Landweber 



thicknesses are in poor agreement with values computed from a for- 

 mula for two-dimensional flow on a smooth flat plate. Although no 

 other analysis was attempted, these data offer an opportunity to test 

 procedures for coraputing a three-dimensional boundary layer, e.g. , 

 by the suggested modification of the method of Webster and Huang. 



Some boundary-layer measurements on a 70-meter research 

 vessel "Meteor" [ 19] and a l:30-scale double model in a wind tunnel 

 [ 20] have been reported by Wieghardt. The full-scale measurements, 

 taken at a point 40 per cent of the draft from the free surface and 

 40 meters from the bow, yielded a value of the shear stress approxi- 

 mately equal to that for a flat plate, but a definitely lower value of 

 the momentum thickness. The results for the boundary layer at the 

 corresponding point on the model were consistent with the full scale 

 measuremients in spite of the neglect of free surface effects in the 

 wind-tunnel tests. Several phenomena peculiar to ship boundary 

 layers were displayed by the model study. One of these is the unusual 

 shape of the boundary layer (vorticity- containing region) around the 

 girth of a fore-ship section, showing bumps at the sides and a great 

 increase in thickness at the keel, attributed by Wieghardt to secondary 

 flow (i.e. , large cross flow) initiated near the bow. The shear-stress 

 coefficient at midship section was nearly constant at about C^ = 0.0035, 

 but decreased to 0.0025 as the keel was approached, and then increased 

 rapidly to 0.0039 at the keel. The momentum thickness 9 varied 

 even more, from a mean value of 9/x = 0.0013 down the sides, in- 

 creasing to a maximum of 0.0028 as the keel is approached, then 

 falling to 0.0018 at the keel. These results indicate that, at least 

 near the keel, the two-dimensional shear stress formulas frequently 

 assumed in computing three-dimensional boundary layers, are very 

 inaccurate. Wieghardt concludes that "much more experimental 

 knowledge about the flow in ship boundary layers, including secondary 

 flows and trailing vortices is needed for semi-empirical calculation 

 methods for such three-dimensional boundary layers ..." 



A project to obtain full-scale measurement of ship boundary 

 layers is under way in Japan, and some results of this work were 

 reported at the 12th International Towing Tank Conference in Rome 

 [ 21] . The unusual shapes of certain velocity profiles astern of the 

 parallel middle body were attributed to the presence of vortices 

 separated from the hull. Clearly these profiles could not be repre- 

 sented by a power law. On one ship an array of five longitudinal 

 vortices was observed in the wake, of which one pair originated at 

 the bow, another pair was shed astern of amidships, and the fifth 

 was due to the propeller. 



A recent paper by Shearer and Steel [17] is noteworthy in 

 that it presents the results of shear-stress and pressure surveys on 

 two ship models at a particular Froude number. The effect of the 

 Froude number on the shear-stress coefficient Cf was found to be 

 small except at the uppermost measurement locations along a water- 

 line at 25 per cent of the draft from the free surface, for which the 



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