HYDRODYNAMIC FORCES 



117 



ship operations is kept in mind. Data on the pitching- 

 oscillation frequencies of several ships will be found in 

 Korvin-Kroukovsky and Jacobs (1957). For the Series 

 60 model of 0.60 block coefficient in head waves of X/L 

 = 1, the parameter o)(B/g)^^- varies from O.U to 1.5 at 

 ship speeds from zero to the maximum expected in 

 smooth water. At synchronism in pitching the param- 

 eter is efjual to 1.25. This narrow range of frerjuency 

 parameters straddles the minimimi of the curve of added 

 mass coefficients in Fig. 6. 



The reader will find it instructive to jjlot the Ursell 

 data for the circular cylinder from Tal)le 2 on Fig. 6, 

 remembering that r = B/2. Both fc^-curves plotted as a 

 function of u{B/g)^^- are similar in form but the curve 

 shown for Golovato's model is seen to be considerably 

 above Ursell's curve. It should be noted that Golo- 

 vato's curve does not asymptotically approadi the F. M. 

 Lewis value l)ut is directed much higher. This raises the 

 question of experimental reliability or jjcrhaps the pres- 

 ence of physical features not accounted for by the theory. 

 Reference to Keulegan and Carpenter (1956) indicates 

 that the added mass may have been increased on the up- 

 stroke of the oscillator by the separation of the water 

 flow. If so, the data would be subject to the degree of 

 model roughness and to a scale effect. 



Gerritsma (1957c, d) tested a Series 60, 0.60 block 

 coefficient model, 8 ft long, by sulijecting it to forced 

 oscillations in heaving and pitching alternately. Fig. 

 7 shows a comparison of measured and calculated virtual 

 masses and virtual moments of inertia; i.e., ship masses 

 plus added water masses. The calculated masses were 

 taken from Korvin-Kroukovsky and Jacobs (1957), and 

 are based on the strip integration of the product of F. M. 

 Lewis' fc2 coefficients and the surface-effect correction 

 coefficient A-4 based on Ursell's data. The discrepancy 

 between measured and calculated data is small, and is in 

 the right direction. In the Series 60 model the after- 

 body ship sections have large inclinations to the water 

 surface, and the surface effect caused by these inclina- 

 tions was not taken into account. A correction for this 

 effect (not known at present, see Section o.l2) can be 

 expected to increase the calculated added masses. 



It is gratifjnng to see that the discrepancies in virtual 

 masses in heaving and in virtual moments of inertia in 

 pitching are similar. This indicates that the three- 

 dimensional effect is not important in added-mass 

 evaluation. 



To summarize the present section: Gerritsma's tests 

 show a satisfactory agreement between added masses as 

 measured and as calculated by the strip theory using the 

 product of Lewis' and Ursell's coefficients, k-tki. The 

 need for an additional correction for the effect of inclined 

 sides is indicated, and a correction for three-dimensional 

 effect may be included in the future. However, the re- 

 sults of the motion analysis of usual ship forms would 

 not be significantly affected by it. Golovato's tests on 

 the idealized ship model show a greater value of the added 

 mass than would be indicated by the method of calcula- 

 tion just described. The failure of the data to approach 



G ^ 



^ 



^ 



IS 



^- 



Calciila+ed Values 

 Measured Values 



J L 



J \ I I L 



20 



^'L/g- 



Fig. 7 Comparison between calculated and measured values of 

 A, B, a, h, for series 60, Cb = 0.60 hull form (from Gerritsma, 



1957^/) 



Lewis' value asymptotically at high frequencies raises 

 suspicion and calls for added investigation. Since only 

 two investigations have been reported, further research 

 is evidently needed.'" 



4 Restained ship forms and other bodies sub- 

 jected to wave action. Three references can be cited 

 in connection with this subject: Keulegan and Car- 

 penter (1956), Rechtin, Steele and Scales (1957), and 

 Korvin-Kroukovsky (1955c, Appendix 2). A .study of 

 the first two, although they are primarily concerned 

 with the forces acting on offshore structures in shallow 

 water, .should be fruitful to a researcher in naval archi- 

 tectural problems. The third reference appears to be 

 the only work concerned directly with the forces acting 

 on ships.'' 



The heaving force, pitching moment, and drag force 

 exerted l:)y wa\'es on a ship model were measured. A 

 Series 60, 0.60 block coefficient model, 5 ft long, was 

 restrained from heaving, pitching and surging by dyna- 

 mometers attached at 0.25 and 0.75 of the model's 

 length. Tests were made in regular waves 60 in. long 

 (i.e. X/L = 1) and 1.5 in. high at six speeds of advance, 

 starting with zero. Fig. 8 is a comparison of test data 

 with calculations made by Korvua-Kroukovsky and Ja- 

 cobs (1957) using strip theory and added-mass coefficient 



'2 Minutes of the S-3 I'auel of the SNAME indicate that such 

 research is in progress at the Colorado State University under the 

 guidance of Prof. E. F. Scluilz. In this program added masses 

 and damping forces are measured on individual sections of a seg- 

 mented ship model so that the distribution of forces along the body 

 length will be obtained. 



" Additional measurements of the wave-caused forces recently 

 were published by Gerritsma (1958, 1960). 



