Panel Discussion 



impracticable to incorporate such corrections in routine wave-resistance 

 calculations. , ; . 



Calculations of the wave pattern generated by practical ship hulls reveal 

 several discrepancies between theory and experiment. In the bow-wave region, 

 the main discrepancy is that the observed waves lie outboard of the predicted 

 ones. It is not thought likely that inclusion of the free- surface pressure cor- 

 rection, if it were thought practicable, would remedy this defect, which prob- 

 ably springs from a nonlinear effect on the propagation speeds of the waves that 

 increased their rate of lateral spreading. However, crudely speaking, the effect 

 is as if the model were upstream of its true position, and therefore, as far as 

 the computation of the wave resistance from downstream wave pattern goes, it 

 may not be very important to remedy this defect of the theory. More significant 

 is the fact that the stern-wave system is greatly overestimated in amplitude by 

 the theory. This seems likely to be mainly a frictional effect. Theory predicts 

 that a large wave crest exists just behind the stern, similar to the bow crest on 

 the hull. Whereas the fluid entering the bow crest has been very little influenced 

 by viscosity, however, the fluid just behind the stern has traveled through the 

 hull boundary layer, and it is doubtful whether it could negotiate the steep slope 

 of the forward face of a wave crest there such as theory predicts. It is not sur- 

 prising, therefore, that in practice the stern-crest amplitude is often greatly 

 attenuated. This could lead to the radiated stern waves being much smaller in 

 practice than in theory. 



Such effects would obviously be very difficult to treat theoretically. A 

 seemingly useful empirical approach is as follows: The total downstream wave 

 pattern is written as = Cb + ^S' where l,^ represents a system centered on the 

 bow and l^ a. stern-centered system. Numerical estimates of ^ are obtained 

 from the theory incorporating second-order hull source corrections; I is decom- 

 posed into ^B aJid Cs in such a way that the amplitude functions of ^b ^^^ ^s ^^^ 

 as smooth as possible, to give the most "natural" subdivision into bow and stern 

 waves. The stern-centered system ^g is then multiplied by the empirical reduc- 

 ing factor k and recombined with ^b to give the total wave pattern, and hence the 

 wave resistance. For a typical 0.60-block-coefficient ship, an appropriate value 

 of k is 0.5, and fairly realistic estimates of downstream wave pattern and wave 

 resistance are then obtained. 



Derivation of Source Arrays from Measured Wave Patterns 



N. Hogben 



Ship Division, National Physical Laboratory 



Feltham, England 



INTRODUCTION 



In Refs. [Ij and [2], a method for deducing theoretical source arrays from 

 measured waves by solving linear simultaneous equations, is described. 



1557 



