THE ARDC MODEL ATMOSPHERE, 1956

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CIA-RDP81-01043R002600070006-6
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U
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229
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March 20, 2014
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6
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December 1, 1956
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REPORT
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Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 R STAT Next 1 Page(s) In Document Denied 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 ... 4' ? --r-4.4-.4*."c` ? ? ? - 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 _ Declassified in Part - Sanitized Copy Approved for Release @ STAT ? 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 PN:Zarr=a0=7Arttl. m mm ^ - ? - - - .73 - ? -1;1 - r.? ? 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 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 , e =MUM 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-A Declassified in Part - Sanitized Co y Approved for Release ? 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6 ? ca749421LiClAt %.i? ftnewriyawsticearMMIIIMEr f.R 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. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 )eclassified in Part - Sanitized Copy Approved for Release - 50-Yr 2014/03/20 CIA-RDP81-01043R002600070006-6 *A " , -....=4z.Log2mtAzow 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. - ii ConrF - Caniti7Pr1 nnpv 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 44: 19). .2:0? ii 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 ;I npHaccified in Part - Sanitized Copy Approved for Release 0 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6 Declassified in Part- Sanitized Copy Approved 4 ve.CAL41,e ? 1 JA-RDP81-01043R002600070006-6 ? ..411 de 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 iv Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: rIA-RnP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ? ...fxszaziasszazzaw 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 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 N.- ????- - F.- 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 - Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 145 147 148 151 I. Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ? a - 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 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 - 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 ??? ? ? \t 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 .4 1 c.Z1ijTI ?7 L'.;."'5 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 ! 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 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 _ Declassified in Part - Sanitized Copy Approved for Release 3120- CIA RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ,?? 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 , .1 npriassified 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 , 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.) - 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 ? , 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 -.. ? ^ ? 0 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 -;;;? 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 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 0 _,=. . _ _ ? 7 ,, ?=-----u---;"---L...a..z.-----'=--t-- ..,,,,,.t,;11.1.T,j-_,,,_,__. , ; _ 1. ? 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 Declassified in Part - Sanitized Copy Approved for Release @?0-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 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 a ? 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 - ,.? ? 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 ^ Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 20. 81 01043Roo26onn7nnns_R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 , 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. - 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 a , ? 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 Declassified in Part - Sanitized Copy Approved for Release @ 20 CIA RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 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 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 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 ? - 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) Declassified in Part - Sanitized Copy Approved for Release @ 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 -7= 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) .-- ! Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr IA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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) Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014 3/20 . CI - -0 Rnn9Rnnn7nnnA Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 1 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 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 II 1 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. 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 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 201 03/20 . CIA-RDP8I- ROfl7fl?n7nnrut R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ; 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) 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 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;- nRclassified in Part - Sanitized Copy Approved for Release @O-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 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 ? Declassified in Part - Sanitized Copy Approved for Re 50-Yr 2014/03/20 ? CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Co .y Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 00 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-010431Rnn9Rnnn7nnnR_a Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 .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 es Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr IA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ? "?.) 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) 4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-m nanpnnoRnnn7nrm0 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6 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 ; 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 ? 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 ?6;11L4 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20. DP81 01043R00260007000A-R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 - 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 _ 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 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, 22 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 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 I 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 ? 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) \ Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr ? CIA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 -\ 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 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 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 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 _ 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 ? 27 Declassified in Part - Sanitized Copy Approved for Release @ 20 CIA RDP81-01043R002600070006-6 D I -s ? ? ? RI 0-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 - ? _ 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; .1 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 0. 8 01043R002600n7nnns-R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 29 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 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 30 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014 3/20 . CI - -0 Rim9Rnnn7nnnA A Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6 1 ...???????????? ? 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). Declassified in Part - Sanitized Copy Approved for Release @,3-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 - - ;?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; 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 ? 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: 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 - ? 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 ? npriaccifiari 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 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 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 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 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 .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) 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 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr IA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 39 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014 03/20 . CI - 1-0 n7snnn7nnnn Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 ? ? S. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 20. 81 01043Roo26onn7nnns_R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20 CIA-RDP81-01043R002600070006-6 131 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 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 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 _ ? ' ! ? '-- Declassified in Part - Sanitized Copy Approved for Release @ 2014/03/20 ? CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 - 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy A ? proved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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) nnr?InccifiPri 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 ^ 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 ? \ ! Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr A RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 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 ;.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 ? 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 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: Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014 03/20 . CI - 1-0 n7Rnnn7nnnR Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 Declassified in in Part - Sanitized Copy Approved for Release @,3-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 ..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 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 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 "--? Declassified in Part - Sanitized Copy Approved for Release @ 2014/03/20 ? CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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. 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 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 Declassified in Part - Sanitized Copy Approved for Release 2014/03/20 ? CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-010431ROn9Rnnn7nnnA_A Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 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 \ 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. Declassified in Part - Sanitized Copy Approved for Release @ /20 ? CIA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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. 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 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. eclassified in Part - Sanitized Copy Approved for Release so ? 50-Yr 2014/03/20 --- Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ; 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 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 ' 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 Declassified in Part - Sanitized Copy Approved for Re (1460 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 ?_1 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) 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 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 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 _ - _ 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 Declassified in Part - Sanitized Copy Approved for Release 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 -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 ? , r%,,,Inecifiarl in Part - Sanitized CODV 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 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-n1nagRnn,,ArInn7rinn0 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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. eclassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20 nIA_PruDszi_ /-11/IA?Jr^, Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 ' 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 ? . . ? 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01n4VIRnn9Annn7nring a Declassified in Part - Sanitized Cop Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-E 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 ,classified in Part - Sanitized Copy Approved for Release 68 ? 50-Yr 2014/03/7n D ? ?? Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 ______ 1.11JULUUUUGUUdE 170 I-0-1-8d 1-,9,10 ? OZ/C0/171-0Z -1A-Og eseeiej .104 panaddv Moo pazillues u!Pe!PsseloaCI aL6Cg? Bc'ta CMS' 9C'fta C9C19' 11'fta Ca119' 51-10 Tg119' 91-ta 6o5Ig' af1518 6/90 665-fig? TS-to LC912' a5-f1a (6919e 45-qa gate' /5?ta o6L10' New L5-qa a6010' 65-qa Lt1610' T9-qa L66tir a9-11a o9o59? itty/a 9o158' 59-qz Caagg' 69-qa o(0' TL'ita frog. uL?ita ICi158* SL'ita TLij 9L-qa L9558' 6/.90 ilo959? 099t3 otL5g* CtLg9' 19'ta O999 ' Firta 60050' Le'tia &mg' a690 cilow a690 9E1E99' 96-1a 9oa98? L6'ta a9(90' ao'5a LLC90' ao'ga 6t59g? Lo'5a 05590" Lo"5a L'9./c 6?Cac r9oC TOC,C 096a L'a6a 44 ..,?,.,g3 EL 5Lact'T iwarft ac5cc'T 62.-fi9c C36S3'1 90'a9c gtgc3'T ar9gc c Si133'I wagc 11603'1 TIT'94c cg6gt ? T 9g ? attc 000'SCT ca'act 000'OCT STC(63I 000'6aT ggc'93T 000 'gat 6a6cLCT 000(5cT ilLe3cT 000'3CT aL9'-ucT 000(IcI oc9 (ocT Ic03-E TigUI ca9w1 OgIWI TOT 65To?T 6g)0'T T8896. 6?1iga 38891' T Tg'9cc 565 'LBT 000'05T 99LL6' L'Iga aT55-uT waCC 000'Lat 605(6aT 09196' T'LLa 615crT oa?Lac iTC/'9aT 000c6aT 0/6i16' 9'CL3 31TOZVT 9WE3c 000(931 0/S'gai 05t16* a'aLa 3CtIT'I 30-rdc CLIT'S3T ococgai 5ao16' og5C6' 6'oLa ? I .. 4..,9a Lagovi 5530TT 9c'6Ic g9'LIC 000'5aT 815'.431 Lo5'LaT 000cLaT CITC6* c'ega CT96o?I 99'STC 000(t3T L911'931 toLa6' v2.9z L906o?1 6IC T55'53T 000'93T toaa6* L'59a 96c9o?T %'atc 000'Cal La/c5aT 1c916* 9919a 66gLo't a6'oic 605'aat 000'58T L6160 T?59a 18-ao-r 99?90c 000'33T L90t5T 09606' T'393 TcL9WT 94*L0c L39'13T 000"t3T c6o6' 5'o9a 6966oT 9C'SCIC 000(1-3I g?K'Cat 16006* 965a a955cy'r 6-utoc 599'O' 0004(ar c6160* 6'Lga ii5Lto-r 90-coC 000coar 6o2:caat 93160' I'L5a cglo'T ag?ooc 50L'6TT 000'83T 96599? c'55a aligo'T 9C'06a 000(6TT OL3'T8T c900" 9915a tUcCrT 5-PrL6a ofrL(grE 000crar (oLLg ' L?aga 5acao?T 99163 000'9TT acacoai logLg' a'a5a ft5oacrt go/6a LLL'Lla 000'OBT 11992' ro5a OTTITT 95*T63 000'LTT -116T(6ET 01990' L?64a tggoo-u TL?o6a cI9'917 000'ect 63650' 9'Lta 656066* 90'L9a 000'917 95T'grr 96L59? aqta aciL66' cc'Lga 058'517 000'grr 61jogg' r5ta ci99g6" 9'i1ga 000(5'n 617(LTT 616tig* g-tita aa1506' 96*C9a 580'ITT 000'LTT 5Litig' 9'Eta ).99L6" woga 0004117 E80'9IT 9o1fi9? icalla 6oLCL6' 05'o9a Ta6'CaT 000'911: 9T9(9? -rota < Ta_a96' 9?LLa 000'cI1 510(511 09ac9? 6?6ca c66196' 1-3'LL3 L56'311 000'5TT wix ow I No 1111 'H tit ez IHDISM HVTIOEIOK 0II2NIX avau 1 aavas uvanaalow SHUVUUMI aanimav UWINIINDO I TIEVI alum ? 9-9000L0009Z0n1C1701-0-1-8dC1I-V10 OZ/C0/171-0Z -1A-09 ? eSeeiei JO4 penal dv ?3 pazwes - 'Jed pawssepac 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 - nnn7nrma a Uthtft.:1701-0-1-8dCll-V10 OZ/?0/171-0Z -1A-09 eseeiej J04 pancuddv Ado Pez!4!ueS - 1-led LI! 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L96*). c6TeeCT 000t5T 6915656* 596oir6 C09*/. 6-L6 6-096 9_9c2.6 000(05.1 ilTL'ECT Tg5L656* ) a...Iiir6 Looc.'9 LIO'I 5530'1 650T 5T51631 000'35T 15E9656 ...93.1t'6 L3599 950T TLSO'T TLo'T 000'6a1 uL9IICT . * ) otzoo96* z911ur6 L594*6 Litt 6531T T1T'T 55Vgat ooer?T i1(cio96* 69516 6_yr086 TOZ'T U99I'T 391T 0001931 059105T oozco96* a5LII*6 e_to90*T 9_66a*T 9--4653'I g-953'T 56cbLat 000'05T LTY/096' BL9It'6 ?OLTI'T , 995'1 5063'T 1,05'1 0001L3T 695'63T 5919096* ctozil*6 6i1oa*1 9L-tri T99C'1 98C'T 1fl'95T 000 62T To5L096 taa16 IgLa*1 995*1 oacirl T5-frI 000'931 9.45'931 5a16o96* cc?atr6 c65*T 599*T 0/T5'i .1155'T 54'53T 000'93T 5950196* 9Lilat'6 sLcirt 19L*I 9565*T +/ITT 000'551 Lo5q5T 6905196* i0951*6 5555'T 598'1 ceL9*T ToL*T UT5'.431 0001LUT oL9CT96* 6LL51.6 .1919T 596*1 L?LL'I 1.6L*1 000'113T L9.4'95T 4505196* 51601*6 cLoL'T z6we ze98*1 Lev( 155(C5T 000(9aT 55L9196* igPot*6 5.11-69'.1 5ca'a 5216*T 4joo*5 000'caT L5-11'5zi 5509196* 905Ct*6 8-TLI6*T 8_91C'e 9_589O*5 g_960*5 685'eaT 0c0(5ut , of/26196* tec-fr6 5650'5 ?55*3 ilLoa'a LCa' 000/gat L9C(tai o66oz96* L6i/C1*6 it otwa 5ooc*5 155'3 LU9'1.3T 000(10T J696 ' L895r6 5935'3 5593TL9f oo5*a ooerat 94-15(53T re 096a96* g9L4T6 59airz CL6*a 5T95'a 565'5 599'oat 000'cur t09596' 6961*6 L5C9'a 653*( 019L*5 86L*5 0001031 605(geT 1569E96' 6Loiliv6 550.'3 T5C'C L559*e 1i69*5 50L'6TI 000'BUT 0016 4l'-596* 4 3,,, Tg96'5 o99'c 6c6o'C 5c-c*c 000t6TT oLatizi to66596' ILcior6 Tego*C c9).*C 1 ggrec96* 5651-4'6 Lz64*c 95rt 9T/Jrc 9T5*? 000'grE aCeoaT 9L8rc o?3*c of0.(9-ur 000'1'31 LL9K96* ?99fIti*6 g_TIOrc 9_L)291 ,_8595*? g..0T9.1. WATT 000'03T 9L55?96" 8621.r6 6L59*? 9aL*.q goo6*? 556'c 000'LTT t6T(6TT 4595?96* t50/1*6 t6 19*-4 cLg6 0t09 Te9TT 000'61T 59?9c96? toz5;(*6 8c6C?ii ?9??5 c69 '$r Ltrfr T 000 '91195Te8?ur ii99trt 83S't 059'SIT 000'911 161(1+196' ?o55-11*6 0a10'5 0fg*9 651641 Lo9v196* gc55v65fito'S '4 489'1117 000fLTT Lego*5 fr? 120 3'9 5?'5 559'5 5 015qq96' Lo95+1*6 59aL*5 5To*L 5195'5 000tira 90'91T LeL1-496' oc85i/*6 5/.91.'5 o6o i19 *L TE6'5IT 000(911 559496' 0119tr6 Of ?9 6ao'9 190C*9 56(*9 000'CIT 5to'511 89Lb196* ca19*/*6 9_9565'9 9_9L0*9 _zaK*9 6_93.fr9 L56(arr 000l5IT 6588?96' 9tia5tr6 t8itf06i1. 5 ITO'S 000(5TI 6TI'LIT 053,2 koogitu,9 F-7:://d 01/51X1 d Ga/a qtala NOLINIEURDOV ALILVAID d1) LIM= =emu mama= aanomoo II alavi onua 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 Declassified in Part - Sanitized Copy Approved for Release @_50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Co.y Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 " i1 ;{ Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20. DP81 01043R00260007000A-R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 ? ??? \\ Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr IA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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 -r? Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP'81-01043R002600070006-6 4 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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! \ ' Declassified in Part - Sanitized Copy Approved for Release 14/03/20 ? CIA RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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- t Declassified in Part - Sanitized Copy Approved for Release 4.? ? ..A...,...._.,,,,,J0 ? 2014/03/20I. ? CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 _ 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr IA RDP81 01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 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) - 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 - 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 Declassified in Part - Sanitized Copy Approved for Release 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 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 , 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 ? ? 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 ? 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 ?!frIr ?P" ? imr???v????.????4,+?%.! 14 r?rifinro,_41471r"VIr7",?--"' "'" 1 000, ? I ?a...s, Xl\N I I I I COMPUTED -- EXTRAPOLATED I 5 '''''*????. NNN Nss?? r o ----6 ...'''sN,,. N 40 e ,.:S'.4 ,e < a o a r a - ,>c....? ..? .., 10.7 a . Viss\,\ ,4 /08,N..\\ /0 VN?sk., ? w /Os % 0/7 _'., ?A 4 ' 0 4 \-s...'..?....................L. 11111%iiii i . I ? t I IOS 103 1/ ..... Mu,,, .. lias.._ \I _Iiiiiiiii. 1 1 1 1 1 1 ORD 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 Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 iononwa.......r. I ?4 ? 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; ; *4 A .t. * TERMS 3,4, AND 5. , (3' 4 I.. * * 11 . 7/ /1111 iii "/r 7/ ,,,.. zz L, 7---- A Pr , A Is ../ 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? ? go 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 '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 _ _ ? _ _ - I .,. 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 ? Declassified in Part - Sanitized Copy Approved for Release 3/20 CIA RDP81-01043R002600070006-6 Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ?-? 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). 177 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 .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) ? 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 - 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 ? 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- "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 Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Co y Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ? ???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 _ Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Co y Approved for Release ? 50-Yr 2014/03/20 : CIA-RDP81-01043R002600070006-6 ? 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 - 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 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? 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 .......-???????,?????-.???????!??????.???-- 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 ? ? 7 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 - 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). 185 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 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 Dnri - niti7PC! r.opv Approved for Release 186 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 ...- _ ? -- - - ?.... .. - -.....: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 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 ? - ? 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 ? 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 ? 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 - npHaRsifien in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 '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. Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ? ' ' -... ^7 ' so7t- r-???,.. :,....m., '1 i Via. 'or :Z. ..-it.:4:1- ,-'`. I - ?, 14- v r I t..' o I ' C. : I E . ! r . 0 tr\ ....1? 0 888S-A p A 0 iiggigigt gIggl.Cd .7.1. .44 ?. H 0 ? i! II l' 0 gg. 0\ N ..% N .. .. F. P. t ! ? ? ? ? ? .--Ntto t I_ ??H? ????? 88-8-AA ..., ? 0 1 P4 I ??1 COMII\ N 0Mte\-1. ......4. a ? o . [ .. ...4, Ao a. 0 gig ??888 ...1- cu pig a) o 4-4 ?ri El . ..... 0 ta gigig ? .. f. M N ... N .. 9.S-I.al.. Mtt"\ ml ? 888 ggggg 88888 taP.A0.* 00Q 000.4.10 glil ? ? ? ? I-I Ol CO1 ? A' ?H, \S g 0 gggg -.1.alC? $4..... O L344-45 Et 9.(:)...-ift tiN 8-1% 000 4 4-) Mg' ????? l'.-.g ggigigigii tcI 4N4 10: Em-4 [ .4... 0 ovE O RI 0 .-INC-UN ..-1 ag D2 0 ?ff s4" NAH C gintl...* ..._. E., ...,?,,.. w 43 00QQQ0 1-7-1',Ztr\CO t^ 0 4 4. 888888 0HN.w 00000 g? PI N Qft s s gs ?A, ? ??? H HN 0\ 1 - - 4A"g@R2 ? r9_ 8 a 88n8 N - 1-91 Table P-II. ? ? ??? \ 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. r :11 ? r 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 cn 2014/03/20: CIA-RDP81-01043R002600070006-6 ????????????,,???????????? j,'"'?'77"?II"rrri-71T1117Irrri,r771.1711FirPT ' if', ., 1 :`.?. ; -, 1 .,' _ *Jia.'Zii.Wo.2041111".:AA?11U114?Adajtjili ? 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 \I\ 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. Declassified in Part - Sanitized Copy Approved for Release a 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 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? 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 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- Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 Declassified in Part - Sanitized Co .y Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 / 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. Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2014/03/20. DP81 01043R00260007000A-R Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/03/20: CIA-RDP81-01043R002600070006-6 ? ? ? ? ? ? ? ? ? ? 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 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 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 Declassified in Part - Sanitized Copy Approved for Release 7- 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 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 Declassified in Part - Sanitized Copy Approved for Release @:)-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 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 ? ? - nRclassified 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 ? ? ? ^ 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. tTh,-.1necifiari in Part - Sanitized CODV Approved for Release a 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 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. Declassified in Part - Sanitized Copy Approved for Release Yr 2014/03/20 ? CIA-RDP81-01043R002600070006-6 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 ? - - Canr+ - qnniti7Pr1 nnIOV 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 ? ? 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