32 



CORRECTION FOR DRAG OF A TRIP WIRE 



Experiments conducted by H. Schlichting 14 have shown that the incre- 

 ment of drag induced by an isolated roughness (small protrusion) in the bound- 

 ary layer of a flat surface may be closely approximated by the drag of the 

 same roughness placed in a free stream where the speed is equal to the 

 boundary-layer velocity at a distance from the surface equal to the height of 

 the roughness. The drag of a trip wire may therefore be approximated by 



D s =|c D dZu 2 [18] 



where u is the speed in the boundary layer at a distance of the wire diameter 

 d from the surface, 



C n is the drag coefficient of an infinite cylinder subjected to the free 

 stream velocity U = u, and 



I is the wire length. 



The velocity u may be conveniently estimated from Pohlhausen's orig- 

 inal approximation 6 for the laminar velocity distribution, which is 



where y is the distance along a normal to the surface and 6 is the boundary 

 layer thickness, i.e., the value of y at which u = 0.99U. 



The boundary-layer thickness which is derived for this velocity dis- 

 tribution is given by the formula: 



*'*■)/¥■ [20] 



where x is the longitudinal distance from the leading edge, and R x is the x- 

 Reynolds number, Ux/v. 



To compute the boundary layer velocity u at the height of the "rough- 

 ness" let y = d in Equation [19]. Then 



2d / d \ r 



TT-f-(f-) l*'l 



Since d/«J varies between 0.11 and 0.17 between towing speeds of 1 .0 and 3-5 ■ 

 knots it was considered sufficiently accurate to drop the square term and use 



JL _ 2d 

 U ~ 6 



[21a 



