404 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 61.11 



0.55 



oafl- 



0.50 

 0.99 ° 040 



-n 0.35 



8 0.995 ^ 



5 



□ 025 



E 998 ^ 



;§ e 0.20 

 0999 " 



^ 



§ 0.15 



0.10 



0.05 







Speed Reduction for 



ABC 5hip in 175 feet of 



To Find ApproKimate Speed Reduction 



Enter Dioqrom with Values of ^/^/h 



and Voo/V^h^ Qfid Interpolate Between Contours 



0.1 



CrilicQl Wave-Speed Ratio 



0.4 V 



Ami 



Intermediote- Speed Ratio rj^ 0,999 0995 0.99 QS 



^00 



Fig. 61.J Geaphs for Determining the Limiting Water Depths for Various Small Speed Reductions 



reductions of 1.0, 0.5, 0.2, and 0.1 per cent, 

 respectively. 



While the statement of this example, and of 

 others in this chapter, gives the impression of 

 straining at small quantities, the principal 

 purpose of the example is to illustrate the method. 

 A secondary purpose is to carry the calculations 

 to a limit beyond which they would probably 

 never go in practice. 



From the 2 per cent curve of Fig. 61. J it 

 appears that at critical-speed ratios V^/'Vgh 

 below 0.4, in the region AB, only the square-draft 

 to water-depth ratio -VAx/h influences the speed 

 reduction. At the liigher critical-speed ratios, 

 but at values of \/^A^/h below about 0.1, in the 

 region DE, only the critical-speed ratio F„/ 'vgh 

 affects the speed reduction. At greater values of 

 both ratios, in the region BCD, both have an 

 effect in diminishing the speed. 



Example 61.11 1. To show how this family of graphs is 

 used, take the case of the ABC ship designed in Part 4, 

 for which Ax is 1,815 ft^ and VH- is 42.6 ft. The limiting 

 depth at which the ship can run slowly, with a reduction 

 of only 1 per cent in speed, is found from the value of 



VAi/h at M on Fig. 61. J, namely 0.393. The limiting 

 depth h is therefore h = \/I^/0.393 = 42.6/0.393 = 

 108.4 ft. For this depth the critical-speed ratio can not 

 exceed 0.4, represented by the point N. The limiting ship 

 speed F„ = O.iVgh = 0.4 [32.174(108.4)]''-'^ = 23.62 

 ft per sec, equivalent to 13.98 kt. Water deeper than 108.4 

 ft must therefore be found in order to run a valid sea 

 trial at 20.5 kt. 



Assume that a region having a depth h of 175 ft is 

 tentatively selected. The square-draft to water-depth 

 ratio is then 42.6/175 = 0.243 an d the critical-speed ratio 

 is [(20.5)(1.6889)l/\/32.174(175) = 0.461. Entering Fig. 

 61. J with these values a point is found (marked by the 

 distinctive circle) at which the predicted speed reduction 

 is only about 0.3 per cent. This is well within the 1 per 

 cent limit. The 175-ft depth is therefore adequate. 



61.11 Cases 2a and 2b: To Find the Limiting 

 Depth for a 2 Per Cent Increase in Resistance. 



Turning to Cases 2a and 2b of the second class of 

 Sec. 61.6, involving a determination of the limiting 

 depth of unrestricted shallow water in which the 

 resistance for a given speed is increased by say 

 2 per cent, or at which the speed for a given 

 resistance is diminished by say 1 per cent, a 

 simplified and approximate procedure is again 

 justified. Water depths in navigable waters are 



