In Part 1 of this article, we saw a step by step guide to calculate the Environmental forces on a vessel based on “Standard” environmental criteria defined in Section 3 of OCIMF Mooring Equipment Guidelines Fourth Edition (MEG-4) in order to determine the ship’s design MBL which in turn can be used to size the various components of the vessel’s mooring system, like bollards, fairleads and winches. Various parameters like loading conditions, tidal variations, WD/T ratio etc. were discussed and calculation of wind and current forces on the vessel based on coefficients was presented.

In Part 2 of the article we will look into how to

1. Select a generic mooring line layout
2. Calculate static Equilibrium of the vessel and stiffness of mooring line layout
3. Determine Ship design MBL

Mooring Pattern

The vessel mooring pattern is to be designed to effectively counter the environmental forces from any direction. This means that the lines should be able to cope horizontal as well as transverse loads. The mooring pattern should therefore have lines along longitudinal direction to prevent motion in forward and aft directions and also in the transverse direction to prevent motion away from the berth. The longitudinal lines are knows as spring lines and the transverse lines are known as breast lines. The pattern also depends on the provisions at the terminal and it should be chosen, as much as possible, to keep the spring lines parallel and breast lines perpendicular to the ship length.

Mooring Pattern (Source: OCIMF MEG-4)

MEG4 provides the below guidelines for a generic mooring line layout.

• Breast mooring lines should be at an angle less than 15^o to the perpendicular axis of the ship.
• Spring mooring lines should be at an angle less than 10^o to the side of the ship.
• Maximum vertical angles of 25 degrees should be assumed for the lightest ballasted condition.

Static Equilibrium

A vessel subject to environmental forces/moments will move in the forward or transverse directions or rotate about the vertical axis i.e. the vessel will have surge, sway or yaw respectively. The vessel motion will change the relative distance of the fairlead from the shore anchor point, changing the length of the mooring lines. The lines, generally speaking, behave like a spring and the force exerted is proportional to the change in length of the line. This characteristic of the lines can be found from the data sheet of the line from the manufacturer. The change in length of the lines increases the tensions in the lines and the combined load exerted by all the lines then balances the total environmental loading. This condition of the vessel where the environmental loading is balanced by the mooring lines is known as static equilibrium.

Ship design MBL calculation

A simple spring formulation can be applied to evaluate the translations/rotations of the vessel in static equilibrium under the effect of the calculated environmental loads. Once a mooring system for the vessel at the berth has been chosen, for given position of the vessel the change in length of each mooring line with respect to its initial (un-stretched) length can be calculated using a simple spring formulation F = k δL where F is the line tension, k is the stiffness of the line and δL is the change in line length. Tension in each line can be aggregated to get the net loading on the vessel.

Hence we can calculate the translation/rotation of the vessel that will result in unit force/moment on the vessel by the mooring lines. Let’s call this the inverse stiffness k’. If k’ is displacement produced by unit force on the vessel, the total displacement X produced by the net environmental loading F can be calculated as X = F k’. The new position for the ship can be used to re-calculate the net mooring loads on the vessel and compared to the environmental forces and the whole process can be repeated until static equilibrium is achieved. The total length of the mooring line from winch to bollard should be used in the calculations. Also the stiffness of the lines change with use and the calculations should use the stiffness of used lines instead of new lines. The above can be summarized in below steps,

1. Calculate total environmental forces/moments on the vessel in surge, sway and yaw directions. E.g. Fx is the net environmental force in the surge direction
2. Determine the inverse stiffness of the mooring system in terms of amount of surge/sway/yaw per unit force/moment. E.g. k’ m/N is the stiffness of the vessel in surge direction.
3. Calculate the total amount of surge/sway/yaw. E.g. Surge (m)= Fx * k’
4. Calculate the resultant mooring forces based on the new position. E.g. Rx is the net mooring force in the surge direction.
5. Compare the environmental forces and resultant mooring forces i.e. Fx = Rx?
6. Several iterations of steps 2-5 may be required until static equilibrium is achieved.

 Once static equilibrium is achieved, maximum mooring restraint force can be determined and used in the flowchart below, provided by MEG4, to calculate the ship design Minimum Breaking Load i.e. Ship design MBL. With the vessel in static equilibrium, the tensions in each mooring line can be determined. Since there are several components in the mooring pattern that support multiple mooring lines, the total loading on such component can be used to calculate the Ship design MBL as

The ship design MBL is the MBL of a new, dry mooring line for which a ships mooring system is designed and that meets the mooring restraint requirements as defined in MEG4, section 3. All other components of a ship’s mooring system are based on this ship design MBL, with defined tolerances.

It must be noted that static analysis may only be suitable for benign environment as we are assuming the lines as simple springs. In other cases dynamic analysis for the vessel motions and line tensions should be performed.

The steps above are also lined out in OCIF MEG-4, and shown in the figure below.

Ship’s Design MBL Calculation Steps (Source: OCIMF MEG-4)

In Part 3, we will further look into using this Ship design MBL for line selection and to determine D/d ratio (bend dia/rope dia) of mooring line and other parameters.

Do check out some products relevant to OCIMF MEG-4 below. The product for calculation of Ship’s Design MBL is in progress and shall be out soon!

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