432 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 62.4 



expect a ship with a soft-rubber hull boundary 

 to set up only trifling amounts of kinetic flow in 

 the surrounding water. The added mass of en- 

 trained liquid would then be extremely small. 

 (3) It has been assumed by many analysts and 

 experimenters that the added-liquid mass in 

 vertical vibration for typical ship sections was 

 independent of both frequency and amplitude 

 for the lower modes of vibration, with two and 

 three nodes. Nevertheless, the model experiments 

 of H. Holstein, described in reference (25) of 

 Sec. 62.8, indicate a large variation in shape 

 factor ^Tsect when the frequency and amplitude 

 are varied, even in a range of frequency encoun- 

 tered on ships. Graphs indicating these variations, 

 and the discrepancy with theory for a ship section 

 approximately rectangular, are included in Fig. 

 32 of the Wendel reference [STG, 1950; TMB 

 Transl. 260, p. 44]. 



Rather than to work out the problem of pre- 

 dicting the added mass of entrained water around 

 the hull of the ABC ship of Part 4 in 2-noded 

 vertical vibration as an example of the method 

 described in this section, there is given hereunder 

 a summary of the steps, with brief comments for 

 each step: 



I. The ship is divided into 21 length segments, 

 19 of them having a full station length of 510/20 = 

 25.5 ft, and the two end segments having a half- 

 length of 25.5/2 = 12.75 ft. The fore-and-aft 

 centers of all but the two end segments fall on 

 the station locations, 1 through 19. For all the 

 21 sections, through 20, it is assumed that the 

 section shape on the body plan is representative 

 of the entire segment length pertaining to that 

 station. 



II. List the whole waterline beams B and the 

 section drafts (not necessarily the ship draft) for 

 the 21 stations. Compute the 21 ratios [(beam B)/ 

 (section draft)]. 



III. Estimate the value of the fullness or section 

 coefficient for each section, by inspection or by 

 some simple method. If there are any concave 

 portions in the section outlines, fill them out 

 by straight tangents before determining the 

 section coefficient. 



IV. Using the graphs of Fig. 62. H, determine the 

 shape factor fcseot for each section. These factors 

 may be checked by entering the half-body dia- 

 grams of F. M. Lewis fSNAME, 1929, Pis. 2, 3; 

 STG, 1950, Fig. 10; TMB Transl. 260, Jul 1956, 

 Fig. 10 on p. 23] with the proper ratio of [(beam 



B)/(section draft)] and selecting by inspection a 

 section shape approximating that for the ship. 

 The shape factor fcgect is then the "coefficient" 

 C of Lewis. The half-body diagrams of C. W. 

 Prohaska may also be used in the same way 

 [ATMA, 1947, Figs. 16, 17, 18 on pp. 191-193; 

 SBMEB, Nov 1947, Fig. 11, p. 593]. Prohaska's 

 "coefficient" C is also the same as kg^^t ■ 



V. Select the proper reduction factor R of J. L. 

 Taylor from the indicated graph of Fig. 62.1, for 

 the L/Bx ratio of the ship. 



VI. Determine the added-liquid weight per unit 

 of ship length for each station by 



mM = (fcsect)(i2)(0.125)7rp(fir)B^ (62.v) 



The shape factor fcsect is usually different for each 

 station but the reduction factor R is the same for 

 all stations. 



VII. Multiply the added-liquid weight per unit 

 length by the length of each of the 21 segments. 

 Apply the weights thus found to the weight 

 curve for the ship, at the proper stations. 



J. C. A. Schokker, E. M. Neuerburg, and E. J. 

 Vossnack give a somewhat-too-brief summary 

 of the available methods for estimating or calcu- 

 lating the added mass of the entrained water for 

 the vertical mode of ship vibration on pages 

 319-321 of their book "The Design of Merchant 

 Ships" [H. Stam, Haarlem, 1953]. On page 340, 

 in Fig. 222, they give a nomogram, apparently 

 first published by C. W. Prohaska [ATMA, 

 1947, Fig. 29, p. 201], for approximating, in 

 vertical vibration, the ratio of (1) the mass of the 

 entrained water to (2) the mass of the ship, 

 taking account of the midship-section coefficient 

 Cm , the beam-draft ratio B/H, the length-beam 

 ratio L/Bx , the ratio of the water depth to 

 draft h/H, and the block coefficient Cb . This 

 ratio is also found by a rather complicated 

 formula in Section 131 on page 326. Neither the 

 nomogram nor the equation suffice, however, for 

 determining the longitudinal distribution of the 

 added mass of the entrained water. These authors 

 fist 32 references on pages 341-342 of their book. 



62.4 The Change of Added Mass Near a 

 Large Boundary. All the comments in the fore- 

 going are based upon the motion of a body or 

 ship at a great distance from any rigid or un- 

 yielding boundary which would interfere with 

 the flow pattern of an ideal liquid. The air-liquid 

 interface or free surface of a body of water 

 represents a boundary which is, in a practical 

 sense, both flexible and yielding. 



