;.o riatimit of crest lag in percent of wave length at any point is given by 



i- 'f -. "<^% i^ + iW)-_ ,^-1 ('^\ (Tf ^\\ 



..'cyt lag ~ .-^^-^.g -.. - tan (•gj (E-3ii; 



Diffraction Coeffinients. - The manner in which lines of equal diffraction 

 c-oBifTexents are fouiid is illustrated in Table E-2o These computations are 

 for diffraction effects where the gap -width is twice the wave length. For a 

 particixlai" value of X/L and various values of Y/L, u,2 and Up2 are calculated 

 by use of equations E-29 and E~30. With these values s, , w, , s- and Wp are 



found from Figure E-7 and when summed in the manner determined by equation 

 E-28j give the (S) and (W) values of equation E-lIi. Diffraction coefficients, 

 K'j are then calculated by use of this equation for each value of X/L and Y/L. 

 These values are plotted as illustrated on Figure 21 of the text. Contour 

 lines of equCl diffraction coefficient, K', may then be drawn. 



Wave _ Cre s t _ Positions . - Equation (E-3I4.), being a tangent function, con- 

 t3ins"~n6 indxcation of the position of a wave crest other than giving the 

 axaount of lag or lead (phase difference) of a diffracted wave crest over an 

 uDdlffracfced one. (Positive values of phase difference indicate a crest 

 lag^ and negative values^ a crest lead). There is no way of telling from 

 the solution of equation (£-2^1 alone to which undiffracted wave crest this 

 lag or lead applies. 



This may be determined however, through the construction of a graph of 

 j/l, vs. eoirplete phase Figure E-8 for various values of X/L, ("Conplete 

 phase" indicates the actual distance in wave cycles of a wave crest from the 

 gap.) A 143^ line is first sketched in. The complete phases along the line 

 for X/L = will lie just below this kS line and successive curves for 

 X/L ~ 0.5', l.Oj 1.5 etc, will lie above and approximately parallel to each 

 preceding cui've . i '".■ 



W 

 ,, ^-L- o) N T p 4. -1 W J tan °1 q- Phase difference (PD) 



From equation {h-Sh) ■) values of tan -s- and X|an____b= __ — ___ i — '- 



b 350 30U 



are calculated. For each integral ^^ '^''a^^ej these ED/36O' values are added 

 to or subtracted from that value of integral phase which will bring the 

 actual complete phase line to the desired positionj slightly above the curve 

 for the next smaller value of XA« For exanplej with X/L = 2,5 and Y/L = 2j 

 ¥\')/36d^ ^ +0.380 which is subtracted from 3, and for Y/L = 3| PD/360° = 

 "•'0.386 which is added to 3 to give complete phase values of 2.62 and 3039 

 respectively. 



Points for the wave pattern are computed by noting from the curves 

 shoirm in Figure E-8 the values of Y/L at the points where the lines of con- 

 stant XA" itersect the line of integral phase. These values are tabulated 



E=12 



