Sec. 61.4 



PREDICTED BEHAVIOR IN CONFINED WATERS 



393 



resistance Rfi at the intermediate speed F/ is 

 applied as the resistance Rrk to the model shallow- 

 water resistance-speed curve at the point Cj , 

 giving the desired shallow-water speed Vh ■ 



One feature of the diagram of Fig. 61.B is 

 important. Since the abscissas represent wave 

 velocities and ship speeds, and since the ratios 

 between the several velocities and speeds are the 

 items of primary interest, the horizontal scale 

 may be laid off in values of what is known as the 

 critical-speed ratio {V„/\/gh), _V„/\/'gL, the 

 ship speed V, or even (VJ-VgL), as may be 

 found most convenient, or in all of them together. 

 The only requirement is that the water depth h 

 and the ship length L remain constant in the 

 problem, and that all the ratios be a function of V. 



61.4 The Square-Draft to Water-Depth Ratio. 

 0. SchUchting found that the ratio V^/Vi is a 

 function of a 0-diml parameter, namely the 

 square root of the maximum section area Ax of 

 the ship, divided by the water depth h. This 

 appears logical because the increased potential- 

 flow velocity under the ship, where most of the 

 water flows in its passage around the hull, is a 

 function of the space occupied by the ship. 

 Although a ship of given maximum section area, 

 corresponding generally to a ship of given overall 

 size, may have a draft deeper than normal, with 

 less bed clearance, this is compensated for by the 

 fact that the beam is then less than normal. In 

 this case more of the water flows around the 

 sides, and less under the bottom. If the beam is 

 very large in proportion to the draft, more water 

 flows under the bottom but with the greater bed 

 clearance there is then more room for it. 



In any case the relationship developed by 

 Schhchting appears to remain reasonably valid 

 for ships of varied form as well as for all speeds 

 below the critical speed of translation of a natural 

 solitary wave in shallow water. It may be some- 

 what optimistic in predicting slightly too small 

 a speed reduction for the general case, and it 

 may be oversimplified, but it is acceptable until 

 something better is worked out. The square root 

 of the area of the maximum section, a linear 

 dimension, is called for convenience the square 

 draft. It is the draft of the equivalent ship having 

 a square maximum section of the given area Ax , 

 with a beam-draft ratio of 1.0. For shallow water 

 of unlimited lateral extent the square draft 

 (Ax)"'^ is related to the water depth h. For 

 restricted channels it is related to a linear dimen- 

 sion known as the hydraulic radius, symbolized 



Notched Retjions ore Moximum iSections of Area Axj 



Broken-Line Squares Have Areos Equal to Ax in Each Cose 

 and Sides Equal to (Ax) , Known as "Square Droft" 



Fig. 61. C Definition Skktch for Term 

 "Square Draft" 



by Rfi , described briefly in Sec. 18.11, and dis- 

 cussed further in Sec. 61.14. 



Fig. 61. C indicates that, for broad, shallow 

 vessels under which the bed clearance may often 



The Center Scale Gives the Value of the Ratio 



= 20 

 ^ 15 



h 



vhere 



Ax is the Mox^ 



I mum-Section 



Area 



h IS the Woter 



Depth, in the 



Same Units 



10,000 

 8.000 — 



6,000 

 5,000 — 

 4,000 — 



Fig. 61.D Nomogram for Determining Square- 

 Draft TO Water-Depth Ratio 



