MAY 10 1971
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ENGINEERING
GOVERNMENT PUBLICATIONS
UNIV. OF WASH. LIBRARIES
APR 17 2018
U.S. DEPOSITORY COPY
STANDARD AERONAUTICAL SYMBOLS
Prepared under Direction of Committee on Aerodynamics
And Approved by
National Advisory Committee for Aeronautics May 28, 1940
1940NOTATION FOR AERONAUTICS
SYMBOLS :
*r X ,	. General scientific.
I I ,	, Airplane dimensions.
III .	, General and applied aerodynamics.
IV. Airplane dynamics
	A x e s . Forces. Force coefficients. M o m e n t s . M o in e n t coefficients. V o 1 o c i t i e s . Angles. Moment s of inertia. Facto rs. Stability derivatives. Stability-derivative coefficient
V. VI . VII . VIII . IX.	S caplane s. Airships. Engines and propellers. Rotor planes. Mi scellaneons: Factors. S ubscripts.
A 3 BRI	IVI AT IOFS :
I .	Aeronautical abbreviations used in N . A . C.A. reports.
II .	Laboratory rules about abbreviationsA .
SYMBOLS :
I .
NOTATION FOB AERONAUTICS
G- e n e r	al scientific:	
cr "3 »	acceleration due	to gravity.
a,	linear acceleration.	
U),	angular velocity.	
v,	velo ci ty.	
Vc,	velocity of sound	. in air.
A,	cross-sectional a	. r e a .
or I ,	1 ength.	
4- u *	thi ckne s s.	
	breadth.	
h,	height.	
x >	radius.	
B,	d i am e t e r.	
w,	weight (mg).	
m,	mass (W/g).	
A,	specific weight.	
P,	d e n s i t y .	
cr,	relative density.	
or t ,	11 m e	
m ~u 3	time for o s c i11at	ion to damp
	amplitude.	
P X ?	period of an osci	llation.
p,	pres sure.	
p,	total pressure.	
CL,	dy nami c pre s sur e	/ 1 _ tt	\ (epf )•
R,	uni versa1 g a s con	s t an t.
or t ,	t emoenature.	
h
T, •y, u-, v,
•p
A »
m,
P ’
absolute temperature, coefficient of friction, coefficient of viscosity, kinematic viscosity ( p./ p ) . strength of circulation, stream function, strength of source or sink, pressure altitude.
Ld’
h,
R.
density altitude altitude or hei< Reynolds IT urn b e r
■P’
k»
E,
altitude or height
fP n
V V-J	2,
rectangular moment of inertia (mk^). polar moment of inertia.
r a di u s of gyration.
Young's modulus of elasticity, shear modulus of elasticity.(ratio of lateral con-

Poisson's ratio t ract i on).
torsion constant, force.
absolute coefficient, section coefficient increment or difference, product of inertia
11 .
Airplane dimensions:
(Symbols ere given for the dimension of the main lifting surface; when more than one surface Is under discussion, they are identified by subscripts: w, wing; t, tail; f, flap; etc.)
Ill .
c ,
h,
S,
A,
r,
,A’ i w ’
i p ,
h ’ a1q ,
8.
chord, span. area.
aspect ratio gap .
di he ci ral angle of
ang1e of angle of angle of
I,
(b"/i
angx e. swe epba ck. wing setting, fin setting, stabiliser setting,
aerodynamic twist of wing.
angle of set of control surface relative to neutral position (particular surface identified by subscript: 5e, 8a,	8r,
distance from c.g. of airplane to some refe: ence point of empennage (usually elevator hinge axis).
center-of-gravity coefficient.
longitudinal coordinate, parallel to the root chord.
lateral coordinate, perpendicular to the plane of symme t ry.
normal coordinate in the plane of symmetry,
pernendi cu 1 a r
,he root chord.
i s 8
f '
G ,
z ,
o
General and applied aerodynamics:
(Subscripts for special cases, and exponents or primes to show values taken about unusual sets of axes.)
L, wing lift.
Ct, wing lift coefficient (L/qS).cl
B
°B
Do
Cp
jJq
Op
■^e
cd
uo
%
c A . al
B„„
'B
p
K
°R
n
h,
rr
n
Sh
h
ch
M
C1I
c
rx
UG
11
cn
c
cc
Gp
7
Vg
7,
o
V
J
7/ ?
section lift.
section-lift coefficient.
total drag.
total drag coefficient (B/qS). profile drag, profile-drag coefficient, effective profile-drag coefficient, section profile-drag coefficient.
induced drag.
induced-drag coefficient.
section induced-drag coefficient.
parasite drag.
parasite-drag coefficient.
resultant force.
resultant-force coefficient, resultant moment.
aerodynamic hinge moment.
aerodynamic hinge-moment coefficient.
section hinge moment.
section hinge-moment coefficient, wi ng normal force.
wing normal-force coefficient (N/qS). cross-wind force.
cross-wind-force coefficient (C/qS).
section
section
normal force.
normal-force coefficient.
s e c t i o n s e c t i o n
cross-wind force, c r o s -wi nd-f o r ce
U
center-of-pressure coeffi
air speed.
stall!ng spe e d.
indicated air so eo d. forward (X-wise) velocity
coeffici en t. ci ent.
in steady flight
longitudinal displacement, lateral displacement, normal disolacement.kx>	radius of gyration	about	X
ky,	radius of gyration	about	Y
Jr 7 z >	radius of gyration	a bout	Z
OS,	angle of attack of	wing	"i + h
	to the chord.	(S	ubscri	p t s
and. T
axi s . axi s . axi s.
respect
o, i, a,
for zero lift, induced, absolute, and. in respect to the thrust axi s.)
flight-path, or glide, angle.
angle of downwash.
wing pitching-moment coefficient about (M n /. / q c 2 h '
El
7
£
C/4
C™
mu
quarter-chord point -moment
m
a . c .
n
c.
c
m»
■c/4/ a- • wing pitching-moment coefficient at zero lift .
wing pitching-moment coefficient about aerodynamic center.
wing pitching-moment coefficient with respect to the center of gravity.
section pitching moment.
section pitching-moment coefficient.
IV.
A i rp1an e dy nami c s
Axes :
X, Y, Z,
airplane axes of reference fixed in the airplane. The X axis is in the plane of symmetry and points generally along the direction of flight.
(The exact orientation varies in different problems.) The Y axis is perpendicular to the Diane of
t ry. symmetry axi s .
he
7
Z4
nd
;ymme-
axis is in the plane of perpendicular to the X

o r c e s :
X
Y
7
longitudinal force (along OX), lateral force (along OY). normal force (along OZ).
force coefficients:
GX’ longitudinal-force coefficients (x/qS). Ov, lateral-force coefficient (Y/qS),
GZ » normal-force coefficient (Z/qS).5
Moments :
h ,	rolling moment (about X axis).
M,	pitching moment (about T axis).
N,	yawing moment (about Z axis).
Moment coeffi	ci ent s :
b-	rolling (L/qbS).
%.	pitching (M/qcS).
Cn,	yawi ng (ll/q bS ) .
Velocities :	
v,	resultant velocity of flight.
n,	longitudinal component of velocity.
v,	lateral (sideslipping) component of velocity.
w,	normal component of velocity.
Q,	resultant angular velocity.
P,	rolling angular velocity.
q,	pitching angular velocity.
r,	yawing angular velocity.
Angles:
(	With	respect to		earth axes)	
		cp,	angle of	roll (bank).	
		0 ,	angle of	pitch.	
		V ’	angle of	yaw (azimuth	an
		<7»	path helix angle (angl		e
			flight	"0 el t Xi el II Cl t (?	ve
			- l .		
			sm UX radius of spin		
	With	r	espect to	relative wind)	
		a,	angle of	a 11 a c k .	
		3,	angle of	sideslin (sin ~ \	—• 1
foment	s of	i	n e r t i s :		
		A,	about X	axis (mky2).	
		3,	about X	axis (mky‘").	
		c,	about Z	axis (mkz2).	
v\
V/
ih<o
Factors-:
T , A,
relative density coefficient (m/pSl). time conversion factor (m/pSV).
dor (used in ez'r ) .
oamm n<
ac
31 a h i i i t y d e r i va t i ve s :

Xv>

variation of longitudinal force due to change of longitudinal velocity f~~/m 'j.
variation of longitudinal force due to
change of lateral velocity
'	\ or /
variation of longitudinal force due to
charge of normal velocity
W 7
‘Q ’

variation of longitudinal force due to
-i i •	ZAv /	\
rolling (Ty®
\dp /
variation of longitudinal force duo
r> i t c h i n g (~~~ / m ).
7
variation of longitudinal force due
to
to
Y,
Y ,
r ’
u ’
zax
yawing g
/nY
variation of lateral force due to change
of longitudinal velocity hf^X/rnY \du 7
of lateral force due to change
e ra1 velocity i7—/m gov'
variation of lateral force duo to change
Vari at of 1
. o
of normal velocity
. _ -/ m i.
7ow 7
tariation of lateral force due to roll-i no
ZdY/ A
Y?z
variation of lateral force due to witch
d<T z
variation of lateral
ga/A
\3*’	/
va. nation of normal force due to change
“orce due to yawing
of longitudinal velocity
AAA
V3w JV
w ’
p >
variation of normal force tine to change
„ -	,	,	,	. ,	/ d Z / h
oi lateral velocity i——/raj.
\dv /
variation of normal force due to change
of norm a 1 velocity f / ra k \d w /'
variation of normal force due to rolling /^-—/mV
kdp' 7
variation of normal force due to pitch-73 Z
ng
k
6 C!
/ra ).
Zr>
^u ♦
T
XJ Y 5
Lw ’
Lp,
Lo»
T.f
1=4. rr ,
variation of normal force due to yawing
\o1	/
variation of rolling moment due to change of longitudinal velocity (hi/rck-A).
\<JU-	/
variation of rolling moment due to
7 3 L / , 2 \ (^S'v/!l"x y
change of lateral velocity variation of rolling moment due to
change of normal velocit
I d L / = P k k 3w' A /
variation of roiling moment due to
rolling f	.
\3PZ A J
rariation of rolling moment due to
i 3L /
-A
<d»
a y
-u ’
variation of rolling moment due to
/AT. / ,	2 \
yawing ; ^-/rik7 i.
\dr' a y
variation of pitching moment due to change of longitudinal velocity I ——/mkv J>
\d P- A 7
variation of pitching moment due to
AK/nkv
change of lateral velocity variation of pitching moment due to
change c
kd v
normal velocity	/ml
\3w'
Ai-,-, ,
of pitching moment du<
/dL

q ’
va r i a t i o n rolling variation
pitching ^/nky2j
t 0
kdP/akl /•
of pitching moment due to /d,,	\Mr ,
^u ’
AT
variation of pitching moment due to
yawing , -—,
\3 r- - /
variation of yawing moment due to change
of longitudinal velocitv —--/mk?2 ).
variation of yawing moment due to change
of lateral velocity ^-/mkc2^.
ye * j
variation of yawing moment due to change
N-,
of normal velocity f—/mk?2 k \dwz “ J
variation of yawing moment due to roil-
v
Nr,
/^kz2^ . c f y /mkz
variation of yawing moment due to pit chi'' 9 IT / „ V 2
\t Q
variation of yawing moment due to vawing rz ' J
S t a. d i 1 i t y - d e r i va t i v e coefficients.’
t
73
= T X,
-vr
V — TV >-U	1 -U
Y.
’U
v.
i/
T --
7
V
T	r
——	z.
c	2
b
T	n
"0 ’
/ 0

u
x w ~
V
T
= T
2 V
= T
■ w
i n g

• V
• w
T Z
w
x
n
X

T
- r9
u	- T	L Lu	7 V "Q	T	■^p
P	- T	1	T	h	= T	Iq
lw	•- T	7	T h*	J. J	T 1/ v»	= T	J.. J
mg	= T		mp	" T	Mp
mv	= T	' Kt	mq	- T	Mq
m.„ V V	= T	V i.-w	mr	= T	Lr
nu	= T	*?	’"T ^u	nP	= T	lTp
nv	= T	1 h v	nQ	= T	hq
n.,,	- T	I 1TW	nr	H- i	Hr
G eapianps :					
v, a ,	speed. acceleration,				
T , trim (degrees).
<i, draft (distance from keel at step to free-water surface).
A, load on water.
Aq , initial load on water.
R, water resistance, w, specific weight, b, beam of hull.
M, trimming moment.
G^» load coefficient (A/wb3).
Gy, speed coefficient (V/v gb).
Gp, resistance coefficient (R/wb3).
, trimming-moment coefficient (M/wb4)
VI. Airships:
vol or V, volume of airship hull.
> virtual volume of airship hull.
L, length of airship.
R, maximum diameter of airship.
a,	major axis of ellipsoid.
b,	minor axis of ellipsoid.ID
VI .
( co nt	. ) :		
n,	fineness	ratio	(a/t>) or (L/D)
r,	radius of hull.		
H,	Reynolds	number	(pVl/p.) .
T	distance	from no	se .
7,	di s tanc e	no rmal	t o hul1.
8 ,	angle of	pit ch.	
f ,	an g 1 e o f	roll.	
V >	angle of	yaw.	
S,	control-	surface	deflection (sub
	for el	evat o r ,	rudder, etc.).
c 1	cont rol-	surf a ce	chor d (sub scrip
c
S,
CE >
p
-ft ,
°L ’ CS ’ CX’
CY,
SS ’ CR’
n
P
t for
fin, rudder, etc.)
control-surface area (subscript for etc.).
coefficient (elevator t o hul 1 ax? s/ q ( vo 1) ) .
f? / ’
tin, nic..a.er, e1evater-fo r c e force normal
r e s ist an ce.
lift c o e: drag ( or
all el
3
cient (lift/q(vol '	~).
shape) coefficient (drug par \ 2 / 3 \
wind. axeszq(vo. longitudinal-force coefficient (force parallel to longitudinal body
axis/qivol; ;.
cross-force coefficient (force normal
to longitudinal body axis/q(vol)° ) cross-wind force coefficient (cross-
wind force/q(vol)“'°).
resultant-force coefficient (resultant
r.	/ Z	-2 / 3 \
t or ce/ q ■. vol	) .
rolling-moment coefficient (rolling Zr. f	'.2 /

0
aoment about C.3,/q(vol)*'	.
pitching-moment coefficient (pitching
moment about C.B./q(vol/° ). yawing-moment coefficient z(yawing mo-
ment about C.B./q(vol)“'^).
VII. Engines and propellers:
E, propeller diameter.
R, propeller radius, r, radius of any blade element.VII. .
Engines and. propellers (con
JL.	i	•
u	• >	.
V
c, P,
n,
i
S ’
e,
chord of propeller blade.
pitch of propeller.
revolutions per second.
inflow velocity.
slipstream velocity.
angle between propeller hlade face end ulane of rotation.
pTTrn
/
effective helix angle ( ta

-1
VIII .
T
CT ’ Q,
c
c
T
Q’
p,
p»
o
C ’
Qc >
propeller thrust, thrust coefficient propeller torque, torque coefficient power.
uower coefficient
D4)
(T/pi (Q/pn2D5)
(P/pnSD5) . /
speed-power coefficient (	pV ° / Pn
propel lei’ efficiency.
net propeller efficiency.
thrust coefficient ( T / p V' " 33 “ ) . torque coefficient (Q/pVL'P3).
Rotor ulanes:
o , wh» c,
Cq-| ,
l,
t ,
m,
r, R, x,
of hlades. weight. chord.
chordwise c.
h’
ov
■Q
number h lade hlade hlade
a . c , ) .
hlade vertical c.g
a. c . ) .
rotor hlade thickness, line density of hlade. hlade-element radius, rotor-hlade radius, ratio of hlade-element hlade radius (r/P). distance from hinge to
rotor solidity (he/up), factor allowing for tip lo moment of
location (aft of location (helow
radius to rotor-
axi s
s e
m
inertia o:
one
fZl -k
rotor
_c_k
2R
/
hlaie about the horizontal hinge.7111. Ho tor planes (cont. ):
I-o, polar moment of inertia.
q, equivalent moment of inertia of the
rotor blade about the elastic axis.
y, mass constant of rotor "blade (cpaH4/li) a, slope of curve of lift coefficient
against angle of attack of "blade airfoil section.
os, rotor angle of attack. osp, blade-element angle of attack from zero
lift (cp + Q > .
cp, angle "between resultant velocity and
the plane perpendicular to the rotor axi s .
9, instantaneons pitch angle measured from zero lift.
90, pitch angle at huh.
8 x , difference "between huh and. tip pitch .angles .
3, blade flapping angle.
, "blade azimuth angle measured from down-
w I n d. direction.
a0 ’	constant term in Fourier series that o xp r e s s e s p ,
an >	coefficient of cos n 4/ in expression
	for p.
»	coefficient of sin n \!/ in expression
	for 9 •
e n »	coefficient of cos n	in expression
	for Q.
n ‘‘n ’	coefficient of sin n y in expression
	for 9.
u,	tip-speed ratio (7 cos c,/QH).
X,	inflow coefficient.
	instantaneous torsional deflection of
	tip of rotor blade.
v,	forward v e10 c i t y.
7 1 ,	resultant air velocity at rotor.
v,	rotor induced velocity	(t/FttH^ pV ’ ) .
Vo>	velocity ^t propeller disk.
	indicated, velocity.
Vi ’	indicated vertical velocity.
n,	angular velocity of rotor blade.
Um ,	velocity component of blade element
	parallel to rotor disk and. perpen-
	dicular to the blade span axis.VIII .
p 1 a n e s	(cent. ) :	
Up»	velo.city component of	b I. a d e e 1 e m e n t
	parallel to the blad	e span axis and
	perpendicular to Up	
Up,	velocity component of	blade element
	p erpendi cular to t h e	bIa d e s p an axis
	and perpendicular to	Urn .
u,	resultant velocity of	UT~ and Up.
Uy ,	component of resultant	velocity (Uij/QE)
	component of resultant	velocity (Up/fiE)
Up,	component of resultant	velocity (Up/QE)
°1’	rotor lift coefficient	(L/i p 7% Ha).
	rotor drag coefficient	(D/l p V2tt h2).
8,	mean profile-drag coef	ficient of rotor-
	blade airfoil section.	
Mw W i	blade weight moment about horizontal	
	hinge.	
mt,	blade thrust moment about horizontal	
	hinge.	
MQ’	b 1 a,do twi st ing moment	at the hub.
x’	blade twisting moment	outboard of any
	station x.	
cM .	moment coefficient of	air forces about
	t ne c.g.	
Cy, lateral-force coefficient of rotor (Y/i p V3n a2).
cm.	pitching-moment co	ef f i ci on t	of	rotor
	about a.c.	(M/i	p v"tt e"	).	
ci •	rolling-momenf coe	~~ ~	h/ X L/ Ij.	of	rotor
c Cm ,	(L'/| p V% 23). torque coefficient	(Q/p	TT	K5 ).
	thrust coefficient	(T/p fi2	'FT	E j .
Mi scellaneous:
Factor s :
slope of lift curve (dCp/da). lift curve a
rat i o.
aQ , slope of lift curve at infinite aspectMi s	cellareous	(cont. ) :
3?	actors:	
	6,	jet-boundary correction factor for wind tunnels.
	e ,	span efficiency factor.
	k .	equivalent monoplane span factor.
	nt.	tail efficiency factor.
<*•< u	ubscript s :	
	A,	airplane or full scale contrasted to model.
	M ,	model contrasted to full scale.
R	or rear,	rear of two objects in tandem.
jT	o r f ro nt ,	front of two objects in tandem.
	u,	upue r.
	»	lower.
(	cipher) 0,	standard conditions; zero time; zero lift .
	P »	projected area; propeller operating.
	a ,	additional force.
	ai ,	additional force when Ck - 1.
	o,	basic force.
	c,	values pertaining to wing-nacelle combinations.
	c ,	critical.
	e ,	effective.
	X J	flap; final value; fuselage.
	-L 9	induced; i n i t i al.
	t,	tail; tab; terminal.
	w,	wing.
	max,	maximum value.
	m i n,	in i n i mum v a, 1 u e .
	opt ,	0 p t imum value.
	corr . ,	corrected value.
ABBE	EVIATIOES :	
I .	Aeronauti	cal abbreviations used in N.A.C.A. report
	a. c. -	aerodynamic center.
	C.3. -	center of buoyancy.
	c. g.	-	center of gravity.
	c . p . -	center of pressure.
	lat. -	lateral (subscript).
	L .3 . -	leading edge.~ 15 -
B. ABBREVIATIONS (cent.):
I. Aeronautical abbreviations used in N.A.G.A.
long. - longitudinal (subscript).
M.	A.G. - mean aerodynamic chord.
N.	A.G.A. - National Advisory Committee for
Aeronaut!cs.
N.D.E. - nacelle drag efficiency factor, s t a. - station.
T.E. - trailing edge.
"eport s

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