Sec. 62.3 



ESTIMATE OF ADDED LIQUID MASS 



427 



more closely, its numerous length segments, 

 separated by adjacent vertical planes, could each 

 be made semielliptic in transverse shape. They 

 could be given proportions corresponding to the 

 ratio [(beam)/(section draft)] of the several 

 sections along the length of the ship in question. 

 The sections forward, for example, could have 

 their major axes vertical; those amidships could 

 have them horizontal. This modification, how- 

 ever, would not assist in the solution being sought 

 since the added-liquid mass around any 2-diml 

 elliptic shape having a unit length and a major 

 axis of length 2a, for unsteady motion normal to 

 that axis, is irpa", the same as for a circle of 

 radius a or diameter 2a. This relationship is 

 indicated in the several elliptic sections of Fig. 

 62.F. The added mass of the liquid surrounding 



KBeam B-2a-»1 



Neqleclino Surface Effects, 

 the Added-Liquid Mass is, 

 in Each Case, m|_- (0.5)Trpa^ 

 - (QI25)tt/3E ' 



Fig. 62.F Series op Elliptic Body Sections, All 

 Having the Same Added Liquid Mass Per Unit Length 



an elliptic section in an ideal fluid is a function 

 of one variable only, namely the square of the 

 beam, reckoned at right angles to the direct- 

 tion of motion. For a section of unit length and 

 beam Bx , either semicircular or semielliptic in 

 shape, the added mass mi is (0.5)p(7r/4)B| or 

 0.125p7rB| . 



It would be an advantage, if it could be done, 

 to modify the shape of the horizontal plane 

 through the major axis of the geometric body so 

 that it would have the same beam, at given 

 0-diml proportions of its length from the nose, 

 as does the designed waterline of the ship. 

 However, this again is not a satisfactory procedure 

 because to determine the longitudinal reduction 

 factor for such a body, non-ellipsoidal in shape, 

 and usually with fore-and-aft asymmetry, would 

 require a determination of the added mass by a 

 lengthy and laborious procedure corresponding 

 to that employed by L. Landweber and A. Winzer, 

 and described in the latter part of Sec. 62.2. 



F. M. Lewis worked out a clever alternative 

 scheme whereby the added mass of an underwater 

 ship hull can be approximated by a much simpler 

 and more straightforward procedure. For this 



method, the representative body is composed of 

 a series of constant-section, vertical segments, 

 say about 20 in number, separated by vertical 

 planes representing the equally spaced stations 

 set up when making the lines drawing of the ship 

 for which the added-mass data are desired. Each 

 constant-section segment has the correct designed- 

 waterline beam B at its appropriate station, at 

 midlength of the segment. However, instead of 

 using elliptic section shapes, Lewis found that by 

 employing conformal transformation, described 

 briefly in Sec. 41.11, he could obtain the added- 

 liquid-mass values for transverse section shapes 

 which resembled closely those found on ships, 

 including rectangles with square corners and 

 V-shapes with sharp keels. Diagrams showing 

 these shapes were published by Lewis in Plates 

 2 and 3 of his SNAME, 1929 paper and were 

 reproduced by K. Wendel in Fig. 10 of his STG, 

 1950 paper; they also appear on pages 21 and 23 

 of TMB Translation 260, July 1956, and in 

 Figs. 186(a) through 186(g) and Fig. 187, on 

 page 320 of the book "The Design of Merchant 

 Ships," by J. C. A. Schokker, E. M. Neuerburg, 

 and E. J. Vossnack [H. Stam, Haarlem, 1953]. 



To make these section shapes more adaptable 

 for comparison with transverse sections on ships, 

 Lewis employed eight separate proportions for 

 the circumscribing rectangles bounding them. 

 These proportions, symboHzed by H in his paper 

 and represented actually by the ratio [(half- 

 beam) /(section draft)], for one side only of a 

 symmetrical ship, varied from 0.2 to 2.0. In the 

 referenced paper by Wendel and in TMB Trans- 

 lation 260 the eight circumscribing rectangles 

 have a half-beam of a and a section draft of 6. 



It is most important to remember, in this 

 connection, that the section draft corresponds to 

 the ship draft (vertical distance between DWL 

 and baseline) only if the section in question 

 extends all the way to the baseplane; otherwise 

 it is the vertical distance from the DWL to the 

 bottom of the section in question. For a transom- 

 stern section, this section draft may be only 0.1 

 the ship draft. The referenced pubUcations are 

 unfortunately not specific on this point but the 

 principal features are shown in diagram 4 of 

 Fig.'62.G. 



Instead of tabulating the added-liquid masses 

 for these 2-diml section segments of unit length, 

 Lewis set up a relationship in which they were 

 referred to halj of the added-liquid mass for a 

 segment having a circular section of radius a 



