbean Wind LLC, and NOAA CO-OPS, a shallow water surface mooring was deployed to explore the influence of buoy tilt on ADCP measurements. The buoy was self-stable with heavy ballast plates to keep it upright, while a low tension mooring helped keep it on station. This is an ideal system to compare with simulated motion predictions from ProteusDS because the buoy is self-stable and the mooring should not have a dominating effect on tilt.
A nearby bottom-mounted AWAC was used to record and verify the sea state condition independent from any measurements on the buoy itself. The Nortek Signature 1000 ADCP mounted on the buoy recorded the tilt angle of the buoy in a range of sea state conditions.
A ProteusDS model of the mooring and buoy was constructed to compare with measured results. The buoy was modelled as a rigid body with a cylindrical hull with viscous drag coefficients and no additional linear damping. The resulting buoy tilt in a 3m significant wave height sea state was measured at 13 deg standard deviation with maximums around 50 degrees. The ProteusDS simulated buoy tilt response showed a 12 degree standard deviation with extremes around 60 degrees tilt.
It’s summary time
All surface buoys will have some damping that will affect their motion. Some of this damping can be from wave radiation effects. But the critical question is how much does this damping affect the function of the buoy and mooring? You may be able to ignore it entirely if the focus is on mooring loads. But larger buoys used for measurements that are sensitive to motion or navigation safety may need to take a closer look at evaluating the buoy motion. A simple approximation based on experience can help. Still, there are also advanced hydrodynamic tools like ShipMo3D that can shed light on the problem, too.
A synchronized swimming performance may look like magic in how the athletes keep their timing. Swimmers need to be precise to get through their routine. When it comes to mooring design, you may or may not need this kind of precision to get through a design process. At least you don’t have to hold your breath the whole time!
Thanks to David Velasco from Nortek for providing data and insight into the shallow water buoy used for the example, and for AXYS Technologies, Caribbean Wind LLC, and NOAA CO-OPS for publishing their work on the collaboration. Read more on their work published here.