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National Advisory Committee for Aeronautics, Technical Notes - The Rolling Moment Due to Sideslip of Triangular, Trapezoidal, and Related Plan Forms in Supersonic Flow

The rolling moment due to sideslip in supersonic flow has been
calculated for a representative group of plan forms. The analysis
was based. on linearized potential theory and was applied. to trian—
gular, trapezoidal, rectangular, and swept-back plan forms without
dihedral.

The only types of plan forms that provided positive dihedral
effect throughout the range of Mach number investigated were the .
rectangular wing of veryr low aspect ratio and a trapezoidal wing
of moderately low aspect ratio having raked—out tips.

The variation of rolling moment with sideslip was found to be
linear over a small range of sideslip angles for practically all
the Mach cone plan—form configurations investigated.

The calculation of the supersonic lateral—stability derivatives
has been undertaken for a group of plan forms of the type shown in
figures 1 and 2 considered to be representative of the plan forms
proposed for flight at supersonic speeds. In reference 1 the
results for the damping—in—roll derivatives were presented. This
report extends the results to include‘the rolling moment due to
sideslip.

The load. distributions for the sideslipping wings were obtained
using the methods presented in references 1, 2, 3, and h. The load
distributions were then integrated to obtain the rolling-moment
coefficient as a function of sideslip.

In general, the plan forms may be described as: (l) triangular
with subsonic leading edges and with supersonic leading edges;
(2) trapezoidal with all possible combinations of raked—in, raked-
out, subsonic or supersonic tips; (3) rectangular; and (1;) two
swept—back plan forms with supersonic trailing edges developed from
the trianguJerwings. Asunllchange has beenmde inane of the
plan forms under investigation since reference 1 was published. In
reference 1, the swept-back plan form having subsonic leading edges
was developed by removing a smll trianguJar portion, having sides
parallel to the Mach cones, from the traiJJng edge of a triangular
plan form having subsonic leading edges. Due to the difficulties
encountered in analyzing the sideslip position for this particular
configuration, the portion removed from the basic triangular plan
form has been changed. A triangular section extending from tip to
tip is now removed leaving the wing tapered to a point at the tip
as shown in figure 2.