Snc. 61.11 



PREDICTED BEHAVIOR IN CONFINED WATERS 



405 



almost never uniform, so that when a limiting 

 depth is determined, someone must decide 

 whether it is to be looked upon as a mean or as a 

 minimum depth. 



For slow and intermediate-speed ships of 

 normal or full form, having a relatively large 

 maximum-section area, the limiting depth h is 

 almost certain to be large enough to make the 

 limiting critical-speed ratio V^/'vgh, as well as 

 the ratio ■\/ Ax/h, rather small, as they are in 

 the region HK of Fig. 61. J. Indeed, the first 

 may be so small as to make the wave-speed 

 ratio F;/F„ practically unity; see the first 

 example following. On the other hand, for a fine, 

 fast ship running at higher critical-speed ratios, 

 the depth h is so great in proportion to the square 

 draft '\/~Ax that the value of the potential-flow 

 ratio Vh/Vi may be practically 1.00, as in the 

 region FG of Fig. 61. J; see the second example 

 following. The ratio V,/V„ then becomes the 

 sole factor in determining the depth. 



The approximate method described here gives 

 quickly the limiting depth of unrestricted shallow 

 water in which a ship must run to insure that its 

 shallow-water total resistance Rth does not 

 exceed 1.02 times its deep-water total resistance 

 i^T-oo . The basis of this method is that the resist- 

 ance varies as a certain — but undetermined — ■ 

 power of the speed in any narrow speed range or 

 at any selected speed. As a rough average it may 



be assumed that R = kV^, in which case dR = 

 2kV{dV). For any small range in which k and 

 V may be assumed constant, a 2 per cent increase 

 in resistance is therefore reflected by a 1 per cent 

 increase in speed. This is the basis for the state- 

 ment that at the limiting depth the shallow-water 

 speed Fa shall be not less than 0.99 times the 

 deep-water speed F„ for the given deep-water 

 resistance Rto, . 



Since the speed reduction may be due to a 

 decreased Velox-wave speed or to augmented 

 potential flow around the ship both factors must 

 be considered. As the first depends upon the 

 critical-speed ratio V„/-vgh and the second 

 upon the square-draft to water-depth ratio 

 'VAx/h, they can not easily be put upon a 

 conunon basis except to say that for any given 

 conditions the value of h to be determined must 

 be the same for both. 



The speed reduction due to either factor man- 

 ifestly can not exceed 0.01. From Fig. 61.E the 

 value of the critical-speed ratio V^c/vgh can 

 not exceed 0.658, for which F//F„ = 0.99. From 

 Fig. 61.G the square-draft to water-depth ratio 

 a/aI/Zi can not exceed 0.393, where VJVi = 

 0.99. Below a critical-speed ratio of 0.40 the inter- 

 mediate speed Vi is practically equal to the deep- 

 water speed F„ so that this part of the theoretical 

 curve need not be considered. Below a square- 

 draft to water-depth ratio of 0.1 the shallow-water 



Critical-Speed f?Qtio Voo/Vqh, where Voq Is Wave Speed m Deep Woter and CQ_='^fqii is Critical 5peed 

 0.400 0.538 0.567 0.586 0.602 0.614 0&Z4 0.634 0.642 0.652 0.658 

 0.515 0555 0577 0.595 0.608 0.619 0.629 0.638 0.647 0655 



0.993 Vj 



0.386 0370 0.353 0334 Q3I3 0291 0265 0235 0199 0.138 

 0.393 0378 0.36Z 0344 0.323 0302 0.278 0.251 Q2I8 QI75 0.000 



Square- Draft to Depth Ratio ''{K^/h, where h is Shallow-Water Depth 



Fig. 61. K Diaqrajh for Determining the Limiting Water Depth for a Speed Reduction op 1 Per Cent 



