TABLE III - COMPARISON OF EXPERIMENT AND THEORY IN 
LONGITUDINAL FLOW — AMPLITUDES AND PHASES 
OF FIRST HARMONIC LOADING COEFFICIENTS 
AT DESIGN J 
Kies 
Kex)4 
K (pdt, EXP K(Ex)1, EXP 
amPLITUDE | 1000- 
(Fx)1 
Experiment 
McCarthy 
(QUASI!) 
Tsakonas et al 
(PPEXACT) 
Kerwin and Lee 
(PUF2) 
Experiment 
McCarthy 
(QUASI) 
Tsakonas et al 
(PPEXACT) 
Kerwin and Lee 
(PUF2) 
The experimental curve presenting 
“(Px)1 versus advance coefficient J 
shows a concave shape with a minimum 
value near design J; see Figure 12. The 
same trend was observed for other loading 
components (not shown). All of the theo- 
retical methods are in good agreement 
with experimental (py) ] near design 
J; however, they did not, in general, 
agree well with experimental (py) 1 
over a wide range of J. The correla- 
tions between experiments and theore- 
tical predictions are somewhat different 
for the two propellers. 
The predictions by the quasi-steady 
method of McCarthy showed different 
trends for different propellers. For 
Propeller 4661, the predicted values of 
and *(px)1 and 90k/dJ increase with 
increasing J. For Propeller 4710, how- 
ever, the predicted values of X(py)1 
and 3k/dJ decrease with increasing J. 
The trends of the predictions by the 
quasi-steady method of McCarthy are quite 
sensitive to small changes in the slopes 
of the open water curves; i.e. Km 
versus J and Kg versus J. 
The phases shown in Figure 13 show 
that the quasi-steady method of McCarthy 
predicts that the maximum value of 
(Fy)1, will occur at approximately 
PROPELLER 4661 | PROPELLER 4710 
CONDITION vy =0 DEG ) =0 DEG 
20 
25 and 10 degrees of blade angular 
position after the experimentally 
determined angles for Propellers 4661 
and 4710, respectively*. 
The unsteady theory of Tsakonas et 
al (6,7) predicts a similar trend of 
K(Fx)] with J in axial and tangential 
wakes; i.e., the predicted (py) 1 
tends to increase with increasing J 
and 0k/dJ to decrease with increasing 
J. These predicted trends are similar 
because this method considers only the 
component of wake resolved normal to the 
blade pitch line, for either longi- 
tudinal or tangential wakes. Thus, as 
discussed previously, this method does 
not distinguish between longitudinal and 
tangential wakes. 
The trend of K(py)] with J 
predicted by the method of Tsakonas et 
al does not agree with the experimental 
results. At low values of J; i.e., high 
time-average loading coefficient, this 
method gives the worst correlation with 
experimental results among the three 
methods evaluated. This occurs, in 
part, because the theory does not 
account for the influence of the time- 
average loading. As discussed in the 
preceding section, it is unclear why 
this method predicts that the loading 
coefficient decreases with decreasing J, 
rather than predicting that it is 
insensitive to J. 
Near design J, the method of 
Tsakonas et al (6,7) predicts kK (py)1 
in longitudinal wakes which is close to 
the predictions by the other calculation 
methods, and reasonably close to 
experimental results. In contrast, in 
inclined flow the method of Tsakonas et 
al predicts much smaller values of 
K(Fx)1 than either the other calcula- 
tion methods or the experiments even at 
design J; see Figure 9. In particular, 
near design J the predictions of k(py)1 
by Tsakonas et al agree with the predic-—- 
tions of Kerwin and Lee in longitudinal 
flow but not in inclined flow. This sug- 
gests that the tangential inflow veloci- 
ties significantly influence the 
periodic blade loads in a manner which is 
considered by the method of Kerwin and 
Lee but which is not properly considered 
by the method of Tsakonas et al. 
*Recall that Propeller 4661 rotates left- 
hand and propeller 4710 rotates right- 
hand, and the phase angle is the angle 
of the blade reference line which the 
maximum positive loading occurs measured 
from the upward vertical positive in the 
direction of propeller rotation. 
