Before concluding the roughness discussion, it may prove useful, with regard to 

 scaling, to compare the foil tip boundary layer thickness 6 with the roughness 

 height k . The detailed calculation is given in the Appendix and assumes fully tur- 

 bulent flat plate flow with zero pressure gradient. For the experimental conditions 



reported, U = 43 ft/sec (13.1 m/sec) and k = 600 microns, the ratio of roughness 



s ° 



boundary layer thickness 6 to the roughness height (grain size) k is estimated to 

 be 



6 /k -^ 0.38 

 r s 



or a roughness height approximately 40 percent of the boundary layer thickness. This 

 calculation is presented for comparative purposes only; obviously the flat plate as- 

 sumption will overpredict 6 at the hydrofoil leading edge. The scaling implications 

 involving the boundary layer parameters and k should be the subject of further 

 research. 



In summary, the roughness experiments identified an optimum roughness pattern 

 and grain size-600-micron grain size applied to both the pressure and suction side 

 tips as prescribed above. This particular roughness arrangement resulted in TVC 

 inception speed increases of up to 92 percent with no measurable loss in foil 

 performance. 



Bulbous Tip 



As discussed earlier, the bulb modification involved only the thickening of the 

 cambered airfoil sections of the parent foil in order to minimize both performance 



loss and local surface cavitation. The maximum bulb thickness was based upon the 



13 

 findings of Crump. The experimental lift curve slope data for the large and small 



bulbous tip foil are shown in Figure 27 and indicate a loss of 7.5 and 2.9 percent 

 in the lift curve slope respectively as compared to the parent foil. Additional 

 insight also is given in Figure 20, which shows that the roll moment arm for the 

 bulbous tips has moved inboard approximately 6.6 and 2.5 percent of the foil span for 

 the large and small bulbs respectively. This result is shown qualitatively in 

 Figure 17 which indicates that the spanwise location of the bulb TVC has moved in- 

 board. These combined results indicate that the bulb sections are not producing the 

 predicted lift. This loss was somewhat unexpected since the bulb was initially de- 

 signed to have a lift curve slope similar to the parent — lifting surface theory 



38 



