Analysis Used in Submerged Body Research 413 
The validity of the force-component-separator and integrator system, shown in Fig. 22, 
has been established on the basis of controlled laboratory tests. A sinusoidal load of known 
amplitude and frequency (0.1 to 1.0 cycle per second) was applied to a gage. The phase 
angle between the gage signal and the sine-cosine: potentiometer was varied known amounts 
over a range of +90 degrees. The study demonstrated that the amplitude of any individual 
component is determined to an accuracy of better than | percent. 
One of the main advantage of this system, over the one described in Ref. 2, is the re- 
duction in test time for the dynamic mode (about 50 percent) and the use of the digital-readout 
system for recording purposes. 
Typical Test Results Obtained with the System 
All the hydrodynamic coefficients required in the equations of motion for submerged 
bodies in six degrees of freedom can be obtained with the DTMB Planar-Motion-Mechanism 
System. This is accomplished by appropriate orientation of the model and mode of operation 
of the system. 
Both the linear and nonlinear coefficients associated with static stability and control 
are determined using the system. In the case of the rotary and acceleration derivatives, 
however, only the linear coefficients are determined. 
The various static, rotary, and acceleration coefficients that can be evaluated using 
this system are presented in Appendix B and Table 2. It is believed to be pertinent, how- 
ever, to include representative samples of test results obtained for each of the three classes 
of coefficients. Examination of these samples should provide insight not only into the nature 
of these coefficients but also the quality with which they can be determined by the system. 
Before proceeding, it is reemphasized that all of the coefficients are obtained from the ex- 
plicit relationships given in Table 2. 
Typical test results for coefficients of the “static” variety are shown in Figs. 25, 26, 
and 27. The variation of normal force and pitching moment with body angle is shown in Fig. 
25 and the variation of normal force and pitching moment with stern plane angle is shown for 
various body angles in Figs. 26, and 27, respectively. The body-angle and plane-angle 
range covered in this case is only +6 degrees. Data are, in general, obtained over a body- 
angle range of +15 degrees and a control-surface angle range of +20 to +45 degrees, depend- 
ing on the particular control surface being investigated. As indicated in the figures, the 
derivatives are obtained from the slopes of the appropriate curves faired through the data 
points. The slopes of the body-angle curves are taken through a body angle of zero and be- 
come the static stability derivatives. The slopes of the control-surface curves for zero body 
angle are taken through a control-surface angle of zero and become the control derivatives. 
The kind of results obtained from pure heaving tests is shown in Fig. 28. The slopes 
of the separate in-phase force component curves are used with the formulas given to obtain 
the linear acceleration derivatives, the added mass Z and associated moment M,. 
Typical results of pure pitching tests which are used to obtain (damping) force and mo- 
ment derivatives are shown in Fig. 29. It may be noted that the quadrature components of 
force measured at each of the two struts are plotted separately. It has been found desirable 
to do so since the slopes of the two curves can then be substituted directly into the two for- 
mulas shown in the figure to obtain the damping force derivative Z , and damping moment 
derivative M,. 
646551 O—62 
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