Aerospace Engineering e-Mega Reference

then the corresponding expressions for the damping and natural frequency become:

2

z

p

u

p

¼x

u

u

p

¼

ffiffiffiffiffiffiffiffiffiffi

gz

u

U

e

r

(4.4.36)

Now

x

u

y



X

u

m

¼

r

V

0

SX

u

2m

and z

u

y



Z

u

m

¼

r

V

0

SZ

u

2m

(4.4.37)

since



X

_

w

is negligibly small and m[



Z

_

w

: Expressions for the dimensionless aerodynamic derivatives may be

approximated as shown in expressions (4.4.38) when the basic aerodynamic properties are assumed to be

independent of speed. This follows from the assumption that the prevailing flight condition is subsonic such that the

aerodynamic properties of the airframe are not influenced by compressibility effects:

X

u

¼2C

D

 V

0

vC

D

vV

þ



1

1

2

r

V

0

S



v

s

vV

y  2C

D

Z

u

¼2C

L

 V

0

vC

L

vV

y  2C

L

(4.4.38)

Expressions ...