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high aspect ratio and with zero dihedral operating at an angle of attack.c! and
sideslip p and moving at a forward velocity Vo as shown in Fig. 3.72. The velocity
components in the spanwise, chordwise, and normal directions are given by
vs - Vo(sin A cosa + p cos A)
Vc -. Vo(cos A cos ct + ~3 sin A)
-. Vo cos A(cos a -1: p tan A)
VN - Vo Sill CL
(3.272)
(3.273)
(3.274)
(3.275)
where the first (upper) sign refers to the right wing and the second (lower) sign
refers to the left wing when the wing is in positive sideslip.
As before, let us assume that both cr and p are small so that higher order terms
involving these two parameters can be ignored. With these assumptions, we have
Vs - Vo cos A(tan A + p)
Vc - 'Vo cos A(l 4: t3 tan A)
VN -. lVoa
(3.276)
(3.277)
(3.278)
As said before, the spanwise component of velocity does not affect the pressure
distribution and hence is ignored in the following calculations. It only adds to skin
friction.
The angle of attack of right (starboard) and left (port) wings are given by
VN
ai = tanat = yc
ct
cos A(l i- p tan A)
- a sec A(l +- p tan A)
(3.279)
(3.280)
(3.281)
Voc
Vo P
STATIC STABILITY AND CONTROL
A
h
r;
yh
267
v, ~-k ~ /::s-OCL
┏━━━━━┳━━━━━┓
┃ ┃ ┃
┗━━━━━┻━━━━━┛
Fig. 3.72 Strip theory analysis of wing sweep effect.
For le'vel fiight with zero sideslip, the local angle of attack is given by
so that
a's - cr sec A
as - ai = +a sec Ap tan A
(3.282)
(3.283)
The dynamic pressures experienced by the right and left wings are given by
qi - 21p(\/c2 + LrF~)
= 2lp Vo2 COS2 A(l i: p tan A)2
(3.284)
(3.285)
Here, we have ignored higher terms such as Ct2, avp, or [112. Forlow subsonic speeds,
we can use the strip theory to estimate the wing contribution to directional stability
due to sweep-back as follows.l0
268 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Consider a strip RT of width dyi on the right wing. Let yh denote the spanwise
coordinate along the quarter chordline and c(yh) denote Lhe local chord normal to
the wing leading edge. The component of force along Ox (the stability axis) for
the righ~wing strip RT is given by
dF = -dL sin(cys - ai) - dD cos(as - ai) (3.286)
- ~dL(as - ui) - dD
(3.287)
Substituting for as - aL from Eq. (3.283) we have
dF : -dLa sec Ap tan A - dD (3.288)
=-;:p, ,s2A(i+ptanA)2[cI.Ra,secAtjtanA
~ p\/o2COS2
+CDO,+CDa., ( +~AA)],(yh)dyh (3.289)
With
aoa' sec A
Ct.R = ~+ p an A (3.290)
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