Sec. 52. 4 



FLOW PATTERNS AROUND SHIPS 



243 



wave profiles as determined from tests of four 

 models of ships having waterline lengths L of 

 from 459.3 ft to 448.2 ft [ATMA, 1948, p. 490]. 

 The ordinates are in meters for the full-scale ships 

 and the abscissas in 0-diml length ratios x/L, 

 with Sta. at the AP and Sta. 20 at the FP. 

 The profiles in diagram a of Fig. 8 on page 490 

 of the reference are plotted with respect to the 

 undisturbed water surface at infinity. Those in 

 diagram b are plotted with respect to the at-rest 

 ship waterplane, so that they differ by the amounts 

 of the sinkage at each station. The T^ values for 

 these plots range from 0.747 for the short ship to 

 0.756 for the long ship; corresponding F„ values 

 are 0.222 and 0.225. 



Wave profiles are shown for the ten tanker 

 models reported upon by R. B. Couch and M. 

 St. Denis [SNAME, 1948, Figs. 2(a)-10(a), pp. 

 360-378]. A single wave profile is reproduced by 

 W. P. A. van Lammeren in RPSS, 1948, Fig, 38, 

 on page 88, for a T, of 0.64, without the body 

 plan of the ship in question. 



Six sets of wave profiles for two self-propelled 

 models, showing the changes in profile over a 

 wide range of speed, are given by S. A. Harvald 

 in SSPA Report 13, published in 1949, entitled 

 "Medstr0mskoefficientens Afhaengighed af Ror- 

 form, Trim og Haekb0lge (The Dependence of 

 Wake Fraction on Shape of Rudder, Trim, and 

 Stern Wave)." The profiles appear on pages 13, 

 14, 34, 35, 36, and 40. On the last-named page 

 there is a set of profiles for the model running 

 astern. On pages 56-60 there is a summary in 

 English. 



Wave profiles at three speeds for seventeen 

 models of coasters are given by A. 0. Warholm in 

 SSPA Report 24, published in 1953, entitled 

 "Nagra Systematiska Forsok med Modeller av 

 Mindre Kustfartyg (Systematic Tests with Models 

 of Coasters)." The profiles, apparently taken 

 during resistance (and not self-propelled) tests, 

 are printed on pages 85-90. On pages 48-50 there 

 is a summary in English. 



Provision is made, on SNAME RD sheets 

 having numbers in excess of 100, to depict the 

 wave profiles at designed speed in either or both 

 of two locations. Examples of these are sheets 

 114, 115, and 144. 



52.4 General Rules for Wave Interference 

 Alongside a Ship. For a ship form having abrupt 

 and localized changes in waterline curvature, 

 resulting in what may be considered as point- 

 pressure disturbances, it is possible to appro.xi- 



mate analytically the resultant wave profile, 

 taking account of wave-interference effects. Fig. 

 lO.F in Volume I, adapted from W. C. S. Wigley, 

 does this for a 2-diml ship having a parallel 

 middlebody and triangular ends. Many barges 

 have nearly square-cornered rectangular water- 

 lines but on most ships the pressure disturbances 

 are regions rather than points. This renders it 

 extremely difficult to predict the shape and fore- 

 and-aft position of the wave form generated by 

 each such disturbance. 



Several further complications in working out 

 wave interferences and their effects along the 

 waterline of a ship of normal form are: 



(1) Lack of information as to the variation of 

 level along the ship of the crests and trough of 

 the Bernoulli contour system, described in Sec. 

 10.3. This is undoubtedly a function of the^ 

 surface-waterline shape and it may also be a 

 function of the section-area curve. 



(2) Lack of a precise determination of the effect 

 of the presence of the ship entrance abaft a point- 

 pressure disturbance such as a stem 



(3) Inadequate knowledge as to the effect of 

 variations in the waterline slopes in such an 

 entrance, discussed briefly in Sec. 10.6 on page 

 174 of Volume I and in Sec. 48.2 



(4) Uncertainty as to the amount of crest lag 

 (and trough lag) in the Velox wave systems 

 generated by pressure disturbances abaft the bow 



(5) Uncertainty as to the factors determining 

 the fore-and-aft position .and shape of a stern- 

 wave crest on an actual ship, in the presence of a 

 separation zone, of boundary layers, and of water 

 coming up from under the ship 



(6) Lack of knowledge as to the lengths of actual 

 (or trochoidal) waves for a given celerity, when 

 occurring abreast a ship instead of in the open, 

 unobstructed sea. 



In the absence of these data it is difficult to 

 set down specific rules for wave interferences and 

 their effects alongside a moving ship. If the 

 individual profiles could be determined and 

 positioned longitudinally, there is every reason 

 to believe that in most cases the interference 

 effects could be determined by simple super- 

 position of the heights of the transverse waves in 

 each system at any selected station. 



K. S. M. Davidson gives a few diagrams [PNA, 

 1939, Vol. II, pp. 66-67] in which this superposi- 

 tion is indicated, in addition to the schematic 



