HYDRODYNAMIC FORCES 



121 



15 



0.10 



en < 



O.OB 



Pitch 



Fr=O.IS Fr=0.2S 



Fr=0.20 Fr=0.30 



Fig. 13 Comparison of measured damping in pitch with one 



calculated by strip theory using Holstein-Havelock method 



(from Gerritsma, 1957£') 



waterline is not taken into consideration in the available 

 methods of calculation. 



In Golovato's tests the calculated damping greatly ex- 

 ceeded the measured damping, and Grim's theoretical 

 method gave the better appro.ximation. With the 

 different rates of increase of measured and calculated 

 damping for a practical ship form, Gcrritsma's heaving 

 test indicates an apparently excellent agreement with the 

 Holstein-Havelock method. Fig. 7 shows that Grim's 

 method underestimated the damping in heave. The 

 word "apparently" was used advisedly. Were the in- 

 crease of damping due to inclined ship sides taken into 

 account in calculations, both curves of theoretical damp- 

 ing in Figs. 7 and 12 would be displaced upwards. 



Examination of Figs. 7 and 13 indicates that the rela- 

 tionship between calculated and measured clamping in 

 pitching is drastically different from that in heaving. 

 In the case of pitching, Grim's method is foimd to agree 

 with the measured data, while the Holstein-Havelock 

 method exaggerates the damping. The calculatetl damp- 

 ing would be further increased if ship side inclinations 

 were taken into account. 



The shift from agreement to disagreement of the cal- 

 culated and measured damping in the cases of heaving 

 and pitching oscillations indicates a strong three-dimen- 

 sional effect. However, application of the three-dimen- 

 sional corrections developed by Havelock and Vossers 

 (to be discussed in Section 3.23) would make the situation 

 still worse. The pitch-damping curves (at synchronous 

 frequency) would l>e displaced upwards, while the heave- 

 damping curves would not be affected. 



To summarize: Prediction of the damping of a ship's 



Fig. 14 Variation of damping coefficient with frequency 

 (from Golovato, 1957) 



heaving and pitching motions is rather uncertain. The 

 iiriier of magnitude and the functional dependence of the 

 damping on oscillation frequency can be estimated 

 roughly. Neither of the two available methods of cal- 

 culating, Grim's or Holstein-Havelock's, gives uniformly 

 satisfactory results. Fortuitously, one or the other will 

 be preferable in a particular case. Currently available 

 calculations of three-dimensional effects (Section 3.23) 

 do not correct discrepancies but apparently make the 

 situation worse. The most pressing need in the theory 

 of ship motions and ship bending stresses is to develop a 

 reliable method of c\'aluating the damping character- 

 istics. 



Experimental measurements on idealized ship forms 

 may be misleading if used directly as an indication of 

 normal ship behavior. Tests on such models are, how- 

 ever, recommended, but only for comparison with calcu- 

 lated values since more advanced methods of calculation 

 can be used for such mathematically defined .ship forms 

 than is possible for normal ship forms (Section G). It 

 would be desirable to develop mathematical ship lines 

 which would be more like the normal ship form and yet 

 permit application of the advanced calculation methods. 



The erratic correlation between computed and meas- 

 ured damping when comparison is made of mathematical 

 and ntjrmal ship forms, and of pitching and heaving mo- 

 tions, indicates that the phenomenon is caused by a com- 

 plexity of conditions. A research program should be 

 directed therefore towards resolving this complex phe- 

 nomenon into its (not now known) parts and towards sub- 

 sequent analysis of these component parts. Two gen- 

 eral directions of approach can be visualized. In one, 

 tests similar to Golovato's and Gerritsma's would be con- 

 ducted on a \-ariet}^ of ship forms, ^^arious factors can 

 then be isolated intuitively after inspection of the test 

 data, and the conclusions can be verified subsequently 

 by synthesis of the elemental findings. The other 



