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^CLASSIFIED — .

■"V

^ AWS TR 105-145 ■ ^JTV AIR WEATHER SERVICE TECHNICAL REPORT

Vo S^ DERIVATION

OF JET-AIRCRAFT CONTRAIL-FORMATION CURVES

V

Herbert S. Appleman

L

^M .& &■

JANUARY 1957

( ^ .

UNITED STATES AIR FORCE

i

\ 1

AWS TECHNICAL REPORT No. 105-145

AWS TR 105-145

HEADQUARTERS AIR WEATHER SERVICE

MILITARY AIR TRANSPORT SERVICE UNITED STATES AIR i^ORCE Washington 25, D. C.

January 1957

FOREWORD

1. Purpose. .To present the data and calculations on which AWS Manual 105-100 (Rev.), August 1956, was based.

2. Scope. The assumptions, calculations, tables, and graphs used In deriving the contrail-formation curves and procedures in the origi- nal edition of AWSM 105-100 (April 1952) are reviewed and revised in this Report in light of more recent data, particularly from Project Cloud Trail. New tables and graphs are presented which were used as the basis for the revision of AWSM 105-100 Issued in August 1956. This Report will be of particular interest to field activities engaged in verifying the procedures in AWSM 105-100 or in adapting them to CüüUI- tions in overseas areas. For all practical purposes AWS TR's 105-103 and 105-112 are made obsolete by this Report and will no longer be stocked; they can still be obtained from ASTIA if desired by research activities.

3. Additional Copies. This Report is stocked at Headquarters MATS, Command Adjutant, Publishing Division. Additional copies may be requisitioned from Headquarters Air Weather Service, ATTN: AWSAD, in accordance with AWSR 5-3, as amended.

r

Approved:

fcU-PTftfcJ^ ROBERT D. FLETCHER Director, Scientific Services

DISTRIBUTION: AWS Wing Hqs AWS Group Hqs AWS Squadron Hqs Plus 'TZ"

fTechnical Services! iTechnical Services, kTechnical Services,

10 copies each 5 copies each 2 copies each

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c January 1957 AWS TR 105-145

TABLE OF CONTENTS

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SECTION I. THEORETICAL DERIVATION

1.1. Introduction 1.2. Method. '.'.'.'.'.'.[ 1.3. Sununary ,,['.,.

SECTION II. EMPIRICAL DERIVATION

2.1. Introduction 2.2. Procedure ! ! 2-3. Comparison of the Theoretical and Empirical

Curves 2.^. Effect of Season on Contrail Probability! '. '. [ 2-5' Effect of Geographical Location on Contrail

Probability . 2.6. Effect of the Tropopause on Contrail'probability 2.7. Summary

APPENDIX

REFERENCES .

Figures la-p.

Figures 2a-J.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

LIST OF ILLUSTRATIONS

Value of N required for formation of a wake saturated with respect to water and saturated with respect to Ice plus an Ice-crystal con- tent of .01gm/m3

Value of N required for formation of a wake saturated with respect to Ice

Value of N at time trail becomes visible, as a function of the pressure, temperature, and relative humidity of the environment

Value of N at time Ice-crystal content of trail falls below .01gm/m3, as a function of the pressure, temperature, and relative humidity of the environment

A graph of the relative humidity reqm -ed for Jet-aircraft contrail formation as a function of pressure and temperature of the environment

Contrail frequency as a function of temperature and pressure. United States, December 1954 - November 1955

Probability of Jet-aircraft contrail formation as a function of pressure and temperature

Theoretical contrall-probablllty-functlon curves obtained by assuming an equal distribution of all relative-humidity values from 0 to 100^ for each pressure point

Page

1 2

15

16 17

19 24

24 25 26

28

46

5

9

12

13

14

18

19

20

i>,

1 AWS TR 105-1^5

Figure 9.

Figure 10.

Figure 11.

January 1957

LIST OF ILLUSTRATIONS (Cont'd)

Theoretical contrail-probability-function curves for 250 mb obtained by assuming an equal distribution of all relative-humidity values between 0^ and each of five arbitrary maxima, and between 100^ and an arbitrary minimum *

Theoietical contrail-probability-function curves obtained by assigning a normal butlon of relative humidity about a 50jg with a a of 20^ ..... .

distrl- mean of

Comparairive contrail-frequency-function curves TT0Lt^eoJr?posphere ^ stratosphere at 200 mb. United States, December 1954 - November 1955

J Page

21

22

26

; Table la. Table lb.

i Table Ic. ; Table Ha

Table lib

1

; 1 Table He

1

Table III

; Table IV.

1

Table Va.

I Table Vb.

•■ Table Vc.

LIST OF TABLES

Density of Water Vapor in Environment 28 Density of Water Vapor in Wake Saturated/Water. 28 Density of Water Vapor in Wake Saturated/Ice, . 29 Density of Water Vapor Required for Wake Satu-

rated/Water for Various Relative Humidities . 29 Density of Water Vapor Required for Wake Satu-

rated/Ice for Various Relative Humidities . . 31 Density of Water Vapor Required for Wake Satu- ^ ^< / ?lus ^ Ice-Crystal Concentration 01 .Olgm/m.3, for Various Relative Humidities. 33

Density of Wake for Various Temperature Differ- ences Between the Wake Temperature and the Initial Temperature of the Environment. ... 36

Density of Water Vapor to Wake by Fuel for vari- ous Temperature Differences Between the Wake Temperature and the Initial Temperature of the Environment -o

Critical Temperature for Formation of Wake Saturated/Water for Various Temperature Dif- ferences Between the Wake Temperature and the Initial Temperature of the Environment. ... 40

Critical Temperature for Formation of Wake Saturated/Ice for Various Temperature Differ- ences Between the Wake Temperature and the Initial Temperature of the Environment. ... 41

Critical Temperature for Formation of Wake Saturated/Ice Plus an Ice-Crystal Concentra- tion of .Olgm/raJ, for Various Temperature Dif- ferences Between the Wake Temperature and the initial Temperature of the Environment 1^2

vi

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January 1957

Table VI.

Table VII.

AWS TR 105-145

LIST OP TABLES (Cont'd) Page

43 Comparison of Contrail Probability for the North

and South i^c

Comparison of Seasonal and Annual Contrail Probability-

1

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vil I

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January 1957 AWS TR 105-145

DERIVATION OP JET-AIRCRAFT CONTRAIL-FORMATION CITRVES

Section I

THEORETICAL DERIVATION

1.1. Introduction

content to be detected visually sZZZ sumele"t Ice-crystal

stals required for a visible oo^t^u Is .OOn0entratlOn ^ l0e 0^-

«t.. „ere used: O.OOW^ ZTZolZj TvT TT' eStl- when actual .eaSure»ents become ^TlTe "u ^tl ZT ^ construct new curves •*„.„ li«I'i«. It might? be necessary to

( several years. ".easurements probably „in not be ^^ ,„

The original tables and graphs „ere „orked out m t.™,. „,. - . -tio (g./.g,, whloh means that oann ^^v:/:^::/^"8

en reworked in terms of vapor density (gm/mS). As shown later it is now a simple matter to derive formation curves based ^ anvT crystal concentration desired AT™ ^ y lce~ avi- x, ^ . aesired. Also, the new tables can readllv bP extended to any altitude and adjusted lor any fuel T^ T^blL r Appendix) and Flares (Flares 1 and 2) ror LT^oTloTll.oZl 31,6 ZZVn thl: ^^ ^ USe ^ ^-^ --tl^atl kerosio ^: ^r1::: r rrr rhydrocarbon fueis (gas— . ue± on, etc.} are heat and water vapor. The heat ™

HT T:*: r"0'the rei"ive hu"idity - *•«- - " ai;. /A»^ ^ ( e^ l8 dePendent on the amount of heat

e^tu" "T :rsr L^r**^in the —-*•«- ^^ - ro^n" y*Z™Z\l])'0™Z1£T T"* (RHE, " ^ enVl- the „ake. Knowing 4H and J" Tf™ ""^"»ent to exhauat gas m

functions of P, £ ^dT 11 1°ir"lble t0 0btalr- '"™" " « " r, rE, and KHg irtiloh „111 result In specific values of

I \ i t c I

AWS TR 105^5 January 1957

relative humidity In the wake. (Hereinafter, the subscript "e" will refer to the wake and "E" to the environment.)

It Is generally accepted that at temperatures below freezing and In the absence of Ice crystals the relative humidity must reach satu- ration with respect to water before any condensation can occur. At the low temperatures (-40oC and colder) necessary for exhaust-trail formation the resulting droplets Immediately freeze. Since the waice Is highly supersaturated with respect to Ice, the excfess water vapor sublimes onto the Ice particles, which continue to grow until the relative humidity In the wake falls to Ice saturation. If the result- ing concentration of Ice crystals Is sufficient, the trail will be visible. The minimum concentration necessary to produce a visible trail is not known, but estimates have ranged as low as 0.004 to 0.01 gm/m [3]. Others have estimated much higher values. In the previous paper [2] it was shown that any wake which reaches a relative humidity of 100^ with respect to water contains .sufficient excess moisture after formation of ice particles to produce an ice crystal concentra- tion in excess of 0.01gm/m3. In that paper, therefore, curves of N va P, Tg, and RHg were constructed for wake relative humidities of water saturation, ice saturation, and ice saturation plus an Ice- crystal content of 0.01gm/m3. As shown below, it Is a relatively simple matter to Insert other concentration values as more information is gained on the actual ice-crystal content of contrails.

1.2. Method..

For every gram of fuel burned there are produced approximately 12 grams of exhaust gases containing 1.4 grams of water vapor and 10,000 calories of heat. Each gram of tne exhaust gas mixes with N grams of the surrounding air, with N Increasing with time from zero to infinity. The Increase In temperature of the wake over the initial temperature of the environment (AT) is equal to 10,000/(l2N x 0.24), where 0.24 is the specific heat of the air. The Increase in water vapor density of the wake (Apwe) is 1.4 x Pe/12N, where pe Is the total density of the wake. Since the earlier study had shown that no trails could form until the value of N exceeded 60 parts of air to one of exhaust gas, all wake densities were calculated on the basis of pure air. Combin- ing the two equations to eliminate N, Apt,ö = .0336 x AT x p . where o

O Vv© 6 Q is In units of kg/m.

The water-vapor density initially present in an environment at i :

i January 1957 .,.„ ,~, <*• * "'-" AWS TR 105-145

relative humidity values of 0, 60, 90, and 100 percent, and at 5»C temperature intervals from -20 to -700C, are shown in Table la. These values were calculated from Table 108 Smithsonian Meteorological Tables. 6th rev. ed. Since the Table extended only to -50oC, graphical extra- ' polation was used to obtain the remaining values. The resulting in-

( accuracies apparently had a negligible effect on the final curves. | Table lb shows the vapor density in a wake saturated with respect ^ . to water^as a function of TE and AT, using AT-values of 35, 20, 10, 5, j 2, and 10C. The saturation density values were obtained from Table 108

of the Smithsonian Tables using waKe temperatures (T ) which were [ obtained by adding TE plus AT. Similarly, Table Ic shows the vapor ; density in a wake saturated with respect to ice, and are based on

Table 109 of the Smithsonian Tables.

,- Part of the water vapor necessary to form a contrail is contained in the environment, as shown in Table la. The amount of additional

;; water vaPor necessary to form a saturated wake, which must come from ! the burning fuel, can be obtained by subtracting the values in Table

la from those in lb and Ic. The results are shown in Tables Ha and

/ IIb' Table Ir~ shows the additional water vapor required to form a wake saturated with respect to Ice plus an ice crystal content of .01 gm/m . It was obtained merely by adding .01 to all values of

Table lib. Any other desired ice-crystal concentration can be added to Table lib in the same manner.

In order to obtain the density of water vapor in the wake provided by the fuel (Apwe), it is first necessary to obtain the density of the wake (pe). These values, shows in Table III as functions of P, T , and AT, were obtained from Table 70 of the Smithsonian Tables. Table IV - the density of water vapor added to the wake by the burning fuel - was then calculated directly from Table III using the aforemen- tioned equation Apwe = .0336 AT p .

Thus, Table Ila shows the additional density of water vapor required to bring the wake to saturation with respect to water and

Table IV shows the water vapor available from the fuel. Both sets of curves can be plotted on a single graph with x- and y- axes of TE and p, respectively, for specified values of P, RHE, and AT. The inter- sections give the critical temperatures for a wake saturated with respect to water as a function of P, RHE, and AT (Table Va). Replacing

^ the curves from Table Ila with those from Tables lib and He gives the

3

AWS TR 105-145 January 1957

critical temperatures for wakes saturated with resnect m i ^ Vb) and wakes saturated with respect to iZl, (Table

tration of .01gm/m3 (Table V) Z P ^ lce-crys^ concen- • wj-gm/m uable Vcj. The values shown In 'P.KI— « are plotted as the solid and dashed curves resplctlvJ . . ^ to lp; those from Table Vb are plotted In J^ P1SUreS la picccea in Figures 2a to 2i

Figures 1 and 2 show the values of M r^ ».4 u

the sPeclflea „.»idit, eon^tiol . a runo Ln ^V T3" Wl11 meet

value, or P an. ^ A11 ourves .„ aoub::.t^ue

0d

f ä^'^«f' temperature excent i-ho ^=0 .. vcixuea with respect to * «uuxc except; the cases where the pnviT'nr>mö^+. ..

=:r::r0:^^^

before the trail can fo«. «n^ ^ <- 12 SpeCt to water must be reached

foiled upward »t^eri.r'18 "" ^ ** T«' the ls°^» " the ordlnaL^r^aa orf ^"r:.13 lnt"~<'t'- ^ ">. value of mteraeots the ippH ««of th ^ . IS ^""""^ "■>"•«> -til it

S Which will result in new vain^« ^ M

N at „hloh the trail starts and ^ E' ^ ""' the value3 of

curves of the ^l^3 ^ ^ .T^ ^ ^^ dete™ln^- ^^

Shown in Plgure 3 (and reproduced as dalhed ^ be0,:"ne •"'"•«•''- obtained by using the l^t^ZT ^ ^^ ^ F1Sare '"• "eTC

curves m Flgu« i si^! ^ , f 0 *" ^"^-^^ eolld «U«. valifof »'selected ^ T ™™ "" "0t a-"*-«^. th. selected „as the muOmm value tested, i.e., 3500.

4

I? I

I

o

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r January 1957

I I

t

I

Ns (gm/gm)

3500

H* (om/gm) 3S00

O O CO 60 90 IOO ^

AT

PIsure la.

0 0 SO SO 30 IOO

Figure 1c

AWS TR 105-1^5

Na (gm/gm)

3500 r

■:

N« (gm/gm)

3500

i nr

-60

Figure lb.

ooeo 60 90 IOO

Figure Id.

with respect to Ice nius «n i^f (solid curves) and saturated (dashed curves). P an lce-crystal content of .01gm/m3

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AWS TR 105-145

Figure le,

N,(8m.'gm) 1HE (X) 3300, 00 g" «"SO 100

AT I

Figure lg.

January 1957

N, (gm/flm) »SOO 1

0 o go «0 SO /OO ~rn r

AT I

-70 -80

Figure If.

N. (gm/gin) **r ^V 3500, 0° BO 6O 90 I0O

^ I \ " TT

AT I

Figure lh.

:

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-,

January 1957 AWS TR 105-145

tnto so 100 N, («m/gm) !°0

60 so 100 ""r <%>

( Figure 11. Figure Ij.

Nl(gm/gi<i) *• ^90

3500

fiMf C/.) Nt(gni^m) I0O 90 1Hr C/.i

35O0 r

90 AT

1 ( Figure Ik. Figure 11.

:

AWS TR 105-143 January 1957

Nt (gm/gm)

3500

RMC (•/.) NjCgm/gn) 100 *° "»e ('''>

P'70 MB

_L -70 -«0 -50 -40 -30 -20

TE CO -70 -60 -30 -40 -30 -20

v

I, I

N« (gm/gm) 100

3500

Figure 1m.

90 RMC (•/.)

Figure In.

N, (gm/gml 100 90 *% ''''>

3500 I r-

P "90 M8

-70 -60 -50 -40

P-40 MB

-70 -60 -50 -40 -30 -20 TE CO

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1

Figure lo. Figure Ip.

Ü

3

I

January 1957 AWS TR 105-145 RHr (•/.) RHe ('M

O SO

Figure 2o. Figure 2d.

Figures 2a-J. Value of N required for formation of a wake saturated with respect to lee.

T

■

AWS TR 105-1^: January 1957

Na (gm/gm) 3500 i

-70 -SO

Figure 2e. Figure 2f.

Nt (gm/gm) eo

1 ^ 1 11 , -

\ / 1750

\ / /

\ / / /

- \ 1 / - \ 1 /

700 - \ / - 1 / -

" // - / _

350 / -

'// -

// 175

J' •P-400MB

IO0 i Xi i i

2 IOOV.

HH£ (•/.)

-70 -60 -50 -40 -30 -20 % CO)

:

Figure 2g. Figure 2h. • U

10

January 1957

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AWS TR 105-145 Nt (gm/gm)

3900 Ns(gm/gm) Wg ('/.)

Figure 21. Figure 2j,

At this point the curve was very nearly asymptotic to the isotherms In all cases the asymptotic value of N on the solid curve lies to the left of the corresponding dashed curve. Indicating that a wake satu- rated with respect to water will contain more than enough moisture to provide a wake saturated with respect to ice plus an ice-crystal con- tent of O.Olgm/nr3.

The isotherm tangent to a solid curve in Figure 1 Indicates the maximum temperature which can exist for the given value of P and RH and still result in a saturated wake. The curves of these maximum E

temperatures are the formation curves in Figure 5 (Figure 1 of

AWSM 105-100 Rev). They can also be considered as curves of the mini- mum relative humidity required for contrail formation as a function of pressure and temperature. This is the more useful fora since T generally is known more accurately than RHE. These curves should be Identical to those in Figure k of the original paper [2] and are very nearly so. To use the curves it is necessary to use known or forecast values of P and Tr ^ ^■-- - ■ - -- If the point falls to the right of the 100^ curve.

11

AWS TR 105-1*5

P(M8)

January 1957

IOO "x x NX RHE 100% 200 N. v \ \N .

300 _ \ \ \ \ \

400 _ N<I00 \

IOO \\

150 200

\ \ NO \ \TRAILS 500 N

" 3500 500 —

\ \\ \ \

600 — \ \ >

V \ \ W 700 —

\ \ X W 800 —

\ N VX V 900

inon

—

1 \ w \

RHE 90%

NO TRAILS

500x

100 150 200 800

-TO -60 -SO -40 -30 -70 -60 -50 -40 -30

IOO

s X \> V RHE 60% 200 _S

\ v s^X 300 -

\ \ \\

400 — N<I00 \ 100

\ \ \ NO TRAILS

ISO 20O 500 500 —

\ \ \ \ 6O0 - \ \ NW 700 - ; XW 8O0 - V X W 90P -

1 I \\\

\^ ^

RHE 0%

_ N<IOo\ v\ NO TRAILS

IOO

: \

ISO 200 3S0

-

\\ i -70 -60 -50 -40

TE (0C)

-30 -70 -60 -SO -40 -SO

TE (0C)

"|

Figure 3. Value of N at time trail becomes visible, as a function of the pressure,, temperature, and relative humi- dity of the environment.

:< t 12

M

t

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January 1957

)

^3500

AWS TR 105-145 P(MB)

100 ^T

200

300

400

500 -

600

700

800 1-

900

1000

r- N> 3500

v RHE 100%

\ \NO TRAILS

\

\

\

\

\

P5 3500 ^T \ RHE 90%

\

\

\

\ NO TRAILS

-70 -60 -50

- N>3500 \

\

-40 -30 -70 -60 J L J

-50 -40 -30

RHE 60%

\ NO TRAILS

500 -

600 - N> 35O0

700 —

800 —

900 —

1000 1 -70 -60 -30

Tp PC) -30 -70

RHE 0%

NO TRAILS

-40 -30

Sf?r»i Va^e 0/3N at tlme ice-crystal content of trail

P

13

AWS TR 105-145

150

200

250

300

400

500 -

600 -

70O 800 900|-

!000 -70

January 1957

Pressure Altitude (JOOO's ft)

Relative' Humidity {%) ^ 60 90 100

Yes

ICAO STANDARD ATMOSPHERE

70

65

60

55

50

45

40

H35

30

•-:

25

20

-115

10

5

-60 -50 -40 Temperature (0C)

-20

^fUff 5' Jt graph of the Elative humidity required for- jet-aircraft contrail formation as a IMnctlon ?f pSssSre

^i^ffii^.rlgon~pt< (same as %£??%

n

.

14

• 1 i

1 January 1957

/ ' ^^ AWS TR 105-145

trails should not form even If the environment Is saturated with re- spect to water. If the point falls to the left of the 0% line, trails should form even If the environment contains no water vapor at all If the point falls between the two boundaries, the value of RH,, must exceed that Indicated by the graph In order for trails to form

1.3. Summary.

The theoretical curves presented In this report (Figure l) indi- cate at what values of N (the ratio of entrained environment to exhaust gas in the wake) visible contrail, start and dissipate. It Is assumed that visible trails start when the wake becomes saturated with respect to water and dissipate when the Ice-crystal concentration falls below 0.01gm/m . The latter assumption Is open to question until actual measurements are made. When data do become available, however, it

W^i l\& SimPle ,natter t0 adJUSt Table VIIb and comblne " graphically with Table IV to obtain new curves to replace the dashed curves of Figure 1.

The use of Figure 1 gives the persistence of visible trails In

IT of N-values. As stated In the earlier paper [2]: "The relatlon- ( ship of N to dlstance behlnd the alrplane ls affected by the type of

aircraft. Its control settings, the stability and density of the surrounding atmosphere, and the radial distance outward from the central axis of the trail. It would be possible to carry out indivi- dual studies for various types of aircraft under various conditions

of atmospheric stability In order to obtain the exact relation between N and distance behind the alrplane. This would enable the translation of the fomatlon and dissipation points of the trail from values of N Into terms of distance, thus giving the length of the trail "

Curves for fuels which, upon combustion, liberate quantities of heat and moisture different from those used in this report can be constructed merely by recalculating Table IV. Also, by extending Table IV to lower pressures, contrail curves can be obtained for any altitude. These studies have now been carried out to 40 mb. Because of the uncertainty in the amount of water vapor required to saturate air at very low temperatures, the curves can be carried no higher at this time.

C

15

V

AWS TR 105-145 January 1957

Section II

EMPIRICAL DERIVATION

\

1

1"

2.1. Introduction.

Chapter II of AWSM 105-100 Rev, and Section I of this Report dis-

cuss theoretically-derived curves (Figures 1-5) which show the pressure-

temperature relative-humidity relationship necessary for contrail forma-

tion by the exhaust from jet aircraft. By forecasting or assuming

temperature and relative-humidity values for the pressure-level of

interest, it is possible to issue a Yes/No type of contrail determin.a-

tion or forecast, unfortunately, in addition to the usual inaccura-

cies inherent in all space and time forecasts, there are special

difficulties in forecasting the temperature and relative humidity at

the altitudes and temperatures where contrails can occur.

Due to instrumental difficulties, relative humidities are not

ordinarily measured at temperatures below -40<>C. Figure 5 shows that

nearly the entire theoretical region of contrail formation lies at

temperatures below -4o0C. In contrail determination and forecasting,

therefore, it is necessary to rely on some assumed value of relative

humidity that has proved useful over a period of time. AWSM 105-100

(RevJ recommends using a relative humidity of 70^ near the tropopause and in high-cloud layers, and 4o$£ Jit all other times.

Temperature data as provided by the radiosonde also are not com-

pletely representative. To begin with, the temperature element Is

subject to a standard error of J^0 - 10C. Another small error Is intro-

duced by the limitation to tha number of slgnilleant levels that can

be worked up and transmitted. Together, these two inaccuracies give a

standard error of close to 1° - l^0c (cf. AWS TR 105-1^). More im-

portant, however, are the very large horizontal temperature gradients

that occasionally exist aloft. Measurements [l] have shown gradients

up to lloC/60 nautical miles with a possible gradient of 13oC/30

nautical miles. This temperature uncertainty must be kept in mind when

using Figure 5 (cf. AWSM 105-100 (Rev.) Chapter II). For all practical

purposes it amounts to a narrowing of the Yes- and No-areas of the

graph, and a widening of the Possible-area. The spacing of the rela-

tive-humidity curves on Figure 5 shows that the left side of the

16

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} AWS TR 105-145

i

January 1957

IIZTITST 1S eXtremely —itive to temperature errors whill th^

o^V s eo* TT:17 lnSenSitlVe- F- —P^- a temperature error

edge of Le r ' relatlve-huml.ity error of 22* on the left

about 15 t! I L y ^ ^ the rlSht edSe - a —itlvlty ratio of

lv affe . ° t ' ^ 1S the left 8lde 0f the SraPh w^ i« Prt-n- ly affected by the temperature uncertainty.

hu.^ by"PaSS ^ PreSently avoidable temperature and relative-

ZTrToll^T I* WaS deClded t0 0btain •^^•«t data to make an empirical study of contrail frequency as a function of pressure and

thHctaT al0ne' ^ thl8 ^ ^^ ^ ^—ature uncertainty and the actual mean relative humidity at each pressure-temperature point are absorbed into the frequency curves Thl«, ^n-v, A T Yea! „ . wu,..acy curves. This method does not allow a Yes-No forecast; It does, however, permit a statement as to the rela!

tlve frequency (i.e., empirical probability) of contrail formation for any given value of pressure and temperature.

2-2. Procedure.

Project Cloud Trail „as established „Ithln the Air Defense commanrt

:f:ruotT "ith Air weather servi"' - ••"-» Z!T:™:~- cle^rit" t Jet alrCra"- The alr0raft -"• to -emulate sufn- clent data to serve as a basis for proved -ethods of forecasting con- tralls clr^s clouds, haze, and turbulence. Only the contrail por ^ of the Project Is considered here. The observational phase of the Project ran fron, 1 December 1954 to 16 Decenber 1955. During this

Period 36 flghter-mteroeptor squadrons based m the UM eTstates collected data over S3 upper-alr sounding stations. The p^cedure employed was as follows: ««-«uure

after 15^'«^"1 ^/^ approxl"ate^ •"• "our before to two hours alter 1530 GOT, t»o aircraft were vectored to a point 25 000 fe.t .K an upper-air sounding station. The aircraft the' 01^ to h .IT ™ altitude obtainable, „alntalnlug position within 3o „lies o^ ^e

b. The wlngman observed whether or not the lead aircraft produced exhaust trails and whether they were continuous or l^"

r^irc::;1-faint' ^^—-* ^ -—"— c Other requested data were gathered.

As the data cards were received at Headquarters Air Weather Serv- ice, the associated soundings were plotted from the Daily Uoner-A^

•

:

17

T1 AWS TR 105-145 T January 1957

Bulletins. The contrail levels were then entered on each sounding. For six selected pressure levels - 350, 300, 250, 200, 175, and 150 mb the occurrence and non-occurrence of contrails and the associated tem- peratures were picked off. A tabulation was made of the number of con- trail, no-contrall, and total cases for each degree of temperature at each pressure level, and the percentage of cases having trails deter- mined. A plot of contrail frequency against temperature was made for each pressure level and smooth curves drawn. The resulting contrail frequency-function curves obtained by lumping together the data from all the stations for the year are shown as solid lines In Figure 6 - (the purpose of the dashed lines Is explained below).

too

90

s?

80 -

70

w 60 O ■ S: so

2 40 -

o o 30

20 -

10

PRESSURE (Mb)

ISO ZOO 250 300 3S0

-64 -62 -60 -58 -S6 - S4 -82 -SO -48 -46 TEMPERATURE (0C)

-44 -42 -40 -38

'

Figure 6. Contrail frequency as a function of tempera- ture and pressure. United States, December 1954 - Novem- oer 1955»

The temperature values for several selected contrail frequencies - 5, 10, 25, 50, 75, 90, and 955* - were picked off from each graph. The pressure-temperature coordinates of these selected frequencies were plottedTand snooth cxirves drawn of contrail probability as a function of temperature and pressure (solid lines. Figure 7). For purposes of i > u

18

January 1957

Pressure (mb) I50i

175

200

95 90\ 75 ^50 25\ 10 -

AWS TR 105-145

Pressure Altitude (ft)

- 40,000

250

300

350

- 30,000

-65 -60 -55 -50 Temperature (0C)

-45 -40

cally-derlved curves o? coSIlf SJöbabSJv It™ are+emPiri-

AWS Manual in^-?nn p^C°ntra11 i0rmatlo«- (Same as Figure 3 of

comparison the four theoretically-derived contrail-formation curves are entered in Figures 6 and 7 as dashed lines. Certain discrepancies be- tween the empirical and theoretical curves are discussed in following sub-sections. &

2-3- Caparison of the Theoretical and Empirical Curv^

Assuming the theoretically-derived curves are exact, perfect data would result in the OJ* probability curve coinciding with the 100*5 humidity line, and the 100^ probability curve with the 0^ humidity line Assuming further an equal chance for all relative humidity values at ' every pressure-temperature point, the 90^ and 60J* humidity lines should also coincide with the 10J* and 4o^ probability curves, respectively

However, one would not expect the distribution of mean relative humidi- ties to be constant with altitude; hence, it is only the bounding

curves that can be tested. Figure 7 shows that although the right side

19 I

AWS TR 105-145 January 1957

of the empirical and theoretical curves are in good agreement, there Is a discrepancy of 5 or 60C on the left side. To thoroughly understand the reason for this dlscrapancy. It is useful to go back to the con- trail-frequency-function curves for the individual levels (Figure 6),

A study of Figure 1 shows that near the C$ relative-humidity line a small change in temperature is equivalent to a large change in rela- tive humidity. The opposite is true near the 100^ line. Assuming an equal chance for all relative-humidity values at every pressure- temperature point, resulting contrail-frequency-function curves would start out flat, then become progressively steeper toward the upper end (Figure 8). If the relative-humidity values were evenly distributed

\

100 r

PRESSURE (mb) 150 200 250 300 350

-54 -52 -50 -48 -46 -44 TEMPERATURE (0C)

42 -40

)

:

.

Figure 8. Theoretical contrail-probability-function curves obtained by assuming an equal distribution of all relative- humidicy values from 0 to 100^ for each pressure point.

20 G

I

ll

i

It'-

January 1957

I

t

100

90

80

C 70

-J 60 m

g 50

d 40 < tr

o o

30

20

10

AWS TR 105-145

0%^RH^ 0

60% =£RH^I00%

\

J L -60

%, 60 75 90 ICO \

Ü L -58 -56 -54 -52 -50 -48 -46 -44 -42 -40

TEMPERATURE (0C) fof^O9^ Srf6^^1 contrall-P^bablllty-functlon curves for 250 mb obtained by assuming an equal distribution or all relatlve^humidlty values between o| and eJch of ?ive ^l™ry ^^ (?0lld curves). and between !S/and aS arbitrary minimum (dashed curve).

but had a minimum cutoff above Of* or a maximvun cutoff below 100^ the flattening effect at the "ower ends of the curves would be reduced. This effect is shown for the 250-mb level in Figure 9. (Note- The curve 0 - RH ^ 100 is identical with the 250-mb curve of Figure 8 ) Figure 10 shows the effect on contrail probability of a normal distri- bution of relative humidity about a mean value of 50^ with a standard deviation of 20^. With this distribution, 68^ of the cases fall be- tween 30 and 70% relative humidity and 95^ of the cases between 10 and 90^ relative humidity. It is seen, then, that any reasonable relative- humidity distribution results in contrail frequency curves which are more or less flat at the lower end and become progressively steeper at the upper ends. j

21

AWS TR 105-145

100 r

PRESSURE (mb)

150 200 250 300 350

January 1957

"

-60 -58 -56 -54 "52 "50 -48 -46 "44 -42 -40

TEMPERATURE (0C)

Slltlve hSi^f^ assrlnS a n°™al distribution of relative humidity about a mean of 50jg with a o of 20^.

The contrail-frequency-function curves of Figure 6 show the ex pected flattening at the lower end. However, the progressive steepen- ing of the curvea continues only to frequency values of 60 to 8o$- thereafter, the curves turn somewhat to the left. This inflection occurs near the left edge of the Possible-area of Figure 5. Since it cannot be attributed to the relative-humidity distribution it 's necessary to consider the other variable, temperature.

It was noted in sub-section 2.1. above that the temperatures from a radiosonde report contain a standard error of about 10C- more im portant are the occasional very large temperature gradients that exist aloft. Because of operational requirements, the aircraft were allowed to take off up to one hour before or two hours after raob release time.

22

Ü 1

c January 1957 AWS TR 105-145

Since It takes the balloon about 30 minutes to get to 30,000 feet, the aircraft might be at this point an hour and a half before or after the balloon. Thus, both a space and time difference may exist. With a fairly strong wind at 30,000 feet, say 60 knots, this Is equivalent to a total space displacement of more than 50 nautical miles. Usually, the difference would be much less, uut In extreme cases it could be more than twice as great. Hence, the temperature measured by the radiosonde could occasionally be 110C different from that encountered by the air- craft, and in some cases even more.

Temperature errors tend to be self-compensating in the Possible- area of the contrail-formation graph (Figure 5), with Just as many cases reported too cold as too warm. However, this compensation Is affected adversely by the non-linearity of the frequency curves and by the 0 and 100^ frequency boundary lines. The increasing steepness of the curves results in theoretically derived contrail frequencies slightly greater than the observed (empirical) values. The boundary lines result in too-large values of derived contrail frequency at the lower end, too-small values at the upper end, or a flattening of both

I ends of the curves on the graph (Figure 7). In the Yes- and No-areas, temperature errors can act in but one direction. Erroneous reports would fall into these regions which properly belong inside the Possible- area. This would result in a flattening of both ends of the frequency curves. However, the lower end is already flat. In addition, as pointed out in sub-section 2.1, the left edge of the contrail-formation graph (Figure 5) (which is equivalent to the upper end of the frequency curves of Figure 7) is about 15 times more sensitive to temperature than the right edge. Hence, the effect of temperature errors would be reflected much more strongly in the upper ends of the frequency curves than in the middle or lower portions.

Apparently, then, the inflection of the upper part of the contrail- frequency curves is due primarily to discrepancies between the tempera- tures measured by the raob and those encountered by the investigating aircraft. This inflection results in a displacement of the higher contrail-frequency values (above about 60$) toward lower temperatures. Hence, the 75, 90, and 95^ contrail-probability curves of Figure 7 are also displaced toward lower temperatures, and cannot be expected to coincide with the theoretical curyes.

^ Extrapolating the frequency-fvinetlon curves smoothly upward with-

23

1.1

I. •

■

' I

AVIS TR 105-145 January 1957

out inflection should give the contrail frequencies that would be obtained with perfect data. These are the dashed curves of Figure 6. The critical temperatures for 100^ contrail frequency obtained in this way are all within 10C of the values shown by the theoretically-derived C$ relative-humidity line.

In using the contrail-probability graph (Figure 7), however, the forecaster must contend with the inherent error of the radiosonde instrument and with the unrepresentativeness caused by the occasional intense horizontal temperature gradients. Consequently, when forecast- ing contrails, he should use the contrail-probability values determined from the actual frequency (empirical) curves, and not (theoretical) curves which would be true only for perfect data.

2-^- Effect of Season on Contrail Probability.

Contrail probability curves similar to those of Figure 7 were constructed for each season (see AWS TR 105-132). Table VI shows a

comparison of the corresponding pressure-temperature values of these curves for the individual seasons and for the year. The differences between the annual and seasonal curves were small. Since the differ- ences that did exist showed no consistent seasonal trends, it is proba- ble that they were caused mainly by the limited sample of data for the individual seasons. It seems that any true seasonal effects are too small to be significant for forecasting purposes.

2'5- Effect of Geographical Location on Contrail Probability. In order to determine whether the contrail probability curves vary

significantly in different regions, separate curves simlDar to those of Figure 7 were constructed for the northern and southern parts of the United States. The dividing line was 390N. The number of southern stations involved in the test was relatively small, and the number of contrails at low altitudes in the south was negligible. Table VII

shows a comparison of the corresponding pressure-temperature values of the contrail-probability curves for the north and south, based on the entire year's data. The average differences between the two sets of points was 0.7oC, with the southern curve averaging 0.2oC colder.

The differences between the two sets of curves were s .all at all levels. At 250 and 200 mb the northern and southern curves coincided almost exactly; at the other levels the contrail probability tended to be a little higher in the north at temperatures above -570C, higher in the south at the lower temperatures. The largest temperature difference

:

c

•

24

i

t AWS TR 105-1^-5

(

1 c

January 1957

between the two sets of curves was never more than 1.30C. The average

of the differences between the two sets of points was 0.7oC, with the northern values averaging 0.2oC warmer.

The differences between the contrail-probability curves for the

north and those for the south, while possibly real, are too small to be

significant for forecasting purposes. Consequently, the curves of

Figure 7 can for the present be considered applicable at all locations.

Further study on climatic effects, based on data taken In Europe and Japan, Is planned for the future.

2.6. Effect of the Tropopause on Contrail Probability.

Various studies have been published comparing the humidity In the

stratosphere with that of the troposphere. Because of the limited

number of measurements actually available near the tropopause levels, •

however, no completely reliable conclusions can be drawn. Since the

mean relative humidity affects contrail probability, separate proba-

bility studies were carried out for the troposphere and stratosphere.

In order to Isolate the effect of the tropopause. It was necessary

to compare stratospheric and tropospherlc frequencies at common

pressure-temperature values. The pressure level containing the best

balance of cases above and below the tropopause was 200 mb. Separate

stratospheric and tropospherlc contrail-frequency-fvinctlon curves were

carried out for this level (Figure 11). It Is seen that throughout

the greater portion of the curve, for a given value of pressure and

temperature the frequency of trails Is greater In the stratosphere than In the troposphere.

The theoretically-derived critical relative-humidity values for

contrail formation have oeen entered on Figure 11 as dashed lines. The

50^ contrail-frequency line Indicates a median relative humidity of

about 40^ In the troposphere, 70^ In the stratosphere. It must be

kept In mind that this measurement applies particularly to the 200-inb

level. At this level, most of the stratospheric cases would be in

lower polar-stratospheres; most of the tropospherlc cases would be In upper tropical-tropospheres.

The tendency for Increased relative humidities near (just above

to just below) the tropopause Is also borne out by Figure J. In gen-

eral, the probability curves are steeper than the relative-humidity

lines up to about 185 mb, then less steep. This Indicates that the

mean relative humidity Increases from 350 mb to about 185 mb, then

25

AWS TR 105-145 January 1957

100

90

80 -

200 Mb

3 70

g 60 u 3 9 u £ 50

I I STRATOSPHERE

<

o o

40

30 -

10

-68 -66 -64 -62

~

-60 -58 -56

TEMPERATURE (0C) -48

Figure 11. Comparative contrall-frequencv-function

function of the 200-mb temperature? J-ormai:ion as a

decreases. Since the mean tropopause height for this study was 210 mb

3000PLT r' T leVel ^ maXlmUin ^^ relatlVe hUmld1^ lies **out 3000 feet above the mean tropopause. (I„ all cases of multiple tropo- pauses only the lowermost was considered In this study.)

2.7. Summary.

Figure 7 presents curves of contrail probability as a function of pressure and temperature. The curves are based on consolidated obser- vations gathered for one year over the entire United States. Inherent data problems encountered by the forecaster In the field are absorbed into the curves. The most Important of these problems are the mean

26 O

.

'\

i

January 1957 AWS TR 105-145

relative humidity at each pressure-temperature point, and the unrepre-

sentativeness of temperatures measured by the radiosonde. The humidity

problem Is caused by the lack of humidity measurements at the levels

where contrails can form. The temperature problem Is due partly to the

small standard error (about 10C) In reported temperatures but mainly to

the fact that occasionally very strong horizontal temperature gradients

exist at the upper levels which can lead to temperature errors of more thrn 10*C.

To use Figure 7 the forecaster merely makes his best possible

temperature forecast for the altitude, time, and place of Interest, and

enters the graph with this pressure-temperature value to get the proba-

bility of contrail formation (see AWSM 105-100 Rev). Unfortunately,

contrail-probability curves are available only from 350 to 150 mb.

Below 350 mb the temperature was nearly always too warm for trail

formation. Above 150 mb there were insufficient observations for the

construction of reliable curves. At altitudes outside the 350-150-mb

range, the forecaster must use the contrail formation graph (Figure 5).

(

f - t 27

^

AWS TR 105-145 January 1957

APPENDIX

TABLE la

Density of Water Vapor In Environment (gra/m3)

Temp, of Environment

(TE, 0C)

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

Relative Humidity of the Environment (^)

100^

.006*

.012*

.021*

.037*

.062

.106

.176

.286

.453

.705 1.074

90<g

Indicates doubtful value

.005*

.011*

.019*

.033*

.056

.095

.158

.257

.406

.634

.966

60^ 0^

.004*

.007*

.013*

.022*

.037

.064

.106

.172

.272

.423 ,644

0 0 0 0

0 0 0 0

0 0 0

TABLE lb

Density of Water Vapor In Wake Saturated/Water (gm/m3)

•;

.' I»»* v e,!"/1 1 J

•

Wake Temp. Minus Initial Environment Temp. (4T, 0C)

—

jl

Temp, of Environment

(TE, 0C) 350C 20 0C 1Ü0C 50C 20C 10C

f -70 -65 -60 -55

.286

.453

.705 1.074

.062

.106

.176

.286

.021*

.037*

.062

.106

.012*

.021*

.037*

.062

.009*

.015*

.026*

.045*

.008*

.014*

.023*

.040*

1 -50 -45 -40 -35

1.605 2.358 3.407 4.847

.453

.705 1.074 1.605

.176

.286

.453

.705

.106

.176

.286

.453

.077

.130

.214

.344

.069

.117

.194

.314 -30 -25 -20 __l

6.797 9.399

12.830

2.358 3.407 4.847

1.074 I.605 2.358

.705 1.074 1.605

.542

.836 1.264

.496

.768 I.I65 O

* Indicates doubtrul value W- -

28

1 I

■ '

January IS57

TABLE Ic AV/S TR 105-145

(

Density of Water Vapor In Wake Saturated/Ice (jpy^j

Wake Temp. Minus Initial Envlronment^emp. -

Temp, of Environment

lE'

-70 -65 -60 -55

-50 -45 -4o -35

-30 -25 -20

35 0C 20 0C

.203

.338 • 552 .884

1.387 2.139 3.246 4.84?

6.797 9.399

12.830

.038

.068

.119

.203

.338

.552

.884 1.387

2.139 3.246 4.8^7

10oC

.011

.021

.038

.068

• 119 .203 • 338 .552

.884 1.387 2.139

20C

.006

.011

.021

.038

.068

.119

.203

.338

.552

.884 1.387

.004

.007

.014

.027

.048

.086

.148

.250

.413

.668 I.060

10C

.003

.006

.013

.024

.043

.077

.133

.225

• 374 .608 .968

TABLE Ha

Density of ^^^^^^^^^^^ ^

f RHE = 100 Percent

Temp. of Environment

Wake Te-P- Minus inltlal^nvlronment Temp, T

35 0C

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

.280

.441

.684 1.037

1.543 2.252 3.231 4.561

6.344 8.694

11.756

20 ""C

.056

.094

.155

.249

• 391 • 599 .898

1.319

1.905 2.702 3.773

10oC

.015

.025

.041

.069

.114

.180

.277

.419

.621

.900 1.234

50C 20C

.006

.009

.016

.025

.044

.070

.110

.167

.252

.369

.531

10C

.003

.003

.005

.008

.015

.024

.038

.058

.089

.131

.190

.002

.002

.002

.003

.007

.009

.018

.028

.043

.063

.091

29 i

AWS TR 105-145 January 1957

TABLE Ha (Cont'd)

Density of Water Vapor Required for Wake Saturated/Water (gm/n^ for Various Relative Humidities / '

RHE - 90 Percent

Temp, of Environment

(T-, 0C)

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

Wake Temp. Minus Initial Environment Temp - (AT, 0C) *'

35 0C

.281

.442

.686 1.041

1.549 2.263 3.249 4.590

6.391 8.765

11.864

20 0C

.057

.095

.157

.253

.397

.610

.916 1.348

1.952 2.773 3.881

100C

.016

.026

.043 • 073

.120

.191

.295

.448

.668 971

1.392

50C 20C

.007

.010

.018

.029

.050

.081

.128

.196

.299

.440

.639

.004

.004

.007

.012

.021

.035

.056

.087

.136

.202 ,298

RH« = 60 Percent

.282

.446

.692 1.052

1.568 2.294 3.301 4.675

6.525 8.976

12.186

10C

.003

.003

.004

.007

.013

.022

.036

.057

.090

.134 199

.058

.099

.163

.264

.416

.641

.968 1.433

2.086 2.984 4.203

.017

.030

.049

.084

• 139 .222 .347 .533

.602 1.182 1.714

.008

.014

.024

.040

.069

.112

.180

.281

.433

.651

.961

.005

.008

.013

.023

.040

.066

.108

.172

.270

.413

.620

.004

.007

.010

.018

.032

.053

.088

.142

.224

.345 • 521

■

1 1

■

1

30 0 I

:■

.

• 1

January 1957 AWS TR 105-145

r

i

TABLE Ila (Cont'd)

Density of Water Vapor Required for Wake Saturated/Water (sm/m3) for Various Relative Humidities

RHE = 0 Percent

Wake Temp. Minus Initial Environment Temp. — (AT, 0C)

Temp, of Environment

(TE, 0C)

350C 20 0C 10 0C 50C 20C 10C

-70

:U -55

-50 -45 -40 -35

-30 -25 -20

.286

.453

.705 1.074

1.605 2.358 3.407 4.847

6.797 9.399

12.830

.062

.106

.176

.286

.453

.705 1.074 1.605

2.358 3.407 4.847

.021

.037

.062

.106

.176

.286

.453

.705

1.074 I.605 2.358

.012

.021

.037

.062

.106

.176

.286

.453

.705 1.074 1.605

.009

.015

.026

.045

.077

.130

.214

.344

.542

.836 1.264

.008

.014

.023

.040

.069 • 117 .194 .314

.496

.768 1.165

TABLE lib

Density of Water Vapor Required for Wake Saturated/Ice (gm/m3) for Various Relative Humidities

RH ■E

100 Percent

Wake Temp, Minus Initial Environment Temp. — (AT, 0C)

Temp. of Environment

(TE,0C)

35»C 20 0C 10 0C 50C 20C I'C

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

.197

.326

.531

.847

1.325 2.033 3.070 4.561

6.344 8.694

11.756

.032

.056

.098

.166

.276

.446

.708 1.101

1.686 2.541 3.773

.005

.009

.017

.031

.057

.097

.162

.266

.431

.682 1.065

.000 -.001 .000 .001

.006

.013

.027

.052

.099

.179

.313

-.002 -.005 -.O07 -.010

-.014 -.020 -.028 -.036

-.040 -.037 -.014

-.003 -.006 -.008 -.013

-.019 -.029 -.043 -.061

-.079 -.097 -.106

5±

K

AWS TR 105-145 January 1957

TABLE lib (Cont'd)

Density of Water Vapor Required for Wake Saturated/Ice (Wm3) for Various Relative Humidities *<*/ /

RHF = 90 Percent

Temp, of Environment

(TE, 0C)

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 ■20

Wake Temp. Minus Initial Environment Temp - (AT, 0C)

350C

.198

.327

.533

.851

1.331 2.044 3.088 ^.590

6.391 8.765

11.864

20 0C

.033

.057

.100

.170

.282 • 457 .726

1.130

1.733 2.612 3.881

10oC

.006

.010

.019

.035

.063

.108

.180

.295

.478

.753 1.173

RHE = 60 Percent

.199 • 331 .539 .862

1.350 2.075 3.140 ^.675

6.525 8.976

12.186

.034

.061

.106 ,181

.301

.488

.778 1.215

I.867 2.823 4.203

.007

.014

.025

.046

.082

.139

.232

.380

.612

.964 1.495

50C

.001

.000

.002

.005

.012

.024

.045

.081

.146

.250

.421

.002

.004

.008

.016

.031

.055

.097

.166

.280

.461

.743

20C

-.001 -.004 -.005 -.006

-.008 -.009 -.010 -.007

-.007 +.034 .094

10C

-.002 -.005 -.006 -.009

-.013 -.018 -.025 -.032

-.032 -.026 .002

.000 -.001

.000 -.001 ,001 .000 .005 .002

.011 .006

.022 .013

.048 .027

.078

1 It «i

• 053

141 .245 .416

,102 .185 ,324

i

32 c I

V

'

January 1957 AWS TR 105-145

!'

i (

I

TABLE lib (Cont'd)

Density of Water Vapor Required for V/ake Saturated/Ice (gm/m3) for Various Relative Humidities

RHE = 0 Percent

Wake Temp. Minus Initial Environment Temp. — (AT, 0C)

Temp. of Environment

(TE, 0C)

350C 20 0C 10oC 50C 20C 10C

-70 -65 -60 -55

-50 -45 -40 -35

-30 -25 -20

.203

.338

.552

.884

1.387 2.139 3.246 4.847

6.797 9.399

12.830

.038

.068

.119

.203

.338

.552

.884 1.387

2.139 3.246 4.847

.011

.021

.038

.068

.119

.203

.338

.552

.884 1.387 2.139

.006

.011

.021

.038

.068

.119

.203

.338

.552

.884 1.387

.004

.007

.014

.027

.048

.086

.148

.250

.413

.668 1.060

.003

.006

.013

.024

.043

.077

.133

.225

.374

.608

.968

TABLE He

Density of Water Vapor Required for V/ake Saturated/Ice (gm/m3) plus an Ice-Crystal Concentration of .01 gm/m3, for Various

Relative Humidities

RHE = 100 Percent

Wake Temp. Minus Initial Environment Temp. - (AT, 0C)

Temp, of Environment

(TE, 0C)

350C 20 0C 10 0C 50C 20C 10C

-70 -65 -60 -55

■n -40 -35

-30 -25 -20

.207 • 336 . 541 .857

1.335 2.043 3.080 4.571

6.354 8.704

11.766

.042

.066

.108

.176

.286

.456

.718 1.111

1.696 2.551 3.783

.015

.019

.027

.041

.067

.107

.172

.276

.441

.692 1.075

.010

.009

.010

.011

.016

.023

.037

.062

.109

.189

.323

.008

.005

.003

.000

-.004 -.010 -.018 -.026

-.030 -.027 -.004

.007

.004

.002 -.003

-.009 -.019 -.036 -.051

-.069 -.087 -.096

33

-»..■- &

y i AWS TR 105-145 January 1957

TABLE lie (Cont'd)

Density of Water Vapor Required for Wake Saturated/Ice (gra/nr*) plus an Ice-Crystal Concentration of .01 sm/m3 for Various

Relative Humidities

RHE = 90 Percent

Wake Temp. Minus Initial Environment Temp. — (AT, 0C)

Temp, of Environment

(Tr 0C)

350C 20 0C 10oC 50C 20C 10C

'-¥ -60 -55

.208

.337

.543

.861

.043 ,067 .110 .180

.016

.020

.029

.045

.011

.010

.012

.015

.009

.006

.005

.004

.008

.005

.004

.001

-35

1.341 2.054 3.098 4.600

.292

.467

.736 1.140

.073

.118

.190

.305

.022

.034

.055

.091

.002

.001

.000

.003

-.003 -.008 -.015 -.022

--it -20

6.401 8.775 11.874

1.743 2.622 3.891

.488

.763 1.183

.156

.260

.431

.003

.044

.104

-.022 -.016 .012

RHE = 60 Percent

-70 -65 -00 -55

.209

.341

.549

.882

.044

.071

.116 • 191

.017

.024

.035

.056

.012

.014

.018

.026

.010

.010

.011

.015

.009

.009

.010

.012

:r5 -40 -35

1.360 2.085 3.150 4.685

.311

.498

.788 1.225

.092

.149

.242

.390

.041

.O65

.107

.176

.021

.032

.058

.088

.016

.023

.037

.063

-30 -25 -20

6.535 8.986 12.196

1.877 2.833 4.213

.622

.974 1.505

.290

.471

.753

.151

.255

.426

.112

.195

.334

34 '.,

t January 1957 AWS TR 105-145

TABLE He (Cont'd)

Density of Water Vapor Required for Wake Saturated/Ice (gm/m^) plus an Ice-Crystal Concentration of .01 ßm/m3, for Various

Relative Humidities

RHE = 0 Percent

1

Temp, of Environment

'Tr >C)

-70 -65 -60 -55

-50 -45 -40 -35

-20

Wake Temp. Minus Initial Environment Temp. — (AT, 0C)

350C

.213

.348

.562

.894

1.397 2.149 3.256 4.857

6.807 9.409

12.840

20 0C

.048

.078

.129

.213

.348

.562

.894 1.397

2.149 3.256 4.857

10oC

.021

.031

.048

.078

.129

.213

.348

.562

.894 1.397 2.149

50C

.016

.021

.031

.048

.078

.129

.213

.348

.562

.894 1.397

20C

.014

.017

.024

.037

.058

.096

.158

.260

.423

.678 1.07C

10C

.013

.016

.023

.034

.053

.087

.143

.235

.384

.618 • 978

35

1J 1

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AWS TR 105-145

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37

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■^

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cy oj aj oj CVJ cy cy o o o o o o o ooo o ooo

on m to ro n en cy o g g o o o o i o o o o ooo

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TABLE VI (Cont'd)

Comparison of Seasonal and Annual Contrail Probability

~1 / H \

!

Pressure (mb)

150 175 200

250 300 350

150 175 200

250 300 350

150 175 200

250 300 350

25^ Probability

Temperature (0C)

Winter

-55.4 -49.5 -50.1

-48.8 -48.4 47.5

Spring

-51.5 -50.5 -50.0

-49.5 -49.O -49.O

Summer

-54.3 -52.0 -51.0

-50.5

10^ Probability

-54.5 -50.6 -48.3

-46.5 -45.8 •45.5

-50.0 -48.3 -^7.3

-47.0 -46.7 -46.5

-52.3 -50.5 -48.8

-47.4 -46.7

5^ Probability

•54.3 -49.6 -^8.0

•46.0 •44.0 •43.0

-47.0

-46.2 -45.3 -44.3

-51.9 -49.6 -47.7

-45.2

Autvunn

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-50.6 -49.3

-50.8 -49.2

-47.7 -46.5

-49.8 -48.2

-46.2 -45.1 -43.2

Annual

-53.6 -51.4 -50.8

-49.8 •48.8 •48.0

-51.5 -49.6 -48.5

-47.0 -46.4 -45.8

-50.6 -48.5 -47.I

-45.1 -44.3 -43.7

t

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44 C

■■

January 1957 AWS TR 105-1^5

V

TABLE VII

Comparison of Contrail Probability for the North (N) and South (S)

Tempera, t^re (0C)

Probability Percent

95

90

75

50

25

10

Area

N S

N S

N S

N S

N S

N S

N S

150

-6I.3 -60.O

-60.I -58.9

-57.8 -57.3

-55.3 -56.2

Pressure (mb)

175

-59.2 -58.6

-57.8 -57.5

-55.2 -55.8

-53.2 -54.2

-51.6 -52.1

-49.6 -50.3

200

-59.0 -58.2

-57.6 -57.1

-55.1 -55.1

-53.0 -53.0

-50.4 -50 A

-48.3 -47.6

250

-56.9 -56.3

-53.6 -54.0

-51.9 -52.0

-49.7 -50.0

-46.6 -47.5

-44.8 -46.0

300

-50.4 -51.3

-48.7 -49.8

-46.2 -47.5

-44.0 -45.4

(.

*5

{

AVIS TR 105-145 January 1957

REFERENCES

[1] Kochanskl A., "Horizontal Temperature Gradient »t onn K

pp. J.4-20. ■-•, ■'0-L- J*» No' 1* January 1953,

[3] ^SSM'NJ- 42' Me? 'Sj/0^^1^.^ Co^enSatlon Trails," l-^o^. Met. Off., Great Britain, Air Ministry, 1943.

'

46 O

OPO 1212(3