Distribution of Hydrodynamic Forces on a Shipmodel 



REPLY TO THE DISCUSSION BY J. N. NEWMAN 



J. Gerritsma and W. Beukelman 



Technological University 



Delft, Netherlands 



For a fully submerged slender body of revolution in unsteady motion, the 

 total hydrodynamic force on a transverse section is equal to the negative time 

 rate of change of fluid momentum. By taking the time derivative in the moving 

 body axis system the expression 



d , ; • , ; •• ,, dm 



-J- (m z\ - m z„ - V -^— z„ , 

 dt ^ o' o dx ° 



is found. 



For the surface ship, it is assumed that the flow over the submerged portion 

 of the ship is similar to the flow over the lower haK of a fully submerged body 

 with circular cross sections. 



Corrections are then necessary for the shape of the sections and for free 

 surface effects. It is assumed that these corrections are introduced by using 

 Grim's values for the sectional damping and added mass coefficients of cylin- 

 ders having ship-like cross sections oscillating at a free surface. It is admitted 

 that this assumption is more or less intuitive and it was clearly necessary that 

 the assumptions being made had to be verified by experiments, as shown in the 

 paper. 



The authors cannot give a similar physical interpretation of the procedure 

 put forward in Dr. Newman's discussion; they have therefore no rational expla- 

 nation why such an approach is not successful. In addition, the result would 

 certainly not agree with the experiments. 



Vossers* results are discussed too shortly in our paper, and the authors 

 are grateful to Dr. Newman for his additional comments. 



However, for the actual ship form, as tested in our case, the forward speed 

 effect cannot be neglected, even at quite low speeds, say Fn = 0.15. 



For pitch, the method, as given in our paper, is valid for such combinations 

 of forward speed and frequency that the motion of the ship in the stationary 

 sheet of water does not depart too much from a harmonic motion (see Ref . [2] ). 



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