148 



THEORY OF SEAKEEPING 



judge the practical value of the models under the pre- 

 ceding subproject (b). They will also ser\-e as the final 

 check on the strip method of analysis using sectional re- 

 sults in conjunction with three-dimensional corrections. 

 Comparative evaluation of damping in pitch of various 

 combinations of bow and stern sections is particularly 

 miportant in A-iew of the suspected nonlinear effects of 

 sections typical for ship ends. 



18 Theoretical Evaluation of Distribution of Sec- 

 tional Damping Forces along the length of a ship is 

 needed in view of its importance in rational calculations 

 of bending moments. Under Michell's thin-ship as- 

 sumptions, this can probably be obtained by recasting 

 Haskind's (1946) and Hanaoka's (1957) ship-motion 

 theories." 



19 Distribution of Nonlinear Damping Forces (in 

 assumed harmonic oscillation) may be of considerable 

 importance in rational bending moment e\-aluation. 

 This project implies a finite beam and finite amplitude 

 of motion. It may well be intractable by advanced 

 mathematical methods of the type used by Haskind and 

 Hanaoka. The author beheves, however, that a cruder 

 intuitive approach based on Holstein and Havelock's 

 pulsating-source distribution may produce valuable 

 results. 



20 Experimental Evaluation of Sectional Damping 

 Distribution is necessary to provide direct data for siiip 

 bending-moment analysis as well as verification of the 

 theoretical results of projects 17 and 18. Conventional 

 ship models and idealized parabolic models should be 

 used.'* 



21 Experimental Evaluation of Sectional Distribu- 

 tion of Wave Forces on restrained ship models of various 

 forms is needed. This project, listed here under damp- 

 ing, is a companion to project 7 on distribution of added 

 masses. Preliminarj' calculations (Korvin-Kroukovsky, 

 1955; Korvin-Kroukovsky and Jacobs, 1957) have indi- 

 cated that damping (i.e., velocity-dependent) forces 

 caused by wa^^es may be negligible in defining ship mo- 

 tions. The}' are important, however, in the distribution 

 of sectional forces since thej' appear to have a strong in- 

 fluence on bending moments (Jacobs, 5-1958). 



22 Theoretical Evaluation of Hydrodynamic Forces 

 and Moments in Side Sway and Rolling is needed for the 

 ultimate analysis of ship motions and stresses in irregular 

 oblique seas. This broad problem e\ddently must be 

 subdivided into a series of lesser projects. Essentially 

 all of the projects listed in the foregoing under heaving 

 and pitching can be rewritten to apply to side sway and 

 rolling. The subject of side sway and roll has been much 

 less developed than that of heaving and pitching. The 

 studies of Grim (1956), Landweber (1957) and Land- 



'^ Independent theoretical research by Dr. Paul Kaplan of 

 S.I.T. is in progress under sponsorship of the Analytical Ship- 

 Wave Relations Panel of the SNAME. 



'■* A current project under the sponsorship of the S-3 panel of 

 the SNAME was mentioned in Section 3.14-4. In this project an 

 attein]3t is made to measure the distribution of sectional hj'dro- 

 dynamic forces. 



weber and de Alacagno (1957) apply only to asymptotic 

 cases of very high or very low frecjuencies. Evaluation 

 of added masses and damping forces is needed for the 

 complete freciuency range of a ship moving in waves. 

 Evaluation is needed of sectional forces, of three-dimen- 

 sional corrections of these, and of forces for complete 

 ships. ^Yhi\e it is difficult to list all possible projects fall- 

 ing under this broad description, a few suggestions will 

 be listed. 



23 Research Based on Haskind (1946) is suggested. 

 Haskind formulated the solution for a ship oscillating 

 in all six degrees of freedom under action of harmonic 

 (but not otherwise defined) wave forces. He has com- 

 pleted the solution, however, only for heaving and 

 pitching. This project would extend Haskind's work to 

 a complete e\'aluation of hydrodynamic forces in six- 

 component ship motions. 5^ 



24 Research Based on Ursell (1949a) is also advised. 

 Ursell presented in his 1949a paper a formulation for 

 the velocity potential and the stream function about a 

 noncircular cylindrical body floating on the water sur- 

 face. He completed the solution for the rolling of a 

 certain family of ship sections. Research projects are 

 suggested for: 



(a) Extension of Ursell's calculations on rolling to 

 other forms of ship sections. 



(b) Extension of Ursell's basic flow expressions to 

 lateral (side-swaying) oscillations. 



(c) Extension of Ursell's basic flow expressions for 

 pitching oscillations. 



25 Experimental Evaluation of Sectional Damping 

 of Bilge Keels on systematic series of models is needed. 

 While it is evident that bilge keels greatly increase the 

 damping in roll of a ship, there exists but few data to 

 permit either rational or empirical evaluation of this 

 damping. Noncircular cylindrical models spanning the 

 width of a towing tank are suggested. The results of 

 experimental work seldom cover suflSciently the variety 

 of forms and proportions found in actual ships and such 

 test results can be better generalized by close correlation 

 with a theorj'. It is suggested therefore that ship sec- 

 tions analyzed by Ursefl (1949a) be chosen as the first 

 subproject. Tests should be made alternately on the 

 bare sections and sections equipped ^\^th bilge keels of 

 \'arious widths. Various draft/beam ratios, should be 

 tried, including the one for zero theoretical damping 

 (Section 5.33; Ursefl, 1949a). 



(a) Tests with a fixed axis of rotation are suggested 

 for the best correlation with theory and so the possibility 

 of generalization. Howe\'er, these tests alone may be 

 misleading. 



(b) In the rolling of a free body, the bilge keels will 

 change the instantaneous axis of rotation and will mod- 

 ify the coupling between roiling, heaving and side sway. 

 The added energy dissipation of additional motions will 

 modify the apparent damping in roll. Alternate experi- 



^* The subject will be further discussed under the heading of 

 ship motions in Chapter 3. 



