Given a steady-state or average towline tension, the curves provide an extreme tension (dynamic plus
average) that has only one chance in a thousand of being exceeded in 24 hours of towing. The allowable
tension for a given wire can therefore be much closer to the hawser's ultimate strength than can tension
computed relying on the traditional factors of safety described in Chapter 5. For a wire in good condition,
limiting the extreme tension to 67 percent of new breaking strength is reasonable. This is equivalent to a factor
of safety of 1.5. Each ship might draw a horizontal line on each of Figures L-2 through L-5 at 67 percent of the
catalogue strength of its towing hawser. This represents the limit of acceptable extreme towline tension for that
The 1.5 safety factor described above does not supersede factors of safety listed in Table 6-4. These latter
factors of safety, which describe limits on average or steady-state tension, still must be checked. Either
criterion may control. The more severe criterion must be considered the limit until significant quantitive
experience is gained with the dynamic theory.
L-4.2 INTERPOLATION WITHIN THE TABLES. The following sub-paragraphs will assist in applying different
conditions to the criteria used in developing the extreme tension predictions.
L-4.2.1 Ship Size. Generally, smaller ships will be affected more by a given sea state than larger ships. For
tugs different from those described (T-ATF 166, ARS 38, ARS 50, ATS 1) use the next-smaller ship listed. For
towing ships smaller than the 2,000-ton ARS 38, use the ARS 38 as the basis for evaluating dynamic tension
Similarly, for tows different from the examples used, use the next-smaller tow unless the actual tow's
displacement is within 25 percent of that of the next larger vessel.
L-4 2.2 Average Tension. Estimation of additional tow resistance due to waves, at normal tow speeds, is not
well-understood. Consequently, the total tow resistance predicted in accordance with Chapter 5 and Appendix
G is always suspect. Whenever there is a difference between computed versus observed towline tension, use
the observed towline tension. This assumes that there is confidence in tension instrumentation onboard the tug.
L-4.2.3 Tow Speed. Speed contributes to extreme tension for two reasons. First, the wave encounter
frequency, for head seas, increases with incremental speed, thereby raising slightly the added resistance due to
tensions. Secondly, the far more significant effect of increased speed is creation of higher average towline
tension. This increases dynamic factors by raising the base to which purely dynamic parameters are added, and
by providing a stiffer (i e., having less catenary) towline system. A stiffer system also increases dynamic effects
Fortunately, the method of data presentation dilutes an incorrect prediction of speed since entry into curves 0
through 99 is through average tension rather than speed. Examination of the curves and tables will show that
the effect of speed, at a given average tension, is not great. Thus, without resulting in major error, the table
values for 3 knots can be applied to speeds from 1.0 to 4.5 knots; similarly, the 6 0 knot table values can be
applied to speeds from 4.5 to 7.5 knots, etc. To reiterate, it is far more important to know the actual average
tension than the actual speed. To find the maximum allowable speed for a given scope, interpolation or
extrapolation is acceptable.
L4.2.4 Towing Hawser Scope. Shorter hawser scope results in a "stiffer" hawser system and higher dynamic
components To be conservative, enter the tables with the next-lower scope-e g., 1,500 feet for a 1,700-foot
hawser scope. Extrapolating beyond 2,100 feet is acceptable.
L-4.2.5 Wave Angle. Data in the tables are presented for relative wave directions of dead-ahead and 60, 120
and 180 degrees. The data for 0 degrees can be used for head seas and