Analysis Used in Submerged Body Research 387 
Symbol Dimensionless Form Definition 
wy The angle of yaw 
ms w' = 4h Circular frequency of oscillation 
ol 
o, a 7 Natural frequency of undamped oscillation 
Subscripts: 
in In-phase component of force or moment 
out Out-of-phase or quadrature component of force or 
moment 
o Maximum amplitude 
1 Associated with forward strut 
2 Associated with aft strut 
m Model. 
INTRODUCTION 
The problems associated with the dynamic behavior of the submarine and other sub- 
merged bodies, that is, stability, performance, and ease of handling, have become increas- 
ingly more and more important with each new increase in submerged speed. This has been 
particularly true for motions in the vertical plane since the submarine must be operated, 
strictly on instruments, within the confines of a layer of water usually no greater than a few 
boat lengths. Also, the increase in submerged speed has given rise to some serious dy- 
namic problems for motions in the horizontal plane and made the problem of emergency re- 
covery increasingly more acute. 
In the early stages of development in the field of submarine stability and control the 
designer was faced with the problem of providing a combination of characteristics and means 
for controlling the submarine which would result in satisfactory dynamic behavior. A major 
difficulty in providing for this was the lack of sufficient information to guide him in the 
choice of a combination of physical characteristics which would result in adequate stability, 
performance, and ease of handling. Another major difficulty was the lack of straightforward 
design methods and experimental or theoretical techniques for obtaining a desired combina- 
tion of characteristics. In those cases where the results of model tests in the form of the 
various hydrodynamic coefficients were available, the interpretations that could readily be 
made relating them to adequate dynamic behavior were rather limited. The designer was 
further handicapped in that he had no standards by which he could evaluate the dynamic be- 
havior of the submarine. 
The mission of the Stability and Control Division at the David Taylor Model Basin has 
been, therefore, to remedy this situation. This has been partially accomplished by the 
