A New Appraisal of Strip Theory 



flow theory, the equivalent mean draft at a specific ship station, which belongs 

 to an infinite cylinder, becomes a(x) H(x) . An overall correction factor such 

 as 



277 



— a(x) H(x) 



will therefore be employed in the calculation of the excitation force at a given 

 section. It must be noted however that the Smith effect should, strictly speak- 

 ing, be a single correction to the wave acceleration force only. 



Since the exact calculation of the total exciting force is a formidable hydro- 

 dynamic problem, the following usual assumptions will be made in the approxi- 

 mate computation: 



a. At each point on the submerged hull surface there is a pressure acting 

 which is the same as the pressure that would occur at the corresponding point 

 in the wave in the absence of the ship. This pressure is computed after the 

 centripetal acceleration of the water particles has been accounted for (Smith 

 effect). 



b. The wave geometry and dynamic state is not affected by the presence of 

 the ship, i.e., any diffraction effects are neglected. 



Assumptions a. and b. constitute the well-known Froude-Kriloff hj^othesis. 



c. The effect of the forward speed of the ship is neglected. 



It is surmised that the differential heaving force as felt by the ship section 

 depends on the instantaneous elevation, velocity and acceleration of the effective 

 subsurface measured relative to the body coordinate system. Thus, 



dx 



Z(h,h,h) exp 



2^ r/ ^ 



(36) 



where ^(x) = a(x) H(x). For small motions, we can expand the function Z(h,h,h) 

 in a Taylor series about the condition of no wave, i.e., h^ = h^ = li^ = o and 

 u = u^ and retain only linear terms. Noting that zch^^.h^^.h^) = o, we finally 

 get, 



dZ_, 

 dx 



3Z^ 



^j h(x.t) . 



Bh 



hCx.t) + 



BZ, 

 Bh 



h(x,t) 



277 



exp — o-(x) H(x) 



(37) 



where the wave elevation is measured positive downwards. The subscript x de- 

 notes that the derivatives (BZ^/Bh)^ etc., correspond to the section under con- 

 sideration only. Since the coefficients of each term are readily computed as 



Bh 



^ Z 



^oC') ' 



BZ, 

 Bh 



= Z 



w(x) 



341 



and 



Bh 



Z. 



w(x) 



