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56 Aircraft
with cyclic stick and pedal connected to rotor controls only for helicopter mode.
7–3 Trim
The aircraft trim operation solves for the controls and motion that produce equilibrium in the
specified flight state. In steady flight (including hover, level flight, climb and descent, and turns),
equilibrium implies zero net force and moment on the aircraft. In general, there can be additional
quantities that at equilibrium must equal target values. In practice, the trim solution can deal with a
subset of these quantities. Usually it is at least necessary to achieve equilibrium in the aircraft lift and
drag forces, as well as in yaw moment for torque balance. The basic purpose of the trim solution is to
determine the component states, including aircraft drag and rotor thrust, sufficient to evaluate the aircraft
performance.
Different trim-solution definitions are required for various flight states. Therefore one or more
trim states are defined for the analysis, and the appropriate trim state selected for each flight state of a
performance condition or mission segment. For each trim state, the trim quantities, trim variables, and
targets are specified. The available trim quantities include:
aircraft total force and moment; aircraft load factor;
propulsion group power; power margin PavP G − PreqPG;
rotor force (lift, vertical, or propulsive);
rotor thrust CT /σ; rotor thrust margin (CT /σ)max − CT /σ;
rotor flapping βc, βs; rotor hub moment, roll and pitch; rotor torque;
wing force; wing lift coefficient CL; wing lift margin CLmax − CL;
tail force.
Targets for aircraft total force and total moment (including inertial loads in turns) are always zero. The
available trim variables include:
aircraft controls;
aircraft orientation, θ (pitch), φ (roll);
aircraft horizontal velocity Vh;
aircraft vertical rate of climb Vz; aircraft sideslip angle β;
aircraft angular rate, ˙ θ (pullup), ˙ ψ (turn).
The aircraft orientation variables are the Euler angles of the body axes relative to inertial axes. The
aircraft controls (appropriately scaled) are connected to the component controls.
A Newton–Raphson method is used for trim. The derivative matrix is obtained by numerical
perturbation. A tolerance ɛ and a perturbation Δ are specified.
7–4 Geometry
The aircraft coordinate system has the x-axis forward, y-axis to the right, and z-axis down, measured
from the center of gravity (fig. 7-1). These aircraft axes are body axes (x is not aligned with the wind),
the orientation determined by the convention used for the input geometry. The center of gravity is the
appropriate origin for describing the motion of the aircraft and summing the forces and moments acting
on the aircraft.
Layout of the geometry is typically in terms of station line (SL, positive aft), buttline (BL, positive