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National Advisory Committee for Aeronautics, Report - Determination of Optimum Plan Forms for Control Surfaces

A theoretical analysis is made to determine the optimum
choral distributihn, location, and extent of control surfaces,
with the ratio of hinge moment to efecticeness as the cri-
terion. Erpressions for the efi‘ectieeness —— for ailerons,
the rolling moment, and for tail surfaces, the change of
lift on the tail due to deflection of the surface—were
derived from lifting-line theory.

Solutions found for a range of airfoil plan forms indi-
cate that, regardless of the characteristics of the tail sur-
face, the chord of the rudder or of the elevator should be
very nearly constant over its span. The optimum ailerons
are also of a characteristic shape, varying little withthe
plan form of the wing.

One of the primary difliculties in airplane design has
been to keep the stick forces required to deflect the
controLsurfaces at reasonably low values. This prob-
lem has inevitably increased in seriousness with the
size and the speed of modern airplanes. There is as
yet, however, no basic principle of control-surface
design that engineers will agree minimizes the ratio of
stick force to efl’ectiveness. Examination of typical
designs indicates that hinge-moment reductions as
great as 40 percent may be achieved in some cases
without lowering the effectiveness of the flap; that is,
the efliciency may be increased by two—thirds.

The present study, which neglects structural and
similar considerations, is a mathematical analysis lead-
ing to the plan forms for. rudder, elevator, and ailerons
that will be most effective in producing a given ammmt
of control with the least operating force. The solutions
are applicable to any airfoil of conventional plan form
to the same extent as are the usual assumptions of the
aerodynamic theory of ail-foils, on which the analysis
is based. Further discussion covers the extent, the
location, and the shape of partial-span control surfaces
to give the greatest efficiency.