194 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 66.28 



fraction / of 0.20 is 189,000/(1 - 0.20) = 236,500 

 lb. 



The disc area A^ of the 20-ft propeller is 314.16 

 ft'. For an estimated wake fraction w of 0.30, 

 the speed of advance V a is 20.5(1 — 0.3) = 14.35 

 kt or 24.24 ft per sec. The ram-pressure load over 

 the disc area is then (0.5)pAoFi = qAo = 0.9953 

 (314. 16) (24.24)' = 183,725 lb. The thrust-load 

 coefficient Ctl is T/qA„ = 236,500/183,725 = 

 1.287. The corresponding real efficiency, taken as 

 0.877, from Fig. 34.B, is 0.636. This is 770 for the 

 working condition of the propeller. 



The hull efficiency r;„ is (1 — t)/{l — w) = 

 (1 - 0.2)/(l - 0.3) = 0.8/0.7 = 1.143. Assuming 

 a relative rotative efficiency ??« of 1.02, the derived 

 value of vp = Voivif)vR = 0.636(1.143)1.02 = 

 0.7415. This is remarkably close to the value of 

 r]p = 0.74 assumed in Sec. 66.9. 



Until something further is known about the 

 new hull shape and its probable performance, the 

 latest derived power and machinery-weight figures 

 from Sees. 66.9 and 66.10 are allowed to stand, 

 namely 16,930 horses and 1,250 tons. 



66.28 Sketching of Wave Profile and Prob- 

 able Flowlines. The Standard-Series procedure 

 developed by Taylor was an effort to predict, in 

 advance of or without a model test, the probable 

 effective power required to drive the bare hull 

 of a ship of given proportions. This procedure 

 omitted any means of judging the effects of 

 changes in shape for fixed proportions. One 

 method of accomplishing this is an analysis of 

 the flow diagrams around a model of the selected 

 shape. However, to employ this method for 

 predictions, in advance of model tests, it must be 

 possible to draw a lines-of-flow diagram from a 

 rough set of lines, such as those of the ABC 

 design at this stage. 



Unfortunately, neither the method of analysis 

 or the techniques of drawing the lines of flow in 

 advance have been worked out. Nevertheless, 

 the latter is attempted here, on the basis of the 

 principles set forth in the sections preceding, and 

 with the background of the diagrams in Chap. 52. 

 If it is possible only to tell whether or not a form 

 has objectionable features the prediction pro- 

 cedure is well worth while. In any case the 

 experience gained will go far toward working out 

 the unknown methods and techniques. 



The first step is to start with the wave profile 

 because the surface contour along the side affects 

 the flow pattern below it. This effect extends all 



the way to the bilge if the Velox system waves 

 are relatively deep. 



It is observed from Figs. 52.1 and 52..J that 

 the height of the bow-wave crest is a function of 

 the Froude number F„ or the speed-length quotient 

 T^ and of the waterline slope z'e in the entrance. 

 The bow-wave crest height (not necessarily the 

 spray of the boAV roll) becomes noticeable at a 

 To of 0.5, F„ of about 0.15; at this low limit a 

 small or a large waterline slope in the entrance 

 appears not to have too great an effect, one way 

 or the other. 



Using the procedure described in Sec. 52.5, the 

 bow-wave crest height for the ABC ship is 

 calculated as 7.17 ft. This is measured from the 

 plane of the undisturbed water level at a great 

 distance from the ship. To find how far this crest 

 may climb up the side of the ship there must be 

 added the predicted sinkage or change of level 

 of the bow. The graphs of Fig. 58.A give this 

 change of level as -0.0046L or -0.0046(510) = 

 — 2.35 ft. At the stern the change is about 

 -0.00145L, corresponding to -0.00145(510) or 

 about -0.74 ft. 



The predicted lag of the bow-wave crest, 

 worked out in Sec. 52.5, is 13.86 ft. This is at 

 about 0.027L abaft the FP, where the sinkage of 

 the bow, by linear interpolation between —2.35 ft 

 and —0.74 ft, is about 0.05 ft less than at the 

 bow. The bow-wave crest may then be expected 

 to rise up the side by (7.17 -|- 2.35 - 0.05) ft or 

 9.47 ft, indicated in Fig. 66.R. 



It is almost certain that the effect of the bulb 

 bow on the ABC ship is to lower the crest height 

 predicted by the referenced formulas. However, 

 no quantitative data are available, so this 

 lowering is not taken into account. Since a small 

 waterline-entrance slope and a bulb bow generally 

 go hand in hand, it is probable that a substantial 

 reduction in height occurs on vessels having these 

 features. 



When there is any flare whatever in the section 

 lines lying inside a bow-wave crest, the wave 

 profile rises higher on the ship's side than it 

 would have if the section lines had been vertical. 



The bow-wave crest heights as predicted for 

 the ship and as observed on the model are intended 

 to be independent of any thin spray roots extend- 

 ing above the crest line. 



The graphs of Fig. 52. H and the procedure 

 illustrated in Sec. 52.5 produce a predicted stern- 

 wave height for the ABC design of 5.32 ft. This is 

 for a normal form of stern, probably of the canoe 



