Symbol

Name

Definition

Unit(s)

a_1P

a_1P

Primary longitudinal thrust offset from port mast in plane of disk.

in or degrees?

ABC

a_1S

a_1S

Primary longitudinal thrust offset from starboard mast in plane of disk.

in or degrees?

ABC

a₁^'

a₁^'

Differential longitudinal cyclic

in or degrees?

ABC

b_1P

b_1P

Primary lateral thrust offset from port mast in plane of disk.

in or degrees?

ABC

b_1S

b_1S

Primary lateral thrust offset from starboard mast in plane of disk.

in or degrees?

ABC

b₁^'

b₁^'

Differential lateral cyclic

in or degrees?

ABC

c

c

Damping

ft lb/rad/sec

c_crit

ccrit

Critical damping

ft lb/rad/sec

c_m

cm

Coefficient of Moment; two-dimensional

c_n

cn

Coefficient of Normal force; two-dimensional

c_m0

cm0

Coefficient of Moment at zero angle of attack; two-dimensional

c_m0.25

cm0.25

Coefficient of Moment about quarter chord; two-dimensional

c_mac

cmac

Coefficient of Moment about aerodynamic center; two-dimensional

e

e

Hinge offset; for flap and for lag

ft or % ??

e

e

Oswald's efficiency factor

h

h

Vertical distance (height) [Is being replaced by z]

in. ??

i

i

Incidence

rad, deg

l

l

Longitudinal distance [Is being replaced by x]

in. ??

m

m

Blade mass per unit length (element)

HT

p

p

Roll rate (angular velocity)

rad/sec.

nP

nP

Rotor revolutions per minute times number of blades

p^{.}

p w/ 1dot over

Roll (angular acceleration)

rad/sec²

q

q

Pitch rate (angular velocity)

rad/sec.

q^{.}

q w/ 1dot over

Pitch (angular acceleration)

rad/sec²

q

q

Dynamic pressure

lb/ft²

r

r

Yaw rate (angular velocity)

rad/sec.

r^{.}

r w/ 1dot over

Yaw (angular acceleration)

rad/sec²

r

r

Radial distance in rotor (cylindrical coordinate)

t

t

Time

sec.

u

x w/ 1dot over

Longitudinal velocity. Same as x^{.}

ft/sec

v

y w/ 1dot over

Lateral velocity. Same as y^{.}

ft/sec

w

z w/ 1dot over

Vertical velocity. Same as z^{.}

ft/sec

x

x

Longitudinal distance in body system (Cartesian)

ft.

x^{.}

x w/ 1dot over

Longitudinal velocity. Same as u

ft/sec

x^{..}

x w/ 2dot over

Longitudinal acceleration

ft/sec²

?

x_cp

x_cp

Location on X-axis of center of pressure as a percentage of chord from leading edge.

y

y

Lateral distance in body system (Cartesian)

ft./in.

y^{.}

y w/ 1dot over

Lateral velocity. Same as v

ft/sec

y^{..}

y w/ 1dot over

Lateral acceleration

ft/sec²

?

z

z

Vertical distance in body system (Cartesian)

ft./in.

z^{.}

z w/ 1dot over

Vertical velocity. Same as w

ft/sec

z^{..}

z w/ 1dot over

Vertical acceleration

ft/sec²

?

A₁

A₁

First lateral harmonic of blade flapping

rad, deg

AC

AC

Aerodynamic center

mine

B₁

B₁

First longitudinal coefficient of blade flapping

rad, deg

C_P

CP

Coefficient of Power; non dimensional

C_m

Cm

Aerodynamic moment in respect to 1/4 of the chord. Positive when pulling up.

C_Q

CQ

Coefficient of Torque; non dimensional

C_T

CT

Coefficient of Thrust; non dimensional

C_T/s

CToverSigma

Coefficient of Thrust/Solidity [see More Helicopter Aerodynamics by Prouty, Chapter 5]; non dimensional

E

E

Efflux (engine exhaust & cooling gasses)

ft³

GW

GW

Gross weight

lb

I_b

Ib

Moment of inertia of blade about flapping hinge

slug ft²

I_xx

Ixx

Rolling moment of inertia of helicopter about CG?

slug ft²

I_yy

Iyy

Pitching moment of inertia of helicopter about CG?

slug ft²

I_zz

Izz

Yawing moment of inertia of helicopter about CG?

slug ft²

J

J

Polar moment of Inertia

slug ft²

K

K

A constant

K_p

K_p

Feedback gain = tan δ₃

K_pβ

K_pβ

Pitch-flap coupling; positive for flap up, pitch down.

K_pζ

K_pζ

Pitch-lag coupling; positive for lag back, pitch down..

K_β

K_β

Flap hinge spring constant

K_ζ

K_ζ

Lag hinge spring constant

K_θ

K_θ

Control system spring constant

L

L

Lift

lb

L

L

Rolling moment (This is Padfield. Use R Prouty)

lb-ft

M

M

Pitching moment

lb-ft

N

N

Yawing moment [weather cocking]

lb-ft

PL_H

PL_H

Power loading, at hover

PL_M

PL_M

Power loading, at maximum power

Q

Q

Torque

ft lb

R

R

Rolling moment [dihedral]

lb-ft

S_β

S_β

Stiffness number

T

T

Thrust

lb

T_P

T_P

Thrust - Port rotor

lb

T_S

T_S

Thrust - Starboard rotor

lb

TC

TC

Center of thrust

mine

VR

VR

Angle between the two masts on intermeshing helicopter

degree

mine

X

X

Longitudinal force

lbs.

X

X

Longitudinal stability axis

Y

Y

Lateral stability axis

Yα

Yalpha

Lateral angle between the mast and Z-axis

radian, degree

Z

Z

Vertical force

lbs.

Z

Z

Vertical stability axis

Λ_LAT

Lambda_LAT

Lateral angle between mast and vertical on an intermeshing helicopter. Negative from vertical.

degree

Λ_LON

Lambda_LON

Rotor shaft angle of attack. Negative into wind

degree

Λ_HOR

Lambda_HOR

Crankshaft (propeller) angle of attack. Positive nose up, spinner dn.

degree

Ω

Omega

Rotational speed of rotor, Ω = (π * RRPM) / 30

rad/sec

ΩR

Omega

Tip speed of rotor

ft/sec

α_s

alpha_s

Rotor shaft angle of attack. Negative into wind Consider alt. Λ_LON

degree

ABC

β

Beta

Helicopter sideslip angle

radian, degree

β

Beta

Blade flap angle (positive upward)

degree

HT

β_p

Beta_p

Precone angle. Also a₀

degree

HT

β₀

Beta₀

Coning angle

degree

HT

β_1c

Beta_1c

Longitudinal tip-path-plane angle (positive forward)

degree

HT

β_1s

Beta_1s

Lateral tip-path-plane angle (positive toward retreating side)

degree

HT

γ

gamma

Blade Lock number

non-dimensional

Γ

Gamma

Control phase angle

degree

ABC

Δθ₀

Deltatheta0

Differential collective

degree

ABC

ζ

zeta

Blade lag angle (positive for motion opposing the rotor's direction of rotation)

degree

HT

η

eta

Mode shape

HT

Θ

Theta

Helicopter pitch angle. Euler

radian, degree

θ

theta

Blade pitch angle (positive when noes up)

radian, degree

θ_P

thetaP

Blade pitch angle of port rotor

radian, degree

θ_S

thetaS

Blade pitch angle of starboard rotor

radian, degree

ν_β

nu_beta

Rotating natural frequency of blade fundamental flap mode

HT

ν_ζ

nu_zeta

Rotating natural frequency of blade fundamental lag mode

HT

Φ

Phi

Helicopter roll angle. Euler

radian, degree

Ψ

Psi

Helicopter yaw angle. Euler

radian, degree

ψ

psi

Azimuth position of blade (cylindrical coordinate) (0º aft)

radian, degree

ψ_P

psi

Azimuth spacing parameter. ψ_P is the azimuth of the advancing blade when the other rotor's blade is at ψ = 0º. Intermeshing ~ 90º for 2-blade rotors, 60º for 3-blade rotors, 45º for 4-blade rotors.

radian, degree

ABC

 Subscript

C

C

Control (used with UniCopter)

E

E

Efflux (exhaust and cooling discharge)

F

F

Fuselage

H

H

Horizontal stabilizer

L

L

Local

M

M

Main rotor

P

P

Port

Q

Q

Torque

S

S

Starboard

T

T

Tail rotor

T

T

Torque

TPP

TPP

Tip path plane

V

V

Vertical stabilizer