Application of Statistically Derived CPAS Parachute Parameters€¦ · Application of Statistically...

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Application of Statistically Derived CPAS Parachute Parameters Co CDS C k CPAS DSS EDU EF e exp open FAST FBCP(s) GEV Log n MDL MMv MPCV Leah M. Romero l and Eric S. Ra / Jacobs Engineering, Houston, TX, 77058 The Capsule Parachute Assembly System (CPAS) Analysis Team is responsible for determining para chute inflation parameters and dispersions that are ultimately used in verifying system requirements. A model memo is internally released semj-annually documenting parachute inl1ation and other key parameters reconstructed from flight test data. Dispersion probability distributions published in previous versions of the model memo were uniform because insufficient data were available for determination of statistical based distributions. Uniform distributions do not accurately represe nt the expected distributions since extreme parameter values are just as likely to occur as the nominal value. CPAS has taken incremental steps to mo ve away from uniform distributions. Model Memo version 9 (MMv9) made the first use of non-uniform dispersions, but only for the reefing cutter timing, for which a large number of sample was available. In order to maximize the utility of the available fli ght test data , clus ters of parachutes were recon tructed individually s tarting with Model Me mo version 10. This allowed for statistical asses ment for steady-state drag area (CDS ) and parachute inflation parameters such as the canopy fill distance (n), profiJe shape expon e nt (expopen), over-inflation factor (CJ, and ramp-down time (t k ) distributions. Built-in MATLAB distributions were applied to the hi stograms, and parameters such as scale (0) and location (fl) were output. Engineering judgment was used to determine th e "best fit" distribution based on the test data. Results include normal, lo g normal, and uniform (wher e available data remains insufficient) fits of nominal and failure (loss of parachute and kipped stage) cases for all CP AS parachutes. This paper discusses the uniform methodolo gy that was prev iously u ed, the process and re ult of the statistical assessment, ho w the di persions were in co rporated into Monte Carlo analyses, and the application of the di tributions in trajectory benchmark testing assessments with parachute inflation parameters, drag area, and reefing cutter timing used by CPAS. Drag coeffi cie nt Drag area Ove r-Inflation Factor Nomenc lature Capsul e Parachute A e mbl y Sy tem = Decelerator Sys tem Simulati on En g in ee rin g Developme nt Unit = En gin ee rin g factor Ree fin g rati o Ope nin g pro fil e hape ex pone nt: < I co ncave down; = I lin ear; > I co ncave up Fli ght An aly i a nd Simul ati on Tool = Forward Bay Cover Parac hut e( ) Genera li zed Ex treme Va lu e di tribution Logarithmic norm al di tributi on Multi - Dimen ional Limits Model Memo ve rsion Multi -Purpose Crew Ve hicl e (Ori on) I Anal y is En gin eer, Aero cience a nd Fli ght Dyn a mic , 2224 Bay Are a Blvd, Houston , TX , AIAA Member. 2 An a ly i En gin eer, Ae ro science a nd Fli ght Dyn a mi c, 2224 Bay Area Blvd , Hou ton , TX, AIAA Me mb er. I Am eri can In stitute of Aeronauti cs a nd Astr onauti cs https://ntrs.nasa.gov/search.jsp?R=20130011421 2020-07-12T05:51:03+00:00Z

Transcript of Application of Statistically Derived CPAS Parachute Parameters€¦ · Application of Statistically...

Page 1: Application of Statistically Derived CPAS Parachute Parameters€¦ · Application of Statistically Derived CPAS Parachute Parameters Co CDS Ck CPAS DSS EDU EF e expopen FAST FBCP(s)

Application of Statistically Derived CPAS Parachute Parameters

Co CDS Ck

CPAS DSS EDU EF e expopen FAST FBCP(s) GEV Logn MDL MMv MPCV

Leah M. Romero l and Eric S. Ra/ Jacobs Engineering, Houston, TX, 77058

The Capsule Parachute Assembly System (CPAS) Analysis Team is responsible for determining parachute inflation parameters and dispersions that are ultimately used in verifying system requirements. A model memo is internally released semj-annually documenting parachute inl1ation and other key parameters reconstructed from flight test data. Dispersion probability distributions published in previous versions of the model memo were uniform because insufficient data were available for determination of statistical based distributions. Uniform distributions do not accurately represent the expected distributions since extreme parameter values are just as likely to occur as the nominal value. CPAS has taken incremental steps to move away from uniform distributions. Model Memo version 9 (MMv9) made the first use of non-uniform dispersions, but only for the reefing cutter timing, for which a large number of sample was available. In order to maximize the utility of the available flight test data, clusters of parachutes were recon tructed individually starting with Model Memo version 10. This allowed for statistical asses ment for steady-state drag area (CDS) and parachute inflation parameters such as the canopy fill distance (n), profiJe shape exponent (expopen), over-inflation factor (CJ, and ramp-down time (tk)

distributions. Built-in MATLAB distributions were applied to the histograms, and parameters such as scale (0) and location (fl ) were output. Engineering judgment was used to determine the "best fit" distribution based on the test data. Results include normal, log normal, and uniform (where available data remains insufficient) fits of nominal and failure (loss of parachute and kipped stage) cases for all CPAS parachutes. This paper discusses the uniform methodology that was previously u ed, the process and re ult of the statistical assessment, how the di persions were incorporated into Monte Carlo analyses, and the application of the di tributions in trajectory benchmark testing assessments with parachute inflation parameters, drag area, and reefing cutter timing used by CPAS.

Drag coeffi cient Drag area Over-Inflation Factor

Nomenclature

Capsule Parachute A embly Sy tem = Decelerator System Simulati on

Engineering Development Unit = Engineering factor

Ree fin g ratio Opening profil e hape exponent: < I concave down; = I linear; > I concave up Flight Analy i and Simulation Tool

= Forward Bay Cover Parachute( ) Generali zed Ex treme Value di tribution Logarithmic normal di tribution Multi -Dimen ional Limits Model Memo version Multi -Purpose Crew Vehicle (Orion)

I Anal y is Engineer, Aero cience and Flight Dynamic , 2224 Bay Area Blvd, Houston, TX, AIAA Member. 2 Analy i Engineer, Aeroscience and Flight Dynamic, 2224 Bay Area Blvd , Hou ton , TX, AIAA Member.

I American Institute of Aeronautics and Astronautics

https://ntrs.nasa.gov/search.jsp?R=20130011421 2020-07-12T05:51:03+00:00Z

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Il , mu n

np

= M ean or expected val ue (general) Canopy fill distance, normalized to reference diameter (fi ll constant) Distance (mea ured in reference diameter) to peak drag area ( infinite ma only) Standard deviation (general)

- --_ ._-- -

0; sigma So tk

Parachute canopy full open reference area ba ed on constructed shape including vents and slots = Time to ramp down after stage over-inflation

T Max

TMin

M ax imum design di per ion Minimum de ign dispersion

I. Introduction

THE Capsule Parachute As embly System (CPAS) i re ponsible for slowing the descent rate of the Orion cap ule to safely land after re-entering the earth 's atmo phere. CPAS utili zes four different parachute type:

Forward Bay Cover Parachutes (FBCP ), Drogues, Pi lot, and M ain , deploying in the equence shown in Figure 1.1 The performance of Mortar:

the parachute system will Deployed :

be verified by analy is so " , it is imperati ve that models accurately represent the parachute dynamics 2 The CPAS Analy is team uses drop test data to reconstruct the parachute sy tem performance in simulations. Results are documented in a model memo released emi­annually. Since sufficient testing for stati tical analy is i not practical with current co t and schedule con traint , di persion are applied to the parameters to account for uncertainties in instrumentation, modeling

/ :r ................... · ......... . : : 151 Stage Mortar: : : Deployed ~

................. FBCPs 2nd Stage

Full · .............. , Open ~ ~ Mortar

:: Deployed

---. .. ................................. : . ..

Drogues , .............. .

Pilots

Pilot Deployed

2nd Stage

Mains limitation , and igure 1: CPAS Par achute deployment equence.

engineering judgment. In previous versions of the model memo, the inflation and drag area parameter were dispersed uni formly, which doe not accurately repre em the expected distribution and likely re ult in overly conservati ve pre-flight prediction. The November 2012 release of the model memo, Model Memo ver ion III (MM v ll ), publi shed nominal and di per ed parameter alue that were tati tically derived from te t data. Table I how the progre ion of disper ion data from MMv8 to MMv II. Change included the method of recon truction

from composite to independent parachutes, di persions from uniform to tati st ical di tribution , de cription of drag

Table 1: Progression of Model Memo disper sion data.

Parachute Reefing Cutter

MMv Reconstruction Type Parameter Co or CDS Dispersions

Dispersions

8 Composite Co only

None 9 Uniform

9A Limited Independent

Both Statistical- GEV 10*

for Skipped Stages On ly Statistica I CDS only

11 Statistical - normal * lnternal release only

2 A meri can Institute of Aeronautic and Astronautics

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from reconstructing and di persing the drag coefficient (CD) onl y to the drag area (CDS), and finally from a uniform rule of thumb to a descripti ve method of tati sti ca ll y disper ing the reefing cutter timing.

A. Parachute Parameters There are five parameter that describe parachute performance and directl y affect the drag area curve: canopy fill

constant (n), profile hape exponent (expopen), over-infl ation factor (C0, ramp down time (lk) , and drag area (CDS). For a detailed explanation and equations of each parameter, ee Ref. 3. All f ive parameter are necessary to describe infinite ma inflations in which the system deceleration is negligible, uch as with small parachutes like the CPAS FBCPs, Drogue , and Pilots. Onl y a ubset of the parameter (n, expopen, and CDS) is nece ary for the larger CPAS M ain parachutes, which are finite ma s inflations where the sy tem deceleration i ignificant. The inflation parameters are determined through drop test recon tnlction . Each stage of each parachute type has a different et of inflation parameter.

B. Reeling Cutter Time The Drogue and M ains each have three tages which are controlled by timed pyrotechnic ree fing cutters. The

cutter for the Drogues are 14 and 28 seconds and the M ai n are eight and 16 seconds. Each parachute canopy has redundant cutter for each stage. There are a total of 20 cutlers on each nominal te t (where rages are not skipped or removed). It is important to under tand the potential variation in the actual cutter firing time , as early or delayed cut could cause parachute in a cluster to lead or lag their neighbor , po sibly resulting in exce i ve loading or even parachute failure. Cutter tolerance values were not provided by the vendor and therefore must be determined from drop te t data.

II. Model Memo 9 and Previous: Traditional Methods

A. Composite to Multi-Parachute Reconstructions Pri or to Model Memo vel' ion 9 (MMv9), the inflation and drag area parameter were reconstructed and

simulated as composite parachute, meaning parachute in a cluster are treated a if they were a single parachute. M odeling the inflation and disreef in thi manner neglected e1u ter effects such as lead-lag, which are ev ident in fli ght te ts. Though a multi -parachute recon truction technique was implemented about the ame time as MMv9 wa relea ed, the memo included a mix of compo ite and multi -chute parameter . The drag area curve for infinite ma skipped stage cases were too complex to be accurately modeled with a composite simulation' therefore they were recon tructed a indi vidual parachute. The a umption that mo t u er of the data had a compo ite simulation drove the des ire to publi h the inflation parameters a such. For tho e u ers who had an independent parachute simulation, MM v9 instructed the u e of imultaneous reefing cut times between parachute in a clu ter for congruity acro imulations. The Decelerator System Simu lation (DSS) ha the ability to model individual parachutes, but it is

unable to output indi vidual load traces. This resulted in the need for continued u e of compo ite data. As the CPAS community continued to u e the MMv9 co mposite parameter , progress on development of multi -parachute reconstructions increa ed the number of data points per te t , allowing parameter to be tati sticall y deri ved.

~

<1> <1> E ro ~

ro 0...

<1> :E -;:) .r:; <.> ~ ro

0...

I

I

3 4

Tes Number

} '" I "'. En n....,g

Recommended Flight T t 01 por Ion

F -101

Figure 2: MMv9A Design and flight test dispersions.

3 American Institute of Aeronautics and Astronautic

B. Uniform Inflation Parameters

MMv9A and previous ver ions were limited by the mailer number of clu ter te ts earli er in the program; a a re ult, two di fferent ets of parameter were publi hed: des ign and fli ght te t di persions. De ign di per ions were based on the range of va lue reconstructed from drop te t data a

----'

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I-I I

shown as purple in Figure 2. These di persion were bounded by the highest and lowe t data point recon tructed from drop tests. The recommended fl ight te t disper ions (green bar) were the de ign disper ions with an engineering factor of ±IO% for inflati on par ameter applied to each limit. This engineering factor, EF, i applied to the mi nimum design dispersion, T Min, and the maximum de ign dispel' ion, T Max, to account for ex treme ca es that may be seen on future tests. T he EF was based on the judgment of engineers with significant recon truction experience.

Test prefli ght prediction used the flight test di per ion to bound previou test experience, and also account for te t mea urement, modeling, and ubjecti ve recon truction uncertainties. Des ign di persions were used in CPAS benchmark test cases to as e s the y tem requirement again t the latest model memo release. It was expected that as CPAS flight te t experience grows, the spread in te t data would approach the fli ght te t disper ion va lue defined earl y in the test program.For ca e where only a ingle data point wa available, an EF of ±IO% of the nominal va lue wa used. Therefore, fli ght test and design di persion were identical.

C. Transition from Co to CDS An update to the technique for

disper ing drag area necessitated the MMv9A revi ion. In the preceding model memos, the drag coeffic ient (CD) was uniforml y di persed ±S% u ing the arne method as de cribed in the

preceding section. The reefi ng ratio (c) was al o di per ed by ± IOo/, in the di persion calculation for reefed tage. The equation used, Co ' So ' £ =(COS)R'

results in the triangular di tri bution hown in Figure 3a. However, the full

open drag area distri bution was determined by multiply ing the uniforml y dispersed drag coefficient by a reefing ratio always exactl y unity (undispersed), re ulting in a uni form distribution. Thi incongruity between the ree fed drag performance and the fu ll open performance was determined to be

Rcsuhin g E distrib uti on

3: Reefed drag a rea dispersion distribution a) traditional fo stages only, and b) updated, to be applied to both reefed

stages.

unacceptable. A more con i tent approach i to characteri ze the drag performance of both types of tage (ree fed and full open) in term of drag area, using (CDS)R IC D ISo =£ . The effecti ve reefi ng i determined from te t data.

Since DSS (the imulation used at the time) accepted onl y drag coeffi cient and ree fing rati o as inputs, not a drag area, both Co and CDS were publ ished and the analyst wa required to pre-compute the ree fing ratio by di viding the CDS by the product of CD COF (loDES randomly generated points)

and the reference area (So) : g L CDFJ , (Figure 3b). ,- -, - -, t;

§ 0.8 u.

, :; D. First Assessment Cutters

Statistical of Reefing

Prior to release of MMv9, reefing cutter timing dispersions were not included in the M odel M emo documentati on. The rule of thumb wa to di per e the des ign cut time by ±I O%.4 This cau ed longer nominal times to have proporti onally larger

" oS! Co

~ en "0 .8 E ~

z

L- __ I ___ I __ I

, , ,

., Time from Target Reefing Cut T ime (sec)

c o '5 0.6

;@ ... '" o 0.4

C1)

.~

i 0.2 ::;, E ::;,

0 .27% = -2 .74 sec 99.73% = 1.13 sec

I

t-

u 0~L-----~~----~~_2------~0--- ~2

Time from Target Cut Time (sec)

b) igure 4: Reefing cutter a) histogram, best fit GEV distribution, and b) associate

CDF.

4 American Institute of Aeronautic and Astronautics

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di per ions without a phy ica l ba i ; thereby warranting a more in-depth under tanding of fli ght ree fing cutter dispersions.

Actua l reefi ng cutter time were evaluated using ePAS te t video timelines. Each cutter time wa computed a the difference in time between the apparent cut event and the skirt expo ure for the given canopy. There i some error in this approach based on the camera frame rate and ubjectivity of when the events occur. A lthough redundant cutter are used for each disreef, only the earliest cut is vi ible (determined by when the parachute kirt begin to expand).

A total of 51 cut event were examined from ePAS testing for nominal cut time of 8, 12, 14, 15 , 16, 20, and 28 econd . The deviation from each nominal was ca lculated. A hi togram of the off ets wa con tructed from the e

data to determine expected reefing cutter tati tic , a hown in Error! Reference source not found.a. The data have a negati ve skew, with a longer tail toward shorter cut times. This is because for any given cut event, onl y the first of the two redundant reefi ng cutter needs to be considered, so data on most longer cutters are not gathered. A Generalized Exu'eme Value (GEV) distribution , shown in red, fit the data be t. Several candidate method were evaluated to determine a suitab le probability di tribution function. For example, a Gauss ian fit fa iled a Kolmogorov-Smirnov (K-S) te t, but the GEY fit pa ed.

The cumulative di u'ibution function based on the GEY parameters i hown in Error! Reference source not found.b . Because thi i not a Gauss ian distribution, the standard deviation (0 ) is not relevant. Therefore, instead of ±30, the upper and lower va lue of equivalent probability (0.27% and 99.73%) are displayed.

The expected and actual cutter time are hown in Figure 5. The deviation from the

expected cut times can be seen by the vert ical off et from the target line. It can be een that the te t data are well bounded by the parallel line ba ed of -2.74 and + 1.13 econd. Absolute va lue were chosen over a percentage of the nominal cutter time becau e the latter ' bounds would expand with time

30

25

'" E j:: :; U 15

'" c

~ cc ~ 10

u:

,- -,

'-r----r-1,---' - ~ ;(: - 8 ,

_ J _

I ,----------------,

CDT-3-2 parachute starv ing cau ed subjecti vi ty in determining

CU( (imes from video ,

- r

- -- - -i

Lot Tested A14 Cutters I

1 ~ Flight E3 Cutters I ~ Flight H3 Cutters

~,' _~_ _,' 0 Flight HS Cutters , Unknown Flight Cutters I

Target Cut Upper Bound (+1 . 13 sec) I

tCUI - ec Lower Bound (-2.74 sec) I

10 15 -~2Q~===25===--~ Target Reefing Cut Time (sec)

igure 5: Target vs. flight actual cut time. ------------------~

resulting in the ame i ue encountered wi th the legacy ± I O~ di per ion.

E. MMv9 Monte Carlo Assessment After a model memo is relea ed, ePAS benchmark testing and analy i are completed to examine the effects of

the new disper ions and any model update. There are eight di fferent benchmark ca e including a nominal configuration, parachute fa ilures, and skipped tage. The MMv9 a e ment wa completed by di per ing on ly the parachute inflation and drag area parameter. The benchmark did not how a need to modify the di per ion .

ImpJementing the uni form di tribution for benchmark a se ment wa a imple proce in all imulation . The u er would refer to the late t model memo for the nominal, and upper and lower bound of each parameter, depending on if they wished to use flight te t or de ign di per ions. They would then create a et of di persion unique to the simulation and , if de ired, ca e type (one or two Drogue , two or three M ain , etc.). This caused ome di fficulties in simulation com pari on because the inputs were not identical.

III. Model Memo vlO: Multi-Parachute Modeling Model M emo version 10 (MMvIO) was internally relea ed in a hort form only in Augu t 20 125

. It included tati stical parachute parameter di persions and a re-parameterization of the fill con tan t, but did not contain an

update to the reefi ng cutter disper ion. Accompanying the memo wa a di per ion rule pread heet which de cribed how to di perse the parachute and a et of tex t file (ca e-type dependent) of 3000 di per ed parameter va lue.

The primary purpose of MMvlO wa to iden ti fy and re 01 e potential i sue the new di persions or with the di tributions themselve . It al 0 wa the fi r t memo to be a e sed with benchmark conducted u ing the Flight Analy is and Simulation Tool (FAST), which i to eventua[l y replace DSS as the primary ePAS analys is simulation.

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FAST ha multi -body simulation capability, contains the high-fidelity parachute model that was developed in the Lockheed Martin 0 iris simul ati on, and is capable of modeling parachutes independentl y.

A. Inflation Parameter Histograms As previou Iy stated, indi vidual parachute test data were reconstructed for MMvIO, resulting in significantly

more data than when clu ters were reconstructed as a single compo ite parachute. The reconstructed lest data were plotted a hi tograms and built-in MATLAB functions were used to fit di stribution curve to the data. Plotting tes t data hi stograms is subjecti ve because the quantity of bins in each hi togram could be varied so that all the data appeared to have a unifo rm distribution. For many of the parameters, the MATLAB default of 20 bins was used. Once the test data was pl otted, di stribution curves were fit , introducing more ubj ecti vity.

LTlllform Normal

A Error! Reference source not found. shows, a few different distributi ons could appropriately describe the test data. However, the unifo rm distribution does not accurately match the potential tail of thi s data, and the normal has a tail that includes negati ve va lues which is not phys icall y poss ible fo r thi s parameter, CDS. That leaves the Generali zed Extreme Value (GEV) and Logarithmic Normal (logn) di stributions as potential choices. Random numbers were

igure 6: Subjectivity of a distribution fit.

generated based on both curves, which showed that the GEV di tribution had a longer right hand tail causing unreali stic parachute parameters. Th is method was employed for each of the parameters of each parachute and stage, re ulting in 38 different di stributions.

B. Re-parameterization of Fill Constant During assessment of the distributi ons curve, theoretical drag area growth curve were generated providing a

rapid eva luation of effects of potential distributi ons on characteri stics such a fill time and peak drag areas. The e curves showed that a few ca es lagged ignificantl y beh ind the majority as shown in Figure 7. Upon further examinati on, the va lue of the fi ll constant, n, was fo und to be the cause. For infinite mass infl ation (e.g., Main

r __ ~ __ =R=n~ll=d=( =n=li~z~=d==n~e ____ ~ __

400

Randomized 11

N-

~ !::.

S ti '" X

{/)o W

v 11)0

U

1 0.2 0.4 0.6 0.8 1 TIme (s - RC) Time (s -RC)

igure 7: Effect of n re-parameterization on CDS.

Ameri can Institute of Aeronautics and Astronautic

parachutes), the peak drag area is based on a combinati on of parameters, ome of which are coupled.

Di per ing the e parameters independentl y can cause the timing of the peak load to be unrea li stic. This was overcome by re-parameteri zing6 n to a new peak fill con tant (np) during reconstruction, and then converting np back to an n ba ed on the other inflati on parameters. Note that the converted n is not the same as an n determi ned through a reconstructi on that uses the MM v9 proces . The converted n eliminated many of the unreali tic inflati on cases. For

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a more detailed discu ion refer to Ref. 6.

C. Dispersion Implementation A tated previously, implementing the uni form

distribution in vari ou simulation wa tra ight­forward , but tended to result in lightly di fferent disper ed va lue. To eliminate thi incon istency between simulation , MMv 10 and ub equent memo incl ude a et of pre-disper ed parachute parameter value, one for each parachute in a clu ter.

Dispersion are created through feeding MATLAB-created di tribution rule (mu and igma) in to a Python scrip t. First, MATLAB

output a .csv fi le that includes flag for items uch as number of parachute in the cluster, whether the par achute is skipping a tage or is a " I agger" , and to which tage the di tribution applies (Table 2).

iTable 2: MA TLAB output of distri bution rules

MMv10 Drogues

CLUSTER SKIP STAGE Parameter Dist . Type Nominal Pa ram{ll Para m(2)

0 0 1 CdSR norma l 115.7 115.68 5.2357

0 0 2 CdSR norma l 168.7 168.69 5.2357

0 0 3 CdSR normal 252.1 251.34 10.51

0 1 1 CdSR normal 168.7 168.69 5. 2357

0 1 2 CdSR normal 168. 7 168.69 5. 2357

0 1 3 CdSR normal 252.1 251.34 10.51

0 2 1 CdSR norma l 115.7 115.68 5.2357

Second, the Python cript use a random number generator with a di fferent seed for each parachute to create the disper i.ons. For a nominal c1 u ter, each parachute u es the same di tribution, but ince a different eed is u ed to generate the dispersion , the re ulting value are di fferent. This reflects how parachute perform in fli ght. Since n i no longer directl y reconstructed, Python fir ( di perses np according to it di tribution and then u e algebra to convert each np to an n value that the imulation can u e.

T hi rd , scatter plot and histogram (Figure 8) are used to veri fy that the generated di persion (blue) fa l l within the distri butions (black line) and match te t data (green bar s). Finall y, the crip t saves the di persed value a a text fi le (Figure 9) . The tex t fi le are used to di tribu te the data to interested partie. The fil e include all nece ary parameters for each tage of that parachute.

~------------------------------------------------------~ 16

14

12

1 0

j 08

0.6

0 4

0.2

6

Figure 8: Example histograms and scatter plots of dispersion

File Edit Format View Help

IF Ru n Msln Ms2n Ms3n MSle MS2 e Ms3 e MS1C ds Ms2cds MS3Cds 0 22 . 7449 1 0 . 0894 1 . 7187 1. 01 86 0 . 5864 1. 3123 283 . 6816 1 01 7 . 3887 94 4 5. 9781 1 1 6. 914 3 7 . 9532 2 . 5355 1 . 2713 0 . 5583 0 . 940 5 308 . 63 71 896 .5 890 961 6 . 2464 2 1 7.532 5 1 6.4 847 6 . 0366 1 .1 572 0 . 6628 1. 1339 310 . 881 9 836 . 6854 8827 . 8802 3 26 . 761 7 43 . 51 59 2 . 4287 1. 0792 0 . 6217 0 . 9179 465 . 9707 963 . 1 779 924 5. 8352 4 2 5. 23 54 1 8 . 95091.6703 0 . 6871 1 .0228 1. 005 5 54 8. 21 24 796 . 6340 95 28.3366 5 26 . 45 73 1 9 . 3586 6.0108 0 . 8994 O. 7606 1 . 2630 406 . 9032 719 . 6513 945 7. 2680 6 20 . 245 8 42 . 9822 1 .6816 1. 2392 0.3979 0. 9700 377.9868 1 080.9766 84 25. 8548 7 24 . 7522 8 . 01 06 2.3117 1. 222 5 0 . 7613 0 . 9721 384.1263 1034 . 6479 8564 . 0405

Figure 9: Exa mple text file of disper ed values.

The simulation then read the tex t file in which each row corre pond to a di fferent M onte Carlo Cyc le. Thi method ha worked ucce sfully in everal independent parachute simulation , and makes simulation compari ons eas ier ince a part icular cycle has identical parachute input .

7 American Insti tute of Aeronautic and A tronautic

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The user creating the di per ions ha the abi l ity to generate any number of values though the default is currentl y 3000. There are known requests for future disper ion files containing up to 10,000 va lues.

D. MMvl0 Monte Carlo Assessment MMv 10 CPAS benchmarks were preliminarily assessed. However, input from other users of the dispersions

provided insight into necessary di per ion update before the CPAS benchmarks were completed. Updates included the need to cap the di tribution tail s and update the reefing cutter dispersion. It was decided to update the di spersions and continue running CPAS benchmarks as part ofMM v l L, which would publish the final versions.

IV. Model Memo vll: Incremental Refin ements

A. Capped Distributions During the first iterati on of M onte Carl os

run with the stati ca lly dispersed parachute parameters, MM v I 0 CPAS benchmark te ting, a handful of cyc les resulted in excess ively large loads or long inflati on times. To mitigate this, the distributions were capped, though the amount by which to cap was conte ted. The options were to cap with an EF applied to the minimum and max imum reconstructed test values or via standard deviation (a) level . Note that for Gauss ian distributions, standard deviation (0') are associated with probability di stributi on , and percentages of data contained within standard deviation interva l are defined. For non-Gauss ian distributions, although the standard deviation cannot be a sociated with a probability, determination of the percentage of data outside a number of standard deviations gi ves u eful insight into the distribution.

Figure LOa and b show capping ba ed on an EF and igma levels, respectively. Since CPAS ha historically used an EF of 5% for the drag coefficient and 10% for all other performance parameters, thi s method wa preferred over using a sigma level. Intere tingly, the engineering factor bounds generall y fall between the second and third tandard deviations as seen in Figure lOb

giving credence to the EF implementati on. The MATLAB cript was updated to

include additional ru les for calculation and output of floor and cap limits (al 0 known as lower and upper bounds). Subsequently, the Python script was updated to di perse between the limits. Problem aro e when di persing the values because values that fell outside the limits were ori ginally set to the fl oor or cap value cau ing a large cluster of data at the limits, thereby corrupting the

;.. o c

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4.5

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·1

Bo und s (fonnerly Righ i TCSI Dispc~ions)

Extent o f Fl ight Tes ts (fo rmerly Design Dispersio ns)

TM~( I +E F)

1

TM,'V( h is expected that future tes ts

wi ll encounter parameters o uts idecurremtes t limits

_ Test O.ta --Best Fit of Te st Data

• Me dian : 2.41

3 4 5 6 10

Canopy Fill Co nstant, n

+20

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_ Test Data

- Best Fi t of Test Data • Bounds: 0.90063 6.7474

• Media n: 2.41

Dis tribution bo unds usuall y fall between 2 a nd

3 (equi va lent )sta ndard devia ti o n from mean

/ 10

Canopy Fill Constant , n

igure 10: Bounding based on a) an engineering factor and b) igma percentage levels.

A merican Institute of Aeronautics and A tronautic

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intended di tribution. Logic was added to force a random redraw.

B. Reefing Cutter Data As more drop tests were completed, the

reefing cutter data was pull ed from the video timelines and increased the number of data poi nts from 5] to 90. The same methodology wa used as discussed in Section II. DFir t Stati ti ca l A es ment of Reefing CuttersFirst Stati stica l Asses ment of Reefing Cutter . When plotted as a histogram, the data began to have more of a Gauss ian distribution as seen in Figure I I . Th i wa expected, but a lot hypothes is test was conducted with a pseudo­random number generator to determine the resulting di t:ribution if thousands of data point were used.

The lot hypothes is test began with a Gauss ian distribution created with a sigma of 0.5 second and mean of 8.0 seconds. Other sigma and mean va lues were tested with the

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Lower Bound (-2.728 se es)

Bound (1.331 secs)

__ ....J _ _ _I

I --1

Highest tes t data po int+10%

I --,--f---- I-

I

same resul t. Then two va lues were chosen at random from the ori ginal lot (Figure 12 top). These two value represented the redundant cutters on a single parachute disreef event. Since the disreef occurs when the fir t cutter

tlomlnal l ot Test lOCO .... ,------- ,_ ..... '.'_.-._,,----_ ..

j ~ 1 l

----_., ....... ..... __ ., ... -_ .. , .. _-_ .. , · . . , , · , . . , • • • 1 , · , . . , · . . , , · . . . ,

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• • I • • · . , , . ······T····r····T····r·····j

a !! Observed Cut Tine (s)

Figure 12: Reefing cutter lot hypothesis test.

fi re, the earlier of the two value was kept wh ile the other wa discarded. This was done thousand of times and a econd lot and histogram were created using the earlier cutter data. A Gauss ian distributi on fit thi s new hi togram, though the mean wa hifted to the left (Figure 12 bottom). Therefore, if suff icient tes t data was available, the cutter time di tribution should be Gaussian. Thi provided more confidence in the decision to use a Gau sian distributi on on the 90 CPAS data points.

To be consi tent with the inflation di persions, a cap and floor of ± I 0% above and below the target va lue were applied as seen in Figure 11 . As the a,forementioned fi gure hows, the fl oor and cap cOITespond to times of 2.728 and 1.33 1 second before and after the target, respectively. This means that for any cutter, whether eight or 40 econds, the fl oor i the target minus 2.728 and the cap is the target plu 1.33 1.

[t i known that the mean nominal reefing cutter time can be bi ased by temperature and the age of the pyrotechnics. Future analyses may define cutter dispersions that include the affect of scenario type (e.g. nominal reentry, pad abort) to account for the expected temperature effects.

C. MMvll Monte Carlo Assessment A co mplete assessment of the di persion was

conducted in conjunction with MMv II , simil ar to that done for MMv IO. The only difference was that the reefing cutter time disper ion were included in the deli vered tex t fi les. Each parachute had its own cutter

9 eronauti cs and Astronautics

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time and therefore, u ing the high f idelity parachute model in the FAST simulation with it multi -parachute modeling capabi li ty, lead-lag dynamics could be examined. Re ults of thi study are covered in the following section.

A. Multi-Dimensional Limits Method After asse ing the MMvl1

di per ion through ePAS Benchmark analy i , many cyc le in the two-Main ca e howed exceedances of load requirements during the M ai n fu ll open inflation. Upon further inve tigation, it was found that unphys ica l combinat ion of in fl ation parameter n and expopen drove the loads to artificially high va lue.

To eliminate the unphysical

V. F urther Improvements

ETe& Da~ ~

- Iogn: 0.14547 0.21556 • Bounds: 0.76275 1.8689

• Median : 1.17

- logn : 0.9209 0.44781 E ".~. • Bounds: 0.90063 6.7474

• Me dian : 2.41 --------'

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combination , reconstructed n and expopen values were plotted a the blue dots in Figure 13. A polygon (cyan curve) was drawn around the extreme data point using a co nvex hull algori thm. Then a lightly larger polygon (black curve) wa generated to bound the data based on an EF of ± I 0%. Thi method was ca lled the multi ­dimensional l imits (MOL) method. As di eu ed in the preceding ection, the

02 4 6 8 onl y bounding of the di tributions for EDU Main Stage 3 n

10

the MMv I I relea e wa through an EF igure 13: MUlti-dimensional limits method of bounding dispersions

applied to the largest and malle I Ie t . . f II ta . m mam u open ge. recon tructed va lue (shown a red Ime ). I Appl ication of the MOL method will '--____________ _

force (through re-draw a nece ary) disper ions to fa ll within the black polygon limi t

_ T." a... =J -- logn: 3.0988 0.2673 • Bounds: 12.716 47.433

• Median: 22. l

_ Te"a.,s ~ -- logn: 2.891? 0.47496

• Bounds: 6.8967 43.787

• Median: 16.4

_~ __ ~ ~ ___ J

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Though this method came about due to an i ue of peak load exceedance in the disreef to full open, it can be applied to the other M ain inflation stages as well. Figure 14 how the reconstructed te t data for stages I and 2 with the MDL method implemented.

Thi s methodology i al 0 being examined for u e on the Drogue parachute. Due to the additi onal infl ation parameters, Ck and tk, the number of combinations makes the appli cation more complicated. Preliminary studie show that the Ck and n parameters dri ve the load .

The MCL method has not yet been implemented in the Python cripts that randoml y di perse parameters within the distributi on, cap, and floor rules. The current plan is to incorporate thi s method into MM v 12 as e sment cheduled to be relea ed in April 20 13.

B. Deficiency in Current Dispersion Method A prev iously mentioned, recall that a ingle parameter for a particular parachute type and stage i di persed

using the same distribution rules but a different seed. Therefore, each parachute in a cluster ha a different value for that particular input. Though this allows each parachute to inflate differently, it does not account for interplay between parachute. A seen in fli ght test, there is u uall y a lead and a lag parachute. In the current method of generating the di persions, each parachute in a cluster has infl ation parameter that can cause them to open early , as though they are all leader , with no lagger , or vice ver a. There is no logic preventing this from occurring, but the benchmark have not hown that is has been a problem in peak load or CDS curve.

VI. Conclusion The u e of stati tically derived parachute parameter wi ll allow CPAS to better predict parachute dynamics that

are out ide the realm of te ting. It wi ll also be used in verifying the parachute ystem for human flight. Inflation parameter are reconstructed from te t data to which a distribution curve i fit. Floor, cap, and multi-dimen ional limits prevent the di persion from being more than 100/£ beyond recon tructed te t data point extremes. A Python script generates disper ion u ing the distribution rules and bound , and en ures that each parachute u e unique parameter va lues. Thi s method doe not take into account c luster effect between the parachute , though additional rules may be incorporated a the need ari e . A the te t program continue , the di tributi on , and therefore di persions, wi ll be updated and refined with each release of the model memo.

Acknowledgements The authors wish to acknowledge the contribution of l ame Moore, previou Iy of the ESCG CPAS Analysis

Team, for writing Python script to operate on MATLAB-created di tributions from and au tomating the di persion creation proces . Special thanks also go to James Dearman of Lockheed Martin for a e ing the disper ion with integrated vehicle simulations and for as isting with the implementation of disper ion into FAST.

References

IRay, E. S, " Engineering Development Un it Operating Modeling Parameter Ver ion II ' J C-659 14 Rev F, Houston, Texas, ovember 20 12. 2M orri s, A. L. , and Ol son, L. , "Verificat ion and Validation of Flight Performance Requirement for Human Crewed Spacecraft Parachute Recovery Sy lems," AIAA-20 I 1-2560-193, 2 I t AI AA Aerodynamic Decelerator Sy lem Technology Conference and Seminar, Dublin , Ireland, May 20 II . 3Schulte, P. , M oore, J., and Morri , A. L. , " Verifi cation and Validation of Requ irement on the CEV Parachute A sembl y System U ing Design of Experiment " AIAA-20 11 -255 -415 , 2 1>l AIAA Aerodynamic Decelerator System Technology Conference and Semjnar, Dublin, Ireland, May 20 I!. 4Barlog, S. J., "Practica l Aspect of Reefi ng Cutter De ign ," 6th AIAA Aerodynamic Decelerator and Balloon Technology Conference, Houston, TX, March 1979, AIAA paper 1979-04 18. SRay, E. S. , "CPA Parchute Parameter Model Memo 10 Data Delivery", ESCG-8400- 12-CPAS-EMO-OO96, August 2012, Jacobs Sverdrup Engineering and Science Contract Group (unpublished). 6Ray, E., "Recon truction of Orion EDU Parachute Inflati on Loads," 22nd ALAA Aerodynamic DeceleralOr Sy tern Technology Conference, Daytona Beach, Florida, March 2013 (submitted for publication).

I I American Institute of Aeronautics and Astronautics

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