777

AAD fz Reports Control Symbol

OSD-1366

"0 •RESEARCH AND DEVELOPMENT TECHNICAL REPORTECOM-5436

THE ACCURACY OF BALLISTIC DENSITY: ~ DEPARTURE TABLES ?9341972

• BY

• ~Marvin J. Lowenthal0D

• ,JUL 27 1972

• April 1972

• Approved for public release; distribution unlimited.

0 0 0 0 9 0 0 0 00 *0 00 a Reproduced, by

INFORMATION SERVICEU S Departm'et of Commerce

Cp~ g~ f VA 221 .51

UNITEDB STATES ARMY ELECTRONICS COMMAND -FORT MONMOUTH, NEW JERSEY /

NOTICES

Disclaimers

The findings in this report are not to be construed as an of-ficial Department of the Army position, unless so designatedby other authorized documents.

The citation of trade names and names of manufacturers inthis report is not to be construed as official Ge;ernment in-dorsement or approval of commercial products or servic:sreferenced herein.

Disposition

Destroy this report when it is no longer needed. Do notreturn it to the originator.

00OC 9UFF SECTION [3U : . A. , :4 0 I, C E D 0 t

... .......GPERl ~ r K A~~ nV ~ O

Din. ~ IeVc

UNCLASS FlEDSecurity Classification

DOCUMENT CONTROL DATA . R & D(Security classification of title, body of abstract and indexing annotation must be entered when the overall report Is etA&-fle#d)

I. ORIGINATING ACTIVIYY (Corporate author) I2a. REPORT SECURITY CLASSIFICAtnN tAtmospheric Sciences Laboratory I UnclassifiedWhite Sands Missile Range, New Mexico Sb. GROUP

3. REPORT TITLE

"THE ACCURACY OF BALLISTIC DENSITY DEPARTURE TABLES 1934-1972

4. DESCRIPTIVE NOTES (Type of report and Inclusive dates)

5. AU THORIS) (First name, zitddle Initial. last name)

Marvin J. Lowenthal

6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS

April 1972 29 5So. CONTRACT OR GRANT NO. go, ORIGINATOR'S REPORT NUM'ItCARI

b. PROJECT NO. ECOM-5436

C. DA Project No. 1T0621 i lAl26-05-57 hb. OTHR REPOPT NOI$) (Any other number, that may be .a...nIdthis report)

d.

10. OISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

U.S. Army Electronics CommandFort Monmouth, New Jersey

13. A0STRACT

The accuracy of ballistic density departure tables is examined, starting withthe earliest available sets in 1934. The extension of the tables (originallydeveloped for the U$) to encompass the enlire Northern Hemisphere is discussedand the shortcomings of the current climatological regional zones described.New tables, based on current data and used for a more limited geographicalarea, are shown to be accurate to one half of one percent, hence furnishexcellent back-up Information when a current sounding is not available forartillery firings. A procedure for minimizing ballistic density errors thataccrue between observational periods is also presented.

/

DD ,oRA7 RLAC O.. .ORM 1478., JAN 04. WHICH ISI NOV 4,14 73 OsoLETi FOR ARMY USE. UNCLASSIFIED

Security Classlfication

UNCLASSIFIEDSecurity Classification

14. LINK A LINK 8 LImK CKEY WOROS

ROLE WT ROLE I ROLE W.

1. Ballistic Density2. Air Density3. Radiosondings4. Station Elevation5. Geographical Regions6. Meteorological Messages

1,.

UNCLASSIFIEDSecurity Classification

Reports Control Symbol IOSD- 1366

Technical Report ECOM-5436

THE ACCURACY OF BALLISTIC DENSITYDEPARTURE TABLES 1934-1972

By

Marvin J. Lowenthal

Atmospheric Sciences LaboratoryWhite Sands Missile Range, New Mexico

April 1972

DA Project No. IT062111A126-05-57

Approved for public release; distribution unlimited.

U. S. Army Electronics Command

Fort Monmouth, New Jersey

ABSTRACT

The accuracy of ballistic density departure tables is examined, startingwith the earliest available sets in 1934. The extension of the tables(originally developed for the US) to encompass the entire Northern Hemi-sphere is discussed and the shortcomings of the current climatologicalregional zones described.

New tablesP based on current data and used for a more I;mited geographicalarea, are shown to be accurate to one half of one percent, hence furnishexcellent back-up information when a current sounding is not availablefor artillery firings.

A procedure for minimizing ballistic density errors that accrue betweenobservational periods is also presented.

CONTENTSPage

INTRODUCTION .C.O............ ....................... I

CONSTRUCTION OF THE TA13LES ............ .................. 16

CONCLUDING REW.RKS . . . .... .............. ........... ... . 24

APPENDIX. COMPUTER DETERMINATION OF METRO MESSAGES FROM RADIO-SONDE DATA .................... ....................... 25

Procedures . . ...... . ....................... 25Method of Solution ........................ 25

Appendix I: Calculation of Zone Temperature ... ....... 28

Preceding page blarkV

INTRODUCTION

One of the basic premises of all firing tables is the "Standard Atmos-phere" - one whose properties are enumerated in the "1962 Standard At-mosphere" [I]. With such a density distribution and zero wind through-out, the shell should describe the calculated trajectory given in thefiring tables. Those conditions are never encountered on earth, hencecorrections for nonstandard conditions are always in order. ArtilleryMeteorological Sections, organic to the Army Artillery, provide meteoro-logical information on winds and density to permit such corrections.

Accurate,.representative, fresh observations are the best method of cor-rection available today. There are, however, occasions when these mea-surements are not availabl;e, and alternate methods are necessary toprovide th- requisite information. In the case of atmcspheric densitysuch an option is available.

Air density at ground level can always be deTermined, the only equipmentrequired being a good barometer and wet- and dry-bulb thermom&-ers. Ifthe upper ai: density can be inferred from the surface measur~iment, theballistic density can be furnished for correction of artillery fire. Thevital question is: Is the assumption justified that the surface densityis a good predictor of ballistic density aloft?

To test the theory, some 3000 radiosondings from Vietnam and 2000 f omthe Korean region were examined. Figure I shows the mean of ballisticdensity aloft as a function of surface density over a wide range ofsurface values.* Values of ballistic density are expressed as a percent

12

II

I0

w8

7

J

5-5

W.J 4-J

2-

90 91 92 93 94 95 96 97 98 99 I00 I01 102 03 104DENSIT ' (% STANDARD)

FI.I VARIATION OF BALLISTIC DENSITY I

[I] US Standard Atmclsphere, US Govt. Printing Office, Dec. 1962.*The values on the abscissa of Figure I represent +0.2% on each sideof The central value.

of standard with the ordinate being the normal NATO zones (Table I).

TABLE I

BALLISTIC ZONES, STANDARD ATMOSPHERE

Height atTop of Zone 3

Line No. (Meters) Temperature (*K) Density (g/m3)

0 Surface 288.2 1225.01 200 287.5 1213.32 500 28:.9 1184.43 1000 283.3 1139.24 1500 280.0 1084.65 2000 276.8 1032.06 3000 271.9 957.07 4000 265.5 863.48 5000 259.0 777.09 6000 252.5 697.410 8000 242.7 590.0II 10000 229.8 467.012 12000 216.8 364.813 i4000 216.7 266.614 16000 216.7 194.815 18000 216.7 142.3

As can be seen, the ballistic densities are a function of the surfacevalue. The various curves do not intersect, although the spread betweenthe extremes continually decreases. The values all seem to trend to-ward a common value at some higher level, beyond the limit of our data.The curves do show that ballistic density is more independent of thesurface value at the high line numbers than at low line numbers. Thus,a climatological value of ballistic density at high altitudes (line 10or above) would have a very small error for all ranges of surface den-sity. This is most fortunate since the range errors due to an incorrectassessment of ballistic density are greatest for high maximum ordinates.

In absolute values, the ballistic density curves exhibit a behavior sim-ilar to that of the Standard Atmosphere (Figure 2). Again, the conver-gence of all curves is seen with increasing altitude. It should benoted that the curves for the tropical region (Vietnam) converge towarda different value than those from the nontropical Korea. This differenceindicates that one set of values is not satisfactory for the entire

2

"10- r

iI

9-

VIE£T NA•M"•

400 €,00 So, 100 'O000

DENSITY (O/M I) MOF STANDARD)

FIC:.2 VARIATION OF BALLISTIC DENSITY

globe, regional tables being required to minimize the error in the esti-mate of the ba• listic density.

It has been shown, therefore, that a surface density measurement canbe used to categorize ballislic densities aloft for a particular geo-graphic region; that a climatological value of ballistic density becomesmore accurate with increasing height (at least to the levels of interestfor conventional tube artillery); and that all geographic localitiescannot be accurately described by a single set of values.

Once the feasibility of the proceoure is established, it is necessaryto determine the accuracy of such a technique. It may well be tha+ eventhough the mean curves of ballistic density do not intersect, the disper-sion within each set is so great that the probability of an accurateestimate from the mean is quite small. This involves, of course, thestudy of the standard deviations of density for aiiy given surface value.A portion of the computer ana;ysis for both Vietnam and Korea is shownin. Table 11.

03

il~~.. . Io i."

.,:20 Z00 004D(0A11,0.CAO.d26 0 2.020 0. ourf 06002. 0 0.04 fl.¶N3j 16: o60o.

AO.5 - 065 3 VI.203 '72 0 1% LI 9 3 9 3.% 0. 27 q2~ 4401 1c.

I0 1.90.0 5 0'' 1. 'o "N, '0:2j9.l 0.02 .. . . .5..... .... .3..... ...ll a 90.0

v.. - .1,.o ~ ., o6 .' 2 920 0.00 1 7.13.5 0.00 2 .00.6 0.00 2 93.36 0.091 9a.9J7. .. 0 . Ui. I I -12.27 4.3% 71 1,.2 0.0 2 33..3. It 09 7. 0 401 .0 if 93.2

90 4 '.26 14.0 6 S07.00 0.47 A 33 32 0 0.021 0.20 4 0 0 ~ 99.0000 *.4 ,.0 6 1.2 .. 4 3 92.20 .6.1 3 93.00 0.410 3 03.117 0.1- 0 00.461 0.3 3 :3.

Oo.11 .:'2 I.No 031 030..s 9 0. 4 1 0.7 943.07 0.02 A 60 .0 0 043 .0 0 9.

0.. *96 . 1 -742. , 0.326 19 S.1 0.6 19 93.30 0.33 1 60 .267 0.340 00.0 6 14 ' 0.

9'.242~2.. 2 4:2. 030: 03.7 .42 76 06.00" 0.03 6N 040 0.0I0.0 t.2 6 0.o2.2 o2.OS y~ ~~.j 23 6v.0 (.0 23 0.0 01 3 036 .0 2 1 0.10 0 4.0 01,3 9.

123127 ..4 20 '1 t 2 ?~~ t00.12 0.42 2- 93..6Y 0.44$ 20" 04.20 0.02 P~ 0. 1 64.4 0 29% 02.0:'024 0 I623 22 :1.73, ,.42 2 63.6 0 .1 424.20 0.16 22 00.62 0.2 20 04.6 0.34 62. 92.6

921 2. 600 22 1146 coO 2 3.7 .1 2 0.0 000 ~ '002 0.41 20 046 0.0 0:l 2 92.1

027 6.: 26 ).02 A42 326 04.0 c..6

26 04.2%0.4 n60.3 04 6 O.3 96 6 '~

A2. '3.1' A. 3 1 6 2 2 10 24 130 047 20 44.47 07.1 2 4' 0.6 76 04.0 0.70 2 01.21

0.6 11 u7.4 I4I.30 32 3.0 0.. 32 6.0 0.6311 32 4.06 06.03 12 06.90 0.62 10 0

.. i0 0.47 Is 02.42.1 l2.i0~. 0 21 '31 2 -.02 21 0".01 0.00 10 94.34 0.60 21 04.00 0.02 20 9S.04 0.74 IT 92.1

0I. 12.-2 9 2 0 3.9IF 0- t.00 20 06.3 0.1 t 7 047 0,3 2 "l.0 0.60 it 02 4 501 7 0.*3.) '14 0 ".'6 62 03.03 2.06 IF 04.10? 0.660. 96.9 6:: . 70 6T' 12 o94.o O.'s 32 60.06 0.06 4p 011.003. V3.13 4,.)0 0 4.3 24.0 6 . 3 0 045 9.04 0.10 3 44 4.66 1.96 12 00.17 0.6 06 '10 .0 9 0.

t3.6 037 65 3 .4 3 94.10 0.11In 1s 14.60 . .2 01. 05.07 6.10 0 0 01 4.0 01 91.003 4.4 64 37 0.0 .03 37 90.6 0.1 37 04.03 0. 402 05.103 .10 37 01.02 0 .4 00 02.3

031 0.3 23 6 ~0 .0 40 0. 0 0.4 40 309 0 .0I 3 9.6 01 9 0.w 01 6 0.03.6 4.'0 4.1p 41 04.30, 16 4ý: :1 %O 4,9, .0.7 41 44.9 o.5 40 01.2 0.6 6% ' 1 .2 0.6 a1 0A.

03.0 6..216 (P.)2 40 64.4o1 4 2. 3* 9 09 .51 *3 0.o 0.1 00 a3 0.1 0' 00.3 0.11 03 03.0,9400 4. 6 6.2 42 096-.6 6 0.40 0.61 42 9S.03 0.514 IS 960 0.00 02 051,O 0.0 6 91.6

03.0 .2 v..3 3I, 04.09 0.09 3 9's. 0,4 61 o,07 37 :% 410 D.1O 7 0.7 o17 3 o 01 7 9.60.6~ ~~~~~~~~0 .. 0.4310.:0.33044065 r 91.03 0.1 IF 1.'24 0.4 310.7031 0.

IF, 4.1 '.6 2 403 20 7 0..90 0.67 22 91.06 0.'12 22 90.61 0.01 20 02.321 6.40 62 000043 4 ,I) . IF 14.Q. 0.26 27 I 4o5.1 0.11 IF 04.00 9.96 It 920 0.1: 6, 00.40 0.46 17 00.

00 C4.0 p.-3 20 64.99 1.924 209 .00.9 0.03 in 9%1.4 0.45 60 05.20 0.09 in 9'..36 0.4"19 0 0.00..1 t. o (.2 37 '.29 0.02 2N 61.23 0.60 I7 0S1.2 0 .3' 27 651.3 0,16 20 900s .2 0 9.

*o ""o 4400 r.j3 20 61.06 0.f6 20 91.00 0.96 20 ~9$.2 6.01 20 91.27 0.60 20 00127 0.91 20 4.

Tsh~c~f V1 etnar

660. (260 2 LI2NE I 6,m 3 LIN6E 4 LINE0 6 00,2SI~6odA $40 120 060. h . 60tw 404 126 . 90 070. 6.1. 9900 Nn7 . 300, 060. 'P. 006162213. 936 .0 30 .06 03. 02 4.4 v0 3 0.2 0 2 2411 64o!000; 43.

................ .. ! ....... .. . . . . 0.

06. * 04.6 0 4.0 90.6 000 2 0.1 00 :9.0 00 3.0 001 30 0.00 2 64.0

"06.3 04. 0 1 10 6 4.9 0.0 1 04.16 0.00 21 66 0.0* 69 0.0 10 .0 2 6.00:Oo2 .0 2 042 4.00 2 9-.5's .00 6 96,23 0.70 6 94.20 0.00A 6 90.39 0.000 1 66.000 044 1.00 6 44..39 000 2 6.36 .3 43 0.050 9 0401 .0.0 1 94.10 00 2 0.

94.0 90.00 v.00

1 o4.#4 6.23 3 04 .00 0 1 90.50900 3 19 94.06 0.00 3 94.09 9.0 3 66990. 0660 .0 3 4.0 9.7 9076 .09 1 4.6 0.7 01 001 .0 3 91.23 0.01 3 60.

01.4, 3~0 . 2 1 ~ v 0 1 -9 .02 0.24 1 05.07 0. 6 1 :so 0 321 0 1 26 0 3 0 0 .

01.2 i v .2 0 5.2. A .2: 7 91.27 0.26 1 03.26 0.30 2 09..2 0. 4 7 '3.21 06 03 1.01.2 0l2 7.1 ) 9-.162 0.14 3 91.90 o670f52 0. 23 1 9 1.66 0. 27 9 9so21 0.29 1 09.20.1

03. 9.4 .320 0 3.3 624 0 29.0 03 3.3 02 1 0.0.2 0 93.60 0.30 9.91.6 l V10 .9 9 9.0 63 9 .2 9 990o03 91 9576I: 0.0 9) 9.66 0.36 6 01.0A

931 0.1 .0 6 ll .3 161 06, 9,.7 0.2 4 04 00 " 3.3 4 5.96 02 3 6.016 1.1 V.2 I 2 011 000f 62 5 0.26 2A 91.00 0.23 22 0.70 0.33 22 91.70 00611 22 99201.7 01.6 6.0: 952. 010 .4 2 19 .3 2 0.9 03 20.0 0 0.47 22 0196 0.1 6.01.0 61.03 036 2* 01.5.06 . 42 00195.0 0.06 20 0191,Y 0.04 00" 016 OO 20 6 00 .60 26 60."01.0 91002 6 20 2 9 5 01S.66 0.30 69 90.04 0.26 0 9.6 33 9 9.6 3.3 20 06.06 0.13 12 69.0962 906 v22 7 903 v23 67 01.0 0.33 37 96.02 3,4 167 96.92A 3.49 20 05.94 0.12 201 6.0029 4.28 4.26 20:3

0 69 0.2 02 91.o

9 0. 3,4 6 09006 0 1602 94S3 06 6 0.00 3.6 20 64.2

00.3 04.13 0.26 it 06.20 0.02 019 60.23 0.3726 06.9 0.37 25 94.23 3.36 21I : 4063 vo).4 21 60,306.4 06.4 4.20 23 90.340 .3 23 ....o1 :3 9 .3 7.0 23 96.15 .02 2o 3 06.33 0.66 23 66.496.1 90.43 6.64 63 96o42 0.20 72 99o3 0.3 23

044 0.3n 967 3 046 3.36 23 94.44 3.6 2. 2 66V .1

96.1 06 11 :1 6 12 20 0,13 0.12 27. 60.4 0.3 261 96.419 39v 96.46 0,67 20 94.64 0.62 26 60.6?06 0 0 . 0 I. 0 3 00 6 0.2 21 06019 0.3 21 6. 0.06 31 006 0 . 0 2 6 1 .0321 6 0

06.0 6~~ ~~6.03 t7130.4 42 3 900 03 3 9 Y O4

' 2 96019 0.43 33 90.,13 0:.412 23 0.990.6 96.S2 06 IV 0 09.01 0.21 24 900 003 76 942 0.4 06 94I 001 2A 046 o 0 6

902 9.3 02 2 0.4 00 2 946 03 20 0426 342 0.3 2 9.4.9 .30.6 22 964.9 0.60 22 67.07. 976 1 V.21 37 94 i 0:26 20 9.A4.9 0.31 20 #~ C 0. 302409 02 2 9 0 06 7 6,

00 o.0 62 1 9::5S 010 21 97.4605 2 ~ 0. 0.0 20 9.7 0.5 0 940 o3 % 6.070 9.3 07 7 9.0 64 7 0.23 0.1 27 0.23 0.302 27 U7o . 56 77'7 0.6126 7.

000 V~3 0. 3 3 0 . 3 2 9 . 6 0 4 6 9 . 0 3,4 26 97.00 0.4 26 4 7.39: 0.49 24 67.906 0 9o 72 22 93 0 ".3 26, 07.28l .3.6 2 173

0,IN4 I 0 9 6*o.13 3.4 22 90.79 ,641 72 67.6

909 7.0 .2 3 00.3 0.3 3 6 : -O9 .30 30 97.10 9,43 t10.0 34 0 '.6 00 0 0.97.9 06 6.2 6 (,.I 00.13o 6.39 2 960 6 0.13 a' '0l9 .069 9.13 0.4 6 20 071 3.6 36 0099.41 00 .0 30 9.0 '3 90.90.0 0.46 292 97,6 '.3 0:9'03.6 2 905 3.4 34 6.009 0.3 .4 3 9.4 ) 30 60.69 03.46 30 976-01 o.41 13 976.61 0.4s 27 36 0 07.43 0. 2 2 9.0

06.4 9. t6..69047. 0.42 26 97.6 0 0.66 26 07.63 0.12 09 9709.1 F6§.00 0.43 6 69, .4960 0.3 3.0 0 2 3.9 4 9091 046 24 00.0 1 .4 24s 99 .4 4 993 26 00.1)O~4 930 4.2 32 9.1 o.0 3 9:4334 3 0.6 43 2 0 963 04 32 0.0 .4 32 0..

90.0 91,6? 0.21 369 1~.32 0.37 20 08

3 0.47 26934 .1 20 920 .0 76 0.2 0.16 20 0.999 0 060 4.0 2791 3 9I. Of 20.4 90.4 0.1 2, 9.4. 0 9 0.0.1 27 00.2 0.6 20 69.9

tob e 5l K.orea % .3 3 ls .3 yk .- n9.105

97-9 91.6 Q'7 29 1.53 c.30234

The standard deviations (STD) are seen to be of the order of 0.5% orless, which suggests that ballistic density aloft can be estimated toabout 1/2% from a measurement of surface density alone. Since densityis calculated from measurements of pressure and temperature from theradiosonde, the accuracy of the density measurement is dependent uponthe accuracy of the pressure and temperature sensors. By use of currentspecification criteria, the error of the density determination is foundto be 0.3 - 0.4% at low iine numbers and greater than 0.5% at high linenumbers. An assessment of ballistic densities to about 1/2 to 1% by asurface measurement alone is an excellent back-up systpm that is alwaysavailable where a radiosonde observation of upper air aensity cannot bemade.

Historically, the use of density tables for the assessmlent of ballisticdensities was the standard procedure before radiosondes were available.The earliest manual available for this rerort was TR-1236-I, "Meteoro-logical Message for the Artillery," 1934. At that time it was stated:

"It is impractical to actually measure the temperature, pressure, andmoisture content of the atmosphere at various heights, compute the bal-listic densities, and get the computed data to the Artillery withoutthe elapse of considerable time. As. atmospheric conditions are contin-ually changing, there must be as little delay as possible between thetimes that meteorological observations are made and the times that tnecompleted reports are available to the Artillery. No attempt is made,therefore, to determine air densities from observations made at variousheights above the ground. Instead, the air density is determined nearthe ground at the meteorological station and the air density is assumedto decrease at a definite rate in height above the ground." [2]

Three decades of technological advances have, of course, made it possibleto obtain an atmospheric measurement of temperature and density andtransmit it to the Fire-Direction Center. The other statements concern-ing atmospheric variability and the necessity for fresh metro informa-tion are as true today as when the original words were written.

The tables given in TR 1236-I were meant to apply to the US only (page24) and values of ballistic density were given for station elevationsnear sea level, and at 1000 and 2000 feet above mean sea level. Forhigher elevdtions, the data given in the table for stations located2000 feet above sea level may be used [3].

[2] TR 1236-I, pp 23-24.

[3] Ibid., pp 82, 92.

5

The data, in part. are shown in Figure 3. The plot shows recognition

-- STATION HEIGHT- SEA LEVEL

- --- STATION H.IGHT-|O0,

12 . . .. STATION HEIGHT -2000'

10- % I/ %, T,~

7 /1 / '\~

a- I % \

,// ,'\\

. I \I

"% %

90 92 94 96 98 100 l02 104 105 lOPSURFACE DEN8ITY IN PERCENT OF STANDARD

FIG.3 BALLISTIC AIR DENSITY FROM TRI1236-I (1934)

of (I) the convergence of all values of ballistic density at higherlevels, (2) the difference in behavior of ballistic densities with in-creasing station elevation.

The main sources of error in the tables are (I) use of the "alues at2000 feet for stations at higher elevations, and (2) assumption thatone set of values will suffice for the entire US. To correct t.'eseerrors, a study was carried out by the Signal Corps General DevelopmentLaboratory, Fort Monmnourh, New Jersey, to revise and extend the tables

L [4]. The results of this study appeared in Sep 1942 as Change 4 toTechnical Manual TM 4-240 which superseded TR 1236-I in Dec 1941.

As a result of that study, the US and its Western Hemisphere territories(Alaska, Hawaii, Canal Zone, Puerto Rico. etc.) were divided into sixgeographical regions*• The boundaries of the regions in the US were

[4] "Preparation and Evaluation of Revised Ballistic Density Tables,"BrasefielId, C., SCL Eng Report #760, SigC Gen Dev Lab, Ft. Monmouth,New Jersey.

**Region 7, the Pacific Northwest, is not mentioned in Ch 4 to TM 4-240,17 Sep 1943. It first appears in TM 20-240 which superseded TM 4-240in Nov 1944. No data are available on the introduction of this newreg ion.

6-6

the same as shown in the current FM 6-16. Appendix I, Change 4 to TM4-240 dated 17 Sep 1943, extended the valid geographical lim.its ofthe density regions to include the entire Northern Hemisphere. Figure4 below, a reproduction p 10, shows the revisions.

TX 4-W00 4 'TECHNICAL MANI'AL

ArIL•iDX I

METEOROLOGICAL TABLES

Table X-In (added by CJ1, 7 Sept. 1942), change title to read asfollows: FOR ANTIAIRCRAFT ARTILLERY AND OTHERIIIGII-ANGLE FIRE: VALID DURING TIlE NIGHT INREGION I (EASTERN U. S. A, BRITISII ISLES, COAST OFNORTH AFRICA, AND EUROPE. EXCEPTING ALPINEREGION, SCANDiNAVIAN PENINSULA, AND RUSSIANORTH OF LATITUDE 55" N.).

Table X-la (added by C 1, 7 S 1942), chiaen .otIe to read isfollows: FOR ANTIAIRCRAFT .. RTILLERY AND OTIHERIIIGII-ANGLE FIRE; VALID DURING TIlE AFTERNOONIN REGION I (EASTERN U. S. A., BRITISH ISLES, COASTOF NORTH AFRICA, AND EUROPE, EXCEPTING ALPINEREGION, SCANDINAVIAN PENINSULA, AND RUSSIANORTII OF LATITUDE 5s. N.).

Table X-3n (added by C 1, 7 Sept. 1942), change title to read afollows: FOR ANTIAIRCRAFT ARTILLERY AND OTIIERIIIGII-ANGLE FIRE: VALID DURING TIlE NIGIIT INREGION 3 (W\ESTERN U. S. A. AND ALPINE REGION OFSOUTIHERN EUROPE).

Table X-3a (added by C I, 7 Sept. 1942), change title to read asfollows: FOR ANTIAIRCRAFT ARTILLERY AND OTIIERIlIGlI-ANGLE FIRE; VALII) DURING TIlE AFTERNOONIN REGION 3 (WFSTERIN U. S. A. AND ALPINE REGIONOF SOUTIIERN EUROPE).

Table X-5 (added by C I, 7 Sept. 1942), change title to read asfolloss. FOR ANTIAIRCRAFT ARTILLERY AND OTIHERIIIGII-ANGLE FIRE; VALID IN REGION I (ALASKA, ICE-LAND, SCANDINAVIAN I'ENINSULA, AND RUSSIA NORTIIOF IATITUDE 550 N.),

Table X-rn (added by C 1, 7 Sept. 1942), change title to read asfollows: FOR ANTIAIRCRAFT ARTILLERY AND OTHERIIIGII.ANGLE FIRES; VALID DURING TIlE NIGIIT INREGION 6 (WEST INDIES, CANAL ZONE, HIAWAII, ANDSOCUTHIWEST PACIFIC AREA).

Table X-6a (added by C I, 7 Sept. 1942), change title to read asfollows: FOR ANTIAIRCRAPT ARTILLERY AND OTIIERIIIGI-ANGLE FIRIlI; VALID DURING TIlE AFTERNOONIN REGION 6 (WEST INDIES, CANAL ZONE, HAWAII.AND SOUTIIWEST PACIFIC AREA).

10

Figure 4. Meteorological Table (from TM 4-240)C4

An examination of the current Chart I (pp 5-6, FM 6-16, Ma, 1961)Figure 5 shows an apparent inconsistency. Note the wording for RegionI "Eastern USA. ..... and Europe, excepting Alpine Regions, ScandinavianPeninsula, and Russia north of latitude 550N,"1 and that for Region 5,"Alaska, Iceland, Scandinavian Peninsula, and Russia north of latitude55°N." Clearly the intent was to place Scandinavia and Northern Russiainto Region 5, and exclude those areas from the rest of Europe whichwere included in Region I. The numbers I anJ 5 in the Eastern Hemisphereare misplaced. Likewise the limits of Region 3, "Western USA and AlpineRegion of Southern Europe" has been rather broadly interpreted - theeastern Mediterranean and Iraq are scarcely Alpine regions of Southe-nEurope. Corrections to the current regional density map will be proposedfor inclusion into the next revision of FM 6-16, tentatively scheduledfor the second quarter of FY-73.

7

7:7 77M -

T __++1

w I W

.. b 4' 14l - .

I. - ,

F g r 5 . Ti m'4ie zon i e .i.omdvr. an., paI.t.1F Ii o. land..i. c ia o g c l regiions f t ie N •hIrlltrn He mlitsph r

The1 departure tables themselv have. been only sltly modified throughthe ear, te geatst hane ocuringwith the issuance or FM C-16 inMay196, oingto he hane i unts romyards to meters, and the

adoption of a new standard surface density, 1225 g/rn3 instead of theolder value of 1203.4 g/m3.

Some of the ballistic density profiles from TR 1236-1 and the revisionare shown in Figure 6. Surface densities 5% above the mean and 5%below the mean were chosen to emphasize the difference in high and lowsurface density conditions.***

***Prior to 1961 (FM 6-16) the mean surface density of a meteorological

station at sea levei was 103%. Currently, the standard mean surfacedensity for a sea-level station is 100%.

8

BALLISTIC DENSITIES FROM TR 1256-1ROMAN NUMERALS REFER TO GEOGRAPPHICALREGIONS IN FM 6-16.

n°I I .M/1 • ,, .r9--

8 , , ,

% %7 / ,/ N

"// IA, ,° , \ \

/ "/ "1. \

Z 5S

97 98 99 100 103 104 105 106 107 108 109SURFACE DENSITY IN PERCENT OF STANDARD

FIG.6 BALLISTIC DENSITY VARIATIONS

The profiles show wide variations between regions, in the example, ashigh as 3%. The profile from TR 1236-I falls between the extremes andis not coincident with any single region - nor is it the mean of allregional values. For 98% and 108%, the old profile is closest tothat of Region 5, the Alaskan area. The figure clearly shows that ageographical area the size of the US cannot be adequately describedwith a single density profile. Thus, it is difficult to comprehendwhy almost the entire Eurasian Continent from the Baltic Sea all theway to the Sea of Japan was considered a single region, or why theNorthern Siberian regions were adjudged similar to Eastern US ratherthan the Polar Regions of North America, or why the mountainous WesternUS is similar to the lands around the northern borders of the Mediterranean.

The revised tables do show, however, that the profiles are dependentupon the elevation of the station, since a given surface density mayrepresent mean conditions, above-normal surface density, or abnormallylow surface density depending on whether the station in question is atsea level or at an elevated location. The behavior of the profile of100% surface density at a sea-level station, at 1000', and at 20001above MSL is shown in Figure 7 for both old and revised tables, Region5 being used since it appears closest to the values in TR 1236-I.

9

I/

STATION ELEVATION STATION ELEVATION STATION ELEVATION-2000 -1000 NEAR SEA LEVEL

9 I

7/

-..... FROM TR 1236-1

W -- FROM FM 6-16

"W4

2

I'

97 98 99 100 101 102BALLISTIC DENSITY IN PERCENT

FIG?. VARIATION OF BALLISTIC DENSITY WITH STATION ELEVATION

The figure clearly indicates that ballistic density aloft decreasesmost rapidly in the cases of high surface densities and increases aloftwhen surface densities are low. Meteorologically, this is known ascompensation, where lighter air overlays dense surface air, and below-normal densities at the surface gradually disappear aloft to be replacedwith higher-than-normal densities. This emphasizes again the fact notedearlier, that at some altitude the atmospheric density is independentof surface density, and at this level horizontal density gradients areminimal .It

The distinction between atmospheric density and ballistic density shouldbe emphasized here. The atmospheric density at any height is dependenton the pressure and temperature of the atmosphere at that elevation.The pressure at that height Is the weight of the column of air abovethat level, irrespective of conditions below.

The ballistic density at any line "n" is the sum of the weighted densi-ties from the surface up to line "n" in question, where the weighting

tThis is the so-called isopycnic level of the atmosphere. In middlelatitudes, it occurs near 8 km and was first discovered by A. Wagnerin 1910 and more closely investigated by F. Linke in 1919.

10

e1

function is described by

j=nZ a.=l

j=l J

and listed in Table III.

TABLE III

DENSITY WEIGHTING FACTORS, IN % (from FM 6-16)Height at Top ofZone Zone #

Line 7#e-ters 1 2 3 1 4 5 61 7 "8 9 1 011 2 13 14 151 200 100 12 500 43 7I-3 1000 22 31 474 1500 15 21 . 32 32:5 2000 II - 17- 25 22 25

6 .. . 30'00 8 II 17 17 15 32_400_ 8T 1413: 12 22 25

8 5000 5 6 11 11 10 19 17 21---9 6000' 4 6-7- 9--9 _8 17 15 14 18"-

10 8000 3 7 7 73 12 II 11 25il 10000 1 3 5 5 6 12 11 '9 9 16 2312120 7 -7 -- - 5 Ti I I0 9 8 14 12 1613 T4000 2 27 4 -5' 5 11 9 9 8 14 10 9 1214 6000 -7- - -- 75 5 110 9 87 13 Ii 8 6 815 180 F 0 9 8712 9 8I 5 54 6'

Hence, while the atmospheric density at the isopycnic level is nearlyconstant around the globe, the ballistic density at the same level willvary somewhat, although far less at that level than at lower altitudes,since the weighting factors are greatest at higher line numbers, asnoted earlier.

It is undoubtedly true that each air mass has a distinctive densitystructure, since the source region determines the temperature and moisturecontent of the air mass. With cold frontal passages, the air mass changesand density changes at low levels (generally line 5 and below) aregreater than normal for a short period of time. It would thus seemlogical to categorize surface densities in terms of air mass, or rela-tion to other meteorological factors (highs, lows, position in relationto a cold front, etc.). However, this technique would require trainedmeteorologists for each metro section, a luxury the current Army Tableof Distribution and Allowances (TDA) cannot afford. Hence, the simplistic

II

climatological approach, that determines the values of ballistic den-sity aloft from the surface density without regard to other meteorolog-ical conditions, was adopted.

The ultimate success of such tabies - accurate assessment of ballisticdensity aloft - will be dependent on restriction of geographic extentof the regions to insure uniformity of conditions, adequate sample ofdata on which to base the tables, and diurnal or season breakdowns whererequi red.

As an example, note the curves in Figures 8 and 9 that show the differ-ences in density for night and day conditions for high and low line numbers.

98

96-95LINE 10 •

>. 95-NIGHT

S941W

P 93 1 95 6

SURFACE DENSITY LE)

FIG. 8 VIETNAM BALLISTIC DENSITIES

12

104

103

102

j-I01

az,'100-_o 99

i-

97- A

96- LINE I10 G

95.LINE I N10

95 97 99 10I 105

SURFACE DENSITY M'

FIG.9 VARIATION IN BALLISTIC DENSITY (KOREA)

In both the tropical Vietnam and temperate Korean regions, there is asignificant difference in upper air density for a given surface condi-

tion. Hence, separate tables are needed for nighttime and daytime, a

fact realized in the first revision of the old tables in TR 1236-1.However,, significant changes in day and night sounding are noted in alllines, not only in line 4 as promulgated in the revised tables ([41,

pp 3-4).

Similarly, plotting the densities as a function of season reveals the

necessity for constructing density tables on a seasonal rather than an

annual basis. In Vietnam (Figure 10), the difference between summerand winter is significant at all levels above line 2, whereas a combin-ation spring-fall table could be developed that would fit these traný-"

sitional seasons.

13

W.INTER

SUMMER0~ ________FALL

--- - SPRING

.j 94 l

sz

I a 3 4 6 8 t0 12LINE NUMBER

FIGAIO SEASONAL VARIATION IN BALLISTIC DENSITY (VIETNAM)

Figures II and 12 show the seasonal density profiles for Korea. Thecontrast between summer and winter could not be depicted, since therewere no corresponding surface densities (lowest surface density inwinter 102%, highest in summer, 100%). There is, however, sufficientspread -to make separate seasonal tables worthwhile.

10 9 FS• FALL

108 - WINTER

107 - - SPRING

105>.

10

"

z 103-

Z10303

102-S104[

100

- I I I I , I ,

I 2 3 4 6 8 10 12

LINE NUMBER

FIG.Il SEASONAL VARIATION IN BALLISTIC DENSITY (KOREA)

14

. SUMMER

I00- FALL

SPRING

-::.

98

97-.o.J

96-

2 4 6 8 10 12LINE NUMBER

FIG,I2 SEASONAL VARIATION IN BALLISTIC DENSITY (KOREA)

The third factor, geographical extent of a region, is harder to define.For the Vietnam area, the density profiles from the most northerly sta-tion (near 160501 N) and the most southerly one (near 100201 N) wereso nearly alike that it was obvious that all of South Vietnam could beincluded in a single region. Data were not available from North Vietnamto delineate the northern extent of the region. It is most probablethat the tables can be extended to 20 0 N and possibly to 250 N. The west-ward extension to the Bay of Bengal is also probable but must awaitfurther checking with data from upper air stations in that area.

For the Korea Region, the ballistic densities in the southern portion(near Pusan) differ markeuly from those in the north (around Pyongyang).The separatior. ;s niost pronouneed in winter (Figure 13) where variationsof more than 1% gre possible between the extreme limits of the Koreanarea.

15

NORTHERN PORTION106 - - -SOUTHERN PORTION

UONE STD DEVIATION

t: 102

z

Q I I

LINE NUMBER

FIGI13 VARIATION OF BALLISTIC DENSITY (KOREA-WINTER)

The one-sigma values shown as vertical lines between the northern andsouthern curves indicate that the differences are significant betweenlines 3 and 7. For that reason, three separate tables were constructed- one for the southern island$ TO 36'N; the second valid between 36*Nand the DMZ; and the third to be used from the DMZ to 40 0 N.

Construction of the Tables

Once the differential criteria for the tables are established, the actualconstruction largely depends on the availability of the data. Wherelarge numbers of Artillery Metro Sections are in operation as in South

VieTnamr, ihe problem is simplified. In fact, zone and ballistic densitiesare available on Forms DA 6-57 and DA 6-59 for processing by computer.Frequency distributions of upper air densities as a function of surfacedensity are produced, and tables are constructed for surface densitysteps of 0.5%. Abrupt changes in slope of the profiles are avoidedboth from zone to zone for a given surface density and for a given zoneas the surface density varies. Such smoothing rarely changes the tabu-lar values by more than 0.2 - 0.3%, much less than the standard devia-tions of the values themselves.

Where sources other than Artillery Metro Sections are used, radiosondedata are available only at mandatory or significant levels. In thosecases, the densities must be computed from the sounding (see Appendix).After this has been completed, the procedure follows that is stated above

16

1.

for the Vietnam data. Recognizing that variations in station altitudecause the greatest difference in density piofi.les (see Figures 3 and 7),the original tables in TR 1236-1 specified density factors for sea level,10001 above MSL, and 2000' above MSL. A similar procedure, incorporatingmetric rather titan English units, was followed for the new Vietnamtables as sufficient data were available. Tables were constructed forstations whose altitudes lay between sea level and 200 meterstt Anotherset was valid for those stations in the range of elevation 200 to 450meters, the next 450 - 650 meters, etc. This procedure has the advantageof allowing for discrimination between density profiles due to elevationwhile keeping the number of tables within reason. In Vietnam, five setsof tables covered all operational station elevations.

The question naturally arises: Can a density profile be constructedfor an elevated station if a nearby sea-level station is available? Aspecial series of Vietnam flights was made every three hours for a weekat a pair'of locations separated by approximately 20 kilomete's, one 30meters above sea level, the other 770 meters above sea level. Theseflights were ideal for determining if ballistic densities from *the sta-tion near sea level could be used to construct a density profile forthe elevated location.

A simplistic approach was attempted. The difference between the surfacedensities of the two stations was computed and the difference subtractedfrom the ballistic densities of the sea-level metro message. The re-sulting values were compared with tne actual ballistic densities fromthe higher station. The results are shown in Table IV below.

TABLE IV

ERROR IN BALLISTIC DENSITY

Line No. 1 2 3 4 5 6 7 8 9 10

Densityerror in .3 .4 .5 .5 .5 .6 .7 .7 .8 .9percent

It is readily seen that the error increases with height and becomesgreater than 0.5% above line five. More complex schemes were tried.The most successful involved subtracting the sum of the difference in

It is believed that by presenting the density for each zone as a tabular

value, rather than a departure from the mean (which involves algebraicaddition before the ballistic density is obtained), arithmetic errorswill be reduced.

17

surface densities and one tenth of the line number from each ballisticdensity at sea level to give the corresponding ballistic density at 770meters. The results of the computations are shown in Table V.

TABLE V

ERROR IN BALLISTIC DENSITY

Line No. 1 2 3 4 5 6 7 8 9 10

Densityerror in .3 .4 .5 .6 .4 .6 .6 .6 .6 .5percent

The errors for high line numbers have been reduced, but the results arestill not encouraging.

Neither of the two techniques is as accurate as the results obtainedusing the new climatological density tables as shown in Table VI.

TABLE VI

DENSITY ERRORS USING CLIMATOLOGICAL TABLES

Line No. I 2 3 4 5 6 7 8 9 10

Densityerror in .2 .2 .3 .3 .4 .4 .4 .4 .4 .4percent

The mean error is seen to be less than 0.5% in all cases and does notcontinuously increase with height. It appears, therefore, that ballisticdensities from a climatological table are superior to values obtainedfrom extrapolating density profiles from a sea-level station.

It has been shown that climatological tables are feasible, seem to bereasonably accurate in one sampie case investigated, and are easy to use.It remains to bE seen whether they are accurate for a much larger sampleand whether they are better or worse than the existing tables.

Since only the data from Artillery Metro Sections in Vietnam are avail-able for direct comparison of tabular and actual ballistic densities,the analysis will be confined to those data. It should be noted thatthe absolute value of the error is the important factor in the applica-tion of the ballistic density to an actual firing. The resulting effectsfrom a shell whose trajectory is 150 meters too short, for example, are

18

K?//

just as bad as those from a thell whose trajectory is 150 meters too

long. The algebraic error is a measure of the amount of bias it) thetables and indicates whether the tables could be improved by changingthe individual values to eliminate the bias. Ideally the algebraicerror should be zero, but, owing to the inherent inaccuracies in thedetermination of density, small biases of a few tenths of a percentappear. These, however, are insignificant.

Tables VII and VIII show sample distribution of errors for the new Vietnamitables. Shown are the errors for the summer daytime and the winternighttime tables for stations below 200 meters elevation.

Hf9TH$0* 6 TO 4

CLEV ATIN- 0 TO 200 METERS90nO HOURS TO t900 HnOURS MONTHS-11 10 0

[LIVATIGN0 0 TO P0I 6t220$2000 HOt1kS 10 760 ,7iw$

34 POINTS OUT Or RANCL[

170 POINTS 5U02 t 54A0GL

"1 2 3 4 5 60 7 8 9 10 31 TOTAL"15 0 0 3 2 0 0 U 0 0 1 0 5 A 4 , 8 r A , 1:2* 0 o 3 4 0 0 3 2 0 0 0 1? -t 0 0 U A 1 6. 7 , I I ,T

I2 0; 3 6 , 5 2 2 2 :' 2 -2 0 1 1 , I5 I U 9 1 I , 40"12 4 6 .2 1 4 7 2 1 2 0 0 47 -13 0 U *? A I P

1i 5 5 9 3 6 5 5 23 4 164 *22 - 9 20 24 24 1- . 9 t 79"00 9 17 23 14 7 15 l 6 5 7 111 211 0 P 5 12 15$ 7 9 7 0 U 9 to"":9 6 ?0 12' 20 13 20 24 5 '4 10 2' I'll 10 2 . I 9 20 P? 25 2- 1- 13 12 17 12*

"-025 29 44 36 40 36 46 26 19 23 252,49 ' 19 3 H 34 3H 3 07. 26 221 is Pp?"7 33 40 53 54 321 2 45 44 48 27 45 00 10 4 4 3 30 2' 20314

SoA 40 50 7 69 55 66 74 67 50 6S 48 602 ' 29 64 01 7I 67 77 F2 I1 11H 36 140"16 52 9 2 29 123 75 116 263 93 61 64 '6 Tul4 -5 62 11 li2 t 1 2 12 2(2 I 2 09 71 2l A9 tool:4 72 66 229 125 118 137 136 116 205 124 94 1252 4 246 143 I22 31i 124 132 226 219 90 9.0 0 1239

' 213 246 241 274 210 240 2 25 130 2 A2 207 20*0 2 216 290 226 It) 231 21 293 207 22| 2',":1 264 163 178 "1, 1 23 2521 179 145 152 145 99 057 *2 239 220 272 239 29 23' 2107 260 129 247 - ! 0 1 53"22Pl4 I74 207 297 173 270 2 39 "t46 45 06 2923 '1 250 286 2ip 17 1 16 o 721 22 20 11 142 174 2077

285 235 IA8 194 267 161 P12 132 252 2•5 96 1977 0 3 o) 223 250 244 266 222 2' 22, 264 2$' 0(0 06$1I 'l l 2 0 8 '06 262 2 3 7 264 20' 24 21 9 236 I6 24 06 2 6 3Pit 202 2 1 6 2 1 6 ID 264 o3 1 S I 13, 4 2 3 76 54 8 4 2 206 274 126 141 143 230 247 144 227) 15 1 4 129I

2268 179 161 242 250 263 02 233 042 054 46 0766 3 24 2s7 1192 9 109 200 . 219 23 0n 123 70 03363 191 174 210 722 230 133 123 229 113 99 85 140 4 6 92 134 1277 2$ 206 IIA lp2 I2 116 06 64 2194

5 51 34 A 7 22 1021 " 04 70 a9 64 66 56 S 3 2 6 5 96 00 200 120 22 II2 IQ/ PA P7 51 2046945 6? 78 67 04 64 77 60 66 60 ) 0 725 6 41 12 A4 200 93 e7 67 09 70 e, 0 ,46 25 45 56 54 71 60 €1 60 40 02 33 S4P 8, 1 $ M 09 IT 5? 73 2' 4 00 I0 7 97 24 33 45 3) 60 46 56 52 33 10 26 '16 .1 7 62 23 A0 $0 Is 67 63 47 3) A'99

6 6 13 27 29 37 41 28 34 22 24 25 264 19 0 6 06 1 ý 66 7$ 46 40 40 00 $449 10 27 20 32 2019 6 24 23 26 22 704 20 6 2I0 5 5 to 9h .96 52 67 54 24 46

26 5 7) 22 1 6 1 9 2. 71 26 22 20 23 274 22 2 6i 39 27 42 47 30 2 7 2 73 336to 2 3 20 24 t'i 23 7 2? 20 13 12 219 13 0 6 1) 0 it 3 P 3 ( We0 2 I2 2 It 171

12 2 6 3 3 6 4 5 10 6 20 26 24 0 3 7 20 16 2t 2'. 22 14 12 14h13 0 3 2 4 5 % 4 121 5 13 60 12 2 ' 5 $ 7 13 17 12 I2 ifI I2 1 924 0 2 3 4 2 2 0 0 2 .325 0 0 0 0 1 2 2 2 2 3 6 18 '207 2196 2107 •104 ,t'2• 223 2 2I7 2259 20.0 260$ 147? T0004S

19621 296i 19A 19021 197 1977 1962 1696 1673 1610 1261 TOTAL0 0.2 0.) Q0. 7.9 (,:.! 0.5 6.90:1. 7,9 0:. A:5 7VFHtgr 04ROCips)9.0 0.e 0¢C.2 0. (.21 . 0.2 6.2 7 . 0.20 6.1 Anew 0H"oxc62.

0.2 .. 4.30.4 0.3 (1,3164 0.:3 0.4 . 003 4 0.9 ovCR1oC (6ROR(CIS$0.0 *0.0 '0.1 '.2 (�'0 :0.0 -0.0 0.0 -0.0 000 0.0 A VIE AC EQoURCAsGi 22083) oj04 7l02

20051DATA OINT Value- in this €o1,rna represent density error# X 10

Values in this tolusnn represent density errors X 10 DISTRIBUTION OF ERRORSNEW VIETNHAM TABLES

DIST2RJBUTION OF ERRORS TABLE ViUNEW VIETNAM TABLES

TABLE VII

It can be seen that the mean absolute error is 0.5% or less for alllines in both seasons and the bias error is not significant. All sea-sons and altitude ranges are similar, although the number of data pointsdecreases markedly with increasing elevation.

Table IX shows a corresponding error distribution using the density de-parture tables in FM 6-16 for region 6. Since the older tales are in-

19

tended for use in all seasons, there is no differentiation for surraerand winter, and the tables include all data for all months.

DISTRIBUTION or OERRORS . '5.L. BALLISTIC DENSITY DEPARTURE TABLES

*'0lIOS* I 0n 1,0114111r'"- fl " .... ..0 (IS

270 1.00'0 '0 .0 7. •T400-.r", n 000 Bun

20 0 , I 2 31 Ia 2 I? I 0 S0"I9 0 I I I I9 23 40 IO .2 0 118

"140 I ; 2 0 I0 33 091 67 34 6 0 7441 0 0 2 6 I? 09 87 III 44 0 0 533"16 0 3 6 I 71 1a, 141 1 00 0 0 450

I. 2 is?2 2 5 211 201 111 12 0 .1,*13 0 3 16 40 A3 197 301 334 213 20 0 0740"7 3 1 14 00 71 214 3? 6 357 289 3- 0 143'"*II 2 | I • I 106 )3 70, 364 11 20 . I IIl:

.11 &L |7• pil |I 54 3A. -5 1) 4 2 75l 1*9 O )6160 , 7' 410 ;52 3 101 4'6t 43 2 90 10 0 M004

-•5 19 •1)+• "Il, l 1 10 .4 1 2 3 T=/I .1T 561411 7n 293 . I93 $10 620 0 11 0 2971

0 IS 17 27.0 310 109 4.7 w )39 S14 279 0 3| 61

° I 3t 3 4 .6 4 59 49 01 T7ý 40. 31 330i 4 0 3900

2 4S 0 51-0 04 490 310 3)0 290 744 20 000 I O 40471306- 0 66 43 .44 '32? 2.% 719 207 501 0 4033

0 007 581 409 490 34 307 3W 0 21 6 I 11 30?1 0 319I 400 '.4 4 3 2"1 lo 153 340 0 31307 $A0 A49 490 300 300 711 173 11. 111 30A 7* 14161

0 n9 401 2P0 232 243 I5l s 09 3 i 16 7 0 2131"6 607 137 700 770 P T0 3 is 24 I03 10 5 14403 9 71 0 " 19 I I' 70 29 14 24 10 2 I190

0 419 1. 3 1 11 I$ I- 1? 01 4 1140

II 10 6) A# 45 40 II 4 4 3 3 21 0 T 012 AS 40 30 49 30 1. , 6 I 313 74 3. 1 le 9 6 2 0 7 I. "0' 7,014 10 5 06 73 13 I 0 I 0 9 173 739

2 1+ 1Zz ' = z ) 0 ,i 1 o 1 - " 1 r tIA II IS 03 I I I I 0 ' 11

11' 5 1 0 7 I 0 0 0 0 3 73 30019 0 I 0 0 I 0 0 0 a 17 ' 540 I I 3 3 0 0 0 0 7 304 3

6091 .416 0914 '401 890t6 640 .944 6042 A1m4 0•30 41)4 0000t30 041944In t101 63 •.43 0 147044441 de•.0t11 40700 X 10

0•.4 6.4 0.4 0.0 0.0. 0.0 0. 0.0• 0.7 0.4 7.7l 4004948 r O•GTl ool+l(.~)

0.3 0.1 0.0 ' "0.I 4 0.2 10. 0,0. QO .0 40".417. 7. • 40744. t : '? 990ll

"--7O0•P0'7'04,-70T5- -.

TABLE IX

It is obvious that the absolute errors are greater and that there is asignificant bias in many zones. Note especially line II, which has anaverage error of more than 2%! It can be seen that fewer than 2000 ofthe 4334 values in line II have errors less than 2.0%, all the othersare off range as far as the table goes. It is all the more surprisingthat lin( 10 is excellent, with mean errors as low as lines I and 2,and no significant bias!

If one wishes to compare the tables on a yearly basis, the seasonalerrors can be combined to give an annual figure. Table X shows thebreakdown into four categories of error.

Cases with errors from 0 to 0.5% can be ciansified excellent, thosefrom 0.6% to 1.0% can be called fair; those from 1.0% to 1.5%, poor;and greater than 1.5% would be disastrous.

20

-'

TABLE X

ANNUAL DISTRIBUTION OF DENSITY ERRORS (SEA-LEVEL STATIONS)

c ENew Tables Old TablesPercent Error Day Night Day Night

0 - 0.5 72.6% 77.1% 50).1% 53.5%0.6 - 1.0 22.4% 19.2% 28.1% 28.5%1.1 - 1.5 4.3% 3.3% 12.5% 10.5%

- 1.5 0.7% 0.4% 9.3% 7.5%

We see that the number of cases of very poor assessment of ballisticdensity when the new tables are used is less than one-tenth the numberwith the old tables; the probability of obtaining an excellent ballisticdensity has increased bý more than 20% and an acceptable density profileis obtained in 95 of every 100 cases. There is no doubt that the tablesoffer an excellent back-up system for obtaining ballistic densities inVietnam in the absence of a direct radiosonde observation.

The lack of a direct measurement may be due to outage of equipment,communication difficulties, or it may be that it is the period betweenscheduled balloon releases, usually every six hours in Vietnam.

Earlier studies have shown that the variation of ballistic density ina I-to-8-hour period is not significant [5]. Should the tables be usedwhen the latest metro message is 3, 4, 5, or 6 hours old?

To answer this question one must examine the diurnal variation of den-sity. The special 3-hourly data from Vietnam (mentioned earlier) areideal for this analysis. Even though the period is short, about oneweek, the changes in density throughout the day will give some clue asto those periods in which the temporal variation is greatest. Figures14 and 15 show the density for the various ballistic zones throughoutthe day for the station near sea level and the elevated location. Theshape of both the curves is the same although the amplitude of the den-sity fluctuation is greater at the lower station. About 2100Z (0500LST).well before sunrise, the surface and ballistic densities decrease rapidly,fluctuating between 0300Z and 0900Z (llO0-1700LST) to a minimum a littlebefore 090OZ. The decrease over this 6-hour period is greater than 3.0%at sea level and more tnan 2.0% at elevated stal'ions.

[5] Lowenthal, Marvin J., "Applications of Accuracy of Upper Air Datato Artillery," ECOM-3122, May 1969.

21

GMT 00 09 12 18 00 GMOT 0 06 12 to 00 OMT CO 0612 If 2 00

940- • 940 1. "90

93JO - -93 0 -93JDLN

SURFACE LIKE IOS9 /i -,20 -e40

SLINE 9

910 -g30

94t) -4.0

I- -94.0

93.0 - 93D0

OSO

LINE I LINE S .93.0

92 0 2.t20

9I0

FIG. 14 DIURIIAL VARIATION OF BALLISTIC DENSITY

VIETNAM STATION 142080 ELEVATION 30 METERS6101 GRE•ENWICH MERIDIAN tIME (Z)

GMT 000306 0912 1518 21 00 GMT 0008 Is 1 00 GMT 00 06 It Is 00

6O -S0o80 -0O

LINE 4"870 870 9170

86- 86o -880.S.i*FACE LINE 2

'ACE LINE 2

0a70

Sao -880

2 -080

4 LINEE6<m 870 870 LINE 3

Y LINE 1I7860 ,860

FIG. 15 DIURNAL VARIATION OF BALLISTIC DENSITY

VIETNAM STATION 140080 ELEVATION 770 METERSGMT - GREENWICH MERIOIAN TIME(Z)

22

Thus, the ballistic density obtained from a sounding made at OOOOZ andused at 0500Z (before a new measurement is customarily made) would bein error by more than 1%. Similarly, a sounding made at 0600Z and usedat IIO0Z would contain an error almost as great, whereas the ballisticdensities from a 1200Z sounding used at 1700Z and from a 1800Z soundingused at 2300Z would be in error by less than 1%. While these valuesare for the tropics, similar curves, although with different amplitudes,obtain for the other climatic regions. This means that the time of dayis the determining factor for the time variability of ballistic densityfor periods of less than 6 hours.

To decrease the error in ballistic density in the interval betweensoundings, the curves of Figures 14 athd 15 may be used to correct theearlier measurement. Even though the daily curves of ballistic densityvariation may not coincide absolutely, the trend is the same. Thus adiminishing of the OOCOZ ballistic density by 1% for use at 0300Zwould give a much better estimate of the density than the use of the un-corrected OOOOZ value. A table could be constructed giving such cor-rections for each measurement hour of the day and the time of usage.

This could be supplied to the Fire-Direction Center to decrease therange error due to improper ballistic density corrections. A sampleof such a table for one location in Vietnam is shown in Table XI.While both location and altitude are different from Figures 14 and 15,the trend is the same.

Corrections for Ballistic Density -- 'Lne 1Station lh(Y015 (Vietnam)

Z. $ Iu ng Tine (LST) 00 01 o2 o3 Oh 0o5 06 07 o8 09 10 11 12 13 14 15 16 17 18 19 20 P1 P2 P .

UE!-r Tirre 00 +.2 +.4 +.6 +.8 4.9+1.0 +.9 +.7 ++. .1-.91-1.7 .231--9 -3. -3.3-3,1-.7-2.2 1-1. -' - -01 -. 2 +.2 -+4 +.5 +.71 +.8 +.5 +.1 -. 5 -1.2 -1.9 -2.6 -3.1-3.1 -3 5-3.1-2.7 -2.- -1 , -.1

_22 -.4 -. 2 1 +.2 +.4 +.5 +.6 +.5 +.3 -. 1 -. 7 -1.3-2.1 -2.7-3. -3.6 -3.7-.5 -3.1 .2.6 -P.1 -1,- -1 .03 -. 6 -. 41 -. 2 +.2 +.3 _L 4 + .I -. = - 2.- 3 -2.9 -3.52 -3.t-3.-3.7-3.3-27 -1 # -1 -

o0h -. 8 -.5 -. h 4 2 - +.1 4.2 +.2 -. 1-. -1.0-1.7-2. -. 1-3.61 -4.0 -4h.O-3.-e-3.5-3.0 .7,1,-1.? -1 Y :I,-0 -. 9 -. 7 -. 5 -. 3 -. 1 +.4 0 -. 2 -. -1.2-1 -2.6-3.2 -3.8 -4.1 -4.2 4.0 -3.6 -3.1 -; 5 -1 _, .1. -1 ;o 6 -i.x -. 6 -. 4 -. 2 -.:1 T -.3 -. 7-1.2 -1.9-2.6 - -3 .2 -4.2 -4.1 - -3.2 2 1 - -107 -. 9 -. 7 -.5 -3 .2 0 . -. 2 -. 6 -1.2-1.9-2.6 -3.2 -3.b-4. . 1b- X•'--• i -3.16 - P1 -2 -1 i3 1 -. 5 -. 3 -. 1 +.1 +.2 4.3 +.2 -. *1.0-I6-2. 3••9 3 . - &.()- • 7 -P 9 -2.L -ij .1 '"0 "-. -.1 + .'1.+6- -. 2 32.} +.6 4,7 4.6 +. -. - •-, -.7-k. -3.5 -. 3J. -3.0O-2.5_-. -! - ' ".

10 +.2 +.5 +.7 +4 .0 1.2 4 1 1.2 +1.0 +. -1.4 -2.1 -2. 9 -2.2 .0 -2.b -2.5 .0 - -91 4+." 41.2 1 '1 41.- +1.7 +1 . 41. 41.4.7 -. 7 -1. -1.9 -2 "-2-23 1 -1. 8 -1.3 - 2. 4 3 +. ,

12_ 41.7 41. 42. 1 + 2. 42.9 . R 4+.2. 4. + 42.0 41. +.7 -. 7 -1.2;-1.5 • "1• - -.5 + 5 I .

1 +4.7 +-.1 .9 +2... + . 1 +. 7 +2.3 +.2 41 1"13 +42. 42.6* 42.7 +2. +. 43.i .2 +3.3 *3 . +3.0 42.7 + 2.0 +1.2 + .5 -.9 -.9 - . 4 + . + 41 -'1 1. 7 4P.2!• 1 +•. f33 +•5 +•7 4.• +.O •.i b.O i.8 4 2.5 + 2. 3 pi+1.• 4.94 +, _ - .I . 4.1 41.0 +lA . 14 -•, + . 2,..

16 43. +3. 4 +3.7 + *'9 +.0 + .2 4s .2 +h. +.2 4 .0 4 +34.0 42.3 41. 4.9 4. 4.1 +_ .2 4.5 +1.1 +*.6 + 4. + A' 4•,

1i 42.79 +.91 +. .+ . 43.5 .7+. +'. +.0+2. 41. 41.0 4.4 -. 2 . i8-.. . .' +. + , 04 1. '-+ +.2 r2., +2.6 +. 43.0 +4 .1 43.2 +43.1 43.9 +2.5 42.0 41.3 +.5 -. 1 -. 7 -1.0 +-1.1 -. 5 -. 0 - .6 +1.1 4- , 4P ; -'

20 41.• rl94. •?+.•+, . •64. 9O~~ 4.7 __0 -. 7 -1.2 -1.5 -'.6j -1. -1.1i * -,, 4.5 41, i

i ,7 +3-1 Q +. !1 +.7 1 +3.8 +74-.o +4.1 +4.04 U +3.0 4 +2 -.8 -1.1 -I.7 -2•2 - 2.1 - ?.2 -. 4 =-_I- r 7.h1 +- 4 . 9 . '7 {. + 37 + +i2+.7 +3.6 +I !L.0 + 2.6 +1-.'9+ 7 -l - . 2 -9 . 5 ? -3, -2.4 +-C,+-1,.9 ) • 1 A-. -. 1

2.21ly appropri1~te correction to r~e~sured B•.1listic tensity to get

corrected value ror u.se at f~iring tirre.

S++ +1TABLE X16

•23

-- +. 2+.T.0+. 7 1 1 -11- 2% . +2 +31+ . 31+. ?1+ . 13-7-. 11.

CONCLUDING REMARKS

In this report, the development of ballistic density departure tableshas been traced over the last three decades from their earliest begin-nings, where elevation of the battery was the only parameter considered,through the promulgation of climatic regions where geography and timeof day were added, to the latest tables that are constructed for a limitedgeographical area far smaller than the previous regions in FM 6-16.

In addition, the possibilities for minimizing interdiurnal densityvariations have been pointed out, as well as impossibility of pre-dicting ballistic densities at elevated locations with sufficientaccuracy for Artillery purposes from measurements at sea level.

The new tables constructed from individual radiosondings have been shownto be much more accurate than the older ones derived mainly from meanvalues at selected locations.

Use of the tables can effect a considerable savings in expendables, aswind measurements can be made every two hours by tracking a balloonalone (without the more costly radiosonde), since the density can becorrected by the tables and associated techniques.

24

APPENDI X

COMPUTER DETERMINATION OF METRO MESSAGESFROM RADIOSONDE DATA

By

Hope S. PerlmanU. S. Army Electronics Command

Computer reduction of radiosonde flights to give thermodynamical quanti-ties is common where a large number of flights must be handled orwhere checking of manual operations is required in data repositories.Less common is the computer determination of NATO or computer meteoro-logical messages since ballistic meteorology is less extensively re-searched than pure synoptic meteorology.

Secondly, the recent change in the format of the computer met messagehas necessitated a change in the reported quantities. That, in turn,requires a program change in any computer routine that produces theartillery met messages.

This paper outlines the procedure for computer determination of ballis-tic and computer met messages, with especial detail given to the evalua-tion of the two new elements of the compuier message - mean virtualtemperature and pressure at the midpoint of the zone.

Procedures

Since data for research purposes is most often obtained from World DataCenters, the analysis begins with the data in the usual card (or tape)format of the mandatory pressure levels - the customary way in whichdata are archived. It must be remembered that heights on the cards areexpressed above mean sea level (MSL). Since artillery met data are con-cerned with heights above ground, the elevation of the station must besubtracted from all given heights of the standard pressure levels. That-is the reason for Steps I and 3(c) below. A complete computer programis available upon request.

Method of Solution

I. Read in surface height (SZ) of station.

2. Read in complete data for one flight. This will include n setsof pressure (P), height (Z), temperature in *C(T) and relativehumidity in %(H).

25

3. Adjust data and number of levels (n) as follows:

a. If H < 0, set it equal to zero.b. Eliminate any level where temperature is missing.c. Subtract SZ from all values of Z.

4. Calculate virtual temperature, in °K, (Tv) at each l6vel, asfollows:

T V -= P(T+273) 25.22T(.O0378I2)(H)(6.iO5)exp( 5.31 In

5. Print out adjusted data (P, Z, T, H, TV) for each level.

6. Set up ballistic zone top heights (ZLT) and standard tempera-tures (ZLTMS) and densities (ZLDNS) at these heights.

7. Print all surface information.

8. For each zone (ZL) compute ZZTM, zone temperature and ZZPR,pressure at the top of the zone, using intermediate data levelvalues of P, Z and Tv, indexed from 0, the bottom of the zone,to d, the top of the zone.

a. Obtain a starting value of Tvd, virtual temperature at thetop of the zone, by interpolating linearly, using values ofTvd+l, Tvd-l, Zd+l' Zd, and Zd-I.

b. ZZTM is calculated by selecting a starting value (1/2 thesum of the maximum and minimum of the Tv values within thezone), and moving it toward the maximum or minimum until

d-I

1/2 Q (Z -, Z i) (Tvi + Tvi+l - 2ZZTM)%O* (2)1=0

In practice, the process is continued until two successive values ofZZTM differ by less than .10K.

c. Pd is found by solving the transcendental equation

29.27 ZZTM I (p Zn - Zo(3)

The rationale for Equation (2) is found in Appendix I.

26

d. A new value of Tvd is computed by interpolating linearly,using iVd+l, TvdIl, Pd+l' Pd' and Pd-l"

e. Steps b, c, and d are repeated until two successive valuesof ZZTM, ca!culated in step d differ by .2°K or less.

f. ZZPR = Pd (4)

9. For each zone level, compute

a. ZZTMPZL zone temperature (% of standard)

ZZTMPzL = 00(ZZTMSZL (5)

b. ZZPR 2 L , pressure at the midpoint cf the zone, is foundby sotving the following transcendental equation:

S(ZZPRzLI )I

29.27(ZZTML) In (ZZPRzLI = 1/2 (Z - ZO) (6)'ZL (ZZPR2ZL d o

c. ZZDNZL, zone density

ZZDNzL = 348.384 ZZPR2zL/ZZTMZL (7)

d. ZZDNP zone density in percent of standardZL'I00(ZZDN= ~ZL 8ZZDNPzL ZLDNSzL

10. For each zone, calculate ballistic weighted temperature (ZZBTL)and ballistic weighted density (ZZBDZL), using temperatureweighting factors (TWF) and density weighting factors (DWG) forthat zone.

/

127

APPENDIX I

CALCULATION OF ZONE TEMPERATURE

T vd, Z d

zone top

T Tv2, Z 2

zone bottomTvo' Z0€4

ZZTM

Given: Tv0 , Z , Tv., ZI -. Tvd, Zd, where the zero subscript denotesthe bottom of ?he zone and the d subscript the top of the zone.

Find: ZZTM, the zone temperature, such that the areas to the right ofZZTM equal the areas to the left of ZZTM, or ZZTM is correct to .['K.

Analysis:

I. Between any successive reading of Tv., Zi and Tvi.l, Zi+Ithe figure is either a trapezoid or ý'triangles.

a. If a trapezoid, Area = 1/2 h (a+b)

= 1/2 (Zi+ - Zi) [(TviMl- ZZTM) - (Tv, - ZZTM)j

= 1/2 (Zi+I - Zi) (Tv, + Tvi+l - 2ZZTM)

and will be positive or negative depending on whether Tvi

and Tvi+l are greater or less than ZZTM.

b. If two triangles, the area equals area of triangle

(Tvi, Zi) (Tvi+I, Zi+I) (Tvi+I, Zi)

minus area of rectangle

"(ZZTM, Zi) (ZZTM, Z i+I) (Tvi+I Zi+I) (Tvi+l Zi)

28

or 1/2 (ZQ Zi) (Tvi - Tvi+)- (Zi+ Zi) (ZZTM- Tvi+)

*.the area of the trapezoid equals the area of the twotriangles, and is

1/2(Zi+ - Zi) (Tvi + Tvi+l - 2ZZTM)

2. ZZTM is calculated by selecting a starting value of ZZTM (halfthe sum of the maximum and minimum values of the Tvts) and movingit AT toward TV min until

d-I1/2 Z iM i (Tvi + Tvi+l - 2ZZTM) n 0.

i=o

29

" - - -• .? V ,'.° - ". '• 4 - 71

ATMOSPHERIC SCENCES RESEARCH PAPERS

"1. Miers, B. T., and J. E. Morris, Mesospl'.ric Winds Over Ascension Island in Jan-uary, July 1970, ECOM-5312, AD 711851.

2. Webb, W. L., Electrical Structure of the D. and E-Region, July 1970, ECOM-5313,AD 714365.

3. Campbell, G. S., F. V. Hansen and R. A. Uise, Turbulence Data Derived from Meas-urements on the 32-Meter Towr ;?acility, White Sands Missile Range,New Mexico, July 1970, ECO1v-5& 14, AD 711852.

4. Pries, T. H., Strong Surface Wind Gusts at Hi'loxwn AFB (March-May), July 1970,ECOM-5315, AD 711853.

5. D'Arcy, E. M., and B. F. Engebos, Wind Effects o.• Unguided Rockets Fired NearMaximum Range, July 1970, ECOM-5317, AD 711854.

6. Matonis, K., Evaluation of Tower Antenna Pedestal for Weather Radar Set AN/TPS-41, July 1970, ECOM-3317, AD 711520.

7. Monahan, H. H., and M. Armendamiz, Gust Factor Variations with Height and At-mospheric Stability, August 1970, ECOM-5320, AD 711855.

8. Stenmark, E. B., and L. D. Drury, Micrometeorological Field Data from Davis, Cali-fornia; 1966-67 Runs Under Non-Advection Conditions, August 1970,ECOM-6051, AD 726390.

9. Stenmark, E. B., and L. D. Drury, Micrometeorological Field Data from Davis, Cali-fornia; 1966-67 Runs Under Advection Conditions, August 1970, ECOM-6052, AD 724612.

10. Stenmark, E. B., and L. D. Drury, Micrometeorological Field Data from Davis, Cali-fornia; 1967 Cooperative Field Experiment Runs, August 1970, ECOM-6053, AD 724613.

11. Rider, L. J., and M. Armendariz, Nocturnal Maximum Winds in the Planetary Boun-dary Layer at WSMR, August 1970, ECOM-5321, AD 712325.

12. Hansen, F. V., A Technique for Determining Vertical Gradients of Wind and Temp-erature for the Surface Boundary Layer, August 1970, ECOM-5324, AD714366.

13. Hansen, F. V., An Examination of the Exponential Power Law in the Surface Boun-dary Layer, September 1970, ECOM-5326, AD 715349.

14. Miller, W. B., A. J. Blanco and L. E. Traylor, Impact Deflection Estimators fromSingle Wind Measurements, September 1970, ECOM-5328, AD 716993.

15. Duncan, L. D., and R. K. Walters, Editing Radiosonde Angular Data, September1970, ECOM-5330, AD 715351.

16. Duncan, L. D., and W. J. Vechione, Vacuum Tube Launchers and Boosters, Septem-ber 1970, ECOM-5331, AD 715350.

17. Stenmsrk, E. B., A Computer Method for Retrieving Information on Articles, Re-ports and Presentations, September 1970, ECOM-6050, AD 724611.

18. Hudlow, M., Weather Radar Investigation on the BOMEX, September 1970, ECOM-3329, AD 714191.

19. Combs, A., Analysis of Low-Level Winds Over Vietnam, September 1970, ECOM-3346, AD 876935.

20. Rinehart, G. S., Humidity Generating Apparatus and Microscope Chamber for Usewith Flowing Gas Atmospheres, October 1970, ECOM-5332, AD 716994.

21. Miers, B. T., R. 0. Olsen, and E. P. Avara, Short Time Period Atmospheric DensityVariations and a Determination of Density Errors from Selected Rocket-sonde Sensors, October 1970, ECOM-5335.

22. Rinehart, G. S., Sulfates and Other Water Solubles Larger than 0.15j Radius in aContinental Nonurban Atmosphere, October 1970, ECOM-5336, AD716999.

23. Lindberg, J. D., The Uncertainty Principle: A Limitation on Meteor Trail RadarWind Measurements, October 1970, ECOM-5337, AD 716996.

24. Randhawa, J. S., Technical Data Package for Rocket-Borne Ozone-TemperatureSensor, October 1970, ECOM-5338, AD 716997.

.30

25. Devine, J. C., The Fort Huachuca Climate Calendar, October 1970, ECOM-6054.26. Allen, J. T., Meteorological Support to US Army RDT&E Activities, Fiscal Year 1970

Annual Rep';rt, November 1970, ECOM-6055.27. Shinn, J. H., An Introduction to the Hyperbolic Diffusion Equation, November 1970,

ECOM-5341, AD 718616.28. Avara, E. P., and M. Kays., Some Aspects of the Harmlonic Analysis of Irregularly

Spaced Data, November 1970, ECOM-5344, AD 720198.29. Fabrici, J., Inv. of Isotopic Emitter for Nuclear Barometer, November 1970, ECOM-

3349, AD 376461.30. Levine, J. R., Summer Mesoscale Wind Study in the Republic of Vietnam, Decem-

ber 1970, ECOM-3375, AD 721585.31. Petriw, A., Directional Ion Anemometer, December 1970, ECOM-3379, AD 720573.32. Randhawa, J. S., B. H. Williams, and M. D. Kays, Meteorological Influence of a

Solar Eclipse on the Stratosphere, December 1970, ECOM-5345, AD720199.

33. Nordquist, Walter S., Jr., and N. L. Johnson, One-Dimensional Quasi-Time-Depend-ent Numerical Model of Cumulus Cloud Activity, December 1970,ECOM-5350, AD 722216.

34. Avara, E. P., The Analysis of Variance of Time Series Data Part I: One-Way Lay-out, January 1971, ECOM-5352, AD 721594.

35. Avara, E. P., The Analysis of Variance of Time Series Data Part I1: Two-WayLayout, January 1971, ECOM-5353.

36. Avara, E. P., and M. Kays., The Effect of Interpolation of Data Upon the HarmonicCoefficients, January 1971, ECOM-5354, AD 721593.

37. Randhawa, J. S., Stratopause Diurnal Ozone Variation, January 1971, ECOM-5355,AD 721309.

38. Low, R. D. H., A Comprehensive Report on Nineteen Condensation Nuclei (Part II),January 1971, ECOM-5358.

39. Armendariz, M., L. J. Rider, G. Campbell, D. Favier and J. Serna, Turbulence Meas-urements from a T-Array of Sensors, February 1971, ECOM-5362, AD726390.

40. Maynard, H., A Radix-2 Fourier Transform Program, February 1971, ECOM-5363,AD 726389.

41. Devine, J. C., Snowfalls at Fort Huachuca, Arizona, February 1971, ECOM-6056.42. Devine, J. C., The Fort Huachuca, Arizona 15 Year Base Climate Calendar (1956-

1970), February 1971, ECOM-6t57.43. Levine, J. R., Reduced Ceilings and Visibilities in Korea and Southeast Asia, March1971, ECOM-3403, AD 722735.

44. Gerber, H., et al., Some Size Distribution Measurements of AgI Nuclei with an Aer-osol Spectrometer, March 1971, ECOM-3414, AD 729331.

45. Engebos, B. F., and L. J. Rider, Vertical Wind Effects on the 2 75-inch Rocket,March 1971, ECOM-5365, AD 726321.

46. Rinehart, G. S., Evidence for Sulfate as a Major Condensation Nucleus Constituent

in Nonurban Fog, March 1971, ECOM-5366.47. Kennedy, B. W., E. P. Avara, and B. T. Miers, Data Reduction Program for RockE

etsonde Temperatures, March 1971, ECOM-5367.48. Hatch, W. H., A Study of Cloud Dynamics Utilizing Stereoscopic Photogrammetry,

March 1971, ECOM-5368.49. Wilamson, L. E., Project Gun Probe Captive Impact Test Range, March 1971,

ECOM-5369.50. Henley, D. C., and G. B. Hoidale, Attenuation and Dispersion of Acoustic Energy

by Atmospheric Dust, March 1971, ECOM-5370, AD 728103.51. Cionco, R.M., Application of the Ideal Canopy Flow Concept to Natural and Ar-

tificial Roughness Elements, April 1971, ECOM-5372, A•D 730638.52. Randhawa, J. S., The Vertical Distribution of Ozone Near the Equator, April 1971,

ECOM-5373.53. Ethridge, G. A., A Method for Evaluating Model Parameters by Numerical Inver-

sion, April 1971, ECOM-5374.

54. Collett, E., Stokes Parameters for Quantum Systems, April 1971, ECOM-3415, AD729347.

55. Shinn, J. H., Steady-State Two-Dimensional Air Flow in Forests and the Disturb-ance of'Surface Layer Flow by a Forest Wall, May 1971, ECOM-5383,AD 730681.

56. Miller, W. B., On Approximation of Mean and Variance-Covariance Matrices of Trans-formations of Joint Random Variables, May 1971, ECOM-5384, AD730302.

57. Duncan, L. D., A Statistical Model for Estimation of Variability Variances fromNoisy Data, May 1971, ECOM-5385.

58. Pries, T. H., and G. S. Campbell, Spectral Analyses of High-Frequency AtmosphericTemperature Fluctuations, May 1971, ECOM-5387.

59. Miller, W. B., A. J. Blanco, and L. E. Traylor, A Least-Squares Weighted-Layer Tech-nique for Prediction of Upper Wind Effects on Unguided Rockets, June1971, .,ýOM-5388, AD 729792.

60. Rubio, R., J. Smith and D. Maxwell, A Capacitance Electron Density Probe, June1971, ECOM-5390.

61. Duncan, L. D., Redundant Measurements in Atmospheric Variability Experiments,June 1971, ECOM-5391.

62. Engebos, B. F., Comparisons of Coordinate Systems and Transformations for Tra-jectory Simulations, July 1971, ECOM-5397.

63. Hudlow, M. D., Weather Radar Investigations on an Artillery Test Conducted in thePanama Canal Zone, July 1971, ECOM-5411.

64. White, K. 0., E. H. Holt, S. A. Schleusener, and R. F. Calfea, Erbium Laser Propa-gation in Simulated Atmospheres II. High Resolution MeasurementMethod, August 1971, ECOM-5398.

65. Waite, R., Field Comparison Between Sling Psychromett.-r and Meteorological Meas-uring Set AN/TMQ-22, August 1971, ECOM-5399.

66. Duncan, L. D., Time Series Editing By Generalized Diffe.'ences, August 1971, ECOM-5400.

67. Reynolds, R. D., Ozone: A Synopsis of its Measurements and. Use as an Aemospher-ic Tracer, August 1971, ECOM-5401.

68. Avara, E. P., and B. T. Miers, Noise Characteristics of Selected Wind and Tempera-ture Data from 30-65 kin, August 1971, ECOM-5402.

69. Avara, E. P., and B. T. Miers, Comparison of Linear Trends in Time Series DataUsing Regression Analysis, August 1971, ECOM-5403.

70. Miller, W. B., Contributions of Mathematical Structure to the Error Behavior ofRawinsonde Measurements, August 1971, ECOM-5404.

71. Collett, E., Mueller Stokes Matrix Formulation of Fresnel's Equations, August 1971,ECOM-3480.

72. Armendariz, M., and L. J. Rider, Time and Space Correlation and Coherence in theSurface Boundary Layer, September 1971, ECOM-5407.

73. Avara, E. P., Some "ffects of Randomization in Hypothesis Testing with CorrelatedData, )ber 1971, ECOM-5408.

74. Randhawa, J. S., (uone and Temperature Change mn the Winter Stratosphere, No-vember 1971, ECOM-5414.

75. Miller, W. B., On Approximation of Mean and Vasriance-Covariance Matrices ofTransformations of Multivariate Random Variables, November 1971,ECOM-5413.

76. Horn, J. D., G. S. Campbell, A. L. Wallis (Capt., USAF), and R. G. McIntyre,Wind Tunnel Simulation and Prototype Studies of Barrier Flow Phe-nomena, December 1971, ECOM-5416.

77. Dickson, David H., and James R. Oden, Fog Dissipation Techniques for EmergencyUse, January 1972, ECOM-5420.

78. Ballard, H. N., N. J. Beyers, B. T. Miers, M. Izquierdo, and J. Whitacre, AtmosphericTidal Measurements at 50 km from a Constant-Altitude Balloon, De-cember 1971, ECOM-5417.

79. Miller, Walter B., On Calculation of Dynamic Error Parameters for the Rawinsondeand Related Systems, January 1972, ECOM-5422.

80. Richter, Thomas J., Rawin Radar Targets, February 1972, ECOM-5424.81. Pena, Ricardo, L. J. Rider, and Manuel Armendariz, Turbulence Characteristics atr Heights of 1.5, 4.0, and 16.0 -Meters at White Sands Missile Range, New

Maico, January 1972, ECOM-5421.82. Blanco, Abel J., and L. E. Traylor, Statistical Prediction of Impact Displacement due

to the Wind Effect on an Unguided Artillery Rocket During PoweredFlight, March 1972, ECOM-5427.

83. 'Williams, B. H., R. 0. Olsen, and M. D. Kays, Stratospheric-Ionospheric InteractionDuring the Movement of a Planetary Wave in January 1967, March1972, ECOM-5428.

84. Schleusener, Stuart A., and Kenneth 0. White, Applications of Dual Parameter An-alyzers in Solid-State Laser Tests, April 1972, ECOM-5432.

85. Pries, Thomas H., Jack Smith, and Marvin Hamiter, Some Observations of Meteor-ological Effects on Optical Wave Propagation, April 1972, ECOM-5434.

86. Dickson, D. H., Fogwash I An Experiment Using Helicopter Downwash, April 1972,ECOM-5431.

87. Mason, J. B., arid J. D. Lindberg, Laser Beam Behavior on a Long High Path, April1972, ECOM-5430.

88. Smith, Jack, Thomas H. Pries, Kenneth J. Skipka, and Marvin Hamiter, OpticalFilter Function for a Folded Laser Path, April 1972, ECOM-5433.

89. Lee, Robert P., Artillery Sound Ranging Computer Simulations, May 1972, ECOM-5441.

90. Lowenthal, Marvin J., The Accuracy of Ballistic Density Departure Tables 1934-1972,April 1972, ECOM-5436.

91. Cantor, Israel, Survey of Studies of Atmospheric Transmission from a 47 Light Sourceto a 27r Receiver, April 1972, ECOM-5435.

92. Barr, William C., Accuracy Requirements for the Measurement of Meteorological Par-ameters Which Affect Artillery Fire, April 1972, ECOM-5437.