NASA Technical Paper 3522

NASA-TP-3522 19960002985

A Longitudinal Aerodynamic DataRepeatability Study for a CommercialTransport Model Test in the NationalTransonic FacilityR. A. Wahls, J. B. Adcock, D. P. Witkowski, and F.L. Wright

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August 1995

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NASA Technical Ubrary

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NASA Technical Paper 3522

A Longitudinal Aerodynamic DataRepeatability Study for a CommercialTransport Model Test in the NationalTransonic FacilityR. A. Wahls and J. B. AdcockLangley ResearchCenter • Hampton, Virginia

D. P. Witkowski and F. L. WrightBoeing Commercial Airplane Company • Seattle, Washington

August 1995

The use of trademarks or names of manufacturers in this report is foraccurate reporting and does not constitute an official endorsement,either expressed or implied, of such products or manufacturers by theNational Aeronautics and Space Administration.

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Abstract

A high Reynolds number investigation of a commercial transport model was con-ducted in the National Transonic Facility (NTF) at Langley Research Center. Thisinvestigation was part of a cooperative effort to test a O.03-scale model of a Boeing767 airplane in the NTF over a Mach number range of O.70 to 0.86 and a Reynoldsnumber range of 2.38 to 40.0 × 106 based on the mean aerodynamic chord. One ofseveral specific objectives of the current investigation was to evaluate the level ofdata repeatability attainable in the NTF. Data repeatability studies were performed ata Mach number of O.80 with Reynolds numbers of 2.38, 4.45, and 40.0 x 106 and alsoat a Mach number of O.70 with a Reynolds number of 40.O x 106. Many test proce-dures and data corrections are addressed in this report, but the data presented do notinclude corrections for wall interference, model support interference, or modelaeroelastic effects. Application of corrections for these three effects would not affectthe results of this study because the corrections are systematic in nature and are moreappropriately classified as sources of bias error. The repeatability of the longitudinalstability-axis force and moment data has been assessed. Coeffic&nts of lifi, drag, andpitching moment are shown to repeat well within the pretest goals of+_0.005,+_0.0001,and +0.001, respectively, at a 95-percent confidence level over both short- and near-term periods.

Introduction Reynolds numbereffects and scaling, and the compari-son of windtunnel data with available flight data.

Every field of studymust contendwith the issue oferror or uncertainty analysis to some degree. Accord- Datarepeatabilityduringprior tests of this and otheringly, the data obtainedand usedin a given analysismust models in the NTF has typically been describedin somebe evaluated and the quality documented. Data evalua- form relative to the observed data scatter, but thosetion includes the broad categoryof uncertainty analysis descriptionshave not includeda consistentmathematicaland can extend from simple observations to complex measureof the scatteror an indicationof how much con-theoretical analysis of errors and comparisons with fun- fidencemay be placed in the data based on the observeddamental principles. Documentationof the evaluation, scatter. Statistical analysis provides an approach towhether simple or complex, is no less important than the addressthese issues.Statisticallymeaningfuldata sampleevaluationitselfbecausepotentialusers of the results of a sizes have been lacking during past tests in the NTFparticularanalysismust havea basis with whichto judge becauseeach cryogenictest condition requires the useofusefulness to their situations.The need for such analysis gaseous nitrogen as the test medium and subsequentand documentation practices in aerodynamic research repeat tests of that condition are considerably moreand development, whether experimental or computa- expensive than typical conditions in other facilities. Intional, is well documented. (Seerefs. 1-6 for examples.) addition, the number of polars per test at the NTF is lessThis report is presented in the spirit of that general thantypicalcomparedwith other facilitiesbecauseof liq-philosophy, uid nitrogenproductionand storage limitations.As such,

each repeat test conditionat the NTF represents a largerThis report documentsa study of data repeatability percentage of an overall test plan. Researchers must

in the National Transonic Facility (NTF) at Langley choose whetherto investigatea wider range of test condi-Research Center performed during a recent high tions and configurations or to investigate repeatabilityReynolds number test of a commercial transport model, more fully. The usualchoice is the former.The test of theThe investigationis part of a cooperative effort between 767 airplane model on which this report is basedplacedLangley, Ames Research Center, and the Boeing more than the usual emphasis on the investigation ofCommercial Airplane Company. The program involves repeatability. The priority to assess data repeatabilitytests on a 0.03-scalemodel of a Boeing 767 airplane at during this investigationwas due to mixed results fromthree facilities: the NTF, the 11-by 11-foottransonicleg previoustests of thismodel in the NTF. (See ref. 7.) Par-of the AmesUnitary Plan Wind Tunnel, and the Boeing ticularattention wasdirected toward drag repeatability.Transonic Wind Tunnel. The primary purposes of theoverall program are the comparison of data and data In addition to better establishment of the repeat-reduction processesfrom each facility, the acquisitionof abilitylevel, the other primaryobjectives of this investi-full-scale Reynolds number data in the NTF to study gation were to obtain data for tunnel-to-tunnel

Normal forcecorrelation at low Reynolds numbers; to decouple CN normal-forcecoefficient,Reynolds number and static aeroelastic effects; and to qSwing meanaerodynamicchord, in.obtain refined, high Reynolds number drag measure-ments for eventualcomparisonwith flight data. Onlythe K order of least squarespolynomialregressionanalysis pertaining to the repeatability assessment is equationpresented in this report. Repeat test conditions were M free-streamMath numberchosen such that the remainder of the test objectiveswould be met. The focus of the investigationwas on the Mref referenceMachnumber basedon staticpres-longitudinal aerodynamic characteristics of the model, suremeasuredin plenumThe repeatability analysis herein emphasizes stability- N number of data points in sampleaxis longitudinalforce andmoment characteristics,but italso addresses body-axislongitudinalforce and moment Px precisionestimate for parameterXcharacteristics, the angle of attack, and the flow condi- PI predictionintervaltions. The repeat conditions were at the cruise Mathnumber of 0.80 with Reynolds numbers of 2.38, 4.45, Pt total pressure, psiaand 40.0 x 106 based on the mean aerodynamicchord Ps staticpressure,psiaand also at a Math numberof 0.70 with a Reynoldsnum- Q data density termber of 40.0 x 106. The Reynolds number range includesthose obtained in the atmospheric conditions of the q free-streamdynamicpressure,psfBoeingfacility (2.38 x 106),in the Ames facilitypressur- Re Reynoldsnumber based onized to 2 atm in air (4.45 x 106),and at the cruise flight S wing referencearea,ft2condition (40.0 x 106). The maximum angle of attackwas limited to 3.5° for high Reynolds number conditions SE standarderrorthat can only be obtainedin the cryogenicmode of oper- s samplestandarddeviationation. This limitation was imposed because of adversemodel and support system dynamics encounteredduring Tbal balance temperature,°Fprevious investigations (refs. 7 and 8) near initial buffet Tgrad temperaturegradientacross balance fromat the full-scale Reynoldsnumber in the Math number frontto rear, °Frange of interest herein.Full-scale cruiseconditionswere Tt total temperature,°Fobtained with tunnel conditions of 63.1 psia total pres-sure and-250°F total temperature, t valueof t distributiondependentupon &andv

Symbols UX uncertaintyestimate for parameterXX genericparameterAll dimensionalvalues are givenin U.S. Customary

Units. Xbest bestestimate for parameterX

AR aspect ratio Xi valueof parameterX for ith data point

BX bias estimate forparameterX Xtrue true valuefor parameterX

b wing span, in. Y genericparameter(71 confidenceinterval Yi valueof parameter Y for ith data point

Axial force Y arithmeticmeanfor N valuesof parameter YCA axial-forcecoefficient,

Co drag coefficient,Drag qS _z curve-fit-basedbestestimateof parameter YqS _ onboardbodyangle of attack,deg

CD,sf drag coefficientdue to skin friction plus & termrepresentativeof confidencelevel, usedoverspeed to determinet value

Ci least squarescoefficients,i = 0, 1,2.....KLift 13 true biaserror

Ct. lift coefficient, --qS _i true precisionerror for ith datapointCm pitching-momentcoefficient, referenced v degreesof freedom

to 0.25_, PitchingmomentqS_ 8i true error for ith data point

2

aT horizontal-tail angle, positive trailing edge without a known true value with which to compare. If thedown, deg true value were known, the true bias error would be

Abbreviations: determined as the difference between the mean of thepopulation of measured values and the true value.

NTF National Transonic Facility Because the population is typically infinite in size, real-rpm revolutions per minute ity dictates that experimenters work with a finite sample

of the population.RSA regression statistical analysis

Unlike the true bias error, the true precision errorSVSA single-variable statistical analysis does not rely on a knowledge of the true value; it does,Model configuration notation: however, depend on the true mean value of the popula-

tion. The true precision error is the random component ofW wing, one piece the true error and is often referred to as the repeatabilityB body (fuselage) error (as is the case throughout this report). The true pre-

M nacelle struts, one per side cision error represents the difference between a measuredvalue and the mean of the population of measured values.

N nacelles, one per side The random nature of the precision error lends itself toT wing flap track falrings, three per side estimation by statistical analysis and is easier to quantify

H = _r horizontal tail at angle ST (positive trailing mathematically than the bias error. Such quantificationof a precision error estimate is discussed in the section,

edge down), deg "Method of Repeatability Analysis."

Background Statistical InformationUncertainty Analysis

Because measurements of any property contain somedegree of uncertainty, any parameter derived from a The result of the uncertainty analysis is the determi-

nation of an interval within which the experimenter canmeasurement also must contain some degree of uncer-tainty. Therefore, the question is how closely does the state with a specified level of confidence that the truemeasured or subsequently derived parameter agree with value lies. That is,

its true value? The difference is the true error Xbest-- UX (3)

Xtrue = Xi 4" _i (1) where Xbestis usually the mean value of the sample mea-surements and UX is the uncertainty in the measurements

where Xi is the measured value, _i is the true error for of parameter X stated with a specified level of confi-measurement i, and Xtrue is the true value for the parame- dence. The uncertainty UX is a combination of both biaster of interest. The true values Xtrue and I$i are never and precision error estimates (Bx and Px, respectively)asknown; the task of an uncertainty analysis is to quantify shown below in its sum-of-squares form:these values by estimation.

The true error of a measurement has two components _x2 2

= +Px (4)as follows:

As described above, estimation of the absolute uncer-_i = [_+ Ei (2) tainty including biases is difficult and is outside the

where the true error _i for measurement i comprises the scope of this report. As such, in the remainder of thisreport the authors concentrate on the estimation of the

true bias error 13and a true precision error ei for measure- precision (repeatability) error only.ment i. The true bias error is considered systematic or

fixed. The determination of the true bias error can be Method of Repeatability Analysismade only if the true value of the measured property isknown. Reference 5 provides a good discussion of the This section describes the approach taken to quantifyclassification of various types of bias errors. Briefly, data repeatability in this investigation. The quantificationbiases can be large or small, each with some combination takes the form of an estimate of the precision error and isof known and unknown sign and magnitude. In general, stated with a specified level of confidence. The approachlarge biases are assumed to be eliminated in a well- builds on the use of simple statistics as used for analysiscontrolled experiment by some means, such as by the of a single variable and extends such statistical conceptscalibration of an instrument. Small biases, however, typi- to the multiple linear regression problem. As describedtally remain and form the bias error. The primary diffi- next, the approach is based on estimating the data meanculty in determining the bias error arises from the fact and representing the data scatter about the estimatedthat both the sign and magnitude are difficult to define mean. The combination of probability and statistical

3

concepts provides an approach to establish a level of tain interval about the estimated mean. The confidence-confidence. The primary underlying assumptions for all interval is defined asstatistical analyses to follow are that the data scatter is

random and that the random scatter can be represented by CI = +_t&/2,v × s × 1 (7)a normal (Gaussian) distribution. Background and fur- 4iNther details on much of the following discussion can be

where t- .. is the value of the t distribution for a spec-found in many statistics textbooks. Several such texts are s/z, vreferences 9-11. ified levelof confidence and number of degrees of free-

dom and N is the data sample size. The t distribution is a

Single-Variable Statistical Analysis modified normal distribution in which the size of the datasample, represented by v = N- 1 degrees of freedom,

The most common situation applicable for statistical is taken into account. The t value is also related to the

analysis involves the quantification of the random scatter specified level of confidence as defined through & byof a single parameter. The method used to analyze such a the relationshipproblem is referred to herein as single-variable statistical

analysis (SVSA). This method uses well-defined, rela- Percent confidence = (1- &) x 100 (8)tively simple statistical parameters to quantify randomscatter. The quantification of total pressure repeatability The t value is tabulated (ref. 9) as a function of & and v.during a test run is an example of a problem appropriate In a similar manner, the prediction interval is defined as

for the use of the SVSA approach. PI = +t_/2, v × s (9)Estimation of the data mean. The most fundamental

statistic for the SVSA approach, or any other statistical The confidence interval, as defined, can be inter-approach for that matter, is a best estimate of the data preted as the bounds about the estimated mean thatmean. This statistic is simply the arithmetic mean encompass the true mean value, with a chance ofdefined in its usual form for a parameter Y as 100 ( 1 - &) percent. The prediction interval, as defined,

can be interpreted as the bounds about the estimatedN mean that will contain any single future observation with

Z Yi a probability of 100 (1 -&) percent. Thus, the predic-tion interval characterizes the data scatter.

_:_ i= I (5)NMultivariable Statistical Analysis

where Yi is the ith data point and N is the data samplesize. Once determined, the data scatter about the best Normal data analysis procedures in which only twoestimate of the data mean can be assessed, variables are involved usually begin with a curve fit to

the data. Curve fitting can be done by eye and provides aMeasures of repeatability. The most fundamental rough idea as to the relationship between the variables.

statistic to describe datascatter is the standard deviation. Unfortunately, because the fit is subjective, the selectedBecause an experimenter typically deals with only a relationship may not be the one chosen by the originalfinite data sample rather than an entire population, the analyst or by some other analyst in the future. In addi-true mean is not known and the true standard deviation tion, some measure is needed of how well the curve rep-can only be estimated. The sample standard deviation s, resents the data. The method of least squares (refs. 9-11)which is used as an estimate of the true standarddevia- provides a consistent method to obtain a. mathematicaltion, is defined as curve fit to a set of data and, in combination with proba-

bility andstatistical concepts, allows researchers to quan-

I N 2.]1/2 tify how well the resulting estimate represents the data

s = Z (Yi- I0 (6) with a specified level of confidence.

i = 1 In terms of wind tunnel data, least squares curves areN- 1 determined by relating two variables obtained during a

test run. If two or more runs are obtained that in theoryThe confidence and prediction intervals, both of are identical (same model configuration and flow

which depend on the sample standard deviation, are two conditions), the repeatability of the dependent variableadditional measures of repeatability. The confidence can be assessed as a function of the independentinterval is related to the location of the true mean, variable. A common approach is to represent each indi-whereas the prediction interval is related to the probabil- vidual run analytically and assess repeatability by inter-it), that a single future observation will fall within a cer- rogating each resulting analytic model at a constant value

of the independent variable and comparing the corre- The parametersXi and Yi are the measured values of thesponding estimates of the dependent variable. This independent and dependent variables, respectively, forapproachis in effect the SVSA methoddescribed earlier the ith data point. Equation (11) is solved for theafter the analytic representations of each run are evalu- K+I constant coefficientsby the methodof least squares;ated at a chosen valueof the independentvariable.In this the result is a mathematical model in the form ofapproach, the repeatabilityassessment is directly related equation (10)that is used as an estimateof the mean.to the set of analytic representationsbut only indirectly

The selectionof the order of the polynomialregres-to the actual data points, sion model K hasa direct effecton the quality of the esti-

An alternate approachis applied here where a single mate of the mean. That selection, however, can bebest estimate curve fit is determined based on all data somewhat subjective. The approach used for the selec-from a set of identical test runs.This approachis referred tion of K in the present investigationwas twofoldas fol-to herein as regressionstatistical analysis (RSA) as it lows. For eachestimateof mean required,severalvaluesrelieson the extensionof simplestatisticsto the multiple of K were evaluatedby inspectionof the data scatterlinear regressionproblem.Repeatabilityis assessed by aboutthe resultingestimate;the standarderror, whichisthe amountof scatteraboutthe singlebest estimateleast definedin equation(14), is the statisticalparameterusedsquarescurve fit (bestestimateof the data samplemean) inthe evaluation.Inaddition,selectionof the orderof theandremains directly relatedto the actualdatapoints.The polynomial regressionmodel is subject to the followingextensions to the statisticalparameters described above guideline"for the SVSA approachare describedbelowfor the RSAapproach.This approachrequires the additionalassump- K < _- 1 (13)tion that random variance of the dependent variable isconstantover the range of the independentvariable. This guideline is described as a useful rule of thumb

(ref. 12) and providesa criterionto limit the maximumEstimation of the data mean. For the RSA ap- orderof the polynomialmodel.

proach, the estimate of the mean is represented by ananalytic equationthat is determinedto be the best model Measures of repeatability.When an estimate of thefor the relationships observed in the data. The true func- data mean _'(X) has been determined, a measureof thetional relationshipmay includedependenceonmore than data scatter about the mean can be applied. The funda-one independentvariableor on powers thereof.The esti- mentalmeasureof the scatterabout an estimatedmean inmated mean is dependent on the functionalrelationship the RSA approach is the standard error SE, which isspecified and is a best estimate for the specified func- definedastional relationship in the context of the method of least

squares.Application of the RSA approachin this report l i_-_!Yt_--]1-N i]i-]1/2

is based on the assumptionthat the functionalrelation-ship between any two variablescan be adequatelyrepre- SE = (14)sented by a polynomial regression equation of order K;the chosen value of K is dependent on the relationshipbetween the variables of interest and its selection isdescribed further herein. The polynomial regression where _'i is the estimatedvalue of Y that correspondstoequationof order K has a generalform as follows: the dependent variableXi of the ith data point. In effect,

the standarderror is an extensionof the sample standarddeviation defined in equation (6) to the multiple linear

_"(X) = CO+ C1X + C2X2 + C3X3 +... + CKXK (10) regressionproblem.

where X is the independentvariable; _"is the resulting The conceptsof the confidence and predictioninter-best estimate of the dependent variable; and the least vals describedin the SVSA approachcan be extendedassquaresconstant coefficientsareC0, C1.....CK.The over- well. In the RSA approach,the confidenceinterval CI isspecified system of N equations can be written in con- definedasdensed matrixnotationas

XN× (K+ I) C(K+ I)xl = YN×I (11) CI(Xo) = + t&/2,v×SE× Q(Xo) (15)

whereeach equationis of the form andthe predictionintervalPI is definedas

Yi = Co+C1Xi+C2X_i +C3X_ +'" +CKX_i (12) PI(Xo) = + t&/2,v ×SE× J1 +Q(X0 )2 (16)

5

As in the SVSA approach, t- .. is the value of the Researchers can define their own hierarchies of confi-_/Z, V

t distribution for a specified level of confidence and dence level descriptors; the one presentedhere is simplythe number of degrees of freedom; the difference in the an example.RSA approachis the definitionof the degrees of freedom(v = N- K- 1) where the order of the polynomial Timescales for Repeatability Analysisregression equation K is taken into account. The term

Three timescalesare defined in this paper to classifyQ (X0) is definedas a given repeatabilitysample--short, near, and long term.

_xT( TX/_Ix 0 The timescales relate to both the period and circum-Q (X0) = X (17) stances in whichdata are collected. A short-termrepeat-ability sample describesdata variabilityover a relatively

where the independentvariable of interest is represented short period with minimal change in circumstance.in vector form as Examples of the short-term time frame with respect to

wind tunnel tests are within a single polar and repeat

[ X_0 Xff01 Mach number polars within a Mach number series. AT (18)

X0 = 1 X0 ... 1x (K+ 1) near-termrepeatability sample describes data variabilitywhen a given configuration is retested during a single

and the matrix X is that used in equation (11). The term tunnel entry and at least one other configurationis testedQ(Xo) is a measure of data density in the neighborhood in between. A long-term repeatability sample describesof the independent variable of interest X0 and accounts the data variabilityfrom entry to entry for a given model.for data densitysuch that highly populatedregions of the Obviously, the potential for the introduction of biases,data sample may have narrower confidence and predie- particularly model-relatedbiases, increases when goingtion intervals than sparselypopulated regions. The effect from short-to long-termcomparisons.Thepresent inves-of this term is observedin the data that follow, tigation includes many examples of short-term repeat-

Interpretationof the confidence and predictioninter- ability and presents a near-term sample. The near-termvals is the same as that describedfor the SVSAapproach, sample was acquired across a significant break in theThe primary difference in application with the RSA cryogenictests and, in some respects,warrantsclassifica-approach is that the intervalsdefine bounds about a least tion of the sampleas long term.squares-basedestimate of the mean, rather than about asimple arithmetic mean. In addition, the defined bounds Experimental Apparatus and Proceduresof the RSA approach are functions of the independentvariable rather than a constant interval that is valid over Facility Description

the range of the independent variable. The NTF (ref. 14) is a unique national facility thatprovidesfull-scale(high)Reynolds number tests of vehi-

Interpretationof ConfidenceLevel cles (suchas commercial transportairplanes)designed toBoth the confidence and prediction intervals are fly in and through the transonic speed regime. The faeil-

associated with a user-specified level of confidence, ity providesa test environment for a scale model that iswhich is stated as a percentage and is based on the similar to that of the full-scaleairplane in flight; that is,numerical probability that an event will occur. In the the Mach and chord Reynolds numbers are identical inpresent context, the events of interest are that the true the tunnel andfull-scale flightenvironments.The NTF ismean value fallswithin the confidenceinterval andthat a a conventionalclosed-circuit fan-drivenwind tunnel thatsinglefuture observationfalls withinthe predictioninter- is capable of operating at elevated l_ressuresand cryo-val. An understanding of what a given confidence level genie temperatures to obtain high Reynolds numbers.implies is useful. One useful tool is the relationship The test section is 8.2 by 8.2 by 25 ft and has a slottedbetween odds and the confidencelevel where, for exam- floor and ceiling.The test-sectionfloor andceilingdiver-ple, 9-to-1 odds are equivalent to a 90-percent confi- gence angles, the reentry flap angles, and the stepheightdence level. A subjective relationship between the for slot flowreentry are adjustableby remote control. Inconfidence level and an appropriate adjective that addition, turbulenceis reduced by four damping screensdescribes the probability of an event is given in in the settling chamber and a contraction ratio of 15:1reference 13 as from the settlingchamberto the nozzle throat. Fan-noise

effects are minimized by an acoustic treatment both75% to 90% confidencelevel ...................Fairly probable upstream anddownstreamof the fan.

90% to 95% confidencelevel .................Highly probable The NTFhas an operatingpressure range of approxi-95% to 100%confidencelevel .........Extremelyprobable mately 15 to 125 psia, a temperature range of-320 °

to 150°F, and a Mach number range of 0.2 to 1.2. The angles of-3 °, -1 °, 0°, and 1%Configurations aredefinedmaximum Reynolds number per foot is 146 x 106 at herein with the component notation described in theMaeh 1. The test gas may be either dry air or nitrogen, symbols list. For example, WB indicates a wing-bodyWhen the tunnel is operated cryogenically, heat is configuration.removed by the evaporation of liquid nitrogen, which issprayed into the tunnel circuitupstream of the fan. Dur- Instrumentationing this operational mode, venting is necessary to main-tain a constant total pressure. When air is the test gas, Aerodynamic force and moment datawere obtainedheat is removed from the system by a water-cooled heat with an internal, six-component, strain gauge balance.exchanger at the upstream end of the settling chamber. The quoted accuracy of the balance (stated in terms of(See ref. 15 for further tunnel details.) the worst outlying point during the calibration) is

_+0.5percent of the maximum design loads; design loadsA detailed assessment of the dynamic flow quality in for the balance and the dataacquisition system resolution

the NTF is reported in reference 16. Fluctuating smile of the channels used to read the balance output are givenpressures were measured on the test-section sidewall in table 1. An internal, heated aecelerometer package wasopposite a 10° cone fairing over the end of a standard used to measure the onboard angle of attack; quotedmodel support system. The root mean square of the flue- accuracy of the package under smooth wind tunnel oper-tuating component of smile pressure nondimensionalized ating conditions is _+0.01° (ref. 17), and the data acquisi-by the free-stream dynamic pressure is approximately tion system resolution of the package output is 0.0021 °.0.0084 at low Reynolds numbers in the ambient airenvi- Model pressure measurements were obtained usingronment and approximately 0.0095 at high Reynolds 5-psid barocells, each with a quoted accuracy ofnumbers in the cryogenic nitrogen environment; each of _+0.01psi (worst case). Model pressure measurementsthese results is for a Mach number of approximately were limited to three internal body locations chosen to0.80. assess flow into and out of the aft-body cavity. The three

pressure measurements near the upper swept strut sealModel Description were made without tubes bridging the balance.

The model is a 0.03-scale representation of the The primary measured flow variables of interestBoeing 767 production airplane. The model is shown in include both the total and static pressures and the totalfigure 1 mounted in the NTF test section; the pertinent temperature. Mach number, Reynolds number, andmodel geometry is given in figure 2. The model was dynamic pressure are calculated from these measureddesigned and constructed specifically for tests in the quantities. Briefly, static pressure is measured by a set ofcryogenic, pressurized conditions of the NTF, where gauges with full-scale ranges of 150, 100, 50, 30, anddynamic pressures reached approximately 2700 psf dur- 15 psia. Each gauge has a quoted accuracy of _+0.01per-ing this investigation. The model was built of maraging cent of full scale (worst case). An autorange systemsteel with a surface finish of 10 Ixin. (root mean square), allows the most sensitive gauge to be used. An identicalThe general wing contour tolerance was _+0.003in.; the system is used to measure the total pressure, except that awing leading-edge tolerance was _+0.0015in. 15-psia gauge is omitted. Total temperature is measured

The model, which contains separable components, by a platinum-resistance temperature probe mounted inallows tests of multiple configurations. The wing compo- the reservoir section of the tunnel near the screens.nent, which includes the wing-body fairing, does not This measurement has an accuracy of approximatelyinclude the wing vortex generatorsthat are found on full- +0.1°F (worst case). A complete description of thesescale production airplanes. (See ref. 7.) The body (fuse- measurements and subsequent calculations is given inlage) design incorporated a nonmetrie upper swept strut reference 18.support system. (See fig. 1.) The upper swept strut sup-port is intended to minimize support interference in the Data Correctionshorizontal-tail region and is integratedinto the body with

Information on the various instrumentation devices,a shape that approximates the airplane vertical tail. How-

the data acquisition and control computers, and the dataever, because greaterstructuralstrength was required, thereduction algorithms for the different measurement sys-strut integration was thicker than the true vertical tail

loft. terns is provided in reference 18. Standard balance,angle-of-attack, and tunnel parameter corrections have

Other model components include flow-through been applied. An additional part of data reduction at thenacelles, which simulate a JT9D-7R4 engine installation, NTF is balance temperature compensation. The tempera-nacelle struts, wing flap track fairings, and a horizontal ture compensation methods are designed to correct hal-tail. The horizontal-tail incidence can be set at nominal ance output due to thermal loads and are discussed in

7

references 18 and 19. A model-specific correction has body cavity, was designed specifically for use in the NTFbeen applied to the drag data to account for the internal environment. This seal is made of polyester fiber fillerdrag of the flow-through nacelles and is based on material in an elastic nylon wrap that was stiffened withunpublished nacelle calibration data obtained by Boeing. thin pieces of DuPont Mylar 1. Tests without the sealThe data herein have not been corrected for model have shown drag and pitching-moment shifts relative toaeroelastics, wall interference, or model support interfer- tests with a seal in place.ence. Application of corrections for these three effectswould not affect the results of this study as the correc- Previous experience (ref. 7) indicates that force andtions are systematic in nature and are more appropriately moment data repeatability can be adversely affected byclassified as sources of bias error, deterioration of the upper swept strut seal. Modifications

to the seal during the investigation described inThe free-stream Mach number is corrected based on reference 7 improved data repeatability to an acceptable

clear-tunnel calibrations that correlate tunnel centerline level (ACL= _+0.0015, ACD = _+0.0002, and ACm =static pressure measurements with the reference static +0.001). In reference 7, repeatability was not quantifiedpressures measured in the plenum. Table 2 contains the because a meaningful data sample size was lacking;free-stream Mach number corrections applied for the instead, the repeatability quote is a more subjective rep-repeat conditions studied herein. As indicated in table 2, resentation of the observed range of a given parameter atthe corrections are functions of both Mach and Reynolds constant conditions. Three modified seals were used dur-

numbers, ing the present investigation. The aft-body cavity was

The angle of attack was corrected for flow angularity instrumented with three static pressure orifices that mon-(upflow) by measurement of both upright and inverted itored airflow within the cavity caused by seal leakage.model force data for a given configuration; in particular, In general, no significant leakage was observed withthe CN-CZoffset method was used. The flow angularity any seal configuration; one exception is described hereinwas evaluated at the beginning of each polar series and in which the seal was damaged during a Mach numberwhen the flow-field total temperature was changed. This series. The seal was not used during tests at Re =approach was taken based on the assumption that flow 2.38 x 106 to allow a direct comparison with dataangularity is primarily a function of cold soaking (time) obtained in the Boeing Transonic Wind Tunnel.and total temperature. Flow angularity was assessed20 times during this investigation, all at M = 0.80; the Transitionobserved variation of flow angularity is discussed later.

Boundary-layer transition was fixed by distributingEmpty-tunnel calibrations allow tunnel wall angles epoxy disks (ref. 20) at specified locations on the model

to be set so as to reduce pressure gradients and buoyancy surface. The distributed disk method minimizes varia-

effects in the test section. However, tunnel wall angles tions in the trip distributions and height and allows thewere set at a nominal angle (0°) before the investigation trip to be easily inspected, repaired, or duplicated. How-and remained fixed throughout the test because wall

ever, the initial application of the distributed disks isactuation is currently problematical at cryogenic condi-

more time consuming than a corresponding applicationtions. Buoyancy drag corrections based on the empty- of the more traditional grit trip method. Transition triptunnel calibrations were about 0.0001 (in coefficient disks were applied to the upper and lower surfaces of theform) or less throughout the investigation. The model wing and horizontal tail, the internal and external sur-and the support system introduce pressure gradients and faces of the nacelles, the nacelle struts, and the nose of

buoyancy effects that could not be accounted for during the body for tests at low Reynolds numbers (R e = 2.38the empty-tunnel calibration of the wall angles. Correc- and 4.45 x 106). Table 3 provides the sizes and locationstions to the data for such effects have not as yet been of the transition trip disks for the conditions at Re = 2.38determined. The solid blockage ratio for the WB config- and 4.45 x 106. The two patterns differ only in the diskuration at an angle of attack of 0° is 0.55 percent; this height on the wing surfaces. The transition trip disksvalue is sufficiently low to minimize blockage effects, were removed from the wing, horizontal tail, and exter-based on conventional criteria. Buoyancy corrections, nal nacelle surfaces for the high Reynolds number testbased on the empty-tunnel calibrations, have been conditions (R e > 21.1 x 106). A comparison of trip-onapplied to the data. and trip-off configurations at Re= 21.1 x 106 (tel 7)

indicates that boundary-layer transition did occur at or,Strut Seal near the 10-percent local chord location of the trip.The upper swept strut support requires a seal at the

junction of the strut and the upper aft body of the model. 1Mylar is a registered trademarkorE. I. duPontde Nemours&The seal, which prevents airflow into and out of the aft- Company.

Test Approach desired confidenceinterval. As is shown later, the datascatterwas less than anticipatedand the number of repeat

Repeatability Goals polars per test conditionwas reducedduring the investi-gation. Table 4 summarizes the repeated test conditions,

The primarydata of interest for this investigationare including the number of polars actually performed andthe longitudinal stability-axis coefficients of lift, drag, the samplesize used with the RSA approach;table4 alsoandpitching moment.Goals for the repeatabilityof these assignsa groupnumber to each repeatedtest conditiontocoefficientswere based on the needs of industry and the facilitate the discussionbelow.information contained in reference 2. The repeatabilitygoals for these coefficientsare given as confidenceinter- Results and Discussionvals about an estimated mean (least squares curve-fitrepresentation)as The purpose of this report is to quantify and docu-

ACL..........................._+0.005 ment the data repeatabilityobtainedduringa recent highReynoldsnumberinvestigationof a Boeing767 model in

ACD........................_+0.0001 the NTF. The approachis to quantifyrepeatabilityusing

ACm.........................._+0.001 the RSA statisticalmethod described earlier.The statis-tical analysisof the force and momentcoefficientrepeat-

and are stated at the 95-percent confidence level, which ability is discussed first and is followed by a discussionindicatesa high to extremeprobabilitythat the true mean of several factorsthat may contributeto nonrepeatabilityvaluelies within the prescribedintervalin the absenceof through eitherbias or precision errors.bias.

The maximum angleof attack waslimited to 3.5° forRepeated Test Conditions high Reynolds number test conditionsbecause of previ-

ous encounters with adverse model and support systemEquation (15) showsthree factors that can affectthe dynamicsin the cryogenicmode of operation; the major-

size of the confidenceinterval for a specifiedconfidence ity of the data obtained lies within the range oc= -2 °level--the standard error, the data sample size, and the to 3°. Previousexperience(ref. 7) indicatesthat the flowdata sample distribution.The data sample sizes and data over this range is well behaved,thus reducingthe poten-sampledistributions,unlike the standarderror, are under tial for unsteady, separated flow phenomena that couldthe directcontrolof the investigatorandare chosenbased affect repeatability.Although data were obtained over aon the goals of a given investigation.The data sample larger angle-of-attackrange for low Reynolds numbersdistribution is typically chosen to define the polar shape (air mode of operation),repeatabilitywas examinedoverover a specified range and is often concentrated in a range consistentwith the high Reynolds number data.regions of particularinterest. Thus, the data sample size As such, the analysisbelow is based on data taken in thebecomes the primaryfactor affectingthe size of the con- range _ = -2 ° to 3° for all repeatedtest conditions.fidence interval for a specified level of confidence.Fig-

ure 3 indicates how the data sample size affects the size Force and Moment Repeatabilityof the confidence interval for a specified level of confi-dence, assuming that the standard error remainsconstant The longitudinal stability-axis coefficients of lift,as N varies;figure 3 is based on the SVSA definitionof drag, and pitching momentare of primaryinterest in thisthe confidence interval given in equation (7). One impli- investigation.The drag coefficientis of particularinter-cation of figure 3 is that for constantdata scatter (s, the est in this investigation because a major goal was thesample standard deviation), increasing N decreases the acquisition of refined drag measurementsfor eventualsize of the confidenceinterval for a specifiedconfidence comparisonwith flight data. Specificrepeatabilitygoalslevel. Figure 3 indicates that a confidence interval equal were establishedbefore the experimentas outlined ear-to the sample standard deviation can be attained at a lier. The data are graphically presented as residualplots95-percent confidence level with a sample size of of the force and moment coefficients,where the residualapproximately6. Based on this result, the importanceof of a parameter Y is defined asdrag repeatability, and the expectation that the standarddeviation of the drag-coefficientdata would be approxi- AY = Yi - _" (19)mately _+0.0001(equal to the confidence interval goal),6 polars per repeated test condition wereperformedin an Selection of polynomial regression model order K.attempt to meet the stated confidence interval goal at a _The process used to select an appropriatevalue of K has95-percentconfidencelevel.Note that thisresult depends been outlined.The rule of thumb (eq. (13)) is evaluatedon s such that if s were smaller, N could also decrease based on the data sample sizes provided in table 4; thewhile maintaining a 95-percent confidence level in the guideline indicates that maximum values of K should

9

be in the range of 3 to 5. The final value of K is chosen and prediction intervals computed at the indePendentbased on a survey of the standard error (eq. (14)) that variable for each data point. Clearly, in each case theresults from curve fits over a range of K and on an exam- repeatability goals as specified on the confidence intervalination of residuals. The random data scatter in the resid- for coefficients of lift, drag, and pitching moment wereual plots validates the polynomial regression model satisfied.relative to the assumption of random data scatter. Figures4 and 5 show the results of this process for the longitudi- Groups 1 and 5 were unique in that a single polarnal stability- and body-axis coefficients, respectively, from each group (run 28 in group 1 and run 29 inThe value of K was varied from 0 to 8 in each case; group 5) was obtained two days after the other five inextending the range to 8, which is beyond the recom- that respective group. In addition, the tunnel environmentmended maximum just identified, is simply for demon- was purged of nitrogen and warmed to ambient tempera-stration purposes. The standard errors for low-order fits ture during the off day. The significant time differenceare often very large and are not always shown in figures and tunnel cycling could allow these two groups to be4 and 5. Based on examination of these figures, a single subdivided and classified as near-term fimescale situa-value of K was selected for each functional relationship tions; as such, the potential was greater for less repeat-modeled. The selected values of K are summarized in able data within the two groups. The results indicate that

table 5 and the two exceptions are noted. The results the repeatability within groups 1 and 5 is essentially theshown in figures 4(b) and 5(b) for the pitching-moment same as for the other short-term, cryogenic-mode groups.

data of groups 11 and 12 indicate a significant reduction Figure 7 shows the residuals of the longitudinalin the standard error when K was increased from 3 to 5; body-axis force and moment coefficients for groups 1-7.the increased order also served to make the data scatter of The results are similar to those presented for the longitu-the residuals significantly more random. Although the dinal stability-axis coefficients. Table 7 provides a sum-selection remains somewhat subjective, an interesting mary of these data; note the very small differences in thenote is that the air-mode groups generally benefit from a results given in table 6 for the drag coefficient comparedslightly higher order model than do the cryogenic-mode with the axial-force coefficient results.groups. As a result, the order of the air-mode regression

models typically defined the final choice of K for the Short-terraanalysis---airmode. Groups 8-13 werecryogenic-mode models, obtained in the air mode of operation and each was

formed from three polars. Repeated polars were obtainedShort-term analysis--cryogenic mode. Groups 1-7 during a Mach number series and followed the pattern

were obtained in the cryogenic mode of operation, they M = 0.80, 0.86, 0.84, 0.82, 0.80, 0.78, 0.75, 0.70,varied in size from three to six polars, and they totaled 20 and 0.80. Figure 8 shows the 95-percent confidence andto 40 data points. Repeated polars were generally prediction intervals and the residuals of the lift, drag, andobtained during a Mach number series in which the Mach pitching-moment coefficients for groups 8-13; figure 9number was alternately set at 0.70 and 0.80. Figure 6 presents the longitudinal body-axis coefficients. As withshows the 95-percent confidence and prediction intervals the cryogenic-mode data, the repeatability in the airand the residuals of the lift, drag, and pitching-moment mode is very good and generally within the pretest goals.coefficients as defined in equation (19) for groups 1-7. Tables 6 and 7 contain the summarized results for the

Note that both the confidence and prediction intervals are stability- and body-axis coefficients, respectively.functions of the independent variable. The magnitude ofthe prediction interval is nearly constant except near the The drag-coefficient (and axial-force coefficient)outer bounds of the data range, whereas the confidence confidence and prediction intervals for group 8 are note-interval varies more throughout. The variability observed worthy because they are significantly larger than those offor both confidence and prediction intervals is a result of the other air- and cryogenic-mode groups; figures 8(a)dependence on the data density term Q. (See eq. (17).) In and 9(a) show the drag- and axial-force coefficient data,regions of high data density, the confidence interval respectively, for group 8. The figures reveal that a singlebecomes more narrow; the widening of both prediction run (run 113) has a lower drag level by roughly 2.5and confidence intervals at the outer bounds is directly to 3 drag counts compared with the other two polars inrelated to this effect as well, an effect that reflects the the group. This disparity was probably due to the strutintuitive result that the mean value of the dependent seal partially tearing loose during the Mach numberparameter is known with more confidence where the data series. (Seal damage was discovered when the model wasare concentrated. Table 6 provides a summary of the inspected after the Mach number series.) As a result,95-percent confidence and prediction intervals over the some seal stuffing was lost and part of the seal cover pro-range of data _ = -2 ° to 3°; the generalized data pre- truded into the flow field and shifted the drag to a highersented in table 6 are simply averages of the confidence level. This error is classified as a bias and invalidates the

10

statisticalanalysis becauseit violatesthe assumptionthat Balance accuracy.Accuracy and repeatability rep-all errorsare random.However,the shift is explainableto resent two distinct areas of interest that relate to the qual-an acceptabledegree such that the nonbiasedpolar could ity of any measurement.A given measurement may bebe used with confidence and the biased polars dis- highly accurate, yet other factors within a system may •regarded during the aerodynamic analysis phase of the inhibit repeatability.On the other hand, a series of mea-investigation.The identificationof this biaserror demon- surements of the same parameter may be highly repeat-strates an extra advantageof the residualanalysisbeyond able,but the accuracycompared with the true value mayits use in quantifyingprecision, be poor.A comparisonis useful, however,of the balance

measurementaccuracybands with the stated repeatabil-Near-term analysis. Groups 2 and 3 can be com- ity goals. Figure 12 shows the accuracy bands for the

bined to form a data set that is suitable for near-term normal force,axial force,and pitching momentin coeffi-repeatability analysis. The acquisition of the two data cient form; figure 12includescurves for the quotedaccu-groups was separated by 15days duringwhich the tun- racy (table 1) and two additional,tighter accuracybandsnel was purged, multiple large changes were made in for reference.Figure 12highlightstwo pointsas follows.tunnel temperature and pressure, and multiple model First, the balance used in this investigation and all bal-changes were made during the low Reynolds number, antes designed for use in the NTF yield significantlyair-modeportion of the investigation.The comparisonof more accuratecoefficients at the high dynamicpressuretwo short-termgroups acquiredin such a manner dem- conditions. Second, the repeatability goals set forth andonstrates the near-term repeatability of the force and satisfiedherein are generallywithin the quoted accuracymomentdata across a break in the cryogenictests, bands of the balance measurements.As shownin figure

12, the exceptionoccurs on the normal-forcecoefficientFigures 10 and 11 show the residuals and the atdynamicpressuresabove approximately2368psf; note

95-percentconfidenceand predictionintervalsfor longi- that the resultsgiven in table 7 show confidenceintervalstudinal stability-and body-axisforce andmomentcoeffi- on the normal-forcecoefficient to be approximatelyonecients,respectively;averagevalues for the intervals are orderof magnitudelowerthan the statedgoal. Thus, theincludedin tables 6 and7. As with the short-termresults, confidencein the accuracy of a repeatablemeasurementthe near-term results demonstrate levels of repeatability due to some unknownmeasurementbias maybe more ofwithin the pretest goals of the investigation.In addition, an issue than the repeatabilityof the measurementitself.the residual analysis clearly shows a small shift in thepitching-moment coefficient of approximately 0.002 Note that the form of the balance accuracyquote hasacross the break in the cryogenic tests. This shift is prob- changed since the last calibration of the balance usedably due to the use of two different strut seals; past during this investigation. (See ref. 21.) Previously, theexperience (ref. 7) has shownthe pitching-momentcoef- accuracyquote was stated in terms of the worst outlyingficient to be sensitive to seal quality,particularly for the point during the calibration,as in this report. This formtail-on configurations.As discussed previously,the bias of quotation is generally overly conservative. Balanceerror technicallyinvalidatesthe statisticalanalysis; how- accuracies are currently quoted based on a 95-percentever, the magnitude of the bias is small and explainable confidencelevel and yield a more realistic assessment;and was not particularly significant during the aero- the revised formof the quotation aligns the balance accu-dynamicanalysis phase of the investigation.This case is racy assessmentmore closely with the methodof repeat-another exampleof the utility of residual plots in detect- ability assessment used herein. Reference 21 showsing bias errors, calibration results for other cryogenic balances used in

the NTF that indicate a consistent improvement from

ContributingFactors to Nonrepeatability 0.5 percent of the maximum design loads previouslyquotedto a quote in the range of 0.1 to 0.3 percent.

The data demonstrate excellent force and momentcoefficient repeatability, particularly in relation to the Balance temperaturegradient effect. References 18complexwind tunnel test environmentin general and the and 19 discuss the balance temperature compensationNTF in particular. A seemingly endless list of possible algorithmused in the data reductionprocess at the NTF.sources for bias and precision errors could be generated. In effect, all balance output is corrected to a referenceFor the sake of brevity,only several possiblesources are temperature (295 K) based on pretest temperaturediscussed here. Highlightingseveral potentialsourcesof cycling of the balance. During the pretest temperatureerror demonstratesthe detail requiredto achievethe level cycling as well as during the test in both air and cryo-of repeatabilitydemonstratedin this investigation, genie modes of operation, a temperature gradient will

U

often occur across the balance. Reference 19 presents coefficient relative to the repeatability goals. Figure 14data indicating a direct effect of the temperature gradi- shows the effect of angle-of-attack errors on the dragents on the balance output. The temperature compensa- coefficient for a range of lift coefficients; an error oftion algorithm is not a function of the temperature 0.01 ° in the angle of attack is shown to affect the draggradient, which, in effect, means that the temperature coefficient by approximately 0.8 drag counts at the cruisecompensation algorithm assumes a zero temperature gra- lift coefficient of 0.45.

dient across the balance. As a result, operational practice The determination of the angle of attack can beincludes time to drive the balance toward thermal equi- affected by several factors. The first and foremost factorlibrium, meaning to some temperature near the flow tem-perature with a minimal gradient of 10° to 15°F, before is the measurement itself. The primary measurement isthe test condition is set and the data are collected. This taken from an onboard accelerometer package that, as

operational practice is used if the highest quality force stated previously, has a quoted accuracy of 0.01% Thisdata are required, and experience has shown that the tem- quoted accuracy is based on calibrations performedperature gradient generally moves toward zero as the test under controlled, laboratory conditions at ambientcondition is set and data collection begins, temperature rather than in an actual wind-on test environ-

ment. One potential factor that affects the onboard angle-

Figure 13 shows the variation of the balance temper- of-attack measurement in the wind-on environment is theature and the temperature gradient across the balance for model and support system dynamics; model and supporteach group of repeat data. The balance temperature pre- system dynamics can be sufficiently large, particularly atsented is measured in the middle of the balance and the high load conditions, to introduce significant centrifugal

gradient is defined as the temperature difference from the forces that cause incorrect (biased) angle-of-attackfront to the rear of the balance. The temperature compen- measurements. (See ref. 17.)

sation algorithm accounts for the variations observed in The flow angularity in the test section is anotherthe balance temperature within a given group; the varia-tions in temperature gradient are potential sources for important factor affecting the determination of the angleerror, as a correction for this effect is not applied, of attack. If the flow angularity were known to be con-Because of the time given to condition the balance, how- stant, it could be assessed once and applied to data for allever, the maximum magnitude of the gradient is a rela- configurations and test conditions. In reality, however,tively small 8°F and does not adversely affect the force the flow angularity should not be assumed to be constant.and moment coefficient repeatability. The gradients gen- This fact is especially true when an error of only 0.01 °

can affect the drag data significantly relative to theeraUy move toward zero over time. Also, cold test condi- repeatability goals. Flow angularity was assessed moretions tend toward negative front-to-rear gradients, frequently than normal during this investigation, all at awhereas the warm test conditions have positive gradi- nominal Math number of 0.80. The variation of the flow

ents; this situation is attributed to the fact that the front angularity throughout the investigation is given inportion of the balance adjusts more rapidly to the flow figure 15. The mean upflow was 0.131 ° with a standardcondition than the rear, sting-connected portion of the deviation of 0.011 °. Note the large variation of more thanbalance. 0.05° on a single day of tests that encompassed a wide

range of operating conditions and the shift of 0.015 ° forAngle of attack. The determination of the angle of the repeated flow condition assessment. No definite con-attack has a direct effect on the calculation of the lift and

clusions can be drawn as to the variability of flow angu-drag coefficients: larity from these data.

CD = CN sinct + CA cosct 1 Figure 16presents residual plots and the accompany-(20) ing statistical intervals for the angle of attack; these data

Ct. = CN cosct-C A sinct J were obtained by representing the angle of attack as afunction of the normal-force coefficient with a third-

The direct effect of angle-of-attack errors on the calcula- order polynomial regression model and applying thetion of CL and CD can be estimated as RSA approach. The residual plots demonstrate the char-

ACD = CL Act (rt/180) _ acteristics of random variation, thereby validating the use

ACL -C D Act (rt/180) J (21) of statistics to quantify repeatability. Average values ofthe 95-percent confidence and prediction intervals arepresented in table 8. The scatter in the angle-of-attack

Equations (21) show that the effect of Act on the drag measurement, as quantified by the prediction interval, iscoefficient is much more significant than that on the lift approximately _+0.02° to the 95-percent confidence level;

12

confidence in the mean value is approximately_+0.005° Reynolds number variations has been assessed basedat a 95-percent confidence level. Although the repeat- solely on predicted variations in the skin-friction dragability is very good, this analysis does not addresspossi- coefficientCD,sf.Skin-frictiondrag-coefficientestimatesble biases that may affect the absolute accuracy of the were made by using an equivalent fiat-plate drag plusangle-of-attackmeasurementsuch as possiblemodel and overspeedfactorsthat were based on the wetted areasofsupportsystem dynamicsas mentionedearlier, the model components.Figure 18 shows the predicted

Reynolds number variation that would cause a shift ofFlow conditions. The repeatability of the flow con- 0.1 drag count (0.00001) in the drag-coefficientdata at

ditions has a direct influence on the repeatabilityof the M = 0.80. Table 9 and figure 17(d) show very goodaerodynamic data. The measured flow parameters are Reynolds number repeatabilitybased on this strict crite-total pressure, total temperature,and static pressure from rion. Note, however,that cryogenic-modegroups 1 and 5which the primary flowparametersof interest are calcu- show greater scatter than all others; this scatter is attrib-lated--namely, the Reynolds number,the Mach number, uted to the fact that a single polar in each group wasand the dynamicpressure.The repeatabilityof these flow obtained at a slightlylower mean total temperature andparameters is summarizedin table 9 where the mean, on a separate day (table 4) than the others within thatsample standard deviation, and 95-percent prediction group.interval are given for each parameter for the combinedshort-term groups of polars; figure 17 shows the varia- The key concerningMach number variations is thetions from polar to polar within each combined short- drag-divergenceMath number, which can be defined asterm group. Table 10presents the variationexpecteddue the Math number at which the drag-rise rate ACD/AMto pure instrumentuncertainty for the four repeated flow reaches 0.1. This criterion implies that deviations ofconditions included in this investigation; the uncertainty about AM = 0.001 near the drag-divergenceMach num-of the measured quantitiesis that describedherein andin ber will cause a drag-coefficientshift of about one drag

count. The drag-divergenceMach number varies fromreference 18, and the uncertaintyof the calculated quan-titiesis based on the propagationof uncertaintyequations configuration to configuration and decreases withgivenby Rind. (See ref. 3.) increasing lift. The general implication is that Mach

number control becomes more important with bothThe measured quantitiesPt, Ps, and Tt are shown in increasing Mach number and increasing lift. Data from

figures 17(a), 17(b), and 17(c),respectively.The repeat- reference7 indicate that the repeat conditionsherein areabilityof these quantities is at least somewhat indicative below drag divergencefor the primary lift range exam-of the flow condition controlin addition to the accuracy ined (_ < 3.0°);however,increaseddrag data scatterwithof the measurement instruments.The maximumstandard increasingliftmay be partiallydue to Machnumber vari-deviation of total pressure withinany singlepolar is less ations, particularly for the test conditions at M = 0.80.than 0.04 psia and less than 0.06 psia for any group of Table 9 and figure 17(e)show the 95-percentpredictionpolars. No distinct difference is apparent between the intervals to be about 0.002 and 0.001 for the cryogeniccryogenic- (groups 1-7) and the air-mode groups and air modesof operation,respectively.(groups 8-13). The trends for static pressure and totaltemperature,however, show more scatter in the air mode Thedynamicpressurevariationsshownin table 9 arethan in the cryogenic mode. The increased scatter in the judged to be negligible compared with the potentialair mode is not truly significant, as the primary flow effects of Math and Reynolds number variations. Thisparameters (figs. 17(d), 17(e), and 17(0) are less sensi- judgment is based on data presented in reference 7 intive to these parameters in the air mode. The maximum which the dynamic pressure was varied over a largestandard deviation of static pressure within any single range. In addition,the effect of dynamicpressure due tocryogenic-modepolar is less than 0.07 psia and less than pure instrumentuncertainty(table 10)on the calculation0.09psia for any cryogenic-modegroup. The maximum of the force and momentcoefficientsis also negligible.standard deviation for static pressure in the air mode isless than 0.02 psia within a polar and less than 0.03 psia Contbinedforee andpressure tests. Another signifi-within a group. The maximumstandarddeviationof total cant source of nonrepeatabilityin the NTF may appeartemperature within any single cryogenic-mode polar is when force and pressure tests are combined. Balanceless than 0.8°F and less than 0.6°F for any cryogenic- repeatabilitycan be adversely affected by pressure tubesmode group. The maximum standard deviationfor total that bridgethe balancein such a way as to cause fouling;temperature in the air mode is less than 1.4°F within a nonrepeatabilitycan result when the tubes contract andpolar and less than 1.6°Fwithin a group, expand over the wide temperature range encountered.

The investigationdescribed herein was conducted as aThe potential effects of the primaryflow parameters force test only to eliminate this situation as a potential

on the drag data are now addressed. The effect of source of nonrepeatability.Note that the three pressure

13

measurements near the upper swept strut seal were made 7. Repeatability of the flow conditions was sufficient towithout tubes bridging the balance, preclude an adverse effect on the force and moment

coefficient data repeatability. However, instancesSummary of Results occurred when a flow parameter varied very little

within a polar, but the mean value was offset from theA high Reynolds number investigation of a 0.03- other polars within a group due to a set point bias.

scale model of the Boeing 767 airplane has been con- Likewise, instances occurred when the set point for aducted in the National Transonic Facility (NTF) at flow parameter was highly repeatable, but specificLangley Research Center; this investigation was part of a polars within a group exhibited more variation thancooperative effort to test this model at the NTF and two the others.other transonic wind tunnels. The model was tested over

a Mach number range of 0.70 to 0.86 and a Reynoldsnumber range of 2.38 to 40.0 x 106 based on the mean NASALangleyResearchCenteraerodynamic chord. The present report focuses on a Hampton,VA23681-0001study of data repeatability during this investigation. Two May 15,1995statistical and probability-based approaches are outlinedand provide the means to quantify data repeatability in a Referencesconsistent, mathematical manner. The results are summa-

rized as follows: 1. Anon.:AerodynamicData Accuracyand Quality:Require-mentsandCapabilitiesin WindTunnelTesting.AGARD-CP-

1. Excellent force and moment coefficient repeatability 429, 1988.(AvailablefromDTICas ADA202496.)was demonstrated in both air and cryogenic modes ofoperation over short-term periods. 2. Steinle, F.; Stanewsky, E.; and Dietz, R. O.: Wind Tunnel Flow

Quality and Data Accuracy Requirements. AGARD-AR-184,2. Excellent force and moment coefficient repeatability 1982. (Available from DTIC as AD A129 881.)

was demonstrated across a 15-day break in the cryo-genic tests. The two cryogenic repeat series were sep- 3. Rind, Emanuel:InstrumentError Analysis as It Applies tomated by 81 runs of tests in air, multiple model W[nd-TannelTesting. NASATP-1572, 1979.changes, multiple large changes in tunnel total tem-

4. Brown, Clinton E.; and Chen, Chaun Fang: An Analysis ofperature and total pressure, and tunnel volume

Performance Estimation Methods for Aircraft. NASAexchanges of air for nitrogen and vice versa. CR-921,1967.

3. Repeatability results for both short- and near-term 5. Abernethy, R. B.: Precisionand Propagation of Error. Thrusttime spans were within the stated pretest goals for the and Drag:Its Predictionand Verification, Eugene E. Covert.confidence interval of _+0.005,:L-0.0001, and _+0.001 ed., AIAA,1985,pp. 281-330.with a 95-percent confidence level for the coefficientsof lift, drag, and pitching moment, respectively. The 6. Roache, P. J.: Need for Control of Numerical Accuracy.repeat series which did not meet these goals could be J.Spacecr. & Rockets, vol. 27, no. 2, Mar.-Apr. 1990,explained by the introduction of a bias that violates pp. 98-102.

the primary requirement of randomness and invali- 7. Wahls, Richard A.; Gloss, Blair B.; Flechner, Smart G.;dates the statistical analysis. The use of residual plots, Johnson, William G., Jr.; Wright, E L.; Nelson, C. E; Nelson,however, was a key factor in identifying biases. R.S.; Elzey, M. B.; and Hergert, D. W.: A High Reynolds

Number Investigation of a Commercial Transport Model in the4. Force and moment coefficient repeatability was insert- NationalTransonicFacility.NASATM-4418,1993.

sitive to the balance thermal gradients of_+8°F experi-enced during data acquisition. 8. Young,ClarenceP., Jr., Hergert,DennisW.; Butler, Thomas

W.; and Herring,Fred M.: BuffetTestin the NationalTran-5. Repeatability assessments herein are based on sonicFacility.AIAA-92-4032,July1992.

data acquired over a limited range of angle of attack(o_ = -2 ° to 3°) and without onboard pressure 9. Walpole, RonaldE.; andMyers, RaymondH.:Probability andinstrumentation. Statistics for Engineers and Scientists. Third ed., Macmillan

Publ. Co., 1972.

6. Repeatability of the angle of attack, which was quanti-fied by the prediction interval as a function of the 10. Draper,N. R.; and Smith,H.: Applied Regression Analysis.

normal-force coefficient, is approximately +0.02° to JohnWiley&Sons,Inc.,1966.

the 95-percent confidence level; confidence in each 11. Coleman,Hugh W.;andSteele,W.Glenn,Jr.:Experimenta-mean value of the angle of attack is approximately tion and Uncertainty Analysis for Engineers.John Wiley &+0.005 ° at a 95-percent confidence level. Sons,Inc.,1989.

14

12. MIDAP Study Group: Guide to In-Flight Thrust Measurement 17. Finley, Tom D.; and Tcheng, Ping: Model Attitude Measure-of Turbojets and Fan Engines. AGARD-AG-237, 1979. ments at NASA Langley Research Center. AIAA-92-0763,(Available from DTIC as AD A065 939.) 1992.

13. Simon, Leslie E.: An Engineers' Manual of Statistical Meth- 18. Foster, Jean M.; and Adeock, Jerry B.: User's Guide for theods. John Wiley & Sons, Inc., 1941, p. 43. National Transonic Facility Data System. NASA TM-100511,

1987.

14. Gloss, B. B.: Current Status and Some Future Test Directions19. Williams, M. Susan: Experience With Strain Gage Balancesfor the US National Transonic Facility. Wind Tunnels and

Wind Tunnel Test Techniques, R. Aeronaut. Sot., 1992, for Cryogenie WindTunnels. Special Course on Advances inpp. 3.1-3.7. Cryogenic Wind Tunnel Technology, AGARD-R-774, 1989,

pp. 18-1-18-14. (Available from DTIC as AD A217 716.)

15. Fuller, Dennis E.: Guide for Users of the National Transonic 20. Chan, Y. Y.: Comparison of Boundary Layer Trips of Disk andFacility.NASA TM-83124, 1981. Grit TypesonAirfoil Performance at Transonic Speeds. NAE-

AN-56 (NRC-29908), National Aeronautical Establ. (Ottawa,16. Igoe, William B.: Analysis of Fluctuating Static Pressure Mea- Ontario), Dec. 1988.

surements in a Large High Reynolds Number Transonic Cryo-genic Wind Tunnel. Ph.D. Diss., George Washington Univ., 21. Fen'is, Alice T.: An Improved Method for Determining ForceMay 1993. Balance CalibrationAccuracy. ISA 93-092, 1993.

15

Table 1. Force andMomentMeasurementCharacteristics

Balance DataFull-scale (FS) accuracya acquisition

Measurement design limit _+0.5%FS resolutionNormal force, lb 6 500 +._.32.5 0.398Axial force, lb 400 +__2.0 .048Pitchingmoment, in-lb 13000 +65.0 1.151Rolling moment, in-lb 9 000 +45.0 .803Yawingmoment, in-lb 6 500 +__32.5 .723Side force, lb 4 000 +_20.0 .255

aQuoted balanceaccuracy (statedin terms of worst outlying point during calibration).

Table2. MachNumber Correctionsfor RepeatedTestConditionsBased on MachNumber Calibrations

as Functionof ReynoldsNumber

[M = Mre f + AM]

R_ M AMc

40.0 x 106 0.80 -0.0037

40.0 .70 -.00324.45 .80 -.0025

2.38 .80 -.0025

Table3. TransitionDisk Sizeand Distribution

[Disk spacing = 0.1 in. from center to center; disk diameters = 0.0455 in.]

Diskheight, in. for--

Component Location R_ = 2.38 x 106 R_ = 4.45 x 106c c

Body...................................... 1 in. aft of nose 0.0060 0.0060Nacelles:

Cowl inside....................... a0.5in. aft of hilite 0.0045 0.0045Cowl outside..................... 0.5 in. aft of hilite 0.0050 0.0050Primaryinside................... 0.5 in. aft of hilite 0.0050 0.0050Primary outside................. 0.5 in. aft of hilite 0.0050 0.0050Bifurcation........................ 0.5 in. aft of hilite 0.0050 0.0050

Nacelle struts......................... 1 in. aft of leadingedge 0.0040 0.0040Horizontaltail:

Upper surface.................... 25-percentlocal chord 0.0045 0.0045Lower surface................... 25-percentlocal chord 0.0045 0.0045

Wing:Upper surface.................... 10-percentlocal chord 0.0060 0.0045Lower surface................... 10-percentlocal chord 0.0060 0.0045

aHilite---leading edge of nacelle components.

16

Table 4. Short-Term Repeat Configurations and Test Conditions

Upper swept Repeat Sample

Group Re M q, psf Configuration strut seala polars b size Date

1 40.0 x 106 0.80 2661 W'BMNT 1 c5+1 40 1-13-921-15-92

2 WBMNTH = -1 1 4 28 d1-16-923 WBMNTH = -1 3 6 40 dl-31-924 WBMNTH = +1 3 4 36 2-3-92

5 40.0 x 106 0.70 2426 WBMNT 1 c5+1 40 1-13-921-15-92

6 WBMNTH = -1 1 4 29 1-16-927 WBMNTH = +1 3 3 20 2-3-92

8 4.45 x 106 0.80 1237 WBMNTH = -1 2 3 37 1-29-929 WBMNT 3 3 39 1-29-92

10 WBMNTH = +1 3 3 42 1-30-92

11 2.38 x 106 0.80 653 WB Out 3 40 1-22-9212 WBMNT Out 3 40 1-24-9213 WBMNTH = 0 Out 3 39 1-24-92

aSealnumberif on, otherwisesealout.bDoes not includeinvertedpolars.CFivepolarson 1-13-92,1polaron 1-15-92:combinefor short-termanalysis.dCombinefornear-termanalysis.

Table 5. Selected Order of Polynomial Regression Model

Order of polynomialDependent variable Independent variable regression model K

CD CL 4

cm cL a3CL a 3

CA CN 4Cm CN a3

C N _ 3

a cN 3aGroups 11 and 12 used K = 5.

17

Table 6. Confidence and Prediction Intervals at 95-Percent Confidence Level for Longitudinal Stability-Axis Coefficients

I Values averaged over range of data. Repeatability goals stated for confidence interval at 95-percent confidence 1level: ACD = __.1.0× 10-4; ACt. = +_5.0× 10-3; ACm= ___1.0× 10-3 d

ACo ACL ACre

Group R_ M CI PI CI PI CI PI

1 40.0 × 106 0.80 +0.5 x 10-4 +1.5 x 10-4 _-+-0.6× 10-3 +_2.0× 10-3 -Z-0.2x 10-3 +0.8 × 10-3

2 +.3 +.9 +.7 +_2.0 +.2 +.5

3 +.3 +1.0 +.7 +_.2.4 +.1 +.5

4 \! +.4 +1.2 +.7 +_2.2 +.1 +.4

5 i .70 +.2 +.7 +.5 +1.6 +.2 +.6

6 .70 +.3 +.7 +.5 +1.5 +.1 +.3

7 \! .70 +.3 +.7 +.6 +1.5 +.2 +.4

8 4.45 .80 +1.1 +__3.2 +.5 +1.7 +.3 +1.1

9 4.45 +.4 +1.2 +.6 +_2.1 +.5 +1.8

10 4.45 +.3 +.9 +.6 +_2.0 +.1 +.5

1I 2.38 +.4 +1.3 +.7 +_2.4 +.1 +.3

12 2.38 +.6 +1.7 +.5 +1.7 +.1 +.3

13 2.38 \! +.4 +1.1 +.6 +_2.0 +.2 +.6

I II .... ...... ....... ........ ? ......

18

Table7. Confidenceand PredictionIntervalsat 95-PercentConfidenceLevel forLongitudinalBody-AxisCoefficients

Values averagedover range of data. Repeatabilitygoals stated for confidenceinterval at 95-percentconfidence 1level: AC D = _1.0 Z 10-4; AC L = +_.5.0× 10-3; AC m = +1.0 × 10-3 _1

Aca ACN XC,.

Group Re M CI PI CI PI CI PI

1 40.0 × 106 0.80 -+0.4 x 10-4 +1.2 × 10-4 _-4-0.6x 10-3 +_.2.0x 10-3 _-t-0.2x 10-3 _-+0.8× 10-3

2 +.4 +1.1 +.7 +_.2.0 +.2 +.5

3 +.4 +1.3 +.7 +_.2.4 +.1 +.5

4 Xr +.5 +1.6 +.7 +__2.2 +.1 +.4

5 .70 +.2 _+.8 _+.5 _+1.6 _+.2 +.6

6 .70 +.2 :!:.6 -+.5 _+1.5 +.1 +.3

7 \ € .70 +.3 -+.7 -+.6 +1.5 -+.2 +.4

8 4.45 .80 _+1.1 +_.3.6 +.5 -+1.7 -+.3 +1.1

9 4.45 _+.5 _+1.5 _+.6 +_2.1 _+.5 +1.8

10 4.45 +.5 _+1.5 _+.6 +_2.0 _+.2 +.5

11 2.38 -+.5 _+1.7 +.7 +__2.4 _+.1 _+.3

12 2.38 _+.7 +_.2.1 _+.5 _+1.7 +.1 -+.3

13 2.38 \/ +.4 -+1.3 +.6 +.+.2.0 +.2 _+.6

19

Table 8. Confidence and Prediction Intervals at 95-Percent

Confidence Level for Angle of Attack

[Values averaged over range of data]

Act,deg

Group R_ M CI PI

1 40.0 x 106 0.80 _+0.005 _+0.018

2 +.006 +.016

3 +.006 +.020

4 \/ +.005 +.018

5 .70 +.005 +.017

6 .70 +.005 +.014

7 _ t .70 +.006 +.014

8 4.45 .80 __+.004 __+.014

9 4.45 +.005 __+.019

10 4.45 -+.005 +.017

11 2.38 -+.006 _+.022

12 2.38 _+.005 __+.016

13 2.38 \/ +.005 +__.017

20

Table 9. Flow Condition Repeatability

Pt, Ps, Tt, q,Group Measure psia psia °F Rc M psf

1 Mean 63.078 41.310 -250.05 39.984x 106 0.7998 2659.2s .013 .032 .46 .126 × 106 .0007 3.1

95% PI +.026 +.064 +.94 +.255 x 106 +.0015 +6.2

2 Mean 63.112 41.341 -250.57 40.149 × 106 0.7996 2659.7s .029 .037 .11 .047 × 106 .0010 4.8

95% PI +.059 +.077 +.22 +.097 × 106 +.0021 +9.9

3 Mean 63.087 41.321 -250.59 40.140× 106 0.7997 2659.0s .007 .032 .17 .050 x 106 .0007 2.9

95% PI +.014 +.064 _+0.35 +.102 × 106 +.0015 +_5.9

4 Mean 63.104 41.308 -250.76 40.217x 106 0.8003 2662.1s .033 .041 .12 .056 × 106 .0011 5.1

95% PI +.067 +.083 +.24 +.114 × 106 +.0022 +10.3

5 Mean 68.416 49.260 -249.88 39.959 × 106 0.6999 2426.1s .025 .043 .46 .145 x 106 .0008 3.5

95% PI +.050 +.088 +.93 +.293 × 106 +.0016 +7.0

6 Mean 68.432 49.271 -250.90 40.260 × 106 0.7000 2426.5s .019 .027 .16 .056 × 106 .0007 3.9

95% PI +.038 +.055 +.34 _.114 × 106 +.0015 +8.0

7 Mean 68.327 49.165 -250.78 40.192 × 106 0.7007 2426.1s .053 .089 .16 .058 x 106 .0013 4.6

95% PI +.111 +.186 +.34 +.122 x 106 +.0026 _+9.7

8 Mean 29.188 19.077 120.55 4.445 × 106 0.8008 1237.7s .011 .017 .90 .008 x 106 .0010 2.0

95% PI +.024 +.035 +1.82 +.016 × 106 +.0020 +4.1

9 Mean 29.I80 19.086 120.72 4.441 × 106 0.8000 1236.1s .010 .010 1.10 .010 × 106 .0004 .9

95% PI +.020 +.020 +_2.24 +.020 x 106 +.0009 +1.9

10 Mean 29.182 19.084 119.66 4.452 × 106 0.8002 1236.4s .014 .013 1.51 .013 × 106 .0005 1.2

95% PI +.027 +.026 +_3.04 +.027 × 106 +.0011 +-2.3

11 Mean 15.595 10.201 120.68 2.373 × 106 0.8002 660.5s .032 .018 .69 .008 x 106 .0004 1.7

95% PI +.064 +.036 +1.39 +.017 × 106 +.0008 +_3.4

12 Mean 15.600 10.204 119.82 2.378 x 106 0.8003 660.8s .024 .017 .40 .005 × 106 .0004 1.1

95% PI +.049 +.034 +.81 +.009 x 106 +.0009 +_2.1

13 Mean 15.600 10.201 120.68 2.374 x 106 0.8005 661.1s .033 .022 1.06 .007 x 106 .0004 1.4

95% PI +.067 +.045 +_.2.14 +.014 × 106 +.0009 +-.2.9

21

Table 10.Flow ConditionUncertaintyBased on QuotedInstrumentUncertainty

Pt, psia Ps, psia Tt, °F Rc, 106 M q, psf

63.10+ 0.010 41.30 + 0.005 -250.0__.0.1 40.00+ 0.031 0.800 + 0.0002 2661+ 1.4

68.40_+0.010 49.30 + 0.005 -250.0 + 0.1 40.00+ 0.031 0.700 + 0.0002 2426+ 1.4

29.20+ 0.003 19.10+ 0.003 120.0+ 0.1 4.45 + 0.001 0.800 + 0.0002 1236+ 0.6

15.60+ 0.003 10.20+ 0.0015 120.0+ 0.1 2.38+ 0.001 0.800 + 0.0002 660 + 0.4

22

L-87-4167Figure 1. Model in NTF test section.

23

Wing area (S) = 2.745 ft2Wing span (b) = 55.8 in.Wing aspect ratio (AR) = 7.877Mean aerodynamic chord (_) = 7.124 in.Sweep back c/4 = 31.5°Taper ratio = 0.267Model scale = 0.03

_ 55.8 in.

55.8 in.

Figure 2. Model geometry.

24

20

!t18

i

16 t _' II

14 ] r jI

I

o 12 '= i i I_" /I ...........J............."_ 10 ',o I I

- /iZ 8 ' ,i

6 ii !:' [

4 i

,,, [ 95% confidence level

i_ ..........................80%confidence level, , i I ! I _0 2 4 6 8 10 12 14 16 18 20

Number of points

Figure 3. Variation of N ll2 and t value with data sample size N.

25

Cryogenic mode Air mode

50 x 10-5

Group Group45

o-- 1 o-- 8

40 D......... 2 D......... 9o---- 3 <>---- 10zx-..... 4 /x...... 1135t,...... 5 t_..... 12b .... 6 r-,.... 13

30 o .... 7 x

SE 25 \%

_ ---__ _- F==_-_)_-_-__4_ _J

_ _.__1 "--- t

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

K K

(a) CDevaluatedas a functionof CL.

Figure 4. Variation of standard error of longitudinalstability-axis coefficients as a function of order of polynomialregressionmodel.

26

Cryogenic mode Air mode

50 x 10--4

Group Group45

(>_ I o-- 8

40 cr......... 2 rn......... 9_---- 3 <>_-- 10z_...... 4 A..... 1135_t_..... 5 Ix- 12

t_ 6 r,,.... 1330 _ O-.... 7

I

SE 25 _ 1,/ ,,I \

20/ ',I \\

15 1 k

10

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

K K

(b) Cmevaluated as a function of Cr.

Figure 4. Continued.

27

Cryogenic mode Air mode

10 x 10-3

Group Group9

o-- 1 o-- 8

8 o-......... 2 c-......... 9_----- 3 _----- 10A-..... 4 , A- 117b ..... 5 h_..... 12

t_.... 6 _ .... 136 c_.... 7

SE 5

4 _\

3

2 'N

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

K K

(c) CLevaluated as a function of o_.

Figure 4. Concluded.

28

Cryogenic mode Air mode

50 x 10-5

Group Group45

o-- 1 o-- 8

40 D......... 2 x D......... 9<>---- 3 \ <>---- I0

/

zx...... 4 _ z_-..... 1135tx- 5 <\/ h,- 12

t_.... 6 _ _ 13

30 cr.... 7

SE 25

20

10 _ '- I_.___1....._...... _____ ______.

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

K K

(a) CAevaluatedas a functionof CN.

Figure5. Variation of standarderror of longitudinalbody-axiscoefficientsas a functionof order of polynomialregres-sion model.

29

Cryogenic mode Air mode

50 x 10-4

Group Group45

o--- 1 o--- 8

40 0-......... 2 t3......... 9O----- 3 O---- 10zx..... 4 z_-..... 1135tx-..... 5 t_..... 12

_ .... 6 _ .... 1330 _ c3.... 7

|

I

SE 25 i J,I \\\ 120

[\\

I \\\

15 I,, '\

,o . ]-----[3-----C....--[.----I....-£

5 x* "_-

_ _ __ _--__ _---_0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

K K

(b) Cm evaluated as a function of CN.

Figure 5. Continued.

3O

Cryogenicmode Air mode

10x 10-3

Group Group9

o-_ 1 o--- 8

8 D......... 2 _ ......... 9O-_-- 3 O----- 10A- 4 A..... 11

7t_..... 5 t_..... 12

t_.... 6 _ .... 136 CY.... 7

SE 5

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8

K K

(c) CN evaluated as a function of cz.

Figure 5. Concluded.

31

Run R_ M q, psf

o 14 39.92x 106 0.800 2660[] 16 39.93 .799 2658<> 18 39.95 .799 2658zx 20 39.93 .800 2660t,.. 22 39.96 .800 2661

r, 28 40.27 .800 265895% confidence interval

95% prediction instal

.005 4,-r--r--_ .... .:.'--t-t i--_-- .,t--.,t...... t-f--i

aCL 0 --'--"--'--"--'--"-'....[-_)-!--f_--_i--t--r--tTt-rz---_ .....t--_--t Goal--i-i-_-_--i--i-i......i-_---i--@-..,--i--i--4--.,--i..i_i---:_ .......__L_.L__--_-_--*.... ";--i-'f..... !--+-_-_--r-ff_ -_'ft_ --_--_ _ _ .............. _ _ _ _--t--!--f--t--t--t--t--t--'_--_ ..... r--'t "r-'-_--_'--*--'_ --,--,--,--,--,--,--,

-.oo5--!--f--t.....t-t--f......t--i--t........i-t-t-:-T::T:-i...._,_ ,,,-4 -3 -2 -1 0 1 2 3 4 T

ct, deg

4 x 10-4i i i i _ _ i i i i i _ i i i i i i l i ] i i i

ACD 0--i--i-;-[-i--i ....... i-i_ '_--i-- _ ......... Goal-,--,-,--,-,--,--,--,-,-,--,--,--,"-,--,--,-,-,-,--,-,--,--"--, _T-I ........... T_.4.__.___.]....... 1.--._-.i...........,.--.r-.i..........,.-.-4..--.,..... 4.... t "-T .................................. r---r ---r ......... r--'r--'r .....

-4 ! i i i i i i i i i i i i _ i _ _ ; i i _ i i i-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

-----._--.'}i i i i ii'.--±--.'--t--'.--..i.--.!ii i.... i iii'-"i--J'-- ] ] ]]_] j,i i i i i i i i _

-----+--.....+--_--_....--_--_--_-<f--_._I_..........._................_-__-_i-_....: i,4 i i _',_ _,i _l_ ,,, i i Goal0 ..... .... ;.....-_.--_--- _--i.--.i::-.i--t_--.i_.i.--_--.-

_.-_.L_-_. i i4-- -.±_.-=.____z -............. i i i ! i i .....T-T-i.....--f-

-.002 -T-T--T.....T-[--7.......[--T--T......!--T--].......T-T--T.......T--T-I........!-T--T.........i-T-i.....-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(a) Group 1.

Figure 6. Statistical results of CL, CD, and Cm short-term repeat data acquired in cryogenic mode.

32

Run R_ M q, psf

o 44 40.17x 106 0.800 2662[] 46 40.18 .800 2664O 48 40.11 .799 2656zx 50 40.12 .799 2656

95% confidenceinterval

.... 95% predictioninterval

.005 i i i i i i i i i _ _ __ _ = ! ! !: ' : i i i i i i i i i--t-t--t ..... *--T--I.... T-"g--[--:ii_ ....[--[-T......t-_--t..... T--r--r-ii_--,-,-si,i ........................, i i ,_ _-T--2_ _--i--r-T-r,_._,_L_ --T-i_T--r--T-'T-T-

i, i _ i i i ' -_ .....P-t-t--'--T--T--T...... [--T--T--'t--T"iil.__+__.a._+ ...... !......b_l__._ ._...q.___.-T_-T--"--T--T--T----t--t--t.__.....t--t--t.... tb_,.__ ....i_i . I .Jl I I 4>_ACL Goal0 ....i__i___.... L_L_i.....i-_--;--_;--_-;--_.--;.--.I.--.j.-_4._i .... i__i.--i--

/

JJJ iiJ liJ JJi iJl JJJ ill -T--T-T--T--.r-- t ..... _.-_--_--_ ..... ,__,.--,--,--.,--,-.,--,.--.,--,--,--,--,--,--,.--,--.,........ __,..__.__.____+ ............ .--+--. ...... +__?__.__._.-__ ............ _....... . ..... +__+__+.... t--#--#---.005 ........... ' , _ E _ _ , , i i , , ,

4 -3 -2 -1 0 1 2 3 4 Ta, deg

4xlO --4....... - ........ -..----- ...... ,--!--.! .... _ ..............

--T--T-T-i if -T-T-T--EI_ TiE --T--T--F--_ _ _ -T-T-F-"--F--T----T.... I'--FF--Tq-y- ---F--FT.... _----------.....i--i--i.....i----'!----i.... l----_--1--""1"

ACD 0 "--T--T--r......T--T-_:::v =_'L7_77"_i_i_=m_:Mi.... _5-r72..... =€__2::.__4,:_._.%%'-.kO__t-=_---T--T-T--Goal

-T-F-T......[--i--i.....I-T--[.....F----T.....!--T--I.......[--i--[....._--!--[.... I--,-T----T--T--T.......F-T--T.....T-T--[.... T--!-T......F-T--T.... T--T--i.......T--T--F-T--T-F-

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002 i i i i i i i i i i i i _L_L_A.... [__L.[.....i__i__i__i il

.... '-....•ACre 0 J i ; i J _--,,; _ ....... '.-, i ; i Goal

....----+......... ?if T--_--i--[.......[-i-- .....F-I-i.....F----[......[--!--T.....F---T.......i--1------T--T--F- 1"

-.002 -!--i--[......T-F-T.......F-F-I........I-T-T--l-i--i ........F-I--T.......F-I-T.....[-T-T--.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(b) Group 2.

Figure6. Continued.

33

Run R_ M q, psf

o 147 40.12 x 106 0.800 2659[] 148 40.17 .800 2659O 149 40.14 .799 2658A 150 40.12 .800 2659_" 151 40.16 .800 2661r, 152 40.14 .800 2659

95% confidence interval

95% prediction interval

.005 $______ii i _ J, i ii--T--T--T...... T--T-I.....F-T--T--]--T-T--Ti j j.... T--T-I!i J J...... T--T--T--_ m j I IiI- Jt i- t_1 _ _ ..... ? -" _--T --_i _ _

-r-T--t.....i--t-i.... t_--._--_-i ......t-x-:-2-h_";-k_.i......i........t......t-

,-......,,. °°"o ...............-- -- - -- __LL__.......................____.._._.......L-L-_.....II!ZIIIiIIiiiiiiiiii -_-T--I.....-.oo5,,, -T-r-T-,,,

-4 -3 -2 -1 0 1 2 3 4 TIx, deg

4 x 10-4i i _ i ! i i i i i _ i l ! ! i i i i i i i i i

--_-_--___......i-N ........H-i .......td-..!........i-T-i.....i--t--t.......H-J........i--i--i.....-i-i--t.....i--i-_-T_!_:_!-_i...._,_-_*-_--_ {-_-Hd ....ACD 0 Goal------i.--.!.--__o____L4L.___z__.-.._-._2-._i_22]3J ii_-.__._.-_.__ . ..... ___..__...._.___._.__.....i-t-.f---- ....i.-_--.i.....--t-.-.....i-f-i- -_ -k --T-,,, Z---_-_--i___, .....L...,, , ,, 7Z-SS--i-----i......."--"--"....if! !-t .... _ _ _ i i i

-4 _ i-i-i ....-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002 ! i i _ i i , i _ _ i i _ i i i i _ _ _ _ _ _

, i I _ ........ r--T--T--T.......T"-r............ i .i_'--'_--_......................J J

__i___L_j.......i___............................i " " i i i i ......................................................... V"I ..........._--'i............... -__._........ !.__.k_...i..... _ _,__,_,__ _--_ _-- - _--."-----_ _ _ _ _ ! -i,, _ i

i i_-tr_ _ T_ T!! --_-_[_-_-I-T-] ....ACm 0 i i _ i i : i i i -_i iOi ,_ i : i-- i _ : : i i _ Goal---.----_.....+--.-_---+---+---.,-.._--.-+---.:o-.-_-_--_ --._--._--.-.--

--i..--.!.--.i.......L-L-.-..........!..--.!.--.!........!.-.!.--.!.....!.--.l..--.-.......i.-...k--.i.........L-I---......L-.-........-.002--i--i--i.......t--P-t.......i--j--i......_-t-".... T,,, ....i-i--i........i--N..........."--"-----,i, ....j--f---i.....

-.2 -.1 0 .1 .2 .3 .4 .5 .6CL

(e) Group3.

Figure6. Continued.

34

Run R_ M q, psf

o 156 40.25 x 106 0.801 2666[] 158 40.21 .801 2662<> 160 40.14 .799 2656A 162 40.23 .800 2661

95% confidence interval

.... 95% prediction interval

,L.005 _ , _ _ _ _ , _ _ _ _ _ _ _ _ [ _ i i : = :....t--t--_-,*-t-t,, ,.....+--!--i,_ ,......,_--*-_,,.....f-t-t--t--t--f--i:_ . . : _......:_--t--f,.....f-i--i-

"--T--I--T-T-:-T--'r ..... _ r--T--r--T--T--r--*--T--T--T.=.&,_,A.=&.," " '

--T-*-?....t--t-?--;_-_--t .... ' ' ' _ .... =T-T-1......T--T--T--ACt. o ___,_ _, ,_,_,, .', ', :,,_'rT-i '_T-I--T--T--T--Goal

.005--t--t--t.....t--t--t....t--t-t.....t--t--t.....t-t--t---i--t--t......t--t-i.......t-_--t--4 -3 -2 -1 0 1 2 3 4 m

IX,deg

4 x 10.4i i i i i i i _ i , _ iI _ E _ i _ ! i i t _ i l ! t E E i ! i i

----'?--i ...... .--t--t- -,--,--. ..... ----T--.t--+--i.--,---r--,--?--.--i--?--?-----, --i"....... r--• . . _ i 1 i _ i --?"-T--T --i------T .... ?--+'--1---"T--T--, .... iI--'J'--'_ -' --?--i'-- ...+--t--?-"?--i .,_

ACD 0 i d r_ _ 1_; i,_ _:_:: i '_'i_ i0 i)1_i i ', Goal--T--T ........ T--T _ _ _--_----T.=---T---:=[=-'_--:I:_': =:'=_'== ='_I: :--&'=_=--_ =--_--_ ..... T--T--T--"

-"+--'i"--+-_ i --+--':'--+--._ .......... _'."-+--+ ....... _"-+--+--+--+ ..... +..... I +--'_ ....... "--'--'--'--"--'--'--'--"

--T--T--T ..... T--T--, ...... T............. i .............. i ................... [-"_" ................... - ............-4 ! ! ! I ! ! ! ! ! ! _ ! ! ! ! ! ! _ ! ! _ _ ! !

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002 ' _ i " i i ! ! ! ! ! ! _ _ _ _ _ _ _ _ _: : : : : : i i i i i i i _ " i i [

i _ i ......... _..... T--T--F--" ........ ,--T ..... _--+--'_ ...... +--+--+--i "--_-'*--+--+~-+ ....... +.... _---+--+ ..... +--+--._ ..... +--+--._ ...... +--.:---+ ..... +~.-+......... +-- v-.- -:.

--T--T--T ...... i-"T'_ _='_ _:'_=_'--5 __. T _.T _--,._.a_? 7T m-T- _. ! i iACm 0 ....... Goal_ _ _ _ _----_i_-_2___i_ .D_____'_" i _ ;-o-_i i i--+--+"--" ..... $--'.--4_ _-_--,;;r=._-_ ..+-..+...-_.......... 7:-- ._-.._.............._-.._-. -+ = .--._'-'_.:=_-_ =-'--'.--.i.--

.... ! ! .).' __ _ ....L-i.--!.... ___ '' _ ___ ' ' _ __'._.-__'__--T--.;--I ........... _ , _ "--T--I-" [ ....... T--T--f-- i i i t _-tt-t....t-- i i--ii ill-.002 i................... +-_--'!i !..... ---*-'+ii I............................i ! !

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(d) Group 4.

Figure6. Continued.

35

Run R_. M q, psf

o 15 39.89 x 106 0.700 242612 17 39.90 .700 2426<> 19 39.91 .699 2424zx 21 39.92 .700 2428tx 23 39.91 .699 2422t_ 29 40.28 .701 2430

95% confidenceinterval

.... 95% predictioninterval

.005 _ _ i i _ , i _ i _ _ _ ...... _ i _ _ i i--*-_--_--*-*-_........... +--i-i--r-++ _ ......Eli i i i ....,--,--,--'--,--,--, ........ r--v--T.... r--r--_

--I--I--I" ..... *--€:'-* ....... _--'_" _'-- --*---_'_--_----i---.4---+--4----_--+-:-+-~+...... +--4---+---

----_----_.-]_--.__s__t--.i...... i_..__Yh----i--T_-_Z_--TS2_.i--:--]-1_-i_£"---J_'&-±.--Ii--[-]_ _ _ , , , 0 c-_c- ,: ,_:: _ _, ,: _: :,,_ :.-r-_o_ -! ! ! GoalACL 0 i i i i i ,--,-,--,--,--,--,--,.....i-_ °'-_i_-_i-_i#_-~i--,--H--i--_'--T--T --T--T--T--T--] ...........I--I--T--T--i--I"-T-'T_~I--T--T--T--T--I--T ....... T--l--t. --T--!--,--,--,--,--,--,--,--,--,--,--,--,--,--,--, --T-T~-T--T--?-T--?--r-t--t-r--r-t-_

-.005--m--t.....r-m.....r-m.....m--r....V-!--t....!--t-!......M--i......f-M--4 -3 -2 -1 0 1 2 3 4 T

_. deg

4 x 10-4i i i i i i i i i i i i

............' i i I i i i I i i i I i i i -T--T-T.....[ "-'-"--'--'-"--' ....,.--T"-]-i:--_--t--i..... .-i--?- --i--,---..._=___..... --- ...... T--r-_..... _--_-_.......]i.__.i.___-]--_--_-?--?-_i i i $'--.,--,--,--.,--,--,--...--'--.'-..=-.... "--._.--.I.-rY_t-t-_-_Trr_ i ......[-i--]i ! i i i i ! l-_r---F_-?:--±--]--i--I--!-i-i....

ACD 0 i i i i i i _ w_ o_ _-_ _ _ _ 7z__,_i i i i Goal

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::-r-.....,_.i........i.__L_[......"......l......l__.[..._.i......l_].__.[.....i__L_i...........,_. L L I-4 _ , , i i i ......... ,,, ,-,]........j-i--,.....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002

--i_--:.-"--i.......i--.L-i --L_L_L_,__!!. { -.,-..,__,__,.__,__.,.__,.....+__+.._!.........!-....!--+......._--".......'--_--"--_-]L-----_--$_--_i_]=.P.-.=........_._.... _-_........M--i:....[-T-I .......T--T--] i i_ ! !_¢ _ _ . _ _! ! ! !

ACre 0 ....[__i__i..... LI__i ...... i_i_ i.'i....i]_....i._..i._._ { b i _ i "L_ i i i ! Goal...._---4-I-44-4--].--.i-..-.'--+:-1..--F--r+---I--+:-%,+<-t;,_{-!_-,;,_1..--:_.,_-_:_-:i:-._:I-7:-I:::--i

.002--H--i.......N--i......i-f--i.....N--i...... .......t--ri.......i--t--!......N--!....-.r-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(e) Group 5.

Figure 6. Continued.

36

Run R_ M q, psf

o 45 40.24 x 106 0.699 2423[] 47 40.25 .700 2428<> 49 40.26 .700 2429A 51 40.31 .700 2429

95% confidenceinterval95% predictioninterval

4 x 10-4J i i i i i " _ i i i J _ i i i i i J i i i i i

......................_.-.±__- __,....,__,__.,_,__,.__,__,.__ _ _ _ _ _ _ _

i i i i i []_ i i i ] i i _ i l iJ ! J J, J i i _ TT -q -T-T----I-T--[ T

JtiIili .--T--_--_--I--_-----_......i--u-.....t--u-t-+------:..---_-_--_.._,t,.....[--[--T......[--- i.....--L--.L--L-- IT--L -i L..... ! _ ! ! ! _ _ _ ! ! ! " ' "

_ ; : ................. _ ..... _ _ i i Goal....b---i.... =----_ '='.---_---_--_ .......-T---I.......J--i--t........r--r--t.... _ _ _ i i , i _ _ ..........---"-"--......._'-----_.... J JJ J ii ---,--r-- _ -_.--.r--._......_i_--_-_..-i i i J J i -_----- ..... "--'--"........ z___,_-__.

/

...._--T.---_....... TTi.......r--r--_.....,_,i--i--i.........i if ,,_'_--r-_......................_---4-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

J J i i i

..__.__-__.!.__.i__.___t__.i.__.i_____.!.__! :-i-:i--i-I:::i-:jzi--Yi-:iZi $i ii i ii ....f-"i--_'--'---?--?--'[.......b-f--i .........--_.--_--_ .... _.--!_.-._-._.-----_--.,.--._-.-i-._.--_--.!-.-$--_--_.-----i.-_-._-..-."--i.--.i

ACre 0 i i i -[--_-r-_---r-r-_ _-_--__-i-_-_, ! ! ! Goal

--i--l-_......i.--._-.--i........j--i--?......i--i--i........r--'T--!......r-"_'--_......"--_--r........t--t---J..........................,,--......'----....--i--J--J........i--t--t-- i i i _ i i i i i T-.oo_-.tti----.......tit j-j--i.......i--J--t.......t--i--i.......t-j--i.....j--p-j.......--'-----,,,-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(f) Group 6.

Figure 6. Continued.

37

Run R_ M q, psf

o 157 40.20 x 106 0.700 2424[] 159 40.16 .700 24230 161 40.22 .702 2431

95% confidence interval

95%prediction interval

002 _i f _'' t:::::::::::::::::::::::::::::::::::::::i::i::i:::::i::_:t:::::::::::::::::::::::::::::i:::i::i:

-.002 i T-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(g) Group7.

Figure 6. Concluded.

38

Run R E M q, psf

o 14 39.92 x 1060.800 2660

[] 16 39.93 .799 2658

<> 18 39.95 .799 2658

zx 20 39.93 .800 2660

tx 22 39.96 .800 2661

t:a 28 40.27 .800 2658

95% confidence interval

95% predictioninterval

$.005 i i i i i i i i _ i i i i i i _ _ J i i i _ i i

......i "_..........i 1 _i........_ _......1 "_"-_--"!_ _.............., ._..-..,--.4.--_.---_...... _--_.--,__ _..... i'--'i"-'i.:--1--i--i--i"..............................................i--_--I--!--1--_--_--_......",--i-i.-_i--]--]--1.--T-.V-. _..... _-i_i---E ......--I-I--I .... -_--t--_..... ,_.-_ _.-4--+_--_+-+-.4--4_-!--_--!......... '................

- _ i t i ! i i i_,i _-_i--_-d--i-f---r--_---_- "-'_"-_'--I--'_"-_-_"-'_" -"--"'-'_'-" '-1"--i--i--'_--i--i--i'-t-i--i--i--1--i--i--i"

._.__....... ' ' ' .....L_J__L_-.oo5-i--......-r-_,_ -t-i-i- ,,,,, , -i-_-! ........!-i-i ......i--!--!......i-!--i--

-4 -3 -2 -1 0 1 2 3 4

_, deg

4 x 10-4i _ i i i i i i ] i i i i i i i _ i i i i i i i

'!-i--T-FT-i--........T-!-;-: $Goal

_c_ 0:_i____.....i-L-J.....iJ___,_i_i__i_o:_,__=___i_____--r-•-i-i-i--Ti--i----,-i-i--i-._--_---_,, ,.......+-H--.,-+-4--i-...,--.H----.,-+-.---

-4 -r--] ......]-7-] ........--]--!'.... _----i,, ,.......i--i-i,, '.......i--i-i'' '.....i--f-i--'' '-.2 -.1 0 .1 .2 .3 ,4 .5 .6

CN

.002 ....... ill i i i

____,-i--r-i-z._ .. _. ,_. _ .._!_'...............__-=._-_--_-"-i--_-_---i-i'-"-;-_....."--_..................i-_-_-"-_-"-"-"--_--*--_---;--E--"--':---_--_--_z-"-'--:-ACre o ....i___.........L_.L.".........L.j__=,_,_,...._._i._i i i,,i ,.i i_:_,,, ....Oo_a:.--i.-i=.--..i.-.-)-..i-_.z-i--.._i.--.i_i--. _-i_ _ _ i i i i i i_-_-_-=i__-_..-;"_==i-j-_i_=-_i_=_-_=.

-.002 _ _ } _ _ _ _ i _ " i i i i i _ _ _ i i i

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(a) Group 1.

Figure 7. Statistical results of CN, CA, and Cm short-term repeat data acquired in cryogenic mode.

39

Run RE M q, psf

0 44 40.17 X lo6 0.800 2662 46 40.18 .800 2664

0 48 40.1 1 ,799 2656 A 50 40.12 .799 2656

95% confidence interval ---- 95% prediction interval

-L Goal

T

L

Goal

7

(b) Group 2.

Figure 7. Continued.

Run R_ M q, psf

o 147 40.12 x 1060.800 2659[] 148 40.17 .800 2659<> 149 40.14 .799 2658A 150 40.12 .800 2659_- 151 40.16 .800 2661r, 152 40.14 .800 2659

95% confidenceinterval

95% predictioninterval

$....!--f-! -7--i-T-i-!-! .......................,'--'-",,......*--+--_......_--'--_........_--"-_.....................................................................'-'-' _-_--_-_j_--,--bM--4........i.-.:l-.b-i---:'.........i-_=_--.q=#----_---=_=._........t-_._=

'-''_---_,_-_.-.-_......4--d-d.....ACN ! ! ! I ! ! ] ! _ !C'_I _ !l_'i I i _ ! I-- i : i0......_ _ _ _ _ , i_-_ _, _..__i -' _' __ _i°! ! i...........! _!i---_.---_....

Goal--f-4"---i ..........i--i"-'_ ........i. " ""I...........i-"k_--i...... i--_--..i .........................."---.... i--'-i .--.'_......... i'--'+---_...... _--'-i-----d....... -i........... .I---.t--._---.-._.................. d...... _....... F-.-r--._---_--._, , , , , , _ , ____---_--___-__.--___.____.___-___7__]_......j__.j__._.....

-.005-!--H-i--H-i......i-i-i.........H--!........H--!..........H-i........i--H........H-i--4 -3 -2 -1 0 1 2 3 4 "f

deg

4 x 10--4

::i::H..............................................................................i i i i I i I i i _ _ _ _ '-i-d-1--i--i-1--1• • • ...-4---i---i....-i-.~-i--4....,i 'T--'I,,..... i"-'!--!--'i"-"_--'i"-'i ....... i--'i--- ........"i--'i'-q ............I--T--'I-- __ L i- _ I i i .l.

....J-i--]......]-J-_ o_,i ._J ; : ,,, ',2-J-m-]E-]-i_--J i j

ACA 0 :]][_-][]-_-]].-,]i i___ _ _ '_ _i , _ , Goal......'--4---' .........'.---_- -..,.--_:.--d.---."-'...-..,.--.-_--_ _.._ ...............-T-T_=--_-r--r_- - --t----'_- _'_--7-_7- _ T..... ---:.--._ ....... _.---_.--.._....... 4.---'--,.i ....... i---..i--,,] ......... _ ............. i---,4 ---[.......... i----_---_ ....

-4 .................i-]-i...........i-i-_..........................l--i-i........---T-]............!---]...................

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.002 i i i i i i , _ i _ t _ - _ _ i i i i i i, i i i.... !--"!---!--"1---i---i'--- ...._----J--H---r---d _ _ I _ _

...... i i i i _ i i i i .-J...-..l-J..... _ i _ i _ iM4I-----T---I-d--._ '-i-t " " " $.....i-J--] .....i-----,.......[--[-, .... • -_--r-i ...... r-q--T--l-T-].......i-]_---u-__

ACre 0 .....h..J..-J........J.-J._'_ _:' ; i'_'_i__ "-+--e-_--@Oi_]_ ..... -_-&-.--i--.lGoali i i l I i I l i l l i I l

----'" ........."'--_- --_--!-_--,-'bbqi_, '' _ ..........._....T_ _ _ _ _ , -Y---q........_-_--- ' ' ' . .i-..--_.......T-T-i--.002 ....i--i--i .....-i--i--i ..........._ _i!-i-"_........................................j i j i j ! j j j

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(C) Group 3.

Figure7. Continued.

41

Run R_. M q, psf

o 156 40.25 x 106 0.801 2666[] 158 40.21 .801 2662O 160 40.14 .799 2656A 162 40.23 .800 2661

95% confidence interval

95% prediction interval

__s---i-"_---_---1--"[--'i---i ---i---i.--..i ....... _-~-4.---4-.... @-"i--_---1---+'-'i--'_ ...... ,,, --.i"-'i--'j--'l---j--!--" [....

_ 0....'"_!+_-_''......_=' _°'......._t_'Y,__'___:_J=......._-:__ t _'- ooo,---_---_---! ...... 1--._--.-r -._ .~--_--_._=_..=-..._.a=._._--- ._.a_._,_,a=-..-..= z_................_: ._._..... -_...... _-----_---_ ....

...._--i-q......_--4-_-_i-..."--._--4 ...... 4--_ .--i-._-.:-._.......i--._...-..i.....-.oo5"_-_--_..... i-_--k-T-!-+-_-+-,--_ --+-4---i......+'-+-+-r-!-+-! --_--..}-.-.i-4 -3 -2 -1 0 1 2 3 4 T

_t, deg

4 x 10-4! ! : ! ! ! _ i i ! _ ! ! _ !

______,.....__-____,_____,..........................____.....--'--i--1 .... ,'-',--," -'_-----"-- ' .............. J,--J"---.t--J........---'--_ --.---J...-,i._ --.4-_--4..... 4.--4.--.._..-r-_-.d,,..,..i.... ' ' ' _ i

: :: ::_::i__-:__:_-:_-_=:_T_ __ '' i i ; i i _ i _ __ -i-d-i-"+-+-<....-4 .....i_--" ...... ,,,'-_-_.....i-q-i--l-i--! ........i----i....-_-"--_,,,....................._ -T---i....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.002 i i i i i i i i i I i i i I i i i i i i , i i i--_--_--,--_-_--i----_--,--i-i--.----.--i---i......i f--i--t-.--,--.. ...........-i-i ........• _ - .I.------_......_--_---......-----'......._-"-_.....i-i-i ......k-+-.!--*-i--'-H-i--+.--!.----_--_............l!_ _ "ACre 0 i i i 7"_:i::_ _ _ :_ _ _=__--=-_ f: _ i [ Goal

...... -__.- _-i_-_,s=_-_-_.._2f______2o___::-_::_:,::-_:_.......,-,..................................................,,...............................,T-,-,-,.............-,---,--,i i _l _--f-i

._.L_J___ ! ! _ _ _ _ 1 _ _ ! ] ] l _ _ t_ "]..-- ---1....... -3..-...---_---:--.! ...... -.-.1--.._-.._.... ]---.--._ .... _-,._---.}.

....r-t-i- .--i--i.--.,.... i......_L_,_,.............].-.-.L..I--_---,,--_.... __..i__J..... L-._---.-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(d) Group4.

Figure 7. Continued.

42

Run R_ M q, psf

o 15 39.89x 106 0.700 2426[] 17 39.90 .700 2426<> 19 39.91 .699 2424A 21 39.92 .700 2428tx 23 39.91 .699 2422r_ 29 40.28 .701 2430

95% confidence interval

95% prediction interval

$.005 ! ! J _ _ _ _ _ _ i i i i i i i _ i i i i i i i

"-_-_-_ ........-]I i--i--i--l--i---i--i ....T--T-Z,.... i--]-i .......i-i--i ........I i--_ i ....... i--Z;---f---4--4--4........4---!--4....... 4---i --4--4--4 --i .........4.......4.-.4--4-.+-4--.i--4.........i--4--4...., i _, i li i_..!__A.... 2 JD,i...... A..-A-...i..........J--J---!........A--..!.--A........J--J--.i....

TT-]s]-]S]]--]-]_T]--i._-!f-9--_=.__---r-_--¢i-i-m-7__T-__J_l__z_J__J__, ! ! !/ _°,i_ c ! !,r, __,,_! ! ! !_cN o:__i_____+_t_£qq_i____i=ie__,_____a=£__._=_.____I.......f-i-_--Go_

--'!-'--!-'1--1--I--I"--1--'1--!--T'-I--1--1--I--!................ ..... i--'i--I ....... "!....... "I'--1--]--'I'--I..,_ ...............I ; I....i-i--'! ..... i--i--i ..... i-i-1--*-i--i-i-"--i--i i........'-+-+-+--+ "-" ........."--"-_ ....

-.oo5--t-_--r--_-i---i.......i-r-i.........rri--i--r-_.......H-i.......4-H......_--H....-4 -3 -2 -1 0 1 2 3 4 m

_, deg

4 x 10--4i i i i i i i i i i ] i i i i i i i i

--i--i--i..____.__._.............k---i--]-i-d-! -i--i--i..................,,-r-- i....7----r-i----T-r--r7• . .-.-l.--_--..i----i.... -l.--J---l----.l-~----i--.i.._j _ _........_,_j i.....2_.] ..!.....L._A__i__

- r----_--,_ , _--_.1 , ,-, i i i ,i,

o-H---i-l-H-q,,,),,i...... _--i-_--i=_",_4o_3..O_4 i i_;'_--_-'_=!--_"6...p_,_L2! _ _-i_ ..... i--i-ii ' Goal

....i--i--4.--.1-.i-{---i--.l--4-4-r-::l:-q-.j-.-{---4-.F4--:l::--i---i--4--.+-i---i-.i--I--q-i--.i--T.....i---I--.i........A__.___._.........i__!__A...... -.......-.... _--..I.--"........L..!___...... "_..i__.i...... -__-_J._-4 i i i i i i i i i i i i i i i i i i i i i ! i i

-o2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.002---.-.i--].........i.._..i..._.i_...__.._.i.....!...__........L_L_.i......i__'_-.........L_L_-.__J_J__i.....J--J--J...."--i---i......---_--)......._-='--]-----'-_.........---".... i $.................. 4--4........ "...... -.

, i _ t , i i _ i -

-i--1---!.....i....................i....F-_...................Y_==_........F= '_ =_ .........____f._..,• i-b_ .._raACm 0 .-.-----i--".........l-.--i--..i.... ' _ ;:iti.......i_._.._.J........i_...i..._..,_...i......_...i.._2..._i ._-__.j__j..... Goal

--.r-'?--i--'--l-_'--l-- --I'-_'--_" .-.--_-_--.r"_ .............i i i....".---i--.i-- _-i-.....i i i............................ i-ri.........i.--rl...........,,-.oo2----i-}.....---i--i........!--!--!.......1-l--i.........!---i ............r-!--i.....!-i--i........i--i-i.....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

c_

(e) Group 5.

Figure 7. Continued.

43

Run R_. M q, psf

o 45 40.24 x 106 0.699 2423n 47 40,25 .700 24280 49 40.26 .700 2429A 51 40.31 .700 2429

95% confidence interval

95% prediction interval

.OO5 $.-LJ-J .....L-4-L-.,......4.-J......_.-L-.i.... L-.LJ_--i--i-J.... L-L-J _ii i E i i i i , _ ] i i _ i i i _ i _ ] _ i _ .....T-I--7--i-q-i ......i--i-i -i--i-? .....t-i--i-"--t--i-i .......i--i-i .....i--i-i .....*-_-_.....

'-i-i--i.:-1-i-i"-i -_-P--:I---T--_-_--; -!--$--I--:'7::7-:_--:--T-_'::_-=.--4...._.._._--1--1--1---r--I--I--i '--i_- --ii/_I---in -1 ...... _........._,-:"_--- -TT_r.t- i l i

ACN 0 i i .... ' -....i-i-i--T--H-i-i......._--=_-:_--:-J-Qi--i-_-7-J-_¢-_7-i-4-2 ..... Goal.....i-q--.i.......i--H........_---_---_......H-4......J--'--J......H-i--i i i i i i

.oo5--.--4--_........r-m .........r-T-_.......i--i-i-- , ,-, -i--i-i-- ,-4 -3 -2 -1 0 1 2 3 4 T

ix, deg

4 x 10-4

ACA 0 i i i ! _4 _-l--k-',z- -_-C _- -.L_-c'ff:_i_-i-_ £ _ i i i i Goal........-----.]--.-_---,--.s........_---,--_..... ---.,---;--.]-..-.-;.----;---.._.....L-if---"--......._--_---........_-_--_....... - .......4-_.--.'.-._____-.......-___..............._.,,........4----........_-4---......L_'_.i. T_.LLJ........I i J -J--J..... J--i---i....l L___ l.._..i.,i i i ii

-4 i i i i I I ill I , , it "i ........i-i-i ........7-7--7 -T-fi--

-.2 -.1 0 .1 .2 .3 .4 .5 .6CN

.oo= ,,, iii ill i,i ,i, ii,............. _'......._ _.........................................---"-_......li--i ............ili ......... ,I,"---_--_..... _----_......*-*-- .........i--i-i....... 4-.....i.--..i..... i---_.--.......----i---i.....i i i _-_= _-=b-_--'-- ........................ : : : --4,--4--.4 ....

ACm 0 o' __ _--_= _ !..... _-__-__L._- -_;.--:,-._z.,u-:_-_.__ i Goal_ -i-i--i ..........i-i-i ........._----__......i--i--i.........l-i-i .......i---_---..i.....-.-.----.. .....

-i-i--i......'--"--"---[XC-_-I,,, ......i----i......-------.........,'-.--'--_,,.....i.--.-i.---.i......._:-.-_.--._....

-.ooz-.--i--i,.........i--i--!......... i-1-i.......--"_!..............------",,,.....i--i--i..........i--i-i....T-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(f) Group6.

Figure7. Continued.

44

Run R_ M q, psf

o 157 40.20 x 106 0.700 2424[] 159 40.16 .700 24230 161 40.22 .702 2431

95% confidenceinterval

95% predictioninterval

.005 _ _ _ , , , _ _ _ $: : : __..=_i i ; ; ; ; i _ i i i ] i i i•--4--,-_---.{ ---1--_--_--4 ...... 4----4---4 ....... 4--4.--4 .--4---4--4 .........7--7--7--']"_--7"-7' -]-_--T , ..... i i i 1 i i i I I i

Ty-]71Y-IL-Z_-::(7_7TI_TZ:]-yL-_7,.:yIi-r-_--r-yi-',:-q(--r-r-r-,-i--i-i

'-i'-'1-i--"-'.h-i'-'!--'1--i--i-'i"_,ACN 0 --i--i--!- _--i-i--t-i--!--t- = = #4zz_ D--_-+-4-_ i __j__L_,, ,'.... Goal-_-q--_--f-t-i--T-l-i--i--i--I-T-r-i-_--i--iq'-i--i--T--_--i'-_--i."--i--i........i--'i--'1--T--"i-_'--'1 .... "fi'--'l;--'i.........i--i--'i--1--i--t---P-1--i--t--'i--1--'i--i--i--1"--'t---{--i ........_--4--4...... 4-~4---.4....... 4"--4..--4...... !--4---.4....... i--4--.-i........,.'--4.--4....... 4.......... 4---4.--J.....

-.005 i ! ! ! i i ! ! ! i i ! ! i ! i _ i _ _

-4 -3 -2 -1 0 1 2 3 4 T

oq deg

4xlO -4i i i i i i i i i i iE l i ! i ! i i i i i i I ! i i i i _ i i / _ i"-i--i--i--1-i ..... i--1--i ...... i--1-i-i--i ......-i-i--i--1"-i--"i--i--1----i-i'-1"-i--i--i ...., _ _ _ _ , _ _ _ _ _ , . _ _ ._,._,__,_......_,__,.... _ _ _--i-"---T'-'Pq--'i--i"--'t--"F--i--'r--"--q---F-i--"--1--q -'] , ..... -'T--T--F'q ..... _,

i i i i i i !__i i I i ! i i i _ i _ _ i "ACA 0 -!--i--i--1--T'q--!--ri':;ai ;;i-i=5q_t=-i__ - :{=-i_74.:....... _, _ :4_......_ i ! !_ ' ' Goal! i ' , i , i i i--_4 _--i----_--_4_._-:'--_2___ i i .-J--L--L-.

------_........_--_.....---r-_......_-_--,.......i--F-I.....I--F-F-__L__,__.I.... ''f i _ ' _ i i I _ J _ I _ -.--:---:--_ ....... _---_.--,,_--. '-'-:--i--":---' --.-;---_---_ .... T

.................. -i--i--7..... i--7--'].......Y-'i--q--"-4 ] i i- --!--i--!,i i......................-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.002 • _ _ _ _ _ _ ' ii i t i i _ i i i _ i i i i

, , , , , , l--r-r-r-l--r-'--:,, , , , , :::::::::::::::::::::::::::::::::::::::"-T'-7--I--T'-'F-q'--I ...... i---i--7--1"--'i--'i--'] ....... 7"-"--'1" _ _ _ _ ,

--4----F--r-+--4_,,, ...........I,,I4-_,,,.4N-4="-4=_4__, ,_, ;-_=€--__._-1--!_.......-'--#--_i i i i _ i i i ! ! _k...': " [Zd : : : : ; ; :

ACre 0--4---..'-.-4.... a---a--l-,-+-_4_.,=_:-4.:_ ,.._.=.._--L-J .........f-L-L-' Goali i i i i i i _ _ i i i i i I i I

-i--,--q.....---i--q......,--,--4_1_-i-_......i--i--i-1-i-J_-1--_--,--i-4--i--"-----T-.002 ....i---i--'i .... --i"--.:."-'l........ i---i--] ..... "'+i--q--'i..... ]-'---'i ........ r'-'i--'i .........---'i--'( ..... ---'Y-- ....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(g) Group7.

Figure 7. Concluded.

45

Run R_ M q, psf

o 113 4.44x 106 0.799 1235[] 117 4.45 .801 1239<> 121 4.44 .801 1239

95% confidence interval

.... 95% prediction interval

$+++ +++ +++ +++ +ii +++ +++.005 --I- --t..... I..... r--T-* --*--'r--'r +_'............................ : + ; + ; ; , i :

...... --T--T--i--T--T--T--r--T--r--T--r-T --T++_ --T--I+--T"-]--T--F--I+-"I'-'I'--T"-T--I--T--T--'[ -"T--I"--I". : ; ; . : : + + ......... : : :

,,_i+ o-T-T-T:--I:-T:T-T-t_-!,_!-+_-!_+--+_-+-_-_-:_+_-+-+-++++I+++_+__++__++++_+_+_._+_++-+-+_+,,:+--+:+--+++---++=++-.=+:,=+-+=+-+-+_+-+-+-+.........ooo,:z2-- 2-_2--_---

+--+-+-+..... P-+-+.... +---[---p.......+---+---+.......f--t--+...... t--t--i...... ;.+-+-+..... +--+--+....

-.oosi--,+-t-t....t-+-f--T--+-P.......+-t--f......f--f--+......t--t--t.....f--f--t--.f--+--t--4 -3 -2 -1 0 1 2 3 4 T

CO,deg

4 x 10-4i i i i i ,_ i i i i i _ _ i i i i

-i---}......+;--i---i----_-=_.......i=-_-q-=-pi=-_-i.......!-=-__- +_ ,+++I++_-_++ + +_++_+++!-lDi-+:-+--r-_....7+--F-F- ,I,--------4--- pm_ +_.=.+...... + m....+._L++ + + + _+ +_ + ++ r+<_+_+b++ _-r-F-ACD 0 + j + + + ! .... +.,_ + + , Goal

_-.---+...... i io! i i i _ i i ! vi'i i..... ....+_q_+_+++-+?-,-,....-r-• -a--B-]7+LT]ZIiT.I.......L.....L....+.._.......L....L....i........=_.='.4.=-4 --..".-F-+--q-+--i- =_=_- --+ + +

•F $ 4.- .l+--+!+--.

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002 + + + i + + i + + + I+ I....b-F-H+-+-F-F-+-+-H-F-+-FF-..........:--+--+........F-+--P......,--+--+....L-.+-.+..........:"--+--:"-.....+-+"--+--++-+":-+_:_=_4 =_=_.=r_.--_._.=.t=.._=.F_=.€:-.i-!-+.I.i I i i i i il_.... l--+--l ..... i"--'p-r_+'+""__ '+'--"-- _ ....... "A"........ +'-"_ ........ _F10r 'r'_--'_ m+'--'i--i .....' + + ' ' + + -"+ +,--,_ + + + '+-'+ +""-'O_,m"+ + + GoalACm 0 i i i i a_i {',7.,ii .+ +14--" + J- + _. ^_ _ +.+'+ _ + +

.....bt-t .......}__+___.+.__+..._+.+__+.+-++¢,+;>...........,++_.........v.++++++<>.........-__+.._++++++++__-._+_.+ + + + + + + + + :q=+_++ +..... _=P4.+ +......_+__+, +..... -, ++=:++ :-+--'----+ -'r

-.002 --T-T-I......+-T-P.... t--i...........T-Ti........F-T--T---.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(a) Group 8.

Figure8. Statisticalresultsof CL, CD, and Cm short-termrepeatdata acquiredin air mode.

46

Run R_ M q, psf

o 124 4.43 x 106 0.800 1237O 128 4.45 .800 1236O 133 4._ .800 1235

95% confidenceinterv_.... 95% pre_cfion intervfl

4 x 10-4I i i I i i I i i I i i I i i i i I i i i i i I

..................".........' ......................................ACD 0 I I i I i i i !-: :_: :_ : : _ ' '_ _ ,_: o [. _) Goal.__,_-,.t___L_-............,.__,_.__L........_...._............,_._._:,____.i I i i I I _ _ _-_---r ..... "T........... _ ........_-__L_-.......L_!__-__J.......-_- ....... -__-...... !_-._i ..... L._ _.

-V-T--T--T-T-T-- i, _ I _ , I , , i ........-4-hi--t---t--t--t.....---_........

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002i i i i i _ i i __ --+--i--4.-- .6--1--4--- .6--1-.6-- .6--_.6--

--'_--"--'i'--__ , "-+--'--#ii ! [...... F...... !"...... +--#........ F t--+ ..................._ F i ii'--+"-_-----"--!--:¢-_-_-i'_i i _ *......... +..... ,--,--,--,--,--,--, --t-----t--t----t--_---.t.--.-_---_-. +--+--+..... ---.i_.!....._----__+._____-..... . _ _ , .L ._........_........L....L...._................._....... _ 01...._= ....

! i ! ! i i i il_l i_i iEil i i [] i i i i iACre 0--.}.--_-.i .... i--i--i-i _d i ' ' ' _ _ i _ _ i i Goal.-----.---._.-..._: :_,_ :...__._..,................L....._........_.... _...._.....___._-........i i i ._'___.'.__L_i i.P-" i i i >i !@ i i L i ) ....]._

i il l il .....F-T-T.....i-"T---.....T-T-i......i-_-9_i-T"-_ .....i--i '!-" T"--'_'--_--_ ...... _-""--'i--'t --t--_--'--T--"--t--_ ....... ?........ "...... I-A--_" --_ ....... t---.002 ._---_---- --r---r---_-_--r---r-r- _ -z_-1- i

-.2 -.1 0 .1 .2 .3 .4 .5 .6

Ct.

(b) Group 9.

Figure 8. Continued.

47

Run R_. M q, psf

o 136 4.44x 106 0.800 1237[] 140 4.47 .800 1236<> 144 4.45 .800 1237

95% confidence interval

95% prediction interval

.005 i _ i _ _ i i _ ! i ! i ! ! ! ! ! ....... ,1,

i ii--iiii i '_ Tii i_i_iil....T--T--T.....i--'i--i---+ .........................7-_-t---7- -.-_4-- .... • • -:--_--:--,--,--,-"--,--,-,--.... -_--T-_"-T_ f!--!_!--FT-_,jt__Vi_ 7T--T--TGoal

•_cL o +++-r-++_--_- "-' '......... _y.__.............. .__+__..__.._.__.;_._____..-_,__._,_•--*-: :. --.r-,-,.-,.- -...{--_4---4;-iililIi--

--f--t--_.......bi--i........t--F-+....-.005 -i--i---r.........F---T..... t---r-_........_--t--t........f--t-f......f-f--i--

-4 -3 -2 -1 0 1 2 3 4 "T

IX,deg

4x 10 -4

i i ] i : i T i _" i _'' i i_i' i i_ '^'_ , _i Goal

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002

i _ i i i _ i i i |_ i I i i i i I i i _ I i i i i

--i--+--i......i.--i..--i--]-.-.i--.i.--_..........i-.i.--i......i-4--i.......i-....i--!.......i.-.!--i......++-+--....H-i......i-+-+.....+-H....._--i.--+--+--H-_-i--+-+-I.-H-.i-.t:::+--+-..i.... 4.

iiiiiiiiiiiiiiiiiiii!-,--!--,.....+-+--.....-,......._.oo2 --bi--i.......t-i--t......t--t-1.........i--t--t....._---r-r.....r--t--,---.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(c) Group10.

Figure 8. Continued.

48

Run R_ M q, psf

o 68 2.36x 106 0.800 658[3 72 2.38 .800 662<> 76 2.38 .800 662

95% confidenceinterval.... 95% predictioninterval

$.005 __,__,_,__,.__,__.,__, i i i' i ' i _ _ _ : i _ ! ! i..... ---'9...... i ....... + " --.--*--':" .... +--'+--+--*--.b " : - ............

--f-H-r-H--+--_4=-._....4--i--_--_-4--_--,--4--_-_....._--'_ --b-+-!....._--+--7-+-w--.r--_--t--t--t ..... t"-t--.t_ o_:_:_ -----'--+--'--

---i---T--i:::[:i-T--i'-_-"__-!_ _"--T-,_..... T--_I_, -_;_ Goal

-.oo5 -!--¢--._--:--H--_......i--_--i......t--i--;---4 -3 -2 -1 0 1 2 3 4 T

a, deg

4 x 10-4] i i ] _ i i _ i i i i i i i i i

...."--'--'--]_--J'--t.......... _--'i'--T"--"-""............. b--'- $...... ,__,__,__.,__.,_!.__,.__.___.T__.__.[_-._..-._..±..... -----J ...... '----'---_-- "_ACD 0 i i i .............. ./, d-, _' ' ' " ' ' : ' '_ ; _ _ X .......... _- "'_ _ Goal

....i--i-i...._-.i--.i......i_--T-.-.i.:-_ _--_--- i.-- I"-4 i i i i

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002 i _ i i i i i i i....i.__i...... _,..... i ............. I ' ' '

ACre 0 i__2__ _:__:2___ _2__.j_,._z__ _._ - i-- .:_ . Goal........T-rT....T-T-,.........................r-T--,........-.002

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(d) Group 11.

Figure 8. Continued.

49

Run RF M q, psf

o 79 2.38 x 106 0.800 661[] 83 2.37 .800 6600 87 2.38 .800 662

95% confidence interval

95% prediction interval

,1,.005 .-L-i-_ .... +-+-.: ....................... ,--,--,-- -,--,--, ..... ,_.__..._...._.__,__._

' ' ' i i i i i i _ i i i _ i

•--_-_-.+..-,-_-_-_-,--,--,--,-,--,--,--r-T--T.................__ __..... ..-,_._.a=____.=_-=4-2=-_--==4-:-_-._.:-

--+-+-.-,-4-i--4-_-!_2--t_,!:-F_=-_D::_ _ ....... .--L_--L-L-f- Goal

-T--r-w,-t-t--i -.-=_"_........r-T--!.......r-::--i.........r=i--i----_-=Y-?-'0,--t--i--i"----'----'--'--'----'----'--'' --T----T----T'--I--T----!"----T ....... F~'T'--T----'i'----'i----T--i ..... i-i--1--*--1-T--1

-.005 -T-T--T.... T--T-T.....T-[--T..... F-T-I.......F-T-T.... T-T-T......F-T--T......I--T-T....-4 -3 -2 -1 0 1 2 3 4 -_

ct, deg

4x 10-4i i i i i i _ i i i

'-+-_---.....F-+'--+.... --'i--+.....+-----+.... !-----._....F--i--_........___,s..__..... :.__:_____....t-.t--i-t--t-+....' .... :_-:)_-_:_:_:.L_-:_-:_+-.--i-t-t--,-f_-+-- +-_-_---.--.,--a.i-:ri--_-+._-_-.!--"_

ACD 0 _ _ _ I i i _ _'--__"_ _ i_! i 7":_1 w"_ _;_._ i _ Goal-i----_ .... t--,+--_-- -__--_0--.----.-----_--" _-I.-._--er._o--_.-._.... T__L____.....--._---_--_._.._.-__._--:=._-.::--.:=-4:::_=._-5.._-,-_--_-._i.......--+--+--+ ...... +--+--_ ...... +--+--+ ........ +--_ ........ _.... +............ *--._-.-._--4.---_ ............

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.O02

=Ti-i-f-ii-ft-i-i-r:i...... Lii L.......i-ii-i-ri..........i-i............,-_,_,......,_.-...........................,............................,-2_LLL.Li__.i.1.

ACre 0 , _ _ : : : _,,_ ___;___L____&i.4____________.____;_.U___i- Goal_-__.., .___ i ; i .__=.;.=_: --._--_.-.-._...... _.--+--._..... __..._., ........._..--._...-._.... . . .i i i ------L-.-........................

H ::::::::_---i--i--i.......i----i-.--i........_--_--._....--¢---- ,,, .....t--!--r....... t--T-T......i--]--i.....]--+--k--I_002

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(e) Group 12.

Figure 8. Continued.

50

Run R_ M q, psf

O 90 2.37 x 106 0.800 660[] 94 2.37 .801 660O 98 2.38 .801 663

95% confidence interval

.... 95% prediction interval

.005 J-J J ! [ i i i i i i i i i i i i i i _ i i i i i

--+--+--+ .... +--+--_ ....... .--+--. ---_----L--4- .... _---4.--_- ...... *--4---4 --4---4---4. .... g--4---4---

d-M ....,--,--,--,--,--,-,--.--,-.,--,--,-,--,-,--,--,--,--,--.--,--,-,__,__,_,_,__

ACL 0 "" ! Ik¢ _ ...... 5or _ _1 i i .-t _.. _F.,- ! !_ _ _ • ! i _ i_ i_, _ _ _ ..... w _,_ _ i i Goal---+--+--?.... t--,+--+......._ _--f--,-.-+--_-i--+-o-.-+.!_.-_s..... +--_ -.+:-+-+---i-M......M-i......"-i-f....f-M....M--r.....f-_--f.....+'-_--i.... Md-

-.oo5-T--T--T......!--r-T.....t--[--!..... T--F-I......f--f--i.......i--t--!.......!--f--i......i--f-i--4 -3 -2 -1 0 1 2 3 4

ix, deg

4 x 10-4.....L&_i_.* J J i ii :'' ' : _ ,'

ill --T--T--T.... T--i--T..... i-T--i.....--+--r..... ,--t-t.....t--t-.-

--tti--[--T- '4--'..... .....T--T--r--................. _ ..... _T '_"-f_-f,=, ..... _"i_ .....i--t--i....ACD o ''' --+--'-_-o=-_d-+-, , , .-.&.---i-.-,,, .-----_---_.....T--.-._--

--]--J--J-i _ I -----i-i-- i i i--:-: ,,, -f--i-f- ' _'--_---i---.r...... --------u-i--i--T-4 ,,, -_--+-_.....Y-f-T......._--i---......i-T--T.....T--T--f.....T-TI........i--i--f---.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

f i i ! ! ! ! ! i _ _ E i I r I i

............. i ............... P--T -- i--'l --"-"'i'-- _ --T--T-- "i" .......................................

.................. i i i i i i i i ii] L..,-- !i .-'--M-.....!.-.r--i--...'--!--_......t--t--._....._----..... t--_--:..-

Ar_.m o '-€.....f ....t--f_ ..... ,........ :"_! IT TTT Goal_! +....... © !.2:,'-" i I J--!--f--f--i _c< ; ,-_, , ,.................. =._._=__.= ----,-----

.__+__+__.___. l l l i i i . i i I

-tn-_--_i_T __:, , ,__i i I.............................- i i T--T-r--Ii i , ,--T,--!-----?.......i--i-i ......_-----',, ,......T--T--T-----?---.002 T--T--r-- i _ i _ T-I .........I"--T--'I................. #-----'_..... ?.--?--?--

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

(f) Group 13.

Figure 8. Concluded.

51

Run R_ M q, psf

o 113 4.44 x 106 0.799 1235[] 117 4.45 .801 1239<> 121 4.44 .801 1239

95% confidence interval

95% prediction interval

$•005 i i i i ! i i i i i i i .........

-Z=z:T_=z-=-':-z.z__:::,:::z-_z:z:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::, . , , . , ] . _ , , , . . , . . . . ...-.£--z--..i......:

ACN 0 .... i .................. -- ' '

--,.--,,-,.--,.--,--,......:_-H4-.i-i-:!:::::::::::::::::::::::::::::::::r::::z: , , ,-4 -3 -2 -1 0 1 2 3 4 m

_, deg

.002 i i i i i i _ i i i i i " i i ...... i i i

l I ! i td i^i i ri i xo _ i -',Dm___q ! i l

Cr. Oji i ..... GoalZZ Z- ZZ ZZ]"-'-" ! i i < ......................... i"-I!--! '

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(a) Group 8.

Fibre 9. SmtisficNresultsof CN, CA, and Cm sho_-term repeat damacqu_ed in mrmode.

52

Run R_ M q, psf

O 124 4.43 X 106 0.800 1237t3 128 4.45 .800 1236

133 4.44 .800 123595% confidenceinterval

95%prediction interval

.005 ,1,..........].........i..................,............._........................I........... I-_---,--i-i--i ........i--i--i .......i--i-t ......¢--P--i.......i-i-1 ......i--i--i ........i-1-i --_--..+--.....+--+-..t-+-+--_.......+-.+=_.=-+-.-+-_,_--+----_-_.-.. _-+_+_......LJ--L-i _ _ + _ _ + + i i i i i i i i i _..+ i iF i i !--i--I--1--1--1"--'I"--'I--"1"--1"--'I"_ _-.-!----'_l'l. ---t--_..--_---i.--!--.':--..t ..... 'i-'t_ "-'i i'-'i

"-i'-'i--7 ....... 1"-"I"1"-"1--'I--1":.z'_ = -- +,,---,,4----,.i_......... .............. ....-.oo i ...... +.......+.......i-+i---4 -3 -2 -1 0 1 2 3 4 "_

e_,deg

4x10 -4" i t ' ! ! + + + i t + i i i [ " i _ i i " ' "

--i--"---'--'1--i ........ i....... 1--1.........................]_ci_---ii ]i[i ]_i , ,".---i........... i....... - ....... q---i--."...... "------.

ACA 0 Goal.._.,.................. + , _ ,_ _ + , ,.,_.+.__+! i i + + J ! ! ! I + i--l.....T-T-i.........i-i-i .........i--l-+......i-rT-

-4-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

J J l i i i l i _--4--_4- .4-i,-.4 -4-P4- 4-_4- .4-j---i........::'--"i--l---i---i--'i........i........................................ :[--............... -....t-----..t ....i----- ........t--t--_.---_........i........-........-................._.+IB-.---.............-._ ....

! i i i _ i i , : : i : i "1_ i i , • ,....+-----+.......-......_1.......-...._ +I-+.................+_1............................o_,=__ACre 0 ........... _ .... + + _ + ' _ + + Gdal

+++ ._.!.....i.._..!.... i i0 i! i?j-)i ! ! i++ !i+ -.-_-.--i

-.2 -.1 0 .1 .2 .3 .4 .5 .6

cN

(b) Group 9.

Figure 9. Continued.

53

Run R_. M q, psf

o 136 4.44 x 106 0.800 1237[] 140 4.47 .800 1236<> 144 4.45 .800 1237

95% confidence interval

95% prediction interval

.005 $, , , , , , 7--7-7....7-7--7........'-"--_-- i 12i-- ii -i iiiiIi ii ] i

_.._._i __L.__.I i i E.... _-....i--4.el-'-_7 m_i:s]E_::_:._--_--_-_.....7--_--_-_-!-_--!_- ....4--_ACN 0 _ _ _ _ i i ,,-........ _-" u i _zk[ _ i ! Goal

•-i--i--i--,--i--i---J _-i--i--t ,---i.-i--'<i.... _0, ..j., , , _,_........ -i......... -b--.-i-._r ----i---;--._---_ ,--d-.-€ -+-.+--_--...-_--_......_--r-r-]_- ..--t-- ,-t_- , ........_ _ z _ i i , i i i _ i i '7-i--i-"--7--i-i.........i--i--i

-.005 -i--!--_-- _ _ i i _ _ i i i-4 -3 -2 -1 0 1 2 3 4 T

(x, deg

4xl -4

--7--t-i.......I--P-I.......,--,-,--,-,-,--,.......i-i--i---i-P--,........i-i---......i-i-i'-1--'I-'i ..... 1--1--'_ ..... i--1"-'i .... 1--'i-"'i ........ 1--i---i ........ i"-'i--i ....... 1---l--'i ..... i---i--'i ,1,...._--.---......._----!--_-_-_.....i--._ -.t.--i_!...._.._.i.-_;-........!-a....•-_--i--, .......i--i--_..... . , , . '._7-T--'-'_7""_-7_----l--"--72---7-'-_.-L;""_TgS-'"-__-"[_>" .....-.i--+--......i-d.... F-----.-_--..F-._........i--_.--.._--._4.-._--_----_'.--.....T

I J........ m_.k_.m_ l L_J..... j J I __J__J...... j l I .J._.l _ _ ! !

-4 J I I i J J _ J i J J I J i J I { i _ _ J i i i-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

i i i i i i i i _ i i i ' --..!--.i.--.J.......[-i-- ' __.002 ][-i]]_-i]-]-_-.][]_-J-J.-_-]J]i]]__-i[j-i-].]iJ_-[i]]_-i]]_-] ' ' ' ; : :-'-J-"i ........_----- i--"j-'-"l"-d'---J'--"--"l'--'::....... "

ACm 0 " "''_! "T_--'_ ----@_"'J".... _._. _._'_ '--'_i ..... Goal....,-.,-..,........_--..,.--.._......;-.-_-._-.-._-E__4S._. _ _' i:'ic__i_..._.._.....• . . "_---i'-- ......--N---i........--d-d.........i--N.....N--.-.......i.--..i---.i.........!.--i---i......_-----_........_.---!--.d.....T•--_--.L-._............. ..... L-_.---!- ....... .........' .............-.oo= i--i-i ,,,--i----i i--i--ii-l-i N--i......i-[-i....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(e) Group 10.

Figure 9. Continued.

54

I Run RF

0 68 2.36 X lo6 0.800 658 0 72 2.38 .800 662 0 76 2.38 300 662 - 95% confidence interval --- - 95% prediction interval

Goal

7-

4, Goal

T

4,

Goal

7-

(d) Group 11.

Figure 9. Continued.

Run RF M q, psf

o 79 2.38 x 106 0.800 661[] 83 2.37 .800 660<> 87 2.38 .800 662

95% confidence interval

.... 95% prediction interval

$

--I--I--'[ ...... I"--'[--I"-- i _ 7---I-- 7---r- 7"-- "!---_ 7"- - 7"--_ 7"- --. --(--[e_I '-1--'i--"i-'--"-"--,-,--,--,......._-__-Tg_!-!_- ......!-!=!_;_;_;_-(-(-(

ACN 0-i--_'--i--I-'i i i "_" ............. _'_; '-'i-_ i | )! _ _ Goal--_-_---H....!--+-_-_---__-T-T-_.....-_-4--i_-_--4--`+_-_--_-_--_--_t--]._-_--_+---i_-+-+_-_!_---+--_._-_--_--_i--_+_--_-_-_!_-_--_-_+--_.....

-.005-4 -3 -2 -1 0 1 2 3 4 "_

(Z,deg

4x 10--4! i _ ! ! ! _ ! ! i _ _ ! ! ! i _ __, ! ! ! --r_-.[_..i.....

-_-4--(.......4-!--4........6__ '" " _ *ACA 0 ?5_ Goal, _ _./',. . ............... ...................... .....-?.----+-m---'--.(--!.........-_..4.:..i-...._.-_-_ ......... -_-_........._--_--.i........_.____._..........i.__.__...........-...... -_-_-_.-_. _-i- --_..................... .J---[.-.4......

-4 ) (( ()) ((( ((( )(( i !! ) ( ) ( ) (-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.002 , _ _ _ _ _ , _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

iii iiilii iii iiimiii ii•--i--_--.........---_--.,......i--.-i---.i.........._.--.._--._-,.--i----.i-...-i........._--_--._........i...-.-i----i...........i-.-._-..i......-......................,............................[....................................................................[ .I.: : , -T-i--T-r-_-F--'__" _-=_ -t'_^__.£,_ _T _ --'.-7--_! GoalACm o -f-i-+ ' ' ' ' ' ' _ ' ' ' ' ' -'--'--'..........'--_-''--'--'-'......

.......... F"'i--i--Z-]_-ZZ--Z]Z-..,--:--i.....'---_--_........_--!-_......... i---[............,-------! ....

-.002 ' ' ' ' ' ' ' ' ' .....i"-"i--'i.......-"-'_--"........_-r-- ............i-!-! ......-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(e) Group 12.

Figure 9. Continued.

56

Run R_ M q, psf

o 90 2.37 x 106 0.800 660

I [] 94 2.37 .801 660

O 98 2.38 .801 66395% confidence interval

.... 95% prediction interval

-44xi 1 + l l i 1 i i i f l i I ] i t 1 i + ! _ i i

:i-:' ' + ' ' + ' ' + ' ' ' ....................=.{=.=._-=.+_d_-_..L..i__.i__,1,

ACA 0 i......i i ' _ + ui +_-_...L._L_.I<'+..............._...._.j................_..+__.+_...,.t+__.-i t i_.,.... Goal.....i--i---.+............ t_- .......................... -i-g_gi_-....++_u._.L.+.........L..i._.+__-+-_-+e..-_.r_._.-..r_-+._.i+ +,., ,._! + + _L_L_+..... i i i + i i , , ,.... _.L.i__.i.... + i i.....,.._..,__..+..........,._..,_..+.........l._..J.._..!.................. i-"i"-'i....-4 ....i--1--l- i I I I I i i i I i ! l l I I l i I

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.002 i i i l " " i i i i ' " ' i i i i i i i ....L_J__J__.... i._.....i.._.i ........... I.__.I.....i ............ I.._.+l ....... +1,.....I.._..i ......... i ....... 1.......... +1.._ 7.__..I ...............

........ I .....l_d_..l.... ,1,, , 1 .... . , i ...... A_i__J__, ..,--.,--_..........-,5_=._.-.,, _........................._, '=__=?_=_ +_il I l / I i _ m : m+ i _'_ l : _ : Goal

ACm 0 ......i---+--.--I........._-._=-_:= =._._o_-:=.+._.=+==-+._=-.==+_._-....I--+i---i.i i I i ! __j7'I" --_ i i I _ t i i i t

...... I,+--.L.--.J .......il .d.-_..i.++ d ....... &.--.J .......... I-..I .......... i ............ I.......1..--..I ........... i-....! .......... !----..i.._.i..+, ,, +,-,............... _._ i i i I i i ....i__L_.I.... T.....4.--.._.--..l....... 4--4 ........ !..........I............................ i ..........i -'u--'_ ..........t.._.___.._....

-.002 i i ! I i I I I I + _ _ i _ + i I I I I i , I I I

-.2 -.1 0 .1 .2 .3 .4 .5 .6

(f) Group 13.

Figure 9. Concluded.

57

Configuration R_ M q, psf Group

o WBMNTH = -1 + Seall 40.15 x 106 0.800 2660 2m WBMNTH = -1 + Seal3 40.14 .800 2659 3

95% confidence interval

95% prediction interval

4x 10-4i i i _ _ i : ' : i i i i i i

-+--+--+--]-i-----_.....+--+-k-i-_--+--_-+-,-_....:::::::::::::::::::::::::::::::......2-i-L ,,, 4.J i ! ! !rd'l_ €'.! !.°Et! !.=.! IB ! !:'-_Tl_"f'h:_-_--i'--f-"i GoalACD 0 _...._ .... --: : ...... _ ....

--'--4.-_---I ' ' _ _ _ "_ _ _ _ _ I i-t_. il:lU _ i i i

' ' ' t .......j ,,-Cf-_'t-c""r-_"-_,, , , , ,'-f<'-1--1"-"'"r'm'-r'ti-r-'_,, i _ i i , i , ,.........., i,i-i-- ---f--...................................i-t --r.........[-i-- ......r-!--t ......i--i---.... ---t--t..... t--r--i----t--t-1.......i---i--i....u----_.......f--f-_.......i--i--_......u-u-f-----u-_--L.u-.u--4

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

.002

__,__-__L__,__i_.]_,, .... ]...I;!_li iOi _ i i /i_ i__u_ i i i_!_ !!! i ii _T-iu;....._-T--[_i--l-'d-[--_i......1--[-i_,..'--_-;£'--_--'--+----.-i................i-.--_--..-.-_-.l----...*--.i__-__.___f.... -__.i._.i6_._.b..i....f.... _ _ _ c _ :a '_-r---'_--_-e----r......o......_" --_.........T--_.....''"1 .... o..... o ,,, --f--.002 ....i--i--. ..... --i-_:]-_ST__"- -'€2-_2 :_-_-_2 Zi__2 S._:ts__ "--i-J .....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CL

Figure 10. Statistical results of CL, CD, and Cm near-term repeat data acquired in cryogenic mode.

58

Configuration R_ M q, psf Group

o WBMNTH = -1 + Seall 40.15 x 106 0.800 2660 2[] WBMNTH = -1 + Seal3 40.14 .800 2659 3

95% confidence interval

95%prediction interval

.005 $i J J _ii_ .i., i __.__i_.!_j ._.i__-L_J._j_-J---! .-_J__4..i........J--J--J

..-4-----q--_.L_.__-_.... 4-_...'_t-_.,.,.i-t_.-q_..'._...,.qO. '.+-,.._._.---.._,=[.L.[._L_'___

ACN 0 _ [ i ) _ ! _ '.-_a _t4 : _ _ .'.' '.,,'_ ,_ ot,.'-7_ i / i : Goal---_.--4.--.l.--..i--i..-.i......._4--4-.._..--., _............4.--4-.._..-__.--.4._--4 .........--)L-L.2........J-.L-.4-.I.--._.-__U.L.I_.&.d=L-,..LJ-L...I=L r'I_..L.... "-_=._--m._--4---i........i-i-i .... i-i-i--I-'i-i--iCq-i--!-4 -i--4--i-q--4-4--4........[-_-"i--]-4-4--i

-.005 i i i-- i I ! i i i ' i i i.... i-7-i ..... id--i--+-1--i..... .......! '-!--]q-4 -3 -2 -1 0 1 2 3 4

Ct,deg

4 X 10--4i i i i i i i i i i i i i i i i i i i i i i _ i

-----i--11 .-1---i-.-1..... :..--1.......... [-1-.i-- _-1-q-q-_ .....__I--,--i ....... i--i---i .........i--i-ii!l i12 iii !ii_ 4,

ACA 0 , , _A_ ___-.._.i i i i 3_ : i i_: !-i ' _ ! i i_ i_.._ _ i i i Goal::::::::::::::::::::::r_:i--:L--:"_::"==_:-_-_-'....-4--4--4:r-:4. Fq..........i--i---i.....--f-I I I i _ l l I ) i _ i [ i l

--4--4---, ..... ---.4-----. i , , --i--i--i ............. -....•.4 i_ ,,, i-i-i .......i--i-i......-------- _,--i--i-i ....-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

.....--_ ............... J--J--4......................... ' .-.4-

• ,, i . i'.°i "i'._ i ...........*, :--:!i .....-_-"i=<-"--'-"'_"-_--,_ii_........_-"-"_,i_............i_i"'_-".....-'_-i--i----i GoalACm 0 i i i _ _ _ i i i i i i , _ i ) i i _ ....., '

--......,-_-_-_,, , ,-,-,--_,-,,-_,,,-,-,---,,, ,, , _,, , , ,_.................,-,,-,--_:_--i-j-J,_,--i ............ 7-7--76 -_7 ........_"-7 .......]-'O-T-7.......i_i ']8 T-.002 ------ --]--_-(j--1---i-----i--"-i-----i--"-!---i---..... -el--i---i_.i-_-o][i-._---|-_--

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

Figure 11. Statistical results of CN, CA, and Cm near-term repeat data acquired in cryogenic mode.

59

Full-scale load+ 0.5% (quoted accuracy)

+0.3%+0.1%Repeatability goal

14 × 10-4.035 ............i......................i........................i.......... •..........i ...........i.............i .007 ...........i........................i......................i..........

iiiiiiiiiiiiiiiiiiiiiii..........._........................'............. '-ii...........030 ......................i_...............................................__....................... :2252552212222221222:i22522:::1:::a::::::::::

_))))}))?)))))37)37}})?}}}733))))?))?))?))_

....................025 i?iiiiii:,:{iiiiiii{ 10 ...........!j........::::::::::::::::::::::::::::::::::::::::::::::::.005 ..t...i.!...........222 :::::::.i::::::::::i

.020 ......I!.......... 8 .004 ?ii?i??: T21iX211 i:

-I-ACN +AC A ....,.....i...\....._ZIIIZIIIII"IIIIIIIIIIIIIIZII+ACm 'il _!iii_ _.015...[..... __ 6 i....., i ii................................... .003

.010 2: ::iZk: 4 \i '\x...i..._ .002

•005 2 .....................__..._i.......................i'""x".. !._..._ .001 _ '" _...........i........................i.......

0 1000 2000 3000 0 1000 2000 3000 0 1000 2000 3000

q, psf q, psf q, psf

Figure 12. Balance accuracy bands in coefficient form based on full-scale loads given in table 1; quoted accuracy interms of worst outlying point during calibration is :k-0.5percent of full-scale load.

60

Run R_ M q, psf Tr°F

o 14 39.92x 106 0.800 2660 -249.8[] 16 39.93 .799 2658 -249.9<> 18 39.95 .799 2658 -249.9A 20 39.93 .800 2660 -249.9

22 39.96 .800 2661 -249.928 40.27 .800 2658 -251.1

10

....i------i........_-----_............._-........................F-----L--_........[ !..--..!--I--I--T--!--L-.I.-_-L--

t t i E 1 _ : E

: : , , | ,oFTgrad, 0 i i i i i i _ i i l: _ *_i, :i ', _ ] i '_ 0: i_ i

....----i--._--i..--------i.----.'--i .............._......... _----..,........._......... [._._....... L_Q_.L_

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

D220

..........................- ,__,.........v____E............[S-_.-_

Tba 1,°F -240 -!--!-! ...... !--!-! ..................!-__-i----i_! ! ! !........!--!-!- _!--i_i _i-_-......i-i--i........i+i---+H-": i.....i---_--_.........._--i--i....... i---i---...... i--i--'-_.........i----!--_........------ .......i---i--_..... i---_---i....

-260......' '"-'---!...............i"-i..................................................................................i ,,!"-""-!....-.2 -. 1 0 .1 .2 .3 .4 .5 .6

CN

(a) Group 1.

Figure13. Variationof balancetemperatureand temperaturegradient (front to rear).

61

Run R_ M q, psf Tt,°F

o 44 40.17 x 106 0.800 2662 -250.6[] 46 40.18 .800 2664 -250.6O 48 40.11 .799 2656 -250.6

50 40.12 .799 2656 -250.6

10 i i i i_ __ _ _ i i i i i i ! i ! i i i j ! ! ,i ii, ,....F--F-----I---i---.F--F--I-.--I---V.-F--r--F--t--.i---i-----r--!.

............ ''' ri !!Z iEi

Tgrad ,°F 0 i i i i i _ i i i _i i i i i i _ , i.--_-._-_-+-._-_--_ _--_--_ i _.._-.... ....... _

-10 i _ i[ ! i ii[ O O! ! i !_i -_-i--_O--i-e-f--d--i--_ii i i' ''i _ ............i i-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

-------- ...._ ?---i-_.......__-__!.__L-__.@.i......O-----..aI-.,--.o..---..,O.-.i--i.o---,-i..--i..-i..r--r--;

-260 -'_-i-i ...... i-_--i ..... _--i--i..... i-i--_ .......i--i-_ ......i--i-"i ......._-i--- ..... i-i--_--.2 -.1 0 .1 .2 .3 .4 .5 .6

Cy

(b) Group 2.

Figure 13. Continued.

62

Run R_ M q, psf Tt,°F

o 147 40.12x 106 0.800 2659 -250.5[] 148 40.17 .800 2659 -250.7

149 40.14 .799 2658 -250.6A 150 40.12 .800 2659 -250.5

151 40.16 .800 2661 -250.6D 152 40.14 .800 2659 °250.6

10 ij I i _ i i ............! . i ] [ ] , ] i i I i ! i E _ i I I i ; i.-4---i.-._....,--,-,--...-,-,-_..,__.,..__,.__,_..,........_--v-...i----t--i---i-----1--i--i--i---t--i--------

,,, ili iiil!ii iil i!i iii iiiTgrad,°F 0 I I i _ _ i

---r-r ....io....... 0............i i i-10 _ _ ! _ ! ! i i _ _ ! _ ! i , I , , , i i i i i

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

-220iil i r iii i_i ii i iii iil....m----i ---........ r-"r r.........--:--...... i-----i---r--i--i--i-_----i-----i--i--i---i-.! i i : i t E i i ! _ E i i F i ! i , : ,

.....!.---,_---_---i-.--_------- -'- -1--- -....... -....... :.__L_...'-......_!_ _ oi_ o i_ 2_ii ic_i ...._---.r--i-_-.-.-----_.--t----.--_--.--._.--i---_---i

---f! ! !t...... _ i I_i--i---, ............Iii I_!i!I-.... ]-.-._-t::9.t-.........i i ! l O .... . .oFTba1, -240 __L_L__I..... ,' '= i i i mi i i --i.--.i.--.i.- _ i imi i i i.... i.--b--!......b--b--_.......P-I--i....

-----_--..... i..--._---_.......-.--.-.i........ --..--.-_.........i.-----i........."--b--i-.-260 .----i--_................... _.-----_.......i..--_--i..... • • • ................... i..-..._.-i.... _ i I....i-i--i.......................

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(c) Group 3.

Figure 13. Continued.

63

Run R_ M q, psf Tt,°F

o 156 40.25 x 106 0.801 2666 -250.8D 158 40.21 .801 2662 -250.8O 160 40.14 .799 2656 -250.7A 162 40.23 .800 2661 -250.8

-220 i I i i I i ill ....i..-.-i..--.F-.--.,---.-i..--F-...i..-.-.,---.--i.--.-_.--.i---i--F-F--t--i--_--_

:'-"i i '7....... i i "F.........F--I'-"I...... r--i"--_-........ -.........

-260-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(d) Group4.

Figure 13. Continued.

64

Run R_ M q, psf Tt,°F

o 15 39.89 x 106 0.700 2426 -249.6[] 17 39.90 .700 2426 -249.70 19 39.91 .699 2424 -249.7

21 39.92 .700 2428 -249.723 39.91 .699 2422 -249.829 40.28 .701 2430 -250.9

...._--_-i-r--F-i-.......t......._......t--!---i---I-_-i-l-t-_---..::----+--_----_-._---_i , _ I z / I I • " " / .....

...... - .... ---i--.:L...... i....... D ........_-I_..........L...... i..... -_..__L.C .___3.L__.L.......... .L.........•i i i i i E : r i

-10 , ! , , i , _ ! ! ! ! ! i , - i _ _ , , , i i ,-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

-220 i ! i i i i i i i _ _ _ _ _ _ ...........,--,---,--,--,---,--,--,---,--,............ .... .......i--i--i

Tba 1,°F -240 .--!.----L-..t.--iii ! i ! !,L ......i ib--il_°[-i_- @_--_i--__ , 3i--_- i-_O................_i_b-_, , ,,i i i• ! ! ! ! i i ! ! i ! ! i i i i i _ ;" " '"--r-t--i'--i--i'--i'-----'l'-"t-----'t" ........ t"........... I".........."........ I....................,,, r--'i"'--i........ r--r ...... i'--r'--'r"" "--_--_"--.."- ......... t--i"--i- ...... i"-"-""_ ...... _'--i"--i .....

.... ------._ ......... ---" ....... b....... - ...... L__L_.L-- ...... L_...L___.......... !..----L----_....-260 ! i i i i i i i i i i i i ! ! ! ! ! _ _ _ _ _ _

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(e) Group5.

Figure 13. Continued.

65

Run R_ M q, psf Tt,°F

o 45 40.24 x 106 0.699 2423 -250.9D 47 40.25 .700 2428 -250.8

49 40.26 .700 2429 -250.8A 51 40.31 .700 2429 -251.0

i i i i i i i i i i i i i [ i i [ l l i Z

i i'i"v ..... ,_, v/_-,-v-_ v--!.... ............ -d- .... ---_ ..... ,---,---....--,---.,--,..... w__w___.............. I3 i i i i i i i " i i i i i i i i i ii i _ _ i i i i t _ _ i i i i i ! i i t t l _ i i

Tgra d, °F 0

_L_L.L.....................__L__L._.....Oi6._...o__i___o...__rorciO' '''i J i i _ _ ............................. j j ii J J i I J

-10 i i i-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

-220 _ L , F _ _ _ i _ _ _ _ _ _ _ _ I

.................::::::::F.....[......i--;.........i---;4---_--i---X......;-i..-_--isii:;=:::_:oFTba1, -240 iii............. ---'--.........i--i--i....-P-_--!.......r--yi- i i i --F-f-i......i ii ---J--i---.....f-T--F-....._i--i---i,,.........J-J--i.....i---i-r.....r--r--_........f-T--i.......i----i.... ,_,

-260....i--V!........r--r--i.......l---!--i..........r--r--i.......r-r--r........!--i-i.........r-r-r.........f--f--F-"-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(f) Group 6.

Figure 13. Continued.

66

Run R_ M q, psf Tt,°F

O 157 40.20x 106 0.700 2424 -250.8[] 159 40.16 .700 2423 -250.7

161 40.22 .702 2431 -250.8

10 _ i_ i_i i ji _ii i_ iii _iii i i l i i i i i i i _ i i

_-_-!--i......_--H..........--!................_--_....--_-!........,:--!--i-_--_--i--_-_-:'--_-ri i i i I i i I i i ! i |''

Tgra d, °F 0 i i i i i i ' _ _ i i i i i i i i i i i i _ i

---L--L__!.................. " " .--_"-_ .... ii" i'--_i........._ i"- ii...... '--"-'"--'-'-"'--'---'--"---"-"i i i i i I " _ _ _ i _ I _ _ i I i

-10 !i_ _i _ i i i i i i i i i

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

-22O i i i i i i i i i i i i i i i _ i i i i i i i i....---i---i....t--i-i......--_i.._i.__i.__i._..i-_...,-_..i._.-__f.__i.._..r.__-__i___i.._..l._.i__-.__i __-__,__i.,, ,....--i-----L---i--i---[-7--i.........., ,,---.7..........i----........._-_.--i.......i.--i---7.... i---f--i•--i..--.i---f ....--...---i...........--9 ......._l.----............I.O.-G.-O--.---._ .--_--:L__!.

i i i i i ! i i I;:I !it'll i i i!_IR I2 i i i-z i i _ _ _"l",-- oF_240--oai' i _ i i i i i i ,v i",,,_ i ! !v!v "f" i Y! ! i i i

-260...... i-_ ......f--_.................i......."--i-P--'' * ''' ''' ''-'---.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(g) Group7.

Figure 13. Continued.

67

Run RE M q, psf Tt,°F

o 113 4.44x 106 0.799 1235 120.3O 117 4.45 .801 1239 119.7O 121 4.44 .801 1239 121.6

1o iJi '_ _ii i,i _ ii_ _i_ ,_...... .-! ie! ....!..d..--b-..4.--p---€__L_L..L.

•-_--.:-_.............--d..d......!,'>i!mlid--i--U----d'eii,'>Di!..... -_--_-- i_! iDjm g--Tgrad,°F 0 i i i J l_ i_ J _J _ _ _r @

'i'Ji_ JJ!i j Jij j j 'jj jij j--i--'..... ..............................................................................

i_i iJi-10-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

140 JJi ii! jil iJJ iil iii iii !i J-i-v-i-.....v-i-i.........._---i--i--r--i---r-i--r-i--i--i-t-r-r-i--t-i-P--_--l--i--i--i

II_ J J J J i J J J J J J J i ]-....v--i--i--_--i---i-_--,--p--j--i--l--i--V--V.........i---i-i...........i---i.........i-_--i-r--i--_---i

Tbal, °F 120....i...............I......._..........iSJ--J..--B-L-j._......J--B....j........8-184l..-_.-:B.-.._-.i.........--._.--._.............v...................i.-.-.i..--.j.........g-4--i........!..-.-i.............i.--._--!........._.-...L-_......!..........--i--?i--i--?.H-l-.H-j..........H.--J........i..-.-i.--.i.........i..--_...-J..--.I..-i..--.i---.i--.I.--j.....-.j-.--j..

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(h) Group 8.

Figure 13. Continued.

68

Run R_ M q, psf Tt,°F

o 124 4.43 x 106 0.800 1237 122.0[] 128 4.45 .800 1236 119.7O 133 4.44 .800 1235 120.4

10

......... --o-i---Jo -i-F ....... _-6..... o L-d_.--!c_._*.._Io..L__!^! !A iA k ^i _. _ _ i^i

Tgrad °F

I

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

......... ...... ......----i--- .....;'--,'---i....... t--------_--------i7-r,l----i-r--r--i--r-_-r--i---_--r ............................... n, ,a mi _...................................I..........._ ........l_l........E 3......_...rn.........J__._ ....... 13...... N. _

Tba 1, F 100 i i i i i i " i i i _ ; , : , _ _ i i i i i

--i-r--......_.......... i-T-i.... i-_............... _--_-_--..... .................._I_ --_--F-V80 .............r--r-r ......r--r---........r-r-i .........i---1--i.......i--i--.-- ! ! ! i i,' --i-[--i-"

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(i) Group 9.

Figure 13. Continued.

69

Run R_ M q, psf Tt,°F

o 136 4.44x 106 0.800 1237 120.9[] 140 4.47 .800 1236 118.00 144 4.45 .800 1237 120.2

10

........ _.-7.G-.B-i iJ _i_ i;i 41¢ i ioi joi_>i_b ; bioF

Tgrad, 0 i _ i i , i i i i _!ii iii !ii iii [ii i[ _....-_,-__, , , ..........,.... , , ___-_.__.-, , , , , ,.....i---i---i......... --.:.__i.....!i ! i i i -rr l l i i i i _ i i

-10 i i i i i i i i !

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

1=0.......i-- .........7-_......i-4--i--.._--7_...........i ........i.-.6-.>i_-.__--b.i.........!--i---........._--r--B.......i--B--L----Ei.--i.-.-lilm..........ai .........o-t_-._-.'.Ei..--.im..-O-[]......• , i : i : , , i _ i i i _ i [ [

--_--_-----I----7--i--_.......F-F-._--f--7-_--F...I--_..........i-...K-!.--!--L--_--H--H-.i--_....Tbal,°F 100 _ d d i_o i ioi ioi G ,.,,id b d _ ,

.--L.--L--_ ...... i _i i ! i ! i _ i ! i i i l i i _ _ i i ii i i i i i i i i i i i i i i i _ i i i i i i

80..................i--i-i............................................................,L--',,.....-.2 -.1 0 .1 .2 .3 .4 .5 .6

c_

(j) Group 10.

Figure 13. Continued.

7O

IL

"ponu!luoD"t;Io.m_!,.q

•IIdnoaD(_

ND

9"g"17"_"_"I"0I'-E'-___iii_iii08 --..........................4--.............----............----............4...............4--.--......---4----

....t-i---_--*-!JM,.-4 _,bid.......;_-'-"o! ....... !_i--"J-"!ic:_ ......... "-----'0! !_......_"--''""! ioi.....]J--J---i !!...... "1!-!"-J "-'i_:,"_i....-_'-""_---,--_-----i---i--',--'i--_--'._._..........-........I.................I.......+---"-I........----"

0ot.40't_qz

.... -M0iJOEI

ND

9"g"t,"_"E"I"0['-_'-iiiiiiiiiiiiiiiiiiiiiiii0[-iiiiii..................

--.--.--4.................... 4--'-4-4............. L-4.--4--.i--..i--.i .......... i--..i--'--._....------]--....

ii-i'-i--i_T_--Tiii•::,(•

"]T-i--" Iiiiii

OI

FOg[E99008"8E'g9Lg0gI_99008"8E'ggLo

_'IEI899008"090lx9E'E89o

_o'_£jsd'bIAI_un_

Run R_ M q, psf Tt,°F

o 79 2.38 x 106 0.800 661 119.8[] 83 2.37 .800 660 119.9

87 2.38 .800 662 119.7

10 i i i i i i i i i i i i " ' i .........

---i.... i--I----"--"---t-_--i-'--"---f---i................. --_--f----- ........[........_---i-....... i---.-.--E _ i t

°F 0 i _ i i i i O! ic i o _ o I_c _oC oi i i _ i i ii i i ! i i i i i ! i ! i ! ! i i i i i ; i i i

I i i i i i ii ! i _ i i i i i i i i i i i ii ] i i l i i ! i i ]

-10 i i i _ _ _ _ _ _ _ _ E _ _ _ _ _ E _ _ _ _ _

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

140 i i i i i i i i J i i i i i i i i i _ i i i i i

--t-----_--f--"-- ' --'-"--"-'--"--'--' .........-- .... _-1 .................. f ............I---F-_........F--i..--i........-!-! ........._-----_......__-_.......'--'--'......i----i.......!--i--i.--,-_-.i-......---F-_......i-i----......_-_--,"-.......F-F-I.........i......!.........i--_--t.......F-FI

Tba1, °F 120 --i.......i...... i ........... _-"i-i_ .........-b..... _t_i-i{_ -i-_i_ "_-__ '-_ ......i-.... ......t-i--i......i--t--i.......i-t-i.........i-i--i........i--t--i........i-l-i.....

1 0 0 .... _----i'l --l" F ....... F-- }'--'1 [ ....... _ _I--'1 _--l__ _ 0........ ill-- ll_" i "l-'l _.31--.f--l_o • l l-- ill-- "Ib-- i11 _ '--6----6"1 !115.... l" --O --l'6--lll_--"

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(1) Group 12.

Figure 13. Continued.

72

Run R_ M q, psf Tt,°F

o 90 2.37 x 106 0.800 660 121.7o 94 2.37 .801 660 119.6

98 2.38 .801 663 120.7

10 ++_ +++ +++ ++i +++ +++ i_i ji+... iii tli i_++ "'" i _i _ill iii + + i,i iii iii Iii ii!

...._......._......._--_-_ ....i---_---_--,---_---_--_....i--b--!--"-i--P-iii IiI_iii _ii i+ ,--+---.. .

i,, ,, ,, ,_+_+.+ ,.,T_d,°F 0 iii i'i i,i _iN?IllJtJ +++ ''' "ii i +i_ _l ++_ r+_ ilii!1 iii !11 !ii !i! iii iii ili

i I i I i I i i i _ i i i i i i iiii i+ ti_ i+! iii ii! iii ili

-10 +i+ ,ii i,i iii iii iii iii ill-.2 -.1 0 .1 .2 .3 .4 .5 .6

120 I ! i i + _ i + t + i + i + + i i--,--,--,-,--,-,-, :--i-_7-i--_--P_ -i---¢-i-i-_-iO-i-__--_-i_-<>--b-----f-::::t-v--t-+,:+--::'::::--+-+_--=.......==..........=.......L=_=+___0_.o__...............

,,,,,.........+ , Lti,+,,,L i+++itiLt+i++,++,+Tbal, °F 100 i i i i i i i i i

__L,_+_.,,,....,L'-L--,o L__+,o+LL,o-F-i°_.......i-+-i.....6--b-i......_-ioi--H--I--L--'--'--I- .... i--_ .....-.__L_.L__

80 .... + + , ! + , i , , ,-.2 -,1 0 ,1 ,2 .3 ,4 .5 ,6

CN

(m) Group 13.

Figure 13. Concluded.

73

0 .O1 .02 .03 .04 .05 .06 .07 -08 .09 .I0

Aa, deg

Figure 14. Effect of angle-of-attack errors on drag coefficient.

• Repeat condition[] Same day

o Same dayo All others

.16 6i []i i.15 _ _,_1_i_ o i

.14 i!i!!!!!!!!!l!!!iiiliii_ii i o ! iii iiiiii iiiili _ _ Si i i_Pii i?ii/_!iqii o _ i

.12 i i

.11 ,_,_,,_,_,,_,_,_, i

.10 !ii!_ !!!!!! i!!!ii ii!iii i _ !0 7 14 21 28 0 10 20 30 40 x 106

Time, days R_

.16 _ _,_ _ iii iii iiiDliii.15 i!! _, D__ _ _ oli i i i : ! ii J ii iil

.14 i i i i i i i i i _ _ _ _ i i i i i i

A_,deg .13 u _ o _ _ i _.12 i i _ i _ i i_i _ _ _ _ _ i i i i: z , _ , i i i ! _ ! ' _ i ! ' ' * ! i !

!!! ..........10 i i i iii i i i ' _' _ __ '''_,_ iii !ii i!i

0 20 40 60 80 150 50 -50 -150 -250

Pt,psia Tt, °F

(5 Relafionsh_ to time,R_nolds number, to_ press_e, _d totfl tempera_re.

Fibre 15. V_ation of test-sectionflow _l_ty atM = 0.80_oughout investigation.

75

• Repeatconditiono Samedayo Samedayo Allothers

.16 ,,, ,,, ,,, ,,, _ i Ji i ii i !!

.15 _ _,_ iij iii ii_,

.14 ! i i i bi i i ! i i i ' _ _ i i io,,_ _ _

Aoqdeg .13 _ _ _ , _i , ,.12 i i i i i i _i i i_'i°, i _ °_ i _i _i _ i '_...... '_' iii iii i i.11 '_i i i i i i i i _ _ ' _ _ _ i i i

ii! iii iii ii! iii _.10 _ _ _ _ _ _ _ _ _ i i ! i _ _ _ i ! _ _ ,200 300 400 500 600 19 20 21 22 23

Fan rpm Fan rpmfr y2

.16 .........

.15 ! i ° i i i _ i i i i i i i i

i i i ° i i _'_ ilii o i ! i 6 i i i i i i i i

A,_,deg .12"13i__° _}:i•°_ i ,ii i ' ii_,, _.,_._?°_=,_ °:_,,,_.11 i i iii iii.10 _ i !! i!!

10 20 30 40 50 -20 -10 0 10 20

Fan power, mW Inlet guide vane angle, deg

(b) Relationshipto fanspeed,fantipspeedcompressibilityfactor,fanpower,andinletguidevaneangle.

Figure 15. Concluded.

76

Run RE M q,psf

O 14 39.92x 106 0.800 2660[] 16 39.93 .799 2658<> 18 39.95 .799 2658zx 20 39.93 .800 2660t,, 22 39.96 .800 2661Ca 28 40.27 .800 2658

95% confidenceinterval95% predictioninterval

Run RE M q, psf

o 44 40.17x 106 0.800 2662[] 46 40.18 .800 26640 48 40.11 .799 2656A 50 40.12 .799 2656

95% confidence interval

95% prediction interval

.05 J i i / J J J J J J : ' i ......... i _ J

--T--i--T .....t F-T--I ....... ;--;--i ....... T-]"T ...... T--T--T..... r--T--T........T--T--T--]--T-T--] .....

--T--T

A_,deg 0 --L--L--]..--.I--'.-'----.'--.'--,-'.---'-'..'.....-.'r..--<-L.....;L:_.._L..:_I.__i.__}_...j--_[--_-.-_---,-.--i-.--_--_.---P--_:-:t-_.-._--l=--t---t-_i---t_:u__ -r-L-t-_---_-- r_-t---...:" r-t-________..-....... ___=__$.... [--TI..-i.-.._..--T-.-I.--.[...............i i i --t--i--t-- J i i ....[--T--] i i i ....T--T-7

-.05 !il --T--T-T.......F-T--T.......F-F-T.......T--T--I........r--T--T-- _i --T-T--T---.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(b) Group 2.

Figure 16. Statistical results of angle-of-attack short-term repeat data in cryogenic and air modes.

77

Run R_ M q, psf

o 147 40.12x 106 0.800 2659[] 148 40.17 .800 26590 149 40.14 .799 2658

150 40.12 .800 2659151 40.16 .800 2661152 40.14 .800 265995%confidenceinterv_

95%predicfionintervfl

Z! - -T--T-T-_.

_,_e_o i__i__i......i__i__.__'_'_.t__i__:._....i_______i_i.____i______.________......,_,__-_--4--j-_-_---.4-L-4- -4--4o--._---i-.-f..........i__i......___i__i.... i__i___.... L_'.__i.....L_____.... _..______-.o5-t--t--t......t--t--t......t-4--t--t--t--t...._--t--t....+--+--+--

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(c) Group 3.

Run RE M q, psf

o 156 40.25 x 106 0.801 2666[] 158 40.21 .801 2662

160 40.14 .799 2656A 162 40.23 .800 2661

95%confidenceinterv_

95%pre_cfionin_rv_

::f-i--i::--i-4-1,--f--ui....+-.-i--.i.....,,_,,_o_o....L__._.L_LL_L..__"o _-.-+-'_--_,-_-_-_......._-_--_'--W!_'_--i--:i---:

;_-- _-_---.--+-+-__---€.__-_-.-_-........i.-q-.-P-.... _. n,i_...___i....•--t-.-+--Z_---'_-_._.=....I_.L_±_=T=__.... _=F-T.........r-r_ ..........=:-' ......L_i__I__

--T-T-T.....T-T-I....i i i --_-T--T.......+--+--+....?--J--?...._-_--_......_'d-!.....-.05--T-T--T.....T--T--T......T--T--T......i--f-i.........i--i-i........i--i-T....i--i-f......f-_i.....

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(d) Group 4.

Figure 16. Continued.

78

Run RE M q, psf

o 15 39.89 x 106 0.700 2426[] 17 39.90 .700 2426O 19 39.91 .699 2424A 21 39.92 .700 2428t-. 23 39.91 .699 2422ta 29 40.28 .701 2430

95% confidenceinterval

95% predictioninterval

Run RE M q, psf

o 45 40.24 x 106 0.699 2423[] 47 40.25 .700 2428<> 49 40.26 .700 2429tx 51 40.31 .700 2429

95% confidenceinterval.... 95% predictioninterval

.05i i i _ , _ _+_.+__._.... +..- +................ +..... _........+...... ,__,__,__,.._,.._,__,

.__t______ _ _ _ _ , _ _ _ _ _ _ _ _ _ _ i i........... t-'t-t- --¢"-t--T........t--¢-'T......?--T--T.... T--F-T...... T-T--T-

..... t..._: t_ : _ i ! . . _ . . . i qJ i _ i i

Act, deg 0 : _ _ _ _ _ , ,l_ _;=___ _i_'_---' ,,=....I'--T"-'[...... T--'_--:" -_'F:-_ -:"

TFT TTT .TT i _ i i i } i i i i i i _ i i

-.05 --?--i--t......T--T-T......t-i-? .....T-!--T......F-T--T......F'i--T......T--F-T......T-T-I....-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(f) Group 6.

Figure 16. Continued.

79

0 157 40.20x lo6 0.700 2424 0 159 40.16 .700 2423 0 161 40.22 .702 2431 - 95% confidence interval

95% prediction interval

.05

Aa, deg 0

-.05 -.2 -. 1 0 .1 .2 .3 .4 .5 .6

(g) Group 7.

Run Rc

x lo6 0.799 1235 1 301 1239

4.44 .801 1239 - 95% confidence interval

95% prediction interval

(h) Group 8.

Figure 16. Continued.

Run RE M q, psf

O 124 4.43 x 106 0.800 1237[] 128 4.45 .800 1236<> 133 4.44 .800 1235

95% confidence interval

95% prediction interval

•05 i i i i i i i i i i i i i i i i i i i i i i i i

--4---+--+ ......t i J ii[i_--4--4..... €-..*--._--. i i i i i L _ i i [ i [ i _ i_7L-_-_7i-.__:::L-L--, _J._.i_L___i__J._.._......i ' _i 2 i _ J J LAct, deg 0 i i i * i i ! ........,, _ ,-_ ........ _,• • • -.... +--....... *--._-_ --_-.:._._--_t...,--_--_---,-_,--, ...... +-.: -_.

-,--,--._----i--]--t--.-L-L-L- ' ' ' --'%_._.--*-'' '.... _.=-_-.-.-t...=_' ' =-_-=-r-_'' '.... -_-_' ._--T--I--I--*-+--+-_ --_--_--_ -i--t--t--J--t--t--t--t--r--t--t--*--T--T--t-- -T--*-[--fll '''....................... aI----i----'L .... iI--Z----& ...... L--±--A....a--_--i--.-.05 i t l --i-F-i.... _ i i _ i i i _ i ! ! ! --t--,---r---

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(i) Group 9.

Run RE M q,psf

o 136 4.44x 106 0.800 1237rn 140 4.47 .800 1236<> 144 4.45 .800 1237

95%confidenceinterval.... 95%predictioninterval

.05 _L__i_i .i__i_.i .... i_ i _ i _ i ; i i i i i i i i i i

r T T -T--T-"T...... r-"T"-T..... T--T--'r.... T--T--T..... T--T--T.... T--T--'T----T--T--T----.,--,--,..-'.-_.,__.,__,......__..._4-.....4-_4-__4-_--4-.-4.-._.......____4-__]_:4-_4.__4-_--4--4_---r--+--i -*--*--__.-F-:---;.m--_._-_--+ _-_-_-F_-<-._*--

Act, deg 0 _ i i i i _ _'_ : _M i_ ;_i i_l_#l_l_ _ _ _ _ _ _

--F-r-v-r--r--F-_s-_=_xu-u __._-2_: -S:--Z-F-.

-.05 -i--1-T......."7-V-_.....V-i-T......7--T--1......i--7-i.... i"-}-}.......I-H ........}---i ....-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(j) Group 10.

Figure 16. Continued.

81

Run RE M q, psf

o 68 2.36 x 106 0.800 658[] 72 2.38 .800 662<> 76 2.38 .800 662

95% confidenceinterval

95% prediction interval

Run RE M q, psf

o 79 2.38x 106 0.800 661[] 83 2.37 .800 6600 87 2.38 .800 662

95% confidence interval

95% prediction interval

.05__.__-$__$

--.--.--.--ii i __.t__t__t_l__i__t._.t_____t__t_t____t__t__t.._t_____t__..._[ii , _ i i i i i i i i i , i i i i ! T i--t--t--t--r..-t.--i_....ot--i _ ! ............ _,__,.__.,.__.,.__,__,__,=+z.=O.o+_---,-.-,--..,--,-.,--.,,

--_--_--_--!--!-i....._-t--T2-_-- aS._.--.i.-..-+._---.i--_ff._]--_--.--+-....-_-..-_....Aa, deg 0 i i i _ _ , _-' i _i _ i i__ ! i !_',0 _i_i-T--T--[..... T-Ir--_.......i'"r--_.........t--. -'i..... ."'r--_........i..... _"-_t--" __ --i.....

--t--1--T .... +"-'i--_...... I"-"T'--T--_"--T---r--_ .....r-"T"-i .... _'-"+"-_.........t--t --t -"_'-"'j'--'i'--_--,--,--,--,-,--,-,......i--!--i--t-i-[--! .....i--i--i.... T-T--T--r-T--i-T-_--T-T-_.....

-.05 --i--T--T.... F-T-F.........i--T-i........[--T--T........T--i--i..........F-i-T .........r--T-1.......!--i--i .....-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(1) Group 12.

Figure 16. Continued.

82

Run RE M q, psf

O 90 2.37 x 106 0.800 660[] 94 2.37 .801 660<> 98 2.38 .801 663

95% confidence interval

.... 95% prediction interval

•05 i i i i i i i i i i i i i i i i i i i i i i i i

....i--+--!--r--#--#--i..... +--+--+..... +--+--_....... _-+-+-r--+--+--+---r--+--+--_-+-+--+--

--T--t--_--i _ i__4-_-4-- ---+--+--+............!..........T---r'-T........__-_.----t;-TT---t---V--_ ----t--t----t-------I";----,#-'-_-_i_--+--+--+

--T--T-T.... T--T'T...........,, ,---*, ....., ', ......................., , , , , , , *--*,,---- ?--? -- ,--.,.-- .--.9--+- -.F -- ,---.! ..........................................-.05 _ _ _ _ _ _ _ _ i t _ _ .t _......t i_......._ _t i _'..;

-.2 -.1 0 .1 .2 .3 .4 .5 .6

CN

(m) Group 13.

Figure 16. Concluded.

83

• Group composite

o Individual polars

.20

.15

95% PI .10...................................................................................{-........................................................................................................................................................I.................!.................I.............._..........._ ...............I.................I.................I.................I.................I.................I.................I................./)

.05 _

.............._......................................__................................................................................................................................o................................._............"..........................._.............'............*............_..........._f...........f_...........!:_Ii!............_............,,.100

......................................................................,..................................., ................., ........................................................................ ................., .................

.075

s .050 .........................................................................................................................."_.........................................................................................................

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...............I....................................................I...............q_............_ ...............................I................................................................

i SIIIIIIII;iiiiiiilS121111111![II121SII'III211111_iZIIS7IIII21Z"IIIISS"IIIIIIIIIIII_211SIIIIIIIIIIIII21L...Z,IIIIII0

.2

.1................,.................,.................,.................,.................,................., ................., .................,.................,.................,................., ................., .................

................I....................................................................._................................................'.................................T I................._.................................{).............................._)............................t 3........................................................................................................_ ...........................Amean 0 _ ,, , _ [_ _, = _ ....

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0 1 2 3 4 5 6 7 8 9 10 11 12 13

Group

(a) p_, psia.

Figure 17. Test condition repeatability for each polar within group; _unean = Polar mean - Group mean.

84

• Group composite

o Individual polars

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Figure 17. Continued.

85

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Figure 17. Continued.

86

• Groupcompositeo Individual polars

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(d) Re, 106.

Figure 17. Continued.

87

Group composite o Individual polars

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(e) Mach number.

Figure 17. Continued.

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12 _

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Figure 17. Concluded.

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Figure 18. Reynolds number tolerancefor ACD,sf= 0.00001at M = 0.80.

9O

REPORT DOCUMENTATION PAGE Fo._op_ovedOMB No. 0704-0188

Publicreportingburdenfor thiscollectionof InformationIs estimatedto average 1 hourper response,includingthe time for reviewinginstructions,searchingexistingdatasources,gatheringand maintainingthe dataneeded, andcompletingand reviewingthe collectionof information.Send commentsregardingthisburdenestimateor anyother aspectofthiscollectionof information,Includingsuggestionsfor reducingthis burden,to WashingtonHeadquartersServices,Directoratefor InformationOperationsand Reports, 1215JeffersonDavisHighway,Suite1204, Arlington,VA22202.4302, andto the Officeof ManagementandBudget,PaperworkReductionProject(0704-0188),Washington,DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

August 1995 Technical Paper4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

A Longitudinal Aerodynamic Data Repeatability Study for a CommercialTransport Model Test in the National Transonic Facility WU 505-59-10-11

6. AUTHOR(S)

R. A. Wahls,J. B. Adcock, D. P.Witkowski, and F. L. Wright

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

NASA Langley Research CenterHampton, VA 23681-0001 L- 17412

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

National Aeronautics and Space Administration NASA TP-3522Washington, DC 20546-0001

11. SUPPLEMENTARY NOTES

Wahls and Adcock: Langley Research Center, Hampton, VA;Witkowski and Wright: Boeing Commercial AirplaneCompany, Seattle, WA.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified-UnlimitedSubject Category 02Availability: NASA CASI (301) 621-0390

13. ABSTRACT (Maximum 200 words)A high Reynolds number investigation of a commercial transport model was conducted in the National TransonicFacility (NTF) at Langley Research Center. This investigation was part of a cooperative effort to test a 0.03-scalemodel of a Boeing 767 airplane in the NTF over a Mach number range of 0.70 to 0.86 and a Reynolds numberrange of 2.38 to 40.0 x 106based on the mean aerodynamic chord. One of several specific objectives of the currentinvestigation was to evaluate the level of data repeatability attainable in the NTF. Data repeatability studies wereperformed at a Mach number of 0.80 with Reynolds numbers of 2.38, 4.45, and 40.0 x 106and also at a Mach num-ber of 0.70 with a Reynolds number of 40.0 x 106.Many test procedures and data corrections are addressed in thisreport, but the data presented do not include corrections for wall interference, model support interference, or modelaeroelastic effects. Application of corrections for these three effects would not affect the results of this studybecause the corrections are systematic in nature and are more appropriately classified as sources of bias error. Therepeatability of the longitudinal stability-axis force and moment data has been assessed. Coefficients of lift, drag,and pitching moment are shown to repeat well within the pretest goals of _+0.005,_+0.0001,and _+0.001,respec-tively, at a 95-percent confidence level over both short- and near-term periods.

14. SUBJECT/k:HMS 15. NUMBER OF PAGESNational Transonic Facility; Repeatability; Uncertainty; Commercial transports 91

16. PRICE CODEA05

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATIONOF REPORT OF THIS PAGE OF ABSTRACT OF ABSTRACTUnclassified Unclassified Unclassified

NSN 7540-01-280-5500 Standard Form 298 (Rev.2-89)Prescribedby ANSI Std. Z39-18298-102