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 TB 55-1900-232-10
calation of the ship motion problem. A mathematical model was developed to predict the behavior of a wire
towline and account for the wire's normal mechanical properties plus the following factors:
a. Cross-flow hydrodynamic drag on the wire that tends to flatten out the catenary and increase dynamic
tensions
b The changing spring constant of the wire.
Tests were conducted in a towing tank where the towline was modeled so that it could be pre-tensioned and
one end point moved longitudinally to simulate the varying separation between tug and tow The test results
validated the numerical model describing the behavior of a wire towline. This work was a prerequisite to the
ship motion studies, because it was necessary to know the coupling forces between the two ships, caused by
the towline.
L-3.2 MOTIONS OF THE TUG AND TOW. The computer provides the capability to predict statistics of ship
motion in a seaway, given ship characteristics, size and frequency of the ocean waves, angle of encounter with
the waves and ship speed. For towing, the motions of two ships connected by the towline model, described
above, are examined. This twelve degree-of-freedom problem does not provide the towline tension directly,
since the motions of both the seas and the ships are random. However, the statistical nature of the effort can
provide the probability that a tension will be exceeded during a 24-hour period of towing. Given a steady-state
tension, and selecting a probability of 0.1 percent, the program provides the extreme tension that has one
chance in a thousand of being exceeded in 24 hours of towing. This is comparable to once in 1000 days of
towing-a very small risk. (Of course, the "once" can occur in the first hour. It is not risk-free.) However, with the
low probability involved, extreme tensions can be compared to the strength of the towline using a lower factor
of safety than is otherwise required when the dynamic effects are unquantified. A factor of safety of 1 5, based
on new wire strength, is appropriate for this effort.
There is no reason to doubt the accuracy of these data. However, until experience is gained in applying the
data to real-life tows, two factors of safety are applicable to towing operations-1.5 when dynamic effects are
quantified, and the appropriate factor of safety from Table 6-4. Both must be checked, as one will control in
some cases, the other in others.
L-3.3 DESCRIPTION OF PHYSICAL VARIABLES AND INFLUENCES ON EXTREME TENSION . The
numerical model describing wire hawser behavior is included in the twelve-degree-of-freedom ship motion
program. Thousands of individual computer simulations were performed, using the following variables:
a. Respective characteristics-displacement and length of tug and tow
b. Wave size, angle and frequency
c. Towline used
d. Average towline tensions
e. Towing speed.
Each of these is discussed in the following subparagraphs.
L-3.3.1 Size of Tug and Tow . Sea motions of both the tug and its tow are unique. It was therefore necessary
to study the problem for the T-ATF 166, ARS 38, ARS 50 and ATS 1 Classes. To provide a range of tow sizes,
each tug was examined while towing the following:
a. 650-ton YRBM berthing barge
b. 3,200-ton FFG 1 Class frigate
c. 6,707-ton DD 963 Class destroyer
d. 20,000-ton AE 26 Class ammunition ship
e. 40,000-ton LHA 1 Class assault carrier
It was found that the motion characteristics of the ARS 50 and ATS 1 were sufficiently alike
L-3
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