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The vertical tail contribution is given by
2
(C ;r)V = b:?,(IU ,oS ct + zu sirity)2Cyp.v
(4.619)
(4.620)
The value of (Cnr)V given by Eq. (4.620) is per radian.
An approximate estimate of (Cnr)W can be obtained using the strip theory as
follows.
Consider once again the elemental strip RT on the right wing of an aircraft
undergoing yawing motion with a positive yaw rate r (Fig. 4.27b). As a result of
this yawing motion, the relative velocity experienced by the wing sections varies
along the span, but the angle of attack can be assumedjto remain approximately
constant. The relative air velocity experienced by the left wing sections is higher
compared to that of the right wing sections. Consequently, the drag of the-left
wing is higher than that of the right wing,leading to a negative or restoring yawing
moment. Thus, conceptually (Cnr)W < O or wing provides a damping effect in
yaw.
We have
dF -. -dD (4.621)
1
= - ;:p(Uo2 _ 2Uory) CDJc(y) dy (4.622)
The yawing moment developed by the elemental strip RT is given by
dYM = lp(U2 _ 2Uory)CDJc(y)y dy (4.623)
The total yawing moment due to the right wing is.given by
Y MR = gp [,' (Uo2 _ 2Uory)CD.lc(y)y dy (4.624)
Similarly, the yawing moment due to the left wing (change y to -y) is given by
1
Y M, = -2 p [,' (Uo2 + 2Uor y)CD.Lc(y)y dy (4.625)
so that the total yawing moment is given by
Y M = -2p Uor [,-' CD.lc(y)y2 dy (4.626)
We have
Y M (4.627)
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