Norrbin 



[ 17] whereas strip theory and two-dimensional added mass values 

 may be used for other forms. The magnitude of ideal side force as 

 well as moment are small, however, and in a real fluid the viscous 

 effects are dominating. 



There are reasons to believe that the main results of the 

 theories for the deeply submerged body will also apply to the case of 

 a surface ship moving in response to control actions at low or 

 moderate forward speeds. Potential flow contribution to damping 

 as well as inertia forces depend on the added mass characteristics 

 of the transverse sections of the hull, and as long as these character- 

 istics are not seriously affected by the presence of the free surface 

 the previous statement comes true. However, an elongated body 

 performing lateral oscillations of finite frequencies will generate 

 a standing wave system close to the body as well as progressive 

 waves, by which energy is dissipated. The hydrodynamic character- 

 istics then are no longer functions of the geometry only. At a higher 

 speed or in a seaway dlsplacenaent and wave interference effects 

 will further violate the simple image conditions. 



VI. CALCULATIONS AND ESTIMATES OF HULL FORCES 



On Added Mass in Sway and Added Inertia in Yaw 



A brief review will here be given of the efforts made to 

 calculate the added mass and inertia of surface ships in lateral 

 motions. Four facts will be in support of this approach: The added 

 masses are mainly free from viscous effects; the added masses 

 appear together with rigid body masses in the equations of motions, 

 and relative errors are reduced — this is especially true in the 

 analytical expression for the dynamic stability lever, which involves 

 only the small X^ the added masses are experimentally available 

 only by use of non-stationary testing techniques , and in many places 

 experimental data must therefore be supplemented with calculated 

 values; the added masses are no unique functions of geometry only, 

 and experiments must be designed to supply the values pertinent to 

 the problems faced. 



The velocity potential for the two-dimensional flow past a 

 section of a slender body must satisfy the normal velocity condition 

 at the contour boundary as well as the klnematlcal condition for the 

 relative depression velocity at the free constant-pressure surface. 

 In case of horizontal as well as vertical oscillations this latter 

 linearized conditions Is co + g(9$/9z) =0 — cf. Larnli^[ 12] — or, 

 introd iiqipg the non- dimensional potentlcil ^" = ^/LygL and 



a$" 



$" 



(6.1) 



832 



