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National Advisory Committee for Aeronautics, Technical Notes - Characteristics of Thin Triangular Wings with Triangular Tip Control Surfaces at Supersonic Speeds with Mach Lines Behind the Leading Edge

A theoretical analysis, based on the linearized equation for
supersonic flow, was made of the characteristics of triangular-tip
control surfaces on thin triangular wings. By restricting the analysis
to the case for which the Mach lines from the wing apex lie behind the
leading edge, a simplified treatment was made possible in that the
results of previous work on the lift of triangular wings could be used
to derive simple expressions for the lift effectiveness, pitching
moment, rolling-moment effectiveness, and hinge moment due to control
deflection. An expression was also obtained for the hinge moment due
to angle of attack. Comparisons were made with the results for the
two-dimensional case.

The ratio of lift effectiveness to the hinge moment which
resulted from.control deflection was equal to the corresponding two—
dimensional ratio for the same ratio of flap area to wing area-

Again for equal ratios of flap area to wing area and for a
flap chord one-half the wing chord, the rate of roll per hinge—moment
coefficient due to control deflection was twice as large for the
present configuration as for the two-dimensional case. This dif-
ference was directly a result of the difference in damping coefficients
between the two cases.

The values of hinge-moment coefficient due to angle of attack
were found to be high when compared with either the hinge-moment
coefficient due to control deflection or with the two-dimensional
hinge-moment coefficient due to angle of attack. The appreciable
balancing effect thus indicated would materially reduce the stick
force in a steady roll and would also have to be taken into account
in the determination of the stick-free longitudinal stability if the
present arrangement were used as a horizontal tail.

There is considerable interest in the use of wings having
triangular plan forms for flight at supersonic speeds. Much work
has been done on the lift and drag characteristics of such wings
(references 1 to 5) Investigation of the lift and hinge -moment __
characteristics of control surfaces which might be used. on tri— ..
angular wings was considered desirable. Several such control surfaces ._
have been suggested; the present paper treats control surfaces which _
are located at the tips of the wing and which have plan forms =
geometrically similar to the plan form of the wing.