Technical Paper 3701

Measurement of Momentum Transfer

Coefficients for H2, N2, CO, and CO2 Incident

Upon Spacecraft Surfaces

Steven R. Cook and Mark A. Hoffbauer

November 1997

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Technical Paper 3701

Measurement of Momentum Transfer Coefficients for H2, N2,

CO, and CO2 Incident Upon Spacecraft Surfaces

Steven R. Cook and Mark A. Hoffbauer

Los Alamos National Laboratory

National Aeronautics

and Space Administration

Lyndon B Johnson Space Center

Houston, Texas 77058-4406

November 1997
Available from:

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Contents

Abstract

1 Background

2 Tile Momentmn Accommodation Coefficients

3 The Reduced Force Coefficients

4 The Nocilla Gas-Surface Interaction Model

5 Experimental Results

6 Conclusions

5

5

6

7

8

10

11

List of Figures

1 The data for 2590 m/s

2 The data for 2590 m/s

3 The data for 2590 m/s

1 The data for 2590 m/s

5 The data for 1870 m/s

6 The data for 18711 m/s

7 The data for 1870 m/s

8 The data for 1870 m/s

9 The data for 1870 m/s

10 The data for 1870 m/s

11 The data for 1870 m/s

12 The data for 1870 m/s

13 The data for 1670 m/s

1,1 The data for 1670 m/s

15 The data tor 1670 m/s

16 The data tbr 1670 ln/S

17 The data tbr 4620 m/s

18 The data for ,1620 m/s

19 The data for 46211 m/s

20 The data for 462/) m/s

21 The data for 3180 in/s

22 The data for 3180 m/s

23 The data for 3180 in/s

2.1 Tile data for 3180 m/s

25 The data tor 3200 m/s

26 The data for 3200 m/s

27 'File data for 3200 m/s

28 The data for 3200 nl/s

29 "I'll(, data for 28411 m/s

30 The data for 2840 m/s

31 The data tbr 28.10 m/s

H2 incident upon the solar panel ................. 13

tt2 incMent upon SiO2-coated Kapton .............. 1.1

H2 incident upon Kapton ..................... 15

[I2 incident upon Z-9%coated aluminum ............ 16

N2 incident upon the solar panel ................. 17

N_ incident upon SiO2-coated Kapton .............. 18

N2 incident upon Kapton ..................... 19

N2 incident upon Z-93-coated ahuninum ............ 20

CO incident upon the solar panel ................ 21

('O incident upon SiO2-coated t(apton ............. 22

CO incident upon Kapton .................... 23

CO incident upon Z-93-coated aluminum ............ 2,1

CO2 inc, ident upon the solar panel ................ 25

CO2 incident upon SiO2-coated Kat)ton ............. 26

CO2 incident upon Kapton .................... 27

CO2 incident upon Z-93-coated alunfinum ........... 28

H2 incident upon the solar panel ................. 29

H2 incident upon SiO2-coated Kapton .............. 30

H2 incident upon Kapton ..................... 31

H2 incident upon Z-93-coated aluminum ............ 32

N2 incident ut)on tile solar panel ................. 33

N2 incident upon SiO2-coated Kapton .............. 3-1

N9 incident upon Kapton ..................... 35

N:_ incident upon Z-93-coated alunfiImm ............ 36

CO incident upon the solar panel ................ 37

CO incidenl upon SiO2-coated Kapton ............. 38

(IO incident upon Kapton .................... 39

(!0 incident upon Z-93-coated aluminunl ............ ,10

('()2 incident upon the solar panel ................ 41

("()2 incident upon Si()2-coated Kapton ............. .12

(_O2 incident upon Kapton .................... -13
32 The data for 2840 m/s CO2 incident upon Z-93-coated aluminum ........... 44

33 The angular distribution functions for 2590 m/s H 2 incident upon the solar panel. 45

34 The angular distribution functions for 2590 m/s H2 incident upon SiO2-coated Kapton. 46

35 The angular distribution functions for 25911 m/s H2 incident upon Kapton ...... 47

36 The angular distribution flmctions tbr 2590 m/s H2 incident upon Z-93-coated aluminum ............................................ 48

37 The ang_ular distribution f\mctions for 1870 m/s N2 incident upon the solar panel. 49

38 The ang-ular distribution functions for 1870 m/s N2 incident upon SiO2-coated Kapton. 50

39 The angular distribution functions for 1870 m/s N2 incident upon Kapton ...... 51

40 The angular distribution functions for 1870 m/s N2 incident upon Z-93-coated ahlminum ............................................ 52

41 The angular distribution functions for 18711 m/s CO incident upon the solar panel.. 53

42 The an_flar distribution functions for 1870 m/s CO incident upon SiO2-coated Kapton. 54

43 The angular distribution functions for 1870 m/s CO incident upon Kapton ...... 55

44 The angular distribution functions for 1870 m/s CO incident upon Z-93-coated aluminum ............................................ 56

45 The anglflar distribution fllnctions for 1670 m/s (!O2 incident upon the solar panel. 57

46 The angular distribution functions for 1670 m/s CO2 incident upon SiO2-coated

Kapton ............................................ 58

47 The angular distribution functions for 1670 m/s CO2 incident upon Kapton ...... 59

48 The angular distribution functions for 1670 m/s CO2 incident upon Z-93-coated

aluminum ........................................... 60

49 The angular distribution functions for 4620 m/s H2 incident upon the solar panel. 61

50 The angular distribution functions for 4620 m/s H2 incident upon SiO2-coated Kapton. 62

51 The angular distribution functions for 4620 m/s H2 incident upon Kapton ...... 63

52 The angxllar distribution functions for 4620 m/s H2 incident upon Z-93-coated aluminum ............................................ 64

53 The angular distribution functions for 3180 m/s N2 incident upon the solar panel. 65

54 The angular distribution functions for 3180 m/s N2 incident upon SiO2-coated Kapton. 66

55 The angaflar distribution functions for 3180 m/s N2 incident upon Kapton ...... 67

56 The angular distribution functions for 3180 m/s N2 incident upon Z-93-coated aluminum ............................................ 68

57 The ang_flar distribution functions for 3200 m/s CO incident upon the solar panel. 69

58 The ang_flar distribution functions for 3200 m/s CO incident upon SiO2-(:oated Kapton. 71}

59 The angular distribution functions for 3200 m/s CO incident upon Kapton ...... 71

60 The angular distribution functions for 3200 m/s CO incident upon Z-93-coated aluminum ............................................ 72

61 The angular distribution functions for 284/) m/s CO2 incident upon the solar panel. 73

62 The angular distribution fimctions for 2840 m/s CO2 incident upon SiO_-coated

Kapton ............................................ 74

63 The angular distribution functions for 2840 m/s CO2 incident upon Kapton ...... 75

64 The angular distribution functions for 2840 m/s CO2 incident _93-coated Munfinum. 76

List of Tables

1 2590 m/s H2 incident upon the solar panel ........................ 13

2 2590 m/s H2 incident upon SiO2-coated Kapton ..................... 14

2
3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

3O

31

32

33

34

35

36

37

38

39

4O

,11

42

,13

44

,15

.16

,17

48

49

5O

2590

2590

1870

187O

187O

1870

1870

1870

1870

1870

1670

1670

1670

1670

4620

4620

4620

4620

3180

3180

3180

3180

3200

3200

3200

3200

2840

2840

2840

284O

The

The

The

The

The

The

The

The

The

The

The

The

The

_l'he

The

The

The

The

m/s H2 incident upon Kapton ............................ 15

m/s t12 incident ut)on Z-93-coated aluininnm ................... 16

m/s N2 incident upon the solar panel ........................ 17

m/s N2 incident upon SiO2-(:oated Kapton ..................... 18

m/s N2 incident ut)on Kapton ............................ 19

m/s N2 incident upon Z-93-coated alumimun ................... 2(1

m/s CO incident upon the solar panel ....................... 21

m/s CO incident upon SiO2-coated Kapton .................... 22

m/s CO incident upon Kapton ........................... 23

m/s CO incident upon Z-93-coated almninum ................... 24

m/s (',O2 incident upon the solar t)anel ....................... 25

m/s ('02 incident upon SiO2-coated Kapton .................... 26

m/s (:()2 incident upon Kapton ........................... 27

m/s (702 incident upon Z-93-c, oated alunfinum .................. 28

m/s 1t2 incident upon the solar palm ........................ 2.(1

m/s |I2 incident upon SiO2-coated Kat)ton ..................... 30

m/s tI2 incident upon Kapton ............................ 31

m/s 1t2 incident ut)on Z-9:{-coated alunfinum ................... 32

m/s N.) incident Ul)On tile solar panel ........................ 33

m/s N,) incident upon SiO2-coated Kapton ..................... 31

m/s N2 incident ut)on Kapton ............................ 35

m/s N2 incident upon Z-93-coated ahmfinum ................... 36

in/s CO incident ui)on the solar l)anel ....................... 37

m/s (IO incident upon SiO:_-coate(t Kapton .................... 38

m/s (IO incident ut)on Kapton ........................... 39

in/s ('O incident ut)on Z-93-coated ahmfinmn ................... 10

nl/s C()2 incident upon the solar panel ....................... 41

m/s CO2 incident upon Si()2-coated Kat)ton .................... 42

nl/s CO2 incident Ul)On Kapton ........................... 43

nl/s (102 incident Ul)On Z-93-coated ahuninmn .................. ,1.1

Nocilla model t)arameters for 2590 m/s I12 incident ut)on the solar t)anel ..... 45

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

Nocilla

No(:illa

Nocilla

Nocilla

Nocilla

model t)arameters for 2590 Ill/S H2 incident upon Si()2-coated Kat)ton.. ,16

model parameters tbr 2590 m/s H2 incident upon Kapton ......... 47

model parameters for 2590 m/s It2 incident upon Z-93-(:oated alunlinunl 48

model t)arameters for 1870 m/s N2 incident upon the solar panel ..... 19

model t)arameters for 1870 m/s N2 incident upon SiO2-coate(t Kapton.. 50

model t)arameters for 1870 in/s N2 incident upon Kaploll ......... 51

model parameters tor 1870 m/s N2 inc, ident nt)on Z-93-coate(t aluminum. 52

model t)arameters for 1870 m/s CO incident upon tile solar t)anel .... 53

model l)arameters for 1870 m/s (IO incident upon SiO2-coated Kat)ton. 5-1

nlodel paranleters for 1870 m/s CO incident upon Kat)ton ........ 55

model parameters for 1870 m/s ('O inci(lent ut)on Z-93-coated aluminmn. 56

model l)arametel's fox' 1670 m/s ('()2 incident upon the solar panel .... 57

model parameters for 1670 m/s (I()2 incident upon SiO2-eoated Kat)ton. 58

model 1)arameters for 1670 m/s (102 inci(lent Ul)on Kat)ton ........ 59

model t)aramcters for 1670 m/s (102 incident upon Z-93-(:oated ahmlinum. 60

mo(lel t)aramelers for 4620 m/s It,2 incident ut)on the solar panel ..... 61

too(tel t)arameters for ,162() m/s tt2 incidenl ut)on Si()2-coaled Kat)lon.. 62

3
51 The Nocillamodel

52 Tile Nocillamodel

53 TheNocilla model

54 The Nocilla model

55 Tile Nocilla model

56 Tlle Nocilla model

57 The Nocilla model

58 The Nocilla model

59 The Nocilla model

60 Tile Nocilla model

61 Tile Nocilla model

62 Tile Nocilla model

63 Tile Nocilla model

64

65

66

67

parameters for 4620 m

parameters for 4620 m

parameters for 3180 In

parameters for 3180 in

paranleters for 3180 m

parameters for 3180 m

parameters for 3200 m

parameters tor 3200 m

/s H2 ilmident upon Kapton ......... 63

/s H2 incident upon Z-93-coated aluminum. 64

/s N2 incident upon the solar panel ..... 65

/s N2 incident upon SiO2-coated Kapton. , 66

/s N_ incident upon Kapton ......... 67

/s N2 incident upon Z-93-coated ahlminmn. 68

/s CO incident upon the solax" panel .... 69

/s CO incident upon SiO2-coated Kapton. 70

parameters fox" 3200 m/s CO incident upon Kapton ........ 71

paralneters for 3200 m/s CO incident upon Z-93-coated almninum. 72

tmrameters tor 2840 m/s CO2 incident upon the solm" panel .... 73

parameters for 28,10 m/s CO2 incident upon SiO2-coated Kapton. 74

parameters for 28,I0 m/s CO2 incident upon Kapton ........ 75

The Nocilla model parameters fox" 2840 m/s CO2 incident upon Z-93-coated aluminum. 76

Colnparison of the Reduced Force CoetIicient measurements fox" 1870 m/s N,_ incident

upon the solar panel made with the carrier gases H2 and He .............. 77

Comparison of the Reduced l%rce Coefficient measurements for 1870 m/s CO incident upon the solar panel made with the carrier gases H2 and He ........... 77

(lomparison of the Reduced Force Coefficient measurements for 1670 m/s (?02 incident upon the solar panel made with the carrier gases H_ and Ile ........... 77

4
Abstract

Measurements of monlentunl trans[er coetlicients were made for gas-surface interactions between

the Space Shuttle reaction (:ontrol jet tflume gases and the solar palml array materials to be used

on the International Space Station. Actual conditions were simulated using a supersonic nozzle

source to produce bealns of the gases with approximately the same average velocities as the gases

have in the Shuttle t)lumes. Samples of the actual solar panel materials were inounted on a

torsion balance that was used to measure the force exerted on the surfaces by the molecular

beams. Measurements were made with It2, N2, CO, and (I()2 incident upon the solar array

material, Kapton, SiO2-coatcd Kat)ton, an(t Z-93-coated A1. The measurements showed that

molecules scatter [rom the sm'faees more specularly as the angle of inciden(:e increases an(t that

the scattering behavior has a strong dependence upon both the incident gas and velocity. These

results show that tot some teetmical surfaces the simple assumption of diffuse scattering with

colnplete thermal accoxninodation is entirely inadequate. It is clear that additional measuremems

are required to produce models that more accurately describe the gas-surface interactions

encountered in raretied flow regimes.

1 Background

This I)roject was motivated by the need to ac<:urately model the forces exerted on the large solar

panel arrays to be used on the International Space Station by gases emitted from the reaction

control .jets on the Space Shuttle. This effort has been one of the largest ever undertaken to

measure and dmraeterize momentmn transferred to sm'faces by incident gases. The experimental

effort has resulted in the most comt)rehensive and accurate measurements ever made in this fieht.

I;sing this data it. is now possible to construct a limited number of accurate empirical models of

forces exerted on spacecraft surfaces by incident gases in rarefied flow regimes. The high accuracv

of these measurements also makes it, possible to obtain an mlderstanding of fllndamenta]

microscopic gas-surface interaction properties. The results of these experiments show that. even

fl'om technical surfaces, molecules scatter more speeularly as the angle of incidence increases, and

that the scattering has a strong dependence 1lt)Oll both the incident gas and velocity.

Theoretical advances were made in addition to the experimental contributions. _lYaditionally, the

momentum accommodation coefficients have been used to analyze the lnonlentllln transferred to

surfaces by incident gases in rarefied flow regimes, ttowever, the momentum accommodation

coefficients contain sing_flarities that render them unusable for a large mlmber of gas-surface

interactions, including those that are of specific interesl to NASA under im_estigation al LANI_.

Therefore, a new formalism was developed based upon two momentum transfer l)arameters <:alled

the reduced force coefficients. We have shown that tile nlacroscopic average momentunl

transferred to a surfa<:e bv incident lnolecules in raretied flow regimes can be completely

characterized using the reduced force coefficients. These coefficients can also 1)e used t<>

determined the magnitude and directioll of the flux-weighte<t average velocity of the scattered

ulole(;llles.

In the past. a kn(>wledge of the energy accommodation coefficient was required to determine the

flux-weighted average translational energy of the scattered molecules. Aeem'ate measurements of

energy a<:cOlninodation coefficients are difficult, however, and would introduce an additional

sour<:e of ml<:ertainty. A forinula was derived using the reduced force coefficients that acenrately
approximatesthe flux-weightedaveragetranslationalenergyof thescatteredmolecules,thereby

eliminatingthe needto measureenergyacconmlodationcoefficients.This breakthroughmakesit

possibleto uniquelydeterminethe adjustableparametersin tile Nocillagas-surfaceinteraction

modelsolelyfrom measurementsof the momentumtransferredto surfacesby incidentgases.

Thisproject,to (latehasresultedin onePh.D.dissertationandsix refereedpublications

[1,'2,3, 4, 5, 6, 7]. Fouradditionalmanuscriptsarenearcompletionandwill besubmittedto

PhysicalReviewE.The apparatushasbeenextensivelyimprovedandis nowfully operational.In

addition,manynewandexcitingresultshavebeenrecentlyobtainedandwill bepublishedin

future articles.

lRecently,a differentiallypumpedtime-of-flightsystemwasaddedto theapparatusthat will allow

accuratemeasurementsof thevelocitydistribution functionsof moleculesscatteredfrom surfaces.

This systemwasdesignedsothat.duringtime-of-flightmeasulvments,the torsionbalancecanbe

usedto simultaneouslymeasurethe Inomentumtransferredto thesurfaceby the incidentgas.

This experimentalcapabilitywill makeit possibleto compareapproximatevelocitydistribution

functionsof tile scatteredmoleculesconstructedfl'omthe nmcroscopicaveragetransferof

momentumandenergyto the surfacest)y the incidentgases,suchasthe Nocillamodel,with the

actualmeasuredvelocitydistribution functionsof tile scatteredmolecules.

In addition,animprovedtorsionbalancehasbeenfabricatedthat canbeusedto measureboth

the momentmntransfercoefficientsand theabsoluteflux densitiesof themolecularbeams.This

newtorsionbalancewill simplit}"theexperimentalprocedures,reducethe timetakento complete

a setof measurements, andincreasethe accuracyof the results.Accuracyis increasedmainlydue

to eliminatingtheuseof massspectrometersto measurethepercentageof eachgasspeciesin the

molecularbeams.

2 The Momentum Accommodation Coefllcients

The tangential cr and normal or' momentum accommodation coefficients can be expressed as [8]

-gi sin Oi - _._ sin 0_

cr = , (1)

_i sin Oi

° r = '_'7i cos Oi -- Ts cos 0s

_ ;' (2)

T'i cos Oi v/rrkT/2m

where ,77.,is the magnitude of the flux-weighted average (hereafter referred to as average) velocity,, 0

is the angle between the average velocity and the surface normal, the subscripts i and s represent

the incident and scattered molecules respectively, k is Boltzmann's constant, T is the temperature

of the scattering surface, and m is the mass of the individual gas molecules. The quantity

v/rrkT/2m is the average velocity of the scattered molecules assmning diffuse scattering from the

surface with complete thermal accomnlodation [8].

For many applications the tangential molnentuln accommodation coefficient has a removable

singularity at an angle of incidence Oi nornml to the surface and is well behaved. However, for

applications where 0., is not equal to zero at normal angles of incidence, the tangential coefficient

would diverge. Problems with the singularity in the normal momentum accommodation

coefficient result in divergent behavior for essentially every application involving a directed gas
flow.In addition,the angleof incidenceat whichtile sinKnlarityoccursis a flmctionof the

averagevelocityof the incidentmoleculesandthe temperatureof the scatteringsurface.For ttl("

gas-surfaceinteractionsconsideredin this report,the angleof incidenceat whichthe singularity

occurredrangedfrom55_ to 85_. Thedivergentbehaviorcausedt)5,this singularitymadeit

nearlyimt)ossit)leto useth(' normal(:oefiicient.

Toover(:omethis singaflarityproblem, Knuth [9] (teiined a norinal momentum transfer coefficient

that elinfinates the fml(:tional det)endenee of the singadarity upon the average veh)city of the

incident mole(:ules an(t lhe surfa(:e tenq)erature. However, the eoetlicient diverges at large angles

of incidence for all non sI)ecular scattering t)rocesses. Therefore, a new formalism was develot)ed

that (:ompletely eliminated the prot)lems (:ause(t t)y singularities.

3 The Reduced Force Coefficients

The definitions of the reduced force <:oetfieients were arrived at by considering the force exerle(t

on a surface by an incident molecular beam. The singulm'ity t)roblems were eliminated by defining

the coefficients with denominators that are independent of the incident flow direction. The

tangential ft and normal .f_ reduce(t force coeflieients are defined as

f,, _ F_,_+_,_ (4)

where _ is the magnitude of the average momentum, and the subscripts t and t_ are the tangential

and norinal components, respectively. The redu(:ed force coefficients can also be written as

where F is the nmgufitu(te of the for(:e exerted on the surface t)y the inci(tcnI gas, and Ni is 1he

total incident ihLx. Thus, the eoeiticicnt s can 1)e (let,ermined fi'om measurements of ['}, F_, 5,},

and "5i. Equations (3) and (4) can be u_d to express the magnitude and direction of the a_'erage

velocity of the st'at tered molecules as

"5._=-5i _(ft - sin Oi)'_ + (.fr_ -cos O_)2 (;)

( sin O_ - ft _

0_ = tan ' kf-_ "'c_s:'O// " (8)

Spherical polar (:()ordinates are use(t to define the directions of the average velocities of the

incident and scattered molecules. The polar angle is measm'ed fl'om the surface normal, the

azimuthal angle is 18() _ for the average veh)('ity of the incident nlole(:ules and is assumed t() be 0 _

for the a_erage velocity of the scattered molecules, and the scattering surface is in the l)lane

define(t t)y the polar angle of 9(F.

A new parameter tt, called the scalar momentum accommodation coetiicient is introduced and

defined as

It-- (.q)
The quantity Pd is the magnitude of tile average monmntum of the scattered molecules assuming

diffuse scattering and is given by' v/rrkTm/2. The scalar momentum accommodation coefficient

ranges between zero for specular scattering and one for diffuse _attering with complete thermal

accommodation and is well defined for all angles of incidence.

For applications where differences between the average energies associated with the internal-state

distribution functions of the incident and scattered molecules can be neglected, the energy

accommodation coefficient e can be written as [8, 10]

= v7- la, (10)

D

where _.,2 is the average of the velocity squared, and 41,'Tim is the average of the velocity squared

of the scattered molecules assuming diffuse scattering. A knowledge of the reduced force

coefficients is not sufficient to determine the energ__y accomnlodation coefficient using Eq. (10).

Additional information is required to determine v_. The simple assumption of equating vr2t._with v-7

can result in errors as large as 60_:.. A more accurate approximation for u"7__ can be nmde with an

energy accommodation coefficient e' based on the average velocities of the incident and scattered

molecules. The coefficient is defined as

= _2 _ rr/,:7/2m ,,) • (11)

From a knowledge of the reduced force coefficients and the velocity distribution function of the

molecular beam, the coefficient e_ can be calculated. The uncertainty associated with the

approximation of equating e' with e has 1)een shown to be less than 4-1_ for gas-surface

interactions where the average energy of the incident molecules is large comt)ared to/,'T [1]. With

""7-

this appi'oximation, ui_ can be written as

(_2)

m

The quantity v/2 can be determined from a knowledge of the velocity, distribution function of the

incident molecules. The average translational energy of the scattered molecules can be obtained

using Eq. (12).

4 The Nocilla Gas-Surface Interaction Model

']?he Nocilla gas-surface interaction inodel assumes that the velocity distrit)ution function of the

scattered molecules can be approximated using a drifting Maxwellian (tistribution fimction with

most probable velocity U defined as [11]

N (v) = ,, exp 2a-T ]' (la)

where n and T, are the number density and temperature of the scattered molecules, respectively.

The adjustable parameters in the Nocilla model are n, T,, and U. The most probable velocity of

the scattered molecules is assumed to lie in the plane formed by the surface normal an(l the
average velocity of die incident molecules. Equations (14)-(17), obtained by integrating Eq. (13),

can be used to determine the four Nocilla model paranleters:

where

T._sin 0_ = g_"sin 0,,.

,,_A<,'_+,/_(_+a') _

7r_cos O_ = ,S' c a_ + v/-ffAE

t,(2+ s")_,:'_++v(}+s")a,_

c_ = 5,2 ( a_ + V/-_AE '

(1.1)

(15)

(16)

(17)

s - (as)

A = N cos Ou, (19)

E = 1 4-erfA. (20)

_ is the flux density of the scatt.ered niolecules, and 0, is t.he angle t)etween the surface nornlal

and the most. probable velocity U. IMng Eqs. (15), (16) and (17) it can t)e shown thai

5'sinO,, (c "_+ x/_,AE)

tail 0,s = ' (21 )

A_. "2 + v_ (1⁄2 +a2) E'

'S'" 0'2(c A2 x/'_AE) ('G sin 0,,)2 (, Slll u) -_-

- (22)

AE"

_lb determine S and 0,,, Eqs. (21) and (22) can be evaluated iteratively. Then Eq. (15) is used to

deterinine U, and E(I. (18) is used to obtain T,.

\Vhen t.he scattering angle 0,, is equal t.o zero, Eq. (15) implies 0,, Inust equal zero or 18W. l_br

this sl)ecial case, ,q can 1)e (teternlined fronl an equation obtained bv confl)ining Eqs. (21) and

(22), given t)y

,,_ a (_ _'_± v_SE ') (2:_)

W] lel'e

E'= 1:1: eft& (21)

a = (e+,_'_)_-'_+ v,__(5t,,:2 +,_") s_' (25)

The phis sign is used if 0u equals zero while the minus sign is used if 0,, equals 180 _. Once ,_,'is

known, U can be evaluated iteratively using Eq. (16). t_br all cases, after 0u, U, and N have been

determined, n cmi be obtained fixmi Eq. (14) 1)y equating the incident and exit fhLx-densities.

The angular dist.ribution function I is (tefine(t l)y letting I (0, O) dt_ ret)resent the fraction of qb,

t.hat scalAers into the differential solid angle dtl about the direction define(t by 0 and 0. where 0 is
the spherical coordinate azimuthal angle. [;sing the Nocilla model to approximate the angular

distribution function of tile scattered molecules Rives

where

and

(-) (,- S 2

I (o, = - cos o (2 s)

O =14- fl2 -1- v/'_p (3 + p2) (l + erfp) e p2, (27)

fl = S (sin 0 cos 0 sin 0,, + cos 0 cos Oct). (28)

Tile angular distribution fimction can also be thought of as representing the probability that a

molecule with incident velocity vi scatters into the solid angle d{/about the direction defined by' 0

and 0- Once the Nocilla model parameters have been determined, Eq. (26) can be used to

approximate the angular distribution ftmction of the scattered molecules.

5 Experimental Results

The experimental results were obtained from measurements of the forces exerted on surfaces by

molecular t)eams of the gases using a torsion balance. The torsion balance apparatus used to

measure the forces, along with the techniques used to measure the flux-densities and velocity

distribution functions of the moleeulm" beams are described elsewhere[l, 2]. The average velocities

of the molecular beams ranged fi'om 1670 m/s for CO2 to 4620 m/s for H2. The total uncertainty

in tile reduced force coefficient measurements is estimated to be less than 4-1@){.

Measurements of the reduced force coefficients for N2, CO, and CO2 incident upon the solar

panel, SiO2-coated Kapton, and Kapton showed that these gas-surface interactions have many

similarities. Scamfing electron microscope measurements revealed that the solar panel,

SiO2-coated Kapton, and Kapton had similar surface roughness and were smooth on a scale of

less than 1 inn. while the Z-93-coated ahmfinum surface was rough on a 100 #m scale. This

contrast in surface roughness could account for the significant differences between the way the

four gases scattered from Z-93-coated aluminum and the other three surfaces.

Figures 1 32 are plots of the reduced force coefficients, -iT,s/Ti, Os, and t t as a flmction of the angle

of incidence Oi for the various gas-surface interactions, while Tables 1-32 contain all actual

experimental data. The gases N2, CO, and CO2 can be seen to scatter from Z-93-coated

alunfinum diffusely with ahnost complete thermal acconlmodation by noting that 0_ is close to

zero and tt is close to one at all angles of incidence. H2 can be seen to scatter froin Z-93-coated

alunfinum diffusely by noting that Os is (;lose to zero ['or all angles of incidence. However, fl varies

widely over the range of angles of incidence.

For the gases incident upon the solar panel, SiO2-coated Kapton, and Kapton gr and 0_ increase

as the angle of incidence inex_ases, consistent with the scattering becoming more specular. For

large angles of incidence, the scattering angles for CO2 are larger than for N2 and CO, and the

scattering angles for N2 and CO are larger thml for H2. ]'his effect can be explained by" noting

that tile mass of H2 is significantly smaller than the mass of N2 and CO, and the masses of N2

and CO axe smaller than the mass of CO_ and that a given force perpendicular to the direction of

motion wouM deltect H2 more than N2 and (IO. and would deflect N._ and CO more than CO2.

10
Thus,forlargeanglesof incidencewherethe scatteringbecomesmorespecular,it.isreasonableto

assumethat thelargerepulsiveforceexertedon themoleculesby thesurfacewill deflect[12more

than N2and(70, andwill deflect,N2andCO morethanC()2.

In Figs.33 61,polarplotsof theangulardistributionfunctionsof the scatteredmoleculesare

shownforthe variousgas-surfaceinteractions.The Nocillamodelparmnetersareshownin Tahles

33 64andwereobtainedfor the gas-surfaceinteractionsusingthepreviouslyoutlinedprocedure.

Negativevaluesfor 0,, imply that 0,, is 180 _'. Equation (26) was t hell used to calculate the

angular distribution functions. In these figures, the origin can be thought of as the impingement

point of the molecular beam, the vertical axis is perpendicular to the scattering surface, and the

horizontal axis is defined by the projection of U onto the plane of the scaltering surface. I:igln'es

33 64 show the intersection of the plane formed by the average velocity of the incident molecules

and the surface normal with the three-dimensional angular distribution functions. The distance

from the origin to a point on a lobe times dt_ represents the pl'obahility that a molecule wilh the

indicated average velocity scatters from the surface into a differential solid angle dft about the

direction defined 1V 0 and 0. These distances are defined by the tick marks on the horizontal and

vertical axis. The portion of the horizontal axis to the right of the vertical axis corresponds to

0 = 0, and the portion to the left of the vertical axis corresponds to 0 = 18(F. The polar angle is

given along the circular axis of the graphs.

The general trend that the scattering t)ecomes more specular with increasing angles of incidence

for gases scattering from the solar panel, SiO2-coated Kapton, and Kapton can b(' inferred fl'om

Figs. 33 64. As the angle of incidence increases, the lobes become much larger 1)ecmlsc of the way

in which the angular distribution function is normalized according to the equation

I (0, 0) d[_ = 1. (2.9)

This hehavior has flm(lamental physical significance. As the angle of incidence increases, the size

of the lobes also increases, meaning fewer partMes scatter out. of the plane formed by the average

velocity of the incident molecules and the surface normal. This effect is lnore t)ronounced for N2.

(:(), and C()2 than for }t2 and for the larger incidenl velocities.

The figmres show that scattering from Z-93-coated aluminum is nearly diffuse for all angles of

incidence. This result was observed for all gases incident upon Z-93-coated aluminum and at all

incident velocities. Nearly diffuse scattering is most likely due to the extremely rough surface

mol3)holog.v of Z-93-coated aluininmn.

Tables 65 67 compare nleasurenlents of the reduced force coefficients for N2. ('O. and ('02 inade

with the carrier gases tt_ and tie. The data agree io within the uncertainty of the lneasuwments

for all angles of incidence except 85 _. AI this angle of incidence aligmnent of the sample with the

molecular beam is extremely critical. A minor misalignment could result in a kaction of the beam

nlissing the sample. The large discrepancy at the angle of incidence of 85 '_ could be due to this

effect.

6 Conclusions

,kt. Ile!.v formalisin has been use(t to analyze the average momentunl transferred to sm'faces 1)v

ineidenl gases. This new tbrmalism eliminates the singularity problems associated with the

11
momentumaccommodationcoefficientsandcanbeusedto uniquelydeterminethe Nocilla

gas-surfaceinteractionmodelparameters.The formalismeliminatesthe needto measureenergy

acconmlodationcoefficients,therebyreducingthe numberof experimentallydetermined

parametersrequiredto obtain th0Nocillamodelparameters.

Tile resultsdiscussedin this report showthat moleculesscatterfrom technicalsurfacesmore

specularlyastheangleof incidenceincreases,andthat thescatteringhasa strongdependence

uponboth theincidentgasandvelocity.The_ resultsshowthat for sometechnicalsurfacesthe

simpleassumptionof diflk_sescatteringwith completethermalaccommodationisentirely

inadequate.

References

[1] S. R. Cook, Ph.D. thesis, The University of Texas at Austin, 1995.

[2] S. R. Cook, M. A. Hoffbauer, J. B. Cross, H. Wellenstein, and M. Fink, Hey. Sci. Instmm.

67, 1781 (1996).

[3] S. R. ('ook and M. A. tIoffbauer, Phys. Rex,. E 55, R3828 (1997).

[4] S. R. Cook, J. B. Cross, and M. A. Hofi%auer, in Ra_'efied Ga._ Dynamics 19, edited by J.

Harvey and G. Lord (Oxford ITniversity Press, Oxford, 1995), Vol. '2, pp. 967 973.

[5] S. R. Cook and M. A. Hoffbauer, in RaTv.fied Gas Dynamics 20, edited by C. Shen (Peking

University Press. Beijing, 1997), pp. -m_ 4_..

[6] S. R. Cook and M. A. Hoffbauer, J. of Spacecraft and Rockets 34, 379 (1997).

[7] S. R. Cook an(t M. A. Hoffbauer, J. of Vac. Sci. and Tech. A 15, 1 (1997).

[8] S. A. Schaaf, in Encyclopedia of Physics, edited by S. F]/igge and C. Truesdell

(Springer-Verlag, Berlin, 1963), No. 2, pp. 591 624.

[9] E. L. Knuth, AIAA Journal 18, 602 (1980).

[10] Dynamics of Cas-5"uffacc Intcvactio't_s, edited by C. T. Rettner and M. N. R. Ashfold (The

Royal Society of Chemistry, (lambridge, 1991).

[11] S. Nocilla, in Rarefied Cas Dynamics, edited by J. A. Laurmann (Academic Press, New York,

1.()63), Vol. 1, pp. 327-346.

12
_0

cO

O

O

(D

o

i,=.

0

U_

"0

0

"0

CK

1.5

1.0

0.5

0.0

75

60

.-. 45

Or)

30

"0

v

_ 15

! • ! • ! ! ! !

I

(a)

• ! , t , I , I i | i

! ! • ! , ! !

(c)

/

m _lf

m--

(b)

I , I

1 • I

(d)

i • i • i • i •

/m _m

__ram/ \i

I i I m I i I *

I • I I I

/

I i I * I , l * l , I , m I , I * I m I

0 15 30 45 60 75 90 0 15 30 45 60

O,(degrees) oi (degrees)

Figure 1: The data for 2590 m/s 1t2 incident upon the solar panel.

1.0

0.8

0.6

0.4 -_ i

0.2

0.0

1.0

0.8

0.4

0.2

, ' , 0.0

75 90

Table 1:2590 m/s [I2 incident upon the solar panel

0i (dcgTees) f, f,, W_/T.'i T., (m/s) 0s (degrees) t' (' c"7 (m/s) 2

0 0 1.59 (1.586 1520 0 0.88_ 0.91_ 5.02x 1() (_

25 0.317 1.48 0.587 1520 10.3 (/.886 0.916 5.02× 10 (_

50 0.612 1.28 0.656 1700 13.6 0.738 0.796 5.25× 10 (;

75 0.750 0.85J 0.633 1640 19.9 0.788 0.839 5.17× 1()_

85 0.619 0.539 0.588 1520 39.8 0.883 0.915 5.03x 10 _i

1;3
1.5

¢/J

¢-.

ID

O

_" 1.0

0

0

0

I,--

0

LL 0.5

"O

0

0.0

75

6O

...-. 45

(/)

3O

"0

v

_' 15

I " I '

-O

J"

e_ (a)

I • I • I . I i | i | i I

I I " I • I I I I

./

fai

jm" (c)

I , i , I • i • I • I . I

0 15 30 45 60 75 90

O,(degrees)

I " I • I " ! ' I

III j

/

11

!

11

(b)

_m _n ---n

I • I • I • I I I a I I I

I I I I I I

_11 111

(d)

I t I t I , I , I , I • I

0 15 30 45 60 75 90

O,(degrees)

Figure "2: The data for 2590 m/s I-I2 incident upon SiO2-coated Kapton.

1.0

0.8

0.6

C:l

*...

0.4 --_ t

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Table 2:2590 m/s H2 incident llpon SiO2-coated Kapton

0 0 1.52 0.520 1350 0

25 0.307 1.48 0.585 1510 11.4

50 0.584 1.26 (/.645 1670 16.4

75 0.733 0.893 0.676 1750 20.1

85 (I.656 0.653 0.660 1710 31.0

1.03 1.02 4.82× 10 6

0.891 0.920 5.02×106

0.761 0.816 5.22× l0 G

0.696 0.760 5.32x10 _

0.129 0.18. 5.27×10 _

t4
..... . , • , 1.0

1.5

c-

.D

0

1.0

0

0

0

0

LL

"0 0.5

0

"0

n'-

0.0

75

60

..-. 45

O9

30

"0

v

_" 15

(a)

I ' I " I " !

ill

....---- III _11 J

jB

(c)

I I I . I I i i i I

0 15 30 45 60 75 90

0i (degrees)

f..J \

mJ •

(b)

0.8

0.6

0.4 -._ i

0.2

I , ! , | , I , I ' ' " ' 00.

I ' I " I ' I ' I I !

1.0

0.8

0.6

0.4

0.2

' ' ' ' ' ' ' 0.0

15 30 45 60 75 90

ei (degrees)

(d)

I , I

0

Figure 3: The data for 2590 m/s H2 incident ut)on Kapton.

Table 3:2590 m/s tt2 inciden! upon Kapton

o_(d_g-,.,_e_) f_ f,, _/_ ,__._(,,/_) O_(d_.g,.e_._) t' _' '_'_(m/_)_

0 0 1.54 0.540 1400 0

25 0.340 1.51 0.606 157/) 7.8/)

50 0.625 1.28 0.657 1700 12..1

75 1/.826 0.907 1}.663 1720 12.2

85 0.833 0.635 /1.571 1480 16.6

0.986 1).990 -1.88× 10(;

0.8,15 0.885 5.118x 10(;

0.735 0.79,1 5.26×10 G

0.721 0.78,1 5.28;_<I(F_

0,920 0.9,12 4.!)7× l()_;

15
1.5

oo

rID

1.0

0

0

(3

0

IJ_

•"o 0.5

0

rr

0.0

75

60

.-.. 45

cf}

30

"13

v

_' 15

! " ! ' I ! • ! , !

• _I --I--_t

/

(a)

I • i i I i i • I , I . I

I " I ' I " I ' I ' I

(c)

• _m -_m

i • i . i " I , I i I m I

0 15 30 45 60 75 90

O,(degrees)

, . , • , • , • , 1.0

/m_ I

i _____._---I -- \

(b)

I m I i I _ I L I , I

! I " I ' ! I ' I '

-= /

(d)

l . I , I • l • I • i I I

0 15 30 45 60 75 90

O,(degrees)

0.8

0.6

0.2

' 0.0

!

1.0

0.8

0.6

0.4

0.2

0.4 ~._ m

Figure 4: The data for 2590 m/s H2 incident upon Z-93-coated aluminum.

0.0

Table 4:2590 m/s H2 incident upon Z-93-coated aluminum

Oi (degrees) St St, T's/'gi '_L'_s(in/s) Os (degrees) t* e' v"7 (m/s) 2

0

25

50

75

85

0 1.53 0.535 1380 0

0.388 1.46 0.551 1430 3.59

0.745 1.26 0.613 1590 1.96

1.02 0.839 0.582 15111 -5.02

1.06 0.594 0.511 1320 -7.25

0.998 0.999 4.87× 106

0.963 0.973 4.91×106

0.830 0.873 5.11x106

0.897 0.925 5.01×106

1.05 1.03 4.80× 10[;

16
-- , ...... 1.0

1.5

(/1

c"

(1)

o_

0

°_::I::

m 1.0

0

0

0

0

LL

•"o 0.5

0

rr

0.0

75

60

45

(/)

o

Im 30

v

_ 15

0

.\

(a)

i • i • i • i • i I l

/

/

(c)

i i | i | i I • | , I i I

0 15 30 45 60 75 90

(degrees)

(b)

1.0

0.8

0.6

\

0.4

0.2

(d)

, . , , , . ' . ' .... 00.

0 15 30 45 60 75 90

(degrees)

[:igure 5: The data for 1870 m/s N2 incident upon the solar pane].

"t::

Table 5:1870 m/s N2 in(:ident upon tile solar panel

Oi (degrees) f, .[,, T._/,_i T8 0n/s) 08 (degrees) t' (' _ (m/s) 2

0

25

50

75

85

0 1.26 0.262 .191 0

0.362 1.17 (}.274 513 12.8

0.628 0.949 0.;}35 629 24.3

0.67.() 0.581 0.431 808 41.7

0.522 0.340 0.537 1010 61.9

0.920 0.96!) -1.487, 105

0.905 0.963 1.69>< 105

0.828 0.924 5.94× l0 s

0.71).(-) 0.847 8.37> 10r,

0.577 0.7,10 1.187,I0(;

17
1.5

GO

t--

CD

1.0

0

0

¢D

0

0

I.t.

._ 0.5

¢.)

-1

CD

cc

0.0

75

6O

.--. 45

O9

3O

CD

v

_' 15

0

(a)

i . i i I i i A i _ I , I

! I l I ' I ' l ' !

./

(c)

i . ! , I . ! I . i . J

0 15 30 45 60 75 90

O_(degrees)

_J"

/

(b)

I , i L I , I _ I . ! • I

! • i . ! • I • i • I !

=\

(d)

I _ l • I • i i i i l , I

0 15 30 45 60 75 90

O_(degrees)

0.8

0.6

0.4 -_ i

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Figure 6: Tile data for 1870 m/s N2 incident upon SiO2-coated Kapton.

Table 6:1870 m/s N2 incident tlpon SiO2-coated Kapton

Oi (degrees) It jr,, vs/v_ v8 (../_) o.,(degrees) # _' _,_(m/s?

0 0 1.25 0.247 46,1 0

25 0.350 1.16 0.-6_9 " 501 15.8

50 0.602 0.945 0.344 645 28.5

75 0.658 0.603 0.462 865 41.9

85 0.578 0.412 0.530 993 52.1

0.938 0.977 4.23x105

0.913 0.966 4.57x105

0.818 0.918 6.13×105

0.671 0.819 9.29× 10r)

0.586 0.748 1.15× 106

18
I " i • I " I • ! I l I i ' i • i " , " I ' I 1.0

1.5

o_

¢-

(..)

1.0

0

0

(1)

E

O

u_

-_ 0.5

O

"ID

rr

0.0

75

6O

,._, 45

if)

tD

3O

tD

"O

v

_ 15

O_

"-O

_m _m

"\.

m/ (a)

| , I i I i i I I I I • I

I I I I l i I

_.jm

(c)

I , I i I i I , I • I i I

0 15 30 45 60 75 90

0i (degrees)

/m _m --m

._...m/

m /

0.8

0.6

0.4 -._ m

0.2

(b)

l m I m I , I , I , i , i 00.

i ' I • I ' i I I I

1.0

0.8

m_m_

kI _m --m

0.6

0.4

0.2

(d)

.... , . , . , .... 00.

0 15 30 45 60 75 90

0i (degrees)

"l:::

Figure 7: The data for1870 m/s N2 incident upon Kapton.

Table 7:1870 m/s N2 incident upon Kapton

Oi (degTees) ft f, V.,/Vi T._On/s) O_ (degrees) t' _' e-_"(m/s) 2

0 0 1.25 0.2-18 465 0

25 0.366 1.19 (3.288 5,1(t 11.3

50 0,638 0.959 0.3,11 639 22.1

75 0.7,10 0.60.9 (t.417 781 32.8

85 0.722 0.40:_ 0.418 78,1 40.9

0.937 0.977 ,1.25× l0 s

0.888 0.95.1 ,1.96x10 r'

O.821 0.920 6.07 × 105

0.727 0.860 7.98× 1()5

0.725 0.858 8.02× 10r,

19
1.5

¢J0

,4,...*

¢-

,m

O

fi5

1.0

0

0

0

0

Ii

•"o 0.5

0

"0

rr

0.0

75

60

.-.. 45

ca0

lm 30

"0

v

15

I • i • I I • i • I

0_

/'\

./ "\ / (a)

I . i i I i I i I , I , I

I ! ! I I • i • I

(c)

i / xI

I , ! • I

l . I i , i , I i I i I

0 15 3o 45 6o 75 9o

(degrees)

I

I

m-

, • , • , • , 1.0

(b)

• __---m ------I --m

i • i I m I m I , I

| • l • I • I . I • I

(d)

--m _m ---__---m /I

i . m • I m I , I m I

15 30 45 60 75 90

(degrees)

0.8

0.6

0.4 -_: m

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Figure 8: The data for 1870 m/s N2 incident upon Z-93-coated aluminun_.

Table 8:1870 m/s N2 incident upon Z-93-coated alunfinum

0 i (de.l_l'ees) It f,, g,/_i t', (m/s) O_ (degrees) # e' v"_"(m/s) 2

0

25

50

75

85

0 1.21 0.211 3q5 0

0.408 1.12 0.218 409 3.82

0.747 0.889 0.247 463 4.45

0.962 0.506 0._4_ 464 0.851

0.987 0.308 0.221 414 2.34

0.984 0.994 3.68× 105

0.975 0.991 3.78×105

0.939 0.977 4.23x105

0.938 0.977 4.23 × 10"_'

0.971 0.990 3.82×105

20
1.5

Or)

E

O

0--

1.0

0

0

0

0

I.L

-o 0.5

0

n"

0.0

75

6O

.-. 45

3O

_'_ 15

_m \

O \

\-

(a)

i I I i I ' u • I

/

f

(c)

I , I a i I l m I * n , I

0 15 30 45 60 75 90

0i (degrees)

(b)

n , I • , • , . , , , . , 0.0

! ' u ' I ' i ' u • i • I

1.0

0.8

m_m_

\

0.6

0.4

0.2

(d)

i . , . , , , , I , ' . ' 00.

0 15 30 45 60 75 90

8i (degrees)

3=

Figure 9: The data for 1870 m/s (!O incident upon the solar panel.

Table 9:1870 m/s ('() incident upon the solar panel

0,: (d,_aT_es) f, .f,, Ts/Ti ,.", (m/s) 0s (deg,'ces) /i " "_ ('"/,_7

0 0 1.26 0.260 488 0

25 0.366 1.18 0.279 524 11.7

50 0.634 0.948 0.333 621 23,,1

75 0.688 0.577 0.123 7.03 ,11.2

85 0.530 0.338 0.530 .0.(_;_ 61.7

0.922 0.970 4.46X 10'_,

0.898 0.959 1.80× l()'_'

0.832 0.925 5.89× 1()r'

0.719 0.855 8.15×10 r,

0.586 0.74.9 1.15×10 (;

21
1.5

¢0

cIll

o_

O

m 1.0

0

0

0

0

U_

•"o 0.5

0

n"

0.0

75

6O

..-.. 45

0

c:m 3o

"0

_' 15

I • i , ! • ! • ! • !

Q_

_D

\

(a)

I , t . I " I , I a i _ I

I ! ' I " I ! " ! ' I

./

(c)

I • i " ' ' I , I , I , I

0 15 30 45 60 75 90

0i (degrees)

, • , • , • , • , • , 1.0

m

• ____.--m _m"

/

(b)

| I i , i i I • i i I

I • ! • i • i I I I

• _m _m

(d)

I , I I i * I , I , I

0 15 30 45 6o 7s 9o

(degrees)

0.8

0.6

0.4 -_: m

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Figure 10: The data for 1870 m/s CO incident upon SiO2-coated Kat>ton.

Table 10:1870 m/s CO incident upon SiO2-coa,ted Kapton

Oi (degTees) ft fr, -#_/'5i "_s (m/s) Os (degrees) tt (' v-7_2 (m/s) 2

0 0 1.25 0.249 :167 0

25 0.352 1.16 0.265 497 15.4

50 0.611 0.944 0.339 635 27.2

75 0.666 0.596 0.451 845 41.7

85 0.589 0.406 0.517 970 51.9

0.936 0.976 4.26×105

0.916 0.968 ,1.54×10 r'

0.824 0.921 6.02× 105

0.685 0.829 8.96×10 _

0.602 0.762 1.11×106

'2'2
, . ....... . , . , . , . , , . , 1.0

1.5

q)

ca)

°_

0

1.0

0

0

0

0

LL

O.G

0

cI

23

rr

0.0

75

60

,,-., 45

30

"0

v

15

O_

11

"\.

(a)

I * I _ I i I • I • I • I

I I I " I " I I I

(c)

I I I I I • I • I • I , l

0 15 30 45 60 75 90

(degrees)

_111 --II

/I j

i1_ IIj

(b)

0.8

0.6

0.4 ~_ i

0.2

' ' ' ' ' ' ' ' " ' ' ' 00.

I I I I I " I " I

1.0

0.8

0.6

0.4

II _11 ___.__

_11 roll

0.2

(d)

I , I , I , I • , • ' " ' 00.

0 15 30 45 60 75 90

0i (degrees)

Figure 11: The data for 1870 Ill/,"; (IO incident upon Kapton.

Table 11:1870 m/s CO incident upon Kapton

0i (degTees) .f, .f,, T._/Ti T.s (m/s) 0_ (degrees) t' " _ (m/s) 2

0 0 1.26 0.259 486 0

25 0.371 1.19 0.290 514 10.3

50 0.6,11 0.956 0.337 633 21. ) -

75 0._4o " _- 0.603 0.409 766 32.6

85 0.728 0.400 0.412 772 -10.6

0.923 0.,971 4.4,1 × l(}r'

(1.885 0.953 5.00× l0 s

0.826 0.922 5..(t9× 10r'

0.737 0.867 7.76× 10'_'

0.733 0.86,1 7.84× lOr'

23
1.5

_0

.O..d

cID

O

o_

1.0

0

0

0

0

ii

._ 0.5

0

n"

0.0

75

60

._. 45

¢/)

0

o_ 30

v

_ 15

I I I I I I " I

O_

_o _o._/..,.......n _u

./ °\

J (a)

• •

I • t • n • | a I . I , I

I u I I • u • I ' u

(c)

._...n .---------------- m

• / _m --m

m • n . i . I * I , I , I

0 15 30 45 60 75 90

O,(degrees)

, • , • , • , 1.0

• __ • ___--m -m"-m

(b)

I . I , I , I I m i I

l I " ! " I I | | ' I

• n _m ----___--m_m

(d)

I . I • I I I • l l I

0 15 30 45 60 75 90

0, (degrees)

0.8

0.6

_o

0.4 --_o

0.2

0.0

1.0

0.8

0.6

0.4

0.2

0.0

"l=:

Figm'c 12: Tile data for 1870 m/s CO incident upon Z-93-coated alunfinum.

Table 12:1870 m/s CO incident upon Z-93-coated aluminum

Oi (degrees) ft fi, Ts/Ti '_s (m/s) 0._(degrees) # e' t,-_s 2 (m/s) 2

0

25

50

75

85

0 1.22 0.215 404 0

0.409 1.13 0.221 414 3.52

0.746 0.890 0.248 466 4.65

0.963 0.507 0.248 465 0.687

0.991 0.309 0.222 416 1.45

0.978 0.992 3.74× 105

0.971 0.990 3.83x105

0.937 0.976 4.25x105

0.938 0.977 4.24×105

0.970 0.98!) 3.84x105

24
1.5

(D

c-

.m

O

1.0

0

0

0

u_

._ 0.5

"0

0

0.0

75

60

..-. 45

_ 30

V

_'_ 15

0

(a)

/

(c)

I • I , I • I . ! , I , I

0 15 30 45 60 75 90

(degrees)

(b)

I , I , I , , • , • J • , 0.0

I " I " ! " I " , I I

1.0

• 0.8

\

0.6

0.4

0.2

' . ' , ' ........ 0.0

0 15 30 45 60 75 90

ei (degrees)

3:::

Figure 13: The data for 1670 m/s CO2 incident upon the solar panel.

Table 13:1670 nl/s (',02 incident upon the solar panel

Oi (degTees) ft f,, Ws/"Yi Ta (m/s) 0,, (de_rees) tt ,:' _ (m/s) 2

0 (l 1.21 0.213 355 0

25 0.381 1.13 0.227 37.9 10.5

50 0.66 ] (/. 891 0.269 449 22.9

75 0.734 0.519 0.348 582 41.7

85 0.562 0.288 0.478 799 65.2

0.957 0.986 2.60>< 10s

0.93.9 0.979 2.77×10 r'

0.888 0.958 3.33× 10r'

0.792 0.907 ,1.6.1× 10s

0.634 0.796 7.52×10 s

25
1.5

or)

E:

(_

°n

0

°_ ::I:=

1.0

o

0

0

0

Im

"0 0.5

0

"0

(3

rr"

0.0

75

6O

..-. 45

00

(_

(:_ 3O

....... 1.0

(a)

I • l , I , I • I , I • l

! I I I " I ' I " I

m

./

(c)

I I • I • I • I • I

15 30 45 60 75 90

0i (degrees)

• _____--m _m

(b)

0.8

0.6

/

0.2

............. 00.

I I I I I I I

1.0

0.8

\

0.6

0.4

0.2

m ---____..._ m

(d)

............. 00.

0 15 30 45 60 75 90

ei (degrees)

Figm'e 14: The data for 1670 m/s CO2 incident upon SiO2-coated Kapton.

0.4 --_ m

Table 14:1670 m/s C()2 incident upon SiO2-coated Kapton

Oi (degrees) ft fr, T's/"Fi _,_ (m/s) 0s (degrees) tt c' v-7 (m/s) 2

0 0 1.19 0.194 324 0

25 0.366 1.lO 0.206 344 16.0

5(1 0.630 ti.889 0.281 469 28.9

75 0.699 0.536 0.385 6,12 44.0

85 0.627 0.350 0.453 757 54.5

0.980 0.994 2.39x105

0.965 0.988 2.53×10 s

0.874 0.951 3.50×105

0.748 0.880 5.35×10 '_

0.664 0.820 6.89×10 '_

26
1.5

(D

r"

.m

{j

zl:=

1.0

0

0

O

Ii

._ 0.5

O

(D

0.0

60

..-. 45

tO

II1

c_ 3O

03

"O

v

_" 15

0

(a)

| I I • I • I , I I , I

./

(c)

I , I , I I I , I , I

0 15 30 45 60 75 90

0i (degrees)

(b)

I _ I

! i

EE_ EE-......._

(d)

0.8

0.6

0.4 -_3 I

0.2

.... ' ' ' ' ' 0.0

i I I I I

1.0

_'m _,, 0.8

0.6

0.4

0.2

l , I , I , I , I , I , I 00.

0 15 30 45 60 75 90

0 i (degrees)

Figure 15: The data for 1670 m/s (102 incident upon Kapton.

Tat)le 15:1670 m/s ('O2 incident upon Kal)ton

Oi (degrees) f, f,, v J-e, r,, (.,/.) o. (deg,._..-,_) /, ,' ,,_ (m/s) _

0 0 1.21 0.210 351 0

25 0.381 1.13 0.232 388 10.3

50 (1.66-1 0.897 0.274 457 21.9

75 0.769 0.511 0.34.1 574 35.0

85 (/.745 0.345 0.360 601 44.2

0.960 0.987 2.572 l0 s

0.933 0.977 2.83× l()r'

0.883 0.955 3.39× 10s

0.797 0.910 4.56× 1(}r)

0.778 0.899 -1.86× 10r,

27
1.5

{D

¢--

O)

.m

O

°m

1.0

0

(O

0

0

1.1_

•._ 0.5

0

or0.0

75

60

,-, 45

Or)

I:_ 30

"0

v

15

0

e_

t_ m _m

.// .\

/ (a)

I , I , I _ I • I . I • I

• • ____-.-m---------m _m

(b)

(c)

_--m.-------m _m ..-.- m

m /

m . i , i • i , i , i , i

0 15 30 45 60 75 90

0i (degrees)

0.8

0.6

0.4 -._ m

0.2

' ' ' ' ' • ' ...... 00.

I • l • m , l • !

• _m -------_---m IN

(d)

!

m . i . , . I m I , I , m

0 15 30 45 60 75 90

0i (degrees)

!

1.0

0.8

0.6

0.4

0.2

0.0

Figure 16: The data for 1670 m/s (!02 incident upon Z-93-coated Muminum.

Table 16:1670 m/s CO2 incident upon Z-93-coated alunfinunl

Oi (degrees) f, f,, _8/_i ,'g, (m/s) O_(degrees) t' e' v-_'_(m/s) 2

0 0 1.18 0.177 295 0

25 0.410 1.08 0.178 297 3.93

50 0.748 0.848 0.206 345 5.07

75 0.957 0.467 0.208 348 2.34

85 0.98,1 0.270 0.184 307 3.85

1.00 1.00 2.22 x 105

0.999 1.00 2.23 x 105

0.964 0.988 2.53× 105

0.962 0.988 2.55×10 r,

0.992 0.998 2.29x105

28
1.5

60

t-

(11

°_

0

Zl=

1.0

0

0

(D

2

O

It.

-o 0.5

¢)

"O

0.0

75

60

.-. 45

¢/)

0)

hi

c:_ 30

(1)

2D

v

15

I I

=/ (a)

I , I , I , I • I . I , !

(c)

I

I

I

• _m ___--m --m

(b)

. I _ I , I • I • a . I

! I I I I I

(d)

• _m _m _m

I , ! • I I I . I

0 15 30 45 60 75 90 0 15 30 45 60 75

(degrees) oi (degrees)

F'igure 17: The data for 4620 m/s H2 incident utlon the solar panel.

• i

90

, 1.0

0.8

0.2

0.0

0.6

0.4 --_ m

1.0

0.8

0.6

0.4

0.2

0.0

Table 17: 462(I m/s tt2 incident upon the solar panel

Oi (degl'ees) J) f,, T_/Ti T_ (m/s) O. (degrees) t' ,, ,,'-_z(m/s)_

0 0 1.57 (1.572 2650 0 0.610 0.738 .().32x106

25 0.370 1.48 (/.575 2660 5.25 0.607 0.735 9.36x l()(_

50 0.656 1.23 0.593 2740 10.7 0.580 0.712 .(1.77x 1()(;

75 0.720 0.823 0.616 2850 2;{.5 0.548 0.682 1.03_, 107

85 0.564 0.538 0.624 2800 ,13.8 0.536 0.670 1.05× lO7

29
1.5

q)

¢-

¢)

°_

_) 1.0

0

0

(1)

¢J

0

Ii

-_ 0.5

¢J

"0

rr

0.0

75

60

..-. 45

(/1

30

"El

v

_" 15

! , . , . , • , • , • , • , 1.0

_0 --II--f t

(a)

I , I , I , I . I • I , I

I I I I I I I

(c)

/

j•l

1tll --II

1

11 ------____.__ 11 J

(b)

0.8

0.6

0.4 -_ t

I • I • I • I • J • I . I

0 15 30 45 60 75 90

8i (degrees)

0.2

............. 00.

1.0

0.8

0.6

0.4

0.2

I I I I I I " t

(d)

• _-I _I

............. 00.

0 15 30 45 60 75 90

0i (degrees)

-=:

Figure 18: The data for 4620 m/s H2 incident upon SiO2-coated Kapton.

Table 18:4620 m/s H2 incident upon SiO2-coated Kapton

m

Oi (deg_'ees) ft f,, _._1"_ v, (res) (degrees) t' _' t'_ (m/s) 2

0

25

50

p,,,_

I,')

85

0 1.55 0.552 2550 0

0.343 1.44 0.539 2490 8.54

0.624 1.22 0.594 2750 13.8

0.693 0.828 0.631 2920 25.6

0.624 0.606 0.639 2950 35.7

0.638 0.76:3 8.90>(106

0.658 0.779 8.62×10 G

0.ot. _'9 0.711 9.79× 106

0.526 0.661 1.06×107

0.515 0.650 1.08×107

30
1.5

0o

cG)

O

::1=

1.0

0

0

(D

0

I.,-

0

IJ-

"o 0.5

0

"0

(1)

rr

0.0

75

6O

45

t,])

o_ 3O

"0

v

15

0

• _ --m--.ft

_0_0 ----0--_

(a)

I , I , I , I , I , I I |

! " I ' ! " ! " ! " ! !

(c)

/

I , I , I . I i I i I . I

0 15 30 45 60 75 90

(degrees)

• .______--m_m _m \m

(b)

0.8

m --------_ m

0.6

0.4 -._ m

0.2

i , i • ' • ' , ' , ' , ' 0.0

i • I • I • ! " i i i

1.0

(d)

0.8

m _m/m 0.6

0.4

0.2

, , , , . i , m , I , L 0.0

0 15 30 45 60 75 90

(degrees)

Figure 19: The data for 4620 m/s [I2 incident upon t(apton.

Table 19:4620 m/s H2 incident upon Kapton

0,: (degTees) It f, T.,/Ti "5, (m/s) 0._ (degrees) I' (' "_'_(m/s) 2

0

25

50

75

85

0 1.48 0.479 2210 0

0.349 1.38 0.484 2240 8.81

0.655 1.19 0.561 2590 11.4

0.748 0.78,1 0.56.() 2630 22.5

0.69,1 0.517 0.525 2,1;{0 35.1

0.7,13 0.846 7.,18× 10(;

0.737 0.841 7.56× 106

0.627 0.753 9.06×106

0.615 0.7-13 9.24× 106

0.678 0.796 8.3-1× 10[;

31
1.5

00

rI1)

O

1.0

0

0

E

O

1.1_

"o 0.5

O

"I3

rr

0.0

75

60

_-. 45

_0

I:_ 30

"13

v

_ 15

I " I • I I I " I • !

i_m Pm

.\.

(a) /

I • I I l I | i I . I , I

I " I " I I I I " I

(c)

• _ai _m

_1 --i

I • i I I i I , l , I , I

0 15 30 45 60 75 90

0i (degrees)

, • , . , • , • , • , 1.0

_m _m

• _u .i \m

(b)

l . m , I , I , l , I , m

I l I I " I • l • m

m" /m

_m _m _m

(d)

i . l , l . l , m . i m

0 15 30 45 60 75 90

0i (degrees)

Figlu'e 20: Tile data for 4620 m/s H2 incident upon Z-93-coated aluminum.

0.8

0.6

0.4 -._ m

0.2

0.0

1.0

0.8

0.4

0.2

0.0

]'able 20:4620 m/s H2 incident upon Z-93-coated aluminum

Oi (degrees) St f. Vs/_ i 'L'_s (hi/S) Oa¢ (degrees) # c' v'_2 (m/s) 2

0

25

50

75

85

0 1.40 0.404 1870 0

0.396 1.28 0.379 1750 3.99

0._8o 1.10 0.461 2130 -2.31

1.04 0.698 0A45 2060 -9.41

1.05 0.465 0.382 1770 -8.85

0.851 0.919 6.24×106

0.886 0.940 5.88× 10 6

0.769 0.865 7.17× 10 6

0.791 0.880 6.90x106

0.882 0.938 5.92× 106

;32
........ . , . , . , . , , , 1.0

1.5

ct)

cO

:1=

0_ 1.0

0

0

0

0

LL

•"o 0.5

0

"0

rr

0.0

75

60

,,-, 45

q)

£

cn 30

"El

v

_" 15

0

0_

• / (a)

I I I • I • I • I . I . I

I ' I " I I 1 I I

ill"

i j

/

/

(c)

I i I * I i I I . I

0 15 30 45 60 75 90

0i (degrees)

(b)

/

0.8

0.6

_ I

0.4 _._ i

0.2

I , I , I , I , I , t . , 0.0

I ' I I | I I I

1.0

• I_i _ 0.8

• 0.6 \

0.4

0.2

(d)

I , I i I , | , I , * ' I :0.0

0 15 30 45 60 75 90

(degrees)

3:::

Figzure 21: The data for 3180 m/s N2 incident upon the solar panel.

Table 21:3180 m/s N2 incident upon the _lar panel

O_(deg,rees) .f, .f,, T,/r'i T, (m/s) O_ (degrees) t' (' _ (m/s) 2

0 0 1.28 0.282 896 0

25 0.400 1.19 0.287 912 4.60

50 0.662 (1.942 0.317 1(}1(} 19.1

75 0.653 0.593 0.,158 1460 43.1

85 0.468 0.371 0.(i00 1910 61.8

0.81;1 0.9:1;1 1.02 × 1()_;

0.807 0.930 1.05× 1()_

0.773 0.912 1.24×1() [;

0.614 0.801 2.35×10 (;

0.453 0.64.() 3.88× 10';

33
1.5

00

c-

(D

.m

O

.u

a=

1.0

O

O

(D

O

I,=.

O

LI_

"O 0.5

{D

O

"O

n0.0

75

60

..-. 45

(D

(D

(D

1,m

c_ 30

(D

"O

v

15

0

I I I I I I I

_O

(a)

i . i i I , I i I , I i I

I • I • I • I I I l

/

(c)

I , I , I , I , l , I • I

0 15 30 45 60 75 90

0i (degrees)

...... • , 1.0

• _m _m

m//m

(b)

l , , , , . , . , . , , n

I I ' I • I I I I

m_m_

"\

(d)

! 0 !

0 15

l • I 0 I , l , m

30 45 60 75 90

0i (degrees)

0.8

0.6

0.4 -_ i

0.2

0.0

1.0

0.8

0.6

Figure 22: Tile data for 3180 m/s N2 incident upon SiO2-coated Kapton.

0.4

0.2

0.0

Table 22:3180 m/s N2 incident upon SiO_-coated Kapton

Oi (degrees) ft f,, -_,,/_i ,'-r, (m/s) 0,_ (degrees) # e' v-7 (,n/s) 2

0

25

5O

75

85

0 1.27 0.273 869 0

0.380 1.16 0.258 820 9.52

0.633 0.937 0.323 1028 24.3

0.613 0.597 0.488 1554 46.2

0.509 0.412 0.585 1862 56.2

0.823 0.938 9.72x105

0.840 0.946 8.89x 10"_

0.766 0.908 1.28x 10 6

0.o19 0.772 2.65x106

0.469 0.666 3.71x106

3,1
, , . , , , . , . , 1.0

1.5

0

1.0

0

0

0

0

1.1_

.._ 0.5

m

o

cc

0.0

75

6O

..... 45

if}

30

v

15

(a)

I • I • I • | " I • l

/

/

(c)

I . I , I , l l , l . l

0 15 30 45 60 75 90

0i (degrees)

i11,/11

• ii_II"

0.8

0.6

%

0.4 --_ i

0.2

(b)

, , , , , , , , i , , • | 00.

l " I " I " | I l " l

1.0

0.8

=\ 0.6

0.4

0.2

(d)

I , I , I , I , I , I , I 0.0

0 15 30 45 60 75 90

Oi(degrees)

Figur(, 2:1: The data for :t180 m/s N2 incident upon t(apt, on.

-r=

Table 2:_: :t180 m/s N2 incident upon Kat)ton

O_(degn'ees) ft f,, "_',_/"_"i '_2,_ (Ill/S) O_ (dl?gl'ePS) It (! 't'7 ('II/S) 2

0

25

50

T5

85

0 1.22 0.219 698 0

0.:_7.(1 1.12 (1.221 704 11.,1

0.656 1/.918 0,297 9i;_ 21.8

0.656 0.559 0.,1:_1 1;_70 -15.9

0.555 0.:t47 0.512 16:_0 59.5

0.884 0.965 T.02× 10_'

0.881 0.96.1 7.11 × 1(1r)

0.796 0.925 1.11×lO (;

0.641 0.825 2.11 × l()';

0.55:_ 0.748 2.88x 10(;

:_5
1.5

if}

c0D

O

1.0

O

0

0

0

IJ_

•o 0.5

0

"0

n,-

0.0

75

60

_,, 45

O9

{D

{D

Tb.=

c:_ 30

"Ov

_ 15

0

I " I • I • I ' I I

.//

// \.

(a)

i . l _ I , I • l i • I

I " I ' ! ' ! ' I ° I ' I

(c)

m_ m

.... <",

0 15 30 45 60 75 90

e, (degrees)

, . , • , • , . , • , 1.0

• _m _U ---_-m \i

(b)

i • I i m , I , i . i

I " I • I ' ! ! " I • I

• -_-----m _m _i _m

(d)

0.8

0.6

0.4 -_ i

0.2

0.0

1.0

0.8

0.6

I • I i I i I _ I , I , I

0 15 30 45 60 75 90

O,(degrees)

0.4

Figure 24: The data for 3180 m/s N2 incident upon Z-93-coated alunfimnn.

0.2

0.0

Table 24:3180 m/s N2 incident upon Z-93-coated aluminum

Oi (dega'ees) ft f,, _/_i Ts (m/s) 08 (degrees) tt _' v"7 (m/s) 2

0 0 1.17 0.170 539 0

25 0.429 1.06 0.157 499 -2.20

50 0. "9i. 8 0.834 0.194 617 -9.33

75 1.00 0.438 0.183 583 -11.6

85 1.01 0.241 0.155 492 -4.48

0.940 0.985 5.05X 105

0.954 0.989 4.62X10 "5

0.912 0.976 5.96X10 .5

(}.925 0.980 5.54× 10'5

0.957 0.989 4.56×105

36
1.5

(D

¢-

(1)

0

1.0

0

0

0

L--

0

u_

-o 0.5

(D

0

"0

rr

0.0

75

6O

..-.. 45

0g

30

15

0

0

(a)

I * I • I J I i • I i |

I • l • 1 I I I i

/

/

f

/I'

• (C)

I • [ , I i I I * I , I

0 15 30 45 60 75 90

0t (degrees)

I 1 " I I I I I " I

/

i __._______- i j

(b)

I I " I ' I I 1 I

\

(d)

0.6

0.4 _l

0.2

1.0

0.8

0.6

0.4

0.2

' ' ' ' ' • ' ' ' ' ' ' ' 00.

0 15 30 45 60 75 90

0_ (degrees)

3::

Figalr(, 25: The data for 3200 m/s CO incident upon t,he solar panel.

Table 25:3200 In/s (IO incident upon th(' solar pallel

0

25

50

75

85

0 1.2.(1 0.285 91 ;I 0

O..lO;} 1.1 i) 0.289 .(t26 3.90

0.665 0.945 0.318 1020 18.5

11.661 0.590 (1.,151) 1441) 42.6

0.472 0.365 0.594 1900 62.1

0.809 0.931 1.05xl() {;

0.801 0.i)2. () ].OTx 10 (;

0.771 O./)ll 1.26_:10 _;

0.622 0.808 2.30>_ 10 (;

0.45.(I 0.656 3.85>< 106

37
1.5

o0

-b.._

C

(D

.B

°B

cD 1.0

o

0

(D

0

0

LL

._ 0.5

"ID

(D

n.-

0.0

75

6o

._. 45

(D

£

_) 30

_' 15

0

I • i , ! • i , I • I

(a)

I i I , I , I

I " I " I " I ' I

/

(c)

I , I • I . I , i l I l I

0 15 30 45 60 75 90

(degrees)

l • I • I • ! i I

• _m _m

mm//m

S

(b)

l m I * I i I i I I I i l

i • i • I i i i l

I

0

"\

(d)

i i l m I i I m I , l

15 30 45 60 75 90

(degrees)

Figure 26: Tile data for 3200 m/s CO incident upon SiO2-coated t(apton.

, 1.0

0.8

0.6

0.4 -_ m

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Table 26:3200 m/s CO incident upon SiO2-coated Kapton

Oi (deg-rees) St f,, "ds/"Q ,'Ts(m/s) 08 (degrees) # e' v-'_s 2 (m/s) 2

0

25

50

75

85

0 1.27 0.268 857 0

0.380 1.16 0.256 819 9.65

0.634 0.935 0.321 1030 24.3

0.619 0.595 0.483 1550 45.9

0.518 0.411 0.578 1850 56.0

0.828 0.941 9.52×105

0.842 0.947 8.87x105

0.768 0.909 1.27x106

0.584 0.777 2.62×106

0.478 0.6_o 3.66× 106

38
, . ............. 1.0

1.5

-I--'

C

O

1.0

0

0

0

k--

o

u_

._ 0.5

(].)

0

rr

0.0

75

60

..-... 45

30

v

./ c,:

(a)

I l I I , l . I . I . I

I I I I I

/

/

(c)

I i I i I i I . I I t I

0 15 30 45 60 75 90

0i (degrees)

/•"

•J

0.8

0.6

0.4 -._ I

0.2

(b)

, . , . , ....... ' 00.

I " ! " I I ' 1 " I " I

1.0

_= 0.8

0.4

0.2

(d)

, , , , , , I • ' . ' , ' 0.0

0 15 30 45 60 75 90

Oi(degrees)

Fig;ure 27: The data for 3200 m/s CO incident upon Kapton.

"=:

Table 27:3200 m/s CO incident upon Kapton

0 (} 1.23 0.226 725 0

25 0.382 1.13 0.229 73,1 10.2

50 0.661 0.925 0.301 965 20.4

75 0.665 0.563 0.,128 1;370 44.7

85 0.562 (}.350 0.507 1620 58.8

0.875 0.962 7.40x 105

0.872 0.960 7.53x105

0.790 (}.921 1.15× 106

0.647 0.828 2.10× it)t;

0.557 0.753 2.87× 106

39
1.5

(D

E

(1)

0

1.0

0

0

2

O

1.1_

"o 0.5

I11

O

ID

rr

0.0

75

6O

_. 45

(D

II1

¢:_ 3O

(D

"O

v

/

• (a)

i , i , I , I • i • I . !

! " ! " ! ' I " I " I " I

(c)

m_ m

J

0 15 30 45 60 75 90

(degrees)

I I " I • I I I I

_ii _'i

• "-'---------i / \1

(b)

I • I | I i I _ I . I . I

I • I " ! ' I • I " I " I

• _m __m _-i _m

(d)

I . I i I • I I I , I . I

0 15 30 45 60 75 90

0i (degrees)

Fig-ure 28: The data for 3200 m/s CO incident upon Z-93-coated ahmfinunl.

1.0

0.8

0.6

0.4 -._ m

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Table 28:3200 m/s CO incident upon Z-93-coated aluminmn

Oi (degrees) ft fn "gs/r.'i T8 (m/s) 08 (degrees) i t (:' v-7, _ (m/s) 2

0 0 1.17 0,172 550 0

25 0.42.(I 1.07 0.160 511 -2.46

50 0.807 0.844 0.205 658 -11.4

75 1.00 0.440 0.185 592 -11.1

85 1.01 0.244 0.157 503 -5.19

0.937 0.984 5.16×105

0.951 0.988 4.74×10 r)

0.899 0.971 6.,17× 105

0.922 0.979 5.65x105

0.953 0.989 4.66×105

4O
1.5

09

cOD

,m

0

,m

1.0

o

0

0

0

LL

•_ 0.5

rO

"0

rr

0.0

75

6O

.-. 45

Q)

o'_ 3O Q_

v

q_ 15

• _ (a)

_O

1 • I • I * l , I , i . I

F " ! " I ' I ! I I

/

J

I a I I I h I i I n a . I

0 15 30 45 60 75 90

O_(degrees)

(b)

/

U j

t I I I

0.8

0.6

0.4 -._ o

0.2

I , I , I , I , I , I , I 00.

I I I

1.0

0.8

0.6

0.4

0.2

• -------m _m

(d) \

n , I , i , i ' " ' ' J 00.

0 15 30 45 60 75 90

0 i (degrees)

Figure 29: The data for 2840 m/s (102 incident upon the solar panel.

rlhble 29:2840 m/s C()2 incident upon tile solar panel

0

25

5o

75

85

0 1.1,1 O.136 387 0

0.369 1.06 0.159 451 19.9

0.619 0.8,11 0.247 700 36.5

0.618 0.525 0.438 1240 52.6

0.44,1 0.322 0.600 1700 67.0

0.964 0.992 2.86× 1() r)

0.939 0.985 3..lOx 10 r)

O. 841 0.9,19 6.30 × l ()r,

0.627 0.817 1.70×1() (;

0.446 0.647 3.07× 1()(_

41
, • , • .... , ..... • , • , 1.0

1.5

o0

rO

._

1.0

o

0

O

u..

-o 0.5

0J

O

ll0

rr

0.0

75

60

.-. 45

0J

¢_ 30

0J

q:

(a)

I , I • I ° I o I a I i I

I U I " I " I " U " I

(c)

J a I , I a I , I , I , 1

0 15 30 45 60 75 90

(degrees)

(b)

J , I , I • I • I i | I |

U ; " I ' I " I " I " U

\

(d)

I . I • n . I o I n I a I

0 15 30 45 60 75 90

0i (degrees)

0.8

0.6

0.4 --_ o

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Figure 30: The data for 2840 m/s (102 incident upon SiO2-coated Kapton.

Table 30:2840 m/s CO2 incident upon SiO2-coated Kapton

Oi (degrees) ft J;, g,,,_,/7 T,, (m/s) 0,. (degrees) it e' u-_'_ _ (m/s) 2

0

25

50

75

85

0 1.21 0.207 587 0

0.383 1.10 0.199 564 11.6

0.635 0.883 0..14)-, 777 28.6

0.625 0.5,18 0.447 1,9"_0 49.6

0.518 0.368 0.555 1580 59.6

0.885 0.968 ,1.83×105

0.895 0.971 4.56×105

0.811 0.935 7.45× 105

0.617 0.80.(I 1.76×10 G

0.497 0.700 2.64×10 (;

42
, . , . , . , . , . ......... 1.0

1.5

c/)

¢-

_D

.m

O

,m

1.0

0

0

0

ii

0.5

0

D

0.0

75

60

..-. 45

30

15

0

0_

m _m \m "\

/ -

• (a)

l , I , I , l , I I l • l

l • l ' m • ! ' l • I I

/

/

(c)

l _m"

0.8

0.6

0.4 -_ I

0.2

(b)

m , m , I , l , I , ' • _ 00.

! ! • i ' i • I • n i

1.0

0.8

0.6

0.4

0.2

I l i , I . I , I . I , I

0 15 30 45 60 75 90

Oi (degrees)

Figure 31: The data for 2840 m/s (!O2 incident upon Kal)ton.

(d)

, , , i , , • , • , • , 00.

0 15 30 45 60 75 90

ei (degrees)

"l::

Tal)le 31:2840 m/s (-!O2 incident ut)on KaI>ton

Oi (degrees) ft f, "_8/"_i L"'Vs (Ill/S) 0 5 ((|e_l'f,es) [' (1 "'_ (Ill/S) 2

0

25

50

75

85

0 1.20 0.198 561 0

0.393 1.10 0.197 559 8.55

0.670 0.883 0.259 735 21.7

0.685 0.530 0.391 1110 16.1

0.574 0.321 0.483 1370 61.1

0.8!)6 0.972 4.52X 1()'_'

0.897 0.972 ,1.50X10 r'

0.827 0.94:{ 6.80× 10r'

0.680 0.857 1.38 × 106

0.578 0.776 2.03× 106

-13
1.5

if)

tO

.m

1.0

0

0

O

LL.

0.5

O

2:3

rr

0.0

75

6O

.... 45

{D

c_ 3O

v

_' 15

--=raft

--'--O m fl I

(a)

m _m /

./ \"

I , I . I • | I I I | , I

I I I I I I I

(c)

• _-m •

I , , m ........,

0 15 3o 45 6o 75 90

O,(degrees)

(b)

• _m/_m _m _m

i • ¢ • i . m , I , I , I

I i i I • I • I • I

• _m _u _m _m

(d)

I i I . I . I • I • I • I

0 15 30 45 60 75 90

0i (degrees)

0.8

0.6

0.4 .c::m

0.2

0.0

1.0

0.8

0.4

0.2

0.0

Figm'e 32: The data for 2840 m/s CO2 incident upon Z-93-coated aluminunl.

Table 32:2840 in/s CO2 incident upon Z-93-coated alunfimun

oi (dea-_) f, y;, "e_/v_ v_ (m/_) 0._(d_,'ee_) # _' _'-7(m/_)2

0

25

50

75

85

0 1.15 0.148 421 0

0.429 1.04 0.134 380 -2.52

0.794 0.809 0.169 479 -9.54

0.998 0.414 0.158 449 -11.6

0.996 0.219 0.132 373 0.076

0.951 0.989 3.13×10 r_

0.967 0.993 2.80× 105

0.928 0.982 3.66×105

0.940 0.986 3.38× 105

0.969 0.993 2.75×105

44
O

e = 50 °

30 °

e. = 75 ° t'. i ..." /.,..: / • ._,:

l ./

"'"_ // 2590 rn/sec H2.

85 °

....... Solar Panel

...................!!iii_.... .......

0.50 0.25 0.00 0.25 0.50

I(e,180 °) I(o,O °)

60 °

90 °

Fig_u'e 33: The angular distribution flmcdons for 2590 m/s tt2 incident 11t)oi1 the solar panel.

Table 33: The Nocilla model parameters for 2590 m/s II2 incident, upon the solar panel.

o,:(d_.gre,,,) ,s' u (,,,/_) o. (de_,.,_,.,)r. (K)

0 0.309 -154 0 263

25 0.334 ,191 33.7 263

50 0.718 968 2,1.3 221

7"5 O. 594 831 42.1 237

85 0.706 1070 114 , _8

45
o

e.= 75 °

[

= 85 °

0.50

I(e,180 °) I(o,o°)

90 °

Figure 34: The angaflar distribution fmmtions for 2590 m/s H2 incident upon SiO2-coated Kapton.

'Fable 34: The Nocilla model parameters for 2590 m/s I-I2 incident upon SiO2-coated Kapton.

Oi (degrees) S U (m/s) 0.. (degrees) T. (K)

0 0.0860 136 180 304

25 0.326 482 38.5 265

50 0.657 901 31.5 228

75 0.831 1090 33.4 210

85 0.757 1030 58.6 225

46
o

e = 25 °

!

\

e= 75 °

!

e= 85 °

z .................... iiii:._....

2590 m/sec Hd

Kapton

0.50 0.25 0.00 0.25 0.50

60 °

s(e,18o°) s(o,o °)

90 °

Figm'e 35: The angular distribution functions for 2590 m/s H2 incident upon Kapton.

Table 35: The Nocilla model paranieters for 2590 m/s H2 incident upon Kapton.

o, (d_a-,-c<_s) S r; (m/_) 0,,(d,,_,'_.) T. (i<)

0 0.0360 55.8 0 2.91

25 0.447 641 19.5 2.1.9

50 0.697 945 22.7 223

7;5 0.758 1010 21.0 216

85 0.308 463 65.9 275

17
0

0.50 0.25 0.00 0.25 0.50

I(e,180 °) I(e,O °)

60 °

90 °

Figure 36: Tile angular distribution functions for 2590 m/s H2 incident upon Z-93-coated almninunl.

Table 36: The Nocilla model parameters for 2590 m/s H2 incident upon Z-93-coated aluinimlm

0 0.00438 6.83 0 291

25 0.115 177 30.4 249

50 0.466 663 4.69 223

75 0.289 428 -17.9 216

85 O.188 300 -146 '275

48
0

0 = 50 °

!

e= 25 °

' \

0._ 0 0

I

30 °

1870 m/sec N2

Solar Panel

0

60 °

3.0 2.0 1.0 0.0 1.0 2.0 3.0

I(e,180 °) I(e,O °)

90 °

Figm'e 37: The angular distribution functions for 1870 m/s N2 incident upon tile solar panel.

Table 37: The Nocilla model parameters for 1870 m/s N2 incident upon the solar panel.

o,(dc_,'ee_) S tv (,,,/_) O,(d_._.,-,_e,) r, (K)

0 0.66.0 266 0 267

25 0.77-1 306 21.7 264

50 1.26 484 32.3 2-17

75 1.91 711 49.0 226

85 2.66 938 71.4 210

49
o

O= 25 °

' \

e= 75 °

e = 85 °

0._- 0 0

l

30 °

0

60 °

3.0 2.0 1.0 0.0 1.0 2.0 3.0

I(e,180 °) I(e,O °)

90 °

Figalre 38: The angular distribution functions for 1870 m/s N2 incident upon SiO2-eoated Kapton.

Table 38: Tile Nocilla model parameters for 187(/m/s N2 incident upon SiO2-coated Kapton.

0i (degrees) S U (m/s) 0_ (degrees) 7; (K)

0 0.531 214 0 273

25 0.718 286 28.4 268

50 1.32 505 37.5 246

75 2.18 781 47.7 216

85 2.68 925 58.0 202

5O
0

e. = 50 °

l

0.= 25 °

l

\

O= 75 °

l .

= 85 °

................. :i!_....

30 °

0

1870 m/sec N2

Kapton

1.5 1.0 0.5 0.0 0.5 1.0 1.5

60 °

I(e,180 °) I(0,0 °)

90 °

Figm'e 39: The angular disU'ibution functions for 1870 m/s N2 incident upon Kapton.

Table 39: The Nocilla model parameters for 1870 m/s N2 incident upon Kat)ton.

o,(dea'e,_) ,S' l: (,,,/_) o,,(de_ree_)'r. (t<:)

t) (I.540 217 0 273

25 0.896 351 17.5 259

50 1.31 ,199 28.8 214

75 1.86 682 38.1 225

85 1.85 682 ,18.9 229

51
O

/I'0.= 250 _1_-=_..._. .. ,,,. /" ",="° .! .,_ <,-_ %. o

°,=5°° ....... ",! o

I o,=7_.5°_._, _...:_

t " "__^'_I_ \_ ' /,/] 1870 m/sec N2

I O,=.85° +_::. % _;._ Z93-Coated AI

I I '''"-i I , "_"_. ,,,_' , I I I

0.50 0.25 0.00 0.25 0.50

I(o,180 °) I(o,O °)

90 °

Figure 40: The angular distribution functions for 1870 m/s N2 incident upon Z-93-coated ahmfinum.

Table 40: The Nocilla model parameters for 1870 m/s N2 incident upon Z-93-coated aluminum.

Oi (degrees) S U (m/s) 0u (degrees) T. (K)

0 0.153 63.4 0 289

25 0.237 97.7 16.2 286

50 0.529 213 9.71 274

75 0.532 214 1.86 273

85 0.265 109 8.92 284

52
o

e = 50 °

l

O= 25 °

' \

O = 75 °

l

0. = 85 °

0 _ 00

!

30 °

1870 m/sec CO

0

Solar Panel

I

3.0 2.0 1.0 0.0 1.0 2.0 3.0

I(e,180 °) 1(o,o°)

90 °

Figure 41: The angular distribution functions for 1870 m/s (IO incident upon the solar panel.

Tat)le 41: The Nocilla model parameters for 1870 m/s CO incident ut)on tile solar panel.

0_ (degrees) 5; U (m/s) 0,, (degrees) 7_ (K)

0 0.655 261 0 268

25 0.822 324 19.0 262

50 1.24 477 31.2 2-18

75 1.88 693 48..q 229

85 2.5!) .()21 71.7 213

53
O

e. = 50 °

l

0.= 25 °

' \

O _ 0 0

l

30 °

1870 m/sec CO

Si02-Coated Ka

0

60 °

3.0 2.0 1.0 0.0 1.0 2.0 3.0

1(0,180 ° ) I(e,O ° )

90 °

Figure 42: The angular distribution flmctions for 1870 m/s CO incident upon SiO2-coated Kapton.

Table 42: Tlle Nocilla model parameters for 1870 m/s CO incident upon SiO2-coated Kapton.

0_ (degrees) S U (m/s) 0. (degq'ees) T_ (K)

0 0.548 220 0 273

25 0.700 ")" - _9 28.2 269

50 1.28 492 36.2 247

75 2.09 756 48.0 220

85 2.57 898 58.2 206

54
_i _= 501

ei -75°

1.0

I(e,180 °)

O

/'"" /se -

_:, II::J/2j '/ y Kapton

I ., _: " " I I I

0.0 1.0

I(O,O °)

90 °

Figqu'e 4:}: The angxllar distribution functions for 187(/m/s CO incident upon Kapton.

Table -13: The Nocilla model parameters for 187(I m/s (IO incident upon Kat)ton.

0 0.645 257 0 269

25 0.913 :t58 15.7 258

50 1.28 490 28.5 245

75 1.80 663 38.6 228

85 1.80 666 .18.9 232

55
o

z" ",--_° .< ,_- _ e

I '.._ _;._ Y,,4i_ V °

l .......',f,, -- I;i: \

/ e,=:s° !_:, J!i 1

' ""o "i \t;, "l" /,'_ 1870 m/sec CO _l

[ et ="85°.,,!_,,., _. I ,f..<'_" Z93-Coated AI I

0.50 0.25 0.00 0.25 0.50

I(e,180 °) I(e,O °)

90 °

Figm'e 44: Tile ang_llar distribution functions for 1870 m/s CO incident llpon Z-93-coated alullli II12 ill.

Table 44: The Nocilla model parameters for 1870 m/s CO incident upon Z-93-coated aluminum.

0i (degrees) S U (m/s) o. (degrees) Ts (K)

0 0.204 84.1 0 287

25 0.268 110 13.3 284

50 0.542 218 9.9/ -c3

75 0.536 216 1.48 273

85 "u.-i')""_ 113 5.3.1 284

56
O

0 = 0° 30o

!

o.= 25 ° 0

' \ 1670 m/sec CO

Solar Panel

3.0 2.0 1.0 0.0

I (0,180 ° ) I(O,O ° )

60 °

1.0 2.0 3.0

90 °

Fig_u'c 45: The angaflar distribution functions for 1670 m/s CO2 incident upon the solar panel.

Table 45: Tile Nocilla model parameters for 1670 m/s (?()2 incident upon the solar panel.

0,:(d_.gr,_e.) ._";' t; (m/.) 0,,(d_aTe_..)'r_(t_:)

0 0.432 140 0 279

25 0.587 189 21.6 274

50 0.975 307 34.7 262

75 1.59 485 52.9 2.18

85 2.47 739 78.8 236

;) t
0

30 °

2.0 1.0 0.0 1.0

1(o,180 °) I(0,0 °)

0

2.0

90 °

Figure 46: The angxllar distribution flmctions for 1670 m/s CO2 incident upon SiO_-coated Kapton.

Table 46: The Nocilla model parameters for 1670 m/s CO2 incident upon SiO2-coated Kapton.

0i (degrees) S U (m/s) 8,, (degrees) T_ (K)

0 0.212 69.7 0 287

25 0.395 129 47.1 284

50 1.07 335 42.5 261

75 1.87 560 52.8 238

85 2.36 692 63.0 227

58
o

e= 25 °

f. o

\

30 °

O,= 75 ° I •

= 85 ° /,/

e

0

.:/"

1670 m/sec CO:

60 °

1.5 1.0 0.5 0.0 0.5 1.0

I(&180 °) I(e,O °)

90 °

1.5

Figure 47: The an#llar distribution functions for 167(/m/s CO2 incident upon Kapton.

Table 47: The Nocilla model t_arameters for 1670 m/s COu incident tlpOll Kapton.

0 0.41)5 132 0 2811

25 0.637 204 19.8 272

51) 1.02 318 32.4 2611

75 1.57 478 43.6 244

85 1.67 509 55.4 246

59
0

O_=_75 ° '_.

= 85 °

, I

0.50 0.25 0.00

I(0,180 °)

30 °

0

1670 m/sec C02] '

/

Z93-Coated AI /

I , 90 °

0.25 0.50

I(o,o°)

Figure 48: The angular distribution functions for 1670 ln/S (2102 incident upon Z-93-coated aluminunl.

Table 48: The Noeilla model parameters for 1670 m/s CO2 incident upon Z-93-coated ahlnlinmn.

Oi (degrees) S U (m/s) O_ (degrees) T8 (K)

0 0.00572 1.92 181) 295

25 0.0613 20.4 85.7 295

50 0.363 118 14.9 282

75 0.382 124 6.55 281

85 0.101 33.4 38.1 292

6O
0

"7.&

O__ 25 °

\

0.= 75 °

= 85 °

30 °

60 °

4620 m/sec H2

Solar Panel

2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5

/(o,180 °) t(o,o °)

90 °

2.0

Figau'e 49: Tile angular distribution functions for 4620 m/s H2 incident upon the solar panel.

Table 49: Tile No(:illa model l)arameters for 4620 m/s It2 incident upon the solar panel.

o,(de_,',,e,_),s' r: (,,,/_) o,,(d,,_,',-e._)"1;(K)

0 1.80 2290 0 197

25 1.81 2310 6.05 197

50 1.93 2420 12.1 191

75 2.06 2540 26.5 185

85 2.06 257(I 50.9 18.9

61
O

0. = 50 °

0.= 25 °

\

O.= 75 °

!

= 85 °

2.0 1.5

30 °

,,/,,4620 m/sec H2

" SiO2-Coated Kapto

60 °

1.0 0.5 0.0 0.5 1.0 1.5 2.0

/(o,18o°) I(o,o °)

90 °

Figure 50: The angular distribution functions for 4620 m/s H2 incident upon SiO2-coated Kapton.

Table 50: Tile Nocilla model parameters for 4620 m/s H2 incident upon SiO2-coated Kapton.

Oi (degrees) S II (m/s) 0,_ (degrees) Ts (K)

0 1.68 ,)_1 -,_(} 0 20,1

25 1.59 2080 10.2 208

50 1.93 2420 15.7 191

75 2.16 2630 28.6 180

85 2.19 2670 40.2 180

62
0

1.5

0i_25 °

\

O= 75 °

= 85 °

/

0

4620 m/sec H 2 ._

Kapton

, I ,/

1.0 0.5 0.0 0.5 1.0

I(e,180 °) I(e,O °)

90 °

1.5

Figure 51: The ang-ular disti'ibution functions for 4620 m/s H2 incident upon Kapton.

Table 51: The Nocilla model parameters for ,1620 m/s [I2 incident upon Kapton.

0 1.23 1680 0 228

25 1.26 1720 11.5 226

511 1.72 2220 13.,1 202

75 1.76 22611 26.-1 200

85 1.46 1970 45.1 220

63
0

0.= 75 °

= 85 °

30 °

0

4620 m/sec H2

Z93-Coated AI

60 °

1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75

I(0,180 °) I(O,O °)

90 °

1.00

Figure 52: The angular distribution functions for 4620 m/s H2 incident upon Z-93-coated aluminum.

Table 52: The Nocilla model parameters for 4620 m/s H2 incident upon Z-93-coated alunfinum.

Oi (degrees) S U (m/s) 0u (degrees) 7"8 (K)

0 0.760 1100 0 254

25 0.598 881 7.95 263

50 1.12 1560 -3.17 234

75 1.02 1440 -13.6 240

85 0.618 910 -17.4 263

64
0

0.= 25 °

1

\

30 °

3180 m/sec N

Solar Panel

0

6.0 4.0 2.0 0.0 2.0 4.0 6.0

I(e,180 °) 1(o,o°)

60 °

90 °

Fig_u'e 53: The angular distribution flmctions for 3180 m/s N2 incident upon the solar panel.

Table 53: The Nocilla model parameters for 3180 m/s N2 incident upon the solar panel.

Oi (degrees) ,S' U (m/s) 0_ (degrees) 7[. (K)

0 2.06 802 0 318

25 2.11 8211 5.12 255

50 2.38 926 20.8 255

75 3.54 1400 45.3 264

85 4.55 1860 64.6 28:t

65
O

e.= 25 °

!

\

30 °

3180 m/sec N2

SiO2-Coated Ka

s

• " /

0(= 75 ° ,/ .- ........... /. ..

= 85 ° Z:....... /"

s

0

6.0 4.0 2.0 0.0 2.0 4.0 6.0

I(0,180 °) I(o,o °)

60 °

90 °

Figure 54: The anglflar distribution flmctions for 3180 m/s N2 incident upon SiO2-coated Kapton.

Table 54: The Nocilla model parameters for 3180 m/s N2 incident 1.1pon SiO2-coated Kapton.

0i (degrees) S U (m/s) 0,, (degrees) T8 (K)

0 1.98 771 0 255

25 1.83 714 10.9 256

50 2.43 947 26.5 256

to 3.77 1500 48.4 -61

85 4.48 1820 58.5 277

66
o

e_= 25 o

\

4.0

3180 m/sec N 2

Kapton

0

2.0 0.0 2.0 4.0

i(o,18o o) ir(o,o°)

60 °

90 °

Figure 55: The angular distribution functions for 3180 m/s N2 incident upon Kapton.

Table 55: Tile Nocilla model parameters for 3180 m/s N2 incident upon Kapton.

0 1.44 565 0 260

25 1.46 572 14.1 260

50 2.1 .q 854 2,1.8 256

75 3.31 1310 48.8 26.1

85 3.89 157'0 63.1 276

67
0

0. = 50 °

0.= 75 °

l

0.= 85 °

30 °

0

3180 m/sec N2

Z93-Coated AI

60 °

1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00

I(0,180 °) I(0,0 °)

90 °

Figure 56: The anDllar distribution functions for 3180 m/s N2 incident upon Z-93-coated aluminum.

Table 56: The Nocilla model parameters for 3180 m/s N2 incident upon Z-93-coated ahmfinum.

Oi (degrees) S U (m/s) 0. (dega'ees) Ts (K)

0 0.846 339 0 260

25 0.669 270 -4.05 260

50 1.15 456 -12.7 256

75 1.02 405 -16.8 264

85 0.64 259 -8.51 276

68
O

j o,

6.0 4.0 2.0

I(o,180 °)

o

3200 m/sec CO'X'_ _'

Solar Panel "_

,%

- .. .... '_ 60°

_:'-i' _ ......I .... , I , I , 190 o

0.0 2.0 4.0 6.0

I(O,O °)

Figure 57: The angular distribution functions for 3200 m/s (_O incident upon the solar panel.

Table 57: The Nocilla model parameters for 3200 m/s CO incident upon the solar panel.

Oi (degrees) H U (m/s) O, (degrees) 7_ (K)

0 2.12 821 0 254

25 2.16 836 4.32 25-1

511 2.12 .9:/!) 20.1 25-1

75 3.51 1380 4-1.9 261

85 4.56 1850 64.9 278

6!)
o

0= 25 °

l

\

0= 75 °

= 85 °

30 °

3200 m/sec CO

Si02-Coated Ka

0

6.0 4.0 2.0 0.0 2.0 4.0 6.0

I(e,180 °) I(O,O °)

60 °

90 °

Figure 58: The ang_tlar distribution functions for 3200 m/s CO incident upon SiO2-coated Kapton.

Table 58: The Nocilla model parameters for 3200 m/s CO incident upon SiO2-coated Kapton.

o_(deg,'ees) S U (n,/s) 0,,(deg,'ee_)T, (t,:)

0 1.95 758 0 254

25 1.83 713 11.1 256

50 2.44 947 26.6 255

75 3.79 1490 :18.1 263

85 4.48 1800 58.2 273

7O
o

O.= 50 °

l

0.= 25 °

I

\

0.= 75 °

l

= 85 °

I(0,180 °)

90 °

Figalre 59: The angular distribution functions for 3200 m/s ('O incident upon Kapton.

Table 59: The Nocilla model parameters for 3200 m/s (IO incident upon Kapton.

0 1.53 5.99 0 258

25 1.56 610 12.3 258

50 2.26 879 22.5 255

7;5 3.33 1310 47 A 261

85 3.91 1570 62.2 271

71
o

0 = 50 °

l

e.= 75 °

[

e.= 85 °

!

e. = 25 s

l

l

\

30 °

0

60 °

3200 m/sec CO

Z93-Coated AI

1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00

I (e,180 ° ) I(&0 ° )

90 °

Figure 60: The angular distritmtion functions for 3200 m/s CO incident upon Z-93-coated aluminnln.

"Fable 60: The Nocilla model parameters for 3200 m/s CO incident upon Z-93-coated aluminunl.

Oi (degrees) S U (m/s) 0u (degrees) T. (K)

0 0.889 356 0 270

25 0. _24 999 -4.31 . _4

50 1.30 511 -14.7 262

75 1.06 420 ) -, -15.7 26_

85 0.688 278 -9.42 275

72
o

0.= 50 °

0.= 25 °

\

30 °

2840 m/sec CO 2

Solar Panel

B

0i = 75 ° / ,/,

= 85 ° ..../- ........

0

60 °

8.0 6.0 4.0 2.0 0.0 2.0 4.0 6.0 8.0

I(0,180 °) I(e,0 °)

90 °

Fig-tire 61: The angular distribution flmctions for 2840 m/s (102 incident upon the solar panel.

Table 61: The Nocilla model parameters for 2840 m/s (102 incident Ul)On the solar panel.

Oi (deg;rees) ,b' (; (m/s) 0u, (degrees) T_ (K)

0 0.605 196 0 278

25 0.942 302 30.5 273

50 1..05 618 42.4 261

75 3.71 12(10 55.5 277

85 4.87 1670 7(I.3 310

73
0

0 = 50 °

[

O_= 25 °

\

0._. 0 0

1

2840 m/sec CO 2

SiOKCoated Ka

0

60 °

8.0 6.0 4.0 2.0 0.0 2.0 4.0 6.0 8.0

I(0,180 °) I(0,0 °)

90 °

Figlu'e 62: Tile angular distribution functions for 2840 m/s CO2 incident upon SiO2-coated Kapton.

rlhble 62: The Nocilla model parameters for 2840 m/s (?02 incident upon SiO2-coated Kapton.

0 1.56 489 0 260

25 1.46 459 14.3 262

50 2.26 707 31.8 260

75 3.80 1230 52.1 ,)_' __6

85 4.61 1540 62.1 295

74
o

0. = 50 °

!

0.= 25 °

' \

30 °

2840 m/sec CO 2

Kapton

6.0 4.0 2.0 0.0 2.0 4.0

I(0,180 °) I(0,0 °)

90 °

6.0

Figm'e 63: The ang_llar distribution functions for 2840 m/s CO2 incident upon Kapton.

Table 63: The Nocilla model parameters for 2840 m/s CO2 incident upon Kapton.

o_(4,_r,,,_) ,s' t: (,,,/_) o,, (d,._roe.) T. (t,:)

0 1.45 455 0 261

25 1.4J 452 10.6 261

50 2.11 660 24.3 25!I

7;5 3.32 1060 ,18.9 270

85 4.03 1380 64.7 288

75
o

0. = 50 °

!

0.= 75 °

1

Oi= 85 °

..................iiii_....

30 °

0

2840 m/sec CO 2

Z93-Coated AI

1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00

I(8,180 °) I(0,0 °)

60 °

90 °

Fig-ure 64: The anDllar distribution flmctions for 2840 m/s (702 incident Z-93-coated aluminum.

Table 64: The Nocilla model parameters for 2840 m/s CO2 incident upon Z-93-coated ahuninunl.

Oi (degrees) S U (m/s) 0,, (degTees) T. (K)

0 0.792 254 0 273

25 0.564 183 -5.25 279

50 1.08 344 -13.3 267

75 0.935 299 17.6 271

85 0.526 171 0.166 280

76
Table65: Conlparisonof the [ReducedForce(!oeflicientmeasurenlentsfor

uponthe solarpanelmadewith the carriergasesII2 and lie.

1870m/s N,eincident

0_ (,tegree_) ft H," f: ti2 f, ';/_Diff. .L, lie f,, I12 L, _ Diff.

1) 0 0 0 1.3,1 1.26 6.0

25 0.379 0.362 4.6 1.2.1 1.17 6.4

50 0.648 t).628 3.2 1.02 (I.9.19 7.7

75 0.696 0.679 2.6 0.643 0.581 111.7

85 0.578 0.522 1/).7 0A30 0.3,111 26.6

Table 66: (!omparison of the Reduee(t Fol"('e Coefficient

upon the solar panel made with the carrier gases tt2 and He.

nleasurements for 1870 Ill/S ("O incident

Oi (degrees) fl lie ./'ttI_ ft _7_Diff. f_, tie .f_, H2 f,, 7( Diff.

0 0 0 0 1.33 1.26 5.6

25 0.382 0.366 4.3 1.24 1.18 5.1

50 0.656 0.631 3.5 0.997 0.948 5.1

7,5 0.725 0.688 5.3 0.632 0.577 9.6

85 (1.595 0.530 12,2 0.414 0.338 22.5

Tabh, 67: ('Oral)arisen of the Reduced Force Coefficient measul"enlents for 1670 m/s (!O_ incident

upon lhe solar panel made with the carrier gases [12 and He.

0_ (degrees) .f, He .ft II.2 f, _7_Diff. J'_ He .f,, ti2 .f,, _/ I)ifl'.

0 0 0 0 1 9" .- t 1.21 5.3

25 (1.37,1 (1.381 1.7 1.19 1.13 5.:_

5/1 0.653 (1.661 1.2 0.961 0.891 7.8

75 [). 71.9 O.734 '2.1 0.588 [).51.9 13.4

85 0.608 0.562 8.3 0.368 11.288 27.6

77
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1. AGENCY USE ONLY (Leave Blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

November 1997 NASA Technical Paper

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Measurement of Momentum Transfer Coefficients for H2, N2, CO, and CO2 Incident Upon

Spacecraft Surfaces

6. AUTHOR(S)

Steven R. Cook* and Mark A. Hoffbauer*

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Lyndon B. Johnson Space Center

Houston, Texas 77058

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

8. PERFORMING ORGANIZATION

REPORT NUMBERS

S-834

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

TP 3701

11. SUPPLEMENTARY NOTES

* Los Alamos National Laboratory

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified/unlimited

Available from the NASA Center for AeroSpace Information (CASI)

800 Elkridge Landing Rd

Linthicum Heights, MD 21090-2934 (301) 621-0390 Subject Category: 15

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Measurements of momentum transfer coefficients were made for gas-surface interactions between the Space Shuttle reaction control

jet plume gases and the solar panel array materials to be used on the International Space Station. Actual conditions were simulated

using a supersonic nozzle source to produce beams of the gases with approximately the same average velocities as the gases have in

the Shuttle plumes. Samples of the actual solar panel materials were mounted on a torsion balance that was used to measure the force

exerted on the surfaces by the molecular beams. Measurements were made with H2, N2, CO, and CO2 incident upon the solar array

material, Kapton, SiO2-coated Kapton, and Z93-coated AI. The measurements showed that molecules scatter from the surfaces more

specularly as the angle of incidence increases and that the scattering behavior has a strong dependence upon both the incident gas and

velocity. These results show that for some technical surfaces the simple assumption of diffuse scattering with complete thermal

accommodation is entirely inadequate. It is clear that additional measurements are required to produce models that more accurately

describe the gas-surface interactions encountered in rarefied flow regimes.

14. SUBJECT TERMS

solar arrays, plumes, momentum transfer, rarefied gas dynamics

15. NUMBER OF

PAGES

81

16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION

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Prescribed by ANSI Std. 239-18

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19. SECURITY CLASSIFICATION

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20. LIMITATION OF ABSTRACT

None