In the actual experiment, the motion 2, of the model cannot be measured directly. In- 

 stead the motion of the oscillating strut above the balance is recorded. Since the balance 

 cannot be infinitely stiff, these two motions may differ in amplitude and phase. This is 

 particularly true at high frequencies; that is, high relative to the natural frequency of the sys- 

 tem. In Appendix A the dynamic system is analyzed, considering the balance to be a spring, 

 and correction factors are obtained which allow the above analysis to be used. 



TEST RESULTS 

 FORCE COEFFICIENTS 



In order to determine the added mass and damping coefficients it has been shown that 

 the complex ratio, F /z or K/s e~'°, must be determined. 



The variation of Fq/z,. with frequency for constant speeds of 0, 1, 2, 3, and 4 knots 

 and displacement apmlitudes of 1/4, 1/2, and 1 inch are shown in Figure 5. 



Figure 6 shows the complementary plots of 5, the phase angle by which the force lags 

 the displacement. At zero speed, for low frequencies, these data scattered excessively and 

 so are not shown in Figure 6a. It is believed that this is due to wave reflections from the 

 basin walls. At low frequencies, the high wave celerity makes it difficult to conclude a test 

 before significant reflections are felt at the body. The phase angle at 3 and 4 knots at high 

 frequencies is not shown due to excessive noise in the trace caused by carriage vibration. 



The dynamic system represented by the model supported on the balance has a natural 

 frequency of about 70 rad/sec. Random disturbances cause the model to oscillate at this 

 frequency, the amplitude increasing as the carriage speed increases. In addition, the oscil- 

 lator is mounted on a carriage which has its own vibratory modes and which is excited by the 

 oscillating model and the motion of the carriage. Thus, the model vibrates at the oscillator 

 frequency and in accordance with these extraneous influences. These additional high frequen- 

 cies appear in the force and moment records and necessitate hand fairing of the traces in order 

 to extract the true fundamental component. 



The damping coefficient B is proportional to the sine of the phase angle 5. At high 

 frequencies, 5 approaches 180 deg and great accuracy is required in the phase angle determi- 

 nation in order to obtain a reasonably accurate coefficient. It was found necessary, for fre- 

 quencies above 7 rad/sec, to determine all phase angles shown in Figure 6 by harmonic 

 analysis using a "Runge Schedule."^ 



The dynamic correction described in Appendix A has already been applied to the data 

 shown in Figures 5 and 6. 



The physcial explanation of the shape of the curves in Figures 5 and 6 can be made as 

 follows: the total force on the model is the sum of three forces; buoyancy, damping, and 

 inertia. The buoyancy force is independent of frequency. The damping force is proportional 

 to frequency, and leads the buoyancy force by 90 deg, while the inertia force is proportional 



