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of this text. Here, we will present empirical relations suitable for preliminary
calculations.l
For subsonic speeds,
~a = 4.44[KA K,.K H(COS Ac/4).l1.19
(3.43)
Here, K A, KA, and K H are wing aspect ratio, wing taper ratio, and horizontal tail
STATIC STABILITY AND CONTROL
location factors as given by
KA
KH -
1+Ain
10 - 3A,
7f
1 - hbj
195
(3.44)
(3.45)
(3.46)
where /h iS distance measured parallel to the wing root chord, between wing mac
quarter chord point and the quarter chord point of the mac of horizontal tail, and
hH is the height of the horizontal tail mac above or below the plane of wing root
chord, measured in the plane of symmetry and normal to the extended wing root
chord and positive for horizontal tail mac above the plane of the wing root chord
(see Fig. 3.23).
The wing quarter chord sweep Ac/4 can be determined using the following
relation:
tan Ac/4 = tan ALE - Cr - Ct
2b
(3.47)
For straight tapered wings, the exposed and theoretical values of A c/4 are identical.
For more complex wing planforms, the two parameters are different.
The following simple formula, which gives the 'variation of downwash wiLh
angle of attack at infinity (the downwash at infinity is twice of that at the wing)
and is based on lifting line theory (see Chapter 1) for elliptical wings, can be used
for crude estimation of downwash at the horizontal tail at low speeds.
d€ 2aw
dct = Tz-A
(3.48)
Note that the values given by Eqs. (3.43) and (3.48) are per radian. The downwash
angle e is then given by
de
e = d7raw
(3.49)
As said before, except for canard airplanes, aw - a.
For supersonic speeds, the estimation of downwash is much more involved
because it depends on many factors such as whether the wing leading- and trailing-
edge conditions are subsonic or supersonic. However, for ver)r approximate
estimation, the following formula may be used:l
1.62CL
e- J
7r A
(3.50)
where € is in radians. It is suggested that adequate care and caution be exercised
1
A
196 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
in using Eq. (3.50). Then,
or
Lr - q,S,a,(aw - /u, + /t - e)
CL.t - Ot(CtLU - /W + /r - e)qq~
dCL.,
dC =..(1_:),7,SS
(3.51)
(3.52)
(3.53)
Here, ar is the horizontal tail lift-curve slope in presence of the fuselage and
th = qr/q is the dynamic pressure ratio at the hori;ontal tail. Just like the wing,
the horizontal tail also experiences the crossflow effect because of aft fuselage. If
the horizontal tail span to body diameter (at tail location) is sufficiently high, then
the aft fuselage interference can be ignored, and ar equals the lift-curve slope of
an isolated horizontal tail. For such cases, Eq. (3.16) can be used to determine ar.
On the other hand, if this ratio is small, then the approach similar to that used for
wing-body combination may have to be used. Additionalinformation,if necessary,
may be obtained from Datcom.l
The dynanuc pressure ratio 17, at the horizontal tail is less than unity because
the horizontal tail comes under the influence of the wing wake, which is a region
of reduced dynamic pressure. For subsonic speeds, Datcoml gives
where
17, - 1 - Aq
q
2.42~ .
= ~+0.30
(3.54)
(3.55)
where lhl iS the distance between the trailing edge of the wing root chord and the
aerodynamic center of the horizontal Lail. CDO.w is the zero-l;~t drag coefficient of
the wing as given by Datcom,l
CDO*,u = C].w 1 + L(tlc) + 1OO(tlc)4l R .s SS (3.56)
where C f.w is the turbulent flat plate skin-friction coefficient. The variation of C f w
with Ma~h number and Reynolds number (based on the mean aerodynamic chord
c) is given in Fig. 3.24. L is the airfoil thickness location parameter. For airfoils
where maximum thickness ratio is located within 0.3c, L = 2.0 and, for those
beyond 0.3c, L - 1.2. The parameter RL.S depends on the sweep angle at that
chord location where t/c is maximum and is given in Fig. 3.25. Swet iS the wetted
area of the wing. For low/moderate angles of attack, Swet ~ S.
For supersonic speeds, the determination of 17r iS much more involved. The
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