662 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 72.5 



diagonal bulges of the maximum section is one 

 means of reducing the effect of the second factor. 

 A better one, because most of the flow passes 

 the ship under the bottom, is raising the floors or 

 decreasing the draft. This gives more flow area 

 between the ship and the stream bed. 



Fortunately, these are equally good solutions 

 to the handicap imposed by lateral boundaries 

 close aboard. It is seldom that the beam or the 

 waterline width of the sections can be appreciably 

 reduced because of the need for deck space, for 

 large metacentric stability, or for lateral room 

 within the hull. In any case, the possible reduc- 

 tions in waterline beam or overall hull width are 

 usually of inconsequential amount, except as 

 they may affect the behavior of the ship in a 

 tight-fitting lock. 



The best and, in fact, the only known method 

 of reducing the sinkage and squat found trouble- 

 some at high speeds is to increase the backflow 

 area and the bed clearance. On the basis that a 

 given restricted channel can not be made wider 

 and deeper the solution is to make the vessel 

 shallower and the maximum-area section smaller. 

 There are no formulas or systematic data available 

 for predicting the sinkage and squat under 

 confined-water conditions but Sec. 58.4 contains 

 some sinkage and change-of-trim values for a 

 few vessels in shallow water. Sec. 58.7 lists 

 references in which other data of this kind, 

 derived from model tests, may be found. 



The importance of this feature is emphasized 

 in the extract from a letter of F. A. Munroe, Jr., 

 Marine Director, Panama Canal Company (of 

 unknown date), published on page 74 of "Marine 

 Engineering" for January 1955: 



"A minimum of 5 feet of water under the keel is con- 

 sidered essential to guard against the squatting effect of a 

 large body moving in a restricted channel and the seiche 

 in the Cut created by the drawing of water at the Pedro 

 Miguel Locks end of the Cut." 



72.5 Transverse Dimensions and Section 

 Shapes for Shallow-Water Riuining. The com- 

 bination of water depth h and speed V^ to be 

 achieved is almost invariably fixed before the 

 design of a shallow-water ship is undertaken. 

 This leaves the designer, if he has some freedom 

 with the length, the choice of the area Ax and 

 the shape of the maximum section and the 

 overall draft H in relation to the water depth h. 

 Within reasonable limits, the hull most easily 

 driven at the relatively high speeds often required 

 of these vessels, where wavemaking in shallow 



water is a factor, is one having a low fatness 

 ratio, F/(0.10L)^, of the order of not more than 

 3.0. Sometimes this ratio is as low as 1.4 or 1.5, 

 corresponding to displacement-length quotients 

 A/(0.010L)' of from 40 to 43. If the overall 

 size is limited, if power is cheap, and if useful 

 load is crowded on, the designer may have to 

 fill the waterway section with all the ship that 

 can be pushed through it, regardless of the 

 square-draft to depth ratio vX^/Zi. 



One way to reduce the maximum-section area 

 Ax is to reduce the draft, but practical considera- 

 tions may set a minimum limit. There must be 

 enough displacement volume to carry the weight 

 of the vessel and its useful load. There must also 

 be enough hull depth to give it structural strength 

 and rigidity. Too large a beam-draft ratio is not 

 advantageous for propulsion because it increases 

 the waterline slopes at the bow and stern for a 

 given displacement volume. However, if propul- 

 sive efficiency is not a major factor, there is no 

 hydrodynamic hmit to the beam of a craft 

 intended for restricted-channel operation. Ob- 

 viously, it must be necessary for two such craft 

 to meet or pass each other in the same channel, 

 or for a single vessel to pass through a lock. If 

 the craft is sufficiently shallow to afford a sizable 

 clearance under the bottom for the passage of 

 displaced water, it may well be that a vessel with 

 a large beam-draft ratio and a small draft is 

 actually easier to handle and less liable to run 

 foul of the banks or of other craft than one which 

 has less beam but also less bed clearance. 



The most efficient solution, considering all 

 phases of the water flow around the hull, is to 

 embody a large rise of floor in the midship or the 

 maximum-area section, together with a large 

 bilge radius. The use of floor slopes as high as 

 10, 15, or 20 deg in the transverse sections acts 

 to increase the draft but this is more of a nominal 

 than an actual increase because of the limited 

 width of the deep-keel portion. If the waterway 

 bed is soft or yielding, occasional encounter of 

 this deep-keel portion with that bed does nothing 

 more than rub off the paint. 



The maximum draft may be limited severely 

 by some especially shallow part of the operating 

 area. The necessary displacement volume is 

 then achieved only by using a nearly flat floor 

 and a relatively large maximum-section coefficient 

 Cx , possibly 0.9 or more. When this occurs, it 

 may be necessary to hold to the relatively flat 

 floor lines for only a limited length amidships. 



