

1 







/ 



\ 































1 









1 



^ 







Distributed Source 





















\ 















\ 







































v 



\ 





Grim 





























/ 



1 



r 



\ 





\ 





















r.Fro„deNu.ber^J 



^ oas/- 



J^ 







\ 



\ 



J^=0.09 

























^■-ozji 



fj 



9^ 





^<^ 





X--0,I8 

















O J^^O.09 



D x = o.ie 





/ 



1'^ 





^ 



\0 



























'/! 







^ 



v\^ 



A 



























1 



t 



1 



























f--o 



A- 



,-- 







.). 



/ 















X^ 



I 











A 



.4'-' 



y 



'^^=0.,8 

















\ 

 \ 



\ 









/■' 



^ " 



• 



— X=0.09 





'i 



/ 

















\^ 



^^ 







J\ 



y 













/ 

















\ 



\- 



"a^ 



■"~o 





$ 















/ 

























A 

















-/I 



Figure 9 - The Variation of Damping Coefficient with Frequency 



A damping coefficient defined by B' = a/-i/^» where L is the length of the model, is 

 given in Figure 9 for nondimensional frequencies between 0.4 and 4. Below w VB/g = 0.4, 

 the accuracy of B is very poor due to the smallness of the phase angle, 8. 



The damping did not show any dependence on the amplitude of motion as was true for 

 the added mass. A decrease in forward speed causes the peak in the damping curve to move 

 to higher frequencies although it has little effect on the maximum value. 



MOMENT COEFFICIENTS 



Equation [4b] indicates that the moment coefficients d and e are determined from the 

 amplitude ratio of pitching moment to displacement, AL/aj, and the phase angle a by which 

 the moment lags the displacement. The amplitude ratio Mq/^q is presented in Figure 10, the 

 dynamic correction described in Appendix A having already been applied. The phase angle 

 is shown in Figure 11. 



Since the model had fore-and-aft symmetry, tests were run both east and west. Although 

 the hydrodynamic moments must be the same in both directions the phase angle clearly is 



13 



