for most conditions evaluated. In 
general, the agreement is better for the 
higher values of advance coefficient J; 
i.e., J near or higher than the design 
value. 
The method of Kerwin (9), which is 
a refinement to the method of Kerwin and 
Lee to account for the effect of the 
inclined slipstream, showed substantial 
improvement over the predictions of 
amplitudes and phases by the method of 
Kerwin and Lee at values of J which are 
substantially less than the design J. 
For higher J values, i.e., J near or 
higher than the design value, where the 
method of Kerwin and Lee was in closer 
agreement with experimental results, the 
improvement by the method of Kerwin was 
smaller. This implies that the 
influence of the non-axi-symmetric wake 
due to shaft inclination on the 
fluctuating forces becomes larger at 
lower values of advance coefficient. 
This trend is expected, as pointed out 
by Kerwin (9), since the effect of wake 
asymmetry is the combined result of the 
time-average loading and the oscillating 
position of the trailing vortex wake 
relative to a point fixed on the blade. 
At low advance coefficients, the mean 
loading is higher, and the pitch of the 
trailing vortex wake is smaller. This 
smaller pitch of the propeller wake 
tends to increase the influence of the 
fluctuating wake position relative to 
the blade on induced velocities since 
the downstream wake is closer to the 
propeller blades. 
In summary, these correlations show 
that the inclination of the propeller 
slipstream relative to the propeller 
axis can significantly influence the 
periodic loads on the propeller blades. 
The importance of this inclination 
increases with increasing time-average 
loading. Of the four methods evaluated, 
the method of Kerwin, which accounts for 
the inclination of the slipstream, gives 
the best predictions of the amplitudes 
and phases of the periodic blade loads. 
The method of Tsakonas et al gives the 
worst prediction of the amplitudes of 
the periodic loads. Further, this 
method failed to predict the trend of 
the variation of the loading 
coefficients with advance coefficient. 
Figure 1]1 presents the variation of 
the periodic loads with inclination 
angle for Propeller 4661 near design J. 
These results show that the rate of 
increase of the periodic loads with 
inclination angle increases with 
increasing inclination angle. Figure 11 
also shows that the correlation between 
experimental resulsts and analytical 
18 
method of Kerwin, which considers the 
inclination of the propeller slipstream, 
is essentially independent of the angle 
of inclination up to 30 degrees. 
PROPELLER 4661 
Oo——O © Experiment 
&r-—-- © Theory (Kerwin-PUF2IS) 
J = 1.062 
INCLINATION ANGLE, y (DEG) 
Fig. 11 — Variation of Periodic Blade Loads with Shaft Inclination 
Correlations in Longitudinal Wakes 
Figures 12 and 13 present the 
amplitudes and phases, respectively, of 
the first harmonic of the Fy component 
on Propellers 4661 and 4710 in the 
longitudinal wake patterns generated by 
the upstream wake screen over a range of 
advance coefficient J. The 
circumferential variation of the 
longitudinal component of the incoming 
velocity is essentially a once-per- 
revolution variation with low velocity 
on the left half of the propeller disk 
and high velocity on the right side of 
the propeller disk looking upstream; see 
Figure 3. Figures 12 and 13 also 
present the correlation between experi- 
mental results and predictions based on 
the three theoretical methods described 
previously.* The results in Figures 12 
and 13 are summarized in Table III for 
design J. 
*For 
the 
the 
Lee 
longitudinal inflow where yp = 0, 
method of Kerwin (9) is identically 
same as the method of Kerwin and 
(8) . 
