o ////;//;///, 



///////;// Y 



Figure 3 - Horizontal Motion, 

 Rigid Wall 



Figure U - Horizontal Motion, 

 Free Surface 



To my knowledge the evaluation of hydrodynamic masses for the 

 boundary condition <t> = has been carried out comprehensively for the first 

 time by Lockwood Taylor. 5 



The foregoing reasoning can be illustrated by well known first 

 order results for the circular cylinder and the sphere (Figure 5)- The ratio 

 radius r, over depth of immersion f, is assumed to be small. 1 



For a motion in a horizontal plane Z = -f parallel to the wall and 

 to the free surface one obtains: 



Cylinder 



k = 

 y 



i 



\ (§)' 



[13] 

 ;i3a] 



Sphere 



V 1 + fc(*)' 



k = 1 - 



y 



3 (LY 



T6 if/ 



[14] 

 "l4al 



In the case of a motion vertical to the wall (surface) similar 

 expressions with larger correction terms are valid. 1 



As compared with the inertia coefficients calculated for infinite 

 depth of immersion, f •*• «>, a dependence upon the wall distance arises. It 

 is easy to estimate the magnitude of f for which this wall influence disap- 

 pears. Such estimates also will be valuable for the general case of a fluid 

 with gravity; this can be, for instance, important in experimental tank work. 



The change in the sign of the correction term [13] and [13a] for 

 the wall and the free surface is due to the difference in the procedure of 

 mirroring the images involved. 



One could assume that the 

 "wave values" k are included between k 

 and k as bounds. This may be frequent- 

 ly a useful approximation, but is by no 

 means exact, as will be proved below. 



It will be shown later that 

 the boundary condition <f> = leads to 

 a further important solution of the 

 general case. Figure 5 



- L e 



