HYDRODYNAMIC FORCES 



133 





1 2 3 4 5^7 



ZTVg 



Fig. 26 Ratio of added mass to mass of ship model: 1 — experimental curve, 2 — theoretical curve (from 



Haskind and Riman, 1946) 



Fig, 27 Variation of damping coefficient with frequency: 1 — experimental curve, 2 — theoretical 



curve (from Haskind and Riman, 1946) 



computed functional relationship between damping 

 coefficient and ship speed was similar to the measured 

 one. The computed values were, howe\'er, much larger 

 than the experimental. Newmann's (1958) report is, 

 however, a preliminary one and the subject is being in- 

 vestigated further. 



The assumption that angle a is small corresponds 

 closely to reality in ships of low prismatic coefficient. 

 However, the assumption that angle ^ is small implies 

 a small beam/draft ratio and a large angle of deadrise 

 which are usually not found in ships. On the other hand, 

 the theory of wave resistance developed in numerous 

 publications of Havelock, Guilloton, Weinblum and Wig- 

 ley, and the ship-motion theories of Haskind and Hana- 

 oka give reasonably good results despite this discrep- 

 ancy. This is explained l>y the fact that the paits of a 

 ship's surface nearest the free water surface are most sig- 

 nificant in causing wa\'es, while deeply submerged parts 

 have less effect. In all cases where comparisons of theo- 

 retical and experimentally measured wa\'e resistance 

 were made, the idealized ship lines were such that a 

 ship's sides were tangent to the vertical at LWL; i.e., 

 the angle /? approached zero. A very large angle /3, 

 which is not compatible with Michell's assumption, oc- 

 curred only at the bottom of a ship's surface where ele- 

 ments have relatively small effect. 



6.3 Experimental Verification. An idealized ship 

 model was also used in the experimental verification of 

 Haskind's theory b.y Haskind and Riman (1946). The 

 \'erification was limited to heaving motion. The ship 

 lines, shown in Fig. 24, are defined by the equation 



2/ = ± .f A'(.r)Z(^) 



(50) 



where X{.x) is a function giving the shape at the water- 

 line, and is taken as a fourth-degree parabola 



A(.v) 



1 



(51) 



X and ij are distances from the midship section and plane 

 of symmetry, respect ix-elj'. L is the length of the ship. 

 The function Z{z) gives the shape of cross sections and 

 is defined by ec|uatinn 



Z{z) 



1 - 



kl 



(52) 



where d is the draft and bd designates the extent of the 

 vertical ship side below LWL as .shown in Fig. 24, where 

 all dimensions are in millimeters. The model used was 

 2000 mm (6.56 ft) long, 250 mm (0.82 ft) wide and had 

 loo mm (0.44 ft) draft. The model was restrained from 

 pitching and was oscillated in heaving by means of a 



