Shear Stress and Pressure Distribution on a Shtp Model 
where {¢ is the wave height inthe oxyz coordinate system and h 
is the distance between o'x' and ox, 
The measured CC. along streamlines A,B,C, and D, and 
along waterline E and the corresponding approximate C, computed 
from Equation (7) and for the double models are shown in Figure 9. 
As shown in Figure 9-e the wave approximation (Equation 7) is in 
good agreement with measured values near the free surface (14% 
draft) for the three Froude numbers tested. However, this approxi- 
mation is not valid near or on the ship bottom. On the after half of 
the flat ship bettom the measured C_ is in general close to the C 
predicted by the double model (Figure 9-a through 9-c), and the 
effect of the surface wave (Froude number) there is small. However, 
some effect of waves (Froude number) on C_ onthe forward half of 
the ship bottom is noted. It should also be noted that C.. near the 
keel (streamline A) ata Fn=0.22 is very close to the C. predict- 
ed by the double model. Figure 9-b shows the C, of the double model 
model computed by the Douglas-Neuman theory * and slender body 
theory *'8 Close agreement between the two computations in the 
middle of the ship is noted. 
(5) Shear Stress Distribution. The local shear stress coef- 
ficient is defined as C; = tw/ (PV*/2), a vector tangent to the hull 
surface. The shear stress magnitude and the angle of the probe 
relative to the waterline for points on the ship side and to the buttock 
lines for points on the ship's bottom were measured by rotating the 
probe to three angular positions (0,+ 0 ). This can be used to compute 
the magnitude and angular position of shear stress vector on the hull. 
This information along with the direction cosines of the waterline or 
buttock line tangents and the surface normal calculated from the sur- 
face equation © , were sufficient to decompose the shear stress 
vector into three components (C, 3 Cry eS ) relative to the 
body axes (x, y, z,). The measured direction cosines of Cy rela- 
tive to the (x, y, z) axes are shown in Figure 10 at the high and low 
Froude numbers of the experiments. Note that these direction cosines 
do not vary much with Froude number except near the station of 
maximum wave slope (i.e., between x = -0.7 and -0.5). 
In Figure 11 we present the measured and calculated distri- 
butions of Crs, along various streamlines and on waterline E. Note 
that the agreement between experiment and calculation is better at 
low Froude numbers and is fairly good on streamline A for the entire 
range of Froude numbers of the experiment. In these cases, wave 
effects were at a minimum and this indicates that the Cumpsty-Head- 
Smith boundary layer calculation is adequate for moderate block- 
1973 
