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National Advisory Committee for Aeronautics, Technical Notes - Boundary Induced Upwash for Yawed and Swept Back Wings in Closed Circular Wind Tunnels

The tunnel- induced velocities for yawed and ewept‘back airfoils
in a closed circular wind. tunnel were determined_ The calculations
were performed for elemental horseshoe vortices having one tip of
the bound vortex on the tunnel axis for a range of yaw angles and
bound-vortex lengths. From these results, the correction for com"
plete yawed and ewept‘back wings of arbitrary span loading may be
obtained by a superposition of solutions

Charts and tables of the induced velocity normal to the plane
of the tunnel axis and bound vortex are presented. In addition,
formulas are given for obtaining the tunnel-induced velocity normal
to any other plane containing the tunnel axis. These velocities
are needed for swept-back wings at high angles of attack, where the
tunnel axis and the two halves of the wing do not all lie in the
same plane. Curves are presented for converting the tunnel-induced
velocities into corrections to the geometric angle of attack of
the wing.

For the case of the unyawed wing, comparison of the present
results for the induced velocities along the tunnel axis with those
obtained.by Irmgard.Lotz and'by J. M. Burgers shows agreement with
Burgers‘ results. Since the method of Lotz was used in the present
study, it would appear that her computations were incorrect.

A proof of the validity of the method presented by Lotz is
given in the appendix.

Wind-tunnel testing of yawed and swept airfoils has con-
siderably increased with the development of maneuvers involving
flight at large angles of sideslip and with the development of
interest in the use of swept wings for transonic, supersonic, and
tailless aircraft. The corresponding_tunnel corrections have
been difficult to derive, inasmuch as the problem is not reducible,
as with a straight unyawed airfoil, to that of a two-dimensional
potential flow. Rectangular tunnels, however, may be treated by
the method of images, as was done in reference 1 in which correc-
tions for 7- by 10-foot closed tunnels are given. The boundary
conditions for tunnels of circular cross-section cannot be satis-
fied by the use of images alone. The purpose of the present
study is to develop a method for treating this case of the closed
circular tunnel and to evaluate the corrections for a range of
conditions.