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Δ Function of κβ, κξ
δ Profile drag coefficient = δ0 + δ1α + δ2α2
δ Lateral deflection at a point on a beam
δ, δc Blade lag and chassis damping coefficients (ground
resonance)
δ1, δ2, δ3 Flapping hinge projected angles
ε Blade hinge offset factor = MbexgR2/B = 3e/2(1 – e)
ε Downwash angle at tailplane
ε Phase angle
ε0 Mean downwash angle at rotor = vi0 /V
ε(x) Modal error function (Duncan)
φ Shaft angle to vertical (roll of fuselage)
φ Velocity potential, or real part of velocity potential
φ Inflow angle at blade element = tan–1(UP/UT)
φ Blade azimuth angle when vortex was shed
φ (x, z) Potential for plane steady flow past a cylinder (Sears)
φi
(t) ith generalised coordinate for flapwise bending
Γ Circulation, vortex strength
Γ Blade rotating lag frequency in absence of Coriolis force
coupling (ground resonance)
Γn Amplitude of bound circulation (Miller)
Γnc, Γns In and out of phase components of Γn
Γq Quasi-static circulation
Γ1 Function of derivatives = – mq + μmB1/zB1
γ Lock’s inertia number = ρacR4/B
γ Vorticity (Theodorsen)
γ Angular displacement of pendulum arm (bifilar absorber)
γ (x) Assumed general blade bending mode shape (Lagrange)
γ1, γ2 Lock number equivalents for flexible blade
η Contraction ratio of slipstream in hover
η Transformed radial position coordinate (Mangler and
Squire) = (1–x2)1/2
xxiv Notation
η Non-dimensional chordwise position (thin aerofoil theory)
η, ζ Coleman coordinates (ground resonance)
κ, κc General blade lag, and chassis frequencies in terms of Ω
κβ, κξ Functions of κβH, κβB and κξH, κξB
κβH, κξH Flap and lag stiffnesses of ‘hub springs’
κβB, κξB Remainder of above stiffnesses outboard of feathering
hinge
κ1 First blade uncoupled natural rotating lag frequency in
terms of Ω
Λ Local wake helix angle
Wake constant (Landgrebe)
Λb Bobweight arm length ratio = d1/d2 (DAVI)
Λ0 Far wake helix angle = w/ΩR0
λ Mean inflow ratio relative to plane of no-feathering
= sin αnf – λ
i
λ Rotating flap bending frequency in terms of Ω
λ, λn General and nth eigenvalue in characteristic equation
λ′ General inflow ratio (function of ψ, r)
= (V sin αnf – vi)/ΩR
λD Mean inflow ratio relative to disc plane = sin αD – λ
i
λc Climb inflow ratio = Vc/ΩR (axial flight), ≈ sin τc (forward
flight)
λi
v i0/ΩR, or vi/ΩR for hovering flight
λiT v iT/ΩR
λre, λim Real and imaginary parts of eigenvalue λ
λ1 First blade uncoupled natural rotating flap frequency in
terms of Ω
μ Constant determining natural undamped frequency of a
non-rotating beam, from standard published results
= ( nr /EI)
mω2 1/4
μ Mass ratio (ground resonance) = 0.5bMb/(M + bMb)
μ, μD Advance ratios = ˆV cos αnf, ˆV cos αD
Magnification factor = x0/xst
μ* Relative density parameter = W/gρsAR
μb Bobweight mass ratio = mbob/M1 (DAVI)
ν Helicopter pitching frequency ratio in terms of rotor
revolutions
ν Far wake velocity ratio
ν Factor depending on disc tilt (Mangler and Squire)
= (1 – sin αD)/(1 + sin αD)
ν Lag bending frequency ratio
Air resonance factor = γ E1/2
Λ
μ
ν
Notation xxv
ω˜
νˆ Incremental frequency term (Floquet) = γ /16
ν1 First blade uncoupled natural rotating torsional frequency
in terms of Ω
ν1, ν2 Exponent constants (Floquet)
θ Blade pitch or feathering angle
θ Fuselage pitch attitude (shaft angle to vertical)
θ Laplace transform of θ (fuselage pitch)
θbar Angular displacement of Bell stabilising bar
θn Amplitude of blade pitch variation at circular frequency
n
θt
Tail-rotor collective pitch
θ0 Collective pitch angle
θ1 Blade twist (washout)
ρ Ambient air density, or material density
ρ Component of inflow angle = tan–1 (vi/W)
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Bramwell’s Helicopter Dynamics(8)
