B265

OTHER: Aerodynamics - Symbols

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Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms

Definitions & Algorithms

Symbols

Symbols

Symbols

 

 

Symbols

The symbols conform to RW Prouty's, where possible.

NACA - Standard Symbols for Helicopters ~ http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930082252_1993082252.pdf

Note: Access database does not distinguish between upper and lower case, there for upper case 'C' in lower case is 'cc'.

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There is, currently, duplication on Dynamics, Aerodynamics & Mechanics.

Symbol

Name

Definition

Unit(s)

 

 

 

 

English

Metric

a

a

Slope of lift curve

1/rad, 1/deg

 

a0

a0

coning angle

rad, deg

 

a1s

a1s

Longitudinal flapping

 

 

ac

ac

Aerodynamic center. [airfoil]

 

 

b

b

Number of blades

 

 

b

b

Span of wing

ft.

 

b1s

b1s

Lateral flapping

 

 

b1'

b1'

Differential lateral cyclic

 

 

c

c

Chord of blade [airfoil]

ft

 

c

c

Damping

ft lb/rad/sec

 

ccrit

ccrit

Critical damping

ft lb/rad/sec

 

cc

cc

Coefficient of Chord force; two-dimensional. [airfoil]

 

 

cd

cd

Coefficient of Drag; two-dimensional. [airfoil]

 

 

cdi

cdi

Coefficient of Induced Drag; two-dimensional. [airfoil]

 

 

cdo

cdo

Coefficient of Profile Drag; two-dimensional. [airfoil]

 

 

cl

cl

Coefficient of Lift; two-dimensional. [airfoil]

 

 

clMax

clMax

Maximum coefficient of Lift; two-dimensional. [airfoil]

 

 

cm

cm

Coefficient of Moment; two-dimensional. [airfoil]

 

 

cn

cn

Coefficient of Normal force; two-dimensional. [airfoil]

 

 

cm0

cm0

Coefficient of Moment at zero angle of attack; two-dimensional. [airfoil]

 

 

cm0.25

cm0.25

Coefficient of Moment about quarter chord; two-dimensional .[airfoil]

 

 

cmac

cmac

Coefficient of Moment about aerodynamic center; two-dimensional. [airfoil]

 

 

d

d

Rotor diameter

ft

RWA

dr

dr

Slant line distance between rotor hub centers

ft

RWA

ds

ds

Stagger (distance between rotor axis)

ft

RWA

g

g

Rotor gap ( elevation of one rotor over another)

ft

RWA

r

r

Radius at blade element

ft

 

e

e

Hinge offset; for flap and for lag

ft

 

e

e

Oswald's efficiency factor

 

 

f

f

Equivalent flat plate area

ft2

 

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'

Dual rotor overlap fraction. Dual rotor overlap ratio.

%

PHA

ov

ov

Overlap, twin rotors

nondimensional

RWA

q

q

Dynamic pressure

lb/ft2

 

r

r

Radial distance in rotor (cylindrical coordinate)

 

 

t

t

Time

sec.

 

t

t

Airfoil thickness

in.

 

v

v

Induced velocity (positive down through the disk)

ft/sec

 

vov

vov

Induced velocity in overlap area (positive down through the disk)

ft/sec

RWA

w

w

Disk loading. Also DL

lb/ft2

 

x

x

Longitudinal distance in body system (Cartesian)

ft.

 

x

x

Nondimensional distance along airfoil chord. [airfoil]

nondimensional

 

xcp

xcp

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

 

 

x0

x0

Blade root cutout

percent

 

y

y

Lateral distance in body system (Cartesian)

ft./in.

 

z

z

Vertical distance in body system (Cartesian)

ft./in.

 

 

 

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A

A

Area

ft2

 

A

A

Area of wing (horizontal or vertical stabilizer, etc)

ft2

 

A1

A1

First lateral harmonic of blade flapping

rad, deg

 

Aone

Aone

Area of individual rotor disk

ft2

mine

AC

AC

Aerodynamic center

 

mine

ΑL0

AL0

Zero lift angle

rad, deg

 

AR

AR

Aspect ratio

 

 

Am

Am

Overlap area of disks

ft2

HT

Asys

Asys

Total effective disk area of rotor system

ft2

HT

Ab

Ab

Area of blades

ft2

 

AI

AI

Autorotation Index (used by Sikorsky)

ft3/lb

 

B

B

Tip loss factor

 

 

B1

B1

First longitudinal coefficient of blade flapping

rad, deg

 

CD

CD

Coefficient of Drag; non dimensional

 

 

CH

CH

Coefficient of (profile drag?); non dimensional

 

 

CP

CP

Coefficient of Power; non dimensional

 

 

Cm

Cm

Aerodynamic moment (section moment coefficient). Positive when pulling up.

 

 

Cm1/4

Cm

Section moment coefficient about quarter chord.

 

 

Cm0.25

Cm

Section moment coefficient about quarter chord.

 

 

Cmac

Cm

Section moment coefficient about aerodynamic center.

 

 

Cnc

Cn

Normal force coefficient (@ 90 to chord)

 

 

CQ

CQ

Coefficient of Torque; non dimensional

 

 

CT

CT

Coefficient of Thrust; non dimensional

 

 

CT

CToverSigma

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

 

 

D

D

Diameter of rotor

ft

 

D

D

Drag

lb

 

De

De

Equivalent Drag

 

 

DL

DL

Disk loading. Also w

lb/ft2

 

E

E

Efflux (engine exhaust & cooling gasses)

ft3

 

F

F

Side force on rotor (F-force)

lb

 

FM

FM

Figure of merit

 

 

GW

GW

Gross weight

lb

 

H

H

Horizontal force on rotor (H-force). Positive aft.

lb

 

K

K

A constant

 

 

Kp

Kp

Feedback gain = tan δ3

 

 

L

L

Lift

lb

 

M

M

Pitching moment

lb-ft

 

M

M

Mach number

 

 

M

M

Free stream Mach number (locally M = 1)

 

 

Mc

Mc

Critical Mach number

 

 

N

N

Yawing moment

lb-ft

 

PA

PA

Projected Area. Area of fuselage, in plan view.

ft2

 

PLH

PLH

Power loading, at hover

 

 

PLM

PLM

Power loading, at maximum power

 

 

Q

Q

Torque

ft lb

 

R

R

Rotor radius

ft

 

Re | RN

RN

Reynolds number [Others | Prouty]

 

 

Sβ

Sβ

Stiffness number

 

 

T

T

Thrust

lb

 

TC

TC

Center of thrust

 

mine

TE

TE

Thrust (efflux)

lb

 

TP

TP

Thrust (port rotor)

lb

 

TS

TS

Thrust (tarboard rotor)

lb

 

V

V

Remote velocity, Free stream velocity

ft/sec, knots

 

VM

VM

Angle between the two masts on an intermeshing. OBSOLETE: see (which is 1/2 VM )

radian, degree

 

U

U

Local velocity

ft/sec, knots

 

X

X

Longitudinal force

lbs.

 

X

X

Longitudinal stability axis

 

 

Y

Y

Lateral force on rotor (H-force). Positive toward advancing side. (sideslip)

lbs.

 

Y

Y

Lateral stability axis

 

 

Yalpha

Lateral angle between the mast and Z-axis

radian, degree

 

Z

Z

Vertical force

lbs.

 

Z

Z

Vertical stability axis

 

 

 

 

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α

alpha

Angle of attack

radian, degree

 

αLO

alphaLO

Angle of attack for zero lift

radian, degree

 

β

beta

Blade flapping angle

radian, degree

 

γc

gammac

Climb angle

radian, degree

 

δ

delta

Rudder angle

degrees

 

δ3

delta3

Pitch-flap coupling angle

radian, degree

 

ε

epsilon

Downwash angle

radian, degree

 

η

eta

Sidewash angle

radian, degree

 

η

eta

Efficiency

percentage

 

ζ

zeta

Blade lag angle. + is opposite of rotor rotation

radian, degree

 

θ

theta

Blade pitch

radian, degree

 

θ0

theta0

Collective pitch angle

radian, degree

 

θT

thetaT

Blade tip pitch angle

radian, degree

 

θ1

theta1

Blade twist

radian, degree

 

θ1A

theta1A

Active Blade Twist

radian, degree

mine

κint

kappa_int

Interference-induced power factor, twin rotors

 

PHA

κOV

kappa_OV

Overlap interference factor, twin rotors

 

RWA

λ

lambda

Induced inflow ratio with respect to swashplate

 

 

λ΄

lambdaprime

Induced inflow ratio with respect to tip path plane.

 

 

λβ

λβ

Flap frequency ratio

 

 

μ

mu

Tip speed ratio (advance ratio)

non-dimensional

 

ρ

rho

Density of air (0.002377 slug/ft3 & 0.07648 lb/ ft3 & 1.204100  kg/m3 @ ISA)

slug/ft3 & lb/ ft3

 kg/m3

σ

sigma

Solidity of rotor

non-dimensional

 

σABC

sigmaABC

Solidity of Advancing Blade Concept rotor

non-dimensional

 

σT

sigmaT

Thrust-weighted solidity

non-dimensional

 

τP

τP

Phase delay between attitude response and control input at high frequency. Is this the same as? Δψ

second

 

φ

phi

Inflow angle

radian

 

φ

phi

Phase angle

degrees

 

ψ

psi

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

radian, degree

 

ωN

omegaN

Natural frequency of blade flapping

radian/second

 

ωbw

omegabw

Bandwidth

radian/second

 

 

 

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Beta

Sideslip angle

radian, degree

 

Γ

Gamma

Circulation

radian, degree

 

Γ

Gamma

Control (swashplate) phase angle (may be the same as Δψ )

radian, degree

N.L.

ΔT

DeltaT

Difference of thrust between rotors. Positive value signifies that the starboard or lower is the greater.

lb.

 

Δψ

Deltapsi

Change in azimuth. Phase lag angle? (may be the same as Γ )

radian, degree

 

Θ

Theta

Helicopter pitch angle

radian, degree

 

Λ

Lambda

Sweep angle

radian/second

 

Φ

Phi

Helicopter roll angle

radian, degree

 

Ψ

Psi

Helicopter yaw angle

radian, degree

 

Ω

Omega

Rotational speed of rotor

radian/second

 

ΩR

OmegaR

Tip speed of rotor

ft/sec

 

 

 

 

 

 

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 Subscript

 

b

b

Per blade

i

i

Induced

O

O

Profile

C

C

Control (used with UniCopter)

CRU

CRU

Cruse

E

E

Efflux (exhaust and cooling discharge)

F

F

Fuselage

H

H

Horizontal, Horizontal stabilizer

HOV

HOV

Hover

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, Vertical stabilizer

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Last Revised: October 29, 2008