Sec. 62.S 



ESTIMATE OF ADDED LIQUID MASS 



441 



"Vibnition of Ships," some of which apply to the 

 present chapter. 



(33) Home, L. R., "Stopping of Ships," NECI, 1944-1945, 



Vol. 61, p. 3Uff 



(34) Havelock, T. H., "Notes on the Theory of Heaving 



and Pitching," INA, 1945, Vol. 87, pp. 109-122, 

 esp. pp. 109-110 discussing the added mass of 

 entrained water for ship forms. For heaving, 

 Havelock gives a Cam of 0.8 to 1.0; for pitching 

 he gives 0.4 to 0.5. 



(35) Lamb, Sir Horace, "Hydrodynamics," 1945, 6th ed. 



The table of contents and the index, between 

 them, list the following pages, among others, for 

 data on added- and virtual-mass coefficients, as 

 well as for data on the body masses themselves: 



Inertia coefficients, of a circular cylinder, 77 

 circular disc, 137 

 of an elliptic cylinder, 85, 88 

 of a sphere, 124 

 of two spheres, 130 

 of an ellipsoid, 153, 155 

 general, 166 

 in cases of symmetry, 172. 



(36) Prohaska, C. W., "Vibrations Verticales du Navire 



(Vertical Vibrations of a Ship)," ATMA, 1947, 

 Vol. 46, pp. 171-219. Discussion of the added mass 

 of the entrained water is found on pp. 189-205. 

 On pages 214 and 215 there is a list of 21 references. 

 Abstracted in English in SBMEB, Oct 1947, 

 pp. 542-546 and Nov 1947, pp. 593-599. Complete 

 English translation, as yet unpublished (1956), at 

 the David Taylor Model Basin. 



(37) Todd, F. H., "The Fundamentals of Ship Vibration," 



SBMEB, May, Jun, Jul, 1947, Vol. 54, pp. 307-312, 

 358-362, 400-403, respectively 



(38) Todd, F. H., and Marwood, W. J., "Ship Vibration," 



NECI, 1947-1948, Vol. 64, pp. 193-210, D113-D128 



(39) John, F., "On the Motion of Floating Bodies," Com- 



munications on Pure and Applied Mathematics, 

 Mar 1949, Vol. II, No. 1 



(40) Ursell, F., "On the Heaving Motion of a Circular 



Cylinder on the Surface of a Fluid;" Quart. Jour. 

 Mech. and Appl. Math., Jun 1949, Vol. II, Part 2 



(41) Kane, J. R., and McGoldrick, R. T., "Londitudinal 



Vibrations of Marine Propulsion-Shafting Sys- 

 tems," SNAME, 1949, pp. 193-252, esp. pp. 

 199-200 



(42) May, A., and Woodhull, J. C, "The Virtual Mass of a 



Sphere Entering Water Vertically," NOL memo 

 10636, 3 Mar 1950; ONR project NR-062-024; 

 copy in BuShips, Navy Dept., library. See also 

 Nat'l. Res. Council, U. S., Bull. 84, 1932, p. 97. 



(43) Wendel, K., "Hydrodynamische Massen und Hydro- 



dynamische Massentraglieitsmomente (Hydrody- 

 namic Masses and Hydrodynamic Mass Moments 

 of Inertia of Entrained Water)," STG, 1950, Vol. 

 44, pp. 207-255. English version in TMB Transl. 

 260, Jul 1956. A bibliography of 27 items appears 

 on p. 252 of the original; pp. 73-74 of the transla- 

 tion. 



(44) Weinblum, G., and St. Denis, M., "On the Motions 



of Ships at Sea," SNAME, 1950, pp. 184-248, esp. 

 pp. 189-192 on Inertia Forces and Free-Surface 

 Effects 



(45) McGoldrick, R. T., "Determination of Hull Critical 



Frequencies on the Ore Carrier S. S. E. J. Kulas 

 by Means of a Vibration Generator," TMB Rep. 

 762, Jun 1951. In an appendix to this report, pp. 

 18-19, E. H. Kennard describes a method for 

 estimating the added mass of entrained water 

 around a ship for any mode of vertical vibration. 



(46) Wendel, K., and Boie, C, "Experimentelle 



Bestimmung der Hydrodynamischen Masse an 

 ganz und Teilweise getauchten Korpern (Experi- 

 mental Determination of Hydrodynamic Masses 

 on Totally and Partly Immersed Bodies)," Hansa, 

 8 Dec 1951, Vol. 88, pp. 1788-1790 



(47) Weinblum, G., "Uber Hydrodynamische Massen (On 



Hydrodynamic Masses)," Schiff und Hafen, Dec 

 1951, pp. 422-427 (in German) 



(48) Weinblum, G. P., "On Hydrodynamic Masses," TMB 



Rep. 809, Apr 1952 



(49) Havelock, Sir Thomas H., "Ship Vibrations: The 



Virtual Inertia of a Spheroid in Shallow Water," 

 INA, 1953, Vol. 95, pp. 1-9. On page 7 there is a 

 list of 7 references. 



(50) Marwood, W. J., and Johnson, A. J., "Vibration 



Tests of an Up-River Collier with Special Reference 

 to the Influence of Depth of Water," NECI, 

 1953-1954, Vol. 70, pp. 193-216 



(51) McGoldrick, R. T., Gleyzal, A. N., Hess, R. L., and 



Hess, G. K., Jr., "Recent Developments in the 

 Theory of Ship Vibration," TMB Rep. 739, Oct 

 1953, esp. pp. 13-15 



(52) Grim, O., "Calculation of Hydrodynamic Forces 



Caused by Oscillation of Ship Hulls," STG, 1953, 

 Vol. 47, pp. 277-299 (in German) 



(53) McGoldrick, R. T., "Comparison Between Theo- 



retically and Experimentally Determined Natural 

 Frequencies and Modes of Vibration of Ships," 

 TMB Rep. 906, Aug 1954, esp. pp. 9, 14 



(54) Havelock, Sir Thomas H., "Waves Due to a Floating 



Sphere Making Periodic Heaving Oscillations," 

 Proc. Roy. Soc, Series A, Jul 1955, Vol. 231, pp. 

 1-7; see Appl. Mech. Rev., Feb 1956, No. 504, 

 pp. 74-75. 



