Fig. 15a and I5b show some results of added mass and damping co- 

 efficients which, next to the exciting forces, are the most important hydro- 

 dynamic ingredients needed in predicting ship motions and wave induced loads. 



It is seen that Chang's predictions agree well with the experimental 

 results throughout the frequency range whereas the strip-theory results only 

 agree well with the experimental values in the high frequency range. 



A complete evaluation of the ship motions by Chang's method is now 

 in progress at DTNSRDC. 



Chapman [ ^] has shown that by applying slender body theory, the 

 three-dimensional problem of a ship oscillating in the lateral modes of 

 motion (sway and yaw) can be reduced to a series of transient unsteady two- 

 dimensional flow problems in the transverse plane. 



Fig. 16 shows some of his results. In some cases Chapman's results 

 are even more accurate than Chang's because Chapman takes into account some 

 non-linear free-surface effects. 

 ^) Hull form approximation 



Exact hull boundary condition is replaced by some approximate con- 

 dition and so the theories are called, thin-ship theory, strip theory, slender 

 body theory, etc. 



Three-dimensional effect 



In the strip method, the three-dimensional ship hydrodynamics problem 

 is replaced by a summation of two-dimensional sectional problems and the for- 

 ward-speed effects are only satisfied approximately. The strip theory provides 

 good results for heaving, pitching motions in moderate seas and moderate ship 

 speeds for most conventional hull forms; however, the method gives inadequate 

 results for low frequencies, higher ship speeds, local pressure distributions 

 and for sway and yaw motions. The forward speed limitations is the most severe 

 restriction for naval applications. 



79 



