Catherine E. McCarthy

Hathaway Brown School, Shaker Heights, Ohio

Bruce A. Banks

Alphaport, Inc., Cleveland, Ohio

Kim K. de Groh

Glenn Research Center, Cleveland, Ohio

MISSE 2 PEACE Polymers Experiment Atomic

Oxygen Erosion Yield Error Analysis

NASA/TM—2010-216903

November 2010
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Catherine E. McCarthy

Hathaway Brown School, Shaker Heights, Ohio

Bruce A. Banks

Alphaport, Inc., Cleveland, Ohio

Kim K. de Groh

Glenn Research Center, Cleveland, Ohio

MISSE 2 PEACE Polymers Experiment Atomic

Oxygen Erosion Yield Error Analysis

NASA/TM—2010-216903

November 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

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7115 Standard Drive

Hanover, MD 21076–1320

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Available electronically at http://gltrs.grc.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

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Level of Review: This material has been technically reviewed by technical management. 

Acknowledgments

We would like to acknowledge and thank former students Jon Gummow of Ohio Aerospace Institute, Doug Wright of Cleveland 

State University, and PEACE Team students for making and characterizing fl ight and back-up samples. We gratefully acknowledge 

Patty Hunt of Hathaway Brown School for making it possible for the students to be a part of this project. Finally, we would like 

to express our sincere appreciation to the MISSE Project Offi ce at NASA Langley Research Center and Gary Pippin, formerly of 

Boeing, for providing the unique opportunity to be a part of the MISSE program.
NASA/TM—2010-216903 1 

MISSE 2 PEACE Polymers Experiment Atomic Oxygen 

Erosion Yield Error Analysis 

Catherine E. McCarthy 

Hathaway Brown School 

Shaker Heights, Ohio 44122 

Bruce A. Banks 

Alphaport, Inc. 

Cleveland, Ohio 44135 

Kim K. de Groh 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

ABSTRACT 

Atomic oxygen erosion of polymers in low Earth orbit (LEO) poses a serious threat to 

spacecraft performance and durability. To address this, 40 different polymer samples and a 

sample of pyrolytic graphite, collectively called the PEACE (Polymer Erosion and 

Contamination Experiment) Polymers, were exposed to the LEO space environment on the 

exterior of the International Space Station (ISS) for nearly four years as part of the Materials 

International Space Station Experiment 1 & 2 (MISSE 1 & 2). The purpose of the PEACE 

Polymers experiment was to obtain accurate mass loss measurements in space to combine with 

ground measurements in order to accurately calculate the atomic oxygen erosion yields of a wide 

variety of polymeric materials exposed to the LEO space environment for a long period of time. 

Error calculations were performed in order to determine the accuracy of the mass measurements 

and therefore of the erosion yield values. The standard deviation, or error, of each factor was 

incorporated into the fractional uncertainty of the erosion yield for each of three different 

situations, depending on the post-flight weighing procedure. The resulting error calculations 

showed the erosion yield values to be very accurate, with an average error of ±3.30 percent. 

1. INTRODUCTION 

1.1 MISSE 2 Polymer Erosion and Contamination Experiment (PEACE) Polymers 

Spacecraft in the low Earth orbit (LEO) environment (between 200 and 2000 km above the 

surface of the Earth) endure extremely harsh conditions, including exposure to ultraviolet, x-ray, 

and charged particle radiation; micrometeoroids and debris; and atomic oxygen, diatomic oxygen 

photodissociated by short wavelength ultraviolet radiation from the sun. Atomic oxygen erosion 

of polymers in LEO poses a serious threat to spacecraft performance and durability. Therefore in 

order to design durable high-performance spacecraft systems, it is essential to understand the 

atomic oxygen erosion yield (E, the volume loss per incident oxygen atom, in cm3

/atom) of 

polymers being considered for spacecraft applications. 
NASA/TM—2010-216903 2 

Figure 1. MISSE 2 PEC 2 Tray 1, containing the PEACE Polymers experiment attached to the ISS, 

exposed to space from August 16, 2001 to July 30, 2005. 

Forty polymer samples (including two Kapton H polyimide atomic oxygen fluence witness 

samples) and pyrolytic graphite, collectively called the PEACE (Polymer Erosion and 

Contamination Experiment) Polymers, were exposed to the LEO space environment on the 

exterior of the ISS as part of the Materials International Space Station Experiment 1 & 2 (MISSE 

1 & 2).1-3 The PEACE Polymers experiment was flown in MISSE Passive Experiment Container 

2 (PEC 2) on the ram-facing tray (Tray 1) in sample tray E5. MISSE PEC 2 (MISSE 2) was 

attached to the exterior of the ISS Quest Airlock, as shown in Figure 1. The one-inch-diameter 

samples encountered atomic oxygen and solar and charged particle radiation during a 3.95-year 

exposure to the LEO environment from August 16, 2001 to July 30, 2005, when the experiment 

was successfully retrieved via spacewalk during Discovery’s STS-114 Return to Flight mission. 

The purpose of the MISSE 2 PEACE Polymers experiment was to obtain accurate mass loss 

measurements of passive samples exposed to atomic oxygen in space to combine with ground 

measurements in order to accurately calculate the atomic oxygen erosion yield of a wide variety 

of polymeric materials exposed to the LEO space environment for a long period of time.1-3 The 

data obtained could then help explain the dependence of erosion yield upon polymer chemistry 

for predictive tool development. Figures 2 and 3 show pre-flight and post-flight photos, 

respectively, of the MISSE 2 PEACE Polymers experiment tray containing the 41 samples. 

MISSE 2 
NASA/TM—2010-216903 3 

Figure 2. Pre-flight photograph of the MISSE 2 PEACE Polymers experiment. Abbreviations are defined 

in Table 1. 

Figure 3. Post-flight photograph of the MISSE 2 PEACE Polymers experiment. 

The 40 different materials (41 samples) tested included those commonly used for spacecraft 

applications, such as Teflon FEP, as well as more recently developed polymers, such as high 

temperature polyimide PMR-15 (polymerization of monomer reactants), and pyrolytic graphite, 

which was included for more diverse chemistry. 

The atomic oxygen fluence for the experiment tray was found to be 8.43 x 1021 atoms/cm2

based on the average of the two fluence witness samples.1-3 The total equivalent sun hours (ESH) 

for the E5 tray was estimated to be 6,300 ESH.1-4 The base-plate thermal cycling temperature 

range for MISSE 2 was nominally between +40°C and -30°C, with occasional short-term 

excursions to more extreme temperatures.*,4 Results of x-ray photoelectron spectroscopy (XPS) 

contamination analysis of two MISSE 2 sapphire witness samples in sample tray E6 (located 

next to tray E5) indicated the experiment had received very little contamination; the sapphire 

witness samples sustained only extremely thin silica contaminant layers, one 1.3 nm thick and 

one 1.4 nm thick.5 

* Details of atomic oxygen fluence calculations, the specific polymers flown, flight sample fabrication, solar and 

ionizing radiation environmental exposure, and pre-flight and post-flight characterization techniques are 

presented in Refs. 1-3. Additional details on environmental exposure are provided by Pippin in Ref. 4. 
NASA/TM—2010-216903 4 

In any experiment, it is critical to determine the accuracy of the data obtained. To address 

this, the error in each polymer’s experimental erosion yield value was calculated using equations 

for fractional uncertainty derived from the equation used to find erosion yield. 

1.2 Erosion Yield 

The equation to find the erosion yield (E) of a polymer calculates the volume lost per 

incident atomic oxygen atom: 

ൌ ܧ

ܯ∆ · 4

ܨ · ଶܦ·ߩ·ߨ

where ΔM is mass loss (g), ρ is the polymer density (g/cm3

), and D is the exposed diameter of 

the polymer (cm). F is the atomic oxygen fluence (atoms/cm2), which is how many atoms of 

atomic oxygen came into contact with the polymer during the period of exposure. Two Kapton H 

witness samples were used to calculate the fluence because Kapton H has a well-established 

erosion yield in LEO, 3.0 x 10-24

 cm3/atom.6 The atomic oxygen fluence for the samples can be 

calculated by solving Equation 1 for F and using the Kapton H mass loss value and density. The 

fluence was based on the frontal exposed area of each sample.† 

1.3 Fractional Uncertainty 

Fractional uncertainty, also called relative uncertainty or percent error, is a way of 

quantifying the error of a data value. In this investigation the fractional uncertainty represents the 

fractional standard deviation of the values and is calculated by dividing the standard deviation of 

the value by the value itself. The general equation for fractional uncertainty in atomic oxygen 

erosion yield is 

ܧߜ

ܧ ൌ ඨ෍ቈ൬1

· ܧ

ܧ߲

iݔ߲

൰ݔߜ ·

ଶ

቉

௜

where E is atomic oxygen erosion yield and xi is the ith variable in the equation for erosion yield. 

The complete equation derivations are explained in Section 4. 

2. MATERIALS 

A list of the different materials exposed to atomic oxygen on the MISSE 2 PEACE polymer 

experiment is given in Table 1, along with the material abbreviation, trade name(s), and material 

thickness. 

†

 It is believed that the 45° slanted edges of the aluminum sample holders contributed to a slight increase in fluence 

around the perimeters of the samples, causing some to erode through only around the edge; however, since this 

was the case for all of the samples, no further calculations needed to be done to correct for this anomalous effect. 

 

(1)

(2)
NASA/TM—2010-216903 5 

Table 1. Materials Included in the MISSE 2 PEACE Polymers Experiment. 

Material Abbrev. Trade Name(s)

Thickness 

(mils)

Acrylonitrile butadiene styrene ABS Cycolac 5

Allyl diglycol carbonate ADC CR-39, Homalite H-911 31

Amorphous fluoropolymer AF Teflon AF 1601 2

Cellulose acetate CA Clarifoil, Tenite Acetate, Dexel 2

Chlorotrifluoroethylene CTFE Neoflon CTFE M-300, Kel-F 5

Crystalline polyvinylfluoride with white pigment PVF-W White Tedlar TWH10BS3 1

Epoxide or epoxy EP Hysol EA 956 88-92

Ethylene-chlorotrifluoroethylene ECTFE Halar 3

Ethylene-tetrafluoroethylene copolymer ETFE Tefzel ZM 3

Fluorinated ethylene propylene FEP Teflon FEP (round robin) 2

High temperature polyimide resin PI PMR-15 12-14

Perfluoroalkoxy copolymer resin PFA Teflon PFA CLP (200 CLP) 2

Poly-(p-phenylene terephthalamide) PPD-T Kevlar 29 fabric 2.2

Poly(p-phenylene-2 6-benzobisoxazole) PBO Balanced biaxial film 1

Polyacrylonitrile PAN Barex 210 2

Polyamide 6 or Nylon 6 PA 6 Akulon K, Ultramid B 2

Polyamide 66 or Nylon 66 PA 66 Maranyl A, Zytel 2

Polybenzimidazole PBI Celazole PBI 2

Polybutylene terephthalate PBT GE Valox 357 3

Polycarbonate PC PEEREX 61 (P61) 10

Polyetheretherketone PEEK Victrex PEEK 450 3

Polyetherimide PEI Ultem 1000 10

Polyethylene PE 2

Polyethylene oxide PEO Alkox E-30 29

Polyethylene terephthalate PET Mylar A-200 2

Polyimide PI LaRC CP1 (CP1-300) 3

Polyimide (BPDA) PI Upilex-S 1

Polyimide (PMDA), sample 1 PI Kapton H 5

Polyimide (PMDA), sample 2 PI Kapton H 5

Polyimide (PMDA) PI Kapton HN 5

Polymethyl methacrylate PMMA Plexiglas, Lucite, Acrylite (Impact Mod.) 2

Polyoxymethylene; acetal; polyformaldehyde POM Delrin (natural) 10

Polyphenylene isophthalate PPPA Nomex Aramid Paper Type 410 2

Polypropylene PP Polypropylene Type C28 20

Polystyrene PS Trycite 1000, Trycite Dew 2

Polysulphone PSU Thermolux P1700-NT11, Udel P-1700 2

Polytetrafluoroethylene PTFE Chemfilm DF 100 2

Polyurethane PU Dureflex PS 8010 2

Polyvinyl fluoride PVF Tedlar TTR10SG3 1

Polyvinylidene fluoride PVDF Kynar 740 3

Pyrolytic graphite PG 80
NASA/TM—2010-216903 6 

3. EXPERIMENTAL PROCEDURES 

3.1 Mass Loss Measurements 

For both pre- and post-flight mass measurements, all samples were vacuum-desiccated at 60-

100 mtorr for a minimum of four days and then weighed with a Mettler M3 Balance. Records 

were kept of time under vacuum, sequence of weighing, and room temperature and humidity.1-3

The same sequence and procedures used for the pre-flight measurements were repeated postflight. 

3.2 Density Measurements 

A material’s theoretical density, provided by the manufacturer, is not always accurate 

because of variation among different sheets of the polymer. To obtain the densities of the exact 

materials used in the experiment, a process known as density column measurement was used. A 

density gradient column was created in a 50-mL buret with solvents of either cesium chloride 

(CsCl) and water (H2O), for less dense polymers, or carbon tetrachloride (CCl4) and bromoform 

(CHBr3), for more dense polymers. Glass standards of known densities were placed in the 

column and allowed to settle, and then small pieces of various polymers were placed in the 

columns. A curve was fit to the positions and relative known densities of the glass standards. 

Plotting the positions of the test polymers on this curve yielded density values for each 

material.1-3

3.3 Diameter Measurements 

The MISSE 2 PEACE polymers were fabricated into one-inch (2.54-cm) diameter discs 

using a double bow punch cutter and an Arbor press. Although the intended diameter of the 

samples was precisely one inch, the samples were flown in a tray with a metal lid that slightly 

overlapped the edge of each polymer, so to account for the overlap as well as for slight variations 

in the size of the openings, 10 diameter measurements were taken of each sample tray opening at 

different positions using a digital micrometer. The average of these 10 measurements was used 

as the sample diameter. This provided a more exact value for the respective exposed diameter for 

each sample.1-3

3.4 Sample Stacking 

MISSE 1 & 2 was originally planned as a one-year mission, and enough layers of each 

polymer were stacked to last 1.5 years, based on estimated erosion yield data.1-3 This set of 

layers was collectively called “flight sample part A.” Retrieval of MISSE 1 & 2 was significantly 

delayed due to the Columbia accident; the experiments were retrieved on July 30, 2005, during 

Discovery’s STS-114 Return to Flight mission. Because of the delay, the PEACE Polymers 

received nearly four years of space exposure. Fortunately, most of the polymers survived the 47-

month exposure to LEO conditions because a second set of sample layers, collectively referred to 

as “flight sample part B,” had been placed behind flight sample part A, giving a total sample 

thickness that, based on estimated erosion yields, would last for three years. Flight sample part A 

and flight sample part B of each polymer were placed together into one stack to form the entire 

flight sample, as shown in Figure 4. 
NASA/TM—2010-216903 7 

Figure 4. Illustration of the flight sample setup. 

3.5 Mass Loss Situations 

As previously mentioned, each flight sample included two sets of sample layers: part A was 

enough material to theoretically last for 1.5 years in space, and the additional layers of part B 

extended the time to three years. Each flight sample also had a corresponding identical “backup” 

sample (including both parts A and B) that was kept on the ground as a control. Though flight 

sample parts A and B were not separated during flight, they were separated for pre- and postflight weighing. Due to mission time constraints, part B of each sample was not weighed preflight, and so a theoretical value for the pre-flight mass of part B was calculated: the pre-flight 

mass of flight sample part A, MF, and the pre-flight mass of control sample part A, MC, were 

used to calculate the average mass per layer, MA, which was multiplied by the number n of layers 

in flight sample part B to get part B’s theoretical pre-flight mass, n·MA. 

There were three different situations for post-flight sample weighing, so three different 

equations to determine mass loss were required. Mass loss (ΔM) is a factor in calculating the 

erosion yield E of a polymer (see Equation 1), and so it was also necessary to develop three 

different equations for fractional uncertainty of the erosion yield. The different mass loss 

equations were simply substituted into the equation for erosion yield, and then from each of the 

three resulting equations an equation for fractional uncertainty was derived to calculate the 

percent error for that situation. 

In the first situation (see Figure 5), referred to as Situation 1, either only one sample layer 

was flown, or the atomic oxygen eroded through only some of the layers in flight sample part A, 

and all of flight sample part B was still pristine. Because flight sample part A and flight sample 

part B were weighed separately pre-flight, in this situation only part A needed to be weighed 

post-flight and compared with its pre-flight mass, so to minimize error, the terms for pre- and 

post-flight mass for flight sample part B were omitted from the Situation 1 mass loss equation: 

∆ܯଵ ൌ ܯி െ ܯி

ᇱ

where MF is the pre-flight mass of flight sample part A and MF' is the post-flight mass of part A. 

Therefore, the Situation 1 erosion yield equation is: 

ܧଵ ൌ 4 · ሺܯி െ ܯி

ᇱ

ሻ

ܨ · ଶܦ·ߩ·ߨ

Flight Sample 

Part A 

(enough layers to 

survive 1.5 years)

Flight Sample 

Part B 

(enough additional 

layers to survive 

a total of 3 years) 

(4)

(3)
NASA/TM—2010-216903 8 

Figure 5. Illustration of Situation 1 sample erosion. 

In Situation 2 (see Figure 6), atomic oxygen erosion occurred through all of the layers of 

flight sample part A and some of flight sample part B. 

Figure 6. Illustration of Situation 2 sample erosion. 

In this situation, flight sample parts A and B were able to be separated to be weighed 

post-flight. However, because flight sample part B was not weighed pre-flight, its theoretical 

pre-flight mass was used. Therefore, the Situation 2 equation for mass loss is: 

∆ܯଶ ൌ ܯி െ ܯி

ᇱ ൅݊·ܯ ஺െ ܯாԢ

where, again, MF and MF' are the pre- and post-flight mass values, respectively, of flight sample 

part A; n·MA is the theoretical pre-flight mass of flight sample part B; and ME' is the post-flight 

mass of part B. The erosion yield equation for Situation 2 is: 

ܧଶ ൌ 4 · ሺܯி െ ܯி

ᇱ ൅݊·ܯ ஺െ ܯாԢሻ

ܨ · ଶܦ·ߩ·ߨ

Flight 

Sample 

Part A 

Flight 

Sample 

Part B 

Pre-Flight 

(pristine)

Post-Flight

completely 

eroded 

through 

partially 

eroded 

through

Flight 

Sample 

Part A 

Flight 

Sample 

Part B 

Pre-Flight 

(pristine)

Post-Flight

partially 

eroded 

through 

pristine

(6)

(5)
NASA/TM—2010-216903 9 

In Situation 3 (see Figure 7), the sample layers were stuck together and fragmented and were 

too fragile to separate without losing particles of the material and therefore compromising the 

erosion yield data. 

Figure 7. Illustration of Situation 3 sample erosion. 

Because of this, flight sample parts A and B were weighed together post-flight. Therefore, 

the Situation 3 mass loss equation is: 

∆ܯଷ ൌ ܯி ൅݊·ܯ ஺െ ܯௌԢ

where MF is the pre-flight mass of flight sample part A, n·MA is the theoretical pre-flight mass of 

flight sample part B, and MS' is the post-flight mass of the entire flight sample. The Situation 3 

erosion yield equation is: 

ܧଷ ൌ 4 · ሺܯி ൅݊·ܯ ஺െ ܯௌԢሻ

ܨ · ଶܦ·ߩ·ߨ

One of the variables in the erosion yield equations is atomic oxygen fluence, F, which is 

itself found from an equation (the erosion yield equation (see Equation 1)) rearranged. Because 

this F value was also based on a series of measurements, the equation for F needed to be 

substituted into the erosion yield equations so that the error calculations could take into account 

all sources of error. 

The equation for the fluence of the Kapton fluence witness samples is: 

௄ܯ∆ · 4 ൌ௄ ܨ

௄ܦ · ௄ߩ·ߨ௄ܧ · ଶ

But the atomic oxygen fluence value used in the experiment was actually the average of the 

two F values of the two Kapton H witness samples that were flown. This needed to be taken into 

account as well; the expression for the average of the two fluence values is found as follows: 

1 ൌ௄ ீ ஺௏ܨ

2 ቆ 4 · ∆ܯ௄ଵ

ଵ௄ܦ · ௄ߩ·ߨ௄ܧ · ଶ

൅

ଶ௄ܯ∆ · 4

ଶ௄ܦ · ௄ߩ·ߨ௄ܧ · ଶ

ቇ ൌ 4

௄ܧ · ௄ߩ · ߨ2

· ቆ∆ܯ௄ଵ

ଵ௄ܦ

ଶ ൅

ଶ௄ܯ∆

ଶ௄ܦ

ଶ ቇ

 

Flight 

Sample 

Part A 

Flight 

Sample 

Part B 

Pre-Flight 

(pristine)

Post-Flight

Partially 

eroded 

through 

(8)

(9)

(7)
NASA/TM—2010-216903 10 

This expression for FAVG K is then substituted into the equation for sample erosion yield: 

ܧௌ ൌ 4 · ∆ܯௌ

ௌܦ · ௌߩ·ߨ௄ீ ௏஺ܨ · ଶ

ൌ 4 · ∆ܯௌ

ௌܦ · ௌߩ·ߨ

௄ܧ · ௄ߩ · ߨ2 · ଶ

4 ൬

ଵ௄ܯ∆

ଵ௄ܦ

ଶ ൅ ∆ܯ௄ଶ

ଶ௄ܦ

ଶ ൰

௄ܧ · ௄ߩ · ௌܯ∆ · 2 ൌ

ௌܦ · ௌߩ

ଶ · ൬

ଵ௄ܯ∆

ଵ௄ܦ

ଶ ൅ ∆ܯ௄ଶ

ଶ௄ܦ

ଶ ൰

Therefore, the erosion yield equations for the three situations are now: 

ܧଵ ൌ 2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

ௌܦ · ௌߩ

ଶ · ൬

ଵ௄ܯ∆

ଵ௄ܦ

ଶ ൅ ∆ܯ௄ଶ

ଶ௄ܦ

ଶ ൰

ܧଶ ൌ 2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ൬

ଵ௄ܯ∆

ଵ௄ܦ

ଶ ൅ ∆ܯ௄ଶ

ଶ௄ܦ

ଶ ൰

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2 ൌ ଷܧ

ௌܦ · ௌߩ

ଶ · ൬

ଵ௄ܯ∆

ଵ௄ܦ

ଶ ൅ ∆ܯ௄ଶ

ଶ௄ܦ

ଶ ൰

In the final equations for fractional uncertainty, ∆ெ಼భ

஽಼భమ ൅ ∆ெ಼మ஽಼మమ is replaced by the variable R. 

3.6 Atomic Oxygen Fluence Uncertainty 

Table 2 shows the values for mass loss, density, erosion yield, exposed diameter, and the 

corresponding uncertainty values for each of these variables, for the two Kapton fluence witness 

samples. The erosion yield for Kapton H polyimide was assumed to be 3.0 x 10-24 cm3/atom6

with a probable error of ±0.05 x 10-24 cm3/atom, which is a standard deviation error of ±7.41 x 

10-26 cm3

/atom (or 0.024700, a ±2.5 percent fractional uncertainty). 

Table 2. Kapton H Witness Sample Measurement and Uncertainty Values. 

Kapton H 

Sample #

ΔMK 

(g)

δΔMK 

(g)

ρ K 

(g/cm3)

δρ K 

(g/cm3)

DK 

(cm)

δDK 

(cm)

EK 

(cm3/atom) 

δEK 

(cm3/atom) 

δEK/EK 

1 0.124785 0.0000513 2.0986 0.00582

2 0.129219 0.0000808 2.1342 0.00410

1.42725 0.0077 3.00E-24 7.41E-26 0.024700

(10)

(11)

(12)

(13)
NASA/TM—2010-216903 11 

4. FRACTIONAL UNCERTAINTY EQUATION DERIVATIONS AND RESULTS 

The equations for fractional uncertainty in erosion yield were derived from the previous three 

erosion yield equations using partial derivatives. In all of the following derivations, ∂x is the 

partial derivative of x, δx is the uncertainty of x, and ఋ௫

௫ is the fractional uncertainty of x. The 

following variable definitions apply to all of the derived equations: 

E = erosion yield, cm3

/atom 

ΔM = mass loss, g

ρ = density, g/cm3

D = diameter of exposed area of sample, cm

F = atomic oxygen fluence, atoms/cm2

MF = pre-flight mass of flight sample part A, g

MF' = post-flight mass of flight sample part A, g

n·MA = theoretical pre-flight mass for flight sample part B, g

ME' = post-flight mass of flight sample part B, g

MS' = post-flight mass of flight sample parts A and B weighed together, g

A subscript of K refers to the value corresponding to the Kapton fluence witness samples, and a 

subscript of S refers to the value corresponding to the flight sample in question. 

4.1 Fractional Uncertainty Equation Derivations for Situation 1 

Using Equation 11, the equation for Situation 1 erosion yield, the equation for fractional 

uncertainty in erosion yield for Situation 1 ቀ

ఋாభ

ாభ

ቁ is derived through the following process. 

Term one: x1 = MF

൬

1

ଵܧ

·

ଵܧ߲

ிܯ߲

ி൰ܯߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

௄ܧ · ௄ߩ·2 ·

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ிܯߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ܯߜி

ଵܯ∆

൰

ଶ

Term two: x2 = MF' 

൬

1

ଵܧ

ଵܧ߲ ·

ிܯ߲

ᇱ · ܯߜி

ᇱ

൰

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

௄ܧ · ௄ߩ · 2െ· 

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ிܯߜ ·

ᇱ

ی

ۋ

ۊ

ଶ

ൌ ቆെܯߜி

ᇱ

ଵܯ∆

ቇ

ଶ

Term three: x3 = ρS

൬

1

ଵܧ

·

ଵܧ߲

ௌߩ߲

ௌ൰ߩߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

· െ2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

ௌߩ

ଶ · ܦௌ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌߩߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬െߩߜௌ

ௌߩ

൰

ଶ

Term four: x4 = DS

൬

1

ଵܧ

·

ଵܧ߲

ௌܦ߲

ௌ൰ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

·

െ4 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

ௌܦ · ௌߩ

ଷ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌܦߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬െ2 · ܦߜௌ

ௌܦ

൰

ଶ
NASA/TM—2010-216903 12 

Term five: x5 = ρK

൬

1

ଵܧ

·

ଵܧ߲

௄ߩ߲

൰௄ߩߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

· 2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ሻ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ߩߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ߩߜ௄

௄ߩ

൰

ଶ

Term six: x6 = EK

൬

1

ଵܧ

·

ଵܧ߲

௄ܧ߲

൰௄ܧߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

· 2 · ሺܯி െ ܯி

ᇱ

௄ߩ · ሻ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ܧߜ௄

௄ܧ

൰

ଶ

Term seven: x7 = ΔMK1

൬

1

ଵܧ

ଵܧ߲ ·

ଵ௄ܯ∆߲

ଵ൰௄ܯ∆ߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

· െ2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଵଶ௄ܦ ·

یଵ௄ܯ∆ߜ ·

ۋ

ۊ

ଶ

ൌ ቆെߜ∆ܯ௄ଵ

ܦ௄ଵଶ · ܴቇ

ଶ

Term eight: x8 = ΔMK2

൬

1

ଵܧ

ଵܧ߲ ·

ଶ௄ܯ∆߲

ଶ൰௄ܯ∆ߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

· െ2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଶଶ௄ܦ ·

یଶ௄ܯ∆ߜ ·

ۋ

ۊ

ଶ

ൌ ቆെߜ∆ܯ௄ଶ

ܦ௄ଶଶ · ܴቇ

ଶ

Term nine: x9 = DK1

൬

1

ଵܧ

ଵܧ߲ ·

ଵ௄ܦ߲

ଵ൰௄ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

·

െ4 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ଵ௄ܯ∆ · ሻ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଵଷ௄ܦ ·

یଵ௄ܦߜ ·

ۋ

ۊ

ଶ

ൌ ቆെ2 · ∆ܯ௄ଵ · ܦߜ௄ଵ

ܦ௄ଵଷ · ܴ ቇ

ଶ

Term ten: x10 = DK2

൬

1

ଵܧ

ଵܧ߲ ·

ଶ௄ܦ߲

ଶ൰௄ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ሻ

·

െ4 · ሺܯி െ ܯி

ᇱ

௄ܧ · ௄ߩ · ଶ௄ܯ∆ · ሻ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଶଷ௄ܦ ·

یଶ௄ܦߜ ·

ۋ

ۊ

ଶ

ൌ ቆെ2 · ∆ܯ௄ଶ · ܦߜ௄ଶ

ܦ௄ଶଷ · ܴ ቇ

ଶ

Therefore the equation for fractional uncertainty in erosion yield for Situation 1 is: 

ଵܧߜ

ଵܧ

ൌ ൥൬ܯߜி

ଵܯ∆

൰

ଶ

൅ ቆܯߜி

ᇱ

ଵܯ∆

ቇ

ଶ

൅ ൬ߩߜௌ

ௌߩ

൰

ଶ

൅ ൬2 · ܦߜௌ

ௌܦ

൰

ଶ

௄ߩߜ൬൅ 

௄ߩ

൰

ଶ

௄ܧߜ൬൅ 

௄ܧ

൰

ଶ

ଵ௄ܯ∆ߜ ቆ൅ 

ܦ௄ଵଶ · ܴቇ

ଶ

ଶ௄ܯ∆ߜ ቆ൅ 

ܦ௄ଶଶ · ܴቇ

ଶ

൅  ቆ2 · ∆ܯ௄ଵ · ܦߜ௄ଵ

ܦ௄ଵଷ · ܴ ቇ

ଶ

൅ ቆ2 · ∆ܯ௄ଶ · ܦߜ௄ଶ

ܦ௄ଶଷ · ܴ ቇ

ଶ

቉

ଵ ଶൗ

Table 3 shows the mass loss, density, exposed diameter, corresponding uncertainty values, and 

calculated fractional uncertainty for each polymer in Situation 1. 

(14)
NASA/TM—2010-216903 13 

Table 3. Situation 1 Fractional Uncertainty in Erosion Yield. 

Material 

Abbrev.

δMF 

(g)

δMF' 

(g)

ΔM 

(g)

ρ 

(g/cm3

)

δρ 

(g/cm3

)

D 

(cm)

δD 

(cm)

δE/E

ABS 0.000042 0.000020 0.033861 1.0500 0.0074 2.1093 0.0058 0.027017

ADC 0.000036 0.000036 0.267295 1.3173 0.0040 2.1228 0.0033 0.025824

AF 0.000004 0.000003 0.012352 2.1463 0.0086 2.0972 0.0034 0.025975

CTFE 0.000005 0.000012 0.052949 2.1327 0.0086 2.1246 0.0030 0.025927

EP 0.000140 0.000220 0.140720 1.1150 0.0079 2.1283 0.0057 0.027020

FEP 0.000002 0.000084 0.012479 2.1443 0.0086 2.0949 0.0039 0.026890

PAN 0.000066 0.000025 0.047281 1.1435 0.0228 2.1040 0.0054 0.032801

PEO 0.000089 0.000022 0.066395 1.1470 0.0028 2.1288 0.0045 0.025948

PFA 0.000079 0.000005 0.010785 2.1383 0.0086 2.0980 0.0052 0.027248

PG 0.002890 0.000100 0.027730 2.2200 0.0074 2.1321 0.0050 0.107496

PI (Upilex-S) 0.000009 0.000003 0.038127 1.3866 0.0212 2.1225 0.0049 0.030056

PI (PMR-15) 0.000065 0.000034 0.118887 1.3232 0.0040 2.1187 0.0018 0.025696

POM 0.000041 0.000018 0.378378 1.3984 0.0233 2.1146 0.0030 0.030556

PP 0.000020 0.000003 0.072357 0.9070 0.0007 2.1211 0.0062 0.026127

PPD-T 0.000041 0.000023 0.026790 1.4422 0.0017 2.1140 0.0061 0.026193

PS 0.000058 0.000001 0.115947 1.0503 0.0079 2.1123 0.0045 0.026884

PTFE 0.000002 0.000001 0.008938 2.1503 0.0086 2.1062 0.0043 0.026089

PVF-W 0.000022 0.000012 0.004714 1.6241 0.0518 2.0860 0.0043 0.041361

4.2 Fractional Uncertainty Equation Derivations for Situation 2 

Using Equation 12, the equation for Situation 2 erosion yield, the equation for fractional 

uncertainty in erosion yield in Situation 2 ቀ

ఋாమ

ாమ

ቁ is derived through the following process. 

One of the variables seen above in the Situation 2 equation for erosion yield, n·MA, was 

found from two different measurements: MA was found by averaging the mass of each layer of 

that flight sample’s part A and control group over the total number of layers, N. So, as with the 

fluence equation, the equation for MA must be substituted into the erosion yield equation to 

account for all sources of error. The equation for MA is: 

஼ܯ ൅ ிܯ ൌ஺ ܯ

ܰ

1 ൌ஺ ܯߜ ׵

ܰ · ඩ෍ቈ൬߲ܯ஺

௜ݔ߲

൰௜ݔߜ ·

ଶ

቉

௡

௜ୀଵ

ൌ 1

ܰ · ඥሺܯߜிሻଶ ൅ ሺܯߜ஼ሻଶ

This expression for δMA will be substituted into term 3 of the error equation for this situation. 

Term one: x1 = MF

൬

1

ଶܧ

·

ଶܧ߲

ிܯ߲

ி൰ܯߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

௄ܧ · ௄ߩ·2 ·

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ிܯߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ܯߜி

ଶܯ∆

൰

ଶ

(15)
NASA/TM—2010-216903 14 

Term two: x2 = MF' 

൬

1

ଶܧ

ଶܧ߲ ·

ிܯ߲

ᇱ · ܯߜி

ᇱ

൰

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

௄ܧ · ௄ߩ · 2െ· 

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ிܯߜ ·

ᇱ

ی

ۋ

ۊ

ଶ

ൌ ቆെܯߜி

ᇱ

ଶܯ∆

ቇ

ଶ

 Term three: x3 = MA

൬

1

ଶܧ

·

ଶܧ߲

஺ܯ߲

൰஺ܯߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

௄ܧ · ௄ߩ · 2݊ ·

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

஺ܯߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬݊ · ܯߜ஺

ଶܯ∆

൰

ଶ

Term four: x4 = ME'

൬

1

ଶܧ

ଶܧ߲ ·

ாܯ߲

ᇱ · ܯߜா

ᇱ

൰

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

௄ܧ · ௄ߩ · 2െ· 

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ாܯߜ ·

ᇱ

ی

ۋ

ۊ

ଶ

ൌ ቆെܯߜா

ᇱ

ଶܯ∆

ቇ

ଶ

Term five: x5 = ρS

൬

1

ଶܧ

·

ଶܧ߲

ௌߩ߲

ௌ൰ߩߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

െ2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌߩ

ଶ · ܦௌ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌߩߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬െߩߜௌ

ௌߩ

൰

ଶ

Term six: x6 = DS

൬

1

ଶܧ

·

ଶܧ߲

ௌܦ߲

ௌ൰ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

െ4 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଷ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌܦߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬െ2 · ܦߜௌ

ௌܦ

൰

ଶ

Term seven: x7 = ρK

൬

1

ଶܧ

·

ଶܧ߲

௄ߩ߲

൰௄ߩߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

2 · ሺܯி െ ܯி

௄ܧ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ߩߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ߩߜ௄

௄ߩ

൰

ଶ

Term eight: x8 = EK

൬

1

ଶܧ

·

ଶܧ߲

௄ܧ߲

൰௄ܧߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

2 · ሺܯி െ ܯி

௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ܧߜ௄

௄ܧ

൰

ଶ

Term nine: x9 = ΔMK1

൬

1

ଶܧ

ଶܧ߲ ·

ଵ௄ܯ∆߲

ଵ൰௄ܯ∆ߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

െ2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଵଶ௄ܦ ·

یଵ௄ܯ∆ߜ ·

ۋ

ۊ

ଶ

ൌ ቆെߜ∆ܯ௄ଵ

ܦ௄ଵଶ · ܴቇ

ଶ

 
NASA/TM—2010-216903 15 

Term ten: x10 = ΔMK2

൬

1

ଶܧ

ଶܧ߲ ·

ଶ௄ܯ∆߲

ଶ൰௄ܯ∆ߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

െ2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଶଶ௄ܦ ·

یଶ௄ܯ∆ߜ ·

ۋ

ۊ

ଶ

ൌ ቆെߜ∆ܯ௄ଶ

ܦ௄ଶଶ · ܴቇ

ଶ

Term eleven: x11 = DK1

൬

1

ଶܧ

ଶܧ߲ ·

ଵ௄ܦ߲

ଵ൰௄ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

െ4 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ଵ௄ܯ∆ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଵଷ௄ܦ ·

یଵ௄ܦߜ ·

ۋ

ۊ

ଶ

ൌ ቆെ2 · ∆ܯ௄ଵ · ܦߜ௄ଵ

ܦ௄ଵଷ · ܴ ቇ

ଶ

Term twelve: x12 = DK2

൬

1

ଶܧ

ଶܧ߲ ·

ଶ௄ܦ߲

ଶ൰௄ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

2 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

·

െ4 · ሺܯி െ ܯி

௄ܧ · ௄ߩ · ଶ௄ܯ∆ · ாԢሻܯ െ஺ ܯ·݊൅ ᇱ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଶଷ௄ܦ ·

یଶ௄ܦߜ ·

ۋ

ۊ

ଶ

ൌ ቆെ2 · ∆ܯ௄ଶ · ܦߜ௄ଶ

ܦ௄ଶଷ · ܴ ቇ

ଶ

Therefore the equation for fractional uncertainty in erosion yield for Situation 2 is: 

ଶܧߜ

ଶܧ

ൌ ൦൬ܯߜி

ଶܯ∆

൰

ଶ

൅ ቆܯߜி

ᇱ

ଶܯ∆

ቇ

ଶ

൅ ቌ݊

ܰ · ඥሺܯߜிሻଶ ൅ ሺܯߜ஼ሻଶ

ଶܯ∆

ቍ

ଶ

൅ ቆܯߜா

ᇱ

ଶܯ∆

ቇ

ଶ

൅ ൬ߩߜௌ

ௌߩ

൰

ଶ

൅ ൬2 · ܦߜௌ

ௌܦ

൰

ଶ

௄ߩߜ൬൅ 

௄ߩ

൰

ଶ

௄ܧߜ൬൅ 

௄ܧ

൰

ଶ

ଵ௄ܯ∆ߜ ቆ൅ 

ܦ௄ଵଶ · ܴቇ

ଶ

ଶ௄ܯ∆ߜ ቆ൅ 

ܦ௄ଶଶ · ܴቇ

ଶ

൅ ቆ2 · ∆ܯ௄ଵ · ܦߜ௄ଵ

ܦ௄ଵଷ · ܴ ቇ

ଶ

൅ ቆ2 · ∆ܯ௄ଶ · ܦߜ௄ଶ

ܦ௄ଶଷ · ܴ ቇ

ଶ

቏

ଵ ଶൗ

Table 4 shows the mass loss, density, exposed diameter, corresponding uncertainty values, and 

calculated fractional uncertainty for each polymer in Situation 2. 

(16)
NASA/TM—2010-216903 16 

Table 4. Situation 2 Fractional Uncertainty in Erosion Yield. 

Material 

Abbrev.

δMF 

(g)

δMC 

(g)

n N δMF' 

(g)

δME' 

(g)

ΔM 

(g)

ρ 

(g/cm3

)

δρ

(g/cm3)

D 

(cm)

δD 

(cm)

δE /E

CA 0.000790 0.000433 6 14 0.000098 0.000069 0.191482 1.2911 0.0025 2.1059 0.0060 0.026573

ETFE 0.000003 0.000002 1 2 0.000003 0.000005 0.049108 1.7397 0.0029 2.1066 0.0022 0.025598

PA 66 0.000088 0.000034 3 8 0.000007 0.000019 0.065562 1.2252 0.1509 2.1185 0.0051 0.125851

PBI 0.000156 0.000141 2 4 0.000040 0.000029 0.082708 1.2758 0.0036 2.1038 0.0056 0.026275

PBO 0.000062 0.000000 5 13 0.000001 0.000004 0.056778 1.3976 0.0752 2.1268 0.0031 0.059587

PC 0.000020 0.000110 1 2 0.000002 0.000012 0.142287 1.1231 0.0079 2.1113 0.0028 0.026545

PE 0.000018 0.000004 2 8 0.000010 0.000013 0.102760 0.9180 0.0007 2.1257 0.0029 0.025620

PEEK 0.000117 0.000026 3 6 0.000001 0.000013 0.107764 1.2259 0.0457 2.1056 0.0054 0.045436

PEI 0.000018 0.000018 1 2 0.000003 0.000009 0.126853 1.2873 0.0036 2.1216 0.0053 0.026088

PI 

(Kapton HN)

0.000052 0.000035 1 4 0.000010 0.000012 0.121315 1.4345 0.0020 2.1313 0.0038 0.025748

PPPA 0.000162 0.000188 3 6 0.000060 0.000102 0.030549 0.7200 0.0074 2.1298 0.0055 0.028987

PSU 0.000035 0.000032 3 6 0.000012 0.000015 0.105948 1.2199 0.0221 2.1113 0.0054 0.031645

PVDF 0.000005 0.000007 1 2 0.000006 0.000001 0.066860 1.7623 0.0086 2.1108 0.0061 0.026549

PVF 0.000011 0.000011 6 13 0.000013 0.000010 0.132537 1.3792 0.0013 2.1331 0.0028 0.025612

4.3 Fractional Uncertainty Equation Derivations for Situation 3 

Using Equation 13, the equation for Situation 3 erosion yield, the equation for fractional 

uncertainty in erosion yield for Situation 3 ቀ

ఋாయ

ாయ

ቁ is derived through the following process. 

Equation 15 will be used to substitute for δMA in term 2 of the final equation. 

 Term one: x1 = MF

൬

1

ଷܧ

·

ଷܧ߲

ிܯ߲

ி൰ܯߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

௄ܧ · ௄ߩ·2 ·

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ிܯߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ܯߜி

ଷܯ∆

൰

ଶ

 Term two: x2 = MA

൬

1

ଷܧ

·

ଷܧ߲

஺ܯ߲

൰஺ܯߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

௄ܧ · ௄ߩ · 2݊ ·

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

஺ܯߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬݊ · ܯߜ஺

ଷܯ∆

൰

ଶ

Term three: x3 = MS’

൬

1

ଷܧ

·

ଷܧ߲

ௌԢܯ߲

ௌԢ൰ଶܯߜ ·

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

௄ܧ · ௄ߩ · 2െ· 

ௌߩ

ଶ · ܦௌ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌԢܯߜ ·

ی

ۋ

ۊ

ଶ

ൌ ቆെܯߜௌԢ

ଷܯ∆

ቇ

ଶ

Term four: x4 = ρS

൬

1

ଷܧ

·

ଷܧ߲

ௌߩ߲

ௌ൰ߩߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2െ

ௌߩ

ଶ · ܦௌ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌߩߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬െߩߜௌ

ௌߩ

൰

ଶ

 
NASA/TM—2010-216903 17 

Term five: x5 = DS

൬

1

ଷܧ

·

ଷܧ߲

ௌܦ߲

ௌ൰ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 4െ

ௌܦ · ௌߩ

ଷ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ௌܦߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬െ2 · ܦߜௌ

ௌܦ

൰

ଶ

Term six: x6 = ρK

൬

1

ଷܧ

·

ଷܧ߲

௄ߩ߲

൰௄ߩߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ߩߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ߩߜ௄

௄ߩ

൰

ଶ

Term seven: x7 = EK

൬

1

ଷܧ

·

ଷܧ߲

௄ܧ߲

൰௄ܧߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧߜ ·

ی

ۋ

ۊ

ଶ

ൌ ൬ܧߜ௄

௄ܧ

൰

ଶ

Term eight: x8 = ΔMK1

൬

1

ଷܧ

ଵܧ߲ ·

ଵ௄ܯ∆߲

ଵ൰௄ܯ∆ߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2െ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଵଶ௄ܦ ·

یଵ௄ܯ∆ߜ ·

ۋ

ۊ

ଶ

ൌ ቆെߜ∆ܯ௄ଵ

ܦ௄ଵଶ · ܴቇ

ଶ

Term nine: x9 = ΔMK2

൬

1

ଷܧ

ଷܧ߲ ·

ଶ௄ܯ∆߲

ଶ൰௄ܯ∆ߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2െ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଶଶ௄ܦ ·

یଶ௄ܯ∆ߜ ·

ۋ

ۊ

ଶ

ൌ ቆെߜ∆ܯ௄ଶ

ܦ௄ଶଶ · ܴቇ

ଶ

Term ten: x10 = DK1

൬

1

ଷܧ

ଷܧ߲ ·

ଵ௄ܦ߲

ଵ൰௄ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௄ߩ · ଵ௄ܯ∆ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 4െ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଵଷ௄ܦ ·

یଵ௄ܦߜ ·

ۋ

ۊ

ଶ

ൌ ቆെ2 · ∆ܯ௄ଵ · ܦߜ௄ଵ

ܦ௄ଵଷ · ܴ ቇ

ଶ

Term eleven: x11 = DK2

൬

1

ଷܧ

ଷܧ߲ ·

ଶ௄ܦ߲

ଶ൰௄ܦߜ ·

ଶ

ൌ

ۉ

ۈ

ௌܦ · ௌߩ ۇ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

௄ܧ · ௄ߩ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 2

·

௄ܧ · ௄ߩ · ଶ௄ܯ∆ · ௌԢሻܯ െ஺ ܯ·݊൅ ிܯሺ · 4െ

ௌܦ · ௌߩ

ଶ · ቆ∆ܯ௄ଵ

ଶ௄ܯ∆ ൅ ଵଶ௄ܦ

ܦ௄ଶଶ ቇ

ଶ

ଶଷ௄ܦ ·

یଶ௄ܦߜ ·

ۋ

ۊ

ଶ

ൌ ቆെ2 · ∆ܯ௄ଶ · ܦߜ௄ଶ

ܦ௄ଶଷ · ܴ ቇ

ଶ

Therefore the equation for fractional uncertainty in erosion yield for Situation 3 is: 

ଷܧߜ

ଷܧ

ൌ ൦൬ܯߜி

ଷܯ∆

൰

ଶ

൅ ቌ݊

ܰ · ඥሺܯߜிሻଶ ൅ ሺܯߜ஼ሻଶ

ଷܯ∆

ቍ

ଶ

൅ ቆെܯߜௌԢ

ଷܯ∆

ቇ

ଶ

൅ ൬ߩߜௌ

ௌߩ

൰

ଶ

൅ ൬2 · ܦߜௌ

ௌܦ

൰

ଶ

௄ߩߜ൬൅ 

௄ߩ

൰

ଶ

௄ܧߜ൬൅ 

௄ܧ

൰

ଶ

ଵ௄ܯ∆ߜ ቆ൅ 

ܦ௄ଵଶ · ܴቇ

ଶ

ଶ௄ܯ∆ߜ ቆ൅ 

ܦ௄ଶଶ · ܴቇ

ଶ

൅ ቆ2 · ∆ܯ௄ଵ · ܦߜ௄ଵ

ܦ௄ଵଷ · ܴ ቇ

ଶ

൅ ቆ2 · ∆ܯ௄ଶ · ܦߜ௄ଶ

ܦ௄ଶଷ · ܴ ቇ

ଶ

൪

ଵ ଶൗ (17)
NASA/TM—2010-216903 18 

Table 5 shows the mass loss, density, exposed diameter, corresponding uncertainty values, and 

calculated fractional uncertainty for each polymer in Situation 3.

Table 5. Situation 3 Fractional Uncertainty in Erosion Yield. 

Material 

Abbrev.

δMF 

(g)

δMC 

(g)

n N δMS' 

(g)

ΔM 

(g)

ρ 

(g/cm3

)

δρ

(g/cm3)

D 

(cm)

δD 

(cm)

δE /E

ECTFE 0.000008 0.000004 1 4 0.000012 0.088869 1.6761 0.0059 2.1141 0.0027 0.025821

PA 6 0.000088 0.000112 4 8 0.000055 0.118376 1.1233 0.0079 2.1304 0.0033 0.026617

PBT 0.000027 0.000017 2 6 0.000049 0.036429 1.3318 0.0040 2.1296 0.0026 0.025798

PET 0.000160 0.000010 4 8 0.000033 0.125187 1.3925 0.0029 2.1240 0.0058 0.026157

PI (CP1) 0.000038 0.000038 2 4 0.000025 0.080648 1.4193 0.0167 2.1205 0.0030 0.028199

PMMA 0.000495 0.000126 5 10 0.000017 0.194588 1.1628 0.0028 2.1247 0.0034 0.025932

PU 0.000051 0.000040 4 10 0.000042 0.057227 1.2345 0.0174 2.1165 0.0039 0.029353

5. RESULTS AND DISCUSSION 

The MISSE 2 PEACE Polymers LEO atomic oxygen erosion yield data are given in 

Table 6.1-3 These results represent the widest variety of extremely accurately measured high 

atomic oxygen fluence data to date. 

 Including enough material in each flight sample to theoretically last for three years was 

crucial to the experiment’s success, because although the experiment received nearly four years 

of atomic oxygen exposure, only one polymer (PBI) was completely eroded away. However, for 

five other samples (PE, ADC, PMMA, PEI, and PMR-15) the atomic oxygen did in some places 

erode through all layers of the flight sample. For these six samples, therefore, the calculated 

erosion yields are less than the actual erosion yields, because if there had been more material the 

mass loss would have been greater. These six erosion yield values are highlighted in Table 6. 

Since the samples in these cases appeared to have eroded partially or completely through at a 

fluence level close to the full mission fluence, the measured erosion yields of these samples were 

still included in the data set as estimates to develop a predictive erosion yield equation.7 These 

samples have been re-flown in LEO for actual erosion yield determination as part of the Stressed 

PEACE Polymers experiment on MISSE 6.8

 Table 6 also includes the uncertainty and fractional uncertainty in erosion yield for each of 

the MISSE 2 PEACE Polymers samples. The highest fractional uncertainty was for PA 66, 

±12.59 percent, and the lowest fractional uncertainty was for Tefzel ZM, ±2.56 percent. The 

average fractional uncertainty in erosion yield was very small, ±3.30 percent. 
NASA/TM—2010-216903 19 

Table 6. MISSE 2 PEACE Polymers Experiment Fractional Uncertainty Data Summary. 

Material Abbrev. Trade Name(s)

Fractional 

Uncertainty in 

Erosion Yield

Uncertainty 

in Erosion 

Yield 

Erosion Yield 

(cm3

/atom)

Acrylonitrile butadiene styrene ABS Cycolac 0.027017 2.96E-26 1.09 ± 0.03 E-24

Allyl diglycol carbonate ADC CR-39, Homalite H-911 0.025824 1.76E-25 >6.80 E-24

Amorphous fluoropolymer AF Teflon AF 1601 0.025975 5.13E-27 1.98 ± 0.05 E-25

Cellulose acetate CA Clarifoil, Tenite Acetate, 

Dexel

0.026573 1.34E-25 5.05 ± 0.13 E-24

Chlorotrifluoroethylene CTFE Neoflon CTFE M-300, 

Kel-F

0.025927 2.15E-26 8.31 ± 0.22 E-25

Crystalline polyvinylfluoride 

with white pigment

PVF-W White Tedlar 

TWH10BS3 

0.041361 4.17E-27 1.01 ± 0.04 E-25

Epoxide or epoxy EP Hysol EA 956 0.027020 1.14E-25 4.21 ± 0.11 E-24

Ethylenechlorotrifluoroethylene

ECTFE Halar 0.025821 4.63E-26 1.79 ± 0.05 E-24

Ethylene-tetrafluoroethylene 

copolymer

ETFE Tefzel ZM 0.025598 2.46E-26 9.61 ± 0.25 E-25

Fluorinated ethylene 

propylene FEP Teflon FEP (round robin) 0.026890 5.39E-27 2.00 ± 0.05 E-25

High temperature polyimide 

resin

PI PMR-15 0.025696 7.77E-26 >3.02 E-24

Perfluoroalkoxy copolymer 

resin

PFA Teflon PFA CLP (200 

CLP)

0.027248 4.72E-27 1.73 ± 0.05 E-25

Poly-(p-phenylene 

terephthalamide)

PPD-T Kevlar 29 fabric 0.026193 1.64E-26 6.28 ± 0.16 E-25

Poly(p-phenylene-2 6-

benzobisoxazole) PBO (balanced biaxial film) 0.059587 8.08E-26 1.36 ± 0.08 E-24

Polyacrylonitrile PAN Barex 210 0.032801 4.63E-26 1.41 ± 0.05 E-24

Polyamide 6 or Nylon 6 PA 6 Akulon K, Ultramid B 0.026617 9.33E-26 3.51 ± 0.09 E-24

Polyamide 66 or Nylon 66 PA 66 Maranyl A, Zytel 0.125851 2.27E-25 1.80 ± 0.23 E-24

Polybenzimidazole PBI Celazole PBI 0.026275 5.81E-26 >2.21 E-24

Polybutylene terephthalate PBT GE Valox 357 0.025798 2.35E-26 9.11 ± 0.24 E-25

Polycarbonate PC PEEREX 61 (P61) 0.026545 1.14E-25 4.29 ± 0.11 E-24

Polyetheretherketone PEEK Victrex PEEK 450 0.045436 1.36E-25 2.99 ± 0.14 E-24

Polyetherimide PEI Ultem 1000 0.026088 8.63E-26 >3.31 E-24

Polyethylene PE 0.025620 9.59E-26 >3.74 E-24

Polyethylene oxide PEO Alkox E-30 0.025948 5.01E-26 1.93 ± 0.05 E-24

Polyethylene terephthalate PET Mylar A-200 0.026157 7.87E-26 3.01 ± 0.08 E-24

Polyimide PI LaRC CP1 (CP1-300) 0.028199 5.38E-26 1.91 ± 0.05 E-24

Polyimide (BPDA) PI Upilex-S 0.030056 2.77E-26 9.22 ± 0.28 E-25

Polyimide (PMDA) PI Kapton H 0.024700 7.41E-26 3.00 ± 0.07 E-24

Polyimide (PMDA) PI Kapton H 0.024700 7.41E-26 3.00 ± 0.07 E-24

Polyimide (PMDA) PI Kapton HN 0.025748 7.24E-26 2.81 ± 0.07 E-24
NASA/TM—2010-216903 20 

Table 6. cont. MISSE 2 PEACE Polymers Experiment Fractional Uncertainty Data Summary. 

Material Abbrev. Trade Name(s)

Fractional 

Uncertainty in 

Erosion Yield

Uncertainty 

in Erosion 

Yield 

Erosion Yield 

(cm3

/atom)

Polymethyl methacrylate PMMA Plexiglas, Lucite, Acrylite 

(Impact Mod.)

0.025932 1.45E-25 >5.60 E-24

Polyoxymethylene; acetal; 

polyformaldehyde POM Delrin (natural) 0.030556 2.79E-25 9.14 ± 0.28 E-24

Polyphenylene isophthalate PPPA Nomex Aramid Paper 

Type 410

0.028987 4.10E-26 1.41 ± 0.04 E-24

Polypropylene PP C28 0.026127 7.00E-26 2.68 ± 0.07 E-24

Polystyrene PS Trycite 1000, Trycite 

Dew

0.026884 1.00E-25 3.74 ± 0.10 E-24

Polysulphone PSU Thermolux P1700-NT11, 

Udel P-1700

0.031645 9.31E-26 2.94 ± 0.09 E-24

Polytetrafluoroethylene PTFE Chemfilm DF 100 0.026089 3.69E-27 1.42 ± 0.04 E-25

Polyurethane PU Dureflex PS 8010 0.029353 4.59E-26 1.56 ± 0.05 E-24

Polyvinyl fluoride PVF Tedlar TTR10SG3 0.025612 8.17E-26 3.19 ± 0.08 E-24

Polyvinylidene fluoride PVDF Kynar 740 0.026549 3.41E-26 1.29 ± 0.03 E-24

Pyrolytic graphite PG 0.107496 4.46E-26 4.15 ± 0.45 E-25

6. SUMMARY

The purpose of the MISSE 2 PEACE Polymers experiment was to obtain the atomic oxygen 

erosion yields of a wide variety of polymeric materials exposed to the LEO space environment 

for a long period of time.1-3 The MISSE 2 PEACE Polymers experiment is unique in that it 

included the widest variety of polymers exposed to identical LEO conditions and received a high 

fluence of atomic oxygen exposure (8.43 x 1021 atoms/cm2). Because of this, the experiment 

provides very valuable erosion yield data for spacecraft design purposes.1-3 It is therefore 

extremely important to know how accurate the atomic oxygen erosion yield data are. To address 

this, the error in each polymer’s experimental erosion yield value was calculated using equations 

for fractional uncertainty derived from the equation used to find erosion yield. Because three 

different situations were required for post-flight sample weighing, a factor in calculating the 

erosion yield E of a polymer, three different equations were derived for determining the 

fractional uncertainty of the erosion yield values. 

 The uncertainty and fractional uncertainty in erosion yield for each of the MISSE 2 PEACE 

Polymers samples have been determined. The highest fractional uncertainty was for PA 66, 

±12.59 percent, and the lowest fractional uncertainty was for Tefzel ZM, ±2.56 percent. The 

average fractional uncertainty in erosion yield was very small, ±3.30 percent. The results listed 

in Table 6 represent the widest variety of extremely accurately measured high atomic oxygen 

fluence data to date. 

 
NASA/TM—2010-216903 21 

References

1. de Groh, K. K., Banks, B. A., McCarthy, C. E., Rucker, R. N., Roberts, L. M., and Berger, L. 

A., “MISSE 2 PEACE Polymers Atomic Oxygen Erosion Experiment on the International 

Space Station,” High Performance Polymers, Vol. 20, no. 4/5, pp. 388-409, Aug. 2008. 

2. de Groh, K. K., Banks, B. A., McCarthy, C. E., Berger, L. A., and Roberts, L. M., “Analysis 

of the MISSE PEACE Polymers International Space Station Environmental Exposure 

Experiment,” Proceedings of the 10th International Symposium on Materials in a Space 

Environment and the 8th International Conference on Protection of Materials and Structures 

in a Space Environment (ISMSE-10 & ICMPSE-8), Collioure, France, June 19-23, 2006ESA 

SP-616, September 2006). 

3. de Groh, K. K., Banks, B. A., McCarthy, C. E., Rucker, R. N., Roberts, L. M., and Berger, L. 

A., “MISSE PEACE Polymers Atomic Oxygen Erosion Results,” Proceedings of the 2006 

National Space & Missile Materials Symposium (2006 NSMMS) in conjunction with the 

2006 MISSE Post-Retrieval Conference, Orlando, Florida, June 26-30, 2006; also NASA 

TM-2006-214482, November 2006. 

4. Pippin, G. and Normand, E., “Estimated Environmental Exposures for MISSE-1 & MISSE-2,” 

proceedings of the 2006 MISSE Post-Retrieval Conference, Jun. 26-30, 2006, Orlando, FL. 

5. Dever, J. A., Miller, S. K., Sechkar, E. A., and Wittberg, T. N., “Preliminary Analysis of 

Polymer Film Thermal Control and Gossamer Materials Experiments on Materials 

International Space Station Experiment (MISSE 1 and MISSE 2),” Proceedings of the 2006 

MISSE Post-Retrieval Conference, Jun. 26-30, 2006, Orlando, FL. 

6. ASTM E 2089-00, “Standard Practices for Ground Laboratory Atomic Oxygen Interaction 

Evaluation of Materials for Space Applications, June 2000. 

7. Banks, B. A., Backus, J. A., Manno, M. V., Waters, D. L., Cameron, K. C. and de Groh, K. 

K., “Atomic Oxygen Erosion Yield Prediction for Spacecraft Polymers in Low Earth Orbit,” 

Proceedings of the International Symposium on Materials in a Space Environment (ISMSE11), September 15-18, 2009, Aix-en-Provence, France, 2009; also NASA TM-2009-215812, 

September 2009. 

8. de Groh, K. K., Banks, B. A., Dever, J. A., Jaworske, D. J., Miller, S. K., Sechkar E. A. and 

Panko, S. R., “NASA Glenn Research Center’s Materials International Space Station 

Experiments (MISSE 1-7),” Proceedings of the International Symposium on 

“SM/MPAC&SEED Experiment,” Tsukuba, Japan, March 10-11, 2008, JAXA-SP-08-015E, 

March 2009, pp. 91–119; also NASA TM-2008-215482, December 2008. 
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MISSE 2 PEACE Polymers Experiment Atomic Oxygen Erosion Yield Error Analysis 

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14. ABSTRACT

Atomic oxygen erosion of polymers in low Earth orbit (LEO) poses a serious threat to spacecraft performance and durability. To address 

this, 40 different polymer samples and a sample of pyrolytic graphite, collectively called the PEACE (Polymer Erosion and Contamination 

Experiment) Polymers, were exposed to the LEO space environment on the exterior of the International Space Station (ISS) for nearly 4 

years as part of the Materials International Space Station Experiment 1 & 2 (MISSE 1 & 2). The purpose of the PEACE Polymers 

experiment was to obtain accurate mass loss measurements in space to combine with ground measurements in order to accurately calculate 

the atomic oxygen erosion yields of a wide variety of polymeric materials exposed to the LEO space environment for a long period of time. 

Error calculations were performed in order to determine the accuracy of the mass measurements and therefore of the erosion yield values. 

The standard deviation, or error, of each factor was incorporated into the fractional uncertainty of the erosion yield for each of three different 

situations, depending on the post-flight weighing procedure. The resulting error calculations showed the erosion yield values to be very 

accurate, with an average error of ±3.30 percent. 

15. SUBJECT TERMS

Atomic oxygen; low Earth orbit (LEO); Polymers 

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