Analysis Used in Submerged Body Research 419 
center of the arm. The positioning apparatus is operated remotely and permits model atti- 
tudes of: yaw, plus or minus 30 degrees; pitch, plus or minus 15 degrees; and roll, 10- 
degree outboard, 40-degree inboard. 
For yaw- and pitch-angle changes, the test location of the submerged body is unchanged. 
However, for roll angles, the center of roll positioning is high about the CG of the body, and 
an adjustment in radial position on the arm is necessary to maintain the proper location of 
the body. The positioning apparatus was made external to avoid large cutouts in the body 
with respect to the towing struts. Individual motor drives and position readouts are used to 
position the body at any attitude. Also, the support struts can be oriented with respect to 
the flow to minimize strut-body interference. The strut spacing is adjustable between 3.5 
feet to 10 feet to accommodate various length bodies. The struts shown in Fig. 32 are simi- 
lar to those used with the Planar-Motion-Mechanism System [2]. The main difference is that 
the upper end of the rotating arm strut has a larger chord (2.5 feet as compared to a 1.0-foot 
chord). 
The internal balance system used with the rotating arm system is identical to that used 
with the Planar-Motion-Mechanism System. Likewise, the measuring, recording, and pro- 
gramming system, shown in Fig. 33, is essentially the same as the static-stability measur- 
ing system used with the Planar-Motion-Mechanism System. 
Test runs are generally made within one turn of the rotating arm. The tangential veloc- 
ity for submerged models is held constant for all radii at about 10 feet per second. For each 
of several discrete radii, the yaw angles (or pitch angles of a submarine model mounted on 
the side): is varied incrementally to investigate planar forces and moments. 
MOTION ANALYSIS SIMULATOR AND FACILITY 
The main purpose of any motion simulation facility is to represent, in the laboratory, 
the characteristics of proposed specific designs of surface ships, submarines, missiles, and 
other vehicles as well as the effects of the surrounding environment. Such a facility enables 
the designer to evaluate and improve the handling qualities or operational characteristics of 
a design, on the basis of established figures of merit, well in advance of construction. The 
facility may be used for parametric studies to investigate the importance of the various hy- 
drodynamic coefficients and other parameters in the equations of motion. For simulating 
manned vehicles, the facility is used to study the responses of the human in the control loop 
as affected by indicators, displays, control linkage design, and environment. In addition, 
operating personnel can be trained well in advance of commissioning. 
A simulation facility consists of a number of general-purpose electronic analog com- 
puters which are used to solve linear and nonlinear differential equations of motion such as 
presented in Appendix D. A general-purpose analog computer is an assembly of electronic 
and electromechanical units, which uses direct-current voltages as variables and can per- 
form specific mathematical operations. When these units are connected together properly 
they can be used to solve mathematical equations. The independent variable is represented 
by time in the computer. The suitability of the computer for solving differential equations 
arises, therefore, from the ease with which an integration of voltage with respect to time can 
be achieved using a high gain direct-current amplifier having capacitance feedback [14,15]. 
The following basic mathematical operations, required to solve differential equations, are 
performed by an electronic analog computer: inversion, algebraic summation of a number of 
variables, multiplication by a constant, integration of a variable with respect to time, 
