How to effectively model oceanographic surface buoy dynamics

Flying sheep may help you get to sleep, but they can save your life, too. In 1934, the Italian army had a huge logistics problem: crossing one of the most inhospitable deserts in the world. Resupply for the trip was vital, and the army had to consider their options carefully.

Flying Sheep

One option was for soldiers to carry their supplies. But weighing down soldiers wasn’t possible: they would move too slowly under the oppressive sun and wouldn’t survive heat stroke.

Another option was trucking in supplies. But that wasn’t going to work either, as the stifling desert heat was already spoiling their food.

The army was left with only one viable option: using aircraft. Soldiers were able to travel quickly through the desert on foot, and supplies were sent by airdrop. Everything, including live sheep, was sent in by parachute! It was the only effective option.

In contrast, there’s often more than one effective option in modelling surface buoys. Surface buoys are a critical component of oceanographic mooring analysis and need to be considered by mooring designers carefully. Without careful consideration of dynamics caused by harsh ocean waves, the buoy and mooring won’t survive. In this article, we’re going to cover a few useful approaches for modelling surface buoys:

  1. point mass
  2. simple rigid body
  3. complex rigid body

First, we’re going to look into point mass approach.

The point mass model is one of the most straightforward approaches to use

They’re straightforward because they ignore all rotational effects of the buoy: a single point represents the hull. It can still account for the linear buoy motions: heave, surge, and sway. But it also means only the most basic shapes can be used to represent the buoy hull, like a sphere or in some exceptional cases, a cylinder.

It’s natural to underestimate simple models

While simple, point mass models can be very extremely useful. Often, a point mass model is more than capable enough to analyze an oceanographic mooring response in currents and waves. This level of detail may be all that’s needed to finalize a robust mooring design.

There are only a few critical parameters needed to get started with a point mass buoy model. Fundamentals like buoy mass, net flotation, and basic hull shape are required and sufficient for many simple systems. But in certain circumstances, buoy rotational effects can be significant. This takes us to the second point on modelling surface buoys: using a simple rigid body approach.

Like a point mass model, a rigid body model accounts for all linear motions

These are heave, surge, and sway. But the difference is that rigid body models also account for rotational effects: roll, pitch, and yaw. These rotation motions may be vital because they can have a significant impact on the equipment used on the buoy. Of course, this means more information is needed to get the model set up correctly.

SOFS buoy in ocean waves

SOFS buoy riding through ocean waves while on station in 4km deep water near Tasmania. Picture credit: Eric Schulz from Australia Bureau of Meteorology / IMOS


But some of this information is not easy to find. For example, most buoy spec sheets provide mass, but usually don’t contain information about what the buoy rotational inertia is. This lack of information is not a surprise because the rotational inertia can change depending on the specific buoy loadout.

This is where the simple rigid body model really shines

With a few assumptions and approximations, mooring designers can estimate many of the additional missing parameters. The first thing is to approximate the hull shape with something simple like a sphere or cylinder. The rotational inertia is easily calculated from these basic shapes and the mass of the buoy.

This is a significant improvement on the point mass model because there is some basis for the rotational effects. A rigid body model can also handle more detail like an offset mooring connection point below the hull. However, it’s still an approximation to the actual buoy shape.

Regardless, it’s certainly a starting point to understand rotational motion. Like the point mass approach, it doesn’t need a lot of information to set up the model. But the simple rigid body model relies on a lot of assumptions to help fill the gaps in knowledge. So what can you do if you have a lot more details on the buoy on hand and want to make use of it? This brings us to the third and final section on modelling surface buoys: using the complex rigid body models approach.

There are a lot of assumptions used in the simple rigid body approach

Complex rigid body models are about reducing some of those assumptions. Using a complex rigid body approach will undoubtedly require a lot more information. In some circumstances, a detailed CAD software model of the buoy may be available. This CAD model can help provide the specific buoy hull geometry. The CAD software can also offer more accurate details like rotational inertia and the location of the centre of mass.

However, it can take a lot of time to set up a detailed CAD model. On top of this, generating a custom mesh of a buoy hull can be a challenging task in its own right. Nevertheless, it is the most flexible and powerful approach to modelling surface buoys.

What about the computational cost of these approaches?

It’s reasonable to expect the computational cost to increase if the model complexity increases. This is always on the top of my mind because more computational cost means more time needed to compute a mooring design. However, in this particular case, it’s not so obvious.

An oceanographic mooring simulation tends to require a fair number of elements in the mooring line. The extra equations introduced between a rigid body and point mass model does not make much of a difference in the computational time. That said, some buoy hulls can have intricate shapes. These intricate shapes mean a lot of geometric detail needs to be used in hydrodynamics calculations to resolve the hull forces. In practice, a complex rigid body model with a detailed hull might take something like twice as long to compute a mooring solution when compared to the other models. But it all depends on how much detail is in the hull.

Let’s look at an example

We’ve looked at the Southern Ocean Flux Station (SOFS) system in previous articles. In 4km deep water off the coast of Tasmania, it uses a 3m diameter buoy at the surface. We set up a detailed configuration of the entire mooring and surface buoy in ProteusDS. The ProteusDS model allowed us to examine what happens to the mooring loads and buoy motions when using the three different model approaches.

The general environmental conditions used for this example were 0.5m/s surface current dropping to zero after a few hundred meters. The wave conditions were 3m significant wave height and 10 second spectrum peak period.

We set up separate ProteusDS projects using the three different surface buoy models configured as a point mass, simple rigid body, and complex rigid body models.

A ProteusDS ExtMassCylinder was used to represent the simplest approach – the point mass surface buoy. The diameter and length of the hull were set to encompass the flotation volume of the SOFS buoy. The mass and maximum wet weight were set equal to the SOFS buoy mass and maximum reserve buoyancy, respectively.

Surface buoy in waves

SOFS surface buoy represented by a point mass approach


The simple rigid body approach was represented in ProteusDS by the Rigid Body model along with a Cylinder Mesh hull. Just like the simplest model, the hull geometry was set to encompass the flotation volume of the SOFS buoy. The mass was set equal to the SOFS buoy mass. The rigid body inertia was approximated using a solid homogenous cylinder with the centre of mass right in the middle of the flotation volume.

SOFS surface buoy represented by the simple rigid body approach


The complex rigid body model was represented using a ProteusDS Rigid Body model along with a Custom Mesh hull. The hull mesh was formed based on the shape of the SOFS buoy hull. The rigid body inertia and centre of mass location were computed by a detailed CAD model provided by CSIRO mooring engineer Pete Jansen.

SOFS buoy represented by the complex rigid body approach


Each model approach produced 3 hour peak mooring tensions of 23kN, 24kN, and 25kN, respectively, in the set environmental conditions. This shows how well the simplest model did at driving the peak loads in this storm condition. But what about buoy motions?

The simple point mass model tells us nothing about the rotational motion of the buoy. But there are results from the simple and complex rigid body models. In the 3m significant wave height conditions, we compared standard deviation and maximum buoy tilt. Each rigid body model produced 5.8deg and 5.7deg standard deviation. The maximum tilts were 37deg and 39deg, respectively. Since they were so close together, it shows for this kind of buoy and mooring combination, the simple rigid body approximation does a reasonably good job.


The Italian army only had one option when crossing a desert to succeed: pass as quickly as possible and airdrop supplies (live sheep included). Fortunately, you have more than one option when analyzing buoys in your oceanographic mooring. Now it’s time to review them.

The first approach is the most direct and straightforward way using a point mass. This approach is the fastest to set up and easiest to use. It often does the job for mooring design. But it does not account for any buoy rotational effects.

When these rotational effects may be significant, it’s time to look at the second approach: the simple rigid body model. The simple rigid body approach is excellent when there’s limited information on the buoy available. It uses underlying approximations and assumptions to fill in gaps in details like those for rotational inertia.

If you have a lot more information on hand, and likely a CAD model to help out, the third approach can be useful: the complex rigid body model. Not for the faint of heart, it can take a lot more time to set up. But you can use more detailed buoy hull geometry, and the rotational inertia computed from a CAD tool for much more accuracy.

Next step: check out this video tutorial comparing point mass and rigid body models

DSA develops ProteusDS as a software tool to help evaluate oceanographic mooring designs. We post a variety of materials online, including video tutorials on our YouTube channel. Check out this video tutorial below showing more detail on a comparison of point mass and rigid body models in the software.


Thanks to CSIRO

Thanks to Pete Jansen from CSIRO Marine National Facility / IMOS for sharing technical pointers, sharing data, and helping assess the SOFS mooring system and buoy dynamics.

How to systematically evaluate oceanographic mooring compliance

People that live in northeastern India use tangled foliage to speed their way through the jungle. But it takes a lot of patience. They can do this with certain kinds of plants, like the rubber tree. As you might expect from a rubber tree, the roots are quite flexible as they grow. It is this flexibility that is used to cultivate and direct the roots so they grow across ravines and streams in the jungle and take root on the other side.

The result? A living bridge that can last for a long time. By tending and adjusting the roots, the problem of getting around is solved with a systematic approach.

Similarly, a systematic approach is needed when evaluating oceanographic mooring compliance. This mooring compliance is what ensures survival in the face of dynamic forces from ocean waves, wind, and currents. In this harsh ocean environment, success for a designer means an oceanographic mooring that can last a long time.

Jungle bridge

A living root bridge in northeastern India

There are a lot of details in designing an oceanographic mooring. It can be easy to get lost in what often will be an iterative process. A roadmap is always helpful when you get lost. That’s what we’re going to talk about in this article: three steps in a systematic approach in assessing oceanographic mooring compliance using:

  1. steady state
  2. regular ocean waves
  3. irregular ocean waves

We will begin by addressing steady state in the first step.

Ocean waves are usually not the only source of forcing from the environment

The first step is to understand steady state effects on the oceanographic mooring. These steady state effects are often from drag forces caused by constant wind and ocean currents. The critical effect of interest here is how these constant forces deflect the oceanographic mooring.

This is particularly important for very long ocean moorings that can deflect a very long distance. It is this deflection that can have a drastic effect on reducing mooring compliance. A mooring that is almost stretched taut from these mean steady state forces will be at risk of breaking when ocean waves come along, which brings us to the next step. In the second step, we check what regular ocean waves will do to the mooring.

In this stage, the analysis picks up from where the first stage left off

The analysis starts with the steady state current and wind and deflected mooring profile. Now is when things get interesting: it’s time to bring in some ocean waves to see what happens to the mooring. But ocean waves also have a lot of parameters. Before we get lost in a vast number of load cases and long computation times, it’s a good idea to start simple. The simplest way to start is with regular ocean waves.

These regular waves are just sinusoidal ocean waves. They are a very simple starting point, but don’t let that simplicity fool you: they can still break your mooring very easily. This simple starting point is ideal because if there’s a problem with the mooring design, you can make adjustments, quickly re-evaluate step 1 again, and be right back to test with regular waves once more.

Regular waves do a great job of adding a dynamic component to test the response of the mooring

If the mooring is near the breaking point from the deflection produced from step 1, often just a short dynamic analysis with regular waves will show whether breaking loads are reached very quickly. But regular waves are very simple and don’t always accurately represent the kinds of ocean wave conditions at sea. This takes us to the third step in the mooring compliance assessment. In the final step, we look at with a wave spectrum, or irregular ocean waves, do to the mooring.

Ususally, when you look at the sea, the water surface doesn’t look very sinusoidal

In reality, it’s most common to see many of these waves of different sizes and wavelengths at the same time: in other words, a spectrum of ocean waves. It is this seemingly random water surface that makes what we call irregular ocean waves. But if they seem random, how can we use irregular waves to design a mooring?

Irregular ocean waves

Irregular ocean waves in a storm

It is the wave spectrum that truly governs this seemingly random nature

While the water surface at any instant might appear to have random waves, over a long period of time, a pattern emerges of typical wave heights and lengths.

However, this pattern is statistical. It isn’t something that can be so easily applied directly to a mooring design to test the mooring compliance. The solution to this is simple but the most time consuming step of all: you have to check what the mooring does in irregular waves over a long period of time.

You don’t need a long time when working with regular waves

This is because regular waves are sinusoidal, and you may see a pattern in the dynamic response of the mooring motion and forces emerge after only a few wave periods. In an irregular sea state, you may never see a specific pattern emerge. However, you will start to see statistical patterns emerge over time.

These patterns may be in a typical envelope of motion or tension of the mooring. But one of the most interesting patterns is in the peak tensions. It is these peak tensions that so often drive the design of the mooring. These are the loads that happen when a single big wave appears and really pummels the mooring.

Mooring designers look for these kinds of events

They’re essential because how high the tensions are provides a more realistic idea of how robust the mooring compliance is and if the mooring will survive or not. And if it doesn’t survive in the analysis? Then the design has to be adjusted, perhaps with stronger or longer components or a different float configuration, and you go back to step 1 and keep going through the systematic process.

But aren’t you going to be looking at irregular wave load cases forever?

It’s true, the final step is not a fully deterministic design step to checking the mooring compliance. It doesn’t mean that you need to look at an infinitely long storm load case. But it does depend on a few factors like the magnitude of the storm, the spectrum type, how long the mooring is, and how it responds to the waves.

The most important thing is that a mooring designer has a way to run load cases that are long enough to see a statistical pattern of the peak loads emerge.

Let’s look at an example

The Southern Ocean Flux Station (SOFS) is an oceanographic mooring deployed in about 4km deep water off the coast of Tasmania. The mooring uses a 3m diameter surface buoy and over 6km of mooring line to provide the compliance needed to ride massive waves in the southern ocean. We configured the entire mooring in ProteusDS and ran through the three steps to determine maximum loads at the top of the mooring, next to the buoy. The general environmental conditions used for this example were 0.5m/s surface current dropping to zero after a few hundred meters. The wave conditions were 3m significant wave height and 10 second spectrum peak period.

SOFS buoy on station in 4km deep water near Tasmania. Picture credit: Pete Jansen from CSIRO MNF/IMOS

In step 1, the steady state profile of the mooring was resolved from the current forces. The top tension of the line was 11kN in this condition. This was only a little higher than the static weight of the system without any current. The deflection of the mooring is significant but expected because of the very long mooring line.

SOFS mooring deflection in steady current profile. This represents 6km of mooring line in 4km of water depth so the buoy and instruments are not visible

In step 2, we used the steady state profile of the mooring as the starting point. It’s a very crude approximation but we used 3m regular waves to represent the sea state condition. These loads were resolved after only a few wave periods so we had the results very quickly. The maximum tension was 13kN so you can see how the loads are increasing from the dynamics. But while it is dynamic, it doesn’t necessarily capture the peak loads caused by a more realistic irregular sea state. This takes us to step 3.

In step 3, we used a JONSWAP sea state with 3m significant wave height and 10 sec spectrum peak period. Running a few separate realizations of this spectrum produced an average 3 hour storm peak tension of 26kN. Note this was just an example to illustrate going through the steps with an existing mooring design and to show how the loads change in each step. In reality, the design may need to be adjusted depending on the needs of the design and strength of components in an iterative fashion.

Because the design process is iterative, it’s easy to get lost in the details

In the steps discussed here, complexity increases with each step. If there’s not enough mooring compliance in any step, a design change is needed and you must go back to step 1. Let’s review the three systematic steps discussed in checking oceanographic mooring compliance:

  1. start with the steady state response: deflection of the mooring to constant currents is the starting point to step 2
  2. rough out the dynamic response to regular ocean waves: it’s a simple but quick check with a dynamic effect
  3. polish with a dynamic response to irregular ocean waves: it’s the most realistic, but most computationally costly.

The systematic process is a roadmap

People living in jungles can use a systematic approach to cultivate living root bridges. It takes a certain amount of time before the roots reach the other side of a river or gulley, and only after the process is completed can the bridge be used. In a similar way, mooring designers need to follow a systematic process to evaluate their designs to ensure they’re safe and will survive.

Next step: evaluate your own mooring designs

DSA develops ProteusDS as a software tool to help evaluate oceanographic mooring designs. Mooring designers use this kind of systematic approach with a tool like ProteusDS to check their work and improve designs. Try the software and judge the results of your own designs. Apply for a free ProteusDS demo here.

Thanks to CSIRO

Thanks to Pete Jansen from CSIRO Marine National Facility / IMOS for sharing technical pointers, sharing data, and helping assess the SOFS mooring system.