gent of the bottom slope angle was computed. 



A simple statistical analysis was then performed on the individual east -west pro- 

 files and the north -south profile. The mean, median and standard deviation for these 

 profiles were obtained and are shown in Figure 5. 



For purposes of estimating sonar fire control performance the data of the diree 

 east -west profiles were lumped together to obtain an east -west composite distribu- 

 tion. The statistical parameters for this composite and the north -south profile num- 

 ber 5 are also shown in Figure 5. 



Figure 6 shows the data of the east -west composite plotted on arithmetic prob- 

 ability paper. Note that the data points fall almost on a straight line between the 10th 

 and 90th percentile lines indicating a close approximation to a normal distribution 

 about a mean of +8. 3 percent bottom slope, where the + sign indicates a downslope to 

 the west. 



Figure 7 shows the data of the north -south profile plotted on arithmetic probabil- 

 ity paper. Note that the data points fall almost on a straight line between the 12th and 

 88th percentile lines indicating a close approximation to a normal distribution about a 

 mean of 2. 5 percent bottom slope where the + sign in this case indicates a doM)iislope 

 to the north. 



The linear transverse error at the target when bottom bounce sonar paths are 

 used is given approximately by 



e = 2 d tan cC 



where d is the bottom depth at the reflection point and ec is the bottom slope. 



Assuming a general water depth of 1000 feithoms (2000 yards), the mean error to 

 be expected for bottom bounce paths with neith -south azimuths is approximately 330 

 yards. This error represents a fire control bias which could be corrected for if it 

 were not for the unfortunate fact diat the standard deviation for the east -west profiles 

 is equivalent to bottom slope deviations of 7. 6 percent which is almost as great as the 

 mean slope. It is important to remember also that essentially 30 percent of the errors 

 will be greater than 330 yards even if allowance is made for the mean slope. 



A typical steeper slope (12 percent) occurring with modest frequency in the east- 

 west direction, will cause a trsms verse error of 480 yards. 



In the case of the north -south profile the mean slope of 2. 5 percent (error of 100 

 yards) is less than for the east -west profiles but the standard deviation of 6.6 per- 

 cent (slope) is almost as great. This implies that even though the correction that 

 could be made is less, it would not help the situation any more than for the east -west 

 profiles. 



Given sufficient coverage of the area of interest one could construct an error map 

 which would give expected errors along particular azimuths for selected bottom re- 

 flection points. With the data on hand one can pass an "average" plane through the 



216 



