Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, July 1996A9637234, AIAA Paper 96-3115

Design of experiments approach to a single-stage-to-orbit take-off thrustaugmentation analysis

Terry GalatiUSAF, Phillips Lab., Edwards AFB, CA

Travis ElkinsUSAF, Phillips Lab., Edwards AFB, CA

AIAA, ASME, SAE, and ASEE, Joint Propulsion Conference and Exhibit, 32nd, Lake

Buena Vista, FL, July 1-3, 1996

Thrust augmentation offers the SSTO space launch vehicle improved payload capability while reducing vehicleweight and cost. Optimization of vehicle configuration and flight profile are studied. Using a 1,350,000 lbs grosslift off weight (GLOW) SSTO with three Castor strap-on motors, payloads in excess of 40,000 to LEO areachievable. Emphasis is placed on finding vehicle optimums in the 20,000 lbs payload range to capture over 80percent of commercial payloads. Strap-on boosters allow a small SSTO vehicle to fly with a mass fraction of only0.88 and LOX/H2 engines operating at 445 sec vacuum specific impulse. Payload sensitivity due to variations ofmass fraction, Isp and pitch rate are quantified. (Author)

Page 1

DESIGN OF EXPERIMENTS APPROACH TO A SINGLE-STAGE-TO-ORBFTTAKE-OFF THRUST AUGMENTATION ANALYSIS

T. Galati, T. EllrinsPhillips Laboratory, Propulsion Directorate

Edwards AFB, CA 93524

Thrust augmentation offers the Single Stage to Orbit (SSTO) space launch vehicle improved payloadcapability while reducing vehicle weight and cost Optimization of vehicle configuration and flightprofile are studied. Using a 1,350,000 Ibs Gross Lift Off Weight (GLOW) SSTO with three Castor*strap-on motors, payloads in excess of 40,000 to Low Earth Orbit (LEO) are achievable. Emphasisis placed on finding vehicle optimums in the 20,000 Ibs payload range to capture over 80% ofcommercial payloads. Strap-on boosters allow a small SSTO vehicle to fly with a mass fraction ofonly 0.88 and LOX/Hj engines operating at 445 sec vacuum specific impulse. Payload sensitivity dueto variations of mass fraction, I, and pitch rate are quantified.

IntroductionA fully reusable Single Stage To Orbit (SSTO)vehicle has been a vision for low cost access tospace for decades. The high recurring cost oflaunch has driven the study of options for lowercost for access to space. SSTO vehicles havepotential for very low recurring costs. Recentstudies point to smaller SSTO vehicles loweringdevelopment cost and technical risk. This studyexamines how smaller SSTOs with strap-onboosters for take-off thrust greatly enhanceSSTO payload capability. Figure 1 illustrates anaugmented configuration with three boosters.

Length: 176'Diameter 24'Wingspan: 86'

Payload Bay: 12'x24'Figure 1: Conceptual Thrust Augmented SSTO

Previous SSTO concepts designed for payloadlift were large (>2.0 M GLOW) with high massfractions (0.91 to 0.93). Such high massfractions may not be realistic—an egg has a massfraction of 0,94 and it has no propulsion^Previous SSTO designs targeted a space stationrendezvous mission. This orbit forces largeGLOWs as demonstrated in Figure 2.

2 Si

222

Figure 2: SSTO Configurations and Weights1

Figure 2's baseline is a 25,000 Ibs payload tospace station orbit (220 nmi, 51.6°). Cuttingpayload weight to 2,000 Ibs (92%) reducesSSTO GLOW from 2,910,000 Ibs to 1,600,000Ibs, a 45% reduction.

In addition to payload capacity, SSTO conceptsneed to maintain controlled development costsillustrated by Figure 3.

10.0

Figure 3: Weight Impact on Development Cost

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Figure 3 represents trend lines based onproprietary data Development costs for a 1,000Ibs payload class vehicle are about 1/100 thecost of a 100,000 Ibs payload class vehicle.2 .Thrust augmentation enables SSTO core vehicleweight reduction and increased payload.

Thrust Augmentation

This paper looks at the Castor9 family of SolidRocket Motors (SRMs)f. A typical Castor*SRM is shown in Figure 4.

Figured Castor* 120SRM

Specifically, five Castor* SRMs are evaluated.Properties for each motor are given in Table 1.

Table 1: Castor SRM Properties

Castor*IVA

Caitor*120

Castor*170

Castor*190

Castor*250

WeightObs)

25,800

118,498

171,081

192.065

238,934

MassFraction0.8643

0.9107

0.9289

0.9235

0.9182

HuunOb.)

108,700

349,000

427,800

500.379

756,700

Length/Diameter36.6ft3.30ft29.6ft7.76ft35.8ft7.70ft41.7ft7.76ft50.4ft9.81ft

NOTE: Outer IV A and 120 motors arc in production whilethe 170, 190 and 250 ate concept* in development.

One to three boosters are considered for take-offaugmentation. Eight of these configurations arelisted below.

• !Cutor250• 2Castorl70«

•2Caitorl20i•2Caitotl90f•3 Caitor 120s• 2Canor250s

• 3 Castor 170s• 2 Castor 120s and 1 Castor IVA

Taking the smallest SSTO GLOW from Figure2 of 1.35 M Ibs, mis study targets a 100 nmi,circular orbit from the Eastern Test Range(ETR). Without thrust-augmentation this smallSSTO has zero payload capability to LEO.Different configurations are modeled using DAB

f Castor9 is a registered trademark of ThiokolCorporation.

Ascent, a three degree of freedom trajectorysimulation program. It uses a fourth-orderRunge-Kutta integrator and state matrixoptimizer.3 DAB Ascent compares well withother trajectory analysis packages such asProgram to Optimize Simulated Trajectories(POST). Payload versus GLOW for eachconfiguration is presented in Figure 5.

Payfoad (K lot)to T

PromisingCombinations

-10 •"•

1.60

GLOW(M Iba)

1.35

Figure 5: Augmented SSTO Payload Capability

The goal of this effort is to optimize a singleconfiguration with a target payload of 20,000 Ibsto LEO. These configurations show potential ofreaching 20,000 Ibs through optimization:

• 1 Castor 250 15,500 It*• 2 Castor 120f 14,130 Ib.• 2 Castor 120s ••• 1 Castor IVA 16,200 Ibi

Vehicle take-off thrust-to-GLOW ratio (T/W) isan important launch vehicle optimizationparameter. Figure 6 shows GLOW versus T/Wfor each augmentation configuration.

1-8 T

155

T/W

1.3

105

0.8

1.35 1.80GLOW (Mite)

1.85

Figure 6: Augmented SSTO T/W Range

PreyiouasludksMve shown a T/W of 1.3 to bea reasonable choice for flight loads and futureman-rating. The following configurations showpromise:

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«!Ci«or250 1.32• 2 Outer 120* 1.2612 Caitor 120i + l Castor IVA 1.31

Promising configurations for payload capabilityand T/W suggest the same strap-on motors. .Assuming a SSTO recurring launch cost (RLQof 1.0, Table 3 presents the cost per pound ofpayload to LEO (100 nmi).

Table 3: Recurring Launch Costs for VariousSSTO Augmentation Configurations

ConfigurationCore Vehicle1 Castor 2502 Castor 120t

2 Castor 120i +1 Castor IVA

RLC1.0001.2501.2741.2971

J/lbs Pay load———2.8253,1562£03

This analysis employs design of experiments tooptimize payload capability for the highlightedconfiguration. Sensitivities to several designparameters are also highlighted.

Design of Experiments (DOE1Edisonian or trial and error experimentation isinefficient and costly.4 DOE is an efficientapproach geared for industrial processoptimizations. DOE shows the relativeimportance of inputs, interactions, and effects onsystems. DOE blends several provenmathematical techniques allowing efficientproblem structuring.

In this effort, DOE is applied to SSTO modelingto discover trends and optimums for factorsaffecting SSTO performance. Of manyavailable designs, Taguchi matrices are usedbecause of their ability to simultaneously modelsystem behavior and screen factors for order ofimportance on system response. Taguchimatrices reduce the number of necessary trials todetermine system behavior. For example, in atypical model with four parameters (A3>CJD)studied at three levels (low [-1], medium [0],high [1]), an experimenter has to run 3* or 81test cases using single parameter variation. Thenumber of required test cases is decreased tonine trials using a Taguchi matrix. This matrixis termed a Taguchi "Lg" design indicating thenine required cases as shown in Table 4.

Table 4: TajExperiment

Number123456789

A

low(-0low(-l)low(-l)med(0)med(0)^med(0)high(l)high(l)hieh(l)

juchi Lo Matrix5

B

low(-l)roed(O)highmIow(-l)med(O)highd)low(-l)med(O)hi£h(l)

C

low(-l)medfO)hi«h(l)mcd(0)high(l)Iow(-l)bighd)lowC-1)med(0)

D

low(-l)med(0)high(l)bigh(l)low(-l)med(0)med(0)high(l)low(-l)

First the experimental design is completed, thecases are run, interactions are checked andsignificant factors identified. A predictionequation is formed using multiple regression.This prediction equation is used for modeloptimization and to investigate performancesensitivities to input factors.

SSTO Optimization

This analysis uses a Taguchi "L^" to look at theeffects of seven parameters affecting SSTOperformance. Each factor was analyzed at threelevels. Table 5 lists each factor with settings.

TableS: Taguchi "W Matrix SettingsFactor

A-SSTOIsp(iec)B-SSTOMaif

FractionC-Pitch Rate (*/tec for

15 sec)D-Thro tried Thrvut

ObOE-Drag ProfileF-Throttle Tune (tec)G-Zero Octree Pitch

Time (tec)

Low(-l)4400.87

-2.50

500.000

-5.0%25580

Mod(0)4450.88

-3.25

625,000

0.0%285100

Kgh(l)4500.89

-4.00

750,000

+5.0%315120

This matrix reduced the required trajectorysimulations from 2,187 (37) to 27. FactorsA,B,C were modeled quadratically; FactorsD,E,F,G were also modeled and screened forimportance.

SSTO flight profile was chosen as follows:• 0.0-3.0sec vertical ascent from launch p«d• 3.0-18.0 »ec constant pitch rate (detennincd

by factor C)• 18.0 - xxx fee 0.0* pitch rate (time determined

by factor G)•xxx-EOB optimized pitch rate (uiing

DAB Aicent)

The dragjwofile for a 1.35 M Ibs SSTO scarredfor strap-on boosters was determined using theAerodynamic Preliminary Analysis System(APAS), a code with sub/supersonic modelling

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for multiple non-planar surfaces flying throughstandard atmosphere.6 The code outputs lift anddrag coefficients for all velocities which are fedinto the trajectory simulation.

The flow of the study approach is shown below:

|1. CTM* and Validate Prediction

13.LOHA»imd« Fighl Opdmmlion| \3. MghAtilud*FightOptimnton]

14. aOKIt»P«yk)«dClp<ima»lkin|

Figure 7: Optimization Analysis Flowchart

First the Ln matrix is created and the trajectorysimulations performed. Multiple regression isused to generate the prediction equation forpayload and other responses. The model isvalidated to ensure model accuracy. Based onthese equations, payload is optimized during lowaltitude flight by varying pitch rate and zero-pitch time interval. High altitude optimizationis achieved by varying throttle-down thrust andthrottle-downtime. Finally, the predictionequation will be used to vary SSTO 1̂ and massfraction to find solutions in the 20,000 Ibsrange.

Payload Validation

Pareto diagrams yield the following factorcoefficient dominance for payload capability.

Coefficient (Ibf)

Significant Factors1. Mass Fraction2. Core Vehicle Isp3. Second Order Pitch Rate4. Second Order Throttle

Time5. Second Order Drag

14.000

12,000

10.000

8,000

6.000

4,000

2,000

B A C2 F2 E2Figure 8: Payload Capability Factor Dominance

The normalized predictor equation using codedvalues (-1 through +1) becomes:

y = 22.401.6+14.729.7B+4347.7A-2205.3C2-2071.0fa-2011.7E2

Maximizing this equation, yields a payloadcapacity of 40,360 Ibs with factor settings:

Table?: Payload Optimization Parameters

ABCDEFG

ParameterSSTO In)Mail FractionPitch RateThrottle ThiustDrag ProfileThrottle Tune0? Pitch Tune

Coded Selling1.00001.00000.0612-0.7288-0.07540.1835-1.0000

Actual Value450 sec0.89

-3.30 '/tec533,900 Ibi-0.075%290.5 sec80.0 «ec

Payload sensitivities to MF and core vehicle l^are also provided through DOE. Leaving allfactors at medium (0) settings and changing MFand I* from low (-1) to high (1), vehiclesensitivities are presented in Figure 9.

40000

Figure 9: Payload Sensitivity to MF an

The ability to raise mass fraction from 0.87 to0.89 (2%) increases payload capability 3%%(7,435 to 36,894 Ibs). Increasing SSTO mainengine l^ by 10 seconds increases payloadcapability 49% (17,854 to 26,549 Ibs).

The prediction equation was validated bycomparing it to trajectory analyses of similarcases as shown in Table 8.

Table 8: Prediction Equation ValidationFactor

Setting!All Low (-1)AUMed(0)AU Hith (1)A3.CJ)(-1)RF.G (0)A.B,C.D<P)BJ.G (1)

PmdictioaEquation

-3003.4 tot21.401.6 Ibs33,988.3 It*4,878.8 It*

18^26.7 Ibf

DAB AccentAnalyni

-3575.0 Ibf20,708.8 Ibf34,245.6 Ibt4,975.1 tot

18,473.9 Ibf

PeiccutDifference10.40%3.24%0.75%1.94%

1.34%

Additionally, errors for the 27 experiments fromthe Taguchi matrix reveal reasonable marginsand error distributions as shown in Figure 10.

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32SOO

-3800 -2900 -1SDO -500 900R%tariOferera»(bB)

1900

Figure 10: Predictor Error Histogram

To further validate this model, consider thevelocity change capability response.

Velocit Chane Caabilit

Velocity change capability is the absoluteperformance capacity of a vehicle. Paretodiagrams show the following factor dominancefor SSTO velocity change capability.

120°i Co«flVa«Bt(l»)

1000

800

600

400

Significant Factors1. Mass Fraction2. Core Vehicle Isp3. Second Order MF4. Second Order Isp

Figure 11: AV Capability Factor Dominance

The simplified AV prediction equation becomes:y = 31,518.3+l,073.0B+546.8A

+206.0 -̂202.̂SSTO AV capability maximum is 33430 ft/swith factor settings of:

Table 9: AV Capability Maximum Parameters

ABCDB

~F'G

ParameterSSTO I vMill FractionPitch Rate•nuottleThruitDrag ProfileThroaieTime0" Pitch Time

Coded Stomc1.00001.0000-1.0000-1.00000.1551Ov4T7i0.1964

Actual Value4SOtec

0.89-Z50*/iec500,000 Ibi

0.78%^99.3 »ec103.93 KC

Looking at AV capability, Figure 12 relatessensitivities to Lp and MF while keeping allother factors at a medium setting.

Figure 12: AV Sensitivity to MF and I,

Changing MF by 2.0%, SSTO AV capabilitychanges by 7.18 % and a ten second variation inLp causes a 3.55 % change.

Validating the model, Table 10 contains thecomparison runs for AV capability. Theseresults show that how the vehicle is flown has alarge effect on payload since AV doesn't changeappreciably with MF and Lp changes.

Table 10: Prediction Equation ValidationFactor

Sating*AJlLowC-lJ_AllMedCO)AJIHigh(l)AJ.CXK-I)E,F,G (0)A.B.C.D (0)E^,G (1)

PredictionEquation

30.040.3 ft/I31.518.3 ft/i33.011.3 ft/i30,280.0 ftA

31,421.7 ft/i

DABAicentAnalvai

30,lS3.4ft/i31.656.3 ft/i33357.1 ft/*30̂ 55.1 ftA

31,656.1 ft/i

PuLeulDifference

0.47%0.44%0.74%0.87%

0.74%

Several additional responses were analyzed, andprediction equations for these factors are:

• Maximum Gravity Force (g's)y = 3.6+0.4D+0.3F+0.2F2-0.2EJ-0.12A

• Maximum Dynamic Pressure (Ibs/ft2)y = 1,132.96+339.7C+49.1£2

• Velocity Losses (ft/s)y = 5829-304.1^2+241.1B2+226.7A2

-213.8F+210.4C2

Sources of error arise from the fact that an LnTaguchi matrix models three Factors (A3.Qquadratically while screening the remainingfactors (DJE^F.G) with some aliasing of thesefactors with main effect interactions. The strongquadratic effects of Factor E and F can multiplylive model error.

The Taguchi matrix allows factor interactionstudies and for this study the interactions wereminimal on the responses studied. Each factor's

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effect on vehicle performance could be treatedindependently of all other factors. In practicethere may be engineering trades between 1̂ andmass fraction.

Another advantage of the Taguchi predictionequation is its ability to be coupled with MonteCarlo simulation. Figure 13 shows a MonteCarlo simulation of pay load using uniformdistribution of all factors to give an idea ofpayload distribution for a thrust-augmentedSSTO.

40

30

20

10

-1200 8250 17,710 27,164 36,620

Figure 13: Payload Capability Range Histogram

Figure 14 shows payload distribution usingnormal distributions for each factor centeredaround a 20,000 Ibs payload. This distributioncan be used to determine the probability ofachieving a given payload and assessingtechnical risk. For instance, to achieve apayload of 20,000 Ibs ± 10%, this distributionshows a probability of 28% with 95%confidence-assuming high confidence of theinput distribution.

i ! I I I 1liliL

S IFigure 14: 20,000 Ibs Payload Capability

Histogram

Targeted Pavload Optimization

This study targeted a 20,000 Ibs payload with atake-off T/W of 1.30. Table 11 lists a few20,000 Ibs payload settings.

Table 11: 20.000 Ibs Payload Solutions

ABCDBFG

Pouibility 1444.78 KC

.8785-3.248 "/we625,700 Ib.

1.55%284.77 KC100.15 KC

Pouibility 2450.0 we

.880-3.25 V»c

734 ,338 ft»3.17%

255.0 sec100.0 KC

Potability 3445.0 «ec

.880-3.25 '/»c651,875 lb§

0.00%260.89 KC100.00 sec

The seven factors selected model both vehicleperformance and flight profile. To optimize at20,000 Ibs payload, consider the followingbreakdown of the problem. Pitch rate and zerodegree pitch time are the dominant factorsduring low altitude flight During this phase(first ISO seconds) aerodynamic forces are theprimary consideration. Dynamic pressure andbending moments limit vehicle acceleration andangle-of-attack during mis portion of flight.Figure 14 shows the relationship of these factorsto achieve maximum payload.

0.8 1.2

Figure 14: Low Altitude Flight Optimization

Previous SSTO studies show designs with 700Ibs/ft2 for maximum dynamic pressure. Thisthrust-augmented SSTO was allowed 1,000 -IJZOOlbs/ft2 to achieve greater pay load. Thisassumption is reasonable because of the lowerMF (.88) and current expendable vehicle flightmaximums. From Figure 14, optimnnr settingsof -3.475°/sec (0.3 coded) pitch rate and 80 sec(-1.0 coded) zero degree pitch time are chosen.

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After approximately 150 sec, the SSTO entershigh altitude flight regime where the trajectorysimulator optimizes pitch rate. The SSTOthrottles back between 250 and 300 sec to reducemaximum g loads (kept between 3.0 and 3.5) onthe vehicle. Throttle down thrust and throttledown time affect high altitude flight Figure 15gives a contour plot of these two factors.

-1.2-1.2 -O.B -0.4 0 0.4

FACTOR D

Figure 15: High Altitude Flight Optimization

Optimum setting of 512,000 IDS throttle backamount and 306 sec throttle back time arechosen to achieve 20,000 Ibs to LEO.

Combining the low and high altitude flightsettings, MF is computed to achieve 20,000 Ibsto LEO with a nominal lv of 445 sec. Dragremains at a medium setting representing ascarred SSTO. These results are contained inTable 12.

Table 12: 20,000 Ibs Payload OptimizationParameters

ABCDEFG

ParameterSSTOI«pMats FractionPitch RateThrottle Thro«Drag ProfileThrottle Timo0" Pitch Time

Coded Settioc0.0000-0.20000.3000-0.90000.00000.7000-1.0000

Actual Value445 KSC0.878

-3.475 'Jtoc512.500 Ibi

0.00*306.0 MC80.00 «ec

A DAB Ascent trajectory was run forconfirmation resulting in 19,227.6 Ibs payload.This represents a difference of 3.86%, withinthe model's estimation accuracy.

Conclusions

Thrust augmentation enables smaller reusablevehicles to capture'over 80% of commercialpayloads. Using 2 Castor* 120s and 1 Castor*IVA, a 1.35 M Ibs SSTO can place up to 40,360Ibs of payload in LEO with a MF of .89. Thissame vehicle can loft approximately 20,000 Ibswith a MF of .88. These MF estimates are moreachievable than the .91 to .93 quoted by studiesof larger all liquid SSTO designs.

Without surprise, MF appears to be the mostsignificant factor affecting payload. Forinstance, increasing MF from .87 to .89increases payload nearly 400%. Other studieshave confirmed the importance of MF estimateson reusable vehicles.7 One can't underestimatethe importance of this point and its relationshipto development risk. An underestimation ofinert mass or technology substitution caneliminate payload.

In addition to MF, core vehicle 1̂ still remains asignificant driver of design sensitivity. Thenon-linear effect of L, on payload impliesdiminishing returns for greater I,p.Consequently, lower L^ is detrimental to smallSSTO designs requiring either higher massfractions or greater flight loads.

Sensitivity to cost-per-pound to LEO is also ofinterest As core SSTO GLOW increases, thecost effectiveness of larger augmentors grows.Additionally, booster tailoring increases costeffectiveness. This is accomplished by changingsize and/or ballistics for a specific mission.

By using DOE to create an accurate predictionmodel with 27 trials rather than an exhaustive2,187 cases, mis study saved 18 man days.Because DOE is not limited by the number ofinputs or outputs considered, it can be used forseveral types of analysis. Additionally, DOE'sability to show interactions between severalinputs adds insight not gained throughEdisonian analysis.

This effort has also shown that DOE predictionmodels coupled with Monte Carlo techniquescan be used to estimate the technical risk ofaehievingxlesigaobgeetiveSf Take-off thrustaugmentation is a serious option to reducereusable vehicle development cost, technical riskand improve payload capability.

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Any launch vehicle requires large thrust at take-off and high efficiency to reach orbit with ameaningful payload. With current propulsiontechnology, high thrust and high L^ areincompatible. For this reason, all currentlaunch vehicles are staged. Smaller SSTOs withstrap-on boosters increase the chances ofdevelopment of a vehicle capable of beingproduced with current aerospace technology.

Acknowledgements

The authors would like to thank Pamela Tanckof the Propulsion Studies Branch, PhillipsLaboratory, Edwards AFB, Ca, for her efforts inproviding baseline SSTO data. Special thanksgoes to Dave Perkins, also in the PropulsionStudies Branch and Capt Gary Flinchbaugh, ofthe Propulsion Resources Business Division,Phillips Laboratory, for their comments andexpertise.

Bibliography1. Hirioki Shirasu, et al., Analysis of Conceptsfor SSTO, AIAA Paper 95-2953, July 10-121995.

2. James H. Sloan, A Two Launch VehicleArchitecture to Reduce Space TransportationCosts, AIAA Paper 95-3089, July 10-12 1995.

3. David A. Baker, DAB Ascent User's GuideVersion 1.04, DAB Engineering Inc. 1993.

4. Robert G. Launsby, Stephen R. Schmidt,Understanding Industrial DesignedExperiments, Air Academy Press, ColoradoSprings, 1988.

5. Douglas O. Stanley, et al., Application ofTaguchi Methods to Dual Mixture RatioPropulsion System Optimization for SSTOVehicles, AIAA Paper 92-0213, Jan 6-9 1992.

6. E. Bonner, et al., APASII Theory Manual,Rockwell International, 1992.

7. J.M. Sponable, Assessing Single Stage ToOrbit Feasibility, AIAA Paper 95-3004, Jul 10-12.1995,

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