-
NASA/TM—2017–219842
Program to Optimize Simulated Trajectories II (POST2) Surrogate
Models for Mars AscentVehicle (MAV) Performance AssessmentM.R.
Zwack and P.D. DeesJacobs ESSSA, Marshall Space Flight Center,
Huntsville, Alabama
H.D. Thomas, T.P. Polsgrove, and J.B. HoltMarshall Space Flight
Center, Huntsville, Alabama
December 2017
National Aeronautics andSpace AdministrationIS02George C.
Marshall Space Flight CenterHuntsville, Alabama 35812
-
The NASA STI Program…in Profile
Since its founding, NASA has been dedicated to the advancement
of aeronautics and space science. The NASA Scientific and Technical
Information (STI) Program Office plays a key part in helping NASA
maintain this important role.
The NASA STI Program Office is operated by Langley Research
Center, the lead center for NASA’s scientific and technical
information. The NASA STI Program Office provides access to the
NASA STI Database, the largest collection of aeronautical and space
science STI in the world. The Program Office is also NASA’s
institutional mechanism for disseminating the results of its
research and development activities. These results are published by
NASA in the NASA STI Report Series, which includes the following
report types:
• TECHNICAL PUBLICATION. Reports of completed research or a
major significant phase of research that present the results of
NASA programs and include extensive data or theoretical analysis.
Includes compilations of significant scientific and technical data
and information deemed to be of continuing reference value. NASA’s
counterpart of peer-reviewed formal professional papers but has
less stringent limitations on manuscript length and extent of
graphic presentations.
• TECHNICAL MEMORANDUM. Scientific and technical findings that
are preliminary or of specialized interest, e.g., quick release
reports, working papers, and bibliographies that contain minimal
annotation. Does not contain extensive analysis.
• CONTRACTOR REPORT. Scientific and technical findings by
NASA-sponsored contractors and grantees.
• CONFERENCE PUBLICATION. Collected papers from scientific and
technical conferences, symposia, seminars, or other meetings
sponsored or cosponsored by NASA.
• SPECIAL PUBLICATION. Scientific, technical, or historical
information from NASA programs, projects, and mission, often
concerned with subjects having substantial public interest.
• TECHNICAL TRANSLATION. English-language translations of
foreign
scientific and technical material pertinent to NASA’s
mission.
Specialized services that complement the STI Program Office’s
diverse offerings include creating custom thesauri, building
customized databases, organizing and publishing research
results…even providing videos.
For more information about the NASA STI Program Office, see the
following:
• Access the NASA STI program home page at
• E-mail your question via the Internet to
• Phone the NASA STI Help Desk at 757 –864–9658
• Write to: NASA STI Information Desk Mail Stop 148 NASA Langley
Research Center Hampton, VA 23681–2199, USA
-
i
NASA/XX—2017–219842
Program to Optimize Simulated Trajectories II (POST2) Surrogate
Models for Mars Ascent Vehicle (MAV) Performance AssessmentM.R.
Zwack and P.D. DeesJacobs ESSSA, Marshall Space Flight Center,
Huntsville, Alabama
H.D. Thomas, T.P. Polsgrove, and J.B. HoltMarshall Space Flight
Center, Huntsville, Alabama
December 2017
National Aeronautics andSpace Administration
Marshall Space Flight Center • Huntsville, Alabama 35812
-
ii
Available from:
NASA STI Information DeskMail Stop 148
NASA Langley Research CenterHampton, VA 23681–2199, USA
757–864–9658
This report is also available in electronic form at
-
iii
TABLE OF CONTENTS
1. INTRODUCTION
.............................................................................................................
1
2. APPROACH
.......................................................................................................................
2
3. GROUND RULES AND ASSUMPTIONS
.......................................................................
3
3.1 Design of Experiments
.................................................................................................
3 3.2 Program to Optimize Simulated Trajectories II Assumptions
....................................... 4
4. VERIFICATION
................................................................................................................
5
5. SURROGATE MODELING
.............................................................................................
6
5.1 Model Fitting in JMP
...................................................................................................
6 5.2 Goodness-of-Fit Testing
...............................................................................................
7
6. RESULTS
...........................................................................................................................
9
REFERENCES
.......................................................................................................................
19
-
iv
LIST OF FIGURES
1. Percentage of error distribution for two-engine TSTO
surrogate ............................... 8
2. Percentage of error distribution for three-engine TSTO
surrogate ............................. 8
3. Liftoff latitude versus gross mass for two target orbits.
Payload = 3 mt, Isp = 360 s, thrust = 100 kN, stage 1 PMF = 0.85,
and stage 2 PMF = 0.75 ............... 10
4. Liftoff TW versus gross mass for two-engine MAV with stage 1
PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude = 30°, and orbit = 1 Sol
.......................................................................................................
11
5. Liftoff TW versus gross mass for three-engine MAV with stage
1 PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude 30°, and 1 Sol orbit
...........................................................................................................
11
6. Liftoff TW versus gross mass for two-engine MAV with stage 1
PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude = 30°, and orbit = 5 Sol
.......................................................................................................
12
7. Liftoff TW versus gross mass for three-engine MAV with stage
1 PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude = 30°, and orbit = 5 Sol
.......................................................................................................
12
8. Liftoff TW versus gross mass for two-engine MAV with stage 1
PMF = 0.8507, stage 2 PMF =0.7898, crew cabin mass = 4 mt, latitude
= 30°, and orbit = 1 Sol
.......................................................................................................
13
9. Liftoff TW versus gross mass for three-engine MAV with stage
1 PMF = 0.8507, stage 2 PMF = 0.7898, crew cabin mass = 4 mt,
latitude = 30°, and orbit = 1 Sol
.......................................................................................................
13
10. Liftoff TW versus gross mass for two-engine MAV with stage 1
PMF = 0.8507, stage 2 PMF = 0.7898, crew cabin mass = 4 mt,
latitude = 30°, and orbit = 5 Sol
.......................................................................................................
14
11. Liftoff TW versus gross mass for three-engine MAV with stage
1 PMF = 0.8507, stage 2 PMF = 0.7898, crew cabin mass = 4 mt,
latitude = 30°, and orbit = 5 Sol
.......................................................................................................
14
-
v
LIST OF FIGURES (Continued)
12. Payload versus gross mass for Isp = 335 s, latitude = 30°,
and orbit = 1 Sol ............... 15
13. Payload versus gross mass for Isp = 360 s, latitude = 30°,
and orbit = 1 Sol ............... 16
14. Payload versus gross mass for Isp = 460 s, latitude = 30°,
and orbit = 1 Sol ............... 16
15. Payload versus gross mass for Isp = 335 s, latitude = 30°,
and orbit = 5 Sol ............... 17
16. Payload versus gross mass for Isp = 360 s, latitude = 30°,
and orbit = 5 Sol ............... 17
17. Payload versus gross mass for Isp = 460 s, latitude = 30°,
and orbit = 5 Sol ............... 18
-
vi
LIST OF TABLES
1. DOE inputs and ranges for two-stage MAV
..............................................................
4
2. MultiPOST versus manual payload comparison
....................................................... 5
3. Excess delta-v values for target orbits
........................................................................
9
4. Stage PMF settings for figures 12–17
.........................................................................
15
-
vii
LIST OF ACRONYMS AND SYMBOLS
ACO Advanced Concepts Office
DOE design of experiments
MAV Mars Ascent Vehicle
PMF propellant mass fraction
POST Program to Optimize Simulated Trajectories II
RSE response to surface equation
Sol Martian solar day
TW thrust-to-weight
-
viii
NOMENCLATURE
Isp specific impulse
mb burnout mass
mp propellant mass
R response
x input parameter
β regression coefficient
-
1
TECHNICAL MEMORANDUM
PROGRAM TO OPTIMIZE SIMULATED TRAJECTORIES II (POST2) SURROGATE
MODELS FOR MARS ASCENT VEHICLE (MAV) PERFORMANCE ASSESSMENT
1. INTRODUCTION
Trajectory optimization is a key component in assessing launch
vehicle performance during conceptual design. For prephase A and
phase A concept definition studies, the Integrated Space
Transportation Team within Marshall Space Flight Center’s Advanced
Concepts Office (ACO) implements Program to Optimize Simulated
Trajectories II (POST2). POST2 is an industry-stan-dard tool that
implements a direct solution method to approximate the control
function for an optimal trajectory.1 Successfully employing POST2
for a trade study requires a trajectory expert in the loop to
ensure that the control variables remain within the feasible space
and produce accept-able trajectories.2 For this reason, trade
studies can only be as broad as the trajectory expert’s time will
allow. A very limited number of cases can be completed by hand in a
given workday.
In an attempt to alleviate the execution time issues associated
with POST2 and allow for much broader trade space exploration, ACO
has developed a tool for automating ascent trajectory optimization.
This tool captures heuristics developed over years of analyst
experience and leverages the power of modern computing to speed up
the evaluation of large sets of vehicle trajectories. The basic
premise of the tool, known as multiple Programs to Optimize
Simulated Trajectories, or mul-tiPOST, is to use multiprocessing to
simultaneously evaluate random repetitions for a single vehicle
case. The analysis-based heuristics are then used to help converge
to acceptable trajectories or reject unrealistic ones. The approach
implemented in multiPOST is detailed further in references 3 and
4.
Although primarily used by ACO for Earth-to-orbit vehicle
studies, multiPOST is capable of executing POST2 for nearly any
valid vehicle input deck. Using this flexibility, multiPOST was
applied to carry out a Mars Ascent Vehicle (MAV) study. The MAV is
a key component to success-ful human exploration of Mars and is
being considered within NASA’s evolvable Mars campaign.5
The primary focus of this MAV study was to use multiPOST to
investigate the effects of mass fraction, liftoff location, and
propulsion on the payload mass delivered to a particular orbit by a
two-stage ascent vehicle. The stages of the vehicle contain the
propulsion related elements, such as engines and propellant tanks.
The payload mass in this case was the crew cabin, which included
the crew and provisions for the trip from the surface of Mars to
rendezvous with the Mars-Earth transportation vehicle. The ultimate
goal was to minimize the MAV gross mass for a given cabin mass. Any
changes in the MAV mass will impact the sizing of other
architecture ele-ments including Earth launch and in-space
transportation as well as entry, descent, and landing.6
-
2
2. APPROACH
The primary purpose of the multiPOST tool is to enable the
execution of much larger sets of vehicle cases to allow for broader
trade space exploration. However, this exploration is not achieved
solely with the increased case throughput. The multiPOST tool is
applied to carry out a Design of Experiments (DOE), which is a set
of cases that have been structured to capture a maximum amount of
information about the design space with minimal computational
effort. The results of the DOE are then used to fit a surrogate
model, ultimately enabling parametric design space exploration.
The approach used for the MAV study includes both DOE and
surrogate modeling. First, the primary design considerations for
the vehicle were used to develop the variables and ranges for the
multiPOST DOE. The final set of DOE variables were carefully
selected in order to capture the desired vehicle trades and take
into account any special considerations for surrogate modeling.
Next, the DOE sets were executed through multiPOST. Following
successful completion of the DOE cases, a manual verification trial
was performed. The trial involved randomly selecting cases from the
DOE set and running them by hand. The results from the human
analyst’s run and multiPOST were then compared to ensure that the
automated runs were being executed properly. Completion of the
verification trials was then followed by surrogate model
fitting.
After fits to the multiPOST data were successfully created, the
surrogate models were used as a stand-in for POST2 to carry out the
desired MAV trades. Using the surrogate models in lieu of POST2
allowed for visualization of vehicle sensitivities to the input
variables as well as rapid evaluation of vehicle performance.
Although the models introduce some error into the output of the
trade study, they were very effective at identifying areas of
interest within the trade space for further refinement by human
analysts.
The next section will cover all of the ground rules and
assumptions associated with DOE setup and multiPOST execution.
Section 3.1 gives the final DOE variables and ranges, while section
3.2 addresses the POST2 specific assumptions. The results of the
verification trials are given in sec-tion 4. Section 5 gives the
surrogate model fitting results, including the goodness-of-fit
metrics for each fit. Finally, the MAV specific results are
discussed in section 6.
-
3
3. GROUND RULES AND ASSUMPTIONS
3.1 Design of Experiments
Primary design considerations for the MAV include mission
parameters such as surface location and destination orbit as well
as vehicle parameters such as propulsion and vehicle masses. At
this point in the MAV design, mass fractions are more appropriate
due to the lack of detailed subsystem masses. Using a Propellant
Mass Fraction (PMF) allows the analysis to be more flex-ible and to
capture many unique vehicle configurations as long as they fit
within the bounds of the study. The PMF for this study was defined
for each stage as:
PMF = mp / (mp + mb) , (1)
where mp is stage usable propellant mass, and mb is stage
burnout mass. The PMFs do not include any mass attributed to the
crew cabin.
In addition to stage PMF, other vehicle parameters were added to
the DOE to represent the MAV propulsion system. In order to capture
many potential propulsion system types, continu-ous parameters were
used for engine thrust and specific impulse (Isp). The ranges for
thrust and Isp were developed to capture potential propellant
combinations for the MAV (e.g. liquid oxygen/liquid methane,
nitrogen tetroxide/monomethyl hydrazine). This allowed the analyst
to dial values representing specific types of propulsion into a
single surrogate model.
The variable for number of engines is discrete, which requires
special treatment. Due to the discrete nature of this variable, the
DOE sets were split to improve the ease of fitting surro-gate
models. Discrete parameters typically cause difficulty in achieving
acceptable fits, therefore a single surrogate is fit to each
discrete dataset. It is important to note that the number of
engines only applies to the first stage of the vehicle. It was
assumed for this study that the second stage would always contain a
single engine. This engine is assumed to be identical in thrust and
Isp to the engines on the first stage.
Two mission parameters of interest were included in the study
DOE. First, the destination orbits for the MAV were defined based
upon current Mars orbit rendezvous options at 1 Sol and 5 Sol.6
These orbit options are discrete; however, they were represented
using a continuous parameter for the required reserve delta-v. The
ranges shown in table 1 for reserve delta-v were developed to
capture orbit options under consideration for the MAV. The second
mission parameter, latitude, is a continuous variable representing
the liftoff location. Since no specific landing sites were
identified for the study, the latitude range was set to capture a
large number of landing sites that have been identified for
consideration.7 The final set of DOE inputs and ranges for the
two-stage MAV can be seen in table 1.
-
4
Table 1. DOE inputs and ranges for two-stage MAV.
Input Variable Min MaxNo. of engines (discrete) 2, 3Reserve
delta-V (m/s) 1,200 1,800Liftoff latitude (°) 0 60Thrust per engine
(kN) 68 200Engine Isp (s) 300 460Stage 1 PMF 0.75 0.95Stage 2 PMF
0.65 0.9Payload (crew cabin) mass (kg) 1,800 5,000
3.2 Program to Optimize Simulated Trajectories II
Assumptions
The POST2 input deck used common assumptions for the Martian
environment. The gravitational model for Mars comes from the 1997
Astronomical Almanac.8 The atmospheric data was taken from the
Space and Planetary Environment Criteria Guidelines for Use in
Space Vehicle Development.9 The reference area for MAV aerodynamics
was set at 22.06 m2 with the speed of sound input as 487.89332
m/s.6
The POST2 input deck was set up to fly to an initial orbit of
100 by 250 km while reserving an excess delta-v required to
transition to a higher target orbit. The excess delta-v required
was set as the variable dvmarr in the deck.
The dependent variables in the POST2 input deck defined the
target orbit using geocentric radius, flight path angle, and
inertial velocity. Independent variables for optimization consisted
of seven pitch rates, launch azimuth, initial weight of the
payload, and throttle level for a throttling event during ascent.
The throttle level was constrained to a minimum of 20%.
The first pitch event occurs at 5 s into the ascent, followed by
a gravity turn at 45 s. Between the end of the gravity turn and
insertion into the initial orbit, six additional pitch events
occur. The gravity turn is ended by the first stage reaching zero
propellant. At this point, the first stage is jet-tisoned, and the
second stage begins thrusting at its optimized throttle level.
The final main-engine cutoff for the two-stage vehicle occurs
when the MAV achieves its initial orbit of 100 by 250 km.
Simultaneously, the MAV is constrained to have a remaining delta-v
equal to the excess amount required to reach the final target
orbit.
-
5
4. VERIFICATION
Using the variables and ranges in table 1, a DOE was executed
through the multiPOST tool. Random cases were then selected from
the DOE to test the multiPOST execution of the MAV POST2 deck.
These cases were extracted from the results and individually
checked by a POST2 expert. It is expected that the POST2 expert
will beat multiPOST in most cases. If any large differ-ences
(>3%) in output are noticed during these checks, the setup and
execution of the automated deck is investigated. Table 2 shows
payload comparisons for a representative set of cases from the MAV
study.
Table 2. MultiPOST versus manual payload comparison.
ManualPayload
(kg)
AutomatedPayload
(kg)
Delta-V(Manual-Auto)
(%)4,818.55 4,818.12 0.0083,608.79 3,608.79 04,563.15 4,555.90
0.162,828.51 2,828.76 – 0.0093,977.55 3,978.55 – 0.0253,409.29
3,401.56 0.2264,447.39 4,428.31 0.4294,529.77 4,517.74
0.2664,145.21 4,119.40 0.6235,331.47 5,331.01 0.0084,041.84
4,041.66 0.0053,815.59 3,815.66 – 0.002
-
6
5. SURROGATE MODELING
5.1 Model Fitting in JMP
Following successful verification testing, surrogate models were
fit for each of the discrete datasets. The statistical software JMP
was used to complete the model fitting. This software pro-vides
tools for fitting many types of models including Gaussian
processes, Kriging, neural net-works, and response surface
equations.10,11 Response Surface Equations (RSE) were selected as
the desired model type for the MAV study due to their relative
simplicity as compared to Gaussian process models or neural
networks. Although the trajectory response space is typically
multimodal and nonlinear, higher order RSEs have been used to
successfully fit results from POST2 for other studies.3
RSEs are typically fit using the method of least squares to
estimate the regression coeffi-cients.12 Equation 1 gives the
generic form of a second order RSE, where R is the response, x
terms are input parameters, and β terms are regression
coefficients. Note that the model is linear in the β parameters and
is therefore a linear regression model, regardless of the order of
the input param-eters12:
R = β0 + β jx jj=1
k
∑ + βijxix jj=i+1
k
∑i=1
k−1
∑ + β jjx2jj=1
k
∑ . (2)
As noted above, higher order RSE models have been successfully
used to fit POST2 output data. However, as the order of the model
is increased, the total number of terms in the equation also
increases. Since k + 1 cases are required to regress the β
coefficients for a model of k terms, this also increases the total
number of DOE cases that must be completed through multiPOST. In
order to keep the number of required cases as well as the overall
length of the equation to a reasonable level, stepwise regression
was utilized in JMP.
Stepwise regression uses a statistical significance level to
determine which terms in the regression model are most beneficial
to the model’s ability to predict the data. During model fitting,
terms are added or removed from the model based upon their
calculated significance levels. The result is a model containing
only terms that are statistically significant for predicting the
response, which tends to be much more compact than the full
model.
In addition to stepwise regression, k-folds cross validation was
implemented when fitting the models in JMP. K-folds cross
validation splits the full set of cases into k different sets or
‘folds.’ The model is fit to k − 1 sets of data, leaving the
remaining set for model validation. After fitting a total of k
models, the one with the best validation statistics is returned as
the final model.10
-
7
5.2 Goodness-of-Fit Testing
When a surrogate model is returned, multiple goodness-of-fit
tests are applied to accept or reject the fit. First, the
coefficient of multiple determination, or R2, is used as an initial
indicator of fit acceptability. The R2 value is a measure of the
reduction in variability of the response obtained from the model.12
Based upon experience with fitting POST2 data, an R2 value greater
than 0.99 warrants further goodness-of-fit testing. Any value below
0.99 will require refitting after investiga-tion of outliers or
execution of additional DOE runs.
When fitting to POST2 data, the investigation of outliers tends
to be the only action required to improve a fit. Although multiPOST
utilizes heuristics to eliminate unreasonable trajec-tories, some
of these trajectories can still pass along into the final data set.
These cases are identi-fied using the residual-by-predicted plot in
JMP. This plot shows the predicted response value for each point
plotted against its residual as compared to the actual response
value. The desired shape of this plot is a ‘shotgun spread’ of
points with no clear trends—an example of which is shown in
reference 3. Any points that are significantly outside the main
point cloud are tagged as outliers for further investigation.
Using the detailed POST2 output for each of the outliers, an
analyst can easily determine whether or not the points can be
excluded from the fit. Typically, these cases illustrate odd
behavior, such as extreme lofting (affectionately dubbed a
‘rollercoaster’ trajectory) or very excessive pitch profiles due to
a high thrust-to-weight (TW). Any case deemed to be unrealistic or
unflyable for a crewed MAV is then removed from the model fitting
dataset.
The final goodness-of-fit test is used to calculate the error
percentage of the surrogate model across the entire dataset. This
percentage encompasses both the points used to fit the model itself
and the points held back for validation purposes. After calculating
the error, the characteristics of the percent error distribution
are used as a final acceptance check of the model. Typically, the
mean is desired to be as close to zero as possible and the standard
deviation must be below one. Figures 1 and 2 provide the final
error distributions for the MAV surrogate models. Note that the
error per-centage was calculated based upon the difference between
the surrogate model and the multiPOST output.
-
8
32.5
21.5
10.5
0– 0.5
–1–1.5
–2–2.5
–3–3.5
– 4
10099.597.5
9075502510
2.50.5
0
Maximum 3.076782.24699
1.36540.68433
Quartile 0.29347Median – 0.0153Quartile – 0.2758
– 0.6375–1.3016–2.6042
Minimum –3.8256
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.00537230.63029910.01192860.0287621– 0.018017
2,792
Quantiles (%)
Summary Statistics
F1_1743Observance
Erro
r (%
)
Figure 1. Percentage of error distribution for two-engine TSTO
surrogate.
33.5
2.52
1.51
0.50
– 0.5–1
–1.5–2
–2.5–3
–3.5–4
– 4.5–5
10099.597.5
9075502510
2.50.5
0
Maximum 3.468952.011681.037870.45785
Quartile 0.18612Median 0.01718
Quartile – 0.1725–0.496–1.989
–1.7967 Minimum – 4.7505
MeanStd DevStd Err MeanUpper 95% MeanLower 95% MeanN
0.00164690.49752310.0071484
0.015661– 0.012367
4,844
Quantiles (%)
Summary Statistics
F2_1743
Observance
Erro
r (%
)
Figure 2. Percentage of error distribution for three-engine TSTO
surrogate.
It is important to note that the resulting surrogate models are
only valid within the bounds shown in table 1. Any case within the
bounds that is evaluated through the surrogate will lie within the
error distributions in figures 1 and 2. If any of the input
variables entered into the surrogates are outside the bounds, the
response of the surrogate is not valid, and it is highly likely
that the percent error will be well outside of the distributions
shown in the figures.
-
9
6. RESULTS
After performing goodness-of-fit testing and accepting the MAV
surrogates, the equations were used to analyze trades of interest.
As discussed in section 3, these trades include propellant types,
crew cabin (payload) masses, and stage PMFs. Propellant types were
represented by varying the engine thrust and Isp. Multiple
destination orbits were represented by fixing the excess delta-v
input variable in the surrogate models. The excess delta-v values
used for the specific orbits can be seen in table 3.
Table 3. Excess delta-v values for target orbits.
OrbitExcess Delta-V
(m/s)1 Sol 1,4345 Sol 1,580
First, the sensitivity to liftoff latitude was analyzed for each
target orbit. Figure 3 shows an example of the latitude sensitivity
for a representative two-stage MAV flying to two different target
orbits. As seen in the figure, increasing latitude increases the
gross liftoff mass by approx imately 2–3 metric tons over the
entire range of latitude settings. This effect, however, is very
small in comparison to the effects of thrust, Isp, and stage PMF,
which can affect gross mass by tens of tons over their respective
ranges. Therefore, the latitude was fixed at the median value of
30° for the rest of the results within this section.
-
10
31,000
30,500
30,000
29,500
29,000
28,500
28,000
27,500
27,000
26,500
26,000
25,500
25,0000 5 10 15 20 25 30 35 40 45 50 55 60
Gros
s Mas
s (kg
)
Latitude (°)
F3_1741
2 Engines, 1 Sol2 Engines, 5 Sol3 Engines, 1 Sol3 Engines, 5
Sol
Orbit and No. of Engines
Figure 3. Liftoff latitude versus gross mass for two target
orbits. Payload = 3 mt, Isp =360 s, thrust = 100 kN, stage 1 PMF =
0.85, and stage 2 PMF = 0.75.
After fixing latitude, a first set of figures was developed to
investigate the optimal thrust level for the two-stage MAV with a
given crew cabin mass. As discussed previously, the Mars mis-sion
architecture is very sensitive to the mass of the MAV. Optimizing
the thrust level for a given payload will result in the smallest
vehicle gross mass, thereby reducing the mass of the
architecture.
To generate these figures, the thrust per engine was varied
across the entire range noted in table 1 for both the two- and
three- engine configurations. The PMFs for each stage were held
constant using values representing a nominal MAV configuration. In
figures 4–7, the first stage PMF was 0.8355, and the second stage
PMF was 0.7639. The first stage PMF was 0.8507, and the second
stage PMF was 0.7898 for figures 8–11. The variations in engine
thrust were carried out at various Isp settings, which are colored
in each figure. Figures 4–7 used a fixed crew cabin mass of three
metric tons, while figures 8–11 used four metric tons. From these
figures, an optimal TW can be identified for a given orbit and
Isp.
-
11
45,000
42,500
40,000
37,500
35,000
32,500
30,000
27,500
25,000
22,500
20,000
17,500
15,0000.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Gros
s Mas
s (kg
)
Liftoff T/W
F4_1743
335360460
Isp
Figure 4. Liftoff TW versus gross mass for two-engine MAV with
stage 1 PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude = 30°, and orbit = 1 Sol.
45,000
42,500
40,000
37,500
35,000
32,500
30,000
27,500
25,000
22,500
20,000
17,500
15,00010.8 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Gros
s Mas
s (kg
)
Liftoff T/W
F5_1743
335360460
Isp
Figure 5. Liftoff TW versus gross mass for three-engine MAV with
stage 1 PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude 30°, and 1 Sol orbit.
-
12
45,00047,500
50,000
42,50040,00037,50035,00032,50030,00027,50025,00022,50020,00017,50015,000
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Gros
s Mas
s (kg
)
Liftoff T/W
F6_1743
335360460
Isp
Figure 6. Liftoff TW versus gross mass for two-engine MAV with
stage 1 PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude = 30°, and orbit = 5 Sol.
45,000
47,50050,000
42,50040,00037,50035,00032,50030,00027,50025,00022,50020,00017,50015,000
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
Gros
s Mas
s (kg
)
Liftoff T/W
F7_1741
335360460
Isp
Figure 7. Liftoff TW versus gross mass for three-engine MAV with
stage 1 PMF = 0.8355, stage 2 PMF = 0.7639, crew cabin mass = 3 mt,
latitude = 30°, and orbit = 5 Sol.
-
13
45,00047,50050,00052,50055,00057,50060,000
42,50040,00037,50035,00032,50030,00027,50025,00022,50020,00017,50015,000
0.60.4 0.8 1 1.2 1.4 1.6 1.8
Gros
s Mas
s (kg
)
Liftoff T/WF8_1741
335360460
Isp
Figure 8. Liftoff TW versus gross mass for two-engine MAV with
stage 1 PMF = 0.8507, stage 2 PMF =0.7898, crew cabin mass = 4 mt,
latitude = 30°, and orbit = 1 Sol.
45,00047,50050,00052,50055,00057,50060,000
42,50040,00037,50035,00032,50030,00027,50025,00022,50020,00017,50015,000
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Gros
s Mas
s (kg
)
Liftoff T/W
F9_1743
335360460
Isp
Figure 9. Liftoff TW versus gross mass for three-engine MAV with
stage 1 PMF = 0.8507, stage 2 PMF = 0.7898, crew cabin mass = 4 mt,
latitude = 30°, and orbit = 1 Sol.
-
14
45,00047,50050,00052,50055,00057,50060,000
42,50040,00037,50035,00032,50030,00027,50025,00022,50020,00017,50015,000
0.60.4 0.8 1 1.2 1.4 1.6 1.8
Gros
s Mas
s (kg
)
Liftoff T/W
F10_1743
335360460
Isp
Figure 10. Liftoff TW versus gross mass for two-engine MAV with
stage 1 PMF = 0.8507, stage 2 PMF = 0.7898, crew cabin mass = 4 mt,
latitude = 30°, and orbit = 5 Sol.
45,00047,50050,00052,50055,00057,50060,000
42,50040,00037,50035,00032,50030,00027,50025,00022,50020,00017,50015,000
0.8 1 1.2 1.4 1.6 1.8 2 2.2
Gros
s Mas
s (kg
)
Liftoff TW
F11_1743
335360460
Isp
Figure 11. Liftoff TW versus gross mass for three-engine MAV
with stage 1 PMF = 0.8507, stage 2 PMF = 0.7898, crew cabin mass =
4 mt, latitude = 30°, and orbit = 5 Sol.
-
15
Using the optimal TW information, a second set of figures was
developed to investigate the effects of various stage PMF settings
on vehicle gross liftoff mass and payload delivered. This was done
by varying the PMF settings of the vehicle stages while maintaining
a near-optimal TW. Therefore, the data in the second set of figures
consists of vehicles with optimal thrust-to-weights that produce a
minimum gross liftoff mass for a given crew cabin mass.
The PMF settings represented worst, nominal, and best cases for
the two-stage MAV and are listed in table 4. Figures 12–14 and
figures 15–17 illustrate the payload delivered versus gross liftoff
mass for various Isp and PMF assumptions for a 1 Sol and 5 Sol
orbit, respectively.
Table 4. Stage PMF settings for figures 12–17.
Setting Name Stage 1 PMF Stage 2 PMFLow 0.75 0.65Nominal 0.85
0.75High 0.95 0.85
11,000
10,000
9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,0002,000 2,500 3,000 3,500 4,000 4,500 5,000
Gros
s Mas
s (kg
)
Payload (kg)
F12_1743
PMF SettingLowNominalHigh
Figure 12. Payload versus gross mass for Isp = 335 s, latitude =
30°, and orbit = 1 Sol.
-
16
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,0002,000 2,500 3,000 3,500 4,000 4,500 5,000
Gros
s Mas
s (kg
)
Payload (kg)
F13_1743
PMF SettingLowNominalHigh
Figure 13. Payload versus gross mass for Isp = 360 s, latitude =
30°, and orbit = 1 Sol.
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
2,000 2,500 3,000 3,500 4,000 4,500 5,000
Gros
s Mas
s (kg
)
Payload (kg)
F14_1743
PMF SettingLowNorminalHigh
Figure 14. Payload versus gross mass for Isp = 460 s, latitude =
30°, and orbit = 1 Sol.
-
17
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,0002,000 2,500 3,000 3,500 4,000 4,500 5,000
Gros
s Mas
s (kg
)
Payload (kg)
F15_1743
LowNominalHigh
PMF Setting
Figure 15. Payload versus gross mass for Isp = 335 s, latitude =
30°, and orbit = 5 Sol.
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,0002,000 2,500 3,000 3,500 4,000 4,500 5,000
Gros
s Mas
s (kg
)
Payload (kg)
F16_1743
PMF SettingLowNominalHigh
Figure 16. Payload versus gross mass for Isp = 360 s, latitude =
30°, and orbit = 5 Sol.
-
18
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
2,000 2,500 3,000 3,500 4,000 4,500 5,000
Gros
s Mas
s (kg
)
Payload (kg)
F17_1743
PMF SettingLowNominalHigh
Figure 17. Payload versus gross mass for Isp = 360 s, latitude =
30°, and orbit = 5 Sol.
-
19
REFERENCES
1. Steffens, M.J.; Edwards, S.J.; and Mavris, D.N.: “Capturing
the Global Feasible Design Space for Launch Vehicle Ascent
Trajectories,” Paper Presented at AIAA Atmospheric Flight
Con-ference, AAIA SciTech Forum, Kissimmee, FL, January 5–9, 2015,
doi:10.2514/6.2015-1910.
2. Steffens, M.J.; and Mavris, D.N.: Launch Vehicle Performance
Analysis using Extreme Value Theory,” Paper Presented at AIAA SPACE
Conference and Exposition, Pasadena, CA, August 31–September
2, 2015, doi:10.2514/6.2015-4679.
3. Dees, P.D.; Zwack, M.R.; Steffens, M.J.; Edwards, S.J.; Diaz,
M.J.; and Holt, J.B.: “An Expert System-Driven Method for
Parametric Trajectory Optimization During Conceptual Design,” Paper
Presented at AIAA SPACE Conference and Exposition, Pasadena, CA,
August 31–
September 2, 2015, doi:10.2514/6.2015-4486.
4. Dees, P.D; Zwack, M.R; Steffens, M.J.; and Edwards, S.J.:
“Augmenting Conceptual Design Trajectory Tradespace Exploration
with Graph Theory,” Paper Presented at AIAA SPACE Conference and
Exposition, Pasadena, CA, September 13–16, 2016.
5. Percy, T.K.; McGuire, M.L.; and Polsgrove, T.T.: In-Space
Transportation for NASA’s Evolv-able Mars Campaign,” Paper
Presented at AIAA SPACE Conference and Exposition, Pasa-dena, CA,
August 31–September 2, 2015.
6. Polsgrove, T.T.; Thomas, D.; Sutherlin, S.G.; Stephens, W.;
and Rucker, M.: Mars Ascent Vehicle Design for Human Exploration,”
Paper Presented at AIAA SPACE Conference and Exposition, Pasadena,
CA, August 31–September 2, 2015.
7. Hoffman, S.J.; and Bussey, D.B.: “Human Mars Landing Site and
Impacts on Mars Surface Operations,” Paper Presented at IEEE
Aerospace Conference, Big Sky, MT, March 3–12, 2016.
8. U.S. Naval Observatory: The Astonomical Almanac, U.S.
Government Printing Office, 1997.
9. Smith, R.E.; and West, G.S.: “Space and planetary environment
criteria guidelines for use in space vehicle development, Volume 1:
1982 revision,” NASA/TR–82478, NASA Marshall Space Flight Center,
Huntsville, AL, 244 pp., January 1983.
10. JMP: JMP 11 Fitting Linear Models, Version 11, SAS Institute
Inc., Cary, NC, 478 pp.,2013.
11. JMP: JMP 11 Specialized Models, SAS Institute Inc., Cary,
NC, 226 pp., 2013.
12. Myers, R.H.; Montgomery, D.C.; and Anderson-Cook, C.M.:
Response Surface Methodology, John Wiley and Sons (3rd ed.),
Hoboken, NJ, 856 pp., 2016.
-
20
REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188The
public reporting burden for this collection of information is
estimated to average 1 hour per response, including the time for
reviewing instructions, searching existing data sources, gathering
and maintaining the data needed, and completing and reviewing the
collection of information. Send comments regarding this burden
estimate or any other aspect of this collection of information,
including suggestions for reducing this burden, to Department of
Defense, Washington Headquarters Services, Directorate for
Information Operation and Reports (0704-0188), 1215 Jefferson Davis
Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should
be aware that notwithstanding any other provision of law, no person
shall be subject to any penalty for failing to comply with a
collection of information if it does not display a currently valid
OMB control number.PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE
ADDRESS.
1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED
(From - To)
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING
ORGANIZATION REPORT NUMBER
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10.
SPONSORING/MONITOR’S ACRONYM(S)
11. SPONSORING/MONITORING REPORT NUMBER
12. DISTRIBUTION/AVAILABILITY STATEMENT
13. SUPPLEMENTARY NOTES
14. ABSTRACT
15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF:a. REPORT b. ABSTRACT c. THIS
PAGE
17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES
19a. NAME OF RESPONSIBLE PERSON
19b. TELEPHONE NUMBER (Include area code)
Standard Form 298 (Rev. 8-98)Prescribed by ANSI Std. Z39-18
Program to Optimize Simulated Trajectories II (POST2) Surrogate
Models for Mars Ascent Vehicle (MAV) Performance Assessment
M.R. Zwack,* P.D. Dees,* H.D. Thomas, T.P. Polsgrove,
and J.B. Holt
George C. Marshall Space Flight CenterHuntsville, AL 35812
National Aeronautics and Space AdministrationWashington, DC
20546–0001
Unclassified-UnlimitedSubject Category 15Availability: NASA STI
Information Desk (757–864–9658)
Prepared by *Jacobs ESSSA Group and the Valves, Actuators, and
Ducts Design and Development Branch, Propulsion Systems Office,
Marshall Space Flight Center.
M–1445
Technical Memorandum
NASA/TM—2017–219842
Mars ascent vehicle, POST2, surrogate model, trajectory
optimization, design of experiments
01–12–2017
UU 32
NASA
U U U
A Mars Ascent Vehicle (MAV) study was carried out using the
Program to Optimize Simulated Trajec-tories (POST2) for performance
assessment. An in-house tool called multiPOST was implemented to
automate the execution of POST2. The results show the effects of
vehicle mass fractions and propulsion parameters on vehicle gross
liftoff mass and payload delivered. In addition to the results
figures, surrogate models created from the POST2 output are
included in a supplement file. These models encompass the trade
space for the MAV study and can be used as a stand-in for POST2
when evaluating vehicle perfor-mance in terms of payload
delivered.
STI Help Desk at email: [email protected]
STI Help Desk at: 757–864–9658
-
NASA/TM—2017–
Program to Optimize Simulated Trajectories II (POST2) Surrogate
Models for Mars AscentVehicle (MAV) Performance AssessmentM.R.
Zwack and P.D. DeesJacobs ESSSA, Marshall Space Flight Center,
Huntsville, Alabama
H.D. Thomas, T.P. Polsgrove, and J.B. HoltMarshall Space Flight
Center, Huntsville, Alabama
October 2017
National Aeronautics andSpace AdministrationIS02George C.
Marshall Space Flight CenterHuntsville, Alabama 35812
Blank Page
Instructions
POST2 Surrogate Models for Two-stage-to-orbit Mars Ascent
Vehicle Analysis
Authors: Mathew R. Zwack, Patrick D. Dees, James B. Holt
This Excel document contains surrogate models for Mars Ascent
Vehicle Performance as described in the NASA/TM "Program to
Optimize Simulated Trajectories II (POST2) Surrogate Models for
Mars Ascent Vehicle (MAV) Performance Assessment". The two
surrogate models are contained in respective worksheets, "2Eng" and
"3Eng" along with error bound calculations for each. In the
surrogate tabs the user will find the vehicle inputs in columns A
through G. Note, each input has a cell comment giving the allowable
ranges for the respective input. Any inputs entered beyond these
ranges will produce results that are NOT valid. The surrogate model
equations are contained from columns K to QW (2Eng) or PA (3Eng)
with the output in column J. The user is advised not to change any
of these cells as any adjustments to the equation coefficients
would render the equation invalid.
Basic Usage:Basic usage involves execution of single vehicle
case. As can be seen in the worksheets, the first row has been
pre-populated with a vehicle case. To analyze a different single
vehicle the user simply changes one or more of the input values and
the surrogate output will update in column J.
Multiple Cases:The surrogate equations were set up in row format
to support easier execution of multiple vehicle cases at once. As
shown in the 2Eng tab, three cases are being evaluated. To do this,
the user can extend all of the surrogate model term columns (J to
QW in this case) down multiple rows. By entering new values for the
inputs multiple cases can be executed at once.
Note, for proper execution of the error bounds, the error bound
calc sheet must be updated for additional cases. To update this
sheet, go to the bottom of the covariance matrix (in
2EngErrorBoundCalcs this matrix is A2 to QM456). The three example
cases can be seen starting in row 459. Steps are as follows:
1. Select all cells in the last row of the list (row 461 cols A
through QM in this case) and extend the equations down additional
row(s) for the desired number of cases.
2. Next, find the sumproduct column (QQ in this case) and extend
the equation in the first cell (QQ2) to the right for the desired
number of cases. Note the first array in the sumproduct equation
should always read A2:QM2, while the second entry should correspond
to the row number of the case in step 1 (i.e. 461 for the third
example case)
3. Extend the equations in the new columns down to row 456
4. Extend the second sumproduct in row 457 to the right for each
of the new columns and ensure the entries are correct. Note the
first entry in the sumproduct should correspond to rows 2 through
456 in the respective column (i.e. for col QQ; QQ2:QQ456). The
second entry should reference cells A through QM of the row number
for the new case from step 1 (i.e. the third example case is
A461:QM461). When entries are correct you must hit CRTL+SHIFT+ENTER
to properly execute the equation.
5. Extend the multiplier cells (i.e. QQ458 and QQ459) to the
right for the newly added columns to get the error bound in row
459
6. Ensure the newly calculated percentile number is being
added/subracted correctly in the surrogate tab. For example, the
third case (row 4 cols H,I) is pointing to the percentile number in
QQ459. If a 4th case were added to the 2Eng tab, cols H and I would
then point to QR459 after the steps above were completed.
2Eng
Payload (lbs)
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 4,000Max: 11,000Thrust per Engine
(lbf)
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 15,000Max: 45,000Isp (s)
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 300Max: 460Stage1PMF
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 0.75Max: 0.95Stage2PMF
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 0.65Max: 0.9Latitude (deg)
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 0Max: 60dvmarr (ft/s)
Zwack, Mathew R. (MSFC-ED04)[ESSSA]: Zwack, Mathew R.
(MSFC-ED04)[ESSSA]:Min: 4,000Max: 6,000Lower 95%Upper 95%Predicted
Gross Mass (lbs)Surrogate Model Terms --->
9087.461933721.33600.8420.7452605321.522394082.242825673194995.04164432594538.6422349991239354.36157514557166.77849732992675.3223697576-100626.217986658-87765.7174254296-63889.79312242663074.15640565128902.0099552398201.987345092945.1163070259-85.22936666851642.9567872542102.79413680881072.241300528451.8520549847-4.962658387254.78258253910.5497321044647.6894128442305.38516358111039.271090834857.8329642662-66.7891731832368.2115711066-103.6359265883446.719604896613.9417182565369.8091278722754.6707452127514.521707181144.0405159875484.528387089314.71650478381.0521292701264.059465214567.305782033743.4008933838-66.9191912556230.15933326873.6804885756227.5207587134-185.3187117136107.289531008558.7764093345-250.3720340989-6.2944241688-152.9203385602-146.8363088179-116.47059401324.047293723559.21923187190.545307997634.937114812928.891178810464.2475259343494.231465838328.866310091565.5170325392342.7693987735323.4693109837-101.9481787719-6.9546464669-165.193307294-132.9612055129-94.2765487295212.310578950816.9020680902367.9572491151254.7324256776224.19084214520.530343702426.70138010545.14296403759.8091365507-0.2310637388-7.8566819782-3.4389627687-4.12324226970.555985676924.81642836658.749990436310.6737642836-0.00358249950.95292621460.17681481220.2763753323161.9840105681156.8149521563235.6179455313-6.6316511799-85.6166708886-100.0783089158261.5225978336247.9913639345275.41269155372.81012830737.88976445447.4268167075179.5808414678134.380913837174.4363263108-72.724521270150.6914464072-170.6250679886-123.8159889189269.174588533884.67578332913.82541099421.6992510545213.860920432152.2886578056-7.8460032566161.108758774831.0030711577-15.04049468844.97793372391.652083631835.56295178737.53116198947.637430372929.7322375086-76.641482384482.4120381892.517124401888.655376326851.759744864315.5406657377131.7746276014-249.622765944-7.5235584143-187.802995532-124.2397301086-59.7839963387168.124327367910.7387932898189.410515747982.145962582748.347940277110.50794427463.68442021910.960544581827.449009413244.338080270753.7116237428-20.6991471757-98.6787736012267.70062907798.5803869265176.155150782363.77355689765.5815110031-325.5452482306-20.0261545255-380.5385763794-104.0195667308-128.0664094309-0.1366863981-19.1523525067-1.6972615747-4.4864792396-68.4183235233-54.0539111005-76.7677144159-88.6606696902-38.981653479-3.336696331226.0668975619-82.4026996137-2.5761503796-52.6871723956-4.8381338886-19.9602317738134.35799973498.0592132912171.434211981930.125357743658.8727947940.07973705347.12412041560.40751645471.96746892441.78346924961.836285996732.65484318383.83450911096.3370739463215.167753404618.9743907033358.150992716885.5924111917106.20136607990.383541146131.30556638574.87959927796.2513390596103.5601902706153.2246379288128.633898510337.5553148916-119.7597293483-10.8954076459-226.8200039001-46.8483991581-78.6753995025-0.2574027357-18.0010998357-3.1038242171-5.0344632652-90.8830154821-56.2719548798-79.2047212999-24.4631645149-38.9109005488-9.441161861592.79229767649.7442545468193.6204966945.601298634563.24384283090.344498505220.85203531522.27054507575.1828924036151.9984256836114.681406647197.5610066117-17.243545687519.04003058490.5582000988-0.05955524980.02724847089.2634548513.64096809737.87579062351.6201666756-0.3424891980.0394696077-0.087048011-6.329154787-2.4716881675-3.87947381230.3932367036-2.2764911188-0.08521688110.00265148010.83424909810.133699532510.91805366295.87525133187.8334422802-0.45817660321.59184012460.76878408650.0061542627-0.00137004560.37866085720.0311054850.197800099822.644393797755.7734081429113.739336448910.8679106869-7.926933010211.3361925081-2.6496510966-45.7760951784-13.125975353567.406671558570.459909569344.214637575949.877371456611.63992635262.06878831014.86825489372.02613779463.98744764550.813870138825.3116158012-6.46929006462.158746661751.0780460167-14.4047007829142.781997061-45.31824589447.374953383531.342490451529.5212396298-1.9761260371116.2889830337143.9978015562-0.74338383280.1871798993-4.2939821794-13.1472499195-38.77058466130.947100527870.396609179233.7323050347-35.5492854041-1.6770855605-48.3679074669-55.0161244883-17.5027967207-11.584618654443.655751709665.7317957388-31.221918624875.24089695422.600024491147.349400277537.182912999716.9286249333-58.1566070304-4.0807033703-47.3695224894-2.83332227210.0984243559-0.5311239223-22.7098572776-40.11759130886.57178053226.88972058212.209181805821.0404484843-20.59461272412.6796358833-1.1096800581-6.9185893451-27.8416540431-2.2070652103-4.388069186918.9936393906-57.8786777179-2.0003712559-32.9832870202-9.637255818983.00509924285.298828014575.263990000917.59031307955.08411080461.076256115135.590817253913.26459188-73.3084774673-6.3572217297-86.032515556918.7376903323-7.8744566367-0.0499270884-10.17357679320.648367283-1.338540011125.7537595601-3.3558219644-13.93804791980.0566580924-4.0312516557-0.843003958421.2826767467-49.2124990879-20.0770939176-5.352360071115.0605442270.55084516999.94496741840.0974674306-27.968092562-1.6481451781-30.0214541605-8.202369405-1.653587057-0.323016963-6.8192832344.761982552834.47254608652.829452631649.22188188859.37559343370.02536531115.05747122321.12030241738.63598862910.0374180223-0.02096279780.01128281862.14666426630.82567505171.03410106030.5765598582-11.5278367338-8.80621321898.151834250742.48979786554.650085946559.5624229370.11239312398.5078963599-11.5377641522-10.35119858250.20976915452.9048119848-0.41694571923.0592390226-28.457322839-3.2879432649-42.8783445428-9.669526177-0.0689004214-6.6626505885-1.15895217429.4159406847-4.2301677545-0.1752138896-0.0266330958-3.6111017522-1.0487822229-0.045870581928.667151843-30.158566401318.52320422232.374027883435.4064300154-6.21984938396.38621714950.08352486756.37757800620.89595588869.73929142740.0013893440.2669297573.1940458016-0.61399701641.5622814332-19.0175330313-0.005415414-1.0966812959-0.0611336378-0.0443030479-1.08277130190.00403057670.19767594220.0299654104-0.5941094851-0.31613274050.00345210790.000645486326.690504144620.2804661254-1.25758741340.68551563070.2671085928-57.4623975046353.47732816469.7562038108
8000330003600.840.7530530076895.925414797577232.89065405877064.4080344277239354.36157514550325.84818634992618.097113753-100626.217986658-87557.2477878395-64301.32158054211537.078202825528785.11901806224.281087353212.8083262652-57.1429908404569.636915447984.16958717141072.241300528435.7740202251-8.0859494875109.01149402912.1767606635205.0289337454228.3027574463948.8667240777105.0706968915-55.6748180929-7.31420782094.8617773535-25.5936891578-1.589439386-19.34424904492.477155513166.847190217333.7273688226453.171340430327.389094599325.3898282506-14.149556513158.87606756521.8089002761-6.586906629327.66766835650.880398379624.97131238271.276324545612.06270001313.6630841398-71.079547769-3.5558598399-39.63697100532.3883071318-30.92561456892.221903958939.70420239760.727520714621.386371817-1.109779879940.2877788692171.357207871519.9155840848179.0169051663-6.8088208356104.8934280244-83.4769023458-11.3316121416-123.49679049456.2374873186-72.1994249845212.310578950833.6333120729335.9492943155-14.5942610303209.68196529720.72809656416.8194524827-0.20328865456.3295927148-0.7491662939-11.68778427560.3210273218-6.28345785832.201522780445.0863872518-0.997551318419.8650932449-0.0282277013.4450475792-0.0401121651.023533515246.81627681-2.844026923869.7589491919-4.52648689383.6670720093-69.9755613712218.0027445711-12.97211546235.18170223684.6613174356-0.821236183612.6197884786136.6750091356-6.4178299884135.9981126673-0.0827653609-0.9417763003-0.45859091585.43256176230.883547322-4.53732942510.0249863977-0.1811875810.6409196081-2.55814379350.00147550990.49460456339.4029282589-10.772968599439.34467121342.875730865228.402763073-0.37743857846.24851611790.4296507105-2.61557215333.43484078340.20876150813.3736296363-0.12359643980.605799325210.620610314-24.5705577275-1.4736145837-16.87756186260.7006307617-5.503753521720.21038237392.568793793720.7885609386-0.56575457175.43582113112.2949217993-0.05049411860.21489905082.750574334-0.27880149885.513556534-2.176621142-18.782625003462.22932398893.9690114737.3867236383-0.849345147514.2583844413-92.4209011836-11.3132189243-98.6356469021.6918885735-34.0045695726-0.153653946-9.87841175680.054933249-2.37048658-16.19138524750.8027128396-18.6104566185-0.08262007840.5930074966-0.82863246111.7175484415-45.2378544799-2.8142427773-26.40838365110.1521725508-10.248713419990.081837379410.7521705867104.941573431-1.157187670336.91743928780.21168664948.6778295918-0.03114917322.455017475123.3523688685-0.064400357318.69566375690.0084387717-0.227668826974.601776689513.090903282113.3742727616-1.700220016134.43858496220.526554740519.7196730727-0.19287849664.033834167329.9307475917-2.778912276338.084389414-0.697725317-98.0613028324-17.7525247552-169.56826496462.1977560637-60.2516604719-0.8345638935-26.77885807130.2897421237-7.6720783541-62.03293377412.4102001223-55.38058043-0.06574992261.7072582653-6.762366689792.792297676419.3900268501176.777789769-2.612613034359.15091415351.364102239337.8838938998-0.25885573829.6459541489126.704438714-5.99883973683.309754091-0.056600768716.65536144580.69967739670.00468435170.03498782225.3275496283-0.13139925334.6399736816-0.0598966536-1.0138406062-0.0073317411-0.2639663065-8.5963699970.2106612079-5.39770378480.00210313160.1987575763-0.12145871970.02089189073.01600248980.495145320518.1103879743-0.611547912413.3107344008-0.0029926674-0.16973457851.33819867460.04427328720.00061847521.2498639257-0.0064427430.6688144795.9753286022-0.92352740440.1181829435-0.184346758-2.19502748867.0645283914-1.6914980173-0.11233050810.525818541351.3017278222-3.365059127134.4716458421-2.44017524229.29636190943.1331050236-0.46265122593.1433643077-0.38818812191.293444190417.58836011230.28208735071.53664659690.13975996130.6434252052-0.0093097726-0.1139197208-0.3026428593-0.00589423080.0906303291-0.01207211590.32595219470.0015514843-0.49800028960.3047323984-3.20749684560.6162577977-0.45875112710.027234149-0.05828241790.9426178961-1.2132035822-0.1138905837-1.50708059370.1075698793-0.5586675777-0.45158645591.5167365976-0.1433064379-2.06045966466.06417381540.41698929473.4842437453-0.17169552091.2760937152-5.7243988339-0.7992739163-4.2570249955-0.5066790632-0.0011044882-0.0972970531-1.86336514690.2065570020.56584866473.23243841860.52845160152.3092732933-2.31547880620.5852291031-0.24826457380.0435046594-2.8579760371-0.4508255338-0.42128910412.9602445207-11.0166904147-0.7576575232-5.7319560045-1.715651767619.29525242922.451067690515.97383886643.82439261452.14717211490.46562289170.027156851-0.1652268687-20.8119626649-3.591335575-22.2996388626-0.3047703924-2.0908488786-0.0561247809-5.2473334838-0.0209849336-0.70723410586.09469833720.04983471730.2120322297-0.0036490368-1.8983718194-0.40666596094.5984788831-0.04187033010.2788541726-1.97006060986.76999079450.49272743924.0815690378-0.0025101797-15.3540661572-1.8004696853-15.0476490422-4.2115609853-1.6492776869-0.3300341565-3.1207000491-0.136748511423.11250760463.774904108230.13063537845.87916545470.0673400576.16046204731.3979189091-0.31026076340.09069649130.00318845590.02801522412.38737346690.94065905070.004528582-0.0412181967-5.8823468999-4.6031894844-0.267390827514.73182836083.208209756518.85474708080.1543019125.35920458-3.3346202407-3.06465933380.2629357041.6706002521-0.2456410101-0.0506565973-23.3013398402-5.3572382145-32.0554023616-7.4051738132-0.2233923574-9.9115151916-1.76614098050.0790615549-3.0299179206-0.5186702445-0.0807627866-4.9046622817-1.4592225771-0.065378855317.8648966971.208133716918.52320422234.724062182632.32648685820.35635080715.97292266680.330731359211.5867580731.66747614028.3166215890.01094710210.96501250465.29814291640.0639102182.6546583830.0035764142-0.00634867080.037016868-0.1652263894-0.12265905610.0863119320.02899565510.6524783970.1013209821-0.8997573136-0.00193124880.0226739125-0.0002660423-1.163814503214.4361123092-1.7388953707-0.06093137520.397030298-0.14705352820.0013204594-0.3744511997
7500330003500.840.7530530078383.631042618778383.631042618778383.6310426187239354.36157514547180.48267470312618.097113753-97831.045264806-87557.2477878395-64301.32158054211537.078202825528785.1190180620.43379923831.7119958543-57.1429908404103.8602248415114.8143053421995.14352139274.7816532034-8.0859494875148.70072887192.176760663527.4047269967228.30275744631294.3329942349105.0706968915-55.6748180929-0.97763698454.8617773535-34.9119170063-1.589439386-19.34424904492.47715551322.301250923733.7273688226618.163334298327.389094599325.3898282506-14.149556513158.87606756520.0043196206-0.11767986490.67427028460.01572895570.44613060910.02280246380.21550888561.8262451252-12.9597250682-0.4752859334-5.29798575030.3192276511-4.13360206772.221903958954.15982863450.727520714621.386371817-1.109779879940.287778869242.61812264783.631149921732.6396262545-1.241432294419.1249104887-155.3273510534-15.4572598032-168.45987593738.5084505893-98.4860102594538.882463689962.5822607766625.1084133205-27.1558699797390.15995225090.09731937442.2481339346-0.02717211650.8460306415-0.7491662939-11.68778427560.3210273218-6.28345785833.003059860861.5015756481-1.36074282327.0976365468-0.0282277013.4450475792-0.0401121651.02353351526.257591363-0.38014040269.3241715852-4.52648689383.6670720093-69.9755613712297.3738439468-17.6950425375320.80736853884.6613174356-0.821236183612.6197884786136.6750091356-6.4178299884135.9981126673-0.0110626441-0.1258803913-0.45859091585.43256176231.2052319065-6.18929406170.0249863977-0.1811875810.6409196081-2.55814379350.00147550990.49460456331.2568210603-10.772968599453.6693982482.875730865228.402763073-0.37743857846.24851611790.0001371377-0.00624593820.01118866820.00049851860.0080561656-0.0002951460.00144663770.1897449071-0.5987926679-0.0263271935-0.30152988510.0125172768-0.09832854890.67185692050.06260235950.5066241477-0.01378762720.13247276980.0410004426-0.00090211410.00383932740.0491410057-0.0049809910.0985036868-0.0388869156-2.51053693311.34608977390.53050890824.9972115442-0.11352579111.9058145887-22.9859330155-2.0627059611-17.9839476460.3084770718-6.1999532433-0.0205378059-1.32037548270.007342528-0.3168457075-2.16418475330.1072927895-2.4875244367-0.01104322520.0792630009-0.110757276811.7175484415-61.7081895233-2.8142427773-26.40838365110.1521725508-10.2487134199167.617302331314.6668534125143.1490192585-1.578500061450.3584523730.21168664948.6778295918-0.03114917322.455017475123.3523688685-0.064400357318.69566375690.0084387717-0.227668826925.30940374483.255828736828.1972303452-0.4228604458.56519463620.09600517853.5954300425-0.03516696950.73547712985.457185253-0.50667090916.9438148059-0.1272142067-248.8972368881-33.0325223774-315.51948718184.0894141737-112.1116207559-1.138414443-36.52858580670.3952323135-10.4653518731-84.6180721443.2877130812-75.5437098504-0.08968835362.3288420243-9.2244296312321.27368193749.215378205448.6938491107-6.6312821319150.13566684272.538215739370.4914140522-0.481658698317.9484439914235.7618009186-11.1621761157155.0163345336-0.105318324230.99100591310.09352079090.00062612320.00467656780.7120948271-0.01756318290.620191549-0.0080059502-1.0138406062-0.0073317411-0.2639663065-8.5963699970.2106612079-5.39770378480.00210313160.1987575763-0.12145871970.02849827364.11407780910.675419328124.704072868-0.834202128218.1569468875-0.0040822468-0.23153205781.82541410020.04427328720.00061847521.2498639257-0.0064427430.6688144790.7986787331-0.1234411940.0157966549-0.0246402909-0.29339336647.0645283914-1.6914980173-0.11233050810.525818541369.979816234-4.590220043847.0221870436-3.328601633512.68100950363.1331050236-0.46265122593.1433643077-0.38818812191.293444190417.58836011230.28208735071.53664659690.13975996130.6434252052-0.0012443696-0.1139197208-0.3026428593-0.00804022020.1236272938-0.01207211590.32595219470.0015514843-0.49800028960.3047323984-3.20749684560.6162577977-0.00014642610.0000086927-0.00001860280.0022509542-0.0039518957-0.0002719686-0.00359888080.0002568749-0.0013340879-0.00147100010.0036219391-0.0003422131-0.03681160650.14778593380.00744981620.0622485419-0.0030674650.0227983399-0.1902970909-0.0194785713-0.1037451157-0.009052189-0.0000197325-0.0017382824-0.033290370.00369029070.01010929680.14657953180.01756739970.0767675354-0.07697382620.014262228-0.00605029030.001060223-0.069649827-0.0080543252-0.00752663540.3956743639-2.0086407893-0.1012705729-0.7661488873-0.22931869884.79890775980.44689596922.91246309930.69729026690.28699688650.06223642680.0036298588-0.0220846743-7.0606678444-0.8931983773-5.5461264563-0.0757992157-0.5200134564-0.0102330664-0.9567308941-0.0038261213-0.12894791621.11122843780.00908621760.0386592134-0.0004877402-0.2537415598-0.05435608250.614645241-0.00559650260.03727241-1.97006060989.23482954310.49272743924.0815690378-0.0025101797-28.5696564808-2.4559901404-20.5262426711-5.7449188618-1.6492776869-0.3300341565-3.1207000491-0.136748511458.66370437877.024049037956.064751414710.93949548710.09185742898.40338172391.9068774585-0.42322144160.09069649130.00318845590.02801522412.38737346690.94065905070.004528582-0.0412181967-5.8823468999-4.6031894844-0.26739082756.81757931291.08841745646.39666275450.03837631281.3328837516-0.829350899-0.76220912440.04794029420.3045956347-0.0447870035-0.0092360685-80.6759551384-13.5976348511-81.3623809258-18.7956640137-0.4156711875-18.4425794008-3.2862982740.1471116147-5.6378364707-0.7075092777-0.1101671465-6.690366577-1.9905007517-0.089182186924.3692023831.647994698987.482289873616.3560649872111.92361561361.233789212220.67997996740.839455718829.40927751884.232354577221.10908252250.02036951921.79562048749.85837377260.11891918124.93958260310.0066547145-0.00084858070.0049477756-0.1652263894-0.12265905610.0863119320.0395524810.89003470760.138210232-1.2273436809-0.00263438380.0226739125-0.0002660423-1.587539611619.6920557926-1.7388953707-0.06093137520.397030298-0.14705352820.0001764962-0.3744511997
2EngErrorBoundCalcs
Covariance Matrix (from JMP)Sum Product (Case 1 on 2Eng tab)
15.4878196248-0.0000201116-0.0000271633-0.0101045479-6.6817017626-4.45618570830.0017533863-0.000283724-0.00000000570.0000000019-0.00000000120.0000003348-0.000000189-0.0000082404-0.0000329409-0.0001759432-0.0336603142-18.92021937460.0003942647-0.0001611092-0.0224288728-8.4532190223-8.9560080631-0.0000002535-0.00000000130.0000204130.02358620530.00394426080.00004691570.0000000291-0.0000000057-0.0000004158-0.0013347777-0.0008312752-0.00000066680.00000000051.91E-123.76E-120.00000000070.00000062250.000000334-0.00000000058.88E-12-2.70E-13-1.77E-10-0.0000000734-0.00000004276.95E-124.02E-122.30E-137.79E-110.00000003670.0000000459-1.41E-111.56E-12-0.0000000166-0.0000135832-0.0000136815-0.00000000132.77E-100.00000000940.00000420260.00000318280.0000000016-1.98E-100.00000361310.00250292630.0013794648-0.0000003670.0000000522-0.000910288-0.0027269844-0.00000123360.00000058930.00075811680.00128239840.0000011298-0.00000007780.85430820121.11653561970.0000475674-0.0000116666446.4713573733309.9930040599-0.1595239170.0038828739-0.00043199310.00000786330.00000008240.0027623303-0.0000010507-0.00000004850.54126071560.0001011121-0.000005782874.6517893566-0.05898667630.0082703122239.6116187292-0.08553116390.00655483660.00000000149.19E-110.00000000435.45E-110.000001153-0.00000001410.0018673233-0.00000966520.00083569780.00002029850.00000015720.00000014221.91E-119.41E-120.00000000090.00000066170.0000012796-0.00000000091.28E-103.25E-16-9.71E-17-1.00E-141.17E-11-2.03E-112.13E-14-1.80E-158.80E-171.42E-141.13E-111.26E-11-1.76E-155.98E-176.42E-14-0.00000000120.0000000005-2.36E-123.74E-14-0.0000009522-0.00000000228.18E-120.0000005998-0.00000000138.85E-114.92E-15-9.49E-18-5.60E-15-2.18E-12-2.09E-121.64E-15-1.72E-17-8.67E-13-0.0000000003-0.00000000128.23E-133.25E-14-0.00000022320.00000015450.0000000004-1.28E-11-0.00000066550.00000000093.18E-127.19E-133.62E-14-1.73E-153.74E-187.90E-168.04E-134.33E-13-2.38E-17-1.65E-183.25E-131.82E-102.87E-10-2.66E-13-1.33E-140.00000011030.0000000206-2.26E-103.79E-120.0000001082-8.95E-11-5.62E-12-2.68E-133.69E-156.29E-110.0000000744-0.00000001243.03E-10-1.17E-110.00001692140.0000556690.0000002531-0.0000000028-0.00009510440.0000001877-0.0000000049-5.36E-124.20E-110.00000003670.0000000463-6.79E-118.15E-130.00000410910.0000226431-0.0000000444-0.0000000020.0000252731-0.0000000648-4.19E-111.98E-11-1.53E-123.10E-14-0.00000000340.00000450920.0000008662-0.00000000492.91E-100.0044951507-0.0009017667-0.00000718520.00000045510.0021136099-0.0000021670.0000002147-0.0000000064-4.58E-120.00262774960.00008057690.00000006820.00415880920.0001288369-0.00000247740.00000000380.0123631407-0.0000173871-0.00000046140.0030892588-0.00005088950.0000007419-0.0000000028-9.83E-116.01E-111.77430126610.90877534780.00003484451.038797682-0.00233734130.0002144962-0.0000069428-0.0000001427-0.0000000052701.7040881933-0.25832761971559.0440298705-0.24595040520.0726976281-0.04894339990.0000398522-0.000000099-0.0000000005-1.27E-100.0150610921-0.0000004530.00000001381.64E-101.7377238365-0.00024275510.00003458150.0000000721-0.0000000076-125.9997621775-0.69124092550.078735635-0.00011162340.000000386684.66844741760.1653603944-0.0144246669-0.0049492982-0.0000146194-2.91E-108.89E-135.63E-140.00000000090.00000000120.00000084690.0000007539-0.00000004864.30E-150.00000000050.00000000061.86E-13-1.24E-19-2.53E-144.44E-172.80E-213.14E-184.85E-15-3.82E-16-6.68E-182.91E-203.76E-17-0.0000000004-1.04E-12-1.17E-20-3.10E-18-2.19E-15-1.51E-157.42E-19-7.02E-20-5.75E-16-2.95E-141.68E-136.81E-114.04E-143.21E-15-2.59E-12-9.57E-14-1.45E-18-1.29E-13-6.52E-11-2.11E-11-4.83E-150.0000000196-2.80E-12-5.58E-11-6.38E-13-0.0000000009-2.78E-131.51E-216.11E-191.12E-163.02E-16-2.78E-201.27E-166.74E-14-1.35E-14-2.22E-18-1.08E-11-5.25E-15-1.42E-16-5.76E-183.55E-141.48E-111.60E-121.64E-14-8.36E-16-0.0000000012-0.00000000651.27E-11-1.21E-13-0.00000000381.68E-11-1.11E-15-0.0000000010.00000018511.66E-11-0.0000013498-4.04E-11-1.00E-12-5.71E-22-2.35E-19-7.89E-17-1.44E-167.79E-20-3.46E-17-1.78E-14-1.22E-142.75E-19-7.28E-125.24E-16-1.37E-111.72E-14-1.10E-14-5.64E-12-4.85E-12-1.67E-16-0.000000002-0.00000000288.97E-142.90E-16-0.00000229070.0000000026-5.82E-12-0.000000688-4.15E-11-1.51E-118.36E-14-0.0000011007-6.49E-113.41E-142.95E-120.00000000131.46E-10-0.0000001602-0.0000004426-0.00000132139.71E-110.0001548772-0.00028330210.0000000418-0.0000000199-1.02E-12-0.0000000012-3.14E-104.25E-14-0.0000004303-0.0000005293.66E-11-2.09E-13-2.05E-15-0.00019038450.000000024-0.00028601540.0000000222-5.27E-140.00013425224.83E-11-0.0000000003-0.0000002231-0.00000008354.60E-11-5.47E-12-0.0001807036-0.0001222577-1.98E-10-0.0000000025-0.1206738057-0.1199320093-0.08331910940.0000532994-0.00000319151.82E-100.0000066051-0.0000000533-0.13122635790.00001258730.0000000433-71.1127658713-43.88630005630.0008763603-38.80647620090.0000000154-63297.83134585744.48142152960.0040540987-0.0003353771-29541.29361011840.0004071824-0.0000000183-0.0000224827-1.80E-113.69E-17-0.04793163110.1733878080.1536002512
-0.00002011160.0000000068-0.0000000003-0.0000000316-0.0000143553-0.0000047850.00000001370.0000000012-1.62E-137.80E-141.98E-14-3.64E-124.36E-130.00000000060.0000000071-1.91E-100.00000072390.0002157601-0.00000000490.0000000010.00000009710.00020933810.0000945332.55E-12-2.98E-121.98E-11-0.0000002525-0.0000003045-1.69E-10-7.04E-137.95E-14-2.51E-14-0.0000000013-0.0000000037-4.28E-12-6.87E-14-5.12E-167.15E-177.51E-152.24E-121.02E-128.19E-15-3.11E-16-5.51E-17-2.86E-15-2.50E-13-2.46E-123.10E-16-2.08E-182.57E-185.95E-161.97E-131.09E-134.46E-16-1.10E-17-1.41E-12-2.78E-10-3.10E-10-1.36E-132.23E-145.91E-149.62E-123.97E-11-6.09E-15-6.58E-167.41E-120.00000000230.0000000063-2.47E-11-2.14E-13-0.00000032570.00000003751.18E-101.09E-110.00000003190.0000000111-2.74E-11-1.60E-120.0000027978-0.0000062217-0.0000000014-0.00000000030.000588359-0.0002056672-0.0000036074-0.0000001397-0.0000005648-8.53E-116.81E-120.0000000411-1.58E-11-4.84E-130.0000035661-2.10E-10-8.59E-110.00013410570.0000022972-0.00000018710.0015529679-0.0000029728-0.0000000273-3.94E-12-3.87E-15-3.76E-14-1.31E-152.78E-113.19E-130.0000000054.79E-110.00000000712.35E-10-2.07E-111.75E-13-1.08E-15-2.12E-175.20E-152.93E-13-1.25E-11-4.67E-14-5.89E-162.22E-20-9.74E-211.08E-18-7.37E-174.65E-163.91E-194.54E-208.87E-221.77E-198.67E-181.49E-171.74E-19-1.39E-20-1.02E-16-1.18E-13-4.54E-14-5.86E-173.74E-18-8.14E-11-5.91E-141.54E-151.04E-112.60E-145.93E-166.60E-20-3.64E-22-2.44E-20-3.59E-17-1.26E-181.24E-205.08E-214.46E-181.27E-14-7.30E-15-1.63E-173.22E-192.15E-126.03E-124.30E-158.78E-17-6.50E-121.39E-141.62E-161.65E-17-3.92E-19-4.78E-21-6.09E-231.57E-213.30E-18-5.28E-181.10E-20-2.21E-22-1.43E-18-2.86E-157.77E-161.66E-18-1.31E-20-9.12E-13-1.05E-121.30E-15-3.48E-17-1.29E-131.22E-155.04E-178.33E-19-9.40E-201.72E-153.81E-121.97E-125.43E-15-6.84E-170.00000000220.00000000471.41E-12-2.13E-13-0.00000000072.99E-13-4.97E-143.66E-16-2.99E-16-5.32E-138.79E-144.40E-16-2.41E-17-2.45E-11-0.0000000007-4.48E-136.21E-150.0000000005-2.44E-13-2.14E-14-2.26E-152.19E-17-9.25E-20-3.79E-14-1.08E-10-3.22E-11-1.70E-141.17E-17-0.000000128-0.0000000532-3.97E-122.94E-12-0.00000001712.49E-111.43E-139.21E-14-8.32E-170.00000219810.00000000074.09E-11-0.0000000364-0.0000000029-1.31E-102.49E-13-0.0000003029-8.78E-116.76E-120.0000000209-2.02E-10-1.88E-127.52E-14-9.22E-15-5.64E-16-0.0000295535-0.0000602160.0000000013-0.00005394530.00000003150.0000000025-0.00000000031.84E-12-2.73E-13-0.01674073770.0000213632-0.01934456020.00004531130.0000008788-0.0000012142-1.79E-105.20E-122.24E-141.00E-140.0000001888-9.99E-12-7.95E-13-1.09E-140.0000333560.0000000213-2.09E-10-8.91E-12-9.01E-14-0.00879921760.0000395130.000001027-1.44E-10-1.09E-100.0103560550.0000179889-0.00000036780.0000001228-0.0000000076-3.17E-15-3.19E-173.35E-189.22E-141.21E-14-1.68E-12-3.66E-12-4.57E-132.54E-21-1.64E-155.76E-151.51E-17-1.13E-241.41E-19-9.03E-223.82E-242.08E-228.48E-211.78E-19-8.51E-233.79E-24-2.07E-224.64E-141.29E-17-5.26E-25-1.06E-22-3.93E-20-3.10E-204.65E-242.50E-24-4.75E-21-6.13E-182.78E-18-5.17E-157.01E-192.87E-19-2.31E-153.00E-181.39E-231.43E-181.36E-151.39E-15-5.31E-201.34E-12-1.62E-174.59E-16-7.01E-17-1.27E-154.77E-181.33E-251.96E-231.59E-219.58E-21-2.78E-254.40E-213.21E-18-2.02E-19-9.96E-232.09E-15-9.25E-201.33E-201.29E-223.33E-201.03E-16-2.30E-164.26E-203.69E-21-3.07E-144.75E-14-6.43E-17-9.07E-18-1.79E-13-1.11E-16-2.71E-20-7.29E-149.25E-11-2.81E-15-7.31E-115.26E-164.47E-18-4.58E-27-2.26E-24-2.74E-22-5.53E-22-2.15E-24-1.31E-22-1.44E-19-7.47E-206.59E-24-2.27E-161.36E-20-7.90E-178.83E-20-4.57E-20-2.63E-176.90E-183.29E-211.13E-142.54E-141.98E-18-3.25E-211.64E-111.18E-144.69E-16-1.90E-118.69E-16-3.20E-175.92E-204.06E-127.91E-18-7.38E-208.23E-17-1.98E-14-1.42E-148.15E-11-9.97E-114.02E-111.55E-15-0.0000000158-0.00000001822.94E-121.51E-11-5.45E-19-1.68E-159.65E-16-1.17E-19-7.65E-125.90E-122.69E-16-5.65E-182.63E-200.0000000006-9.20E-140.0000000053-4.05E-142.72E-17-0.0000000009-1.46E-15-8.49E-166.71E-14-5.66E-134.33E-151.60E-17-0.00000000040.00000000145.34E-14-4.34E-15-0.00000004780.00000030160.0000010676-0.0000000005-4.87E-126.18E-150.0000000011-2.87E-120.0000002771-2.80E-105.82E-130.00036264290.0000688668-0.00000002430.00055176912.60E-130.0264103462-0.0003369845-0.0000004574-0.000000010.0507177998-0.00000001871.80E-13-2.86E-102.97E-15-9.52E-22-0.00000236920.0000012488-0.0000002425
-0.0000271633-0.00000000030.00000000050.00000001380.00000450310.0000082786-0.0000000143-1.97E-10-2.81E-14-1.16E-142.86E-151.23E-121.26E-136.50E-120.00000000050.00000000060.00000005950.00004566390.00000000050.0000000004-0.00000001450.0000577712-0.0000211082-5.63E-122.11E-131.71E-10-0.0000000315-0.0000000519-2.62E-10-4.46E-143.23E-146.52E-120.00000000190.0000000071-2.63E-12-1.37E-133.40E-17-5.68E-17-1.97E-15-8.98E-13-1.28E-123.54E-159.22E-186.74E-181.37E-153.08E-134.47E-13-2.17E-16-2.87E-17-4.90E-18-2.58E-16-1.57E-14-2.14E-131.32E-172.64E-186.06E-141.10E-114.76E-11-1.66E-14-3.89E-16-1.08E-13-1.41E-11-3.52E-11-1.64E-141.45E-15-3.91E-12-0.0000000013-0.00000000282.46E-122.54E-140.00000001680.0000000089-1.99E-11-1.30E-12-0.00000001380.0000000079-3.72E-121.66E-13-0.000000928-0.0000008126-0.0000000009-5.84E-110.0001543376-0.00047247590.00000104510.00000005050.0000000501-3.00E-11-1.27E-12-0.0000000363-1.34E-114.62E-13-0.0000014-0.00000000061.05E-10-0.0012531577-0.0000005392-0.0000000349-0.00046730230.00000047580.00000007621.88E-14-1.64E-15-9.30E-147.11E-16-1.92E-124.07E-140.00000000177.63E-110.0000000014-4.95E-119.13E-12-1.78E-136.25E-18-1.12E-16-1.54E-15-5.52E-13-2.24E-124.79E-16-8.56E-178.59E-227.82E-23-1.97E-19-1.93E-168.88E-192.66E-196.70E-21-3.70E-22-2.30E-206.03E-18-4.87E-177.31E-219.94E-229.39E-181.02E-14-4.81E-16-1.21E-17-9.56E-195.01E-121.67E-14-5.94E-16-4.95E-123.18E-15-1.84E-164.34E-206.48E-231.97E-201.26E-177.14E-18-5.09E-21-4.40E-223.50E-19-8.28E-163.83E-15-3.81E-181.14E-193.82E-13-7.52E-13-5.04E-151.90E-164.27E-12-6.58E-15-3.14E-17-6.30E-18-1.16E-193.63E-21-2.02E-23-2.57E-21-5.30E-18-1.33E-183.17E-21-3.89E-23-8.39E-19-5.75E-16-4.99E-167.63E-194.19E-21-6.04E-15-5.84E-131.17E-151.43E-17-2.27E-131.28E-15-1.53E-172.29E-183.21E-20-2.72E-16-4.61E-13-1.18E-132.74E-162.01E-17-2.24E-10-0.0000000004-6.42E-133.81E-140.00000000041.98E-138.64E-15-5.31E-17-6.74E-18-1.94E-14-1.14E-131.22E-17-8.80E-182.62E-11-2.91E-111.11E-13-1.88E-15-1.27E-101.28E-13-2.46E-155.45E-16-1.43E-173.22E-195.65E-15-7.80E-121.07E-11-2.63E-14-1.07E-15-0.00000001410.00000000875.99E-12-8.59E-13-0.0000000035-4.37E-12-1.24E-12-8.02E-15-4.20E-17-0.0000002154-9.52E-112.17E-110.0000000442-0.00000000058.74E-12-3.55E-140.00000005861.79E-10-3.19E-12-0.00000004664.81E-119.98E-13-4.98E-15-8.70E-155.18E-18-0.00000146290.0000022167-0.00000000050.00000030790.0000000222-0.0000000006-2.18E-118.56E-13-1.49E-14-0.0034070455-0.0000039869-0.00047376320.0000031954-0.00000055790.00000019248.06E-11-6.53E-13-1.23E-14-7.24E-17-0.00000007772.85E-131.63E-13-2.54E-15-0.00000707350.0000000055-0.0000000003-2.19E-122.74E-14-0.0026884163-0.00000371770.00000015670.0000000006-1.79E-110.00031210110.00000751190.00000010566.06E-11-0.00000000094.90E-15-1.19E-17-1.13E-18-5.00E-14-4.36E-15-2.92E-12-7.08E-132.60E-13-3.87E-20-1.79E-15-4.65E-151.02E-171.89E-246.18E-20-2.43E-22-4.27E-25-6.58E-23-2.70E-20-1.35E-206.80E-232.71E-24-3.09E-22-2.63E-154.16E-182.32E-252.12E-233.56E-221.07E-20-1.05E-23-3.94E-254.32E-211.44E-18-1.41E-18-1.97E-161.18E-18-4.03E-207.67E-16-1.06E-191.17E-232.30E-19-1.93E-169.97E-171.22E-20-2.82E-131.43E-172.78E-162.33E-184.83E-151.42E-19-2.80E-26-7.63E-24-5.00E-22-2.61E-211.59E-25-5.41E-22-1.14E-192.32E-199.86E-24-1.80E-161.99E-202.57E-212.02E-23-4.27E-203.54E-174.98E-171.25E-19-8.93E-231.13E-147.41E-14-7.12E-18-1.05E-184.12E-144.99E-172.72E-21-4.61E-14-1.40E-11-2.11E-152.46E-111.87E-161.78E-181.35E-261.15E-243.01E-239.23E-222.56E-254.43E-225.97E-201.92E-19-4.57E-241.42E-17-4.05E-211.73E-165.90E-211.92E-201.44E-183.84E-18-2.86E-223.35E-15-4.07E-15-1.05E-19-2.53E-23-1.49E-12-1.34E-14-8.76E-167.20E-124.89E-16-4.19E-17-9.63E-203.21E-12-1.80E-162.07E-20-2.18E-185.70E-155.08E-16-5.77E-131.78E-11-2.45E-12-4.59E-160.00000000560.0000000063-2.96E-13-6.44E-124.36E-188.77E-161.67E-16-1.08E-192.69E-12-4.16E-123.24E-172.08E-172.00E-200.0000000007-3.12E-14-0.00000000071.06E-14-4.59E-18-0.00000000059.57E-173.03E-161.13E-131.42E-13-9.77E-17-3.96E-191.37E-10-2.52E-101.76E-143.24E-15-0.00000002730.0000001431-0.0000001586-2.65E-108.07E-12-4.12E-15-8.04E-117.70E-130.00000072526.04E-12-7.67E-140.0001621372-0.00006314020.00000000380.0000768796-1.16E-130.0605991501-0.0000121088-0.000000092-0.00000000150.0536502161-0.00000000516.19E-15-2.95E-11-4.17E-17-9.47E-22-0.00000005060.00000032460.0000003993
-0.0101045479-0.00000003160.00000001380.00001885170.00168864050.0011810506-0.00000286650.0000000744-3.00E-121.22E-13-1.50E-13-1.84E-101.62E-10-0.0000000280.00000009980.00000007120.00002737060.0072991947-0.0000000370.00000000790.00001173460.00141918180.00194140981.80E-102.32E-100.0000000023-0.000013879-0.0000109174-0.0000001027-1.77E-116.28E-12-0.00000000070.00000143390.0000014743-2.01E-10-4.04E-118.76E-16-1.13E-15-1.26E-12-1.60E-10-2.92E-111.57E-134.14E-153.68E-161.99E-13-1.83E-113.53E-115.53E-15-2.89E-16-7.61E-17-1.13E-13-1.14E-11-1.44E-111.57E-14-8.07E-163.64E-110.0000000120.0000000169-1.37E-12-4.09E-13-9.59E-12-0.0000000022-0.0000000031-1.48E-121.54E-13-0.0000000069-0.0000017765-0.00000106840.00000000071.55E-110.0000017927-0.0000018650.000000005-0.0000000007-0.0000005368-0.0000001155-0.0000000017.72E-11-0.0013478201-0.00044754960.00000010440.0000000167-0.025760175-0.15036057350.00023374840.00000431910.0000028859-0.000000006-8.87E-11-0.00000159380.00000000084.61E-11-0.0006517943-0.0000005893-0.0000000026-0.32386518910.0004250862-0.0000127361-0.03540841540.0000491609-0.00000071986.48E-11-8.77E-14-5.18E-12-1.21E-13-0.00000000235.19E-11-0.0000002715-0.0000000039-0.00000069880.00000000290.00000000121.26E-111.12E-14-3.16E-16-1.52E-12-1.07E-101.66E-109.06E-13-4.84E-141.17E-191.42E-19-7.14E-18-9.92E-15-1.46E-148.38E-192.02E-18-2.39E-20-1.05E-17-3.28E-151.30E-15-8.98E-187.32E-202.49E-152.22E-121.26E-121.84E-15-3.18E-170.00000000226.78E-13-6.49E-141.11E-102.74E-12-1.44E-137.06E-18-5.95E-211.83E-18-6.49E-17-9.17E-173.24E-18-1.69E-201.96E-164.98E-143.50E-13-2.07E-16-4.17E-173.07E-11-1.77E-10-1.53E-13-2.44E-142.23E-10-9.34E-134.17E-15-6.94E-162.64E-17-3.54E-191.13E-21-5.35E-19-1.88E-162.35E-16-1.60E-18-1.12E-20-3.13E-17-1.06E-13-1.26E-137.53E-178.64E-18-2.50E-11-1.97E-121.03E-13-4.54E-15-2.38E-11-2.13E-141.34E-152.63E-166.69E-18-1.20E-13-1.80E-10-9.20E-11-3.22E-131.03E-14-0.0000000155-0.0000001563-1.09E-108.28E-120.000000012-1.91E-105.21E-125.55E-15-4.36E-14-1.97E-11-1.37E-117.21E-141.99E-16-0.00000000420.00000000272.30E-111.93E-12-0.00000001165.14E-117.45E-131.49E-13-3.89E-16-5.04E-177.61E-12-0.00000000230.00000000183.58E-12-2.44E-13-0.00000098230.00000444490.0000000059-0.00000000050.00000097290.0000000022-0.00000000049.57E-141.13E-14-0.0000259863-0.000000055-0.0000000017-0.0000073319-0.00000008760.00000000394.38E-12-0.0000012967-0.00000000533.15E-10-0.00000123740.0000000373-1.05E-10-1.63E-111.23E-12-4.38E-14-0.00243190450.00082372920.00000001520.000906104-0.0000043718-0.00000020080.0000000139-1.29E-102.24E-11-0.9675121375-0.0015590563-0.7649613684-0.0001204478-0.00012467320.0000287902-0.00000007647.36E-129.56E-12-1.21E-13-0.00000859881.91E-101.60E-11-3.20E-12-0.00128843160.0000031452-0.0000000731-2.05E-111.23E-110.40842680690.0011326612-0.00002935950.000000206-0.0000000009-0.11141324290.0006864837-0.00006271440.0000017629-0.0000001026.60E-14-5.85E-15-1.14E-16-3.01E-11-4.52E-13-1.04E-10-0.00000000111.32E-10-3.60E-18-1.94E-13-3.96E-14-7.10E-16-3.80E-23-3.05E-18-9.79E-21-2.38E-24-5.29E-212.86E-18-1.30E-184.26E-21-2.93E-22-5.68E-20-1.68E-135.94E-163.90E-244.30E-214.70E-191.43E-19-3.27E-22-2.69E-256.18E-193.31E-17-8.11E-17-8.49E-161.10E-16-7.83E-185.72E-14-1.07E-17-5.55E-232.35E-164.33E-14-4.87E-143.26E-186.36E-121.47E-158.67E-141.78E-154.95E-13-3.07E-17-9.97E-25-4.34E-221.84E-19-3.11E-201.46E-23-1.51E-19-8.11E-171.51E-175.88E-213.02E-145.94E-185.03E-216.85E-21-4.17E-17-1.94E-146.24E-15-1.02E-173.56E-19-2.23E-12-4.89E-12-1.39E-148.55E-162.74E-124.51E-15-1.94E-191.73E-12-2.56E-103.46E-13-0.00000000045.05E-165.61E-163.71E-262.47E-222.26E-205.51E-20-3.83E-232.50E-209.36E-18-5.44E-188.14E-24-8.92E-16-7.14E-196.16E-15-1.31E-171.65E-174.90E-151.18E-155.81E-202.35E-121.02E-12-1.21E-16-6.01E-190.0000000006-3.50E-12-5.32E-140.00000000045.71E-15-6.94E-16-6.28E-175.64E-137.77E-14-6.77E-17-5.97E-15-3.27E-138.60E-13-0.00000000030.00000000160.0000000021-9.17E-14-0.00000111420.0000003182-9.74E-120.00000000121.23E-159.86E-133.77E-13-6.09E-170.00000000062.12E-10-4.07E-144.46E-161.22E-180.0000003303-2.43E-110.0000000632-3.15E-11-7.50E-160.0000000854-6.32E-156.48E-132.35E-106.55E-11-4.10E-14-2.30E-150.0000002888-0.00000000092.23E-135.09E-120.00004186540.0001192491-0.0000161819-0.00000008410.000000005-6.97E-130.00000001229.80E-110.0000283244-0.0000000111-7.47E-110.03538564610.0808833019-0.0000015318-0.0018455613-2.64E-1124.2833043686-0.04028621770.00001073130.000000725310.5822110396-0.00000397227.52E-120.0000000054-4.96E-142.40E-190.000004108-0.0002401215-0.0002107135
-6.6817017626-0.00001435530.00000450310.00168864058.1112098152-1.0463715243-0.0009141840.00001051620.0000000018-0.0000000018.41E-110.0000000440.0000000874-0.0000171143-0.0001596720.00013953330.00525997067.91087112380.0001527426-0.000018979-0.00807298970.7460209556-11.04925584350.000000664-0.0000000982-0.0000321035-0.0250611403-0.0129296317-0.00003167110.00000000070.0000000006-0.0000001878-0.00014149090.00014538250.0000008049-0.00000000071.19E-12-1.07E-12-1.09E-10-0.00000064670.0000000629-2.67E-111.11E-123.57E-135.48E-110.00000006740.000000017-3.42E-11-8.17E-13-4.00E-14-2.30E-11-0.00000004970.00000000945.78E-128.15E-140.00000000940.0000111220.0000001142-0.000000001-2.98E-10-0.0000000026-0.0000029746-0.00000083860.00000000062.76E-11-0.0000008281-0.0021742080.00011626620.0000004785-0.00000000140.00288858430.0042727874-0.0000043593-0.00000033350.0000103582-0.0021551931-0.0000009351-0.0000000027-0.2313915993-0.62487447250.00003995880.0000113122-600.60908435767.90497096050.22758110620.0063011543-0.0016802969-0.00000267630.0000000285-0.00005563660.0000015525-0.00000000230.02174027610.0002177256-0.0000025689-902.5306524596-0.1804775646-0.000285150369.31934517010.0826041234-0.00188657530.00000000052.32E-100.00000000193.51E-11-0.0000000296-0.0000000075-0.0023366466-0.00000183060.0007513232-0.00001051680.0000000823-0.0000000255-4.38E-12-1.04E-12-3.09E-10-0.00000110540.00000027040.0000000013-8.40E-12-4.10E-16-4.18E-19-1.90E-141.46E-11-1.45E-11-2.33E-14-8.74E-17-1.52E-175.09E-15-9.40E-128.87E-128.13E-15-3.91E-162.72E-120.00000000150.00000000262.51E-12-8.07E-140.00000028260.0000000037.15E-110.00000114455.95E-11-1.11E-10-3.17E-157.57E-181.23E-151.63E-12-6.57E-13-4.32E-159.02E-17-1.13E-130.0000000005-0.0000000004-5.67E-131.24E-150.0000001528-0.0000000303-2.32E-101.95E-11-0.00000004265.34E-119.60E-12-5.55E-14-3.40E-141.27E-15-6.19E-19-5.13E-16-6.25E-138.28E-141.59E-162.23E-18-6.09E-14-8.04E-11-3.36E-112.40E-136.47E-15-0.00000003780.00000000851.21E-10-3.70E-12-0.00000002691.17E-104.18E-121.64E-13-3.44E-15-7.93E-11-0.000000094-0.0000000914-2.00E-107.12E-12-0.0000623776-0.000050672-0.00000025460.0000000016-0.0000214291-0.00000004230.0000000026-2.36E-12-1.27E-11-0.00000002820.00000000972.27E-112.58E-13-0.0000139895-0.00000302640.00000004060.00000000110.00000063760.00000000883.29E-111.44E-122.22E-12-3.13E-150.0000000027-0.00000023720.00000220290.0000000033-8.88E-11-0.00029954920.00069304240.0000027298-0.00000022790.00137988910.00000150120.00000004580.00000000657.59E-12-0.03756313-0.0001053557-0.00000082530.02931045610.00000522730.0000003032-0.0000000073-0.01285166360.00002552040.00000049-0.00113802970.0000274549-0.00000012590.0000000595-4.04E-11-4.33E-110.63432192780.0432937576-0.00009402360.05859579020.0021800525-0.00005887820.00000405980.00000036360.0000000019696.47941084551.6581899025-1045.1577961639-2.23254626-0.0514434953-0.01365775910.0000164561-0.00000002650.0000000047-5.11E-120.00024192570.0000000203-0.00000003060.00000000060.14766169180.00241792670.00003140810.0000000735-0.0000000005-160.45784550343.5079446944-0.0140385040.00014525920.0000077723671.9516084040.64664059580.0134525070.0015967009-0.0000414007-2.28E-103.35E-13-1.39E-130.0000000018-6.14E-110.0000006343-0.00000029870.0000000077-1.55E-15-8.38E-11-2.93E-10-5.64E-135.34E-202.09E-142.61E-18-3.24E-20-2.25E-18-3.85E-15-2.53E-155.30E-184.91E-211.31E-171.60E-114.98E-143.84E-212.38E-183.10E-152.03E-16-5.33E-20-3.25E-203.01E-167.26E-148.00E-14-2.54E-111.19E-135.25E-156.38E-12-1.73E-148.09E-194.63E-155.49E-11-2.59E-111.07E-15-0.00000003839.59E-13-4.64E-121.17E-120.00000000184.87E-14-1.22E-21-3.03E-19-2.03E-16-1.37E-161.09E-20-8.50E-17-7.29E-14-4.41E-151.26E-18-1.35E-111.19E-15-1.80E-16-1.77E-18-1.59E-14-1.14E-11-3.23E-12-9.74E-155.68E-16-0.00000000230.0000000076-9.48E-12-2.80E-13-0.0000000032-5.77E-121.95E-15-0.000000002-0.0000001249-0.0000000006-0.0000008477-3.23E-128.14E-131.32E-226.78E-201.17E-16-2.39E-17-4.31E-207.21E-181.40E-149.30E-16-7.73E-209.18E-121.96E-175.18E-13-7.10E-153.55E-154.83E-12-4.49E-13-8.03E-170.00000000110.0000000013-3.87E-14-1.89E-170.0000008085-0.0000000022-4.63E-110.00000131491.40E-102.23E-11-1.87E-14-0.0000002569-2.66E-111.22E-14-1.02E-12-1.39E-10-5.66E-110.00000044830.00000039890.0000000723-4.65E-110.00026437150.0002800975-0.0000000504-0.00000017414.17E-130.00000000078.26E-11-1.62E-140.00000009450.0