Application of Theodorsen's theory to propeller design Page: 4 of 17
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REPORT 924-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Interference velocities for dual-rotating propellers.--The
average axial interference velocity far behind the propeller
obtained from the momentum considerations is
2Va==K
where K is the mass coefficient and w is the axial displacement
velocity. This mean value is equally due to each of the two
oppositely rotating propellers. The average axial interfer-
ence velocity due to each is therefore exactly
The average interference velocity at the propeller plane is
one-half the value in the final wake and, therefore,
1 1
2 4
where V, represents the average axial interference velocity
at the propeller plane due to each component of the dual-
rotating propeller. With the two propellers separated by
a small axial distance, this velocity refers to a plane between
the two propellers. The interference velocity at the front
propeller is smaller and at the rear propeller is larger than at
the plane between the propellers. In the following treat-
ment, the propellers are considered to be very close together
so that the axial interference velocity is the same on both
propellers.
In the final wake, the mean value of the rotational inter-
ference velocity for the ideal case is given by
2V,=0
For an infinite number of right and left blades equally loaded,
rotational components would cancel exactly. However, the
average rotational interference velocity immediately behind
each propeller may be considered as
-1
r=~ KW tan 4
In summary, the mean interference velocities acting on the
front propeller from the rear propeller are
Axial:
1 1
Rotational:
The mean interference velocities acting on the rear propeller
from the front propeller are
Axial:
Rotational:-=12Itan
VT= Kw tan t
2It is useful to recognize that the mean self-interference of
each propeller in its own plane isAxial:
Rotational:1
- Kw
4- Kw tan 4
Velocity diagram for the dual-rotating propellers. -The
velocity diagram for the dual-rotating propellers is shown
in figure 2. As in the case for the single-rotating propeller,
the axial displacement velocity at the propeller is equal to
1 w. In figure 2 the vector AB gives the mean axial inter-
1
ference velocity 4 K4 of each propeller acting on the other
propeller. The vector BC gives the mean rotational inter-
1
ference velocity Kaw tan of the front propeller acting on
the rear propeller. The total interference velocity acting
on the front propeller from the rear propeller is therefore
given by AB, and the total interference velocity acting on the
rear propeller from the front propeller is equal to the vector
AC. The local self-interference velocity of the front pro-
peller is given by Ws,, and the corresponding helix angle is
given by 4,F. The local self-interference velocity of the rear
propeller is given by 1,, and the corresponding helix
angle is given by R. The angle 4, is slightly larger than
the ideal helix angle 4 given by the displacement velocity
1 w and 4, is slightly smaller than 0. The design condition
of most interest is the one for which rF for each blade of the
front propeller is equal to re for each blade of the rear
propeller. The number of blades on the front and rear-Velocty diagram for dualrotatn pro lr.
FrGE 2.-Velocity diagram for dual-rotating propeller.
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Crigler, John L. Application of Theodorsen's theory to propeller design, report, March 15, 1948; (https://digital.library.unt.edu/ark:/67531/metadc60237/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.