214 



THEORY OF SEAKEEPING 



coefficients consume the largest part of the time spent 

 in evahiating the pitcliing and heaving motions of a 

 ship. 



4 Programming Digital Machine Computations of the 

 coefficients of equations (2) is desirable. In the case of 

 section shapes obtained by transformation of a circle 

 (Lewis, 1929; Prohaska. 1947), the machine can solve 

 directly the expres.sions resulting from such a transforma- 

 tion. The results of more complicated computational 

 methods (of Haskind, Ursell, Hanaoka for example, 

 suggested in Chapter 2) can be approximated by simple 

 expressions using a eur\-e-fitting technique. 



5 Towing-Tank Test to evaluate coupled heaving- 

 pitching motion of a ship will be needed for \-erifying the 

 results of projects 1 and 2. 



6 Tests in Wide Tanks are needed in order to estab- 

 hsh the amplitudes and phase lags of coupled hea^•iilg- 

 pitching motions at low speeds. Previous tests have 

 shown considerable uncertainty in this speed range. 

 This uncertainty is usually attributed to wave reflec- 

 tions from towing-tank walls. The difficulty may con- 

 ceivably also be caused by the erratic behavior of damp- 

 ing coefficients b and B at low speed, Section 2-3.24. 

 One of the aims of the experimental program suggested 

 here is to separate these two effects by eliminating the 

 tank-wall reflections. 



7 Solutions for Transient Response of the coupled 

 hea\-ing-pitching equations of motion. Section 2, are 

 suggested in order to provide the material needed in 

 projects 20 and 21 on irregular ship motions under condi- 

 tions in which the superposition principle is inapplicable 

 (aonlinearities and variable coefficients). 



8 Attenuation of an Incident Wave as it progresses 

 along a ship was discussed by Grim (1957, second part). 

 Further de\'elopment and experimental verification of 

 the subject is recommended. The object is to establish 

 a correction to the usual strip theor\' in which each 

 element of a ship's length is assumed to be acted upon 

 by an undistorted wave. 



9 Changes of a Ship's Mean Trim during pitching 

 and heaving oscillaticjns are known to occur and may be 

 significant in defining a ship's seakindliness. A ship 

 which increases its mean trim in head seas is evidently 

 a drier sliip than one exhil)iting a decrea.se in mean trim. 

 Linearized theories so far have treated only oscillations 

 about a mean and have not taken up the changes of mean 

 trim from the .still-water trim. Formulations to correct 

 this defect are recommended. 



It is presumed that in calculating the trajectory of a 

 nonlinear motion by a step-by-step integration the change 

 of the ship's attitude will automatically be shown. 



10 Interpretation of Computations and Model Data 

 should be made specifically for the appraisal of a ship's 

 seakindliness. The computation and model test data 

 are often presented as tables or curves-of-motion ampli- 

 tudes. Such quantitative data can be used directly 

 only in a few specialized na\'al problems. They do not 

 describe the seakindliness of a cargo ship, for instance, 

 as a mariner would appraise it. It is necessary to estab- 



lish which properties are desired in a ship and how these 

 l)ro])erties are indicated by the results of theory or of 

 model tests. The amplitude and pha.se data must be 

 supplemented by information on the freciuency and 

 severity of shipping of water and of slamming. Methods 

 are needed for estimating this "severity" quantitatively. 

 Geometric superposition of wave and ship motions does 

 not necessaril.v define tlie shiiiping of water, since, on the 

 one hand, the water surface rises at a submerging flared 

 bow, and, on the other hand, the deflection of water 

 by the bow delays the shipping of water. It is suggested 

 that a project be established to investigate these various 

 effects, with the ultimate aim of preparing a specifica- 

 tion for model tests and test reports. 



11 Rolling, Heaving and Side-Sway motions of a 

 ship at zero speed in regular beam seas should be investi- 

 gated. By formally .setting a system of three coupled 

 differential equations, a procedure analogous to that 

 used by Korvin-Kroukovsky and Jacobs (1957) for the 

 heaving-pitching motion can be followed. The sup- 

 porting material for the e\-aluation of coefficients can be 

 found in Ursell (1949a), Grim (1956. 1957fl and b) 

 and Landweber and de Macagno (1957). 



It is suggested that the series 60, 0.60 block coefficient 

 model be used for the first project. The information ob- 

 tained, added to the already available data on behavior 

 in head seas, will be valuable in the subsequent multi- 

 mode motion investigations. Attention should be paid 

 to the wave lengths (frequencies) which are significant 

 in pi-actice. 



12 Rolling, Heaving and Side-Sway motions of non- 

 circular c.ylindrical and prismatic bodies should also be 

 investigated theoretically in connection with project 11 

 in order to verifj' the theoretical procedure in a simpler 

 ca.se and to provide the data for a three-dimensional cor- 

 rection. 



13 Model Experiments in regular waves (o) on 

 cylindrical and prismatic bodies, and {b) on ship models 

 are needed in connection with projects 11 and 12. The 

 experiments on ship models should be conducted in 

 wide tanks or ponds in order to avoid interference of 

 the wall-reflected wa\es. 



14 Experiments on Model Rolling in Long-Crested 

 Irregular Waves are reconnnended as a supplement to 

 project 11. The objective is to provide information on 

 the applicability of irregular-wave theories to the rolling 

 of ships, which are characterized by low damping. 

 The results also are expected to contradict certain 

 conclusions in regard to nonlinear rolling. Section 2.22, 

 which were ba.sed on excessive attention to regular waves. 



15 Transient Response of a Ship to an Excitation in 

 Roll should be tleri\-('d on the basis of the differential 

 e(|uations of motion formed under project 11. This is 

 the preliminary step to project 16 which follows. 



16 Theory of a Ship's Response to Irregular Waves 

 ba.-<ed on a succession of transient respon.ses to excitation 

 in roll should be developed. This would be a verifica- 

 tion and elaboration of the brief calculaticms made by 

 Kriloff (1896, 1898) in which it was demonstrated that a 



