for the left-hand propeller) intersects the plane normal to the pro- 
peller axis at the angle $6 Tia tan (Py ,/ (0.47D)) and is directed 
so that a positive M puts the face (pressure side) of the blade 
0.4 
in tension. In calculating M from the experimental values of the 
0.4 
three measured forces and three measured moments, an adjustment was 
necessary to allow for the contribution of loading in the region 
0.4R>r>r, =0.3R where Th is the hub radius. It was estimated that for 
all harmonics including the time average values, 3 percent of M, and 
ah was contributed by the loading in the region 0.4R>r>r, These 
estimates were based on a refinement of the method of Cummings for 
the time-average values, and the method of Tsakonas et pile for the 
unsteady values. 
Hydrodynamic, centrifugal, and gravitational loads may contribute to 
each of these components of loading; however, for some components the 
centrifugal loads and/or gravitational loads are zero, as discussed in 
the section on centrifugal and gravitational loads. 
Each component of loading is generally presented as a variation of 
the instantaneous value with blade angular position ® and as a Fourier 
series in blade angular position in the following form: 
F,M(6) = (F,M) + ae (F,M) cos (né - ) 
(OF Mn 
where F,M = circumferential average value of F,M 
(F,M)_ = amplitude of the nth harmonic of F,M 
6 = angular position about the propeller axis, positive counter- 
clockwise from the vertical upward looking upstream for 
starboard propeller (left-hand rotation) positive clockwise 
looking upstream for port propeller (right-hand rotation) 
(OF wn = phase angle of nth harmonic of F,M 
where the reference line of the blade is the spindle axis; see Figure 2 
and Table 1. 
The components SS and M, are the most important for determination of 
the time-average and unsteady stresses in the hub mechanism of an actual 
BS) 
