438 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 62.7 



McGoldrick on pages 199 and 200 of SNAME, 

 1949. Subsequent experience has indicated a single 

 average value of 25 per cent increase in / due to 

 added-liquid mass for the pure torsional mode of 

 motion [Garibaldi, R. J., "Procedure for Torsional 

 Vibration Analysis of Multimass Systems," 

 BuShips, Navy Dept., Unclassified Res. and 

 Dev. Rep. 371-V-19, 15 Dec 1953, p. 6]. 



For the axial mode of vibration the situation is 

 rather complicated, since the blade sections 

 usually lie at rather large angles to each direction 

 of motion, forward and aft, and the blade width 

 is a major factor. Kane and McGoldrick explain 

 it in most readable terms on pages 199 and 200 

 of their paper "Longitudinal Vibration of Marine 

 Propulsion Shafting Systems" [SNAME, 1949]. 

 For axial vibration they recommend that, as an 

 approximate estimate, the added Uquid mass m^ 

 be taken as 40 to 60 per cent of the propeller 

 mass mprop • Further experience on their part 

 indicates a single value of 60 per cent. In other 

 quarters, a value of 50 per cent "is normally used" 

 [E. F. Noonan, BuShips, Navy Dept., unpubl. 

 memo to HES of 15 Jun 1956]. 



Kane and McGoldrick also give a dimensional 

 equation having a semianalytic basis, of the 

 following form: 



wii for the axial mode of motion, in lb, 

 1 



0.23(^ at 0.6772Ma«) + 1 J 



= k 



•(Z)(0.010D in inches)'! ^1 (62.vi) 



where k has an empirical value of about 9,100. 



This formula is converted to 0-diml form by 

 inserting the weight density w of the water in 

 which the propeller is working. Incorporating the 

 constant k = 9,100, and eliminating the units of 

 measurement for the diameter D, the 0-diml 

 equation then becomes 



rrij, for the axial mode of motion 

 = 0.245«; F^ 



0.231^^ at 0.67/?^.,J + Ij (62.vii) 



■iZ){D)f-^ 



For the ABC transom-stern ship of Part 4, 

 having a final design of propdler shown in Fig, 



70.O, the P/D ratio at 0.67/2 m.x is 1.199, Z = 4, 

 D = 20 ft, and the mean-width ratio Cm/D = 

 0.229. Then for salt water having a weight density 

 w of 64.0 lb per ft^, the added mass m^ for the 

 axial mode is, by substitution in Eq. (62.vii), 



mr. = 0.245(64.0) 



1 



[0.23(1.199)' + 1] ' 



•(4)(20.0)'(0.229)' 



= 19,790 lb. 



The estimated weight of this propeller in man- 

 ganese bronze is 40,750 lb, which gives an 

 mi/mprop ratio of only 48.6 per cent. 



For the lateral mode of vibration, depicted in 

 diagram 3 of Fig. 62.M, no analytic solution or 

 test data appear to be available in published form. 

 A percentage increase of 10 in the propeller mass 

 is recommended by R. T. McGoldrick (Conf. of 

 7 Jun 1956). 



For the diametral mode of motion, diagrammed 

 at 4 in Fig. 62. M, McGoldrick recommends a 

 percentage increase of 50 in the mass moment 

 of inertia, in air, of the propeller for the same 

 mode of motion about the same axis, due to the 

 moment of the added mass of the entrained water. 



62.7 Added-Mass Data for Water Surround- 

 ing Ship Skegs and Appendages. Fins, deep 

 keels, fixed stabilizers, and thin skegs of moderate 

 to large area are subject to lateral vibration when 

 excited by mechanical or hydrodynamic forces. 

 The frequency of resonant vibration must be 

 clear of any exciting-force frequency, especially 

 for a periodic force of large magnitude, if magnifi- 

 cation of the resonant vibration is to be avoided. 

 The graphs in EMB Report R-22 of April 1940, 

 describing full-scale vibration tests of one of the 

 twin skegs of the battleship Washington (BB55), 

 illustrate the mode of vibration and the resonance 

 variations with frequency for a ship structure of 

 this kind. 



When a large, thin, vibrating appendage with 

 moderately sharp edges is surrounded by water, 

 the kinetic energy in the velocity field is high. 

 This means a large added mass of entrained liquid. 

 Indeed, the added-mass coefficient Cam may easily 

 reach 2, 3, or 4. For a thin-plate structure like a 

 sailing-yacht centerboard, it may exceed 6 or 8. 

 Not only must the magnitude of this mass be 

 known to predict the resonant frequency when 

 in water, but the frequency is often drastically 

 lowered, so that it lies in an undesirable position, 

 within the range of exciting-force frequencies. 



