412 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 61.17 



Width of Wate 

 ■345.6 ft 



Sorfoce A^- IHI 3 ft^ 



^ ■/%- 33,34 ft 



I Wetted Girth 98 fl (opprox.) 



U-eo.eftU— 



Wetted Perimeter is Shown in Heavy Lines 



Net Area of Water Seotion (less Ax) 



Hvdrovilic Radius Ku- .,, ^, , o : f — TT — Trzi — TTT — 



' " Watted Perimeter, Includino that of Ship 



^^^^ 



ForDeterminincj Vo„/y^, Vj/y^ ond V^/y^ i 



of Non-Uniform Depth, Use the Etjuivolent Depth hgg 



E<iuqI to (Water-Section Area)/(WQter Surface Width)' 



Offset from Centerlii 



l^pical Suez Lonol Profile of j About 1950 as Given b>y 

 R. Brand, "Moneuverinfj of Ships." 3NAME, 1951. Fici.lO, p. 241, 

 with Larqe Ship in Offset Position 



T^picol Test Condition in the Sho I low- Water Basin at the 

 David Ta-^lor Model Basin, for which the H-ydraulic. Radius is 

 Appreciably Less Thon the Water Depth h 



Fig. 61.N Explanatory and Illustrative Sketches 



FOR Equivalent Depths and Hydraulic Radii op 



Restricted Channels 



constant and all other variables allowed to change. 

 The water depths may fluctuate widely with 

 ship location in the shallow area or along the 

 channel; the resistances and perhaps the speeds 

 fluctuate with them. 



Unless a ship is designed for special service in 

 confined waters, only rarely does it have any 

 great reserve of power to match the increase in 

 resistance in the shallower channel depths and 

 narrower widths, assuming that it is advisable 

 or permissible to maintain the deep-water speed. 

 If it is so designed, the limiting conditions become 

 the basis of the design, and the operator gets 



whatever improved performance he can from the 

 ship ui deeper and more open water. 



When the ship speed is reduced because of the 

 diminished velocity of the Velox-wave system in 

 shallow water, the speed of the ship through the 

 surrounding water — in other words, its relative 

 speed — is correspondingly reduced because the 

 water stands still, generally speaking, while the 

 wave moves by. This is the reason why the friction 

 resistance is reduced when the ship slows from 

 its deep-water speed to its intermediate speed. 



The ship resistance Rt is reduced by this 

 decrement in Rp , represented by the ordinate 

 MBi in Fig. 61. B, but not by as much as it would 

 be for a corresponding speed reduction in deep 

 water. Thus point Bj in the figure is higher than 

 point L. For the mtermediate speed F/ , therefore, 

 the shallow- water power, RrhiVi), is greater 

 than it would be for the same speed in deep 

 water. The rate of rotation drops by a ratio 

 somewhat greater than Vj/V^ , assuming the 

 wake fraction w constant, because of the greater 

 resistance that must be overcome and the greater 

 thrust to be developed. Furthermore, as the 

 thrust loading at point Bj is greater than it 

 would be at point L, the propeller efficiency 

 drops slightly, still further increasing the power 

 at the point L. 



As the ship speed diminishes from the inter- 

 mediate value Vr to the shallow-water value V^ , 

 with no change in total resistance, the effective 

 power P E diminishes, as do the thrust T and the 

 speed of advance V a , unless the augmented 

 backflow occurs in a region occupied by the 

 propulsion device(s). From here on, the data are 

 scanty and the analysis is nearly nonexistent. 



At a sufficiently low value of V^/'s/gJi; the 

 ship speed is reduced solely because of the ratio 

 \/ Ax/h. The speed drops from F„ to V^ but the 

 resistance remains the same. All the water ahead 

 of the ship has to get around astern, it must flow 

 backward in this process, and the backward 

 flow is much faster close to the ship. The ship 

 thus has to move against what amounts to a 

 contrary current in the channel, so that the lost 

 of speed is equal to the effective velocity of this 

 counter current. Assuming that the ship moves 

 through the water close around it with the same 

 relative speed, the shaft power and rate of rota- 

 tion of the propulsion device (s) should remain 

 substantially the same as at the speed V„ in 

 deep water. 



61.17 Data on Confined-Water Operation at 



