Tag: hydrodynamics

Why it’s hard to distinguish between the effects of buoy and line drag on mooring knockdown

The southern border between the Canadian provinces of British Columbia and Alberta is, in places, very irregular. It might even seem to be random at first glance. Yet, there is some logical reasoning behind what is there. This border was measured and established over one hundred years ago – far before GPS or other advanced survey techniques were around to help out. So how was the border established?

It has to do with hydrology. In other words, at the highest peak, the direction of rainfall flow establishes the border. Where rainfall flows to the west, it’s British Columbia, and when it flows to the east, it’s Alberta. It’s this clear reasoning that helps to distinguish things.

But we’re not always so lucky to have something to help distinguish things. At first glance, you might be looking at a seemingly random result without any clue how you landed there. When it comes to oceanographic mooring deflection, there are two primary sources of drag: the buoy and the mooring. However, distinguishing between what is more critical to mooring deflection can be a real challenge.

The southern portion of the border between BC and Alberta highlighted in red is highly irregular, but it’s not random. The direction of the flow of rainfall is used to define the border and distinguish between provinces. Picture credit: Google Maps

The vertical deflection of a mooring is crucial to understand

This vertical deflection, also called knockdown, is an increase in depth of all the mooring components from steady drag loads. Because it’s an increase in depth, you need to watch any parts approaching their depth rating. Flotation that exceeds depth rating may fail and result in the mooring collapsing to the seabed. But knockdown may have detrimental effects on instrumentation data quality, too. But regardless, you can’t get a good idea of mooring knockdown without considering the drag loads on the system.

Why is drag significant in calculating knockdown?

Without any currents and the resulting drag load, subsurface moorings are perfectly vertical in the water column. Knockdown results when a subsurface mooring leans over from the effects of steady loads like current drag. All components on the mooring will have some drag. But often, there are two primary sources of drag that tend to dominate mooring deflection and knockdown. The first is the drag on the primary buoy.

The primary buoy is a significant source of drag for a few reasons

The primary buoy is at or near the top of the mooring and often does the bulk of the work holding everything up in the water column. This means it tends to be relatively large compared to other components. On top of this, generally, but not always, currents tend to be larger higher up in the water column. This means the primary buoy is likely in higher flows than the rest of the mooring. Drag is proportional to structure size and flow speed, which explains why the primary buoy is a significant source of total drag on the mooring. But it’s not the only source to consider. The other source of drag to consider is the mooring line itself.

The NOAA CO-OPS DWEAB mooring uses a low-profile Mooring Systems Inc ellipsoid buoy. Picture credit: Laura Fiorentino

At first glance, a mooring line may seem minuscule compared to the primary buoy

Often the diameter of the mooring wire is only a tiny fraction of the size of the primary buoy. But the problem is that the drag area of the mooring is a function of both the diameter and the mooring length. When you consider the entire length of the mooring, the drag area can often be comparable to the top float. There is often at least some kind of current profile through the water column, and this means there can be a substantial amount of drag that accumulates over the whole system.

However, there are more details to the drag on the mooring than the drag area. The actual current profile is vital to get right. The inclination angle the mooring makes in the flow is a factor, too. The effect of inclination on drag is not something you can estimate as quickly by hand as by comparing drag areas. But suffice to say, it’s important enough that you shouldn’t ignore it, and it may even surprise you how important it can be.

How are these effects calculated?

Mooring deflection is typically calculated using well-established numerical techniques that factor in all mooring components, dimensions, and forces in a specific current profile. Purpose-built software like ProteusDS Oceanographic uses geometry, weight and buoyancy of the parts, and typical drag parameters to resolve the mooring deflection. The mooring deflection is a calculation of all these effects together.

So what’s more important: mooring or buoy drag?

It’s not easy to know, in general, what is more important. But we can use a validated example to show mooring and buoy drag contributions. NOAA CO-OPS uses the Deep Water Elliptical ADCP Buoy (DWEAB) design as a standardized design to measure the top portion of the current profile in various locations in the coastal United States. In a recent deployment in a high current region of the Gulf Stream, mooring knockdown field measurements show 48m in 2m/s flow. Mooring knockdown calculated by ProteusDS Oceanographic reached 52m in a 2m/s flow, reaching reasonably close to the field data results. The primary buoy is a large 58″ Mooring Systems Inc Elliptical float, while the mooring is only a 1/4″ in diameter. At first glance, it may seem like the primary buoy would dominate the mooring deflection because of its larger drag area. So how can we get an idea of how much buoy and mooring drag contribute to the knockdown?

To conceptually illustrate this, we looked at two additional load cases. Mooring deflection was calculated with drag on the primary buoy turned off and then again with the drag on the mooring line turned off.

The resulting numerically calculated knockdown with only primary buoy drag was 25m, while the knockdown with only mooring drag was 20m. Note that the total expected knockdown is not calculated by adding these deflections together. This particular example aims to give a rough idea about their contributions to the mooring knockdown for this system. In this specific example, the mooring drag is almost as significant as the buoy drag.

The 200m long DWEAB mooring deflection to scale in 325m water depth in 2m/s current

What if you don’t know the current profile ahead of a deployment?

A knockdown calculation is only as good as the information you have. Of course, before deployment, you may not have much information about the water flow in a region. In this case, it helps to think more about the boundaries of the problem rather than finding the most accurate or probably current profile. The most conservative approach is a uniform current profile. But that may only be appropriate in areas of intense flow. A linear shear, or power profile, may be more realistic. Still, it’s up to the designer to use their judgement and experience for what works best.


Mooring knockdown is crucial to understand ahead of deployment. This deflection can compromise data quality and damage equipment if depth ratings are exceeded. Knockdown happens in subsurface moorings as it leans over from steady current drag. The primary buoy is often a sizable source of drag in the system. But it’s a mistake to ignore the drag from the mooring line because it can make a surprising contribution to deflection. Unlike considering rainfall to determine a border between two Canadian provinces, there isn’t a way to easily distinguish the contribution of deflection from the primary buoy and mooring. Instead, the best approach is to make sure your analysis considers drag from all components at some point in the design process.

Next step

Download and explore the ProteusDS Oceanographic DWEAB 325m mooring file in the collection of designs available for download here.


Thanks to Laura Fiorentino and Robert Heitsenrether from NOAA CO-OPS for providing data and pictures for the DWEAB mooring deployment used in the example.

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.

Why drag force is more than just resistance

It’s tough to beat Nature. You don’t have to look in a top secret lab to find one of the most miraculously slippery fluids on the planet. You can just look at your knee! Lining many of your joints is an egg-white coloured substance called Synovial Fluid. Among its many purposes is to keep your joints moving. But not just for a few days – for your entire life. And through all this time, it manages to control and minimize joint resistance.

Certainly, when resistance gets out of control, everything can come to a grinding halt. When it comes to hydrodynamics, when you think of resistance, drag forces may be the first thing that comes to mind. But there’s more to drag than just resistance, and this is what we’re going to cover in this article.

What is the drag force?

Forces appear when there are changes in momentum. Momentum means mass in motion, so for the specific case of fluids, this could mean water or air flowing in a current. The drag force arises when there is a change in momentum in fluids. More specifically, the drag force transfers momentum between a structure and a fluid it is immersed in. This might sound like an abstract idea, but you already have some experience with it every day.

You feel this effect when your hand is in water

A big part of this is the drag force. But if you are in a pool or bathtub, the water isn’t moving around – it’s your hand – and so the drag force in this case will feel like resistance to you. In this case, it’s your hand that has momentum: it is the mass in motion. The drag force is then transferring momentum from your hand into the water.

You can feel drag when moving your hand around in water

What does momentum look like in water?

Well, if it’s your bathtub, there will be swirling and churning water – turbulence, and probably some waves. All this moving water is mass in motion, too. But the drag force does work in reverse, too – it can transfer momentum from water into structures.

What happens when there are ocean waves or currents in the water?

Ocean waves and water currents are also examples of mass in motion, too. If a structure, like a mooring buoy or ship gets in the way of moving water, there’s going to be some drag forces. These forces will transfer momentum from the waves and currents into the structure. So in this way, drag force is really about the exchange and transfer of momentum.

Sometimes this means it creates resistance and slows down a structure. But it can create motion in floating structures, too. The key is that drag is proportional to the relative velocity between a structure and the fluid.

The drag force is one of the essential forces in hydrodynamics

It acts like a resisting effect on many structures. If you are trying to understand what will happen to an ocean robot driving around in the water, it will have a big impact on energy consumption as well as how it can maneuver.

But the drag force is also a key element in mooring designs. In oceanographic mooring designs, the aggregate drag on all the components and the mooring line causes the system to deflect in an ocean current. In reality, the water current loses some momentum from this drag force from the mooring – the wake from the float and mooring components reduces the ocean current flow speed by some small amount.

In an ocean current with speed U, the drag force from all mooring components causes deflection.

Drag is also a key element in the excitation forces when ocean waves are around. You need to know these excitation forces to properly design a system to perform the way you want in the ocean environment. But knowing drag forces is one thing. Knowing how big they are is really the million-dollar question.

How do we know what the actual drag force is?

The drag force is measured from an experiment. These experiments might be a physical test in a lab, or in more modern times, they might be virtual tests using fluid dynamics software. These experiments resolve what the drag forces are in certain specific conditions. There have been hundreds of thousands of tests completed in laboratories for many decades measuring the drag force on a vast array of shapes in different flow speeds and fluid mediums. But how do we take all this information on drag force and then use it in a specific application?

The key is the drag coefficient

Similar shapes produce similar and predictable drag forces. The concept of a drag coefficient works well and covers a wide range of fluid types and conditions. Ultimately, if you’re looking at something like a sphere, you can use a drag coefficient associated with a sphere and predict reasonably well what the drag forces will be for a good range of wind or water current speeds. These drag coefficients are often available in look up tables to help the design process.

But what about the drag on mooring lines?

A mooring line is indeed a much more complicated structure than a sphere. Depending on its orientation to the flow, the local drag can change drastically. The drag forces on mooring lines require a calculation that considers the local flow speed and tilt of the line of the whole system. Suffice to say, it’s not a back-of-the-envelope type calculation you can do like that of the drag on a sphere! But this is what we have programs like ProteusDS Oceanographic that help address these complexities.

It’s summary time

The drag force is an effect that arises when momentum transfers between a fluid and a structure. Yes, a structure will feel resistance when it’s moving in a fluid, but the reverse is true, too: a moving fluid, like ocean currents and waves, can also cause a structure to move around, too – and the drag force plays a big role in that. The drag force is a very important effect that affects a range of systems from vehicle dynamics to oceanographic mooring design.

Even super low friction fluids like those in your knee joints have some drag effects, too. While you don’t need to do much over your life to keep your knee joints going, you do need to be mindful of drag when designing structures in the ocean.

Next step

Figuring out a drag coefficient for a particular structure isn’t always obvious. While ProtesuDS Oceanographic includes drag coefficients for a variety of shapes, you can learn more about different ways to resolve drag coefficients here.