It was 333 BC and a puzzle tormented Alexander the Great. Still early in his military conquests, things were going well and his army had recently taken the city of Gordium in what is now modern-day Turkey. The city was host to an ancient wagon tied with the legendary Gordian knot, so intricate and elaborate in its form that a prophecy declared anyone who could untie it would rule over all Asia.
Alexander the Great cuts the Gordian Knot, by Jean-Simon Berthélemy (1743–1812)
The story cuts off there
Alexander realized the prophecy didn’t specify how the knot was to be untied, and solved the problem with a swift sword stroke. He recognized the problem could be addressed differently.
In this article, a different way of solving a static mooring line profile is presented and the effects on calculation speed, mooring profile design, and limitations for dynamic analysis are discussed.
How you calculate affects the speed
A starting point for mooring design is to calculate the mooring deflection due to forces from a current profile and mooring weight and buoyancy. However, how do you calculate this? One way to do this in an analysis software program like ProteusDS is to start with a straight line and let the forces move the mooring model so it relaxes into a steady-state profile over time. But this is almost like untying the Gordian knot: the drag forces can be weak, the mooring can be very long, and it can take hours of calculations showing in exquisite detail the slow deflection of the mooring over time until it reaches a steady profile. Is there another way?
Shoot for the moon
Another way of thinking calculates the mooring deflection directly from the balance of drag and internal tension on the mooring. Developed decades ago, this algorithm is known as the shooting method. Much like Alexander’s approach to solving the Gordian knot, it solves directly for the mooring shape needed to balance drag and internal tension – and out pops the final profile after a few calculations. This calculation speed can be critical in cases when a mooring design needs to be checked in a short time frame. In ProteusDS, the QuasiStaticCable model uses the shooting algorithm and computes the mooring profile in steady currents. But why is the shape of the mooring so important in design?
How the mooring profile affects oceanographic equipment
The resulting mooring profile can be a complex curve in the water, and it changes depending on the materials, lengths, distribution of floats and weights, drag forces, and the current profile. There are three ways the profile affects the design: knockdown, tilt, and tension.
The profile is the shape: the shape is the design
Oceanographic moorings have sensors at various locations along the span and the intent is often to make measurements at a consistent water depth. Much like a flower that bends over in a breeze, too much mooring deflection can significantly change the actual depth of each instrument, known as knockdown. In addition to this, some sensors stop working properly if there is too much tilt angle, leaving either gaps or unreliable data. Finally, for in-line mooring sensors, the line tension is essential to ensure there is no damage. These parameters are easy to check with the built-in reporting tools in ProteusDS.
The shooting method quickly calculates the static profile of a mooring when knockdown, tilt, and tension does not change in time. But what happens when things are dynamic?
The image shows four buoys of various styles (spherical, elliptical, and streamlined) being loaded by current. As the current ramps up to 3.6 knots, the knockdown and pitch of the buoys increase.
When there’s no way around untying the knot
Alexander cut straight to the chase and solved his problem when he cut the knot in two. By ignoring acceleration and inertia, the shooting method cuts straight to the chase and solves the steady mooring profile. However, what about when acceleration or inertia is important? This might happen if the effects of ocean waves are significant, if the flow is turbulent, or if there is flow induced vibration caused by the mooring components.
In these cases, there’s no way around untying the knot: the time history of the mooring profile must be calculated to show how the knockdown, tilt, and tensions change in time. Single leg moorings can be very complex systems, and the moment in time of the maximum knockdown, or tilt, can be very difficult or impossible to know in advance. Nevertheless, this knot can be unravelled eventually with dynamic analysis.
Example: 4500m mooring
But what if I have experience deploying equipment without these techniques?
Oceanographic data is very expensive: sensors themselves cost thousands of dollars and even more costly is the ship time to deploy the equipment for months or even years on station in very remote locations.
It’s all about the consistent design process
Using a systematic approach with validated algorithms minimizes the risk of inconsistent quality in design loss of data, or worse yet, requiring even more expense to repair or deploy replacement moorings.
In summary, a different way of calculating the mooring profile can save a lot of computational time. This method provides rapid design feedback when checking a mooring profile in a steady current. Checking for knockdown, tilt, and line tension allows a quick initial check for many mooring designs. When waves or changing currents are present, there may not be any way around using dynamic analysis. But with the right tools, like Alexander’s sword, some problems can be cut through rather than exhaustively unravelled.
Next step
Oceanographic mooring analysts can quickly assess their designs using software like ProteusDS. Check out this video tutorial that shows how to instantly assess oceanographic moorings in ProteusDS.