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National Advisory Committee for Aeronautics, Technical Notes - Charts and Tables for Use in Calculations of Downwash of Wings of Arbitrary Plan Form

Values of the downwash of a horseshoe vortex in incompressible flow
are presented in the form of charts and tables. The use of the charts
and tables in the calculations of the downwash of wings of arbitrary plan
form is discussed. The results of a few calculations are compared with
experimental results.

A knowledge of the downwash behind the wing is required for the
rational design of the horizontal tail surfaces as well as for the
analysis of the longitudinal stability of an airplane. The design charts
of reference 1, which are based on the experiments and analysis of refer-
ence 2, afford a convenient means of estimating the downwash behind
unswept wings. These charts are basically inapplicable to swept wings
and to wings of more complicated plan form because the assumed bound
vortex is unswept and because the assumed spanwise lift distributions
are those of unswept wings and differ from those of swept wings.

Inasmuch as sweep constitutes an additional geometric variable and
because the use of more complicated plan forms introduces still further
variables, the preparation of extensive charts that give directly the
downwash field for any arbitrary plan form is not considered practical.
When the spanwise lift distribution is known for any particular case
the representation of the wing by a vortex pattern and calculation of
the downwash field associated with that pattern in the tail region with-
certain simplifying assumptions, such as that of a plane vortex sheet,
is a fairly straightforward, although somewhat time consuming problem.

This paper presents a method, together with the necessary charts »
and tables, for facilitating such calculations. As is described herein,
the tables and charts give the downwash field of an elemental rectangular
horseshoe vortex. The method c0nsists basically of distributing these
vortices along the wing span in such a way that they approximate the
lifting action of the wing and of superimposing the downwash fields of
the individual vortices.