136 



HYDRODVNAMIQS I\ SHIP DESIGN 



Sec. 46.3 



J_ 



Borge Form with Wide Beom 



T 



Buttock Slope Ig T 

 Hy 1^ " — ^,__^_ 14 de<) or lets 



I than 3 ft for ig Limit Given 



Hy left& than "^^ <:r Buttock Slope Lg 



I 5 ft for tg Limit Giv»n^^ ^^ I Zt6*a or leas p 



Fio. 46.C Typical Separ-^tion Criteria for Buttocks 



Stern of diagram 2 of Fig. 46. C, the separation-free 

 buttock or profile slope near the surface niaj' be as 

 great as 25 deg with the liorizontal. However, 

 separation may normally be expected bej'ond the 

 range of 22 to 25 deg, assuming a full-scale depth 

 not more than 5 or G ft below the wavehne. 



A special case is presented by the immersed- 

 transom stern described and illustrated in Sec. 

 25.14 of Volume I, where separation is known to 

 e.xist in the region abaft the transom. The quanti- 

 tative information usually desired is the speed at 

 which the transom will clear in service; in other 

 words, the speed at which the transom surface 

 is entirely free of water contact. This depends 

 upon a number of factors, not yet evaliiated in 

 adequate fashion: 



(a) The transom corner angle, illustrated and 

 defined in Fig. 25.1 on page 379 of Volume I and 

 in Fig. 4G.Ii. The sharp corners define the trans- 

 verse extent of the stern separation zone, regard- 

 less of the speed at which the craft is running. 



(b) The transom edge angle, at the lower edge 

 of the tran.som. This is a measure of the dis- 

 continuity in a buttock line in the vertical plane. 

 As illustrated in Fig. 25.1, the edge angle defines 

 the lower edge of the separation zone if it has a 

 value of about IGO deg or less, if the lower edge 

 ia not rounded, and if the buttock slope ahead 

 of the transom is not too large. 



(c) The submergence llu of the deepest portion 

 of the transom. By one line of reasoning this 

 should be reckoned below the waveline at the 

 outer transom corners, but for wide transoms, 

 where Bu = 0.5/i or more, the pressures and flow 

 conditions are certainly not the same all the way 

 acroHS the stern. For design purpo.scs it is almost 

 necessary to u.se //„ , the nmximuin immersion 

 belrjw the at-rcst \VL. 



(d) The slope of the flowlines, with reference to 

 the horizontal, for a considerable distance below 

 the lower edge of the transom, say at least 1.0 

 and possibly 2.0 times the transom immersion Hv ■ 

 If the buttock slopes are nearlj' constant for a 

 considerable portion of the length, say 0.3L, 

 ahead of the transom, it may be assumed that 

 tlie flowline slojie equals the buttock slope. If 

 this is not the case, as on the transom-stern ABC 

 ship hull of Part 4, the actual flowline slopes at 

 the transom edge may be appreciably larger than 

 the buttock slopes. 



Further information as to the application of 

 these criteria to a transom-stern design are 

 included in Sec. 67.20. 



Notwithstanding the long and extensive use of 

 tunnel sterns for shallow-water craft, and the 

 fitting of twin skegs with tunnels between them 

 on large vessels, there is little systematic quanti- 

 tative information about the tunnel-roof slopes 

 at which separation would occur under the 

 conditions represented by the.se various designs. 

 Sees. 67.16 and 67.17 describe the design of the 

 tunnel roof for the alternative arch-type stern 

 of the ABC ship of Part 4, and Fig. 78. F reveals 

 that, at a nominal submergence of about 12 ft 

 in the steepest region, there was no separation 

 for a maximum tunnel-roof slope of about 18.5 deg. 



In those tunnel-stern craft having tuiuiel roofs 

 above the at-rest WL, the nominal submergence 

 and the hydrostatic pressure at the top are 

 negative. Only rarely do tunnel-roof slopes 

 exceed 20 deg, at or near the at-rest WL, but it is 

 doubtful that the critical slope for separation is 

 as large as this. So far as known, at the time of 

 writing (1955), very few craft of this type have 

 been tested in model scale in a circulating-water 

 channel. 



It is realized that the slopes mentioned in the 

 preceding paragraphs are not always tiiken along 

 lines or surfaces of constant pressure, as was 

 pointed out at the beginning of this section. 

 However, no better method of defining po.ssible 

 separation zones ajjpears to be available at this 

 time. 



46.3 Detection of Separation; Extent of the 

 Zone. In smooth water and at close range, such 

 as abaft the square stern of a punt or skiiT, 

 .separation can be "spotted" with a little practice 

 l)y noting the vertical-axis vortexes or whirls at 

 ami near the surface. At longer range, and on 

 larger craft, the .scparalion zone is made clearly 



