condition, between 20 and 40 values of 
advance coefficient were evaluated in 
order to well define the manner in which 
the loading varies with advance 
coefficient. In general, each 
experimental condition was run three 
times, once for each of the three 
flexures. This was necessary in crder 
to obtain all six components of force 
and moment. Data were also collected 
with the propellers rotating in air at 
0, 10, 20, and 30 degrees of shaft 
inclination over the range of rotational 
speeds evaluated in water. This 
provided the gravitational and centri- 
fugal loads that were later subtracted 
from the total propeller blade loads 
measured in water. 
Data Acquisition and Analysis 
Data were collected and analyzed in 
the same manner as in the steady ahead 
runs described in References 1 through 
4. For each flexure, an Interdata 70 
Computer was used to collect and average 
the force and moment data for each 
4-degree increment of blade angular 
position over 200 to 300 propeller 
revolutions. Propeller rotation speed, 
n, and model (or carriage) velocity, V, 
were recorded for every set of two 
propeller revolutions, and averaged over 
the period during which data were 
collected. 
At the end of each run, the 
computer analyzed and printed the data. 
The average force and moment signals for 
each 4-degree angular position were 
printed along with the average model 
velocity and propeller rotation speed 
for the run. The standard deviation of 
the accumulated data for the run was 
also calculated for V, n, and the force 
and moment signals at each position. A 
harmonic analysis was performed on the 
force and moment data providing the mean 
signal and amplitude and phase of the 
first 16 harmonics. 
First, the experimental agenda was 
completed for all three flexures at each 
Major condition (each propeller, wake 
screen, and value of ~) except wp = 30 
deg. Then the corrections for 
interactions were calculated at five 
values of J at which measurements with 
all three flexures were made using the 
same procedures outlined in Reference 1 
through 4. After the correction for 
interactions, the centrifugal and 
gravitational loads were subtracted from 
the total experimental loads to obtain 
the hydrodynamic loads. 
Accurac 
The accuracy of the experiment was 
generally similar to that of the steady 
ahead runs in References 1 through 4. 
During a single run, where signals were 
averaged over many revolutions, the 
standard deviation of the measured 
forces and moments maintained a similar 
error (95 percent confidence band) of +5 
to +10 percent of the averaged signal at 
each angular position. For a given run 
the average error in model speed V was 
approximately +1.0 percent, and the 
error in rotational speed n was less 
than +0.01 percent 
Except for the fluctuations in 
signals occurring in a given run, the 
accuracy of the data is indicated by the 
repeatability of an identical condition. 
An effort was made to set experimental 
conditions identically on repeat runs; 
however, some variation was unavoidable 
due to manual setting of the model speed 
and propeller rotation speed, random 
zero shift in data channels, and minor 
variations in basin water conditions. 
This resulting error is approximately +2 
percent of the measured first harmonic 
loading component. A more detailed 
error analysis based on the repeata- 
bility of the hydrodynamic, centrifugal 
and gravitational loads will be presented 
in a future DTNSRDC Report. 
EXPERIMENTAL RESULTS 
Loading Components 
The basic loading components are 
shown in Figure 1. For a right-hand 
propeller the sign convention follows 
the conventional right-hand rule with 
right-hand Cartesian coordinate system. 
For a left-hand propeller all the loads 
are the same, but for this case the sign 
convention follows a left-hand rule with 
a left-hand Cartesian coordinate system. 
Each component of loading is 
generally represented as a variation of 
the instantaneous values with blade 
angular position, 6, and as a Fourier 
series in blade angular position in the 
following form: 
epee N 
F,M(0) = (F,M)+ > (F,M), cos{nd-(d¢ m),} (2) 
n=1 
In general, the loads consist of 
hydrodynamic, centrifugal and gravita- 
tional components. However, in this 
