Ablative materials are often used for spacecraft heatshields to protect underlying structures from the extreme environments associated with atmospheric reentry. NASA's Orion EM-1 capsule has been designed to use a molded Avcoat material system. In order to determine the required heatshield thickness, a Monte Carlo approach to the sizing process was proposed. To perform the Monte Carlo simulation, statistical uncertainties on all material property input parameters were required. Obtaining these values for measured properties is straightforward, however input parameters that are derived analytically have historically used uncertainties based on engineering judgment. A MATLAB program was created to use laboratory generated thermogravimetric analysis (TGA) data to calculate uncertainties on the Arrhenius parameters for molded Avcoat. Uncertainties associated with the normalized ablation rate and pyrolysis gas enthalpy were also generated using a wrapper script and the ACE code. These uncertainties could then be tied directly to measured values of individual elemental constituents. The resulting uncertainty values will allow for a probabilistic sizing approach on molded Avcoat with a higher level of confidence in the input parameters

Coughlin, Scott J.

McGuire, M. Kathleen

Sepka, Steven A.

Sixel, William R.

NASA Technical Reports Server

1 
 
Determination of Uncertainties for Analytically Derived 
Material Properties to be used in Monte Carlo Based Orion 
Heatshield Sizing  
Scott J. Coughlin* 
NASA Johnson Space Center, Houston, Texas, 77058 
William R. Sixel† 
University of Wisconsin-Madison, Madison, Wisconsin, 53706 
Steven A. Sepka‡ 
AMA Corporation, Moffett Field, California, 94035 
and 
M. Kathleen McGuire§ 
NASA Ames Research Center, Moffett Field, California 94035 
 
Ablative materials are often used for spacecraft heatshields to protect underlying 
structures from the extreme environments associated with atmospheric reentry.  NASA’s 
Orion EM-1 capsule has been designed to use a molded Avcoat material system.  In order 
to determine the required heatshield thickness, a Monte Carlo approach to the sizing 
process was proposed.  To perform the Monte Carlo simulation, statistical uncertainties 
on all material property input parameters were required.  Obtaining these values for 
measured properties is straightforward, however input parameters that are derived 
analytically have historically used uncertainties based on engineering judgment.  A 
MATLAB program was created to use laboratory generated thermogravimetric analysis 
(TGA) data to calculate uncertainties on the Arrhenius parameters for molded Avcoat.  
Uncertainties associated with the normalized ablation rate and pyrolysis gas enthalpy 
were also generated using a wrapper script and the ACE code.  These uncertainties could 
then be tied directly to measured values of individual elemental constituents. The 
resulting uncertainty values will allow for a probabilistic sizing approach on molded 
Avcoat with a higher level of confidence in the input parameters.  
 
Nomenclature 
𝐵′𝑐 = no dimensional char mass loss rate 
𝜌 = density 
𝜑 = decomposition reaction order 
                                                          
* Aerospace Engineer, NASA Johnson Space Center, Thermal Design Branch, ES3, Houston, TX 77058 
† Graduate Student, University of Wisconsin, Dept. of Mechanical Engineering, Madison, WI 53706 
‡ Sr. Research Scientist, AMA Corporation, Thermal Protection Materials and Systems Branch, NASA Ames Research 
Center, MS-234-1, Moffett Field, CA 94035, Senior Member, AIAA 
§ Aerospace Engineer, NASA Ames Research Center, Systems Analysis Office, MS-258-1, Moffett Field, CA 94035 
https://ntrs.nasa.gov/search.jsp?R=20190029074 2019-09-26T19:40:02+00:00Z
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𝑘 = decomposition pre-exponential coefficient 
?̃? = elemental mass fraction 
𝑟 = residual char mass fraction 
𝜎 = standard deviation 
𝑢 = uncertainty 
𝜇 = mean 
 
I. Introduction 
Ablative thermal protection materials are often used for spacecraft heatshields to protect underlying 
structures from the extreme environments associated with atmospheric reentry.  NASA’s Orion capsule for 
Exploration Mission 1 (EM-1) has been designed to use a molded block version of the Avcoat ablative 
material.  Based on extensive material property testing, a high fidelity thermal response model for molded 
Avcoat was developed for use in the CHarring Ablator Response (CHAR) code1.  To determine the required 
heatshield thickness, the Orion program currently uses a four-branch, root-sum-squared (RSS) method to 
account individually for the effects of uncertainty on trajectory dispersions, aerothermal heating and 
material properties along with a nominal case.  Those sizing results, combined in an RSS process, and 
further adjusted by either a recession margin or thermal factor of safety determine the final sized heatshield 
thickness for a given bodypoint.  This process for Orion TPS2 sizing was also used for the sizing of the 
Mars Science Laboratory TPS3.   
 
The current method used to account for the material property uncertainties in the appropriate RSS sizing 
branch is to reduce the allowable bondline temperature limit by 60°C.  This value has been used consistently 
since the early phases of the Orion program and is based on resulting two sigma values from earlier 
planetary mission studies using a number of different materials.  Understandably, there is a desire to 
determine whether this value is appropriate for the case of molded Avcoat on Orion. 
 
Additionally, in place of this existing sizing approach, it has been proposed that a probabilistic design 
approach be taken for future heatshield sizing that makes use of a Monte Carlo simulation4. This simulation 
would use the material property and modelling uncertainties, randomize these variables according to an 
appropriate probability distribution, size the TPS, and report the thermal sizing for each iteration.  The 
output of a Monte Carlo based heatshield sizing would be a distribution of sizes that could be approximated 
as normal.  As a final sizing of a heatshield, a 3σ value from the simulation could be used as a replacement 
for a factor-of-safety based sizing.  This methodology is explained in detail in multiple studies5, 6. 
 
As part of the proposed Monte Carlo simulation, statistical uncertainties on all material property inputs to 
the CHAR model were required for the molded Avcoat material.  The overall uncertainty in the TPS sizing 
and reliability results from the combined effect of all the uncertainties in the model input parameters.  
Therefore, without accurately determining these material property uncertainties that are inputs to the 
process, there cannot be a great deal of confidence in the resulting system reliability values.  Fortunately, 
many of the required uncertainty values for this effort are obtained directly via statistical analysis of material 
property measurements.  Multiple laboratory measured values for density or specific heat for example can 
be used to calculate a mean and standard deviation.  The uncertainties associated with analytically derived 
input parameters, however, cannot be determined via traditional methods.  These model inputs include the 
pyrolysis gas enthalpy, the non-dimensional mass loss rate (Bc
′ ), and parameters associated with the material 
decomposition.   
 
3 
 
Similar Monte Carlo based sensitivity studies have been performed in the past on numerous types of TPS 
materials6,7,8 to investigate ablator model performance with respect to input parameters and to assess the 
reliability of the ablative thermal protection system design.  None of these studies, however, attempt to 
calculate the uncertainties on analytically derived material property inputs and instead rely on estimates 
based on engineering judgment or on holdover values from earlier studies.  This paper will present a method 
for calculating the uncertainties of analytically derived ablative material properties.   
 
 
II. Method 
A. Decomposition Parameters 
Ablator decomposition, the transition from the virgin to char state and production of pyrolysis gas, is 
modelled in CHAR using the Arrhenius reaction equation.  The complete molded Avcoat decomposition 
was modelled using three Arrhenius equations of the form show in equation 1. 
 
𝜕𝜌𝑖
𝜕𝑡
= −𝑘𝑖 𝜌𝑣,𝑖 (
𝜌𝑖(𝑡)−𝜌𝑐,𝑖
𝜌𝑣,𝑖
)
𝜑𝑖
𝑒
− 
𝑇𝑎,𝑖
𝑇(𝑡)      (1) 
 
The virgin material density 𝜌𝑣 and the char density 𝜌𝑐 are determined from initial volume and mass 
measurements and from thermogravimetric analysis (TGA) residual char yield. The remaining parameters 
must be determined from TGA data: the pre-exponential factor k, the reaction order 𝜑𝑖, and the activation 
temperature 𝑇𝑎.  
 
Common Arrhenius curve fitting techniques were not able to be directly applied to the TGA data available. 
Avcoat cannot be accurately modelled as a single Arrhenius reaction and constant-temperature reaction 
data was not available. For these reasons, a general curve-fitting approach was used to fit Arrhenius 
equations to TGA data.  A MATLAB program was written to optimize Arrhenius parameters from the TGA 
data. For each of the six laboratory measurements available, an initial guess for the parameters was 
provided, and the Arrhenius equation was solved using MATLAB’s differential equation solver. The 
goodness-of-fit was evaluated by residual sum-of-squares calculation between the computed result and the 
test data. The parameters were randomized and iterated using a multivariable derivative-free optimization 
algorithm to minimize the residual sum-of-squares.  MATLAB optimized the nine independent Arrhenius 
parameters to produce the fitted curves shown in Figure 1.   
 
 
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Figure 1. Curve fits to TGA data. 
 
 
The mean, standard deviation, and uncertainty were calculated for each of the nine parameters using the six 
sets of TGA data.  As a check on the calculated mean values and uncertainties for each equation, the 
Arrhenius parameters and char density were randomized according to a normal distribution as they would 
be in the full Monte Carlo simulation. The resulting randomized curves were then shown to bound the 
available TGA data as seen in Figure 2 for all but one outlier.   
 
 
 
Figure 2. Randomized Parameter Curves. 
 
 
B. Pyrolysis Gas Enthalpy 
The enthalpy of the pyrolysis gas was calculated using the Aerotherm Chemical Equilibrium code (ACE)9, 
as a function of temperature and pressure.  The strategy to generate uncertainties was to run selected 
5 
 
conditions rather than the full enthalpy table for a large number of pyrolysis gas elemental fraction 
possibilities. The elemental composition of the pyrolysis gas is derived as follows:  
  
?̃?𝑝𝑔𝑖 =
?̃?𝑣𝑖−𝑟?̃?𝑐𝑖
1−𝑟
      (2) 
 
Where ?̃?𝑝𝑔𝑖, ?̃?𝑣𝑖, and ?̃?𝑐𝑖 are the elemental mass fractions in the pyrolysis gas, virgin material and char 
material, respectively. The residual mass fraction is represented by r.  So the average elemental composition 
of the pyrolysis gas is derived from the compositions of the virgin and char materials and knowledge of the 
ratio of char to virgin density.   
 
Elemental analysis was performed on four virgin molded Avcoat material samples, four char samples and 
the residual char yields from six TGA runs were used to calculate the uncertainties going into the analysis.  
The pyrolysis gas composition calculated for each run and an ACE wrapper script varied the elemental 
constituents and residual mass fraction on a random normal distribution. 
 
The wrapper script performing the Monte Carlo ACE analysis was run at varying temperatures and 
pressures across the nominal pyrolysis gas enthalpy table to determine the pyrolysis gas uncertainties. The 
resulting distributions for a number of pressure, temperature combinations are shown in Figure 3. 
 
 
Figure 3. Pyrolysis Gas Enthalpy Uncertainties 
 
 
C. Normalized Ablation Rate, 𝐁𝐜
′  
The B’ tables are likely the most influential of inputs to an ablation model in terms of recession.  Much like 
the pyrolysis gas enthalpy, these tables are typically generated with the use of a thermochemical equilibrium 
code.    Fixed mass molecular compositions are evaluated from relative elemental quantities, species 
thermochemical data and two-state properties (temperature and pressure).  The environment gas 
6 
 
composition, pyrolysis gas composition, and char composition are required inputs.  In addition, the allowed 
resultant chemical species are required in the form of JANAF thermochemical tables.  A representative set 
of Bc
′  curves for a single pressure is shown in Figure 3. 
 
 
Figure 3. Normalized Ablation Rate Curves for molded Avcoat at a Single Pressure 
 
 
For this analysis multiple laboratory measurements were made for both virgin and char elemental 
composition which allowed the calculation of mean mass percentages of carbon, silicon, hydrogen, etc. 
Variability in the elemental composition of Avcoat char and char yield percentage was determined and a 
series of Monte Carlo runs were made using an ACE wrapper script at a number of different flight-relevant 
B’ table combinations of pressure, temperature and pyrolysis blowing rates.  The distribution of the 
resulting Bc
′  values from these runs were assumed to be normal and uncertainty values were calculated.  
 
 
III. Results 
 
For the purposes of ease-of-comparison between parameters, the standard deviation was normalized to an 
uncertainty calculated as twice the coefficient of variance. 
 
𝑢 = 2 ∙
𝜎 
𝜇
      (3) 
  
The resulting uncertainties form this study are given in Table 1.  Values assumed in earlier studies3,6,7,8 are 
also given for comparison. The Arrhenius parameter uncertainties calculated from the test data and 
computed best-fit curves are reported in Table 2. Notably, the best-fit reaction orders varied greatly and 
produced a high uncertainty, while the best-fit activation temperatures were grouped closely together. 
 
  
7 
 
Table 1. Resulting uncertainty values compared with past studies. 
 
 
Equation 1 
Pre-exponential factor 0.109 
Reaction Order 0.263 
Activation Temperature 0.060 
Equation 2 
Pre-exponential factor 0.179 
Reaction Order 0.388 
Activation Temperature 0.061 
Equation 3 
Pre-exponential factor 0.188 
Reaction Order 0.263 
Activation Temperature 0.033 
Table 2. Decomposition Parameter Uncertainties 
 
 
IV. Conclusion 
 
In previous Monte Carlo based sensitivity studies, there was no uncertainty applied to the individual 
decomposition parameters. Uncertainties on pyrolysis gas enthalpy and normalized ablation rate tables were 
estimated based on engineering judgment or in some cases not used at all.  A MATLAB program was 
developed to allow for faster, more accurate and automated computation of Arrhenius reaction parameters. 
This MATLAB program, along with TGA data, was used to generate uncertainties on the Arrhenius 
parameters for molded Avcoat.  Uncertainties associated with the normalized ablation rate and pyrolysis 
gas enthalpy were also generated with the use of the ACE code wrapper script, using the uncertainties in 
individual elemental constituents based on a number of laboratory measurements. The resulting calculated 
uncertainty values allow for new TPS sensitivity studies and sizing efforts on molded Avcoat using values 
having a higher level of confidence and a better tie to measured data.   
 
 
Acknowledgements 
 
The authors would like to recognize the members of the Orion TPS Team. They are spread across multiple 
NASA centers including Johnson Space Center, Ames Research Center and Langley Research Center as 
well as team members from Lockheed Martin Space Systems.  
 
 
References 
 
1.  Amar, A.J., Calvert, N.D., and Kirk, B.S., “Development and Verification of the Charring Ablating 
Thermal Protection Implicit Solver System,” AIAA Paper-2011-0144, January 2011. 
 
Current Study 
7Chen et al.  
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6Wright et al. 
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8Sepka et 
al. 2009 
3Wright et al. 
2014 
Ablative Material Molded Avcoat PICA, SLA-561v SLA-561v PICA SLA-561v 
Decomposition Table 2 0.20 0.20 0.15 0.16 
Char Recession Rate, Bc
′  .15 1.0 n/a 0.15 n/a 
Pyrolysis gas Enthalpy .18 0.75 0.50 0.15 n/a 
8 
 
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Mountainview CA: Aerotherm Corporation, May 1969. 
 
 
 


Determination of Uncertainties for Analytically Derived Material Properties to Be Used in Monte Carlo Based Orion Heatshield Sizing

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