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National Advisory Committee for Aeronautics, Technical Notes - Empirical Corrections to the Span Load Distribution at the Tip

An analysis of existing pressure-distribution data
was made to determine the variation of the tip loading
with wing plan form. A series of empirical tip corree:
tions was derived that may be added to theoretical curves
in certain cases to obtain a closer approach to the ac-
tual loading at the tip.

The analysis indicated that the need for a tip cor—
rection decreases as either the aspect ratio or the wing
taper is increased. In general, it may be said that, for
wings of conventional aspect ratio, corrections to the
theoretical span load curves are necessary only if the
wing is tapered less than 2:1 and has a blunt tip. If that,
tip is well rounded in plan form, no correction appears
necessary even for a wing with no taper.

The recent trend toward the use of airfoil theory for
determining the load distribution for structural design
arose principally because it was found that the various
combinations of wing taper and wing twist that were being
used called for a rational system of specifying the load
distribution. Although it was known that the lifting—line
theory gave load distributions that were, in general, in
good agreement with those experimentally obtained, it did
not indicate the presence of a tip_ effect that was known
to exist for certain wing shapes.

The results of flight tests, reported in reference 1,
indicated that, contrary to theory, the distribution of
the normal-force coefficient for a rectangular wing was
practically independent of the tip plan form when no twist
was built into the wing and also that the shape of the dis—
tribution curve Varied with the wing lift. This result is
also verified by windutunnel tests of untwisted rectangu-
lar wings as shown by figure 1. Figure 1(a) shows typical
wind—tunnel distribution curves for a rectangular wing
with a square tip; figure 1(b) shows corresponding curves
for a wing with a circular tip. The dotted curves show
that the theoretical values of on at the tip increase
rather rapidly as the rounding proceeds from the blunt to
the more slender circular plan form. Also it can be seen
that the shape of.the theoretical curves does not vary
with wing 0N as the ratio of the ordinates of any two
curves is equal to the ratio of the wing GN values.