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298 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Effect of wing sweep. In general, the sweep-back has a stabilizing effect,
and the sweep-forward has the opposite or destabilizing effect. To understand
how the wing leading-edge sweep infiuences the wing contribution to static lateral
stability, let us refer back to F.gY '3.72 and consider a swept-back wing with no
dihedral and operating at an angle of attack a and sideslip P and moving with a
forward velocity Vo.
As before, let us assume tbat both ct and t3 arc small so that higher order
terms involving these two parameters can be ignored. Then, from Eqs. (3.280) and
(3.285), the effective angle of attack and effective dynanuc pressure are given by
a -.
(1 :1 p tan A)cos A
qt = ,}:P Vo)- COS2 A2(1 +- p tan A)2
(3.352)
(3.353)
where the first (upper) sign applies to the right wing and second (lower) sign
applies to the left wing when the sideslip is positive.
At low speeds, the contribution of a sufficiently high-aspect ratio swept-back
wing to lateral stability can be approximately evaluated using the strip theory as
follows.
Consider a strip RT of width dyh on the right wing. Let yh denote the spanwise
coordinate along the quarter chordline and c(yh) denote the local chord normal
to the wing leading edge. Then the lift on the right wing elemental sU:ip RT is
given by
d Lift - qtc(yh) dyhaoaf
= gp Vo2 ,OS2 A(l + p Mri A)2tro
(1 + p tan A)cos A
= /Z p Vo2 COS A(l + p tan A)aoac(yh)dyh
The rolling moment due to strip RT is given by
(3.354)
] (yh)dy,
(3.355)
(3.356)
dL = - ~p Vo2 COS A(l + p tan A)aoac(yh)yhcos A-dyh (3.357)
The rolling moment due to the right wing is given by
~ sec A
LR=-;pVo7-cos2A(l+ptanA aoc(yh)yhdyh (3.358)
Similarly, the rolling moment due to the left wing is given by
g sec A
~~ = ~pjo2,OS2 A(l - p tan A)a aoc(yh)yh dyh (3.359)
)
The total rolljng moment is given by
.: sec A
L = -p'Vo2ap cOS2 A tan A aoc(yh)yh dyh (3.360)
)
Then,
STATIC STABILITY AND CONTROL
299
2ctp cos A sin
ci-- _)l,"ec\aoc(y.r)ytidyh (3.361)
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