The computers to be used for the programs cited in the appendices 

 are the IBM 1620 (with floating-point hardware and 60K memory) and the 

 IB4 7094. FORTRAN II is the language used for the 1620 programs; FORTRAN 

 IV is used for the 7094 programs. The computer and language for a given 

 program are specified on the first comment card of each program print-out. 



The number of digits carried by a computer during internal computations 

 for floating-point numbers (designated by f) and the number of digits carried 

 for fixed-point numbers (designated by k) vary with the different programs. 

 For the 1620 programs, f is given in Columns 2 and 3 and k is given in 

 Columns 4 and 5 of the first card of each program print-out. For the 7094 

 program, f = 8 and k = 5. 



Example of Sample Output . Sample input and output listings are given 

 in Appendix D for three wave rays. These three rays, numbered 1, 2, and 3 

 in the OUTPUT listings, correspond to rays numbered 33, 32, and 31, respec- 

 tively, of Table 1 and Figures 2 and 6. 



Representation of Output 



Possible Methods. Output from the computer programs could be presented 

 in a variety of ways, depending upon the requirements of the investigator. 

 Precision work on caustics, for example, might entail skillful plotting of 

 the values at MAX points with precision drafting techniques. If a rapid 

 analysis of ray paths from deep water to the shore is all that is required, 

 however, the investigator might consider an X-Y plotter attachment for 

 rapid printing of the computer output. For many shore engineering studies, 

 only the final few hundred yards of the wave rays will be of practical 

 value, while for studies of energy or wave-power distribution along a 

 fixed segment of the shore, it is possible that only the terminal points 

 of the rays at some specified distance from shore would be of value for 

 presentation. 



Example. The results of the computer refraction of the 52 wave rays 

 of Figure 2 are presented in Figures 3-8, which show only the last portions 

 of the wave rays relatively close to shore. Successive calculation points 

 were plotted on a grid and then connected by a smooth curve. The rays 

 themselves vary from the almost unmodified ones for 4-second waves that 

 approach the beach relatively head on (Figure 5), to the 6-second ones 

 that actually cross (Figure 8) within the limits of the figure. 



Attention is drawn to the terminal points of the wave rays; some of 

 these points (such as those of rays Nos. 14, 37, and 52 as shown in Figures 

 4, 7, and 8, respectively) are closer to the shoreline than others. These 

 variations are due to the fact that a ray terminates because either the 

 next calculation point is in an area of zero or negative velocity, or 

 curvature approximations are not converging. Thus, with a constant in- 

 cremented distance (D), all rays do not reach a similar distance from the 

 shoreline. Ray No. 24 (Figure 5), on the other hand, makes a pronounced 



