Motora and Koyama 



wave elevation (under cancel). At (^Vg)a = 0.238, the heaving force almost 

 vanishes. At (oj^/g)a = 0.402, where the buoyancy is less than the inertia force, 

 the heaving force is 180 degrees out of phase with the wave elevation (over can- 

 cel). These oscillograms gave valuable information in determining a suitable 

 breadth of the strut. 



To examine the effect of the breadth of the strut as well as the depth of the 

 cylinder, results are shown in Fig. 7. As predicted by theory, c.^o shifts to 

 lower frequency as the breadth of the strut decreases. However, change of 

 depth does not affect oj^. Frequency w^ for a = 10 cm, T = 30 cm is 5.03, which 

 corresponds to ^o = 0-873 for a full-scale ship of length 140 m and draft 10 m. 

 This frequency corresponds to wavelength 61 m for beam seas. However, in 

 case of longitudinal waves, this frequency corresponds to wavelength 200 m at 

 ship speed 18 kts. 



2.2 Elliptic Cylinder with Strut 



To make the draft relatively small, an elliptic cylinder was chosen as the 

 main body. The ratio of major axis and minor axis was varied from 2 to 4, 

 where the breadth of the strut was kept to be a half of the major axis (Fig. 8). 



Results are as shown in Fig. 9. Different from the result of the former 

 case, Wq seems to shift toward lower frequency as the depth increases. Abso- 

 lute value of the heaving force is about the same as the former case. 



2.3 Fins with Strut 



To make the inertia term greater, it is necessary to increase the added 

 mass k^/oV. The virtual mass for a thin plate of breadth 2a is p^a^ per unit 

 length. Therefore, it will be possible to replace ellipse by adequate size of fins 

 as shown in Fig. 10. 



A model in which 2a = 25 cm, B = 15 cm, f = 7 cm was tested in the same 

 technique. Results are as shown in Fig. 11. In general, it can be said that ef- 

 fectiveness of fins are almost equivalent to a thin ellipse. 



3. HEAVING AMPLITUDE 



As shown in Section 2, there are several variations of bodies which are not 

 acted on by wave-induced heaving force at specified frequency. However, it will 

 be premature to conclude that these bodies do not heave at the specified 

 frequency. 



As shown in Eq. (3), damping factor is proportional to the square of the 

 heaving force. This means that a wave-excitationless body is also a damping- 

 less body. 



In fact, in the case of the circular cyclinder as described in 2) of Section 2.1, 

 measured heaving amplitude is quite large as shown in Fig. 12. There appears 

 a high peak at resonant frequency and a minimum point at a frequency about u}^. 



390 



