

























/ 











/ 





















/ 











/ 



















/ 











/ 

















/ 













/ 

















/ 











/ 





n 

















/ 











/ 

















1 



' 











/ 



























J 



















1 









10 20 



CO 













/ 











■ 



h 



















/ 











o 



ilfji 



o~-c 















/ 



r 



















X 











/ 





o 1 in. 

 a '/2 in. 

 a '/4 in. 

 4 knots 

















\ 







y 



/ 





















N 



"^t-o 



/ 









































cj in rod/sec 

 Figure 5e - 4 Knots 



to (x?^ and leads the buoyancy force by 180 deg (Figure 7). Assuming the coefficients 4, S, 

 and C to be approximately constant and the damping to be small, it can be seen that at very 

 low frequencies the total force is essentially all buoyancy force and the phase angle is very 

 small. As the frequency increases the inertia force increases and cancels part of the buoy- 

 ancy force so that the total force drops and the phase angle increases toward 90 deg. When 

 the two are equal, the total force curve is at its minimum, the phase angle is 90 deg. and we 

 see the pure damping force in the record. As frequency increases, the inertia force increases 

 as £u^ so that the total force at high frequencies is essentially the inertia force. The total 

 force rises sharply and the phase approaches 180 deg. 



The data shown in Figures 5 and 6 are substituted in Equation [la] to obtain the added 

 mass m and damping coefficient S. Below co = 7, values obtained from the faired curves of 

 fT/s and S were used. Above o) = 7, however, due to the sensitivity to small errors in S, the 

 measured values for each run were combined to yield m^ and B and then these results were 



faired. 



m 

 Figure 8 is a plot of an added mass coefficient k „ = — — where A is the displacement 



of the model and g is the acceleration of gravity. In Figures 5 and 6 no systematic amplitude 

 effects were observed so that the added mass in Figure 8 represents all amplitudes used in 

 the tests. At low frequencies, the added mass appears to decrease with increased forward 

 speeds. However, at higher frequencies for Froude numbers 0, 0.09, and 0.18, there does not 

 appear to be any variation of m^ with speed. 



10 



