## Why you should be careful about fixating on buoy drag coefficient (and what else affects hydrodynamic performance)

We’re going to start off with a magic trick: you are about to make something disappear right before your eyes. Cover your left eye and focus your right eye on the letter R in the image below. Hold the screen away from your face about three times the distance between the characters R and L. As you slowly move toward and away, there will be a point when the character L will disappear from your peripheral vision. So why does this happen?

Everyone has a small blind spot. This is caused by the area on the retina that connects to the optic nerve: there’s a gap in your visual senses, and your brain automatically blends the image around this area to compensate. In other words, you have a blind spot when you are fixating on details.

While this is a literal blind spot, there’s no shortage of figurative blind spots that can creep up in your work, especially when you are fixating on details. When it comes to the world of mooring systems, designers sometimes overly fixate on the drag coefficient of specific components. This may be especially true when moorings are planned for locations with high-speed ocean currents. Yet obsessing over the drag coefficient can leave you vulnerable to missing other essential details on the hydrodynamic performance of the entire system. In this article, we will cover a few facets of why you need to be careful when considering buoy drag coefficient and hydrodynamic performance.

### There’s more to hydrodynamic performance than drag coefficient

The drag coefficient is helpful, but it can sometimes be misleading and doesn’t give a complete hydrodynamic picture of a system. A more complete picture considers the total absolute drag (rather than only the coefficient) and what happens to a buoy in dynamic flow conditions. We will use three different subsurface buoy shapes to explore some essential facets of hydrodynamic performance:

- drag coefficient vs drag area
- vortex shedding
- turbulence and buoy rotational inertia

First, we’re going to cover drag coefficient vs drag area.

### Drag coefficient can mislead when comparing different shapes of buoys

The drag coefficient is a handy dimensionless parameter that boils down all the details, including the effect of geometry, into a single number. What it’s then useful for is anticipating what the total drag could be for a completely different size of buoy. However, because the geometry is baked into the drag coefficient, you can only use it for buoys with geometric similarity.

### It’s a mistake to compare only the drag coefficient of differently shaped buoys

After all, the total drag force is proportional to the drag coefficient and a specific reference area. If you haven’t accounted for the differences in reference area, you may be misled into what has better hydrodynamic performance.

### The solution is to consider the drag area

When you factor the drag coefficient and reference area together, it’s called drag area. The buoy drag area may be very different between different buoy shapes. If you know the reference area, you can compute the drag area and make a more accurate comparison. The true total drag will then be only missing water velocity and density – but these are common to all the buoy shapes in the same conditions.

For example, the drag coefficient of some torpedo-shaped buoys with a tail ring is higher than a spherical buoy. But you don’t get a complete picture of total drag without accounting for the reference area. The reference area of a sphereical buoy is the frontal area, and for the torpedo-shaped buoy it’s the frontal area of the hull only (excluding the tail ring). The total drag, proportional to the drag area, is then much lower for a torpedo shaped-buoy. For a long torpedo-shaped buoy with the same net uplift as a spherical buoy, the drag area, and therefore total drag, is a factor of 2.5 smaller!

While drag is a crucial factor to consider in steady conditions, but often there are dynamic conditions that are worth considering, too. This brings us to the second point on buoy hydrodynamic performance about vortex shedding.

### It’s almost impossible to escape vortex shedding in a steady flow

Almost every structure sheds alternating swirls of water, called vortices, in a steady flow. It’s remarkable how predictable the effect is, including the frequency, which increases steadily with current speed. But the challenge this introduces is the dynamic imbalancing forces lateral to the main current flow from the alternating flow pattern of the vortices. When the conditions are right, the vortex shedding can cause severe shaking of the buoy and strumming of the mooring, referred to as Vortex Induced Vibration or VIV. In the worst case, this can cause accelerated wear of mooring components and premature mooring failure. While faster flow speeds mean higher frequency vortex shedding, the complex nature of VIV makes it hard to anticipate the exact detailed dynamic response. Usually, the focus of mooring design is on avoiding or disrupting vortex shedding altogether. So, how can you disrupt it? One key is to prevent vortex shedding in the first place.

### Streamlined shapes shed fewer and weaker vortices

The more streamlined a buoy shape is, the fewer and weaker the vortex shedding effect will be. For example, a spherical float would be the ideal shape to have the most potent vortex shedding effect in a steady flow. An ellipsoid float, on the other hand, has a decent amount of streamlining. Though ellipsoid floats won’t necessarily eliminate vortex shedding, it should be a significant improvement compared to a sphere. Similarly, a torpedo-shaped buoy can be significantly streamlined, further reducing the potency of vortex shedding to a minimum. While vortex shedding is one dynamic effect, it shows up in relatively steady flow conditions. In the highest speed conditions, turbulence can introduce a lot of chaotic hydrodynamic loads on buoy. This brings us to the last point on turbulence and buoy inertia.

### Turbulence is a measure of the chaotic nature of the flow

The more turbulence, the less the flow is an ideal smooth and unchanging speed in time. This also means there can be many rapidly changing hydrodynamic loads on the buoy. Because of the complex interaction between the high speed turbulent flow and the buoy itself, calculating detailed high frequency buoy motion in these dynamic conditions is no simple matter. But rather than trying to find a way to anticipate these detailed motions, you can get some insight into what characteristics of the buoy might affect the resulting motion. This is where considering the buoy rotational inertia comes into play.

### Buoy rotational inertia can act like a shock absorber in turbulent flow

Inertia is resistance to motion. The more there is, the less rapidly changing forces move things around. More specifically, the more buoy inertia there is, the less the chaos of turbulence affects buoy motion. Yet inertia doesn’t help at all in resisting the forces from the average flow speed, which creates a steady drag that deflects the buoy and mooring together. So what does inertia mean when considering common buoy shapes? It’s the particular form factor of the torpedo shaped buoy that has the greatest advantage.

For the same net uplift, a torpedo shaped buoy has the largest rotational inertia compared to sphere and ellipsoid buoys. This rotational inertia will help keep the buoy aligned to the flow in spite of the chaotic hydrodynamic disturbances from turbulence. The drag area of torpedo shaped buoys means that the effects of steady flow or average flow drag on the buoy are kept under control, too.

### But what are the downsides of using more complex than spherical buoys?

Hydrodynamic performance is not the be-all, end-all for design of mooring systems. There’s more to consider, like availability of components, preparation, and handling. While it may seem the torpedo shaped buoy has the most advantages, it’s far from the simplest to work with. Because they tend to be long and slender, they need careful consideration to ensure they are trimmed and float level in water after installing heavy instruments like ADCPs.

The rotational inertia of a torpedo shaped buoy can be a downside when handling, too. The inertia and length can makes them awkward to work with on the deck of a ship during deployment and recovery. But nevertheless, with careful planning they can be very effective.

### It’s summary time

We covered a few aspects of hydrodynamic performance and it’s time to summarize. While drag coefficient is useful, you may not get a complete understanding because the total drag is proportional to drag area, which factors in a reference area for each form factor. Dynamic performance is another issue altogether, and vortex shedding can cause significant problems with motions and damage to moorings. The more streamlined a float is, the weaker vortex shedding is, helping avoid this issue. Finally, turbulent flow introduces an element of chaotic hydrodynamic loading on the buoy. But larger buoy inertia can act like a shock absorber to smooth out the effects of these high speed flow conditions, and the torpedo shaped buoy may be an important option to consider in the most extreme conditions.

In short, be careful if you find yourself fixating on the drag coefficient of a buoy. It’s might leave you with a blind spot!

### Next step

The ProteusDS Official Parts Library has dozens of floats from DeepwaterBuoyancy, Mooring Systems Inc, and other commercial suppliers. Quickly explore different mooring configurations using commercially available parts in ProteusDS Oceanographic Designer for free as a Community User. Get started by downloading ProteusDS here:

proteusds.com/downloads