ship Maneuvering in Deep and Confined Waters 



lated from the sectional area curve slope and the added mass 

 characteristics of the transverse sections , as shown by Munk [ 17] 

 and experimentally verified for the submerged doublebody ship form 

 in Ref. [ 18] . The good agreement obtained between total yawing 

 moments measured on this form and its surface ship geosim suggests 

 that the deeply submerged added mass values should apply in this 

 case. It is observed, however, that the water particles in way of a 

 certain section station here are not repeatedly accelerated from 

 rest as is the case when considering the cylindrical part of the hull. 

 Again, if the principle of superposition of damping and inertia com- 

 ponents to the total hydrodynamic force shall be retained for general 

 motions it shall be necessary to adopt the zero-frequency added 

 mass values . 



An illustrative discussion of added masses with special 

 application to the design and analysis of experiments is due to 

 Motora in Ref. [ 3 5] . For the determination of the added mass in 

 sway to be used in the aperiodic equations of a maneuvering ship he 

 recorded the direction of the acceleration imparted to a model by a 

 force suddenly applied in a certain direction. The added mass then 

 could be found from a reasonable estimate of virtual mass in surge. 

 To obtain the added moment of inertia in yaw he recorded the angular 

 acceleration following the impact by a pendulum, the momentum 

 loss of which was also known. He suggested that the inertia values 

 so derived should correspond to the impact or high-frequency type, 

 but the results included from tests with a series of ship models indi- 

 cate sway mass values of the same order as those valid for the deeply 

 submerged case, and moments of inertia in yaw of magnitudes cor- 

 responding to finite frequency surface values. 



In a recent paper Motora and co-authors [36] compare the 

 results of new experiments and calculations of an "equivalent" 

 added mass for a ship model in a sway motion, which is initiated 

 by a ramp- or step-form impact input of finite duration. The calcu- 

 lations are based on Tasai's section values in the frequency domain 

 [ 26] , and in agreement with the experiments they confirm that the 

 value of the equivalent added mass defined is a function of impact 

 duration. (Cf. Fig. 9.) If the duration is infinitely small only the 

 equivalent added mass is equal to its high-frequency value, and it 

 becomes larger the longer the duration. Thus these results help to 

 explain the earlier findings for added masses as well as for added 

 moments of inertia, for which latter the impact technique then used 

 did generate rather short input impulses. 



For application to normal ship maneuvers it may now seem 

 justified to use the low-frequency or deeply submerged values. 



In recent years it has been widely accepted that the accelera- 

 tion derivatives for a surface ship model may be evaluated from a set 

 of "planar-motion-mechanism" tests in pure sway or yaw. The 

 acceleration amplitudes are varied by an adjustment of oscillator 



837 



