Wave Resistance 



resistance.) The latter problem was also treated in two dimensions, but in- 

 cluding surface tension, in the earlier work of Wu and Messick (1958). 



MISCELLANEOUS 



One of the most important experimental developments, which has brought us 

 to our present state of inquiry, is the determination of wave resistance from 

 analysis of wave records. Several different methods exist for performing this 

 analysis, and none can be regarded as "exact," but the results are fairly consist- 

 ent and seem likely to be at least as reliable, for their stated purpose, as the 

 Froude or Michell approaches are for theirs. However, the wave analysis tech- 

 niques are still being examined critically, and Sabuncu (1968) has examined the 

 effects of the local disturbance which are neglected in the usual free-wave analy- 

 sis, and has also proposed the use of the wave-height measurements to deter- 

 mine the "equivalent body shape" which is the source of the disturbance. This 

 appears to be an interesting scheme for experimentally finding the effective hull 

 shape, including the displacement effects of the boundary layer and the separated 

 wake. (The same scheme has been employed by Hogben (1967, 1968), who has 

 demonstrated its success in the case of a parabolic model.) 



Inui and Kajitani (1968 a,b) have investigated the bow wave system of a 

 Wigley model and have compared the experimentally measured waves with cor- 

 responding theoretical predictions. It is found that good agreement results for 

 wave angles 20" <6 <60°, but that for smaller or larger angles the theoretical 

 prediction of wave amplitude is substantially greater than that which is meas- 

 ured. For wave angles greater than 60" (i.e., very short wavelengths), this dis- 

 crepancy is attributed to nonlinear effects, associated with the high values of 

 the wave steepness in this region. For the angles less than 20°, the discrepancy 

 is attributed to sheltering effects of the hull. Correcting empirically for the 

 sheltering effect improves the experimental agreement considerably and also 

 appears to lead to a superior approach for the investigation of low-resistance 

 hull forms. 



A recent experiment of fundamental significance has been performed by 

 Sharma (1968), which might be conveniently described as a modern version of 

 the Weinblum-Kendrick-Todd friction plank experiment. Sharma towed a wall- 

 sided parabolic strut, of length 2.0 m, beam 0.1 m, and draft 0.3 m, at Froude 

 numbers ranging from 0.2 to 1.0. Measurements were made of the free-wave 

 spectrum using a longitudinal cut, and the wave resistance was computed from 

 these data and also from Froude's method using the Prandtl-Schlichting fric- 

 tional drag estimate and a constant form factor C^/Cp = 1.15. The results of 

 both experimental methods show quite good agreement with each other and with 

 Michell's integral over the entire Froude-number range. Some significant dis- 

 crepancy was found in the phase of the free waves at low Froude numbers, 

 which Sharma attributes to nonlinear wave effects. (The satisfactory agreement 

 achieved for this model, and for the parabolic hull discussed by Shearer and 

 Cross (1965), is the principal evidence to suspect the importance of separation 

 and nonlinear effects.) 



Since attention has been focused on the low-Froude-number regime by the 

 practical speeds of merchant ships and by the lack of satisfactory theories and 



1552 



