SHIP MOTIONS 



215 



ship's rolliiif^ in its iialiiral pcriotl pcvsislcd in v\v\\ 

 slightly in'cguiar wax'cs. 



17 Ships' Rolling When Anchored sliduld he investi- 

 gated theoretically and experimentally. Dangerously 

 large rolling lias lieen observed in a ease which has l)een 

 attributed to the regularity of swells (Saunders' discus- 

 sion of Korvin-Kroukovsky, 1957). However, swell 

 records invariably disclose a large degree of irregvdarify. 

 It is concei\'al}l(> that niooring-cablc forces, resulting 

 from several ship mentions incited by wa\-es, may act as 

 sufficient excitation for rolling. 



18 Investigation of Environmental Conditions can be 

 suggested as a companion project to 17. It shoulil be 

 investigated to what extent the usual swell may become 

 more regular in the process of entering a shallow-water 

 harbor and possibly refracting after approaching a sea 

 shore ol)liquely. To what (>xtent can the sex'ere rolling, 

 attrit)uted to an allegetl swell regularity, be relieved by 

 changing the anchorage jioint to a greater water deptli? 



19 Rolling and Yawing Moments Caused by Oblique 

 Waves should be determined theoretically and meas- 

 ured experimentally. Theoretical evaluation may follow 

 the pattern used for heaxing-pitching motion by Kor\in- 

 Kroukovsky and Jacol)s (1!).57) with the supporting 

 material of'Ursell (194!)rt), Grim (1956, 1957) and Land- 

 weber and de Macagno (1957). Presently available 

 material ijermits making these calculations only for the 

 zero-speed case. Completion of certain pi'ojects listed 

 in Chapter 2 may permit extension to cases in\'ol\"ing 

 forward speed. 



The yawing moment caused by wa\-es depends on a 

 ship's trim. Calculations at: several trim angles are 

 therefore needed. 



In towing-tank tests, the forces and moments acting 

 on a lestrained model are to be measured. Vertical 

 and lateral forces and rolling and yawing moments are 

 involved. The effect of the wa\'e direction, model's 

 forward speed and model's angle of trim are to be deter- 

 mined. Several wave heights should be used, since there 

 is the ])robability of a strong nonlinear I'ffect at certain 

 trim angles. 



It is customary to express the wa\'e forces and moments 

 as amplitudes in a harmf)nic variation. This is the form 

 in which the data are used in the now accepted theory 

 of linear superposition. There is a possibility, however, 

 that this will not be suitable in the analysis of yawing 

 and rolling in which nonlinear characteristics may be 

 decisive. This may make it neces.sary to use super- 

 position of transient responses to a series of successive 

 impulses. To provide the material for such an even- 

 tuality, detailed information on the pattern of cyclic 

 variations of all (|uantilies must be repoi'tcd. 



20 Theoretical Evaluation of Four-Mode Model 

 Motions in long-cre.sted regular waves is suggested, as 

 described under the second project in Section 2.33';. 

 Fi\'e degrees of freedom are involved; namely liea\'ing, 

 sidesway, yawing, pitching, and rudder movements. 

 The effect of surging is disregarded, and restraint in roll 

 is assumed. After evaluation of all variables, except the 



roll angle 0, the rolling moment is ccjmputed. As a 

 sub.sequent step, the rolling motion is comj^inted using 

 the fourth of equations (12). 



It is suggested that the initial acti\-ity be centered 

 about the .series (iO, O.GO Ijlock coefficient model. Waves 

 approaching a ship from 60 deg oft' the bow, and 45 and 10 

 (leg off' the stern are suggested as likely to be critical for 

 the i-udder control, Kydill (1959); also Section 2.38a. 



In Section 2.33« tiie author expre.ssed an opinion that 

 nonlinear l)ehavior is decisive in yawing and rolling 

 motions. Step-by-step integration with \-ariable co- 

 efficients in the equati<ins of motion is therefore \'isualized 

 under this project. 



21 Towing-Tank Tests in Regular Oblique Waves 

 are suggesteil under conditions matching tho.se of project 

 20. The model is to be self-propelled and free in every 

 respect, except for tlie resti'aint in I'oll, witli iiro\-ision for 

 measuring the rolling moment. 



A well-dehned rudder-control function must be chosen, 

 suitable for both projects 20 and 21. The optimum 

 rudder-conti'ol function will differ in Itow and quartering 

 seas. Papers l)y Schiff and Gimprich (]!)49) and Rydill 

 (1959) can be used as a guide in choosing a suitable 

 function. .Motions of the rudder must be recorded. 



Alternative tests are suggested in which the model will 

 be left free in rolling as w'ell as in all other modes. The 

 compari.son of the two .series of tests will indicate the 

 error resulting from neglect of the effect of rolling f)n other 

 modes, which was implied in project 20. 



There ai'e large differences in the motion characteristics 

 of ships, and tests on one model cannot arbitrarily be 

 assumeti to apply to another. The particular \-alue c:f 

 this project lies, therefore, in confirming the calculations 

 of project 20. The calculational procedure, once con- 

 firmed, can be used subsequently for predicting char- 

 acteristics of other ship forms of comparable prisma! ic 

 coefficients. A separate confirmation is needed 'or 

 ships with large prismatic coefficient. 



22 Measurement of the Derivatives dl'/d;/' and 

 dN/dv at various angles of trim and ship speeds is 

 recommended in order to provide the supporting mate- 

 rial for project 20. The effect of the trim on the rudder 

 effectiveness No = Ndid) should also be measured. The 

 angles of trim in these tests .should be chosen to give the 

 stern emergence corresponding to that found experi- 

 mentally in project 21. 



23 Results of Project 20 should be examined in an 

 attempt to derive .simple relationships between direct 

 roll response to waves and the roll response resulting 

 from various couplings, particularly that of yaw-roll. 

 It is hoped to ck'rive the optinumi proportions of bilge 

 keels and skegs to minimize the angle of roll. Section 

 2.33. 



The presence of nonlinear effects should be remem- 

 l)ered. Transient roll response may be excited at 

 instants of positive dN/d^p (at bow submersion) or 

 unusually large negative dN/di// (at bow emersion and 

 stern submersion) during a pitching cycle in waves. 

 Once excited, lightly damped rolling oscillations in a 



