• Optimoor papers


  • Computer Mooring Load Analysis to Improve Port Operations and Safety

    John F. Flory, Stephen P. Banfield, Dr. Alan Ractliffe


    Mooring analysis of a vessel alongside a pier usually involves a number of non-linear mooring lines, extending at different vectors in both the horizontal and vertical planes, with elastic fenders, acted upon by wind, current, and sometimes other forces, which may vary in time and direction. Computer programs are now available which can quickly and accurately analyze such complex mooring arrangements.

    In this paper, a number of example cases, calculated by a mooring analysis computer program, are used to demonstrate that the characteristics, qualities, and arrangements of the lines can greatly affect the mooring line tensions experienced at a pier.


    A vessel's mooring arrangement is seldom a concern, until a gust of wind, a passing ship, or inattention to changes in tide or freeboard causes mooring line failure and sudden vessel movement. Such an accident can result in costly damage to cargo handling equipment or other nearby vessels and structures, oil or chemical pollution, and personal injuries and fatalities.

    Proper analysis of the adequacy of a vessel's mooring gear, a pier's mooring points, and the mooring arrangement can significantly reduce the likelihood of such mooring accidents. Some ports which handle hazardous materials, such as LPG, require such an analysis for each vessel mooring. Other ports simply prescribe the use of a minimum number of mooring lines, without concern for the character, quality or arrangement of those lines.

    In this paper, a typical large-tanker mooring is analyzed with variations of the number, type, and arrangement of mooring lines. Cases are compared in which winch-mounted wire mooring lines are used together auxiliary synthetic fibre lines. Cases involving several alternative synthetic fibre ropes are examined. Finally, several variations of mooring bollard positions are evaluated.

    Mooring Analysis Simplified

    Figure 1

    Simplified mooring arrangement

    Figure 1 shows a simplified mooring arrangement, comprised of bow and stern breast lines, spring lines, and fenders. With only four mooring lines, the analysis involves six unknowns the mooring line forces and the fender reactions. Only three force and moment summation equations can be written. The vector and elasticity of each mooring line must also be considered. Thus a complete, proper solution of even this simplified mooring arrangement is not an easy matter.

    Real vessel mooring arrangements usually have many mooring lines. If fender deflection is considered, the solution becomes more complicated. The solution becomes very complex if non-linear mooring line elasticity is included. Thus the typical mooring arrangement is too complex to be properly analyzed by hand.

    Computer programs are now available which can perform a complete mooring analysis of even a complex system in a few minutes on a personal computer. One such mooring analysis computer program is the Optimoor program, developed by Tension Technology International.

    The Optimoor Mooring Analysis Program

    Within Optimoor, the vessel is defined by its dimensions as well as by data on fairlead positions and mooring line size and material. Based on the mooring line information, Optimoor determines the appropriate break strength and non-linear force-extension characteristics. The berth is defined by data on mooring point positions and fender characteristics. These data are entered in spread-sheet-like screens and stored in files, which are then used in setting up analyses cases.

    The Optimoor user defines a mooring analysis case by calling up the vessel and the berth files and describing which vessel lines are connected to which mooring points on the pier. Wind and current velocities and directions are then entered. Optimoor contains appropriate wind and current force and moment coefficients for typical vessels, and additional data files can be prepared as necessary. Tide table data can be entered, and then used to determine tidal currents as well as tide elevation with time.

    As data is entered or updated, the program calculates the resulting mooring line loads due to the wind and current conditions and state of tide. Wind and current velocities can be increased to check limiting conditions. The wind vector can be swept through 360° to determine the most severe direction. Mooring line pretensions can also be varied.

    A mooring analysis can be set up based on the vessel's arrival and departure times and corresponding drafts and trims. Tide elevation and current information can be input or called from an existing data file. Optimoor can then perform a mooring analysis over time, predicting the effects of changes of draft, trim, tide, and tidal current on mooring line tensions. This technique can be used to determine when mooring lines may need to be tended and also to plan the best way to tend the lines in order to minimize the need for further mooring line tending.

    Example Mooring Arrangement Analyses

    Figure 2

    The mooring arrangement figure 2

    The following examples involve a 250,000 dwt tanker moored alongside a pier. The vessel length is 330 m (1080 ft) between perpendiculars. Its beam is 52m (170 ft), and its molded depth is 24 m (79 ft). In the example cases, the vessel has a draft of 6 m (20 ft) and a trim of 5 m (16.4 ft) by the stern. This particular tanker is used because it was used in several mooring analyses examples in the Oil Companies International Marine Forum Guidelines and Recommendations for the Safe Mooring of Large Ships at Piers and Sea Islands.(1) The mooring forces calculated by Optimoor are compared with those OCIMF examples in a previous paper.(2)

    The mooring arrangement which is used in these analyses is shown in Figure 2. The bollards, other than those used for spring lines, are positioned 38 m (125 ft) back from the fender face. Later, the case of 53 m (175 ft) bollard setback is examined. The bollards for the bow and stern lines are positioned substantially ahead and abeam of the moored vessel. Later, a case in which these bollards positioned essentially in line with the bow and stern is examined.

    In these examples, the forcing environment is a 60 kt wind pushing the moored tanker off the pier combined with a 3 kt current from ahead. This corresponds with the criteria given in the OCIMF Guidelines. Note that these guidelines apply to mooring gear onboard the vessel and do not necessarily apply to mooring analysis of a particular pier. The pier should normally be designed and outfitted in accordance with the most severe environment which is expected at the site.

    All-Wire Cases

    Case 1, 14 Wire Mooring Lines Alone

    In Case 1 the vessel is moored by 14 wires, arranged as 2 head lines, 3 forward breast lines, 2 forward springs, 2 aft springs, 3 aft breast lines, and 2 stern lines. The wires are 45 mm (1-¾ in.) diameter steel with fibre core, with a rated break strength of 52.9 GN (235 kip). Each line is pretensioned to 2.2 GN (10 kip).

    In the case tables at the end of this paper, connection designates the number of the vessel line and the letter of the shore mooring point to which it is attached. Thus for example, 5-C indicates that line 5 is attached to mooring point C. The spring lines are not shown in the tables, because in these examples they were only lightly tensioned.

    Line 8-G is tensioned to 58% of the rated breaking strength of the wires. This exceeds the 55% maximum mooring line tension criteria permitted by OCIMF. Thus this is probably an unacceptable situation.

    The common solution is to require the use of auxiliary lines. Here the term auxiliary refers to lines other than winch-mounted mooring lines which are deployed on bitts to provide additional mooring capacity.

    Case 2, 14 Wire Mooring Lines plus 4 Wire Auxiliary Lines

    In Case 2, four additional wire ropes are deployed as auxiliary lines. These are mounted on bitts near the edge of the deck and run essentially in parallel with the breast lines. Auxiliary lines 11-D and 12-D are forward breast lines, and auxiliary lines 19-G and 20-G are aft breast lines.

    Because the wire auxiliary lines are relatively short, as compared to the winch-mounted wires, they are more heavily loaded. In this arrangement the most highly loaded line, 11-D, is tensioned to only 45% of its breaking strength.

    Wire and Synthetic Mixed-Line Cases

    Figure 3 shows typical load-extension curves for wire rope and several types of synthetic fibre rope. These curves are for broken-in ropes which have been cycled a few times to a modest load. Steel wire rope extends about 1% when loaded to 50% of its new breaking strength. Ropes made of high-modulus fibres extend about twice as much as steel wire rope. Broken-in polypropylene and polyester ropes typically extend about 6% at 50% of new breaking strength. At 50% strength, nylon rope typically extends between 12% to 15%, depending on other variables.

    Case 3, 14 Wire Mooring Lines with 4 Polypropylene Auxiliary Lines

    Polypropylene rope is frequently used as auxiliary mooring lines. Polypropylene rope is light-weight, is easy to handle, and it floats, but it is relatively low in strength.

    In Case 3, the auxiliary lines are 75 mm (3 in.} diameter polypropylene rope, with a rated break strength of 24 GN (107 kip). Four auxiliary polypropylene lines are used in the same arrangement as was used with the auxiliary wires in Case 2. These are lines 11-D, 12-D, 19-G and 20-G.

    In Case 1, wires without auxiliary lines, the most highly tensioned line was 8-H. Through the use of these polypropylene auxiliary lines, the load in that line was reduced by 4.2 GN (19 kip), a relative reduction of 14%. Similar tension reductions are achieved in several other breast lines.

    Note that the polypropylene ropes are only lightly loaded. These polypropylene auxiliary lines are generally tensioned to only about 25% of the tension in the adjacent wire breast lines. This is because the polypropylene ropes are much more elastic than the wires. Thus they are not very effective in reducing mooring tensions.

    Use of High-Modulus Fibre Ropes

    High performance fibre ropes are now sometimes used for mooring lines. The fibre materials used in these ropes are much stronger and also stiffer than the conventional rope-making fibres nylon, polyester, and polypropylene. Examples of such materials are aramid (duPont "Kevlar" and Akzo Nobel "Twaron") and high-modulus polyethylene (HMPE) (Allied "Spectra" and DSM "Dyneema"). Because they are much stiffer, the ropes made of this new class of fibres are called high-modulus fibre ropes. (3)

    These high-modulus fibre ropes are almost as strong as wire ropes of the same size, and they are also almost as stiff. At 50% of new break strength, wire rope extends about 1%, and broken-in high-modulus fibre rope extends about 2%.

    Case 4, 14 Wire Mooring Lines with 4 High-Modulus Auxiliary Lines

    Case 4 illustrates the use of high-modulus fibre rope in place of polypropylene in the above example. The high-modulus fibre auxiliary lines are used in the same positions as the auxiliary lines in the preceding examples. And as before, they are pretensioned to 2.2 GN (10 kip).

    The resulting maximum line tensions are much less than with polypropylene auxiliary lines. The tension in line 8-H, which was overloaded in Case 1, is reduced by 10.4 GN (46 kip), a 35% relative reduction in tension.

    Note that tensions are relatively equally distributed among the various lines, including the high-modulus fibre auxiliary lines. The maximum line tensions in this case are lower than those of Case 2 where wire auxiliary lines were used. The high-modulus lines, which are about twice as elastic as the wire auxiliary lines, are not as greatly affected by the relatively short leads from the bitts to the shore mooring points.

    Use of Synthetic Fibre Mooring Lines

    Case 5, All High-Modulus Fibre Mooring Lines and Auxiliary Lines

    Some vessels now use high-modulus fibre rope instead of wire rope as winch-mounted mooring lines. The principal advantage is the lighter weight, which requires a smaller deck crew to handle the lines and also reduces the chances of injuries. Other advantages are; the high-modulus fibre ropes do not corrode, do not require greasing, and generally last longer than wire ropes in typical service. But the high-modulus fibre ropes cost more than conventional fibre ropes and much more than wire ropes of the same strength.

    In Case 5, 14 high modulus fibre ropes are mounted on winches in place of the wires, and 4 additional high modulus fibre ropes are deployed as auxiliary mooring lines. The high modulus fibre ropes have a rated breaking strength of 56.7 GN (252 kip), slightly greater than the wires which they replace. This strength could represent either aramid or HMPE rope of approximately 50 mm (2 in.) diameter.

    Compared to Case 2, in which wire rope was used in the same arrangement, the line tensions are very similar. Compared to Case 4, in which wire was used as mooring lines and high-modulus fibre rope was used only as auxiliary lines, the maximum tensions are about the same, but now the relatively short auxiliary lines are more highly tensioned and the tensions in the winch-mounted mooring high-modulus lines are less.

    Case 6, 14 High-Modulus Fibre Mooring Lines Alone

    What would happen if only the 14 winch-mounted high-modulus fibre ropes were used, without the use of auxiliary lines? With only 14 high-modulus fibre mooring lines, the maximum tensions are within the OCIMF 55% limitation criteria.

    This is in contrast to Case 1, with wire mooring lines, in which line 12-H was tensioned to 58% of its rated breaking strength. This is because the tensions were more equally shared among the more elastic high-modulus fibre lines.

    Case 7, 18 Nylon Mooring Lines

    Nylon rope is much more elastic than wire rope and high-modulus fibre rope. In some mooring and towing applications, this is a desirable property. But it is generally undesirable where the motions of the moored vessel must be restricted. Case 7 shows what happens when nylon is used for all of the mooring and auxiliary lines.

    The line loads in this all-nylon 18 line case are similar to those for the all-high-modulus 18 line Case 5 above. However, the vessel motions are much greater. The moored vessel shifts forward 3.4 m (11 ft) and moves out almost 6.1 m (20 ft) from the berth. These vessel motions would be unacceptable for a tanker connected by hoses or loading arms to a terminal and would probably be unacceptable in other applications.

    Case 8, 18 Polypropylene Mooring Lines

    Some vessels are equipped only with polypropylene mooring lines. Polypropylene fibre ropes are relatively inexpensive. However, they are also weak compared with other conventional fibre (nylon and polyester) ropes of the same size and with wire rope and high-modulus fibre rope of the sizes typically used as vessel mooring lines.

    The following case illustrates the use of 18 polypropylene ropes in the example situation discussed here. The vessel movement is much greater than with wire or with high-modulus fibre rope, although it is not as great as with nylon.

    The mooring line tensions are similar to those of the above all-high-modulus fibre and nylon rope cases. But because the polypropylene rope is not as strong, several auxiliary lines are tensioned to over 90% of the rated break strength and others are tensioned to over 80%. Several breast lines are tensioned to over 70% of the rated break strength. Tensions in a number of other mooring lines exceed the 55% criteria. Clearly, this is an unacceptable situation, even though a total of 18 mooring lines are used.

    Changes in Mooring Line Arrangement

    figure 3

    Elongation, Percent broken-in lengths

    Thus far only the effects of changing the types and numbers of mooring lines have been considered. What if the mooring line arrangement is changed?

    Case 9, 14 Wire Mooring Lines, Bow and Stern Lines to Alternative Mooring Points

    As shown in Figure 3, two additional mooring points are available on the pier. These bollards B and I are positioned such that bow and stern lines respectively will be essentially perpendicular to the vessel. Case 9 shows the 14 wire mooring lines of Case 1with the bow and stern lines run to these alternative mooring points.

    In this case, none of the mooring lines exceed the OCIMF 55% line tension limitation criteria. The bow lines and also the stern lines now act essentially as breast lines, more effectively sharing the force of the broadside wind, and thus relieving tensions from the other breast lines. The spring lines still serve to resist the longitudinal force due to the 3 kt current.

    Case 10, 14 Wire Mooring Lines, Change in Bollard Set-Back Distance

    In all of the above examples, the bollards (except spring-line bollards) were positioned at 38.1 m (125 ft) back from the fender face. What happens if this bollard set-back distance is altered? In Case 10 these bollards are moved back to positions which are 53.4 m (175 ft) from the fender face. The 14 wire mooring lines are placed on the same bollards as in Case 1.

    In this case, none of the mooring lines exceeds the 55% OCIMF criteria. In all of the above examples, the maximum tensions would be less if the bollards were moved back. Conversely, if the mooring bollards were moved closer to the pier face, the maximum tensions would be greater. This is because the longer mooring lines provide greater elasticity which better shares mooring loads.


    Many ports establish criteria for a minimum number of mooring lines, without regard to the character, quality, or arrangement of the mooring lines which might be employed by a particular vessel. This practice does not necessarily guarantee an adequate mooring.

    Case 1 illustrated a situation in which 14 wire mooring lines were not adequate, meaning that the OCIMF 55% maximum line tension criteria was exceeded. In Case 2, an additional 4 wire auxiliary lines made the situation acceptable.

    Case 9 and also Case 10 demonstrated how repositioning the original 14 wire lines achieved an acceptable mooring arrangement. Case 6 demonstrated how 14 high-modulus fibre mooring lines in the original arrangement provided an acceptable mooring situation. Thus 14 lines are sufficient in some circumstances.

    Case 3 demonstrated how the use of 4 polypropylene auxiliary lines turned Case 1 into an acceptable situation. The use of 4 high-modulus fibre auxiliary lines in Case 5 created an even better situation.

    In Case 7, 18 nylon lines would be judged acceptable by the maximum tension criteria. However, the greater elasticity of these nylon lines permit excessive vessel movement. In Case 8, a total of 18 polypropylene lines was not sufficient, because the break strength of at least one of these lines was exceeded. Thus specifying a minimum of 18 mooring lines does not always ensure an adequate mooring.

    These example cases demonstrate that each particular mooring situation should be individually analyzed to determine its acceptability, instead of simply specifying a general criteria without considering the character, quality, or arrangement of the mooring lines. In some cases, 14 lines alone was sufficient, and the additional auxiliary lines were not necessary. In other cases, even 18 lines was not sufficient.


    1. OCIMF, Guidelines and Recommendations for the Safe Mooring of Large Ships at Piers and Sea Islands, Witherby & Co., London, 1978.

    2. Flory, J.F. and A. Ractliffe, "Mooring Arrangement Management by Computer", 1994 Ship Operations, Management, and Economics Symposium, SNAME, Jersey City, NY, 1994.

    3. Flory, J.F., H.A. McKenna, and M.R. Parsey, "Fibre Ropes for Ocean Engineering in the 21st Century", pp 934-947, Proceedings of Civil Engineering In the Oceans V, ASCE, New York, Nov. 1992

      • Optimoor Mooring analysis software view
      • Mooring Consultancy Preliminary and detailed design of mooring systems view