Gyrostatic terms discussed in Ref. 1 are omitted in the process of linearization. 

 This agrees with a recommendation made by Chadwick and can be considered as a 

 necessary first step from a formal point of view. But the appraisal of the order of 

 magnitude of inertia and hydrodynamic forces is a serious task in itself. Very prob- 

 ably in the case of roll the term (m' 66 — w'as) <pQ ls important because of the high 

 value of the difference in added masses m 66 — m 55 as compared with m' 44 . In general 

 by neglecting such coupling terms peculiar effects may be omitted. 



Some further remarks on nonlinearities appear to be appropriate. 



It is natural to treat the roll simultaneously with sway and heave as done so 

 far, but separate investigations are needed because of the basic importance of transverse 

 stability and the nonlinear character of the motion at large angles. In fact, studies on roll 

 serve as a prototype when dealing with nonlinear ship motions. 



Efforts are being continued to determine the actual stability in a seaway. It has 

 been shown that stable models capsized when advancing on oblique courses in regular 

 waves although some experiments do not support results obtained by elementary cal- 

 culations with respect to heavy losses of metacentric height on wave crests in a follow- 

 ing sea. Theoretical work has not progressed appreciably either in this field or with 

 respect to roll at large angles. Baumann [49] has discussed the latter problem under 

 simplifying assumptions which admit the solution of the equation of forced roll in a 

 closed form. 



Equations with higher order terms in the restoring expressions for heave and 

 pitch have been solved by a step by step method [50], but results so obtained do not 

 present especially interesting features. 



Nonlinear effects in roll damping are well known [51]. Recent experiments on 

 forced heave have yielded similar pronounced effects [34]. So far they have not been 

 detected by model investigations in regular seaways of various but moderate height, 

 which generally yield a reasonably linear relation for motion amplitudes. 



4. Hydrodynamic Impacts 



Within the last five years the application of hydrodynamic impact theory to 

 problems of naval architecture has successfully developed. At present, shock phenomena 

 are considered to be as important as the approximately periodic effects experienced by 

 a ship in a seaway. 



A first step has been to borrow from sea plane mechanics the fundamental 

 theory due to Wagner; however, quite a bit remains to be done to arrive at quantitative 

 results in the case of a ship. 



Special studies had to be devoted to the investigation of conditions under which 

 "slamming" occurs. With regard to notation, by "slamming" we denote essentially 

 impacts which act in a direction not too far from the vertical and mostly on bottom 

 parts of the ship. However, important impact effects can arise in other cases, e.g. 

 when a rather blunt forebody heads into steep waves, when green water on deck hits 

 the bridge superstructure or when wave impacts are exerted on the side of the ship. 

 All that is needed for the occurrence of such phenomena is a high relative normal 

 velocity between a flat part of the ship and a free water surface bounding a consider- 

 able amount of liquid. 



It is, therefore, preferable to restrict the use of the expression "slamming" to 

 the "vertical effects" only mentioned earlier and to use the expression hydrodynamic 

 impact as the more general concept. Reference is made to the work of V. Szebehely 

 and collaborators at TMB [52], which rests on analysis, model experiments and full- 

 scale research. Interesting experimental studies have been performed by Akita and 

 Ochi [53]. 



Although approximate calculations have been made to determine the influence 

 of elasticity on the impact process in seaplanes, no comparable work has been per- 

 formed in ship theory nor has Cauchy's Law been observed when experimenting. Pos- 



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