Vassilopoulos and Mandel 



of motion can be computed on the basis of a strip technique. The extension of 

 this approach to the other coefficients will be fairly apparent so that the values 

 of the other coefficients will be given without derivation. 



Equation (28) indicates that, after linearization, the coefficient of the heave 

 acceleration term a(a)^) consists in fact of two additive terms; the mass of the 

 ship, m, which is known and is constant with time and the partial derivative of 

 the total vertical hydrodynamic force with respect to heave acceleration, z- . 

 This is the force that is exerted on the body when oscillating in smooth water 

 and its derivative is computed at the equilibrium condition characterized by a 

 constant ship speed u = u^,, and byzQ=6'=w=q=w=q=o. 



The statement of the problem has been given but the exact solution for the 

 complete three-dimensional body is available only for special mathematically 

 defined forms. Theoretical results are however available from two-dimensional 

 theory; hence, it will be assumed that an arbitrary three-dimensional body can 

 be replaced by the sum of a large number of two dimensional segments or strips. 

 This is the essence of strip theory. It involves the following simplifications: 



a. The underwater hull geometry is defined by an arbitrary number of typi- 

 cal sections. 



b. These sections are arbitrarily assumed to be equally spaced. 



c. To date, these sections are defined in terms of two geometrical parame- 

 ters; the sectional area coefficient, o-(x) and the beam/draft, B(x)/H(x), ratio 

 of section or its reciprocal. 



d. Each of the strips is assumed to belong to a specific infinite cylinder 

 oscillating at zero forward speed and its behavior is assumed independent and 

 isolated from the neighboring strip. 



e. Loi^itudinal perturbation velocities which exist in the three dimensional 

 problem are totally neglected. 



f . Since the available theoretical data to be used are based on an ideal 

 fluid, viscosity is ignored. 



FoUowii^ strip theory, 



+L/2 



Z. = - Z.(w x) dx (32) 



-^-L/2 ^ 



where the integrand is the partial derivative of the force on the strip, which on 

 the basis of extensive theoretical data is defined as 



Z.(C0^,K) = kjk^C B(x)2 . (33) 



The integrand is more commonly known as the added mass of the section or 

 strip where the constant c = np/s. 



332 



