Page 304 - Aeronautical Engineer Data Book

246 Aeronautical Engineer’s Data Book
Table A2.2 Lateral-directional response transfer functions
in terms of dimensional derivatives

is aileron input
2
4
3
Demoninator polynomial ∆(s) = s(as + bs + cs + ds + e)
2
a m(I x I z – I xz )
˚
˚
˚
˚
˚
2
b –Y v (I x I z – I xz ) – m(I x N r + I xz L r ) – m(I z L p + I xz N p )
˚
˚
˚
˚
˚
˚
˚
c Y v (I x N r + I xz L r ) + Y (I L p + I xz N p ) – (Y + mW e )(I
z
v z p
˚
˚
L v + I xz N v )
˚
˚ ˚
˚
˚
˚ ˚
– (Y – mU e )(I x N v + I xz L v ) + m(L p N r – L r N p )
r
˚ ˚
˚
˚ ˚
˚ ˚
˚ ˚
˚
d – (Y (L N – L p N r ) + (Y p + mW e )(L v N r – L r N v )
v r p
˚
˚ ˚
˚ ˚
(Y – mU e )(L p N v – L v N p )
r
˚
˚
˚
˚
– mg cos e (I z L v + I xz N v ) – mg sin e (I x N v + I xz L v )
˚ ˚
˚ ˚
˚ ˚
˚ ˚
e mg cos e (L v N r – L r N v ) + mg sin e (L p N v – L v N p )
2
v
3
Numerator polynomial N (s) = s(as + bs + cs + d)
˚
2
a Y (I x I z – I xz )
˚
˚
˚
˚ ˚
˚
˚
b Y (–I x N r – I z L p – I xz (L r N p )) + L (I z (Y + mW e ) +
p
˚
I xz (Y r – mU e ))
˚
˚
˚
+ N (I x (Y – mU e ) + I xz (Y p + mW e ))
r
˚
˚ ˚
˚ ˚
c Y (L p N r – L r N p )
˚
˚
˚
˚
˚
+ L (N p (Y – mU e ) – N (Y p + mW e ) + mg(I z cos +
e
r
r
I xz sin e ))
˚
˚
˚
˚
˚
+ N (L r (Y p – mW e ) – L p (Y + mU e ) + mg(I sin e +
r
x
I xz cos e ))
˚
˚
d L (N p mg sin – N r mg cos e ) + N (L mg cos – L p e ˚ ˚ ˚ r e ˚
mg cos e )