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N A S A C O N T R A C T O R f&Ktek N A S A C R - 2 4 9 9 R E P O R T
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HIGH REYNOLDS NUMBER TEST
OF A NAG A 651-213, a = 0.5 AIRFOIL
AT TRANSONIC SPEEDS
Kenneth P. Burdges, James A. Blackwell, Jr.,
and Gerald A. Pounds
Prepared by LOCKHEED-GEORGIA COMPANY Marietta, Ga. 30060 s 19l& for Langley Research Center "' - NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • MARCH 1975 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA CR-2H99 4. Title and Subtitle 5. Report Date March 1975 [L AT HIGH -REYNOLDS NUMBER TEST OF A NACA 65-213,a = 0.5 AIRFOi 6. Performing Organization Code TRANSONIC SPEEDS 7. Author(s) 8. Performing Organization Report No.
Kenneth P. Burdges, James A. Blackwell, Jr., and Gerald A Pounds 10 Work Unit No 9. Performing Organization Name and Address 505-06-31-02 Lockheed Aircraft Corporation 11. Contract or Grant No.
Lockheed-Georgia Company 86 South Cobb Drive NAS1-12325 Marietta, GA 30060 - 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Contractor Report National Aeronautics & Space -Administration 14. Sponsoring Agency Code Washington, DC 20546 15. Supplementary Notes Topical report.
16. Abstract Wind-Tunnel tests have been conducted in the Lockheed-Georgia Company's Compressible Flow Facility to determine the transonic two-dimensional aerodynamic characteristics of a NACA 65.-213 a = 0.50 airfoil. The results are correlated with data on this same airfoil section obtained in the NASA-Langley 8-Foot Transonic Pressure Tunnel and the NAE high Reynolds number 15x60-inch two-dimensional test facility. The tests were conducted over a Mach number range from 0.60 to 0.80 and an angle of attack range from -1° to 8°. Reynolds numbers, based on the airfoil chord, were varied from about 3.0 x 10 to 32.0 x 10 .
17. Key Words (Suggested by Author(s)) 18. Distrib ution Statement NACA 65-213 airfoil High Reynolds number test Unclassified - Unlimited Transonic aerodynamics Data correlation STAB Category 02 21. No. of Pages 22. Price* 19. Security dassif. (of this report) 20. Security Classif. (of this page) 162 $6.25 Unclassified Unclassified For sale by the National Technical Information Service, Springfield, Virginia 22151 HIGH REYNOLDS NUMBER TEST OF A NACA 65!-213, a = 0.5 AIRFOIL AT TRANSONIC SPEEDS By Kenneth P. Burdges, James A. Blackwell, Jr.,.
and Gerald A. Pounds Lockheed-Georgia Company SUMMARY An investigation was conducted in the Lockheed-Georgia Company Compressible Flow Facility to determine the transonic two-dimensional aerodynamic character- istics of a NACA 65i~213, a = 0.5 airfoil over a wide Reynolds'number range indicative of both conventional wind tunnel and full scale flight values. The results are correlated with unpublished data on this airfoil section obtained in the NASA 8-foot transonic pressure tunnel and the NAE high Reynolds number 15 x 60 inch two-dimensional test facility. The tests were conducted over a Mach number range from 0.60 to 0.80 and an angle of attack range from -1° to 8°. Reynolds 6 6 numbers based on the airfoil chord, were varied from about 3-0 x 10 to 32.0 x 10 .
The results of the investigation indicated that variations in wind tunnel wall porosity had a significant effect on the airfoil performance for conditions where shock-induced separation was present. Correlation of the data obtained in this investigation with test data on the same airfoil section from the NASA 8-foot transonic pressure tunnel and the NAE 15 x 60 inch two-dimensional high Reynolds number test facility indicated that generally good agreement was obtained. The effects of varying Reynolds number on the normal-force and pitch- ing moment characteristics were generally small. For attached flow conditions, the effect on drag coefficient for large changes in Reynolds number was generally consistent with conventional flat plate drag variations. Also, for attached flow large Reynolds number variations had practically no effect on airfoil shock location. For shock induced separated flow conditions, Reynolds number had a substantial effect on t r a i l i n g edge pressure coefficients and the shock location moved aft about 5 percent of the airfoil chord.
INTRODUCTION Over the past decade, there have been several correlations of wind tunnel and flight data to determine the effects of large changes in Reynolds number on the aerodynamic performance of transport aircraft; These correlations have covered a wide range of aircraft size and technology, such as the NASA F-8 supercritical wing airplane, the Lockheed C-5A, the Lockheed C-1^1, and the Lockheed T-33. The results of these studies have indicated that the magnitude of Reynolds number scale effects on aerodynamic performance varies considerably depending upon both airplane configuration geometry and airfoil technology.
As new full-scale transport aircraft are designed which incorporate the latest advances in aerodynamic technology, it is imperative that the effect of large Reynolds number variations on the aerodynamic performance of these air- craft be known and understood. In particular, the relationship of configuration geometry and airfoil technology to Reynolds number scale effects needs to be established.
Recognizing the need for an experimental facility to evaluate Reynolds number scale effects, the Lockheed-Georgia Company has constructed a new transonic wind tunnel capable of simulating Reynolds numbers of conventional transonic wind tunnel facilities as well as those near full-scale aircraft flight values. This tunnel, referred to as the Compressible Flow Facility (CFF), is described in reference 1 and has the capability of performing both two- and three-dimensional testing at transonic speeds and at large Reynolds numbers.
As a result of the need to establish experimentally the effects of large variations of Reynolds number on airfoils of varying technology, NASA has contracted with the Lockheed-Georgia Company to test in the Lockheed CFF a series of airfoils. These airfoils w i l l be representative of various types of aircraft such as those mentioned above and w i l l be investigated over a large Reynolds number range indicative of both wind tunnel and flight values.
It is the purpose of this report to present the experimental results and establish the Reynolds number scale effects on the first airfoil of this test series - the NACA 65j-213, a = 0.5 airfoil. This airfoil was selected as representative of conventional airfoil technology and has been used on aircraft such as the Lockheed T-33- A second airfoil typical of that used on the NASA F-8 supercritical wing airplane was also tested in this series. These results are reported in reference 2.
In this report, a description of the model and test facility w i l l be pre- sented followed by the test procedures and test conditions. The discussion of the results w i l l be divided primarily into two sections. The first section presents the basic force data and representative pressure data on the NACA 65}-213, a=0.5 airfoil to establish the transonic characteristics of the air- foil at various angles of attack, Mach numbers, and Reynolds numbers. A complete set of the pressure distribution data measured during this test is given in the Appendix. Correlation of data from the present tests with unpublished measure- ments of Aryo Luoma of NASA-Langley on the same airfoil section in the NASA 8-foot transonic pressure tunnel and the NAE high Reynolds number 15 x 60 in. 2-D test facility are included where test conditions match. In the second section, the Reynolds number scale effects on the NACA 65 -213, a =.0.5 airfoil based on the CFF data w i l l be established and discussed.
SYMBOLS Values are given both in St and the U. S. Customary Units. The measure- ments and calculations were made in the U. S. Customary Units.
a mean-line designation b model span, cm (in.)
Cp pressure coefficient Cp.sonic pressure coefficient for local Mach number .of 1.0 c chord of a i r f o i l , cm (in.)
C(j section profile drag coefficient c'd point drag coefficient C'H maximum value of c'j in wake u u m c section pitching-moment coefficient about quarter chord m c section normal force coefficient n d external diameter of wake rake total head tubes, cm (in.)
h vertical distance in wake profile, cm (in.)
2 2 H total pressure, N/m (lb/ft ) k roughness height, cm (in.)
M freestream Mach number 2 2 p static pressure, N/m (lb/ft ) 2 2 q dynamic pressure, N/m (lb/ft ) R Reynolds number based on freestream conditions and a i r f o i l chord N R^ roughness Reynolds number based on roughness height and velocity and kinematic viscosity at top of roughness x ordinate along a i r f o i l chord l i n e measured from a i r f o i l leading edge, cm (in.)
y ordinate along airfoil span measured from tunnel centerline, cm (in.)
z ordinate vertical to airfoil chord line, cm (in.)
a geometric angle of airfoil chord line, degrees 6 flat plate laminar boundary-layer height, cm (in.)
Y ratio of specific heats Subscripts: t.e. trai1 ing edge T transition strip location 0 zero normal force 1 tunnel station one chord length downstream of model « denotes freestream conditions .
Abbreviations: • . . .
CFF Lockheed Compressible Flow F a c i l i t y 1. s. lower surface ' NASA NASA 8-foot transonic pressure tunnel u.s. upper surface NAE NAE 15 x 60 inch two-dimensional test f a c i l i t y APPARATUS AND TEST PROCEDURES Model The two-dimensional model of the NACA 65^-213, a = 0.5 a i r f o i l used in this investigation is shown installed in the Lockheed CFF in'figure 1. A sketch of the a i r f o i l section is given in figure 2 and the design ordinates are listed in table I. The model has a chord of 17-78 cm (7.00 in.) and a span of 50.80 cm (20.00 in.) so that the model completely spans the CFF two-dimensional test section. The model was fabricated from 17-^PH stainless steel.
Surface pressure orifices were installed near the mid-span region of the model on the upper and lower surfaces so as to provide a chordwise d i s t r i b u t i o n of pressures. A d d i t i o n a l pressure orifices were placed strategically along the span to measure the two-dimensionality of the flow. Orifice locations for the pressure tubes are shown in table II.
The model contour accuracy was checked at three spanwise stations by template and feeler gage. The deviations from the mean contour are generally w i t h i n ±.025 (.001 in.), except for small areas on the lower surface where the deviation reached ±.050 mm (.002 in.). The variation in angle of attack across the span of the model was found to be 3 minutes. The a i r f o i l surface was fair and smooth with conventional transonic model surface finish.
Test F a c i 1 i t y The general arrangement of the Lockheed Compressible Flow Facility (CFF) is shown in figure 3- The tunnel is of the blow-down type, exhausting directly 3 3 to the atmosphere. The air storage capability is 368 m (13,000 ft ) at 413 dynes/cm (600 psia). A sleeve-type control valve accurately maintains the settling chamber stagnation pressure at selected pressure less than or equal to the 172 dynes/cm (250 psia) maximum and at mass flow rates less than 1089 kg/sec (2^00 Ib/sec). The test section is 50.8 cm (20.0 in.) wide by 71.2 cm (28.0 in.) high by 183 cm (72.0 in.) long and is enclosed in a 3.7 m (12.0 ft.)
diameter plenum chamber. The top and bottom walls of the two-dimensional test section have variable porosity capability (from 0 to 10 percent), obtained by s l i d i n g two parallel plates with .635 cm (.250 in.) diameter holes slanted 60 degrees from the vertical. The 2-D test section side walls are not porous. A more detailed description of the f a c i l i t y may be found in reference 1.
Wake Survey Rake The fixed wake survey rake used for section drag measurements is described in figure ^ and shown installed in the tunnel in figure 1. The wake rake was mounted at the tunnel centerline one chord length behind the a i r f o i l model. The rake has a total of 90 total head measurement tubes and *t static pressure tubes.
The wake rake tubes are .15 cm (.06 in.) in diameter. Two static tubes are located on a horizontal plane at the tunnel centerline and the other two static tubes are located .64c above and below the tunnel centerline. The wake rake has been calibrated in the tunnel without a model present.
Data has been obtained in previous- CFF a i r f o i l tests s i m i l a r to that conducted herein with the wake rake installed and removed to determine its in- fluence on the flow over the a i r f o i l . These unpublished data indicated the wake rake had n e g l i g i b l e effects on the normal-force coefficient, the pitching- moment coefficient, and the airfoil pressure distribution. Although no such investigation was done for the present tests, i t - i s felt, based on this previ- ously obtained data, that the wake rake did not have any effect on the flow over the NACA 65T213, a = 0.5 airfoil.
Instrumentation Measurements of the static pressures on the a i r f o i l surfaces and the wake rake pressures were made using electronically actuated pressure scanning valves.
The full-scale range of the quarter percent accuracy statham transducers in the valves were selected to provide maximum accuracy for the wind tunnel conditions tested (wake rake ±12.5 psi and a i r f o i l pressures ±50 psi). CEC force balance pressure transducers were used in conjunction with CEC servo amplifiers to provide a precise measurement of the atmospheric pressure, stagnation pressure, and test section static pressure to 0.05% of the 250 psi capacity. These trans- ducers allow determination of the test section Mach number to an accuracy of : ±.002 at'the highest stagnation pressure. • • : • . • ' • ". ' Angle of-attack was'measured with a calibrated potentiometer operated-by the angle-of attack drive mechanism. • Raw pressure data was recorded on magnetic tape u t i 1 i z i n g the CFF h i g h •- speed data a c q u i s i t i o n system. The data acquisition system consists of a Lockheed Electronics Company MAC-16 computer and associated peripheral equip- ment. The raw data was reduced to coefficient form with a CDC 1700 computer.
. ; - . - • • TESTS A N D METHODS Test Conditions .; The aerodynamic characteristics of the NACA 65^-213, a = 0,5 airfoil were investigated over a wide range of test conditions. The angle of attack of the airfoil was varied from.-1 to 8 degrees and the Mach number range investigated was from 0.60 to 0.80. The Reynolds number based on airfoil chord was varied 6 6 from 3-0 x 10 to 32 x 10 by varying tunnel stagnation pressure. A tabulation of the nominal test conditions is presented in table I I I .
Data Reduction x '. ' .' •' The static pressure measurements at the airfoil surface were reduced to standard pressure coefficients and then machine integrated by a double para- bolic integration routine to obtain section normal force and section pitching moment coefficients about the quarter chord using the following equations: f J /A\ _ , /A\ / . .
Cp d (-; - c d (-; (1)
p J l. s. u. s.
and c - j C (0.2 - f) d (J) - J C (0.25 - £) d (f) (2) m p 5 p Section profile drag measurements were computed from the wake survey rake measurements by the method of reference 3 u t i l i z i n g the following equations: f c = Jc' d(£) + Ac (3) d d d wake
nl '
PI -^~-'- i
1 - ( °°) ^
*
H p > ^ i 7, c Y Y
i - <
'd^(-) (-) <
r
, . ni
• oo . o p P M V oo ^T~ « _ / \ I i ' n j The Acj is a correction for the wake rake total head tube displacement effect when in a transverse velocity gradient. This correction is discussed in reference 3 and is given by equation 5- = 0.36 - c' (5) m Transition The airfoil was tested with roughness particles located on both surfaces at 0.05c for Reynolds numbers from 3 to 12 m i l l i o n . The roughness size was chosen for each Reynolds number according to reference A. At Reynolds numbers greater than 12 m i l l i o n , the airfoil was tested with free transition (natural boundary layer transition).
The roughness particle height used for each test Reynolds number is shown in figure 5- The roughness strips, were 0.13 cm (0.05 in.) wide and consisted of Ballotini glass beads set .in a plastic adhesive. Oil flows were conducted to verify.that transition occurred at the strip.for the selected particle heights.
A typical oM flow photograph demonstrating .boundary layer transition at the strip is presented in figure 6. .
Additional tests to investigate the effects of particle height and density were accomplished. Tests were made over the entire Reynolds number- range with the roughness strip removed to establish the movement of the natural transition point dn the airfo.il as a'function of Reynolds number. These additional tests w i l l be analyzed in the DISCUSSION section.
Tunnel Porosity The wind tunnel wall porosity of the Lockheed CFF is variable between 0 and 10%. Since one of the objectives of this test was to obtain a good correlation with data obtained in other facilities, it was desirable to simulate as closely as possible the wind tunnel wall interference present in these tests. Therefore, the criteria for selecting the porosity for the CFF tests was that the pressure distribution level and shape and the force data be the same, at a given angle of attack, for the data obtained in the NASA 8-foot transonic pressure tunnel and the present tests. The NASA 8-foot transonic pressure tunnel has slotted upper and lower walls and the slot opening in the region of the airfoil was about 6 percent of the upper and lower walls.
To determine the required porosity a range of porosity values were run in the CFF. These data w i l l be presented and discussed in detail in the DISCUSSION section. It was concluded from this study that a wall porosity of k% achieved the best data correlation and was used for the entire test program unless other- wise noted.
Tunnel Wall Effects An estimate of the standard subsonic wind tunnel boundary corrections (lift interference and blockage) has been calculated for this test using the method of reference 5- The corrections to pressure coefficient, normal force coefficient, pitching moment coefficient, and drag coefficient for a porosity of k% were generally less than 1 percent of the measured values.- The- correction to angle of attack was, however,-quite large. This is illustrated in figure 7- These corrections have not been applied to the data presented herein.
As shown in table II, orifices were located at various spanwise stations on the airfoil to determine the effect of the tunnel side walls on the two- dimensionality of the flow. Analysis of the pressure data for various flow conditions indicated very l i t t l e variation in the pressure coefficient across the airfoil span. A typical variation at both subcritical and supercritical flow conditions is presented in figure 8. This conclusion was further substan- tiated by observations of oil flow patterns at the airfoil-wall intersection.
Disturbances in this juncture were confined to a very small region.
. Test Repeatab!1ity A measure of the data accuracy is its repeatability. A repeatability check for two runs at M = 0.6, a = 3°» and R^ = 26 x 10 are shown in figure 9- As can be seen, the difference in pressure distribution and force data are n e g l i g i b l e indicating the data to be of good quality.
RESULTS AND DISCUSSION The results obtained in the transition study and the tunnel-wall porosity effects study w i l l be presented and analyzed first to provide the framework for the presentation of the basic airfoil results. This w i l l be followed by a discussion of the basic data for the various test conditions obtained in the CFF. Completing the discussion w i l l be the analysis of the Reynolds number effects on the aerodynamic performance of the airfoil. As appropriate, the data from the present investigation w i l l be compared in various sections to data obtained on the same a i r f o i l in the NASA 8-foot transonic pressure tunnel and the NAE high Reynolds number 15 x 60 inch two-dimensional test f a c i l i t y to establish the degree of correlation present between the various facilities.
Transition Study The objective of this study was to verify that the transition fixing techniques (following ref. 'O used in this test resulted in turbulent boundary layer flow behind the transition strip without excessive particle drag. This was accomplished by testing the airfoil (l) transition free, (2) transition fixed with particle height varying, and (3) transition fixed with varying particle density w i t h i n the transition strip.
This variation of airfoil drag with normal force coefficient for transition free and for four, particle heights at a Mach number of 0.6 is shown in figure 10- The effect on a i r f o i l drag of increasing particle height at low normal force co- efficients is generally to shift the curve to a higher level by a constant increment. At the higher normal force coefficients, where separation is beginning to occur on the a i r f o i l , increases in p a r t i c l e height tend to aggravate the separation and result in s i g n i f i c a n t l y h i g h e r drag.
The drag data from figure 10 at normal force coefficients of 0.2 and 0.5 are plotted versus particle height in figure 11. From t h i s figure, it can be seen that no excess particle drag should be expected for particle heights s l i g h t l y lower than the laminar boundary layer height. The effect of various particle sizes on a i r f o i l pressure d i s t r i b u t i o n is small as shown in figure 12.
The effect of transition strip particle density on drag is shown in figure 13. As can be seen, the data is very sensitive to the manner in which the particles are applied.. Generally, the very dense particle application resulted in an excessive particle drag of six drag counts. The transition fixed data with varying particle height of figure 11 was obtained with the very dense particle applications. These data were run at the beginning of the test program before the effect of strip density was known. To be consistent with the remainder of the data in this report which was obtained with sparce particle applications, the effects of varying transition particle height on section drag, shown in .figures 10 and 11, have been corrected downward by six drag counts.
Tunnel Wall Porosity Effects Study ',• " H\- This study had two primary objectives. The first was to determine the general effects of varying wall porosity on the NACA 65i~213, a = .5 a i r f o i l .
The second objective of this study was to select the value of wall porosity for which the test would be conducted.
The general effect of varying wall porosity on the airfoil pressure d i s t r i - butions at subcritical and supercritical conditions are shown in figures 14 and 15. The effect of increasing porosity, subcritically, is to lower the negative r pressure coefficient level on both the upper and lower surfaces. At super- critical speeds (fig. 15), the same variation in pressure level with increasing porosity is evident. For the 2% porosity case, the flow behind the shock over ,;ti the aft part of the airfoil upper surface is separated. As porosity is in- creased, this flow approaches an unseparated flow condition and the shock moves aft siightly.
•• ' • . : '• :v.v •- • -• ~ - ..v_ The variation of normal-force and drag coefficients with porosity for the above subcritical and supercritical cases are shown in figures 16 and 17.
Subcritically, most of the force data variation takes place between porosities of 0 and k%. At supercritical conditions (fig. 1?), larger variations are noted in the data with increasing porosity. This is due to the effects of porosity on the airfoil upper-surface separation characteristics as noted in figure 15 ea r 1 i e r.
To obtain a good correlation of the present data with data obtained in other f a c i l i t i e s on this same airfoil section, it was desirable to select a value of wall porosity in the CFF that yielded s i m i l a r wall interference effects to those inherent in other investigations. As set forth in the TEST AND METHODS section, the criteria for determining the CFF wall-porosity value was that the force data and the pressure distribution level and shape for the NASA 8-foqt transonic pressure tunnel tests and the present investigation to be same at a given angle of attack'...'
Pressure coefficient data and force data for the present tests with varying wall porosity are shown in figures 16 and 17 compared to the NASA 8-foot tran- sonic pressure tunnel data for both subcritical and supercritical conditions, respectively. The pressure data correlation is for both upper and lower surfaces, and the pressure data points are representative of variations over the entire chord. It is evident that a wall porosity value of 'k% yields the best overall correlation with the NASA data. Therefore, this value was used for the remainder of the test program reported herein.
Basic Results Complete basic force data for the various test conditions are presented in this section. The most comprehensive tests on this airfoil were made for a s "* - -• Reynolds number of six m i l l i o n and are described first. Only selected pressure distributions are shown in this section with a complete set included in the appendix.
Reynolds number of six m i l l i o n . - The basic force data at a Reynolds number of six m i l l i o n are presented in figures ]8 to 23. At Mach numbers of 0.60, 0.70 and 0.75, the force data from the NASA 8-foot transonic pressure tunnel are also shown. Good agreement of the slopes of the normal-force coefficient versus angle of attack curves for the present tests and the NASA data, through the Mach number range, demonstrate that the wind tunnel wall interference effects between the two tunnels are closely matched.
At all Mach numbers, the correlation of the pitching-moment coefficient versus normal-force coefficient curves generally indicate a slight difference in zero-lift pitching moment, but otherwise the/agreement is good.
The correlation of drag coefficient with normal-force coefficient between the CFF and NASA data is excellent at Mach numbers of 0.60 and 0.70. The drag correlation at a Mach number of 0.75 is s t i l l good considering the large amount of drag present on the airfoil at this Mach number. Also, slight deviations in Mach number can cause large changes in drag when the airfoil is well into the drag rise. Since some s l i g h t deviations from the nominal Mach number.occur in the data, constant Mach number fairings are included on the basic drag data plots (solid line). The constant Mach number fairings were obtained from the drag-rise plots presented in figure 23.
An a i r f o i l pressure distribution for a subcritical test condition (M = 0.60, a = 0°) is presented in figure 2k. Correlation between the CFF pressure data and the NASA 8-foot transonic pressure tunnel results is very good over the entire a i r f o i l . A minor difference occurs .on the upper .surface in the mid-chord region. The NASA data has a subtle difference in shape from the CFF data which is smoother. This difference becomes more apparent as Mach .number is increased (fig. 25). . • .'
At supercritical conditions with a strong shock where the flow is not separated '(M = 0.75, a = 0°, fig. 26) agreement between the NASA data and the CFF data remains very good. Correlation is shown in figure 27 (M = 0.75, a = 3°) for a case with supercritical flow followed by extensive shock-induced separation. There is a small difference in shock location which may be due to the s l i g h t differences in mid-chord a i r f o i l geometry or by small differences in wind tunnel wall effects. Otherwise, the correlation of the pressure d i s t r i b u - tions is good.
Reynolds number of three m i l l i o n . - Test data and correlations are pre- sented for three m i l l i o n Reynolds number in figures 28 through 36- Agreement between the CFF data and the NASA data generally follow the same patterns, as were described for the six m i l l i o n Reynolds number data.
Reynolds number of nine million. - No NASA data were available at nine m i l l i o n Reynolds number. Therefore, the data for this Reynolds number are pre- sented without any correlation in figures 37 through 42• These data, however, appear to be consistent with the other results.
Reynolds number of twelve m i l l i o n . - Data for R^ = 12 m i l l i o n are given in figures 43 through 5^. Correlation of the subcritical force characteristics for M = 0.6 between the NASA and CFF data is presented in figure ^3.
Agreement is good, except that the drag of the CFF data is higher than the NASA data. This difference is believed to be associated with movement of the boundary layer transition location to the airfoil leading edge in the CFF .tests. This w i l l be discussed further in the Reynolds Number Effects section.
Correlation of force data from the CFF, NASA and NAE tunnels is presented for a Mach number of 0.70 in figure ^5- Agreement between the three sets of • - . ' ' • ; - ' ' ' normal-force and pitching-moment data is generally good. The main differences are in that the NAE data has a more positive ot than the NASA and CFF data which o agree closely. All three sets of data have difference values of C but show m s i m i l a r variation of pitching-moment with increasing normal-force. The drag data at M = 0.70 from the NASA and NAE tunnels agree fairly well and the CFF drag data is influenced by an apparent difference in transition location.
Correlation of force data for a Mach number of 0.75 from the three tunnels is shown in figure ^7. Normal-force and pitching-moment characteristics follow the same patterns as described for a Mach number of 0.70. The drag data show a spread that is exaggerated by the differences in Mach number at which the data were taken. At M = .75, the airfoil is well into the drag rise, as can be seen ' ' - "t ^ ' ' • T - in figure k8, and small differences in Mach number cause large variations in drag.
Correlation of airfoil pressure distributions between the NASA data and the CFF data at a Reynolds number of 12 m i l l i o n are shown for Mach numbers of 0.60, 0.70, and 0.75 in figures ^9 through 52. Agreement follows .the same pattern as was discussed for the six m i l l i o n Reynolds number data.
1 7 Correlation of the NAE pressure distribution data with the CFF data is shown in figures 53 and 54- Inspection of the subcritical comparison (M = 0.70, a = 0°), shows slight differences over most of the airfoil surface. These dif- ferences are most likely due to the difference in wall effects between the CFF data (porosity = k%, slanted) and the NAE data (porosity = 20%, normal). • The apparent influence of the wind tunnel walls can be more dramatically seen in figure 5/» which shows the airfoil pressure distributions at super- critical conditions (M = .75, a « 3°). The more aft shock location and reduced trai1 Ing-edge separation of the NAE data follows the trend shown In figure 15 for increasing porosity. It should be noted that the Mach number differences for the two sets of data may account for part of the difference in shock loca- tion and separation pattern. • • Reynolds number of seventeen m i l l i o n . - An additional set of correlation data for the three tunnels is presented In figures 55 through 67 for a Reynolds number of 17 m i l l i o n . Generally, the correlations indicate similar trends to that previously discussed for 12 m i l l i o n Reynolds number. The one exception Is the variation in angle of attack for zero normal-force. The NASA data show a positive shift in a that does not occur at other Reynolds numbers. In o addition, the NAE data show a slightly different o as previously mentioned.
o For a given angle of attack, this results in small differences -in normal-force coefficient. Part of the disagreement in correlation of the pressure distri- butions in figures 61 to 67 i'S due to the differences in normal-force coefficient f for a constant angle of attack. ' Reynolds number at facility maximum. - The facility maximum Reynolds number data are shown in figures 68 through 77- The comparison of CFF and NAE data at this Reynolds number indicates the same trends as the lower Reynolds number'data.' ' Trailing Edge Pressure Coefficient Variation The variation of airfoil t r a i l i n g edge pressure coefficient with Mach number is presented in f.igures 78, 79 and 80 for all the Reynolds numbers tested.
As can be seen the Mach number for trailing edge pressure divergence decreases rather rapidly with increasing angle of attack. Also, as Reynolds number is increased the Mach number for trailing edge pressure divergence increases. The largest improvement occurs between 3 and 9 m i l l i o n Reynolds number.
Shock Location . The shock locations for various flow conditions are summarized in figure 81. The shock location is defined as the chordwise point on the airfoil where the shock discontinuity in the pressure distribution is initiated. For condi- tions where the flow behind the shock remains attached, the data in figure 81 indicates the shock location moves progressively rearward as Mach number is increased and there is very l i t t l e change in shock location as angle of attack is varied (at a constant Mach number). As shock-induced separation occurs, the shock location begins to move forward with increasing angle of attack.
For conditions where a strong shock exists but no shock-induced separation is present (e.g. M = 0-75, a = 0°), the effect of Reynolds number on shock location, as shown in figure 81, is minimal. However, for cases where shock- induced separation is present (e.g. M = 0.75, a = 3°) a small change in shock location does occur (approximately 5% chord).
Reynolds Number Effects -i . In this section the effects of Reynolds number on airfoil characteristics w i l l be summarized. Some correlation of Reynolds number effects obtained from the NASA 8-foot transonic pressure tunnel and the NAE 15 x 60 two-dimensional test facility w i l l be included.
A summary of airfoil force parameters at a Mach number of 0.6 is shown in figure 82. The corresponding parameters obtained from the NASA 8-foot transonic pressure tunnel data are included. The angle for zero normal force for the CFF data was found to be unaffected by Reynolds number. The normal-force curve slope was found to show a modest scale -effect up to Rjg = 10 x 10 . The pi'tching moment at zero normal force was found to be unaffected by Reynolds number,' but the parameter, dc /dc , shows a modest scale effect up to Rjg = 10 x 10 . The m n NASA data agree well with the Reynolds number effects observed in the CFF data.
S i m i l a r Reynolds number data for M = 0.7 is shown in figure 83 for the data from the CFF, NASA, and NAE tunnels. The Reynolds number effects shown by the CFF data follow the same pattern as the M = .6 data and are generally supported by the NASA and NAE data.
The Reynolds number effects upon subcritical airfoil drag are shown in figure 84 for M = 0.6. The NASA data show a conventional scale effect that would match theoretical drag calculations for transition at 5% chord. The CFF free transition drag data indicate that transition moves to the airfoil leading"" edge at R = 9 x 10 . The fixed transition data for a g r i t strip at 5% chord N matches the NASA data at R = 3 and 6 x 10 , but at 9 and 12 m i l l i o n Reynolds N number, the fixed transition drag data matches the free transition data at a level 6 to 8 counts higher than the NASA data for transition at 5% chord. This same trend is evident in the Reynolds number effects on drag at M = 0.7 shown in figure 85. It is significant to note that the NAE data serves to bridge between the NASA data and CFF data at Reynolds numbers between 12 and 17 m i l l i o n Reynolds number. It is suspected that this transition movement 5% chord to the leading edge in the CFF tests relative to the NASA data is caused by differences in either the freestream turbulence levels or model relative surface finish.
The effect of Reynolds number on t r a i l i n g edge pressure for attached and separated flow are presented in figure 86. The attached flow condition of M = 0.75 and a = 0° shows a modest effect of Reynolds number. The separated flow condition chosen is M = 0.75 and a = 3° which exhibits a substantial Reynolds number effect. S i m i l a r effects are shown for the movement of upper surface shock location in figure 86. At attached flow condition of M = 0.75 and a = 0° the shock does not move at all over the entire Reynolds number range investigated. However, for the separated .flow conditions of M = 0.75 and a = 3° the shock does move aft about 5% of the airfoil chord over the Reynolds number range from 3 t o 3 2 m i l l i o n . . • • • • ' .
CONCLUSIONS A test program has been conducted on a NACA 65]~213, a = 0.5 a i r f o i l over the Mach number range from 0.6 to 0.8 at various angles of attack and at Reynolds, numbers from 3 to 32 m i l l i o n based on chord. These data have been presented in both basic data form and summary form with correlation data from two other test f a c i l i t i e s included.
Analysis of these data has produced the following conclusions: 1. Variations in wind tunnel wall porosity resulted in small changes in the aerodynamic performance of the airfoil for conditions where the flow was attached. However, for cases where shock-induced separation was present, wall porosity was found to have a significant effect on the a i r f o i l characteristics.
2. Correlation of the test data from the present tests with the NASA 8-foot transonic pressure tunnel data and the NAE 15 x 60 inch two-dimensional test f a c i l i t y data indicated that generally good agreement was obtained.
3. The effects of varying the Reynolds number on the normal-force and pi ten ing-moment characteristics were found to be generally small. For attached flow conditions, the effect of varying Reynolds number on drag co- efficient was generally consistent with conventional flat plate drag variations. Also, for attached flow large Reynolds number variations had practically no effect on shock location. For shock induced separated flow conditions, Reynolds number had a substantial effect on trai1 ing-edge pressure coefficients and the shock location moved aft about 5 percent of the airfoil chord.
REFERENCES 1. Pounds, G. A.; and Stanewsky, E.: The Research Compressible Flow •Facility. Lockheed-Georgia Company ER-9219, 1967. • 2. Burdges, Kenneth P.; Blackwell, James A., Jr.; and Pounds, Gerald'A.: Hiqh Reynolds Number Test of a NASA 10-Percent-Thick Supercritical A i r f o i l Section at Transonic Speeds. NASA CR132468, 1974.
(Title unclassified, paper classified).
3. Pankhurst, R. C.; and Holder, D. W. : Wind-Tunnel Technique.
Sir Isaac Pitman & Sons Ltd., London, p 276, 1965.
4. Braslow, Albert L.; and Knox, Eugene C.: S i m p l i f i e d Method for Determining of C r i t i c a l Height of Distributed Roughness Particles for Boundary Layer Transition at Mach Numbers from 0 to 5- ,NACA .
TN 4363, 1958.
5. Garner, H. C.; Rogers, E. W. E.; Acum, W. E. A.; and Maskell, E. C.: Subsonic Wind Tunnel Wa1] Corrections, AGARDograph 109, 1966.
TABLE I. - DESIGN ORDINATES FOR.NACA 6 5 ] ~ 2 \ 3 > a = 0.5 A I R F O I L • UPPER SURFACE LOWER SURFACE X/C 2/C , X/C Z/C- 0.000 0.000 0.000 0.000 .384 0.924 1.062 0.616 .621 1.291 .879 -1.097 1.105 1.643 1.395 -1.349 2.335 2.283 2.665 -1.765 4.814 3.258 5.186 . -2.376 7.305 4.024 -2.836 7.695 9.804 4.672 10.196 -3.220 • 1 4 . 8 1 2 15.188 5.713 -3.817 19.831 6.511 20.169 -4.263 7.116 24.857 25.143 -4.592 29 . 889 7.559 30.111 -4.823 34.924 7.848 35.076 -4.962 39.964 40.036 -5.011 7.983 45.008 44.992 7.943 -4.947 50.066 49.934 7.707 -4.767 55.115 7.255 54.885 -4.469 60.134 6.63* 59.866 -4.072 65.138 • 64.862' 5.889 -3.599 70.130 5.044. 69.870 -3.062 75.112 4.138 74.888 -2.486 80.089 3.191 79.911 -1.885 2.244 . 84.939 -1.286 85.061 1.332 89.965 - .718 90.035.
94.988 0.530 - .242 95.013 0.0 100.0 0.0 100.0 Leading Edge Radius = 1 . 1 7 4 Percent Chord Slope of radius through L . E . = 0.084 • TABLE II. - O R I F I C E LOCATIONS FOR NACA 65T213, a = 0.5 AIRFOIL MODEL Location Location Orifice Model Location Distance Orifice Model Location Distance Surface X/C No. Surface X/C off <t No. off (£ i % Span -% Span Upper 0. .05 34 .01 . 0 5 1 Lower . .01 .02 2 35 .02..
3 36 .05 4 .05 37 • .075 .075. 38 .10 .10
6 39 .15
7 .15' 40 • 1 7 -20 41 8 .30 .25.. 42 9 .35 10 , . 3 0 ' - . 43 .40 • .
.35 44 .45 11 , 12 . .375 45 .50 .40 = 13 46 . .55 14 , .425 47 .60 : .45 48 .65 16 .475 49 .70 • .50 ' 17 50 .80 ' .
18 .525 51 .90 19 .5375 52 .95 .
. .55 53 .25 20 Upper .35 21 .5625 54 .40 22 .575' 55 . .45 23 .5875 56 .48 24 .60 57 .55 ; .625- 58 • .60 25- 26 .65 59 .65
', -
27 • 71 60 .70 28 .75 61 .50 0.00 .1 29 .80 62 .85 30 63 .15 31 .90 64 .35
r
.1
32 .95 .45
'
' i
• 97 TABLE I I I . - NOMINAL TEST CONDITION MATRIX FOR 65]-213, a = 0.5 AIRFOIL LOW REYNOLDS NUMBER STUDY RM = 3, 6, 9, 12 x 10 M = .60 .68 .70 .72 .75 -78 \. : .80 a X X . X- X
-1 X X x
X X . X ' X X X X X X :" . . X X X 1 X ;
x
;
X X X • . .-. x . • "'' •
2 x
X X X X X
X X x
l»
. . x
X X X X X 6 X 8 X HIGH REYNOLDS NUMBER STUDY R = 17 x 10 AND FACILITY MAXIMUM* N .78 ">• ' M = .60 .68 .70 ..72 .75 a x ; ; X
-1 . X X . x
X ...': - •• '-' Ui *•
X x
0 X X X X ; •;i " X , X X X X
1 x
x X X
2 X X X X
x •':•', X ' ' . X
X . X X x ; V : ( . c
• • ' , - . >.;; ^V''
8 : ' I . ( ^Facility Maximum R = 25 x 10 for M = 0.60 N Facility Maximum R .= 32 x 10 for M = 0.68 to .80.
N .
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D BOUNDARY CORRECTION
Figure 7 • - Effect of standard subsonic wind tunnel wall boundary corrections on the variation of section normal force with angle of attack. M = 0.60, Rjg = 6 x 10 , porosi ty =-k%.
Figure 8 • ~ Variation of airfoil pressures across tunnel, RN= 6 x io , a = o°.
.5987 .4652
,5977
•1,0
Figure 9 . - Repeatability check at M = 0.6, R = 26 x 10 , a = 3° N (Flags denote l.s.).
PARTICLE SIZE
O FREE
D ,00039t
O ,00046c
A ,00077c
k ,00130c
. 0 0 4 .006 . 0 0 8 .010 .012
.014
d
Figure 10 . - Effect of transition p a r t i c l e size on drag, M = 0.6, R = 6 x 10 , X/C = .05, porosity = 6%.
N T
.0100
c
d .008
.0060
r4
0 12 16x10
.0120
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.6, Effect of transition particle size on drag,M Figure 1 1 . - R = 6 x 10 , X/C = .05.
N T
-1.4
c K /C
C d m T
.0057 ,0310 FREE
O .604 6,3 .000
-1.2
,0294 .00039
.117 ,0084
-O .605 6.4 .005
.0297 .00130
.119 ,0093
Q ,GQ3 7.3 .000
particle size on a i r f o i l pressure Figure 12. - Effect of t r a n s i t i o n di s t r i b u t ion, M = .6 , R = 6 x 10 , X/C = .05, N T denote 1.s.)
porosi ty = 6% (Flags
-1.4
3° .413 ,0077 -.0331 FREE
3° ,402 .0085 -.03.13 .00039
-1.2
3° .402 .0095 -.0300 .00]30
i
F i g u r e 12.- Concluded.
TRANSITION POROSITY
O VERY DENSE 6%
D
SPARSE
.004 .006 .006 .010 .012 .014
C, Figure 13 . - Effect of t r a n s i t i o n p a r t i c l e d e n s i t y on drag, M = 0.6, R = 6 x 10", X/C = .05, k = .00039c.
N T Figure - Effect of wall porosity on a i r f o i l pressure d i s t r i b u t i o n at subcritical conditions for M = 0.6 and a = 0.0* (Flags denote 1 . s . ).
-1.41=3
-1.2 -
Cp/soni c pressure distribution Figure 15. - Effect of wall porosity on a i r f o i l at supercritical conditions for M = 0.75 and a = 3-0° (Flags denote 1. s .).
POROSITY
O 21
O 4%
D 6%
j LOHER SURFACE]
C OF NASA DATA
n
C OF NASA DATA
m
C. OF NASA DATA
2 4
POROSITY ~ !
Figure 16 . - Summary of porosity effects at subcritical conditions, M = 0.6, R = 6 x 10 , X/C = .05, a = 0°.
N T
C OF NASA DATA
n
. 4 0
0 2 4
POROSITY - %
.032
C , t.:
C OF NASA DATA
d
>K>
0 2 4
POROSITY - %
Figure 17. - Summary of porosity effects at supercritical conditions, My ui y u i u a i L y ei ecis at supercritica .75 R = 6 x 10 , X/C = .05, a = 3°.
N T
-.04
2 4
POROSITY ~ I
-1.0
-1.0
CFF Figure 17 . - Concluded.
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.004
. 6 4
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.80 .8 4
Figure 23. - A i r f o i l drag r i se character i s t i cs , R = 6 x 10'' X/Cj = .05.
N
,603 0,0 ,127 ,0084
.597 0,0 128 .0082
Figure 2k. ~ A i r f o i l pressure d i s t r i b u t i o n correlat ion at M = 0.6, R = 6 x 10 , a = 0° (Flags denote 1.s.
N
-1.4
C C n d m
,0315 -O CFF ,704 0.0 ,140 ,0087
D NASA .699 ,03 ,129 ,0086 -.0400
-1.2
-1.0
f i g u r e 25 . - A i r f o i l pressure d i s t r i b u t i o n correlation at M = 0.7, RN = 6 x 10 , a = 0 (Flags denote l.s.)
-1.4
,0483
,756 0,0 ,153 ,0139
-O CFI
,0474
.751 -.01 136 ,0112 D NASA
Figure 26. - A i r f o i l pressure d i s t r i b u t i o n c o r r e l a t i o n at M = .75, R = 6 x 10 , a = 0° (Flags denote l.s.).
N n -d
3,00 ,438 ,0310
-O CFI
3.02 ,449 ,0260
D NASA
Figure 27. - A i r f o i l pressure d i s t r i b u t i o n correlation at M R = 6 x 10 , a = 3° (Flags denote l.s.).
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o
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Figure 33- ~ A i r f o i l drag rise characteristics, RN = 3 x 10, X/Cj = .05.
-1.4
O CFF .602 0.0 ,118 .0096 -.0305
—D NASA .601 0.0 .123 .0096 -.
F i g u r e 3^. - A i r f o i l pressure d i s t r i b u t i o n c o r r e l a t i o n at M = 0.6, RN = 3 x 10 , a = 0' (Flags denote l.s.).
-1.4
.761 0,0 .147 .0166 -.0494
O CFF
.750 0.0 .138 .0129 -.0470
-D NASA
-1.2
: Figure 35. - A i r f o i l pressure d i s t r i b u t i o n c o r r e l a t i o n at M - 0.75, ; RN = 3 x UT , i = 0° (Flags denote I.S.).
-1.4
M
C C C
n d m
.756 3.00 .392 .0256 -,OW»
O CFF
.750 3.04 ,^29 .0270 -.0566
,-Q NASA
-1.2
-1.0
-.8
C
-.6
-.4
-.2
Figure 36. - A i r f o i l pressure d i s t r i b u t i o n c o r r e l a t i o n at M = 0.75, e R = 3 x 10 , :, = 3° (Flags denote l.s.).
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i en CD O
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.032
.028
Figure ^2. - A i r f o i l drag rise characteristics, RN = 9 x 10^ X/Cj - .05.
-,00
o
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.028
.024
.020
.016
.012
.008
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.60 .64 .68 .72 .76
.80 .84
M
b F i g u r e ^8- - A i r f o i ) drag r i s e c h a r a c t e r i s t i c s , Rfj = 12 x 10 , X / C j .05.
~ A i r f o i l pressure d i s t r i b u t i o n correlation at M = .6, Figure R = 1 2 x 1 0 , a = 0° .
N
-1.4
n ~d ~m
.00 ,146 .0085 -.0370 -O CFI .700
.02 141 .0075 -.0404 NASA .702
-1.2 —f-—
F i g u r e 5 0 . - A i r f o i l p r e s s u r e d i s t r i b u t i o n c o r r e l a t i o n a t M = . / , 78 R = 12 x 10 , <x = 0 ° ( F l a g s denote I . S . ) .
N
-1.4
n "a
,754 0,00 ,151 .0129 -.0455 -O CFI
,750 -.08 .127 .0098 -.0479 NASA
-1.2
; I Figure 51. - A i r f o i l pressure d i s t r i b u t i o n correlation at M R = 12 x 10 , a = 0° (Flags denote l.s.)
N
-1.4
-n "d - m
,457 ,0325 -.0556
.753 3,00
.463 .0257 -.0629
,752 2.99
-1.2
F i g u r e 52. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = .75, ; R = 12 x 10' , i = 3° (Flags denote l.s.)
N n -d
.700 0.00 ,146 .0035 -.0370
-O CFI
.704 -0.07 115 .0075 -.0414
O NAE
Figure 53. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = .7, R = 12 x 10 , a = 0° (Flags denote l.s.).
N 81
-1.4
,457 ,0325 -.0556
,482 ,0172 -.0567
Figure 5A. - A i r f o i l pressure distribution correlation at M = .75, R = 12 x 10 , a = 3° (Flags denote 1 . s.).
N L.
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F i g u r e 60. - A i r f o i l drag r i s e c h a r a c t e r i s t i c s , R = 17 x 10 .
N
-O CFF ,608 0.0 .124 .0075 -.0299
D NASA .600 .05 .112 .0069 -.0350
-1.2
-1.0
Figure 61 . - A i r f o i l pressure d i s t r i b u t i o n correlation at M = .6, R = 17 x 10 , a = 0° (Flags denote 1 . s . ).
N 89
-1.4
C a n d m
-O CFF .700 0.0 ,146 .0079 -.0370
__ D NASA .700 -.04 .119 .0071 -.0401
-1.2
-1.O
Figure 62. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = -7, R = 17 x 10 , a = 0° (Flags denote l.s.).
N
-O CFF ,753
PNASA ,750
Figure 63- ~ A i r f o i l pressure d i s t r i b u t i o n correlation at M = -75, R = 17 x 10 , a = 0° (Flags denote 1 .s.).
N 91 n d
.477 .0298 -.0560
.476 .0234 -.0686
/I
F i g u r e 64. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = -75, R = 17 x 10 , a = 3° (Flags denote l.s.).
N
-1.4
-1.2
.2
.4
Figure 65- " A i r f o i l pressure d i s t r i b u t i o n correlation at M = .7, C R - 17 x 10 , ^ = 0° (Flags denote 1 . s.). 93 N
-1.4
M a C C C n d m
•-O CFF .753 0.0 .126 .0126 -.0464
ONAE .754 -.07 .120 0.0133 -.0539
-1.2
-1.0
-.8
c
P
-.6
-.4
-.2
Figure 66. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = .75, R = 17 x 10 , < = 0' (Flags denote I . s. ).
N
-1.4
-O CFF .752 2,99
ONAE ,764 3,01
-1.2
Figure 67- - A i r f o i l pressure d i s t r i b u t i o n c o r r e l a t i o n at M = -75, R = 1 7 x ]Q', / = 3° (Flags denote 1 . s.).
N ,-J •J L.
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Figure 73- ~ A i r f o i l drag rise characteristics, RN = 25 x 1O e for M = 0.60 and R = 32 x 1 O for M = .68 to 0.80.
N
-1.4
,601 .00 .133 .0072 -.0312
. I.
-1.2
Figure Ik. - A i r f o i l pressure d i s t r i b u t i o n at M - 0.6.
R - 25 x 10", i = 0" (Flags denote 1 . s . ).
N
-OCFF .703 0,0 ,150 .0073 -,0
ONAE ,701 -,12 ,099 ,0074 -,(M15
Figure 75. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = .7, G R = 32 x 10 , a = 0°(Flags denote l.s.).
N
-O CFF ,750
ONAE ,754
: 1,0
Figure J6. - A i r f o i l pressure d i s t r i b u t i o n c o r r e l a t i o n at M = ./5, R = 3?. x 10 , t = 0° (Flags denote l.s.).
N Figure 77. - A i r f o i l pressure d i s t r i b u t i o n correlation at M = -75, R = 32 x 10 , a = 3° (Flags denote l.s.).
N
-.4
R = 3 x 1
N e>
SYM
-.2
D
0 2
A
A
.84
Figure 78. - A i r f o i l t r a i l i n g edge pressure vs. Mach number,
-At- ~
R = 9 x 10
N Figure 79. - A i r f o i l t r a i l i n g edge pressure vs. Mach number.
A
R = 17 x 10
N
.2
C
Figure 80. - A i r f o i l t r a i l i n g edge pressure vs. Mach number.
4 6
• x/c -
RM = 6 x 10'
RM = 3 x 10 RM = 9 x 10'
Figure 81. - A i r f o i l shock location for various Reynolds numbers.
-O CFF
D NASA
'm.
Figure 82 . ~ Effect of Reynolds number on a i r f o i l force data, M = .6, X/C = .05.
T 1 1 0
O
:F
n M SA
NA i: -
•
1 j j j j
1 i I Ill i i 1 1 .
. • 1
1 ' ' '
i I r
fj r \ ,(• ; , , . i ; i-t
jQ
v 3 f£i
^\ ... .
°*0 t C
f J . • •:•
. <
.
• ^
1 < 1 1 •
-
i i
i
• 1 1 n
5O
-.06
-02
Figure 83. - Effect of Reynolds number on force data, M = .7, X/C = .05.
T 11 I
A CFF FIXED TRANSITION X/Cj = .05
—O CFF FREE TRANSITION
--D NASA FIXED TRANSITION X/C = ,05
T
.012
C
C
.008
.004
Figure 8*4 • ~ Effect of Reynolds number on a i r f o i l drag, M = 0.6.
1 1 2
—O CFF
--D NASA
O NAE
.016
.004
10 50
R-10
N Figure 85. - Effect of Reynolds number on a i r f o i l drag, M - -7, C = .3, X/C = .05.
n T • C- . . . ....
•\ • • - Ct SB - • ' • < V • J
r* i
c —-
>* — -< .
.... .... .... .... ..~.
H
p
- "11" ' '1 . , , tp -\ 1ST.
\ II; . . , , A
. 6
, a ^_ .. .
( *
t ^*
n
»! •" "• •v V. 0 " ^
X/C
....
:::SfflS:lffi ,. ,,,, - i i
bii
.4
R -10
N Figure 86- ~ Variation of airfoi1 t r a i 1 ing edge pressure and shock location w i t h Reynolds number at a Mach number of 0.75- A P P E N D I X TABLE I. FORCE DATA M R a C C N n d m .6007 -1.0000 3.13 -.0289 .0183 .0103 .6019 .0000 3.01 .1183 .0100 -.0305 .6014 1.0000 3.00 .2265 .0102 -.0312 .6012 2.0000 3.01 .3358 .0104 -.0316 .6030 3.0000 2.96 .4408 -.0312 .0105 .6025 4.0000 2.96 .5528 .0114 - . 0322 .6010 6.0000 2.98 .7567 .0131 -.0281 .5994 8.0000 2.99 .9375 .0178 .0001 .6829 - 1 . 0000 2.94 .0228 .0103 -.0352 .6844 .0000 2.95 .1269 .0105 -.0328 .6834 1 . 0000 2.96 .2423 .0106 -.0348 .6843 2.0000 3.18 .3580 .0113 - . 0352 .6861 3.0000 3.08 .4702 .0118 -.0346 .6849 4.0000 2.90 .5909 .0127 -.0343 .6831 5.0000 2.92 .7018 .0145 -.0318 .6798 6.0000 .8291 2.87 .0176 -.0310 .6961 -1.0000 2.98 .0189 .0100 -.0340 .6987 .0000 2,94 .1319 .0102 -.0345 .7007 1.0000 2.89 .2458 .0108 - . 0352 .7019 2.91 2.0000 .3654 -.0367 .0114 2.91 .7046 3.0000 .4828 .0127 -.0377 .7058 4.0000 2.91 .6062 .0156 -.0414 .7020 5.0000 2.92 .7047 .0225 -.0413 .7014 6.0000 2.95 .7448 .0397 -.0398 .7250 -1.0000 3.06 .0198 .0104 -.0363 .7253 .0000 .1419 3.04 .0108 -.0386 .7280 1.0000 3.06 .2562 .0119 -.0393 .7275 2.0000 .0139 3.06 .3821 -.0431 .7249 3.0000 3.05 .4941 .0183 - . 0459 .7257 4.0000 3.03 .5482 .0258 -.0478 .7604 -1.0000 3.04 .0281 .0137 -.0448 .7610 .0000 3.02 .1469 .0166 -.0494 .7601 1 . 0000 3.06 .2400 .0199 -.0507 .7584 2 . 0000 3.06 .3223 .0212 - . 0487 .7562 3.0000 3.06 .3922 .0255 - . 0444 -1.0000 .7846 3.08 .0070 .0195 - . 0525 .7846 .0000 3.09 .0856 .0213 -.0501 1 . 0000 .7836 3.03 .1650 .0236 -.0483 .8040 -1.0000 3. 11 -.0439 - . 0687 .0247 .8069 .0000 3.00 .0064 .0261 - . 0395 .8067 1 . 0000 3.01 .0210 .0084 -.0307 1 1 6 TABLE I. (Continued) M a C R C C N n d m .6021 -1.0000 6.43 .0183 .0087 -.0298 .6024 - .5000 6.49 .0701 .0084 -.0303 .6029 .0000 6.10 .1271 .0083 -.0315 .6026 .5050 6.09 .1780 .0084 -.0314 .6028 1 . 0000 6.10 .2343 .0084 -.0324 1.5000 6.06 .2911 .6029 .0085 -.0332 .6042 2.0000 6.02 .3463 .0088 -.0335 .6053 2,5000 6.00 .3969 .0085 -.0343 .6044 3.0000 6.00 .4550 .0087 -.0346 .6035 3.5050 6.01 .5106 .0089 -.0348 4.0000 .6058 6.02 .5653 .0091 -.0350 .6017 5.0050 5.92 .6837 .0098 -.0349 .6006 6.0000 5.97 .7959 .0112 -.0313 .5997 8.0000 5.87 .9863 .0146 -.0013 .6843 -1.0000 6.29 .0214 .0087 -.0344 .6856 .0000 6.29 .1333 .0086 -.0347 .6843 1 . 0000 6.06 .2550 .0088 -.0371 .6857 2.0050 5.96 .3788 .0092 -.0388 .6862 3.0050 5.77 .4991 .0092 -.0395 6849 4.0000 6.07 .6305 .0103 -.0402 .6834 5.89 5.0000 .7605 .0117 -.0395 .6817 6.0000 6.28 .9018 .0165 -.0387 .7016 -1.0000 6.17 .0203 .0085 -.0353 .7044 .0000 5.97 .1398 .0087 -.0371 .7039 1 . 0000 5.88 .2631 .0088 -.0392 5.79 .7063 2.0000 .3880 .0096 -.0405 .7040 3.0000 5.75 .5206 .0111 -.0435 .7010 4.0000 5.77 .6526 .0134 -.0458 .7022 5.0000 5.79 .7853 .0186 -.0478 .7010 6.0000 5.65 ,8271 .0504 -.0627 6.02 .7207 -1.0000 .0213 .0088 -.0368 .7218 .0000 6.20 .1424 .0087 -.0384 .7222 1 . 0000 5.88 .2725 .0097 -.0418 .7212 2 . 0050 5.68 .4042 .0112 -.0448 .7195 3.0000 5.88 .5371 .0149 -.0479 .7218 4.0000 5.75 .6539 .0262 - . 0585 .7548 -1.0000 6.16 .0313 .0123 -.0436 .7557 .0000 6.30 .1527 .0138 -.0483 .7515 1 . 0000 6.36 .2774 .0172 -.0524 .7523 2.0050 6.11 .3717 .0238 -.0554 .7527 3.0000 6.04 .4384 .0310 -.0518 TABLE I. (Continued) C C M a. R C m N n d -.0540 5.94 .0222 .0186 7829 - 1 . 0000 .0223 -.0554 .0000 6.08 .1096 -.0507 5.97 .1711 .0277 7871 1 . 0000 -.0501 - . 0463 .0257 -1.0000 5.77 .0288 -.0444 .0000 6.05 .0156 -.0428 6.03 .0956 .0317 8051 1 . 0000 -.0347 .4625 .0074 6042 3.0000 5,81 .0058 -.0363 6019 3.0000 2.98 .4717 - . 0353 8.73 .4644 .0086 6039 3.0000 ,0082 -.0347 .4630 6017 3.0000 11.73 .0210 .0084 -.0307 -1.0000 9.21 -.0314 9.59 .1266 .0087 6019 .0000 -.0329 9.19 .2334 .0084 6011 1 . 0000 .0082 -.0338 2.0000 9.27 .3455 .0087 -.0349 3.0050 9.20 .4596 .5711 .0090 - . 0357 6021 4. 0000 9.15 .7969 .0104 -.0334 5997 6.0000 9.11 -.0018 8.0000 9.06 .9933 .0145 9.09 .0220 .0086 -.0345 6842 -1.0000 .1388 .0085 - . 0358 .0000 9.31 .0087 -.0379 1 . 0000 9J9 .2597 .3803 .0092 -.0387 6831 2.0000 9.16 .5094 .0094 -.0404 6832 3.0000 9.16 .6367 .0101 -.0412 4.0000 9.00 .0127 -.0415 5.0000 9.23 .7673 -.0400 9.12 .9095 .0184 6815 6.0000 .0088 -.0358 -1.0000 9.05 .0241 .0082 -.0371 .0000 9.40 .1434 9.01 .2656 .0087 -.0394 7023 1.0000 .3944 .0096 -.0412 2.0000 9.18 .0109 -.0438 3.0000 9.20 .5256 .6596 .0150 -.0475 4.0000 , 9.15 9.04 .7723 .0237 -.0498 7037 5.0050 -.0481 6.0000 9.02 .8323 .0385 -1.0000 9.61 .0207 .0095 -.0381 9.44 .1457 .0094 -.0394 7247 .0000 9.32 .2705 .0106 -.0413 7256 1 . 0000 .3940 .0117 -.0422 2 . 0000 9.55 .5253 .0150 -.0456 3.0050 9.24 .6399 .0249 -.0512 4.0050 9.20 9.42 .0255 .0111 -.0424 7503 - .9950 9.21 .1545 .0128 -.0452 7517 .0000 TABLE I. (Continued) M a C R C C n N d m 9.39 7514 1 . 0000 .2877 .0165 -.0530 7490 2 . 0000 9.33 .4015 .0221 -.0565 7499 3 - 0 0 5 0 9.04 .4646 .0306 -.0549 -1.0000 9.12 .0177 .0175 -.0543 7836 .0000 8.80 .1239 .0216 -.0594 7825 .9950 8.81 .1939 ,0266 -.0548 8051 -l.OCOO 8.78 -.0625 .0253 -.0523 8044 .0050 8.80 .0262 .0283 -.0489 8049 1 . 0000 8.86 .1036 .0312 -.0452 6035 - .9950 12.30 .0241 .0201 -.0297 6053 .0000 1 .93 .1278 ,0082 -.0312 6049 1 . 0000 1 .83 .2372 .0082 -.0325 6036 2.0000 1 .90 .3490 .0082 -.0337 6035 3.0050 1 .93 .4642 .0087 -.0347 6041 4. 0000 1 .79 .5742 .0089 - . 0349 6.0050 6016 .71 .8061 .0106 -.0324 6002 8.0000 .62 1 . 0006 .0154 -.0005 6825 -1.0000 .73 .0263 .0085 -.0337 6833 .0000 .70 .1406 .0083 -.0350 6831 1 . 0000 1.75 .2604 .0086 -.0369 6820 2.0000 1.52 .3833 .0089 -.0383 6820 3.0000 1.58 .5108 .0093 -.0400 6827 4.0050 1.52 .6393 .0101 -.0405 6811 5.0000 1.50 .7728 .0123 -.0403 6789 6.0050 11.43 .9171 .0173 -.0381 7000 -1.0000 11.39 .0267 .0085 -.0351 7007 .0000 11.47 .1463 - . 0370 .0086 7008 1 . 0000 11.39 .2683 .0086 -.0388 7003 2.0000 11.43 .3943 .0095 - . 0406 7018 2.9950 11.38 .5191 .0104 -.0423 7018 4.0000 11.45 .0140 - . 0442 .6488 11.42 -.0459 7003 5.0000 .7713 .0205 6987 6.0000 11.37 ,8643 .0338 - . 0447 7225 -1.0000 11.50 .0089 -.0368 .0256 7193 .0000 .0092 -.0383 11.85 .1475 7203 -.0410 1 . 0000 11.81 .2722 .0101 7206 2 . 0050 11.67 .0119 -.0441 .4004 7193 - . 0473 3.0050 11.96 .5265 .0161 7226 4.0000 11.79 .6430 .0252 -.0518 -1.0000 11.70 .0271 .0112 -.0413 7544 .0000 11.67 .1511 .0131 -.0455 7529 1 . 0000 11.58 .2794 .0167 -.0509 TABLE I. (Continued) C C M C a R N n d m .3962 .0225 -.0550 2.000 11.60 - . 0556 3.0000 11.62 .4571 .0325 -.0549 11.59 .0159 .0186 7835 - 1 . 0000 .1169 .0233 -.0564 ,0000 11.59 .2019 -.0546 1 . 0000 11.59 .0275 .0255 .0077 -.0298 6085 - 1 . 0000 17.77 -.0299 .1244 .0075 .0000 17.67 -.0322 1 . 0050 17.54 .2356 .0075 -.0330 .3406 .0074 6079 2.0000 17.35 .0077 -.0324 1.5000 18.35 .2888 .0074 -.0325 .3369 6042 2 . 0050 17.75 -.0326 .3880 ,0077 6090 2.5000 17.63 .0078 -.0333 3.0000 17.42 .4463 .0079 -.0335 .5014 6044 3.5000 17.31 -.0340 .0081 6019 3.9950 17.08 .5614 .0080 -,0348 -1.0000 17.55 .0328 -.0355 .0000 17.62 .1515 .0078 .2604 .0078 -.0351 6822 1 . 0000 17.56 .3877 .0084 -.0381 2.0050 17.41 -.0393 17.41 .5050 .0086 3.0000 -.0392 17.24 .6365 .0093 4.0000 .0294 .0080 -.0346 -1.0000 17.07 .0080 -,0370 17.23 .1456 .0000 .0084 -,0384 17.30 .2745 7009 1 . 0000 .0079 -.0387 .2772 1 . 0000 17.26 .4011 .0088 -.0414 2 . 0000 17.36 .5240 .0098 -.0418 3.0000 17.38 .0129 -.0448 16.92 .6608 4.0050 -.0355 ,0280 .0083 -1.0000 17.01 ,0089 -.0392 .1494 .0000 17.06 .0101 - . 0390 1 . 0000 17.01 .2776 .0108 -.0402 .4061 7169 2 . 0000 17.55 -,0461 ,5447 .0157 3 . 0000 17.07 6640 .0258 -.0545 4.0000 17.20 .0369 .0112 -.0426 17.39 7541 -1.0000 -.0463 .1632 .0126 .0000 17.46 -.0507 .2948 .0155 1 . 0000 17.30 .0215 -.0568 2 . 0000 17.22 .4173 .0297 - . 0560 17.19 .4766 2 . 9950 -.0542 17.14 .0332 .0160 - 1 . 0000 17.09 . 1 484 .0206 - . 0585 .0000 .0268 -.0566 17.11 .2244 7814 1.0000 TABLE I. (Continued) C M C i R C N n d m .0282 .0075 -.0304 6007 -1.0000 26.15 .0072 -.0312 6007 .0000 25.67 .1325 6002 1.0000 25.29 .2383 .0074 -.0317 5990 2 . 0000 25.11 .3537 .0077 -.0332 25.57 .5824 .0080 -.0345 5965 4.0000 .0075 -.0342 -1.0000 31.66 .0395 .1540 .0000 31.37 .0073 -.0354 .2691 .0072 1 . 0000 30.06 - . 0366 30.21 .3956 .0078 -.0379 6819 1 . 9950 .5180 .0085 -.0387 6799 3.0000 30.80 .6389 .0090 -.0400 4.0000 30.54 3.0000 24.82 .4653 .0078 -.0340 29.90 .0350 .0077 -.0353 6983 -1.0000 .1501 -.0362 .0000 32.48 .0075 1 . 0050 31.94 .2775 .0076 - . 0378 .3952 .0081 -.0373 7030 1.9950 31.37 .0094 -.0389 3.0050 31.14 .5275 -.0318 4.0050 32.90 .6483 .0116 32.00 .0240 .0076 -.0332 7210 -1.0000 -.0349 .1458 .0080 7203 .0050 31.06 -.0407 1 . 0000 30.57 .2828 .0085 .4127 .0100 -.0427 7178 2 . 0000 32.14 .0125 -.0457 7191 3.0050 32.10 .5474 .6732 .0234 -.0518 7228 4.0000 31.91 - .9950 31.63 .0297 .0098 -.0377 .0000 31.81 .1661 .0123 -.0445 .2972 .0147 -.0493 1 . 0000 31.14 2.0050 30.93 .4251 .0206 -.0555 .4909 -.0518 31.06 .0293 7515 3.0050 .0163 -.0537 -1.0000 32.17 .0398 -.0580 .0000 32.26 .1537 .0206 .0264 -.0582 32.33 .2388 7826 1.0000 TABLE I I. POROSITY STUDY Poros i ty .1123 .00824 -.0306 5994 .000 6.51
4.97
5996 .000 6.54 .1196 .00828
-.0311 3-99
.1236 3.00
5996 .000 6.58 .00850 -.0311 5988 .000 6.40 .00849 -.0322 2.01 .1327
.000 .1436
5993 6.53 .00869 -.0331 1.07
5988 .00884 -.0340
.000 6.61 .1598 0.73
5970 .000 6.42 .00838 -.0302
.1187 5-99
3.000 .02550 -.0518 6.01
7555 6.75 .4229
3.000 .4528
7503 6.57 .02735 -.0539 3-99
3.000 .03260 2.01
7495 6.47 ' .4313 -.0527
TABLE I I I . T R A N S I T I O N STUDY K /C T m -1.000 6.84 6036 .0134 .0090 0302 .00039 .000 6036 6.97 .00864 .1155 0305 .00039 1.000 .00902 6.94 .2240 6033 0319 .00039 6056 3.000 6.64 .4458 .00920 0337 .00039 6072 6.44 4.005 .00950 0350 .00039 .5635 6041 6.000 .7861 6.77 .01134 0318 .00039 8.000 6029 6.35 .9434 0050 .01511 .00039 -1.000 6.62 .0211 .00927 .00046 6017 .000 6.66 .1120 .00899 0291 .00046 1.000 .2084 .00909 6.77 0305 .00046 3.000 • 3990 6.33 .00911 0315 .00046 4.000 6.48 6029 .4950 0324 .00046 .00979 6008 6.44 6.005 .683 .00046 .01095 0307 6001 8.000 6.32 .801 .01320 .00046 -1.000 6007 .0196 0298 6.79 .00969 .00077 6018 .000 .1124 6.93 .00963 0297 .00077 6028 1.000 6.62 .2066 .00954 0298 .00077 6056 3.000 .3986 6.55 .00993 0307 .00077 4.000 6.58 .4964 .01041 6039 0303 .00077 6029 .000 .1190 7.25 .00983 0297 .00129 1.000 6043 6.96 .2109 .00966 0294 .00129 6066 3.000 6.67 .4021 .01000 0300 .00129 4.000 6051 6.87 .01082 .4991 0309 .00129 -1.000 7.27 Free 6023 .019 .00835 0305 0.500 0314 Free 6030 6.45 .069 .00709 6.28 Free 0.000 .114 .00570 0310 0308 Free 6016 0.500 6.46 .160 .00688 1.000 6.48 .211 .00784 0322 Free 2.000 6.34 .310 .00782 0322 Free 3.000 Free 6036 6.23 .413 .00778 0331 3-500 6.41 0334 Free 6034 .463 .00810 6038 4.000 0341 Free 6.25 .511 .00811
-1.4
- Airfoil pressure distribution M = 0.6 R., = 3 x 10 .
- m
.4 .llJLLd.!
Figure 2 .
Airfoil pressure distribution M =0.68 R,- = 3 x 10 Figure 3 .- Airfoil pressure distribution M - 0.70 R, = 3 x 10 Airfoil pressure distribution M = 0.72 R.. = 3 x 10 .
..._:._.l M L
- Airfoil pressure distribution M = 0.75 R, = J x 10 .
I 2 8 Figure 6 .- Airfoil pressure distribution K = 0.78 R = 3 x 10 .
-1.4
- Airfoil pressure distribution K = 0.80 R,. = 3 x 10 .
-1.4
- Airfoil pressure distribution M = 0.6 ^a ~ 6 x 10 .
Figure 9 .- Airfoil pressure distribution M = 0.68 R, = 6 x 10 oi
o -1
X 0
+ 1
A
D 3
Figure 10.- Airfoil pressure distribution M = 0.70 6 x 10 .
Figure 11 .- Airfoil pressure distribution M = 0.72 R = 6 x 10 .
-1.4
Airfoil pressure distribution M = 0.75 R,. = 6 x 10 .
.2 : fr•---{"- . 4 Figure 13.- Airfoil pressure distribution M = 0.78 R., = 6 x 10 .
- Airfoil pressure distribution M = 0.80 R,, = 6 x 10 .
Figure 15.- Airfoil pressure distribution K = 0.6 R. = 9 x 10
-1.4
Figure 16 .- Airfoil pressure distribution M = 0.68 R, = 9 x 10 .
-1.4
Figure 17.- Airfoil pressure distribution K = Q.JO R. = 9 x 10
-1.4
-1.2
-1.0
Figure 16.- Airfoil pressure distribution M = 0.72 R. = 9 x 10 .
T Figure 19 .- Airfoil pressure distribution M = 0.75 R,, = 9 x 10 .
-1.4
Figure 20.- Airfoil pressure distribution M = 0.78 PL = 9 x 10 .
- Airfoil pressure distribution M = 0.80 R., = 9 x 10 .
-1.4
- Airfoil pressure distribution M = 0.6 R,, = 12 x 10 .
Figure 2J.- Airfoil pressure distribution M = 0.68 R,, = 12 x 10 Figure 24.- Airfoil pressure distribution M = 0.70 TL, = 12 x 10 .
-1.4
-1.2
Figure 25.- Airfoil pressure distribution M = 0.72 R . . . = 12 x 10 .
.- Airfoil pressure distribution M = 0.75 = 12 x 10 .
Figure 27.- Airfoil pressure distribution M = 0.78 R = 12 x 10 .
-1.4
-1.2
Figure 28.- Airfoil pressure distribution M = 0.6 FL = 17 x 10 .
-1.4
-1.2
Figure 29.- Airfoil pressure distribution M = 0.68 R., = 17 x 10 .
-1.4
Figure 30.- Airfoil pressure distribution M = 0.70 R, = 1? x 10 .
T Figure 31.- Airfoil pressure distribution M = 0.72 17 x 10 .
5*4 Figure 32.- Airfoil pressure distribution M = 0.75 = 17 x 10 .
-1.4
Figure 33 •- Airfoil pressure distribution K = 0.?8 li. = 17 x 10
-1.4
oi
O -1
X 0
+ 1
-1.2
A 2
D 3
O 4
-1.0
Figure 34.- Airfoil pressure distribution M = 0.6 IL. = 25 x 10 .
.- Airfoil pressure distribution M = 0.68 R,j = 32 x 10 .
-1.4
- Airfoil pressure distribution M = 0.70 R = J2 x 10 .
Figure 57.- Airfoil pressure distribution K = 0.12 R, = 32 10 x
.2
A
Figure J8.- Airfoil pressure distribution M = 0.75 R,- = 32 x 10 .
Airfoil pressure distribution M = 0.78 R. = 32 x 10 »U.S GOVERNMENT PRINTING OFFICE: 1975-635-049 70 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON. D.C. 2O546 POSTAGE AND FEES PAID IATIONAL AERONAUTICS AND SPACE ADMINISTRATION OFFICIAL BUSINESS PENALTY FOR PRIVATE USE «3OO SPECIAL FOURTH-CLASS RATE BOOK If Undeliverable (Section 15f POSTMASTER : Postal Manual) Do Not Retu "The aeronautical and space activities of the United States shall be conducted so as to contribute . . . to the expansion of human knowl- edge of phenomena in the atmosphere and space. The Administration shall provide for the widest practicable and appropriate dissemination of information concerning its activities and the results thereof."
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