THE ARDC MODEL ATMOSPHERE, 1956

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• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 229
• Document Creation Date: January 4, 2017
• Document Release Date: March 20, 2014
• Sequence Number: 6
• Publication Date: December 1, 1956
• Content Type: REPORT

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AIR FORCE SURVEYS Jt GCOPHYSICS
No:86
IHE ARDO MODEL
tiTMOSPHERE,
i956
?
R.A. MINZNER
W.S. RILEY
DECEMBER 1956
OV.
GEOPHYS 'S RESEARCH DIRECTOR TE
AIR FORCE i,,,IMBR'DGE RE! E4RCH .;ENTER
AIR RESEARCH AND DEVELOPMENT 1.0MMAND
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AIR FORCE SURVEYS Ii GEOPHYSICS "
No.86
THE ARDC MODEL
ATMOSPHERE,
1956
R . A . ZNER
W.S. RIPLEY
DECEMBER 1956
GEOPHYSICS RESEARCH DIRECTORATE
AIR FORCE CAMBRIDGE RESEARCH CENTER
BEDFORD. MASSACHUSETTS
- STAT
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The representation of the atmosphere contained
betwev, thes, covers is deeignated "THE ARM MODEL ATMOS-
PHERE, L956" since it is in this Command that these tables
a.e accopted and directive in all design pro-
blems.
T. an altitude of 300 kilmaters the basic
propertiAs et this atmosphere are the result of the cord,
bined .-41' the scientists and engineers listed in the
preface uhore acknovledgements are accorded. Without
their holp ttis representation .t.r.tnld not have been posable.
/1
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PREFACE
-
PREFACE
The 1956 ARDC MODEL ATMOSPHERE, defined and tabulated to 542,248 meters
or 1,850;870 feet in this Air Force Survey in Geophysics, has been prepared in
partial fulfillment of ARDC Technical Requirement 140-56. This MODEL is to be
used as the basis for engineering and design work performed within ARDC and by
its contractors, insofar as the work requires the use of a model representing
the average condition of atmospheric properties within the altitude limits of
this MODEL.
This MODEL ATMOSPHERE is designed to be used for the same purposes as a
standard atmosphere. For some of these purposes the MODEL should serve in the
following ways:
1. As a reference atmosphere to be used in calculating flight performance
of aircraft.
2. As the basis for calibrating barometric altimeters, where observed
departures of atmospheric properties from the values of the MODEL
provide the means for computing altimeter correction.
3. As the basis for ballistic tables where the observed departures of
the atmospheric properties from the values of the MODEL provide the
basis of corrections to be put into gunnery-and bombing computers.
4. As a time average of the actual physical conditions existing at
various altitudes for aircraft engineering and design purposes,
and for use in solving geophysical problems.
It should be emphasized, particularly in regard to item 4, that this
MODEL most probably will never completely match the actual atmosphere, and may
only rarely approximate the average value at all altitudes simultaneously.
While the properties at some altitude may exactly fit the values of the MODEL
at any ,stant, the properties at other aititudes simultaneously may depart
drastically from tabulated values. The greatest percentage departures probably
occur at the higher altit- '-s. Maximum and minimum pressures at 120 km, for
example, may differ by as much as a factor of 3. Neither this MODEL nor any
other calculated model will accurately depict the total atmosphere at any par-
ticular moment.
The tables and graphs of this MODEL approximate the best average of avail-
able temperature, pressure, and density data, compiled and processed under Project
7603, "Atmospheric Standards." The tables are also consistent with the recently
adoptee Extension to the United States (ICAO) Standard AtmosphereA51 (1956)
wre prepared concurrently under the same project. Both are consist-
ent with the basic properties of the International Civil Aviation Organization
(ICAO) Standard Atmosphere26-28 adopted by the United States on November 20, 1952.
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The tables of this MODEL partially duplicate the tables of the ICAO Standard
AtmospYare, ;in the altitude region of -5,000 to +20,000 geopotential meters),
although the tables of this MODEL are given in larger increments. This partial
duplication is desirable and necessary, not only for the sake of continuity, but
because this MODEL includes values of seven additional altitude-dependent prop-
erties not found in the ICAO Standard: Acceleration of gravit4, scale height,
molecular weight, particle speed, number density, mean free path, and collision
frequency.
The ARDC MODEL differs from the standard atmosphere not only because of
the greater altitude of the former but because the MODEL is intended to be re-
viewed annually and modified at any time, if necessary, to reflect significant
changes in thinking brought about by more reliable atmospheric data.
We wish to acknowledge the assistance of the several members of the Geo-
physics Research Directorate who participated in various ways in the preparation
of this survey: Dr. R. Penndorf and Mr. M. Dabin for helpful suggestions and
counscl, and Mr. L. R. Shedd for his eveditious handling of many details.
We also wish to thank the members of the Working Group on Extension to the
Standard Atmosphere for their helpful suggestions and encouragement. This Work-
ing Group consisted of:
Dr. Fred L. Whipple, Chairman
Dr. Charles J. Brasefield
Dr. William G. Brombacher
Dr. Austin R. Brown
*Mr. LeRoy Clem
Major R. F. Durbin
Dr. Sigmund Fritz
**Dr. Boris Garfinkel
Dr. Ralph J. Havens
***Dr. D. P. Johnson
****Dr. Hildegard K. Kallman
Dr. William W. Kellogg
Mr. Raymond A. Minzner
-1*-*-1xADr. Homer E. Newell, Jr.
Mr. William J. O'Sullivan
Mr. William A. Scholl
**ff***Mr. William G. Stroud, Jr.
Mr. Norman Sissenwine
Executive Secretary
Harvard University and Smithsonian Inst.
Formerly at Signal Corps Engineering Lab.
National Bureau of Standards
Formerly at Ballistics Research LAI?rat:TY
Air Weather Service
Formerly at Air Weather Service
U. S. Weather Bureau
Ballistics Research Laboratory
Formerly at Naval Research Laboratory
National Bureau of Standards
Rand Corporation
Rand Corporation
Air Force Cambridge Research Center
Naval Research Laboratory
NACA. Langley Aeronautical Laboratory
Wright Air Development Center
Signal Corps Engineering laboratory
Air Force Cambridge Research Center
* Replacement for Major Durbin upon his departure .rom Air Weather Service.
** Replacement for Dr. Brown upon his departure from Ballistics Research Lab.
*** Substitute for Dr. Brombacher upon his retirement from National Bureau
of Standards to status of consultant for the same organization.
**** Substitute for Dr. Kellogg.
***** Replacement for Dr. Havens upon his departure from Naval Research Lab.
**u*** Replacement for Dr. Brasefield upon his departure from Signal Corps Eng. Lab.
-
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We are especially indebted to two subcommittees of this Working Group:
The first subcommittee, consisting of Dr. H. Newell, Dr. H. EalIman,
and Mr. R. A. Minzner, formulated the general aspects of the temperature-
altitude profile between 130 and 300 kilometers, and made recommendations
concerning the degree of dissociation of 02 and N2 in this region.
The second subcommittee, consisting of Mr. L. P. Harrison, Mr. W. J.
O'Sullivan, Mr. W. Scholl, and Er. R. A. Ninzner, studied some of the aspects
of the following atmospheric properties: coefficient of viscosity, kinematic
viscosity, and the speed of sound. This subcommittee recommended departures
from the ICAO values of these properties and thereupon suggested values of
constants, empirical expressions, and maximum altitude of tabulation for these
properties.
We are particularly grateful to Dr. F. L. Whipple whose efficient
manship expedited the accomplishment of the Working Group, and to Mr. N. Sis-
senwine who in the capacity of Executive Secretary handled a flood of detail.
Finally we uisb to thank Dr. H. Wexler of the Us S. Weather Bureau.
Dr. Wexler served with Mr. Sissenwine as Co-chairman of the Parent Committee
on Extension to the Standard Atmosphere, and though not an official member of
the WGESA, was over in the background to lend his advice and support wherever
needed.
iii
R. A. MiNZNER
W. S. RIPLEY
Geophysics Research Directorate
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CONTENTS
Section
?
of Tables
of Illustrations
of Abbreviations and Symbols
East
via
ix
XV
Preface
List
List
List
Abstract
1.
Introduction
1
1.1
Background and Early History of Standard Atmospheres
1
1.2
First U. S. Aeronautical Standard Atmosphere
1
1.3
First International Standard Atmosphere
2
1.4
ICAO Standard Atmosphere - New U. S. Standard
Atmosphere
2
1.5
High Altitude Models - Warfield, Grimminger
2
1.6
New Data from Rocket-Borne Experiments
2
1.7
Extension to the Standard Atmosphere
3
2.
Systems of Altitude Measure and Related Parameters
4
2.1
Acceleration of Gravity
5
2.2
Relation of Geopotential to Geometric Altitude
3.
Basic Atmospheric Properties of the MODEL
1/
3.1
Molecular-Scale Temperature and Its Development
12
3.2
Pressure
17
3.3
Density
22
3.4
Validity of the Basic Properties
23
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a CONTENT? (Contd.)
Section
h.
Secondary Properties Defined as Functions of TIM
24
4.1 Scale Height
24
4.2 Speed of Sound
28
4.3 Air Particle Speed (Arithmetic Average)
29
?
4.4 specific Weight
31
S.
Other Secondary Properties
33
5.1 Molecular Weight
33
5.2 Mol Volume
36
5.3 Number Density
39
5.4 Man Free Path
40
5.5 Collision Frequency
43
5.6 Temperature (Real Kinetic)
1414
5.7 Coefficient of Viscosity
45
5.8 Kinematic Viscosity
48
5.9 Summary of Ratio Equations
50
6.
Metric Gravitational System of Units
50
6.1 Unconventional Form
50
6.2 Basic Concepts
50
6.3 Modified Definition of the Kilogram Force
51
6.4 Conversion from the Absolute System
51
6.5 Properties Requiring Conversion
52
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CONTENTS (Contd.)
Section
Page
6.6 Converted Sea-Level Values 52
6.7 Conversion for All Altitudes 52
7. Preparation of the Metric Tables 53
7.1 Computation of the Tables 53
7.2 Detailed Computational Procedure 53
7.3 Tabulations Presented 58
7.4 Significant Figures 58
7.5 Accuracy of Tabulations 58
8. Preparation of the English Tables 59
8.1 Conversion of Basic Units 59
8.2 Other Necessary Conversions 60
8.3 Sea-Level Values of Atmospheric Properties
in English Units 62
8.4 Calculation of the English Tables 611
9. Conclusions and Recommendations 66
10. Metric Tables, ARDC MODEL ATMOSPHERE, 1956 67
11. English Tables, ARDC MODEL ATMCWHERE, 1956 129
Appendixes
Appendix A Comparison of Prominent Aeronautical
Standard Atmospheres
Appendix B Constants
Appendix C Conversions
Appendix D Assumptions
vi
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147
148
151
I.
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ARRMILIM
Appendix E
Appendix F
Appendix G
Appendix H
Appendix J
Appendix
Appendix L
Appendix It
Appendix N
Appendix 0
Appendix P
Ref er enc es
CONTENTS (Contd.)
Sea-Level Values of the Atmospheric
Properties in Metric Units
Sea-Level Values of the Atmospheric
Properties in English Units
Abbreviated Metric Tables of the ARDC
ZODEL ATMOSPHERE (1956) to 942,686 nt
Abbreviated English Tables of the ARDC
MODEL ATMOSPHERE to 1,7803465 Ft
Systems of Mechanical Units
Comparison of the Magnitudes of Comparable
Units in the Metric Absolute cgs and mks
Systems of Mechanical Measure
Atmospheric Density Expressed as a Single
Function of Altitude
Effective Radius of the Earth
Acceleration of Gravity
Scale Height
More accurate method for computing Geopotential
vii
MO.
153
155
156
157
158
159
160
162
164
178
184
198
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LIST OF TABLES
Metric Table ---
I. Temperatures and Molecular Weight as Functions
of Geometric and Geopotential Altitude 67
II. Pressure, Density, and Acceleration of Gravity
as Functions of Geometric and Geopotential 77
Altitude
III. Velocity of Sound, Particle Speed, Molecular-Scale
Temperature Gradient, and Scale Height as Functions
of Geometric and Geopotential Altitude
Viscosity, Kinematic Viscosity, and Specific Weight
as Functions of Geometric and Geopotential Altitude
V. Mean Free Path, Collision Frequency, and Number
Density as Functions of Geometric and Geopotential
Altitude
English Table
87
97
105
I. Temperatures, Molecular Weight, and Gravitational
Acceleration as Functions of Geometric and
Geopotential Altitude 129
II. Pressure and Density as Functions of Geometric
and Geopotential Altitude 134
a
III. Sound Speed, Viscosity, and Kinematic Viscosity
as Functions of Geometric and Geopotential
Altitude
139
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LIST OF ILLUSTRATIONS
Figure (Metric Units)
1. Molecular Scale Temperature vs. Geopotential Altitude
US
1
2. Real Kinetic Temperature vs. Geopotential Altitude
3. Molecular Weight vs. Geopotential Altitude
117
I. Pressure vs. Geopotential Altitude
11.8
S. Density vs. Geopotential Altitude
119
6. Scale Height vs. Geopotential Altitude
120
7. Particle Speed vs. Geopotential Altitude
121
8. Sound Speed vs. Geopotential Altitude
122'
9. Coefficient of Viscosity vs. Geopotential Altitude
123
10. Kinematic Viscosity vs. Geopotential Altitude
124
11, Specific Weight vs. Geopotential Altitude
125
12. Mean Free Path vs. Geopotential Altitude
126
13. Collision Frequency vs. Geopotential Altitude
127
14. Number Density vs. Geopotential Altitude
128
Figure (English Units)
15. Kinetic Temperature vs. Geometric Altitude
342
16. Pressure vs. Geometric Altitude
1143
17. Density vs. Geometric Altitude
1144
ix
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ABBREVIATIONS AND SYMBOLS
acceleration II
b subscript indicating base or reference level
/
?C degrees, in thcrmodynamic Celsius scale
Cs speed of sound
/
/
sea-level value of Cs
/
cp specific heat of dry air at constant pressure
cv
cgs specific heat of dry ai at constant volume
centimeter-gram-second system of units
cm centimeter .
d differential symbol
base of natural logarithms
.F degrees, in thermodynamic Fahrenheit scale
F
f(H) force
undefined function of H representing TM
fps foot-pound-second system of units
ft foot
ft' standard geopotential foot
dimensional constant in the geometric-geopotential relationship
effective value of acceleration of gravity
sea-level value of g
r. go sea-level value of g at latitude 0
F
gm gram
t!
Pgm-mol gram mole
cb
...,
te. .
. t _
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ABBREVIATIONS AND SYMBOLS (Contd.)
altitude in geopotential measure
Ho sea-level value of H, (zero)
altitude at base of layer, or reference level in
geopotential measure
Hg mercury
Hs scale height
H' geopotential scale height
(Hdo sea-level value of H
in inch
I n mi international nautical mile
6K degrees, in thermodynamic Kelvin scale
kg kilogram
kgf kilogram force
kg-mol kilogram mole
km geometric kilometer
km' standard geopotential kilometer
mean free path
Lo sea-level value of L
Lbi molecular-scale-temperature gradient alve H
length
lb pound
lbf pound force
in natural logarithm
Xi
,
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ABBREVIATIONS AND SYMBOLS (Contd.)
log logarithm
apparent molecular weight of air
Mo sea-level value of M
M' mass numerically equal to the molecular weight (a mole)
?
(geometric) meter
m' standard geopotential meter
nib millibar
mks meter-kilogram-second system of units
mass
Avogadro's number (standard)
xi atmospheric number density
nt newton
no sea-level value of n
n.
number density of a gas at temperature Ti and pressure Po
(Loschmid's number)
atmospheric pressure
ro sea-level value of P
Pdl poundal
Pb value of P at base of layer or reference level
conatant, GM ..2
Fr*
degrees, in thermodynamic Rankine scale
R71 universal gas constant
effective radius of earth (at 45 32' 4o" N. lat.)
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,
ABBREVIATIONS AND SYMBOLS (Contd.)
r0 radius of earth at latitude 0
Sutherland's constant
sec second
temperature (real kinetic) in the absolute thermodynamic scales
To sea-level value of T
Ti temperature of the ice point in the absolute thermodynamic
scales
TM molecular-scale temperature in the absolute thermodynamic
scales
(Tm)0 sea-level value of T
(Tm)b value of T at base of layer or reference
temperature in nonabsolute thermodynamic scales, also signifies
time
to sea-level value of t
ti temperature of the melting point of ice at 1013.250 mb air
pressure in the nonabsolute thermodynamic scales
molecular-scale temperature in the nonabsolute scales
particle speed (arithmetic average)
o sea-level value of V
volume of one mole of air at existing conditions of T and P
vo sea-level value of v
v volume of one mole of air at a temperature Ti and pressure Po
(mol-volume)
altitude in geometric measure
real temperature gradient ?T/dZ
xiii
-..
?
^
?
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ABBREVIATIONS AND SYMBOLS (Contd.)
real temperature gradient a To H
constant used in the empirical expression for the coefficient
of viscosity
ratio of specific heats, spicy
partial differential symbol
kinematic viscosity
0 sea-level value of n
coefficient of viscosity
sea-level value of ?
collision frequency
sea-level value of V
ratio of circumference to the diameter of a circle
atmospheric density
sea-level value of p
ice-point value of p
effective collision diameter of a mean air molecule (standard)
latitude of the earth
specific weight
sea-level value of w
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ABSTRACT
A realistic model of atmospheric properties based on reliable observa-
tions and current theories is presented.
Fifteen atmospheric properties are discussed and tabulated, thirteen
to 500 km and two to only 90 km. The values of these prcperties are inter-
nally consistent through classical equations, and are dependent upon (1), a
defined, linear, segmented, molecular-scale temperature function, (2) a mol-
ecular weight function, and (3) an acceleration of gravity function. Values
of twelve physical constants required in the computations are adopted as
exact. Internationally agreed-upon, exact transformation factors are employed
in converting from Metric to English units. Both Metric and English tables
are presented, and computational procedure is discussed. A thorough discus-
sion of geopotential altitude, effective radius of the earth, and molecular-
scale temperature is given. The relative virtues and validity of two methods
for computing the acceleration of gravity are discussed. The concept and
validity of the various properties as applied to high altitudes are considered
briefly.
XV
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17.
THE ARDC MODEL ATMOSPHERE
1956
(Tables and Graphs for kltitudes to 542,686 Meters or 1,850,870 Feet)
1. Introduction
1.1 Background and Early History of Standard Atmospheres
Standard atmospheres have been usej for nearly a hundred years for
altimetry purposes. The earliest of these were very simple and were based on
an isothermal atmosphere. With the development of aircraft and precision artil-
lery during the First World War, 1914-1918, the need for more extensive atmos-
pheric tables for aeronautical and ballistic purposes became apparent. Atmospher-
ic temperatures were measured at various locations in southern and western Europe.
Several functions approximately fitting these temperature data were proposed and
used in various countries for deriving an analytical expression for atmospheric
pressure and density. No generally agreeable function was proposed, however,
until 1919 when Toussaint4Y suggested a segmented straight-line function as the
basis for an international standard. Toussaintls temperature function was de-
fined by a value of 15 degrees Celsius (00) at sea level, a constant gradient of
-.00650C per meter from sea level to 11,000 meters, (in), (yielding -56.500 for
11;000 m), and a constant gradient of zero degrees per meter from 11,000 in to
20,000 in altitude.
-
1.2 First U. S. Aeronautical StRndard Atmosphere
The Toussaint formula with minor variaLions has remained the basis
for all major aeronautical standards prepared for the 0 - 20 km altitude region.
These include the first United States Standard Atmosphere prepared by Greggel in
1922, and the modification,extension,and amplification of the Gregg standard
prepared by :Diehllit in 1925. Neither of these agreed exactly with the Toussaint
proposal, however: Gregg terminated his analytically derived atmosphere at
10 km altitude although he presented observed data to 20 km; Diehl extended the
analytical atmosphere to 20 km but established the tropopause at an altitude of
10,769.23 in (65,000 ft) with a temperature of -55?C, instead of at 11,000 in and
-56.500, as suggested by Toussaint. Thus Diehl's stratosphere, 10,769.23 in to
20,000 ;was warmer by 1.5?C than that used by Toussaint.
Brombacher425 amplified the Gregg Standard Atmosphere in 1926 and
again in 1935 by adding tables of altitude as a function of pressure for altimetry
purposes.
1
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1.3 First International Standard
In 1924 the International Committee on Air Navigation (ICAN)29 prepared
an international standard atmosphere based exactly on Toussaint's temperature-
altitude function. This standard was adopted throughout most of Europe. It was
never adopted formally by the United States, however, because of two small but
basic differences between this and the Diehl-U. S. Standard.
In addition to using different altitudes and temperatures for the tro-
popause, the ICAN and EL S. Standard also used different values for the acceler-
ation of gravity at sea level, 9.8 and 9.80665 respectively. These dgferences
prevented United States and European agreement on a standard atmosphere until
1952 when a new international organization, ICAO, reached a compromise.
1.4 ICAO Standard Atmosphere28-- New U. S. Standard2627
Between June 1950 and November 1952 the International Civil Aviation
Organization (ICAO), of which the United States was a member, proposed and
adopted a compromise standard atmosphere in which the United States standard sea-
level value of gravity, and the MAN values of tropopause altitude and trorepause
temperature were employed. This ICAO Standard Atmosphere was formally adopted
as the United States Standard Atmosphere by NAGA vote on 20 November 1952.
1.5 High Altitude Models Warfield, Grimminger
The activities of ICAO emphasized international agreement and refine-
ment of atmospheric tables within the altitude range of existing standards; i.e.,
sea level to 20,000 meters altitude. The ICAO did not concern itself with high
altitude tables. The advances in aeronautics and ballistics during and since
World War II resulted in demands for atmospheric tables to much greater altitudes.
In 1947 these demands were met in part by Warfield's uTentative Tables for the
Properties of the Upper Atmosphereu52 which depicted the atmosphere to 120,000
meters altitude and which were designed to be a continuous extension of the
tables of the Diehl-U. S. Standard14 at 20,000m altitude. The Warfield tables
were based on the best 1946 estimates of atmospheric temperature, and considered
the variations of molecular weight of air and the acceleration of gravity with
increasing altitude.
The 120 km altitude upper limit of the Warfield tables was inadequate,
however, even before the publication of the report, and Griming er22 in 1948
published tables of atmospheric properties to altitudes of over 8,800 km. These
tables were essentially in agreement with the Warfield tables up to 120 lam and
were based on the best 1947 theoretical and experimental data.
1.6 New Data from Rocket-Borne Experiments
Simultaneously with the preparation of the Warfield and Grimminger
tables, a new research tool, the upper air sounding rocket, was beginning to be
exploited. This new device permitted making measurements of the atmosphere by
2
0
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direct probing methods not previously possible. The new data compiled in 1952
as the Rocket Panel Atmosphere45 indicated that preasures in the Warfield and
Grimminger tables were 2 times higher than observed at 70 km, 5 times higher than
observed at 90 km, and over 10 times higher than observed at 120 km. These dis-
crepancies, plus the fact that the Warfield tables were not continuous with the
newly adopted ICAO Standard, initiated the preparation of this extension of the
ICAO Standard to high altitudes.
1.7 Extension to the Standard Atmosphere
In November 1953 the Geophysics Research Directorate, Air Force Cam-
bridge Research Center, of ARDC, USAF, together with the U. S. Weather Bureau
sponsored a three-day "Open Meeting on Extensions to the Standard Atmosphere."17
Standard atmosphere requirements and scientific data supporting various models
were presented. Brombacher? presented a Standard Atmosphere proposal which was
not accepted because of an unrealistic stratosphere and because the constant
gravity assumption employed was inconsistent with the ICAO Standard and this
assumption introduced errors in the analysis. A Working Group on Extension to
the Standard Atmosphere (UassA) was appointed to recommend the temperature-
altitude profile and other constants necessary for the preparation of the desired
extension.
The discussions of the first meeting18 of the Working Group dealt prin-
cipally with the temperature-altitude profile in the 20 to 53 kilometer region.
Temperatures were also recommended for the region between 53 and 83 km, although
these were replaced by slightly different values at a later meeting. Recommen-
dations were also made at this first meeting regarding the atmospheric properties
to be included in the standard. Differences of opinion existed on the manner
of accounting for variable gravity, and some conflicting recommendations resulted
from this meeting.
The task of preparing the text and tables for the extension to the
Standard Atmosphere was assigned to GRD (Geophysics Research Directorate). The
recommendations were studied, and Hinzner 40 prepared a paper, "Three Proposals
for U. S. High Altitude Standard Atmosphere," which was presented at the second
meeting19 of the Working Group. Each of the three proposals suggested a dif-
ferent method for handling the acceleration of gravity and molecular weight as
variables in the hydrostatic equation. Only one of these three proposals was
consistent with the ICAO Standard Atmosphere and that one, using geopotential to
account for variable gravity, and molecular-scale temperature to account for
variable molecular weight, was adopted by the Working Group.
Preliminary tables of atmospheric properties to 130 km,111 prepared at
GRD, were teLtatively adopted at this meeting. These tables were consistent
with the temperature-altitude function to 83 km recommended by the Working
Group and consistent with the temperatures of the Rocket Panel Atmosphere above
this altitude. A subcommittee was appointed, however, to make recommendations
concerning molecular weight and temperatures for extending the Staniard Atmos-
phere to 300 km altitude.
3
1:
i.
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,
?
This subcommittee met with several consultants and then agreed upon
certain boundary conditions for oxygln and nitrogen dissociation, as well as
for atmospheric temperature. Using these boundary conditions and all the
available atmospheric pressure, temperature, and density data above balloon
altitudes, two separate proposals were prepared, one at Rand Corporation34,35
and the other at GRD.4z
The Rand proposal assumed a density-altitude function and a molecular
weight gradient arbitrarily related to this density function. From these, there
was derived a nonlinear temperature-altitude profile with no discontinuous first
or second derivatives.
The GRD proposal, in keeping with previous Working Group recommen-
dations, assumed several constant gradients of molecular_scale temp mmture for
as many altitude regions. These gradients were chosen to yield values of pres-
sure and density consistent with the average of observed values of these proper-
ties below 160 km altitude, and consistent with current estimates of these
properties at higher altitudes. Molecular weights39 were computed from diffu-
sion theory and the agreed-upon boundary conditions. The GRD proposal was
adopted at the third and final meetingn of the Working Group.
A summary of the adjusted recommendationsla resulting from the Wee
meetings of theWGESA was prepared. A supplemental net of recommendations43
on previously-unresolved questions was also prepared. Within the framework
of these recommendations, this ARDC MODEL ATMOSPHERE and the Extension to the
U. S. Standard Atmosphere have been prepared.
2. Systems of Altitude Measure and Related Parameters
In accordance with agreements concerning publication of international aero-
logical tables30 and in keeping with the existing United States (ICAO) Standard
Atmosphere, the basic altitude parameter of this MODEL is taken to be geopo-
tential H, expressed in standard geopotential meters, mt. Supplemental to the
existing (ICAO) United States Standard, this MODEL has been prepared with
parallel tabulations in integral values of both geopotential and geometric
altitude measure so that the values of tabulated properties are given for both
integral geopotential and integral geometric kilometers.
ft
The relationship between geopotential and geometric altitude depends
directly upon the value of the acceleration of gravity at sea level at a par-
ticular altitude and upon the variation of the acceleration of gravity with
altitude and latitude. The definition of the special unit of geopotential used
in this MODEL is also related to the specific sea-leiel value of gravity,
adopted by ICAO and used in this MODEL. Therefore, a digression is made to
present a detailed discussion of the acceleration of gravity before geopotential
is discussed further.
14
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2.1 Acceleration of Gravity
2.1.1 Sea-level value
ri
. . ? _ L
. P.
The sea-level value of the acceleration of gravity used in
this MODEL is defined to be 9.80685 in see-2 exact" . This value was originally
announced by Defforges and Lubanskil3 at the 1891 meetings of the International
Committee on Weights and Measures as the best value for 450 latitude. Since
then, it has been used by physicists and others as an arbitrary standard and
was receqtly adopted as an international standard in the ICAO Standard Atmos-
phere. It has long been recognized, however, that this value of g not correct
for 45? latitude but rather is the value for 450 321 40" /atitude.1, This cor-
rected latitude is the one to which all tables in this MODEL apply.
2.1.2 Altitude variation - classical expression
The variation of the acceleration of gravity with geometric
altitude is classically expressed by the equation
g go [rfirj6 2
+ 1
where
?
(1)
g = the acceleration of gravity of a point (in in
Z = the geometric altitude of the point (in m),
the sea-level value of g at the latitude of the point
(in in sec-2), and
= the radius of the earth at latitude 0.
In its fundamental form this equation applies rigorously only for a nonro-
tating sphere composed of spherical shells of equal density. The earth, how-
ever, is definitely not spherical; furthermore, its rotation introduces cen-
trifugal acceleration which varies with latitude and which increases with
altitude. The sea-level value of the ctatrifugal acceleration at any selected
latitude may be accounted for, in equation (1), by the proper choice of an
effective value of go. The increase of centrifugal acceleration with increas-
ing altitude is not accounted for in the simple unadjusted inverse square law,
which describes only the decreasing Newtonian component of the effective value
of g. Hence, values of g cemputed from equation (1) become increasingly in-
accurate as altitude increases. An adjustment of the value of ro to an effective
/ Basic constant
5
,
I
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i371 , j- ? c;
radius, however, was found to greatly improve the validity of that equation even
at altitudes as great as 500 km.
2.1.3 Effective earth's radius
Harrison23using a suggestion by Lambert37? developed an ex-
pression for an effective earth's radius as a function of latitude. This ef-
fective radius is derived in a manner consistent with the effective sea-level
value of g at latitude 0 , and consistent with the vertical gradient of g at
the given latitude (neglecting local anomalies), assuming the International
Ellipsoid represents the figure of the earth. The value of effective earth's
radius at 45? 321 40u, computed from Harrison's equation (given in Appendix M)
is
r = 6,356,766 meters
which, for purposes of this MODEL, will be considered as an exact constant.
.2.1.4 Computational equation
The exact form of the equation used to compute the acceleration
of gravity and to relate geopotential to geometric altitude in this MODEL is
where
g g
o r z
(la)
g = the acceleration of gravity in meters per second squared,
On sec-2) at altitude Z and at latitude 45? 321 401', hereafter,
= 9.80665 m sec-2(exact)/, the sea-level value of g at 45? 321 40*
go
latitude, and
r = 6,356,766 a (exact)71, the effective earth's radius at latitude
450 32' 401.
(For purposes of this MODEL, this equation is assumed .uo apply in free air
below sea level as well as above sea level.)
2.1.5 Best available analytical expression
A more exact equation for g as a function of Z and 0 in free
air, based directly on the International E4ip?oid and the International
Gravity Formula, was developed by Lambert31?2-30 in the form of an infinite,
Basic constant
_
6 ?
? I
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alternating power series (see AppendaM). The values of g computed from equa-
tion (la) are in good agreement with those computed from Lambert's more exact
equation. For an altitude of 500 km the value of g from the two methods differs
only by 3 parts in the fifth significant figure, or less than 1/1000 of 1 per
cent. For lower altitudes the agreement is much better. Values of geopotential
computed for specific values of Z. on the basis of equation (la) are also in
good agreement with corresponding values of geopotential computed on the basis
of the more exact equation for g. The percentage departures are similar. The
more exact expression for g was not employed in this MODEL because of its much
greater complexity. In the U. S. Standard Atmosphere, the tables will be
recomputed by machine and will be based on the more exact equation.
2.2 Relation of Geopotential to Geometric Altitude
2.2.1 Basic definition of geopotential /
The geopotential of a point is defined as the increase in
potential energy per unit mass lifted from mean sea level to that point against
the force of gravity.
2.2.2 Analytical development
The increase in potential energy of a body lifted against the
force of gravity, from sea levell through a vertical distance to a given point
is:
A E 8.fmgdZo (2)
whers
increase of potential energy over the sea-level value, in joules,
m = mass of the body in kilograms, kg.
The geopotential of that point AB/m is therefore:
E
If geopotential is given a special designation, Ft, with special units, we
have:
or
(2a)
E
GH = ? lgdZ, (2b)
GdH gdZ, (2c)
7
(2d)
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where
H geopotential (in unspecified units), and
G a proportionality factor depending upon the units of H.
When H is in units of joules kg-1 or equivalently in m? sec-2, G is nondimensional
and unity. If H is expressed in some other units, standard geopotential meters
for example, the value and dimensions of G must be correspondingly changed.
2.2.3 The standard geopotential meter26-28
The basic unit of geopotential employed in this MODEL is the
standard geopotential meter where one standard geopotential meter, in', is de-
fined to be an increment of potential energy per unit mass equal exactly to
9.80665 joules kg-1 (or m2 sec-1); i.e.,
1 ml 1. 9.80665 m? sec-2 (exact)! (3)
It is evident from equation,(2b) that if H is expressed in ms, G is equal
to 9.80665 m2 sec-2 mt-1. ff One standard geopotential meter is therefore the
vertical distance through which one kilogram mass must be lifted against the
force of gravity to increase its potential energy by 9.80665.joules. If a region
deleted where the value of the acceleration of gravity were constant at
9.80665 in sec-2 over an altitude interval of one geometric meter, in this region
one geometric meter and one geopotential meter would then be exactly equal. This
condition is very closely approximated at sea leveat 49 321 40n latitude. Since
g normally does decrease with altitude, however, even over a one meter interval,
an altitude of one geometric meter at this latitude has a geopotential altitude
of slightly less than I a', (sea table in Section 2.2.5). Above sea level, at
all points where the altitude gradient of g is continuously negative from sea
level, the altitude in standard geopotential meters is always numerically less
than the altitude in geometric meters, and the numerical difference increases
with increasing altitude.
2.2.4 Standard geopotential kilometer and standard geopotential
centimeter
The basic concept of the metric system of units leads directly
to the conclusion that one geopotential kilometer, km', is equal to one thousand
geopotential meters; i.e.,
1 lant mi 1 x 103 my.
* Basic conversion of units
ki Derived constant, inferred from transformation of units
8
(3a)
.--
!
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Also, it follow that one geopotential centimeter, cm*, is equal to one one-
hundredth of a geopotential meter; i.e.,
1 cmi .^ 1 x 10-2 ml.
(311)
One cm' may also be defined in cgs units directly by analogy with equation
(3),
where
in
where
1 cm: in 980.665 ergs gel w 980.665 cm2 sec-2 .01 mt? (3c)
980.665 is the numerical value of go in the cgs units.
2.2.5 Conversion of standard geopotential meters to
geometric maters
The replacement of g in equation (2h) by equation (1a) results
H.f5.1jr[L...1 dZ,2
G r Z
H geopotential in standard geopotential meters,
Z u geometric altitude tam,
G 9.80665 m2 see-2 m1-1(exact)21,
go = 9.80665 m sec-2 (exact/,
? 6,356,766 in (exact)'t.
Performing the indicated integration leads to
rgol rZ
H i77721
Or
rit
Z -
[g?
r - H
Basic constant *
9
(5)
(6)
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7 The ratio go/G appearing in equations (4), (5), and (5) is numerically unity
while its dimensions are intim. Home while the ratio go/G may be ignored for
numerical purposes, in this MODEL it must be retained in a dimensional analysis.
(The definition of the standard geopotential meter was in fact chosen to make
the ratio go/G numerically unity for the case when g, = 9.80665 m 3ec-2, the
standard sea-level value of gravity in the ICAO Stanaard Atmosphere and in this
MODEL.)
Using equation (5), the following tables of geopotential in
m2 sec-2, as well as in standard geopotential meters, have been prepared for
specified geometric altitudes.
Geometric
Altitude
Geopotential
AE/a,
Differences in
Values of H
in
2 -2
m sec
int by equation (5)
ml
1 x 100
9.806,648,45 x 100
.999,999,839 x 100
.000,000,0
1 x 101
9.806,634,56 x 10 -
.999,998,423 x 101
.000,CC0,0
1 x 102
9.806,495,72 x 102
.999,984,265 x 102
.000,C00,0
1 x 103
9.805,107,53 x 103
.999,842,719 x 103
.000,000,0
1 x 104
,
-
9.791,247,11 x 10)
.998,429,339 x 104
.000,07
1 x 105
9.654,768,23 x 105
.984,512,367 x 105
.088
.5 x 106
4.545,771,23 x 106
.463,539,663 x 106
9.9
1 x 106
8.473,638,99 x 106
.864,070,707 x 107
70.6
Equations (4) through (6) do not represent the only possible
equations for converting geometric measure to geopotential measure. While
equation (2d) is the fundamental and rigorously correct equation for convert-
ing geopotential measure to geometric measure, equations (4) through (6) are
only as good as the expression for g introduced into equation (2d). A more
precise expression for g is discussed in Appendix N. This expression is an
alternating infinite-power series in terms of latitude and altitude. Evalu-
ating this expression for latitude 45? 32' 140" and introducing it into equation
(2d) yields another alternating power series as the expression for H in terms of Z.
The departures of the result of equation (5) from the results of this more exact
. ,
10
3
4
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method are small. The differences in the values of H computed by both methods ,
for 45? 32' 1,0" Jatitude are given in the above table. For altitudes of 1 x 10)
meters and below, the number of sign4ficant figures limits difference determin-
ations. For altitudes above .8 x 100 meters, the number of available terms in
the series limits thc difference determinations. From these results it is
obvious, however, that for practical applications, at least, equations (4) and
(5) are quite adequate. (See appendix P)
2.2.6 Other special units of geopotential
Two other special units of geopotential, neither of which is
employed in this MODEL, preceded the standard geopotential meter. ,The geodynamic
meter, the first of such units to be used, was defined by Bjerknes) to be equal
to 10 joules kg-1. Thus a geodynamic meter differed in magnitude from a geo-
metric meter by about 2% at sea level.
The second special unit of geopotential to be introduced, and
the one generally used by meteorologists, is the geopotential meter23,32 equal
to 9.8 joules kg-1 or 9.8 121 sec-2. This latter unit was defined on the basis of
a sea-level value of g equal to 9.8 m sec-2. The numerical differences between
altitudes measured in geopotential meters and the same altitudes expressed in
standard geopotential meters are small, of the order of 1/10 of 1 per cent, and
in many instances may be neglected.
2.2.7 Analytical usage
Geopotential has its greatest appeal, for use in this MODEL,
from an analytical point of vielq, because it is a parameter involving both g
and Z, and hence its use reduced by one the number of variables in the differ-
ential form of the barometric equation relating the basic atmospheric properties
of this MODEL. This reduction in the number of variables comes without requiring
the erroneous assumption of constant acceleration of gravity, used in some of
the earlier standards. (The constant gravity-assumption would result in a
computed pressure which, at 500 km, is 140 per cent lower than one finds when
variations in gravity are accounted for.) This pressure discrepancy is equivalent
to an altitude discrepancy of 42.6 km at 500 km. If variable gravity is retained
in the hydrostatic equation explicitly, rather than being concealed in the geopo-
tential altitude, the algebraic expression resulting from the integration of the
hydrostatic equation is excessively complicated.
3. Basic Atmospheric Properties of the MODEL
The basic properties of this AREC MODEL are those properties rigorously
related by the hydrostatic equation and the equation of state (perfect gas law).
These are pressure, density, and the ratio of temperature to molecular weight of
air (which will be expressed in terms of molecular-scale temperature). Defining
the altitude function of any one of these properties specifies the remainder of
these basic properties in any In this MODEL, according to custom, the
temperature function is the defining property.
N4.
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k
aTa"
TJ-
_ . _
3.1 Molecular-Seale Temperature and Its Development
3.1.1 Ratio of temperature to molecular weight, T/M
The property, TIM, is a composite of two variables which
are conveniently handled as an entity because of the frequent occurrence of this
ratio in atmospheric equations. In fact, the occurrence is so frequent and so
fundamental that all so-called atmospheric-temperature measuring experiments
successfully used in rockets to date measure TIM, rather than T independently.
The combining of the two variables into a single parameter is
of particular convenience in the computation of atmospheric tables to great al-
titudes because:
a. The values of T and M have not been independently measured
above 90 km with any degree of reliability; and
b. The introduction of T/M, as a single function of H, into
the differential form of the barometric equation greatly simplifies the inte-
gration and resulting algebraic computational equations over the case when two
independent functional relationships are used.
Until recently, aerologists have not been concerned with re-
lating pressure-altitude gradients or speed of sound etc., to the ratio TIM,
since within the altitude region of their concern (below about 90 km), the
molecular weight of air, M, is known to remain essentially constant at its sea-
level value2 M. For the same reason, the preparation of tables of atmospheric
o
models and standards did not require the consideration of 11 as a variable; and
hence the increased complexity of equations resulting from considering M a
variable was not a problem. Defining the atmosphere in terms of TIM instead
of in terms of T alone solves the problem of cdmplexity but introduces the
problem of consistency with existing standards. This consistency problem is
solved by defining a new property, the molecular-scale temperature, such that
it'is a function of T/M and is equal to T at all altitudes where M is equal to
3.1.2 Molecular-scale temperature concept
The molecular-scale temperature, TM, which Minzner0,41
suggested as the basic parameter for the Standard AlMosphere, is a parameter
which combines the ratio of two fundamental variables T/M with a constant in
such a manner the T is equal to T whereverM Mo, and simultaneously ac-
,
counts for variations in H without specifying its functional variation. Mol-
ecular-soale temperature is that temperature derived from essentially all
rocket experiments when variations in molecular weight from its sea-level value
are unknown and hence neglected. Molecular-scale temperature is an amplifica-
tion and redefinition ofIlhipplefs T29 in the Rocket Panel Atmosphere.45
Analytically TM is defined by the following equation:
12
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II
? \
-
A.
where
TM ,
= temperature (kinetic) in the absolute thermodynamic
scales, ?
T = molecular-scale temperature in the absolute thermo-
dynamic scales,
= molecular weight (nondimensional),
Mb = sea-level value of. molecular w4ght egual to
28.966 (nondimensional, exact)?0-20,31,47
(See section 5.1.)
The use nf TH in the ARDC MODEL retains consistency with th existing United
States Standard Atmosphere, since over the altitude region of the Standard
(0 to 20,000 mi) as well as to considerably greater altitudes, the ratio of
Mo/M is unity; and hence TM = T for these altitulas.
3.1.3 Form of altitude function of molecular-scale temperature
(7)
Molecular-scale temperature is the key or defining property
of this MODEL, in that the specification of the variation of TM with altitude
simultaneously ad completely establishes the altitude variation of more than
half of the fifteen properties of this MODEL. (The determination of the re-
maining properties requires a definition of the altitude variation of molecular
weight above 90 km in addition to the altitude variation of the molecular-
scale temperature.)
In accordance with precedent26-28 and by agreement of the
Working Group on Extension to the Standard Atmosphere,18 the temperature param-
eter of this MODEL is defined to be a continuous function of altitude consist-
ing of a consecutive series of functions linear in geopotential H, whose first
derivatives are discontinuous at the intersections of the linear segments.
Tho use of such a function implies that the atmosphere is made up of a finite
number of concentric layers, each layer characterized by a specific constant
value of the slope of the temperature parameter with respect to altitude. This
slope will hereinafter be referred to as the gradient. The following is the
general form of each segment of the function:
(8)
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where
?
= geopotential altitude in mf,
TM = the molecular-scale temperature in ?K at altitude H,
= the gradient of the molecular-scale temperature in terms
of geopotential altitude; i.e., a Twat', in OK m1-1,
constant for a particular layer,
H = geometric altitude in in' at the base of a particular
layer characterized by a specific value of .1.m, and
(Tm)b = the value of TH at altitude Hb.
3:1.4 Kelvin or absolute temperature scale
In agreement with Resolution 164 of the 1947 meeting of the
International Meteorological Organization,31 and consistent with the ICAO
Standard Atmosphere, the absolute temperature in degrees Kelvin of the melt-
ing point of ice subjected to atmospheric pressure of 1013.25 nib (or 101,325.
newtons m-2) is taken* to be Ti = 273.16?K. Temperatures on tile absolute
Kelvin scale are related to temperatures on the Celsius scale44 by the rela-
tiOnship:
where
T(?K) Ti
Ti 1. ice-point temperature, 273.16?K (exact)/,
t(?C) = temperature in the thermodynamic Celsius scale.
The magnitude of Kelvin degrse and the Celsius degree are equal and hence tem-
perature gradients are numerically the same in both systems.**
The Tenth General Conference on Weights and Measures12'48 has adopted
273.150K for ti but this value will not be used in this mom.
** For relations between the two metric and two English temperature scales
commonly used in scientific and engineering fields refer to Appendix C.
pt Basic constant
114
?
0
(9)
?
9
a;-
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3.1.5 Specific altitude function of molecular-scale temperature
In accordance with the ICAO Standard Atmosphere, Crm)0, the
sea-level value of Tm, is taken to be 15?C (exact) or 288.16?K (exact) by
equation (9). This sea-level temperature plus the values of Lm, and the extent
of the respectively associated layers completely define the profile of molecular-
scale temperature with respect to altitude. The following are the values of LK
and their respectively associated altitude layers employed in this MODEL.
Table of Molecular-Scale Temperature
Gradients Versus Altitude/
Lm in nK al/ -1
-0.0065 exact
-0.0065 exact
Atmospheric Layers in ml
-5,000 to 0
0 to 11,000
0.0
exact
11,000 to
25,000
.vax03
exact
25,000 to
47,000
0.0
exact
47,000 to
53,000
-0.0039 exact
53,000 to
75,000
0.0
exact
75,000 to
90,000
40.0035
exact
90,000 to
126,000
400100
exact
126,000 to
175,000
40.0058
exact
175,000 to
500,000
These values of L together with equation (8), imply ten specific functions
of H to define Tm over the desired altitude intervals. This molecular-scale
temperature profile results in the following values of molecular-scale temperature
(rii)b associated with the base of the respective layers, lib:
Base Altitudes and the Respective Base Values of Molecular-Scale Temperatures
Hb in ml
(T14)b in 41
0
288.16
11,000
216.66
25,000
216.66
47,000
282.66
53,000
282.66
75,000
196.86
90,000
196.86
126,000
322.86
175,000
812.86
)[ Entire table consists of basic constants.
15
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3.1.6 Basis for selecting the temperature-altitude function
?
The temperature-altitude function of this MODEL was selected
to be in exact agreement with the present ICAO Standard Atmosphere which ex-
tends from -5,000 ml to 20,000 ml. (The temperature-altitude function is also
in agreement with the recently adopted Extension of the Standard Atmosphere to
300,000 ml which was prepared concurrently with this MODEL.) The values of the
function between 20,000 ml and 53,000 ml were suggested by Whipple and adopted
at the First Meeting18 of the WOESA. Between 53,000 my and 500,000 ml, the
temperature-altitude function is that presented by Minzner20,42 and adopted
to 300,000 ml for the Standard Atmosphere at the Third Meeting of the womx.
The linearized temperature-altitude function of this MODEL
follows approximately along the average of observed temperatures up to about
90 or 100 km, the highest altitude for which "direct" temperature observations
have been reliably made. The pressures and densities inferred by this linear-
ized temperature-altitude function at the various altitudes agree very well with
the average of all measured pressures and densities up to 160 km, the maximum
altitude of such observations. Agreement between the inferred pressures or
densities and the average of observed values was, in fact, the primary criterion
for choosing the temperature-altitude function between 70 and 160 km.
Above 160 km, only theoretical approaches are presently avail-
able for estimating temperatures, pressurcs$ or densities. Between 160 and 300
km, this MODEL represents an approximate mean value of the recent theoretical
estimates of these properties.
For the region above 300 km, there are two basic theories on
which to base a temperature-altitude profile. This MODEL follows that theory
which results in the higher atmospheric densities at 500 km.
One of these theories, fostered principally by Bates,1,2
assumes an upward conduction uf energy from layers of high solar energy absorp-
tivity, between 100 and 250 km. The proponents of this theory generally deduce
an essentially isothermal atmosphere at a temperature between 8500 and 1100011
extending upward from 250 or 300 km.
A second theory, proposed by Chapman, 8-10 suggestu that the
earth is bathed in the solar corona which extends outward from the sun beyond
the earth's orbit around the sun. Some of the energy of the very high-temper-
ature (high-velocity) particles comprising the corona, through which the earth
is said to move in its orbin, is conducted dowuward toward the earth's surface.
Thus a temperature of the order of 2 x 105 01C, a few earth's radii away from
the earth, drops to the order of 1000011 at 300 km altitude as the conducted
energy is shared by increasing numbers of particles. This theory, therefore,
implies a positive real-temperature gradient which Chapman suggests might be
of the order of 2.5011 per kilometer, in the 300 to 500 km region. This value
corresponds closely with the molecular-scale temperature gradient of 5.8011/km
used in that region of this MODEL.
16
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.73
?
Neither theory has any strong experimental support at present.
The positive temperature-altitude gradient above 300 km was selected for this
HODEL, however, because it inferred a higher atmospheric density at 500 km than
is inferred by an isothermal atmosphere above 300 km. Higher densities in the
vicinity of 500 km altitude are conservative from the point of view of satellite
design.
?
3.2 Pressure
3.2.1 Development of the general pressure-altitude equation
Atmospheric pressure is expressed as a function of altitude
through the hydrostatic equation,
dP = -gpdZ,
where
P = atmospheric pressure in newtons m-2,
g = accelerat.I.n of gravity in m scc-2,
p = atmospheric density in kg m-3, and
Z u altitude in m.
The density, p, may be eliminated by replacing it with
of pressure and temperature in the form of the perrect
PM
P
12*T
where
T = atmospheric temperature in o1E, and
its equivalent in terms
gas law,
R* = universal gas ccnstanti
8.31439 x 103 joules (l) -1 kg-1 (exact).,1 11,16,46,47
(10)
The value of R7* was chosen to be in agreement with recent determinations of its
value and consistent with the ICAO Standard Atmosphere.
The substitution of equation (11) into equation (10) plus some
manipulation, leads to the differential form of the barometric equation,
Basic constant
17
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? "?.) 1;7; %T.',
-
-14
d in P Lea ?
14.^T
It is to be noted that the pressure is now expressed as a function of TM.
The introduction of molecular-scale temperature from equation (7) and geo-
potential from equation (2c) changes equation (12) in five variables to
the following equation in only three variables:
d In P
Equation (13) in turn leads to
where
P
---
Pb da
Hb '
Pb ... pressure at altitude lib,
Q G Mo/e, a constant equal to 0.034,164,794,2?K ml -1
f(H) ?i a functional representation of Tm.
(12)
(13)
3.2.2 Pressure-altitude equations for linear temperature functions
For purposes of this MODEL, f(H) is defined by equatior)(8).
Thus the integration of equation (14) yields two different forms of the baro-
metric equation, depending on whether Im of equation (8) is equal to zero or
equal to a nonzero constant:
For Iv 0 0,
-Q01 -
P Pb exponential
(Tm)b
For not equal to zero,
Ai Derived constant
es
P = Pb (TH)b V ;
(TH)b /(H - lib)
18
(is)
(16)
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where
(TM)1.. = the value of molecular-scale temperature in
?K at the baso of a layer characterized by a
constant value of Lm,
= the value of Tm/H in ?K m1-1 for a particular altitude
region.
The formzof equations (15) and (16) are such that pressure may be computed in
any units merely by introducing Ph in terms of the desired units. For numerical
computationl purposes equation (157 is more usable in the form
where
a
Pb
logioeQ
antilogio 01 - HO
(Tm)b
Logioe - .434,2 94,462 the modulus of common logarithms.
(17)
3.2.3 Sea-level value of pressure
Pressures at all altitudes computed from equation (15) or (16)
depend directly on the sea-level value of pressure. In keeping with the ICAO
Standard Atmosphere26 -28 and implicit in the Resolution of the Proceedings of the
International Committee on Weights and Measures,44 the sea-level value of pressure,
Po, is taken to be 101,325 newtons m-2 or 1,013.25 mb./ This pressure corresponds
to the pressure exerted by a column of mercury 760 mm high having a density of
13.595,1... gm cm-3 and subject to a gravitational acceleration of 9.80665 in sec-2.
3.2.4 Base pressures for various layers
With Po used for Pb in equation (16) and using suitable values
of (Tm)b and Lm, the value of P is computed for 11,000 ml, the top of the tro-
posphere, the first atmospheric layer above sea level. This value of P, designated
by Pi', in turn becomes the value of Pb for use in computing the pressure within
and at the top of the next layer. In this way the values of 1,11, for each succes-
sive layer are determined. The value adopted in this MODEL for Po, i.e., 1,013.250
mb or 101,325.0 newtons m-2 (exact) is identical to that adopted by ICAO and other
prominent groups .31,46
/ Basic constant
/// Numerical constant
?
19
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?
It
S
3.2.5 Specific computational equations
The specific equations for computing pressure for each of ten
atmospheric layers (determined by ten molecular-scale temperature functions) are
as follows:
For 4,000.0 ms H 1 0.0 al,
[ JH288.160 - 6.500,00 x lo_
?15256h122318
.1 5.256,122,18
288.160
where
For 0.0
P Po
Pou atmospheric pressure at sea level, defined to?13e
101,325.0 newtons m-2, or 1,013.25 mb (exact)./.
m 1 in
H u 11,000 ml,
(16a)
Po (16b)
P u
5.256,122,18
[288.160 - 6.500,00 x 10-3HI
For 11,000 ms H .1 25,000 ms,
P x
where
288.160
pii
antilogio [(0.068,483,253,0 x 10-3)(H - 11,000.0)]
P11 u the pressure at 11 km' computed from equation
(16b).
For 25,000 ms 1 H 1 47,000 ms,
P25
/ Basic constant
141.660 + 3.000 00 x 10-3H I
216.660
11.388,264,73
CO
(17a)
(16c)
?
1
.t
1 . ,
I.1 - - .- --
20
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where
P25 = the flressure at 25 km' computed from equation (17a).
For 47,000 m1 H 53,000 m1,
P
147
P =
where
antilogio [ (0.052,492,682,3 x 10-3)(H - 47,000.0)]
P47 = the pressure at 41 kint computed from equation (16c).
For 53,000 m1 1 H 1 75,000 ml,
a
where
P53
[ 439.860 - 3.900,00 x 10-3H
282.660
8.760,203,64 '
-
(17b)
(16d)
4
P53 = pressure at 53 km' computed from equation (17b).
< <
For 75,000 m1 = H = 90,000 ms,
P75 I
P - (17c)
anti1og10 [(0.075,371,236,14 x 10-3)(H - 75,000.0)]
where
P7? = the pressure at 75 km' computed from equation (16d).
.
For 90,000 m1 1 H = 126,000 10,
21
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where
a
P90
[3.500,00 x 10-3H - 118.140]
196.860
9.761,369,77 '
P90 = the pressure at 90 km' computed from equation (17c).
For 126,000 ms H 175,000 ms,
2126
r
[10.000,0 x 10-3H - 937.140 ]
3.416,479,42
322.860
where
PI26 a the pressure at 126 kms computed from equation (16e).
For 175,000 mi H 500,000mf,
P175
=
5.890,481,75
[5.800,00 x 10-3F1 - 202.140 I
812.860
where
P175 = the pressure at 175 kms computed from equation (16f).
3.3 Density
3.3.1 Computational equation
(16e)
(3.6r)
(16g)
Atmospheric density at altitude H is readily computed from the
perfect gas law, equation (11), implicit in the barometric equation. With the
introduction of the molecular-scale temperature concept, equation (11) for
density in kg m.-3 becomes,
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1-
3
11? P 3.4831839,46 x 10- P .
"R TM
where
(18)
P mg atmospheric pressure in newtons m-2 (or sub x 102),
expressed by eouations (16a - 16g)and(17:: 170),
TM Is molecular scale temperature in ?K expressed by
equation (8) with its various values of LK.
The computational equation for p is left in terms of P and TM instead of in
terms of H, for to convert to the latter would revire ten different functions,
as in the case of Tm and P. The copputational equations of all other properties
of this MODEL will Be similarly expressed in terms of P or TM, rather than in
terms of H.
3.3.2 Sea-level value - ratio equation
Evaluating equation (18) at sea level yields the sea-level
value of density:
P 1-t
? 1.225,013,998 kg mr3, ,A1
where
Po sea-level value of PI
101,325.0 newtons m-2 (exact)/, and
(TM)0 ?, sea-level value of Tm, 288.16?K (exact)!
Dividing equation (18) by equation (18a) yields
p p (T00
? .
Po Po
3.4 Validity of the Basic Properties
The three basic properties of this atmospheric MODEL are rigorously
self-consistent through the perfect gas law and the hydrostatic equation, which
accounts for the variations of the effective acceleration of gravity with altitude,
(18a)
(18b)
/ Basic constant
Ill Derived constant
23
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1
through the use of geopotential. The user of these tables is warned that the
validity of the hydrostatic equation as well as some of the other classical
equations, in their simple forms, may decrease considerably at great altitudes.53
The uncertainties at high altitudes in most equations relating the variuus at-
mospheric properties, however, are perhaps small compared with the present uncer-
tainties at these altitudes in the defining property of this MODEL, T/M.
4. Secondary Properties Defined as Functions of T/M
. This section is devoted to all those atmospheric properties of the ABDO
MODEL ATMOSPHERE, except P and p, which are classically defined as functions
of the ratio T/M and which are, therefore, conveniently redefined in terms of
molecular-scale temperature without otherwise involving 11 or T explicitly.
(Some of the properties of this group depend also upon the acceleration of
gravity.) Properties which depend also upon P or p , or combinations of these,
are implicitly in this group. The properties of this group tabulated in this
MODEL are scale height, speed of sound, air-partiele speed (arithmetic average),
and specific weight.
4.1 Scale Height
4.1.1 Definition
If both sides of equation (12) are divided by dZ, we have
d in P -104
dz Rib/
(12a)
A dimensional analysis of the quantities in the right-hand side of this equation
show that the net dimensions are reciprocal meters. The reciprocal'of the right-
hand side of equation (12a), by virtue of its dimensions has been given the name
"scale height." Thus scale height as tabulated in this MODEL is defined as
where
R.*'T
H3 g 141
Hs = scale height in in (not ml),
g = acceleration of gravity in m sec-2,
and R*T and M have their usual
significance.
(19)
\
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4.1.2 Concepts
Using equation (19), equation (12a) may now be rewritten as
ln P -1
dz '
and scale height is seen to be the negative reciprocal of the slope of the
in P versus Z curve.
(12b)
The geometric-altitude-pressure equation for an isothermal
atmospheric layer may be manipulated to show that when gravity is considered to
be constant, the scale height at any altitude represents the vertical distance
above the reference altitude at which the atmospheric pressure has dropped to
a value of i/o of its value at the reference altitude. This concept for scale
height is often erroneously thought to apply to an atmosphere in which temper-
ature and gravity vary. A check of pressures and scale heights in the tropo-
sphere of this MODEL shows the scale height at sea level to be 8.4344 km. The
pressure, however, has dropped to Ve of its sea-level value at an altitude of
7.68 km, where the scale height is 7.0 km. Since this concept of scale height
is developed from the equation for an isothermal constant-gravity atmosphere,
the concept will not hold for other conditions.
From the same basic, isothermal, pressure-altitude equation one
may demonstrate that the scale height at any altitude is the length to which
the total of a unit cross-section column of the atmosphere above that point
would be compressed, if subjected to the pressure and gravity of that altitude.
That is, the reduced thickness of the residual) isothermal, constant-gravity
atmosphere above a given altitude, when subjected to the pressure of that alti-
tude, is equal to the scale height, Again this concept does not apply rigor-
ously anywhere in this MODEL since the atmosphere is not indefinitely isothermal
above any point, neither is the gravity constant.
4.1.3 Definition of geopotential scale height
The limitations imposed by constant gravity in the latter
two concepts of scale height can be eliminated through the use of a geopotential
scale height. If both sides of equation (13) are divided by dE, we obtain
d in P
dE
RThrm
(3.3a)
A dimensional analysis of the right-hand side of this equation shows the net
dimensions to be reciprocal geopotential meters. Thus the reciprocal of this
equation serves to define geopotential scale height:
25
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where
R*T
H a-,
G
E geopotential scale height in mIl and
a
1.1 9.80665 m2 sec-2 mt-1 .
4.1.4 Concept of geopotential scale height
The combining of equation(13a) and (13b) yields
d in p
dH Hat'
0
(13b)
(13c)
and the geopotential scale height is seen to be the negative reciprocal of the
slope of the In P versus H curve.
The manipulation of equation (15) (for a variable-gravity,.
isothermal atmosphere) leads to the conclusion that for a variable-gravity, iso-
tbermal atmosphere, the geopotential scale height at any altitude represents the
increment in geopotential above the reference altitude at which the atmospheric
pressure has dropped to a value of l/e of its value at the reference altitude.
Th1a. concept does apply rigorously to isothermal regions of this MODEL. Equation
(15) also leads to the conclusion that the geopotential scale height at any al-
titude is the reduced thickness in geopotential of the residual, isothermal,
variable-gravity atmosphere above a given altitude when subjected to the pressure
of that altitude. Even though this concept accounts for variable gravity, it
still is not rigorously applicable to the MODEL since no indefinite isothermal
atmosphere to great altitudes is speculated in this MODEL.
The geopotential scale height at any altitude is readily trans-
formed to a geometric length by adding the geopotential scale height to the
reference geopotential altitude and converting the resulting geopotential
measure to geometric altitude, by means of equation (6). Then the reference
geopotential altitude is converted to geometric altitude with the same equation.
Finally, the smaller geometric altitude is subtracted from the larger. The
difference is the equivalent geometric length for the geopotential scale height
at the reference altitude.
dhiie geopotential scale height is obviously the preferable
parameter from the point of view of using the several concepts in a variable-
gravity atmosphere, only geometric scale height from equation (19) will be
tabulated in this edition of the ARDC MODEL.
26
(I
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0
4.1.5 Computational equation for (geometric) scale height
Introducing TM from equation (7) into equation (19) leads to
the computational equation for He
Hs
is 267.039,63216
(19a)
4.1.6 Sea-level value and ratio equation
The sea-level value of H3 isobtained by evaluating equation
(19a) at sea level, such that
RNTI4)0 . 8
where
(113)0 140g0
.434,413,43 x 103 m
(3.9b)
(H3)0 is sea-level value of B:110
(T00 m. sea-level value of TIP ' 288 16?11 (exact),14.
go sea-level value of g, 9.806,65 in sec-2 (exact/
Dividing equation (19a) by (19b) yields
Hs Tm go
(H3)0 WO?Io g
which is an alternate form for computing values of Hs.
(19c)
4.1.7 Validity
Because the analytical expression for scale height is implicit
in the barometric equation, as is evident from equation (12), the validity of
the value of HsLat various altitudes depends directly on the validity of the
barometric equation. (Scale height from this consideration might also be con-
sidered one of the basic properties along with pressure and density.) The use
Basic constant
// Derived constant
1
?
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-s
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of the tabulated values of scale height, however, in connection with several
commonly accepted concepts of scale height is to be avoided except for rough
approximations.
4.2 Speed of Sound
4.2.1 Defining equation ?
The square of the speed of sound propagabion is defined in
this MODEL to be
where
2 VP
4?MMIONa. p
3 p
Cs = speed of sound in in sec-1
P = pressure in newtons n-2,
p Is density in kg m-3, and
(2o)
= ratio of specific heat of air at constant pressure
to the specific heat of air at constant plume,
defined to be 1.4 (dimensionless, exact))
4.2.2 Computational equation
Eliminating p between equations (18) and (20) and extracting
the square root results in:
where
4.2.3
Cs
Sea-level value
Evaluating
(03)0 -
YR
- 20.046,333,0 (TH)1. (20a)
ratio equation
(20a) at sea level yields
(TN). = 340.292,046 in (2ob)
Ho M
and
equation
[Ye
711:- ?
(C3)0 = sea-level value of C.
Basic constant
Derived constant
28
i
I'
I
t;
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uvUA:1--- 'L. 0
\-7 -
::!
?
Dividing equation (20a) by equation (20b) reduces the number of constants so
that:
Cs [ (TmTlifis
(Cs)0
4.2.4 Validity
(20e)
These equations for computing the velocity of sound apply
only when the sound wave is a small perturbation on the ambient condition.
Harrison24 has shown that even when this condition is met, the above definition
for the velocity of sound is not quite correct for two reasons: First, 7 is
not really a constant, but rather, varies with pressure and te-uperature over a
small region around the value 1.4; second, the form of the above relationship
is not completely correct, since even if the best value of 7 is used for a
given set of conditions, computed values of Cs differ slightly from experimen-
tally determined values. In spite of these discrepancies, however, the stated
relationships are adopted in accordance with Subcommittee recommendations43
which are in conformity with established aerodynamic practice but at variance with
the present United States Standard Atmosphere.
The limitations of the concept of velocity of sound due to
extreme attenuation are also of concern. This situation exists for high frequen-
cies at sea-level pressures and applies to successively lower frequencies as
atmospheric pressure decreases, or as mean free path increases. For this reason
the concept of speed of sound progressively loses its meaning at high altitudes,
except for frequencies approaching zero and for very short distances. To call
attention to this limitation, it was agreed to terminate at 90 km' the tabula-
tion of the velocity of sound, in the Extension to the United StaLes Standard
Atmosphere. In conformity with this agreement, tabulations in this MODEL are also
similarly terminated. Because of the relationship between sound velocity and
air particle speed (Section 4.3), sound velocities for altitudes above 90 km'
may readily be obtained for use with suitable caution.
4.3 Air Particle Speed (Arithmetic Average)
4.3.1 Concept
The mean air particle speed is the arithmetic average of the
distribution of speeds of all air particles within a given elemental volume.
This quantity has significance provided that the volume considered contains
a sufficiently large number of particles so that their velocities follow a
Maxwellian distribution, and provided that variations of p and T/M in any
direction are negligible within the volume element.
?
4.3.2 Defining equation
Arithmetic average of air particle speed is defined to be:
o 0
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where
?
(21)
1. air particle speed (arithmetic average) in m sec-1,
-1r 3.14.1,592,654 (dimensionless)&'
4.3.3 Computational
The introduction
yields the computation equation
4.3.4 Sea-level
Evaluating
'70 -
equation
of.Tm
for
plE!:TM
714.
value and
equation
8 RII
(T1do
Vs
m
ratio
(21a)
from equation (7) into equation (21)
27.035,909,86 (T1)1 (21a)
equation
at sea level leads to
458.942,035 m see-1 (21b)
7r No
[
where
e= sea-level value of
Equation (21a) divided by equation (21b) yields
[T
I. (To.
(21c)
4.3.5 Validity
On considering the restrictions applied to the volume element
for which we desire the value of V, it is evident that these restrictions come
# Derived constant
//,? Numerical constant
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...???????????? ?
into conflict with each other at high altitudes and the validity of the concept
of V decreases with altituda. It is uncertain whether or not the concept re-.
? tains reasonable significance at altitudes as great as 500 km. Nevertheless, as
in the case of pressures and densities, etc., values have been tabulated to
this altitude, 'on the basis that with suitable caution, such values are better
than no values.
4.3.6 Relationship to sound velocity
From a comparison of equation (20c) and equation (21c) it
is evident that
(cdo
Since values of Vflo are tabulated to 500 kat, values of 0.0/(05) and hence
values of C are readily available to the same altitude, even though their
significance is extremelYqUostiondble?
4.4 Specific Weight
4.4.1 Concept
(20
? The specific weight co of a body of uniform density at any
Partidular point in space is the weight per unit volume of that bed; at that
point. The weight per unit volume is equal to the mass per unit volume times
the acceleration of gravity., which in tura is equal to the density of the body
? times the acceleration of gravity, g. Since g is assumed to vary in this MOM
in accordance with equation (la), the specific weight of a body will vary pro-
portionately.
The density of the air mass also varies with altitude and
hence w is dependent upon two variables, p and g. This is at variance
with the procedure in the ICAO Standard Atmosphere in which specific weight is
? defined to vary only with p
. .
4.4.2 Defining and computational equation
In this NODEL specific weight is defined by
p g,
-
where
to mg specific weight in kg m7.2 sec-2 or newtons m73 (at any point),
p 1. density in kg m73 (at the point),
g acceleration of gravity in m sec-2 (at the point).
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-
- ;?L.
Eliminating p by means of equation (18) results in
g P 3.483,819,46 x lo-3g2 ?
R.81%? Tx
4.4.3 Sea-level value and ratio equation
where
(23a)
The evaluation of equation (23) and (23a) at sea level yields
in
14.,P
2 m ?-' 2' 12.013,283,5 kg m72sec-2, (23b)
Po -0 evil
we = sea-level value of ou $
go
... sea-level value of p p 1.225,014,00 kg m73,
= sea-level value of g, 9.806,65 (exact). /
Dividing equations (23) and (23a) by the appropriate portions of equation (23b)
results in:
tuo
P
P0 g0
P (Tm)4, g
NB -??=?????????? ??????? ?
Po Tx g
Introducing Ha from equation (19a) into the right-hand member of equation
(23c) leads to:
PM P
?
4.4.4 Validity
The validity of the values of w dcp ends only upon the
validity of the values of g and p which have already been discussed.
/ Basic constant
/X Derived constant
?
32
(23c)
(23d)
L.
_
t;
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?
S. Other Secondary Properties
The last group of properties of this ARDC MODEL ATMOSPHERE includes all
those properties considered in this MODEL which are defined by functions of
T and M, in forms different from T/M, so that these functions cannot be re-
defined in terms of molecular-scale temperature without the additional use
of either M or T in its independent form. This group includes molar volume,
number density, mean free path, collision frequency; coefficient of viscosity,
and kinematic viscosity, as well as temperature and molecular weight. Either
molecular weight or temperaturo must now be defined in terms of altitude be-
fore any of these remaining secondary properties can be computed. The molec-
Oar weight is the one specifically defined in this MODEL.
5.1 Molecular Weight
5.1.1 General definition
Molecular weight is defined to be dimensionless. On the
chemical scale* molecular weight (of a compound) is defined to be 16 times the
ratio of the average mass of a molecule of the compound to the average mass
of an oxygen atom, where both the oxygen and the compound are assumed to
have their natural distribution of isotopes, and where average is to be con-
strued as the arithmetic mean.
5.1.2 Concept applied to air
The definition of molecular weight includes the concept of
a mixture of the several isotopes of an atomic species and the resulting
mixture of similar molecules of different masses. Therefore, it is not un-
reasonable to extend the definition of molecular weight to include mixtures of
different kinds of molecules as in the atmosphere. Such an extension of the
basic definition is employed in this MODEL in establishing the concept of the
molecular weight of air.
The definitions of atomic or molecular weights on the physical scale
are more specific than the equivalent definitions on the chemical scale, in
that on the physical scale, the ratios are estabpshed with reference to the
ma9s of an atom of a specific oxygen isotope, 010. Because the mass of an
010 atom is less than the mass of an average oxygen atom, the atomic or
molecular weights on the physical vale are greater than on the chemical
scale by approximately the ratio 32.0087/32.0000 . When the physical scale
is used for expressing molecular weight, values of the universal gas constant,
R,*, and other constants must be proportionately changed.
33
ar1..A.161a:
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?
1
1
5.1.3 Molecular weight of air and mole defined
Molecular weight of air, M, is defined es 16 times the ratio
of the arithmetic mean mass of a single molecule of the air mixture to the
arithmetic mean mass of a single atom of oxygen in a natural mixture of the
several oxygen isotopes.
A kilogram mole of air is defined as a quantity of air having
a mass in kilograms numerically equal to the molecular weight of the air.
5.1.4 Sea-level and low-altitude value of molecular weight of air
The value of M at sea level is determined from an assumed
distribution of the several atmospheric constituents at sea level. In
accordance with the ICAO agreements the atmosphere of this ARDC MODEL is
assumed to be dry and to have the following, composition at sea level and at
all altitudes up to and including 20 km/. This model has assumed a continuation
of this composition up to 90 km'.
Constituent Gas
Mol. Fraction
Molecular Wei ht
1
1
i
Nitrogen (12)
Oxygen (02)
Argon (A)
Carbon dioxide (002)
Neon (Ne)
Helium (He)
Krypton (Kr)
Hydrogen(H2)
(H2)
Xenon (Xe)
Ozone (03)
(Rn)
Per Cent
mi 16.000
78.09
20.95
0.93
0.03
1.8 x 10-3
5.24 x 10:44
1.0 x 10-4
x 10-5
-6
8.0 x 10
1.0 x 10 -6
-18
6.0 x 10
28.016
32.0000
39.94/4
44.010
20.183
4.003
83.7
2.0160
131.3

148.0000Radon
222.
The above data yield a value of 28.966 (nondimensional) for the molecular
weight of air. In this MODEL the molecular weight of air at sea level, and for
ee
314
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c.7
-N-9 - 1
a considerable altitude above and below sea level, is defined as a constant. Thus
for -5,000 mf = H = 90,000 mf,
M = 28.966 . (24)
5.1.5 Molecular woight of air at high altitudes and
validity of the values
Atmospheric composition at high altitudes is thought to vary
considerably from that near sea level. The variation in composition may result
from dissociation of various molecules of the atmosphere as well as from dif-
fusive separation of molecules of various masses in a gravitational field.
While several theories describing these phenomena exist, there are only a few
data to support or disprove these theories. The choice of 90,000 mt as the
top of the region of constant composition is quite arbitrary but is as good as
any other current choice.
It is thought that the dissociation of 02 is the principal
factor in producing a change in molecular weight between 90,000 and 175,000 mi.
Rocket measurements of 02 concentration obtained by Byram, Chubb, and Friedman
provide partial support to this contension. Diffusive separation and the dis-
sociation of N2 is thought to dominate the variation of molecular weight of the
mixture of atmospheric gases above 175,000 ml .
Miller-39 combined these theories, assumptions, and data with
scale height gradients of this MODEL and computed molecular weights for specific
altitudes between 90,000 and 500,000 mt. A plot of these data versus altitude
suggested the possibility of approximating the graph with two analytical func-
tions. Campen of GRD developed the desired functions in the form of the fol-
lowing two equilateral hyperbolae which for this MODEL define molecuinr weight
from 90 to 500 km.
For 90,000 ml = H = 175,000 ml,
23.160,126,7 H - 1,757,856.05
M (24)
H - 78,726.25
For 175,000 mf = H 1 500,000 ml,
13.139,119,0 H 5'4,492.02
M = ? (214b)
H - 56,969.89
For purposes of defining other atmospheric properties, it is convenient to
35
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establish the the following rolationships:
where
M? 'Mil and
MI is a kilogram mole of air, a mass in kg numerically equal
to the molecular weight, and
MIo is the sea-level value of Ml.
Using equation (5), relating geopotential and geometric alti-
tude, equations (24), (24a) and (24b) are converted to the following in terms of
Z:
For -4,996.070,27 in Z.1 91,292.532,7 in,
M ? 28.966.
(25)
For 91,292.532,7 in
Z1 179,954.085 in,
23.170 552 5 z'- 779 899.46
Z - 79,713.475,7
(25a)
For 179,954.085 m
Z 1 542,685.673,
13.339.605,8 z 519,144.64
(25b) '
N
Z - 57,485.075,2
These equations yield results within ? 1% of Miller's values at all altitudes
except for a small region around 105 km where the analytical results are
about 3% higher than Miller's values.
5.2 Mol Volume
5.2.1 Concept and definition
"Ensity of the air at any altitude is expressed as the mass
per unit volume at that altitude. If the mass is that of a mole of air, the
related volume is that of a mole of air. Thus the mol velume of air is given
? by,
H,
36
(26)
0
I
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.where
v = the volume (in m3) of a mole of atmospheric gas at
a particular altitude,
p - the density (in kg m73) of air at the same altitude, and
?
MI = the kilogram molecular weight, the mass in kg of a
kilogram mole of air having the composition of this
altitude. (This mass is numerically equal to the molecular
weight defined by equations (24), (2)4a), and (24b). )
5.2.2 Computational equation
Eliminating p between equations (18) and (26) yields a
computational* expression for v in terms of basic properties and constants:
where
?M/TM M.1Tv
v = = 287.039,632,6
Mp
= universal as constpt, 8.314,39 x 103 joules
(o10 k
-1 1
j g- (exact)",
= sea-level value of mol9cular weight, 28.966
o
(dimensionless, exact)'
T = molecular scale temperature, in ?K, at the altitude
in questionl and
P = atmospheric pressure in newtons m-2 (or mb x 102).
* Values of v are not tabulated for various altitudes in this edition of
the MODEL but the equations are developed for use in the expressions for
number density and implicitly mean free path. It will be noted from a
comparison of equations (26c) and (28c) that vivo = Lao . Thus values of
v for any altitude are readily available from these tables.
/ Basic constant
37
(26a)
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where
5.2.3 Sea-level value and ratio equation
Equations (26) and (26a) evaluated at sea level yield:
2.16 . Imp? (r.14)0 . 23.645,444,1 m3,
- P
o o
(26b)
ve = the sea-level value of v,
M/0 = a mole of air at qqa level,
28.966 kg (exact)tt,
= sea-level value of p , 1.225,013,998 kg m-3,
(r14). a the sea-level value of TM, 288.16?K (exact)ii, and
Po a the sea-level value of P, 101,325.0 newtons m-2(exact)'f
From equations (24d), (26), (26a), and (26b) it is obvious that
v .Hi Po M TK Pe
-- . . . . ..P?T? ?
v a 200 P Ho (TM). P
5.2.4 Ice-point value
The (standard) ice-point value* of the volume of a mole of
gas is considered to be one of the basic physical constants. This value may
be computed by evaluating equation (27) at the ice point, i.e., at a temper-
ature of 273.160 K and a pressure of 101,325.0 newtons m-2 (1013.250 mb),
(26c)
IVINO (rM)i . 22.414,594,3 m3, /4
M P
o 0
(26d)
)1/
Basic constant
Derived constant
These conditions referred to as standard conditions by chemists are
not to be confused with the standard sea-level values of the standard atmos-
phere where the To a (T24)0 = 288.16 .
?
38
a
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where
vi = the ice-point value of v, and
(TH)i = the ice-point value of Tm = 273.16? K (exact)ti,
= the ice-point value of p y 1.292,283,037 from
the left-hand members of equation (264).
The above value of vi for a kilogram mole is in keeping with 22.4146 m3, the
value currently accepted outside of the realm of this standard. (The latter
is equivalent to 22,414.6 cm3 for a gram mole.)
5.2.5 Validity
The validity of the concept of molar volume at great altitudes
becomes vague because the volume becomes so large that density and molecular
weight cannot be assumed to remain constant throughout the volume and hence
the specified volume will most probably not contain exactly one mole of atmos-
pheric gases.
5.3 Number Density
5.3.1 Concept and definition
The number density of air is defined to be the number of
atmospheric particles per unit volume, considering only neutral or ionized
atoms or molecules. (Electrons and other subatomic particles are ignored.)
The number of particles contained in a mole of air is by definition Avogadrots
number. Thus Avogadrots number divided by the mol volume yields number den-
sity, i.e. :
where
(27)
n = atmospheric-particle, number density, at a specified
altitude, in w-3,
v = mol volume at that altitude in m3, and
N = Avogadrots number, 6:023,80 x 1026 (dimensionless, exact)IL 16,46
A more recent value of N might have been used but that would not be consistent
with the current values adopted by the National Research Counci1.46
/ Basic constant
?
0
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0K? a1J Ti
5.3.2 Computational equation ?
Introducing equation (26a) into equation (27) leads to that
computational form of the expression for number density in terms of basic
properties and constants:
?
obtains:
where
NMP
U_____u 2.00,595,21 x 102,4 --T--P
R A TX M T
(27a)
5.3.3 Sea-level value and ratio equation
Upon evaluation of equation (27) and (27a) at sea level, one
NM P
no . 1,17 00
2.547,552,07 x 1025 -3, (27b)
-o p*Ile (T..) m
- 0 -fro
n = the sea-level value of n,
= the sea-level value of v.
The manipulation of equations (27), (27a), and (27b) and ref-
erence to equations (26c) and (24d) show the following relationships to exist:
v P NO Ho CA00 P
---.i.--.?
v? 7... .
no
11 It X TM o
n
(27c)
5.3.4 Validity
In the form of equation (27) the validity of n would be
open to considerable question at high altitudes. In terms of equation (27a),
however, where all the parameters are defined at a point or within a volume
considerably crlAiler than v, the validity of n is probably limited principally
by the validity of the values of TM and M.
5.4 Mean Free Path
5.4.1 Concept and definition
Hean free path is the mean value of the distances traveled
by each of the molecules of a given volume between successive collisions with
other molecules of that volume, provided that a sufficiently large number of
140
?
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molecules are contained within the volume. It is usually considered necessary
that the volume be the cube of a length many orders of magnitude greater than
the mean free path. From kinetic theory and assuming a gas of uniform temper-
ature and density, the following expression for mean free path is developed:
L
./27Tcr4 n
where
(28)
L = mean free path in at at a particular altitude,
n = number density in m-3 at the same altitude,
= a numerical constant, 3.141,592,654 )1
cr a average effective collision diameter, taken
to be exactly 3.65 x 10-10 at for this MODEL;
This value of a is an arbitrarily adopted average of several published values.
5.4.2 Computational equation
Eliminating n between equation (27a) and equation (28) yields:
eniTH
mi714
L - 8.c50,460,475 x 10-5 (28a)
r0-2N110P
5.4.3 Sea-level value and ratio equation
The evaluation of equations (28) and (28a) at sea level
results in:
where
L, a 6.631,722,3 x 10-8at, (28b)
- vcr2 no IAINY2 NMoPo
Lo a sea-level value of
no a sea-level value of number density, 2.547,552,07 x 1025 m-3.
1? Basic constant
- - ?
41
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Equation (28a) divided by the right-hand member of equation
(28b) and the use of equation (2hd) leads to the following ratio equation:
L m C44)0 P
Lb 140 Tm Po
A comparison of equations (26c), (27c), and (28c) shows that:
L v
nn
0 X m (TM)0 . P
Lo vo n p ? 14.0 14:0 ? Tm Po
(28c)
(28d)
5.4.4 Validity
Equation (28) for mean free path is based on the concept
that temperature and density are uniform throughout a volume equal to the
cube of a length many orders of magnitude greater than the mean free path.
At 90,000 m: the mean free path is 2.5 cm. A length two orders of magnitude
greater than L would be 2.5 meters and a cube of this dimension is perhaps
approaching the smallest size cube which contains a sufficient number of
molecules at this altitude to rigorously apply the derivation of equation (28).
Temperatures and densities within this volume may certainly be considered con-
stant. At higher altitudes, however, this may no longer be true for the neces-
sary size cube.
In this NOEL, the value of L from equation (28) becomes 1
meter at 114,000 mt. A cube of length two orders of magnitude larger, a
100-meter cube, would have a change in density from top to bottom of about 1%.
This amount is considerably more than should be tolerated for the conditions
of rigorous validity of the equation for L. At an altitude of 210,000 ms,
the value of L is 1 kilometer; while at 390,000 r0, the value of L is 100
kilometers. Certainly at these altitudes the density is not uniform throuc:hout
a sufficiently large cube and the distance through which a molecule will travel
between successive collisions depends on its direction of motion. The value of
L from equation (28) for a given altitude requires that conditions along the
path of the molecule remain equal to those at the particular altitude. At high
altitudes this condition can only be met for those molecules moving in a horizon-
tal direction. For molecules moving vertically downward, the distance traveled
between collisions will be less than L, because the motion is into a region of
exponentially increasing density. For molecules moving vertically upward, the
distance traveled between collisions will be greater than L because the motion
is into a region of exponentially decreasing density. Some kind of average of
these directional mean free path lengths, considering all possible directions,
is suggested as a more general concept of mean free path at these altitudes.
An unpublished study at GRD shows that the horizontal mean free path, obtained
from equation (28), yields values which agree well with this newly suggested
mean free path concept to altitudes of about 220,000 ms. Above this altitude,
zr
_
?
' !
? '--
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LLLLLL. L
LLLOL.L.LLi ?
-
equation (28) should only apply to a horizontal mean free path.
5.5 Collisicn Freq.ency
5.5.1 Concept and definition
The average velocity of the molecules or atoms within any given
volume of air, divided by the mean free path of the molecules within that volume
yields the mean collision frequency of the molecules of that volume. That is,
any particular molecule in that volume will collide successively with other mol-
ecules at a mean rate given by the collision frequency. Analytically collision
frequency is defined by
where
to:
= the collision frequency in sec-1,
= the average particle velocity in m sec-1, and
L = the mean free path in in.
(29)
5.5.2 Computational equation
Equation (21a) for V divided by equation (28a) for L leads
v = iter2 N. [-41-?7R12 .
* Mt(T)2 3.358,306,019 x 107 (29a)
(Tm)i
5.5.3 Sea-level value and ratio equation
From the evaluation of equations (29) or (29a) at sea level
one obtains:
where
/7.0
Lo
= 02 N
Po
Mo t (T )2
mo
= 6.920,404,9 x 109 sec-1, (29h)
Vo 458.942,034 m sec-1,
Lo = 6.631,722,29 x 10-8 m.
C ra
1:3
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Equations (29), (29a) and (29b) permit the following ratio expression:
. Larra
Vo
v
Lo p Mo (TM)0 1 1.
Po H TM
f
5.5.4 Validity
(29e)
?
The validity of the value of v is limited principally
by the validity of L. Even with the broader concept of L suggested in Section
5.4.4, the value of L should not apply without restrictions above 220 to 250 km.
Similarly, values of v must not be used without caution above this altitude.
5.6 Temperature (Real Kinetic)
5.6.1 Concept and validity
Temperature in this MODEL is a measure of the kinetic energy
of the molecules and atoms comprising the atmosphere at any specified altitude.
Tabulated values most probably will not indicate the temperature of anybody
suspended in or passing through the region.
The determination of the value of atmospheric temperature, T,
at any given altitude, from conventional measuring techniques requires a knowl-
edge of molecular weight M of the air at thlt altitude. Without this knowledge of
molecular weight, the measurement yields only the value of TiM. Because values
of H have not been measured at high altitudes, the so-called temperature meas-
urements from rockets yield only the ratio TIN. This ratio, however, was shown
to relate the basic atmospheric properties of pressure, density, specific weight,
scale height, particle speed and sound speed. The altitude function of this
ratio, TIM, in the form of molecular scale temperature, TM, defines the altitude
functions of these properties.
With the establishment of the independent assumption regarding
the altitude function of molecular weight in Section 5.1, it is now possible to
specify values of T with the same degree of reliability as exists in the values
of N. These values of T will then permit the determination of the coefficient
of viscosity and kinematic viscosity from empirical expressions involving T.
5.6.2 Computational equation
The computational equation for real temperature follows di-
rectly from the definition of molecular-scale temperature in equation (7).
Thus,
T TM M .034,523,234,1 m ? TM ,
144
(30)
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^
where
T.= temperature (real kinetic, absolute scale)
at any specified altitude, and
TM = molecular scale temperature (absolute scale)
at that altitude.
5.6.3 Sea-level value and ratio equation
Equation (30) evaluated at sea level yields:
er
140 - 288.16? K (exact),/4
To (m 1do 7R-- - m)o
where
To = sea-level value of T, and
(T11)0 = sea-level value of TH defined to be
288.16? K (exact)' N
the division of equation (30) by (30a), one Obtains:
T Tm m
To (TM)o Ho
5.7 Coefficient of Viscosity
(30a)
(300
5.7.1 Concept
Viscosity of a fluid (or gas) is a kind of internal friction
which resists the relative motion between adjacent regions of a fluid. If two
very large parallel plates surrounded by a gas (at normal pressures) are moving
relative to each otner so that their separation remAins constant, experiments
show that the layer of gas directly at the surface of each plate is at rest with
respect to that plate. It has also been shown that each layer of gas exerts a
/ Basic constant
// Derived constant
?
\ !
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1_1?, 11,N? I
/
ii '1 I
drag on the neighboring layers so that there exists a velocity gradient normal
to the surface of the plates. If the plates are sufficiently close, the vel-
ocity gradient is constant. The relative motion of the plates is resisted by
a drag force proportional to the product of the area of the plates times the
normal velocity gradient of the fluid. The proportionality factor in this
relationship is known as the coefficient of viscosity IL . This proportionality
factor has been found to vary with the temperature of the gas, but to be inde-
pendent of the gas pressure within limited ranges of pressure. Various people
have contributed to the development of a theoretical expression for it from
kinetic theory and Chapman? has recently derived cumbersome formulas which ac-
curately represent the dependence of p. on the temperature, at least over the
range of 100-1500? K. Because of the complexity of the Chapman equations,
however, the values for coefficient of viscosity in this MODEL are computed
from the well-known empirical Suthgrland's equation, with coefficients as used by
the Rational Bureau of Standards.22
5.7.2 Computational equation
Sutherland's empirical equation for computing viscosity is
, 3/2
T + S
where
p.= viscosity in kg sec-1 m-1
(1 kg sec -1m 10 poise),
. 1.458 x 10-6 kg sec-1 ra-1 (?0-1 (exact)/
S = 110.4? K (exact),/
T = temperature in ?K .
5.7.3 Sea-level value and ratio equation
The sea-level value of p. is
where
9 Lo
Po a
(31)
/
=
To + 1.789,428,53 x 10-5 kg m-1 sec-
S
= 1.789,428,53 x 10-4 poise, 1 IF (31a)
ito = the sea-level value of it ?
To = the sea-level value of T.
/ Basic constant
46
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;.01 to,) V?A'j ?
[.
-
Equation (31) divided by equation (31a) yields the ratio equation:
T I3/2
116 To
5.7.4
Validity
[To + S]
T + S ?
(31b)
The users of this MODEL are cautioned that the value of the
coefficient of viscosity determined by equation (31) is open to question for
conditions of yery high and very low values of pressure and density. While
equation (31) suggests that the coefficient of viscosity is independent of pressure
and depends only on temperature, the measurement of /1 with an oscillating disk
viscometer indicates this situation to be true only within certain limits of pres-
sure, of the order of 2 to .1 atmospheres.
As the pressure decreases below .1 atmosphere; a point is
reached where begins to fall off with further decrease in pressure in a
manner which depends upon the size of the viscometer. This change in the de-
pendence of first occurs when the mean free path of air molecules becomes
some small fraction of a linear dimension characteristic of the apparatus or
other body. Such a dimension in the case of the viscometer would be the dis-
tance between plates.
As the pressure is decreased still further, a point is
reached when the mean free path becomes equal to or greater than this charac-
teristic dimension. At this point the viscous stress (drag force per unit area)
becomes directly proportional to the quadruple product of density of the gas,
velocity of the moving plates or other body, one-fourth the mean speed of the
molecules, and a function indicating the reflective properties of the surfaces.
This situation characterizes the "free-molecule region!' of the gas.
For pressures in between the free-molecule region and the region
characterized by independent of pressure, there exists for any partic-
ular viscometer a transition region where the coefficient of viscosity is
neither independent of pressure nor directly- proportional to it, and the rela-
tionship is rather difficult to treat theoretically. Studies indicate, however,
that as the dimensions of the viscometer are made larger, both the high and low
pressure boundaries of the transition region are moved to smaller values of
pressure. Thus by greatly increasing the size and plate separation of the vis-
cometer, the pressure region for which equation (31) yields satisfactory values
of p. is extended to very low values of pressure.
It may well be that this procedure can be extended until
the characteristic dimension becomes so great that appreciable differences in
density or temperature exist over a vertical distance equal to this dimension.
At this point, equation (31) would begin to become inaccurate regardless of
further increase in viscometer size. By dividing atmospheric density by the
47?
?
? e
?
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s'?L
?
density gradient at various altitudes, it maybe shown that 0.1 per cent
variation in density occurs over a vertical distance of 5 to 10 meters at
all altitudes below 130 km. Viscometers with plate separations of 10 meters
would be expected to yield values of p, consistent with equation(31) for
pressures as low as those found at 90 kilometers altitude.
Thus values of IL tabulated in this MODEL only from-5,000 ms
to 90,000 ms are probably reliable for suitable conditions over this entire
range of altitudes, but only when these conditions incltde body dimensions
which are sufficiently large. For altitudes above 40 km, each case ought
to be examined with caution before using the tabulated values of L. ?
5.8 Kinematic Viscosity
5.8.1 Definition and computational equation
Kinematic viscosity is defined as the ratio of the coef-
ficient of viscosity of a gas to the density of the gas. Analytically it is
expressed as:
where
-
17 1. kinematic viscosity of air in a2
p. coefficient of viscosity of air ix
kg sec-1 Er', and
? atmospheric density in kg a-3.
(32)
Because of the empirical nature of the expression for is and since no other
atmospheric properties of this MODEL depend upon /7 , the expression for 17
has not been transformed to an expression in terms of the three properties,
pressure, molecular-scale temperature, and molecular weight. Computations of .9
have been made directly front equation (32).
5.8.2 Sea-level value and ratio equation
Equation (32) evaluated at sea-level yields:
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where
-
alb
" `' 1460,741,29 x 104 m2 sec-1,
im sea-level value of
ite m. sea-level value of $
1.789,428253 x 10-5 kg m-1 sec-1, Ai
p = sea-level value of p,
e 1.225,01306 kg m-3. ki
From the division of equation (32) by equation (32a) and from equations
(7), (18b), and (31b), one obtains:
77 P
p? m
P Po I. To J L T + Si
(32a)
(32b)
5.8.3 Validity
The validity of the tabulated values of 77 is no better
than the validity of either p. or p . Within the altitude range of
tabulation of 17 , values of ? are the more uncertain and the use of
values of 72 should be subject to the same restrictions applied to the use
of .
Derived constant
149
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..r?-? ? ?
- ?????
5.9 Summary of Ratio Equations
Because of the coJtmon relationship of molecular-scale temperature or
real temperature and molecular weight to all the properties of this MODEL, the
ratio of these properties to their sea-level values are all interrelated in the
following multiple equation:
TM Po
?
(TN)0 P P
Hs
(15)0
2
2
i
g Po c Po [ V P
go o
s . ?
(Cs)0 P V*o
n g No no 14o L N0ve ri No T 24s.
m Lo m V .1.0 14 MI To P
(a go v M n
6. Metric Gravitational System of Units
6.1 Unconventional Form
(33)
In this MODEL, as in the ICAO Standard Atmosphere, the system of units
employing the dimensions of the TypeI gravitational system is not strictly a
gravitational system; rather, it is a form of absolute system employing the
names of gravitational units, (see Appendix J). In order that there be no con-
fusion between the kilogram force as used in this mccm, and the kilogram force
as used in a pure gravitational system of units, the following development is
presented.
6.2 Basic Concepts
All properties in this MODEL maybe expressed in terms of mass 0),
length., time t, and temperature T. The metric absolute system of mechanical
units, which has been employed throughout the discussion to this point, uses the
kilogram as the unit of mass, the meter as the unit of length, and the second
as the unit of time. The unit ef acceleration a, therefore, has the dimension
of m sec-2, while the unit of force F, expressed by Newton's second law as
F Pa , has the dimensions of kg m sec- and has been named the "newton."
The metric gravitational system of units is based on the kilogram force
kgf, meter, and second. These units through Newton's law imply a unit of mass
equal to the unit of force divided by the unit of acceleration, and having the
dimensions of kgf sec2 m-1, for which there is no specific, commonly used name.
The English counterpart of this unit of mass is the lug or lbf sec( ft-1.
50
r
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In its fundamental concept, the kilogram force is the force which
gravity exerts on a kilogram mass at the particular altitude and latitude under
copslieration, and the relationship between the absolute and the graviGational
system of units thus depends upon the location. For any fixed latitude, as
applied to this MODEL, the variations of gravity with altitude could be used to
i rigorously relate the kilogram mass and the kilogram force at various altitudes.
6.3 Modified Definition of the Kilogram Force
The drafters of the ICAO Standard Atmosphere, on which this MODEL
is based, have chosen not to follow the fundamental concept of the gravitational
system of units. They have in effect defined the kilogram force as the force
which gravity exerts on a kilogram mass at a location where g is equal to go,
i.e., at sea level and at 49 321 40" latitude. This definition makes the
kilogram force an absolute unit, and makes the resulting system of units aa
absolute system, employing only the dimensions, of a gravitational system. The
system might therefore be called an absolute-force, gravitational system of units.
In equation form, the definition of this absolute kilogram force in terms of the
kilogram mass is:
1. kgf = 9.80665 m sec-2 x 1 kg, (34)
or conversely,
1

1 kg . 9.80665 kgf sec2 n-1.
The dimensions of the right-hand side of equation (35) are these previously
associated with mass in the metric gravitational system. Thus it appears that
the metric units of mass in this absolute-force, gravitational system is
always exactly 9.80665 times as great as the kilogram mass.
(35)
6.4 Conversion from Absolute System
Since units of length, time, and temperature are the same in both
absolute and gravitational systems of units, only those properties of the
MODEL which inherently involve the dimensions of mass have different magnitudes
in the two ystems. Thus solving equation (35) for unity provides the neces-
sary factor for converting in either direction between the absolute system and
the absolute-force gravitational system of units:
1 = 9.80665 m sec-2 kg ke-1(exact). (36)
The factor required for converting from the absolute system to the pure grav-
itational system of units varies according to the geographic location and is
expressed by:
1
1 g kg kgr
Si.
(36a)
,r
1
"--?
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1:_Nry It it ._\/ LN JL. ,.411 V 0 S
_
where g is the acceleration of gravity in In sec-2 at the particular altitude
and latitude in question.
6.5 Properties Requiring Conversion
A dimensional analysis of the various properties of this MODEL in
terms of mass, length, and time :i.ndicates that only pressure, density, specific
weight, and coefficient of viscosity involve the dimensions of mass. Hence,
MI-These properties are expressia-differently in the two systems of units.
For each of these properties the conversion from the metric, absolute system to
the metric, absolute-force, gravitational system at any altitude is accomplished
by dividing the magnitude and dimensions of the property in the former system by
the right-hand side of equation (36), (which is equal to unity).
6.6 Converted Sea-Level Values
tar 'T) 1;i
The sea-level values of atmospheric pressure, density, specific weight,
and coefficient of viscosity in units of the metric, absolute-forcel gravitational
system are obtained by dividing the defined value of Po in newtons-4 and the right-
hand members of each of equations (18a), (23b), and (31a) respectively by the
right-hand side of equation (36). Thus:
101,325. nt
Po = = 10 332.2745 kgf m-2,
-1
9.80665 in sec-2 kg kgf
(37)
1.225,013,998 kg m-3 m-4,
. - .124,916,663 kgf sec2 (38)
9.80665 in sec-2 kg kgf-1
6 . 12.013,283,5 kg m-2 see-2
1.225,013X2 kgf m-3,
9.80665 In sec-2 kg kgf-1
1.789,428,53 x 10- kg m
see1
9.80665 in see-2 kg kg.17-1
- 6.7 Conversion for All Altitudes
= 1.824,709,28 x 10-6
kgf sec m-2
The ratios P/P pi/pc, , col% , and FL /?0 in the absolute
system of units, when multiplied by the respective sea-level values given
above, yield the values of P, p, w , and p. in the absolute-force, gravitational
52
.t.
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s? ?
system of units.*
7. Preparation of the Metric Tables
7.1 Computation of the Tables
The acceleration of gravity, molecular-scale temperature, pressure,
and molecular weight are the only properties which were computed directly as
functions of H alonej g in terms of a single function for all altitudes, TM
and P in terms of ten different functions for ten altitude regions respectively,
and 2.11 in terms of three different functions for three altitude regions respec-
tively. The remaining properties were. computed from expressions in terms of g,
TM, P, and M, W. in terms of T derived from TM and M. To have computed each
of the properties in terms of H alone would have required the development of
ten functions for each property, each function applying to a specific altitude
region.** Such a procedure would have been unwieldy, and would not have added
to the accuracy or validity of the tables. Even the stated computational equa-
tions for each of the properties, while serving well for isolated calculations,
do not necessarily represent the best approach for development of the tables.
From the multiple equation (33) it is evident that if the ratios of
certain basic atmospheric properties to their sea-level values are determined,
the remaining ratios are readily computed from products or quotients of not
more than two previously determined ratios. The tabulated ratios, when mul-
tiplied by the sea-level values of the respective properties in any desired
absolute system of unitsj then yield the required absolute tables.*"
7.2 Detailed Computational Procedure
The following procedure is suggested as one of the better methods
for use in any expansion or,revision of these tables by desk calculator
* For conversion to the pure gravitational system, these values in the
absolute-force, gravitational system of units would have to be multiplied
by go/g .
** A single function of altitude, closely approximating the densities of this
MODEL, particularly above 100 km, was developed by L. Jacchia33 of the
Astrophysical Observatory, Smithsonian Institute and is presented in
Appendix L.
*** The tabulation of properties in the absolute-force, gravitational system
employed in this MODEL is also made in this manner, although this proced-
ure would not apply to the pure gravitational units.
53
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techniques:
A. List all integral multiples of the desired increment of geometric al-
titude for which atmospheric properties are to be computed and determine
the corresponding values of geopotential altitude to nine significant
figures by means of equation (5).
B. List all integral multiples of the same increment of geopotential
altitude for which atmospheric properties are to be computed and determine
the corresponding values of geometric altitude to nine significant figures.
C. Combine the entries of lists compiled in steps A and B into a binele
list arranged in numerically ascending values of geopotential.
D. Compute values of g/go to nine significant figures for all tabulated
values of H by means of equation (la).
E. Compute values of TM in ?K to nine significant figures for all tab-
ulated values of H, using equation (8) and the values of LK tabulated in
Section 3.1.5 .
F. Compute values of TION), to nine significant figures for all tabu-
lated values of H, using the defined value of CrOop 288.16?K.
G. Compute values of [TM/(TM)0] I. to nine significant figures for all
tabulated values of H.
H. Compute values of P/Po to nine significant figures for all tabulated
values of H from equations (17a) through (17c), as each applies to its
respective altitude range.
I. Compute value of 14 to nine significant figures for all tabulated
values of H, using equations (20: (24a)? and (24b) as each applies to its
respective altitude region.
J. Compute values of 1.1/H0 to nine significant figures, using the defined
value of 140, 28.966.
K. Compute values of T in ?K to nine significant figures, and T/To for
all tabulated values of H above 90,000 mf, using equations (30) and (30b),
in terms of previously determined quantities. (Below 90,000 ms, T TM,
and T/To Tm/(Tu) ' ? hence T and T To need not be computed for this ,.al-
titude region.) o
?
L. Compute values of (T/T0)3/2 to nine significant figures for all
tabulated values of H up to and including 90,000 mt only. For this
511
3
i
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altitude region,
4
? ?
- - - - - -
(T/T0)3/2 as [Til(Vo] ? [TH/(TH)0
To S
it. Compute values of - T to nine significant figures for all tabulated
S
values of H up to and including 90,000 mt only, using S 110.4 ?X from
equation (31).
N. Using the previously established ratios and the following equations,
compute to nine significant figures the values of the eleven ratios of
atmospheric properties to their respective sea-level values, for all
tabulated values of H, except in the case of C3/(03)0, IL/140 $ and
which are computed only to 90,000
P (TI4)0
mt inclusivelys
P (18b)
Po
go
(190)
g
(20c)
(21c)
(23c)
(26c)
fle
H3
?
Tx
(Hs)o
C3
(TH)0
TMi*
(cs)o
ff
io
Tx 11
(Tx)0
g
0
1r
0
n
P0 go
it f,
?
MO P
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\ f
P: .
DO P0 M
[To + S
o T + S
ja.._ ?
P P.
3/2
To
_
(27e)
(28d)
(29c)
(31b)
(32b)
0. Compute the mks values of g, P, P $ Hs, Cs, V, U , n,
, p. $ and 17 to nine significant figures in the mks absolute
units by multiplying the tabulated values of g/go, P/Po and the
tabulated values of each of the eleven ratios listed under step N
respectively, by the following corresponding, sea-level values,
as they are basically defined or as they are derived by the
several equations, .sing the mks system of units.
= 9.80665 in sec-2, defined (Section 2.1.1)
288.16?K, defined (Section 3.1.5)
= 101,325 newtonsm-2, defined (Section 3.2.3)
= .76 m 144 defined (Section 3.2.3)
1.225,013,998 kg m-3 from equation (18a)
= 8.434,413,43 in R R (1%)
= 340.292,046 in sec-1 a a (20b)
* These properties are listed here only for completeness and are
not used in step 0 of the computational procedure since values
of TEL,H, and T have already been tabulated.
56
NO.
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r_L
VC
m sec from equation (21b) "1 458.942,035 -1
0)0 "1 12.013,283,5 kg 1072(23b) sec-2 u
Mc = 29.966, defined M N (24)
23.645,444,1 (26b)
n0 = 2.547,552,07 x 1025 m73 (27b)
Lb = 6.631,722,3 x 10-8m (28b)
v0 a 6.920,40 (29b)419 x 109 sec (29b)
28806
-o (30a)
/10 1.789,428,53 x 31)-5 ke sec-1 .11 (312.)
no . 1.460,741,29 x lo -5 .2 sec-1 (32a)
P. Compute the values of P, p ,(0 , and p in the mks, absolute-force,
gravitational units** to nine significant figures by dividing the tab-
ulated mks absolute values of these four properties by 9.80665 in sec-2
kg kgf-1 (exact) from equation (36). In principle this procedure is
equivalent to multiplying the tabulated values of P/Pc, ,
and /L //L by the following sea-level values in gravitational
units: ?
P = 10,332.274,5 kgf m72, from equation (37)
m .124,916,663 kgf se-02 mr4, M (38)
4) u 1.225,013,998 kgf m-3, n n (39)
0
- 1.824,709,28 x 10-6 kgf sec m-2. n n (4o)
Q. Independently repeat the entire procedure of steps A through P,
compare the two results, and account for any discrepancies.
* See footnote on page 56.
** The remaining atmospheric properties of this MODEL are numerically
and dimensionally equal in both mks systems tabulated.
57
4.
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7
J
-.:
R. Tabulate the corrected results to any desired number of significant
figures less than nine, with values of the ratios always given to one more'
significant figure than the values of the property itself.
7.3 Tabulations Presented
Of the sixteen properties discussed, only one, the mol-volume, is not
tabulated for other than sea-level values. In the present edition of the metric
tables, the values of pressure, density., specific weight, and coefficient of
viscosity are given only in the absolute system of units.
7.4 Significant Figures
The number of significant figures to which these tables might be
computed is limited only by the capabilities of the machine. The constants,
the defining properties, and the functional relationships are all specified as
being exact, and thus they do not limit the number of significant figures of
the tables. Such a procedure makes for internal consistency to any degree desired.
The choice of the number of significant figures tabulated in this MODEL resulted
from arbitrary decisions and does not in the slightest amount indicate the val-
idity of the values in depicting the actual atmosphere.
The sea-level values of the various properties are given to eight or
nine significant figures depending on whether the first significant figure is
greater than or less than 5. Tabulated values of geopotential and geometric
altitude are listed to the nearest meter or standard geopotential meter. Tabu-
lated values of g are given in six significant figures* and values of TM to five
significant figures for all altitudes. The values of the remaining properties
are given to five significant figures from -5,000 my to +75,000 mi. Above
75,000 in', the values of these properties are given to only four significant
figures. The ratios of the various properties to their respective sea-level
values are given to one more significant figure ,han the corresponding value
of the property.
7.5 Accuracy of Tabulations
The metric tables were prepared with the aid of desk calculators
from the equations developed above. The values of the atmospheric properties
discussed in Sections 3 and 14 were computed independently by two people and
any discrepancies in results were resolved. Any errors which may in the
tabulated values of these properties will be due to inaccurate copying. The
tables of properties in Section 5 have been computed only once and here some
possibility of computational error exists.
* A comparison with a more accurate method for computing g indicates that
the sixth significant figure is not meaningful for indicating the actual
effective gravity above about 49 km.
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8. Preparation of the English Tables
8.1 Conversion of Basic Units
- ? eeraLsaa?IL?meat.swietttaJJ tr.0?1,
The English tables of THE ARDC MODEL ATMOSPHERE are given in terms
of the foot (ft), pound (lb), second (sec), and degree Rankine (?R), each
of which is defined exactly in terms of the corresponding units employed in
the metric tables. The second, of course, is common to both the English and
metric systems of measurement. The foot and the pound are defined as follows:
1 ft = 0.3048 in (exact)* (41)
1 lb = 0.453,592,3 kg (exact)." (42)
The magnitude of the degree Rankine in terms of the degree. Kelvin is derived
from the defined relationship of the two temperature scales:
voR) . 1.8 T(olo (Ref. 60) (43)
where T(?R) is the absolute temperature in the thermodynamic Rankine scale.
From equation (43) one infers that
1?K = 1.8ctR (exact), (43a)
and from equations (41), (42), and (43a) respectively, one determines the
following three conversion factors:
1 = 0.3048 in ft-1 (exact) (41a)
1 = 0.453,592,3 kg lb-1 (exact)
(42a)
1 = 1.8?R (?K)-1(exact). (43b)
These three factors are sufficient to convert values of all atmospheric pro-
perties in the mks PK absolute system of units to the correct values in the
fps oR absolute system of units.
* "The round value has been accepted by the U.S. National Bureau of Standards
and the Commonwealth Standards laboratory as the common basis on which the
American and British representation of the 'foot' should be unified when neces-
sary legal provision is forthcoming." 26-28
** "This value is based on an informal understanding between the National Bureau
of Standards (Washington, D.C.) and the National Physical Laboratory (Teddington,
England) that this rounded quantity would be convenient if the English-speaking
nations could arrive at a u,ifrm basis of conversion from the metric to the
English system of units.".2 -20
59
0 v
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'
8.2 Other Necessary Conversions
8.2.1 'English absolut'e to English gravitational units
As in the metric system of units, the English gravitational
system employed in this MODEL is not a pure gravitational system where the
unit of force varies with the location in accordance with the value of g.
Rather, the unit of force, the pound force (lbf) is taken to be that force
which gravity exerts on a pound mass (lb) at a point where g has the standard
sea-level value of this MODEL, go. The definition of the pound force in equa-
tion form is
1 lbf = go x 1 lb.
Dividing the defined metric value of go by the conversion factor of
equation (41a) yields
Thus,
(1414)
9.80665
ft sec-2 (45)
go ' .3048
32.174,048,55 ft sec-2. (4511)
9
1 lbf =.80665 ------- ft 30e 41b.
.3048
(1414a)
Since force has the dimension of lbf, and acceleration is in
ft sec-2 by New-tents second law, mass must have the dimensions of lbf sec2 ft4.
This unit is called the slug. Solving equation (44a) for 1 lbf sec2 ft-1, one
ob+ains:
1 slug = 1 lbf sec2 ft-1 = 21826-6g lb
.3048
Thus we find that the slug, the unit of mass in the English (absolute-
force) gravitational system of units is exactly 9.80665/.3048 times as
large as 1 lb (masa The factor for converting back and forth between the
two Englsih systems of units employed in this MODEL is therefore:
(145)
or
. 9.80665 ft sec_2 lb 1bf-1 (46)
.3048
9.80665
1 = lb slug-1
.3048
60
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0
?
8.2.2 Metric gravitational to English gravitational units
The combining of equations (35), (42a), and (h5) yields the
following direct relationship between the metric and English gravitational
units of mass:
1 slug = 1 (lbf sec2 ft-1) . .453,592,3 (kgf 2 -1%
.3o48 sec m J.
Dividing the two right-hand members of equation (47) respectively by the cor-
responding parts of equation (41a) yields
1 lbf = .453,592,3 kgf.
This equation provides the factor for converting directly between the two
gravitational systems of this MODEL:
1 = .453,592,3 kgf
8.2.3 Rankine-to-Fahrenheit scale and Kelvin-to Fahrenheit scale
conversions
The relationship of the thermodynamic Fahrenheit temperature
scale to the thermodynamic Rankine scale is established by the following def-
inition:
t (?F) - ti(?F) = T (?R) Ti(?R),
where ti(?F) is defined to be 32?F (exact)4, the ice-point temperature.
Using the definition of Ti in ?K (see Section 3.1.4)
equation (43), one obtains
and
Ti(?R) = 1.8 x 273.16 = 491.688?R.
Introducing equations (43) and (51) into equation (50) yields
t (?F) = 1.8 (T?K - 273.16) + 32.
8.2.4 Standard geopotential meter to standard geopotential
foot
From equation (41) it follows directly that
1 std. geopotential foot (it') = 0.3048 x 1 std. geopotential meter
Thus the factor for converting mt to it' and vice versa becomes:
1 = 0.3048 in ftt -1(exact).
/ Basic constant
61.
?
(147)
(48) /
(149)
(52)
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8.2.5 Geometric meter to nautical mile
The defined conversion* from meters to the international
nautical mile (i n mi) in this MODEL is:
1 (i n mi) = 1,852 meters (exact). (54)
The conversion factor is therefore:
1 = 1,852 et (i n
(54a)
8.3 Sea-Level Values of Atmospheric Properties in English Units
By means of equation (43a) for TM or by the proper application of
equations (41a), (42a), and (43b) bo the mks, absolute, sea-level values of the
various other atmospheric properties listed under computational procedure, step 0
of Sectinn 7.2, the following sea-level values in English absolute units** are
derived. The English absolute values of P p0, coo, and p6 , when divided
by the conversion factor given in equation (16) yield the sea-level values of
these properties in the English (absolute-force) gravitational system.***
or
go
(TM)0
p
'0
po
32.174,048,55 ft sec-2, from equation (45a)
- 1.8(288.16?K) = 518.688?R
. 101,325 X .3048 = 68,087.266,9 lb ft-1 sec-2
(55)
(56)
(56a)
(56b)
.453,592,3 or poundals ft-2
. 101,325 x (.3048)2
= 2,116.216,95 lbf ft-2
.453,592,3 x 9.80665
.76 x 12
= 29.921,259,84 in Hg
.3048
* United States Department of Defense Directive 2045.1, 17 June 1954, directed
the adoption of the international nautical mile (equal to 1852 meters) as a
standard value with the Department oi DefeLe effective 1 July 1954.
** See Appendix J.
*** All remaining properties are numerically and dimensionally the same in both
systems.
62
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_
-
_
106 . 1.225,013,998 x (.3048)3
- .076,475,137,4 lb ft-3
.453,592,3
. 1.225,013,998 x (.3048)4 - 2.376,919,99 x 10-3 lbf sec2 ft44
.453,592,3 x 9.80665 or slugs ft-3 (57a)
(57)
(H3)0 . 8,434.413,43 1. 2.767,196,007 x 104 ft
.3048
(C2)0 241MA-46 . 1.116,443,720 x 103 ft sec-1
.30148
. 458.942,035 . 1.505,715,337 x 103 ft 3e2-1
.3048
6 . 12.013,283,5 x (.3048)2
2.460,51 ft
4,77 lb -2
.1153,592,3 sec-2
w . 12.013,283,5 X (.3048)3
.453,592,3 x 9.80665 - 7.647,513,72 x 10-2 lbf rt-3
Mo .g 28.966 (nondimensional) (unchanged)
. 23.645,444,08 . 835.030,977 rt3
0 (.3048)3
no .? 2.547,552,07 x (.3048)3 x 1025 - 7.213,864,115 x 1023
L
0 .3048
vo - 6.920,404,91 x 109
6.631,722,29x 10-8
2.175,761,906 x 10-7 ft
sec-1 (unchanged)
(58)
(59)
(6o)
(61)
(61a)
(62)
(63)
ft-3 (64)
(65)
(66)
. 1.789,428,53 x .3048 x 10-5 . 1.202,440,640 x 1051b ft-lsec -1 (67)
.453,592,3
63
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-W ? \n--i C-9 0
-
_=1.1
'
n ..1.789,428,53 x (.30118)2x lo -5 . t
'16 - 3.737,299.76 x 10-7 lbf sec ft-2 (67a)
.453,592,3 x 9.80665
r ;
no ? ?.?.?
1! 4602 741? 29 x 10--'
= 1.572,328,83 x 10-4 ft2 sec-1 (68)
(.3048)2
1'
!?I
It is to be noted that. only three exactly defined numerical constants Here employed
in all the above conversions. Hence the English values may reliablY (melted to
any number of significant figures consistent with the metric absolute talus.
8.4 Calculation of the English Tables
8.4.1 Functions employed
This MODEL ATMOSPHERE is defined exactly in terms of various
gradients of molecular-scale temperature in 0K m1-1 between specific exact values
of altitude expressed in and in terms of constants defined exactly in metric
units. These definitions cannot be converted exactly to English units. Thus it
is preferable to compute English tables from exactly-the same equations used
for the metric tables, after first making the necessary conversion of the English
altitudes to metric altitudes, and then obtaining the English values of the various
* properties by another conversion.
8.4.2 Altitude increments
The argument of the English tables, similar to the metric tables,
is given in. consecutive integral multiples of a fixed altitude increment in both
geometric feet and standard geopotential feet, i.e.,
n x 2500 ft and n x 2500
where n -6, -5, -4, -3, -2, -1, 0, +1,2,3 'etc. to 24. From -15,000 ft' to
60,000 it' the increment is 2500 ft or ft'; from 60,000 it' to 300,000 ft I, the
increment .18 10,000 ft or ft1; from 300,000 it' to 500,000 it', the increment is
25,000'ft or ft'; from 500,000 ft' to 1,000,000 ft', the increment is 50,000 ft
or ft'; and from 1,000,000 ft' to 1,700,000 ft.', the increment is 100,000 ft or
ft/.
8.4.3 Altitude conversions
In order to use identically the same equations for converting
between geopotential and geometric altitude for the English tables as was used
in the metric tables, these conversions must be made in metric units. Thus, to
convert the tabulated integral multiple values of ft to mg, multiply the altitudes
in ft by exactly .3048 m ft-1, from equation (41a), to. obtain the equivalent in
meters, and then convert the results to m1 by using equation (5). This value of ,
m1 is then converted to the equivalent in.ft1 by dividing by exactly .3048 at ft1-4'
Co
?
,
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To;11,.......swassane
from equation (53a). Starting with tabulated, integral, multiple values of It',
thp conversion to in' is directly by means of equation (53m). This value of ml
is then converted to in by means of equation (6), and the corresponding value
of ft is then obtained by means of equation (41a). Since the conversion factors
cited and the constants of equations (5) and(6) are all defined to be exact, the
conversions maybe carried to any desired number of significant figures.
8.4.4 Computational procedure
Having arranged in sequence the values of mt for each English
altitude to be tabulated, the computation of the tables proceeds exactly as
indicated in Section 7.2, steps D through 16 but stopping short of 0.
Compute the values of TN and T in 00 to nine significant
figures from the Kelvin values by means of equation (9). Compute the values
of Ty and T in oF to nine significant figures from the Kelvin values by using
equation (50).
Compute the values of the remaining properties in English
units from the multiplication of the ratios of the various properties determined
in step N by their respective sea-level values in tho desired English absolute and
absolute-force units.
8.4.5 Tabulated values
In this edition of the NODEL, only half of the properties dis-
cussed are contained in the English tables. The properties tabulated are those
designated by g, 12, p , Co, H, T, L, end"; . It should be noted that p and it
are given only in Type I, absolute-force, gravitational units, while P is given
not only in this system (lbf ft-2) but also in mb and in inches of Hg. Temper-
atures in the English tables are given in CIO, ?F, and ?R.
These tables were prepared from a single computation using
desk calculators; as the values have not been checked by independent calculations,
some chance of error exists.
Above 60,000 ft the altitude increments of the English tables
are conSiderably larger than the increments of thelnetric tables.
0
65
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9. Conclusions and Recommendations
The tables included in this report are based on the totality of the
available, reputable, atmospheric data from observations of the upper
atmosphere to 160 km, and above this al4tude, on estimates and theories
acceptable at the time of this writing, 1956, The Geophysics Research
Directorate, AFCRO, ARDC?believes that tIlese tables provide the best rep?
resentation of the properties of the upper atmosphere consistent with a
segmented, linear, temperature-altitude function.
It is recommended that these tables be used as the basis for all aircraft
and missile design work within ARDC and by its contractors.
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I
;?
?
Section 3.0
METRIC TABLES
OF THE
ABDO MODEL ATMOSPHERE, 1956
NOTE: Superscripzs appearing in the following
tables indicate the power of ten by which each
tabulated value should be multiplied.
t '
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? . .
?
3
METRIC TABLE I
TEMPERATURES AND MOLECULAR WEIGHT AS FUNCTIONS
OF GEOMETRIC AND GEOPOTENTIAI MaTUDE
I
ALTITUDE
TEMPERATURE
MOLECULAR SCALE
I REAL KINETIC
I;
MOLECULAR WEIGHT .1
Z,m
H,mt TM,
Tm/Tmo
T, ?K
T/To
M
mlmo
?
-5,000
-5,003.9
320.69
1.11287
-4,966.1
-5,000
320.66
1.11278
-4,000
-4,002.5
314.18
1.09028
-3,997.5
-4,000
314.16
1.09023
-3,000
-3,001.4
307.67
1.06770
-2,998.6
-3,000
307.66
1.06767
-2,000
-2,000.6
331.16
1.04513
-1,999.4
-2,000
301.16
1.04511
-1,000
-1,000.2
294.66
1.02256
- 999.8
-1,000
294.66
1.02256
o
o
288.16
1.000000
1,000
999.8
281.66
.974443
1,000.2
1,000
281.66
.974443
2,000
1,999.4
275.16
.954886
2,000.6
2,000
275.16
.954886
3,000
2,998.6
268.67
.932364
3,001.4
3,000
263.66
.932329
4,000
3,997.5
262.18
.909842
4,002.5
4,000
262.16
.909772
5,000
4,996.1
233.69
5,003.9
5,000
255.66
.887215
:88:77:77
6,000
5,994.3
249.20
6,005.7
6,000
249.16
.864659
7,000
6,992.3
242.71
.842273
7,007.7
7,000
242.66
.842102
8,000
7,989.9
236.23
.819788
8,010.7
8,000
236.16
.819545
9,000
8,987.3
229.74
.797265
9,012.8
9,000
229.66
.796988
10,000
9,984?3
223.26
.774778
10,016
10,000
223.16
.774431
11,000
10,981
216.78
.752290
11,019
11,000
216.66
.751874
12,000
11,977
216.66
.751874
12,023
12,000
216.66
.751874
13,000
12,973
216.66
.751874
13,027
13,000
216.66
.751874
14,000
13,979
216.66
?
14,031
14,000
216.66
:775511781714
67
23.966 1.00000
28.966 1.00000
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tAr,r_v 9
4J
METRIC TABLE I CONTINUED
ALTITUDE
1
MOLECULAR SCALE IREAL KINETIC i
0
MOLECULAR WEIGHT
ITEMPERATURE
TM' ?K
T14/T140
T?K
T/To
14/140
15,000 14,965 :.g:2 :.g127,14
15,035 28.966 1.00000
16,000 1.3:09,g0
216.66 .751874
16,040 16,000 216.66 .751874
17,000 16,955 216.66 .751874
17,046 17,000 216.66 .751874
18,000 17,949 216.66 .751874
18,051 18,000 216.66 .751874
19,000 18,943 036.66 .751874
19,057 19,000 216.66 .751874
20,000 19,937 216.66 .751874
...11
20,063 20,000 216.66 .751874 -,Il
21,000 20,931 216.66 .751874 -.4a &
21,070 216.66 .751874
+3
21,000 a 0
22,000 21,924 216.66 .751874 Ek
R4 a
0
..
22,076
22,000 216.66 .751874 22,917
P 0 0
0
23,000 216.66 .751874
e +3
+3 P.
23,084 23,000 216.66 .751874
24,000 !'
23,910 216.66 .751874
m ,11
O 0
24,091 24,000 216.66 .751874
4, 4.)
0 ???4 r4
O i
nzt 0
0
44 ., 4
43
,4 ri 0
24,902 216.66 .751874 4.3.
25,000 43
'W m
t4 s4
0
25,099 2:g 216.66 .751874
$4 m
44 44
4,
26,000 219.34 .761182
44
o c..
1 $4
26,107 26,000 219.66 .762285 o
x ei. tv4
z
27,000 26,886 222.32 .771507
03 0
27,115
27,000
222.66 .772696
28,000 27,877 225.29
.781828
28,124 28,000 d
0
1
0
4.)
d
? X
225.66 .783107 N 4-)
29,000 28,868 228.26 .792146 2
co 4? ri
1 M
29,133 29,000 228.66 .793517 m 0
0
30,000 29,859 231.24 .802461 0
30,142 30,000
31,000 30,850 g1142. 2.3g
31,152 31,000 234.66 .814339
32,000 31,840 237.18 .823081
32,162 32,000 237.66 .824750
33,000 32,830 240.15 .833597
33,172 33,000 240.66 .835161
34,0040 33,819 243.12 .843689
34,183 34,000 243.66 .845572 28.966 1.0000o
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w- -Cur --419---91-E
-iL
-
METRIC TABLE I CONTINUED
ALTITUDE
TEMPERATURE
MOLECULAR SCALE I REAL KINETIC
Z,m
H,m '
T ?K
M'
Tm/Tmo
T, ?K IT/TO
35,000
35,194
36,000
36,205
37,000
37,217
38,000
38,229
39,000
39,241
40,000
40,253
41,000
41,266
42,000
42,279
43,000
43,293
44,000
44,307
45,000
45,521
46,000
46,335
47,000
47,350
48,000
48,365
49,000
49,381
50,000
50,396
51,000
51,412
52,000
52,429
53,000
53,446
54,000
54,463
34,808 246.09
35,000 246.66
35,797 249.05
36,000 249.66
36,786 252.02
37,000 252.66
37,774 254.98
38,000 255.66
38,762 257.95
39,000 258.66
39,750 260.91
40,000 -261.66
40,737 263.87
41,000 264.66
41,724 266.83
42,000 267.66
42,711 269.79
43,000 270.66
43,698 272.75
44,000 273.66
44,684 275.71
45,000 276.66
45,670 278.67
46,000 279.66
46,655 281.63
47,000 282.66
47,640 282.66
48,000 282.66
48,625 282.66
49,000 282.66
49,610 282.66
50,000 282.66
50,594 282.66
51,000 282.66
51,578 282.66
52,000 282.66
52,562 282.66
53,000 282.66
53,545 280.53
54,000 278.76
.853988
.855983
.864283
.866394
.874575
.876805
.884865
.887215
.895151
.897626
.905433
.908037
.915713
.918448
.925989
.928859
.936262
.939270
.946532
.949681
.956798
.960092
.967062
.970503
.977322
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.980913
.973535
.967379
-0
Sk
0
4'
R
.
P
?,-4
,--1
0
k
0
44
x
H
0
0
1
-.0
0
4.
R.
.
4S:
?,-1
4.,
,-i
s-,
0
41
0
EF
-----
z
E-4
0
1
?.
69
MOLECULAR WEIGHT
/4 M/Mo
28.966 1.00000
-1!
Declassified in Part - Sanitized Copy Approved for Re
50 -Yr 2014/03/20 ? CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20 CIA-RDP81-01043R002600070006-6
? I
ALTITUDE
Z,m H,m'
METRIC TABLE I CONTINUED
1TEMPERATURE
MOLECULAR SCALE REAL KINETIC'
T ,e1C 1 Tm/Tmo T, ?K IT/To ,
MOLECULAR WEIGHT
m/mo
55,000
54,528
276.70
.960230
55,480
55,000
274.86
.953845
56,000
55,511
272.87h4
.9-929
56,498
56,000
270.96
.940311
57,000
56,493
269.04
.933633
57,516
57,000
267.06
.926777
58,000
57,476
265.21
.920340
58,534
58,000
263.16
.913243
59,000
58,457
261.38
.907052
59,553
59l000
259.26
.899709
60,000
59,439
257.55
.893767
60,572
60,000
255.36
.886174
61,000
60,420
253.72
.880487
61,591
61,000
251.46
.872640
62,000
61,401
249.90
.867211
62,611
62,000
247.56
.859106
63,000
62,382
246.07
.853939
63,631
63,000
243.66
.845572
64,000
63,362
242.25
.840672
64,651
64,000
239.76
.83208
65,000
64,342
238.43
.827408
65,672
65,000
235.86
.818504
66,000
65,322
234.61
.814148
66,692
66,000
231.96
.804969
67,000
66,301
230.79
.800893
67,714
67,000
228.06
.791435
68,000
67,280
226.97
.787642
68,735
68,000
224.16
.777901
69,000
68,259
223.15
.774395
69,757
69,000
220.26
.764367
70,000
69,238
219.33
.761152
70,779
70,000
216.36
.750833
71,000
70,216
215.52
.747913
71,802
71,000
212.46
.737299
72,000
71,194
211.70
.734678
72,825
72,000
208.56
.723765
73,000
72,171
207.89
.721448
73,848
73,000
204.66
.710230
74,000
73,148
204.08
.708221
74,872
74,000
200.76
.696696
70
same as TM for altitudes up to 90 km'
S.
28.966 1.00000
0
altitudes
28.966 1.00000
-
Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20 CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
---
-
METRIC TABLE I CONTINUED
ALTITUDE
Z,m I H,m'
1 TEMPERATURE
MOLECULAR SCALE 1 REAL XINETIC
Tm,?K TmiTml o T,?K
1
TiT
MOLECULAR WEIGHT
mim
75,000
75,895
76,000
76,920
77,000
77,944
78,000
78,969
79,000
79,994
80,000
81,000
81,020
82,000
82,045
85,000
83,072
84,000
84,098
85,000
85,125
86,000
86,152
87,000
87,179
88,000
88,207
89,000
89,235
90,000
90,264
91,000
91,293
92,000
92,322
93,000
93,351
94,000
94,381
74,125
75,000
75,102
76,000
76,078
77,000
77,055
78,000
78,030
79,000
79,006
79,981
80,000
80,956
81,000
81,930
82,000
82,904
83,000
83,878
84,000
84,852
85,000
85,825
86,000
86,798
87,000
87,771
88,000
88,744
89,000
89,716
90,000
90,688
91,000
91,659
92,000
92,630
93,000
200.27
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
196.86
199.27
200.36
202.67
203.86
206.07
207.36
.694999
.683162
.683162
.683162
.683162
.683162
.683162
.683162
.683162-
.683162 .0
5:
.683162 0
.633162 43
.683162 R.
.683162
.683162 ,i
.683162 o
43
.683162 ?,4
4)
.683162 .-
d
.683162 s4
0
.683162 44
x
.683162 El
.683162 o
d
.683162
.683162 1
.683162 m
.683162
.683162
.683162
.683162
.683162
.683162
.683162
.683162 196.9
.691526 197.0
.695308 197.1
.703325 197.5
.707454 197.7
.715109 198.3
.719600 198.6
71
Ek
0
04
28.966 i.00000
constant at 28.966 for altitudes up to 90 kW
0
4-4
0
.68316
28.96
1=000
.68355
28.63
.98848
.68395
28.49
.98367
.68523
28.22
.97429
.68609
28.09
.96980
.68799
27.87
.96208
.68929
27.75
.95787
/.-
0
Declassified in Part - Sanitized Copy Approved for Release @
014/03/20 ? CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release
?
50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
-
-
- ... _ _ ' ? : .
.. ,....,,,, .-... . .............._?.....1.1."5..; .4'.......:....,-,---,.. ....., - .
. . .. -
.?
-...
. s
- _
. ?
1
METRIC TABLE I CONTINUED
;
ALTITUDE
TFMPERATURE
MOLECULAR SCALE I REAL KIIMC I MOLECULAR WEIGHT
4
i
Z,m
11,m`
TM, ?K
TM /TMo
T, 'K
T/To
M
WM?
95,000
93,601 209.46
.726902
199.3
.69163
27.56
.95147
95,411
94,000 210.86
.731746
199.8
.69334
27.45
.94751
96,000
94,572 212.86
.738691
200.6
.69597
27.29
.94217
96,441
97,000
95,000 214.36
95,542 216.26
.743892
.750477
201.2
202.0
.69e08
.70090
27.18
27.05
-93842
.953914.
97,472
96,000 217.86
.756038
202.7
.70340
26.95
.93038
98,000
96,512 219.65
.762258
205.5
.70632
26.84
.92661
98,503
97,000 221.36
.768184
204.4
.70920
26.74
.92322
99,000
97,482 223.05
.774037
205.2
.71215
26.65
.92004
99,534
98,000 224.86
.780330
206.2
.71541
26.56
.91680
100,000
98,451 226.44
.785811
207.0
.71833
26.48
.91412
100,566
99,000 228.36
.792476
208.0
.72196
26.39
.91102
101,000
99,420 229.83
.797582
208.9
.72481
26.32
.90876
101,598
100,000 231.86
.804622
210.0
.72881
26.24
.90578
102,000
100,389 233.22
.809549
210.8
.73155
26.18
.90387
102,631
101,000 235.36
.816768
212.1
.73592
26.10
.90103.
105,000
101,358 236.61
.8P1113
212.8
.73852
26.05
.89941
? k
103,663
102,000 238.86
.828914
214.2
.74325
25.97
.89665
104,000
102,326 240.00
.832873
214.9
.74568
25.93
.89531
104,696
103,000 242.36
.841061
216.3
.75078
25.86
.89265
105,000
103,294 243.39
.844629
217.0
.75302
25.82
.89154
105,730
104,000 245.86
.853207
218.6
.75848
25.75
.88897
106,000
104,261 246.78
.856382
219.1
.76051
25.72
.88806
106,764
105,000 249.36
.865353
220.8
.76633
25.65
.88557
107,000
105,229 250.16
.868131
221.3
.76814
25.63
.88483
107,798
106,000 252.86
.877499
223.1
.77432
25.56
.88241
Si
108,000
106,196 253.55
.879876
223.6
.77590
25.54
.88182
108,832
107,000 256.36
.889645
225.5
.78243
25.48
.87948
109,000
107,162 256.93
.891618
225.8
.78376
25.46
.87903
109,867
108,000 259.86
.901791
227.8
.79065
25.40
.87675
110,000
108,129 260.31
.903356
228.1
.79172
25.39
.87642
110,902
109,000 263.36
.913937
230.2
.79897
25.32
.87420
111,000
109,095 263.69
.915091
230.5
.79976
25.32
.87397
111,937
110,000 266.86
.926083
232.7
.80738
25.25
.87182
112,000
110,06124 4 .07
.926822
232.8
.80789
25.25
.87168
['
I,.
112,973
113,000
114,000
114,009
111,000
270.36
270.45
273.83
273.86
.938229
.938549
.950273
.950375
235.1
235.2
237.5
237.6
.81586
.81609
.82435
.82443
25.19
25.19
25.13
25.13
.86958
.86952
.86749
.86747
I '1
s
111,026
111,992
112,000
72
leclassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20 ______
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
tt)C,7
"CIF co).- \II
\t
METRIC TABLE I CONTINUED
ALTITUDE
VWMATURE
MOLECULAR SCALE MAL RIEETZC
MOLECULAR WEIGHT
14 M/140
140,000
136,983
432.69
1.50157
143,153
140,000
462.86
1.60626
145,000
141,766
480.52
1.66755
148,385
145,000
512.86
1.77978
150:o00
146,542
528.28
1.83329
153,625
150,000
562.86
1.95329
155,000
151,311
575.97
1.99877
158,874
155,000
612.86
2.12680
1601,000
156,072
623 58
2.16399
164,131
160,000
662.b6
2.30032
165,000
160,826
671.12
2.32897
169,397
165,000
712.86
2.47383
170,000
165,572
718.58
2.49369
174,671
170,000
762.86
2.64735
175,000
170,311
765.97
2.65815
179,954
175,000
812.86
2.82086
180;000
175,043
813.11
2.821711
185,000
179,768
840.52
2.91684
185,245
180,000
841.86
2.92150
190,000
184,486
867.88
3.01179
190,545
185,000
870.86
3.02214
195,000
189,196
895.20
3.10660
195,854
190,000
899.86
3.12278
200,000
193,899
922.48
3.20127
201,171
195,000
928.86
3.22342
205,000
198,595
949.71
3.29579
206,497
200,000
957.86
3.32406
210,000
203,284
976.91
3.39016
211,831
205,000
986.86
3.42469
215,000
207,966
1004.1
3.48440
217,175
210,000
1015.9
3.52533
220;000
212,641
1031.2
3.57849
222,526
215,000
1044.9
3.62597
225,000
217,308
1058.2
3.67243
227,887
220,000
1073.9
3.72661
230,000
221,969
1085.3
3.76624
233,256
225,000
1102.9
3.82725
235,000
226,622
1112.3
3.85990
238,634
230,000
1131.9
3.92789
714
362.7
387.2
401.4
427.6
440.0
467.9
478.5
508.2
516.8
548.4
555.1
588.6
593.2
628.8
631.3
669.0
669.1
679.7
680.2
690.4
691.6
701.3
703.1
712.2
714.8
723.2
726.5
734.3
738.3
745.4
750.3
756.6
762.3
767.8
774.3
779.1
786.5
790.4
798.6
1.2588
24.28
.83835
1.3435
24.23
.83644
1.3931
24.20
.83541
1.4837
24.15
.83366
1.5269
24.13
.83288
1.6237
24.08
.83127
1.6604
24.06
.83069
1.7635
24.02
.82919
1.7935
24.01
.82878
1.9032
23.97
.82737
1.9263
23.96
.82709
2.0428
23.92
.82575
2.0587
23.91
.82558
2.1823
23.88
.82432
2.1909
23.87
.82424
2.3217
23.84
.82303
2.3220
23.84
.82290
2.3588
23.42
.80869
2.3606
23.41
.80802
2.3960
23.04
.79555
2.4001
23.00
.79418
2.4336
22.69
.78337
2.4401
22.63
.78138
2.4715
22.36
.77204
2.4804
22.29
.76951
2.5097
22.06
.76149
2.5212
21.97
.75846
2.5481
21.77
.75162
2.5622
21.67
.74816
2.5867
21.50
.74238
2.6036
21.39
.73854
2.6256
21.25
.73371
2.6452
21.13
.72953
2.6645
21.02
.72555
2.6871
20.89
.72106
2.7037
20.79
.71787
2.7292
20.66
.71310
2.7429
20,58
.71062
2.7715
20.44
.70561
Declassified in Part - Sanitized Copy Approved for Release @
0 4/03/20 ? CIA R-DP81-01043R002600070006-6
D I
-s
?
?
III ?
-
?
RI
0-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
METRIC TABLE I CONITNUED
ALTITUDE
TEMPERATURE
MOLECULAR SCALE REAL KINETIC
MOLECULAR WEIGHT
11,m1
TM: ?K
Tm/Tmo
T,?K
T/To
240,000 231,268 1139.2 3.95342 801.7 2.7823
244,021 235,000 1160.9 4.02853 810.9 2.8140
245,000 235,908 1166.1 4.04680 813.1 2.8218
249,417 240,000 1189.9 4.12916 823.2 2.8567
250,000 240,540 1193.0 4.14003 824.5 2.8613
254,821 245,000 1218.9 4.22980 835.5 2.8995
255,000 245,165 1219.8 4.23313 835.9 2.9010
260,000 249,784 1246.6 4.32608 847.4 2.9407
260,235 250,000 1247.9 4.33044 847.9 2.9425
265,000 254,395 1273.4 4.41890 858.8 2.9804
265,657 255,000 1276.9 4.43108 860.3 2.9856
270,000 258,999 1300.0 4.51157 870.3 3.0202
271,088 260,000 1305.9 4.53172 872.8 3.0289
275,000 263,597 1326.7 4.60411 881.8 3.0600
276,528 265,000 1334.9 4.63236 885.3 3.0722
280,000 268,187 1353.3 4.69650 893.3 3.0999
281,977 270,000 1363.9 4.73300 897.8 3.1157
i 285,000 272,7711379.9 4.78876 904.8 3.1398
275,000 1392.9 4.83363 910.4 3.1592
287,435
290,000 277,347 1406.5 4.88088 916.3 3.1797
11 292,902 280,000 1421.9 4.93427 922.9 3.2029
295,000 281,917 1433.0 .97286 927.8 3.2197
4
1
298,377 285,000 1450.9 5.03491 935.5 3.2466
300,000 286,480 1459.4 5.06470 939.3 3.2596
i
1 303,862 290,000
1479.9 5.13555 948.2 3.2905
305,000 291,036 1485.9 5.15640 950.8 3.2995
309,356 295,000
1508.9 5.23619 960.8 3.3344
11 310,000 295,585 1512.3 5.24797 962.3 3.3395
1 4 314,859 300,000 1537.9 5.33683 973.5 3.3783
1 1 320,000 304,663 1564.95.?30w h g
9 985.3 3.4194
i 325,893 310,000 1595.9 5.53810 988.9 3.4665
330,000 313,714 1617.4 5.61286 1008 ? 3.4993
I 336,963 320,000 1653.9 5.73938 1024 3.5549
340,000 322,738 1669.7 5.79449 1031 3.5791
I 348,069 330,000 1711.9 5.94066 1050 3.6435
75
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr
0.
mAto
20.39
.70377
20.23
.69853
20.20
.69729
20.04
.69184
20.02
.69114
19.86
.68550
19.85
.68530
19.69
.67975
19.68
.67950
19.54
.67447
19.52
.67379
19.39
.66943
19.36
.66837
19.25
.66463
19.21
.66321
19.12
.66005
19.07
.65829
18.99
.65566
18.93
.65359
18.87
.65146
1St
.64911
18.
.64744
18.68
.64482
18.64
.64359
18.56
.64072
18.54
.63989
18.45
.63679
18.43
.63634
18.34
.63302
18.24
.62964
18.13
.62593
18.06
.62344
17.94
.61938
17.89
.61767
17.77
.61331
I.
8 01043R002600n7nnnR_R
Declassified in Part - Sanitized Copy Approved for Release
? -,
?
50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
METRIC TABLE I CONfINUED
- ?
.. ?
ALTITUDE
TEMPERATURE
MOLECULAR SCALE I REAL KINETIC
Z,m
H, m'
?K
Tm/Tmo
T,?K
T/T
MOLECULAR WEIGHT
)4 IM/Mo
350,000
559,215
331,735
540,000
1721.9
1769.9
5.97558
6.14194
1,054
1,075
3.6588
3.7322
31.7:t
7
360,000
340,705
1773.9
6.15613
1,077
3.7385
17.59
370,000
349,648
1825.8
6.33614
1,100
3.8181
17.45
370,394
350,000
1827.9
6.34321
1,101
3.8212
17.45
380,000
358,565
1877.5
6.51561
1,123
3.8975
17.33
381,612
360,000
1885.9
6.54449
1,127
3.9103
17.31
390,000
367,456
1929.1
6.69456
1,146
3.9768
17.21
392,867
370,000
1943.9
6.74577
1,153
3.9996
17.17
400,000
376,320
1980.5
6.87297
1,169
4.0560
17.09
404,160
380,000
2001.9
6.94704
1,178
4.0889
17.05
410,000
385,158
2031.8
7.05086
1,192
4.1351
16.99
415,491
390,000
2059.9
7.14832
1,204
4.1784
16.93
420,000
393,970
2082.9
7.22823
1,214
4.2140
16.89
426,860
400,000
2117.9
7.34960
1,230
4.2680
16.82
430,000
402,756
2133.8
7.40507
1,237
4.2928
16.79
438,267
410,000
2175.9
7.55087
1,256
4.3577
16.72
440,000
411,536
2184.7
7.58139
1,260
4.3713
16.70
449,713
420,000
2233.9
7.75215
1,282
4.4475
16.62
450,000
420,250
2235.3
7.75719
1,282
4.4498
16.62
460,000
428,959
2285.8
7.93247
1,305
4.5280
16.53
461,197
430,000
2291.9
7.95343
1,307
4.5374
16.52
470,000
437,642
2336.2
8.10725
1,327
4.6061
16.46
472,721
440,000
2349.9
8.15471
1,333
4.6273
16.44
480,000
446,300
2386.4
8.28151
1,350
14.6840
16.38
484,283
450,000
2407.9
8.35598
1,359
4.7173
16.35
490,000
454,932
2436.5
8.45526
1,372
4.7618
16.31
495,884
14.60,0002465.9
8.55726
1,385
4.8074
16.27
500,000
463,540
2486.4
8.62851
1,394
4.8393
16.25
507,525
470,000
2523.9
8.75854
1,411
4.8976
16.20
510,000
472,122
2536.2
8.80125
1,417
4.9167
16.18
519,205
1180,000
2581.9
8.95981
1,437
4.9877
36.12
520,000
480,679
2585.8
8.97348
1,439
4.9939
16.12
530,000
489,212
2635.3
9.14522
1,461
5.0709
16.06
530,925
490,000
2639.9
9.16109
1,463
5.0780
16.06
540,000
497,719
2684.6
9.31646
1,484
5.1489
16.01
542,686
500,000
2697.9
9.36237
1,489
5.1683
15.99
76
:234.7
.60728 1
.60259
.60241
.59818
.59750
.59404
.59290
.59014
.58859
.58647
.58454
.58299
.58072
.57971
.57712
.57659
.57372
:Ngg
.57050
.56815
.56744
.56560
.56455
.56317
.56179
.56085
.55918
.55864
.55668
.55651
.55448
.55430
.55266 1
.55203
1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-0104riRnn9snnn7nrma a
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
---
VEURIC TABLE II
PRESSURE, DENSITY AND ACCELERATION OF GRAVITY AS FUNCTIONS
OF GEOMETRIC AND GEOPOrENTIAL ALTITUDE
ALTITUDE
PRESSURE
DENSITY
ACCElEiRATICif
OF GRAVITY
Z,m
H,m'
P,mb
P/Po
p ,kg1m31
g,misec I ego
-5,000
-5,003.9
1.7776+3 1.75438
1.9312 1.57644
9.82210 1.001575
-45996.1
-5,000
1.7769 1.75365
1.9305
1.57591
9.82209
1.001574
-4,00.0
-4,002.5
1.5960 1.57515
1.7698
1.44472
9.81901
1.001260
-3,997.5
-4,000
1.5956 1.57469
1.7694
1.44437
9.81900
1.001259
-3,000
-3,001.4
1.4297 1.41104
1.6189
1.32157
9.81592
1.000945
-2,998.6
-3,000
1.4295 1.41082
1.6187
1.32140
9.81591
1.000944
-2,000
-2,000.6
1.2778 1.26112
1.4782
1.20667
9.81283
1.000630
-1,999.4
-2,000
-1.2777 1.2610
1.4781
1.20660
9.81282
1.000629
-1,000
-1,000.2
1.1393 1.12441
1.3470
1.09960
9.80774
1.00015
- 998.8
-1,000
1.1393 1.12439
1.3470
1.09958
9.80774
1=0315
o
1.01325+3 1.00000
1.2250
1.00000 9.80665
1.000000
1,000
999.8
8.9876+2 8.87008-1
1.1117
9.074771 9.8056
.9996854
1,000.2
1,000
8.9875 8.86994
1.1117
9.07464 9.8056
.9996854
2,0100
1,999.4
7.9501 7.84615
1.0066
8.21671 9.80048
.9993710
2,000.6
2,000
7.9495 7.84556
1.0065
8.21622 9.80048
.9993708
3,000
2,998.6
7.0121 6.92039
9.0926-1
7.42243 9.79740
.999068
3,001.4
3,000
1.0108 6.91917
9.0913
7.42137 9.79740
.9990563
4,000
3,997.5
6.1660 6.08537
8.1935
6.68847 9.79432
.9987427
4,002.5
4,000
6.1640 6.08339
8.1913
6.68671 9.79431
.9987419
5,000
4,996.1
5.4048+2 5.33413-1
7.3643-1
6.01161-1 9.79124
.9984287
5,003.9
5,000
5.4020 5.33133
7.3612
6.00906 9.79123
.9984275
6,000
5,994.3
4.7217 4.65998
6.6011
5.38859 9.78816
.9981149
6,005.7
6,000
4.7181 4.65635
6.5969
5.38519 9.78815
.9981131
7,000
6,992.3
4.1105 4.05676
5.9002
4.81643 9.78509
.9978013
7,007.7
7,000
4.1060 4.05233
5.8950
4.81216 9.78506
.9977988
8,000
7,989.9
3.5651 3.51851
5.2578
4.29206 9.78201
.9974877
8,010.1
8,000
3.5599 3.51339
5.2516
4.28701 9.78198
.9974846
9,000
8,987.3
3.0800 3.03977
4.6706
3.81270 9.77894
.9971744
9,012.8
9,000
3.0742 3.03401
4.6634
3.80685 9.77890
.9971704
10,000
9,984.3
2.6500+2 2.61532-1
4.1351-1
3.37554-1 9.77587
.9968612
10,016
10,000
2.6436 2.60903
4.1270
3.36896 9.77582
.9968562
11,000
10,981
2.2700 2.24030
3.6480
2.97792 9.77280
.9965481
11,019
11,000
2.2632 2.23358
3,6391
2.97069 9.77274
.9965421
12,000
11,977
1.9399 1.91455
3.1193
2.54637 9.76973
.9962352
12,023
12,000
1.9330 1.90774
3.1082
2.53731 9.76966
.9962281
13,000
12,973
1.6579 1.63626
2.1659
2.17624 9.76666
.9959224
13,027
13,000
1.6510 1.62943
2.6548
2.16716 9.76658
.9959140
14,000
13,969
1.4170 1.39849
2.2785
1.86001 9.76360
.9956098
14,031
14,000
1.4102 .1.39172
2.2675
1.85100 9.76350
.9956001
77
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr
3/20. -
1 043R0n7Annn7nnnR_R
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
"
J
METRIC TABLE II CONTINUED
ALTITUDE I PRESSURE
DENSITY
ACCELERATION
OF GRAVITY
11
Z,m R,mi 1_ P,mb P/P0 p,kg/m3 p/p,?
----
15,000 14,965 1.2112+2 1.19533-1 1.9475-1 1.58980-1
15,035 15,000 1.2044 1.18869 1.9367 1.58097
16,000 15,960 1.10353 1.02173 1.6647 1.35891
16,040 16,000 1.0287 1.01528 1.6542 1.35033
17,000 16,955 8.8496+1 8,73388-2 1.4230 1.16162
17,046 17,000 8.7866 8.67167 1.4129 1.15334
18,000 17,949 7.5652 7.46623 1.2165 9.93016-2
18,051 18,000 7.5048 7.40662 1.2067 9.85088
19,000 18,943 6.4674 6.38285 1.0399 8.48925
19,057 19,000 6.4099 6.32611 1.0307 8.41379
20,000 19,937 5.5293+1 5.45694-2 8.8909-2 7.25779-2
20,063 20,000 5.4748 5.40323 8.8034 7.18634
21,000 20,931 4.7275 4.66564 7.6016 6.20534
21,070 21,000 4.6761 4.61498 7.5191 6.13797
22,000 21,924 4.0420 3.98918 6.4995 5.30565
22,076 22,000 3.9940 3.94173 6.4222 5.24255
23,000 22,917 3.14562 3.41101 5.5575 4.53667
23,084 23,000 3.4113 3.36670 5.4853 4.47774
24,000 23,910 2.9554 2.91677 4.7522 3.87934
24,091 24,000 2.9137 2.87555 4.6851 3.82451
25,000 24,902 2.5273+1 2.49428-21: 3.31742-2
25,099 25,c00 2.4886 2.45606 1:(26-2 3.26658
26,000 25,894 2.1632 2.13493 3.4359 2.80476
26,107 26,000 2.1278 2.10001 3.3748 2.75490
27,000 26,886 1.8555 1.83126 2.9077 2.37361
27,115 27,000 1.8233 1.79943 2.8528 2.32877
28,000 27,877 1.5949 1.57407 2.4663 2.01332
28,124 28,000 1.5655 1.54504 2.4169 1.97296
297000 28,868 1.3737 1.35573 2.0966 1.71147
29,133 29,000 1.34 N? 69 1.329 2.0521 1.67520 .
30,000 29,859 1.1855+1 1.17002-2 1.7861-2 1.45803-2
30,142 30,000 1.1611 1.14592 1.7461 1.42540
31,000 30,850 1.0251 1.01167 1.5248 1.24472
31,152 31,000 1.0028 9.89735-3 1.4889 1.21538
32,000 31,840 8.8801+? 8.76402 1.3044 1.06478
32,162 32,000 8.6776 8.56423 1.2721 1.03840
33,000 32,830 7.7068 7.60604 1.1i80 9.12666-3
33,172 33,000 7.5224 7.42412 1.0390 8.88944
34,000 33,819 6.7006 6.61300 9.6019-3 7.83821
7.62473
34,183 311,coo 6.5307 6.44726 9.3404
?
78
g,misec2
g/go
9.76053
.9952973
9.76042
.9952862
9.75747
.9949849
9.75735
.9949723
9.75441
.9946728
9.75427
.9946585
9.75135
.9943607
9.75119
.9943448
9.74829
.9940448
9.74811
.9940311
9.74523
.9937371
9.74504
.9937174
9.74218
.9934255
9.74196
.9934038
9.73912
.9931140
9.73889
.9930902
9.73607
.9928027
9.73581
.9927767
9.73302
.9924916
9.73274
.9924633
9.72997
.9921805
9.72967
.9921498
9.72692
.9918697
9.72659
.9918365
9.72387
.9915589
9.72352
.9915232
9.72083
.9912484
9.72045
.9912099
9.71778
.9909379
9.71738
.9908967
9.71474
.9906276
9.71431
.9905835
9.71170
9.71124
.9902704
:999?049::77:
9.70866
9.70816
.9899573
9.70562
.9896977
9.70510
.9896443
9.70258
.9893879
9.70203
.9893314
Declassified in Part - Sanitized Copy Approved for Release 0 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
ta. -
l I I
METRIC TABLE II CONTINUED
?
?
,
II,
ACCELERATION
ALTITUDE
PRESSURE
DENSITY 11
OF GRAVITY
Z,m
H,m'
P,Mb J P/P0
p'kem3
PifPo I
1
g,m/sec2
gigs
35,000
34,808
5.8359+C)
5.75960-3
8.2619-3
6.74437-3
9.69955
.9890784
35,194
35,000
5.6829
5.60855
8.0265
6.55217
9.69896
.9890184
36,000
35,797
5.0914
5.02486
7.1221
5.81390
9.69651
.9887690
36,205
36,000
4.9519
4.88717
6.9101
5.64082
9.69589
.9887056
37,000
36,786
4.4493
4.39115
6.1507
5.02089
9.69348
.9884597
37,217
37,000
4.3221
4.26562
5.9597
4.86497
9.69282
.9883927
38,000
37,774
3.8944
3.84344
5.3209
4.34354
9.69045
.9881506
38,229
38,000
3.7785
3.72908
5.1489
4.20313
9.68975
.9830800
39,000
38,762
3.4142
3.36952
4.6112
3.76419
9.68742
.9878416
39,241
39,000
3.3084
3.26514
4.4560
3.63753
9.68669
.9877672
40,000
39,750
2.9977+0
2.95851-3
4.0027-3
3.26751-3
9.68439
.9875328
40,253
40,000
2.9013
2.86333
3.8629
3.15332
9.68362
.9874546
41,000
40,737
2.6361
2.60159
3.4803
2.84105
9.68136
.9872241
41,266
41,000
2.5481
2.51474
3.3541
2.73803
9.68056
.9871420
42,000
41,724
2.3215
2.29110
3.0310
2.47-422
9.67834
.9869155
42,279
42,000
2.2411
2.21176
2.9169
2.38115
9.67749
.9868294
43,000
42,711
2.0474
2.02060
2.6438
2.15815
9.67531
.9866072
43,293
43,000
1.9739
1.94812
2.5408
2.07408
9.67443
.9865169
44,000
43,698
1.8082
1.78454
2.3096
3.88534
9.67229
.9862989
44,307
44,000
1.7411
1.71828
2.2165
1.80933
9.67136
.9862044
45,000
44,684
1.5991+?
1.57820-3
2.0206-3
1.64946-3
9.66927
.9859908
45,321
45,000
1.5378
1.51765
1.9364
1.58073
9.66830
.9856920
46,0oo
45,670
1.4161
1.39763
1.7704
1.44523
9.66625
.9856828
46,335
46,000
1.3600
1.34224
1.6942
1.38304
9.66523
.9855796
47,000
46,655
1.2558
1.23936
1.5535
1.26812
9.66323
.9853750
47,350
47,000
1.2044
1.18866
1.4845
1.21179
9.66217
.9852673
48,000
47,640
1.1147
1.10014
1.3739
1.12155
9.66021
.9850673
48,365
49,000
48,000
48,625
1.0673
9.8961-1
1.05333
9.76671-4
1.3155
1.29(
1.07383-4
9.9567511
9.65911
9.65719
.9849550
.9847598
49,381
49,000
9.4578
9.33411
1.1657
9.
9.65605
.9846428
50,000
49,610
8.7C58-1
8.67088-4
1.0829-3
8.83961-4
9.65418
.9844524
50,396
50,000
R.5810
8.27142
1.0330
8.43237
9.65299
.9843306
51,000
50,594
7.8003
7.69829
9.6140-4
7.84809
9.65117
.9841452
51,412
51,000
7.4269
7.32973
9.1537
7.47235
9.64992
.9840185
52,000
51,578
6.9256
6.83507
8.5360
6.96807
9.64815
.9838381
52,429
52,000
6.5813
6.49524
8.1116
6.62162
9.64686
.9837064
53,000
52,562
6.1493
6.06886
7.5791
6.18694
9.64515
.9835311
53,446
53,000
5.8320
5.75576
7.1881
5.86775
9.64380
.9833944
54,000
53,545
5.4588
5.38738
6.7790
5.55383
9.64214
.9832243
54,463
54,000
5.1637
5 09615
6.4534
5.26800
9.64074
.9330824
79
?
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
. . V
L Ili I
*.s!P ?1.!3- s;_r
a
i
1ETRIC TABLE II CONTINUED
ALTITUDE
PRESSURE
DEMITY
ACCELERATION
OF GRAVITY
Z,m
H,me _
P,mb
P/Po
p,kg/m3
P/Pc,
g,m/sec2
g/go
55,000
54,525
4.8358-1
4.77557-
6.0924
11..973354-
9.63913
.9529176
55,430
55,000
4.5641
4.50445
5.7850
4.72241
9.63769
.9827705
56,000
55,511
4.2822
4.22624
5.4674
4.46310
9.63612
.9826111
56,498
56,000
4.0270
5.97438
5.1777
4.22666
9.63463
.9824586
57,000
56,493
3.7833
3.73354
4.8991
3.99926
9.63312
.9523047
57,516
57,000
3.5467
3.5C036
4.6268
3.77692
9.63157
.9821467
58,000
57,476
3.3367
3.29306
4.3832
3.57809
9.63012
.9819985
58,534
58,000
3.1179
3.07713
4.1276
3.36945
9.62851
.9818350
59,000
58,457
2.9375
2.89912
3.9154
3.19620
9.62711
.9816924
59,553
59,000
2.7356
2.69987
3.6761
3.00083
9.62545
.9815232
60,000
59,439
2.5814-1
2.54761-4
3.4918-4
2.85042-4
9.62411
.9813864
60,572
60,000
2.3955
2.36417
3.2681
2.66784
9.62240
.9812116
61,000
60,420
2.2641
2.23453
3.1089
2.53783
9.62111
.9810806
61,591
61,000
2.0934
2.06598
2.9002
2.36750
9.61934
.9808999
62,000
61,401
1.9820
1.95606
2.7631
2.25558
9.61812
.9807749
62,611
62,000
1.8255
1.80159
2.5689
2.109705
9.61629
.9805884
63,000
62,382
1.7315
1.70885
2.4514
2.00114
9.61512
.9804694
63,631
63,0100
1.5884
1.56764
2.2711
1.85394
9.61323
.9802768
64,000
63,362
1.5096
1.48982
2.1709
1.77218
9.61213
.9801640
64,651
64,000
1.3790
1.36099
2.0038
1.63573
9.61018
.9799653
65,00o
64,342
1.3132-1
1.29606-4
1.9189-4
1.56640-4
9.60913
.9798588
65,672
65,000
1.1945
1.17885
1.7643
1.44026
9.60712
.9796539
66,000
65,322
1.1399
1.12503
1.6928
1.38185
9.60614
.9795537
66,692
66,000
1.0322
1.01866
1.5502
1.26546
9.60407
.9793425
67,000
66,301
9.8726-2
9.74349-5
1.4903
1.21658
9.60315
.9792455
67,714
67,000
8.8969
8.78052
1.3591
1.10944
9.60102
.9790312
68,000
67,280
8.5301
8.41856
1.3093
1.06883
9.60016
.9789439
68,735
68,000
7.6491
7.54912
1.1888
9.70447-5
9.59796
.9787199
69,000
68,259
7.3523
7.25615
1.1479
9.37010
9.59717
.9786393
69,757
69,000
6.5590
6.47323
1.0374
8.46874
9.59491
.9784087
70,000
69,235
6.3212-2
6.23854-5
1.0040-4
8.19618-5
9.59419
.9783347
70,779
70,000
5.6088
5.53547
9.0313-5
7.37244
9.59186
.9780975
71,000
70,216
5.4206
5.34974
8.7624
7.15289
9.59120
.9780304
71,802
71,000
4.7826
4.72010
7.8424
6.40188
9.58881
.9777864
72,000
71,194
4.6357
4.57513
7.6286
6.22739
9.58822
.9777261
72,825
72,000
4.0662
4.01299
6.7922
5.54461
9.58576
.9774753
73,00072,171
3.9535
3.90181
6.6252
5.40830
9.58524
.9774220
73,848
73,000
3.4464
3.40132
5.8666
4.78903
9.58271
.9771642
74,000
73,145
3.3619
3.31794
5.7391
4.68489
9.58225
.9771181
74,872
745000
2.9118
2.87373
5.0529
4.12479
9.57966
.9768532
80
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
I
METRIC TABLE II CONTINUED
ALTITUDE
PRESSURE
DENSITY
ACCELERATION
OF GRAVITY
Z,m
H,m'
P,mb
P/Po
p,kg/m3
PO
g,misec2
g/go
75,000
74,125
2.8503-2 2.81229-5 4.9582-5
4.04747-5
9.57928
.9768142
75,895
75,000
2.452
2,4200 4.339
3.5423
9.57661
.9765423
76,000
15,102
2.409
2.3775 4.263
3.4801
9.57630
.9765106
76,920
76,000
2.061
2.0344 3.648
2.9780
9.57356
.9762314
77,000
76,078
2.04
2.0069 3.599
2.9377
9.57332
.976207o
77,944
77,000
1.733
1.710 3.067
2.5035
9.57051
.9759206
78,000
77,0.5
1.717
1.6942 3.038
2.4799
9.5705
.9759036
78,969
78,000
1.457
1.4378 2.578
2.1046
9.56746
.9756098
79,000
78,00
1.449
1.4303 2.565
2.0936
9.56737
.9756004
79,994
79,000
1.225
i.2087 2.167
1.7695
9.56442
.9752990
80,000
79,006
1.224-2
1.2075-5 2;165-5
1.76765
9.56440
.9752973
81,000
79,981
1.033
1.0195 1.828
1.4924
9.56143
.9749943
81,020
80,000
1.00
1.0162 1.822
1.4874
9.56137
.9749883
82,000
80,956
8.723-3
8.6085-6 1.544
1.2601
9.55846
.9746915
82,045
81,000
8.656
8.5425 1.532
1.2504
9.55832
.9746777
83,000
81,930
7.365
7.2690 1.30
1.0640
9.55549
.9743888
83,072
82,000
7.277
7.1815 1.288
1.0512,
9.55528
.9743671
84,000
82,904
6.220
6.1383 1.101
8.9851-0
9.55252
.9740862
84,098
83,000
6.117
1.083
6:8013;6
8.8373
9.55223
.9740566
85,000
83,878
5.252-5
5 9.295-6
7.5878-6
9.54956
.9737838
85,125
84,000
5.143
5.0754 9.101
7.4293
9.54919
-9737461
86,000
84,852
4.436
4.3778 7.850
6.4081
9.54659
.9734816
86,152
85,000
4.323
4,2668 7.651
6.2456
9.54614
.9734356
87,000
85,825
3.746
3.6974 6.630
5.4121
9.54363
.9731795
87,179
86,000
3.635
3.5870 6.432
5.2506
9.54310
.9(31253
88,000
86,798
3.164
3.1229 5.600
4.5712
9.54067
.9728774
88,207
87,000
3.055
3.0155 5.407
4.4140
9.54006
.9728149
89,000
87,771
2.673
2.6378 4.730
3.8611
9.53771
.9725756
89,235
88,000
2.569
2.5351 4.546
3.7108
9.53701
.9725046
90,000
88,744
2.258-5
2.2282-6 3.995-6
3.2615-6
9.53475
.9722739
90,264
89,000
2.159
2.1312 3.822
3.1196
9.53397
.9721944
91,000
89,716
1.907
1.8823 3.375
2.7552
9.55179
.9719724
91,293
90,000
1.815
1.7916 3.213
2.6225
9.53093
.9718842
92,000
90,688
1.612
1.5913 2.819
2.3012
9.52884
.9716709
92,322
91,000
1.52Er
1.5085 2.658
2.1695
9.52789
.9715740
93,000
91,659
1.367
1.3490 2.350
1.9181
9.52588
.9713697
93,351
94,000
92,000
92,630
1.291
1.162
1.2739 2.206
1.1468 1.965
1.8006
1.607
9.52485
9.52293
.9712639
.9710685
94,381
93,000
1.093
1.0789 1.837
1.4992
9.52180
.9709539
Declassified in Part - Sanitized Copy Approved for Release
81
Yr 2014/03/20 ? CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Co .y Ap roved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
'...fteAs
-
METRIC TABLE II CrATINUED
?
ALTITUDE
PRESSURE
DENSITY
P ,kg-iml PIP,
ACCELERATION
OF GRAVITY
g,m/scc2
ego
Z,m
H,m'
P,mb
PP?
?
95,000
93,601
9.9o5-4
9.7759-7
1.647-6
1.3449-6
9.51998
.9707675
95,411
94,000
9.284
9.1622
1.534
1.2521
9.51876
.9706439
96,000
94,572
8.466
8.3552
1.386
1.1311
9.51703
.9704666
96,441
95,000
7.905
7.8021
1.285
1.0488
9.51573
.9703339
97,000
95,542
7.254
7.1590
1.169
9.5392-7
9.51408
.9701659
97,472
98,000
96,000
96,512
6.749
6.231
6.6612
6.1492
1.079
9.882-i,
8.8106
8.0671
9.51269
9.51113
.97o024o
.9698654
98,503
97,000
5.777
5.7015
9.092
7.4220
9.50965
.9697142
99,000
97,482
5.365
5.29)1.4
8.379
6.8399
9.50818
.9695649
99,534
98,000
4.957
14.8920
7.680
6.2691
9.50661
.9694o44
100,000
98,451
4.629-4
4.5689-7
7.123-7
5.8142-7
9.50524
.9692646
100,566
99,000
4.263
4.2073
6.5o4
5.3091
9.50357
.9690946
101,000
99,420
4.004
3.9516
6.069
4.9345
9.50230
.9689644
101,598
100,000
3.675
3.6268
5.522
4.5074
9. 50053
.9687849
102,000
100,339
3.471
3.4253
5.184
4.2321
9.49935
.9686644
102,631
101,000
3.175
3.1333
4.699
3.8363
9.149750
.9684753
103,000
101,353
3.015
2-9753
4.439
3.6234
9.49641
.9683645
103,663
102,000
2.749
2.7129
4.009
3.2728
9.49446
.9681657
104,000
102,326
2.624
2.5896
3.809
3.1092
9.49347
.9680646
104,696
103,000
2.355
2.3558
3.428
2.7986
9.49143
.9678561
105,000
103,294
2.288-4
2.2585-7
3.276 -7
2.6739-7
9.49o53
.9677652
105,730
104,000
2.073
2.0463
2.938
2.3984
9.48839
.9675466
106,000
104,261
2.000
1.9735
2.823
2.3o44
9.148760
.9674657
106,764
105,000
1.806
1.7826
2.523
2.0600
9.48536
.9672372
107,000
105,229
1.751
1.7277
2.438
1.9901
9.48466
.9671664
107,798
106,000
1.576
1.5559
2.172
1.7731
9.48232
.9669278
103,000
106,196
1.535
1.5153
2.110
1.7222
9.48173
.9668672
103,332
109,000
107,000
107,162
1.378
1.349
1.3605
1.3314
1.873
1.829
1.5292
1.4932
9.47929
9.47880
.9666184
.9665682
?
109,367
103,000
1.208
1.1918
1.619
1.3216
9.47626
.9663o91
110,000
103,129
1.187-4
1.1718-7
1.589-7
1.2972-7
9.47586
.9662692
110,902
109,000
1.060
1.0459
1.402
1.1444
9.47322
.9659999
111,000
111,937
109,095
110,000
1.047
9.316-5
1.0331 a
9.1941-u
1.383
1.216
1.1289 .
9.9280-o
9.47293
9.47019
.9659705
.9656906
112,000
110,061
9.244
9.1229
1.206
9.8432
9.47001
.9656718
112,973
111,000
8.203
8.0961
1.057
8.6292
9.46716
.9653815
113,000
111,026
8.176
8.0692
1.053
8.5975
9.146708
.9653733
314,000
111,992
7.243
7.1484
a
9.215-0
7.5224
9.46415
.965o75o
114,009
112,000
7.235
7.14o8
9.204
7.5137
9.46413
.9650724
11.
82
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CI -
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9-9000L0009Z0a1?1701-0-1-8dCll-V10 OZ/?0/171-0Z -1A-09 ? 3Se3I3j JO4 penal dv do o pazwes - 'Jed pawssepaa
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
?
?
METRIC TABLE II CONTINUED
ALTRUDE
I PRESSURE
DENSITY
ACCELERkTION
OF GRAVITY
Z,m
H,m'
1 P,M1)
P/P0
p,kg/m3
P/Po
g,m/sec2
g/go ?
140,000
136,983
5.336-
5.2662-9
1l..2969
3.5071-9
9.38855
.9573660
/
143;153
140,a0,0
4.238
4.1831
3.190
2.60142
9.37945
.9564375
145,000
141,766
3.729
3.6807
2.704
2.2072
9.37412
.9558941
148,385
145,000
2.985
2.9464
2.028
1.6555
9.36437
.9548996
150;000
146,542
2.698
2.6628
1.779
1.4525
9.35972
.9544256
153,625
150,000
2.173
2.1442
1.345
1.0977
9.34930
.9533630/
155,000
151,311
2.008
1.9820
1.215
9.9162-10
9.34535
.952967.5:
158,874
155,000
1.624
1.6032
9.234-10
7.5380
9.33424
.9518276
160,000
156,072
1.531-6
1.5110-9
1
8.5540 -
6.982410 -
9.33101
.9514 7
164,131
160,000
1.243
1.2264
6.531
5.3312
9.31920
.9502935
165,000
160,826
1.191
1.1756
6.183
5.0476
9.31671
.9500403
169,397
145,000
9.692-7
9.5657-10
4.737
3.8668
9.30416
.9487606
170,000
165,572
9.431
9.3080
4.573
3.7326
9.30244
.9485852
174,671
170,000
7.689
7.5881
3.511
2.8663
9.28914
.9472289
175,000
170,311
7.582
7.4832
3.100
2.8152
9.28821
.9471335
179,954
175,000
6.189
6.1085
2.653
2.1655
9.27413
.9456985
180,000
175,043
6.178-7
6.0974-10
2.647-10
2.1609- 10
9.27400
.9456852
185,000
179,768
5.082
5.0159
2.107
1.7196
9.25983
.94424?1
185,245
180,000
5.035
4.9689
2.083
1.7008
9.25913
.9441693
190,000
184,486
4.208
4.1533
1.689
1.3790
9.24569
.9427984
190,545
185,000
4.124
4.0704
1.650
3.3469
9.24415
.9426413
195,000
189,196
3.506
3.4602
1.364
1.1138
9.23159
.9413599
195,854
190,000
3.400
3.3559
1.316
1.0747
9.22918
.9411146
200,000
193,899
2.938-7
2.8995-10
1.11010
9.0572-11

9.21751
-9399247
201,171
195,000
2.821
2.7840
1.058
8.6369
9.21422
.9395891
205,000
198,595
2.475
2.4427
9.079 -11
7.4117
9.20347
.9384929
206,497
200,000
2.354
2.3229
8.560
6.9880
9.19927
.938?648
210,000
203,284
2.096
2.0685
7.474
6.1014
9.18946
.9370643
211,831
205,000
1.974
1.9486
6.970
5.6899
9.18433
.9365418
215,000
207,966
1.783
1.7600
6.188
5.0511
9.17548
.9356389
217,175
210,000
1.665
1.643?
5.709
4.6605
9.16941
.9350200
220,000
212,641
1.524-7
1.5004-10
5.150-11
4.2039 -11e
9.U15h14.
.9342168
222,526
215,000
1.410
1.5920
4.703
3.8389
9.15450
.9334995
225,000
217,308
1.308
1.2914
4.308
3.5164
9.14762
.9327979
227,887
220,000
1.200
1.1846
3.894
3.1789
9.13960
.9319802
230,000
221,969
1.128
1.1131
3.620
2.9554
9.13374
.9313823
233,256
225,000
1.026
1.0126
3.241
2.6457
9.12472
.9304621
235,000
226,622
9.759-8
9.6315-11
3.057
2.4953
9.11989
.9299699
238,634
230,000
8.805
8.6900
2.710
2.2124
9,10984
.9289453
I.
V-
%
Declassified in Part - Sanitized Copy Approved for Re
50 -Yr 2014/03/20 ? CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
a7f 13,11 rr
1
METRIC TABLE II CONTINUED
ALTITUDE
PRESSURE
DENSITY
ACCELERATION
OF GRAVITY
' Z,m
H,m'
P,mb
P/Po '
p,2g/m3
Wo
g,m/sec2
g/go
240,000
231,268
-6
8.475
8.3646-
2.592-11
-
2.115811
9-10607
.9285607
244,021
235,000
7.586
7.4869
2.277
1.8535
9.09498
.9274297
245:000
235,908
7.387
7.2900
2.207
1.8014
9.09228
.9271547
249,417
240,000
6.560
6.4741
1.921
1.5679
9.08013
.9259154
250,000
240,540
6.459
6.3746
1.886
1.5398
9.07852
.9257519
254,821
245,000
5.692
5.6179
1.627
1.3282
9.06529
.9244?22
255,000
245,165
5.666
5.5920
1.618
1.3210
9.06480
.9243522
260,000
249,7814.
4.986-8
4.92014-11
-
1.39311
1.1574-11
9.05110
.9229558
260,235
250,40
4.956
4.8913
1.384
1.1295
9.05046
.9228904
265,000
254,395
4.400
4.3421
1.204
9.8261-12
9.05744
.9215625
265,657
255,000
4.329
4.2722
1.181
9.6414
9.03565
.9213797
270,000
258,999
3.893
3.8423
1.043
8.5166
9.02381
.9201724
271,088
260,000
3.792
3,7428
1.012
8.2591
9.02085
.9198703
275,000
263,597
3.454
3.4092
9.071-12
7.4048
9.01021
.9187854
276,528
265,:.(10
3.332
3.2886
8.697
7.0992
9.00606
.9183622
280,000
,
3.073-8
3.0327-11
7.910-12
6.4574-12
8.99664
.9174015
281,977
2') '
;`.936
2.8975
7.499
6.1220
8.99128
.9168552
285,000
=.740
2.7044
6.918
5.6473
8.98509
.9160207
287,435
2.594
2.5598
6.487
5.2958
8.97651
.9153496
290,000
27;,,,r
2.449
2.4173
6.067
4.9525
8.96958
.9146431
292,902
280,000
2.297
2.2672
5.629
4.5948
8.96176
.9138451
295,000
281,917
2.194
2.1655
5.334
4.3546
8.95611
.9132686
298,377
285,000
2.040
2.0130
4.898
3.9980
8.94702
.9123419
300,000
286,480
1.970-8
1.9442-11
4.70-2
,13.8388-12
8.94266
.9118972
303,862
290,000
1.815
1.7914
4.273
3 4883
8.93229
.9108399
505,000
291,056
1.772
1.7492
4.156
3.3923
8.92924
.9105288
309,356
295,000
1.619
1.5979
3.738
3.0517
8,91757
.9093391
310,000
295,585
1.598
1.5769
3.681
3,0048
8.91585
.9091636
314,859
.300,000
1.447
1.4284
3.279
2.6765
8 90287
.9078396
320,000
504,663
1.306 -8
0,,,-11
1.2uvu
2.908-12
203736-12
8,88916
.9064422
325,893
310,000
1.164
1.1485
2.541
2.0739
8.87549
.9048444
350,000
356,963
513,714
320,000
1.075
9.431-9
1.0613
9.30--f)-12
2.316
1.987
1.8909
1.6217
8.86259
8.84417
.9037331
.9018540
340,000
322,738
8.914
8.7978
1.860
1.5183
8.83615
.9010361
348,069
330,000
7.698
7.5971
1.567
1.2788
8.81489
.8988686
85
Declassified in Part - Sanitized Copy Approved for Release @
0 ? CIA RDP81 01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
C.0
17$
METRIC TABLE II CONTINUED
ALTITUDE
' PRESSURE
DENSITY '
ACCELERATION
OF GRAVITY
Z,m
H,ms
P,mb 1 P/Po
P,kg/m)
P/R,
g,m/sec2
g/go
350,000 331,735 7.437-9 7.3393-12
1.5o5-12 1.2282-12 8.80982 .8983512
359,213 340,000 6.326 6.2432 1.245 1.0165 8.78566 .8958882
360,000 340,705 6.241 6.1589 1.226 1.0005 8.78360 .8956782
370,000 349,648 5.266 5.1973 1.005 8.2026-13 8.75751 .8930172
370,394 350,000 5.23? 5.1631 9.971-13 8.1396 8.75648 .8929127
380,000 358,565 4.467 4.4088 8.289 6.7665 8.73153 .8903680
381,612 360,000 4.352 4.2954 8.040 6.5634 8.72735 .8899421
390,000 367,456 3.808 3.7584 6.877 5.6141 8.70566 .8877305
392,867 370,000 3.641 3.5934 6.526 5.3270 8.69827 .8869765
400,000 376020 3.262-9 3.2190-12 5.737-13 4.6836-13 8.67991 .8851048
404,160 380,000 3.062 3.0220 5.329 4.3501 8.66923 .8840159
410,000 385,158 2.806 2.7691 4.811 3.9273 8.65428 .8824907
415,491 390,000 2.586 2.5517 4.373 3.5696 8.64025 .8810602
420,000 393,970 2.424 2.3922 4.054 3.3096 8.62876 .8798882
426,860 400,000 2.197 2.1687 3.615 2.9508 8.61131 .8781094
430,000 402,756 2.102 2.0747 3.432 2.7848 8.60335 .8772971
438,267 410,000 1.874 1.8496 3.000 2.4495 8.58242 .8751636
440,000 411,516 1.830 1.8062 2.918 2.3824 8.57805 .8747175
449,713 420,000 1.605 1.5841 2.50 2.0434 8.55358 .8722228
450,000 420,250 1.599-9 1.57E10-12 2.492-13 2.0343-13 8.55286 .8721492
460,000 428,959 1.402 1.3834 2.136 1.7440 8.52779 .8695923
461,197 450,000 1.380 1.3621 2.098 1.7126 8.52479 .8692869
470,000 437,642 1.233 1.2168 1.839 1.5008 8.50282 .8670466
472,721 440,000 1.191 1.1756 1.766 1.4417 8.49605 .8663559
480,000 446,300 1.088 1.0735 1.588 1.2963 8.47797 .8645120
484,283 450,000 1.032 1.01841.493 1.2187 8.46735 .8634299
1+90,000454,932 9.625-10 9.11990-15 1.376 1.1234 8.45322 .8619885
495,884 460,000 8.969 8.8512 1.267 1.044 8.43871 .8605088
500,000 463,540 8.541-10 8.4293-13 1.197-13 9.7692-14 8.42858 .8594761
507,525 470,000 7.821 7.7184 1.080 8.8124 8.41011 .8575927
510,000 472,122 7.600 7.5003 1.044 8.5219 8.40405 .8569746
519,205 480,000 6.841 6.7515 9.231-14 7.5353 8.38156 .8546816
520,000 480,679 6.780 6.6912 9.135 7.4567 8.37963 .8544840
530,000 489,212 6.064 5.9842 8.016 6.5435 8.35531 .8520043
530,925 490,000 6.002 5.9234 7.921 6.4658 8.35306 .8517754
540,000 497,719 5.436 5.3647 7.054 5.7583 8.33110 .8495354
542,686 500,000 5.281 5.2117 6.819 5.5666 8.32461 .8488741
86
F:
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr
3/20. -
1 043R0n7Annn7nnnR_R
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
11
METRIC TABLE III
Veliwity of Sound, Particle Spedh Molecular-SceJe Temperature Gradient,
and Scale Height as MT-lotions of Geometric and Geonotential Altituda
ALTITUDE?
mul,-S...iaLE
TEMP.GRAD
SCALE HEIGHT
PARTICLE SOUND

SEM SPEED
7.,m
Rim'
1.1).0/In'
H, km
115/H8
'il-Wsec
Vflo
Cs/Cs
Cs,m/sec
-51000
-53003.9
9.3717
1.11112
484.15
1.05493
358.98
-4,996.1
-5,000
9.3709
1.11104
484.15
1.05489
358.97
-4,000
_44002.5
9.1843
1.08891
479.21
1.04417
355.32
-3:997.5
-4,000
9.1839
1.08886
479.20
1.04414
355.31
-3,cco
-3,001.4
8.9969
1.06670
474.22
1.03330
351.62
-2:998.6
-33000
8.9967
1.06666
474.22
1.03328
351.62
-moo
-2,000.6
8.8095
1.04447
469.19
1.02232
347.89
-1,999.4
-21000
8.8o94
1.010016
469.18
1.0231
347.88
-1,000
-1,coo.2
8.6220
1.02224
464.09
1.01122
344.11
- 999.8
-10000
8.6220
1.02224
464.09
1.01122
o
o
8.444
1.00000
458.94
1.00000
3440.29
1,000
999.8
8.2468
.977754
453.74
.988659
336.43
1:000.2
1,000
8.2468
.977751
103.74
.988657
336.43
2,000
13999. 4
8.0591
.955501
03.47
.977190
332.53
21000.6
2,000
8.0590
.955487
448.47
.977183
332.53
woo
2,998.6
7.8713
.933241
443.15
.965589
328.58
3,001.4
3,000
-0.0
65
7.8711
.933210
443.11
.965572
328.58
4,000
3,997.5
7.6835
.910975
437.76
.953850
324.59
4,002.5
4,000
7.6831
:910918
437.75
.953820
324.58
5,000
4,996.1
7.4957
.888700
43c.31
.941968
320.54
5,003.9
53000
hnbn
7S.
.888613
432.29
.941921
320.53
6,000
5,994.3
7.3077
.866419
426.79
.929939
516.45
6,005.7
6,000
7.3067
.866293
426.76
.929370
316.43
7,000
6,992.3
7.1198
.844131
421.20
.917756
312.30
7,007.7
7,000
7.1183
.843959
421.15
.917661
312.27
8,000
7,989.9
6.9317
.821836
415.53
.905412
308.10
8,010.1
8,000
6.9298
.821611
415.47
.905287
308.06
9,000
8,987.3
6.7436
.799534
409.79
.892902
303.85
9,012.8
9,000
6.7412
.799249
409.72
.892742
303.79
10,000
9,984.3
6.5554
.777225
403.97
.880219
299.53
10,016
10,000
6.5525
.776873
403.88
.880018
299.46
11,000
10,981
6.3672
.754908
393.07
.867354
295.15
11,019
11,000
6.3636
.754483
397.95
.867107
295.07
12,C00
11:977
6.3656
.754715
397.95
.867107
295.07
12,023
12,000
6.3656
.754720
397.95
.867107
295.07
13,000
12,973
6.3676
.754952
397.95
.867107
295.07
13,027
13,000
o.
6.3676
.754959
397.95
.867107
295.07
14,000
13,969
6.3696
.755189
397.95
.867107
295.07
14,031
14,000
6.3696
.755197
397.95
.867107
295.07
Declassified in Part - Sanitized Copy Approved for Release
87
14/03/20 ? CIA RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6
-
METRIC TABLE III CONTINUED
,
ALTITUDE
MOL-SCALE
TEMP.GRAD.
SCALE HEIGHT
PARTICLE pATT, SCUND
SPEED ------`"E-SPEED
1
Z,m
I H,m'
Lm,s0/m'
Hs, km
Hs/Hss
.1.7,misec
Vflo
C8/C80
Cs,m/see
15,000
14,965
6.3716
.755426
397.95
.867107
295.07
15,035
15,000
6.3717
.755435
397.95
.867107
295.07
16,000
15,960
6.3736
.755664
397.95
.867107
295.07
16,040'
16,000
6.3737
.755673
397.95
.867107
295.07
17,000
16,955
6.3756
.755901
397.95
.867107
295.07
17,046
17,000
6.3757
.755915
397.95
.867107
295.07
18,000
17,949
6.3776
.756140
397.95
.867107
295.07
18,051
18,000
6.3777
.756152
397.95
.867107
295.07
19,000
18,943
6.3796
.756377
397.95
.867107
295.07
19,057
.19,000
6.3797
.756389
397.95
.867107
295.07
20,000
19,937
0.0000
6.3816
.756615
397.95
.867107
295.07
20,063
20,000
6.3817
.756626
397.95
.867107
295.07
21,000
20,931
6.3836
.756852
397.95
.867107
295.07
21,070
-21,000
6.3837
.756864
397.95
.867107
295.07
22,000
21,924
6.3856
.757089
397.95
.867107
295.07
22,076
22,000
6.3857
.757101
397.95
.867107
295.07
23,000
22,917
6.3876
.757326
397.95
.867107
295.07
23,084
23,000
6.3878
.757350
397.95
.867107
295.07
24,000
23,910
6.3896
.757563
397.95
.867107
295.07
24,091
24,000
6.3898
.757587
397.95
.867107
295.07
25,000
24,902
6.3916
.757800
397.95
.867107
295.07
25,099
25,000
Y._ 6.3918
.757824
397.95
.867107
295.07
26,000
25,894
6.4728
.767427
400.41
.872458
296.89
26,107
26,000
6.4823
.768554
400.70
.873089
297.11
27,000
26,886
6.5626
.778074
403.11
.878355
298.90
27,115
27,000
6.5730
.779307
403.42
.879031
299.13
28,000
27,877
6.6525
.788733
405.80
.884206
300.89
28,124
28,000
6.6636
.790049
406.13
.884933
301.14
29,000
28,868
6.7424
.799392
408.58
.890026
302.87
29,133
29,000
+0.0030
6.7543
.800803
408.82
.890796
303.13
30,000
29,859
6.8323
.810050
411.12
.895802
304.83
30,142
30,000
6.8451
.811568
411.50
.896621
305.11
31,000
30,850
6.9223
.820721
413.75
.901539
306.79
31,152
31,000
6.9360
.822345
414.15
.902407
307.08
32,000
31,840
7.0123
.831392
416.37
.907238
308.13
32,162
32,000
7.0269
.833123
416.79
.908158
309.04
33,000
32,830
7.1023
.842062
418.97
.912900
310.65
33,172
33,000
7.1178
.843900
419.41
.913871
310.98
34,000
33,819
7.1923
.852733
421.55
.918525
312.57
34,183
34,000
7.2088
.854689
422.02
.919550
312.92
88
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0
?
IEMIC TABLE III C0721-111ED
,AITITODE
MOL. SCALE
TEMP .GEAD.
SCALE HEIOT
1 PARams E031.1D
--r-Iiii'lE0 = ? x 10
?
(N-1)
* The fifth term (in Z) has not been published, 'alit was provided by
Col. C. Spohn, of Air Weather Service USAF, who probably obtained it
from Lambert or Harrison.
164
"
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W
41
For the case when p = 45' 32, 40", as in this MODEL, chosen to agree
with go = 9.806,65 m scc-2,
cos 20 = cos 91? 5, 20" = - sin 1? 5' 20" = - .019,003,7. (N-2)
For this value of 0, Eq. (N-1) becomes
g = ci - c2Z + c3Z2 - c40 + c5Z4 - (N-3)
where
cl = 9.806,65 (exact) m sec-2
c2 = .338,541,88 x 10-5 m9 sec-2
e3 = .007,253,81 x 10-1? m-1 sec-2
ch. = .000,151,689 x 10- m-2 sec
15 -2
c5 = .000,002,9696 x 10-20 m-5 sec-2
The reliability of the limit of this series in expressing the true val-
ue of g at any altitude is unknown to the authors of this report. It is
assumed that this function represents the best available analytical expres-
sion for g in terms of Z and 0. The small number of available terms and
significant figures, however, places limitations on the evaluation of the
series at high alLitades.
2. Problem
It is necessary to determine the limitations which the small number of
terms and the small number of significant figures place upon the evaluation
of the function at various altitudes. It is further necessary to compare
the results of the adjusted, inverse-square-law function for g with the
values obtained from the infinite series function for g.
The extent to which the availability of only five terms limits the value
of g at various altitudes has been studied for the case where 0 = 45" 32' 40"
with the results indicated below. In the course of the analysis it was found
that several additional terns were necessary to determine the value of g to
the desired accuracies at altitudes above lO km. The values of the addi-
tional terms were estimated by graphical extrapolation, and refined values
of g were computed for various altitudes. These values of g were then com-
pared with values from the inverse square law: using the effective P.Arth's
radius at 450 32' h0" as determined in Appendix M.
3. Results. Concerning Required Number of Terms in Equation Og-5) For
Various Degrees of At:curacy
Equation (N-3), limited to four terms as published, provides accuracies ?
3.65
?
???
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of one part in 9,800,000, or seven significant figures, for altitudes up to
only about bo km. The fifth term permits the equation to be .used up to
about 150 km with the same accuracy, provided that the coefficient of the
third term has one additional significant figure. By means of extrapola-
tion it was estimated that with five additional terms in Eq. (N-3), g could
be determined to the stated accuracy for altitudes up to 1,140 km, provided
a sufficient number of significant figures are added to all the terms be-
yond the first two. For other accnracics the maximum altitude to which g
may be computed with a given number of terms in Eq. (N-3) is given in Table
(N-I), neglecting significant figures in existing terms.
Nutber of
Terms
Available
2
Number of Significant Figures Required in g
3 4 5 6 7
? 8
2
260
8o
25
8
3
700
330
150
75
6o
20
4
1100
65o
370
200
110
6o
35
5
low
64o
400
250
150
loo
6
950
610
420
260
180
7
1300
Wo
610
440
320
8
1100
860
610
480
9
1200
830
620
10
1140
800
Table N-I. Estimated maximum altitude in km for which a specified
number of terms in Eq. (N-)) will yield accuracies of
a specified number of significant figures in g, pro-
vided the various coefficients have a sufficient number
of significant figures.
4. Results. Concerning Limitations Due to Available Significant Figures in
Equations (N-1) and (N-)).
The number of significant figures in the coefficients of Eq. (N-)) stems
directly from the number available in the coefficients of Eq. (N-1). An
analysis of the limitations of these equations shows that for g accurate to
four significant figures, these equations may be used up to 1,400 km.
For five-significant-figure accuracy in g, the accuracy of the coeffi-
cients limits the calculations to altitudes below 1,300 km; ror six-signifi-
cauL-figure accuracy in g, the calculations are restricted to altitudes be-
low 500 km; while for coven-and eigh6-significant-figure accuracy in g, the
maximum perndssible altitudes are only 150 and 50 km, respectively. (see
figure N-6)
166
0
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Applying these restrictions to Table N-I, cue obtains Table N-II.
Number of
Terms
Available
2
Number of Significant Figures Required in g
3 if 5 6 7
8
2
260
80
25
8
3
700
330
150
75
Go
20
if
lioo
650
370
200
no
60
35
5
low
640
400
250
122
52
6
950
610
420
2.-22
22
7
1300
900
500
122
.22
?
8
imo
coo
15o
5.2
9
500
150
22
lo
/
Table N-II. Estimated maximum altitude in km for which a specified
number of terms of Eq. (N-2) will yield a specified num-
ber of significant figures' accuracy in the value of g,
with the significant figures of existing coefficients
limiting the results.
NOME: Underlined fioltrea are thane limited by the number of
significant figures in coefficients.
5. Results of Comparison of Values of g from Equation (N-3) with Inverse-
Square-Law Values of g
The inverse-square-law values of g, for 0 = 450 32' 40", when the effec-
tive earth's radius is used, are in goud agreement with the values of Eq.
(N-3), with no differences occurring in the fifth significant figure below
100 km. Above this altitude the differences increase rather rapidly to a
peak at 500 km, after which they fall off to zero somewhere between 700 and
800 km and increase negatively above that altitude. This large fall-off is
due principally to the omission of term six which becomes extremely signif-
icant in the series at this altitude. Since this term is negative, its
presence would reduce the value of Eq. (N-3) at these altitudes and tend to
retain the increasing difference with the inverse-square-law value.
Values of g were recalculated from Eq. (N-3) on the bases of four Addi-
tional terms determined graphically, and these new values of g were then
compared with the inverse-square-law values. In this latter comparison,
the differences increased uniformly with altitude. Curves B and C of Fig.
N-1 show the graphs of the two comparisons. Curve A in this figure shows
the departure of the five-term-series value of g from the estimated nine-
term-series value of g. Curves A and C are essentially the error curves
of the five-term-series function and the inverse-square-law function,
? 167
1!
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respectively, assuming the nine-term-series value of g to be the most cor-
rect. At 150 km, the five-term-series function provides two more signifi-
cant figures than the inverse square law. As altitude increases, however,
the differential in accuracy drops proportionately to one significant fig-
ure at 330 km, and no difference at 750 km. A comparison of the maximum
altitudes to which the five-term-sries funution and the inverse-square-law
function may each be used for various accuracies is given in Table N-III.
Significant Figures
4 5 6 7 8
5 term series
640
400
250
150
50
inverse square
500
130
40
10
5
Table N-III. Comparison of marl:mum altitude to ..tich each
of two funcLIons of a may be used ror five
different, degrees of accuracy.
The numerical value of g by the several methods and the numerical differ-
ences between these values are given in Table N-VI.
6. Method of Analysis
The analysis was performed by using twenty-one values of Z between 1
and 1,000 km, and independently evaluating each of the five terms of Eq.
(N-3). The logarithms of the absolute values of each term were plotted as
a function of the number of the term, and points corresponding to the same
value of Z were connected to form the solid line portion of Fig. N-2. The
lines were then extrapolated to regions corresponding to higher order terms.
The values indicated for these terms by the extruolations then served as
estimated values for these terms.
The values of the several terms were then plotted as a function of alti-
tude, as in Fig. N-3, with solid lines connecting the computed terms, and
broken lines connecting the estimated terms. .The analysis of the contribu-
tion of varying numbers of terms to the value of the total function was then
made visually from this graph.
The significant figure analysis was performed on tabulated values of
the several berms (Table N-IV and Table N-V) and the net results are plotted
on Figs. N-4, N-5, and N-6.
168
f-
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_
Alt.
km.
2nd Term
3rd Tenn
4th Term
5th Term
1
.003,085,418,8
.000,000,725,38
.000,000,000,151
.000,000,000,000,029
5
.015,427,094
.000,018,134,52
.000,000,018,965
.000,000,000,018,56
10
.030,854,1813
.000,072,538,1
.000,000,151,62q
.000,000,000,296,91
20
.061,708,37g
.000,29o,152,
.000,001,213,51
.000,000,004,711
53
.092,562,565
.000,652,84,
.000,004,095,g5
.000,000,024,055
40
.123,416,752
.001,160,Q
.000,009,708,0
.000,000,076,022
50
.154,270,940
.001,813,452
.000,018,961,1
.000,000,185,60
60
.185,125,1-0
.002,611,3 2
.000,032,7g,13
.000, 000,
70
.215,979,53
.003,554,, 7
.000,052,029,3
.000,000,713,00
80
.2146,835,5Y
.004,642,44?
.000,077,6.g
.000,001,216,35
90
.277,687,6'g
.005,875,22
.000,110,561
.000,001,948,3
100
,308,541,880
.007,2;43,81
.000,151,6.2
.000,002,962,6
200
.617,083,77i
.029,015,75
.001,213,a
.000,047,513
300
.925,625,64-
.065,284,2
.004;095.60
.000,240,JE-
400
1.234,167,52
.009,708,1
.000,760,22
500
1.542,709,40
.181,345,2
.018,961,1
.0o2., 856, c
6?0
1.851,251,28
.261,137,2
.032,764,8
.003,848,6
700
2.159,793;3
.355,4A1
.052,02,3
.007,130,0
800
2.468,335,04
.464,244
.077,6614
.012,16V
900
1000
2.776,876,2g
3.085,418,60
.587,55
.725,
.110,51
.151,611-2'
.019,48)
.029,6.E
Table N-IV. Values of the first four
w..riuus altiLudes from 1
variable terns of Eq. (N-3) for
km to 1,000 km.
NOTE: The underlined figures are beyond the limit of significance but
are carried for smoothness.
169
?Vr.
\ F
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fyi
^
-No" .s.:1???*,"
? ?
_
?-.1)
6th Term
7th Term
8th Term
9th Term
100
.000,000,05
.000,000,001
.000,000,000
.000,000,000
200
.000,001,8
.000,000,08
.000,000,002
.000,000,000
300
.000,012
.000,000,8
.000,000,04
.000,000,000
400
.000,055
.000,003,5
.000,000,2
.000,000,001
500
.000,15
.000,012
.000,001
.000,000,05
600
m00,42
.000,045
.000,004
.000,000,3
7040
.000,9
.000,ii.
.000,014
.000,001,5
800
.001,7
.000,24
.000,03
.000,003,5
900
.002,6
.000,4
.000,05
.000,006,5
1000
.004,5
.000,7
.000,10
.000,013
?
Table N-V. EstimAtc.A values of terms 6 through 9 of Eq
for altitudes between 100 and 1,000 km.
170
0
? (N-3)
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-
1
I.
asio
2
Alt. g = g r
o
e from 5
terns of
Eq. (N-3)
g** from
estimated
9 terns of
Eq. (N-3)
g g g** g* le*
1 9.803,565,30
5 9.791,241,06
10 9.775,868,42
20 9.745,231,56
30 9.714,738,52
40 9.684,388,35
50 9.654,180,19
60 9.624,113,15
70 9.594,186,36
80 9.564,398,93
90 9.534,750,01
100 9.505,238,75
200 9.217,512,92
300 8.942,656,38
400 8.679,912,89
500 8.428,581,04
600 8.188,009,42
wo 7.957,592,42
800 7.736,766,50
900 7.525,006,62
moo 7.321,823,24
9.803,565,306
9.791,241,021
9.775,868,19
9.7)15,230,56
9.714,736,2
9.684,384,2
9.654,173,7
9.624,103,8
9.594473,1
9.564,382
9.534,729
9.505,2'3
9.217,415
8.942,45
8.679,59
8.428,18
8.187,61
7.957,31i
7.737,0
7.526,2
7.324,6
identical
to
adjacent
column
departures
from g*
are
underlined
below
9.217,414
8.942,44
8.679,51
8.428,a
8.187,24
7.9564:2
7.735,b
7.525,0
7.320,1
.000,000,00
.0400,000,04
.000,000,23
.000,001,00
.000,002,32
.000,004,1
.0?0,006,5
.000,0?9,3
.000,012,6
.000,016
.000,021
.000,026
.oco,o98
.000,20
.000,32
.000,lpo
-000,39
-000,20
-.000,3
-.001,2
-.002,8
)1'
.3
o3 c;
a) UP a)
Tal
-01 .91
.ci
O)
o
.000,099 .000,001
.000,21 .000,01
.000,38 .000,05
.000,54 .0400,14
.000,76 .000,37
-001,00 .000,80
.001,2 .001,4
.001,0 .002,2
.001,1 .003,9
ta3
co
Table N-VI. Values of the acceleration of gravity for various altitudes
computed from three different equations as indicated, and
the differences between these values of the acceleration of
gravity.
NOTE: Underlined numbers in Column g*indicate figures of questionable
significance.
Underlined numbers in Column indicate figures differing from
Column g*.
171
0
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7. Conclusions
a. For mcct engineerlag purposes, the adjusted inverse-square-law
function for g provides adequate accuracy.
b. For the standard atmosphere, and for future editions of this MODEL,
the values of g should be computed on the basis of an expanded version of
Eq. (N-3) in which a minimum of three, and preferably five, additional
terms are employed, and in which sufficient additional significant figures
are provided for the various limiting coefficients, particularly coeffi-
cients cf terms 3, 4, and 5.
172
,
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?
?
ALTITUDE IN KILOMETERS
800
700
600
NEGATIVE
BRANCH OF 8
--- A,
Bo 9_9K
g gkX
WHERE g g )1/
? v.*:
500? III IS EQUATION (N-3) TERMINATED
AFTER 5 TERMS,
g" IS EQUATION (N-3) TERMINATED
AFTER 9 TERMS.
400
300
BOO
100
1/
if
.000,000,1 .000 001 .000,01 .000,1 .001 .005
DIFFERENCE IN .m SSC"
o FIGURE N-I DIFFERENCES BETWEEN THE VALUES OF THE ACCELERATION
"-
OF GRAVITY COMPUTED FROM THREE DIFFERENT EQUATIONS.
S RD 173
MARCH 1911
?
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MARCH I1157
.UO,0I .000,1 .001 .01
ACCELERATIONS IN M/seat
MAGNITUDE OF SUCCESSIVE TERMS OF LAMBERT'S ALTERNATING
POWER SERIES FOR g WHEN EVALUATED FOR VARIOUS ALTITUDES
II
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iononwa.......r. I
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ALTITUDE IN KILOMETEDS
1000
900
900
70
50
40
30
20
10
-
I i
COMPUTED
/
--
???? ESTIMATED FRO1A FIG. N-1I
?
???-- ERROR INTRODUCED BY
SIGNIFICANT FIGURE
LIMITATIONS IN 4-
,4v
t
t
4/
I..
lic 14
us, #.
A.
r
dt
31
gr?
s..
2
t
us
s-
2
M
lIJ
1.-
e -?
4?2 *4
U
..
4
4*
*
4 4 4
?? 47; ;
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A
.t.
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TERMS
3,4, AND
5. ,
(3'
4
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11
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7/
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7/
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zz
L,
7----
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Pr
,
A
Is
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V
,........,
.......---
.000.0001,01 .00 0,00 0,01 .000,000,1
WINCH int
.000,001
.000,01 .000,1 .001
ACCELERATIONS IN M/sitc2
.01
MAGNITUDES OF EACH OF THE FIRST TEN TERMS OF LAMBERT'S ALTERNATING
POWER SERIES FOR g, FOR VARIOUS ALTITUDES, BETWEEN 10 AND 1000 km.
FIGURE N-3
910665
-
I.
i:?
; ?
I ^
l? ?
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'11
V 1.S
-
PERCENTAGE ERROR
PERCENTAGE ERROR
10"
10
10-4
10-g
10-4
1 0-7
10-s
10"
lb?
10-0
10-i
_
111
4/
411
4.t
1
a
V 1
I
3 5 10 30 50 100 300 500 1000 3000
ALTITUDE IN KILOMETERS
FIGURE N-4 PERCENTAGE ERROR IN THE VALVE OF
THE ACCELERATION OF GRAVITY AT VARIOUS ALTITUDES
INTRODUCED BY THE SIGNIFICANT FIGURE LIMITATIONS
OF THE SEVERAL TERMS OF EQUATION N-3.
10-3
10-5
lo-7
I
?
_
I
1
1
1
1
_
_
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-
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.,.
I
K.
,...
43
I
/
K.
,\
r
I
.c.
..
I
_
?
3 5 10 30 50 10.0
ALTITUDE IN KI LOME TrliS
300 500 1000
3000
FIGURE N-5 ESTIMATED PERCENTAGE ERROR IN THE
VALUE OF THE ACCELERATION OF GRAVITY AT VARIOUS
ALTITUDES INTRODUCED BY THE OMISSIONS OF TERMS
6,7, 8 AND 9 OF EQUATION (N-3).
176
?7;
0_
;
II
a
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?-?
II
10
9
SIGNIFICANT
6
5
4
3
?
I
i
1
1
1
.
i
_
_
N
N
NNB
?
7
_
\
\
I
(
t
t
_
-
I
\
\
I
3 5 10 30 50 100
300 500 1000
ALTITUDE IN KILOMETERS
FIGURE N-6 (A) MAXIMUM NUMBER OF SIGNIFICANT
3000
FIGURES AVAILABLE FROM THE EXISTING 5 TERM VERSION
OF EQUATION N -3. FOR VARIOUS ALTITUDES.
(B) THE MAXIMUM NUMBER OF SIGNIFICANT
FIGURES. OF THE VALUE OF g AT VARIOUS ALTITUDES,
COMPUTED FROM THE ADJUSTED INVERSE SQUARE LAW,
WHICH ARE IN AGREEMENT WITH VALUES COMPUTED FROM
EITHER THE 5 TERM OR 9 TERM VERSION OF EQUATION
(N-3).
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.1
-I
_71
1 1. Geometric Scale Height
First Concept - Scale height is equal to the height above any reference
altitude at which the atmospheric pressure falls to l/e of the pressure at
Ithe reference altitude in a constant gravity, isothermal atmosphere.
i (Section 3.2.1), the following equation is developed in terms of Z:
In a manner analogous to the development of Eq. (15) in terms of H
i-in P = 74r
P: TN i b R1'
IZb
For the case of an isothermal layer in a constant gravity atmosphere,
Di. (0-1) upon integration leads to
APPENDIX 0
Scale Height
P = Pb exponential -
R*(Tm)b
It Jo noted that in a constant gravity atmosphere:
H*(Tm)b (Hel)b
goMo
and it follows that
(Z Zb)
P = Pb exponential -
(Hs)b
For the case that
Eq. (0-4) .simplifies to
?
P = Pb e-1 = Pb/e ?
178
(0-2)
(0-3)
... (0-4)
(0-5)
(0-6)
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-
It appears, therefore, that in a constant gravity atmosphere and in a
layer of constant Tm, the scale height at any reference level is the incre-
ment in geometric altitude required for the pressure to fall to 1/e of the
value at the reference level. Since this MODEL does not assume constant
gravity, the above concept does not apply rigorously in these tables. In the
special case, where sea level is the reference altitude the same concept
would apply but only if the isothermal layer is assumed to extend down to
there, and only for a constant gravity atmosphere.
Second Concept - In an atmosphere of constant g and constant Tk, the
scale height at any altitude Zu is equal to the total mass of air in a unit
column extending upward from tgat altitude to infinity, divided by the den-
sity at the reference altitude.
From Eq. (33) one obtains
Ph
Pb %%lb
In a constant Tim atmosphere, TM = (VII and thus,
P
rb Pb
Equation (0-2) may then be rewritten as
p pb exponential - gg4?
WilTm)b
(0-7)
(o-8)
(o-9)
The total mass in a unit column from the reference level to infinity is:
OD goMo
j2?: pdZ = Pb! exponential
R*(Tm)b
o
Zh
(z - zb) ? (0-10)
= pb[R*('14)1] [exponential - goMo
?7/VAT 17*(1P,M)b
179
z
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,??????
i- "1--_- -a ? .
= {R*(TM)lai [ _ CO
-g?140 e e
R*(Tm)b
= Pb ? --g-diro-
(0-10b)
137* m
Since (T-)- - scale height at Hb in a constant gravity atmosphere, it
g M
o o
follows that
CO
(Hs)b
Zb
Thus the assertion of Concept 2 is demonstrated.
(0-11)
Third Concept - In a constant-g, constant-TR, constaut-M atmosphere, the
scale height at any altitude is equal to the total number of particles in a
column of unit cross section extending from a reference level to infinity,
divided by the number density at that altitude.
From Eqs. (26) and (27) of Sections 5.2.1 and 5.3.1, respectively, it
? follows that:
but
n
14,
(0-12)
(0-13)
where co = the mass of a single air particle.
Thus p = nm (0-14)
and ? Pb nbrn b (0-15)
Thus it follows directly from Eq. (0-11) that
CO
(116)bpdZ, (0-16)
neb
Zb
180
?
?
?
?
1.1
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?
???i
co
r
(H )L nmdZ.
nifilb
"b
(0-17)
The right-hand side of this equation would not strictly equal the total
number of atmospheric particles in the column, unless the molecular weight
were constant. Thus, for the assertion of the third concept to be rigor-
ously correct, it was necessary to make the restriction of constant molec-
ular weight in addition to the restrictions made in the first and second
concepts. With this constant-M restriction, Eq. (0-17) becomes
(Hdb
Zb
(0-18)
and the assertion is demonstrated. It is noted that a corollary to the
third concept is that scale height is the length of the unit column neces-
sary to enclose all the atmospheric particles normally present in an infi-
nitely long unit column, extending vertically above the reference altitude,
when these particles are compressed to the number density at the reference
level. Hence, this quantity is the basis for computing reduced thickness of
the atmosphere. Such computations are limited by the fact that constant
gravity, constant TM, and constant molecular weights are assumed in the
derivation of the expression.
2. Geopotential Scale Height
Geopotential scale height was defined in Section 4.1.3 of this paper as
Hs' GM0 ?
11:11TNI
In terms of this property the several concepts developed above do not have
the restriction of a constant gravity atmosphere. Thus Eq. (15) of Section
3.2.2 may be rewritten as
GM0
p = Pb exponential - 11*(Ti,)b (H - HO.
ri
(0-19)
For a geonutential altitude increment equal to the geupotential scale height
- R*(TM)b =g
GMo s '
?
181
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?
4.
(5--Irsy-72,1J-
,
r
`.7.1
-
2
and hence Eq. (0-19) reduces to
P = Pb/C.
-77=7:45
(0-19a)
Note that no assumption of constant gravity is made, only constant TM.
Hence, a revision of Concept 1, eliminating the constant gravity restric-
tions, will apply rigorously in this MODEL in isothermal layers. For ex-
ample, Hs' at 11 km' is 6.341,615,82 x 103 m'. Thus, at 17.341,615,82 km',
the pressure will be Pule, where Pil is the pressure at 11 km. At 14 km',
Hs' has the same value; hence at 20.341,615,82 x 103 m' altitude, the pres-
sure will be P1' '-
Th geometric altitude increment, however, will be
=
different in the two instances, accounting for the effect of variable g on
the pressure.
In geopotential form, Eq. (0-10) may be rewritten as
r co
J Hb
GM?
pdH = pbcr exponential - R*(Tm)b (H - Hb). (0-20)
Hb
By analogy this reduces to
,
(H ')b = pdH.
$
Pb
Hb
(0-21)
This equation and concept rigorously apply to isothermal layers of this
MODEL.
Equation (0-16) is. converted by analogy to
pdH
(118913
nbr%
If constant molecular weight is assumed, this equation becomes:
(H,') = 1-11:11ndR.
nb
(0-22)
n7. \
This equation would provide a better basis for computing reduced thickness
182
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for this MODEL than Eq. (0-18), but Eq. (0-23) is similarly limited by con-
stant M and constant T assumptions. Thus, for still greater accuracy of
reduced-thickness ,vacuaations consistent ulth this MODEL, additional equa-
tions accounting for variable 14 and TM must be developed.
183
7?
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.......-???????,?????-.???????!??????.???-- re- - - ?
t..
r
P
?
7-
- ??
"e?Gli,o,
_? -
APPENDIX P
More Accurate Method for Computing Geopotential in this Model
]. Adjusted Classical Approach
Equation (2d) of this paper indicates the rigorous relationship between
geopotential H, geometric altitude Z, and the acceleration of gravity g to
be
1
H _ -0/ gdZ.
a?-?
When g iu expressed by the classical, inverse-square law, adJusted for
45* 3P' 40" latitude,
g =
r )
the expression for geopotential becomes
Hgo ( rZ),
G r+Z
(p-i)
(P-2)
(P-3)
where gc) and r have the values 9.80665 in sec-2 and 6,356,766 m, respective-
ly, as indicated in Section 2.1.
62. Lambert Series Method
In Appendix N, another expression for g in terms of Z for latitude
450 32' 40" was developed from Lambert's general alternating power series.38
This specific expression is
where
g = el - c2Z + c3Z2 - c4Z3 + c5Z4 - (P-4)
cl = 9.806,65 (exact) in sec-2
c2 = 30,854.188 x 10-10 m? see4
C3 = 725.381 x 10-15 m-1 sec- ,
C4 = 15.1689 X 10-2? m-2 sec-2,
C5 = .29696 x 10-25 m-5 sec-2,
Z is in meters, and
g is in meters sec-2.
MIN
184
?
?
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r.e
11
?
S.
?0
When this expression for g is intro4uced into Eq. (P-1) the expression for
H becemes
Z
H = dZ - cif ZdZ + c3diciddZ - Z3dZ + c5of Z4dZ-...
0
where H is in standard geopotential meters.
Performing the indicated integration one obtains
H ci
C. e c3
2G
3 -140 Z4 + ;g z5-...,
(P-5)
(P-6)
where the coefficients of the various powers of Z have the following numer-
ical values:
c1
G 9.806,65
c2 30,854.188 x 10-1?
20 2 x 9.806,65
f2 725.3- x10-15
3G 3 x 9.806,65
'4 15.168 x 10-2?
4G - 4 x 9.b06,65
f_2 .29696 x 10-25
50 5 x 9.806,65
= 1.0 exact
- 1,573.12578 x 10-10
= 24.6561 x 10-15
= .386,699 x 10-2?
= .006,0563 x 10-25
Hence one obtains
H = Z - 1,573.12578 x 10-10Z2 +24'6561 x 10-15Z3
.386,6 x 10-2?z4 + .006,0563 x 10-2525-- (P-7)
(where the exponents have beea selected for convenience when Pis expressed
in units of 105 meters).
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11
11
:
0
Evaluating the five defined terms of Eq. (P-7) for various altitudes
yields the daLK presented in Table P-I. An examination of the logarithms
of successive terms of the series evaluated for particulnx altitudes shows
that the absolute magnitudes of successive terms fall off very nearly at a
constant rate, or, in other words, the logarithmic decrement of successive
terms is very nearly constant. Examples of this nearly constant logarith-
mic decrement, Alog, are given for 1,000, 300, and 100 km.
Alt. 1,000,000 m 300,G00 in 100,000 is
Term # Logic) Term Alog Logic) Term Alog Logi? Term Eilog
1 6.000,00 5.477,12 5.000,00
.803,24 1.326,11 1.803,24
2 5.196,76 4.151,01 3.196,76
.804,84 1.327,72 1.804,84
3 4.391,23 2.823,22 1.391,92
.804,55 1.327:43 1.8o4,.22
If 3.587,37 1.495,86 9.5870.1
.892,16 1.331,64 1.805,16
5 2.782,21 .164,22 7,782,21
NOTE: Underline indicates non-significant digits.
3. Extension of the Lambert Series
The departure of the logarithmic decrement from linearity is less than
one half of one perccnt uvcr the five available terms for the altitudes dis-
cussed. On the average, the differerles between the logarithms of successive
terms increase very slightly with increasing term number. It is not unrea-
sonable to assume that this pattern of logarithmic decrement with slowly in-
creasing differences might continue for a considerable number of additional
terms in the series. Employing this pattern, the values of the ninth term
of Eq- (P-7) for 1,000, 300, and 100 km are 3.6 x 10-1, 4.9 x 10-, and
3.6 x 10-10, respectively, in standard geopotential meters.
Estimated values of the 6th, 7th, 8th, and 9th terms of Eq. (P-7) for
various altitudes may also be determined graphically by plotting the loga-
rithms of the various terns as functions of term number, and connecting
those points corresponding to each specific altitude as in Fig. P-1. These
lines are then extended linearly to higher term numbers as in the dashed
line portion of Fig. P-1. The estimated values of terms 6, 7, 8, and 9 of
Eq. (P-7) determined graphically on a figure three times as large as Fig.
P-1 are given in Table P-II. Graphically determined values of the ninth
term of Eq. (P-7) for altitudes of 1,000, 300, and 100 km differ from the
three computed values given above by less than 10 per cent.
A replotting of the data of Table P-I in terms of the value of each
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...- _ ? -- -
- ?.... .. - -.....:J
-
-7 '7":"-'1=-' ' - - ? - ......3a---...-. -
- - -
LI. 1 _ ..7
C- - -
E- _ 3
---_-? Ti
a-,--7---f----
/
t
_
term of Eq. (P-7) as a function of altitude is given in Pig. P-2. The es-
timated values for the 6th, 7th, 8th, and 9th terms of the equation come
from Fig. P-1. Figure P-2 cletorly shows the contribution which each terra
in the series makes to the value of geonotential of a given geometric alti-
tude. Figure P-2 demonstrates that for errors in geopotential of less than
.1 m', the five term version of Ea (P-7) ;Toy be used only to altitudes of
about 280 km, neglecting the possible limitations due to significant fig-
ures.
4. Comparison of the Three Methods
The values of geopotential in standard geopotential meters for various
geometric altitudes are given in Table P-III. Values designated by H are
computed from the simple Eq. (P-3). Values designated by H* are computed
from the five defined terms of Eq. (P-7). Values designated by H** are
those resulting from the estimated nine-term version of Eq. (P-7). The
values of the differences H - H*, H - H**, and H* - B.-1-* are also given in
Table P-III. The difference H - H** is cf particular interest, since it
indicates the amount of error in geopotential altitude incurred by using
the simple Eq. (P-3) instead of the nine-term version of Eq. (P-7). (Below
100 km altitude the error is less than 0.1 m'.)
5. Limitation of the Five Term Lambert Serint: Illys to Nvm),..,.. of 714.emn
Because of the increase of centrifugal acceleration with altitude wnich
is not accounted for in Eq. (P-3), the departure between the value of H
from Ea. (F-3) and the value from Eq. (P-7) lb expected to increase with
altitude. The reversal of the trend resulting in smaller departures (i.e.
smaller values in H H*) above 800 km suggests the inadequacy of the five-
term version of Eq. (P-7). The difference H - H** involving the nine-term
version of Eq. (P-7) continues to increase te altitudes well over 1000 km.
A graph of the various differences is given in Fig. P-3.
6. Limitations of the Five Term Lambert Series Due to Significant Pictures
An analysis of the values and number of significant figures of terms 2,
3, 4, and 5 of Ea. (P-7) as listed in Table P-I indicates the limitations
which the nuaaer of significant figures of each term place upon the computed
value of geopotential. The results of this analysis are presented in Fig.
P-4. Below 10 km altitude, the number of significant figures in term num-
ber 2 is seen to limit the accuracy of Eq. (P-7). From 10 km to about
3,200 km altitude, term number 3 limits the accuracy of the equation, pro-
vided a sufficient number of terms is employed so that the number of terms
does not limit the accuracy at some altitude below 3,200 km.
7. Combined Limitations of the Lambert Series
The minimum numerical error obtainable with the existing five-term ver-
sion of Eq. (P-7) is given as the three-segment curve A of Fig. P-5.
187
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?
?
I ?
-
?
Segment a represents the limitation due to significant figures of term 2;
segment b represents the limitation due to significant figures of term 3;
while segment c represents the limitation due to the termination of the
series after term 5. Line B of that same graph represents the minimum nu-
merical error incurred in using the simple equation for geppotential, Eq.
(P-3). This error is determined from the values of H - H. The differ-
ence between these two curves (given more accurately by values of H - H*
in Table P-III) shows that for altitudes between 10 and 500 km, an improve-
ment of only one significant figure in geopotential altitude is obtained by
switching from Eq. (P-3) to the presently available form of Eq. (P-7).
8. Requirements Which the Extended Lambert Series Must Meet
In order to obtain the ten significant figure accuracy desirable for
standard atmosphere computations at altitudes of 300, 500, and 1,000 km;
three, four, and eight additional terms, respectively, must be developed
for Eq. (P-7). Also, the following numbers of significant figures should
be available for the several coefficients:
4
Alt.
300 km
500 km
1 000 km
Term #
Number of Sig. Fig.
Number of Sig. Fig.
Number of Sig. Fig.
2
9
9
10
'
3
7
8
9
4
6
7
8
5
5
6
7
6
3
5
7
7
2
4
6
8
1
2
5
9
1
4
10
3
11
2
12
2
13
3.
These requirements reflect back directly upon LaMbert's general expres-
sion for g as a function of Z and 0; i.e.,
g = ci - (a2 + b2 cos 20)Z + (a3 + b3 cos 20)Z2
4
- (8 b cos 20)Z3 + (a5 + b5 cos 20)&4'
4 .
- + (ref. 38)(P-8)
188
ri
3
?1
!
I
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r'
To meet the above requirementn for latitude 90?, the coefficients a2, a3,
114, ... an and b2, b3, b4, ... by, of Eq. (P-8) must have nuMbers of eighif-
leant figures graphically estimaed to be the following:
Alt.
7j00
500 km
1.000 km
an
bn
an
bn
abn
n
2
9
7
9
7
lo 7
3
7
5
8
6
97
4
6
3
7
4
85
5
5
3
6
4
75
6
3
1
5
3
75
7
2
4
n
a
6 4
8
1
2
1
5 4
9
1
4 3
10
3 3
II
2 2
12
2 2
13
1 1
To meet stAndard atmosphere reauirement at latitude 45 32' 4o", the num-
ber of significant figures required for bn would be one to two less than
required for the case when 0 = 90?. In any case, ba must have enough sig-
nificant figures so as not to invalidate the accuracy of an.
9. Conclusions
This analysis is strictly mathematical and does not consider whether it
is physically possible to obtain the required number of terms or the neces-
sary accuracy in Eq. (P-4) or Eq. (P-8). If no substantial improvement of
Eq. (P-7) is physically possible through a better expression for the accel-
eration of gravity in Eq. (P-4) or Eq. (P-8) and if one must resort to ar-
bitrary detinitions as in the standard sea level pressure, then it is sug-
gested that Eq. (P-2) for g be retained by definition, in which case geo-
potential is given by the simple Eq. (P-3), sufficiently accurate for most
engineering purposes. Only a study of Lambert's unpublished method for the
development of Eq. (P-8) will suggest the course to follow.
189
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'71 "*P?Irmerrr",...v. -*re - tr,*.min?
1st Term
1,000
5,000
10,000
20,000
30,000
40,000
50,000
60,000
70,000
30,000
90,000
100,000
200,000
300,000
400,000
500,000
2nd. Term
.157,312,58
3.932,814,p
15.731,257,_
62.925,031,2
141.581,320
251.700,125
393.281,445
566.325,281
770.831,0
1,006.800,4--
1,274.231,
1,573.125,78
6,292.503,12
14,158.1so
25,170.012,5
39,328.115
3rd. Term
.m0,024,656
.003,082,01
.024,656,1-
.2.91,21I2
1.577,22
3.082,01
5.325,72
8.45-1,-67
12.623,2
3.7.9yg,2
24.656,1
197-2.'12
665.715
1,577.22
3,082.01
600,000
56,632.528,1
5,325.72
700,000
77,4083.16V
8,457 .ij
800,000
100,680.047,1
12,623.r
900,000
127,423.1:4
17,974.3
1000,000
157,312.51E
24,65.6:r.
Table P-I.
Values of the
NCEE:
4th Term
.000,000,003,866,2
.000,002,416,.?1
.000,038,662,2
.000,618,718
.003,132,2r
.009,899;g
.024,168,7.
.050,1'0,2
.158,391,2
.253)712
.386,622
6.187,18
31.322,T-
98.994,72
241.6,g1
501.162
1,583.9172
2,537.12
3,866.22
5th Term
.0000,000,000,000,6
.000,000,001,892,2
.000,4000,060,56
.0?0,(X1,938,02
.000,o14,716 r8
.000,062,016
.000,189,222
.000,470,211
.001,017,88
.001,984,53
.003,576,2
.006,056,2
.193,802
6.201,7
18.925,2 .
47.0211
101.788
198.1g
357.62
605.:E
First Five Terms of Eq.(P-7)for Various Geometric Altitudes as
Indicated by the Value of the First Term. (Value of terms in
The underlined figures are beyond the limit of significance, but are
carried for smoothness.
I.
I.
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
n.)
0
--r,r!irnirrsmq(PrtnliEMI'DVIKTr--'"""""'"-"'-
Alt.
km
1
5
10
20
30
140
.....????????,..?????????
?
???? ?? " r -
.ro.7./1.? ?
H = rZ
r-1-Z
999.242,712,0
4,996.070,273,2
9,984.293,4-58
19,937.272,75
29,859.083,6T
39,749.87-5;65
50 49,609.787,52
6o 59,438.9?22,72
70 69,237.*3;63
80 79,005.711;8I
90 88,743.356,2i
100
200
300
400
500
600
700
Boo
900
1,000
98,451.237,0
193,892:431,5
286,472.921;3
376,320.032,3
463,532:6(32,8
548,251.817,0
630,563.222,6
710,57X.133,13
788,31Z.-635,4
864,ODYIE
H*, 5 Terms H**, 9 Terms
of Eq. (P-7) of Eq. (P-7)
999.842,712,0
4,996.070,265
9,984.293,360
399:97:7:8:6:
29,859.081,27
49,609.776,6
59,438.950,8
69,237.533,6
79,005.667
88,743.492
98,451.149
193,898.75
286,477.72
376,315.2
463,531.1
548,239.1
630,547.2
710,558.4
78B,371.6
8611,082.2
A
same as H*
286,477.6
576,314.8
463,529.8
548,235.1
630,537.1
710,531.9
788,325.7
8610?0'1
H - H**
.000,000 .000,000
.000,008 .000,008
.000,078 .000,078
.000,68 .000,68
.002,3 .002,3
.005,6 .005,6
.010,9 .010,9
.018,9 .018,9
0030,1 .030,1
.045 .045
.064 .o64
.088 .o87,4
.68 .685
2.2 2.26
4.8 5.22
8.6 9.85
12.7 16.7
15.9 26.0
15.7 036.2
8.4 50.3
-11.5 70.6
.000,000,000
.000,000,005
.000,000,063
.000,000,397
.000,001,329
.000,004,36
.000,011,08
.000,022,7
.000,047,3
.000,093,c
.005,874
.061,42
.377,3
1.297,6
4.03o
10.12
20.50
41.86
82.o4
Table Values of Geopotential in Stand-.rd Geopotential Meters for Various Geometric
Altitudes at Latitude 450 32, ho" Computed from Three Different Equations as
Indicated, and the Differences Between Those Values of Geopotential, also in
Standard Geopotential Meters.
7
NOTE: The underlined portion of valuea of H indicates the degree of departure from
values of H* and H.
Nonsimificant figures in values of B* and H** are depressed.
The difference tabulations are reliable to not Imre than three significdht figures
and usually only to two.
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9
7
6
3
2
N
N
too km
\,.
\.km
NI
"
\*
\:?DOkm
N--
\\\\
N
N
\
\
\
\
N
\
\
\ \t?
COMPUTED
ESTIMATED
BY
EXTRAPOLATION
_
NN.
NN
NN
Nsx
N\
\
\
NN
I
I..
\
111
Makam
Mal
a.
_Ilumml4.
METERS
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L \\
\ \)
\
lel
--N? .
\
0.k.
.
ihk\
I
.,,zim
\
,
I
STANDARD GEOPOTENTIAL
lo-9 icr? I O i cr` I o" I 0-4 10-5 io? id lot IO 3 104 los los
FIGURE P-1 COMPUTED AND ESTIMATED ABSOLUTE VALUES OF 9 TERMS OF EO.(P-7) FOR
VARIOUS ALTITUDES.
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Declassified in Part - Sanitized Copy Approved for Release . 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
I
I
I
I
1st It"
f..9'
1
/
I
r
tt6
/ ////
k 'S
r
"V"
k
I / //
ke
k
c2, 11.1 e ei
, (,
I
/
,
/ 1 , I I
5 10 30 50 100
300 500
ALTITUDE IN GEOMETRIC KILOMETERS
FIGURE P-2 ABSOLUTE VALUE OF THE FIVE DEFINED AND FOUR
ESTIMATED TERMS OF EQUATION P-7 AS A FUNCTION OF ALTITUDE
. Itil
APRIL III?
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A, H-114
A., NEGATIVE
BRANCH
OF A
B, HH"
C, HI- HXX
H ?-.tii--
WHERE 2
H12 5 TERM VERSION OF EQ. (P-7)
H" 2 ESTIMATED
?OF
EQ.(12-7)
9 TERM
VERSION
0 100 200 500 400 500 600 700 800 900
ALTITUDE IN KILOMETERS
FIGURE P-3 DIFFERENCES BETWEEN VALUES OF GEOPOTENTIAL
FROM THREE DIFFERENT EQUATIONS AS SeECIFIED, FOR VARIOUS
ALTITUDES.
P
A?IIIL 1)57-
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/
ip
* 4
re
q- t
e.
A
I I
1 I
II
10 30 50 100
300
000
ALTITUDE IN KILOMETERS
FIGURE P-4 NUMERICAL ERROR CONTRIBUTED BY SIGNI?
FICANT FIGURE LIMITATIONS IN EAcH OF TERMS 2,3, 4
AND 5 OF EQUATION (P-7) FOR VARIOUS ALTITUDES.
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? ? ? ? ? ? ? ? ? ?
y!
NUMERICAL ERROR IN
( LOGAR ITHMIC UAL( 1
0
?
103 -r I I ii
II
I Oa
C
I0' I
3 .5 I 3 5 10 30 50 100 300 500 1000 5000
ALT IT UDE IN KILOMETERS
FIGURE P-5 THE ALTITUDE VARIATION OF
(A), MINIMUM NUMERICAL ERROR ASSOCIATED WITH
THE EXISTING 5 TERM VERSION OF EQUATION P-7
FROM BOTH SIGNIFICANT FIGURE CONSIDERATIONS,
AND A LACK OF SUFFICIENT NUMBER OF TERMS.
1 I
I 1
I I
(13), MINIMUM NUMERICAL ERROR ASSOCIATED WITH THE
pSE OF THE ADJUSTED VERSION OF H=
r +z z AT
VARIOUS ALTITUDES AT 45? 32'40" L.
? R
? APRIL 111117
197
,
1
, . . . \ ' Li
L
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0
REFERENCES
1. Bates, D. R., "The Temperature of the Upper Atmosphere," Proc. Ph.
Soc. London, 64 B, 805-821, Sept. 1951.
2. Bates, D. R., "A Discussion on 'Radiative Balance' in the Thermosphere,"
Proc. Royal Soc. Iondon, Series A, 236 No. 1205, 206-211, 1956.
3. Bjerknes, V. et al, "Dynamic Meteorology and Hydrography," Carnegie
Institute of Washington Publication 88, Washington, D. c.,73511T7-
4. Brombacher, W. G., "Tables for Calibrating Altimeters and Computing
Altitudes Based on the Standard Atmosphere." NAM Rnt, 2116, 1926.
5. Brombacher, W. G., "Altitude-Pressure Tables Based on the United States
Standard Atmosphere," NACA Rpt. 538, Sept. 1935, Reprint 1948.
6. Brombacher, W. G., "Proposed Standard Atmosphere to 160 km (500,000 ft),"
Nat. Bur. Stand. Rpt. 2680, 5 June 1953.
7. Chapman, S. and T. G. Cowling, Mathematical Theory of Non-uniform Gases,
p. 101, Cambridge University Press, Cambridge, England, 1952.
8. Chapman, S., "The Solar Corona and the Temperature cf the Ionosphere,"
Proc. of the Washington Conf. on Theoretical Geophysics, 1956, J. Geophm.
Res. 61, No. 2, Part 2, 350-351, June 1956.
9. Chapman, S., "Speculations on the Atomic Hydrogen and the Thermal
Economy of the Upper Ionosphere," Threshold of Space, Pergamon Press, Inc.,
New York, N.Y., in press, 1957.
10. Chapman, S., "Notes on the Solar Corona and the Terrestrial Ionosphere,"
Smithsonian Contributions to Astrophysi, No. 1, 1957.
U. Cohen, E. R., et al, "Analysis of Variance of the 1952 Data on the
Atomic Constants and a Low Adjustment," Rev. Mod. Phys.. 27,, 363-380,
1955.
12. Crittenden, C. E., Nat. Bureau Stand., "International Weights and
Measures, 1951.0, Science 120, 1007, 1954.
13. Defforges and Lubanski, Com. Internat. des Poids et Mes., Ann. I,,
135, Paris, 1892.
14. Diehl, W. S., "Standard Atmosphere Tables and Data," MCA Rpt. 218,,
Oct. 1925.
198
-t
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F.?r-i
1? ... al-
7....1 rt r t.;-)..._ - ___ , -
1.?.?
,--
._?
..
?
-
&
a
REFERENCES (contd.)
15. Dryden, H. L.. " A Re-examination of the Potsdam Absolute Determination
or Gravity." Ngt, Bur. Stand. J. Res., 29, 303, 1942.
16. Du Mond, J. W. M. and E. R. Cohen, "Least-Squares Adjusted Values of the
Atomic Cnnstants as of December 1950," Phys. Rev., 82 555, 1951.
17. Geophysics Research Directorate, "Minutes - Open Meeting on Extension
to the Standard Atmosphere on 2-4 Nov. 1953," (unpublished).
18. Geophysics Research Directorate, " Minutes of the First Meeting of the
Working Group on Extension to the Standard Atmosphere," 5 August 1954,
(unpublished).
19. Geophysics Research Directorate, "Background and Summary of Proceedings -
Second Meeting, NCESA, 25 May 1955," (unpublished).
20. Geophysics Research Directorate, "Background and Summary of Proceedings -
Third Meeting, WIIESA, 2 March 1956", (unpublished).
21. Gregg, W. R., "Standard Atmosphere," RAGA Rpt. 147, 1922.
22. Grimminger, O., "Analysis of Temperature, Pressure, and Density of the
Atmosphere Extending to Extreme Altitudes," Rand Corporation, Santa
Monica, Cal., November 1946.
23. Harrison, L. P., "Relation Between Geopotential and Geometric Height,"
Smithsonian Meteorological Tables. Sixth Edition, 217-219, Washington,D. C.,
1951.
24! Harrison, L. P? Private communication to WGESA Subcommittee on Constants.
25. Hilsenrath, J., et al., "Tables of Thermal Properties of Gases," Nat.
Bur. Stand. Circular 564, Washington, D. C., issued 1 Nov. 1955.
26. Ineernational Civil Aviation Organization, Montreal, Canada, and Langely
Aeronautical Laboratory, Langely Field, Va., "Manual of the ICAO
Standard Atmosphere - Calculations by the NAGA," NAGA Technical Note
22L, May 1954.
27. International Civil Aviation Organization, Montreal, Canada, "Manual
of the ICAO Standard Atmosphere," ICAO Document 7488, May 1954.
28. International Civil Aviation Organization, Montreal, Canada, and Langely
Aeronautical Laboratory, Langely Field, Va., "Standard Atmosphere -
Tables and Data for Altitudes to 65,800 Ft.," NAGA Rpt. 1235, 1955.
)99
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Declassified in Part - Sanitized Copy Approved for Release
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7
"0, C11.1)1 11/21IntrtiVroNVIM4?"11,7
REFERENCES (Contd.)
?
29. International Commission for Air Navigation, Official BulieLin NO. 7,
Resolution No. 192, Paris, France, Dec. 1924; also Official Bulletin
1121_2.t2. Resolution No. 1053, Dec. 1938; also Smithsonian netcorolo ice].
Tables, Sixth Revised Edition, p.268, Washington, D. C., 1951.
30. International Commission for the Exploration of the Upper Air, "Report
of the Meeting in London, April 16-22, 1925," Meteor. Off. Publ. 281,
London, Eng., 1925.
31. International Meteorological Organization, Conference of Directors,
Resolution 164, Washington, D. C., 1947.
32. International Meteorological Organization, Aerological Commission,
Abridged Final Report, Publication 62, Lausanne,Switz., 1949.
33. Jacchia, Luigi, G. Private communication.
34. Kallman, H. K. and W. B. White, "Physical Properties of the Speculative
Standard Atmosphere from 130 Km to 300 Km," Rand Corporation, Santa
Monica, Cal., Feb. 1956.
35. Kallman, H. K., W. B. White, and H. E. Newell, Jr., "Physical Properties
of the Atmosphere from 90 to 300 Kilometers,:: J. Geophys. Res., 61, NO. 3,
Sept. 1956.
36: Lambert, W. D., "Formula for the Geopotential, Including the Effects of
Elevation and of the Flattening of the Earth," unpublished mss., 15 Oct.
1946.
?
37. Lambert, W. D., "Some Notes on the Calculation of Geopotential,"
unpublished mss., 1949.
38. Lambert, W. D., "Acceleration of Gravity in the Free Air," Smithsonian
Meteorological Tables Sixth Edition, p. 490, Washington, D. C., 1951.
39. Mfller, L. E., Molecular Weight of Air at High Altitudes," Geophysics
Research Directorate, unpublished, 15 Feb. 1956.
Minzner, R. A., 'Three Proposals for U. S. High Altitude Standard
Atmosphere," Geophysics Research Directorate, unpublished, April, 1955.
41. Hinzner, R. A., "Proposed Extension to the ICAO Standard Atmosphere,Model
16 - Using Variable Gravity, Molecular-Scale Temperature and Geopotential
Altitude," Geophysics Research Directorate, unpublished, April, 1955.
200
? ?
-
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- Sanitized Copy Approved for Release
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?
?
?
^ f? d?-,.Pars-....""????'.?????-????????..-----""??'
?
4 REFERENCES (Contd.)
42. Minzner, R. A., "The 1956 ORD Proposal for a Speculative Standard Atmos-
phere," Geophysics Research Directorate, unpublished, Feb. 1956.
43. OISullivan, W. J., Jr., "(NCA) Supplemental Report of Recommendations,
Subcommittee on PhyRical Constants, WGESA, to Parent Organization,"
unpublished, 1955.
44. ProceS-Verbaux des &canoes du Comitd International des Poids et Measures,
Tome XXI, 1948.
)45.
Rocket Panel, The, "Pressures, Densities, and Temperatures in the Upper
Atmosphere," Phys. Rev., 88. No. 5, 1027-1032, 1 Dec. 1952.
46. Rossini, F. T. et al, "Status of the Values of the Fundamental Constants
for Physical Chemistry as of 1 July 1951," J. Amer. Chem. Soc. 74, 2699,
1952.
47. Sissenwine, N., "Report on Recommendations, MESA to Parent Organization,"
Geophysics Research Directorate, unpublished, 15 Feb. 1956.
Lo
Stimson, H. F., "Heat Units and Temperature Scales for Calorimetry,"
Amer. J. Phys,., 23,, 614, 1955.
49. Toussaint, A., "Etude des Performances diun Avion Nuni dlun Moteur
Suralimente," IdAeronautiquel 2, 188-196, 1919: No.2, Part 2, 350-351,
June 1956.
50. U. S. Weather Bureau and Geophysics Research Directorata,"CoTmittee
on Extension to the Standard Atmosphere Announcenent, 26 Octoner, 19:6"
Monthly Weather Rev. 84, 333, 1956.
51. U. S. Weather Bureau and Geophysics Research Directorate, AFCRC, "ICAO
Standard Atmosphere Extension," Jet Propulsion, 26, 1097, 1956.
52. Warfield, C. N., "Tentative Tables for the Properties of the Upper
Atmosphere," NACA. Technical Note No. 1200, Jan. 1947.
53. Yerg, D. G. "The Applicability of Continuous Fluid Theory in the Higher
Atmosphere," J. Meteor, 11, No. 5, 387-391, October 1954.
201
? ?-?
.t.
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7.1
41
I I
LIST OF Am FORCE SURVEYS IN GEOPHYSICS''
(Unclassified)
Security
Number
Title
Author
Date
Class.
1
W. K. Widger, Jr.
Mar 52
S-RD
2
Methods of Weather Presentation for Air
W. K. Widger, Jr.
Jun 52
Defense Operations
3
Some Aspects of Thermal Radiation From the
R. M. Chapman
Jun 52
Atomic Bomb
4
Final Report on Project 8-52M-1 Tropopause
S. Coroniti
Jul 52
5
Infrared as a Means of Identification
N. Oliver
Jul 52
J. W. Chamberlain
6
Heights of Atomic Bomb Results Relative to
R. M. Chapman
Jul 52
S-RD
Basic Thermal Effects Produced on the Ground
G. W. Warns
Peak Over-Pressure at Ground Zero From High
N. A. Haskell
Jul 52
Altitude Bursts
8
Preliminary Data From Parachute Pressure
N. A. Ilaskell
Jul 52
S-RD
Gauges. Operation Snapper. Project 1.1
Shots No. 5 and 8
9
Determination of the Horizontal
R. M. Chapman
Sep 52
M. II. Seavey
10
Soil Stabilization Report
C. Moline
Sep 52
11
Geodesy and Gravimetry, Preliminary Report
R. J. Fcrd,
Maj., USAF
Sep 52
12
The Application of Weather Modification
C. E. Andzrson
Sep 52
Techniques to Problems of Special Interest
to the Strategic Air Command
13
Efficiency of Precipitation as a Scavenger
C. E. Anderson
Aug 52
S-RD
14
Forecasting Diffusion in the Lower Layers of
the Atmosphere
B. Davidson
Sep 52
15
Forecasting the Mountain Wave
C. F. Jenkins
Sep 52
16
A Preliminary Estimate of the Effect of Fog and
J. H. Pertly
Sep 52
S-RD
Rain on the Peak Shock Prescure From an
H. P. Gauvin
Atomic Bomb
1.
*Titles that arc omitted ars classified.
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Declassified
in Part - Sanitized Copy Approved for Release
41
it
?
50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6
111:-
_
. ?
-
r:r
:
?
?
"
Securay
Number
Title
Author
Date
Class.
17
Operation Tumbler-Snapper Project 1.IA. Thermal
M. O'Day
Sep 52
C-RD
Radiation Measurements With a Vacuum Capacitor
J. L. Bohn
Microphone
F. II. Nadig
R. J. Cowie, Jr.
18
Operation Snapper Project 1.1, The Measurement
of FrLe Air Mona Blast Pressures
J. 0. Vann,
Lt Col., USAF
Sep 52
S-RD
N. A. Haskell
19
The Construction and Application of Contingency
E. W. Wahl
Nov 52
Tables In Weather Forecasting
R. M. White
II. A. Salmela
20
Peak Overpressure in Air Due to a Deep Under-
N. A. Haskell
Nov 52
Wta.Cr. Explosion
21
Slant Visibility
R. Penndorf
Dec 52
B. Goldberg
D. Lufkin
22
Geodesy and Gravimetry
R. J. Ford,
Maj., USAF
Dec 52
23
Weather Effect on Radar
D. Atlas
Dec 52
V. G. Plank
W. H. Paulsen
A. C. Chmela
J. S. Marshall
T. W. R. East
K. L. S. Gunn
24
A Survey of Available Information on Winds
C. F. Jenkins
Dec 52
Above 30,000 Ft.
25
A Survey of Available Information on the Wind
W. K. Widger, Jr.
Dec 52
Fields Between the Surface and the Lower
Stratosphere
26
A. L. Aden
Dec 52
S
L. Katz
27
N. A. Haskell
Dec 52
S
28
A-Bomb Thermal Radiation Damage Envelopes for
R. If. Clnyman
Dec 52
S-RD
Aircraft
G. W. Wares
M. S. Seavey
29
A Note on High Level Turbulence Encountered
by a Glider
J. Kuettner
Dec 52
a
?
-
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?
?
LJ'-' 1.1
,
1
-
41
tt
Number
Title
Author
Date
Security
Class.
30
Results of Controlled-Altitude Bf11/001i Flights
at 50,000 to 70,000 Feet During September 1952
T. 0. llaig
Maj., USAF
Feb 53
II. A. Craig
31
Conference: Weather Effects on Nuclear
13. Grossman, Ed.
Feb 53
S-RD
Detonation
32
Operation IVY Project 6.11. Free Mr Atomic
N. A. Ilaskell
Mar 53
S-RD
Blast Pressure and Thermal Measurements
P. R. Gast
33
Variability.of Subjective Cloud Observatiens - 1
A. M. Galligan
Mar 53
34
Feasibility of Detecting Atmospheric Inversions
by Electromagnetic Probing
A. L. Aden
Mar 53
35
Flight Aspects of the Mountain Wave
C. F. Jenkins
Apr 53
J. Kuettner
36
Report on Particle Precipitation Measurements
A. J. Parziale
Apr 53
S-RD
Performed During the Bustei Tests at Nevada
37
C-1 Envelope Study for the XB-63, 13-52A,
and F-89
N. A. Haskell
M. H. Scavey
Apr 53
R. M. Chapman
38
Notes on the Prediction of Overpressures
N. A. Haskell
Apr 53
From Very Large Thermo-Nuclear Bombs
39
Atmospheric Attenuation of Infrared Oxygen
N. J. Oliver
Apr 53
Afterglow Emission
J. W. Chamberlain
40
R. E. Hanson,
Capt, USAF
May 53
41
The Silent Area Forecasting Problem
W. K. Widger, Jr.
May 53
42
An Analysis of the Contrail Problem
R. A. Craig
Jun 53
43
Sodium in the Upper Atmosphere
L. E. Miller
Jun 53
44
Silver Iodide Diffusion Experiments Conducted
at Camp Wellfleet, Mass., During July-August
P. Goldberg
A. J. Parziale
Jun 53
1952
Q. Faucher
B. Manning
H. Lettau
45
The Vertical Distribution of Water Vapor in the
L. E. Miller
Sep 53
Stratosphere and the Upper Atmosphere
a
46
Operation IVY Project 6.11. Free Air Atomic
N. A. Haskell
Sep 53
S-RD
Blast Pressure and Thermal Measurements ?
Final Report
J- 0. Vann,
Lt Col, USAF
P. H. Gast
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
lassified in Part -Sanitized Co Approved for Release
16,y,
t.
i!
50-Yr 2014/03/20 CIA-RDP81-01043RUuzouvu,
?
Security
Number
Title
Author
Data
47
Critical Envelope Study for the I161-A
N. A. Haskell
Sep 53
S-RD
R. M. Chapman
M. H. Seavey
48
Operation Upshot-Knothole Project 1.3. Free
N. A. Haskell
Nov 53.
S-RI)
Air Atomic Blast Pressure Measurements.
Revised Report
R. M. Brubaker,
Maj., USAF
49
Maximum Humidity in Engineering Design
N. Sissenwine
Oct 53
50
Probable Ice Island Locations in the Arctic
A. P. Crary
May 54
Basin, January 1954
I. Browne
51
Investigation of TRAC for Active Air Defense
G. W. Wares
Dec 53
S-RD
Purposes
R. Pentalorf
V. G. Plank
B. H. Gritssman
52
Radio Noise Emissions During Thermonuclear
T. J. Keneshea
JIM 54
Reactions
53
A Method of Corre?cting Tabulated Rawinsonde
Leviton
Jun 54
Wind Speeds kr Curvature of the Earth
54
A Proposed Radar Storm Warning Service for
M. G. H. Ligdr
Aug 54
Army Combat Operations
55
A Comparison of Altitude Coe:action,* or
N. A. Haskell
Sep 54
Blast Overpressure
56
Attenuating Effects of Atmospheric Liquid
H. P. Gauvin
Oct 54
Water on Peak Overpressures from Blast Waves
J. H. Healy
M. A. Bennet
57
Windspeed Profile, V7indshear, and Gusts for
N. Sissenwine
Nov 54
Design of Guidance Sys.ems for Vertical Rising
Air Vehicles
58
The Suppressiou of Aircraft Exhaust Trails
C. E. Anderson
Nov 54
59
Preliminary Report on the Attenuation of Thermal
R. M. Chapman
Nov 54
S-RD
Radiation From Atomic or Thermonuclear Weapons
M. H. Seavey
60
Height Errors in a Rawin System
R. Leviton
Dec 54
61
Meteorological Aspeas of Constant Level
W. K. Widger, Jr.
Dec 54
Balloon Operations
M. L. Baas
E. A. Doty, Lt
E. M. Darling, Jr.
S. B. Solot
fru- Release
-
50-Yr 2014/03/20: CIA-RDP81-01043R00260007000(
Declassified in Part - Sanitized Copy Approved for Release
?
50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
?
Security
Number
Title
Author
Date
Class.
62
Variations :n Geometric Height of 30 to 60,000 Ft.
N. Siasenwine
Dec 54
C-MA
PICtbillta Altitudes
A. E. Cole
W. Baginsky
63
Review of Time end Space Wind Fluctuations
W. Bugitusky
Dec 54
Applicable to Conventional BaHistic Dater-
minations
Sissenwine
B. Davidson
H. Lettau
64
Cloudiness Above 20,000 Feet for Certain
A. E. Cole
Jan 55
Stellar Navigation
65
The Feasibility of the Identification of Hail
and Severe Storms
D. Atlas
R. Donaldson
Jan 55
66
The Rate or Rainfall Frequencies Over Selected
A. E. Cole
Mar 55
Air Routes and Destinations
N. Sissenwine
67
Some Considerations on the Modelling of
N. A. Haskell
Apr 55
S-RD
Cratering Phenomena in Earth
68
The Preparation of Extended Forecasts of the
R. M. White
May 55
Pressure Height Distribution in the Free Atmos-
phere Over North America by Use of Empirical
Influence Functions
69
Cold Weather Effects on 13-62 Launching Personnel
N. Sissenwine
Jun 55
70
Atmospheric Pressure Pulse Measurements:
E. Flauraud
Acg C5
S-RI)
Operation Castle
71
Refraction of Shock Waves in the Atmosphere
N. A. Haskell
Aug 55
72
Wind Variaoility as a Function of Tillie at Muroc,
California
B. Singer
Sep 55
73
The Atmosphere
N. C. Gerson
Sep 55
74
Areal Variation of Ceiling Height
Baginsky
Oct 55
.C-MA
A. E. Cole
75
An Objective System for Preparing Operational
I. A. Lund
Nov 55
Weather Forecasts
76
The Practical Aspect of Tropical Meteorology
C. E. Palmer
Sep.55
C. L. Wise
L. J. Sternpson
G. H. Duncan
77
Remote Determination of Soil Trafficability
by Aerial Penetrometer
C. Molineux
Oct 55
?
npe.lassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03120: CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Cop Approved for Release
?
50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
'!?
Number
78
79
80
81
82
83
at
85
Title
Effects or die Primary Cosmic Radiation
on Mutter
TropeephcriO Variations of Refractive Index
at MicrowavP Frequencies
A Program to Test Skill in Terminal
Forecaating
Extrme Atni',spheres and Ballistic Densities
Rotational Vrequencies and Absorption
Coefficients of Atmospheric Gases
10,00pheric gIfects on Positioning of Vehicles
at High AltitPdes
Pre.Trough qinter Precipitation Forecastidg
Geomagnetic Field Extrapolation Techniques ?
An EvalttatioP of the Poisson Integral for a Plane
Author
H. 0. Curtis
_
C. F. Catnpen
A. E. Cole
I. I. Gringorten
I. A. Lund
M. A. Miller
N. Siasenwine
A. E. Cole
S. N. Ghooh
H. D. Edwards
W. Pfister
T.J. Keneshea
P. W. Funks
J. F. McClay
P. Fougere
?
Security
1)ce Man.
Jan 56
Oct 55
Jun 55
Jul 55
Mar 56
Mar 56
Feb 57
Feb 57
?
?
?
'
?, ?
,
1
,
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6
STAT
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6