CORRELATION BETWEEN EXPERIMENTAL RESULTS 
AND THEORETICAL PREDICTIONS 
Theoretical Methods 
The experimental results were 
correlated with predictions based on the 
following methods: 
IG The quasi-steady method developed 
at DTNSRDC by McCarthy (5); 
Computer Program QUASI. 
aie The procedure developed 
Laboratory by Tsakonas, 
based on lightly-loaded 
lifting surface theory; 
Program PPEXACT. 
3}6 The procedure developed at MIT by 
Kerwin and Lee (8) based on 
moderately-loaded unsteady lifting 
surface theory; Computer Program 
PUF2. 
4. A refinement of the method of 
Kerwin and Lee (8) developed at MIT 
by Kerwin (9), to allow the axis of 
the propeller slipstream to depart 
from the propeller axis for opera- 
tion in inclined flow; Computer 
Program PUF2IS. 
at Davidson 
et al (6,7) 
unsteady 
Computer 
The procedure developed by McCarthy 
(5) is a simple quasi-steady procedure 
utilizing the open water characteristics 
of the propeller. It is assumed that 
the thrust and torque developed by the 
propeller blade at any angular position 
in a circumferentially nonuniform wake 
is the same as would be produced by the 
propeller blade if it were operating 
continuously at the advance coefficient 
J and rotational speed n based on the 
local wake at the angular position 
corresponding to the mid-chord of the 70 
percent radius. It is further assumed 
chat the instantaneous thrust and torque 
can be adequately estimated by entering 
the propeller open water characteristics 
at the values of J and n based ona 
weighted average over the propeller 
radius of the wake at the local blade 
angular position. This simple method 
can be expected to yield reasonable 
results only if the reduced frequency of 
interest is low, the propeller projected 
skew is small relative to the wave 
length of the pertinent wake harmonic, 
and the wake harmonic corresponding to 
the force harmonics of interest does not 
vary substantially in amplitude or phase 
with radius. These conditions are met 
for propellers and wakes being evaluated 
in the present paper. 
The procedure developed by 
Tsakonas, et al (6,7), is based on the 
linearized unsteady lifting surface 
theory for a lightly-loaded propeller 
using an acceleration potential. The 
10 
numerical procedure applies the mode 
approach and collocation method in 
conjunction with the "generalized lift 
operator" technique. This procedure 
based on the frequency domain assumes 
that a given harmonic of blade loading 
depends upon the corresponding harmonic 
of the wake velocity normal to the blade 
chord line, independent of whether the 
normal velocity results from axial or 
tangential components of the wake. 
The blade load does not depend upon the 
radial variation of the circumferential 
mean wake. The shed and trailing 
vortices are assumed to lie on an 
"exact" helicoidal surface of constant 
pitch extending to downstream infinity 
determined by the propeller rotational 
speed and a single axial inflow 
velocity. The axis of this helicoidal 
surface coincides with the propeller 
axis, regardless of the inclination of 
the propeller shaft to the incoming 
flow. This method does not consider the 
contraction or roll-up of the propeller 
slipstream. All geometric characteris-— 
tics of the propeller are considered, 
except rake, camber, and thickness which 
are assumed to be zero. 
Valentine (20) developed a 
refinement to the method of Tsakonas, et 
al (6,7) for operation in slightly 
inclined flow. This refinement, in 
effect, replaces the "exact" helicoidal 
wake whose axis coincides with the 
propeller axis with a slightly distorted 
one in the direction of the inflow 
velocity. The refinement, which is 
incorporated as a perturbation for small 
inclination angles, relates the unknown 
loading at the first harmonic of shaft 
frequency with the loadings at the mean 
and second harmonics of shaft frequency 
evaluated without the distorted helicoi- 
dal wake. All other assumptions of the 
Method of Tsakonas et al, are retained. 
Calculations made by Valentine (20) 
showed that his modification to the 
method of Tsakonas et al, did not 
significantly improve the poor 
correlation between this method and 
experimental blade loads in inclined 
flow. Further, with the modifications 
by Valentine the disagreement in phase 
between predicted and experimental blade 
loads in inclined flow were even worse 
than the agreement obtained with the 
method of Tsakonas et al. Valentine 
concluded that the effects of shaft 
inclination required a moderately-loaded 
propeller theory, and could not be 
adequately calculated based on the 
lightly-loaded formulation of Tsakonas 
et al. Therefore, the theory of 
Tsakonas et al, as modified by Valentine 
was not correlated with the experimental 
results in the present paper. 
