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National Advisory Committee for Aeronautics, Report - Charts and Approximate Formulas for the Estimation of Aeroelastic Effects on the Loading of Swept and Unswept Wings

A knowledge of the spanwise lift distribution and of some
of the aerodynamic parameters associated with it is required
for the design of a wing structure. Under certain conditions,
such as high dynamic pressures,' thin wings, swept wings,
or wings designed for low wing loadings, the spanwise lift
distribution may be affected to a significant extent by
aeroelastic effects, because a wing which carries a certain lift
necessarily deforms under that lift. If the angles of attack
along the span are changed as a result of this deformation, the
lift carried by the wing is changed as well; in turn, this
change in lift causes a change in the deformation of the wing
and hence another change in lift, and so on, until an equilib-
rium condition is reached. The changes in the magnitude
and the distribution of the lift are reflected in changes of the
wing lift-curve slope, the wing bending and rolling moments,
the spanwise center of pressure of the lift, and, on a swept
wing, the longitudinal center of pressure.

Inasmuch as the lift produced by a given change in'angle
of attack is proportional to the dynamic pressure, the various
aeroelastic effects tend to increase with dynamic pressure.
In fact, for certain wings a sufficiently large dynamic pressure
may produce a condition of instability in which the change in
lift caused by deformation is greater than the amount of
lift required to produce the deformation, so that a given
deformation will tend to increase until the structure fails.
This phenomenon is aeroelastic divergence; since it involves
only torsional deformations 1n the case of unswept wings, it is
often referred to as torsional divergence.

Several methods are available for calculating these effects
(ref. 1, for instance), but since these effects depend on the
structural characteristics of the Wing, which are not ac-
curately known in advance of its design, the relatively large
amount of time required for even the most efficient of these
methods militates against their use in connection with
preliminary design calculations. A need exists, therefore,
for means of estimating some of the more important aero—
elastic effects on the spanwise lift distribution quickly and
with an accuracy that is sufficient for preliminary design
purposes.