If choosing the more elaborate expression for <^ given by equation 

 (127) the implicit relationship for i> becomes 



tan2, = 0.29 (^] (^J^L,) F^ . (139) 



OS 



The preceding calculation based on the simple formula for i> , may be used 

 as a first guess for the value of <}> . Therefore, with <t> = 3.3° and 

 Si /L = 0.12, Figure 16 gives: 



R = 1AL= 1.3 (140) 



u 2a. 



or 



2.6a. = 2.6(0.069) = 0.138 foot , (141) 



and Figure 17 gives F =0.83 as before. Equation (139) therefore 

 becomes 



2 3 



tan2* = 0.29 (^) CrnFTlVw^ O-^^ = 



0.29 (0.64) (0.64) (0.83) = 0.099 (142) 



or 



^ = ^-^y = 2.8° . (143) 



One should now return to Figures 16 and 17 with this new value of (j> 

 to reevaluate the values of R^ and F3. In the present example the values 

 corresponding to this new estimate of ^ (eq. 139) are practically 

 identical to those obtained for <i> = 3.3° so convergence is, in this 

 example, rapidly achieved. 



With cj) = 2.8° and £ /L = 0.12, Figure IS yields a reflection 

 coefficient of 



R = 0.95 . (144) 



P 



Due to the steep 1 on 1.5 slope this estimate should be corrected 



by the factor < Rj^/Rp> in Table 2, corresponding to <}> obtained from 



equation (127), i.e., the best estimate of the reflection coefficient 

 becomes 



78 



