.
.—-
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
,
TECHNICAL NOTE
No. 1120
,
STANDARD NOMENCLATURE
.
FOR AIRSPEEDS WITH TABLES
AND CHARTS FOR USE IN CALCULATION OF AIRSPEED
.
By William S. Aiken, Jr.
Langley hCemoriaI Aeronautical Laboratory
Langley Field, Va.
Washington
September 1946
,.
-..
*
.
*
.
NA!215EAL ADVW3RY
COMMITTEE FOR AERONAUTICS
.
. .
● ✌
TECHNICAL NOTE No, 1120
.
.-
.
-.
.
AND CEM?TS FOR USE IN CALCULATION W
By
●
.
.“
William
S . Mbn,
AIRSPEED
Jr.
Symbols and definitions of various airspeed terms
that have been adopted as st~dard by the NACA Subc GEP
mittee on Aircraft structural Design are presented.
The
equations, charts, and tablgs required In the evaluation
of true sirspeed, calibrated airspeeds equivalent air~
s-peed, im-p.actand dynamic nressures, and }:achand Reynolds
nlmnbers have been cor,piled~ Tables of the standard
akmosghera to an alt?tude of 65,.200feet and a tentative
extension to an altitude of 1009000 feet are given along
with tha basic equations and ccfistants on whi~h both the
standard atmosphere and the tentative extension are based~
INTI?ODUCTION
In s.nalyses of aerodynamic data very often windtunnel or fligb.t measurements must bs converted into airspeed and related quar.ttties that are used in engineering
calculatt ons, Attsmpts to accomplish such confers!.on by
use of available m.etkods have been corc~licated by the
diversity of s~mbols and definitions and by the necessity
of referring to equations, charts, and tables from a
nwn”oer of different sources. A standard set of symbols
and definitions of v.micms atrsgaad terms that were
adopted by the KACA Subcommittee on Aircraft Structural
Design and a cow~ilation of th~ necessary equations, charts,
‘
and tables f~r converting measured pressures and temperatures into airs~eeds, determining Mach numbars sand
Re~~~ds zi’~ber~, snd determtnir.g otker quantities such
and iwqp.ct pressures that are of interest are
as dynamic
therefore presented Mrein.
-.-—
In the preparation of tha pres~nt paper results
that have been included in ~reti.ous papers have been
ext,?nded to includ~ higher qltitudas and quantities not
.
.
.,,
~i.ven h the ~i~~vious pa~a.=:? since recsnt raquests have
indicated the need for such an extension of stani!ardatuosphere tables.
●
●
The tables and figuz-es have been arranged for ease
‘Hb.fich
ts usually bcsed
in determination of the ~irSP6f3ds
on the interpretation of measurements of’differential
Fressures obtained with “some pttct-static &rranSe?nent.
The Interrelation of the various airspeed quantitie= is
used in the measurement.
independent Of the method
Instrument and installation errors have been ass-wed to
have been taken into account.
ST.AKDARD SYH13GZS A.liDXFIN121CNS
At the ??ovem’oar191f4meeting of tileNACA Subcommittee
on .Aircrai’tStructural .Wsign, reprcsent=tivsti frozU tins
A??M7’
Yavy, CAA, ??AC-A,and several aircraft manufacturers
ado~;ed as standard the folloring symbols and def:nttions
for air,sneecls
:
..-i
true ai.rspoecl
vq
indicated airspeed (the reading of’a differer.tialnressure airs~eed indicator,
~ccordance wi>bi the accepte~ standtird adiabattc
formula to ii~d.icatetrue &irspeed for stmdard
sea-level conditions only, unccrr~cted for
instrument and installatim tirrors)
calib~-ated
in
.
.
.
.
Ve
equivalent airspeed
(,,.1/2)
uce of’equivalent ai~s~eed in combination with
various subscripts is custor.ary, particularly in stvuctursl desi~n, to d~si~gate various design conditions.
Zt is sug~ested that the i’oregolng 8P301s tieretained
Intact when furtb-er subscripts are necessary.
.
.
NA.CA TN Na, 1120
3
.
D
~~ostof tjhefollowing symbols, which ar”eused herein,
.
.
.
have already been accepted as standard and are used
throughout aeronautical literature. The units given apply
to the development Of the equationsin the present report.
.
<
.-
v,
true airspeed, feet per second
Vc
calibrated airspeed, feet per second
Ve
equivalent airspeed, feet per second
a
speed of sound in ambient air, feet per second
M
Mach number
P
mass density of ambient air, slugs per cubic foot
Po
standard mass density of dry ambient air at sea
level, 0.002578 slug per cubic foot
CY
density ratio
q
dynamic pressure, pounds per SW=’Q
qc
impact pressure, pounds per square foot (total
pressure minus static pressure p)
P
static pressure ,of free stream, pounds per squsre
foot
‘o
static pressure of free stuesm under standard seaMvel conditions, pounds per s“quare foot
t
temperature, oF or oC
At
difference between free-air temperature and temperature of standard atmosphere,
‘F
T
absolute temperature, ‘F absolute or ‘C absolute
T S td
star.dard-atmospb.erefree-air temperature, %
TO
standard sea-level absolute temperature,
518.4 ‘F absolute
.
.
.
;
.-
.
(V/a)
(p/PO)
foot
1 2
()
~pv
,.
.
.
.
.
.,9
.
.
absolute
.
hnrmonic mean absolute temperature, ‘F absolut~
(defined in equation (E5))
?
.
.
.’.
.
compressibility factor defined in equation (11)
compressibility factor d6fined in equation (1~)
ratio of’specific beat at constant pressure to
specific heat at constant volume (assumed equal
to l.1+for air)
.
I
,
absolute altitude, feet
pressure altitude, feet
feet per second
acceleration of gravity, 32.174.0
per second
modulus for common “logarithms, lo~lOe (O .k3&Th
coefficient of viscosity, SIUGS pm
foot-second
kinematic viscosity, square fe6t per second
ReWolds
number
)
(P/P)
.
“-
()
p~
w
Reynolds number f’or standard s.tmospheric conditions
characteristic lerigth, feet
CALCULATIOiJ OF AIRSPEED AND PLELATED QUANTITIES
.
.
~ecause pit”ot-static arrangements are used as the
basis for the determlnati.on of atrspeed, aeronautical
engineering practice has develop6d to include the use of
a number of’airspeed terms and quantities, each of which
has a particular field of usefulness.
True airspeed is
:Irincipally of use to aerodynamicists, and indicated and
c&librated airspeeds are principally of use to pil.ota.
Equivalent airspeed is used by structural engineers,
since all load specifications have long b6en based on
this quantity.
Ik5finite r61ationshi~s exist between true airspGecl,
Mach number, Reynolds number, calibrated airspeed, and
Equivalent airspeed, and all these quantities may be
., s
.
NJLCA TN
.
~0,
1120
5
.
,
related either to the dynamic Qressure
q or to the
impact pre3sure
qc . Some of the relations presented
hsreln apply to the calculation of true airspeed and
Mach number from airspeed measurements obtained with an
airspeed indicator of standard calibration,
C?therrelations apply to the calculation of true airspeed when the
impact pressure is measured directly.
.
.,.
\
.
.-
.
If it is assumed that tb.6 total-head tl~be and the
static-head tube measure their respective p~essures correctly and that these ,tubes are connected to an a~propriate instrument, the impact pressure measured is given
bT tb.eadiabatic equation wb.en V <, a:
(1)
Standard airspeed indicators usefl in Aruy and Navy
airplanes since 1~25 have been calibrated according to
equation (1) for standard sea-level conditions; that is,
according to the equation when V < a,
w-here t~ie subscript
O denotes standard sea-level conthe calibrated airspeed. The c8.1ib~ated airspeed is, therefore, equal to true airspeed
only for standard sea-level cor.ditions.
&itiorIs
and
VC
1s
Determination
.
.-
of True Airspeed
from Calibrated Airspeed
The formula that relates the true airspeed to the
calibrated airspead may be found “Qy equating the rigb.t- “
hand terms of equations (1) and (2) as follows:
6
NACA TN No. 1120
●
Because the exact numerical solution of equation (j) for
true airspeed is involved and requires a great deal of
time, a number of charts for the determination of the
from
the
cal~brated
airspeed for vartous
t~ue airspeed
(See referatmospheric conditions have been derived.
ences 1 to 3.) A typical chart (taken from reference 1)
Wiiatshows the relationship between Mach number, cali‘orated airspeed, pressure altitude, temperature, and
true airspeed is given in figure 1. ~iS chart iS Widely
used. because of’ its convenience. Airspeed may be obtained
froii~this chart with an accuracy within 2 miles per hour
wl~c:nstandard conditions hold and when values of airspeed”
and pressure altitude explicitly given by the chart are
ehcsen; the possible errors increaoe to within ~ miles
peimhour, however, when the temperature conditions are
not standard and when interpolation is required for both
altitude and airspeed.
.
. .:.
\
,’
.-
.
For some prposes, charts such as figure 1 are not
sufficiently accurate . A series of logarithmic tables
that may be used to determine the true airspeed in knots
from observed values of calibrated airspeed, pressure
altituile, and free-air temperature is given in reference 4.
LoCarithwdc tables of the type given in reference )A are of
limited usefulness since they cannot bb used conveniently
to evaluato the intermediate quantities (impact pressure
and ?.:ach
number) that are involved. in the computation of
true airspeed.
A series of tables (tables T to V) is given in the
prc.sent report to permit determination of impact pressure !lC in pournds per square foot, Uach number 1;, and
true airspeed V in mil(ss per hour or knots for okscrved
values of Vc in miles par hour or knots, press-are altitude h~ In f~et, and t~mperature in dcErees Fahrenheit
or Centlgratie. The accuracy of the tables is far greater
than that with which experimental data can normally be
obtained. ~~~th ordinar;~ care in interpolation, errors
should be less than 0.25 mile per hour throughout the
greater part of tlie airspeed and altitude ranEes.
!’able I, which gives values of impact pressure qc
in pounds per square foot for values of Vc in miles per
hour, was computed directly from equation (2]; standard
values were used for all the constants occurring in this
equation. Table II gives values of impact pressure qc
in pounds per square foot for values of Vc in knots.
.
.
.
.
“
.
.
.
*
.
.
in table II, the conve~.=
In computing the values of’
‘f es used was as follows:
sion from feet to nautical ni
.
1 nautical nile = 6080.2 feet
Tables I and II give the impact pressures for Vc in
increments of 1 mile peP hour and 1 knot for speeds cor-responding to Mach numbers at sea level from O to 1.000.
.
Table III gives values of static pressure p in
pounds per square foot for various values of pressure
altitude hn from -1000 to 60,co0 feet in incremerits of
3.00feet an~ from 60,000 to 100,000 in increments of
(The use
1000 feet for standsrd ~tmospheric conditions.
of the term standard atmosphere throughout this report
includes values for the standard atmosphere up to an
altitude of 65,000 fee~ and for the tentative extension
of the standard atmosphere from 65,000 to 100,000 f’eet.)
The values given in table 111 were computed from the
equation
‘?
)?0 Tm
Po
10B107
‘P = Po&W —
To
.
-“
(q
which is given a,sequation (4) of reference 5 with slightly
different symbols.
From tables I or 11 and 111 the ratio of impact
pressure to static pressure
qc/p MELY be established
and the Mach nimber, which is a function of this ratio,
may then be found, The relation between Mach number
~d
qc/p is given in reference 6 as
M{{@+I~2/7-]}1/2
(5,
-.
.
.
Table IV, which is taken directly from reference 6, gives
values of”Mach number for various values of the
r~tio cl~/P
●
The Mach number M is defined as the ratio of’the
true airspeed to the speed of sound in ambient air and
-.
.
N“ACA T3TN:
8
●
112:;
I
tnns, w!.th the Mach numb: r date rmimd,
may he found by the llSe of
..
(~)
v = ?&3
1
m
the tr-ue airspeed
.,
.
.
.
‘Ihe sveod of sound in ambient af.ris found from the
equation
“
a =,;?
(’/)
J
which may be rewrt tten in the f nllowing forms when the
value of y is assumed equal to 1.4 and the air ia
assumed to follow the gas law
If a is in miles ‘per hour a~ld T
hgit absolute
.
is in degrees F61xren.
Xf a is in knots and
abzolute
T
,
is in degrees Fahrenheit
If s is in miles per hour and
gr~de atisclute
T
“-
is in degrees C!snti-
.
a = 33.94@
(h}
Table V giv?s the speed of s~umd. for values of frefi-air
temperature in degrees Fahrenhe~t, and table VI gives t~le
s>ecd of sound for temperatures in degrees centigrade.
!l’~blesV and VI give the speed of ,sound both in milfis Jer
h?ur and in knots.
In order to illustrate the use of tablas I t~ VI to
determine the true airsgeed from- calibrated airspe=d, the
fnllowing example is presented:
.*=
,.
9
?WCA TN No. 1120
.
Given:
~zli’~rated air speed Vc = 398 miles per h~ur
:?ress~e altitude
% = 22,000 feet
Temperature
t = -12° F
,
“-
.
To find:
True atrsaeed
.
V
in miles per hour
Ste-p (1)
Fri~mLtable I, far
Vc = 595 miles per hour,
‘%3 = !435.7pounds ~qer square fo~t
Step (2)
From table 111, for ho = 22$990 feet,
~=
~~~.~ pounds-per square foot
.
Stez. ;:;F
-. these values,
“,
.
.“
Step (4)
F~om table IV, for
l’! =
.
.
CIC
~
= 0.lJ355,
9.7736
Step (~)
From. ts.ble V, for t = -12° E’,
706.9 miles per hour
step (5)
equatton (6),
w!.= 0,7736 x ‘706.9miles ~er haur
~h6.8 tiles per hour
Determlnatim
of ‘True Airspeed frcm Impact ?ressure
.
.
...
Tn order t~ convert rnessur-euer-t~
of impact m?essure
to true airspeed, the static prsssure and the s?eed of
sound must be known. It is convenient first to determine
the Mach number from measurements of “tine
im~act ~ressure
and tb.e static gressure.
Table IV may be used to find
the :fachnumber from the ratio of qc to p and
10
NACA TN NO o 112.;
.
.
tables V.and VI may bu used to fifid thG speed of sound
for various values of tk.e fr~e-air temperature. Tkle true
airspeed may then be deterinined from equation (6).
.’
Determination of Dynamic Pressure and
Equivalent Airspeed
In order to reduce fliglht-test data to coefficient
fcrm or to demonstrate compliailce with certain structural
requirements, either the dpamic pressure q or the
equivalent airspeed V must be determined,
The relations
of dynamic pressure and equivalent airspeed to inps.ct
pressure, static pressure, calibrated airspeed, and l;ach
nmnber are there”~ore presented.
q
Since the dymamic pressure
is by definition
12
c1= pv
,’
it
may be expressed a s a function of the impact pr5s3ure
by soiving equatton (1) fOr true a irspead and substiimting
the Yesultant express ion Intc equa tion (9), which reduces
to
.
Values of the compressibility factor f are given in
fi.qure 2 as a function of @?
The dynamic pressure
nay also be expressed as a f’uncticn of Mach numbdr and
static pressure from equations (6), (7), and (~) as
●
(12)
Since the equivalent airspeed
Ve
.
is by definition
.,
.,
k-.
11
N:.CLTIJNO . 1120
.“
t~~erele.tion between the equivalent airspeed in miles
and pressure ratio can be derive?.
per hour, Yach number
f’rmn equaticr~ (6), (~), (15), ‘Md the gas-law equation
as
.
..,
The variation, determined from equation (1.4),of eq-~ivalent airspeed with Xaeh .nunber for p~essure altitudes
I?OLI1(jto 100,OUO feet is given in ftghre ~. ~70r convenience, the true airspeed that ap~iies to the standard
atw-o
s:phere computed fro-m equatior.s (1>) and (14) is also
included in fi,gu.re3.
Finally, expressions that will i-elate the true airspeed, the calibrated airspeed, ami the e ql~ivaler,tairs~e~d are determined.
If equation (2) is solved fop Vc :
r
(15)
.
.’
If
equation
(15) becoitles
:
.
,
(17)
J’PO
\
.
r
&c!
,--=
Vc=fo
The compre.7sibility factor f~ is given in figure 2 as
a i’unction of %@c “ Similarly, the true airspeed may
be written
(13)
...
“.
i%cnn equations (17) and (18)
‘,
pi”
v=
v~ g
oJ P
‘~-;hen
equations (15) and (l(j)are summarized
=
Vvc+
—
P%l=v
~
(?O
i
od P
(2(’)
Fc.r convenic;nce, eGuations relattrigthe v~rioua
,.
.
*
charts rel atitigthe Reynolcis number tc t-hel,iacl~
rnunbor
have been f ou.ndconvenient.
Reynolds number is Wi’inoi! by the formula
‘.
.
.
,.
.
,.
‘
15
NJ*CL TN No . 1120
.
In orden to account for free-air conditions other
than standard, figme ~ is given to be used in conjunc2c518 T3/2
(justifi—
tion with r igure 4. Whenv=—
10S T + 216
cation for the use ef this equation given in the section
Properties of Stand&u?d Atmospheretl) is substientitled II
tuted into equation (21),the Ee-polds number factor ~~ay
.
be written
‘.
.
~06
(23)
sphere
The Reynolds number factor in the stamiard atzno
becomes
.
‘std = I .232pL1
‘std + 216 ~06
.
L
.
(24)
T3td2
8
When equation (.25)is divided by equation (24-)
.’
—=R
‘std
2 ~+ 216”
T~td
( T )( T~td + 216)
(25)
.
as a function of press-ure altiR/R@d
the deviation At oi’the free-air temperature
from standard temperature for a given pressure altltude.
Ilzequation form,
FQw2e
t~’de
~
gives
anti
A~=T
~std
-
.
.
..
In order to illustrate the procedure to be used in
determining Reynolds nnnbe~, the f’ollowlng example is
presented:
,
.
. .,
(26)
Given:
Mach number
M =
0.75
Pressure altitude
.’
1+ = >~,OCIC)feet
.2
Characteristic length
Z = 10 feet
Deuiation of free-air temperature from standard
temperature &~ = -10° F
To find:
Re~riclds number
R
step (1)
From figure h(a), for
M = O.’~~ and
~ = 35s000 feet,
Rstd
—
= 1,800,000 per foot
1
,..
.
t = 10 feet,
For
R
=
std
18,000,000
Step (3)
From figure ~, for
and
‘P = 5~,0C0 feet
ht = -10° F,
R
-~std = 1.036
.
~tep (4)
.
From these values,
R =
18,600,000
.
15
.“
.
“.
.-
.
.
.
,
.
. .
!
>,
I
The quantities mass density
p ald density
Pgtfo r are also tzken directly from. reference 5 for
the altitudes from O to 35,000 fzet. For altftudes Cver
j~,220 feat the nressures, the mass densiti~, and tka
density ratio were recalculated, stnce a tingr error was
dl.scovored in the calculations of refereni~e ~ for the
:;re~sure .r~tio for altitudes E-oove35,35.2 feet.
.
., .
.
.
.
.
,
\
“.
..
.
?
. .
●
W*CL
.
ml ,Nc)
. 11.20
17
✞
~b.eNACA Special subcommittee on the TJppar At:nOsresolved
that the
pb+ere e.t a r,eeting m June ~, ?.946
tentative extension of tha standar.~ atmosphere frarn
6~,W0 to 100,9QO feet be based upon a constant cowzositi on of the atrncsghere and an i sotherrial tem~ersture
whleh are tine same es standard conditions at 655039 i’act,
This tentative extended isothermal region snds at
52 kilometers (apgraxiw.ately 10530W ft). It is pOssible
that as results of higher altitude temperature ~i>~dings
became availeble End tbe standard e.tm~sphare is extended
ta very high altitudes the areser.t recmmendatian
r,aybe
.
Uhe
Subcommittee also recommended that th3 values of
temperature given in the followinS table be considered as
maximum and r.inimum values occurring for the givan. altitudes with the variations b~tveen the specified 2oints
to be linear:
‘.
A tentativa axtsnsion of th3 stmdard atr.osphere
cmputed from. tha equattons Givsri in apaendix B usir.~ the
rscommnded
isothermal
temperature
is @ven
in table
‘HI I
65~QOCl to 102~OCt0 feet. All qusntitias
for
sltitudes
from
given
in table
V’11 &re
included
in table
VIII.
.
.
.
L$.T@ey
Kemorial
Astronautical
La_90r&tory
Yaticnal
Advisory
Comrittce
for
Aercrimltics
17, 1946
Lkn.gley
Fisld,
\rs.,, July
-
1.3
The Gquat ions ,re?.at.
in~ the various airspeed qU~;itlt:.
es, which are Liven in the present paper, are P.sfollc”.-;
c:
1-
G
i
.——
.
-,
I
(Al )
q
for
c = PO
V<a
,.
f=
J_
Qc
+
1
4
..i
.
.
.
f=
o
(id;
8 ..
, 19
.’
.
={J(’’+9’’J2J2
(li9)
.
(Ale)
If a is in miles per hour and
heit absolute
If
.
a
is in knots and
T
T
is in de~rees Fahren-
is in debgrees Fa?werineit
absolute
‘w
.
,’
is In miles per hour and
.grad: abs olv.t
a
If
If
a
is
in knots and
T
T
Is in degrees C&lIti-
is in degrees Centigrade
&bsolutt3
a = 32*?4’q,~
V
.
.-8
= Itia
(4)
(A15 )
2C
.J
●
I
.
,.
ccrrssponding to 55,552 ft ) the ter.perature is ass,u-ed”to
decrease lir.ea,zzl~
. according to ihe equ~tion
n=~
1
is
Fur ther, the atmosphere
~as Wat obeys the Mws
of
the mass densit~
corresponding
~erature 13
cJ-
$gh
(El )
assuned
to be a tky perfect
Char ltis arid Eoyl.e,
ao that
tc the pressure
and
tm-
.
i-.
‘cl
p=—~ Poppo
.
(e
)
21
~f~~~fsTN NO, 1120
.
.
“.
In
re~erence
~
the
and altitude ape
press7me
by’
related
.
.
(B3)”’
.
./’
.
.
t
‘I?r:is given by
sm~er ature
Ahl
+Ali2
+
+ Ah2
—+
q
T avl
-.aVz
. . .
, (E5]
Ahl
●
ee
“.
sre t.ne sverase
.
“*
L
the
.
.
.-
S
..*
.
alt i t~&e
increz29nts Ahlj ~~2, ....
terLperatmes
fcr
Nf,rA TN
22
N?,
1120
.
.
R.E,3’ERE
KCES
-1 13aals, llmald D. , and RJ.tchie, Vir.q:l s ,:
-.
“.,
.
A Sinollfiecl
.“
.
.“
.
,,
.
14ACA TN No, 1120
25
.
TDIE III
STATIO PRESSQRE
.
:.
PR2SSORE
p
IN
PCUSD3
ALTITUD2~
PER SWARE
FOOT FCR VALJJESOF
FRCU-1000TO 100,000
F?RT
.
.
.,
.
,.
.
.
..
.
.
.
,.
.
NATIONAL ADVISORY
CGWI’ITEE FOR AERONAUTICS
.. ..... ..... .. ... ..... ..... ....
%%
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NACA TN No. 1120
TABIE V
SFEEDOF S-
FOR
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1
2
OF FREE-AIR
IN DEGREE8FAHREmIT
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&
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NATIONALADVISORY
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FOR AERONAUTICS
NACA TN No.
20
1120
.
TABLE VI
~
SPEED OF SOUND FOR VARIOUS VALUES OF FREE-AIR
TEMPERATURE IN DEGREES CENTIGRADE
.
.
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