Robert A. Ziemke

Glenn Research Center, Cleveland, Ohio

Solar Simulation for the CREST Preflight

Thermal-Vacuum Test at B-2

NASA/TM—2013-217720

March 2013
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Robert A. Ziemke

Glenn Research Center, Cleveland, Ohio

Solar Simulation for the CREST Preflight

Thermal-Vacuum Test at B-2

NASA/TM—2013-217720

March 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Aerospace Testing Seminar (ATS)

sponsored by The Aerospace Corporation

Los Angeles, California, October 16–18, 2012
Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

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Trade names and trademarks are used in this report for identification 

only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2013-217720 iii

Contents

Abstract..........................................................................................................................................................................1

Introduction ...................................................................................................................................................................1

Requirements.................................................................................................................................................................1

Engineering Approach...................................................................................................................................................1

The Line Sources...........................................................................................................................................................3

Projected Longitudinal Flux Distribution...............................................................................................................3

Projected Normal On-Axis Output Level...............................................................................................................4

Projected Radial Flux Distribution .........................................................................................................................4

Sizing the Planar Arrays................................................................................................................................................6

Layout of the Planar Arrays...........................................................................................................................................7

Optimizing Flux Uniformity..........................................................................................................................................7

The Crest Planar Arrays ................................................................................................................................................9

Setting the Infrared Flux Density Levels.....................................................................................................................11

Terrestrial Sun Level ............................................................................................................................................11

Surface Film Evaluation .......................................................................................................................................13

Aluminized Mylar Skin.................................................................................................................................13

Silvered Teflon Skin......................................................................................................................................13

Corrections to SSA...............................................................................................................................................14

Power Regulation Methodology ..................................................................................................................................14

Corrections to Automatic Control Setpoints.........................................................................................................14

Corrections to Manual Setpoints ..........................................................................................................................15

Conclusion...................................................................................................................................................................16

Appendix A.—Distance Exponent Development ........................................................................................................17

Appendix B.—B-2 Power Control Capability.............................................................................................................19

Appendix C.—Spreadsheets........................................................................................................................................21

Spreadsheet C.1 ....................................................................................................................................................21

Spreadsheet C.2 ....................................................................................................................................................22

Spreadsheet C.3 ....................................................................................................................................................23

Spreadsheet C.4 ....................................................................................................................................................24

Spreadsheet C.5 ....................................................................................................................................................25

Spreadsheet C.6 ....................................................................................................................................................26

Spreadsheet C.7 ....................................................................................................................................................27

Spreadsheet C.8 ....................................................................................................................................................28

Spreadsheet C.9 ....................................................................................................................................................29

Spreadsheet C.10 ..................................................................................................................................................30

Spreadsheet C.11 ..................................................................................................................................................31

Spreadsheet C.12 ..................................................................................................................................................32

Spreadsheet C.13 ..................................................................................................................................................33

Spreadsheet C.14 ..................................................................................................................................................34

Spreadsheet C.15 ..................................................................................................................................................35

Spreadsheet C.16 ..................................................................................................................................................36

References ...................................................................................................................................................................37

Biography ....................................................................................................................................................................37

NASA/TM—2013-217720 1

Solar Simulation for the CREST Preflight

Thermal-Vacuum Test at B-2

Robert A. Ziemke

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

In June 2011, the multi-university sponsored Cosmic Ray 

Electron Synchrotron Telescope (CREST) has undergone 

thermal-vacuum qualification testing at the NASA Glenn 

Research Center (GRC), Plum Brook Station, Sandusky, Ohio. 

The testing was performed in the B-2 Space Propulsion 

Facility vacuum chamber. The CREST was later flown over 

the Antarctic region as the payload of a stratospheric balloon.

Solar simulation was provided by a system of planar infrared 

lamp arrays specifically designed for CREST. The lamp 

arrays, in conjunction with a liquid-nitrogen-cooled 

cryoshroud, achieved the required thermal conditions for the 

qualification tests. This report focuses on the design and

analysis of the planar arrays based on first principles.

Computational spreadsheets are included in the report.

Introduction

Since the B-2 chamber currently has no large-aperture 

collimated solar simulator, it was decided to utilize 

components of the existing B-2 infrared (IR) thermal

simulator to produce the incident flux needed for the CREST 

thermal-vacuum test. A sufficient quantity of 12 ft infrared 

line sources and power control channels were available. These 

were recently refurbished to operational status, and appeared 

to be a good fit for this application considering the size of the 

test article and the quantity of units available. The line sources 

were assembled into planar arrays, each incident on the 

appropriate test article surface.

From the beginning it was readily apparent that the solar 

and infrared spectra had to be reconciled and the incident 

infrared flux density adjusted to transfer the correct solar 

energy equivalent to the test article.

Requirements

With the B-2 vacuum chamber operating at 3 torr, and the 

cryoshroud at 77.2 K, provide the following solar simulation:

1. The equivalent heating of one low Earth orbit (LEO) sun

at 1 AU at 22° incident on the front (+X) and top (+Y) 

surfaces of the test article.

2. The equivalent heating of earth’s albedo at levels of 0.65 

and 0.95 LEO sun incident on the bottom (–Y) surface of 

the test article.

3. Manually controlled auxiliary heating at a level of 

0.5 LEO sun incident toward the rear (–X) surface of the 

test article.

4. While the incident flux uniformity wasn’t specified by 

the customer, a nominal tolerance band of ±5 percent 

was mutually agreed upon by the customer and NASA.

Engineering Approach

The Antarctic LEO sun was resolved into horizontal and 

vertical components of 0.927 and 0.375 sun, respectively, with 

separate planar lamp arrays provided for the front and top 

surfaces. The bottom surface (albedo) was heated by a third 

array, and a single line array was provided to supply auxiliary 

heat to the rear surface of the test article. A profile of the 

complete test setup is shown in Figure 1. The terms “surface,” 

“face,” and “zone” all refer to the heated outer surfaces of the 

test article and are used interchangeably throughout this 

report.

The infrared line sources were assembled into appropriately 

sized planar arrays. The line sources were spaced and aimed, 

and their individual power levels proportioned to optimize the 

transverse (perpendicular to line source axis) incident flux 

uniformity of each planar array. In Figure 1, the end view of 

each line source is shown. Figure 2 and Figure 3 show a 

portion of the arrays as installed in the vacuum chamber.

In the longitudinal (parallel to line source axis) direction, 

the line sources introduce the usual fall-off of flux density 

each side of center. The line sources also overhang the test 

article width somewhat, producing a small amount of heating 

on its normally dark side surfaces. Both of these undesirable 

characteristics are difficult to correct and were accepted by the 

customer as necessary tradeoffs. 

The incident flux uniformity in the transverse direction was 

optimized based on theoretical prediction. Verification by 

optical scanning was considered, but was beyond the scope and 

budgetary constraints of this qualification test. According to the 

customer, it was sufficient that the average heating of each 

surface be equivalent to that produced by the 22° LEO sun.

Inside the vacuum chamber, the incident infrared flux levels 

were set to produce average surface heating equivalent to that of 

the 22° LEO sun, taking into account the optical properties of 

the surface films. The flux level settings were based on 

measurement of radiant energy absorbed by film test samples 

exposed first to the terrestrial sun and then to the infrared lamp 

arrays.
NASA/TM—2013-217720 2

Figure 1.—Layout of infrared lamp arrays, CREST thermal-vacuum test.
NASA/TM—2013-217720 3

Figure 2.—CREST package with top array and front array 

(far left).

Figure 3.—Top array lit during electrical checkout.

Figure 4.—Parabolic reflector and its adjustable mounting.

The Line Sources

Each 12 ft line source consists of 16 parallel-connected 120 V

750 W infrared quartz T3 lamps with the filaments collinearly 

oriented and closely spaced. The lamps share a common highgain faceted aluminum parabolic reflector which projects a 

narrow wedge of illumination at high intensity. The reflector is 

cooled by radiation. See Figure 4.

When assembling a group of line sources into a planar 

array, the line sources must first be characterized. Following is 

a description of the three fundamental line source 

characteristics. 

Projected Longitudinal Flux Distribution

The longitudinal projection characteristic of a single 12 ft 

line source is described by the following sequence of 

equations. This is a two-dimensional description where the 

line source and receiving line lie in the same plane. The 16 

lamp filaments, each considered a unit point source, are 

oriented parallel to the receiving line. The flux density 

contribution (ETU) at the receiving line of each point source is 

given by:

XT XS

YS YT A −− = − −1 tan (1)

2 2 S = (YS −YT) + (XT − XS) (2)

2

2 cos

S

A ETU = (3)

where 

ETU unit flux density contribution at receiving line 

S oblique distance from point source to receiving point

A source angle and angle of incidence at receiving line 

(radians)

XS horizontal source distance from origin to line array 

(ft)

YS vertical distance from origin to point source (ft) 

XT horizontal distance from origin to receiving line 

YT vertical distance from origin to receiving point (ft)

For the longitudinal projection, each filament is treated as a 

point source if S is greater than or equal to ten times the 

filament length. Otherwise, the filaments should be divided 

into smaller elements and the elements treated as point 

sources. As shown in Figure 5, each sampled point on the 

receiving line represents a summation of the flux contributions 

from all 16 point sources. Figure 6 and Spreadsheet C.1 show 

the longitudinal flux distribution along the receiving line at a 

projection distance of 6 ft. The parabola-like flux density falloff each side of center is an intrinsic projection characteristic 

of a line source. 
NASA/TM—2013-217720 4

Figure 5.—Flux summation at receiving line.

Figure 6.—Line source longitudinal flux distribution.

Projected Normal On-Axis Output Level

The flux producing capability of the line sources was 

determined by measurements made in the B-2 vacuum 

chamber during the course of the Integrated Systems Test 

(IST) conducted in April 2011. At full lamp voltage (120 V), 

three 12 ft line sources stacked vertically end-to-end produced 

approximately 1500 W/m2 as read by a Hukseflux SR03-C01-

05 thermopile pyranometer located at the midpoint, at a 

normal distance of 6 ft from the lamp filaments. Since the line 

sources were not stacked for the CREST test, the Hukseflux 

reading was converted to indicate what would have been 

generated by energizing the center 12 ft line source only.

By treating each lamp filament as a point source, the flux 

contributions of each filament were calculated using Equations 

(1), (2), and (3) and summed at the sensor location. This twodimensional analysis was performed in Spreadsheet C.2 for 

both the 12 ft case and the 36 ft case. The flux density 

conversion was accomplished using the following 

proportionality. 

36

36 12

12 ET

EO ET EO ⋅ = (4)

where

EO12 calculated normal on-axis flux density of a single 12 

ft line source at 6 ft (W/m2

)

EO36 measured normal on-axis flux density of 36 ft line 

source at 6 ft (W/m2

)

ET12 average unit flux density at sensor from 12 ft unit 

line source (see Spreadsheet C.2)

ET36 average unit flux density at sensor from 36 ft unit 

line source (see Spreadsheet C.2)

Therefore,

2 2

12 1247 W/m

0.344

(1500 W/m ) (0.286) = ⋅ EO = 

This result is a prediction of the full power radiant output of a 

single 12 ft line source that would have been read by the 

Hukseflux sensor at a normal distance of 6 ft from the source 

center. 

Projected Radial Flux Distribution

The radial directional characteristic of a single line source is 

shown in Figure 7. This polar plot (Ref. 1) was produced by 

direct measurement of a 12 ft lamp/reflector assembly as part 

of the original acceptance testing of the B-2 thermal simulator 

components performed in 1965. Figure 8 shows the 

normalized directional characteristic in Cartesian form. 

The following equation was developed to emulate the radial 

directional characteristic as a spreadsheet formula. It was finetuned by adjusting the exponents and angular coefficients to 

obtain a behavior that closely approximates the original 

directivity data. 

13.1

(| 57.3 | 1)

cos(15 ) 16cos 2.9 0.2

16 















+ −

= A

A A

D (5)

where

D normalized radial directivity function

A source angle or angular deviation from normal (radians)

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Package

W=8.7 ft
NASA/TM—2013-217720 5

Figure 7.—Radial directional characteristic.

Figure 8.—Measured radial directivity.

Figure 9.—Emulated radial directivity.

Direct radiation from the filaments at large angles (± 20° to

± 40°) was not included in the emulation. Figure 9 shows a 

directivity plot of Equation (5). Spreadsheet C.3 shows the 

original measured directivity data along with the emulated 

directivity data.

The following sequence of equations mathematically 

projects the flux density contribution of a single 12 ft line 

source onto the receiving plane. Here, the line source and 

receiving plane, or test article surface, are both perpendicular 

to and are bisected by the XY plane, and their intersections 

with the plane represent a point source and transverse 

receiving line respectively in the two-dimensional analysis.

Figure 10 shows the geometric relationship of the projection. 

The projection is a locus of points (ET as a function of YT) 

along the receiving line describing the transverse flux density 

distribution. Note that once the projection occurs, the flux 

distribution terminology transitions from “radial” to 

“transverse”. The flux density (ET) at each sampled point on 

the receiving line is given by:

XT XS

YS YT A −

− = − −1 tan (1)

2 2 S = (YS −YT) + (XT − XS) (2)

G = −B + A (6)

13.1

(| 57.3 | 1)

cos(15 ) 16cos 2.9 0.2

16 















+ −

= G

G G

D (7)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-90-80-70-60-50-40-30-20-10 0 10 20 30 40 50 60 70 80 90

Normalized Level

Deviation from Normal (°)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-90-80-70-60-50-40-30-20-10 0 10 20 30 40 50 60 70 80 90

Normalized Level

Deviation from Normal (°)
NASA/TM—2013-217720 6

Figure 10.—Flux projection from a single source.

( ) U S

R ET = 2.93(EO12 )D cos A (8)

where

ET flux density at receiving line (W/m2

)

A source angle and angle of incidence at receiving line 

(radians)

S oblique distance from point source to receiving line 

(ft) 

G substitution variable (–B+A)

D normalized radial directivity function

B reflector offset angle (radians)

R original (IST) source-to-sensor distance (6 ft)

U 1.6 (see Appendix A)

EO12 1247 W/m2 (from Eq. (4))

XS horizontal source distance from origin to line array 

(ft)

YS vertical distance from origin to point source (ft)

XT horizontal distance from origin to receiving line (ft)

YT vertical distance from origin to receiving point (ft)

Figure 11 and Spreadsheet C.4 show the projected 

transverse flux distribution for a single line source. Note that 

Equation (8) is referenced to a 6 ft source-to-sensor distance, 

i.e., when S = 6 ft and A = 0 radians, the value of ET is EO12

(1247 W/m2

).

Sizing the Planar Arrays

The size of an array refers to its area as well as the quantity 

and wattage of the IR lamps employed. For the CREST test 

the lamps are arranged in collinear groups of 16, each forming 

a 12 ft line source, so the design challenge is to determine the

Figure 11.—Projected transverse flux distribution with line 

source at 6-ft distance.

number and spacing of the line sources for each heated face of 

the test article, such that each array will have sufficient 

heating capacity plus a generous (at least 50 percent) margin.

Initially we are merely estimating the number of line 

sources needed in the array based on the response of the 

Hukseflux pyranometer to the IR-rich lamp spectrum. In terms 

of infrared heating capability, this estimate will be 

conservative because the Hukseflux (wavelength range 0.305

to 2.8 μm) favors the solar spectrum, but is blind to much of 

the long wave radiation produced by the lamps (Ref. 2).

Assuming an original in-chamber measurement of EO36 at 6 ft, 

the size of each lamp array can be estimated as follows:

0

200

400

600

800

1000

1200

1400

1600

-5 -4 -3 -2 -1 0 1 2 3 4 5

Incident Flux Density (W/m2)

Distance from Center (ft)
NASA/TM—2013-217720 7

(2.93)

1.6

12 ⋅ = ⋅ ⋅ ⋅

R

S

WS

WT

EO

ES NE SF (9)

where

NE estimated number of line sources in planar array

SF required incident sun fraction

ES 1370 W/m2 (one LEO sun)

EO12 1247 W/m2 (from Eq. (4))

WT transverse length of test article face (ft)

WS projected transverse beam width at 1⁄2 power points 

(ft)

S normal distance from filament plane to test article 

surface (ft)

R original (IST) source-to-sensor distance (6 ft)

Example:

For the CREST bottom zone:

(6ft) (2.93)

6 ft

3.4ft

10.4ft

1247W/m

1370 W/m 0.95

1.6

2

2

⋅ = ⋅ ⋅ ⋅ NE = 3.19

In order to reduce the tendency of developing a hot spot at 

the center of the zone, it is desirable not to have a line source 

at the transverse center of the array. It is also desirable to 

preserve symmetry about the transverse center when laying 

out the array. Therefore N, the number of line sources in the 

array, should be an even integer. The value N is then rounded 

up to the next higher even integral value, and the margin (M) 

and relative lamp power (RLP) values calculated over a range 

of increasing even values of N.

1 ⋅100 













 = − NE

N M = ⋅100

N

N RLP E

For N = 4: M = 25.4 percent RLP = 79.8 percent

For N = 6: M = 88.1 percent RLP = 53.2 percent 

For N = 8: M = 151 percent RLP = 39.9 percent

From a flux density margin standpoint, the N = 6 case 

would probably be a good choice. In producing 0.95 IR suns, 

the lamps would run at only 53.2 percent of their full power 

capability, thus assuring long lamp life. However, for the 

CREST bottom zone it was decided to err toward the 

conservative and go with N = 8 for the following reasons:

a. Our design experience with these line sources was 

limited.

b. A higher value of N would enhance the transverse 

incident flux uniformity.

c. Tight scheduling required that the arrays be designed 

before the analysis tools were fully developed.

The sizing method just described provides the starting point 

for the layout and optimization processes. Compared to the 

final optimized array, it tends to overestimate the margin 

somewhat because it doesn’t take into account the measures 

implemented to optimize the transverse flux uniformity.

Layout of the Planar Arrays

For the CREST configuration, array layout means 

transverse positioning and spacing of the line sources within 

the boundaries of the heated zone. The end line sources are 

positioned near the boundaries but must remain within the 

boundaries to prevent crosstalk to the adjacent zones. The 

remaining line source positions should initially be evenly 

spaced between the end ones, with all positions symmetrical 

about the center of the zone. When optimizing the flux 

uniformity it may be necessary to introduce a mild spacing 

gradient favoring the zone boundaries, while still maintaining 

symmetry about the center. The gradient will compensate for 

the natural flux density falloff as the boundaries are 

approached (Ref. 3).

Each power controller channel is capable of powering three 

line arrays. For the CREST test each channel powers a 

transverse symmetrical pair of line sources. In addition to 

providing a well-balanced array, the symmetry serves as a 

trouble-shooting aid if a layout or computational problem arises. 

If possible, the final line source positions should be 

specified to fall on major division markings of the layout ruler 

to aid the technician in positioning the line sources. It’s highly 

recommended to make all line source positions and aiming 

angle settings mechanically adjustable.

Optimizing Flux Uniformity

The sizing and layout methods just described will produce 

an array that is conservative in terms of flux density margin 

and lamp operating level. In general, flux uniformity and 

layout take precedence over sizing, and the array margin is 

increased as necessary to fulfill a desired layout sweet spot. As 

the number of line sources grows, the electrical power level 

can be reduced accordingly to maintain the correct average 

incident flux density level.

In the longitudinal direction, the flux uniformity for an array 

of line sources is described by Equations (1), (2), and (3), 

Figure 6, and Spreadsheet C.1. The parabola-like fall-off is 

intrinsic to the line source and little can be done to improve 

the longitudinal flux uniformity. This characteristic can be 

flattened somewhat by removing a few central lamps or by 

decreasing the distance from the array to the irradiated 

surface. However, for the CREST test, the customer agreed to 

live with the amount of fall-off shown in Figure 6, across the 

width of the test article, with the line source bars fully 

populated with lamps.

In the transverse direction, three line source adjustment 

parameters (degrees of freedom) exist and are defined as 

follows:

1. Line Source Position

a. The transverse distance of a line source to the array 

centerline.

2. Offset Angle
NASA/TM—2013-217720 8

a. The transverse angular deviation of line source 

reflector from normal incidence.

3. Power Ratio

a. The power drive level of an individual line source 

within an array divided by the maximum line source 

drive level within the array. This ratio is expressed as 

a percentage. One 100 percent channel per array is 

considered the master to which all others are slaved 

by an assigned power ratio. Normally the line 

sources of like power ratio are paired symmetrically 

about the center. 

The flux uniformity optimization process is a trial and error 

procedure whereby the designer manually adjusts the above 

parameters in a two-dimensional mathematical model of the 

array and observes the effect of each adjustment on the 

calculated transverse flux distribution. The optimizations are 

performed for each degree of freedom in the order shown 

above.

The mathematical model produces a summation of the flux 

contributions of all the line sources within the array at each 

selected sampling point on the receiving line. The model is 

based on Equations (1), (2), (6), (7), and (8), and is 

implemented in Spreadsheet C.4 through Spreadsheet C.13. 

For each line source, the designer inputs the parameters XS, 

YS, XT, YT, B, and E0 in the columns, and the output produced 

is a plot of relative flux density versus distance from the center 

of the receiving line. Also, the average flux density (ET

average) at the longitudinal center of the zone is calculated 

and should be monitored as the optimization proceeds. If the 

average flux density is not satisfactory it might be necessary to 

adjust N (the number of line sources in the array) up or down 

to restore the desired margin. It also may be necessary to 

increase N in order to achieve satisfactory transverse flux 

uniformity.

The bottom (albedo) zone is used as a design example. 

Figure 12 and Spreadsheet C.5 show the flux uniformity 

obtained with the line source positions shown in Figure 1, with 

B = 0, and the power ratios at 100 percent. For CREST the line 

source positions were not optimized, but were based on a best 

guess because the analysis tools were not fully developed 

when the line source positions for all the zones were specified. 

This was done so that the mechanical build-up could proceed 

on schedule.

Figure 13 and Spreadsheet C.6 show the flux uniformity 

obtained with the tilt angles (B) optimized, and Figure 14 and 

Spreadsheet C.7 show the flux uniformity obtained with the 

power ratios also optimized. The final angles and power ratios 

for the bottom zone are shown in Figure 1. The improvement 

in uniformity obtained at each level of optimization is readily 

apparent. It was necessary to tilt the end line sources out 

almost beyond the zone boundaries in order to keep the flux 

density relatively flat out to the boundaries. Figure 15 and 

Spreadsheet C.8 show an overlay of the optimized 

contributions of each of the line sources.

Figure 12.—Bottom zone not optimized.

Figure 13.—Bottom zone tilt angles optimized.

Figure 14.—Bottom zone tilt angles and power ratios optimized.

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Bottom

L=8.75 ft

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Bottom

L=8.75 ft

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Bottom

L=8.75 ft
NASA/TM—2013-217720 9

Figure 15.—Bottom zone line array contributions superimposed. Figure 16.—Top zone tilt angles and power ratios optimized.

TABLE 1.—CREST PLANAR ARRAYS

Zone Face 

dimensions,

ft by ft

Required 

flux 

density,

LEO suns

Full power

flux 

density,

IR suns

Full power

flux 

density,

W/m2

Line

sources,

N

Total 

lamps,

750 W ea.

Max.

power,

kW

Distance 

to face

[XT-XS], 

ft

Figure Spreadsheet

Bottom 8.75 by 8.7 0.95 2.15 2943 8 128 96 6 Figure 14 Spreadsheet C.7

Top 10.6 by 8.7 0.375 1.2 1638 6 96 72 8 Figure 16 Spreadsheet C.9

Front Upper 2.08 by 8.7 0.927 2.04 2793 2 32 24 6 Figure 17 Spreadsheet C.10

Front Lower 2.69 by 8.7 0.927 1.64 2252 2 32 24 6.83 Figure 18 Spreadsheet C.11

Rear ------------ 0.5 1.37 1880 1 16 12 4.27 Figure 22 Spreadsheet C.13

The Crest Planar Arrays

The solar simulation system built for the CREST thermalvacuum test consisted of three planar arrays, each made up of 

several 12 kW infrared line sources. In each array, the 12 ft

line sources spanned the 8.7 ft width of the test article with an 

overhang of approximately 1.6 ft on each side. Figure 1 shows 

the side view of the arrays, where the axes of the line sources 

are normal to the plane of the figure. The line sources for each 

zone were supported by a steel frames which surrounded the 

test article. The frames held the line sources in the positions 

and at the tilt angles specified in Figure 1. The transverse 

positions and angles were made adjustable by design.

Of the twelve 36 kW SCR power controllers available at the 

facility, ten were used to power the infrared lamps. Two 

12 kW line sources were assigned to each power control 

channel, where each line source of the pair were placed 

symmetrically about the center of each zone. Each pair is 

identified by a like control channel number in Figure 1. The 

previously discussed power ratios, also symmetrical about 

each zone center, are shown in Figure 1. Table 1 summarizes

the sizing parameters of each CREST array, and lists the 

spreadsheet and figure numbers associated with the flux 

uniformity optimizations for each zone.

The front face of the CREST package was split into two 

zones separated by a thin galvanized steel shield plate as 

shown in Figure 1. The front upper zone surface (detector 

housing), covered with aluminized Mylar film, projected out 

11 in. from the lower surface (gondola) which was wrapped 

with a silver-Teflon film. Since the two films have different IR 

absorption characteristics, it was necessary to operate the 

upper and lower lamp banks at different power levels. The 

shield plate prevents radiant crosstalk between these zones.

The shield plate also acts as a partial reflector, producing an 

image of the two line sources of the zone. The reflectivity of 

the galvanized plate was assumed to be approximately 0.5, 

making the image contribution to the incident flux half that of 

the direct line sources. The images are entered into 

Spreadsheet C.10 and Spreadsheet C.11 as additional sources 

of reduced intensity at the image positions. Thus, the images 

are taken into account when optimizing the flux uniformity for 

these two zones. The theoretical flux uniformities achieved are 

shown in Figure 17 and Figure 18.

Figure 19 and Figure 20 show the transverse distribution of 

the flux incident on the bottom surface of the front and rear 

projections. These distributions are referenced to the average 

flux incident on the bottom face of the gondola. They take into 

0

200

400

600

800

1000

1200

1400

1600

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Incident Flux Density (W/m2)

Distance from Center (ft)

CREST Bottom

L=8.75 ft

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Top

L=10.6 ft
NASA/TM—2013-217720 10

account the shadows introduced by the gondola front and rear 

lower edges, and the reflections introduced by the silverTeflon film wrap on its front and rear faces. The simulation of 

shadows and reflections was accomplished by the use of 

correction coefficient columns in Spreadsheet C.12 to correct 

the incident flux density. For the shadows, a coefficient of 

1.000 transitioning to 0.000 was used to go from full 

transmission to full extinction. For the reflections, a direct 

incidence coefficient of 1.000 transitioning to 1.900 (direct 

plus reflected) was used. The width of the transitions (approx. 

0.67 in.) as projected onto the bottom surfaces are an 

approximate 3:1 reduction of the line source reflector width of 

approximately 2.0 in. The geometry describing the shadow 

and reflection boundaries is shown in Figure 21.

Figure 17.—Upper front zone optimized.

Figure 18.—Lower front zone optimized.

Figure 19 and Figure 20 show that the incident flux density at 

bottom surface of the projections is quite low (less than 

60 percent of the flux density at the gondola bottom surface). 

This is mainly due to the shadows and the increased distance 

from the bottom lamps. Because of this, supplementary heating 

was provided at the rear of the package at the customer’s 

request, to be used if needed to prevent this area of the package 

from becoming too cold. This heating capability, composed of a 

single line source, is identified as control channel 20 in 

Figure 1. Its incident flux density and directional characteristic 

are described in Figure 22 and Spreadsheet C.13.

Figure 19.—Simulated albedo illumination of front projection 

bottom.

Figure 20.—Simulated albedo illumination of rear projection 

bottom.

-25

-20

-15

-10

-5

0

5

10

15

20

25

-3 -2 -1 0 1 2 3

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Front

H=2.08 ft

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-3 -2 -1 0 1 2 3

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Front

H=2.69 ft

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

-5.3 -5.2 -5.1 -5.0 -4.9 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Front Projection

D=0.92 ft

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3

Relative Flux Density (percent)

Distance from Center (ft)

CREST

Rear Projection

D=0.92 ft
NASA/TM—2013-217720 11

Figure 21.—Shadow and reflection boundaries affecting simulated albedo illumination of front

projection bottom.

Figure 22.—Rear supplementary heat distribution.

Setting the Infrared Flux Density Levels

As mentioned previously, the CREST package was wrapped 

with two skin materials. The detector housing (the long upper 

portion) was wrapped with 4 mil aluminized Mylar film, while 

the gondola (shorter lower section) was wrapped with 5 mil 

silvered Teflon film. See Figure 1. The optical properties of 

these materials are wavelength sensitive and exhibit different 

absorption characteristics under T3 incandescent lamp 

illumination (2500 K) versus LEO solar illumination (6000 K). 

The optical properties of the skins under 2500 K illumination 

were not readily available from the manufacturers. 

The objective is to simulate the LEO solar illumination 

using the T3 incandescent lamps in the vacuum chamber 

adjusted to transmit the equivalent heat flux is through the 

skins. The T3 illumination levels were developed using an

empirical approach based on field measurements of terrestrial 

solar flux absorbed by skin samples. An instrument rake 

consisting of a 1 in. thick aluminum heat sink plate equipped 

with a Hukseflux SR03-C01-05 thermopile pyranometer and 

two Omega HFS-4 thin film thermopile heat flux sensors was 

constructed to enable the field measurements. See Figure 23. It 

is assumed that the spectral differences between the terrestrial 

sun and the LEO sun do not significantly affect the energy 

absorbed by the skins.

Terrestrial Sun Level

With the instrument rake set-up outdoors at high noon, the

Hukseflux pyranometer was used to measure the density of the 

terrestrial sun flux incident on the rake. See Figure 23. The 

measurement was obtained by “shuttering” or intermittently 

casting a shadow on the pyranometer, where the terrestrial sun 

flux density was read as the difference between direct incident 

sun and shadow (diffuse skylight). A calibrated strip chart 

0.0

0.5

1.0

1.5

2.0

-20 -15 -10 -5 0 5 10 15 20

Incident Flux Density (IR suns)

(S = 4.35 ft)

Deviation (°) from 32° Center
NASA/TM—2013-217720 12

recorder was used to record the pyranometer signal. See 

Figure 24 (lower trace). The TSL was calculated as follows:

C D

A B TSL ⋅

⋅ = (10)

where

TSL terrestrial sun level (expressed in LEO suns)

A pyranometer signal amplitude (expressed in chart div)

B chart recorder calibration (uV/div)

C pyranometer sensitivity (uV/W-m2

)

D LEO solar constant (W/m2

)

Therefore,

( ) ( )

( ) 0.661LEO sun

8.8 W/m (1370 W/m -LEOsun)

3.982 2000

2 2 = ⋅

⋅

=

uV

div uV div

TSL

Figure 23.—Instrument rake set-up outdoors with Hukseflux 

Pyranometer (rear), and thin film heat flux sensors with 

material samples (front and left).

Figure 24.—Outdoor “shuttered” measurement of ISA for aluminized Mylar (upper trace) and 

accompanying pyranometer signal (lower trace).
NASA/TM—2013-217720 13

Surface Film Evaluation

Aluminized Mylar Skin

The solar radiation absorption properties of the 4 mil 

aluminized Mylar film (second surface mirror side facing the 

Sun) were explored by attaching a sample to one of the Omega 

thin film thermopile heat flux sensors and exposing it to the 

terrestrial Sun. The back side of the sensor was adhered to the 

aluminum heat sink plate which was kept at ambient 

temperature prior to Sun exposure. A cardboard tube was 

installed to shield the sensor from outdoor wind disturbance. 

The sensor was shuttered from sun to shadow as previously 

described, and its output recorded on the strip chart. See Figure 

24 (upper trace). The ISA, expressed in chart units (div), was 

read from the chart as step transitions between direct incident 

Sun and shadow. In generating the chart of Figure 24, the 

Omega sensor and the Hukseflux pyranometer were shuttered 

and recorded simultaneously to minimize differential errors 

caused by minor atmospheric and/or incident angle dynamics. 

The solar incident angle was manually kept very close to zero 

during the measurement period.

Using the TSL as the basis, the ISA was scaled down based 

on the required flux density to give the SSA as shown below.

TSL

ISA F SSA ⋅ = (11)

where

SSA scaled solar absorption (expressed in chart div)

ISA indicated solar absorption (expressed in chart div)

F required flux density (expressed in LEO suns)

TSL measured terrestrial sun level (expressed in LEO 

suns)

Therefore, for a required level of 0.375 LEO suns (top zone):

( ) ( ) div div SSA 0.844

0.661 LEO sun

1.488 0.375 LEO suns = ⋅ =

The ISA and SSA values for all of the zones are given in Table 

2 and Spreadsheet C.14.

Silvered Teflon Skin

The 5 mil silvered Teflon (second surface mirror side facing 

the sun) didn’t absorb terrestrial solar energy well enough to 

permit a direct measurement of its ISA. Therefore, it was 

necessary to derive the ISA from the material’s solar 

absorptance. The typical solar absorptance was estimated at 

0.07 based on the manufacturers stated maximum value of 

0.09. The typical solar absorptance was converted to the 

equivalent ISA as follows: 

B

K ISA = J ⋅TSL ⋅ D⋅ (12)

where

ISA indicated solar absorption (expressed in chart div)

J solar absorptance for silvered Teflon (alpha)

TSL measured terrestrial sun level (expressed in LEO 

suns)

D LEO solar constant (W/m2

)

K heat flux sensor calibration (uV/W/m2

)

B chart recorder calibration (uV/div)

Therefore, for the bottom zone:

( )

( ) div

uV div

uV

ISA

0.697

200

2.2 W/m 1370W/m LEOsun

0.07 0.661 LEOsun

2 2 − ⋅ =

= ⋅ ⋅

This result together with the required heating flux density 

(expressed in LEO suns) was substituted into Equation (11) 

above to give the SSA for the bottom zone at 0.95 LEO suns as 

follows: 

TSL

ISA F SSA ⋅ = (11)

TABLE 2.—DEVELOPMENT OF CREST IN-CHAMBER ILLUMINATION LEVELS

Surface Face 

dimensions,

ft by ft

Required

flux density,

LEO suns

Skin

material

Skin

thickness,

mils

ISA,

div

SSA,

div

SSA

correction

CSSA,

div

Lg,

%

Xv,

%

Bottom 8.75 by 8.7 0.95 Silvered Teflon 5 0.697 1.002 8.0 0.5 1.087

0.65 0.685 8.0 0.5 0.744

Top 10.6 by 8.7 0.375 Aluminized Mylar 4 1.488 0.844 8.0 2.5 0.933

Front upper 2.08 by 8.7 0.927 Aluminized Mylar 4 1.488 2.087 8.0 2.0 2.295

Front lower 2.69 by 8.7 0.927 Silvered Teflon 5 0.697 0.977 8.0 2.5 1.080

Rear ------------ 0.25 Aluminized Mylar 4 1.488 0.563 8.0 –3.0 0.591

0.5 1.126 8.0 –3.0 1.182

0.75 1.688 8.0 –3.0 1.773
NASA/TM—2013-217720 14

( ) ( ) div div SSA 002.1

661.0 LEOsun

95.0697.0 LEOsun = ⋅ =

A later search of spacecraft thermal-control coating 

characteristics revealed that the correct solar absorptance for 

5 mil silvered Teflon (Ref. 4) is 0.08. However, 0.07 was the 

value used in the calculations for the CREST test. 

Corrections to SSA

Since, as previously shown, the flux distribution has 

residual transverse ripple and longitudinal parabola-like

falloff, the SSA must be adjusted so that the average flux 

density produced for the zone is very close to the required 

level. Figure 16 shows the transverse ripple of the top zone. It 

can be seen that the flux density is approximately 2.5 percent

high at the center (sensor location). Figure 6 shows the 

longitudinal distribution where the flux density is 

approximately 8 percent high at the center. Therefore, the SSA 

must be corrected as follows: 





 



 +

+=

100

1 Lg Xv SSACSSA (13)

where 

CSSA corrected scaled solar absorption (expressed in chart 

div) 

SSA scaled solar absorption (expressed in chart div) 

Lg deviation due to longitudinal flux density fall-off 

(percent) 

Xv deviation due to residual transverse ripple (percent) 

Therefore, for the top zone:

CSSA 933.0 div

100

5.20.8 1844.0  =



 



 +

+=

These corrections are summarized in Table 2 and Spreadsheet 

C.14 for all zones.

The instrument rake was then taken into the vacuum 

chamber, with the sensors placed at the center of the test 

article surface plane, and exposed to the quartz lamp arrays. 

See Figure 25. The voltage applied to the lamp array was

adjusted to produce the CSSA calculated above as indicated by 

the chart recorder. At this level, the heating of the sample by 

the IR lamps is equivalent to the heating produced by 

0.375 LEO suns. In effect, the IR heat lamps of the top zone

are now “calibrated” at this sun level, skin material, voltage 

level, and sensor location.

Figure 26 (upper trace) shows a typical dynamic response to 

a voltage step applied to the lamps. It is believed that the

initial rapid rise (right-hand side of chart) is caused by shortwave radiation directly from the lamp filaments, whereas the 

long exponential rise is due to radiation from the filaments

Figure 25.—Instrument rake setup in vacuum chamber. 

being absorbed by the quartz envelopes and reradiated at 

longer wavelengths as the envelopes heat up less rapidly. 

Power Regulation Methodology

A Hukseflux pyranometer was installed at the center of each 

illuminated face of the test article for the purpose of providing 

a feedback signal to stabilize the incident flux density level. 

Even though the pyranometer doesn’t cover the full infrared 

spectral range it was, in effect, “calibrated” when the lamp 

intensity levels were set in the chamber. These readings were 

subsequently used as setpoints for automatic closed-loop

control of the incident flux levels. As a backup, the manual 

settings required to achieve the required flux levels in the 

chamber were also recorded, and could have been applied if 

manual control would have become necessary.

Small corrections were applied to the setpoint and manual 

values to compensate for chart reading errors which occurred 

in the test chamber environment when the intensity levels 

were set. These are calculated as follows.

Corrections to Automatic Control Setpoints 

ICC

CSSA ACS HF ⋅= (14)

where 

ACS auto control setpoint (W/m2

) 

HF Hukseflux pyranometer reading (W/m2

) 

CSSA corrected scaled solar absorption (chart div) 

ICC final in-chamber chart setting achieved (chart div) 

Therefore, for the bottom zone:

ACS = ( ) div

div

076.1

09.1 W/m100 2 ⋅ = 101.3 W/m2
NASA/TM—2013-217720 15

Figure 26.—In-chamber step response of lamp-sensor system. Aluminized Mylar on thin film thermopile (upper 

trace) Hukseflux pyranometer signal (lower trace)

Corrections to Manual Setpoints

0.6





 



 = ICC

CSSA CM UM (15)

where

CM corrected manual setting (percent)

UM uncorrected manual setting (percent)

CSSA corrected scaled solar absorption (chart div)

ICC final in-chamber chart setting achieved (chart div)

Therefore, for the bottom zone:

CM = 

0.6

1.076

1.09 (21.0 percent) 



 





div

div = 21.2 percent

Note 1: For CM, 100 percent corresponds to the maximum 

voltage output (120 VAC) of the power control channel.

Note 2: The 0.6 exponent (Ref. 5) in Equation (15) accounts for 

the temperature-dependent filament resistance characteristic 

of incandescent lamps.

The above corrections as applied to the four control zones 

are calculated and summarized in Spreadsheet C.15 and Table 

3 respectively. The ACS values were dialed-in to the thermal 

simulator programmable logic controller (PLC) as incident 

flux density setpoints based on what the Hukseflux sensors are 

seeing. When it was time to “turn on” the sun, these setpoints 

were enabled, and the infrared lamp arrays came up to the 

proper level to produce the required simulated solar heating of 

the test article surfaces. The manually controlled auxiliary heat 

provided at the rear of the package successfully maintained 

this region above the safe low temperature limit.
NASA/TM—2013-217720 16

TABLE 3.—DEVELOPMENT OF CREST IN-CHAMBER POWER CONTROL LEVELS

Surface Original 

illumination 

source

Required 

flux 

density, 

LEO suns

Skin 

material

Master 

channel

Hukseflux 

reading, 

W/m2

Correction,

CSSA/ICC

Auto 

control 

setpoint,

W/m2

Uncorrected 

manual,

%

Correction,

CSSA/ICC0.6

Corrected 

manual, 

%

Bottom Albedo 0.95 Silvered Teflon 15 100 1.013 101.3 21 1.008 21.2

0.65 52 1.000 52.0 17 1.000 17.0

Top 22° Sun 0.375 Aluminized Mylar 12 191 0.979 187.0 36 0.987 35.5

Front upper 22° Sun 0.927 Aluminized Mylar 10 700 0.962 673.2 50 0.977 48.8

Front lower 22° Sun 0.927 Silvered Teflon a11 none none none 24.5 1.017 24.9

Rear Dark Side 0.25 Aluminized Mylar 20 none none none 31 1.007 31.2

0.5 51 1.011 51.6

0.75 69 0.987 68.1 a

Channel 11 command voltage slaved at 50.1 percent of channel 10.

Conclusion

This report described how we accomplished the solar 

simulation for CREST on a very tight time schedule, and to 

the extent possible, utilizing existing equipment. It heavily 

emphasized the development of planar arrays built from line 

sources, and the supporting theory. The customer was very 

pleased with the solar simulation achieved.
NASA/TM—2013-217720 17

Appendix A.—Distance Exponent Development

When the receiving point is at a far distance from the line 

source, i.e., where the separation distance is more than ten 

times the length of the line source, the incident flux density at 

the receiving point varies approximately as the inverse square

(Ref. 6) of the distance. When the receiving point is close to 

the line source, i.e., where the line source length is long 

compared to the separation distance, the incident flux density 

varies approximately as the inverse of the distance.

For the CREST test the transverse separation distances, (S) 

in Figure 10, ranged from 6 ft to approximately 13 ft.

Compared to the 12 ft line sources, these separation distances 

fall into the intermediate range which suggests an inverse 

exponent which is greater than unity, but less than two.

This was explored mathematically by analyzing a single 

12 ft line source where the receiving point was on a line 

perpendicular to and centered on the filament axis. The 

separation distance (XT-XS) was varied over the range of 6 to 

13 ft as shown in Spreadsheet C.16. Several inverse 

exponential functions of distance were evaluated, plotted, and 

compared to the finite element analysis generated reference 

function (ET sum). Each was plotted as a function of the 

separation distance as shown in Figure 27. It can be seen that

the inverse (1/S) and inverse squared 1/(S2

) functions diverged 

significantly from the reference, and the 1/(SSK

) function 

tracked the best. Error-wise the 1/(S1.6) function is almost as 

good, and was ultimately chosen for CREST analysis work 

because of its simplicity.

Figure 27.—Exponent development.

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

6 7 8 9 10 11 12 13

Deviation from Reference Fall-Off 

(Percent)

Distance XS-XT (ft)

 

 

 1/S

 1/S(MS+B)

 1/(SSK

) 

 1/S1.6

 1/S2

NASA/TM—2013-217720 19

Appendix B.—B-2 Power Control Capability

The B-2 facility is equipped with twelve 60 Hz variable 

voltage power supply channels feeding the vacuum chamber for 

the purpose of operating incandescent lamps or heaters. These 

are transformer isolated feeds, each supplying 0 to 120 VAC 

60 Hz single phase up to 50 KVA each. Each channel is SCR

phase-angle controlled, and driven by command signals from a 

remotely located Programmable Logic Controller (PLC). The 

command signals can be controlled manually, or automatically 

utilizing feedback parameters and Proportional-IntegralDerivative (PID) algorithms. The PLC human operator interface 

is located in a separate control building approximately 2300 ft

from the SCR power controllers.

NASA/TM—2013-217720 21

Appendix C.—Spreadsheets

Spreadsheet C.1

Column A

 ↓

CREST001C

ARRAY BAR AXIAL DISTRIBUTION 05/27/2011

Lamp XS(ft) YS(ft) XT EO(W/m2) YT A(rad) A(deg) S(ft) D ET(W/m2) ET Sum:

1.000 0.000 -5.625 6.000 1.000 4.400 1.031 59.099 11.683 0.514 0.002 0.221

2.000 0.000 -4.875 6.000 1.000 4.400 0.997 57.101 11.047 0.543 0.002

3.000 0.000 -4.125 6.000 1.000 4.400 0.958 54.862 10.425 0.576 0.003

4.000 0.000 -3.375 6.000 1.000 4.400 0.914 52.342 9.821 0.611 0.004

5.000 0.000 -2.625 6.000 1.000 4.400 0.864 49.499 9.239 0.649 0.005

6.000 0.000 -1.875 6.000 1.000 4.400 0.808 46.283 8.682 0.691 0.006

7.000 0.000 -1.125 6.000 1.000 4.400 0.744 42.640 8.156 0.736 0.008

8.000 0.000 -0.375 6.000 1.000 4.400 0.672 38.514 7.668 0.782 0.010

9.000 0.000 0.375 6.000 1.000 4.400 0.591 33.855 7.225 0.830 0.013

10.000 0.000 1.125 6.000 1.000 4.400 0.500 28.627 6.836 0.878 0.016

11.000 0.000 1.875 6.000 1.000 4.400 0.398 22.823 6.510 0.922 0.020

12.000 0.000 2.625 6.000 1.000 4.400 0.288 16.480 6.257 0.959 0.023

13.000 0.000 3.375 6.000 1.000 4.400 0.169 9.694 6.087 0.986 0.026

14.000 0.000 4.125 6.000 1.000 4.400 0.046 2.624 6.006 0.999 0.028

15.000 0.000 4.875 6.000 1.000 4.400 -0.079 -4.526 6.019 0.997 0.027

16.000 0.000 5.625 6.000 1.000 4.400 -0.201 -11.539 6.124 0.980 0.026

YT Values ET Sum ET Average Pct. Dev.

-4.400 0.221 0.264 -16.1

-4.200 0.227 0.264 -13.9

-4.000 0.233 0.264 -11.8

-3.800 0.238 0.264 -9.7

-3.600 0.243 0.264 -7.8

-3.400 0.248 0.264 -6.0

-3.200 0.252 0.264 -4.3

-3.000 0.257 0.264 -2.7

-2.800 0.261 0.264 -1.2

-2.600 0.264 0.264 0.1

-2.400 0.267 0.264 1.4

-2.200 0.270 0.264 2.5

-2.000 0.273 0.264 3.6

-1.800 0.276 0.264 4.5

-1.600 0.278 0.264 5.3

-1.400 0.280 0.264 6.0

-1.200 0.281 0.264 6.7

-1.000 0.283 0.264 7.2

-0.800 0.284 0.264 7.6

-0.600 0.285 0.264 7.9 Formulas:

-0.400 0.285 0.264 8.2 D = AVERAGE(C24:C68)

-0.200 0.286 0.264 8.3 E = (C-D)/D*100

0.000 0.286 0.264 8.4

0.200 0.286 0.264 8.3 I = -ATAN((C-G)/(D-B))

0.400 0.285 0.264 8.2 J = H*180/3.1416

0.600 0.285 0.264 7.9 K = ((C-G)^2+(D-B)^2)^0.5

0.800 0.284 0.264 7.6

1.000 0.283 0.264 7.2 N = COS(I)

1.200 0.281 0.264 6.7 O = F*N*COS(I)/K^2

1.400 0.280 0.264 6.0 P = SUM(O4:O19)

1.600 0.278 0.264 5.3

1.800 0.276 0.264 4.5

2.000 0.273 0.264 3.6 Macro:

2.200 0.270 0.264 2.5 Sub CERST001CM()

2.400 0.267 0.264 1.4 Dim i As Long

2.600 0.264 0.264 0.1

2.800 0.261 0.264 -1.2 For i = 24 To 68

3.000 0.257 0.264 -2.7 Cells(4, 7) = Cells(i, 2)

3.200 0.252 0.264 -4.3 Calculate

3.400 0.248 0.264 -6.0 Cells(i, 3) = Cells(4, 16)

3.600 0.243 0.264 -7.8 Next i

3.800 0.238 0.264 -9.7 End Sub

4.000 0.233 0.264 -11.8

4.200 0.227 0.264 -13.9

4.400 0.221 0.264 -16.1

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 6 Line Source Longitudinal

CREST

Package

W=8.7 ft.
NASA/TM—2013-217720 22

Spreadsheet C.2

Column A

 ↓

CREST001B

ARRAY BAR RATIO CALIBRATION 05/27/2011 06/14/2011 ET36

Lamp XS(ft) YS(ft) XT EO(W/m2) YT A(rad) A(deg) S(ft) D ET(W/m2) SUM(O4:O51)

1.000 0.000 0.375 6.000 1.000 18.000 1.243 71.200 18.618 0.322 0.000 0.344

2.000 0.000 1.125 6.000 1.000 18.000 1.229 70.427 17.910 0.335 0.000 "

3.000 0.000 1.875 6.000 1.000 18.000 1.215 69.590 17.205 0.349 0.000 "

4.000 0.000 2.625 6.000 1.000 18.000 1.199 68.682 16.504 0.364 0.000 "

5.000 0.000 3.375 6.000 1.000 18.000 1.181 67.694 15.808 0.380 0.001 "

6.000 0.000 4.125 6.000 1.000 18.000 1.163 66.615 15.117 0.397 0.001 "

7.000 0.000 4.875 6.000 1.000 18.000 1.142 65.433 14.431 0.416 0.001 "

8.000 0.000 5.625 6.000 1.000 18.000 1.119 64.133 13.753 0.436 0.001 "

9.000 0.000 6.375 6.000 1.000 18.000 1.094 62.700 13.082 0.459 0.001 "

10.000 0.000 7.125 6.000 1.000 18.000 1.067 61.113 12.420 0.483 0.002 "

11.000 0.000 7.875 6.000 1.000 18.000 1.036 59.349 11.769 0.510 0.002 "

12.000 0.000 8.625 6.000 1.000 18.000 1.001 57.381 11.131 0.539 0.002 "

13.000 0.000 9.375 6.000 1.000 18.000 0.963 55.175 10.507 0.571 0.003 "

14.000 0.000 10.125 6.000 1.000 18.000 0.920 52.696 9.900 0.606 0.004 "

15.000 0.000 10.875 6.000 1.000 18.000 0.871 49.899 9.315 0.644 0.005 " ET12

16.000 0.000 11.625 6.000 1.000 18.000 0.816 46.736 8.754 0.685 0.006 " SUM(O20:O35)

17.000 0.000 12.375 6.000 1.000 18.000 0.753 43.152 8.224 0.730 0.008 " 0.286

18.000 0.000 13.125 6.000 1.000 18.000 0.682 39.094 7.731 0.776 0.010 " "

19.000 0.000 13.875 6.000 1.000 18.000 0.602 34.508 7.281 0.824 0.013 " "

20.000 0.000 14.625 6.000 1.000 18.000 0.512 29.358 6.884 0.872 0.016 " "

21.000 0.000 15.375 6.000 1.000 18.000 0.412 23.629 6.549 0.916 0.020 " "

22.000 0.000 16.125 6.000 1.000 18.000 0.303 17.354 6.286 0.954 0.023 " "

23.000 0.000 16.875 6.000 1.000 18.000 0.185 10.620 6.105 0.983 0.026 " "

24.000 0.000 17.625 6.000 1.000 18.000 0.062 3.576 6.012 0.998 0.028 " "

25.000 0.000 18.375 6.000 1.000 18.000 -0.062 -3.576 6.012 0.998 0.028 " "

26.000 0.000 19.125 6.000 1.000 18.000 -0.185 -10.620 6.105 0.983 0.026 " "

27.000 0.000 19.875 6.000 1.000 18.000 -0.303 -17.354 6.286 0.954 0.023 " "

28.000 0.000 20.625 6.000 1.000 18.000 -0.412 -23.629 6.549 0.916 0.020 " "

29.000 0.000 21.375 6.000 1.000 18.000 -0.512 -29.358 6.884 0.872 0.016 " "

30.000 0.000 22.125 6.000 1.000 18.000 -0.602 -34.508 7.281 0.824 0.013 " "

31.000 0.000 22.875 6.000 1.000 18.000 -0.682 -39.094 7.731 0.776 0.010 " "

32.000 0.000 23.625 6.000 1.000 18.000 -0.753 -43.152 8.224 0.730 0.008 " "

33.000 0.000 24.375 6.000 1.000 18.000 -0.816 -46.736 8.754 0.685 0.006 "

34.000 0.000 25.125 6.000 1.000 18.000 -0.871 -49.899 9.315 0.644 0.005 "

35.000 0.000 25.875 6.000 1.000 18.000 -0.920 -52.696 9.900 0.606 0.004 "

36.000 0.000 26.625 6.000 1.000 18.000 -0.963 -55.175 10.507 0.571 0.003 "

37.000 0.000 27.375 6.000 1.000 18.000 -1.001 -57.381 11.131 0.539 0.002 "

38.000 0.000 28.125 6.000 1.000 18.000 -1.036 -59.349 11.769 0.510 0.002 "

39.000 0.000 28.875 6.000 1.000 18.000 -1.067 -61.113 12.420 0.483 0.002 "

40.000 0.000 29.625 6.000 1.000 18.000 -1.094 -62.700 13.082 0.459 0.001 "

41.000 0.000 30.375 6.000 1.000 18.000 -1.119 -64.133 13.753 0.436 0.001 "

42.000 0.000 31.125 6.000 1.000 18.000 -1.142 -65.433 14.431 0.416 0.001 "

43.000 0.000 31.875 6.000 1.000 18.000 -1.163 -66.615 15.117 0.397 0.001 "

44.000 0.000 32.625 6.000 1.000 18.000 -1.181 -67.694 15.808 0.380 0.001 "

45.000 0.000 33.375 6.000 1.000 18.000 -1.199 -68.682 16.504 0.364 0.000 "

46.000 0.000 34.125 6.000 1.000 18.000 -1.215 -69.590 17.205 0.349 0.000 "

47.000 0.000 34.875 6.000 1.000 18.000 -1.229 -70.427 17.910 0.335 0.000 "

48.000 0.000 35.625 6.000 1.000 18.000 -1.243 -71.200 18.618 0.322 0.000 "

Formulas:

I = -ATAN((C-G)/(D-B))

J = I*180/3.1416

K = ((C-G)^2+(D-B)^2)^0.5

N = COS(I)

O = F*N*COS(I)/K^2

P = SUM(O4:O51)

Q = SUM(O20:O35)
NASA/TM—2013-217720 23

Spreadsheet C.3

Column A

 ↓

CREST001J

LINE ARRAY POLAR PLOT 07/20/2011

Bar R(ft) A(deg) A(rad) D

1.000 6.000 90.000 1.571 0.000

Column Heading Notes

RI Level: Reseasch Inc. Raw Directivity Data

RI Level/1.3: Normalized Measured Directivity, Fig 8

D Level: Emulated Directivity, Fig 9

A(deg) RI Level RI Level/1.31 D Level Pct. Dev.

-90.000 0.010 0.008 0.000 -0.8

-85.000 0.010 0.008 0.088 8.0

-80.000 0.010 0.008 0.046 3.8

-75.000 0.010 0.008 -0.066 -7.3

-70.000 0.010 0.008 -0.082 -8.9

-65.000 0.010 0.008 0.025 1.7

-60.000 0.240 0.183 0.097 -8.6

-55.000 0.260 0.198 0.026 -17.3

-50.000 0.280 0.214 -0.086 -30.0

-45.000 0.290 0.221 -0.068 -28.9

-40.000 0.300 0.229 0.070 -15.9

-35.000 0.310 0.237 0.155 -8.2

-30.000 0.330 0.252 0.122 -13.0

-25.000 0.360 0.275 0.142 -13.3

-20.000 0.470 0.359 0.391 3.2

-17.500 0.740 0.565 0.588 2.3

-15.000 1.100 0.840 0.791 -4.8

-12.500 1.310 1.000 0.962 -3.8

-10.000 1.420 1.084 1.075 -0.9

-7.500 1.490 1.137 1.120 -1.8

-5.000 1.480 1.130 1.109 -2.1

-3.750 1.410 1.076 1.090 1.4

-2.500 1.350 1.031 1.066 3.6

-1.125 1.310 1.000 1.035 3.5

0.000 1.310 1.000 1.000 0.0

1.125 1.330 1.015 1.035 2.0

2.500 1.380 1.053 1.066 1.3

3.750 1.410 1.076 1.090 1.4

5.000 1.460 1.115 1.109 -0.5

7.500 1.480 1.130 1.120 -1.0

10.000 1.420 1.084 1.075 -0.9

12.500 1.300 0.992 0.962 -3.0

15.000 1.040 0.794 0.791 -0.3

17.500 0.700 0.534 0.588 5.4

20.000 0.460 0.351 0.391 4.0 Formulas:

25.000 0.380 0.290 0.142 -14.8 E4 = C4*3.1416/180

30.000 0.340 0.260 0.122 -13.7 F4 = (16*(COS(E4))^16-2.9*COS(15*E4)/((((E4*57.3)^2)^0.5+1)^(1/5)))/13.1

35.000 0.320 0.244 0.155 -9.0

40.000 0.300 0.229 0.070 -15.9 D = C/1.31

45.000 0.300 0.229 -0.068 -29.7 F = (E-D)*100

50.000 0.290 0.221 -0.086 -30.8

55.000 0.260 0.198 0.026 -17.3

60.000 0.200 0.153 0.097 -5.5 Macro:

65.000 0.010 0.008 0.025 1.7 Sub CERST001JM()

70.000 0.010 0.008 -0.082 -8.9 Dim i As Long

75.000 0.010 0.008 -0.066 -7.3

80.000 0.010 0.008 0.046 3.8 For i = 12 To 60

85.000 0.010 0.008 0.088 8.0 Cells(4, 3) = Cells(i, 2)

90.000 0.010 0.008 0.000 -0.8 Calculate

Cells(i, 5) = Cells(4, 6)

Next i

End Sub

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-90-80-70-60-50-40-30-20-10 0 10 20 30 40 50 60 70 80 90

Normalized Level

Deviation from Normal (degrees)

Fig. 9 Emulated Directivity

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-90-80-70-60-50-40-30-20-10 0 10 20 30 40 50 60 70 80 90

Normalized Level

Deviation from Normal (degrees)

Fig. 8 Measured Directivity
NASA/TM—2013-217720 24

Spreadsheet C.4

Column A

 ↓

CREST001A3A

REAR PROJECTION BOTTOM 05/27/2011 06/14/2011

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 0.000 6.000 0.000 1247.0 5.000 0.695 39.805 7.810 0.695 39.805 0.075 47.28

ET Sum: 47.28

YT Values ET Sum ET Average IR Suns Avg. IR Suns

-5.000 47.28 545.65 0.035 0.398

-4.800 68.62 545.65 0.050 0.398

-4.600 88.22 545.65 0.064 0.398

-4.400 104.19 545.65 0.076 0.398

-4.200 114.83 545.65 0.084 0.398

-4.000 119.10 545.65 0.087 0.398

-3.800 117.06 545.65 0.085 0.398

-3.600 110.36 545.65 0.081 0.398

-3.400 102.59 545.65 0.075 0.398

-3.200 99.34 545.65 0.073 0.398

-3.000 107.88 545.65 0.079 0.398

-2.800 136.31 545.65 0.099 0.398

-2.600 192.19 545.65 0.140 0.398

-2.400 280.87 545.65 0.205 0.398

-2.200 403.67 545.65 0.295 0.398

-2.000 556.56 545.65 0.406 0.398

-1.800 729.72 545.65 0.533 0.398

-1.600 908.40 545.65 0.663 0.398

-1.400 1075.25 545.65 0.785 0.398

-1.200 1213.69 545.65 0.886 0.398 Formulas:

-1.000 1311.54 545.65 0.957 0.398 I = -ATAN((C-G)/(D-B))

-0.800 1363.91 545.65 0.996 0.398 J = I*180/3.1416

-0.600 1374.27 545.65 1.003 0.398 K = ((C-G)^2+(D-B)^2)^0.5

-0.400 1352.90 545.65 0.988 0.398 L = -E*3.1416/180+I

-0.200 1311.93 545.65 0.958 0.398 M =L*180/3.1416

0.000 1246.93 545.65 0.910 0.398 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

0.200 1311.93 545.65 0.958 0.398 O = 6*F38*N38*COS(I38)*2.93/(k38^1.6)

0.400 1352.90 545.65 0.988 0.398

0.600 1374.27 545.65 1.003 0.398 D12 = AVERAGE(C12:C62)

0.800 1363.91 545.65 0.996 0.398 F12 = C12/1370

1.000 1311.54 545.65 0.957 0.398 G12 = D12/1370

1.200 1213.69 545.65 0.886 0.398

1.400 1075.25 545.65 0.785 0.398

1.600 908.40 545.65 0.663 0.398 Macro:

1.800 729.72 545.65 0.533 0.398 Sub CERST001A3A()

2.000 556.56 545.65 0.406 0.398 Dim i As Long

2.200 403.67 545.65 0.295 0.398

2.400 280.87 545.65 0.205 0.398 For i = 12 To 62

2.600 192.19 545.65 0.140 0.398 Cells(4, 7) = Cells(i, 2)

2.800 136.31 545.65 0.099 0.398 Calculate

3.000 107.88 545.65 0.079 0.398 Cells(i, 3) = Cells(9, 16)

3.200 99.34 545.65 0.073 0.398 Next i

3.400 102.59 545.65 0.075 0.398 End Sub

3.600 110.36 545.65 0.081 0.398

3.800 117.06 545.65 0.085 0.398

4.000 119.10 545.65 0.087 0.398

4.200 114.83 545.65 0.084 0.398

4.400 104.19 545.65 0.076 0.398

4.600 88.22 545.65 0.064 0.398

4.800 68.62 545.65 0.050 0.398

5.000 47.28 545.65 0.035 0.398

0

200

400

600

800

1000

1200

1400

1600

-5 -4 -3 -2 -1 0 1 2 3 4 5

Incident Flux Density (W/m2)

Distance from Center (feet)

Fig. 11 Projected Transverse Flux Distribution

(Line Source at 6 feet)
NASA/TM—2013-217720 25

Spreadsheet C.5

Column A

 ↓

CREST003A-1

BOTTOM 05/27/2011 10/18/2011 

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -5.000 6.000 0.000 1247.0 5.200 1.039 59.534 11.834 1.039 59.534 0.097 20.63

2.000 0.000 -4.000 6.000 0.000 1247.0 5.200 0.993 56.889 10.984 0.993 56.889 0.068 17.48

3.000 0.000 -2.500 6.000 0.000 1247.0 5.200 0.909 52.073 9.762 0.909 52.073 -0.048 -16.83

4.000 0.000 -1.000 6.000 0.000 1247.0 5.200 0.802 45.939 8.628 0.802 45.939 -0.084 -40.88

5.000 0.000 1.000 6.000 0.000 1247.0 5.200 0.611 34.992 7.324 0.611 34.992 0.155 114.83

6.000 0.000 2.500 6.000 0.000 1247.0 5.200 0.423 24.228 6.580 0.423 24.228 0.163 160.41

7.000 0.000 4.000 6.000 0.000 1247.0 5.200 0.197 11.310 6.119 0.197 11.310 1.024 1213.69

8.000 0.000 5.000 6.000 0.000 1247.0 5.200 0.033 1.909 6.003 0.033 1.909 1.054 1311.93

ET Sum: 2781.26

YT Values ET Sum ET Average Pct. Dev. IR Suns Avg. IR Suns

-5.200 2781.26 3461.57 -19.7 2.030 2.527

-5.000 2888.05 3461.57 -16.6 2.108 2.527

-4.800 3109.79 3461.57 -10.2 2.270 2.527

-4.600 3296.70 3461.57 -4.8 2.406 2.527

-4.400 3460.20 3461.57 0.0 2.526 2.527

-4.200 3593.23 3461.57 3.8 2.623 2.527

-4.000 3671.41 3461.57 6.1 2.680 2.527

-3.800 3835.10 3461.57 10.8 2.799 2.527

-3.600 3926.78 3461.57 13.4 2.866 2.527

-3.400 3958.34 3461.57 14.4 2.889 2.527

-3.200 3933.73 3461.57 13.6 2.871 2.527

-3.000 3862.60 3461.57 11.6 2.819 2.527

-2.800 3758.72 3461.57 8.6 2.744 2.527

-2.600 3632.36 3461.57 4.9 2.651 2.527

-2.400 3551.13 3461.57 2.6 2.592 2.527

-2.200 3518.52 3461.57 1.6 2.568 2.527

-2.000 3474.94 3461.57 0.4 2.536 2.527

-1.800 3420.89 3461.57 -1.2 2.497 2.527

-1.600 3356.18 3461.57 -3.0 2.450 2.527

-1.400 3285.64 3461.57 -5.1 2.398 2.527

-1.200 3217.14 3461.57 -7.1 2.348 2.527 Formulas:

-1.000 3144.02 3461.57 -9.2 2.295 2.527 I = -ATAN((C-G)/(D-B))

-0.800 3219.44 3461.57 -7.0 2.350 2.527 J = I*180/3.1416

-0.600 3288.65 3461.57 -5.0 2.400 2.527 K = ((C-G)^2+(D-B)^2)^0.5

-0.400 3354.55 3461.57 -3.1 2.449 2.527 L = -E*3.1416/180+I

-0.200 3402.65 3461.57 -1.7 2.484 2.527 M =L*180/3.1416

0.000 3420.30 3461.57 -1.2 2.497 2.527 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

0.200 3402.65 3461.57 -1.7 2.484 2.527 O = 6*F*N*COS(I)*2.93/(K^1.6)

0.400 3354.55 3461.57 -3.1 2.449 2.527

0.600 3288.65 3461.57 -5.0 2.400 2.527 D15 = AVERAGE(C15:C39)

0.800 3219.44 3461.57 -7.0 2.350 2.527 E15 = (C15-D15)/D15*100

1.000 3144.02 3461.57 -9.2 2.295 2.527 F15 = C15/1370

1.200 3217.14 3461.57 -7.1 2.348 2.527 G15 = D15/1370

1.400 3285.64 3461.57 -5.1 2.398 2.527

1.600 3356.18 3461.57 -3.0 2.450 2.527

1.800 3420.89 3461.57 -1.2 2.497 2.527 Macro:

2.000 3474.94 3461.57 0.4 2.536 2.527 Sub CERST003AM()

2.200 3518.52 3461.57 1.6 2.568 2.527 Dim i As Long

2.400 3551.13 3461.57 2.6 2.592 2.527

2.600 3632.36 3461.57 4.9 2.651 2.527 For i = 15 To 67

2.800 3758.72 3461.57 8.6 2.744 2.527 Cells(4, 7) = Cells(i, 2)

3.000 3862.60 3461.57 11.6 2.819 2.527 Calculate

3.200 3933.73 3461.57 13.6 2.871 2.527 Cells(i, 3) = Cells(13, 16)

3.400 3958.34 3461.57 14.4 2.889 2.527 Next i

3.600 3926.78 3461.57 13.4 2.866 2.527 End Sub

3.800 3835.10 3461.57 10.8 2.799 2.527

4.000 3671.41 3461.57 6.1 2.680 2.527

4.200 3593.23 3461.57 3.8 2.623 2.527

4.400 3460.20 3461.57 0.0 2.526 2.527

4.600 3296.70 3461.57 -4.8 2.406 2.527

4.800 3109.79 3461.57 -10.2 2.270 2.527

5.000 2888.05 3461.57 -16.6 2.108 2.527

5.200 2781.26 3461.57 -19.7 2.030 2.527

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 12 Bottom Zone

(Albedo)

CREST

Bottom

L=8.75 ft.
NASA/TM—2013-217720 26

Spreadsheet C.6

Column A

 ↓

CREST003A0

BOTTOM 05/27/2011 10/18/2011

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -5.000 6.000 -10.000 1247.0 5.200 1.039 59.534 11.834 1.214 69.534 -0.075 -16.10

2.000 0.000 -4.000 6.000 -3.000 1247.0 5.200 0.993 56.889 10.984 1.045 59.889 0.097 25.19

3.000 0.000 -2.500 6.000 0.000 1247.0 5.200 0.909 52.073 9.762 0.909 52.073 -0.048 -16.83

4.000 0.000 -1.000 6.000 2.000 1247.0 5.200 0.802 45.939 8.628 0.767 43.939 -0.044 -21.29

5.000 0.000 1.000 6.000 -2.000 1247.0 5.200 0.611 34.992 7.324 0.646 36.992 0.137 101.63

6.000 0.000 2.500 6.000 0.000 1247.0 5.200 0.423 24.228 6.580 0.423 24.228 0.163 160.41

7.000 0.000 4.000 6.000 3.000 1247.0 5.200 0.197 11.310 6.119 0.145 8.310 1.112 1317.84

8.000 0.000 5.000 6.000 10.000 1247.0 5.200 0.033 1.909 6.003 -0.141 -8.091 1.115 1388.10

ET Sum: 2938.95

YT Values ET Sum ET Average Pct. Dev. IR Suns Avg. IR Suns

-5.200 2938.95 3140.20 -6.4 2.145 2.292

-5.000 3015.91 3140.20 -4.0 2.201 2.292

-4.800 3034.92 3140.20 -3.4 2.215 2.292

-4.600 3009.62 3140.20 -4.2 2.197 2.292

-4.400 2954.92 3140.20 -5.9 2.157 2.292

-4.200 2957.03 3140.20 -5.8 2.158 2.292

-4.000 3007.65 3140.20 -4.2 2.195 2.292

-3.800 3059.79 3140.20 -2.6 2.233 2.292

-3.600 3108.57 3140.20 -1.0 2.269 2.292

-3.400 3143.53 3140.20 0.1 2.295 2.292

-3.200 3157.59 3140.20 0.6 2.305 2.292

-3.000 3150.85 3140.20 0.3 2.300 2.292

-2.800 3129.82 3140.20 -0.3 2.285 2.292

-2.600 3099.90 3140.20 -1.3 2.263 2.292

-2.400 3125.07 3140.20 -0.5 2.281 2.292

-2.200 3204.63 3140.20 2.1 2.339 2.292

-2.000 3272.99 3140.20 4.2 2.389 2.292

-1.800 3322.45 3140.20 5.8 2.425 2.292

-1.600 3343.52 3140.20 6.5 2.441 2.292

-1.400 3332.89 3140.20 6.1 2.433 2.292

-1.200 3295.01 3140.20 4.9 2.405 2.292 Formulas:

-1.000 3238.67 3140.20 3.1 2.364 2.292 I = -ATAN((C-G)/(D-B))

-0.800 3160.70 3140.20 0.7 2.307 2.292 J = I*180/3.1416

-0.600 3204.16 3140.20 2.0 2.339 2.292 K = ((C-G)^2+(D-B)^2)^0.5

-0.400 3235.79 3140.20 3.0 2.362 2.292 L = -E*3.1416/180+I

-0.200 3258.06 3140.20 3.8 2.378 2.292 M =L*180/3.1416

0.000 3266.30 3140.20 4.0 2.384 2.292 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

0.200 3258.06 3140.20 3.8 2.378 2.292 O = 6*F*N*COS(I)*2.93/(K^1.6)

0.400 3235.79 3140.20 3.0 2.362 2.292

0.600 3204.16 3140.20 2.0 2.339 2.292 D15 = AVERAGE(C15:C39)

0.800 3160.70 3140.20 0.7 2.307 2.292 E15 = (C15-D15)/D15*100

1.000 3238.67 3140.20 3.1 2.364 2.292 F15 = C15/1370

1.200 3295.01 3140.20 4.9 2.405 2.292 G15 = D15/1370

1.400 3332.89 3140.20 6.1 2.433 2.292

1.600 3343.52 3140.20 6.5 2.441 2.292

1.800 3322.45 3140.20 5.8 2.425 2.292 Macro:

2.000 3272.99 3140.20 4.2 2.389 2.292 Sub CERST003AM()

2.200 3204.63 3140.20 2.1 2.339 2.292 Dim i As Long

2.400 3125.07 3140.20 -0.5 2.281 2.292

2.600 3099.90 3140.20 -1.3 2.263 2.292 For i = 15 To 67

2.800 3129.82 3140.20 -0.3 2.285 2.292 Cells(4, 7) = Cells(i, 2)

3.000 3150.85 3140.20 0.3 2.300 2.292 Calculate

3.200 3157.59 3140.20 0.6 2.305 2.292 Cells(i, 3) = Cells(13, 16)

3.400 3143.53 3140.20 0.1 2.295 2.292 Next i

3.600 3108.57 3140.20 -1.0 2.269 2.292 End Sub

3.800 3059.79 3140.20 -2.6 2.233 2.292

4.000 3007.65 3140.20 -4.2 2.195 2.292

4.200 2957.03 3140.20 -5.8 2.158 2.292

4.400 2954.92 3140.20 -5.9 2.157 2.292

4.600 3009.62 3140.20 -4.2 2.197 2.292

4.800 3034.92 3140.20 -3.4 2.215 2.292

5.000 3015.91 3140.20 -4.0 2.201 2.292

5.200 2938.95 3140.20 -6.4 2.145 2.292

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 13 Bottom Zone

(Albedo)

CREST

Bottom

L=8.75 ft.
NASA/TM—2013-217720 27

Spreadsheet C.7

Column A

 ↓

CREST003A

BOTTOM 05/27/2011 06/14/2011

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -5.000 6.000 -10.000 1247.0 5.200 1.039 59.534 11.834 1.214 69.534 -0.075 -16.10

2.000 0.000 -4.000 6.000 -3.000 1247.0 5.200 0.993 56.889 10.984 1.045 59.889 0.097 25.19

3.000 0.000 -2.500 6.000 0.000 1122.3 5.200 0.909 52.073 9.762 0.909 52.073 -0.048 -15.14

4.000 0.000 -1.000 6.000 2.000 1122.3 5.200 0.802 45.939 8.628 0.767 43.939 -0.044 -19.16

5.000 0.000 1.000 6.000 -2.000 1122.3 5.200 0.611 34.992 7.324 0.646 36.992 0.137 91.47

6.000 0.000 2.500 6.000 0.000 1122.3 5.200 0.423 24.228 6.580 0.423 24.228 0.163 144.37

7.000 0.000 4.000 6.000 3.000 1247.0 5.200 0.197 11.310 6.119 0.145 8.310 1.112 1317.84

8.000 0.000 5.000 6.000 10.000 1247.0 5.200 0.033 1.909 6.003 -0.141 -8.091 1.115 1388.10

ET Sum: 2916.56

YT Values ET Sum ET Average Pct. Dev. IR Suns Avg. IR Suns

-5.200 2916.56 2942.93 -0.9 2.129 2.148

-5.000 2984.29 2942.93 1.4 2.178 2.148

-4.800 2991.06 2942.93 1.6 2.183 2.148

-4.600 2950.72 2942.93 0.3 2.154 2.148

-4.400 2878.77 2942.93 -2.2 2.101 2.148

-4.200 2862.41 2942.93 -2.7 2.089 2.148

-4.000 2894.49 2942.93 -1.6 2.113 2.148

-3.800 2929.08 2942.93 -0.5 2.138 2.148

-3.600 2961.96 2942.93 0.6 2.162 2.148

-3.400 2982.77 2942.93 1.4 2.177 2.148

-3.200 2983.91 2942.93 1.4 2.178 2.148

-3.000 2964.47 2942.93 0.7 2.164 2.148

-2.800 2929.99 2942.93 -0.4 2.139 2.148

-2.600 2885.74 2942.93 -1.9 2.106 2.148

-2.400 2890.27 2942.93 -1.8 2.110 2.148

-2.200 2944.28 2942.93 0.0 2.149 2.148

-2.000 2989.96 2942.93 1.6 2.182 2.148

-1.800 3021.32 2942.93 2.7 2.205 2.148

-1.600 3030.30 2942.93 3.0 2.212 2.148

-1.400 3013.95 2942.93 2.4 2.200 2.148

-1.200 2975.89 2942.93 1.1 2.172 2.148 Formulas:

-1.000 2923.43 2942.93 -0.7 2.134 2.148 I = -ATAN((C-G)/(D-B))

-0.800 2853.00 2942.93 -3.1 2.082 2.148 J = I*180/3.1416

-0.600 2892.68 2942.93 -1.7 2.111 2.148 K = ((C-G)^2+(D-B)^2)^0.5

-0.400 2921.96 2942.93 -0.7 2.133 2.148 L = -E*3.1416/180+I

-0.200 2942.67 2942.93 0.0 2.148 2.148 M =L*180/3.1416

0.000 2950.34 2942.93 0.3 2.154 2.148 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

0.200 2942.67 2942.93 0.0 2.148 2.148 O = 6*F*N*COS(I)*2.93/(K^1.6)

0.400 2921.96 2942.93 -0.7 2.133 2.148

0.600 2892.68 2942.93 -1.7 2.111 2.148 D15 = AVERAGE(C15:C39)

0.800 2853.00 2942.93 -3.1 2.082 2.148 E15 = (C15-D15)/D15*100

1.000 2923.43 2942.93 -0.7 2.134 2.148 F15 = C15/1370

1.200 2975.89 2942.93 1.1 2.172 2.148 G15 = D15/1370

1.400 3013.95 2942.93 2.4 2.200 2.148

1.600 3030.30 2942.93 3.0 2.212 2.148

1.800 3021.32 2942.93 2.7 2.205 2.148 Macro:

2.000 2989.96 2942.93 1.6 2.182 2.148 Sub CERST003AM()

2.200 2944.28 2942.93 0.0 2.149 2.148 Dim i As Long

2.400 2890.27 2942.93 -1.8 2.110 2.148

2.600 2885.74 2942.93 -1.9 2.106 2.148 For i = 15 To 67

2.800 2929.99 2942.93 -0.4 2.139 2.148 Cells(4, 7) = Cells(i, 2)

3.000 2964.47 2942.93 0.7 2.164 2.148 Calculate

3.200 2983.91 2942.93 1.4 2.178 2.148 Cells(i, 3) = Cells(13, 16)

3.400 2982.77 2942.93 1.4 2.177 2.148 Next i

3.600 2961.96 2942.93 0.6 2.162 2.148 End Sub

3.800 2929.08 2942.93 -0.5 2.138 2.148

4.000 2894.49 2942.93 -1.6 2.113 2.148

4.200 2862.41 2942.93 -2.7 2.089 2.148

4.400 2878.77 2942.93 -2.2 2.101 2.148

4.600 2950.72 2942.93 0.3 2.154 2.148

4.800 2991.06 2942.93 1.6 2.183 2.148

5.000 2984.29 2942.93 1.4 2.178 2.148

5.200 2916.56 2942.93 -0.9 2.129 2.148

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 14 Bottom Zone

(Albedo)

CREST

Bottom

L=8.75 ft.
NASA/TM—2013-217720 28

Spreadsheet C.8 

Column A

 ↓

CREST003A2

BOTTOM 05/27/2011 06/14/2011 EO

Bar XS(ft) YS(ft) XT B(deg) E0(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -5.000 6.000 -10.000 1247.0 5.200 1.039 59.534 11.834 1.214 69.534 -0.075 -16.10

2.000 0.000 -4.000 6.000 -3.000 1247.0 5.200 0.993 56.889 10.984 1.045 59.889 0.097 25.19

3.000 0.000 -2.500 6.000 0.000 1122.3 5.200 0.909 52.073 9.762 0.909 52.073 -0.048 -15.14

4.000 0.000 -1.000 6.000 2.000 1122.3 5.200 0.802 45.939 8.628 0.767 43.939 -0.044 -19.16

5.000 0.000 1.000 6.000 -2.000 1122.3 5.200 0.611 34.992 7.324 0.646 36.992 0.137 91.47

6.000 0.000 2.500 6.000 0.000 1122.3 5.200 0.423 24.228 6.580 0.423 24.228 0.163 144.37

7.000 0.000 4.000 6.000 3.000 1247.0 5.200 0.197 11.310 6.119 0.145 8.310 1.112 1317.84

8.000 0.000 5.000 6.000 10.000 1247.0 5.200 0.033 1.909 6.003 -0.141 -8.091 1.115 1388.10

YT Values ET1 ET2 ET3 ET4 ET5 ET6 ET7 ET8

-5.200 1388.1 1317.8 144.4 91.5 -19.2 -15.1 25.2 -16.1

-5.000 1340.1 1348.7 209.0 105.2 -8.5 -21.0 25.8 -15.0

-4.800 1238.9 1345.0 304.3 112.5 4.6 -26.7 25.9 -13.4

-4.600 1089.1 1317.7 429.2 113.1 19.8 -31.9 25.1 -11.3

-4.400 905.1 1273.7 577.3 107.8 36.4 -36.2 23.5 -8.8

-4.200 707.5 1288.2 737.5 99.7 53.4 -39.0 20.9 -5.7

-4.000 518.9 1342.0 895.0 93.9 69.5 -40.0 17.3 -2.1

-3.800 358.6 1379.5 1034.0 97.5 83.5 -38.5 12.5 2.0

-3.600 238.9 1390.3 1141.4 118.6 93.8 -34.3 6.6 6.5

-3.400 163.4 1361.4 1209.0 165.0 99.7 -26.9 -0.3 11.4

-3.200 127.6 1284.7 1236.4 242.3 100.5 -16.2 -8.0 16.5

-3.000 121.0 1160.8 1230.1 352.6 97.0 -2.3 -16.4 21.7

-2.800 130.8 999.1 1200.9 492.3 91.0 14.3 -25.1 26.7

-2.600 144.5 815.9 1156.7 652.1 85.7 32.9 -33.4 31.3

-2.400 152.5 630.4 1156.7 818.0 86.2 52.2 -41.0 35.2

-2.200 149.2 460.8 1200.9 973.1 98.3 70.9 -46.9 38.0

-2.000 133.1 320.7 1230.1 1101.6 128.6 87.1 -50.5 39.3

-1.800 106.0 217.2 1236.4 1191.7 182.9 99.2 -50.8 38.8

-1.600 71.7 150.8 1209.0 1238.9 265.0 106.0 -47.2 36.1

-1.400 34.9 116.6 1141.4 1246.7 375.5 106.9 -39.1 31.0

-1.200 0.2 106.4 1034.0 1224.7 510.6 102.7 -26.0 23.3 Formulas:

-1.000 -29.0 110.4 895.0 1184.7 661.9 95.7 -8.3 13.1 I = -ATAN((C-G)/(D-B))

-0.800 -50.4 119.9 737.5 1124.9 816.9 90.0 13.6 0.5 J = I*180/3.1416

-0.600 -63.1 127.7 577.3 1173.3 961.3 91.5 38.4 -13.7 K = ((C-G)^2+(D-B)^2)^0.5

-0.400 -67.4 129.5 429.2 1206.9 1081.2 107.2 64.2 -28.7 L = -E*3.1416/180+I

-0.200 -64.4 123.2 304.3 1223.5 1166.4 144.4 88.6 -43.3 M =L*180/3.1416

0.000 -55.7 109.1 209.0 1212.8 1212.8 209.0 109.1 -55.7 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

0.200 -43.3 88.6 144.4 1166.4 1223.5 304.3 123.2 -64.4 O = 6*F*N*COS(I)*2.93/(K^1.6)

0.400 -28.7 64.2 107.2 1081.2 1206.9 429.2 129.5 -67.4

0.600 -13.7 38.4 91.5 961.3 1173.3 577.3 127.7 -63.1 D15 = AVERAGE(C15:C67)

0.800 0.5 13.6 90.0 816.9 1124.9 737.5 119.9 -50.4 E15 = (C15-D15)/D15*100

1.000 13.1 -8.3 95.7 661.9 1184.7 895.0 110.4 -29.0 F15 = C15/1370

1.200 23.3 -26.0 102.7 510.6 1224.7 1034.0 106.4 0.2 G15 = D15/1370

1.400 31.0 -39.1 106.9 375.5 1246.7 1141.4 116.6 34.9

1.600 36.1 -47.2 106.0 265.0 1238.9 1209.0 150.8 71.7

1.800 38.8 -50.8 99.2 182.9 1191.7 1236.4 217.2 106.0 Macro:

2.000 39.3 -50.5 87.1 128.6 1101.6 1230.1 320.7 133.1 Sub CERST003A2M()

2.200 38.0 -46.9 70.9 98.3 973.1 1200.9 460.8 149.2 Dim i As Long

2.400 35.2 -41.0 52.2 86.2 818.0 1156.7 630.4 152.5

2.600 31.3 -33.4 32.9 85.7 652.1 1156.7 815.9 144.5 For i = 15 To 67

2.800 26.7 -25.1 14.3 91.0 492.3 1200.9 999.1 130.8 Cells(4, 7) = Cells(i, 2)

3.000 21.7 -16.4 -2.3 97.0 352.6 1230.1 1160.8 121.0 Calculate

3.200 16.5 -8.0 -16.2 100.5 242.3 1236.4 1284.7 127.6 Cells(i.3) = Cells(4,15)

3.400 11.4 -0.3 -26.9 99.7 165.0 1209.0 1361.4 163.4 Cells(i.4) = Cells(5,15)

3.600 6.5 6.6 -34.3 93.8 118.6 1141.4 1390.3 238.9 Cells(i.5) = Cells(6,15)

3.800 2.0 12.5 -38.5 83.5 97.5 1034.0 1379.5 358.6 Cells(i.6) = Cells(7,15)

4.000 -2.1 17.3 -40.0 69.5 93.9 895.0 1342.0 518.9 Cells(i.7) = Cells(8,15)

4.200 -5.7 20.9 -39.0 53.4 99.7 737.5 1288.2 707.5 Cells(i.8) = Cells(9,15)

4.400 -8.8 23.5 -36.2 36.4 107.8 577.3 1273.7 905.1 Cells(i.9) = Cells(10,15)

4.600 -11.3 25.1 -31.9 19.8 113.1 429.2 1317.7 1089.1 Cells(i.10) = Cells(11,15)

4.800 -13.4 25.9 -26.7 4.6 112.5 304.3 1345.0 1238.9 Next i

5.000 -15.0 25.8 -21.0 -8.5 105.2 209.0 1348.7 1340.1 End Sub

5.200 -16.1 25.2 -15.1 -19.2 91.5 144.4 1317.8 1388.1

0

200

400

600

800

1000

1200

1400

1600

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Incident Flux Density (W/m2)

Distance from Center (feet)

Fig. 15 Bottom Zone

(Albedo)

CREST

Bottom

L=8.75ft.
NASA/TM—2013-217720 29

Spreadsheet C.9

Column A

 ↓

CREST002A

TOP 05/27/2011 06/14/2011

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -4.500 8.000 -12.500 1247.0 5.200 0.881 50.486 12.573 1.099 62.986 0.068 16.61

2.000 0.000 -3.250 8.000 -3.000 997.6 5.200 0.813 46.567 11.636 0.865 49.567 -0.091 -21.73

3.000 0.000 -1.500 8.000 1.000 1159.7 5.200 0.697 39.946 10.435 0.680 38.946 0.098 35.87

4.000 0.000 1.500 8.000 -1.000 1159.7 5.200 0.433 24.820 8.814 0.451 25.820 0.125 71.16

5.000 0.000 3.250 8.000 3.000 997.6 5.200 0.239 13.699 8.234 0.187 10.699 1.050 613.33

6.000 0.000 4.500 8.000 12.500 1247.0 5.200 0.087 5.001 8.031 -0.131 -7.499 1.120 872.46

ET Sum: 1587.70

YT Values ET Sum ET Average Pct. Dev. IR Suns Avg. IR Suns

-5.200 1587.70 1637.64 -3.0 1.159 1.195

-5.000 1638.74 1637.64 0.1 1.196 1.195

-4.800 1669.29 1637.64 1.9 1.218 1.195

-4.600 1679.70 1637.64 2.6 1.226 1.195

-4.400 1672.71 1637.64 2.1 1.221 1.195

-4.200 1652.94 1637.64 0.9 1.207 1.195

-4.000 1625.75 1637.64 -0.7 1.187 1.195

-3.800 1595.01 1637.64 -2.6 1.164 1.195

-3.600 1579.55 1637.64 -3.5 1.153 1.195

-3.400 1599.07 1637.64 -2.4 1.167 1.195

-3.200 1619.73 1637.64 -1.1 1.182 1.195

-3.000 1642.00 1637.64 0.3 1.199 1.195

-2.800 1662.51 1637.64 1.5 1.214 1.195

-2.600 1677.25 1637.64 2.4 1.224 1.195

-2.400 1682.98 1637.64 2.8 1.228 1.195

-2.200 1678.09 1637.64 2.5 1.225 1.195

-2.000 1662.97 1637.64 1.5 1.214 1.195

-1.800 1639.70 1637.64 0.1 1.197 1.195 Formulas:

-1.600 1610.91 1637.64 -1.6 1.176 1.195 I = -ATAN((C-G)/(D-B))

-1.400 1575.40 1637.64 -3.8 1.150 1.195 J = I*180/3.1416

-1.200 1587.14 1637.64 -3.1 1.158 1.195 K = ((C-G)^2+(D-B)^2)^0.5

-1.000 1606.68 1637.64 -1.9 1.173 1.195 L = -E*3.1416/180+I

-0.800 1626.62 1637.64 -0.7 1.187 1.195 M =L*180/3.1416

-0.600 1646.44 1637.64 0.5 1.202 1.195 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

-0.400 1663.57 1637.64 1.6 1.214 1.195 O = 6*F*N*COS(I)*2.93/(K^1.6)

-0.200 1675.24 1637.64 2.3 1.223 1.195

0.000 1679.38 1637.64 2.5 1.226 1.195 D15 = AVERAGE(C15:C67)

0.200 1675.24 1637.64 2.3 1.223 1.195 E15 = (C15-D15)/D15*100

0.400 1663.57 1637.64 1.6 1.214 1.195 F15 = C15/1370

0.600 1646.44 1637.64 0.5 1.202 1.195 G15 = D15/1370

0.800 1626.62 1637.64 -0.7 1.187 1.195

1.000 1606.68 1637.64 -1.9 1.173 1.195

1.200 1587.14 1637.64 -3.1 1.158 1.195 Macro:

1.400 1575.40 1637.64 -3.8 1.150 1.195 Sub CERST002AM()

1.600 1610.91 1637.64 -1.6 1.176 1.195 Dim i As Long

1.800 1639.70 1637.64 0.1 1.197 1.195

2.000 1662.97 1637.64 1.5 1.214 1.195 For i = 15 To 67

2.200 1678.09 1637.64 2.5 1.225 1.195 Cells(4, 7) = Cells(i, 2)

2.400 1682.98 1637.64 2.8 1.228 1.195 Calculate

2.600 1677.25 1637.64 2.4 1.224 1.195 Cells(i, 3) = Cells(13, 16)

2.800 1662.51 1637.64 1.5 1.214 1.195 Next i

3.000 1642.00 1637.64 0.3 1.199 1.195 End Sub

3.200 1619.73 1637.64 -1.1 1.182 1.195

3.400 1599.07 1637.64 -2.4 1.167 1.195

3.600 1579.55 1637.64 -3.5 1.153 1.195

3.800 1595.01 1637.64 -2.6 1.164 1.195

4.000 1625.75 1637.64 -0.7 1.187 1.195

4.200 1652.94 1637.64 0.9 1.207 1.195

4.400 1672.71 1637.64 2.1 1.221 1.195

4.600 1679.70 1637.64 2.6 1.226 1.195

4.800 1669.29 1637.64 1.9 1.218 1.195

5.000 1638.74 1637.64 0.1 1.196 1.195

5.200 1587.70 1637.64 -3.0 1.159 1.195

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 16 Top Zone

CREST

Top

L=10.6 ft.
NASA/TM—2013-217720 30

Spreadsheet C.10

Column A

 ↓

CREST001F

UPPER FRONT W/REFLECTOR 05/27/2011 06/16/2011

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -1.600 6.000 -3.000 623.5 2.400 0.588 33.690 7.211 0.640 36.690 0.141 54.53

2.000 0.000 -0.600 6.000 -3.000 623.5 2.400 0.464 26.565 6.708 0.516 29.565 0.118 55.22

3.000 0.000 1.000 6.000 3.000 1247.0 2.400 0.229 13.134 6.161 0.177 10.134 1.070 1245.85

4.000 0.000 2.000 6.000 3.000 1247.0 2.400 0.067 3.814 6.013 0.014 0.814 1.027 1273.66

ET Sum: 2629.26

YT Values ET Sum ET Average Pct. Dev. IR Suns Avg. IR Suns

0.200 2618.29 2792.89 -6.3 1.911 2.039

0.400 2732.56 2792.89 -2.2 1.995 2.039

0.600 2814.36 2792.89 0.8 2.054 2.039

0.800 2861.92 2792.89 2.5 2.089 2.039

1.000 2876.29 2792.89 3.0 2.099 2.039

1.200 2856.47 2792.89 2.3 2.085 2.039 Formulas:

1.400 2850.61 2792.89 2.1 2.081 2.039 I = -ATAN((C-G)/(D-B))

1.600 2876.55 2792.89 3.0 2.100 2.039 J = I*180/3.1416

1.800 2863.75 2792.89 2.5 2.090 2.039 K = ((C-G)^2+(D-B)^2)^0.5

2.000 2813.76 2792.89 0.7 2.054 2.039 L = -E*3.1416/180+I

2.200 2720.82 2792.89 -2.6 1.986 2.039 M =L*180/3.1416

2.400 2629.26 2792.89 -5.9 1.919 2.039 N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

O = 6*F*N*COS(I)*2.93/(K^1.6)

D15 = AVERAGE(C26:C37)

E15 = (C26-D26)/D26*100

F15 = C26/1370

G15 = D26/1370

Macro:

Sub CERST001FM() EO (direct):

Dim i As Long 1500*0.286/0.344 = 1247 W/m2 

For i = 26 To 37 EO (reflector image):

Cells(4, 7) = Cells(i, 2) 1247*0.5=623.5 W/m2

Calculate

Cells(i, 3) = Cells(13, 16)

Next i

End Sub

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-3 -2 -1 0 1 2 3

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 17 Upper Front Zone

CREST

Front

H=2.08 ft.
NASA/TM—2013-217720 31

Spreadsheet C.11

Column A

 ↓

CREST001G

LOWER (RECESSED) FRONT W/REFLECTOR 05/27/2011 06/16/2011

Bar XS(ft) YS(ft) XT B(deg) EO(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -2.000 6.833 -1.500 1247.0 0.200 0.311 17.847 7.178 0.338 19.347 0.440 392.02

2.000 0.000 -1.000 6.833 -1.000 1247.0 0.200 0.174 9.961 6.938 0.191 10.961 1.040 1012.05

3.000 0.000 1.400 6.833 1.000 623.5 0.200 -0.174 -9.961 6.938 -0.191 -10.961 1.040 506.03

4.000 0.000 2.400 6.833 1.500 623.5 0.200 -0.311 -17.847 7.178 -0.338 -19.347 0.440 196.01

ET Sum: 2106.11

YT Values ET Sum ET Average Pct. Dev. IR Suns Avg. IR Suns

-2.600 2098.66 2251.95 -6.8 1.532 1.644

-2.400 2160.33 2251.95 -4.1 1.577 1.644

-2.200 2180.27 2251.95 -3.2 1.591 1.644

-2.000 2253.85 2251.95 0.1 1.645 1.644

-1.800 2300.57 2251.95 2.2 1.679 1.644

-1.600 2322.73 2251.95 3.1 1.695 1.644

-1.400 2323.87 2251.95 3.2 1.696 1.644

-1.200 2301.71 2251.95 2.2 1.680 1.644

-1.000 2310.66 2251.95 2.6 1.687 1.644

-0.800 2331.09 2251.95 3.5 1.702 1.644

-0.600 2329.23 2251.95 3.4 1.700 1.644

-0.400 2306.07 2251.95 2.4 1.683 1.644

-0.200 2260.70 2251.95 0.4 1.650 1.644

0.000 2193.34 2251.95 -2.6 1.601 1.644

0.200 2106.11 2251.95 -6.5 1.537 1.644

Formulas:

I = -ATAN((C-G)/(D-B))

J = I*180/3.1416

K = ((C-G)^2+(D-B)^2)^0.5

L = -E*3.1416/180+I

M =L*180/3.1416

N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1

O = 6*F*N*COS(I)*2.93/(K^1.6)

D15 = AVERAGE(C12:C26)

E15 = (C12-D12)/D12*100

F15 = C12/1370

G15 = D12/1370

Macro:

Sub CERST001GM() EO (direct):

Dim i As Long 1500*0.286/0.344 = 1247 W/m2 

For i = 12 To 26 EO (reflector image):

Cells(4, 7) = Cells(i, 2) 1247*0.5=623.5 W/m2

Calculate

Cells(i, 3) = Cells(9, 16)

Next i

End Sub

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

-3 -2 -1 0 1 2 3

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 18 Lower Front Zone

(Recessed)

CREST

Front

H=2.69 ft.
NASA/TM—2013-217720 32

Spreadsheet C.12

Column A

 ↓

CREST003A4

PROJECTION BOTTOM 05/27/2011 06/14/2011

Bar XS(ft) YS(ft) XT B(deg) E0(W/m2) YT A(rad) A(deg) S(ft) G(rad) G(deg) D ET(W/m2)

1.000 0.000 -5.000 8.500 -10.000 1247.0 5.300 0.881 50.469 13.354 1.055 60.469 0.096 21.27

2.000 0.000 -4.000 8.500 -3.000 1247.0 5.300 0.830 47.573 12.599 0.883 50.573 -0.078 -19.96

3.000 0.000 -2.500 8.500 0.000 1247.0 5.300 0.742 42.541 11.536 0.742 42.541 -0.005 -1.77

4.000 0.000 -1.000 8.500 2.000 0.0 5.300 0.638 36.545 10.580 0.603 34.545 0.155 0.00

5.000 0.000 1.000 8.500 -2.000 0.0 5.300 0.468 26.834 9.526 0.503 28.834 0.113 0.00

6.000 0.000 2.500 8.500 0.000 1247.0 5.300 0.318 18.232 8.949 0.318 18.232 0.528 329.98

7.000 0.000 4.000 8.500 3.000 1247.0 5.300 0.152 8.695 8.599 0.099 5.695 1.116 773.67

8.000 0.000 5.000 8.500 10.000 1247.0 5.300 0.035 2.021 8.505 -0.139 -7.979 1.116 795.75

ET1 Refl. ET2 Shadow ET3 Shadow ET Average

YT Values ET1 Correction ET2 Correction ET3 Correction ET Sum (bottom) Pct. Dev.

-5.300 795.8 1.0 773.7 1.0 330.0 1.0 1899.4 2942.9 -35.5

-5.250 793.3 1.0 773.3 1.0 347.1 1.0 1913.7 2942.9 -35.0

-5.200 790.0 1.0 772.3 1.0 364.5 1.0 1926.8 2942.9 -34.5

-5.150 785.8 1.0 770.9 1.0 382.1 0.5 1747.8 2942.9 -40.6

-5.100 780.7 1.0 769.1 1.0 400.0 0.0 1549.8 2942.9 -47.3

-5.050 774.6 1.0 766.9 1.0 418.0 0.0 1541.5 2942.9 -47.6

-5.000 767.5 1.0 764.3 1.0 436.1 0.0 1531.8 2942.9 -47.9

-4.950 759.5 1.0 761.4 1.0 454.2 0.0 1520.9 2942.9 -48.3

-4.900 750.6 1.0 758.2 1.0 472.4 0.0 1508.7 2942.9 -48.7

-4.850 740.6 1.0 754.7 1.0 490.4 0.0 1495.3 2942.9 -49.2

-4.800 729.7 1.0 751.0 1.0 508.4 0.0 1480.7 2942.9 -49.7

-4.750 717.9 1.0 747.0 1.0 526.2 0.0 1465.0 2942.9 -50.2

-4.700 705.2 1.0 742.8 1.0 543.8 0.0 1448.0 2942.9 -50.8

-4.650 691.7 1.5 738.2 1.0 561.0 0.0 1775.7 2942.9 -39.7

-4.600 677.3 1.9 733.2 1.0 578.0 0.0 2020.0 2942.9 -31.4

-4.550 662.1 1.9 727.5 0.5 594.5 0.0 1621.7 2942.9 -44.9

-4.500 646.1 1.9 720.9 0.0 610.6 0.0 1227.6 2942.9 -58.3

-4.450 629.5 1.9 712.5 0.0 626.2 0.0 1196.0 2942.9 -59.4

-4.400 612.2 1.9 720.6 0.0 641.2 0.0 1163.2 2942.9 -60.5

4.400 612.2 1.9 720.6 0.0 641.2 0.0 1163.2 2942.9 -60.5

4.450 629.5 1.9 712.5 0.0 626.2 0.0 1196.0 2942.9 -59.4

4.500 646.1 1.9 720.9 0.0 610.6 0.0 1227.6 2942.9 -58.3

4.550 662.1 1.9 727.5 0.5 594.5 0.0 1621.7 2942.9 -44.9

4.600 677.3 1.9 733.2 1.0 578.0 0.0 2020.0 2942.9 -31.4

4.650 691.7 1.5 738.2 1.0 561.0 0.0 1775.7 2942.9 -39.7

4.700 705.2 1.0 742.8 1.0 543.8 0.0 1448.0 2942.9 -50.8

4.750 717.9 1.0 747.0 1.0 526.2 0.0 1465.0 2942.9 -50.2

4.800 729.7 1.0 751.0 1.0 508.4 0.0 1480.7 2942.9 -49.7

4.850 740.6 1.0 754.7 1.0 490.4 0.0 1495.3 2942.9 -49.2

4.900 750.6 1.0 758.2 1.0 472.4 0.0 1508.7 2942.9 -48.7

4.950 759.5 1.0 761.4 1.0 454.2 0.0 1520.9 2942.9 -48.3

5.000 767.5 1.0 764.3 1.0 436.1 0.0 1531.8 2942.9 -47.9

5.050 774.6 1.0 766.9 1.0 418.0 0.0 1541.5 2942.9 -47.6

5.100 780.7 1.0 769.1 1.0 400.0 0.0 1549.8 2942.9 -47.3

5.150 785.8 1.0 770.9 1.0 382.1 0.5 1747.8 2942.9 -40.6

5.200 790.0 1.0 772.3 1.0 364.5 1.0 1926.8 2942.9 -34.5

5.250 793.3 1.0 773.3 1.0 347.1 1.0 1913.7 2942.9 -35.0

5.300 795.8 1.0 773.7 1.0 330.0 1.0 1899.4 2942.9 -35.5

Formulas: Macro:

I = -ATAN((C-G)/(D-B)) Sub CERST003A4M()

J = I*180/3.1416 Dim i As Long

K = ((C-G)^2+(D-B)^2)^0.5

L = -E*3.1416/180+I For i = 15 To 31

M =L*180/3.1416 Cells(4, 7) = Cells(i, 2)

N = (16*(COS(L))^16-2.9*COS(15*L)/((((L*57.3)^2)^0.5+1)^(1/5)))/13.1 Calculate

O = 6*F*N*COS(I)*2.93/(K^1.6) Cells(i, 3) = Cells(4, 15)

Cells(i, 5) = Cells(5, 15)

I15 = C15*D15+E15*F15+G15*H15 Cells(i, 7) = Cells(6, 15)

K15 = (IC15-J15)/J15*100 Next i

For i = 33 To 49

Cells(4, 7) = Cells(i, 2)

Calculate

Cells(i, 3) = Cells(11, 15)

Cells(i, 5) = Cells(10, 15)

Cells(i, 75) = Cells(9, 15)

Next i

End Sub

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

-5.3 -5.2 -5.1 -5.0 -4.9 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 19 Front Projection Bottom

(Albedo)

CREST

Front

Projection

D=0.92 ft.

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3

Relative Flux Density (percent)

Distance from Center (feet)

Fig. 20 Rear Projection Bottom

(Albedo)

CREST

Rear

Projection

D=0.92 ft.
NASA/TM—2013-217720 33

Spreadsheet C.13

Column A

 ↓

CREST001A3

REAR PROJECTION BOTTOM 05/27/2011 06/14/2011

Bar EO(W/m2) S(ft) G(deg) G(rad) D ET(W/m2)

1.000 1247.0 4.350 20.000 0.349 0.391 816.13

ET Sum: 816.13

G Values

(degrees) ETSum ET Average Pct. Dev. IR Suns Avg. IR Suns

-20.000 816.13 1880.36 -56.6 0.596 1.373

-18.000 1141.43 1880.36 -39.3 0.833 1.373

-16.000 1485.00 1880.36 -21.0 1.084 1.373

-14.000 1805.26 1880.36 -4.0 1.318 1.373

-12.000 2065.50 1880.36 9.8 1.508 1.373

-10.000 2241.79 1880.36 19.2 1.636 1.373

-8.000 2327.47 1880.36 23.8 1.699 1.373

-6.000 2333.36 1880.36 24.1 1.703 1.373

-4.000 2282.87 1880.36 21.4 1.666 1.373

-2.000 2201.98 1880.36 17.1 1.607 1.373

0.000 2085.94 1880.36 10.9 1.523 1.373

2.000 2201.98 1880.36 17.1 1.607 1.373

4.000 2282.87 1880.36 21.4 1.666 1.373

6.000 2333.36 1880.36 24.1 1.703 1.373

8.000 2327.47 1880.36 23.8 1.699 1.373

10.000 2241.79 1880.36 19.2 1.636 1.373

12.000 2065.50 1880.36 9.8 1.508 1.373

14.000 1805.26 1880.36 -4.0 1.318 1.373

16.000 1485.00 1880.36 -21.0 1.084 1.373 Formulas:

18.000 1141.43 1880.36 -39.3 0.833 1.373 M = L*3.1416/180

20.000 816.13 1880.36 -56.6 0.596 1.373 N = (16*(COS(M))^16-2.9*COS(15*M)/((((M*57.3)^2)^0.5+1)^(1/5)))/13.1

O = 6*F*N*2.93/(K^1.6)

D = AVERAGE(C12:C32)

E = (C-D)/D*100

F = C/1370

G = D/1370

Macro:

Sub CERST001A3M()

Dim i As Long

For i = 12 To 32

Cells(4, 12) = Cells(i, 2)

Calculate

Cells(i, 3) = Cells(9, 16)

Next i

End Sub

0.0

0.5

1.0

1.5

2.0

-20 -15 -10 -5 0 5 10 15 20

Incident Flux Density (IR suns)

( S = 4.35 ft)

Deviation (deg) from 32 deg Center

Fig. 22 Rear Projection Supplementary
NASA/TM—2013-217720 34

Spreadsheet C.14

 Column A

 ↓

CREST000

Table 2 CREST Illuminated Surfaces 04/04/2012

 Table 2 Development of CREST In-Chamber Illumination Levels

Face Required Skin Skin SSA

Dimensions Flux Density Material Thickness ISA SSA Correction CSSA

Surface (ft. x ft.) (LEO suns) (mils) (div) (div) Lg(%) Xv(%) (div)

______________________ __________ __________ __________ _______ __________ _____ _____ __________

Bottom 8.75 x 10.6 0.95 Slvr. Teflon 5 0.697 1.002 8.0 0.5 1.087

0.65 0.685 8.0 0.5 0.744

Top 10.53 x 10.6 0.375 Alum. Mylar 4 1.488 0.844 8.0 2.5 0.933

Front Upper 2.09 x 10.6 0.927 Alum. Mylar 4 1.488 2.087 8.0 2.0 2.295

 Front Lower 2.95 x 10.6 0.927 Slvr. Teflon 5 0.697 0.977 8.0 2.5 1.080

Rear -- 0.25 Alum. Mylar 4 1.488 0.563 8.0 -3.0 0.591

0.5 1.126 8.0 -3.0 1.182

0.75 1.688 8.0 -3.0 1.773

Formulas: G12=F12*C12/0.661 J12=G12*(1+(H12+I12)/100)

G13=F12*C13/0.661 J13=G13*(1+(H13+I13)/100)

G15=F15*C15/0.661 J15=G15*(1+(H15+I15)/100)

G17=F17*C17/0.661 J17=G17*(1+(H17+I17)/100)

G19=F19*C19/0.661 J19=G19*(1+(H19+I19)/100)

G21=F21*C21/0.661 J21=G21*(1+(H21+I21)/100)

G22=F21*C22/0.661 J22=G22*(1+(H22+I22)/100)

G23=F21*C23/0.661 J13=G13*(1+(H23+I23)/100)
NASA/TM—2013-217720 35

Spreadsheet C.15 

 Column A

 ↓

CREST000

Table 3 CREST In-Chamber Calibrated Levels 04/05/2012

 Table 3 Development of CREST In-Chamber Power Control Levels

Original Required Skin Master Hukseflux Correction Auto Control Uncorrected Correction Corrected

Illumination Flux Density Material Channel Reading CSSA/ICC Setpoint Manual (CSSA/ Manual

Surface Source (LEO suns) (W/m2) (W/m2) (percent) ICC)^0.6 (percent)

______________________ __________ __________ __________ __________ __________ __________ __________ __________ __________

Bottom Albedo 0.95 Slvr. Teflon 15 100 1.013 101.3 21 1.008 21.2

0.65 52 1.000 52.0 17 1.000 17.0

Top 22 Deg. Sun 0.375 Alum. Mylar 12 191 0.979 187.0 36 0.987 35.5

Front Upper 22 Deg. Sun 0.927 Alum. Mylar 10 700 0.962 673.2 50 0.977 48.8

 Front Lower 22 Deg. Sun 0.927 Slvr. Teflon *11 none none none 24.5 1.017 24.9

Rear Dark Side 0.25 Alum. Mylar 20 none none none 31 1.007 31.2

0.5 51 1.011 51.6

0.75 69 0.987 68.1

 *Channel 11 command voltage slaved at 50.1 % of channel 10.

 CSSA/ICC (CSSA/ICC)^0.6

Formulas: G12=1.09/1.076 H12=F12*G12 J12=(1.09/1.076)^0.6 K12=I12*J12

G13=.74/.74 H12=F13*G13 J13=(0.74/0.74)^0.6 K13=I13*J13

G15=.93/.95 H15=F15*G15 J15=(0.93/0.95)^0.6 K15=I15*J15

G17=2.26/2.35 H17=F17*G17 J17=(2.26/2.35)^0.6 K17=I17*J17

J19=(109.6/1.065)^0.6 K19=I19*J19

J21=(0.59/0.583)^0.6 K21=I21*J21

J22=(1.18/1.158)^0.6 K22=I22*J22

J23=(1.77/1.81)^0.6 K23=I23*J23
NASA/TM—2013-217720 36

Spreadsheet C.16

 Column A

 ↓

CREST001E1

ARRAY BAR FALLOFF VS DISTANCE (S EXPONENT DEVELOPMENT) 06/06/2011 07/14/2011

Lamp XS(ft) YS(ft) XT EO(W/m2) YT A(rad) A(deg) S(ft) D ET(W/m2) ET Sum:

1.000 0.000 -5.625 13.000 1.000 0.000 0.408 23.398 14.165 0.918 0.004 0.083

2.000 0.000 -4.875 13.000 1.000 0.000 0.359 20.556 13.884 0.936 0.005

3.000 0.000 -4.125 13.000 1.000 0.000 0.307 17.605 13.639 0.953 0.005

4.000 0.000 -3.375 13.000 1.000 0.000 0.254 14.554 13.431 0.968 0.005

5.000 0.000 -2.625 13.000 1.000 0.000 0.199 11.416 13.262 0.980 0.005

6.000 0.000 -1.875 13.000 1.000 0.000 0.143 8.207 13.135 0.990 0.006

7.000 0.000 -1.125 13.000 1.000 0.000 0.086 4.946 13.049 0.996 0.006

8.000 0.000 -0.375 13.000 1.000 0.000 0.029 1.652 13.005 1.000 0.006

9.000 0.000 0.375 13.000 1.000 0.000 -0.029 -1.652 13.005 1.000 0.006

10.000 0.000 1.125 13.000 1.000 0.000 -0.086 -4.946 13.049 0.996 0.006

11.000 0.000 1.875 13.000 1.000 0.000 -0.143 -8.207 13.135 0.990 0.006

12.000 0.000 2.625 13.000 1.000 0.000 -0.199 -11.416 13.262 0.980 0.005

13.000 0.000 3.375 13.000 1.000 0.000 -0.254 -14.554 13.431 0.968 0.005

14.000 0.000 4.125 13.000 1.000 0.000 -0.307 -17.605 13.639 0.953 0.005

15.000 0.000 4.875 13.000 1.000 0.000 -0.359 -20.556 13.884 0.936 0.005

16.000 0.000 5.625 13.000 1.000 0.000 -0.408 -23.398 14.165 0.918 0.004

XT-XS --------------------- ET Approximations --------------------- --------------------------- % Error ----------------------------

Values ET Sum 1/S 1/(S^1.6) 1/S^(MS+B) 1/(S^S^K) 1/(S^2) 1/S 1/(S^1.6) 1/S^(MS+B) 1/(S^S^K) 1/(S^2)

6.000 0.286 0.286 0.286 0.286 0.286 0.286 0.074 0.069 0.074 0.143 -0.093

6.200 0.273 0.277 0.271 0.277 0.273 0.266 1.388 -0.593 1.330 -0.119 -2.701

6.400 0.261 0.268 0.258 0.268 0.260 0.248 2.733 -1.174 2.505 -0.346 -4.811

6.600 0.250 0.260 0.246 0.259 0.248 0.234 4.110 -1.682 3.599 -0.543 -6.459

6.800 0.239 0.252 0.234 0.250 0.237 0.220 5.516 -2.123 4.611 -0.712 -7.984

7.000 0.229 0.245 0.223 0.242 0.227 0.208 6.949 -2.504 5.543 -0.855 -9.399

7.200 0.220 0.238 0.214 0.234 0.218 0.196 8.410 -2.829 6.392 -0.975 -10.712

7.400 0.211 0.232 0.204 0.226 0.209 0.186 9.896 -3.103 7.161 -1.073 -11.935

7.600 0.203 0.226 0.196 0.219 0.200 0.176 11.406 -3.331 7.847 -1.152 -13.074

7.800 0.195 0.220 0.188 0.211 0.192 0.167 12.939 -3.516 8.454 -1.213 -14.138

8.000 0.187 0.215 0.180 0.204 0.185 0.159 14.494 -3.662 8.979 -1.258 -15.131

8.200 0.180 0.209 0.173 0.197 0.178 0.151 16.070 -3.773 9.425 -1.288 -16.062

8.400 0.174 0.204 0.167 0.191 0.171 0.144 17.666 -3.850 9.791 -1.305 -16.933

8.600 0.167 0.200 0.161 0.184 0.165 0.138 19.281 -3.896 10.079 -1.310 -17.751

8.800 0.161 0.195 0.155 0.178 0.159 0.131 20.914 -3.915 10.289 -1.304 -18.520

9.000 0.156 0.191 0.149 0.172 0.154 0.126 22.565 -3.908 10.423 -1.289 -19.243

9.200 0.150 0.187 0.144 0.166 0.148 0.120 24.233 -3.876 10.481 -1.265 -19.924

9.400 0.145 0.183 0.139 0.160 0.143 0.115 25.916 -3.823 10.466 -1.233 -20.566

9.600 0.140 0.179 0.135 0.155 0.138 0.110 27.614 -3.750 10.378 -1.194 -21.172

9.800 0.135 0.175 0.130 0.149 0.134 0.106 29.327 -3.657 10.219 -1.149 -21.744

10.000 0.131 0.172 0.126 0.144 0.129 0.102 31.053 -3.547 9.990 -1.099 -22.285

10.200 0.127 0.168 0.122 0.139 0.125 0.098 32.793 -3.421 9.694 -1.044 -22.798

10.400 0.123 0.165 0.119 0.134 0.121 0.094 34.546 -3.280 9.331 -0.985 -23.283

10.600 0.119 0.162 0.115 0.129 0.118 0.091 36.310 -3.125 8.904 -0.923 -23.743

10.800 0.115 0.159 0.112 0.125 0.114 0.087 38.086 -2.957 8.415 -0.857 -24.180

11.000 0.112 0.156 0.108 0.120 0.111 0.084 39.874 -2.777 7.866 -0.789 -24.595

11.200 0.108 0.153 0.105 0.116 0.107 0.081 41.672 -2.586 7.258 -0.719 -24.990

11.400 0.105 0.151 0.102 0.112 0.104 0.078 43.480 -2.385 6.594 -0.647 -25.365

11.600 0.102 0.148 0.100 0.108 0.101 0.076 45.298 -2.175 5.876 -0.573 -25.723

11.800 0.099 0.145 0.097 0.104 0.098 0.073 47.125 -1.955 5.106 -0.499 -26.063

12.000 0.096 0.143 0.094 0.100 0.096 0.071 48.962 -1.727 4.286 -0.424 -26.388

12.200 0.093 0.141 0.092 0.096 0.093 0.068 50.807 -1.492 3.418 -0.348 -26.698

12.400 0.091 0.138 0.090 0.093 0.090 0.066 52.660 -1.249 2.504 -0.272 -26.994

12.600 0.088 0.136 0.087 0.090 0.088 0.064 54.521 -1.000 1.548 -0.197 -27.277

12.800 0.086 0.134 0.085 0.086 0.086 0.062 56.391 -0.745 0.550 -0.121 -27.547

13.000 0.083 0.132 0.083 0.083 0.083 0.060 58.267 -0.484 -0.487 -0.046 -27.806

Upper Formulas: Lower Formulas:

J = -ATAN((C-H)/(E-B)) E = 6/B*0.286

K = J*180/3.1416 F = 6*2.93/((B)^1.6)*0.286

L = ((C-H)^2+(E-B)^2)^0.5 G = (6/B)^(0.0857*B+0.486)*0.286

O = COS(J) H = 6*1.496/((B)^(B^0.113))*0.286

P =G*O*COS(J)/L^2 I = 6*5.99/(B)^2)*0.286

Q = SUM(P4:P19)

K = (E-C)/C*100

Macro: L = (F-C)/C*100

Sub CERST001EM() M = (G-C)/C*100

Dim i As Long N = (H-C)/C*100

O = (I-C)/C*100

For i = 25 To 60

Cells(5,5) = Cells(I,2)

Calculate

Cells(i,3) = Cells(5,17)

Next i

End Sub

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

6 7 8 9 10 11 12 13

Deviation from Reference Fall-Off 

(Percent)

Distance XS-XT (feet)

Fig. 27 Exponent 

Development

1/S^2

1/S^(MS+B)

1/S^1.6

1/(S^S^K)

1/S
NASA/TM—2013-217720 37

References

1. Pauls, Edward (Research Incorporated), “Energy 

Distribution Curve,” Acceptance Test Results for Thermal

Simulator Test Fixture (December 14, 1965): figures 2-2

and 2-5.

2. Ziemke, Robert, “Infrared Heater Used in Qualification 

Testing of International Space Station Radiators,” 

NASA/TM—2004-212332 (2004): 12, figure 7a.

3. Ziemke, Robert, “Infrared Heater Used in Qualification 

Testing of International Space Station Radiators,” 

NASA/TM—2004-212332 (2004): 7, step 5.

4. Henninger, John, “Solar Absorptance and Thermal 

Emittance of Some Spacecraft Thermal-Control 

Coatings,” NASA Reference Publication 1121 (April 

1984): 16.

5. Forsythe, W. E., and Worthing, A. G., “The Properties of 

Tungsten and the Characteristics of Tungsten Lamps,” 

Astrophysical Journal, vol. 61 (1925): 171

6. Smith, Warren, “The Inverse Square Law,” Modern 

Optical engineering (1966): 182.

Biography

Mr. Ziemke works in the Plum Brook Management Office 

at the NASA Glenn Research Center’s Plum Brook station in 

Sandusky, Ohio. He is currently serving as an electronics 

engineer specializing in solar and thermal simulation, and 

analysis. He designed the infrared heating system for the 

qualification testing of the International Space Station 

radiators and has consulted on proposed design concepts for 

the Orion Crew Exploration Vehicle thermal simulation. In 

1971, he designed the 7.2 megawatt SCR power control 

system for the Viking Centaur heated fairing jettison test

performed at NASA Plum Brook’s Space Power Facility. He 

has over 35 years experience as a NASA instrumentation and 

controls engineer. He holds a Bachelor’s degree in electrical 

engineering from the Cleveland State University.
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Solar Simulation for the CREST Preflight Thermal-Vacuum Test at B-2 

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In June 2011, the multi-university sponsored Cosmic Ray Electron Synchrotron Telescope (CREST) has undergone thermal-vacuum 

qualification testing at the NASA Glenn Research Center (GRC), Plum Brook Station, Sandusky, Ohio. The testing was performed in the B2 Space Propulsion Facility vacuum chamber. The CREST was later flown over the Antarctic region as the payload of a stratospheric 

balloon. Solar simulation was provided by a system of planar infrared lamp arrays specifically designed for CREST. The lamp arrays, in 

conjunction with a liquid-nitrogen-cooled cryoshroud, achieved the required thermal conditions for the qualification tests. This report 

focuses on the design and analysis of the planar arrays based on first principles. Computational spreadsheets are included in the report.

15. SUBJECT TERMS

Thermal vacuum tests; Infrared radiation; Luminaries; Flux density; Solar spectra; Pyranometers; Albedo 

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