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A1, B1c, C1, D1, E1 Coefficients in longitudinal characteristic equation
A2, B2, C2, D2, E2 Coefficients in lateral characteristic equation
Aij, Bij Normalised generalised coefficients = Aij , Bij /0.5mΩ2R3
a Lift curve slope of blade section
a Distance from edge of vortex sheet
a Offset of fixed pendulum point from rotor centre of rotation
(bifilar absorber)
a, b, c, d, e Square matrices, and column matrix (e) (Dynamic FEM)
a*, b*, c* Subsidiary square matrices (Dynamic FEM)
ag Acceleration of blade c.g.
aT Tailplane lift curve slope
a0 Acceleration of origin of moving frame = ax i + ay j + azk
a0 Coning angle
a1, b1 Longitudinal and lateral flapping coefficients
a0, a1, a2, b1, b2 Sine and cosine coefficients in equation for Cm
Analogous to a0, a1, b1 for hingeless rotor
B Tip-loss factor (Prandtl) = Re/R
B Vector of background vibration responses
a0, a1, b1
xiv Notation
Coefficients B1c, C1 with speed derivatives neglected
Laplace transform of B1 (cyclic pitch)
b Number of blades
b Aerofoil semi-chord
b Effective pendulum length (bifilar absorber)
C Torsional moment of inertia per unit blade length
C, S Cosine and sine multi-blade summation terms
C, F, G, H, S Coefficients in solution for normal acceleration
C(k) Theodorsen’s function
CD Drag coefficient
CH H-force coefficient = H/ρAΩ2R2
CL Lift coefficient
CLT Tailplane lift coefficient
CT Thrust coefficient based on disc area = stc = T/ρAΩ2R2
CM Pitching moment coefficient
CN Normal force coefficient
CL Equivalent CL = 3
0
1 ∫ x2CLdx
Cl Rolling moment coefficient of blade
Cm Pitching moment coefficient of blade
Cmf Pitching moment coefficient of fuselage = Mf /ρsAΩ2R3
Cms Pitching moment coefficient due to hinge offset
= Ms/ρsAΩ2R3
Cp Pressure coefficient
C1, C2, S1, S2 Coefficients in less usual solution for normal acceleration
C1, D1, F1, G1 Integrals of blade flapping mode shape functions (first
and second moments, and powers)
Cξ˙ Fβ˙ , Flap-lag cross coupling damping coefficients
c Blade or aerofoil chord
c Viscous damping coefficient
c Offset of c.g. of oscillatory mass from pivot point (bifilar
absorber)
ccrit Critical damping coefficient = 2(k/m)–1/2
ce Equivalent chord
cl Linkage ratio on Bell stabilising bar
cn, dn, en, fn, gn, hn, jn, kn Coefficients relating to Sn, Mn, αn, Zn at blade station n
(Myklestad)
c0, cn Downwash factors (Mangler and Squire)
c1, c2, c3, c4 Constants determined from initial conditions
D Drag of fuselage, or local blade section
D Diameter of holes in fixed arm and oscillatory mass (bifilar
absorber)
D, E, F Blade or helicopter products of inertia
B1′c, C1′
B1
Notation xv
Denominator in integral for ω
t
d Drag factor, where blade drag = dΩ2
d Diameter of pin connecting fixed arm and oscillatory
mass (bifilar absorber)
d0 Fuselage drag ratio = SFP /sA
d1, d2 Bobweight arm lengths (DAVI)
E Young’s modulus
Es Modulus of rigidity or shear modulus
E1 Generalised inertia of first flapping mode
E1, E2 Wake energy contributions
e Rotor blade hinge offset, as fraction of R
eA Distance between blade centroid and elastic axis
e1, e2, e3 Orthogonal unit vectors fixed in hub
F Aerodynamic force on blade or helicopter, or general
external force vector
= Xi + Yj + Zk
Ratio of Lock number equivalents for hingeless blade
= γ2 /γ1
FR, FI Real and imaginary parts of L/Lq
Fy, Fz Lagwise and flapwise forces acting on a blade section
Lag damping coefficient
f Lateral distance of c.g. from shaft, as fraction of R
f Function affecting the k correction factor
= 0.5b(1 – x)/sin φ (Prandtl vortex sheet model)
f Bending flexibility matrix
f (n), g(n) Generalised inertias for nth flap and lag bending modes
fb Factor dependent on number of blades
fin Forcing term assumed constant for ith step in nth mode
G Centrifugal tension in blade
g Gravitational constant
H Rotor force component perpendicular to thrust axis
(positive to rear) (H-force)
H Total head pressure
H Absolute angular momentum vector = h1i + h2 j + h3k
Non-dimensional quantities (air resonance)
HB, HD Flap and pitch damping coefficients (Coleman and
Stempin)
HD H-force referred to disc axes
HP H-force due to profile drag
Hi H-force due to induced drag
H0, H1, H2 Coefficients used in longitudinal response solution
Aerodynamic damping terms (Coleman and Stempin)
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Bramwell’s Helicopter Dynamics(4)
