:n 



HYDRODYNAMICS IN SHIP DFSICN 



Sec. 52.5 



tli:iRrain.s in Figs. lO.C;, 10..I, uiul 10. K of C'liap. 

 10 of \olume I. 



W. P. A. van I^mmorcn, L. Troost, ami J. G. 

 Koniiig discuss the features and effects of wave 

 interference along somewhat difTerent lines [RPSS, 

 1918, pp. 54-')ol. 



52.5 Estimate of Bow-Wave and Stem-Wave 

 Heights and Positions. Prediction of the surface- 

 wave profile, outlined in Sec. 52. (i, recjuires in 

 particular an estimate of the heights and positions 

 of the bow-wave and stern-wave crests. There is 

 an appreciat>le space lag in the bow-wave crest 

 position al)aft the stem, described in Sec. 10.15 

 on page ISO of Volume I, especially if the speed 

 is high. This lag is particularly noticeable in 

 Fig. 52.B of Sec. 52.2 and in Figs. 52.1 and 52.J 

 of Sec. 52.6. 



J. Scott Russell, in Plate 1 18 of MSXA, 18G5, 

 Vol. II, Fig. 31, shows a ves.sol being driven so 

 fast that the bow-wave crest lags back to a 

 point abreast midships. He explains this feature in 

 Vol. I of the reference, page G3G. A situation 

 almost exactly similar is reproduced in the familiar 

 photograph of Parsons' Turbinia at full speed 

 (SNAME, HT, 1943, p. 439]. 



An empirical formula for estimating "good 

 average values" of the height of the bow-wave 

 crest is given by J. L. Kent [NECI, 1949-1950, 

 Vol. 66, p. 435]. This is in the dimensional 

 form h = k{B/LE)V', where h, B, and Lg are in 

 ft, V is in kt, and Jc = 0.083. It resembles a formula 

 given by Laubcuf many years ago [ATMA, 1897, 

 p. 211]. 



Kent's /:-value is for "ordinary merchant 

 ships," derived from wave jjrofiles observed when 

 towing a number of ship models at the XPL, 

 Teddington. Presumably it appHes to ships with- 

 out bulb bows. Furtiiermore, it takes no account 

 of angle of entrance at the stem, hollowness or 

 fullness in the entrance wnterlines, flare of bow 

 sectioiKS, rake of the stem profile, or of any other 

 feature which might reduce or augment the 

 bow-wave crest height. Preliminary plots indicate 

 that the value of /; varies rather widelj', from tlie 

 order of 0.015 to 0.13 or more. 



Transformed into a dimensionally consistent 

 equality for any units of measurement, Kent's 

 formula becomes, for the height h of the bow- 

 wave creat above the at-rest WL: 



For the range of fcjrni of displacenicnl-lyije 



ships, />-,r for the 0-dinil Eq. (52. i), as indicated 

 by the wave profiles ob.servcd on tiieir models, 

 varies from 0.3 to nearly 3.0, indicate*! graphically 

 in Fig. 52. F. This extreme variation is undoubtedly 



40 

 3. 

 32 

 26 

 5 2" 



I 



5 08 



6r 



azo 



ojso ^ 



ZHflST 





D«st. Tender *v 



\\, Seoplane lender 



^"-L— n_ ''""feS^^I 



Cruiser 



t,-vm: 



DeslroYer 



0.6 0.6 



1.0 1.2 



1.4 



16 



^ 



i.a 20 



Fig. 52.F Graph for Estimati.n'o Bow-Wave Crest 



Height 

 The spot .ipplying to each vessel is ealeulutcti for the 

 designed speed of tiiat vessel 



due to the fact that the ratio Bx/Le does not take 

 adequate account of the WL slopes at and just 

 abaft the stem. A large waterline slope not only 

 produces a high value of pressure coefficient close 

 behind the stem, but the large slope throws the 

 projection of the crest on the centerplane farther 

 forward, toward the stem. 



The models on which pressure distributions 

 were observed by E. F. Eggert, EMH 2861 and 

 3383 [SNAINIE, 1935, pp. 129-150; 1939, pp. 

 303-330], sliow bow-wave crests considerably 

 higher than those given by either formula, in the 

 T, range of 0.76 through 1.2. On the other hand, 

 the bow-wave crest heights measureil on two 

 narrow models by W. C. S. Wigley, in the same 

 speed range, are lower than the fonnida values 

 [NECI, 1930-1931, Vol. 47, pp. 153-196; INA, 

 1935, Fig. 6, PI. XXVI]. It is po.s.sil)le that on 

 some towed models it is difficult to tell where the 

 wave profile ends and the spray root begins; also 

 that factors additional to those in the formulas 

 affect this phenomenon. For either or both of these 

 regions E(|. (52. i) and the Air-curvc of Fig. 52. F 

 arc consiiiercd lus preliminary only. 



The estimated bow-wave crest height for the 

 ABC ship of Part 4 at 20.5 kt (34.62 ft per sec), 

 using a h,r of 1.385 from Fig. 52.F and employing 

 Eq. (52.i), is 



, , (l^A ^" , oor 73(l,198.r>) _- ,-f, 

 '' - '"\J 2y = ' ••^^•'(■2ii2T5J647rrs ' ' ' f' " 



