Tag: ShipMo3D

Why the sensitivity of ship roll damping makes naval architects sweat

Dolphins might act like they have x-ray vision. But it’s not their eyes that help them see through the ground. Their fine-tuned sonar capabilities have made them a valuable part of maritime security and the protection of coasts and harbours for decades. They’re used to living and working in all ranges of conditions, including murky water and acoustically noisy environments – where there are many other animals and lots of marine traffic. Trained Dolphins can easily find intruders or even mines in places and conditions where our own sonar technology completely falls flat. In fact, Dolphins can differentiate between entirely distinct types of metal, like brass, aluminum, and steel, buried almost a meter under the seabed because their natural sonar is so sensitive.

But a high level of sensitivity can be both a blessing and a curse. It can be a curse because seemingly minor changes can cause a completely different response. When it comes to ship motions, roll is extremely sensitive. Small changes in the ship design can result in significant changes in motion characteristics. In this article, we’re going to talk about why naval architects sweat the details to really understand just what will happen to a ship in roll. So why are ship roll motion so sensitive?

Dolphins have sonar so sensitive it can differentiate different metals buried in the soil.

Not all ships have sensitive roll

Barges and multi-hull ships like catamarans and trimarans don’t tend to have sensitive roll. The kind of ships we are talking about are smooth monohull systems. The key is that there is a single primary hull that is relatively slender in terms of length to beam ratio. Often, monohull ships are quite smooth with a round form, which is one crucial reason roll motion is so sensitive. The rounded shape means there is very little damping resistance when it rolls.

What do you mean by resistance?

By resistance, I mean either ocean wave radiation or viscous damping. Barges are large and flat – almost like floating paddles – and their particular shape is ideal for generating waves when rolling. These radiated ocean waves absorb massive energy, making an enormous amount of resistance that slows down barge motion in roll. A multi-hull vessel like a catamaran also does an excellent job of radiating waves when rolling. This is because of the way the flotation hulls are offset from the centerline. But a rounded monohull makes almost no waves when it rolls and, as a result, relies heavily on viscous drag for resistance.

But viscous drag damping doesn’t work very well in oscillation

Even if the ship roll velocities are high, because of the back-and-forth motion, drag loads tend to be weak. Because of the low resistance, even relatively mild ocean wave conditions can lead to significant roll motions and accelerations. This can limit ship operations or, worse, cause injuries. Equipment, cargo, or the ship itself can be damaged, too.

The result is that naval architects spend a lot of time and energy thinking about ship roll

A lot of time and energy goes into the design details of the shape of the hull and appendages that help amplify viscous drag resistance. Features like bilge keels are often added specifically to create viscous resistance to help reduce roll motion. Other technologies can help, including passive and active systems like antiroll tanks and stabilizers, but simple appendages are the most straightforward place to start. But with hull appendages, it’s vital to understand the viscous drag effects reasonably well because of how they can substantially impact roll motion performance. So how is viscous roll damping evaluated?

Slender monohull ships like the Uchuck III can have very round and smooth hulls which can make controlling roll motion a design priority


Hull appendages like rudders and skegs can help with roll damping, but they can only do so much

One way to evaluate roll motion is from physical scale model testing

But this approach is by far the most costly and time-consuming. A scale model of a ship in a wave basin will verify the ship’s expected roll response based on the design details used. But because of the costs involved, it’s not an economically viable approach to iterate on the design of the hull and appendages – it serves more as a confirmation of the expected roll performance. Yet there are alternative numerical methods that work well in evaluating roll.

Roll damping can be computed with Computational Fluid Dynamics tools

These software tools resolve the physics and details of the water flow interacting with the hull and appendages. While they provide a great deal of useful information and are helpful for a degree of design iteration, it can be a computationally costly and time-consuming approach. A tight project timeline won’t leave room for investigating many different loading conditions or design iterations on hull and appendage configurations. But there is more than one numerical approach to resolve ship motion.

Some numerical models use empirical relationships to resolve the viscous forces

Empirical equations describing viscous roll resistance are helpful but have more significant uncertainty than the other approaches. Yet ship designers can use them across various conditions and appendage configurations. They are also very computationally efficient and can help screen out different designs quickly. Dynamic analysis tools like ShipMo3D are designed to set up typical hull design, including appendages and resolve ship motion in a broad range of sea and ship conditions much faster than CFD tools.


The RV Investigator hull is also very smooth, but has multiple tricks to help with stability in roll like bilge keels and an antiroll U-tube tank. Picture credit: Mike Watson

It’s example time

So how much difference can something like bilge keels make to damp roll motion on a smooth bottomed monohull vessel? Here is a comparison of ship roll response of the Generic Frigate computed by ShipMo3D with and without bilge keels.

The ShipMo3D Generic Frigate model with bilge keels on the left and without on the right

A roll decay comparison starting the vessels at 10 degrees shows a significant difference. While bilge keels don’t eliminate roll oscillations entirely, they are substantially better than nothing at reducing roll motion. But this is only the roll decay response. What happens to the ship motion response across a range of wave frequencies? The RAO can give some insight.

In a roll decay test computed by ShipMo3D, bilge keels are significantly better than nothing at reducing roll motions

The RAO gives a broad spectrum idea of how the ship will respond, including at resonance. Often, for slender monohull ships, one of the worst-case loading conditions is in a beam sea. The roll RAO of the Generic Frigate with and without bilge keels in a beam sea condition is illustrated below. The RAO shows that maximum roll motion is reduced by a factor of two! There is also much lower roll motion in the region around the peak as well. This implies that the bilge keels help significantly control roll motion, especially around the natural frequency in roll.

The bilge keels have a substantial effect at reducing the roll RAO peak by a factor of two. This implies significantly lower accelerations and motions especially around the natural roll frequency.

It’s time to summarize

We covered a few details on ship roll response, and now it’s time to review. Roll response is something to get right because the stakes are high – large roll motions can make the ship inoperable, cause injuries, or even damage. Not all ships have sensitive roll response, and usually, it’s an essential issue for monohull vessels. The slender form of the vessel with a rounded bottom means there is little resistance in roll.

These vessels don’t radiate ocean waves very well compared to other vessel forms like barges or multi-hulls like catamarans and trimarans. So monohulls rely almost totally on viscous damping to control roll motions. Viscous forces are weak in the back-and-forth oscillatory motion in roll. So ship designers and naval architects spend a lot of time characterizing the viscous roll effects however they can. Like dolphins measuring different materials through seabed soil and mud layers, ship designers will use whatever tools they can to measure ship roll response.

Next step

Validation of dynamic analysis tools like ShipMo3D is crucial to trust the results. Read more on validation of ShipMo3D in the report posted here.

Why drag loads are underwhelming at damping floating system motion

Snow is rare in my Canadian city. This might surprise you, given Canada’s reputation as a northern and wintry country, but I am lucky to live near the coast. The marine climate helps keep the weather surprisingly mild. Despite this, I do own a snow shovel. It’s a big one, too. It has a wide scoop, all the better to clear a large swath along the path on our driveway. I expected it to do well and help quickly clean up any snow that came along.

But that expectation threw me off on our last rare snowfall. The problem with snow in a marine climate is that it often comes down super wet and thick. Because wet snow is so dense, a massive scoopful in my large shovel was too heavy to lift. Piling up a giant heavy glob of dripping snow almost broke my shovel and my back at the same time! I had big expectations for my large shovel, but in wet, heavy snow, it was underwhelming.

An underwhelming response can throw anyone off. It can cause nasty surprises, especially if there are big expectations. In the world of hydrodynamics, there are often big expectations with drag loads. Any analyst should be wary of drag forces – after all, they are very sensitive to current speed and can become a dominating effect. But there are some circumstances when they fall flat and have little impact on ships and buoys. But first, it helps to understand why drag loads can be so powerful in the first place.

In wet, heavy snow, larger shovels are underwhelming

Why can drag loads be overwhelming?

Viscous drag forces appear when there is relative flow past a structure. Whether the structure is moving, the flow is moving, or a combination of both, you’ll see drag loads. The key is that there needs to be some relative motion involved. Generally, the greater this relative motion, the greater the magnitude of forces involved.

One portion of drag on a hull is a skin friction effect, and while important in some ways, it tends to be a much smaller effect in general. The other critical portion of drag is a pressure differential caused by eddies and wake structures that form in the lee of the relative flow behind the hull. Eddies and wakes are regions of low pressure in the flow field, and the resulting imbalance in pressure on the hull causes the drag force. But when are these effects overwhelming?

Drag forces from current can be overwhelming

The drag on the side of a ship hull or buoy in a current can be so significant as to dominate all other effects, overpowering a ship or destroying a mooring system. When a hull and flow have a large relative velocity, the pressure differential from these wake structures grows larger.

These forces increase rapidly with the square of relative flow speed. But it doesn’t mean they are always significant just because they are so sensitive. Viscous forces can also be weak in certain circumstances, and in particular, this can happen in oscillation.

Drag forces are underwhelming at damping oscillation

Oscillation, or any cyclical back-and-forth motion, is common for any hull in the marine environment. For example, a ship or a buoy will bob up and down vertically in heave. You see this in the tilt degrees of freedom of pitch and roll, too. So why does oscillation mean underwhelming drag forces?

Buoys or ship hulls, like the HMCS Halifax, have lots of drag. But drag from steady effects like currents or forward speed is different from viscous drag loads in oscillation.

A fully developed wake structure doesn’t appear instantly: it takes time for the low-pressure region to form behind the hull. Only once it is fully formed is the pressure differential greatest. This means there will be a time lag for the drag forces to come up to full strength.

But when a hull oscillates back and forth, it’s also constantly changing the flow structure back and forth. There’s almost no chance for a wake to form on either side of the system as the flow regularly reverses one way and the other. In the short term, fluid flows over the contours of the hull, causing some skin friction drag but without forming these larger low-pressure regions, preventing significant drag forces from forming.

The key is that in any kind of back-and-forth motion, the relative flow speed hovers around zero, as you would expect when you see a buoy or ship roll back and forth. The flow speeds can be high at a moment in time if the motion is violent, but the resulting drag loads are underwhelming because the flow structures haven’t had time to form and create large pressure differentials.

The Generic Frigate hull head on. The yellow portion is the wetted hull in this displacement. In a lateral ocean current, a steady wake forms in the lee of the hull and drag would be enormous. But drag during side-to-side sway oscillations, it is less likely these pressure regions can form and the effects of drag can be underwhelming.

But aren’t there other more significant hull damping forces?

Drag and viscous effects are not the only sources of damping in motion oscillations. Wave radiation can be substantial in certain conditions. Ship motion in pitch is usually controlled with damping by a totally different force: wave radiation. Smaller structures like buoys can some wave radiation effects, but it’s not as significant. Regardless, buoys often use a mooring that helps to control motion to some degree.

Sometimes drag is the only source of motion damping

This is a particular issue in specific buoy systems in pitch and roll and spar hulls in heave. It’s also a common problem in ship roll. These are only a few particular cases. Generally, it’s best if you are careful to understand both how your real system will work and how that reflects in your analysis of the floating hull dynamics.

Let’s look at an example

Here are two motion decay tests of the Generic Frigate computed by ShipMo3D. These are time-domain simulations in calm conditions with an initial deflection. The first is a decay test with the Generic Frigate starting at 10 degrees pitch. In this case, wave radiation dominates the damped system response, and after about 20 seconds, the motion is entirely damped.

Generic Frigate pitch decay test. Wave radiation effects are substantial and create a strong damping effect that stops pitch motion after about 20 seconds.

The second scenario is a decay test with the Generic Frigate starting at 10 degrees roll. The big difference from pitch motion is that there’s no significant wave radiation in roll because of the slender hull, and this means the damping effects are essentially completely from viscous drag loads. The decay response is far different than in pitch: after 100 seconds, it’s still going!

Generic Frigate roll decay test in calm seas. In roll, motion damping is almost completely from viscous drag effects. The system is still oscillating after 100 seconds and will likely keep going for a while!

In summary

Drag loads can be devastating when there are high relative flow speeds. Low-pressure wake structures cause a large differential pressure on the hull that we think of as the drag force. But when a floating hull oscillates, these wake structures don’t often have time to develop fully. Even if the oscillation velocity can be high, it’s only for a moment in time before the system reverses backward. It can mean drag loads become vanishingly small and ineffective at damping oscillatory motion. The result can be underwhelming – much like my disappointing giant snow shovel. By the way, my son’s toy snow shovel ended up working much better at clearing my driveway of heavy snow. Because it had a small scoop, it was far easier to quickly scoop and heave loads of snow out of the way, and it took far less time to get the job done!

Next step

In this article, we saw how viscous drag forces fizzle in oscillation motion – particularly in rotation.  In the next article, we focus on roll motion and see why it’s such an important topic in ship design. Read more on why the sensitivity of roll damping makes naval architects sweat here.


When you need to fine tune surface buoy damping (and when you don’t)

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.

Special underwater speakers help artistic synchronized swimmers keep coordinated even when their ears are below the water surface

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.

Surface buoy configuration with ballast plates and Nortek Signature 1000 ADCP

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.

Surface buoy moored profile in 19m water depth

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.

How to take the guesswork out of wave radiation forces

In 1830, the Swedish Navy was reeling after a major continental war. Their fleet was decimated, with many of their wooden sailing ships lost or badly needing repair. Securing wood to rebuild and maintain their fleet in the future was a top priority. The Navy estimated they would eventually need 300,000 oak trees and immediately set to work planting them. It turned out they needed precisely zero.

Planting so many seemed like a reasonable assumption to help with supply in the future. Yet the particular oak trees needed are slow to grow and mature, and they weren’t ready to be used until 1975. But by then, the Navy didn’t need trees anymore because of technological transitions to steel ships. Still, nobody in 1830 knew what the future would hold, and with such long timelines involved, there was no getting around the guesswork involved.

Guesswork may come up when there’s lots of uncertainty. You try to make reasonable assumptions to help find a way forward and solve your problem. When it comes to floating systems, there’s often uncertainty on some aspects of hydrodynamics. The amount of motion damping caused by wave radiation can be an important question. However, with the right software tools, you can eliminate the guesswork using a straightforward process, and take a closer look at the effects of wave radiation.

The forest of oak trees on Visingsö in Sweden were planted years ago to use for wooden naval ships

What are wave radiation forces?

When floating structures move in the water, they create waves at the water surface. These waves radiate away just like the ripples you see after dropping a stone in a pond. Wave radiation forces are the loads that act on the floating structure as these new radiating waves are created.

Wave radiation can cause substantial damping effects

The effects from these radiated waves can be substantial, even dominating, on the motion of floating systems. The momentum and energy of these radiated waves come directly from the floating structure. One crucial effect they can have is damping. This damping can significantly slow down the motion of the floating system in specific ways. But damping is not the only thing affected. The inertia of the floating structure can be affected, too.

The ripples you see in a pond are waves radiating away from the splash. All floating structures radiate waves when they move in the water. But the important question is to figure out how much it affects floating system motions

Wave radiation can also change added mass

Generally, added mass tends to be constant for completely submerged hulls far from the water surface. But near the water surface, the effect of radiating waves causes shifts in the magnitude of added mass. Further complicating things is that wave radiation may increase or decrease the added mass depending on how fast the structure moves around. This effect is sometimes called motion frequency-dependent added mass.

It’s not always easy to tell when wave radiation is important

Generally, one sign wave radiation is critical is if a floating structure looks like it would be a good wavemaker. Good wavemakers displace a lot of water when they move around – and that causes a lot of wave radiation. For example, a typical barge hull is like a large flat paddle sitting on the water surface. It’s hard to think of a better wave maker! Wave radiation forces are significant in almost all degrees of freedom of motion of a barge. But it also depends on how the hull moves in the water. For example, barge yaw may not cause a lot of wave radiation.

What about a more typical ship-shaped hull with a rounded bottom? Typically, in heave and pitch, they are excellent wavemakers, too. Like a barge, there’s often a lot of water displacement, and powerful wave radiation effects are possible. Essentially all the damping of ship and barge motion in heave and pitch will be from wave radiation. But the rounded hull produces an entirely different effect in roll. With very little water displaced as the ship rolls in the water, there aren’t many significant waves generated.

How are wave radiation forces calculated?

There’s no back-of-the-envelope calculation to estimate these effects. Suppose you expect a damped motion response of your floating system. In that case, it’s possible to model wave radiation with a linear damping effect. But the problem with this is that you need to know the nature of the damped motion response from experience and data. You will miss the frequency-dependent added mass effects, too. Without enough information, it might introduce a lot of guesswork to fill the gaps.

But instead of using experience and guesswork, there is a myriad of numerical tools available. One of the most common ways to resolve wave radiation effects is with a potential flow calculation that determines the interaction of a hull form with the water surface. These numerical techniques developed and used for many decades are helpful to resolve all aspects of wave radiation forces – including the damping and added mass effects – for many types of hull shapes. One example of a program that does this is ShipMo3D. ShipMo3D uses potential flow techniques to resolve the interaction of the hull with ocean waves, including radiated waves.

It’s time for an example

The Generic Frigate is a sizeable ship. At 120m in length, there is a lot of displaced water when the entire hull heaves or pitches in the water. So what do the wave radiation forces look like? Rather than focus on the forces themselves, let’s look at a heave decay response of the ship in calm water. This is a simple test that shows the heave motion of the ship after some initial displacement in heave. By far, the dominating damping effects in heave motion are wave radiation.

At 120m long, the Generic Frigate has strong wave radiation effects in heave and pitch motion

The heave decay response was calculated in ShipMo3D. The Frigate was offset by 1m out of the water and dropped. Even though 1m may not seem like much, in this configuration, the total ship displacement is 1000 tonnes, so it will take a lot to stop the oscillations. Yet a little more than 10 seconds later, wave radiation has damped out the heaving motion to a bit of a ripple. For this kind of hull in this particular motion, wave radiation forces are substantial.

After only little more than 10 seconds, the multi-thousand-tonne Generic Frigate heave motion settles out from wave radiation forces. This shows the major influence wave radiation has on this particular hull shape in heave.

It’s a mistake to use potential flow tools for every problem

Though wave radiation forces may be present in a floating system, they are not necessarily a dominating factor. For example, in the problem of oceanographic mooring design, the focus tends to be on loads and deflection of the mooring line itself. Many oceanographic buoys are relatively small and generally follow the water surface in extreme conditions with large ocean waves that drive extreme mooring loads. In specific circumstances, wave radiation may be key in oceanographic mooring problems. Still, most oceanographic mooring design problems do not necessarily require this level of detail.


Floating systems moving in the water create waves. These waves radiate away from the hull and carry momentum and energy away. When this happens, the result is wave radiation forces that appear on the hull. Radiated waves may have strong damping effects and can also shift the added mass of a system. Generally, you can get an intuitive idea if wave radiation forces are significant if you expect the hull to be a good wavemaker. In other words, if a hull displaces a lot of water when in motion, much like a typical barge would be in heave or pitch. Wave radiation forces can be resolved in specialized software tools like ShipMo3D, but it doesn’t mean they need to be used for every problem. Still, it’s good to have options to reduce the amount of guesswork involved. But guesswork that goes sideways isn’t all bad. At least the Swedish Government now has a forest of 300,000 trees they can use as a national park rather than building Navy ships!

Next Step

Learning about the concept of wave radiation is one thing, but applying it in a specific application is something else. Learn more about what you can do about the effects of wave radiation in the specific application of surface buoys for oceanographic systems here.


The oak trees on Visingso island in Sweden were cultivated to be particularly straight to make them better to use for shipbuilding. Take a closer look at Visingso forest in Sweden on Google Street View here.

Why an RAO is the dynamic fingerprint of a hull

The Great Blue Hole in Belize looks mysterious from above. It stands out as a perfect dark blue circle – almost black – amid a shallow water atoll. It’s such a dark blue because it is a marine sinkhole. In other words, it’s a large cavern that expands over 100m below the surface. Yet, though it looks mysterious, there’s a lot we know about how it formed.

Thousands of years ago, during an ice age and shallow sea levels, a cavern formed. As it aged, this cavern grew in size and formed many giant stalagmites and stalactites. But eventually, the ice age waned, and sea levels rose. Finally, the weight of seawater collapsed the cavern roof and submerged it. How can we tell all this happened?

The key is the stalagmites and stalactites: they can not form underwater. They tell us the historical characteristics of the cave that became a marine sinkhole and act as a historical fingerprint.

Fingerprints reveal a lot of information. They can even capture a unique identity. When it comes to floating systems, a Response Amplitude Operator (RAO) acts just like a fingerprint. But in this case, the fingerprint gives a hint about how these floating systems respond to ocean waves. All the details of a hull go into making this unique dynamic fingerprint. In this article, we’re going to talk about an RAO and what it tells us about ships and floating structures.

The Great Blue Hole of the coast of Belize looks mysterious, but we know a lot about its history from its geological fingerprints.

What is an RAO?

The RAO shows how much a floating hull responds to ocean waves of different periods. A motion RAO shows how much the hull moves in each degree of freedom. For example, a heave motion RAO will show how much a hull will move up and down across a wide range of ocean wave periods. There will be a different RAO curve for each degree of freedom of the hull – the linear motions surge, sway, heave, and the orientation motions roll, pitch, and yaw.

An RAO gives a hint about motions at sea

The RAO can show you in a single view just how sensitive the hull will be to different ocean wave periods. Depending on the hull type, a few degrees of freedom are often susceptible to a dangerous resonance condition. A resonance condition is when the hull motions or accelerations may get very large. Either of those conditions can lead to injury, damaged equipment, or damage to the vessel itself.

An RAO allows comparison between two different vessels. RAOs can be helpful to understand what might be a more suitable ship for a particular operation. But it can also be beneficial feedback in the design process, where a designer can see how subtle changes to the hull form or load out will affect the overall ship response.

How is an RAO calculated?

A common way to produce RAOs is with a seakeeping analysis based on potential flow theory, such as ShipMo3D. These tools take a wide range of input on the hull shape, hull appendages, system mass and inertia, and then calculate the RAO.

Seakeeping software typically assembles the RAO from calculated steady-state sinusoidal ship movement in sinusoidal ocean waves. The magnitude of the RAO is then the steady-state ship motion amplitude in individual sinusoidal ocean waves. Ultimately, the RAO illustrates the variation in ship motion amplitude across a range of ocean periods.

Since the goal is to show the variation independent of wave height, the RAO may be nondimensionalized by individual sinusoidal wave heights for linear motions and wave slope for rotational movements.

While you get a lot of information from an RAO, it isn’t necessarily representative of motion in an actual sea state.

Ship motion in a sea requires more than the RAO

An actual wave state in the ocean is rarely just a single sinusoidal wave. Typically, there is a combination of many different ocean waves, each with a slightly different direction and period. One way to compute the expected ship motion response in a realistic sea state is with the RAO. But to do this, you need the RAO in combination with the ocean wave state spectrum.

The mathematical combination of the sea state and RAO produces the ship response spectrum in that sea. The ship motion spectrum then tells you precisely the characteristics of the ship’s motion in that sea state.

So the RAO is not in itself the absolute ship motion in a specific sea state. But it is very much a unique dynamic fingerprint. So this fingerprint is then what you can use to determine how the ship will move in a wide range of ocean wave states.

US Navy Ship in a heavy sea state. An RAO tells us a lot about the characteristics of a ship hull. But you need both the RAO and the sea state spectrum to predict ship motion at sea.

Are there other ways to compute ship motion response in the ocean?

Absolutely: physical scale model tests predict ship motion response. Commercial Computational Fluid Dynamics software tools resolve fluid physics much more accurately than potential flow methods. But there are advantages and disadvantages to each approach. Calculating an RAO and ship motion response with a potential flow tool like ShipMo3D is typically very fast – on the order of minutes – and generally cost-effective.

On the other hand, physical tank tests may reach tens or even hundreds of thousands of dollars depending on the testing required. Commercial Computational Fluid Dynamics software tools are sophisticated and powerful but incur high computational costs – and that means more time to compute ship motions or higher prices in using a more powerful computational facility to get answers faster.

Example time

In a previous article on seakeeping, we used a Generic Frigate to showcase ship motions in a particular sea state. Part of this process includes calculating the Generic Frigate motion RAO. The RAO for this Generic Frigate configuration at 10kts forward speed in a beam condition is below. The roll motion RAO, the middle plot on the right side, shows a peak around 0.6 rad/s or 10 seconds. The roll RAO peak reaches almost 3 here, which hints that the ship is pretty sensitive to waves around a period of 10 seconds in a beam loading condition.

Generic Frigate motion RAO summary at 10kts in beam condition. Note the roll motion RAO shows a peak around 0.6 rad/s or 10 seconds. This shows the ship is fairly sensitive to roll from ocean wave periods around 10 seconds.

Remember, these values indicate the ship hull response to a single sinusoidal wave. A ship motion time-series requires a combination of the RAO and a specific sea state spectrum. With a particular sea state spectrum, you can compute a ship motion spectrum and time series to predict specific motions and accelerations. A sample time series created from these RAOs in an irregular sea state is below.

A typical sample time series of the Generic Frigate motion in a beam sea condition with short crested, irregular seas.


The RAO shows how a particular hull will respond to a wide range of ocean wave periods. It’s a helpful calculation that helps with a comparison of different ships or how design or configuration changes affect a ship’s response. Most often, it’s a standard computation from commercial seakeeping analysis tools, like ShipMo3D. Calculating the ship motion response in a specific sea state needs the RAO combined with the sea state spectrum, producing the overall ship response spectrum. In this way, the RAO represents a dynamic fingerprint of a specific ship.

A marine sinkhole may look mysterious, but we have many clues about how they formed through their detailed rock formations. Similarly, RAOs provide valuable clues about predicting ship motion in any sea state – so you don’t leave safety at sea as a mystery.

Next step

ShipMo3D is an example of a seakeeping tool that you can use to calculate motion RAOs and better understand all ship motions in various sea conditions. Read more and apply for a free demo of ShipMo3D here.


Read more about the Great Blue Hole near Belize here.