Sec. 12A 



DESIGN FOR CONFINED WATERS 



661 



speed of the solitary wave or wave of translation 

 can and does change rapidly with the depth of 

 water and the configuration of the bed. Since 

 the wave itself is short, a change in depth that 

 is relatively short in the direction of motion 

 changes the speed of advance of the wave rather 

 suddenly. For instance, in passing over a narrow 

 rock ledge its speed is changed in proportion to 

 the clear depth over the ledge. It may be more 

 than disconcerting to the pilot of a ship moving 

 at just below the critical speed in the deeper 

 water to find the sohtary wave suddenly dropping 

 back and raising the bow of his vessel. 



The contours of Fig. 61. L indicate the regions 

 of both the critical-speed ratio V J -sfgh and the 

 square-draft to depth ratio a/Aj/Zi, where the 

 total shallow- water resistance Rn is only slightly 

 greater than the total deep-water resistance Rt , 

 as well as the regions where the ratio of these 

 two values mounts rapidly. If the square-draft 

 to depth ratio 's/A^/h is low, the point where 

 the resistance begins to increase rapidly is at 

 about 0.8 Vgh or 0.8cc ■ 



This corresponds to a speed, in ft per sec, of 



TABLE 72. a — Solitary-Wave Speeds for a Range 

 OF Uniform Shallow- Water Depths 



The celerity c of the soUtary wave or wave of translation 

 is related to the depth h by the formula c = y/gh, where 

 g is the acceleration of gravity. In Enghsh units <; is taken 

 as 32J74 ft per sec*. For this table, 1 kt is 1.6889 ft per sec. 



about 4.54 V^, when the depth h is in ft. In kt, 

 the value is about 2.69 V/i. In metric units, the 

 Hmit is, in meters per sec, about 2.5 V^ when h 

 is in meters; in kt, it is about 1.29 \//i when h 

 is in meters [Kempf, G., "Wirtschaftliche Gesch- 

 windigkeiten bei Fahrt auf flachem Wasser 

 (Economical Speeds When Running in Shallow 

 Waters)," WRH, 7 Dec 1923, pp. G01-G02; 

 SBSR, 5 Jun 1924, pp. 671-672].' 



In the reference cited Kempf makes the state- 

 ment that the maximum increase in resistance has 

 been found to occur at a critical-speed ratio 

 Vh/cc of about 0.927. Examination of the graphs 

 of Figs. 35. D and 61. A reveals that, despite 

 somewhat erratic data, this ratio is perhaps on 

 the high side. A better practical ratio of the 

 shallow-water ship speed to the critical speed is 

 about 0.9. The critical-wave speed ratio at which 

 the highest percentage increase of the ratio 

 [(total resistance in water of depth /i)/ (total 

 resistance in deep water)] occurs is slightly lower 

 still. 



It is true that in the 1820's, and possibly for a 

 century before that time, horse-drawn canal 

 boats traveled at supercritical speeds, taking 

 advantage of the reduction in resistance gained 

 thereby. However, the canals of those days were 

 shallow affairs, probably not more than 5 or 6 

 ft deep, so that a towing speed of 8 mph lay in 

 the supercritical range. With the deeper depths 

 of modern inland waterways, of 10 ft or more, 

 travehng at supercritical speed involves traffic 

 and other risks. Furthermore, with a long string 

 of barges it is not possible to have all of them ride 

 simultaneously on the face of a solitary wave. 



72.4 Design for Reduction of Confined-Water 

 Drag, Sinkage, and Squat. If the deductions 

 made by Otto Schlichting and described in 

 Sees. 61.3, 61.4, and 61.5 are correct, two major 

 factors — and only two — are responsible for the 

 changes in resistance and speed which occur 

 between deep-water and confined-water condi- 

 tions. The first is the increased pressure drag from 

 the augmented surface wavemaking. The second 

 is the increased friction drag from the augmented 

 water velocities in the backflow under and along 

 the hull. The remedy for the first is to use a 

 hull that has small pressure drag due to wave- 

 making to begin with. That for the second is, if 

 practicable, to provide more room for the water 

 to get around the ship and thus to reduce the 

 backflow velocity. 



Cutting away the lower outer corners or the 



