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How forward speed codes add a missing ingredient to ship motion prediction

Most frogs spend their lives in and around water. Yet some thrive in hot and dry deserts, where there’s no water to be found. This is odd, because frogs typically start life hatching as fish-like tadpoles, swimming around looking for food. It takes time for them to grow, and slowly their limbs form, as they metamorphose into adults. But how can some species of amphibians thrive in a place like a desert where there isn’t any water?

The Desert Rain Frog found a solution to this. It short-circuited the typical lifecycle process. With no water available in a desert environment, they adjusted the way they develop. Unlike most other frogs, they skip the tadpole stage altogether. Out of their eggs, they pop out in final form, as tiny versions of adults, ready to go hunt for food. For most frogs, life revolves around some form of standing water. Their lifecycle demands it, as they hatch and transform over time through the aquatic environment. While the Desert Rain Frog makes it work in arid deserts, the majority of other frogs would falter without this missing ingredient.

Similarly, a missing ingredient can cause significant headaches in our work. These might be elements that can make or break a project. But understanding what’s missing and what that implies is crucial to getting answers and moving forward with confidence. This is precisely the case when using zero or forward speed ship motion prediction software. Using zero speed tools sometimes yields forward speed results. But doing so can short-circuit the analysis process, and might leave you high and dry without realistic answers. In this article, we’re going to talk about the missing ingredient that forward speed ship motion prediction codes bring to the analysis process.

What does a forward speed ship motion prediction code mean?

Many publicly available software tools evaluate the interaction of ocean waves with floating hulls. Among these software tools, there is a clear distinction between two groups. One group of tools resolves ocean wave interaction at zero speed, and the other resolves wave interaction at both zero and forward speed. The distinction is really about these forward speed effects. These forward speed effects arise from the effect of a mean forward velocity of the hull in water – in other words, considering the changes of hydrodynamics and motion from a ship moving through the ocean with waves. So what changes does this actually introduce? One change affects the frequency of loading.

Forward speed introduces the encounter frequency effect

One way to think of this is what the ship experiences, or encounters, as it moves over the waves. The encounter frequency means a shift in the hydrodynamic loading and motion based on the hull’s mean velocity relative to the waves. But it depends on the relative direction between the waves and the hull. For example, in a head wave condition, the faster the ship speed, the higher the encounter frequency is. You experience something similar when you drive your car (or bicycle!) over speed bumps – the faster you go, the faster the impact of the bump you feel. However, encounter frequency can also cause a decrease in frequency when a following sea is present. In this case, the ship is moving with waves, which decreases the rate of hydrodynamic loading and the resulting dynamic motion. The encounter frequency is a crucial aspect of forward speed hydrodynamics, but it’s not the only change. There’s another vital detail that can fundamentally change the hydrodynamics relating to the amplitudes of motion.

Forward speed introduces a new hydrodynamic interaction with ocean waves

When calculating the interaction between ocean waves and the hull, a forward speed ship motion prediction program introduces a new boundary condition between the ocean domain and the hull that zero speed codes don’t consider. This new boundary condition is the mean velocity of the hull in the water. And this is the missing ingredient that truly makes the difference in the resulting hydrodynamic physics calculated between the ocean surface and the moving hull.

Both zero and forward speed codes have a boundary condition that enforces no water flow through the hull as it calculates how waves radiate from a moving hull or how waves bend and diffract around the hull footprint. But only a forward speed code introduces a forward speed velocity boundary condition around the entire hull, in addition to this. This introduces new momentum effects on the flow domain around the hull and can make dramatic changes in the resulting forces on the hull as the forward speed increases.

Beware that some zero speed codes include an encounter frequency effect, but don’t include velocity boundary conditions

Ship motion prediction codes that apply zero-speed forces at a forward speed encounter frequency might give some insight into ship motion at very low speed conditions. But the hazard here is that without truly considering this missing ingredient of the velocity boundary condition, the wave forces and resulting ship motion might be significantly different. It’s not intuitive or easy to predict how these forces might change without running direct comparisons with and without forward speed. That said, the magnitude of speed is a general indicator of when this might be a problem or not.

The speed itself is an indicator of how significant these effects may be

The lower the speed, the more the hydrodynamics and resulting motion might be well approximated by a zero speed code. But speed itself may not be enough to consider, because what’s crucial is understanding how that relates to the size of the hull itself. Normally, the nondimensional Froude number is helpful to gauge when forward speed effects may be important. Yet nondimensional or otherwise, speed is still a qualitative indicator, because there can be surprising differences in loads and resulting motions even in moderate speeds among different hull forms.

It’s time for an example

Let’s clarify some of the differences by looking at a few specific cases. Three ship types were used to explore how specific forces compare when resolving them with zero and forward speed terms. The general idea is to spot-check the magnitudes of the diffraction forces in a few scenarios. This way, we can focus on comparing zero and forward speed forces to gauge the difference it makes.

For each ship type, a characteristic forward speed was selected that represents a reasonable operational condition. A diffraction force corresponding to a wave frequency that was close to each ship’s roll natural period was selected. This means it is likely to be a meaningful force that more likely influences ship motion. Finally, we focused on a bow quartering case as a realistically meaningful condition as well.

The Generic Frigate was evaluated at 20 kn (Fr 0.3), the Generic Yacht 50m at 12 kn (Fr 0.27), and the KRISO Container Ship (KCS) at 24 kn (Fr 0.25). The resulting diffraction forces were resolved for both Generic Frigate and Yachts at 7 seconds, and KCS at 21 seconds.

The net diffraction force on each ship was resolved at both zero and forward speed in these conditions. The results are summarized in the table below. Generally, forward speed forces are often less in magnitude than zero speed. However, in some circumstances, the forward speed forces were significantly higher. When the magnitudes of the forces are much higher at forward speed, the risk is that the resulting motions and local accelerations throughout the hull may be different and potentially much higher as well.

Notably, in the bow quartering condition, the forward speed sway loads tended to be notably higher than zero speed for all hulls, and significantly so for the Generic Frigate. Roll loads were also notably higher than zero speed forcing.

So what does this mean?

All else being equal, it gives a sense for these ships of whether the assumption of using zero speed derived forces in a forward speed condition is conservative or not. For example, surge and heave forces are consistently lower when determined with a forward speed code. However, this is not the case for sway and roll – the forces determined from a forward speed code are significantly higher. Since the most sensitive motions that affect people and equipment on board monohulls are in roll, it suggests using a forward speed code is crucial for more accurately resolving motion and accelerations.

Table 1: Ratio of forward speed load magnitude to zero speed for specific ship types in bow quartering (BQ) condition

	Surge	Sway	Heave	Roll	Pitch	Yaw
Generic Frigate (20 kn, 7 sec)	0.3	9.0	0.5	1.2	0.3	1.0
Generic Yacht 50m (12 kn, 7 sec)	0.8	1.4	0.4	1.8	0.1	0.5
KRISO Container Ship (24 kn, 21 sec)	0.5	1.1	0.8	1.2	0.7	0.6

But diffraction is only one force on the hull that affects motions. How does this compare with everything else going on?

Diffraction, sometimes referred to as scattering forces, is specific to the effect of how waves bend or deflect around the presence of the hull. Yet they are the essential excitation forces from ocean waves. The other primary wave excitation force is the incident wave force, also known as the Froude-Krylov force. This is the force from the pressure field around the hull from the undisturbed ocean wave field. Together, the incident and diffracted force produces the net wave excitation force on the hull. There’s no intuitive way to know what these forces are acting on a specific hull shape. But it’s enough to know that these are the primary excitation forces in a seakeeping analysis. In the case of the Generic Frigate, the forward speed diffraction loads can be up to three times higher in magnitude than the incident loads. In other words, the changes in excitation force from forward speed effects are likely to have a significant effect on accelerations.

It’s summary time

We covered a few nuances on forward speed hydrodynamics, and now it’s time to summarize. Among hydrodynamic tools that calculate wave interaction with floating hulls, there is often a distinction between two groups: zero and forward speed codes. Forward speed codes account for changes in hydrodynamics and the resulting motion, affecting both the frequency and amplitude of these effects. The encounter frequency is a shift in the rate of loading that depends on the relative direction of the hull velocity and wave direction. This may increase or decrease the frequency of loading. To account for changes in the amplitude of loading, forward speed codes introduce a new boundary condition when solving the wave interaction with the hull that accounts for the mean velocity. This introduces a momentum and forcing effect on the flow domain and can significantly change the resulting magnitude of forces acting on the hull and the resulting motion. A hazard to be aware of is when zero speed codes that include an accounting of encounter frequency but don’t include this velocity boundary condition – it can give inside in very low speed conditions, but the uncertainty can grow quickly as the speed increases. And trying to gauge how significant this uncertainty is for a ship motion project can leave you with a grumpy look, much like a desert rain frog!

Next step

The ProteusDS ShipMo3D toolset uses a forward speed approach and incorporates mean ship velocity in solving the interaction with the ocean domain. Read more about how it can be used to get insight in early stage design here.