Reference is made to some results obtained by Grim [31] for sections of the 

 Lewis class and circular segments. These findings have been recently supplemented by 

 values m 44 (0), i.e. of the hydrodynamic moment of inertia of cylindrical bodies in roll 

 for a frequency parameter cog* — > 0, which change somewhat the shape of curves 

 communicated earlier. 



ni 22 {co) 4 



For the elliptic section we have the well-known result ■ = — which 



m 22 (0) 7T- 



pictures the conditions $ — and — z respectively; and for a flat plate Haskind [25] 



dz 

 m 44 (0) 



obtained the relation^ ~ 1.6. In Grim s presentation the inertia coefficient i£ 44 



m 44 (co) 

 is referred to the moment of inertia of the homogeneous elliptic halfcylinder. 



The variability of the added mass coefficients with the frequency parameter is 

 impressive. Nonetheless, Haskind proposed recently to use in heave and pitch the 

 approximations ra 33 — ra 33 (oo) and m 55 = m 55 ( oo ) ; in sway and roll m 22 = ra 22 (0) 

 and m 44 = m 44 (0), since free heave and pitch oscillations are in general short perioded 

 as compared with those of sway and roll. This means in effect that the earlier practice 

 of substituting the deeply immersed double body for the ship should be applied as first 

 approximation. We do not agree with this proposal which, in our opinion, is permis- 

 sible not as a first approximation but as a first orientation only. In the later part of 

 our study it will be pointed out that it can become quite important to determine added 

 mass values more rigorously. 



In [25] expressions are communicated for added masses m 22 , m^, m 2i of 

 bodies belonging to the class of Lewis' forms. Previously, only ra, 3 was known. The 

 total added masses of the ship are determined by a strip method. Approximate expres- 



2« 2 _ 2/? 2 __ 



sions are given in the form m^, = m 033 L m n ^ = m 022 L with m the 



l+o l+(3 



added mass of the midship section, a the waterline area coefficient, and /? the area 

 coefficient of the longitudinal section generally close to 1. These formulas are based 

 on a rather rough assumption on the average distribution of m 33 etc. and on Chapman's 

 parabolas as waterline equation; a correction coefficient has to be used for the finite 

 length of the ship. 



a$ 



Haskind suggests use of the condition — zz to determine added masses in 



dz 

 the aperiodic motions of sway and yaw, which again appears to be rather arbitrary. 



The vertical added mass of half a sphere oscillating at the free surface has been 

 calculated by Havelock [32]. Its dependency upon the frequency parameter is similar 



m 33 (0) 

 to that found by Haskind for a ship; the ratio £i 1.6, is somewhat lower 



m 33 (oo) 

 than for the latter. 



The magnitude of added mass values in transient conditions depends upon the 

 time history. There exists a solution [33] for the wholly immersed circular cylinder 

 moving sidewise from rest with a constant acceleration, which yields an added mass 

 value m., 2 ( oo ) , i.e. corresponding to the assumption 4> z= 0. Suggestions have been 

 made to approximate transient motions by parts of a sine curve and thus to determine 

 a frequency parameter. This procedure, obviously, is questionable. 



So far, no consistent theory is known to us which deals with the influence of 

 speed of advance on added masses of bodies moving at or near the free surface. 

 Haskind indicates however, that following his theoretical and experimental work, this 

 influence is not strong in case of the heave motion, and recent experiments by Golovato 

 [34] support this statement reasonably well. 



68 



