198 PERFORMANCE, STABILITY, DYNAMICSf AND CONTROL
The horizontal tail contribution to pitching moment is obtained by taking mo-
ments about the center ofgravity (see Fig. 3.4) as
Mt - Mac.r - Lrlr
(3.57)
We ignore Mact, the zero-lift pitching moment of the horizontal tail, because this
term is usually quite small. Then,
or, in coefficient form,
Mr - -Lrlr
Cm*r = _Cuqq SS~
= -CL.r Vir7t
-. -at(alo - iw + /r - e)r7t V i
(3.58)
(3.59)
(3.60)
(3.61)
where
r Srlr
Vl= S~ (3.62)
The parameter V i is often called the horizontal tail volume ratio. Differentiating
with respect to CL, we get
dC..' -.(l-j)r7rV/ (3.63)
d~L =-a~
3.3.5 Effect of Power
The effect of the propulsive unit on Iongitudinal stability and trim can be both
significant and difficult to evaluate. These effects also depend on the mode of
propulsion such as turbo props or piston props, turbo fans, or turbo jets. Owing to
these complexities,it is difficult to make a comprehensive evaluation of the power
effects on longitudinal stability and trim. However, to gwe the reader some idea, a
qualitative discussion ofthe major effects is presented in the following paragraphs.
For simplicity, we restrict this discussion to propeller and jet aircraft.
For propeller-driven aircraft, the effect of power on static longitudinal stability
consists of two parts: 1) direct effect caused by forces developed by the propulsion
unit and 2) indirect effect caused by propeller slipstrcam passing over wing or tail
surfaces.
The direct effect caused by thrust depends on the vertical location of the thrust
line with respect to the center of gravity. A high thrust line is stabilizing, whereas
a low thrust line is destabilizing. The direct effect also includes a normal force Np
acting on the propulsion unit, which for a propeller airplane is destabilizing and
for a pusher airplane is stabilizing as shown in Fig 3.26.
The indirect effects arise because oftheinfluence ofpropeller slipstream passing
over wing and tail surfaces as shown in Fig. 3.27. The wing sections exposed to
the propeller slipstream experience a higher dynamic pressure and hence develop
STATIC STABILITY AND CONTROL
a) Propeller airplane
l- jP J
b) Push,Lrpa:.,.4e
Fig.3.26 Schematicillustration ofpower effects.
Fig. 3.27 Schematicillustration of propeller slipstream effects.
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