F max= 2af[24n(N)]l'2.+ ( 0^772 \\ (45) 



where a 2 is the variance of the force (area under the spectrum curve), and 

 N is the expected number of waves in a specific storm system. 



III. PONTOON FLOATING BREAKWATERS 



To be effective as a breakwater, the motions of a floating structure must 

 be of small amplitude so that the structure does not generate waves into the 

 protected region. Although at resonance the generated waves can be out of 

 phase with the transmitted waves (resulting in lower coefficients of transmis- 

 sion), the structure must respond to a spectrum of incident wave conditions. 

 Hence, the design of a floating structure for resonance characteristics only 

 would not be satisfactory. Designers seek to achieve small wave transmission 

 by incorporating a large mass to resist the exciting forces, and a natural 

 period of oscillation which is long with respect to the period of the waves 

 (Wiegel, 1964). To obtain a long natural period, it is generally necessary to 

 combine large mass with small internal elastic response of the entire system. 

 A floating breakwater should also extend deep enough into the water so that 

 little of the wave kinetic energy can be transmitted beneath the structure. 

 To make the internal elasticity small and the mass large at the same time, the 

 bulk of the breakwater should be below the water surface at all times. A 

 moored structure has an additional elastic restraining force due to the 

 mooring lines, and the mass to be considered is the virtual mass (which 

 includes the added mass term). The simplest forms of floating breakwaters 

 include pontoon structures, although various modifications in geometry have 

 been investigated in an effort to optimize the mass (and ultimately the cost) 

 of potentially viable alternative systems. 



1. Single Pontoon. 



The rectangular, prismatic (single) pontoon floating breakwater has been 

 considered by several investigators (Carr, 1950; Hay, 1966; Ofuya, 1968; 

 Carver, 1979; Bottin and Turner, 1980) either as a possible system or as a 

 reference for comparison with other potential systems. Patrick (1951), as 

 part of his investigations of a special form of pontoon (the inclined pontoon 

 system), evaluated the efficiency of rectangular blocks in a model study. 

 Blocks of various lengths parallel to the incident wave crest were tested in 

 three different depths of water, at a constant wave steepness and relative 

 water depth, to determine the relationship between the relative breakwater 

 width and the coefficient of transmission. Patrick's analysis showed the 

 existence of transmitted secondary waves in many cases, and showed that trans- 

 mitted wave heights varied with distance away from the structure. The period 

 of the major transmitted wave was the same as the incident wave, but a second- 

 ary wave was superposed. Because the draft-to-depth ratio was found to be a 

 significant variable, studies were conducted with an irregular bottom on the 

 structure which effectively made the draft much deeper. The investigations 

 showed that the irregular bottom was not quite as effective as the prismatic 

 structure; however, the mass was relatively less in the irregular version. 



The floating single pontoon investigated experimentally by Ofuya (1968) 

 was a massive structure of rectangular cross section (Fig. 20). This design 



51 



