Propeller -Hull Interaction 



and 



s = the thickness of the boundary layer measured to the point where 

 u = 0.99 u. 



The power coefficient n depends on the pressure gradient or on a form 

 factor Hj2, which is the ratio between the displacement thickness s^ and mo- 

 mentum thickness ^2 of the boundary layer, where h.^/h2= (2 + n)/n. The 

 thickness of the boundary layer can be calculated approximately by the relation 



(2) 



RnO ■ 2 



where 



I = the length of the boundary flow, 



c = a constant depending on the pressure gradient or on the form 

 factor Hj2 > 



and 



Rn = the Reynolds number f u / v. 



For the flat plate without pressure gradient, n is about 7, and C is about 

 0.37. Substituting the value of 5 in the first expression, 



u /y Rnl/5\ 1/n 

 U ~ W C / 



Using the subscripts M and S for the model and ship, respectively, an 

 equation like this can be written for model and ship. Usually, n will be a little 

 larger on the full scale, and little is known about the values of C^ and Cg. As- 

 suming that n and c are the same for model and ship, then approximately the 

 velocity ratios at equal relative positions y/? in the propeller plane of ship and 

 model are related as follows: 



Us Um 



Rrij 

 Rn. 



0. 2/n 



By Froude's relation, R^s/^m = '^■^^^, where ^ is the scale ratio between 

 ship and model, so that 



• 1 0.3/n„ 



Us ^u 



For a flat plate, if n is 7 and the scale ratio ^ is 30, the value of the ratio 

 ug/u^, is 1.16; for X equal to 40, it is 1.17. K n is less than 7 (say, 5) these 

 ratios become 1.23 and 1.25. 



The program for the cavitation committee is to do a test first in the uncor- 

 rected wake field and then to determine the value of n from a model test at 

 various water lines and correct the wake field for the scale ratio. The new 

 wake field would then be simulated in the cavitation tunnel and the cavitation 

 pattern studied. The same methods will be used to calculate the thrust and 



1654 



