However, the meaning of these terms may be 

 examined in the hght of refractive effects in shallow 

 water by considering the velocities and angles 

 involved. 



The velocity and length of a wave decreases in 

 shallow water as shown in the following tables: 

 dILo 0. 4 0. 3 0. 2 ' 0. 1 



CI Co 0. 98 0. 96 0. 89 0. 71 



The angle through which a wave crest will 

 turn between deep water and any value of dlL^, 

 may be obtained from figure 4. By selecting a few 

 values to represent the effect, table 2 shows that 

 the limits of "shallow water" depend upon the 

 angle a„ and the accuracy to which the diagram 

 is to be constructed. If a, = 70 degrees and if the 

 construction is at an accuracy of ± 1 degree, the 

 diagram should start in depths even greater than 

 rf=0.5 Lo, but if a„ is only 10 degrees, a negligible 

 error is introduced if the diagram is started from 

 c?=0.3 L„. 



As a working rule, to be modified if circum- 

 stances so indicate, refraction diagrams should 

 start from straight wave crests in a depth equal to 

 half the deep water wave length or at d=0. 5X5.12 



Table 2 

 Values of oc as a function of d/L„ and a„ 



The velocity of a wave in deep water is 5.12 T. 

 As the wave moves into shallow water, its velocity 

 decreases and, if the crest makes an angle with 

 the bottom contours, the wave velocity will vary 

 from point to point a,long the crest. Graphical 

 construction of a refraction diagram consists 

 simply in moving each point of the crest in a direc- 

 tion perpendicular to the crest by a distance equal 

 to the wave velocity times the time interval 

 selected. The initial form of the wave is a straight 

 line in the deep water area, as previously defined. 

 Figure 5 shows scales constructed in such manner 

 as to give the advance of the wave crest at any 

 value of d/Lo on a chart of any scale S. (These 

 scales have been printed on thin paper and are 

 available for distribution.) The two scales of 

 figure 5 differ only in that scale A gives the wave 



advance during an interval which is twice that of 

 scale B. 



To construct a refraction diagram, the chart 

 first is contoured with an interval which will 

 represent accurately the details of the bottom 

 topography. Each contour on the map is con- 

 verted to mean sea level — or any other desired 

 stage of the tide — adding the proper constant to 

 the chart soundings. For the wave_period selected 

 the deep water wave length is computed from the 

 relationship, io = 5.12 T^. The contour values, in 

 depth in feet below the tide stage selected, are 

 then divided by Lo (in feet) to give contours in 

 terms of d/Lo. Thus, in figure 6, for example, the 

 contours in fathoms have been re-labeled in terms 

 of values of d/Lg. Additional contours of d/Lo may 

 be added if considered desirable. In figure 6, for 

 example, contours of d/Lo of 0.5 and 0.4 have 

 been added. 



Generally, it is sufficient to draw every nth 

 crest, where the value of the crest interval, n, 

 depends upon the scale of the chart and the 

 complexity of the bottom topography. The crest 

 interval is determined by the scales used and may 

 be expressed as n, a multiple value of wave length, 

 or as a time interval, t. The crest interval does not 

 have to be an even value, nor does it have to be 

 the same for the entire chart, since more crests 

 often should be drawn where the bottom topo- 

 graphy is particularly complex. The two trans- 

 parent scales (fig. 5) for plotting the wave advance 

 are provided so that the crest interval in one scale 

 (scale A) is just twice that for the second scale 

 (scale B). These scales are applicable to charts 

 of any scale and of any wave period. The only 

 variable between refraction diagrams prepared by 

 the use of the scales is the crest inter-val, this 

 interval being a function of the scale of the 

 hydrographic chart. Formulas are provided for 

 computation of the crest interval, n, or time 

 interval, t, for any particular refraction diagram 

 (fig. 5). 



It is often advantageous, as well as sometimes 

 necessary, to draw a refraction diagram for a 

 particular locality in several steps; First, the 

 over-all pattern for a long stretch of coast line is 

 drawn on a relatively small scale chart, following 

 the waves from deep water to within a few 

 thousand feet from shore; finally, the results are 

 transferred to larger scale charts, and a detailed 

 pattern is constructed of the waves close to shore in 

 bays, harbors, and other areas of particular 

 importance. Where the tidal range is large, it 



6 



