Application of Wavemaking Resistance Theory- 

 Very low wave drag at v/\/T = l . , such a gain in viscous drag can be realized 

 without the penalty of increased wave drag. 



This idea of reducing the wetted surface through the application of wave- 

 making resistance theory is quite useful. However, this is not the only way the 

 theory can be used to reduce viscous drag — the form drag can also be reduced, 

 as described below. 



Ever since the comparison of the results of Models 4946 and 4953 (repro- 

 duced here as Fig. 9) were published (Ref. 4), some uneasiness has been felt. 

 The body plans are given in Fig. 10. Model 4953 has 28 percent less displace- 

 ment and 7 percent less wetted surface than Model 4946, and yet has greater 

 total resistance at the lower Froude numbers. It was thought that this was 

 mainly due to the wavemaking resistance, but considering the fact that the dif- 

 ference between these two models is confined to areas much below the free sur- 

 face, it should not produce a big difference in wavemaking resistance, especially 

 at lower Froude numbers. 



One possible explanation for the larger total resistance of Model 4953 is a 

 greater form drag. Due to the flat bottom, large eddies may be created in the 

 water which flows over the bilge to reach the flat bottom. Such eddies are not 

 likely to be created in the case of Model 4946 because of its rounded bottom. 

 However, the turn of the bilge in the case of Model 4953 is not particularly hard. 

 If large eddies do exist under the flat bottom of this model, it is likely that a 

 majority of flat bottom models have the same drawback. 



In searching for evidence of eddies beneath a flat bottom model, the wake 

 survey results behind a smaller version of Model 4210, reported by Wu (Ref. 5), 

 have been studied with great interest. Some of the figures of Ref. 5 have been 

 reproduced here as Fig. 11. This model has a draft of only 0.53 ft and yet the 

 wake is still quite strong at a depth of 0.7 ft. This cannot happen without the 

 presence of large eddies underneath the flat bottom. 



It is quite possible that although Model 4953 has less displacement volume 

 and wetted surface than Model 4946, it may have a stronger wake belt trailing 

 behind it. It would be very desirable to conduct wake surveys behind these mod- 

 els, but these are quite tedious and expensive, and it was thought that a flow 

 visualization test might give a general picture of the flow near the bilge and 

 bottom. Such tests have been conducted on both Models 4953 and 4946 in the 

 circulating water channel. 



Figures 12 and 13 show the corresponding pictures of these two models. 

 Ink was introduced at nearly the same longitudinal stations. All the photographs 

 were taken at a speed of 3 knots. It is quite clear from these pictures that large 

 eddies do exist in Model 4953. These may account for a large portion of the in- 

 creased total resistance. The bottom picture in Fig. 13 shows the ink flow near 

 the stern of Model 4946. The ink was introduced at the bow, and there was no 

 noticeable change in the thickness of ink marks as viewed from the other side of 

 the model. If there is strong eddying, the diffusion of ink is very great, as ob- 

 served in a similar test on Model 4953. (Unfortunately, the corresponding pic- 

 ture was not successful.) 



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