CATENARY DEPTH. To avoid dragging or fouling the towline on the bottom, while maintaining a sufficient
catenary depth to absorb changes in tug-tow separation, it is necessary to estimate the catenary depth, or sag, of the
towline. A number of methods have been utilized for estimating towline catenary.
Do not allow the tow hawser to drag on the bottom.
In order to estimate catenary depth it is necessary to have the following data available:
a. Steady tension in the towline
Lengths of the towline components and their weight per unit length in water
Total scope of the towline.
The steady tension in the towline may be estimated by using the tension meter on the towing machine, by the estimating
procedure in Appendix G, or by using the chart in Figure 6-1 which presents the calculated tug pull available versus
speed through the water. The composition and total length of the towline should be known Appendices B and D provide
the weight per unit length for various towline components. When weight in water of steel components is not given,
multiply weight in air by 0.87 to obtain weight in salt water.
An initial estimate of the catenary depth of the towline may be determined using the following formula'
C = T/W - T/W 1-(WS/2T)2
C = Catenary or sag (ft)
= Steady tension (lbs force)
W = Weight in water per unit length (lbs/ft)
S = Total scope (ft)
Total weight in water per unit length is computed as the sum of the weights of the individual towline components divided
by the total towline scope This formula applies to single component wires hanging under their own weight similar to
power lines However, for towline configurations where the ratio of towline scope (S) to catenary (C) is greater than 8:1,
this formula provides an acceptable estimate of tow-line catenary.
Figures 5-4 through 5-12 show the calculated catenary for various compositions and lengths of towline. These curves
may be used for towing speeds up to 12 knots. In order to decrease catenary, towline scope may be shortened or the
towing speed increased.
To quantify effects of changes in tension, the user can draw in his own curve representing the scope actually used, and
proceed along that curve to different tensions to find the new catenary. For example, with a scope of 1,500 feet of 2-inch
hawser and no chain, Figure 5-7 shows that increasing tension from 20,000 pounds to 30,000 pounds will decrease the
catenary depth from about 100 feet to about 65 feet. Slowing down to a tension of 10,000 pounds will almost double the
catenary to about 190 feet.
Likewise, the user could plot curves of catenary versus tension for several tension figures to provide a graphical
representation of the effect of change in hawser scope. For a fixed limit on depth, the user could plot scope versus
tension for several catenary figures to assist in determining scope/tension combinations required by the water depth.
Some towing machine technical manuals include tables or curves to assist in solving scope/catenary/ tension questions.