ADDED RESISTANCE OF 

 SHIPS IN WAVES 



W. P. A. Joosen 

 Netherlands Ship Model Basin 

 Wageningen, The Netherlands 



ABSTRACT 



An expression is derived for the drift force acting on a slender ship in 

 waves. The speed effect in the added resistance is taken into account 

 by using the frequency of encounter. Numerical calculations based on 

 a two-dinnensional strip theory are carried out for various ship forms 

 and the results are connpared with experimental data. 



INTRODUCTION 



The problem of a ship heaving and pitching in the presence of incident 

 waves can be treated by a linear hydrodynamical theory. The forces acting on 

 the ship are purely harmonic and have a linear relation with the motion amplitude 

 or the wave height. Within the framework of the linear theory it is possible, 

 however, also to determine higher order steady forces in the horizontal plane 

 which are due to various nonlinear effects. 



After the work of Havelock (1) and Hanaoka (2) the first complete analysis 

 of the drift forces was obtained by Maruo (3). He derived expressions in terms 

 of the Kochin function. The drift force appeared to be composed of two effects: 

 the motion of the ship and the reflection of the waves. Maruo carried out cal- 

 culations for simple ship shapes. 



The work of Maruo was extended by Newman (4), who included the determi- 

 nation of the vertical moment. He further obtained approximate expressions for 

 slender ships in waves of moderate or large lengths. 



In the present paper a slender body approximation will be developed for 

 short waves. It is well known that in the theory of ship motions this procedure 

 leads to a two-dimensional strip theory, the resulting values being in good 

 agreement with the experimental data. It is expected that a strip theory will 

 give useful results for the drift force as well. Therefore Maruo's expression 

 will be expanded into an asymptotic series with respect to the slenderness 

 parameter, taking into account the first order term only. 



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