Figures 6, 7, and 8 show the added mass and damping coefficients. The presently 

 computer results are compared with those of strip theory. The results of strip 

 theory were computed by the computer program MOT35 (Reference 16) which is based on 

 the analytical method developed by Lee. The two-dimensional potential (strip 

 theory) is solved by the Frank close-fit method. The effects of fins and viscosity 

 are included in the computation of added mass, damping forces, and excitation forces. 



This computer program has been improved by adding surge effect to the pitch excita- 



2 

 tion moment due to the incoming waves and by correcting for viscous damping. 



The results for added mass by the present method are almost 70 to 80 percent 



higher than those from strip theory, while the damping coefficients are slightly 



less than those from strip theory. In the present method the results of the unified 



slender-body theory are added to those of the strip theory as a correction term 



(Equation (63)). For the added mass coefficients, these correction terms are too 



large. The large discrepancy may result from the different methods used to solve 



3 

 the strip theory. In the derivation of the unified slender-body theory, Newman 



solved the strip theory with the multipole expansion method (Equation (50)). In 

 Equation (50) a is a source located at the origin and is used to solve the three- 

 dimensional source strength (Equation (62)), from which the correction factor C. is 

 computed as in Equation (61) . The only part of the source located at the origin is 



a^ . The other part of the source is a from Equation (50), which is included in the 

 J m 



computation of the two-dimensional added mass and damping coefficients, but is not 

 included in the three-dimensional source strength. 



In the present approach for solving the two-dimensional problem, the Frank 

 close-fit method (Equation (100)) was applied. In Equation (100) O is distributed 

 on the contour of the section, and the corresponding source a , which is located 

 at the origin, is computed by the relation in Equation (105) . To solve the three- 

 dimensional source strength, a_ was replaced with a , but O includes the effect of 



3 o o 



o„ and a . It is difficult to decompose a into o„ and a in the Frank close-fit 

 J m o 3 m 



method. If a ^s not computed accurately, the three-dimensional source q. in 

 Equation (62) cannot be solved correctly, even though the kernal function f (x) has 

 been evaluated properly. Therefore, the difference between a„ and a could possibly 

 cause the large discrepancy in added mass coefficients. 



36 



