396 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 61.6 



Fig. 61. G Graphs of Potential-Flow Ratio on a Base of Square-Draft to Water-Depth Ratio 



there was some wall effect in Schlichting's shallow- 

 water experiments 



(3) Extending the graph derived by Landweber 

 and mentioned in (1) preceding, which carried 

 to a a/A^/Zi ratio of only 1.6, to a value exceeding 

 3.0. This extension was made by plotting the 

 available data on log-log paper and extrapolating 

 the curve by eye. The portion so extrapolated is 

 shown in broken lines in the lower right corner 

 of Fig. 61.G. 



The modified curves of Fig. 61.G are in two 

 parts; the left-hand curve is a large-scale version 

 of the corresponding portion of the larger right- 

 hand one. 



The Schlichting method takes no direct account 

 of the slope drag involved in the shallow-water 

 resistance problem, or of the change in attitude 

 and slope drag when running from deep into 

 shallow water. This drag becomes appreciable 

 when approaching the critical speed, and it 

 diminishes rapidly as this speed is exceeded. 

 However, no method has been developed as yet 

 for assessing the amount of slope drag under 

 any given conditions. All that is known about it 

 is that it represents an increased resistance. 



Fig. 35. D of Sec. 35.6 demonstrates that in the 

 case of the scout-cruiser model reported upon 

 there, the maximum increase in shallow-water 

 over deep-water resistance, as well as the maxi- 

 mum increase in trim by the stern, occur at a 

 speed less than the critical speed or celerity Cc ■ 



Fig. 61. A of Sec. 61.2 shows definite trends in this 

 direction. Whether this phenomenon is a function 

 of slope drag, of the cross-sectional area of the 

 water region in which the ship is moving, as 

 brought out by O. Schlichting [TMB Transl. 56, 

 p. 19], of other factors not yet evolved, or of 

 some combination of these, is not yet certain. 



The fact that there is fittle or no reduction in 

 wave speed in shallow water until the ship speed 

 reaches about half the critical speed, and that 

 there is likewise a negligible speed reduction due 

 to potential flow for small values of the square- 

 draft to water-depth ratio is brought out more 

 clearly in the examples which follow. 



61.6 Practical Cases Involving a Given Depth 

 of Water. Five cases, in two classes, appear to 

 cover all normal shallow-water situations en- 

 countered in service: 



(1) When the depth of shallow water is known or 



given : 



Case la. To determine the reduced shallow-water 

 speed for a given resistance when the 

 deep-water speed and resistance are 

 known 



Case lb. To determine the increased shallow- 

 water resistance for a given speed when 

 the deep-water resistance is known 



Case Ic. To determine the deep-water speed and 

 resistance when the shallow-water speed 

 and resistance are measured. 



