Wave Resistance 



due to flow at the ship's bottom, the ship- surface corrections remain 

 negative and large. This is in contrast to experimental evidence as 

 well as to results from a slender-body-theory approach. Tentative cal- 

 culations support the conclusion that at high Froude numbers the first- 

 order approximation should be constructed according to slender -body 

 theory (this would even imply a reduction of the computational effort) 

 with less flow intensity at the ship's bottom area, and then improved by 

 the iteration method developed. 



It is found that the procedure developed is not affected by singular be- 

 havior of the first-order flow at the bow, stern, and keel, resulting from 

 that part of the flow which would persist at zero Froude number, if ap- 

 propriate methods of quadrature are selected and if the flow is evalu- 

 ated on the hull rather than on the centerplane. This is considered to 

 be even more pertinent for analytical reasons. 



The second-order corrections found explain a significant part of the 

 discrepancies between experimental wave resistance and predicted val- 

 ues from first-order theories . The rest m.ust be attributed either to 

 viscous wave interactions or to resistance components of still higher 

 order. At least in the range of Froude numbers larger than 0.2, where 

 the present investigations were performed (mostly for reasons of econ- 

 omy), it is felt that the computational effort is moderate, once a com- 

 puter program has been established, and attempts to apply the method 

 to more conventional forms should be encouraged. 



Wave- Resistance Calculations for Practical Ships 



G. E. Gadd 



Ship Division, National Physical Laboratory 



Feltham, England 



A computer program has been written which appears to give fairly realistic 

 estimates of the wave-making of practical ship hulls which are not too blxiff . 

 Kelvin sources are distributed over the vertical plane of symmetry of the hull, 

 which is divided into a grid of rectangular panels, the hull shape being defined 

 by the lateral offsets corresponding to the grid intersection points. The source 

 density is assumed uniform over each of the panels in the computation of the 

 downstream waves, but for computing local effects near the hull the cruder ap- 

 proximation is made of replacing each source panel by a concentrated source of 

 equal flux output at its center. 



Source strengths are calculated using second- order corrections as de- 

 scribed by the author (J. Inst. Maths. Applies. Vol. 4, p. 43, 1968). The free- 

 surface pressure distribution, which should be imposed (K, W. H. Eggers, Pro- 

 ceedings of the Sixth Symposium on Naval Hydrodynamics, p. 649) to compensate 

 for linearization errors in the free-surface boundary condition, is neglected. 

 This pressure distribution was computed for the simple case of a single sub- 

 merged point source, but so much computer time was involved that it was judged 



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