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Forward speed normalised on thrust velocity = V/v0
Forward speed normalised on tip speed = V/ΩR
V′ Total velocity at the rotor
VC Rate of climb in axial flight, or axial velocity
Climb speed normalised on induced velocity (actuator
disc) = VC/vi
Tail volume ratio = STlT/sA
ˆt
u , v, w
u ˆ, vˆ, wˆ
VˆV
VC
VT
Notation xxi
Vdes Descent velocity
v Absolute velocity vector
vi General induced velocity at rotor
viT Downwash at blade tip (with linear distribution)
vi0 Mean induced velocity
vrel Relative velocity vector
Induced velocity normalised on thrust velocity = vi/v0
v0 Mean induced velocity in hover (thrust velocity)
v0 Velocity of origin of moving frame
v2 Slipstream velocity in far wake
v3/4 Induced velocity component at 3/4 chord point
W Helicopter weight
W Total relative flow velocity at blade section
W Work done
W Torque on blade element
W Total velocity vector at blade section
Wi Vibration measurement weighting (active vibration
control)
W0, W1, W2 Coefficients used in longitudinal response solution
w Velocity of wake sheets near rotor
w Wake velocity
w Induced velocity normal to disc, or aerofoil
wD Disc loading = T/A
wP, wQ Induced velocity components normal to rotor at P, Q
wb Downward component of induced velocity due to bound
vortices
wc Weight coefficient = W/ρsAΩ2R2
ws Induced velocity component for shed part of wake
wt Downward component of induced velocity due to trailing
vortex
X, Y, Z General or aerodynamic force components
X Vector of higher harmonic control (HHC) inputs
Mean hub force components
Xu, Xw, etc. X force derivatives
x, y, z Position coordinates (dimensional, or non-dimensionalised
on R)
Distance of datum point on aerofoil from mid-chord
xk General variable measured with respect to rotating kth
blade
xkg, ykg Coordinates of the kth blade relative to centre of hub
(ground resonance)
xrg, yrg Coordinates of rotor c.g. (ground resonance)
xst Static deflection of single degree of freedom system
= F0/k
vi
x
X, Y, Z
xxii Notation
xu, xw, etc. Non-dimensional X force derivatives
x1 Non-dimensional position of vortex filament on blade
= r1/R
Y, Z Displacement of point on blade relative to axes rotating
with blade
Y Vector of measurement vibration components (active
vibration control)
Yf Fuselage side-force
Yv, Yp, etc. Y force derivatives
Y0, Y1 Bessel functions of first and second kinds (Miller)
yv, yp, etc. Non-dimensional Y force derivatives
Z Blade bending deflection vector
ZE Elastic deflection vector of blade bending
ZR Rigid body rotation deflection vector (about flapping
hinge)
Zu, Zw, etc. Z force derivatives
z Distance along rotor axis
Tip vortex axial coordinate (Langrebe)
zu, zw, etc. Non-dimensional Z force derivatives
z0 Wake coordinate
α Incidence of blade section
α Blade torsional stiffness constant = ω0(CR/EsJ)1/2
Equivalent lag damping coefficient (Ormiston and Hodges)
αD Disc incidence
αT Tailplane incidence
αT0 No lift setting of tailplane (with respect to fuselage)
αi
Downwash angle relative to blade
αi
Stiffening effect due to rotation = ( – )/ i
2
nr
ω ω2 Ω2
αi
Spanwise slope at RH end of ith element (Myklestad)
αnf Incidence with respect to plane of no-feathering
αs Rotor hub incidence (i.e. shaft tilt)
α0 Incidence in the absence of induced velocity
α0, α1 Coefficients in polynomial expression for α
α1, α2 Amplitudes (Floquet)
α1, α2, α3 Lag hinge projected angles
β Blade flapping angle, at hinge
Analogous to β for hingeless rotor blade
βs Blade flapping, relative to shaft
βss Side-slip angle
β0 Built-in coning angle
χ Wake angle
Flap bending frequency difference term (air resonance)
= λ1
2 – 1
zT
α
β
χ
Notation xxiii
χi
(t) ith generalised coordinate for lagwise bending
ξ Blade lagging angle
ξ Distance of vortex element from centre of aerofoil, based
on semi-chord b
ξ, ζ Aft and downwards position coordinates based on on R
and aligned with mean downwash angle (for defining
tailplane position)
ξk Lag angle of kth blade (ground resonance)
Δ Stability quartic in Laplace variable p
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Bramwell’s Helicopter Dynamics(7)
