Propellers in yaw Page: 1 of 23
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REPORT No. 820
PROPELLERS IN YAW
By HnsnT S. RBxeaSUMMARY
It was realized as early as 1909 that a propeller in yaw
develops a side force like that of a fn. In 1917, R. G. Harris
expressed this force in terms of the torque coefficient for the
unyawed propeller. Of several attempts to express the side
force directly in terms of the shape of the blades, however, none
has been completely satisfactory. An analysis that incorpo-
rates induction effects not adequately covered in previous work
and that gives good agreement with experiment over a wide
range of operating conditions is presented herein. The present
analysis shows that the fin analogy may be extended to the form
of the side-force expression and that the effective fin area may
be taken as the projected aide area of the prompeller. The effec-
tire aspect ratio is of the order of 8 and the appropriate dynamic
pressure is roughly that at the propeller disk as augmented by
the inflow. The variation of the inflow velocity, for a fied-
pitch propeller, accounts for most of the variation of aide force
with adrance-diameter ratio T/nD.
The propeller forces due to an angular relocity of pitch are
also analyzed and are shown to be very small for the pitching
velocities that may actually be realized in maneuvers, with the
exception of the spin.
Further conclusions are: A dual-rotating propeller in yaw
develops up to one-third more side force than a single-rotating
propeller. A yawed single-rotating propeller experiences a
pitching moment in addition to the aide force. The pitching
moment is of the order of the moment produced by a force equal
to the side force, acting at the end of a lever arm equal to the
propeller radius. This cross-coupling between pitch and yaw
is small but possibly not negligible.
The formulas for propellers in yaw derived herein (with the
exception of the compressibility correction) and a series oJ
charts of the side-force derivative calculated therefrom have been
presented without derivation in an earlier report.
INTRODUCTION
The effect of power on the stability and control of aircraft
is becoming of greater importance with increase in engine
output and propeller solidity. An important part of this
effect is due to the aerodynamic forces experienced by the
propeller under any deviation from uniform flight parallel
to the thrust axis. The remaining part is due to the inter-
ference between the propeller slipstream and the other parts
of the airplane structure.
A number of workers have considered the forces experi-enced by the propeller. It was pointed out in 1909 (reference 1)
apparently by Lanchester, that a propeller in yaw
develops a considerable side force. The basic analysis was
published in 1918 by R. G. Harris (reference 2), who showed
that a pitching moment arises as well. Glauert (references 3
and 4) extended the method to derive the other stability
derivatives of a propeller.
Harris and Glauert expressed the forces and moments
in terms of the thrust and torque coefficients for the unyawed
propeller, which were presumably to be obtained experi-
mentally. The analyses. did not take into account certain
induction effects analogous to the downwash associated with
a finite wing. It is noteworthy that with a semiempirical
factor the Harris equation for side force does give good
agreement with experiment. (See reference 5.) Pistolesi
(reference 6) in 1928 considered the induction effects but his
treatment was restricted to an idealized particular case.
Klingemann and Weinig (reference 7) in 1938 published an
analysis neglecting the induction effects; the treatment
appears almost identical with the account given in 193k by
Glauert in reference 4.
There have been several notable attempts to express the
side force directlyin terms of the shape of theblades. Bairstow
(reference 8) presented a detailed analysis in 1919 that
neglected the induction effects. Misztal (reference 9) pub-
lished an investigation in 1932 that did not have this limita-
tion and that is probably the most accurate up to the present.
MIisztal's result, however, is in a very complex form from the
point of view of both practical computation and physical
interpretation; there is, in addition, an inaccuracy in the
omission of the effects of the additional apparent mass of the
air disturbed by the sidewash of the slipstream.
Very recently Rumph, White, and Grumman (reference 10)
published an analysis that relates the side force directly to
the plan form in a very simple manner. Reference 10, how-
ever, (1) does not include the ordinary inflow in the analysis
and (2) applies unsteady-lift theory in an improper manner to
account for the induction effects. As a consequence of (1),
the equations are badly in error at high slipstream velocities.
As a consequence of (2), the equations fail to predict the
substantial increase in side force that experiment shows is
provided by dual rotation. The improper use of unsteady-
lift theory consisted in using formulas that apply to the case
of a finite airfoil with an essentially rectilinear wake. The
vortex loops shed by the finite airfoil, which produce the
interference flow, are distributed along this rectilinear wake.
193
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Ribner, Herbert S. Propellers in yaw, report, October 11, 1943; (https://digital.library.unt.edu/ark:/67531/metadc60102/m1/1/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.