144 



THEORY OF SEAKEEPING 



be reserved for iin-estigation of nonlinear beha\'ior of a 

 few models. It is hoped that a much larger number of 

 models will be tested by the simpler "flexible" methods. 



In any case it is strongly recommended that familiarity 

 with the Haskind-Riman, Golovato, and Gerritsma pa- 

 pers be required of all prospective investigators. 



The prismatic models and ship models should be tested 



m: 



(a) Heaving oscillations. 



(b) Side-sway oscillations. 



(c) Rolling oscillations. 



The complete ship models should be tested in addition 

 in: 



(d) Pitching oscillations. 



(e) Ya^nng oscillations. 



The series of tests intended for analj'sis of symmetric 

 motion, i.e., heave-pitch, and unsymmetric motion, i.e., 

 side sway, roll and yaw, need not necessarily be con- 

 ducted by the same in\'estigators, since as a rule differ- 

 ent types of apparatus will be needed. 



8.12 Prismatic models. Those investigators of ship 

 motions using strip theory have usually estimated the 

 added masses in hea\'ing motion on the basis of the theo- 

 retical studies of F. M. Lewis (1929). Lewis devised a 

 conformal transformation by means of which he de- 

 veloped potential flow patterns for a number of ship- 

 like sections starting from the known velocity potential 

 of the flow about a circle. Lewis assumed the water 

 flow around a siu'face ship to be identical with that 

 around a fully submerged douljle body, and on this basis 

 computed added masses. Grim (1953) used Lewis' sec- 

 tions in computing damping forces in heaving motion and 

 also made a certain (not yet adequate) amount of com- 

 putations of added masses in the presence of a free water 

 surface. Grim (1956) also has calculated added masses 

 and damping forces for side-swaying and rolling motions 

 of floating bodies of Lewis' sections. 



It is believed important to obtain experimental data 

 on added masses and damping forces in heaving, side- 

 swaying and rolling for prismatic bodies of the type used 

 by Lewis. This will provide experimental A'erification of 

 Grim's work, and at the same time furnish data on sec- 

 tions of practical type with large section coefficients. 

 Lewis' results are not realistic for small section coeffi- 

 cients since free-surface effects are expected to be par- 

 ticularly strong in sections having sloping sides at the 

 LWL. Experiments with prismatic bodies of cross sec- 

 tions used by Haskind (1946) are therefore recommended. 

 These are defined by equations (50) and (54). At .small 

 section coefficients, their sides at the LWL are tangent to 

 an inclined line; they are pointed at the keel and repre- 

 sent reasonably well the V and concave V-sections at the 

 bow and stern of many ships. 



The foregoing program is particularly recommended 

 since there is strong evidence'^ that the slope of a ship's 

 sides at the LWL has a large effect on hydrodynamic 

 forces. 



" Korvin-Kroukovsky and Jacobs, 1954, 1957. 



Use of these two families of mathematically defined 

 lines is recommended not only because they pro\'ide an 

 opportunity to compare theoretical and experimental 

 data, but also because hydrodynamic forces can be ex- 

 pressed systematically by a plot against a pair of param- 

 eters defining the section. Were tests made on unrelated 

 profiles, subsequent use of the data for a new ship would 

 involve rather uncertain comparisons. 



8.13 Complete ship models. Tests of complete ship 

 models are recommentlcd in order to provide data on the 

 relationship between a true three-dimensional flow and 

 the two-dimensional one assumed in strip theory. They 

 also are \'aluable in cases when only ship motions are 

 of interest and the question of force distribution is not 

 in\'olved. Three types of tests are recommended here: 



(a) Tests of mathematically defined lines symmetrical 

 about the midship plane, with sections of one family and 

 the same parameter (affine sections), such as Haskind's 

 (1946) for which theoretical computations are available. 



(b) Tests of mathematically defuied lines in which 

 sections vary from full ones amidship to V or concave V 

 at the ends; also possibl.y un.symmetrical fore and aft. 

 The ship-surface equation and theoretical forces for these 

 forms are not yet available and must be developed. 



(c) Tests of selected ships of normal practical type. 

 Comparison of test data with theory should be based on 

 matching true ship sections to those closest to them in 

 F. jNI. Lewis' or Haskind's families of sections. 



8.2 Theoretical Research. It has been pointed out in 

 the text that information on added masses of ship forms 

 in two-dimensional flow is only available for two asymp- 

 totic cases of very high or very low freciuency. Added- 

 mass information at all frequencies is only available in the 

 work of Ursell for a semi-cylinder. Additional theoreti- 

 cal work is needed to obtain the added masses for other 

 sections at all frequencies. Lh-sell's (1949a) paper can 

 serve as a foundation for this work. 



It is necessary to evaluate the distribution of added 

 masses along the length of a ship and this can possibly 

 be done by extension of Haskind's (1946) and Hanaoka's 

 (1957) work. Early translation of the complete set of 

 Hanaoka's papers is desirable. 



Theoretical work on hydrodynamic forces acting on 

 three-dimensional bodies (Haskind, Hanaoka, Vossers) 

 has been in\'ariabl}' based on parabolic forms with affine 

 sections, symmetric fore and aft. It is desirable to ex- 

 tend it to hull forms with nonaffine sections, more nearly 

 resembling actual ships. The availability of high-speed 

 computing machines will permit a ■\\ider scope of activity 

 in the futvn-e than was feasible for the original investi- 

 gators. 



Grim's (1953) theoretical computations of damping 

 forces in heaving appear to be the most complete at pres- 

 ent. However, their application to the damping on a 

 complete ship model did not lead to good agreement 

 with Gerritsma's test data. The discrepancy may lie 

 in the assumptions made in the original development of 

 the theory for cylindrical bodies, or it may have been 

 caused by the three-dunensional effect. The corrections 



