Norrbin 



practical range of swaying frequencies, [ 26] . His results are con- 

 densed In a number of convenient tables and diagrams; the added 

 mass values are seen to vary even outside the limit values cor- 

 responding to zero and infinite frequencies. 



An application of a generalized mapping function technique 

 to ship section forms of arbitrary shape was performed by Porter, 

 who studied the pressure distribution and forces on heaving cylinders, 

 [ 27]. A way of solving the two-dimensional problem without resort 

 to conformal mapping was developed by Frank, who represented the 

 velocity potential by a distribution of wave sources over the sub- 

 merged part of the contour, now defined by a finite number of off- 

 sets. The varying source strength was determined from an Integral 

 equation based on the klnematlcal boundary condition 



Vugts [ 29] contributed an extensive experimental and theo- 

 retical study of the hydrodynamlc coefficients for pure and coupled 

 swaying, heaving and rolling cylinders, based on the previous works 

 by Ursell, Porter and de Jong, [ 30] , The coefficients of the 

 THEODORSEN mapping function were defined by a least square fit 

 of the geometry of the cylinder contours to off-sets In 31 points. Of 

 special Interest Is the good agreement obtained between experiments and 

 the theoretical predictions for the added mass of a typical midship 

 section; the oscillation experiments do not cover the very low fre- 

 quencies, however. Although small the difference in the calculations 

 for the actual section fit and for an approximate LEWIS form was 

 mainly confirmed by the experiments. 



When used with the strip method the Integrated section contri- 

 butions to total added mass and inertia shall be reduced by the 

 appropriate "longitudinal Inertia factors" for three-dimensional 

 effects. Following Lewis these factors are usually taken equal to 

 those derived for the prolate sphereold In a similar mode of motion. 

 This Is only an engineering artifice, and It Is certainly not correct, 

 say, In case of accelerations In yaw for normal hull forms; thus 

 these correction factors are mostly omitted In hydrodynamlc studies 

 of sufficiently slender bodies. 



In a discussion of the strip theory Tuck [ 31] Included the 

 results of all the added mass and dannplng coefficients of a surface 

 ship at zero forward speed, calculated by use of Frank's close-fit 

 method with 15 off- sets for each of 23 stations. The total added 

 mass (-A° ) and moment of Inertia (AgJ of a Series 60 Block , 70 form 

 are here represented by full lines In Fig. 8. Tuck also examined the 

 forward speed corrections to be applied to the integrated values; 

 thus, especially, he put Agg = Agg + (U /oj^) • A°^, or in present 

 notation 



N^u",.") = N!'(c."K ^ +^ • Y!'(c.")^..^^ (6.3) 



834 



