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Rotor 81
plane command. The collective control variable is the rotor thrust amplitude T or CT /σ (in shaft axes),
from which the collective pitch angle can be calculated. This approach eliminates an iteration between
thrust and inflow, and allows thrust limits to be applied directly to the control variable.
The relationship between tip-path plane tilt and hub moment is M = N
2 IbΩ 2 (ν 2 − 1)β = Khubβ,
where N is the number of blades, Ω the rotor speed, and ν the dimensionless fundamental flap frequency.
The flap moment of inertia Ib is obtained from the input Lock number: γ = ρacR 4 /Ib, for SLS density
ρ and lift-curve slope a =5.7. The flap frequency and Lock number are specified for hover radius and
rotational speed. The flap frequency and hub stiffness are required for the radius and rotational speed
of the flight state. For a hingeless rotor, the blade-flap spring is Kflap = IbΩ 2 (ν 2 − 1), obtained from the
hover quantities; then Khub = N
2 Kflap and
ν 2 =1+ Kflap
IbΩ 2
For an articulated rotor, the hinge offset is e = Rx/(1 + x), x = 2
3 (ν2 − 1) from the hover quantities; then
ν 2 =1+ 3
2
e/R
1 − e/R
and Khub = N
2 IbΩ 2 (ν 2 − 1), using Ib from γ (and scaled with R for a variable diameter rotor) and Ω for
the flight state.
Optionally the rotor can have a variable diameter. The rotor diameter is treated as a control, allowing
it to be connected to an aircraft control and thus set for each flight state. The basic variation can be
specified based on the conversion schedule, or input as a function of flight speed (piecewise linear input).
For the conversion schedule, the rotor radius is Rhover for speeds below VChover, Rcruise = fRhover for
speeds above VCcruise, and linear with flight speed in conversion mode. During the diameter change, the
chord, chord radial distribution, and blade weight are assumed fixed; hence solidity scales as σ ∼ 1/R,
blade-flap moment of inertia as Ib ∼ R 2 , and Lock number as γ ∼ R 2 .
11-3.1 Tip-Path Plane Command
Tip-path plane command is characterized by direct control of the rotor thrust magnitude and the
tip-path plane tilt. This control mode requires calculation of rotor collective and cyclic pitch angles
from the thrust magnitude and flapping.
a) Collective: magnitude of the rotor thrust T or CT /σ (shaft axes).
b) Cyclic: tilt of the tip-path plane, hence tilt of the thrust vector; longitudinal tilt βc
(positive forward) and lateral tilt βs (positive toward retreating side). Alternatively,
the cyclic control can be specified in terms of hub moment or lift offset, if the
blade-flap frequency is greater than 1/rev.
c) Shaft tilt: shaft incidence (tilt) and cant angles, acting at a pivot location.
The relationship between tip-path plane tilt and hub moment is M = Khubβ, and between moment and
lift offset is M = o(TR). Thus the flapping is
βs
=
βc
1
rMx
=
Khub −My
TR
ox
Khub −oy
for hub moment command or lift offset command, respectively.