Norrbin 



product - N" • B/T, are displayed in Fig, 10b, compiling experiment 

 data from different sources. Here the two-dimensional LEWIS-form 

 values for high as well as low frequencies are indicated by off-sets 

 to the left in the diagram. Motora's i960 impact test data, which 

 appear on a level close to the high-frequency prediction, do not 

 indicate any definite dependence on draught-to-length ratio. These 

 data as well as low-frequency PMM data clearly indicate an increase 

 of moment of inertia with reduced fullness. This trend may be 

 expected in view of the deep and narrow bow and stern sections in 

 fine forms — certainly the deeply- submerged ellipsoid is not repre- 

 sentative for a ship form in yaw acceleration* 



Semi-Empirical Relations for the Four Basic Stability Derivatives 



Among the large number of first-order force and moment 

 derivatives, that are used to describe the linearized hydrodynamics 

 of the moving hull, only four appear in the analytical criterion for 

 inherent dynamic stability with fixed controls. These are the stability 



derivatives proper, Yy 



Nuv» Yur and 



N., 



From simple analogy 



with the zero-aspect- ratio wing theory of Jones [37] they turn out 

 as in Table III. 



TABLE III 



Although this analogy has been verified in principle for a submerged 

 double -body model as well as for the surface model at small Froude 

 numbers [ 18] , it shall not be expected to furnish an adequate nu- 

 merical prediction. It suffices to point on the alternative relation 

 for a closed body in a perfect fluid, given by Eq, (5.7), and to the 

 fact that at least some negative lift is still carried on the run of 

 normal ship-form hull. The bow lift or transverse force is not 



840 



