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Aircraft 59
For steady-state flight, ˙ θF = ˙ φF =0; ˙ ψF is nonzero in a turn.
Accelerated flight is also considered, in terms of linear acceleration a F AC =˙vFI/F = gnL and pitch
rate ˙ θF . The nominal pullup load factor is n =1+ ˙ θF Vh/g. For accelerated flight, the instantaneous
equilibrium of the forces and moments on the aircraft is evaluated for specified acceleration and angular
velocity; the equations of motion are not integrated to define a maneuver. Note that the fuselage and
wing aerodynamic models do not include all roll-moment and yaw-moment terms needed for general
unsteady flight (notably derivatives Lv, Lp, Lr, Nv, Np, Nr).
The aircraft pitch and roll angles are available for trim of the aircraft. Any motion not selected for
trim will remain fixed at the values specified for the flight state. The pitch and roll angles each can be
zero, constant, or a function of flight speed (piecewise linear input). The flight state input can override
this value of the aircraft motion. The input value is an initial value if the motion is a trim variable.
7–6 Loads and Performance
For each component, the power required and the net forces and moments acting on the aircraft can
be calculated. The aerodynamic forces F and moments M are typically calculated in wind axes and then
resolved into body axes (x, y, z) relative to the origin of the body axes (the aircraft center of gravity).
The power and loads of all components are summed to obtain the aircraft power and loads. Typically
the trim solution drives the net forces and moments on the aircraft to zero.
The aircraft equations of motion, in body axes F with origin at the aircraft center of gravity, are the
equations of force and moment equilibrium:
m(˙v FI/F + ω FI/F v FI/F )=F F + F F grav
I F ˙ω FI/F + ω FI/F I F ω FI/F = M F
where m = W/g is the aircraft mass; the gravitational force is F F grav = mCFIgI = mCFI (0 0 g) T ; and
the moment of inertia matrix is
I F ⎡
⎤
=
⎦
⎣ Ixx −Ixy −Ixz
−Iyx Iyy −Iyz
−Izx −Izy Izz
For steady flight, ˙ω FI/F =˙v FI/F =0, and ω FI/F = R(0 0 ˙ ψF ) T is nonzero only in turns. For accelerated
flight, ˙v FI/F can be nonzero, and ω FI/F = R(0 ˙ θF ˙ ψF ) T . The equations of motion are thus
m(a F AC + ω F ACv F AC) =F F + F F grav
ω F ACI F ω F AC = M F
The body axis load factor is n =(CFIgI − (aF AC + ωF ACvF AC ))/g. The aFAC term is absent for steady flight.
The forces and moments are the sum of loads from all components of the aircraft:
F F = F F
fus + F F rotor + F F
force + F F wing + F F tail + F F engine + F F tank
M F = M F fus + M F rotor + M F force + M F wing + M F tail + M F engine + M F tank
Forces and moments in inertial axes are also of interest (F I = C IF F F and M I = C IF M F ). A particular
component can have more than one source of loads; for example, the rotor component produces hub
forces and moments, but also includes hub and pylon drag. The equations of motion are Ef = F F +
F F grav − F F
inertial =0and Em = M F − M F inertial =0.