182 



THEORY OF SEAKEEPING 



model tests in regular long-crested waves using suitable 

 restraints and oscillating devices. This procedure will 

 be an elaboration of the one used for heaving and pitch- 

 ing motions liy Haskind and Riman, Golovato, and Ger- 

 ritsma. Extending these measurements to all param- 

 eters involved in equations (12) would be a very large 

 undertaking of questionable usefulness. It is the author's 

 opinion that this work should be preceded by a step-by- 

 step integration of equations (12) based on the best 

 available theoretical estimates (however crude) of the 

 parameters. Further theoretical and experimental work 

 can then be directed towards a more complete evaluation 

 of the limitetl number of parameters of greatest signifi- 

 cance. 



(b) Tests connected ivith a statistical theory. A statisti- 

 cal project was described by Marks (1957). In this proj- 

 ect a ship's responses are to be measured in a series ofwave 

 lengths and wave directions at a series of forward speeds. 

 Ship responses, considered independently in each motion 

 mode and combined with the wave directional energj^ 

 spectrum, will give the spectrum of ship motions in each 

 particular mode. The average characteristics of each 

 mode are then given by the Longuet-Higgins relation- 

 ships. The procedure is an exact repetition of the one 

 described in Section 3 for heaving and pitching motions 

 in irregular long-crested head seas and used by Lewis 

 and Numata (195G). It is made, howe\-er, more com- 

 plicated by consideration of a directional wave spectrvun 

 which necessitates the use of the "frequency mapping." 



A few ciuestions arise in connection with this project. 

 The necessity of making tests at a series of wave direc- 

 tions, in addition to a series of wave lengths and ship 

 speeds, makes the experimental program so large that it 

 is questionable whether it remains practical. It appears 

 to the author that this program can be carried out once 

 for the verification of the statistical theory, but that it 

 is too cumbersome for either ship-design use or motion 

 evaluations under specific weather conditions. The 

 method, as described by Marks, may still be valuable 

 for computational prediction of ship-l)eha\-ior char- 

 acteristics on the basis of theoretically evaluated re- 

 sponses to regular long-crested waves. Once the pro- 

 gramming of computations is established, application 

 to individual cases may not be laborious. The results 

 of computations can be verified by comparison with the 

 model test data described in Section 4.41, as well as 

 with ship tests at sea. 



The author feels, however, that scientific foundations 

 of the procedure described need further investigation. 

 In the case of the heaving-pitching motion, the super- 

 position principle for ship mentions is compatible with 

 the linear superposition of velocity potentials on which 

 all hydrodynamic forces depend. The nonlinearities ap- 

 pear to lie of secondary importance in these motions. In 

 six-component motions, defined by equation (12), the 

 products of velocities are found on the left-hand sides. 

 Is their superposition permissible? Apart from mathe- 

 matical principles, the practical significance of this 

 fjuestion depends on the motion mode under considera- 



tion. In the pitching motion the hydrodynamic forces 

 are expected to predominate strongly over the gyro- 

 scopic components of inertial forces. The procedure 

 described by Marks can be expected, therefore, to give 

 good results. In the rolling motion the hydrodynamic 

 moments L are small and gyroscopic forces can be ex- 

 pected to exert large influence. In the yawing motion, 

 sixth of equations (12), there is no restoring force in 

 xp and the factors {ly - Ii) and often p, are large. The 

 applicability of Marks' independent consideration of 

 motion modes needs, therefore, further investigation 

 in application to rolling and yawing, which are the par- 

 ticular characteristics of interest in connection with 

 oblique waves. \i\ investigation of the yawing be- 

 havior of ship models at large roll amplitudes and short 

 rolling periods is desirable in view of the important posi- 

 tion of the rolling velocity ^ p in the sixth equation 

 (12). 



The non-constant behavior of coefficients is much more 

 important in the case of j'awing (and yaw-induced roll- 

 ing) than in the case of pitchin g because the most signifi- 

 cant derivatives dN/d4' a nd dN/dv change their signs 

 with bow emergence and submergence (and the opposite 

 movements of the stern). This behavior of the coef- 

 ficients indicates that linear theory, generally satisfactory 

 for pitching, is probably inadequate for yawing. Yet, 

 the evaluation of the coupled rolling and yawing char- 

 acteristics represents the most important objective of 

 model testing in oblique seas. An experimental evalua- 

 tion of these aspects of ship-motion theory is needed 

 and can be accomplished by applying Marks' recom- 

 mended procediu'e to the model motions in oblique ir- 

 regular long-crested waves at one or two headings, and 

 one or two forward speeds. Such a limited test program 

 and computations can be carried out easily. 



5 Observations on Ships at Sea 



The bulk of the quantitative information on ship be- 

 havior at sea has been obtained by theoretical methods 

 and by towing-tank tests. The need of obtaining data 

 by observations of actual ships at sea has been felt for 

 a long time, but has been difficult to fill. The dif- 

 ficulty lies in the technical complexity of recording and 

 interpreting the complex motions of a ship at sea, and 

 also in the prodigious cost of comprehensive investiga- 

 tions. It is presumed that governmental naval research 

 establishments, such as the David Taylor Model Basin 

 in the United States, the Admiralty Experiment Works 

 in England, and the Bassin d'Essais des Carenes in France 

 have maintained contact with other naval activities and 

 have conducted many trials. Most of their observa- 

 tions, however, have not been published and so are not 

 a\ailable to naval architects in general. Independent 

 laboratories have need for a close contact with the opera- 

 tion of ships at sea. Steps have been taken to fill this 

 need even though only to a limited extent. Thus, J. L. 

 Kent (1924, 1927a), of the National Physical Labora- 

 tory in England, made research voyages on six ships. 



