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A M E R I C A N

C a p 7 Z

S T A N D A R D

Letter Symbo ls for

Aeronaut ica l Sciences

ASA Y10.7-1954 UDC 003.62:533.6

Prepared by Sectional Committee on

Letter Symbols

The American Society of Mechanical Engineers

National Advisory Committee for Aeronautics

Institute of the Aeronautical Sciences

American Rocket Society

T H E A M E R I C A N S O C I E T Y O F M E C H A N I C A L E N G I N E E R S 29 West 39th Street, New York 18, N. Y.

T A B L E OF CONTENTS

General Pr inc ip les o f L e t t e r Symbol Standardization ....................................... L e t t e r Symbols f o r Primary C o n c e p t s ................................................................ L e t t e r Symbols for Secondary C o n c e p t s ...........................................................

Symbols for u s e a s Subscripts .......................................................................... Symbols for u s e a s Superscr ipts ......................................................................

............................................................................................................ Appendix I Recommended Des igna t ions for Sys tems of Axes, Angular Relat ion-

s h i p s , and Quanti t ies R e l a t e d There to

Appendix 11 .............................................................................................................. Alphabet ical Index b y C o n c e p t s

P a g e

5

Sectional Committee on Letter Symbols H.M. Turner, Chairm.an, A s s o c i a t e Professor , E lec t r ica l Engineering,

Y a l e Universi ty , New Yaven, Conn.

P e r s o n n e l of Subcommittee No. 7 on Le t te r Symbols for Aeronaut ical S c i e n c e s

Thomas F. Ball, Chairman, Bureau of Ordnance, Department of the Navy, Washington, D.C. Roy C. Hopgood, Secretary, 420 Lexington Ave., New York, N.Y.. J.V. Charyk, Department of Aeronautical Engineering, Princeton University, Princeton, N. J. Charles W. Chillson, Curtiss-Wright Aeronautical Corporation, Caldwell, N.J. W.M. Coates, U.S. Naval Post Graduate School, Monterey, Calif. W.S. Diehl, Captain, USN, Bureau of Aeronautics, Department of the Navy, Washington, D.C. Hugh L. Dryden, Director of Aeronautical Research, National Advisory Committee for Aeronautics,

Washington, D.C. Donne11 W. Dutton, Director, Daniel Guggenheim School of Aeronautics, Georgia Institute of Technology,

Atlanta, Ga. Maurice A. Garbell, President, Maurice A. Garbell, Inq., San Francisco, Calif. 1.E. Garrick, National Advisory Committee for Aeronautics, Langley Aeronautical Laboratory,

Langley Field, Hampton, Va. Newman A. Hall, Mechanical Engineering Department, University of Minnesota, Minneapolis, Minn. James A. Hootman, National Advisory Committee for Aeronautics, Washington,, D.C. H.C. Johnson, Glenn L. Martin Co., Baltimore, Md. C.T.G. Looney, Department of Civil Engineering, Yale University, New Haven, Conn. Clark B. Millikan, Director, Guggenheim Aeronautical Laboratory, California Institute of Technology,

Pasadena, Calif. F.T. Morse, Department of Mechanical Engineering, University of Virginia, Chartlottesville, Va. John D. Nicolaides, Bureau of Ordnance, Department of the Navy, Washington, D.C. R. Hosmer Norris, General Engineering Laboratory, General Electric Co., Schnectady, N.Y. G.L. Shue, Consolidated Vultee Aircraft Corporation, San Diego Division, San Diego, Calif. Harold K. Skramstad, Naval Ordnance Laboratory-Corona, Corona, Calif. M.J. Thompson, Defense Research Laboratory, University of Texas, Austin, Tex. R.J. Volluz, Ordnance Aerophysics Laboratory, Consolidated Vultee Aircraft Corporation,

Daingerfield, Texas Calvin N. Warfield, Applied Phys ics Laboratory, The Johns Hopk~ns University, Silver Spring, Md. John M. Wuerth, Aerophysics Laboratory, North American Aviation Corporation, Los Angeles, Calif. Charles H. Zimmerman, National Advisory Committee for Aeronautics, Langley Aeronautical Laboratory,

Langley Field, Hampton, Va.

Copyright, 1954, by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

Printed in U.S.A.

Foreword (This Foreword i s not a part of the American Standard Let ter Symbols for Aeronautical Sc iences , Y10.7-1954.)

This standard was prepared by Subcommittee No. 7 on Aeronautical Sciences, one of fifteen subcommittees appointed by Sectional Committee Y 10 on Letter Symbols, for the purpose of prepar- ing American Standard letter symbols. The other subcommittees cover mathematics, hydraulics, mechanics of solid bodies, structural analysis, heat and thermodynamics, illuminating engineering, electrical and magnetic quantities, radio, physics, chemical engineering, acoustics, meteorology, feedback-control systems, rocket propulsion, and general principles.

Sectional Committee Y10 (originally designated Z10) was organized under the procedure of the American Standards Association in January, 1926, with the American Society of Civil En- gineers, American Institute of Electrical En- gineers, American Society for Engineering Edu- cation, American Society of Mechanical Engineers, and the American Association for the Advance- ment of Science,, a s joint sponsors. The commit- t ee was reorganized in 1935, in 1947, and igain in April, 1951, with ASME sole sponsor. It now consis ts of representatives of 42 national socie- t ies and associations.

Subcommittee No. 7 was originally constituted in April, 1926, and submitted a proposal which was issued a s a standard in 1930. Rapid develop- ments in concepts relating to the aeronautical sciences rendered the 1930 standard obsolete, and the subcommittee was reconstituted in June, 1947, with substantially i t s present membership, for the purpose of developing a new standard. A proposed standard was published in January, 1949, for trial and criticism, and the resulting American Standard in this field was published in January, 1950.

The 1950 standard was admittedly deficient in certain respects, for compromises had been made in order to expedite approval and publication. Since the 1950publication, the subcommittee has attempted to rationalize some of the original in- consistencies, and the re quired number of changes has appeared to justify reissue of the standard in i t s present revised form. Concepts beyond those listed in the present revised standard are the subject of further subcommittee work, con- templating a possible later revision.

During the course of i ts work the subcommittee

has considered a number of special letter symbols relating particularly to meteorology, to feedback- control systems, and to jet propulsion (including rockem).* I t has been the consensus that some , - - - ~~

let ter symbols and concepts in these fields are s o specialized a s not properly to fall within the scope of Subcommittee No. 7. Special Y10 subcommittees have now been established in these fields, and therefore no attempt h a s been made to be exhaustive (in the present standard) in the matter of letter symbols for special concepts in meteorology, in feedback-control systems, and in internal aspects of propulsion.

Recognizing the practical fact that most p u b lished and duplicated papers and other works in the fields of aeronautics and aerodynamics are duplicated by some process relying upon the use of a typewriter, the subcommittee has made no u s e of type-face variations in orderto distinguish le t ter symbols. I t i s believed that this feature will simplify thepreparatibn of typewritten dupli- cations, but, of course, General Principle 4 (see page 6) will st i l l be applicable to printed publi- cations.

In the present standard there are two listings of the same symbols and quantities (in the case of letter symbols for primary concepts and for secondary concepts) in order to facilitate use of the standard. The first l ist ing i s alphabetical by symbol, and the second i s alphabetical by concept (see Appendix 11, page 23). The first two columns (namely, the Symbol column and the Concept column) of the first l ist ing constitute the American Standard, and all other columns and listings (including Appendix Ion axes, angu- l a r relationships, and related quantities) are merely to facilitate use of the standard. In the third column of the first l ist ing of letter symbols for primary concepts, illustrative dimensions are given, but these dimensions are not a part of the standard; in the fourth column of the first listing the extent of agreement with current American Standards is indicated and i t will be noted that this agreement i s substantial; in the fifth column of the first listing are certain remarks including definitions, but these form no part of the standard.

'Pending recommendations by other ASA-Y10 subcommit- teen on tbeae topica, aome aymbola and concepts in theae fields a m recommended herein.

In general, any of the recommended let ter s y m bols for primary concepts may b e employed a s subscripts i n application to another symbol for a primary concept. This recognizes the fac t that a given primary concept may in certain circum- s tances be employed a s a modifying or secondary concept. F o r this reason, there h a s been no deliberate attempt made to include in the subscr ip t l i s t a l l the symbols which may be employed a s subscripts, particularly where such'symbols maybe found in the published l is t ing o r principal le t te r symbols. In certain c a s e s , recommended subscripts may be used a s superscripts.

Multiple subscripts and superscripts a re fre- quently necessary in the more complex phases of t he aeronautical sc iences and are condoned provided the following system i s observed:

(a) Two adjacent subscripts (superscripts) impiy that the second subscript (superscript) modifies the first subscript (superscript) or that both subscripts together represent an abbreviation (e.g. z, , - position of aerodynamic center).

(b) Two adjacent subscripts (superscripts) separated by a comma imply that t he second modifies the quantity represented by the principal symbol.

(c) A subscript to a subscript denotes t h e derivative of the quantity, represented by the principal symbol, with respect to the quantity related to the second subscript.

Thus, for example:

~ C L '~ ,denoteh 7 , and

ck!

a s subscripts whenever the terms occur in mathematical expressions; e.g., be-elevator span; S,- wing area. Capital let ters should be used to designate component parts of a configuration, a s used in models for wind-tunnel testing, and various components of the model under t e s t should be distinguished by means of numer~ca l sub scripts; thus, F,B,N,would represent a model including the No. 1 fuselage, the No. 3 wing, and the No. 2 nacelle. Since such configuration symbols are not usually employed a s subscr ip ts , they are not included in the present l i s t of subscripts; thus, in the present l is t of subscripts , symbols for aircraft components generally appear a s lower-case letters.

In the field of turbulent-flow analysis , practice i s not well enough established to permit the recommendation of symbols pertaining to turbulence intensity, to turbulence energy distribution (i. e., the so-called spectrum of turbulence), and to turbulent-fluctuation frequency. Meanwhillt, the limited needs for such symbols should be met by use 'of symbols for analogous concepts in other fields. I t will be noted, however, that recommendations are made herein for symbols to ex- press mean-velocity component (E) and turbulent- velocity' component (u ' ) , the recommended symbols being the bar and the prime, respectively, to be applied to a suitable velocity symbol.

Since publication of ASA Standard 210.7-1950, the subcommittee has given careful consideration to the subjects of axis conventions (with attend- an t problems of moment designations, coefficients, etc.), number designations, and flutter. Much i s now standardized in these fields, and Appendix I contains further recommendations on the first of these t o ~ i c s .

dCl denotes - A draft, dated April, 1954, was presented to the members of Sectional Committee Y 1 0 for letter ($1 ballot vote. Following its approval and that of the sponsor, i t was submitted to the American

In designating aircraft components, i t i s recom- Standards Association for approval and designa- mended that lower-case let ters be general1 y used tion. T h i s mas granted on 0 ctober 7, 1954.

Any part of this standard may be quoted. Credit l ines shoutd read: "Extracted from American Standant Let ter Symbols for Aeronautical Sciences (ASA Y10.7-1954) wi th the pennisswn of the publisher, The American Society of Mechanical Engineers, 29 U'est 39th Street, New York 18, N.Y."

AMERICAN STANDARD

LETTER SYMBOLS FOR AERONAUTICAL SCIENCES

General Principles of

Letter Symbol Standardization

1 Letter Symbols. A letter symbol for a phy si- cal quantity 1s a single letter, specified a s to general form of type. It i s available for use within 3 mathematical expression. This primary symbol may be modified by subscript or superscript. In a published work, the same primary letter symbol should appear throughout for the same generic physical quantity, regardless of the units employed, and of special values assigned.

Usually, one may readily distinguish between letter symbols for physical quantities, and other published symbols and signs. The latter, while more or less analogous, belong largely to topics not treated here, such as , (i) mathematical signs, (ii) chemical symbols, (iii) punctuation, (iv) proofreading signs, and (v) abbreviations (widely used in tabulations).

2 Four General Requirements for Published Symbols and Signs. A s i s generally recognized, each published symbol or sigfl, of whatever kind, should be a t least:

(a) Standard, where ~ o s s i b l e . In the use of published symbols, authors of technical works (including textbooks) are urged to adopt the symbols in this and other current standard l is ts , and to conform to the principles stated here. An author should give a table of the symbols he uses and their respective interpretations, or e l se refer to a standard l ist a s source for symbols which he i s using but does pot explain. For work in a specialized or developing field, the author may need symbols in addition to those already contained in standard lists. In such a case he should be careful to select simple suggestive symbols which yet avoid conflict in the given field and in other closely related special fields. Except in this situation, he should not introduce new symbols or depart from currently accepted notation.

(b) Clear in reference. One should not assign to a given symbol different meanings in such a manner as to make i t s interpretation in a given context ambiguous. Conflicts must be avoided. Often a listed alternative symbol or a modi+ing subscript i s available and should be adopted. Except in brief reports, any symbol not

familiar to the reading public should have i t s meaning defined in the text. The units should be indicated whenever necessary.

( c ) Easily 'identified. Because of the many numerals, letters and signs which are sirni- lar in appearance, a writer should be careful in calling for separate symbols which in published form might be confused by the reader. For example, many letters in the Greek alphabets (lower case and capital) are practically indis- tinguishable from English letters; the zero i s easily mistaken for a capital (A

(d) Economical in ~ubl icat ion. One should try to keep a t a minimum the cost of publishing symbols. In particular: ( i) Notations which call for handsetting of movable type should be rejected in favor of forms adapted to modem mechanical methods of composition. (ii) No one work should use a great variety of types and special characters. (iii) Handwriting of inserted symbols, in copy largely typewritten and to be reproduced in facsimile, should not be excessive. (iv) Often a complicated expression appears as component part of a complex mathematical f o r mula, for example, a s an exponent of a given base. Instead, one may introduce, locally, a single letter to stand for such a complicated component. An explanatory definition should then appear in the immediate context.

3 Secondary Symbols. Subscripts and superscripts are widely used and for a variety of conventional purposes. For example, a subscript may indicate: (i) the place of a term in a sequence or matrix, (ii) a designated state, point, part, or time, or system of units, (iii) the con- stancy of one independent physical quantity among others on which a given quantity depends for i ts value, (iv) a variable with respect to which the given quantity, is a derivative. Like- wise, for example, a superscript may indicate: (i) the exponent for a power,(ii) a distinguishing label, ( i i i) a unit or (iv) a tensor index. The intended sense must be clear in each case. Several subscripts or superscripts sometimes separated by commas may be attached to a single letter. A symbol with a superscript such a s a prime (') or second ("), or a tensor index,

October, 1954 5

AMERICAN STANDARD

should be enclosed in parentheses, braces or brackets before an exponent i s attached. So far as logical clarity permits, one should avoid attaching subscripts and superscripts to subscripts and superscripts. Abbreviations, them- selves standardized, may appear among subscripts. A conventional sign, or abbreviation, indicating the adopted unit may be attached to a letter symbol, or corresponding numeral. Refer- ence marks, such a s numbers in distinctive type, may be attached to words and abbreviations, but not to letter svmbols.

4 Typography. Letter symbols for physical quantities, and their subscripts and superscripts, whether upper case, lower case, or in small capitals, when appearing a s light-face letters of

the English alphabet, are printed in italic (sloping) type. Arabic numerals, and letters of other alphabets used in mathematical expressions are normally printed in vertical type. When a special alphabet is required, boldface type i s to be preferred to German, Gothic or Script tvpe. In material t6 be reproduced in facsimile, tram copy largely typewritten, letters which would be boldface in print, may be indicated to be such by special underscoring, while the few distinct letters used from other alphabets, if carefully made, should be self-explanatory. It i s important to select a type face which has italic forms, and with clearly distinguished upper case, lower case, and small capitals. Only type faces with serifs are recommended.

Letter Symbols for Aeronautical Sciences A symbol designated as an alternate isnot preferred. Symbolshaving equal rank are not designated a s alternates. The dimensions given in the third column and the definitions given in the fifth column are merely illustrative and

form no part of the present standard. With regard to the indicated dimensions, and in a particular system of units, M represents Mass, L represents Length,. T represents Time, 'and 8 represents Temperature.

Symbol

Ai (written together)

b b

Letter

Concept

Slope of lift curve

Velocity of sound Area, cross-sectional

Aspect ratio

Aspect ratio, alternate for

Blade width (propellers) Semichord, alternate for

c/2 (flutter)

Chord, of an airfoil

Section coefficient Section coefficient

(flutter)

Symbols for Primary Concepts

Dimensionless

Dimensions

Dimensionless

Use c for alternate Use S for surface or

projected area See (written together)

for alternate

Also Appears in ASA Publication

Dimensionless Dimens'ionless

Remarks

L Used in Z10.3,Z10.6, 1 210.8 for breadth

L

In flutter, section coefficients reduce to steady-flow coefficients under steady-flow conditions. Use subscripts or superscripts to indicate any or all of the following items:

Use s for alternate for semispan (b/2)

Use b as alternate for c/2, semichord (flutter)

(1) whether for lift or moment,

(2) acting on what component or about what axis,

(3) due to what kind of motion (or degree of free- dom),

(4) of what component. These items may be indicated in the form c ::

h w 34 (e.g. c l o ); since c ,, is , in general, a complex quantity, i t can be divided into its real and imaginary Darts. as:-

AMERICAN STANDARD

L E T T E R SYMBOLS FOR PRIMARY CONCEPTS (Cont.)

Symbol

Velocity of sound, alternate for; g a s velocity (rockets)

Specific heat, a t constant

Concept

pressure Specific heat, at constant

volume Circulation function, for

harmonic oscillations ( flutter)

Also Appears Dimensions in ASA Publication

Coefficient

Concentration I Diameter

D i arne ter

Drag

Span effectiveness Internal energy, per unit

mass or per unit weight, alternate for

Energy

Modulus of elasticity; Young's modulus

2T-28-1

L2T-20-1

Dimensionless

Dimensionless

Dimensionless

Remarks

Used in expressing a function, as C(k), meaning circulation function of reduced frequency k (see NACA Report 496 by Theodorsen). C(k) = F(k) + iG(k), or, in terms of Hankel functions,

See Appendix I and Figure 2; also, see K for factor which may have dimensions

Interchangeable, but conflicts with differential operators shall be avoided

Dimensionless L ~ T - ~ (per unit

mass); L (per unit weight)

M L ~ T - ~

ML' IT-2

Cyclic frequency

Force; resultant force

Thrust; stream thrust (combus tion)

Acceleration due to gravity

S tructur a1 damping coefficient (flutter)

LT-2

Dimensionles s

Distinguish from u for circular frequency

See Appendix I

Use T for propeller thrust

Use with appropriate subscript to indicate type of vibra- tion. Section damping force or moment may be introduced proportional to amplitude and in phase with velocity, as , for example, by applying the factor(1tig) to the stiffness term

L E T T E R SYMBOLS FOR AERONAUTICAL SCIENCES

Mass velocity; mass- flow, per unit cross- sectional area, per unit time; weight-flow, per unit cross-sectional area, per unit time

Shear modulus

Symbol

ML-'T- (mass flow)

ML-'T'~ (weight flow)

M L - ~ T - ~

A 1 ti tude Blade thickness

(propellers) Deflection, from a speci-

fied plane, due to bending (flutter)

Concept

Enthalpy, per unit mass or per unit weight: specific enthalpy

Heat-flow rate, per unit of area, per degree, across a boundary surf ace

Angul ar mom en tum

Dimensions

Enthalpy; total heat con tent

Angle of incidence


Impulse

Remarks

Mass moment of inertia Mass moment of inertia,

per unit length Area moment of inertia

L ~ T - ~ (per unit mass)

er unit weight)

M T - ~ O - '

I

Dimensionless I

Function of space coordinates and time; use z (lc) for alternate, when with reference to z-y plane

Usually characterized by a sub script

Subscripts should be used to connote type of impulse

Advance ratio of propeller

Mechanical equivalent of heat; Joule's constant

Torsional st iffness con stan t

Dimensionless

Dimm sionless Numerical value is a function of mechanical and thermal units used

Used in torsional stiffness GI; same a s area polar moment of inertia only for a circular cross-section

Radius of gyration k I Ratio of specific heats,

alternate for Reduced frequency

(flutter) Thermal conductivity Factor, for comparison

purposes

Length; distance

Li ft Lift, per unit length

(flutter)

L 1 Z10.3,Z10.6,Z10.8 Dimensionless 210.4

Dimensionless ob "% 'P

M L T ' ~ ~ -' May have

dimensions

L

MLT-2 MT-2

210.4,Z10.6,ZlO. 12

ZIO.3,Z10.4,21O.6 Recommend useof italicized symbol, and script ell (lower case) if italicized symbol i s not available.

AMERICAN STANDARD

LETTER SYMBOLS FOR.PRIMARY CONCEPTS (Cod.)

Remarks

Use NMo for alternate

See Appendix I; see also Q

See Appendix I Usually characterized by

subscript; see Appendix I1

See Appendix I; use ox

for alternate

See Appendix I; use o for alternate

v2 PT

See also

See Appendix I; use oZ for alternate

Always used with appropriate subscript

Identification i s to be made by suitable subscripts, superscripts, or indication of functional dependence

A s occuringin pv =RT


Z10.2,Z10.3,Zl0.4, Z10.6,ZlO. 12

Z10.3,Z10.8

~10.2,Z10.3,Zl0.6,Z10.12

Z10.2,Z10.3,Z10.4,Z10.12

Z10.2,Z10.3,Z10.4,Zl0.6, Z10.8,Z~10.12 Z10.2,Z10.3,Z10.6,Z10.12

210.4

Z10.4,ZlO. 12

'210.4,Z10.6,ZlO. 12

Z10.2,Z10.3,Z10.4,210.6, Z10.8,Z10.12

210.4,Z10.6,ZlO. 12

Dimensions

L

M

ML" Dimensionless

M L ~ T - ~

MLT'~

Dimensionless

T"

M L T ' ~ Dimensionless

T'l

ML"T'~

M L ~ T ' ~

T"

ML-'T '~ ML2T'3

L'T-~ (per unit mass) (. (per unit wei9 t )

M L ~ T ' M L ~ T - ~

T ' ~

L

Dimensionless

Dimensionless

L 2 ~ - 2 0 - 1

L

Symbol

L

rn

rn M M M

n

n

N N

P

P

P

9

4 9

9

Q Q

r

r

r

R

R R

Concept

Turbulence scale; correlation length (turbulence)

Mass

Mass,per unitlength(f1utter) Mach number

Moment, torcpe

Moment, per unit length (flutter)

Load factor

Revolutions per unit time

Normal force, alternate for Number, in general

Angular velocity of body- axis system about X-axis

Pressure; static pressure

Power

Angular velocity of body- axis system about Y-axis

Dynamic pressure Quantity of heat, per unit

time Quantity of heat,.per unit

mass or per unlt weight; specific quantity of heat

Quantity of heat Torque (propellers and

rotary-wing aircraft)

Angular velocity of body- axis system about Z-axis

Radius

Reduced radius of gyration (flutter)

Correlation coefficient (turbulence)

Gas constant Range


LETTER SYMBOLS FOR PRIMARY CONCEPTS (Cont.)

Symbol I Concept

Entropy, per unit mass or per unit weight; specif ic entropy

R R

/ Semispan, alternate for S

Entropy s Area, surface or projected

Reynolds number Richness; equivalence

ratio (combustion)

t Thickness t Time

t

T I Temperature, absolute

Temperature, general

Thrust (propellers and rotary-wing aircraft)

Internal energy, per unit mass or per unlt weight specif ic internal energy

Velocity, component of, along X-axis

Internal energy Heat transfer coefficient,

over-all Velocity, alternate for;

gust velocity

Velocity, component of, along Y-axis

Volume, per unit mass or per unit weight; specif ic volume

1 Velocity, resultant; speed

Dimensions

V

Dimensionless ~ i m e n s ionless

Volume

L ~ T - ~ B - (pkr unit mass)

LO-1 (per unit weight)

L ML 2 ~ - 2 8 - 1 L

( L ~ T - ~ (per unit

( L ( p ~ r unitweight) LT- .

h 4 - l ~ ~ (per unit mass]

M - ~ L ~ T (per unit weight)

LT-I

Use N R for a1 ternate Richness i s >1 on the rich

s i d e of the stoichiometric mixture, and <1 on the lean side; u s e K meaning rich- f

Also Appears in ASA Publicat ion

ness of the- fuel, when necessary to distinguish $ram other concepts con- noted by R

Remarks

Alternate for b/2

U s e A for cross-sectional area

Use 8 for al ternate

Use T for al ternate

Use F for other types of thrust

Z10.4,Z10.6,210. 12 I U s e e for al ternate

S e e Appendix I and Figure 1 for designation of axes

Use E for alternate;

z10.2,z10..4,z10.12 I

Use U for alternate; u s e ei ther subscripts ( e S g . , V X , V y , V z ) O r U 7 V7 W for velocity components

210.2,210.6

Z10.4,210.6,ZlO.12

See Appendix I and Figure 1 for designation of axes


Velocity, component of, along Z-axis

Weight flow, per unit time; mass-flow per unit time

LT'

MT-I $mass flow) Weight MLT-

AMERICAN STANDARD

LETTER SYMBOLS FOR PRIMARY CONCEPTS (Cod.)

Remarks


See Appendix I and Figure 1

See Appendix I andFigure 1 See h

W Defined a s arctan --; see u

Appendix I and Figures 1 and2 -

Oefined a s arcsinV V ; See Ap- pendix I and Figures 1 and 2

Use k for alternate

Angle between a horizontal plane and instantaneous direction of motion of body center of gravity, positive in climb; see Appendix I and Figure 1

Use 8 for momentum thickness of boundary layer

Differential deflections must be clearly defined; in flutter, symbol 6 i s often employed for con trol-surface angular displacement

--

Ratio of a pressure to the standard pressure of atmos- pheric air a t sea level


210.2,Z10.3,Z10.6,Zl0.8

Z10.4,Z10.6,Z10.12 Z10.3,210.8

-

210.3, 210.8

ZlO.4,ZlO.6,ZlO. 12

Dimensions

L

L

L L

Dimensionless

T - ~ L ~ T - ~ Dimensionless

Dimensionless

Dimensionless Dimensionless

Dimensionless

Dimensionless Dimensionless Dimensionless

L~T-'

Dimensionless

L

Dimensionless

Dimensionless

Dimensionless

Dimensionless Dimensionless Dimensionless ML -IT-

Divensionless

Symbol

x

Y z z

Q

a! a! Q

P

P P

P

Y Y Y

r I-

6

6

6

6

c c c f

c

Concept

Coordinate along X-axis

Coordinate along Y-axis

Coordinate along Z-axis Deflection normal to X-Y

plane (flutter)

Angle of attack

Angular acceleration Diffusivity, thermal Nozzle-divergence half

angle

Angle of sideslip

Blade angle (propellers) Mach number relation,

I I - M ~ 1 % o r IMZ-1 1 % Nozzle-convergence half

angle

Ratio of specific heats Strain, shear Flight-path angle

Circulation; strength of a single vortex

Dihedral angle

Boundary-layer thickness

Displacement, angular, of control surface or tab

Logarithmic decrement of viscous (or equivalent viscous)damping

Relative pressure

Angle of downwash Error signal Strain, normal Turbulence-exchange

coefficient Emissivity (for radiant

heat)


LETTER SYMBOLS FOR PRIMARY CONCEPTS (cont.)

I Also Appears

Symbl I Concept Dimensions in ASA Publication Remarks I Efficiency Dimensionless

Dimensionless Temperature-recovery factor

Usually employed with

Symbolar i s often employed as an alternate in flutter

Angle of pitch Angle of twist of an

elastic component Momentum thickness of

boundaty layer


L

8 1 Z10.3,210.4,Z10.6 I Use t if possible Temperature, alternate for

Temperature ratio Ratio of an absolute temperature to the standard absolute temperature for atmos- pheric air at sea level

Dimensionless

I I I

h Mean free path L A Microscale (turbulence) L Associated with turbulence

I I 1 I decay Nozzle-divergence factor Dimensionless

Dimensionless

L

The theoretical ratio of thrust of a diverging nozzle to the thrust without divergence of the flow

In any given tapered wing element, the ratio of chord a t the up end to chord at the root end

Taper ratio

Wave length

Sweepback angle

Mach angle

Dimensionless

Dimensionless

Dimensionless rn M B p --, wherel i s the reference

PSI 4 m 1 length

p = - ; symbol --ii; has npc been used as an dtemate

Mass parameter of airplane (stability)

Mass parameter of air- Dimensionless plane component (flutter)

Viscosity absolute; ML"T" Z10.2,Z10.4,Z10.12 viscosity, cnefficientof

Poisson's ratio Dimensionless z 10.3

Kinematic viscosity L ~ T " Z1O.2,21O.4,ZIO.6,210.12 v =

P

P Mass density ML" Z10.2,210.3,Z10.4,210.6, Such h a t pl/P = pressure Z10.8,Z10.12 2

Angle of sidewash Relative density


Dimensionless

Ratio of a density to the standard density of aanos- pheric air at sea level

Solidity (propellers)

u Stress, normal; stress ML"T'~ 210.2,210.3 (intensity)

T

7 Stress, shearing M L ' ' ~ ~ 210.2,210.3 7 Time, alternate for T Z10."4,210.6,Z1O.12 Use t (Ic) if possible 7 Time ratio Dimensionless

AMERICAN STANDARD

LETTER SYMBOLS FOR PRIMARY CONCEPTS (Cont.)

Remarks



Use a a s alternate for angular velocity


210.2,210.3,Z10.4,210.6 210.8,210.12

Dimensions

Dimensionless Dependent on

definition Dimensionless

Dimensionless

Dependent on definition

T'

Symbol

9 9 9

9

+ I

o

If possible, use o for I angular velocity

Concept

Angle of 1011 (or bank) Potential function

Helical angle of advance (propellers)

Angle of yaw; effectiw helix angle

Stream function

Angular velocity; circular frequency

T" 8 Angular velocity, a l t e r nate for; mrticity

Letter Symbols for Secondary Concepts SYMBOLS FOR USE AS SUBSCRIPTS

(Note: Letter symbols for primary concepts may also be used for subscr ip ts ; s e e Foreulord)

--- ---

Subscript Symbols Concept Remarks

a Absolute Added; additional

I Adiabatic See also ad for alter-

I nate; u se aw for adiabatic wall

Ai 1 eron Air; relative to air Allowable Ambient See am for alternate Available

ac Aerodynamic center (of a surface or airfoil section)

ad Adiabatic, alternate for

Subscript 1 s y ~ b o h ~ Concept 1 Remarks

Damping, general When possible, II I

- -

I replace bv subscript 11 1 1 indicating directio;

Diffuser, duct d ischarge

Dry Drag

1 of motion-or of angular velocity causing the damping

Use only for the dis- charge coefficients of nozzles and orifices

Use d with section coefficient

a m Ambient, 1 1 e Earth bound As applied to axes alternate for i or to vector

av Average See also m for mean A Axial components; s e e

See A~pend ix I / Appendix I1 b Base Effective Use eff a s alternate

Basic Elevator B ending See h for alternate Endurance Blade Engine Burner; burnt; Equivalent 1

I - burning Exhaust; exhaust , I t i c I 1 nozzle; exi t see also i for fuselage e ff ' Effective, alternate I for

Calibrated Use cal for alternate ELL / Euler (number) I I ____-__- Chord -- -A

I / -_ _ - --- -

corr C P C r

Climb Combustion; com-

bustion chamber

I

I Compressibility,

I I f Use b for combustion I chamber in gas- 1 turbine power plants to distinguish from c for compressor

Fin Flap: flipper Fluid; l i a ~ i d phase Flutter Friction, friction

factor - I! i Fuel

- ---- - -. - -- - - -- -. -- - -- Set I for alternate

- - - -

compressible, -- / Fuselage; body / See also 4 for body compression, - I

1; ~ compressor Force; thrust ; See also 7' for thrust Coolant Use c l for alternate Frontal -

Critical Use c r for alternate /;r I Froude (nunber) 1 - - - - - . .

Calibr ated, alternate for

Calculated Center of gravity Coolant,

alternate for Corrected Center of pressure Critical,

alternate for Cross wind Cauchy (number)

See Appendix I

Gage Gas; combustion

gases ; exhaust gas Gross

Grashof (number) Graetz (number)

May require care in definition

Bending, alternate fo -- - - --

Heat; heat exchanger -- - - - --

Hinge 1 -

AMERICAN STANDARD

Remarks


See also N

See Appendix I

-


See o x for alternate

See superscript asterisk (*) for charac-

value; s e e sl for teristic or reference

alternate for sea- level conditions

See para for alternate

See also for moment

May require care in I definition 1

LETTER SYMBOLS FOR SECONDARY CONCEPTS (Cont.) SYMBOLS FOR USE AS SUBSCRIPTS

Subscript Symbols

n

nP

N

Nu

o

Remarks

See also r for root Used primarily a s

applied to heat of combus tion

As applied to axes

Subscript Symbols

h

H

i

Concept

Net

Normal to a surface Nozzle Yawing moment

Neutral point (of a configuration)

Normal Normal, perpendic-

ular to X-Y plane Nusselt (number)

Initial Outer Oxidizer Profi le (drag) Standard or refer-

ence condition;

R

Concept

Horizontal Hub Higher

Ideal Incidence (angle) Indicated; observed Induced Inertial

min M Ma

Reference condition, alternate for

Relative Root Rotor; rotational Rudder

Resultant Right

conditions standard sea-level

Zero lift Oxidizer, alternate

for

Paras i te ; parasitic Polar Potential Pressure, based on Propellant; propel-

1 er; propul sive; tailpipe

Paras i te , alternate for

Power P ec le t (number) P randtl (number)

Torque (propellers and0rotary-wing aircraft)

--- Radial Ram

Recovery

1 Inlet; intake; input Inner; internal Interference

S e e l? for alternate

I O X

P

para

P P e P r

Q

r

i

k

1

lam lat le L

m

max

or to vector components; s ee Appendix I

M inimum Moment, in general

i Mach (number) When used as a sub- s cript,thi s double- 1 etter form i s recommended for consistency with designations for other dimension- l e s s numbers

J e t

Kinetic

Liquid phase,

/ alternate for Local condition,

just outside boundary layer

Lower (surface) Rolling moment Section l if t

Laminar Lateral Leading edge Landing conditions Lef t Level Lift

Lower

Mean

Pitching moment

Maximum


Recommend use of

I i tal icized symbols, and script ell (lower case) if italicized symbol i s not available

See Appendix I

Use 1 with section coefficient

Use primarily a s a p plied to heat of combustion

See a lso av for average

See Appendix I

-- Subscript Symbols

R

tab

turb T


LETTER SYMBOLS FOR SECONDARY CONCEPTS (Cont.)

A -- - -

Remarks

------& See s for alternate

--

--

Positive in positive X direction; see Appendix I

Positive in positive Y direction; see Appendix I

-- . - --

Concept

Ultimate Upper (surface)

Vertical Vapor Volumetric

Wall; surface Wind \king U'eber (nuvber) Wave

Excess Component parallel

to X-axis

--- Yield Component parallel

to Y-axis

---

AS SUBSCRIPTS --

Subscript Symbols

u

-

v

vol

U)

we W

x s X

Y Y

Concept

Rotor, alterwte for; rotational, alternate for

Reynolds (number)

Shaft Shear Slipstream Speed-power Stability

Stabilizer Surface, alternate

for Standard sea-level,

alternate for Specific Static Standard, alternate

for Stall conditions Stanton (number)

SYMBOLS FOR USE

Remarks

-

As applied to axes o r to vector components; see Appendix I

z

6

6

8

P

a

0,1,2,3,4,.

m

Tab Tail Tangential Tensile Throat Tip Total; isentropic

stagnation conditions

Turbine

Tab, alternate for Trailing edge Theoretical Throat, alternate for Turbulent Take-off and termi-

nal velocity conditions

Thrust (for propellers and rotary- wing aircraft

Tunnel

Component parallel to Z-axis

Angular deflection of a control surface or tab

Boundary-lay er thickness, based on ---

Elastic angular deflection; twist --

Density, based on

Condition which applies immediately after shock

Station subscripts

Undisturbed; free- stream

See Tab for alternate

See th for alternate

See also 'superscript zero ( O )

-

-

-

*

See also F for force; thrust

Positive in positive Z direction; see Appendix I

--- -

-

-

AMERICAN STANDARD

LETTER SYMBOLS FOR SECONDARY CONCEPTS (Cont. )

SYMBOLS FOR USE AS SUPERSCRIPTS

Super- script

Symbol Concept Re marks

'(Dot)

"(Double- dot

'(Prime)

'(Prime)

"(Double prime)

- (Bar)

+ (Plus)

(7.ero)

* (Asterisk)

First derivative, with respect to time

Second derivative, with respect to time

First derivative, with respect to distance; effec-

These symbols are written o-rer, not after, the principal symbol to which they are applied

Used in turbulent-flow analysis to identify a turbulent-veloci ty component, e.g., - u ' = u - U ; also used to designate the pressure measured by a total-head tube

To designate a

in a supersonic , stream, e.g., p

Alternate for sub- second s e t of axes, or quan- t i t ies related

scripts

to such a x e s Second derivative,

with respect to distance

Mean value

A dimensionless measure of the quantity considered

Total; isentropic stagnation condi tion s

Characteristic or reference value; critical conditions at (M = 1

Commonly used for value per unit area

This symbol i s written over, not after, h e principal symbol to which i t i s applied

Commonly used for boundary-layer flow and for flow in pipes

See also subscript t

A s applied to u for friction velocity (u*); as applied to 6 - displacement thickness of boundary layer (6*)

Appendix I

RECOMMENDED DESIGNATIONS F O R SYSTEMS O F AXES, ANGULAR RELATIONSHIPS, AND QUANTITIES R E L A T E D T H E R E T O

1 1. Axes:

X - Longitudinal body axis, in vertical plane of symmetry and preferably coincident with centerline of symrnPtrical body or parallel to thrust line of asymmetrical fuselage; positive forward' .

Y - Lateral body axis, perpendicular to vet- tical plane of symmetry; positive to right when looking forward (Same a s lateral s tab~l i ty axis)'

Z - Vertical body axis, in vertical plane of symmetry and perpendicular to the longitudinal and lateral body axes; positive downward'

xw - Longitudinal wind axis, parallel to the relative wind; posltive forward','

Yw - Lateral wind axis, perpendicular to the longitudinal and vertical wind axes positive to right when looking forward"'

zw - Vertical wind .axis, in vertical plane of

symmetry and perpendicular to the relative wind, positive downward (Same a s vertical stability axis)'"

xs - Longitudinal stability axis, parallel to the projection of the relatlve wind on the vertical plane of symmtry,positive forward

Ys - Lateral stability axis (same a s lateral body axis)

Zs - Venical stability axis (same a s vertical wind axis)

Xc - Longitudinal earth axis, lying in plane tangent t o earth's average surface or in plane perpendicular to the direction of gravitational force"4

Ye - Lateral earth axis, lying in plane tangent to earth's average surface and perpen- dicqly to the longi tdinal earth axis; positive to right when looking along positive direct Ion of longitudinal earth axis'

Ze - Vertical earth axis, mutually perpendicular t o longitudinal and lateral earth axes, positive downward'

Xi - Longitudinal inertial axis, usually assumed to l ie initially in plane tangent to earth's average surface, but fixed with relation t o space"4

Yi - Lateral inertial axis, usually assumed to lie initially in plane tangent to earth's average surface and perpendicular to the longitudinal inertla1 ax+ but fixed with relation to space; posltlve to right when looking along pos~t ive direction of longitudinal inertial axis'

Zi - Vertical inertial axis, mutually perpendicular to longitudinal and lateral inertial axes; positive downward initially'

2. Angles:

,, 0 - Angles of attack and sideslip, respective- l y , a s defined in Letter Symbols for Primary Concepts (page 12); a lso see Figures 1 and 2.

y - Flight-path a n le, a s defined in Letter Symbols tor ffrlrnary Concepts (page 12).

$, 6,+- Angles of yaw, pitch, and roll, respec- tlvely; a system of three angles which uniquely define with reference to one coordinate s ys tem (e.g., earth axes), the orientation of a second coordinate system (e.g., body axes). Any orientation of the second system is obtainable from that of the first by rotation through each of the three angles in turn,the sequence of which is important. The preferred order is !l!usuated in Figure 1, where the posltive directions are defined. Any deviation from this order must be clearly indicated.

'nody axes are orthogonal axes fixed in the body, Choice of origin and orientation depend on nature of problem and should be clearly defined (See Figures 1 and 2.)

2 ~ i n d axes are orthogonal axes fixed with respect to the instantaneous relative wind. Origin i s at the center of gravity or designated moment reference point.

3 ~ f only one set of a3es i s involved, the subscript may be omitted provided the e x e s ere clearly defined. If desired, for simplicity, a prime ( ) may be used a s an alternate for the subscript provided it8 significance i s clearly indicated.

'~ irec t ions of longitudinal earth and inertial axes must be clearly defined.

APPENDIX I

1 Ezample: Let the orientation an les ($, ?, 4) be zero

when the aircraft axes ate afigned wlth the earth axes (i.e., straight and level flight along the positive direction of t h X - axis). Any other orientation of the aircraft is then %ached by:

Rotation (1). Yaw about Z-axis, through angle $, until X-axis l ies in the vertical plane con- taining i t s ultimate position:

Rota ion (2). Pitch about Y-axas, through angle b, until X-axis points in its final direction. Rotation (3). Roll about X-axls, through angle 4,

until aircraft has the required orientation. 3 . Angular Velocities:

p, q, r - angular velocities of bodpaxis system (X, Y , 2, respectively), p-ositive clockwise w k n looking in pos~tive direction of axes

4. Linear Velocities: u, v , w - components of resultant velocity V

along body axes (X, Y, Z, respectively)

5. Forces and Force Coefficients:

Name Positive - Force Coefficient Directim

BODY AXES: axial FA f-Fx) C A ( z x ) -X side F~ Y Y

WIND AXES: h a g F~ C~ 'Xw crosswind F~ C~ w

I lift FL C~ -zw STABILITY AXES:

drag (approx.) Ff) Co' -Xs side C~ Y,fY) lift F~ L -Zsf-2 J

6. Moments and Moment Coefficients:

Name Moment Coefficient Positive Direction

ABOUT BODY AXES: rolling M~ c 1 is clockwise look-

ing forward

pitching yawing

MY m raises nose

C n rotates nose to right

ABOUT WIND AXES: rolling M ~ w is clockwise look-

C l * ~ ing forward

pitching 'm, w raises nose

yawing M ~ ~ v 'n, w rotates nose to right

ABOUT STABILITY AXES: rolling M ~ s C1, i s clockwise look-

ing forward

pitching /My) 'rn raises nose yawing M ~ s f"zw) 'n,w rotates right nose to

NOTES:

1.) Symbols in parentheses may be used a s alternates.

2.) Force coefficient i s d e f i ~ e d a s force d i v i d ~ d by the product of two quantities, namely, the dynamic pressure (g) and a reference area.The choice of reference area depends on the nature of the problem, and the particular reference area del,ends on the nature of the problem, and the particular reference area must be clearly indicated.

3.) Moment coefficient i s defined a s mon~ent divided by tt,e product of three quantities, namely the dynamic pressure (9). a reference area, arid a reference length. The choices of reference area and reference length depend on the nature of the problem. The reference arec. must be the some a s that used for the force coefficients. The reference length need not be the same for p-itching, yawing and rolling moments and, along with the respective moment reference points, m u s t be clearly indicated for each:

APPENDIX I

Xe Figure I.- Orientation of coordinate systems, showing direction and sense of Euler angles.

NOTE:

P O S I T I V E SENSE OF AXES, VELOCIT IES, AND ANGLES I S l NDl CATED BY ARROWS.

Appendix II

ALPHABETICAL INDEX BY CONCEPTS 1

Sub- Super- script script

Symbols Symbols 1 Concept 'rincipal Symbols

SU b- script

Symbols Principal Symbols Concept

Angular velocity of body-axis system about X-axis

Angular velocity of body-axis system about Y-axis

Angular velocity of body-axis system about Z-axis

Absolute Absolute temperature Acceleration, angular Acceleration due to

gravity Added; additional

Adiabatic

Adiabatic wall Advance, helical angle

of (propellers) Advance ratio

(propellers) Aerodynamic center Aileron Air; relative to air Airplane Allowable

Area, cross-sectional Area moment of inertia Area, surface or projected Aspect ratio

Attack, angle of, relative to wind

Avail able Average Axial Bank, angle of Barometric Base Basic Bending

a av

- bar b b

1: b - - -

I7 -

A1 ti tude

Ambient

Angle of attack, Angle of bank Angle of blade

(propellers) Angle, dihedral Angle of downwash Angle, effective helix Angle, flight-path ,

Angle, helical, of advance (propellers)

Angle of incidence Angle, Mach Angle of pitch Angle of roll Angle of sideslip Angle of sidewash Angle of sweepback Angle of twist of an

elastic component Angle of yaw Angular acceleration Angular displacement

of control surface or tab

Blade Blade angle

(prope 11 ers ) Blade thickness Blade width

(propellers)

Boundary layer, displacement thickness of

I Boundary layer, momentum thickness of

Boundary-layer thicknes: , Burner; burnt; burning I

6 b

calc

c:1 Ca ac cg C P

C

Calculated

Calibrated

Cauchy (number) Center, aerodynamic Center of gravity Center of pressure Chamber, combustion Characteristic or

reference value

Angular momentum h g u l ar velocity;

circular frequency

APPENDIX I1

I APPENDIX I1

I Note: Axis designations for particular coordinate systems may 'be used to connote direction (e.g. . F X , F Y , Fzl.

Super- script

Symbols

- -

- - - - - -

- -

- - - - -

-

- - -

- -

-

-

-

- - - - -

- - - - - -

Principal Symbols

1 i k

- u*

N ~ r

-

R c

N~ z

N~ r g

- U k r

- i,

(2 4

C'

d

4 -

1 i

1 I

Concept

Frequency, circular; angular velocity

Frequency, reduced (flutter)

Friction; friction factor Friction velocity Frontal Froude (number) Fuel Fuselage; body

Gage Gas; combustion gases ;

exhaust gas Gas constant Gas velocity (rockets) Graetz (number) Grashof (number) Gravity, accelerat ion

due to Gravity, center of Gross Gust velocity Gyration, radius of Gyration, reduced

radius of (flutter)

Heat; heat exchanger Heat-flow rate, per unit

area, per degree, across a boundary surface

Heat, quantity of Heat, specif ic quantity

of; quantity vf heat , per unit mass or per unit weight

Heat transfer coefficient , over-all

Helical angle of advance (propellers)

Helix angle, effective Higher Hinge Hori ton t a1 Hub

Ideal Impulse Incidence (angle) Indicated: observed Induced Inertia, area moment of Inertia, mass moment of Inertial Initial

Sub- script

Symbols

-

-

- f F

Fr f f

g g

G z Gr

Cg g

h -

H h h h

1

i i i

--- i o

Super- scr ip t

Symbols

- - - - - - -

- - - - - -

-

- -

-

- - - . - -

- -

-

- -

- - - - - - - - -

-

Sub- script

Symbols

- - -

8

-

e -

e

: e -

-

- -

-

e - Eu xs

h e

g e

-

f f f -

i f

F See

footnote -

N (D

-

Concept

Effect ive helix angle Effectiveness, span Efficiency Elas t ic angular deflec-

tion; twist Elasticity, modulus of;

Young's modulus Elevator Emissivity (for radiant

heat) Endurance Energy

Energy, internal

Energy, internal, per unit mass or per unit weight

Engine Enthal~y, ner unit mass

or per unit weight; specific enthalpy

Enthalpy; total hea t con t en t

Entropy Entropy, per unit mass

or per unit weight; specific entropy

Equivalence ratio; richness(combustion)

Equivalent Error Signal Euler (number) Excess Exchange, he at Exhaust; exhaust

nozzle Fxhaust gas Exit

Factor, for comparison purposes

Factor, friction Fin Flap Flight-path angle Flipper Fluid; liquid phase Flutter Force: resultant force

Force cornponen t s

Force, cross-wind Force, normal Free-stream;

undisturbed Frequency, cyclic

Principal Symbols

6 e 'I -

E

- a

-

[ i -

h

fi

s s

6 c - - - -

- -

k'

-

- Y - - -

F -

c f l -

f

APPENDIX I1

Concept

Inlet Inner Input Intake Interference Internal

Internal energy

TnternaI energy, per clnit mass or per unit weight

Isentropi c stagnation conditions; total

Jet Joule's constant;

rnechan ical equivalent of heat

Kinemaric viscosity Kinetic

Laminar Landing (conditions) Lateral Leading edge Left Length; distance Length, correlation

(turbulence) Level Lift; lift, per unit

length (flutter) Lift curve, slope of Lift, section Lik, zero Liquid phase; fluid Load factor Local condition, just

outside boundary layer

Logarithmic decrement of viscous (or equivalent viscous) damping

Lower Lower (surface)

Mach angle Mach number

Mach number relation

1-,Va ' a M a - 1 % Mass; mass, per unit

length (flutter)

S u p ~ r - scnp t

Symbols

- - - - - - -

-

-

O (zero)

- -

-

-- -

-

-

-

- - - -

-

-

- -

-

-

Principal Symbols

{: 1: - -

- 1

v -

- - - - -

1 L -

L

a - - -

n -

8

- -

n; {c.

P

m

Sub- script

Symbols

I

i i i I

i -

-

t - i -

- k

lam I,

lat le L - -

L C

- 1 o I -

1

-

L 1

- Ma

-

-

Concept

Mas's density Mass-flow, per unit

cross- sec t~ona l area, per unit time; mass velocity

Mass-flow , per unit time4 weight flow, per unit time

Mass moment of inertia; mass moment of inertia, per unit length

Mass parameter of alr- plane (stability);

Mass parameter of airplane component (flutter)

Mass velocity; mass- flow, per unit cross- sectional area, per unit time

Maximum Me an Mean free path Mean velocity compo-

nent (turbulent flow) Measure (dimensionless)

of the quantity considered (boundary- layer flow; flow in pipes)

Mechanical equivalent of heat; Joule's constant

Microscale, turbulence Minimum Modulus of elasticity;

Young's modulus Modulus, shear Moment; torque Moment per unit

length (flutter) Moment of inertia, area Moment of inertia, mass;

mass moment of i n e ~ tia, per unit length

Moment, pitching Moment, rolling Moment, yawing Momentum, angular Momentum thickness of

boundary layer

Net Neutral point Normal

Principal Symbols

P G

w

I

-

CL

G

- - X -

' -

1

X - E

G M M

1 I

- - - H 8

- - N

Sub- script

Symbols - -

-

-

- - -

max m - -

-

-

- min - - - -

- -

m 1 n - -

n nP -

Super- script

Symbols

- -

-

-

- - ---

- - (bar) - - (bar)

+ (plus)

- - - -

- - -

- -

- - - - -

- - -

APPENDIX I1

Sub- script

Symbols

P CP - - d -

P o -

P P P - - -

r - - -

r - - -

r - - -

- i; r a - -

I2 - - -

Principal Symbols

P - i P -

- - S

- - -

Q 9

4

- r k r

- R

I 1 r

- Tr

k

r

-

-

- -

o 6 - F

n 1 'U

Super- script

Symbols

- - - - -

'(prime)

- - -

- - - - -

-

- - - - - - - - - -

-

- -

* (asterisk)

- - - - - - - -

Concept

Pressure Pressure, center of Pressure, dynamic Pressure, relative Pressure, static Pressure, total-head

(measured by total- head tube)

Profile Profile (drag) Projected area; surface

area Propellant Propeller Propulsive

Quantity of heat Quantity of he at, per

unit tirn e Quantity of heat, per.

unit mass or per unit weight; spec~fic quantity of heat

Radial Radius Radius of gyration Radius, reduced, of

Ram gyration (flutter)

Ran ge Ratio of specific heats

Ratio, time Recovery Recovery factor,

temperature Reduced frequency

(flutter) Reduced radius of

gyration (flutter) Reference (or standard)

con di ti on s Reference (or charac

teristic) value Relative Relative to air Relative density Relative pressure Resultant Resultant force Resultant velocity

Revolutions, per unit time

Concept

Normal, perpendicular to X-Y plane

Normal (perpendicular to a surface)

Normal force Normal strain Normal stress; stress

(intensity) Nozzle Nozzle, exhaust Nozzle-convergence

half angle Nozzlcdivergence

factor NO zzl e-divergence half angle

Number, in general Numbers:

Cauchy Euler Froude Graetz Grashof

Mach

Nussel t Peclet Prandtl

Reynolds

Stanton Weber

Nussel t (number)

Observed; indicated Outer

Oxidizer

Parasite; parasitic

Peclet (number)

Phase, liquid

Pitch, angle of Pitching moment Poisson's ratio Polar Potential Potential function Power Prandtl number Precise or effective

value

Sub- script

Symbols

N

n

N - -

n e -

- - - Ca Eu Fr Gz Gr

,Ma

Nu Pe P t

Re

S t We

Nu

i o

{ o z

P

{P;;

( f . - - -

P P

P - P r

-

Principal Symbols

- -

N c (I

- -

0

h

a

N

N gu Pr 4:

{ to Pu

{ $: N": G e

N~ u

- - -

-

'P e -

8 m CL - - $' "'P I

-

S F ' scrlpt

Symbols

- -

- - - - - - - a

- - - - - - -

- -

- -

, -

- - - - -

- - - - - - - - - - -

'(prime)

Sub- script

Symbols

-

- s s

s t

S

1 st:

/: st -

0,1,2,3,4.. St

- - - - -

-

- -

W

S - -

-

- - - - - - - - -

t T

th -

Principal Symbols

v

V - - - - - -

- -

P - "'s t

J

c

5 F

T

T

g

.t- - S

A

L b t

P T t h T

1 f!i 8

q r - -

- k

Super- script

Symbols

-

- - - - -

O (zero) - -

- - - - - - - - - -

- - - - - - -

-

- - - - - - - - - -

- -

II

Concept

Specific volume; volume per unit mass or per unit weight

Speed Speed-power Stability (see Appendix

n) Stabilizer Stagnation conditions,

isentropic Stall conditions Standard (or reference)

conditions

Standard sea-level conditions

S t a t ~ c Static pressure Station subscripts Stanton number

Stiffness constant, torsion a1

Strain, normal Strain, shear Stream function Stream thrust; thrust

(combustion) Stress, normal; stress

(intensity) Srress, shearing Structural damping

coefficient

Surface

Surface area; projected area

Sweepback angle

Tab

Tail Tailpipe Take-off conditions Tangen ti a1 Taper ratio Temperature, absolute

Temperature, general

Temperature ratio Temperature-recove ry

factor Tensile Terminal-velocity

conditions Theoretical Thermal conductivity

APPENDIX

Super- script

Symbols

-

-

- - - - - -

- - - -

- - - - - -- -

- - - - - - - - - -

-

--

-

- -

-

Sub- script

Symbols

Re

-

R - 1 r

{R' r

- -

1 -

- s S

- - -

o

- - s - - - - -

S P -

-

-

-

- -

-

Concept

Reynolds number

Rithness; equivalence ratio (combustion)

Right Roll, an#e of Rolling moment Root

Rotor; rotational

Rudder

Scale, turbulence 'Section coefficient 9ection lift Semichord, alternate for

c/2 (flutter) Semispan, alternate for Shaft Shear Shear modulus Shear strain Shearing stress Shock, condition which

applies immediately after

Sideslip, angle of Sidewash, angle of Slipstream Slope of lift curve Solidity (propellers)

Sound, velocity of

span Span effectiveness Specific Specific enthalpy;

enthalpy per unit weight

Specific entropy; entropy per unit mass or per unit weight

Specific heat, at constant pressure

Specific heat,at constant volume

Specific heats, ratio of

Specific internal energy; internal energy, per unit weight

Specific quantity of heat; quantity of heat, per unit mass or per unit weight

Principal Symbols

{ 4e (4 - + - - -

-

L c

-- b

s - - G Y T

-

I3 u - a u

/: b e - h

s

c P

cr

I r u

4

Super- script

Sypbols

-

-

-

-

- (bar)

'(prime)

-

--

- - - - -

- - - - -

- - -

7

- - - -

- - - -

Note: Axis designations for particular coordinate systems may be used to connote direction (e.g., V x , V y , Vz).

Principal Symbols

P

4

r

U y v , W

- -

u

C'

w

u* c U C

- 1: w

- P

P

s" V 2'

v - r !2 - -

A

I1

Concept

Velocity, angular, of body-axis system about X-axis

Velociw, angular, of body-axis system about Y-axis

Velocity, angular, of body-axis system about Z-axis

Velocity components

Velocity (mean) component (turbulent flow:

Velocity (turbulent) component, particular

Velocity, component o f , along X-axis

Velocity, component of, along Y-axis

Velocity, component of, along Z-axis

Velocity, friction Velocity, gas (rockets) Velocity, gust Velocity, mass; mass-

flow, per unit cross- sectional area, per unit time

Velocity of sound

Velocity (conditions), terminal

Velocity vector, magni- tude of

Vertical Viscosity, absolute;

viscosity, coefficient of

Viscosity, coefficient ofi absolute viscosity

Viscosity, kinematic Viscous damping, loga-

rithmic decrement of Volume Volume, per unit mass

or per unit weight; specific volume

Volumetric Vortex, strength of a

single; circulation Vorticity Wall; surface Wave Wavelength

Sub- script

Symbols

-

-

-

See footnote

-

-

- -

- - - - -

- T

- v -

- - - - -

- vol -

- w B -

APPENDIX

Super- script .

Symbols - - -

-

-

- -

-

- - - -

-

O (zero)

'(prime)

-

- - - -

- - - -

'@rime)

-

- -

-

- -

Sub- script

Symbols

- -

8

-

1 t i F

T

- -

t M Q

-

t

-

-

t e T

1 -

- - -

twb -

H

u m

u

v -

Concept

Thermal diffusivity Thickness Thickness, blade

(propellers) Thickness of boundary

1 ay er Thickness (momentum)

of boundary layer

Throat

Thrust; stream thrust (combustion)

Thrust (propellers and rot ary-wing aircraft)

Time

Time ratio Tip Torque; moment Torque (propellers and

rotary- wing aircraft) Torsional stiffness

constant Tota1;isentropicstag

nation conditions Total-head pressure

(measured by total- head tube)

Total heat content; enthalpy

Trailing edge Tunne 1 Iurbine Turbulence correlation

coefficient Turbulence exchange

coefficient Turbulence mi croscale Turbulence scale Turbulent Turbulent-velocity

component, particular Twist of an elastic

component, angle of

Ultimate Undisturbed; free-

stream Upper (surface)

vapor

Velocity, resultant

Velocity, angular; circular frequency

Principal Symbols

(Y

t h

2

8

- F

T

1: T -

M Q

1 --

-

H

- - -

R

45

X L -

0

- - -

p w R

APPENDIX I1

American Standards for Abbreviations.

Symbols and Charts 'I

TITLE OF STANDARD

Let te r Symbols for Aeronautical S c i e n c e s ( Y 10.7.1954) ................... .... ............................. Abbreviations for Scient i f ic and Engineering Terms ( Z 10 . 1- 194 1) .................................... L e t t e r Symbols for I ~ y d r a u l i c s ( 2 1 0 . 2- 1942) .......................................................................... Let te r Symbols for l l echanics of Solid Bodies (210.3- 1948) ...............................................

........... Let te r Symbols for Heat and Thermodynamics, Including Heat F l o w (210.4- 1943) Let te r Symbols fnr P h y s i c s (210.6. 1948) ......................................................................... Let te r Syrribols for Structural Analys i s (Z10.8- 1949) .......................................................... Let te r S y r b o l s for Radio ( Y 10.9. 1953) ............................................................................. Let te r Symbols for Meteorology (Y 10 . 10- 1953) .................................................................. Let te r Symbols for Acous t ics (Y1O.ll-1953) ................................................................ Let te r Symbols for Gear Engineering (86.5- 1954) .......................................................... Drawings and Drafting Room P r a c t i c e (Z14 . 1- 1946) ...................................................... Graphical Symbols for

. :Y'elding and Instruct ions for The i r U s e ( Z 3 2 . 2 1- 1949) ........................................ Plumbing (232.2.2-1949) . . . . . . . . . . . . . . . . . . : .......................................................... P i p e F i t t ings , Valves, and Piping (232.2.3-1949) ...................................................... FIeating, Ventilating, and Air Conditioning (71.32.2.4- 1949) ............................................. Railroad U s e ( 7 3 2 . 2.5- 1950) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ..

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ileat-Power Apparatus (232.2.6- 1950) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abbreviations for U s e on Drawings (232.13-1950)

Engineering and Scient i f ic Char t s for Lantern S l ides (213.1- 1932; reaffirmed 1947) . .

. . . . . Fngineering and Scient i f ic G r a ~ h s for Publ ica t ions (Z15.3- 1943;reaffirmed 1947) . . . . . . . . . . . . . . . . . . . . Time Ser ies Char t s (215.2-1938; reaffirmed 1947)

PRICE . 81.25 0.50 0.50 0.50 0.65 1.00 0.50 1.00 1.00 1-00 1.00 1.50

20% Discount to ASllE r.rernbers .

A binder is available for holding these standards . It holds ttc~enty-five (25) pamphlets and gives every advan. tage of a bound booh v i t h tlze at!(l'ed convenience zuhich comes from t h e ability t o insert. remove. or transpose s ec t ior~s o f the contents . Price $3.25 postpairl .

A corirplete l i s t of Alr~erican Stanrlarrlr pub l i s l~er~ by I'Ae American Society o f : lechanicd bz7r~gineers obtairlable upon request .

letter symbols for aeronautical sciences - nasa · pdf fileletter symbols for aeronautical...

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