Shear Stress and Pressure Ditstrtbutton on a Shtp Model 
misaligned probe is also shown. Since the angular response is a 
cosine function, the angle between the maximum shear stress anda 
reference line, 2 can be obtained by rotating the probe +6 with 
respect to this line, i.e., 
cei ens Os 2i 250 we! (Al) 
where (e)+, is the output when the probe is rotated at an angle equal 
to t g respectively. The values of @ used in the study were 45 deg. 
and 30 deg. depending upon the angle of the shear stress vector with 
respect to the reference line. The film on the probe element was 
aligned parallel to the waterlines for points on the ship side and 
parallel to the buttock lines for points on the ship bottom. The angle 
between the maximum stress and the reference line is obtained 
through Equation (Al). The magnitude of the shear stress along the 
reference line and the angle 2 , along with the direction cosines of 
the waterline and buttock line tangents and the surface normals cal- 
culated from the surface equation 2© were sufficient to decompose 
the shear stress coefficient vector Cy into the components (Cy, , 
Cry, C4,), relative to the body axes (x, y, 2). 
One of the difficulties in using the hot-film shear probe is 
mounting the probe perfectly flush to the surface. As shown in 
Figure A3, the response is very sensitive to the probe protuberance. 
In order to keep the accuracy within 5%, the probe protuberance 
should be kept within 0.002 inches. This was accomplished by using 
a flat face pressure transducer as a probe feeler. 
(2) Preston Tube and Directional Preston Probe 
The Preston method of measuring skin friction in the turb- 
ulent boundary layer makes use of a circular pitot tube resting on 
the wall. The Preston tube pressure, together with the static pres- 
sure at the same point, permits the computation of the skin friction 
at that point. The use of the Preston tube is based on the assumption 
that the tube lies within the law-of-the-wall region of the boundary 
layer. In this study we limit the diameter of the Preston tube to 
less than 15% of the boundary layer thickness in order to satisfy this 
assumption, The calibration of a Preston tube reported by Landweber 
and Siao 33 , by Patel?* , and many others is shown in Figure A4. 
The Preston tube used was also calibrated ina 1l-inch pipe flow. 
PSFe 
