Figure 2 presents a plot of w for the entire range of critical angles from to 180 degrees. 



The tables of Report 687 covered values of the frictional resistance parameter / of 0.01, 

 0.02, and 0.03. The present tables include, in addition, /= 0.1. 



NUMERICAL METHODS AND PROCEDURES 



The numerical computations were executed with the UNIVAC by the Applied Mathe- 

 matics Laboratory at the David Taylor Model Basin. All numerical integrations were made 

 using Simpson's rule with a correction term. Explicitly, the form.ula used was 



ydx 



iVn + 4y„_i +y„-2]-^[yn-42/„_i +62/„_2 -42/„-3 + Vn-^'^ t2] 



-2h 



90 



The integrations of the functions for Table 1 (Quadrant 1) of this supplement were 

 started at = 90 degrees. Except for the case (^ ^ = Q the integrations were performed in 

 steps of -0.5 degrees until the value (^ = (f>^ + ^ degrees was reached. Tlien the method 

 described in Appendix 3 of TMB Report 687 was applied using steps of -0.1 degrees. The 

 integrations were term.inated either when cf} - <p^ became less than 0.5 degree or when a 

 exceeded 300. 



The methods described in Appendix 3 of TVB Report 687 were applied for evaluating 

 the functions given in Table 2 (Quadrant 3). The integrations were started at ^ =180 degrees 

 and performed in steps of +0.1 degree. Computations were terminated either when 180^+^^-0 

 became less than 0.5 degree or when a exceeded 300. 



The integrations for Table 3 (Quadrant 2) were started at q6 = 180 degrees and carried 

 to (^ = 90 degrees. The integrations were performed in steps of -0.1 degree for the critical 

 angles c^ = 1, 2 and 3 degrees. For the other critical angles, steps of -0.5 degree were used. 



The methods given in Appendix 4, of Report 687 were used to determine the values of 

 the functions in Table 1 for the case where ^^ = 0. The following intervals of the independent 

 variables were used: 



Range of c^ 



Interval of Intergration 



degrees 



degrees 



90 >c6>15 



-0.5 



15 >cS>10 



-0,25 



10 >0> 5 



-0.1 



50 >cb> 1.2 



-0.05 



1.2>0> 0.5 



-0.001 



