Analysis Used in Submerged Body Research 441 
c 22") ou. I eee 
Note SS (B31) 
q z ag. 
where 
Cea (2 sin *) ae (B32) 
and 
Go ag (22 sin 5) a (B33) 
are the maximum amplitudes of the angular velocity and acceleration, respectively. 
The relationships for pure yawing and rolling, presented in Table 2, can be derived in a 
similar manner. 
The model mass m,, and metacentric stability (M4), are evaluated experimentally by 
performing inclining tests (standstills). The model moment of inertia], is determined from 
oscillation tests performed in air. For these tests, the model-ballast condition is the same 
as during the regular tests. 
APPENDIX C 
Mathematical Operations Performed by Instrumentation System 
As indicated in the section entitled “Instrumentation for Static and Dynamic Stability 
Tests,” the operation of the present electronic system differs from that described in Ref. 2 
in that a true integration of the gage signal is performed. 
To illustrate, assume a ‘pure heaving condition which results in a gage signal of the 
form such as given in Fig. 4: 
Ze => Zy + Ze sin (at = d) (C1) 
which can be written as 
Zr = 2, + Z, (cos ¢) sin wt - Z, (sin ¢) cos at (G2) 
Z, = 2, + Z,, sin wt - Z,,, cos oat. (C3) 
ut 
The in-phase and quadrature (out-of-phase) components can be obtained by operating on 
the gage signal in the following manner: 
