438 Alex Goodman 
Since 0 = g = q=0, Eq. (A9) reduces to Z y= w. Therefore 
W = awcos wt (B9) 
and 
2 
WwW = -aw? sin ot. (B10) 
Substituting Eqs. (B9) and (B10) in Eqs. (B2) and (B3), results in 
2 
Z= -aw*(Z.-m_) sin wt + aw (3 pt uz) cos at + Z, (B11) 
and 
; 1 3 
NS — ae. sin wt + aw (3 pt uw) cos wt + M, (B12) 
where m,, is the model mass. 
The component of force and moment in phase with the motion can be written as 
Z,, = -aw*(Z.-m) (B13) 
in 
and 
Ho = -aw lH. . (B14) 
in 
The internal balance system, shown in Fig. 6, measures the components of force at two 
points spaced equidistant from the body CG. Therefore, Eqs. (B13) and (B14) can be rewrit- 
ten as 
fs), eas 2 bape 
(21), + (25). = -aw*(Z.-m) (B15) 
and 
es 2 
x|(29),, - (21),,] = -aw"M.. (B16) 
The heaving acceleration derivatives, written in nondimensional form can be expressed 
as 
eZ), + 22), 
(Z.'-m") = Me NAMEN RS NC eae (B17) 
Ww m ow, 7 
and 
CAC aca et 
5 (B18) 
ow 
2 
os |x 
