118 



THEORY OF SEAKEEPING 



1.2^ 



its 

 .11 



0:234 



Forward Speed, V, F+/Sec. (Against the Waves) 



Fig. 8 Comparison of computed and experimentally meas- 

 ured exciting force and moment amplitudes for ETT Model 

 1445 in waves 5 ft by 1.5 in. (from Korvin-Kroukovsky, 

 1957) 



4 0.5 

 Period T »- 



(a) — Prism 1 2 cm wide, 5 cm draft — Holstein's experimental 



data 

 (A) — Same computed by source distribution along the bottom 

 (c) — Semi-cylinder of 6 cm radius — on basis of Ursell's (1949) 



computations 

 ((/) — Semi-cylinder computed by source distribution over the 



surface 



Fig. 9 Ratio, A, of wave amplitude to amplitude of heaving 



motion of cylinder and of rectangular prism of same width and 



sectional area (from Korvin-Kroukovsky, 1955a) 



/i:2/i'4." A good agreement is demonstrated except at 

 zero model speed. It is possilile that at zero speed the 

 reflections of model-radiated wa\'es from towing-tank 

 walls was affecting the test data. The influence of these 

 reflections was not recognized at the time of the tests, 

 but has since been found important by Golovato and 

 Gerritsma. 



While L'ig. 8 appears to pro^'ide a satisfactory confir- 

 mation of the calculational procedure, it should be re- 

 meml)ered that it is only the result of a single project of 

 small scope. Additional tests by other investigators with 

 several model forms and different wave lengths and 

 heights are desirable. 



The tests of Korvin-Kroukovsky ju.st described, as 

 well as those of Golovato and Gerritsma point to diffi- 

 culties caused by wave reflections at low model speeds. 

 Tests in wide (maneuvering) tanks are therefore recom- 

 mended. 



Attention should l)e calletl t<j the fact that the h_ydro- 

 dynamic force caused liy waves is in composition like 

 the force cau.sed by ship oscillations; i.e. it has force 

 components proportional to acceleration (inertial), to 

 velocity and to displacement. In the analysis of ship 

 m(jtions, Korvin-Krouko\-sky and Jacobs (1957) neg- 

 lected the wave-force component proportional to veloc- 

 ity, since this component became very small after inte- 

 gration of sectional forces over a ship's length. This 

 component cannot be neglected, however, for individual 

 sections when the force distribution along the length is 



important, as in the calculation of hull bending moments 

 (Jacobs, 5-1958) . Therefore, research planning must pro- 

 \-ide for the measurement of the distribution of velocity- 

 proportional forces as well as the inertial ones. 



3.2 Damping Forces. The work of Grim (1953) is 

 particularly valuable in that it contains a comprehen- 

 sive set of curves for estimation of damping. These 

 curves are of A, the ratio of the progressive waves' am- 

 plitude to the amplitude of heaving oscillation, as a 

 function of nondimensional frc(|uenc,v w-B/2g for Lewis- 

 type .sections. From the \-alues of A , the damping force 

 coefficients A''(^) per unit length can be computed readily 

 (Havelock, 19426; St. Denis, 1951) by 



N{^) = pg'A-/w/ 



(21) 



" The method of calculation is described in .\ppcndi.\ C. 



One of the drawbacks to following Grini's study is 

 the extensive interpolation needed to obtain the values 

 of A and the damping-force coefficients for various ship 

 sections. A more convenient approximate evaluation 

 of damping had been developed earlier by Holstein 

 (1936, 1937a, b) and Havelock (1942). Their method 

 is based on the fact that formation of surface waves by a 

 single pulsating source at a depth / can be evaluated as 

 a preliminary step. The solution gives two types of 

 wave systems, the standing waves and the progressive 

 waves. The expression representing a progressive-wave 

 .system at a great distance from a body takes on a simple 

 form. The action of a prismatic body in heaving oscil- 

 lation is replaced by a .series of pulsating sources on the 

 body surface, and the total wave formation is obtained 

 by integration of the effects of separate sources o\'er the 



