Tag: hydrodynamics

When to avoid a static solver in oceanographic moorings

It was when the traffic light turned green, and my car lurched forward from a stop when it happened. A warning light flickered on the dash, but then quickly turned off again. Fortunately for me, it wasn’t a sign of disaster with the engine – it was just a light indicating more window washer fluid was needed. But the warning light wasn’t on all the time – yet.

Dashboard with warning light

The to-do list just got a bit longer

Now, it’s right at this stage that I turn into Mr. Scrooge with my window washer fluid. The little bit left in the tank is sloshing around, and I know if I use one tiny spritz more to clean my windshield, the light will stay on. And if the light stays on? Well, it’s another problem I need to solve on my long to-do list! So my short term solution? Never clean the windshield. It may seem counterintuitive because that’s exactly what washer fluid is supposed to be for – cleaning my windshield. But instead, I completely avoid it.

Likewise, there’s some things I also completely avoid in mooring analysis. In particular, when we’re looking for a static mooring profile, it may seem counterintuitive to avoid using a static solver. But there’s good reason to avoid them in some circumstances. In this article, we’re going to focus on when to avoid using a static solver and what to do instead.

A static solver can mean many different things depending on the problem you’re trying to solve

In the case of mooring analysis, one problem we’re trying to solve is to find the static deflection of a mooring system to steady loads. Most often, these steady loads are from effects like ocean currents and wind. In the case of mooring design, this is what we mean by a static solver.

A static solver is a great tool to have

Ideally, they work quickly to give you a solution that shows what the mooring deflection looks like to specific steady loads. These static solvers compute the tensions in the mooring lines, too. This feedback is really helpful in the early stages of the mooring system’s design, so you can narrow down the materials and concepts to find something workable.

Often, you may need to screen mooring designs to make sure the deflection isn’t too high and check the lines are strong enough to handle the loads. But timelines are often tight in these projects. So getting to the next step in mooring design in short order is crucial.

Finding a static mooring deflection may sound like a straightforward problem

But it can be tricky depending on the complexity of the mooring system. Because of this complexity, there’s no single static solver algorithm that’s useful for all mooring systems. Ultimately though, there’s a common idea behind these static solvers. The idea is that they look for a mooring configuration in which the external forces, such as those from ocean currents and wind, are in balance with the internal forces, such as the mooring tensions.

As a static solver goes through a solution process, it can make large jumps to test what the mooring profile looks like. These jumps aren’t random. But they certainly do depend on how the forces are balanced between the environmental effects and the mooring loads. These jumps are a static solver’s greatest advantage: when they work well, they jump instantly to the right solution! But then sometimes they also struggle. When they struggle, it looks like they jump around and around a potential solution, but never quite land on one. Or, in some circumstances, there just may not be any solution at all.

It’s when static solvers struggle that they lose their advantage of speed

Suddenly, the static solver process is churning away, but just not getting anywhere. It can take a long time to process, whirring away on calculations, and never end up with anything useful. We call this a failure to converge to a solution. Suddenly, the trusty tool that quickly got you to the next step has betrayed you!

Now what do you do?

One alternative is dynamic relaxation. Dynamic relaxation is a very simple and direct approach, and there’s only a few steps. First, you start with a basic crude guess for the mooring system layout. This crude guess might look like diagonal straight lines from the anchor to the fairlead. Next, you simply run a dynamic analysis solver to let the system respond dynamically to steady forces from ocean currents and winds. The mooring system “relaxes” and deflects naturally to its steady state configuration.

The advantage here is that it’s a typically very robust approach: there’s no guessing about mooring profiles – it evolves a realistic deflection of the mooring over time and eventually to a steady state profile.

Why don’t we use dynamic relaxation all the time?

It all has to do with time. Unfortunately, dynamic relaxation can be quite slow! The longer the mooring lines and the deeper the water, and the lower the forces involved, the longer it takes to relax and settle to a steady state profile. A full ocean depth mooring might take over 24 hours to compute a steady state profile by dynamic relaxation – but only a few minutes for a static solver. So when do you want to use dynamic relaxation?

It’s hard to know when to use dynamic relaxation ahead of time

But there are a few guidelines you can keep in mind. Generally, what you need to keep your eyes peeled for are strong forces or abrupt changes in the environmental effects. This might look like a very severe shear profile in the ocean current, or perhaps an abruptly varying sea bottom. But one of the most common effects you’ll see is the effect of shallow water. In shallow water, small changes in mooring deflection can mean big changes in forces acting on the mooring – from buoyancy if the lines come out of the water, or ground contact if they touch the seabed.

This is where those jumps that static solvers make in guessing the mooring profile can run into problems. It can take a long time to settle and often you may find it fails to converge to a solution. But the good news is that dynamic relaxation can really shine in shallow water conditions. After all, often, mooring lines are shorter in shallow water. It doesn’t take much time for a mooring to deflect a short distance and reach a steady state.

Wait a minute. What do you mean by shallow water?

It’s one of those grey areas. There isn’t an exact answer. But fortunately, it’s often easy to try both techniques in parallel – static solver and dynamic relaxation – so really it’s up to you to learn what works. I think you will find that there is a range where one works better, and a range where they both work OK, too.

NOAA COOPS Currents Buoya (CURBY) mooring in 10m water is pretty shallow water. Picture credit: Laura Fiorentino

No really, can you give me a specific water depth?

Ok. Fine. For oceanographic moorings, I would suggest definitely trying dynamic relaxation if your mooring is in less than 100m of water depth. But again, it’s ultimately up to you to judge what works best for your specific problem.

Let’s look at an example

The CURBY (CURents BuoY) is a shallow water mooring deployed in the Delaware River. It’s certainly shallow at just over 10m depth. But the currents can rip through there fairly quick. The mooring is a simple design with a surface buoy and a few different sizes of chain along the span. In this example, the ProteusDS static solver struggles to find a solution in certain environmental conditions. But the shallow water is so short, that a dynamic relaxation finds a solution in only about 20 seconds of simulation in a strong current.

CURBY mooring static deflection calculated by ProteusDS

It’s time for a summary

We covered a fair bit on static mooring solutions, so now it’s time to review. There are many different techniques that may be used in static solver algorithms. It’s common for them to use an iterative approach that jumps to a solution, continually seeking a balance of internal tensions with external environmental loads from ocean currents and winds. But sometimes they just don’t work. When they don’t work, either they take way too long or fail entirely to reach a solution. You may find this when there are big discontinuities in the environment, like a very strong current shear, or a shallow water depth. In these cases, you may consider dynamic relaxation as an alternative.

Dynamic relaxation is a process that uses a dynamic solver that lets the system evolve through time from the effects of constant loads. While it’s often much slower than static solvers, in shallow water conditions, it should be plenty speedy – and at least there are no problems like failing to converge. Think about using dynamic relaxation in 100m water depth or less – but always be sure to judge for yourself what works best.

You may not be as annoyed as me when the window washer fluid light goes on. Of course, it seems counterintuitive to avoid using the window washer in your car. In a similar way, avoiding static solvers in mooring design may seem counterintuitive. But fortunately, there are only a few circumstances in which you need to use a workaround.

Next step

Learn more about how static solvers work with an article using an example with a deep water oceanographic mooring example here.

Thanks to NOAA CO-OPS

Thanks to Laura Fiorentino from NOAA CO-OPS for sharing technical pointers and data for the CURBY mooring for the example.

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.

Is your WEC hydrodynamics software up to the task?

Image of IEA-OES Task 10 Wave Energy Converter Modelling Verification and Validation logo

DSA Continues to Support IEA-OES Task 10 Wave Energy Converter Modelling Verification and Validation.

Calculating the effects of wind, waves, and currents on devices in the ocean is complex. We know the value of numerical modelling that reduces risks in physical prototyping. How do you know your software’s calculations are right? One way to ensure that your software is producing expected results is through cross-validation and comparison with different analysis programs.

DSA is pleased to continue our participation in an international group of experts that been working together on the validation of numerical modelling tools for wave energy converters (or WECs) under the Ocean Energy Systems (OES) Technology Collaboration Programme of the International Energy Agency.

The initial results published in a joint paper prepared by 13 countries and over 20 companies with experts from academia and industry was presented at the European Wave and Tidal Energy Conference (EWTEC), held in Cork (Ireland) in late August 2017. Focused on ocean energy, EWTEC is an international technical conference with attendees and contributors from both academic and industry.

Phase two of the project is about the launch, and it will incorporate validation aspects using experimental test data from the US Navy wave test facility, MASK basin.

In this second phase, DSA and the group are looking to further improve their confidence and the accuracy of numerical models for wave energy converters and to identify future research needs.


“At what point do you realize there is a problem? It becomes costly, quickly, to learn lessons while putting steel in the water,” cautions DSA CTO, Ryan Nicoll. “Cross-validation of numerical models is one way to find out much earlier if there is a discrepancy. Critical initiatives like the IEA-OES Task 10 allow international experts to compare their analysis capabilities and ensure our independently derived calculations make sense,” notes Nicoll. “We are grateful to represent Canada with our colleagues from Cascadia Coast Research and engage with such an esteemed international group.”


Participation in Task 10 is voluntary; the Canadian Government provides registration fees for participating Canadian companies.

An overview of findings achieved by the international team so far is summarized here.


  • Aalborg University, Denmark
  • BCAM, Spain
  • Cascadia Coast Research, Canada
  • Chalmers University, Sweden
  • DSA, Canada
  • EC Nantes, France
  • EDRMedeso, Norway
  • Floating Power Plant, Denmark
  • Glosten, USA
  • Hawaii Natural Energy Institute, USA
  • INNOSEA, France
  • KRISO, South Korea
  • KTH, Sweden
  • MARIN, Netherlands
  • Plymouth University UK
  • Queen’s University Belfast, UK
  • Technical University of Denmark
  • Tecnalia, Spain
  • University College Cork, Ireland
  • Wave Venture, UK
  • WavEC, Portugal


Ocean Energy Systems (OES), also known as the Technology Collaboration Programme on Ocean Energy Systems, is an intergovernmental collaboration between countries, which operates under a framework established by the International Energy Agency in Paris. Presently, the OES has 24 member countries and the European Commission with a number of other observer countries in the process of joining.


We want you to fail

We want you to fail. Virtually. So you don’t fail in reality. With Dynamic Analysis, you can reduce real-life failure.


With dynamic analysis, you can test your virtual prototypes; pushing your designs to their breaking point before going full scale.

But what is dynamic analysis? And what does it mean in the ocean engineering industry?

In ocean engineering, dynamic analysis uses virtual prototypes of vessels and equipment operating in ocean conditions using simulation software.

These virtual prototypes capture the dynamic response caused by the effect of wind, waves, and ocean currents. Easy to use software tools allow for much quicker design iteration and optimization compared to rules of thumb or rough calculations. Providing a swift and accurate analysis of the vessels and equipment’s response in various environmental conditions and reduces the need for physical prototypes and testing.

When you perform dynamic analysis, you reduce the risks and uncertainty of a project by considering the nonlinear and complex effects of current, wind and waves.

With dynamic analysis, you can apply industry best practices for installation and maintenance processes and explore design alternatives efficiency using an easy to use and flexible unified modelling environment.

At any stage of the project, virtual prototypes can be used to answer questions related to engineering design, planning, training, operations, and safety.

Some common questions our clients look to answer are;

  • How will my mooring system respond to wind and waves?
  • How will my ship behave in a seaway?
  • How can I safely tow this barge?
  • How will my towed body respond?
  • How will the pipeline be loaded during install?
  • How do tidal energy platforms behave in current and waves?
  • How much energy can my wave energy converter extract from the waves?

To answer these questions Dynamic Systems Analysis created ProteusDS, a powerful finite-element based analysis tool with intuitive pre and post-processing capabilities.

With ProteusDS, users can create virtual prototypes of marine, offshore, and subsea technologies. For example, DSA recently led an ecoEnergy Innovation Initiative (ecoEII) and launched the ecoSPRAY system to gather data and verify the behaviour of floating tidal energy platforms and their moorings in high-energy turbulent tidal flows.

The NRCan ecoEII project is helping to reduce the cost of in-stream tidal energy through the development of comprehensive site assessment methods and technologies. Lessons learned from this project will help smaller and remote communities deploy smaller scale tidal energy systems and support them with their local equipment and capabilities.

Image of a ProteusDS simulation of the ecoSpray tidal energy platform


The ecoSPRAY is deployed in Grand Passage between Freeport and Westport, NS, in the Outer Bay of Fundy. The Bay of Fundy has the highest tides in the world with current speeds that can reach up to 11 knots. With the help of ProtuesDS and its advanced finite-element capabilities, DSA was able to simulate the floating platform and mooring configuration before deployment.


The ability to view and understand how a system will react is a significant advantage in any ocean industry. It allows you to plan and gain insight into how a system will respond to a wide range of conditions. Determining areas of potential problems will reduce project risk and assures that the design can withstand the extreme ocean conditions.

Dynamic analysis is used for a wide variety of marine industries including;

Designing for the ocean environment is a constant challenge. Dynamic analysis allows rapid innovation and optimization while reducing risk to fail in the harsh ocean environment.

Interested in DSA’s ocean engineering numerical modelling expertise? A quick email to see if ProteusDS is the right solution for you is a great place to start.

button to contact dynamic systems analysis




DSA Employee Featured in World Aquaculture Magazine

Bridging the Gap

Environmentally Friendly Aquaculture Design

Did you know that aquaculture is responsible for the production of roughly 50% of the world’s seafood? In Canada aquaculture accounts for 14% of the total Canadian fisheries production and 33% of its value. The aquaculture industry plays a vital role in all Canadian provinces and territories, employing nearly 10,000 people primarily in small communities.

Aquaculture has been around for thousands of years but has only been recognized as an industry in western society for four decades. During this time period, poor government regulation, environmental impacts and lack of industry promotion has had a negative impact on the image of the aquaculture industry.

In steps Adam Turner, a recent graduate of the Master of Science in Mechanical Engineering program at the University of New Brunswick, who is currently a Mechanical Engineer in Training at Dynamic Systems Analysis (DSA). Adam’s master’s thesis focused on the hydrodynamic wake properties of scale model fish cages and fish cage arrays, to gain a better understanding of wake velocity, wake topology, wake turbulence and wake recovery. The results of his work are being used to better understand how to place extractive species in aquaculture farms for optimized nutrient extraction.

By focusing his studies on how water moves through fish cages and cage arrays, Adam is helping the aquaculture industry understand how current flow will impact nutrient and waste flow, and how that impacts surrounding habitats. Adam also draws attention to the vital role extractive species (mussels, sea cucumbers, kelp, etc.) play in and around aquaculture farms, as they have a natural ability to recycle nutrients or waste, making them a living filter.

Green dye can be seen moving with the current flow.

Adam’s scale model testing research (currently featured in the December Issue of the World Aquaculture Magazine), suggests that the placement of extractive species, and current flow through cages should be an important consideration for any aquaculture farm as it will help to reduce the environmental impact these farms have on the surrounding marine environment.

From theory to practice, Turner is focusing his attention on aquaculture engineering projects at Dynamic Systems Analysis using their ProteusDS software. The software plays a vital role in allowing Adam to easily and effectively conduct mooring, motion and anchoring analyses, with use of ProteusDS’ built in hydrodynamic cable and net models. The data gained from these assessments will play a vital role in helping producers and site managers in the protection and maintenance of their aquaculture farms.


Heading to Aquaculture 2016 in Las Vegas? Check out Adam’s session IMTA/Aquaculture on Wednesday, February 24th at 10:30am.