A Longitudinal Aerodynamic Data Repeatability Study for a Commercial Transport Model Test in the National Transonic Facility

Transcription

1 NASA Tehnial Paper 3522 A Longitudinal Aerodynami Data Repeatability Study for a Commerial Transport Model Test in the National Transoni Faility R. A. Wahls and J. B. Adok Langley Researh Center Hampton, Virginia D. P. Witkowski and F. L. Wright Boeing Commerial Airplane Company Seattle, Washington August 1995

2 The use of trademarks or names of manufaturers in this report is for aurate reporting and does not onstitute an offiial endorsement, either expressed or implied, of suh produts or manufaturers by the National Aeronautis and Spae Administration. Available eletronially at the following URL address: Printed opies available from the following: NASA Center for AeroSpae Information National Tehnial Information Servie (NTIS) 8 Elkridge Landing Road 5285 Port Royal Road Linthium Heights, MD Springfield, VA (31) (73)

3 Abstrat A high Reynolds number investigation of a ommerial transport model was onduted in the National Transoni Faility (NTF) at Langley Researh Center. This investigation was part of a ooperative effort to test a.3-sale model of a Boeing 767 airplane in the NTF over a Mah number range of.7 to.86 and a Reynolds number range of 2.38 to based on the mean aerodynami hord. One of several speifi objetives of the urrent investigation was to evaluate the level of data repeatability attainable in the NTF. Data repeatability studies were performed at a Mah number of.8 with Reynolds numbers of 2.38, 4.45, and and also at a Mah number of.7 with a Reynolds number of Many test proedures and data orretions are addressed in this report, but the data presented do not inlude orretions for wall interferene, model support interferene, or model aeroelasti effets. Appliation of orretions for these three effets would not affet the results of this study beause the orretions are systemati in nature and are more appropriately lassified as soures of bias error. The repeatability of the longitudinal stability-axis fore and moment data has been assessed. Coeffiients of lift, drag, and pithing moment are shown to repeat well within the pretest goals of ±.5, ±.1, and ±.1, respetively, at a 95-perent onfidene level over both short- and nearterm periods. Introdution Every field of study must ontend with the issue of error or unertainty analysis to some degree. Aordingly, the data obtained and used in a given analysis must be evaluated and the quality doumented. Data evaluation inludes the broad ategory of unertainty analysis and an extend from simple observations to omplex theoretial analysis of errors and omparisons with fundamental priniples. Doumentation of the evaluation, whether simple or omplex, is no less important than the evaluation itself beause potential users of the results of a partiular analysis must have a basis with whih to judge usefulness to their situations. The need for suh analysis and doumentation praties in aerodynami researh and development, whether experimental or omputational, is well doumented. (See refs. 1 6 for examples.) This report is presented in the spirit of that general philosophy. This report douments a study of data repeatability in the National Transoni Faility (NTF) at Langley Researh Center performed during a reent high Reynolds number test of a ommerial transport model. The investigation is part of a ooperative effort between Langley, Ames Researh Center, and the Boeing Commerial Airplane Company. The program involves tests on a.3-sale model of a Boeing 767 airplane at three failities: the NTF, the 11- by 11-foot transoni leg of the Ames Unitary Plan Wind Tunnel, and the Boeing Transoni Wind Tunnel. The primary purposes of the overall program are the omparison of data and data redution proesses from eah faility, the aquisition of full-sale Reynolds number data in the NTF to study Reynolds number effets and saling, and the omparison of wind tunnel data with available flight data. Data repeatability during prior tests of this and other models in the NTF has typially been desribed in some form relative to the observed data satter, but those desriptions have not inluded a onsistent mathematial measure of the satter or an indiation of how muh onfidene may be plaed in the data based on the observed satter. Statistial analysis provides an approah to address these issues. Statistially meaningful data sample sizes have been laking during past tests in the NTF beause eah ryogeni test ondition requires the use of gaseous nitrogen as the test medium and subsequent repeat tests of that ondition are onsiderably more expensive than typial onditions in other failities. In addition, the number of polars per test at the NTF is less than typial ompared with other failities beause of liquid nitrogen prodution and storage limitations. As suh, eah repeat test ondition at the NTF represents a larger perentage of an overall test plan. Researhers must hoose whether to investigate a wider range of test onditions and onfigurations or to investigate repeatability more fully. The usual hoie is the former. The test of the 767 airplane model on whih this report is based plaed more than the usual emphasis on the investigation of repeatability. The priority to assess data repeatability during this investigation was due to mixed results from previous tests of this model in the NTF. (See ref. 7.) Partiular attention was direted toward drag repeatability. In addition to better establishment of the repeatability level, the other primary objetives of this investigation were to obtain data for tunnel-to-tunnel

4 orrelation at low Reynolds numbers; to deouple Reynolds number and stati aeroelasti effets; and to obtain refined, high Reynolds number drag measurements for eventual omparison with flight data. Only the analysis pertaining to the repeatability assessment is presented in this report. Repeat test onditions were hosen suh that the remainder of the test objetives would be met. The fous of the investigation was on the longitudinal aerodynami harateristis of the model. The repeatability analysis herein emphasizes stabilityaxis longitudinal fore and moment harateristis, but it also addresses body-axis longitudinal fore and moment harateristis, the angle of attak, and the flow onditions. The repeat onditions were at the ruise Mah number of.8 with Reynolds numbers of 2.38, 4.45, and based on the mean aerodynami hord and also at a Mah number of.7 with a Reynolds number of The Reynolds number range inludes those obtained in the atmospheri onditions of the Boeing faility ( ), in the Ames faility pressurized to 2 atm in air ( ), and at the ruise flight ondition ( ). The maximum angle of attak was limited to 3.5 for high Reynolds number onditions that an only be obtained in the ryogeni mode of operation. This limitation was imposed beause of adverse model and support system dynamis enountered during previous investigations (refs. 7 and 8) near initial buffet at the full-sale Reynolds number in the Mah number range of interest herein. Full-sale ruise onditions were obtained with tunnel onditions of 63.1 psia total pressure and 25 F total temperature. Symbols All dimensional values are given in U.S. Customary Units. AR B X b CI C A C D C D,sf C i C L C m aspet ratio bias estimate for parameter X wing span, in. onfidene interval Axial fore axial-fore oeffiient, Drag qs drag oeffiient, qs drag oeffiient due to skin frition plus overspeed least squares oeffiients, i =, 1, 2,..., K Lift lift oeffiient, qs pithing-moment oeffiient, referened Pithing moment to.25, qs K Normal fore normal-fore oeffiient, qs wing mean aerodynami hord, in. order of least squares polynomial regression equation M free-stream Mah number M ref referene Mah number based on stati pressure measured in plenum N number of data points in sample P X preision estimate for parameter X PI predition interval p t total pressure, psia p s stati pressure, psia Q data density term q free-stream dynami pressure, psf R Reynolds number based on S wing referene area, ft 2 SE standard error s sample standard deviation T bal balane temperature, F T grad temperature gradient aross balane from front to rear, F T t total temperature, F t value of t distribution dependent upon α and ν U X unertainty estimate for parameter X X generi parameter X best best estimate for parameter X X i value of parameter X for ith data point X true true value for parameter X Y generi parameter Y i value of parameter Y for ith data point Y arithmeti mean for N values of parameter Y Ŷ urve-fit-based best estimate of parameter Y α onboard body angle of attak, deg α term representative of onfidene level, used to determine t value β true bias error ε i true preision error for ith data point ν degrees of freedom true error for ith data point δ i 2

5 δ T horizontal-tail angle, positive trailing edge down, deg Abbreviations: NTF rpm RSA SVSA National Transoni Faility revolutions per minute regression statistial analysis single-variable statistial analysis Model onfiguration notation: W B M N T H = δ T wing, one piee body (fuselage) naelle struts, one per side naelles, one per side wing flap trak fairings, three per side horizontal tail at angle δ T (positive trailing edge down), deg Bakground Statistial Information Beause measurements of any property ontain some degree of unertainty, any parameter derived from a measurement also must ontain some degree of unertainty. Therefore, the question is how losely does the measured or subsequently derived parameter agree with its true value? The differene is the true error X true = X i + δ i (1) where X i is the measured value, δ i is the true error for measurement i, and X true is the true value for the parameter of interest. The true values X true and δ i are never known; the task of an unertainty analysis is to quantify these values by estimation. The true error of a measurement has two omponents as follows: δ i = β + ε i (2) where the true error δ i for measurement i omprises the true bias error β and a true preision error ε i for measurement i. The true bias error is onsidered systemati or fixed. The determination of the true bias error an be made only if the true value of the measured property is known. Referene 5 provides a good disussion of the lassifiation of various types of bias errors. Briefly, biases an be large or small, eah with some ombination of known and unknown sign and magnitude. In general, large biases are assumed to be eliminated in a wellontrolled experiment by some means, suh as by the alibration of an instrument. Small biases, however, typially remain and form the bias error. The primary diffiulty in determining the bias error arises from the fat that both the sign and magnitude are diffiult to define without a known true value with whih to ompare. If the true value were known, the true bias error would be determined as the differene between the mean of the population of measured values and the true value. Beause the population is typially infinite in size, reality ditates that experimenters work with a finite sample of the population. Unlike the true bias error, the true preision error does not rely on a knowledge of the true value; it does, however, depend on the true mean value of the population. The true preision error is the random omponent of the true error and is often referred to as the repeatability error (as is the ase throughout this report). The true preision error represents the differene between a measured value and the mean of the population of measured values. The random nature of the preision error lends itself to estimation by statistial analysis and is easier to quantify mathematially than the bias error. Suh quantifiation of a preision error estimate is disussed in the setion, Method of Repeatability Analysis. Unertainty Analysis The result of the unertainty analysis is the determination of an interval within whih the experimenter an state with a speified level of onfidene that the true value lies. That is, X best ± U X (3) where X best is usually the mean value of the sample measurements and U X is the unertainty in the measurements of parameter X stated with a speified level of onfidene. The unertainty U X is a ombination of both bias and preision error estimates (B X and P X, respetively) as shown below in its sum-of-squares form: U X = B X + P X (4) As desribed above, estimation of the absolute unertainty inluding biases is diffiult and is outside the sope of this report. As suh, in the remainder of this report the authors onentrate on the estimation of the preision (repeatability) error only. Method of Repeatability Analysis This setion desribes the approah taken to quantify data repeatability in this investigation. The quantifiation takes the form of an estimate of the preision error and is stated with a speified level of onfidene. The approah builds on the use of simple statistis as used for analysis of a single variable and extends suh statistial onepts to the multiple linear regression problem. As desribed next, the approah is based on estimating the data mean and representing the data satter about the estimated mean. The ombination of probability and statistial 3

6 onepts provides an approah to establish a level of onfidene. The primary underlying assumptions for all statistial analyses to follow are that the data satter is random and that the random satter an be represented by a normal (Gaussian) distribution. Bakground and further details on muh of the following disussion an be found in many statistis textbooks. Several suh texts are referenes Single-Variable Statistial Analysis The most ommon situation appliable for statistial analysis involves the quantifiation of the random satter of a single parameter. The method used to analyze suh a problem is referred to herein as single-variable statistial analysis (SVSA). This method uses well-defined, relatively simple statistial parameters to quantify random satter. The quantifiation of total pressure repeatability during a test run is an example of a problem appropriate for the use of the SVSA approah. Estimation of the data mean. The most fundamental statisti for the SVSA approah, or any other statistial approah for that matter, is a best estimate of the data mean. This statisti is simply the arithmeti mean defined in its usual form for a parameter Y as N Y i i = 1 Y = (5) N where Y i is the ith data point and N is the data sample size. One determined, the data satter about the best estimate of the data mean an be assessed. Measures of repeatability. The most fundamental statisti to desribe data satter is the standard deviation. Beause an experimenter typially deals with only a finite data sample rather than an entire population, the true mean is not known and the true standard deviation an only be estimated. The sample standard deviation s, whih is used as an estimate of the true standard deviation, is defined as s = N ( Y i Y ) 2 i = N (6) The onfidene and predition intervals, both of whih depend on the sample standard deviation, are two additional measures of repeatability. The onfidene interval is related to the loation of the true mean, whereas the predition interval is related to the probability that a single future observation will fall within a er- tain interval about the estimated mean. The onfidene interval is defined as 1 CI = ± t α s (7) 2, ν N where t α is the value of the t distribution for a speified level of onfidene and number of degrees of free- 2, ν dom and N is the data sample size. The t distribution is a modified normal distribution in whih the size of the data sample, represented by ν = N 1 degrees of freedom, is taken into aount. The t value is also related to the speified level of onfidene as defined through α by the relationship Perent onfidene = ( 1 α ) 1 (8) The t value is tabulated (ref. 9) as a funtion of α and ν. In a similar manner, the predition interval is defined as PI = ± t α s 2, ν The onfidene interval, as defined, an be interpreted as the bounds about the estimated mean that enompass the true mean value, with a hane of 1 ( 1 α ) perent. The predition interval, as defined, an be interpreted as the bounds about the estimated mean that will ontain any single future observation with a probability of 1 ( 1 α ) perent. Thus, the predition interval haraterizes the data satter. Multivariable Statistial Analysis Normal data analysis proedures in whih only two variables are involved usually begin with a urve fit to the data. Curve fitting an be done by eye and provides a rough idea as to the relationship between the variables. Unfortunately, beause the fit is subjetive, the seleted relationship may not be the one hosen by the original analyst or by some other analyst in the future. In addition, some measure is needed of how well the urve represents the data. The method of least squares (refs. 9 11) provides a onsistent method to obtain a mathematial urve fit to a set of data and, in ombination with probability and statistial onepts, allows researhers to quantify how well the resulting estimate represents the data with a speified level of onfidene. (9) In terms of wind tunnel data, least squares urves are determined by relating two variables obtained during a test run. If two or more runs are obtained that in theory are idential (same model onfiguration and flow onditions), the repeatability of the dependent variable an be assessed as a funtion of the independent variable. A ommon approah is to represent eah individual run analytially and assess repeatability by interrogating eah resulting analyti model at a onstant value 4

7 of the independent variable and omparing the orresponding estimates of the dependent variable. This approah is in effet the SVSA method desribed earlier after the analyti representations of eah run are evaluated at a hosen value of the independent variable. In this approah, the repeatability assessment is diretly related to the set of analyti representations but only indiretly to the atual data points. An alternate approah is applied here where a single best estimate urve fit is determined based on all data from a set of idential test runs. This approah is referred to herein as regression statistial analysis (RSA) as it relies on the extension of simple statistis to the multiple linear regression problem. Repeatability is assessed by the amount of satter about the single best estimate least squares urve fit (best estimate of the data sample mean) and remains diretly related to the atual data points. The extensions to the statistial parameters desribed above for the SVSA approah are desribed below for the RSA approah. This approah requires the additional assumption that random variane of the dependent variable is onstant over the range of the independent variable. Estimation of the data mean. For the RSA approah, the estimate of the mean is represented by an analyti equation that is determined to be the best model for the relationships observed in the data. The true funtional relationship may inlude dependene on more than one independent variable or on powers thereof. The estimated mean is dependent on the funtional relationship speified and is a best estimate for the speified funtional relationship in the ontext of the method of least squares. Appliation of the RSA approah in this report is based on the assumption that the funtional relationship between any two variables an be adequately represented by a polynomial regression equation of order K; the hosen value of K is dependent on the relationship between the variables of interest and its seletion is desribed further herein. The polynomial regression equation of order K has a general form as follows: Ŷ ( X) = C + C 1 X + C 2 X 2 + C 3 X C K X K (1) where X is the independent variable; Ŷ is the resulting best estimate of the dependent variable; and the least squares onstant oeffiients are C, C 1,...,C K. The overspeified system of N equations an be written in ondensed matrix notation as X N ( K+ 1) C ( K + 1) 1 = Y N 1 where eah equation is of the form (11) The parameters X i and Y i are the measured values of the independent and dependent variables, respetively, for the ith data point. Equation (11) is solved for the K+1 onstant oeffiients by the method of least squares; the result is a mathematial model in the form of equation (1) that is used as an estimate of the mean. The seletion of the order of the polynomial regression model K has a diret effet on the quality of the estimate of the mean. That seletion, however, an be somewhat subjetive. The approah used for the seletion of K in the present investigation was twofold as follows. For eah estimate of mean required, several values of K were evaluated by inspetion of the data satter about the resulting estimate; the standard error, whih is defined in equation (14), is the statistial parameter used in the evaluation. In addition, seletion of the order of the polynomial regression model is subjet to the following guideline: K N 1 (13) This guideline is desribed as a useful rule of thumb (ref. 12) and provides a riterion to limit the maximum order of the polynomial model. Measures of repeatability. When an estimate of the data mean Ŷ(X) has been determined, a measure of the data satter about the mean an be applied. The fundamental measure of the satter about an estimated mean in the RSA approah is the standard error SE, whih is defined as SE = N Y i Ŷ 2 i i = N K (14) where Ŷ i is the estimated value of Y that orresponds to the dependent variable X i of the ith data point. In effet, the standard error is an extension of the sample standard deviation defined in equation (6) to the multiple linear regression problem. The onepts of the onfidene and predition intervals desribed in the SVSA approah an be extended as well. In the RSA approah, the onfidene interval CI is defined as CI ( X ) = ± t α 2, ν SE Q ( X ) and the predition interval PI is defined as (15) 2 3 K Y i = C + C 1 X i + C 2 X i + C 3 X i + + C K X i (12) PI ( X ) = ± t α SE 1 + Q( X 2, ν ) 2 (16) 5

8 As in the SVSA approah, t α is the value of the 2, ν t distribution for a speified level of onfidene and the number of degrees of freedom; the differene in the RSA approah is the definition of the degrees of freedom ( ν = N K 1) where the order of the polynomial regression equation K is taken into aount. The term Q( X ) is defined as T T 1 Q( X ) = X X X X (17) where the independent variable of interest is represented in vetor form as T X = 2 K 1 X (18) X X 1 ( K + 1) and the matrix X is that used in equation (11). The term Q(X ) is a measure of data density in the neighborhood of the independent variable of interest X and aounts for data density suh that highly populated regions of the data sample may have narrower onfidene and predition intervals than sparsely populated regions. The effet of this term is observed in the data that follow. Interpretation of the onfidene and predition intervals is the same as that desribed for the SVSA approah. The primary differene in appliation with the RSA approah is that the intervals define bounds about a least squares-based estimate of the mean, rather than about a simple arithmeti mean. In addition, the defined bounds of the RSA approah are funtions of the independent variable rather than a onstant interval that is valid over the range of the independent variable. Interpretation of Confidene Level Both the onfidene and predition intervals are assoiated with a user-speified level of onfidene, whih is stated as a perentage and is based on the numerial probability that an event will our. In the present ontext, the events of interest are that the true mean value falls within the onfidene interval and that a single future observation falls within the predition interval. An understanding of what a given onfidene level implies is useful. One useful tool is the relationship between odds and the onfidene level where, for example, 9-to-1 odds are equivalent to a 9-perent onfidene level. A subjetive relationship between the onfidene level and an appropriate adjetive that desribes the probability of an event is given in referene 13 as 75% to 9% onfidene level...fairly probable 9% to 95% onfidene level...highly probable 95% to 1% onfidene level... Extremely probable Researhers an define their own hierarhies of onfidene level desriptors; the one presented here is simply an example. Timesales for Repeatability Analysis Three timesales are defined in this paper to lassify a given repeatability sample short, near, and long term. The timesales relate to both the period and irumstanes in whih data are olleted. A short-term repeatability sample desribes data variability over a relatively short period with minimal hange in irumstane. Examples of the short-term time frame with respet to wind tunnel tests are within a single polar and repeat Mah number polars within a Mah number series. A near-term repeatability sample desribes data variability when a given onfiguration is retested during a single tunnel entry and at least one other onfiguration is tested in between. A long-term repeatability sample desribes the data variability from entry to entry for a given model. Obviously, the potential for the introdution of biases, partiularly model-related biases, inreases when going from short- to long-term omparisons. The present investigation inludes many examples of short-term repeatability and presents a near-term sample. The near-term sample was aquired aross a signifiant break in the ryogeni tests and, in some respets, warrants lassifiation of the sample as long term. Experimental Apparatus and Proedures Faility Desription The NTF (ref. 14) is a unique national faility that provides full-sale (high) Reynolds number tests of vehiles (suh as ommerial transport airplanes) designed to fly in and through the transoni speed regime. The faility provides a test environment for a sale model that is similar to that of the full-sale airplane in flight; that is, the Mah and hord Reynolds numbers are idential in the tunnel and full-sale flight environments. The NTF is a onventional losed-iruit fan-driven wind tunnel that is apable of operating at elevated pressures and ryogeni temperatures to obtain high Reynolds numbers. The test setion is 8.2 by 8.2 by 25 ft and has a slotted floor and eiling. The test-setion floor and eiling divergene angles, the reentry flap angles, and the step height for slot flow reentry are adjustable by remote ontrol. In addition, turbulene is redued by four damping sreens in the settling hamber and a ontration ratio of 15:1 from the settling hamber to the nozzle throat. Fan-noise effets are minimized by an aousti treatment both upstream and downstream of the fan. The NTF has an operating pressure range of approximately 15 to 125 psia, a temperature range of 32 6

9 to 15 F, and a Mah number range of.2 to 1.2. The maximum Reynolds number per foot is at Mah 1. The test gas may be either dry air or nitrogen. When the tunnel is operated ryogenially, heat is removed by the evaporation of liquid nitrogen, whih is sprayed into the tunnel iruit upstream of the fan. During this operational mode, venting is neessary to maintain a onstant total pressure. When air is the test gas, heat is removed from the system by a water-ooled heat exhanger at the upstream end of the settling hamber. (See ref. 15 for further tunnel details.) A detailed assessment of the dynami flow quality in the NTF is reported in referene 16. Flutuating stati pressures were measured on the test-setion sidewall opposite a 1 one fairing over the end of a standard model support system. The root mean square of the flutuating omponent of stati pressure nondimensionalized by the free-stream dynami pressure is approximately.84 at low Reynolds numbers in the ambient air environment and approximately.95 at high Reynolds numbers in the ryogeni nitrogen environment; eah of these results is for a Mah number of approximately.8. Model Desription The model is a.3-sale representation of the Boeing 767 prodution airplane. The model is shown in figure 1 mounted in the NTF test setion; the pertinent model geometry is given in figure 2. The model was designed and onstruted speifially for tests in the ryogeni, pressurized onditions of the NTF, where dynami pressures reahed approximately 27 psf during this investigation. The model was built of maraging steel with a surfae finish of 1 µ in. (root mean square). The general wing ontour tolerane was ±.3 in.; the wing leading-edge tolerane was ±.15 in. The model, whih ontains separable omponents, allows tests of multiple onfigurations. The wing omponent, whih inludes the wing-body fairing, does not inlude the wing vortex generators that are found on fullsale prodution airplanes. (See ref. 7.) The body (fuselage) design inorporated a nonmetri upper swept strut support system. (See fig. 1.) The upper swept strut support is intended to minimize support interferene in the horizontal-tail region and is integrated into the body with a shape that approximates the airplane vertial tail. However, beause greater strutural strength was required, the strut integration was thiker than the true vertial tail loft. Other model omponents inlude flow-through naelles, whih simulate a JT9D-7R4 engine installation, naelle struts, wing flap trak fairings, and a horizontal tail. The horizontal-tail inidene an be set at nominal angles of 3, 1,, and 1. Configurations are defined herein with the omponent notation desribed in the symbols list. For example, WB indiates a wing-body onfiguration. Instrumentation Aerodynami fore and moment data were obtained with an internal, six-omponent, strain gauge balane. The quoted auray of the balane (stated in terms of the worst outlying point during the alibration) is ±.5 perent of the maximum design loads; design loads for the balane and the data aquisition system resolution of the hannels used to read the balane output are given in table 1. An internal, heated aelerometer pakage was used to measure the onboard angle of attak; quoted auray of the pakage under smooth wind tunnel operating onditions is ±.1 (ref. 17), and the data aquisition system resolution of the pakage output is.21. Model pressure measurements were obtained using 5-psid baroells, eah with a quoted auray of ±.1 psi (worst ase). Model pressure measurements were limited to three internal body loations hosen to assess flow into and out of the aft-body avity. The three pressure measurements near the upper swept strut seal were made without tubes bridging the balane. The primary measured flow variables of interest inlude both the total and stati pressures and the total temperature. Mah number, Reynolds number, and dynami pressure are alulated from these measured quantities. Briefly, stati pressure is measured by a set of gauges with full-sale ranges of 15, 1, 5, 3, and 15 psia. Eah gauge has a quoted auray of ±.1 perent of full sale (worst ase). An autorange system allows the most sensitive gauge to be used. An idential system is used to measure the total pressure, exept that a 15-psia gauge is omitted. Total temperature is measured by a platinum-resistane temperature probe mounted in the reservoir setion of the tunnel near the sreens. This measurement has an auray of approximately ±.1 F (worst ase). A omplete desription of these measurements and subsequent alulations is given in referene 18. Data Corretions Information on the various instrumentation devies, the data aquisition and ontrol omputers, and the data redution algorithms for the different measurement systems is provided in referene 18. Standard balane, angle-of-attak, and tunnel parameter orretions have been applied. An additional part of data redution at the NTF is balane temperature ompensation. The temperature ompensation methods are designed to orret balane output due to thermal loads and are disussed in 7

10 referenes 18 and 19. A model-speifi orretion has been applied to the drag data to aount for the internal drag of the flow-through naelles and is based on unpublished naelle alibration data obtained by Boeing. The data herein have not been orreted for model aeroelastis, wall interferene, or model support interferene. Appliation of orretions for these three effets would not affet the results of this study as the orretions are systemati in nature and are more appropriately lassified as soures of bias error. The free-stream Mah number is orreted based on lear-tunnel alibrations that orrelate tunnel enterline stati pressure measurements with the referene stati pressures measured in the plenum. Table 2 ontains the free-stream Mah number orretions applied for the repeat onditions studied herein. As indiated in table 2, the orretions are funtions of both Mah and Reynolds numbers. The angle of attak was orreted for flow angularity (upflow) by measurement of both upright and inverted model fore data for a given onfiguration; in partiular, the -α offset method was used. The flow angularity was evaluated at the beginning of eah polar series and when the flow-field total temperature was hanged. This approah was taken based on the assumption that flow angularity is primarily a funtion of old soaking (time) and total temperature. Flow angularity was assessed 2 times during this investigation, all at M =.8; the observed variation of flow angularity is disussed later. Empty-tunnel alibrations allow tunnel wall angles to be set so as to redue pressure gradients and buoyany effets in the test setion. However, tunnel wall angles were set at a nominal angle ( ) before the investigation and remained fixed throughout the test beause wall atuation is urrently problematial at ryogeni onditions. Buoyany drag orretions based on the emptytunnel alibrations were about.1 (in oeffiient form) or less throughout the investigation. The model and the support system introdue pressure gradients and buoyany effets that ould not be aounted for during the empty-tunnel alibration of the wall angles. Corretions to the data for suh effets have not as yet been determined. The solid blokage ratio for the WB onfiguration at an angle of attak of is.55 perent; this value is suffiiently low to minimize blokage effets, based on onventional riteria. Buoyany orretions, based on the empty-tunnel alibrations, have been applied to the data. Strut Seal The upper swept strut support requires a seal at the juntion of the strut and the upper aft body of the model. The seal, whih prevents airflow into and out of the aftbody avity, was designed speifially for use in the NTF environment. This seal is made of polyester fiber filler material in an elasti nylon wrap that was stiffened with thin piees of DuPont Mylar 1. Tests without the seal have shown drag and pithing-moment shifts relative to tests with a seal in plae. Previous experiene (ref. 7) indiates that fore and moment data repeatability an be adversely affeted by deterioration of the upper swept strut seal. Modifiations to the seal during the investigation desribed in referene 7 improved data repeatability to an aeptable level ( C L = ±.15, C D = ±.2, and C m = ±.1). In referene 7, repeatability was not quantified beause a meaningful data sample size was laking; instead, the repeatability quote is a more subjetive representation of the observed range of a given parameter at onstant onditions. Three modified seals were used during the present investigation. The aft-body avity was instrumented with three stati pressure orifies that monitored airflow within the avity aused by seal leakage. In general, no signifiant leakage was observed with any seal onfiguration; one exeption is desribed herein in whih the seal was damaged during a Mah number series. The seal was not used during tests at R = to allow a diret omparison with data obtained in the Boeing Transoni Wind Tunnel. Transition Boundary-layer transition was fixed by distributing epoxy disks (ref. 2) at speified loations on the model surfae. The distributed disk method minimizes variations in the trip distributions and height and allows the trip to be easily inspeted, repaired, or dupliated. However, the initial appliation of the distributed disks is more time onsuming than a orresponding appliation of the more traditional grit trip method. Transition trip disks were applied to the upper and lower surfaes of the wing and horizontal tail, the internal and external surfaes of the naelles, the naelle struts, and the nose of the body for tests at low Reynolds numbers ( R = 2.38 and ). Table 3 provides the sizes and loations of the transition trip disks for the onditions at R = 2.38 and The two patterns differ only in the disk height on the wing surfaes. The transition trip disks were removed from the wing, horizontal tail, and external naelle surfaes for the high Reynolds number test onditions ( R ). A omparison of trip-on and trip-off onfigurations at R = (ref. 7) indiates that boundary-layer transition did our at or near the 1-perent loal hord loation of the trip. 1 Mylar is a registered trademark of E. I. du Pont de Nemours & Company. 8

11 Test Approah Repeatability s The primary data of interest for this investigation are the longitudinal stability-axis oeffiients of lift, drag, and pithing moment. s for the repeatability of these oeffiients were based on the needs of industry and the information ontained in referene 2. The repeatability goals for these oeffiients are given as onfidene intervals about an estimated mean (least squares urve-fit representation) as C L... ±.5 C D... ±.1 C m... ±.1 and are stated at the 95-perent onfidene level, whih indiates a high to extreme probability that the true mean value lies within the presribed interval in the absene of bias. Repeated Test Conditions Equation (15) shows three fators that an affet the size of the onfidene interval for a speified onfidene level the standard error, the data sample size, and the data sample distribution. The data sample sizes and data sample distributions, unlike the standard error, are under the diret ontrol of the investigator and are hosen based on the goals of a given investigation. The data sample distribution is typially hosen to define the polar shape over a speified range and is often onentrated in regions of partiular interest. Thus, the data sample size beomes the primary fator affeting the size of the onfidene interval for a speified level of onfidene. Figure 3 indiates how the data sample size affets the size of the onfidene interval for a speified level of onfidene, assuming that the standard error remains onstant as N varies; figure 3 is based on the SVSA definition of the onfidene interval given in equation (7). One impliation of figure 3 is that for onstant data satter (s, the sample standard deviation), inreasing N dereases the size of the onfidene interval for a speified onfidene level. Figure 3 indiates that a onfidene interval equal to the sample standard deviation an be attained at a 95-perent onfidene level with a sample size of approximately 6. Based on this result, the importane of drag repeatability, and the expetation that the standard deviation of the drag-oeffiient data would be approximately ±.1 (equal to the onfidene interval goal), 6 polars per repeated test ondition were performed in an attempt to meet the stated onfidene interval goal at a 95-perent onfidene level. Note that this result depends on s suh that if s were smaller, N ould also derease while maintaining a 95-perent onfidene level in the desired onfidene interval. As is shown later, the data satter was less than antiipated and the number of repeat polars per test ondition was redued during the investigation. Table 4 summarizes the repeated test onditions, inluding the number of polars atually performed and the sample size used with the RSA approah; table 4 also assigns a group number to eah repeated test ondition to failitate the disussion below. Results and Disussion The purpose of this report is to quantify and doument the data repeatability obtained during a reent high Reynolds number investigation of a Boeing 767 model in the NTF. The approah is to quantify repeatability using the RSA statistial method desribed earlier. The statistial analysis of the fore and moment oeffiient repeatability is disussed first and is followed by a disussion of several fators that may ontribute to nonrepeatability through either bias or preision errors. The maximum angle of attak was limited to 3.5 for high Reynolds number test onditions beause of previous enounters with adverse model and support system dynamis in the ryogeni mode of operation; the majority of the data obtained lies within the range α = 2 to 3. Previous experiene (ref. 7) indiates that the flow over this range is well behaved, thus reduing the potential for unsteady, separated flow phenomena that ould affet repeatability. Although data were obtained over a larger angle-of-attak range for low Reynolds numbers (air mode of operation), repeatability was examined over a range onsistent with the high Reynolds number data. As suh, the analysis below is based on data taken in the range α = 2 to 3 for all repeated test onditions. Fore and Moment Repeatability The longitudinal stability-axis oeffiients of lift, drag, and pithing moment are of primary interest in this investigation. The drag oeffiient is of partiular interest in this investigation beause a major goal was the aquisition of refined drag measurements for eventual omparison with flight data. Speifi repeatability goals were established before the experiment as outlined earlier. The data are graphially presented as residual plots of the fore and moment oeffiients, where the residual of a parameter Y is defined as Y = Y i Ŷ (19) Seletion of polynomial regression model order K. The proess used to selet an appropriate value of K has been outlined. The rule of thumb (eq. (13)) is evaluated based on the data sample sizes provided in table 4; the guideline indiates that maximum values of K should 9

12 be in the range of 3 to 5. The final value of K is hosen based on a survey of the standard error (eq. (14)) that results from urve fits over a range of K and on an examination of residuals. The random data satter in the residual plots validates the polynomial regression model relative to the assumption of random data satter. Figures 4 and 5 show the results of this proess for the longitudinal stability- and body-axis oeffiients, respetively. The value of K was varied from to 8 in eah ase; extending the range to 8, whih is beyond the reommended maximum just identified, is simply for demonstration purposes. The standard errors for low-order fits are often very large and are not always shown in figures 4 and 5. Based on examination of these figures, a single value of K was seleted for eah funtional relationship modeled. The seleted values of K are summarized in table 5 and the two exeptions are noted. The results shown in figures 4(b) and 5(b) for the pithing-moment data of groups 11 and 12 indiate a signifiant redution in the standard error when K was inreased from 3 to 5; the inreased order also served to make the data satter of the residuals signifiantly more random. Although the seletion remains somewhat subjetive, an interesting note is that the air-mode groups generally benefit from a slightly higher order model than do the ryogeni-mode groups. As a result, the order of the air-mode regression models typially defined the final hoie of K for the ryogeni-mode models. Short-term analysis ryogeni mode. Groups 1 7 were obtained in the ryogeni mode of operation, they varied in size from three to six polars, and they totaled 2 to 4 data points. Repeated polars were generally obtained during a Mah number series in whih the Mah number was alternately set at.7 and.8. Figure 6 shows the 95-perent onfidene and predition intervals and the residuals of the lift, drag, and pithing-moment oeffiients as defined in equation (19) for groups 1 7. Note that both the onfidene and predition intervals are funtions of the independent variable. The magnitude of the predition interval is nearly onstant exept near the outer bounds of the data range, whereas the onfidene interval varies more throughout. The variability observed for both onfidene and predition intervals is a result of dependene on the data density term Q. (See eq. (17).) In regions of high data density, the onfidene interval beomes more narrow; the widening of both predition and onfidene intervals at the outer bounds is diretly related to this effet as well, an effet that reflets the intuitive result that the mean value of the dependent parameter is known with more onfidene where the data are onentrated. Table 6 provides a summary of the 95-perent onfidene and predition intervals over the range of data α = 2 to 3 ; the generalized data presented in table 6 are simply averages of the onfidene and predition intervals omputed at the independent variable for eah data point. Clearly, in eah ase the repeatability goals as speified on the onfidene interval for oeffiients of lift, drag, and pithing moment were satisfied. Groups 1 and 5 were unique in that a single polar from eah group (run 28 in group 1 and run 29 in group 5) was obtained two days after the other five in that respetive group. In addition, the tunnel environment was purged of nitrogen and warmed to ambient temperature during the off day. The signifiant time differene and tunnel yling ould allow these two groups to be subdivided and lassified as near-term timesale situations; as suh, the potential was greater for less repeatable data within the two groups. The results indiate that the repeatability within groups 1 and 5 is essentially the same as for the other short-term, ryogeni-mode groups. Figure 7 shows the residuals of the longitudinal body-axis fore and moment oeffiients for groups 1 7. The results are similar to those presented for the longitudinal stability-axis oeffiients. Table 7 provides a summary of these data; note the very small differenes in the results given in table 6 for the drag oeffiient ompared with the axial-fore oeffiient results. Short-term analysis air mode. Groups 8 13 were obtained in the air mode of operation and eah was formed from three polars. Repeated polars were obtained during a Mah number series and followed the pattern M =.8,.86,.84,.82,.8,.78,.75,.7, and.8. Figure 8 shows the 95-perent onfidene and predition intervals and the residuals of the lift, drag, and pithing-moment oeffiients for groups 8 13; figure 9 presents the longitudinal body-axis oeffiients. As with the ryogeni-mode data, the repeatability in the air mode is very good and generally within the pretest goals. Tables 6 and 7 ontain the summarized results for the stability- and body-axis oeffiients, respetively. The drag-oeffiient (and axial-fore oeffiient) onfidene and predition intervals for group 8 are noteworthy beause they are signifiantly larger than those of the other air- and ryogeni-mode groups; figures 8(a) and 9(a) show the drag- and axial-fore oeffiient data, respetively, for group 8. The figures reveal that a single run (run 113) has a lower drag level by roughly 2.5 to 3 drag ounts ompared with the other two polars in the group. This disparity was probably due to the strut seal partially tearing loose during the Mah number series. (Seal damage was disovered when the model was inspeted after the Mah number series.) As a result, some seal stuffing was lost and part of the seal over protruded into the flow field and shifted the drag to a higher level. This error is lassified as a bias and invalidates the 1

13 statistial analysis beause it violates the assumption that all errors are random. However, the shift is explainable to an aeptable degree suh that the nonbiased polar ould be used with onfidene and the biased polars disregarded during the aerodynami analysis phase of the investigation. The identifiation of this bias error demonstrates an extra advantage of the residual analysis beyond its use in quantifying preision. Near-term analysis. Groups 2 and 3 an be ombined to form a data set that is suitable for near-term repeatability analysis. The aquisition of the two data groups was separated by 15 days during whih the tunnel was purged, multiple large hanges were made in tunnel temperature and pressure, and multiple model hanges were made during the low Reynolds number, air-mode portion of the investigation. The omparison of two short-term groups aquired in suh a manner demonstrates the near-term repeatability of the fore and moment data aross a break in the ryogeni tests. Figures 1 and 11 show the residuals and the 95-perent onfidene and predition intervals for longitudinal stability- and body-axis fore and moment oeffiients, respetively; average values for the intervals are inluded in tables 6 and 7. As with the short-term results, the near-term results demonstrate levels of repeatability within the pretest goals of the investigation. In addition, the residual analysis learly shows a small shift in the pithing-moment oeffiient of approximately.2 aross the break in the ryogeni tests. This shift is probably due to the use of two different strut seals; past experiene (ref. 7) has shown the pithing-moment oeffiient to be sensitive to seal quality, partiularly for the tail-on onfigurations. As disussed previously, the bias error tehnially invalidates the statistial analysis; however, the magnitude of the bias is small and explainable and was not partiularly signifiant during the aerodynami analysis phase of the investigation. This ase is another example of the utility of residual plots in deteting bias errors. Contributing Fators to Nonrepeatability The data demonstrate exellent fore and moment oeffiient repeatability, partiularly in relation to the omplex wind tunnel test environment in general and the NTF in partiular. A seemingly endless list of possible soures for bias and preision errors ould be generated. For the sake of brevity, only several possible soures are disussed here. Highlighting several potential soures of error demonstrates the detail required to ahieve the level of repeatability demonstrated in this investigation. Balane auray. Auray and repeatability represent two distint areas of interest that relate to the quality of any measurement. A given measurement may be highly aurate, yet other fators within a system may inhibit repeatability. On the other hand, a series of measurements of the same parameter may be highly repeatable, but the auray ompared with the true value may be poor. A omparison is useful, however, of the balane measurement auray bands with the stated repeatability goals. Figure 12 shows the auray bands for the normal fore, axial fore, and pithing moment in oeffiient form; figure 12 inludes urves for the quoted auray (table 1) and two additional, tighter auray bands for referene. Figure 12 highlights two points as follows. First, the balane used in this investigation and all balanes designed for use in the NTF yield signifiantly more aurate oeffiients at the high dynami pressure onditions. Seond, the repeatability goals set forth and satisfied herein are generally within the quoted auray bands of the balane measurements. As shown in figure 12, the exeption ours on the normal-fore oeffiient at dynami pressures above approximately 2368 psf; note that the results given in table 7 show onfidene intervals on the normal-fore oeffiient to be approximately one order of magnitude lower than the stated goal. Thus, the onfidene in the auray of a repeatable measurement due to some unknown measurement bias may be more of an issue than the repeatability of the measurement itself. Note that the form of the balane auray quote has hanged sine the last alibration of the balane used during this investigation. (See ref. 21.) Previously, the auray quote was stated in terms of the worst outlying point during the alibration, as in this report. This form of quotation is generally overly onservative. Balane auraies are urrently quoted based on a 95-perent onfidene level and yield a more realisti assessment; the revised form of the quotation aligns the balane auray assessment more losely with the method of repeatability assessment used herein. Referene 21 shows alibration results for other ryogeni balanes used in the NTF that indiate a onsistent improvement from.5 perent of the maximum design loads previously quoted to a quote in the range of.1 to.3 perent. Balane temperature gradient effet. Referenes 18 and 19 disuss the balane temperature ompensation algorithm used in the data redution proess at the NTF. In effet, all balane output is orreted to a referene temperature (295 K) based on pretest temperature yling of the balane. During the pretest temperature yling as well as during the test in both air and ryogeni modes of operation, a temperature gradient will 11

14 often our aross the balane. Referene 19 presents data indiating a diret effet of the temperature gradients on the balane output. The temperature ompensation algorithm is not a funtion of the temperature gradient, whih, in effet, means that the temperature ompensation algorithm assumes a zero temperature gradient aross the balane. As a result, operational pratie inludes time to drive the balane toward thermal equilibrium, meaning to some temperature near the flow temperature with a minimal gradient of 1 to 15 F, before the test ondition is set and the data are olleted. This operational pratie is used if the highest quality fore data are required, and experiene has shown that the temperature gradient generally moves toward zero as the test ondition is set and data olletion begins. Figure 13 shows the variation of the balane temperature and the temperature gradient aross the balane for eah group of repeat data. The balane temperature presented is measured in the middle of the balane and the gradient is defined as the temperature differene from the front to the rear of the balane. The temperature ompensation algorithm aounts for the variations observed in the balane temperature within a given group; the variations in temperature gradient are potential soures for error, as a orretion for this effet is not applied. Beause of the time given to ondition the balane, however, the maximum magnitude of the gradient is a relatively small 8 F and does not adversely affet the fore and moment oeffiient repeatability. The gradients generally move toward zero over time. Also, old test onditions tend toward negative front-to-rear gradients, whereas the warm test onditions have positive gradients; this situation is attributed to the fat that the front portion of the balane adjusts more rapidly to the flow ondition than the rear, sting-onneted portion of the balane. Angle of attak. The determination of the angle of attak has a diret effet on the alulation of the lift and drag oeffiients: C D = sinα + C A osα C L = osα C A sinα (2) The diret effet of angle-of-attak errors on the alulation of C L and C D an be estimated as C D = C L α ( π 18) C L = C D α ( π 18) (21) Equations (21) show that the effet of α on the drag oeffiient is muh more signifiant than that on the lift oeffiient relative to the repeatability goals. Figure 14 shows the effet of angle-of-attak errors on the drag oeffiient for a range of lift oeffiients; an error of.1 in the angle of attak is shown to affet the drag oeffiient by approximately.8 drag ounts at the ruise lift oeffiient of.45. The determination of the angle of attak an be affeted by several fators. The first and foremost fator is the measurement itself. The primary measurement is taken from an onboard aelerometer pakage that, as stated previously, has a quoted auray of.1. This quoted auray is based on alibrations performed under ontrolled, laboratory onditions at ambient temperature rather than in an atual wind-on test environment. One potential fator that affets the onboard angleof-attak measurement in the wind-on environment is the model and support system dynamis; model and support system dynamis an be suffiiently large, partiularly at high load onditions, to introdue signifiant entrifugal fores that ause inorret (biased) angle-of-attak measurements. (See ref. 17.) The flow angularity in the test setion is another important fator affeting the determination of the angle of attak. If the flow angularity were known to be onstant, it ould be assessed one and applied to data for all onfigurations and test onditions. In reality, however, the flow angularity should not be assumed to be onstant. This fat is espeially true when an error of only.1 an affet the drag data signifiantly relative to the repeatability goals. Flow angularity was assessed more frequently than normal during this investigation, all at a nominal Mah number of.8. The variation of the flow angularity throughout the investigation is given in figure 15. The mean upflow was.131 with a standard deviation of.11. Note the large variation of more than.5 on a single day of tests that enompassed a wide range of operating onditions and the shift of.15 for the repeated flow ondition assessment. No definite onlusions an be drawn as to the variability of flow angularity from these data. Figure 16 presents residual plots and the aompanying statistial intervals for the angle of attak; these data were obtained by representing the angle of attak as a funtion of the normal-fore oeffiient with a thirdorder polynomial regression model and applying the RSA approah. The residual plots demonstrate the harateristis of random variation, thereby validating the use of statistis to quantify repeatability. Average values of the 95-perent onfidene and predition intervals are presented in table 8. The satter in the angle-of-attak measurement, as quantified by the predition interval, is approximately ±.2 to the 95-perent onfidene level; 12

15 onfidene in the mean value is approximately ±.5 at a 95-perent onfidene level. Although the repeatability is very good, this analysis does not address possible biases that may affet the absolute auray of the angle-of-attak measurement suh as possible model and support system dynamis as mentioned earlier. Flow onditions. The repeatability of the flow onditions has a diret influene on the repeatability of the aerodynami data. The measured flow parameters are total pressure, total temperature, and stati pressure from whih the primary flow parameters of interest are alulated namely, the Reynolds number, the Mah number, and the dynami pressure. The repeatability of these flow parameters is summarized in table 9 where the mean, sample standard deviation, and 95-perent predition interval are given for eah parameter for the ombined short-term groups of polars; figure 17 shows the variations from polar to polar within eah ombined shortterm group. Table 1 presents the variation expeted due to pure instrument unertainty for the four repeated flow onditions inluded in this investigation; the unertainty of the measured quantities is that desribed herein and in referene 18, and the unertainty of the alulated quantities is based on the propagation of unertainty equations given by Rind. (See ref. 3.) The measured quantities p t, p s, and T t are shown in figures 17(a), 17(b), and 17(), respetively. The repeatability of these quantities is at least somewhat indiative of the flow ondition ontrol in addition to the auray of the measurement instruments. The maximum standard deviation of total pressure within any single polar is less than.4 psia and less than.6 psia for any group of polars. No distint differene is apparent between the ryogeni- (groups 1 7) and the air-mode groups (groups 8 13). The trends for stati pressure and total temperature, however, show more satter in the air mode than in the ryogeni mode. The inreased satter in the air mode is not truly signifiant, as the primary flow parameters (figs. 17(d), 17(e), and 17(f)) are less sensitive to these parameters in the air mode. The maximum standard deviation of stati pressure within any single ryogeni-mode polar is less than.7 psia and less than.9 psia for any ryogeni-mode group. The maximum standard deviation for stati pressure in the air mode is less than.2 psia within a polar and less than.3 psia within a group. The maximum standard deviation of total temperature within any single ryogeni-mode polar is less than.8 F and less than.6 F for any ryogenimode group. The maximum standard deviation for total temperature in the air mode is less than 1.4 F within a polar and less than 1.6 F within a group. The potential effets of the primary flow parameters on the drag data are now addressed. The effet of Reynolds number variations has been assessed based solely on predited variations in the skin-frition drag oeffiient C D,sf. Skin-frition drag-oeffiient estimates were made by using an equivalent flat-plate drag plus overspeed fators that were based on the wetted areas of the model omponents. Figure 18 shows the predited Reynolds number variation that would ause a shift of.1 drag ount (.1) in the drag-oeffiient data at M =.8. Table 9 and figure 17(d) show very good Reynolds number repeatability based on this strit riterion. Note, however, that ryogeni-mode groups 1 and 5 show greater satter than all others; this satter is attributed to the fat that a single polar in eah group was obtained at a slightly lower mean total temperature and on a separate day (table 4) than the others within that group. The key onerning Mah number variations is the drag-divergene Mah number, whih an be defined as the Mah number at whih the drag-rise rate C D / M reahes.1. This riterion implies that deviations of about M =.1 near the drag-divergene Mah number will ause a drag-oeffiient shift of about one drag ount. The drag-divergene Mah number varies from onfiguration to onfiguration and dereases with inreasing lift. The general impliation is that Mah number ontrol beomes more important with both inreasing Mah number and inreasing lift. Data from referene 7 indiate that the repeat onditions herein are below drag divergene for the primary lift range examined (α 3. ); however, inreased drag data satter with inreasing lift may be partially due to Mah number variations, partiularly for the test onditions at M =.8. Table 9 and figure 17(e) show the 95-perent predition intervals to be about.2 and.1 for the ryogeni and air modes of operation, respetively. The dynami pressure variations shown in table 9 are judged to be negligible ompared with the potential effets of Mah and Reynolds number variations. This judgment is based on data presented in referene 7 in whih the dynami pressure was varied over a large range. In addition, the effet of dynami pressure due to pure instrument unertainty (table 1) on the alulation of the fore and moment oeffiients is also negligible. Combined fore and pressure tests. Another signifiant soure of nonrepeatability in the NTF may appear when fore and pressure tests are ombined. Balane repeatability an be adversely affeted by pressure tubes that bridge the balane in suh a way as to ause fouling; nonrepeatability an result when the tubes ontrat and expand over the wide temperature range enountered. The investigation desribed herein was onduted as a fore test only to eliminate this situation as a potential soure of nonrepeatability. Note that the three pressure 13

16 measurements near the upper swept strut seal were made without tubes bridging the balane. Summary of Results A high Reynolds number investigation of a.3- sale model of the Boeing 767 airplane has been onduted in the National Transoni Faility (NTF) at Langley Researh Center; this investigation was part of a ooperative effort to test this model at the NTF and two other transoni wind tunnels. The model was tested over a Mah number range of.7 to.86 and a Reynolds number range of 2.38 to based on the mean aerodynami hord. The present report fouses on a study of data repeatability during this investigation. Two statistial and probability-based approahes are outlined and provide the means to quantify data repeatability in a onsistent, mathematial manner. The results are summarized as follows: 1. Exellent fore and moment oeffiient repeatability was demonstrated in both air and ryogeni modes of operation over short-term periods. 2. Exellent fore and moment oeffiient repeatability was demonstrated aross a 15-day break in the ryogeni tests. The two ryogeni repeat series were separated by 81 runs of tests in air, multiple model hanges, multiple large hanges in tunnel total temperature and total pressure, and tunnel volume exhanges of air for nitrogen and vie versa. 3. Repeatability results for both short- and near-term time spans were within the stated pretest goals for the onfidene interval of ±.5, ±.1, and ±.1 with a 95-perent onfidene level for the oeffiients of lift, drag, and pithing moment, respetively. The repeat series whih did not meet these goals ould be explained by the introdution of a bias that violates the primary requirement of randomness and invalidates the statistial analysis. The use of residual plots, however, was a key fator in identifying biases. 4. Fore and moment oeffiient repeatability was insensitive to the balane thermal gradients of ±8 F experiened during data aquisition. 5. Repeatability assessments herein are based on data aquired over a limited range of angle of attak (α = 2 to 3 ) and without onboard pressure instrumentation. 6. Repeatability of the angle of attak, whih was quantified by the predition interval as a funtion of the normal-fore oeffiient, is approximately ±.2 to the 95-perent onfidene level; onfidene in eah mean value of the angle of attak is approximately ±.5 at a 95-perent onfidene level. 7. Repeatability of the flow onditions was suffiient to prelude an adverse effet on the fore and moment oeffiient data repeatability. However, instanes ourred when a flow parameter varied very little within a polar, but the mean value was offset from the other polars within a group due to a set point bias. Likewise, instanes ourred when the set point for a flow parameter was highly repeatable, but speifi polars within a group exhibited more variation than the others. NASA Langley Researh Center Hampton, VA May 15, 1995 Referenes 1. Anon.: Aerodynami Data Auray and Quality: Requirements and Capabilities in Wind Tunnel Testing. AGARD-CP- 429, (Available from DTIC as AD A ) 2. Steinle, F.; Stanewsky, E.; and Dietz, R. O.: Wind Tunnel Flow Quality and Data Auray Requirements. AGARD-AR-184, (Available from DTIC as AD A ) 3. Rind, Emanuel: Instrument Error Analysis as It Applies to Wind-Tunnel Testing. NASA TP-1572, Brown, Clinton E.; and Chen, Chaun Fang: An Analysis of Performane Estimation Methods for Airraft. NASA CR-921, Abernethy, R. B.: Preision and Propagation of Error. Thrust and Drag: Its Predition and Verifiation, Eugene E. Covert, ed., AIAA, 1985, pp Roahe, P. J.: Need for Control of Numerial Auray. J. Spaer. & Rokets, vol. 27, no. 2, Mar. Apr. 199, pp Wahls, Rihard A.; Gloss, Blair B.; Flehner, Stuart G.; Johnson, William G., Jr.; Wright, F. L.; Nelson, C. P.; Nelson, R. S.; Elzey, M. B.; and Hergert, D. W.: A High Reynolds Number Investigation of a Commerial Transport Model in the National Transoni Faility. NASA TM-4418, Young, Clarene P., Jr.; Hergert, Dennis W.; Butler, Thomas W.; and Herring, Fred M.: Buffet Test in the National Transoni Faility. AIAA , July Walpole, Ronald E.; and Myers, Raymond H.: Probability and Statistis for Engineers and Sientists. Third ed., Mamillan Publ. Co., Draper, N. R.; and Smith, H.: Applied Regression Analysis. John Wiley & Sons, In., Coleman, Hugh W.; and Steele, W. Glenn, Jr.: Experimentation and Unertainty Analysis for Engineers. John Wiley & Sons, In.,

17 12. MIDAP Study Group: Guide to In-Flight Thrust Measurement of Turbojets and Fan Engines. AGARD-AG-237, (Available from DTIC as AD A ) 13. Simon, Leslie E.: An Engineers Manual of Statistial Methods. John Wiley & Sons, In., 1941, p Gloss, B. B.: Current Status and Some Future Test Diretions for the US National Transoni Faility. Wind Tunnels and Wind Tunnel Test Tehniques, R. Aeronaut. So., 1992, pp Fuller, Dennis E.: Guide for Users of the National Transoni Faility. NASA TM-83124, Igoe, William B.: Analysis of Flutuating Stati Pressure Measurements in a Large High Reynolds Number Transoni Cryogeni Wind Tunnel. Ph.D. Diss., George Washington Univ., May Finley, Tom D.; and Theng, Ping: Model Attitude Measurements at NASA Langley Researh Center. AIAA , Foster, Jean M.; and Adok, Jerry B.: User s Guide for the National Transoni Faility Data System. NASA TM-1511, Williams, M. Susan: Experiene With Strain Gage Balanes for Cryogeni Wind Tunnels. Speial Course on Advanes in Cryogeni Wind Tunnel Tehnology, AGARD-R-774, 1989, pp (Available from DTIC as AD A ) 2. Chan, Y. Y.: Comparison of Boundary Layer Trips of Disk and Grit Types on Airfoil Performane at Transoni Speeds. NAE- AN-56 (NRC-2998), National Aeronautial Establ. (Ottawa, Ontario), De Ferris, Alie T.: An Improved Method for Determining Fore Balane Calibration Auray. ISA 93-92,

18 Table 1. Fore and Moment Measurement Charateristis Measurement Full-sale (FS) design limit Balane auray a ±.5% FS Data aquisition resolution Normal fore, lb 6 5 ± Axial fore, lb 4 ±2..48 Pithing moment, in-lb 13 ± Rolling moment, in-lb 9 ± Yawing moment, in-lb 6 5 ± Side fore, lb 4 ± a Quoted balane auray (stated in terms of worst outlying point during alibration). Table 2. Mah Number Corretions for Repeated Test Conditions Based on Mah Number Calibrations as Funtion of Reynolds Number [M = M ref + M] R M M Table 3. Transition Disk Size and Distribution [Disk spaing =.1 in. from enter to enter; disk diameters =.455 in.] Disk height, in. for Component Loation R = R = Body... 1 in. aft of nose.6.6 Naelles: Cowl inside... Cowl outside... Primary inside... Primary outside... Bifuration... a.5 in. aft of hilite.5 in. aft of hilite.5 in. aft of hilite.5 in. aft of hilite.5 in. aft of hilite Naelle struts... 1 in. aft of leading edge.4.4 Horizontal tail: Upper surfae... Lower surfae... Wing: Upper surfae... Lower surfae... a Hilite leading edge of naelle omponents. 25-perent loal hord 25-perent loal hord 1-perent loal hord 1-perent loal hord

19 Table 4. Short-Term Repeat Configurations and Test Conditions Group R M q, psf Configuration Upper swept strut seal a Repeat polars b Sample size Date WBMNT WBMNTH = 1 WBMNTH = 1 WBMNTH = WBMNT WBMNTH = 1 WBMNTH = WBMNTH = 1 WBMNT WBMNTH = WB WBMNT WBMNTH = Out Out Out d d a Seal number if on, otherwise seal out. b Does not inlude inverted polars. Five polars on , 1 polar on : ombine for short-term analysis. d Combine for near-term analysis. Table 5. Seleted Order of Polynomial Regression Model Dependent variable Independent variable Order of polynomial regression model K C D C L 4 C m C L a 3 C L α 3 C A 4 C m a 3 α 3 α 3 a Groups 11 and 12 used K =5. 17

20 Table 6. Confidene and Predition Intervals at 95-Perent Confidene Level for Longitudinal Stability-Axis Coeffiients Values averaged over range of data. Repeatability goals stated for onfidene interval at 95-perent onfidene level: C D = ± ; C L = ± ; C m = ± C D C L C m Group R M CI PI CI PI CI PI ± ± ± ± ± ± ±.3 ±.9 ±.7 ±2. ±.2 ±.5 3 ±.3 ±1. ±.7 ±2.4 ±.1 ±.5 4 ±.4 ±1.2 ±.7 ±2.2 ±.1 ± ±.2 ±.7 ±.5 ±1.6 ±.2 ± ±.3 ±.7 ±.5 ±1.5 ±.1 ± ±.3 ±.7 ±.6 ±1.5 ±.2 ± ±1.1 ±3.2 ±.5 ±1.7 ±.3 ± ±.4 ±1.2 ±.6 ±2.1 ±.5 ± ±.3 ±.9 ±.6 ±2. ±.1 ± ±.4 ±1.3 ±.7 ±2.4 ±.1 ± ±.6 ±1.7 ±.5 ±1.7 ±.1 ± ±.4 ±1.1 ±.6 ±2. ±.2 ±.6 2 & ±.2 ±1. ±.5 ±2.1 ±.4 ±1.8 18

21 Table 7. Confidene and Predition Intervals at 95-Perent Confidene Level for Longitudinal Body-Axis Coeffiients Values averaged over range of data. Repeatability goals stated for onfidene interval at 95-perent onfidene level: C D = ± ; C L = ± ; C m = ± C A C m Group R M CI PI CI PI CI PI ± ± ± ± ± ± ±.4 ±1.1 ±.7 ±2. ±.2 ±.5 3 ±.4 ±1.3 ±.7 ±2.4 ±.1 ±.5 4 ±.5 ±1.6 ±.7 ±2.2 ±.1 ± ±.2 ±.8 ±.5 ±1.6 ±.2 ± ±.2 ±.6 ±.5 ±1.5 ±.1 ± ±.3 ±.7 ±.6 ±1.5 ±.2 ± ±1.1 ±3.6 ±.5 ±1.7 ±.3 ± ±.5 ±1.5 ±.6 ±2.1 ±.5 ± ±.5 ±1.5 ±.6 ±2. ±.2 ± ±.5 ±1.7 ±.7 ±2.4 ±.1 ± ±.7 ±2.1 ±.5 ±1.7 ±.1 ± ±.4 ±1.3 ±.6 ±2. ±.2 ±.6 2 & ±.3 ±1.2 ±.5 ±2.1 ±.4 ±1.8 19

22 Table 8. Confidene and Predition Intervals at 95-Perent Confidene Level for Angle of Attak [Values averaged over range of data] α, deg Group R M CI PI ±.5 ±.18 2 ±.6 ±.16 3 ±.6 ±.2 4 ±.5 ± ±.5 ± ±.5 ± ±.6 ± ±.4 ± ±.5 ± ±.5 ± ±.6 ± ±.5 ± ±.5 ±.17 2 & ±.4 ±.17 2

23 Table 9. Flow Condition Repeatability Group Measure p t, psia p s, psia T t, F R M q, psf 1 Mean s 95% PI ± ± ± ± ± ±6.2 2 Mean s 95% PI ± ± ± ± ± ±9.9 3 Mean s 95% PI ± ± ± ± ± ±5.9 4 Mean s 95% PI ± ± ± ± ± ±1.3 5 Mean s 95% PI ± ± ± ± ± ±7. 6 Mean s 95% PI ± ± ± ± ± ±8. 7 Mean s 95% PI ± ± ± ± ± ±9.7 8 Mean s 95% PI ± ± ± ± ± ±4.1 9 Mean s 95% PI ± ± ± ± ± ±1.9 1 Mean s 95% PI ± ± ± ± ± ± Mean s 95% PI ± ± ± ± ± ± Mean s 95% PI ± ± ± ± ± ± Mean s 95% PI ± ± ± ± ± ±2.9 21

24 Table 1. Flow Condition Unertainty Based on Quoted Instrument Unertainty p t, psia p s, psia T t, F R, 1 6 M q, psf 63.1 ± ± ±.1 4. ±.31.8 ± ± ± ± ±.1 4. ±.31.7 ± ± ± ± ± ±.1.8 ± ± ± ± ± ±.1.8 ±.2 66 ±.4 22

25 Figure 1. Model in NTF test setion. L