CATENARY CALCULATION:
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A catenary mooring line will have a part which is laying on the seafloor and a part of the mooring line suspended in the seawater. The part that is suspended in the seawater will take on a catenary shape. Based on the ship's Allowable displacement and it's weight; the forces one the mooring line varies. This, in turn determines the length of the mooring line required and also the shape of the suspended catenary.
Firstly, the length of the suspended mooring line S in [m] is calculated based on the water depth d, the weight of the mooring line W, and the force applied to the mooring line at the fairlead, F:
In the figure,above a catenary moorings line is shown. The angle between the moorings line at the fairlead and the horizontal shown as angle j. The applied force to the mooring line at the fair lead is given as F.
The water depth plus the distance between sealevel and the fairlead in [m] is d in this equation. W is the unit weight of the mooring line in water in [t/m].
The horizontal distance X in [m] between the fairlead and the touchdown point of the mooring line on the seabed can be calculated with:
The water depth plus the distance between sealevel and the fairlead in [m] is d in this equation. W is the unit weight of the mooring line in water in [t/m].
The horizontal distance X in [m] between the fairlead and the touchdown point of the mooring line on the seabed can be calculated with:
As the Force applied to the mooring line at the fair lead increases, the horizontal distance between fairlead and the touchdown increases. This is logical because more length of chain is required to withstand the load applied at the fairlead.
It is useful to know the weight of the suspended chain V [tonnes] because this weight is crucial in determining the restoring forces of the mooring lines to the force at the fairlead. This load can be obtained the following formula:
Where S is the length of the suspended mooring line as calculated above.
Now that we know the weight of the mooring line, it is now important that we determine the shape of the mooring line so that we can calculate how much of the motion of the vessel will the mooring line accommodate safely while holding the vessel in place.
Now that we know the weight of the mooring line, it is now important that we determine the shape of the mooring line so that we can calculate how much of the motion of the vessel will the mooring line accommodate safely while holding the vessel in place.
The shape of a catenary mooring line is given by the function:
Where the shape of the catenary line is uniquely determined by parameter a given by:
upper angle of incidence of chain with horizontal in degrees фs and lower angle of incidence of chain with horizontal in degrees ф1 are the angles which help maintain the catenary shape of the mooring line and they can be calculated from the following formulas;
Now that we know the shape parameters, length and the weight of the mooring line, the next step to be carried out is to fix the mooring line to the sea bed. This is usually done with the help of an anchor. thre are many types of anchors, but since we are permanently mooring the vessel at a particular location, we choose a suction pile anchor. The suction pile anchor fixes the mooring line to the sea bed with the help of suction. For this anchor to remain fixed on the sea bed at all times, it should overcome a certain load exerted on it directly by the mooring line(indirectly by the vessel). This load is an axial load and it can be determined by the following formula;
This axial load is needed for calculating the bearing capacity of the suction pile(anchor), which is shown in the anchor calculations on the next tab.
Also, it is observed that when the force applied on the fairlead is comparatively small at a certain given depth, the calculator shows errors. This is because the weight of the mooring line will exert an resisting force much higher than the force applied at the fairlead. This leads to unwanted forces on the vessel due to the mooring line.
Thus, the above calculator provides a detailed design of the catenary of the mooring line.
Also, it is observed that when the force applied on the fairlead is comparatively small at a certain given depth, the calculator shows errors. This is because the weight of the mooring line will exert an resisting force much higher than the force applied at the fairlead. This leads to unwanted forces on the vessel due to the mooring line.
Thus, the above calculator provides a detailed design of the catenary of the mooring line.