Analysis Used in Submerged Body Research 391 
The hydrodynamic forces and moments which enter into the equations of motion as coef- 
ficients are usually classified into three categories: static, rotary, and acceleration. The 
static coefficients are due to components of linear velocity of the body relative to the fluid, 
the rotary coefficients are due to angular velocity, and the acceleration coefficients are due 
to either linear or angular acceleration. Within limited ranges the coefficients are linear 
with respect to the appropriate variables and thus may be utilized as static, rotary, and ac- 
celeration derivatives in linearized equations of motion. 
It may be concluded from the foregoing classification, that the experimental determina- 
tion of the coefficients of the equations of motion requires facilities which will impart linear 
and angular velocities and accelerations to a given body with respect to a fluid. For exam- 
ple, the usual basin facilities have carriages designed to tow models in a straight line at 
constant speed. Such facilities can be equipped to orient models in either pitch or yaw to 
obtain the static coefficients. However, more specialized types of facilities, such as rotat- 
ing arm or oscillator, are required to impart the angular velocities that are necessary to ob- 
tain rotary coefficients. The oscillator type of facility provides also linear and angular ac- 
celerations so that the acceleration coefficients may be determined experimentally. 
The choice of a suitable facility for determining hydrodynamic coefficients involves 
many considerations pertaining to accuracy, expediency, and ease of data analysis. A de- 
tailed treatment of these problems is beyond the scope of this paper. However, of primary 
concern is the degree to which the experimental technique involves explicit relationships 
and avoids the need for solutions of matrices. Also techniques which involve extrapolations 
should be avoided. To illustrate, a carriage which tows a model at uniform velocity in 
straight-line pitched or yawed flight is a direct and explicit means of determining static 
coefficients. Similarly, a rotating arm which:tows a model at uniform angular velocity and 
tangential to the circular path at each of several different radii is a means for determining 
rotary coefficient explicitly. On the other hand, the use of the rotating arm to obtain static 
coefficients should be considered as an indirect procedure since the data must be extrap- 
olated to infinite radius. The usual oscillator techniques are even more indirect and, at 
best, require solutions of simultaneous equations to.obtain rotary and acceleration derivatives. 
Each of the techniques mentioned can be used most advantageously for obtaining one 
category of hydrodynamic coefficients. The straight-line towing carriage supplies only the 
static coefficients. The rotating arm supplies rotary coefficients directly and static coef- 
ficients indirectly. The oscillator supplies all three categories of coefficients, but all in- 
directly. 
The foregoing considerations suggest the desirability of having a single system to de- 
termine explicitly all of the coefficients required in the equations of motion for six degrees 
of freedom. To accomplish this objective, it is necessary to develop a facility which can 
move a body through water with “hydrodynamically pure” linear velocities, angular veloci- 
ties, linear accelerations, and angular accelerations in all degrees of freedom. This con- 
cept forms the basis of the DTMB Planar-Motion-Mechanism System. 
Principles of Operation 
The DTMB Planar-Motion-Mechanism System as it physically exists is described briefly 
in the next section. It is desirable, however, to consider first the principles underlying the 
operation of the mechanism so that the design concept can be generally understood. In the 
interest of simplicity the mode of operation applicable only to submerged bodies in the 
