to eliminate separate studies for these two towing ships.
L-3.3.2 Wave Size, Angle and Frequency. The motions of the tug and the tow, caused by ocean waves, result
in variations in towline tension. The ship motion having the most influence on towline tension is surge, but the
other motions-sway, heave, roll, pitch and yaw-play a role as well Generally, the larger waves cause the
greatest tension, but it is not only the size of any one wave that counts; ship position and motion at any point in
time depend on the most recent several waves. In addition to wave size, the wave frequency is influential. For
very high frequencies, ships do not have time to respond to the waves, so the motions resulting from such
waves are small. At very low frequencies, ships move significantly, but there is sufficient towline catenary
adjustment that ship motion is accommodated by geometric changes in catenary depth. At somewhat higher
frequencies, changes in catenary depth are restricted by the cross-flow drag of the water on the catenary as it
tries to rise and fall. Thus, at these medium frequencies, the frequencies of interest, ship motions cannot be
accommodated by geometric changes in catenary. This results in larger extreme tensions.
The wave height estimated by an experienced seaman has been found to be approximately the average height
of the third-highest waves, called H 1/3. Values of H 1/3 used in the computer program for predicting extremal
tensions are as follows:
9 1 feet
L-3.3.3 Influences of Towline and Average Towline Tension . For a wire rope towline, the average (mean)
towline tension has a major effect on the extreme tension, since it is the base to which the dynamic tension
effects are added in the analyses. When average tension is low, the towline hangs in a deep catenary which
can change its depth to accommodate large ship motions without large changes in the tension. When the
average tension is high, the towline is nearly straight and can accommodate ship motions only by stretching,
which requires large increases in the tension of wire rope. Of course, the catenary depends upon the weight
and scope of the wire used. All of the computations were based on the actual hawsers used by each towing ship
and an assumed 70 feet of 2 1/4-inch chain pendant extending outward from the tow's bow Computations were
made for hawser scopes of 1,000, 1,200, 1,500, 1,800 and 2,100 feet.
Methods for estimating average towline tension appear in Chapter 6 and Appendix G of this manual One of the
effects influencing average tension, the added resistance due to waves, cannot be estimated with great
accuracy. Results for added resistance, obtained from the methods of Appendix G, are approximate. Because
average tension can have such a pronounced effect on extreme tension, especially for wire rope towlines, it is
preferable to use mean tension measured with an accurate tension meter for entering the extreme tension
graphs, rather than using calculated mean tension.
L-3.3.4 Influence of Tow Speed. The greatest influence of tow speed on extreme tension derives from its
impact on mean towline tension. Both mean tension and dynamic tension contribute to extreme tension Speed
also affects the frequencies at which waves are encountered, providing a second-order effect on tension. All
these effects have been included in the analysis.
Because of the association between mean tension and extreme tension, estimates of the latter must be based
on accurate estimates of mean tension. This is facilitated by presenting data in the form of curves relating
these two forms of tension. These curves "automatically" include the primary effect of speed-its in-