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National Advisory Committee for Aeronautics, Technical Notes - Calculation of Lift and Pitching Moments Due to Angle of Attack and Steady Pitching Velocity at Supersonic Speeds for Thin Sweptback Tapered Wings with Streamwise Tips and Supersonic Leading and Trailing Edges

On the basis of linearized supersonic—flow theory the stability
derivatives 0mm. and Cmq (moment coefficients due to angle of attack
and steady pitching velocity, respectively) and CLq (lift coefficient
due to steady pitching velocity) were derived for a series of thin swept-
back tapered wings with streamwise tips and supersonic leading and
trailing edges. The results are valid for a range of Mach number for
which the Mach lines from the_leading edge of the center section cut the
trailing edges. An additional limitation is that the foremost Mach line
from either tip may not intersect the remote half of the wing.

The results of the analysis are presented as a series of design
charts. Some illustrative variations of the derivatives and of the Chord—
wise center—of—pressure location with the various wing design parameters
are also included.

To facilitate the transformation of the calculated results to arbi-
trary moment—reference locations, the required data for CLQ have been
selected or computed from the charts and equations in NACA TN 211% and
are also presented in the form of design charts.

The develOpment of the linearized supersonic—flow theory has enabled
the evaluation of stability derivatives for a variety of wing configura-
tions at supersonic speeds. Fairly complete information is now available
for the theoretical stability derivatives of rectangular, triangular, and
arrowhead plan forms (references 1 to 6). For the sweptback tapered wing
with streamwise tips, some of the available stability derivatives are the
lift—curve slope CLCL (references 7 to 10) and the damping—in—roll
derivative Clp (references 9 to 12). For this same wing, reference 13
treats the longitudinal-stability derivatives Cm“ and Cmq (moment
coefficients due to angle of attack and steady pitching velocity,
respectively) and CLq (lift coefficient due to steady pitching
velocity) for a range of Mach number for which the leading edge is sub-
sonic and the trailing edge is supersonic. Reference 1h treats the
derivative Cm for cases where all edges are subsonic.