line was too taut to allow it to become tangent to the bottom at the 

 anchor. If this condition occurs, or as it is approached, the catenary- 

 equations no longer apply. For many full-scale installations, a combi- 

 nation chain and synthetic line anchor cable is used. This combination 

 anchor cable presents problems in attempting to use the catenary equa- 

 tions . 



Comparisons between the mooring line forces calculated using the 

 catenary equations to predict spring constants showed poor agreement 

 with measured results (Adee, 1975) . While the general trends were re- 

 produced, an increase in the predicted spring constants of about a factor 

 of 4 would have been required to bring the theoretical prediction into 

 agreement with the measured results. 



To overcome the problems encountered in using the catenary equa- 

 tions, a system based on discretization of the mooring line and static 

 equilibrium was developed. This method is described in Appendix B. 



(1) Proposed Oak Harbor Breakwater . One of the few model 

 tests in which mooring line forces were measured was performed by David- 

 son (1971) for the floating breakwater proposed for Oak Harbor, Washing- 

 ton. The model configuration with properties scaled to the prototype 

 is included in Appendix F. The shape of this breakwater is basically an 

 inverted bathtub with foam flotation. 



Applying the theory to predict the mooring line force in the seaward 

 anchor line at a water depth of 29.5 feet, one obtains the results shown in 

 Figure 17. The mooring-force coefficient is defined as the amplitude 

 of the force oscillation divided by incident wave amplitude times the 

 weight per unit length of the breakwater. In this figure, the large 

 range of the experimental results is directly related to incident wave 

 amplitude. The smaller incident wave amplitudes generally produce lower 

 measured mooring line forces per unit amplitude except at the beam to 

 wavelength ratio of 0.49. Since the linear theory is mathematically cor- 

 rect only in the limit as wave amplitude tends to zero, one would expect 

 the best correlation between theoretically predicted and measured results 

 for small amplitude incident waves. The results shown in Figure 17 are 

 consistent with this expectation. However, the very large difference in 

 mooring line forces as incident wave amplitude increases indicates a 

 highly nonlinear response. 



A potential explanation for the nonlinear response observed in 

 these experiments results from the condition of the mooring lines at the 

 29.5-foot water depth used for the model tests. Under these conditions, 

 the mooring lines no longer maintain a catenary shape. When the initial 

 tension in the mooring lines is increased to this level, they respond 

 with very large changes in mooring line force for very small displacements 

 of the breakwater. Consequently, small deviations in the planned posi- 

 tioning of the anchors will lead to large changes in forces in the moor- 

 ing line. This condition clearly should be avoided in prototype instal- 

 lations where very large mooring line forces are to be avoided. 



41 



