



— 





' compressional ^S^ 

 / wave angle ^^^ 





^^ ' ^V reflected angle 





X**""" \ lope ingle \ 



-f 



refracted angle ^"^^^ \ 



u KS 



i i i i 



1 



Figure 1 3 Angles at which rays emerge after striking or passing 

 through the keel of Fig. 10. as a function of position on the wave 

 front The slope of the keel at the point of contact is labeled 

 "slope angle." 



-20 degrees. This causes the vertical discontinuity of 40 degrees in the reflected angle. Reflected 

 angles less than degrees are headed upward after reflection and reflect from the surface 

 behind the keel, becoming downgomg or positive angles of the same size. 



The final angle at which refra .ted rays emerge from ti t keel cannot be easily 

 characterized. Figure 14 shows the change in angle at the interlace for the water wave to ice 

 si. ear wave interaction for the sound ..f^eeds of Table I. A 45-degree line is drawn in to indicate 

 the size of the angle change. At high grazing angles or near-normal incidence, very little change 

 occurs. These angular changes occur at transmission both into the keel and from it. The 

 additional change in ray angle is a result of change in slope of the keel at the entering and 

 exiting points. The ray may also reflect from the fiat upper surface of the keel model. 



A compressional wave begins when the grazing angle equals 66 degrees and ends when 

 the rays reach ihe upper corner of the keel. The upper end of this line has a small transmission 

 coefficient, hut towards the lower end provides occasional downward-directed rays, as can be 

 seen in Fig. 4 and other such scatter diagrams. 



The accumulation of the above effects produces exiting angles for z 20-degree ray sei, 

 shown by the dashed lines in Fig. 13. At the critical grazing angle near 26 degrees, the reflected 

 and refracted rays correspond in angle. The dashed line therefore meets the reflected angle 

 curve at the points where the slope angle is 26 ± 20 degrees. The nearly fiat section through the 

 middle of the refracted angle line is from rays that reflect from the upper surface of the keel. 

 The discontinuity at either end of this section is the ray that intersects either the leading or 

 trailing comer of the keel and surface. 



14 



