• Version
• 135 Downloads
• 1.05 MB File Size
• 1 File Count
• December 14, 2016 Create Date
• December 14, 2016 Last Updated

National Advisory Committee for Aeronautics, Technical Notes - Theoretical Supersonic Characteristics of Inboard Trailing Edge Flaps Having Arbitrary Sweep and Taper

Generalized expressions in closed form have been obtained by means
of linearized theory for the aerodynamic characteristics (lift-, rolling-
noment-, pitching—momen -, and hinge—moment-coefficient derivatives) due
to deflection of inboard trailing—edge flaps. The analysis considers the
effects of Mach number and flap aspect ratio, taper ratio, and sweep for
the conditions where the Mach lines lie behind the flap leading and
trailing edges. The flap configurations analyzed are limited to the
case of streemwise tips where the foremost Mach lines from the flap tips
do not intersect the root and tip chords of the wing. The expressions
for the hinge-moment-coefficient derivative are limited to configurations
where the flap-root-chord Mach line does not intersect the flap tip chord.

Design charts are presented for the rapid estimation of the charac-
teristics due to flap deflection for control surfaces for which the Mach
lines from the flap tips do not intersect on the control surface. Some
illustrative variations of the characteristics with leading—edge sweep,
aspect ratio, taper ratio, and Mach number are also presented.

The lift-coefficient derivative at constant Mach number is dependent
only on the trailing-edge sweep; whereas the moment-coefficient deriva-
tives depend on the complete flap geometry.

The characteristics of control surfaces at supersonic speeds have
been extensively investigated by means of linearized theory. Reference 1
presents the flmda'mentals of the control-surface problem; whereas a pro-
cedure for obtaining solutions for general configurations was ,given in
reference 2. Another investigation, reference 3, presents detailed
analyses of specialized plan forms. The present paper presents the
effects of sweep, aspect ratio, taper ratio, and Mach number on the
lift-, rolling-moment-, pitching-moment-, and hinge-moment-coefficient .
derivatives of inboard trailing-edge flaps at supersonic speeds.

The analysis covers a range of Mach numbers in which the leading and
trailing edges of the control surfaces are supersonic (component of
free—stream Mach number normal to the leading and trailing edges is
greater than 1). The plan forms considered have streamwise tips, and
the location of the flap on the wing is limited to cases where the fore-
most Mach lines from the flap tips do not intersect the root and tip
chords of the wing. The analysis for the hinge-moment-coefficient
derivative was limited to configurations where the flap-root—chord Mach
line does not intersect the flap tip chord.