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20 



Figure 11 - a, Phase Angle Between Moment and Displacement 

 "^ at Various Speeds 



different at higher frequencies. This is due to a mass unbalance in the model which yields 

 a moment signal proportional to the square of the frequency. This moment must change sign 

 relative to the apparent bow as the direction of travel reverses. Thus it either adds or sub- 

 tracts from the hydrodynamic moment so that the phase angle for travel east and west is dif- 

 ferent. The amplitude ratio is essentially unaltered. 



The magnitude of this extraneous inertia loading can be obtained from the moment 

 versus frequency curve at zero speed since at this speed no hydrodynamic moment can exist. 

 It was found that the unbalance was equivalent to a weight of 32 pounds at an arm of 1 foot. 



In Figure 11 it was necessary to draw the two curves ("east" and "west") so that 

 when the inertia moment correction is made to the data in applying Equation [4b], the east 

 and west tests will yield the same coefficients d and e. That is, the two curves are a best 

 fit to the data spots while being consistent with each other. At low forward speeds, the 

 accuracy of the hydrodynamic moment is low since its magnitude is small relative to the 



15 



