Analysis Used in Submerged Body Research 389 
Consequently, to obtain solutions for any given configuration by means of this technique, it 
is necessary to know these coefficients with reasonable accuracy. Many attempts have been 
made in the past to fulfill this requirement by utilizing various experimental (captive model) 
and theoretical techniques, or combinations of both. 
Among the various captive-model techniques used, fairly refined methods have been de- 
veloped by model basins and wind tunnels for measuring forces and moments due to body 
orientation and control deflection; the so-called static stability and control coefficients. 
However, the various experimental methods used to determine forces and moments associ- 
ated with variations in linear acceleration, angular velocity, and angular acceleration have 
been successful in only a limited number of cases. The techniques that have been tried in 
this respect have required the use of facilities such as the rotating arm, free oscillator, 
forced oscillator, curved-flow and rolling-flow tunnels, and curved models in a straight flow 
facility [3]. Each of these techniques has certain limitations and problems associated with 
either accuracy of instrumentation, model support, friction, accuracy of flow (curved and 
rolling flow) [5,6], and accuracy of model construction (curved model). Also, none of these 
techniques provide a direct measure of all the hydrodynamic coefficients required in the equa- 
tions of motion for six degrees of freedom. The DTMB Planar-Motion-Mechanism System re- 
cently developed at the David Taylor Model Basin, however, incorporates in one device a 
means for experimentally determining all of the hydrodynamic-stability coefficients required 
in the equations of motion for a submerged body in six degrees of freedom. 
A comparison of the main advantages and disadvantages of several of the basic experi- 
mental techniques that have been discussed is presented in Table 1. Based on this compar- 
ison, it can be seen that the mathematical model technique, in conjunction with accurately 
determined hydrodynamic coefficients, provides the most powerful and versatile design and 
research tool for the study and analysis of stability and control problems. 
PLANAR-MOTION-MECHANISM SYSTEM 
The DTMB Planar-Motion-Mechanism System incorporates in one device a means for ex- 
perimentally determining all of the hydrodynamic-stability and control coefficients required 
in the equations of motion for a submerged body in six degrees of freedom. These include 
the static-stability and control, rotary-stability, and acceleration coefficients. The unique 
features of the system are the methods used to impart hydrodynamically pure pitching, heav- 
ing, and rolling motions to a given submerged body, as well as the dynamometry and data 
analysis equipment employed. These enable the explicit and accurate determination of indi- 
vidual derivatives without resort to the solution of simultaneous equations as is necessary 
when other types of oscillation devices are used. Although the system was designed prima- 
rily for submerged body research it can also be used to determine the hydrodynamic coef- 
ficients for other types of marine vehicles such as hydrofoil boats and ground effect machines. 
General Considerations 
The derivatives and composition of the equations of motion have formed the subject of 
numerous text books and papers [7-9]. For the purpose of this paper, therefore, only the 
general nature of these equations are considered. This is done to give some insight into 
the problems which must be faced in the design of experimental facilities for the evaluation 
of the equations. 
