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60 Aircraft
The component power required Pcomp is evaluated for all components (rotors) of the propulsion
group. The total power required for the propulsion group PreqPG is obtained by adding the transmission
losses and accessory power. The power required for the propulsion group must be distributed to the
engine groups. The fuel flow is calculated from the power required. The fuel flow of the propulsion group
is obtained from the sum over the engine groups. The total fuel flow is the sum from all components of
the aircraft: ˙w = ˙wreqEG + ˙wforce.
7–7 Aerodynamics
Each component has a position z F in aircraft axes F, relative to the reference point; and orientation
of component axes B relative to aircraft axes given by the rotation matrix C BF . It is expected that the
component axes are (roughly) x forward and z down (or in negative lift direction). The aerodynamic
model must be consistent with the convention for component orientation. Acting at the component
are interference velocities v F int (velocity of air, in F axes), from all other components. Then the total
component velocity relative to the air is
v F = v F AC + ω F ACΔz F − v F int
where Δz F = z F − z F cg. Then v B = C BF v F is the velocity in component axes. The aerodynamic
environment is defined in the component axes: velocity magnitude v = |v B |, dynamic pressure q = 1/2ρv 2 ,
angle-of-attack α, and sideslip angle β. The angle-of-attack and sideslip angle provide the transformation
between airframe axes and velocity axes:
C BA = YαZ−β
This is the conventional aircraft definition, corresponding to yaw-then-pitch of the airframe axes relative
to the velocity vector. By definition, the velocity is along the x-axis in the A axes, v B = C BA (v 00) T ;
from which the angle-of-attack and sideslip in terms of the components of v B are obtained:
α = tan −1 v B 3 /v B 1
β = sin −1 v B 2 /|v B |
This definition is not well behaved for v B 1 =0(it gives α = 90 sign(v B 3 )), so for sideward flight a
pitch-then-yaw definition can be useful: C FA = Z−βYα. Then
which gives β = 90 sign(v B 2 ) for v B 1 =0.
α = sin −1 v B 3 /|v B |
β = tan −1 v B 2 /v B 1
From v, q, α, and β, the aerodynamic model calculates the component force and moment, in wind
axes acting at zF :
F A ⎛
= ⎝ −D
⎞
Y ⎠ M
−L
A ⎛
= ⎝ Mx
⎞
My ⎠
Mz
where D, Y , and L are the drag, side force, and lift; Mx, My, and Mz are the roll, pitch, and yaw moments.
The aerodynamic loads in aircraft axes acting at the center of gravity are then:
F F = C FB C BA F A
M F = C FB C BA M A + Δz F F F