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Czq = -CLq
Cz8 - -CL siri0o
The expressions for other lateral-directional stability derivatives essentially remain
the same as those derived earlier for steady ffight. However, we have to note that
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 389
all the stability derivatives have to be evaluated for curved flow conditions to sim-
ulate the steady pull- out maneuver prior to disturbance. However, if qo iS small,
for approximate purposes, the curved flow effects can be ignored, and relations
derived for steady flightin a vertical plane can be used with one difference that Cma,
should be evaluated considering the increase in stability level during the pull- out
maneuver.
4.4 ' Estimation of Stability Derivatives
To solve motion Eqs. (4.417-4.419) and (4.459-4.461) for studying the stabil-
ity (free response) or the response of the airplane to a given pilot input (forced
response), we need to know the values of all the static and dynamic stability deriva-
tives appearing in those equations. These derivatives can be determined either by
analytical, serniempirical, computational fluid dynamics (CFD), or experimental
methods. The analytical methods based on classical aerodynamic theories can be
applied only to idealized wings and bodies. Aircraft configurations ofpractical in-
terest cannot be analyzed using the classical aerodynamic theories.ln view of this
difficulty, several empiricaVsemiempirical methods have been developed over the
years for evaluating the stability and control derivatives of aircraft configurations
of practical interest. Datcom is one of the most widely used sources for estimat-
ing aircraft stability and control derivatives.7 It is a comprehensrve compilation
of all the available engineering methods for obtai:rung the stability and control
derivatives of airplane- type configurations.
The modern CFD methods are capable ofproviding more accurate estimates of
static and some dynamic derivatives. But, at present, the level of effort imtolved
precludes their application at preliminary design stages. In view of this, the CFD
methods are usually used at a sufficiently later stage in the velucle design process
when the configuration takes its final form.
The experimental methods for obtaining dynamic stability derivatives in ground-
based test facilities8-10 mainly consist ofeither forced oscillation or free oscillation
technique wherein the test model undergoes an oscillatorjr motion in pitch, roll, or
yaw. Another approach that is often used to obtain dynamic stability derivatives
in ground-based test faciMes is the so-called free fiight or semifree fiight test
technique.ll Here, the test model is allowed to fly either free or semifree [loosely
constrained in some degree(s) of freedom] in the viewing area of the test facility.
The model motion is recorded in the form ofvarious accelerometer outputs or higX-
speed motion picture records. The dynamic stability derivatives are then obtained
implicitly by matching the predicted time history of the model with the observed
time history. Because the time and effort involved in fabricating and testing aircraft
models in the ground-based facilities are considerable, these approaches are also
usually used in the final stages of the vehicle design.
On the other hand, the semiempirical or engineering methods provide quick and
cost-effective estimates of the static and dynamic stability derivatives, which can
be readily used for assessing the vehicle fiyability, stability, and control. Also, the
predictions based on these engineering methods can be used in the design of fiight
control and guidance systems. The only disadvantage is that such predictions are
less accurate compared to the CFD or the wind-tunnel test data. However, this type
ofinformation is very useful in the early stages of the design to quickly evaluate
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