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ze [ m ] Z-coordinate in Earth-fixed reference frame FE
z f [ m ] Z-coordinate in runway-fixed reference frame FF
Zgr [ N ] gravity force along ZB-axis
Zp [ N ] propulsive force along ZB-axis
a [ rad ] angle of attack, see figure 2.1
b [ rad ] sideslip angle, see figure 2.1
g [ rad ] flight-path angle
g [ – ] ratio of specific heats of air
ggs [ rad ] nominal glide-path angle on final approach (ILS glide-path)
Ggs [ rad ] angle between localizer reference plane and the line through the ground
position of the aircraft and the glideslope antenna
Gloc [ rad ] angle between localizer reference plane and the line through the ground
position of the aircraft and the localizer antenna
GVOR [ rad ] angle between selected and actual VOR radial
da [ rad ] deflection of ailerons (da = daright
− daleft ), see figure A.5
de [ rad ] deflection of elevator
df [ rad ] deflection of flaps
dr [ rad ] deflection of rudder
D increment
Dpt [ Nm−2 ] increase of total pressure over the propeller
Dda [ rad ] change in deflection of the ailerons
Dde [ rad ] change in elevator deflection
Ddr [ rad ] change in rudder deflection
#gs [ rad ] glideslope error angle above/below the nominal ILS glide-path
q [ rad ] pitch angle
l [ Km−1 ] temperature gradient (¶T/¶h)
μ [ rad ] aerodynamic angle of roll
μ [ kgm−1s−1 ] dynamic viscosity
r [ kgm−3 ] air density
s standard deviation
sgs [ μA ] standard deviation of glideslope noise
sloc [ μA ] standard deviation of localizer noise
su [ ms−1 ] standard deviation of turbulence velocity in XB-direction
sv [ ms−1 ] standard deviation of turbulence velocity in YB-direction
sw [ ms−1 ] standard deviation of turbulence velocity in ZB-direction
j [ rad ] roll angle
F [ rad ] bank angle
A.2. Vectors 289
c [ rad ] azimuth angle
y [ rad ] yaw angle
yw [ rad ] wind direction (wind from the North: yw = p)
yRW [ rad ] runway heading
w [ rad s−1 ] angular frequency
w0 [ rad s−1 ] natural frequency of undamped system
wn [ rad s−1 ] natural frequency of damped system
W [ radm−1 ] spatial frequency
A.2 Vectors
a body-axes acceleration vector
Caero vector with non-dimensional aerodynamic force and moment coefficients
Cprop vector with non-dimensional engine force and moment coefficients (‘propulsive’)
F resulting force vector acting on rigid body; F = [Fx Fy Fz]T
h resulting angular momentum of rigid body about c.g.; h = [hx hy hz]T
M resulting moment vector about c.g. of rigid body; M = [L M N]T
r position vector
u... input vectors
V true airspeed vector
Vw wind velocity vector
x state vector
y... output vectors
W rotational velocity vector
A.3 Matrices
A system matrix of linear state-space system
B input matrix of linear state-space system
C output matrix of linear state-space system due to x
D output matrix of linear state-space system due to u
TP!Q transformation matrix from a reference frame FP to a reference frame FQ
Q transformation matrix for first Euler rotation from FE to FB
F transformation matrix for second Euler rotation from FE to FB
Y transformation matrix for second Euler rotation from FE to FB
A.4 Functions
f(t) general vector-equation for the time-derivatives of the state variables
g(t) general vector-equation for the output variables
H(w) frequency response of forming filter
S(w) power spectral density function
S(W) power spectral density function
A.5 Indices and subscripts
0 nominal value
0 value at sea level
a ailerons
290 Appendix A. Symbols and definitions
a relative to the surrounding atmosphere (used for velocity components)
aero aerodynamic forces and moments or force and moment coefficients
c.g. center of gravity
dpt stability derivative with respect to non-dimensional pressure increase across propeller
e elevator
e relative to Earth axes (used for velocity components)
f flaps
f referenced to runway-fixed reference frame FRW, f stands for ‘field’
grav gravity force components
gs related to glideslope deviation
k ‘kinematic’ (used for accelerations)
loc related to localizer deviation
p stability derivative with respect to non-dimensional rolling speed
q stability derivative with respect to non-dimensional pitching speed
r stability derivative with respect to non-dimensional yawing speed
r rudder
RW runway, used for defining runway parameters
prop engine forces and moments or force and moment coefficients (‘propulsive’)
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(103)
