Strumpf 



ORIGIN OF FIXED AXES 



ORIGtM OF BODY AXES 



ORIGIN OF FLUID AXES 



The weight w of the submersible is positive and includes internal water. 

 The buoyancy B, also positive, is the weight of water displaced by the volume 

 enclosed in the external boundary of the submersible. The coordinates x^.y^,, z^ 

 of the center of gravity (CG) are measured in the body axes frame. The pitch 

 moment of inertia of the body is lyy and is referred to the y axis, and the mass 



m is W/g. 



Derivatives with respect to time t are denoted by a dot over the symbol, 

 e.g., u is the x -component of acceleration. Hydrodynamic force and moment 

 derivatives are evaluated at zero angular velocity, zero acceleration, and zero 

 angles of attack a, sideslip /3, and elevator s . These are denoted by the force 

 or moment with a velocity, acceleration, or angle symbol as subscript, e.g., 

 BZ/3w = z^ and BM/BS = Mg, Second derivatives are denoted in a similar man- 

 ner, e.g., B^x/BwBq = X^„. 



Stability indices are given by a^ , subscript 

 the angular velocity of the longitudinal propeller. 



being an integer. 



denotes 



Subscripts used include a for the change in a value due to addition of an 

 appendage, b and s for bow and stern, respectively, c for thruster control 

 forces and moments, e for the equilibrium value of a quantity, h for bare hull 

 value, and m for maximum value of a quantity. 



The length -^ and the frontal area A of the hull are used in forming dimen- 

 sionless coefficients, which are denoted by the prime of a symbol. Some exam- 

 ples of these are 



x^ = J , Z' = Z/I AU2 , M' = M/f A^U2 , m' = m/f A-C , q' = y ' 



z; = zy4 Au , z; = z /| a^u , h' - ^ ^ i', - i.Vf A-e^ , 



'w w/ 2 



and 



r-tAJ 



where p is the mass density of water and U is the magnitude of U. 



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