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Fz -- Fzo + AFz = -(Lo + AL) + W cos(0o + AO) - ( v~ [(Uo +RAf/
so that
AFx -. -AD - W cos 0o AO
AFz = -AL - W sinOoAO - (V;~) [2URAU ]
Proceedingin a similar way as we did for the small disturbance equations ofmotion
for a steady flight in a vertical plane, we obtain
Cxu - -2CD - CDu
xcr : -CDa
Cx0 - -CL COS 0o
Cxct - -CDd - 0
Cxq = -CDq - 0
Czu = -2CL - CLu - 2tTl,iqo
zct : -Cln
zd - -CLdt
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-
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