



/ 





N 



Source Distribution 



^ 1 1 1 







f\ 





, , 



r4\ 













A 



f' 







"O' \ 











' 





Haskind Model 

 V = 



s 





^ 





1) 



I 



III 



1 















-o> 



'/ 





















-n 



Figure 16 - The Variation of Damping 



Coefficient with Frequency for the 



Haskind Model 



These data afford another opportunity 

 to compare the Grim method and source method 

 for computing damping. Again, the sections 

 of the Haskind-Riman model were compared 

 with the forms derived by Grim. Sections of 

 equal fullness and beam-draft ratio were as- 

 sumed to have equal damping. Suitable inter- 

 polation and integration over the body length 

 gave the curve shown in Figure 16. Distri- 

 buting pulsating sources on the surface of the 

 sections, computing the waves generated and 

 therefore the damping, and then integrating 

 over the length gave the curve marked "Source Distribution." Again, as in the case of the 

 present experiments, the Grim method is seen to yield a closer prediction of the damping 

 although both methods predict excessive damping. Application of a three-dimensional cor- 

 rection would improve the correlation. 



QUADRATIC DAMPING OF THE HEAVING OSCILLATION 



It has been shown earlier that a measurable amount of second harmonic content is pre- 

 sent in the lift>force traces and that this could be attributed to the existence of quadratic 

 damping of the heaving oscillation. It is intended at this point to evaluate its effect on the 

 motions of a surface ship. 



The method of Kryloff and Bogoliuboff ^^ allows one to find an approximate solution to 

 nonlinear equations of the form 



3 + V^Z + f /(3,3) = 



where the motion is nearly sinusoidal. 



The free oscillations of a heaving ship, assuming both linear and quadratic damping, 

 can be written 



z + V z + — - z + — ^ \sgn z) z-^ = 

 m m 



If the damping forces are small compared to the restoring forces, the approximate so- 

 lution has been given ^^ as 



z = a sin (t/< + 0) 



2a 



