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C" = ~-p U2Sb
Cnr = aa(:c: ) (4.628)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 417
For an untwisted rectangular wing of constant chord and an identical airfoil
section along the span, Eq. (4.629) reduces to
(Cnr)W = -/3 CD,l (4.630)
The strip theory estimate is based on neglecting the induced drag and mutual
interference effects between adjacent wing sections. Hence, this prediction will be
in error for low-aspect ratio wings.
For wings oflow aspect ratio, the following Datcoml formula may be used:
(Cnr)W = (C~)CZ + (CL.)cDO (4.631)
The data to evaluate (Cnr/C~.) and (Cnr/CD) are presented in Figs. 4.29a and
4.29b.
For supersonic speeds, no general method suitable for engineering purposes is
available to evaluate (Cnr)W.
Lateral-directiona/ acce/eration derivatives.
Cyp. rrhis derivative is a measure of the unsteady effects or the effects of
time rate of change of sideslip on the side-force coefficient. At low angles of
attack, the contributions of the wing and body are small and can be ignored. The
largest contribution comes from the vertical tail, which can be estimated using the
following expressionl
}- zv sin /Y'
(CyB)V=2ar,ap(SS [-s :2-' -] (4.632)
where ay is the lift-curve slope of the vertical tail and can be estimated using the
methods discussed in Chapter 3. From Datcom]
op - Opcr Ct + opr (57F3 ) + Up,WB (4.633)
r
where cr is the angle of attack in degrees and F is the dihedral angle in degrees.
Here, we have assumed that the wing has zero twisL
The term Crptr gives the variation of the sidewash with angle of attack, upr
represents the influence ofdihedral angle r on the sidewash, and ap.WB represents
the influence of the wing-body interference effect on the sidewash. The wing-
body interference effects depend on the location of the wing with respect to the
fuselage, i.e*, whether it is a low, middle, or high wing configuration.
Data to estimate ap(y, opr, and ap,WB for typical airplane configurations are pre-
sented in Figs. 4.30-4.32. The results presented in Fig. 4.31 for Crpr are applicable
for O < A .< 1. The data on op,wn given in Fig. 4.32 are for only one value of the
ratio of body diameter to wing semispan of 0.12 and apply for O < A < 1 and
r "
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