Sec. 52 J 



FLOW PATTERNS AROUND SHIPS 



245 



It appears proper that this height be measured 

 from the undisturbed water level rather than 

 from the at-rest WL of the ship, as might be 

 painted on its hull, because of the drop (or rise) 

 of the bow due to the combined effects of the 

 Bernoulli contour system and the Velox wave 

 system at the ship speed in question. Adding to 

 the calculated h the value of this drop for the 

 ABC ship, —2.35 ft, as measured during the 

 model resistance test, and allowing for the lag 

 in the bow-wave crest, to be determined presently, 

 gives a value of 9.47 ft for the bow-wave crest 

 height, measured above the 26-ft DWL. The full 

 details of this calculation are given in Sec. 66.28. 



Based upon observations of EMB model 2861 

 E. F. Eggert evolved a rule for estimating the 

 bow-wave crest lag, defined as the fore-and-aft 

 distance of that crest abaft the intersection of the 

 stem and the at-rest WL, when projected on the 

 centerplane [EMB Rep. 392, Nov 1934, p. 1]. 

 The +Ap peak may not always lie exactly at the 

 intersection just mentioned, but it is near enough 

 for all practical purposes. Eggert's formula, in 

 dimensional form, says that the crest lies at a 

 distance x = 0.033 F^ abaft this intersection, 

 where the x-distance is in ft and V is in kt. In 

 0-diml form this becomes, for the distance abaft 

 the stem at the WL at rest. 



7' 

 X = 0.372 — 



This equation is plotted in Fig. 52. G to give 

 values of the crest lag x in fractions of the water- 

 line length L ^l , on a basis of both Taylor quotient 



Crest Lag- 



-n-V^ 





0.6 0.8 1.0 I.Z 1.4 1.6 1.6 2.0 



Fig. 52. G Graph for Estimating Bow-Wave Crest 

 Lag Abaft Stem 



T„ and Froude number /*"„ . For the ABC ship at 

 20.5 kt, or 34.62 ft per sec, this crest lag works 

 out as 0.372(34.62)732.174 = 13.86 ft. From 

 Fig. 52. G the value of the crest lag for a T„ of 

 0.908 is 0.0272L„.z, . The value observed on TMB 

 model 4505 of the ABC ship and indicated on 

 Fig. 66. R, where the crest occurs at about Sta. 

 0.7, is 17.85 ftor0.035L;pi . 



Model data for a variety of ship forms, from 

 which the graph of Fig. 52. G was derived, show 

 rather wide variations from the value predicted 

 by Eq. (52. ii) in some cases and exact agreement 

 in others. Thus this equation and the broken-line 

 curve of Fig. 52. G are both to be considered as 

 preliminary. 



S. A. Harvald, in his "Wake of Merchant 

 Ships" [Danish Tech. Press, 1950, pp. 81-84], 

 gives a diagram by which the stem-wave height 

 may be estimated, as a means of predicting the 

 amount of wave wake in any particular case. 

 Fig. 52. H, adapted from Harvald's Fig. 41 on 



0.05 



0.04 L \\^ \^ 



(52.ii) s\^ 



? - 



= \\ 



0.03 



o — 



0.02- 



0.01 



^ \\\ \ \ 

 \\ \ \ 



\\\ 



W \ s \ 

 \\\ W 





L 



h = Stern-Wave Crest Height 

 Ly/ "= Lenqth of Tro- 

 choidal Wave of 



Velocitv^ V — 



\ \\ 



\ \ \> 

 .\ \ \ 



\ 



N^O.14 \Q.I6 \ 



0.1 z a 



-r- V 



\0.20 

 \ 



0.5 

 Fig. 52.H 



0.7 



0.9 



1.3 



Graphs for Estimating Stern-Wave 

 Crest Height 



page 83 of the reference cited, indicates the 

 parameters employed, B/L, h/Lw , and T, . Har- 

 vald admits that a number of apparently import- 

 ant factors are not taken account of in his diagram 

 but, like the other diagrams of this section, it 

 will serve until something better is developed. 



For the ABC ship, or one of its proportions, 

 B = 73 ft and L = 510 ft, whence B/L = 0.143. 

 At a Tj of 0.908, Harvald's diagram gives a value 



