Sec. 61.7 



PREDICTED BEHAVIOR IN CONFINED WATERS 



399 



Rtoi for these spots is indicated by the successive lines of 

 Table 61. a. Plotting these values gives the curves through 

 A2-K2 and through E2-F2 of Fig. 61. H. 



The next step is to derive the values of Yhlyfgh for 

 five (or more) selected values of Vm/\/gh. These latter 

 may correspond to the five Fn's of the first line of Table 

 61. a or, what is slightly easier for plotting, to certain 

 principal abscissas on the diagram of Fig. 61.H. In this 

 example the value of Vo:,/\/gh for the 13-kt speed happens 

 to lie at one of these points, namely 0.790. 



The method of determining the values of Vh\/gh for 

 the selected values of V^l\fg]\ is set down in Table 61. b. 

 The Fz/Fco and Vhiyj ratios give the values of the ab- 

 scissas Vail\/ gh for the horizontal locations of the points 

 B2 and C2 on Fig. 61. H, corresponding to the points Bi 

 and Ci on Fig. 61.B. Determining the ordinates of a series 

 of points such as B2 and C2 for a series of points such as 

 A2 enables the shallow-water total-resistance curve 

 C21-C25 to be laid down. 



The value of the total resistance at the point B2 on 

 Fig. 61. H may be derived from that at a selected point Ao 

 by picking off the value TJ^a, at A2 and using the formula 



Rth = Rtcd — Rfoi + Rft ■ However, it is easier and 

 quicker to draw the line A2B2 on the graph, parallel to the 

 corresponding segment of the friction-resistance curve 

 (that is, for the same range of Vco/\/gh), and to mark 

 the point B2 at its intersection with the vertical line for 

 the corresponding Vi/\/gh ratio. The ordinate of B2 gives 

 the ordinate of C2 and value of Rn for the corresponding 

 point on the shallow-water curve. Through the six points 

 such as C21 through C26 the shallow-water Rn-V curve 

 is drawn, remembering that the abscissas are really 

 values of Vai/^/gh. A horizontal line drawn from A2, 

 where Vai/\/gh is 0.790, representing the 13-kt ship 

 speed, to the point Ho , gives the value Vh/\/gh of 0.643. 

 Since s/gh is, from Table 61. a, equal to 27.79 ft per sec, 

 Vk is (27.79) (0.643) or 17.87 ft per sec, equivalent to 

 10.58 kt. This is the answer desired. The speed reduction 

 is (13 - 10.58) /13 = 2.42/13 or about 18.6 per cent. 



Using the contours published by O. Schliohting [STG, 

 1934, Fig. 9; TMB Transl. 56, Fig. 9, p. 11 ; van Lammeren, 

 W. P. A., RPSS, 1948, Fig. 30, p. 57]_to determine the 

 speed loss, V^/Vgh is 0.790, (V^/VghY is 0.624, and 

 y/ Axlh is 1.389. Entering with these arguments, the 



TABLE 61. a — Calculation op Dbep-Watbr Resistance-Speed Data for Example 61.1, Plotted on P^g. 61.H 

 Data marked with an asterisk (*) are taken from SNAME RD sheet 9. The value of aCj? is 0.4(10"'). 



