X/L = ( +) 0,707 u \Aa + 0.125 u^ (E-20) 



A diffraction diagram consisting of lines of equal wave height reduction 

 (K') and wave crest advance positions may be drawn from ocmputations similar to 

 those shown in Table ^.-l). Values of K' are chosen (including the mscxLmmti and 

 minimum at the points of reversal of the curve |f(u)j = K' vs. u), and are en- 

 tered in Column 1. From Figure E-3 corresponding values of u sre found and en- 

 tered in Column 2. Columns 3 and h are coitputed as indicated. With columns 3 

 and li, for every value of Y/L in the heading of columns $ through 12 (these values 

 represent distances in wave lengths leeward of the end of the breakt-Jater) 

 corresponding values of X/L are computed with equation E-20 and are entered in 

 the table o Curves of constant K' may be drawn from these X/L and l/L values of 

 columns ^ through 12. (See Figure 19 of text). 



Along these curves, since u is constant, arg f (u) will also be constant; 

 which means that the lines of constant K' may be considered to be lines of con- 

 stant phase lago The amount of crest lag in percent of wave length along any 

 of these lines is given by 



erestlag= ^^ (E-21) 



in which u is taken to correspond to each value of K', and arg f(u) is taken 

 from Figure E-3, and entered in column 13» With arg f (u), the crest lag is 

 conputed from equation (E-21) and entered in column ll;. 



Since the wave crest lag is constant along ar^r one line of K', crest positions 

 along these lines after diffraction may be plotted as on Figure 19 by marking 

 points on them, from and normal to the undiffracted position of any wave crest, a 

 distance equal to the calculated values of crest lag. Positive values of crest 

 lag represent lag and negative values represent lead of the new position of wave 

 crest. All linear dinensions on the graph. Figure 19, are divided by L the incident 

 wave length. Note that Figure 19 being dimensionless may be used for all wave con- 

 ditions and for all size drawings by increasing or decreasing the scale of the 

 diagram to correspond to the scale of the drawing. 



Equation (E-l^) may be ifiritten in the following forms by use of the relation- 

 ship (E-I9). VJhen the upper limit in equation (E-ll) is positive; 



F(x,y) = e~^^'^-f for X S 



aad^x ^ 0) (E-22) 



^0] 



ViThen the upper limit in equation E~ll is negative; 



F(x,y) = f forfx ^ o] 



(E-23) 



where f = e'^^f^) 



E-5 



