Sec. 61.5 



PREDICTED BEHAVIOR IN CONFINED WATERS 



395 



speed F„ , again provided that the intermediate 

 speed remains well below the critical. 



Referring back to Fig. 61. B, the solution in the 

 various cases presented in practice involves 

 finding points such as Gi and Hi when the position 

 of Ai is known, or in finding the depths of water 

 for which G, and H, lie at certain positions 

 relative to Aj . 



This is not as easy as it looks or sounds because, 

 first, there is not available, for a typical ship, a 

 family of curves giving the resistances for a 

 series of speeds, in waters of many different 

 depths. Second, the pairs of points such as Ai 

 and Ci in Fig. 61. B are not directly related to 

 each other. Both the speed and the resistance are 

 different for the two spots of a pair. When making 

 calculations of the kind represented graphically 

 by this figure it is generally necessary to plot two 

 resistance-speed curves, one for shallow water 

 of the given depth h and one for deep water, 

 marking the companion spots Ai and Ci on each. 

 Assuming that the water depth h is known, the 

 plots are conveniently made at values of the 

 critical-speed ratio Va./'vgh (using a range of 

 speeds F<„), because it is then easier to determine 

 the intermediate-speed position c^ or Vj for the 

 point Bi . A small range of the critical-speed 

 ratio, embracing from three to five points, rather 

 close together, is adequate if the problem is of 

 limited application. If the water depth h is not 

 known it may be convenient to plot the resistance 

 curves on a basis of ship speed V or of Froude 

 number F„ , depending upon the nature of the 

 problem. 



The ratio of the intermediate speed F/ to the 

 deep-water speed F„ , called hereafter the wave- 

 speed ratio, is determined by inspection from a 

 theoretical curve giving Vj/V:^ on a basis of 

 critical-speed ratio V„/\'gh. Fig. 61.E shows 

 two parts of such a curve; the shorter is a large- 

 scale edition of a portion of the longer one, for 

 easier reading in the lower critical-speed range. 

 The nomogram of Fig. 61.F, also designed and 

 generously furnished by Professor Seward, gives by 

 inspection the value of the ratio V^/y/gh when 

 the deep-water speed V^ and the water depth h 

 are known. There is a double scale for F„ , by 

 which the right-hand line may be entered either 

 in ft per sec or in kt. 



The ratio of the shallow-water speed V^ in a 

 depth h to the intermediate speed F/ , called 

 hereafter the -potential-flow ratio, is determined by 

 inspection from experiment curves such as those 



The Center Scale Gives the Value of the Rotio 

 Va, Speed of Ship in Unlimited Deep Water 

 -y^ Speed of Wove of Translation in Depth h 

 By the Intersection of o Stroicjht Line Drov^n 

 Between q Point on the Rioht-Hond Scole at 

 the Ship Speed V^o in Deep Water and a 

 Point on the Left-hand Scole at the Depth 

 h of the Shallow Water Under Considerotion 



The Value of Q is Token as 32.174 ft per sec^ 



Vqh- 



— 5 



— 4 



— 3 



— JC _ 



■ ?. — M_ 



Example: 



V„- 10 kt.or 16.89 ft per sec 



Depth of Water h-28ft 



-p^ot Point R» 0.563 



90 -5p 



10 ■ 



-2D 



— 0.5 — ^ 



025 

 — O.E 

 0.15 



-2 



— 0.08 

 0.07 



— 0.06 



— 0.05 



— 0.03 

 O.0Z5 



— O.Oi 



7 -4 

 6 — 



3 — 



25- 



■ 250 C 

 -300 5 



- 400 ^" 

 -500 % 



- 600 'S 



-700 t -^"' 



-800 ^ g. 



L 1000 ■" 



Fig. 61. F Nomogram for Determining Critical- 

 Speed Ratio 



of Fig. 61.G, in which the ratio V JV i is plotted 

 on a basis of the square-draft to water-depth 

 ratio \/~Axlh,. The curve determined by Schlich- 

 ting [STG, 1934, Fig. 9, p. 135; EMB Transl. 56, 

 Jan 1940, Fig. 2, p. 3; EMB Rep. 460, May 1939, 

 Fig. 9, p. 11] has been modified by: 



(1) Decreasing slightly the potential-flow ratios 

 YulV I for small values of the square-draft to 

 water-depth ratio. This was done to bring the 

 potential-flow ratios in agreement with those 

 determined by L. Landweber for restricted 

 channels [EMB Rep. 400, May 1939, p. 11]. 



(2) Increasing the potential-flow ratios YJYi 

 rather markedly for the larger values of the square- 

 draft to water-depth ratio because tests made in 

 other model basins indicate conclusively that 



