Wave Excitationless Ships Forms 



where 



K = wave number, 



= encounter angle of an incident wave, and 



h = the wave height. 



Substituting Eq. (3) into (2), we can get approximate value of the amplitude of the 

 heaving force F^^ as follows: 



Fzw 7 (-7ik,pVa.2 + 73pgA)Zw-,/l + (-7ik^/^Va>2 + y^pgk)^ (-^Tt) ^"^^ 



Therefore, heaving force will vanish when the frequency co takes the following 

 value: 







73 gA 



or 



Let us call -Jq ^-S "excitationless frequency" for convenience. To bring this ex- 

 citationless frequency toward low-frequency range of probable wave encounter, 

 it will be necessary to make A/v smaller than usual proportion. It will be noted 

 that results of measured external force to oscillate different bow section models 

 by Paulling (7) indicate the similar tendency, though in his case the inertia force 

 includes the mass of a model itself. 



2. TWO-DIMENSIONAL CASE 



2.1 Submerged Circular Cylinder with a Strut 



1) Theoretical consideration 



In seeking a body which has relatively greater inertia force, one may be 

 aware that an extreme case of such a body is a completely submerged body. 

 The main part of the heaving force acting to a submerged body is an inertia 

 force which is reverse in sign of the wave elevation. Therefore, if a vertical 

 strut of narrower width is attached to a submerged body so that it gives small 

 amount of buoyancy, it will be possible to eliminate the heaving force at a speci- 

 fied frequency of waves. 



Therefore, let us choose a combination of a circular cylinder of radius a, 

 depth f , and a vertical strut of breadth B as shown in Fig. 1. 



385 



