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92 Rotor
inflow angles are obtained, and then the angle-of-attack:
uT = r + μx sin ψ + μy cos ψ
uR = μx cos ψ − μy sin ψ
uP = λ + r( ˙ β +˙αx sin ψ − ˙αy cos ψ)+uRβ
U 2 = u 2 T + u 2 P
cos Λ = U/
u 2 T + u2 P + u2 R
φ = tan −1 uP /uT
α = θ − φ
In reverse flow (|α| > 90), α ← α − 180 signα, and then cℓ = cℓαα still (airfoil tables are not used). The
blade pitch consists of collective, cyclic, twist, and pitch-flap coupling terms. The flap motion is rigid
rotation about a hinge with no offset, and only coning and once-per-revolution terms are considered:
θ = θ0.75 + θtw + θc cos ψ + θs sin ψ − KP β
β = β0 + βc cos ψ + βs sin ψ
where KP = tan δ3. The twist is measured relative to 0.75R; θtw = θL(r − 0.75) for linear twist. The
inflow includes gradients caused by edgewise flight and hub moments:
λ = μz + λi(1 + κxr cos ψ + κyr sin ψ)+Δλm
= μz + λi(1 + κxr cos ψ + κyr sin ψ)+
From the hub moments
−CMy
the inflow gradient is
Δλm =
fm
μ 2 + λ 2
σa
8
ν 2 − 1
γ/8
CMx
= σa
2
fm
μ 2 + λ 2 (−2CMyr cos ψ +2CMxr sin ψ)
ν 2 − 1
γ
βc
βs
(rβc cos ψ + rβs sin ψ) =Km
The constant Km is associated with a lift-deficiency function:
ν 2 − 1
γ/8
1
1
C = =
1+Km 1+fmσa/ 8 μ2 + λ2 (rβc cos ψ + rβs sin ψ)
The blade chord is c(r) =crefĉ(r), where cref is the thrust-weighted chord (chord at 0.75R for linear
taper). Yawed flow effects increase the section drag coefficient, hence cd = cdmean/ cos Λ. The section
forces in velocity axes and shaft axes are
L = 1
2 ρU 2 ccℓ
D = 1
2 ρU 2 ccd
R = 1
2 ρU 2 ccr = D tan Λ
Fz = L cos φ − D sin φ = 1
2 ρUc(cℓuT − cduP )
Fx = L sin φ + D cos φ = 1
2 ρUc(cℓuP + cduT )
Fr = −βFz + R = −βFz + 1
2 ρUccduR
These equations for the section environment and section forces are applicable to high inflow (large μz),
sideward flight (μy), and reverse flow (uT < 0). The total forces on the rotor hub are
T = N Fz dr
H = N Fx sin ψ + Fr cos ψdr
Y = N −Fx cos ψ + Fr sin ψdr