and surge can be neglected. 



The heaving motion in response to simple harmonic waves of amplitude 

 a can be described by equation (8. 26)» 



(8. 26) Mz + f z + pgA^z = pgAj^[<^((jL)]aQCOs fj.t 



where Qi[i-) is determined from the wave pressures on the horizontal areas of 

 the wave pole, and M includes the added mass of the water set in motion by 

 the moving wave polCo 





is given by equation (8. 27) 

 (8.27) ((l(H.) = e" g +^ je" g -e ^ k ^i 



where A,, A28 and A_ are the cross sectional areas of the top, middle, and 

 bottom portions of the wave pole respectively. 



Note that as \i. approaches infinity ^i{\i) approaches zero and there is no 

 force on the wave pole. As [x approaches zero p,(^) approaches one and the 

 wave pole follows the wave profile exactly. 



For this particular wave pole as shown in figure 8. 1, (A2/A-,) = (6/2o5) , 



and (A^/Aj) = (12/2.5) . The function ^([i) is graphed in figure 8.2. Because 



of the greater magnitude of the areas of the larger submerged tanks and the 



rate of change of the wave pressure with depth, a wave crest actually produces 



a downward force instead of an upward force for most wave frequencies and 



this force is 5— tinaes greater than that which would have been produced by 



a very long wave acting on a pole of constant diameter A, . 



The wave pole was calibrated in still water by measuring the period of 



74 



