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 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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390                PERFORMANCE, STABFLITY, DYNAMICS, AND CONTROL
several candidate configurations for their suitability in meeting design goals. As
the design matures, these estimates can be replaced by more accurate CFD results
or the wind-tunnel test data on high fidelity models as they become available to
revise/update the stability and control characteristics as well as the design of flight
control and guidance systems.
   In this section, we will discuss the engineering methods suitable for evaluat-
ing the important stability derivatives appearing in the longitudinal and lateral-
directional equations of motion. We will use the simple strip theory wherever
applicable. The strip theory analysis is helpful to understand the basic aerody-
namic concepts underlying the dynanuc derivatives. The senuempirical methods
discussed in this text are taken from Datcoml These relations usually involve sev-
eral empirical parameters, and Datcom gives numerous charts to evaluate them.
It is neither the objective of this text nor it is possible to include all the Datcom/
information here. Instead, an effort is made to present sufficient information that
should be useful for the estimation of static and dynanuc stability derivatives of
generic aircraft configurations typically used in classroom instruction and study
projects.If the reader finds that the data for any fuselage, wing.fr tail configuration
of interest is not available in this text, please refer to Datcom]
4.4.1   Estimation of Longitudinal Stabdity Derivatives
    Estimation of CLn,.   This is the lift-curve slope of the airplane. Essentially,
 CLa -. (CLa,)/W. The methods to evaluate (CLu)lW were discussed in Chapter 3.
   Estimation of Cmu.   This is the slope of the pitching-moment curve, and
 essentially Cma  =  (Cma) WB.The methods to evaluate this derivative were discussed
in Chapter 3.
     Estimation of CDa,.    Forlinearliftcocfficient CL -. CLcra and quadratic drag
polcrr CD - CDO + kC2, the der:ivative CDu can be expressed as
CD" = G~ )(ddC.)
          - 2k CLCIAr
(4.476)
(4.477)
where k  -.  l/:rr Ae. The planform or Oswald's efficiency parameter e is given by7
  l.lCLtr
e--
      RCLa + (     R n-A
(4,478)
The parameter R is girren by the following expression, which is a curve fit to
Datcom data:7
R = ai~ + a2A{ + a3Al + a4
(4.479)
where  ai -0.0004,  a2~-0.0080,  a3 -0-0501,  a4-0.8642,  ancl  A,i = AA/
cos ALE where A is the aspect ratio, A.is the taper ratio, and ALE is theleading-edge
sweep of the wing.
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 391
Estimation of CDu.   With u = AU/Uo, this derivative can be expressed as
ac =MaacDM
au
(4.480)
The derivative acDlaM represents the variation of drag coefficient with Mach
number when the angle of attack is held constant. At low subsonic speeds (M  <
0.5), the drag coefficient is practically constant so triat acDlaM  - O. However,
as the fiight Mach number approaches the critical Mach number Mcr,.the drag
coefficient starts rising.lt assumes apeak valuein the transonic Mach number range
and starts decreasing as Mach number becomes supersonic. It tends to assume a
　
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