Analysis Used in Submerged Body Research 415 
In-Phase Component of 
Normal Force Coefficient 
, OZ) in + (Z2 Vind 
Ma x 8[(Za)in-(Z) in] 
wit rs 
eo. 
fo) 002 004 O06 O08 O10 Ol2 O14 O16 
Linear Acceleration Parameter Wo 
Fig. 28. Typical curves of forces versus linear acceleration 
amplitude from pure heaving tests used to obtain added mass 
(and associated moment) 
Fig. 29. '‘l'ypical curves of forces versus 
angular velocity amplitude from pure pitching 
tests used to obtain damping force and damp- 
ing moment derivatives 
= 
3, 
Py 
fe} 
8 (Zour +(Za' out J 
849 
(2g +™m )* 
& 
GB 
Quadrature Component of Normal Force Coefficient 
O 002 004 O06 O08 O10 Ol2 O14 
Angular Velocity Parameter q, 
The curves of in-phase force components shown in Fig. 30 are also typical of the results 
obtained from pure pitching tests. Here again, the force components measured at each strut 
are plotted separately. The angular acceleration derivatives, the added moment of inertia 
M; and associated force Z;, are obtained from the slopes of the curves using the formulas 
given in the figure. 
Results are obtained in a similar manner for all the other hydrodynamic coefficients. 
ROTATING ARM FACILITY 
Another captive-model technique that has been used extensively in submerged body re- 
search, to determine explicitly the rotary coefficients for the differential equations of motion, 
