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Fig.4 27 Wingin rolling and yawing motion.
The resultant velocitjr at the strip RT is given by
VR
= ~Z+ (Py)2
N Uo
(4.559)
(4.560)
Let c(y) be the local chord and ao(Y) be the local sectionallift-curve slope of the
wing. The lift on the elemental strip RT is given by
dL - ;:p Uo2ao(y)rytc(y)dy
1
= ~pUo2ao(Y) [ + 7jY],(y)dy
The drag ori the elemental strip RT is given by
dD = ;:'pU2CD,lc(y)dy
(4.561)
(4.562)
(4.563)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 409
where
CD,I = CDO,L + CDor,ICt (4.564)
Here, CD OJ iS the sectional zero-lift drag coefficient (profile drag coefficient when
CL - O), and CDa,l is the incremental sectional profile drag coefficient per urut
angle of attack Note that the strip theory ignores the induced drag.
The normal force on the elemental strip RT is given by
dZ ~ -dL cos aP - dD sin a'P (4.565)
- -dL -
- L-dDap (4.566)
- pUo2[ao(y)ry+[ao(y)+CD.,](7jY)l,(y)dy (4.567)
= -;pl
The rolling moment due to the elemental strip RT is given by
dRM=-l2pUo2[ao(y)a,+[ao(y)+CD,l](ZrY)].(y)ydy (4.568)
The total rolling moment due to the right wing is given by
, 1
RMR = _~p Uo2 l,b/2 [ao(y)a- + [ao(Y) + CD.d (7jY) ].(y)y dy (4.569)
Similarly, the rolling moment due to the left wing (change +y to - y) is given by
RM,=;pUo2l,'/2[ao(y)u-[ao(y)+CD.,]7jY],(y)ydy (4.570)
The total rolling moment
RM=-pUo2(3)l,%[ao(y)+CD.tlc(y)y2dy (4.571)
We have
CL= pRUMS7 (4.572)
Ctp= lCt (4.573)
a~)
Then, '
(C,p)W = Sb4 f.g[ao(Y) + CD,tlc(y)y2dy (4.574)
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