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D
F
H, Hˆ, Jˆ
H1′, H5′
F˙ξ
xvi Notation
h Height of hub above c.g. as fraction of R
h Vertical spacing between vortex sheets (Loewy and Jones)
h Relative angular momentum vector
h′ Tail rotor height above c.g. based on wind axes
= ht cos αs – lt sin αs
hc H-force coefficient = CH/s
ht Tail rotor height above c.g., as fraction of R
h1 Height of hub above c.g. based on wind axes
= h cos αs – l sin αs
I Second moment of area of blade section
I Blade moment of inertia in both flap and lag (Southwell)
I The unit matrix
IA, IB Non-dimensional inertia factors (Coleman and Stempin)
Iy, Iz Second moments of inertia of blade section for lagwise
and flapwise bending
Iβ, Iθ Blade flap and pitch moments of inertia
i, j, k Unit vectors fixed in blade
iA, iB, iC Non-dimensional rolling, pitching and yawing inertias
of helicopter
iE Non-dimensional roll-yaw inertia product term for
helicopter
J Modal error squared integral (Duncan)
J Polar second moment of area of blade section
J Performance index (active vibration control)
J0, J1 Bessel functions of first and second kinds (Miller)
j1, j2, j3, j4 Quantities dependent on first blade flapping mode shapes
of hingeless blade
K Induced velocity gradient (Glauert)
K Stiffness between gearbox and fuselage (DAVI)
Hingeless rotor blade constant = γ2F1/2
K(x) Elliptic integral
Kθ′ Stiffness of pitch control (Coleman and Stempin)
K0 (ik), K1(ik) Bessel functions of the second kind (Theodorsen)
k Correction factor to induced velocity for number of blades
(Prandtl and Goldstein)
k Incremental correction factor to induced power relative
to that for constant induced velocity
k Frequency parameter = nc/2V (Theodorsen),
= ωb/ΩR (Miller)
k Blade structural constant = EI/mΩ2R4
k Spring stiffness
kA, kB Non-dimensional pitching and flapping radii of gyration
= c(A/M)1/2, R(B/M)1/2
kT Correction factor to trim due to tailplane
K
Notation xvii
ki Induced velocity ratio (axial flight) = vi/v2
ks Equivalent flap hinge stiffness for hingeless blade
kβ, kξ Pitch/flap bending and pitch/lag bending coupling
coefficients
kθ Stiffness of control system about feathering axis
Non-dimensional artificial lag damping
k1, k2 Wake constants (Landgrebe)
k1, k2 Constants associated with transient motion
kA, kB Effective pitching and rolling stiffnesses (air resonance)
L Blade sectional lift force
L Lagrangian = T – U
L, M, N Moments about i, j, k for a rigid body, or of helicopter in
roll, pitch and yaw, or of blade in pitch, flap and lag
Non-dimensional quantity (air resonance) = 2a0J
LA Aerodynamic torsional moment
Lb Lift due to bound circulation
Le Elastic moment in flap plane
Lq Quasi-steady lift
Lv, Lp etc. Rolling moment derivatives
L0 Steady lift, and at instantaneous incidence
l Distance forward of c.g. from shaft in terms of R
l Position vector to vortex = l1 i + l2 j + l3 k
l′ Tail rotor arm based on wind axes = lt cos αs + ht sin αs
lT Tailplane arm, as fraction of R
lb Blade inertia to mass moment ratio (ground resonance)
= I/Mbrg
ln Length of nth beam element (Myklestad)
lt Tail rotor arm, as fraction of R
lv, lp etc. Non-dimensional normalised rolling moment derivatives
etc. Non-dimensional rolling moment derivatives
l1 Distance forward of c.g. from hub based on wind axes
= l cos αs + h sin αs
M Mass (general), chassis mass (ground resonance)
M Bending moment
M Column vector of blade bending moments
Rotor figure of merit = Tvi/P
MA Aerodynamic moment about flapping hinge, or hub
MT Pitching moment due to tailplane
Mb Blade mass
Mc Blade root bending moment coefficient = M/ρbcΩ2R4
Me Elastic moment in lag plane
Mf Pitching moment of fuselage
Mr Moment of rotor forces about c.g.
k˙ξ
L
M
lv′, lp′
xviii Notation
Ms Pitching moment per unit tilt of all the blades due to
hinge offset
Mu, Mq, etc. Pitching moment derivatives
M1 Unit load bending moment
M1, M2 Combined rotor/gearbox, and fuselage mass (DAVI)
m Mass, or mass per unit length
m Frequency ratio (Miller) = ω/Ω
mbob Bobweight mass (DAVI)
mu, mq, etc. Non-dimensional normalised pitching moment derivatives
mu′, mq′, etc. Non-dimensional pitching moment derivatives
NA Aerodynamic lagging moment on a blade
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本文链接地址：
Bramwell’s Helicopter Dynamics(5)
