B265
OTHER: Aerodynamics  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'.
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 

a_{0} 
a0 
coning angle 
rad, deg 

a_{1s} 
a1s 
Longitudinal flapping 


ac 
ac 
Aerodynamic center. [airfoil] 


b 
b 
Number of blades 


b 
b 
Span of wing 
ft. 

b_{1s} 
b1s 
Lateral flapping 


b_{1'} 
b1' 
Differential lateral cyclic 


c 
c 
Chord of blade [airfoil] 
ft 

c 
c 
Damping 
ft lb/rad/sec 

c_{crit} 
ccrit 
Critical damping 
ft lb/rad/sec 

c_{c} 
cc 
Coefficient of Chord force; twodimensional. [airfoil] 


c_{d} 
cd 
Coefficient of Drag; twodimensional. [airfoil] 


c_{di} 
cdi 
Coefficient of Induced Drag; twodimensional. [airfoil] 


c_{do} 
cdo 
Coefficient of Profile Drag; twodimensional. [airfoil] 


c_{l} 
cl 
Coefficient of Lift; twodimensional. [airfoil] 


c_{lMax} 
clMax 
Maximum coefficient of Lift; twodimensional. [airfoil] 


c_{m} 
cm 
Coefficient of Moment; twodimensional. [airfoil] 


c_{n} 
cn 
Coefficient of Normal force; twodimensional. [airfoil] 


c_{m0} 
cm0 
Coefficient of Moment at zero angle of attack; twodimensional. [airfoil] 


c_{m0.25} 
cm0.25 
Coefficient of Moment about quarter chord; twodimensional .[airfoil] 


c_{mac} 
cmac 
Coefficient of Moment about aerodynamic center; twodimensional. [airfoil] 


d 
d 
Rotor diameter 
ft 
RWA 
d_{r} 
dr 
Slant line distance between rotor hub centers 
ft 
RWA 
d_{s} 
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 
ft^{2} 

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/ft^{2} 

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 

v_{ov} 
v_{ov} 
Induced velocity in overlap area (positive down through the disk) 
ft/sec 
RWA 
w 
w 
Disk loading. Also DL 
lb/ft^{2} 

x 
x 
Longitudinal distance in body system (Cartesian) 
ft. 

x 
x 
Nondimensional distance along airfoil chord. [airfoil] 
nondimensional 

x_{cp} 
x_{cp} 
Location on Xaxis of center of pressure as a percentage of chord from leading edge. [airfoil] 


x_{0} 
x_{0} 
Blade root cutout 
percent 

y 
y 
Lateral distance in body system (Cartesian) 
ft./in. 

z 
z 
Vertical distance in body system (Cartesian) 
ft./in. 






A 
A 
Area 
ft^{2} 

A 
A 
Area of wing (horizontal or vertical stabilizer, etc) 
ft^{2} 

A_{1} 
A_{1} 
First lateral harmonic of blade flapping 
rad, deg 

A_{one} 
A_{one} 
Area of individual rotor disk 
ft^{2} 
mine 
AC 
AC 
Aerodynamic center 

mine 
Α_{L0} 
AL0 
Zero lift angle 
rad, deg 

AR 
AR 
Aspect ratio 


A_{m} 
A_{m} 
Overlap area of disks 
ft^{2} 
HT 
A_{sys} 
A_{sys} 
Total effective disk area of rotor system 
ft^{2} 
HT 
A_{b} 
Ab 
Area of blades 
ft^{2} 

AI 
AI 
Autorotation Index (used by Sikorsky) 
ft^{3}/lb 

B 
B 
Tip loss factor 


B_{1} 
B_{1} 
First longitudinal coefficient of blade flapping 
rad, deg 

C_{D} 
CD 
Coefficient of Drag; non dimensional 


C_{H} 
CH 
Coefficient of (profile drag?); non dimensional 


C_{P} 
CP 
Coefficient of Power; non dimensional 


C_{m} 
Cm 
Aerodynamic moment (section moment coefficient). Positive when pulling up. 


C_{m1/4} 
Cm 
Section moment coefficient about quarter chord. 


C_{m0.25} 
Cm 
Section moment coefficient about quarter chord. 


C_{mac} 
Cm 
Section moment coefficient about aerodynamic center. 


C_{nc} 
Cn 
Normal force coefficient (@ 90º to chord) 


C_{Q} 
CQ 
Coefficient of Torque; non dimensional 


C_{T} 
CT 
Coefficient of Thrust; non dimensional 


C_{T}/σ 
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 

D_{e} 
D_{e} 
Equivalent Drag 


DL 
DL 
Disk loading. Also w 
lb/ft^{2} 

E 
E 
Efflux (engine exhaust & cooling gasses) 
ft^{3} 

F 
F 
Side force on rotor (Fforce) 
lb 

FM 
FM 
Figure of merit 


GW 
GW 
Gross weight 
lb 

H 
H 
Horizontal force on rotor (Hforce). Positive aft. 
lb 

K 
K 
A constant 


K_{p} 
K_{p} 
Feedback gain = tan δ_{3} 


L 
L 
Lift 
lb 

M 
M 
Pitching moment 
lbft 

M 
M 
Mach number 


M_{∞} 
M_{∞} 
Free stream Mach number (locally M = 1) 


M_{c} 
M_{c} 
Critical Mach number 


N 
N 
Yawing moment 
lbft 

PA 
PA 
Projected Area. Area of fuselage, in plan view. 
ft^{2} 

PL_{H} 
PL_{H} 
Power loading, at hover 


PL_{M} 
PL_{M} 
Power loading, at maximum power 


Q 
Q 
Torque 
ft lb 

R 
R 
Rotor radius 
ft 

Re  RN 
RN 
Reynolds number [Others  Prouty] 


S_{β} 
S_{β} 
Stiffness number 


T 
T 
Thrust 
lb 

TC 
TC 
Center of thrust 

mine 
T_{E} 
T_{E} 
Thrust (efflux) 
lb 

T_{P} 
T_{P} 
Thrust (port rotor) 
lb 

T_{S} 
T_{S} 
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 Yα (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 (Hforce). Positive toward advancing side. (sideslip) 
lbs. 

Y 
Y 
Lateral stability axis 


Yα 
Yalpha 
Lateral angle between the mast and Zaxis 
radian, degree 

Z 
Z 
Vertical force 
lbs. 

Z 
Z 
Vertical stability axis 







α 
alpha 
Angle of attack 
radian, degree 

α_{LO} 
alphaLO 
Angle of attack for zero lift 
radian, degree 

β 
beta 
Blade flapping angle 
radian, degree 

γ_{c} 
gammac 
Climb angle 
radian, degree 

δ 
delta 
Rudder angle 
degrees 

δ_{3} 
delta3 
Pitchflap 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 

θ_{0} 
theta0 
Collective pitch angle 
radian, degree 

θ_{T} 
thetaT 
Blade tip pitch angle 
radian, degree 

θ_{1} 
theta1 
Blade twist 
radian, degree 

θ_{1A} 
theta1A 
Active Blade Twist 
radian, degree 
mine 
κ_{int} 
kappa_int 
Interferenceinduced power factor, twin rotors 

PHA 
κ_{OV} 
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. 


λ_{β} 
λ_{β} 
Flap frequency ratio 


μ 
mu 
Tip speed ratio (advance ratio) 
nondimensional 

ρ 
rho 
Density of air (0.002377 slug/ft^{3 }& 0.07648 lb/ ft^{3 }& 1.204100 kg/m^{3 }@ ISA) 
slug/ft^{3} & lb/ ft^{3} 
kg/m^{3} 
σ 
sigma 
Solidity of rotor 
nondimensional 

σ_{ABC} 
sigma_{ABC} 
Solidity of Advancing Blade Concept rotor 
nondimensional 

σ_{T} 
sigma_{T} 
Thrustweighted solidity 
nondimensional 

τ_{P} 
τ_{P} 
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) (0º aft) 
radian, degree 

ω_{N} 
omegaN 
Natural frequency of blade flapping 
radian/second 

ω_{bw} 
omegabw 
Bandwidth 
radian/second 






ß 
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 






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 
Introduction
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Last Revised: October 29, 2008