Effects of independent variation of Mach and Reynolds numbers on the low-speed aerodynamic characteristics of the NACA 0012 airfoil section

NASA Technical Memorandum 4074

Effects of Independent Variation

of Mach and Reynolds Numbers

on the Low-Speed Aerodynamic

Characteristics of the

NACA 0012 Airfoil Section

Charles L. Ladson

LangZey Research Center

Hampton, Virginia

National Aeronautics

and Space Administration

Scientific and Technical

Information Division

Summary theoretical estimates are also discussed. The Langley

Low-Turbulence Pressure Tunnel is the facility used

Presented in this report is a description of a test

for these tests. The Mach number varied from 0.05 to

program conducted in the Langley Low-Turbulence

0.36. The Reynolds number, based on model chord,

Pressure Tunnel to produce the low-speed aero-

generally varied from about 2 to 12 x lo6. One ad-

dynamic characteristics of the NACA 0012 air-

ditional run at a Reynolds number of about 19 x lo6

foil section. During the program, Mach number

and a Mach number of 0.15 with free transition is in

independently varied from 0.05 to 0.36 and the

the tabulated data base but is not in the summary

Reynolds number independently varied from about 2

figures.

to 12 x lo6. The angle of attack variation covered

the range from zero lift coefficient to maximum lift

Symbols

coefficient

All measurements and calculations are in U.S.

An analysis of the data shows that changes in

Customary Units. The International System of Units

Mach number affect lift-curve slope and maximum

(SI) values are in parentheses.

lift coefficient. These changes have little effect on

either minimum drag or maximum lift-drag ratio. b airfoil model span, 36.00 in.

Changes in Reynolds number affect all parameters (91.44 cm)

to some extent. Theoretical predictions of lift-curve

C airfoil model chord, 23.66 in.

slope generally show the trends of the experimen-

(60.10 cm)

tal data with varying Mach number but do not

Cd section drag coefficient from

accurately give the trends with Reynolds number.

integration of wake survey (CD

The magnitude of the predictions is generally higher

in computer-generated figures)

than that of the experiment. Predictions of mini-

mum drag are as much as 0.001 lower than exper-

Cd,o section drag coefficient at zero

iment at the higher Mach and Reynolds numbers

lift

for the free-transition case. With transition fixed

ce section lift coefficient from

at the 5-percent-chord model station, the agreement

integration of model surface

between theory and experiment is excellent.

pressure coefficients (CL in

computer-generated figures)

Introduction

ce,a section lift-curve slope, per deg

Aeronautical researchers have been and are still

using the NACA 0012 airfoil section as a reference

C m section pitching-moment coeffi-

model for the assessment of wall interference and

cient about 0.25~ point from inte-

correction procedures. This airfoil section is also an

gration of model surface pressure

AGARD standard used in the testing of numerical so-

coefficients (CM in computer-

lutions (ref. l) and is in the AGARD two-dimensional

generated figures)

experimental data base (ref. 2). Although a large ex-

lift-drag ratio (L/D in computer-

perimental data base exists for this airfoil through- t l d

generated figures)

out the subsonic and transonic speed range, there

are some areas in which additional data are desir-

M average free-stream Mach number

able. One such area is the low-speed regime. In

R Reynolds number based on model

this regime, the independent effects of Mach num-

chord

ber and Reynolds number on the aerodynamic char-

acteristics of the airfoil are lacking. To supplement

angle of attack, deg (“Alpha” in a

the data available in this area, researchers at Lang-

computer-generated figures)

ley Research Center conducted an investigation of

Subscript:

this airfoil in the Langley Low-Turbulence Pressure

max maximum

Tunnel i n late 1975.

The purpose of this paper is to present a com-

Apparatus

prehensive data base of the low-speed aerodynamic

characteristics of the NACA 0012 airfoil section. In-

Wind Tunnel

cluded are the effects of varying Mach number and

Reynolds number independently and the effects of The Langley Low-Turbulence Pressure Tunnel, fixiig transition location. Comparisons of some of used to conduct the tests on this model, is a closed- the results with previously published data and with throat, single-return facility. The tunnel operates at stagnation pressures from 1.0 to 10.0 atm. The we use an automatic pressure scanning system and Mach number is variable from about 0.05 to 0.46. An variable-capacitance-type pressure transducers. Pre- air-to-water heat exchanger maintains the stagnation cision quartz pressure transducers measure the tun- temperature at or near ambient conditions. The nel stagnation pressure and the reference static pres- maximum Reynolds number is about 15 x lo6 per sure. The angle-of-attack measurement device is a foot (4.92 x lo7 per meter) at a Mach number of calibrated digital shaft encoder operated by a pinion 0.22. The test section is 36.0 in. (91.4 cm) wide gear. A rack attached to the circular plates drives the and 90.0 in. (228.6 cm) high. Descriptions of the pinion gear. A high-speed computer-controlled digi- operational characteristics and calibration results for tal data-acquisition system records the analog output this tunnel are in the appendix of reference 3. At of all measurement devices on magnetic tape. This the time of this test program the turbulence level magnetic tape is the input for post-run data reduc- of the tunnel was unknown, but there were many tion and analysis of the aerodynamic data.

indications that it had increased from the original low

Accuracy

level measured in the early 1940's. This increase was

the result of successive damage to the heat exchanger

The differential pressure gauges used to measure

because of freezing as well as deterioration of the

the model pressures have a maximum range of 50 psi.

screens. After these tests, the tunnel was refurbished

The gauges for measurement of wake total-pressure

and the turbulence level reduced. A description of

loss have a maximum range of 7.5 psi. These preci-

the refurbishment and results of calibration are in

sion transducers have an accuracy of 0.25 percent

reference 4.

of reading from 25 percent of negative full scale

The tunnel sidewalls contain circular end plates

to 100 percent of positive full scale. The preci-

40.0 in. (101.6 cm) in diameter. These plates are for

sion quartz gauges used to measure stagnation pres-

positioning and attachment of the two-dimensional

sure and the difference between reference static pres-

airfoil models. These hydraulically actuated plates

sure and stagnation pressure have full-scale ranges of

rotate with the model and are flush with the test

150 psi and 15 psi, respectively. These gauges have

section sidewall. The airfoil ends attach to rectan-

an accuracy of about 0.01 percent of full scale at low

gular model attachment blocks in these plates. The

pressures to about 0.02 percent of full scale at the

sta-

airfoil mounting blocks locate the 0.25~model

high end of their range.

tion on the center of rotation. Air gaps between the

rectangular blocks and the circular plates are sealed

The repeatability of data is also an indication

with flexible sliding metal seals. For a sketch of these

of the overall data accuracy. On many of the runs

seals, see figure 1.

shown in the tabulated data, two points at a = 0 ' are

listed. An analysis of these repeat points shows that

Wake Survey Rake

when the two points are within 0.01' of each other,

A fixed wake survey rake is cantilevered from

drag coefficient varies by 0.0002 or less, normal-

the test section sidewall. This rake, located at the

force coefficient varies by 0.004 or less, and pitching-

model midspan, is about IC downstream of the model

moment coefficient varies by 0.0002 or less.

trailing edge. The rake consists of 91 total-pressure

tubes 0.060 in. (0.152 cm) in diameter and 5 static-

pressure tubes 0.125 in. (0.318 cm) in diameter. The

Model

total-pressure tubes are oval in cross section for the

last 0.24 in. (0.61 cm) of the tube. A minimum The model, machined from a solid aluminum bil- opening of 0.040 in. (0.102 cm) remains at the tube let, had a chord of 23.66 in. (60.10 cm) and a span

end. The static-pressure tubes each have four flush

of 36.00 in. (91.44 cm), which is the span of the tun-

orifices drilled 90' apart. These orifices, located eight nel. Instrumentation consisted of a total of 81 ori- tube diameters from the end of the tube, are in the fices. There were 24 orifices located in each chord- plane of measurement of the total-pressure tubes. wise row on both the upper and the lower surface.

on the test section sidewall in the plane

Also located These chordwise rows were 4.20 in. (10.67 cm) to

of the total-pressure tubes is an array of flush static- the left of the model center lime. There were also

a sketch of the

pressure orifices. Shown in figure 2 is 33 additional orifices arranged in 3 spanwise rows on

wake survey rake. the upper surface. Grooves, machined in the surface

of the model, accommodated the pressure tubing for

Instrumentation

each orifice location. After the tube installation, the

To make measurements of both the airfoil sur- grooves were covered with a plastic resin. The ori- face static pressures and the wake total pressures, fices, drilled through the plastic and into the tubing,

had a diameter of 0.060 in. (0.152 cm). After com-

coefficients. These basic data plots and tabulations

pletion of this potting process and the drilling of the

are presented as follows:

orifice, the airfoil surface was machined to provide a

surface finish of about 32 rms microinches. The sur-

face was then hand polished in a chordwise direction Mach

with No. 400 carborundum paper to provide the final lumber Transition

aerodynamic surface. The ordinates of the finished 0.15 Free

model were within 0.0002~ of the design ordinates. .20 ~

.25

.30

.36

Tests and Procedures

0.05 Fixed (No. 60-W grit) VI

.15 I 9 VI1

The airfoil test program covered Mach numbers

10 VIII

.30

from 0.05 to 0.36 over angles of attack from about

0.15 Fixed (No. 80 grit) 11 IX

-4’ to 18’. The Reynolds number based on model

.30

chord varied from about 2 to 12 x lo6. Both

0.15 Fixed (No. 120 grit)

the Reynolds number and the Mach number varied

.30

independently for this test program.

0.15 Fixed (No. 180 grit) 4 + - XIV

Included in the program were tests with both

-30

k e d and free boundary-layer transition. For the

fixed-transition runs, carborundum strips were ap-

plied to both the model upper and lower surfaces

Discussion

at the 0 . 0 5 ~ station. The strips were about 0 . 0 1 ~

in width. The carborundum grit size varied with

To summarize the results of these basic data

test Reynolds number to provide enough height to

plots, we present some of the important parameters

trip the boundary layer but not add incremental

as separate figures. These summary figures show

drag. The method of reference 5 was used to deter-

some of the effects of variations of Mach number,

mine the appropriate grit size. Also included in the

Reynolds number, and transition fixing. The discus-

test program were tests made with an NACA-type

sion which follows is the result of an analysis of these

wraparound transition strip. This strip extended

summary figures.

from the 0 . 0 5 ~ location on the upper surface, around

the leading edge, to the 0 . 0 5 ~ location on the lower

Lift-Curve Slope

surface. The grit size was No. 60 for these tests. The

Figures 17 to 23 illustrate the experimental lift-

label “#60-W” indicates these runs on the data plots.

curve slope obtained by a least-squares curve-fit pro-

This series of tests is for comparison with previously

gram. This program used data only from the linear

published data on this airfoil.

angle-of-attack range. Figure 17 illustrates the ef-

All data presented include corrections for the

fects of Mach number and Reynolds number on the

standard low-speed wind tunnel boundary effects

lift-curve slope for the free-transition case. There

described in reference 6. This correction amounts

is a gradual increase in the slope with increasing

to about 2 percent of the measured coefficients.

Mach number and Reynolds number. This increase

in slope amounts to about 5 percent for increases in

Mach number from 0.15 to 0.36. A similar percentage

Presentation of Results

increase results from increases in Reynolds number

from 4 to 12 x lo6. It is thus clear that the effects

of Mach number and Reynolds number are equally

Computer-generated plots of lift coefficient, drag

important in these ranges. Ignoring either of these

coefficient, pitching-moment coefficient, and lift-drag

effects in a comparison of data can be misleading.

ratio as a function of angle of attack present the

Illustrated in figure 18 is a comparison of the lift-

basic results of this investigation. For a few of the

curve slopes for both free- and fixed-transition cases

polars presented, data at the angle of attack for

at a Mach number of 0.15. Fixing the transition at

maximum lift were not available. On the plots of

0.05~ has little effect on the data presented compared

these data, the lift coefficient wits extrapolated to

obtain the maximum value. A dashed line indicates with the free-transition ‘case. The effects of grit these extrapolations. Also included in this report size are small and not consistent. For the case of are tabulations of these integrated force and moment wraparound transition (No. 60 grit), however, the

lift-curve slope decreases about 3 percent. This loss

This percentage decrease is about the same for all

is about the same for all Reynolds numbers. Data at

Reynolds numbers. The maximum lift coefficient in-

a Mach number of 0.30 (fig. 19) show essentially the

creases with increasing Reynolds number for all test

same trends. M = 0.15, this increase amounts

Mach numbers. For

Presented in figures 20 and 21 are comparisons R = 2 to 12 x lo6.

to 20 percent for

of the experimental and theoretical lift-curve slopes

As shown in figure 25 for M = 0.15 and in

for the free-transition case. The theoretical values

figure 26 for M = 0.30, fixing transition at the 0 . 0 5 ~

labeled Stevens are from the analysis program pre- location has very little effect on the maximum lift

sented in reference 7, and the values labeled Eppler

coefficient. Using the wraparound transition method

are from the program presented in reference 8. Fig-

(No. 60 grit) produces a large loss in maximum lift.

ure 20 shows that both theories predict higher val-

This loss is about 25 percent at M = 0.15 and about

ues than the experimental data throughout the Mach M = 0.30. Again, these data show

half this value at

number range. The trends of the theories with Mach

that Mach number and Reynolds number effects are

number, however, are very similar to the experimen- at low speeds. Ignoring these effects in

appreciable

tal data. Figure 21 shows that the overprediction of

data comparisons can lead to erroneous conclusions.

the magnitude of the experimental data reduces from

Minimum Drag

about 7 percent at R = 4 x lo6 to about 3 percent

at R = 12 x lo6. The results are about the same for

Figures 27 to 29 summarize the minimum drag

both Mach numbers shown. This figure also shows

characteristics of this airfoil. For the free-transition

that neither theory accurately predicts the trends of

data (fig. 27) there are no consistent trends in the

the data with increasing Reynolds number. The Ep-

data. Drag levels remain essentially constant with

pler theory shows no effect of Reynolds number, and

increasing Mach and Reynolds number. Fixed tran-

the increase in slope of the Stevens theory is only

sition (figs. 28 and 29) increases the drag over that for

about half the experimental value.

free transition for both Mach numbers. There is little

Figure 22 presents the comparison of theoreti-

effect of grit size on drag for transition fixed at the

cal and experimental lift-curve slopes for the fixed-

0 . 0 5 ~ location. With the wraparound grit, however,

transition case. Like the free-transition results, the

drag increases by about 0.01 for both Mach numbers

theory gives higher slopes and does not give the

throughout the Reynolds number range. This incre-

proper trends with Reynolds number. The Eppler

ment is greater than expected from the increase in

code is in better agreement with experiment than

length of turbulent flow. Drag from the grit particles

the Stevens code, but it shows essentially no varia-

is the probable source of most of this drag increment.

tion with Reynolds number.

Shown in figure 30 is a comparison of the ex-

Figure 23 shows a comparison of data from ref-

perimental and theoretical values of minimum drag.

erence 9 with results from the present investigation.

Once again, results of both the Stevens code (ref. 7)

Both sets of data are from the same facility. The

and the Eppler code (ref. 8) are shown. For both

agreement is good for the free-transition case except

Mach numbers, the experimental drag values with

at the low Reynolds numbers. With the transition

free transition are higher than theoretical values. At

fixed with wraparound grit, the lift-curve slopes from

the lower Mach number, the experimental values are

the present investigation are higher for Reynolds

as much as 0.0006 higher than those from the Stevens

numbers below 6 x lo6. The variation with Reynolds

theory. The results from the Eppler code show only

number is much greater for the data of reference 9.

about half this difference. At the higher Mach num-

The agreement at R = 6 x lo6 is a crossover point

as much as 0.0010 higher than the

ber, the data are

and is probably not typical of the results. The sus-

Stevens code results. The Eppler code results again

pected higher turbulence level of the facility during

in the

show only about half this difference. As stated

the present tests may account for some of these dif-

discussion of lift-curve slope, the higher experimen-

ferences. The density of the grit may also be a con-

tal values are probably the result of the tunnel turbu-

tributing factor.

lence level. Turbulence will move the transition point

forward on the model compared with the theoretical

Maximum Lift Coefficient

M = 0.30, the ex-

location, thus increasing drag. At

The maximum lift coefficient attained before stall

perimental drag with free transition approaches that

is an important parameter for low-speed airfoil tests. for fixed transition at the higher Reynolds numbers.

Figures 24 to 26 present this parameter for the This shows that the transition location is approach- present tests. For the free-transition case (fig. 24), ing the 0 . 0 5 ~ station on the model. The orifice lo- the maximum lift coefficient decreases about 25 per- cations on this model are about 23 percent of the cent as the Mach number increases from 0.15 to 0.36. model semispan to the left of the tunnel center line.

slope or maximum lift coefficient. Minimum drag This offset reduces the possibility of orifice-induced increases with fixed transition and the maximum turbulence on the measurement of wake drag, which lift-drag ratio thus decreases. is measured on the tunnel center line.

With the transition location fixed, figure 30 shows

4. The theoretical values of lift-curve slope are

that the agreement between theory and experiment

higher than the experimental values by as much

is excellent. Both theoretical programs give nearIy

as 7 percent at the lower Reynolds number with 1

identical results.

I

free transition. Both theories presented generally

Figure 31 presents a comparison of the present

predict the experimental trends with variation of

test results with those from reference 9. With free

I

Mach number but do not adequately predict the

transition, the present test results are about 0.0005

trends with Reynolds number. With fixed transi-

higher at most Reynolds numbers. This again is

tion, the Stevens theory predicts values as much

likely the result of differences in tunnel turbulence

as 10 percent higher than experimental values,

levels. With fixed transition, the present test results

5. With free transition, both theories underestimate

are lower by about 0.001 for all but the lowest

the minimum drag level. The Stevens theory

Reynolds number. This difference may be the result

is as much as 0.0010 low at the higher Mach

of differences in density of grit application.

numbers and Reynolds numbers. The Eppler

Maximum Lift-Drag Ratio

code is within 0.0005 for most cases. Theoretical

Plotted in figures 32 to 34 are the variations

values of minimum drag with fixed transition are

with Mach and Reynolds number of the maximum

in excellent agreement with the data.

lift-drag ratio. For free transition, figure 32 shows

NASA Langley Research Center little variation in this parameter with Mach number.

Hampton, Virginia 23665-5225

Maximum lift-drag ratio increases with increasing

August 23, 1988

Reynolds number up to about 6 x lo6. Above this

value little variation occurs.

With k e d transition (figs. 33 and 34), the values References

of this maximum ratio are slightly less than for

1. Experimental Data Base for Computer Program Assess-

free transition. The data also show a continual

ment. AGARD-AR-138, May 1979.

increase with increasing Reynolds number. The use

2. Lock, R. C.: Test Cases for Numerical Methods in Two-

of wraparound grit produces a 20- to 30-percent

Dimensional Itansonic Flows. AGARD Rep. No. 575,

decrease in maximum lift-drag ratio when compared

Nov. 1970.

with that produced for the 0 . 0 5 ~ transition location.

3. Beasley, William D.; and McGhee, Robert J.: Experi- mental and Theoretical Low-Speed Aerodynamic Charac-

Conclusions

teristics of the NACA 651-219, a = 0.50, Airfoil. NASA

An investigation conducted in the Langley Low-

TM X-3160, 1975.

Turbulence Pressure Tunnel has produced the low-

J.; Beasley, William D.; and Fos- 4. McGhee, Robert speed aerodynamic characteristics of the NACA 0012 ter, Jean M.: Recent Modifications and Calibration of the Langley Low- Turbulence Pressure Tunnel. NASA

airfoil. This investigation covered a Mach number

TP-2328, 1984.

range of 0.05 to 0.36. The corresponding Reynolds

5. Braslow, Albert L.; and Knox, Eugene C.: Simplified

number range was about 2 to 12 x lo6. The angle-

Method for Determination of Critical Height of Distrib-

of-attack variation covered the range from zero lift

uted Roughness Particles for Boundary-Layer Itansition

coefficient to maximum lift coefficient. An analysis

at Mach Numbers From 0 to 5. NACA TN 4363, 1958.

of the data yields the following conclusions: 6. Allen, H. Julian; and Vincenti, Walter G.: Wall Inter-

1. Increasing Mach number at constant Reynolds

ference in a Two-Dimensional-Flow Wind Tunnel, With

number increases the lift-curve slope and de-

Consideration of the Effect of Compressibility. NACA

creases maximum lift coefficient, but it has little

Rep. 782, 1944. (Supersedes NACA WR A-63.)

effect on minimum drag and maximum lift-drag Stevens, W. A.; Goradia, S. H.; and Braden, J. A.: 7.

Mathematical Model for Two-Dimensional Multi- ratio.

component Airfoils in Viscous Flow. NASA CR-1843,

2. Increasing Reynolds number at constant Mach

1971.

number increases the lift-curve slope, maximum

A Computer Pro- Eppler, Richard; and Somers, Dan M.: 8.

lift coefficient, and, to some extent, maximum

gram for the Design and Analysis of Low-Speed Airfoils.

lift-drag ratio. Minimum drag decreases with

NASA TM-80210, 1980. '

increasing Reynolds number only for the fixed-

9. Loftin, Laurence K., Jr.; and Smith, Hamilton A.: Aero- transition case.

dynamic Characteristics of 15 NACA Airfoil Sections at 3. Fixing transition at the 5-percent-chord location Seven Reynolds Numbers From 0.7 x lo6 to 9.0 x lo6.

on the model has little effect on either lift-curve NACA TN 1945, 1949.

Table I. Force Coefficients at M = 0.15 for Free Transition

R = 2.00 x lo6 a t deg.

t/d Cd CL cm -4.25 -00730 -.4300 -.0040 -58.90

-2.10 .00620 -. 2150 -.0020 -34.68

.oo .00620 .oooo * 0000 .oo 1.85 .00620 .1940 -0030 31.29 4.25 .00670 .4450 .0040 66.42 6.05 -00870 .6250 .0070 71.84 8.15 .01270 .8550 .0080 67.32 10.15 .01350 1.0450 * 0120 77.41 11.15 -01490 1.1350 .0140 76.17 12.10 -01640 1.2180 .0180 74.27 13.08 -01880 1.2900 .0190 68.62 14.25 -02280 1.3620 -0220 59.74 15.25 .02910 1.4080 -0250 48.38

16.25 .7530 -. 1060

R = 3.94 x lo6 a, deg.

e/d Cd ce cm -4.06 .00701 -.4019 .0022 -57.33

-.04 .00659 -.0033 -.0002 -. 50

3.96 .00631 ,4203 .0015 66.61 6.00 .00712 .636 -0019 89.33 8.17 .00985 .8657 .0077 87.89 10.02 .00934 1.0629 .0071 113.79 11.07 .01069 1.1622 .0080 108.72 12.08 .01289 1.2489 .0095 96.93 13.37 .01523 1.3587 .0116 89.22 14.10 .01725 1.4215 .0145 82.41 15.14 .02045 1.4844 .0196 72.60 18.09 -22773 1.0946 -.0800 4.81 R = 5.97 x 106 a t deg.

l/d Cd cm -4.05 .00700 -.4280 .OOOO -61.14 -2.00 .00650 -.2150 .OOOO -33.08 05 .00650 -0040 .OOOO .62 1.98 .00680 .2080 -0020 30.59 4.18 .00760 -4520 .0030 59.47 6.20 .00680 -6630 .0040 97.50 8.22 .00800 -8800 .0050 110.00 10.18 .01050 1.0880 .0070 103.62 11.08 .01140 1.1800 .0080 103.51 12.25 .01250 1.2920 .0090 103.36 13.10 .01300 1.3680 .0110 105.23 14.28 .01620 1.4580 .0150 90.00 15.20 .01870 1.5280 -0180 81.71 16.18 .02180 1.5900 -0210 72.94

16.90 ,. 02440 1.6180 .0230 66.31

17.35 .02750 1.6600 .0250 60.36 17.65 1.6450 -0270 18.65 1.0050 -.lo80

Table I. Concluded

R = 8.86 x lo6 a, deg.

L/d Cd

-4.00 -00680 -. 4300 .0030 -63.24

-1.98 .00630 -.2150 .OOlO -34.13

-.lo .00630 -. 0050 .oooo -.79

2.13 .00650 -2300 .0020 35.38 4.13 .00700 .4500 -0030 64.29 6.08 .00720 .6650 -0050 92.36 8.02 .00850 .8750 .0060 102.94 10.30 -00980 1.1150 .0080 113.78 11.18 .01050 1.2050 .0080 114.76 12.22 .01150 1.3050 .0090 113.48 13.42 .01280 1.4120 .0130 110.31 14.13 .01480 .0150 99.32 1.4700 15.12 .01680 1.5430 .0180 91.85 16.48 .02250 1.6300 -0240 72.44 17.38 .02470 1.6730 -0280 67.73 18.42 .02950 1.6930 .0320 57.39 R = 11.90 x 106 a, deg.

e/ d

Cd C L cm

-4.20 ,00684 -. 4665 .0006 -68.23

-2.01 .00611 -. 2286 .0006 -37.45

-.05 -1.74

.00637 -. 0111 -0001

-.03 .00634 -. 0090 .0003 -1.42

2.00 .00692 -2159 -. 0001 31.20

4.17 .00687 .4575 .0002 66.60 6.10 .00713 .6693 .0007 93.84 8.11 -00826 .8885 .0016 107.53 10.40 -00975 1.1289 .0040 115.84 116.28 11.43 .01058 1.2308 -0057 12.52 .01166 1.3331 -0078 114.31 13.25 .01293 1.3963 -0096 107.95 16.05 .02156 1.6004 .0198 74.25 18.04 .05429 1.6174 .0225 29.79 18.25 .25587 1.2188 -.1341 4.76 19.46 -29135 1.1064 -.1823 3.80 R = 18.90 x 106 a, deg.

L/ d Cd '3 =m -2.07 -00617 -.2369 .0009 -38.36

-.03 .00655 -. 0091 .0006 -1.39

-03 .00664 -. 0019 .0005 -. 28

1.99 .00716 .2177 -.0001 30.40 64.90

4.20 .00716 - 4 644 -. 0001

6.05 .00737 .6694 0000 90.82 ,0016 101.44 8.37 .00916 .9290 10.02 .01075 1.1007 -0036 102.40 1.2557 .0060 104.42 11.57 .01203 12.40 -01292 1.3339 .0079 103.25 ,01345 .0094 103.86 13.12 1.3968 14.16 .01514 1.4833 -0127 97.96 15.14 .01900 .0167 81.79 1.5541 16.17 -02175 1.6169 .0215 74.35 44.51 17.84 .03728 1.6593 .0288

18.69 .26619 1.0867 -. 1108 4.08

.32534 1.1321 -. 1148 3.48

20.17

Table 11. Force Coefficients at M = 0.20 for Free Transition

R = 2.66 x lo6 (I, deg.

l/ d

Cd ce cm

-4.11 .00729 -. 4265 -.0034 -58.53

-2.00 .00655 -. 2138 -. 0012 -32.63

-00 -00599 -. 0058 .0006 -.97

.oo .00607 -. 0062 .0004 -1.02

2.07 .00612 .2138 .0016 34.96 4.27 -00663 .4457 .0033 67.25 81.80 6.03 .00771 .6304 .0051 8.21 .8590 .0052 10.19 .01318 1.0593 -0099 80.39 11.15 .01410 1.1497 .0116 81.55 12.25 .01549 1.2444 -0139 80.36 74.25 13.27 -01784 1.3246 -0165 14.29 -02140 1.3937 .0198 65.13 15.18 .02592 1.4420 .0233 55.63 16.28 .03599 1.4604 .0266 40.58 -.0827 4.41 17.25 .25283 1.1140 18.16 .26666 1.1328 -.0830 4.25 19.24 .28507 1.1597 -.0846 4.07 R = 3.99 x lo6 a, deg.

e/ d

Cd C L c, -4.09 .00695 -.4416 -.0002 -63.54 -2.04 .00638 -.2219 -.0009 -34.78

-. 04 -00648 -.0097 .OOOO -1.49

-03 .00670 -.0016 -.0001 -.25 .00687 .2119 .0016 30.84 2.04 4.02 .00654 .4220 .0023 64.53 6.08 -00717 .6446 .0034 89.91 8.07 .00963 -8553 .0060 88.80 10.18 -0ii7a 1.0789 .0070 91.61 11.19 .01242 1.1749 .0094 94.58 12.45 .01412 1.2902 .0122 91.40 87.65 13.08 .01532 1.3430 .0140 14.24 -01817 1.4299 .0177 78.68 15.27 .02136 1.4976 .0220 70.12 16.34 -02660 1.5489 .0263 58.23 17.34 .07842 1.5745 ,0146 20.08

18.08 .29925 1.0123 -. 1022 3.38

19.00 -28959 1.1632 -.0839 4.02 R = 5.95 x lo6 (I, deg.

l / d Cd CL cm

-4.08 .00688 -.4313 -. 0007 -62.65

-2.11 .00631 -. 2210 .0002 -35.01

-.12 .00637 -. 0080 .0003 -1.25

-.11 .00638 -. 0042 .0002 -.65

1.95 .00680 .2152 .OOOl 31.66 .00731 .4375 .ooos 59.82 3.97 6.03 .00686 .6623 -0018 96.51 -00796 -8674 .0033 108.93 7.91 9.99 .01044 1.0843 .0053 103.85 11.15 -01156 1.1994 .0073 103.78 12.12 .01244 1.2902 .0093 103.72 13.13 .01422 1.3792 .0121 96.99 14.04 .01591 1.4539 .0153 91.37 15.03 -01918 1.5238 .0189 79.43 68.26 16.29 .02339 1.5966 .0244 17.08 .02723 1.6258 .0279 59.70

18.00 -26026 1.1169 -. 1062 4.29

19.04 .28442 .9393 -. 1086 3.30

Table 11. Concluded

R = 8.93 x lo6 LY, deg.

t/d Cd =t cm

-4.05 .00696 -. 4490 .0002 -64.53

-2.17 -.2464 .0002 -38.62 .00638

-.03 .00619 -. 0101 -. 0001 -1.63

.02 .00625 -. 0025 -. 0004 -. 40

2.07 -. 0003

-00685 .2245 32.78 4.03 -00721 .4431 .0002 61.47 6.05 .00719 .6683 .0009 92.94 8.21 .00864 .9046 0023 104.67 10.22 .0047 112.04 .00995 1.1147 11.09 .01117 1.2070 .0061 108.01 12.13 .01189 1.3089 .0084 110 * 12 13.33 .01359 1.4162 .0116 104.22 14.17 .01553 1.4845 .0145 95.60 15.16 .0181 .01835 1.5586 84.93 16.24 .02220 1.6231 .0230 73.10 17.53 .02784 1.6681 .0283 59.92

18.23 .26063 1.2387 -. 1230 4.75

19.08 .28015 1.1290 -. 1032 4.03

R = 11.95 x lo6 LY, deg.

t/d Cd ct cm -4.08 .00679 -.4602 -0007 -67.76

-2.12 .00626 -.2422 -. 0004 -38.69

-. 05 .00633 -. 0101 .OOOl -1.60

2.00 .00694 -2190 -. 0001 31.54

4.12 .0002 .00705 .4576 64.93 6.05 .00711 .6719 -0007 94.49 8.12 .00830 .9056 .0020 109.08 10.47 .00978 1.1547 .0052 118.06 11.32 -01082 1.2400 .0066 114.60 13.13 -01309 1.4101 .0109 107.69 14.73 .01738 1.5376 .0164 88.47 15.21 .0185 .01886 1.5713 83.33 16.18 -02249 1.6279 -0237 72.39 17.46 .03427 1.6669 .0295 48.64

18.35 .25142 1.2593 -. 0980 5.01

19.10 -30417 1.0541 -. 1288 3.47

Table III. Force Coefficients at M = 0.25 for Free Transition

R = 3.29 x lo6 a, deg.

l/d

Cd ce cm

-4.00 .00736 -. 4258 -. 0028 -57.88

-2.00 .00656 -. 2178 -. 0011 -33.21

.oo

.00662 -. 0045 .0003 -.68

.05 .00661 .0005 .0004 07 2.06 -00614 .2169 .0015 35.34 4.25 .00662 .4509 .0030 68.12 6.09 .00738 .6491 .0044 87.91 8.33 .01189 .8916 .0068 74.99 10.13 .01263 1.0752 -0096 85.16 11.39 .01403 1.1982 .0134 85.43 12.28 .01529 1.2713 .0146 83.17 13.10 -01759 1.3397 .0170 76.18 14.32 .02165 1.4185 .0222 65.52 15.20 .02708 1.4576 .0262 53.83

16.16 .23673 1.1493 -. 0883 4.85

17.66 .25620 1.1435 -. 0869 4.46

18.61 .27777 -. 0868

1.1636 4.19 R = 3.98 x lo6 a , deg. cd

e/ d

ce cm

-4.00 -00717 -. 4284 -.0024 -59.76

-2.08 .00648 - * 2214 -. 0010 -35.11

-. 0019 .oooo

.Ol .00653 -.29 1.99 ,00688 .2104 .OOlO 30.57 4.04 .00655 .4326 .0023 66.01 6.24 .00723 .6542 ,0154 90.49 8.19 .01047 .8794 .0067 83.98 10.36 .01229 1.1089 .0091 90.22 12.51 -01490 1.3071 .0147 87.76 13.24 .01677 1.3658 .0172 81.45 14.11 .01953 1.4269 ,0209 73.05 15.17 .02487 1.4860 .0258 59.75 16.34 .05556 1.4104 .0183 25.39

17.11 -25278 1.1775 -. 0904 4.66

-. 0897 4.41

18.19 .26552 1.1703

19.12 .28717 1.1760 -. 0881 4.10

R = 5.95 x lo6 a, deg.

l/d Cd c t cm

-4.22 .00715 -. 4512 .OOlO -63.12

-2.13 -00630 -. 2329 -.0040 -36.97

-. 0002

-.03 .00623 -. 0119 -1.92

-.01 .00634 -.0078 -. 0002 -1.23

2.09 .00672 -2245 .0005 33.41 3.99 .00725 .4325 .0012 59.66 6.00 ,00694 -6557 .0026 94.45 8.06 .00803 .8740 .0046 108.84 -0074 10.13 .01173 1.1034 94.10 11.17 .01189 1.2096 .0092 101.73 12.09 .01262 1.2960 .0116 102.69 13.14 ,01465 1.3929 .0152 95.07 14.34 .01784 .0204 83.16 1.4835 15.15 .02157 1.5364 .0248 71.22 16.21 .02903 1.5616 .0310 53.80 17.32 .23316 1.1335 -.0924 4.86

.25539 1.1233 -. 1069 4.40

18.41

Table 111. Concluded

R = 8.92 x lo6 a, deg.

L/ d

Cd CL cm

-4.01 .00696 -.4493 .OOOl -64.58 -36.49

-2.02 -00638 -. 2327 .OOOl

-00 I 00673 -. 0043 -. 0004 -.63

1.93 .00728 .2116 -. 0002 29.07

4.13 -00744 .4625 .0002 62.17 .0014 87.39 6.07 -00778 .6801 8.09 .00874 .9081 .0031 103.86 10.12 -01006 1.1258 .0060 111.94 11.20 .01165 1.2352 .0080 106.05 12.15 .01218 1.3285 .0109 109.03 13.14 .01412 1.4188 .0141 100.46 14.14 -01646 1.5002 .0183 91.14 1.5724 76.28 15.28 .02061 .0241 16.13 .02642 1.5948 .0297 60.37

17.29 .23437 1.2748 -. 1173 5.44

18.21 .26412 1.1905 -.0907 4.51 R = 11.95 x lo6 a, deg.

@/d Cd C@ Cm -4.04 .00680 -.4630 .0004 -68.13 -2.10 .00629 -.2443 .0006 -38.86 -.03 .00653 -.0078 .OOOO -1.20 -1.34 -.03 .00633 -.0085 .0001 1.99 .00705 .2211 -.0003 31.37 3.97 .00719 62.08 .4464 .0001 6.23 .00742 .7028 .0011 94.73 8.13 .00879 .9203 .0029 104.64 10.10 .01076 1.1327 .0056 105.31 .01085 1.2321 .0078 113.61 11-08 108.77 12.09 .01225 1.3329 .0103 13.23 .01406 1.4385 .0141 102.29 .01683 90.56 14.29 1.5240 .0184 15.26 -02065 1.5807 .0234 76.54 1.6007 .0284 57.79 16.19 .02770 17.43 -24160 1.2119 -.0942 5.02 .26570 1.1466 -.lo01 4.32 18.19

Table IV. Force Coefficients at M = 0.30 for Free Transition

R = 3.90 x lo6 a I deg.

e/ d Cd cm

-4.11 .00727 -. 4479 -.0026 -61.60

-1.96 .00651 -.2191 -. 0011 -33.66

.04 .00657 .OOOl .oooo .02 .05 00657 0013 .OOOl .19 2.05 -00698 .2216 .OOll 31.73 4.19 .00672 .4561 .0028 67.93 6.20 .00743 -6781 ,0048 91.27 8.06 -01030 .8821 -0074 85.62 10.15 .01270 1.1089 87.32 .0112 11.11 .01374 1.2014 .0139 87.46 12 * 10 .01569 1.284 .0167 81.84 13.16 ,02122 1.3468 * 0221 63.48 14.13 .03118 1.3466 .0292 43.18

15.33 .17380 1.0964 -. 0656 6.31

16.46 .24760 1.1197 -. 0995 4.52

17.09 .25661 1.1578 -.0878 4.51

18.61 .27777 1.1636 -. 0868 4.19

R = 5.93 x lo6 a I deg.

v d

Cd ce cm

-4.37 .00648 -.4894 -.0015 -75.54 -2.02 -00630 -.2316 -.0005 -36.80 -.01 .00635 -.0079 -.0002 -1.25 .03 .00659 -.0026 -.0002 -.40 4.03 .00728 .4452 .0015 61.19 6.08 .00711 .6762 -0031 95.13 8.13 .00822 .9039 .0057 110.01 10.12 .01200 1.1251 .0094 93.78 11.13 .01232 1.2273 -0117 99.58 12.12 -01397 1.3172 .0155 94.26 13.32 .01994 1.3939 .0226 69.91 14.27 .03023 1.3917 .0294 46.04 15.14 .12487 1.2273 -0278 9.83 16.25 .20698 1.1132 .0124 5.38 R = 8.96 x lo6 a I deg.

(/d Cd CL cm

-4.12 .00706 -. 4587 -.0001 -64.96

-2.14 .00649 -. 2367 .OOOl -36.50

-. 12 .00673 -.0065 -. 0001 -. 96

1.85 .00729 .2184 .oooo 29.95 3.96 -00752 .4608 .0004 61.30 6.04 .00783 .6995 * 0019 89.35 7.97 .00918 .9228 .0041 100.54 10.02 .01023 1.1454 .0079 111.99 11-09 .01215 1.2536 .0105 103.20 12.01 .01336 1.3442 .0147 100.58 13.13 .01829 1.4241 .0223 77.87 14.14 .02821 1.4274 .0298 50.59

15.20 .16128 1.3001 -. 0772 8.06

15.99 .20284 1.2011 -.0818 5.92

Table IV. Concluded

R = 11.90 x lo6 a, deg.

e/ d

Cd ce = u t -64.17

-4.03 -00720 -. 4620 * 0010

-2.01 .00680 -.2330 .oooo -34.26 .02 .00680 .0030 .oooo .44 2.02 -00780 .2350 .OOlO 30.13 3.92 .00770 .4550 .0020 59.09 6.05 .00800 .7030 .0050 87.88 8.08 -00890 .9350 .0060 105.06 10.05 .01120 1.1580 .OlOO 103.39 11.13 .01170 1.2700 .0130 108.55 12.10 -01300 1.3700 .0150 105.38 13.20 .01780 1.4500 .0240 81.46 14.28 .02910 1.4400 .0330 49.48

15.30 1.2950 -. 0550

Table V. Force Coefficients at M = 0.36 for Free Transition

R = 3.93 x lo6 a , deg.

L/d

Cd ce cm

-3.97 .00727 -. 4467 -. 0026 -61.48

-.2335 -. 0009 -35.41

-2.03 .00659

-.03 .00668 -. 0108 .oooo -1.61

. 00 -00672 -. 0075 .0003 -1.12

2.06 .00702 .2243 .OOlO 31.97 4.01 -00678 -4460 .0027 65.77 91.38 6.34 .00777 .7097 .0053 8.03 .01036 -8981 .0090 86.69 10.15 .01415 1.1260 .0163 79.60 11.27 ,02119 1.1828 .0269 55.81 12.14 .03128 1.2044 -0322 38.51

13.36 .14591 1.1093 -. 0394 7.60

14.12 .18655 1.0554 -.0774 5.65 R = 5.88 x lo6 a, deg.

l/d Cd cm

-4.00 -00618 -. 4722 -. 0017 -76.41

-2.04 .00636 -. 2387 -.0005 -37.54

-. 0003 -1.49 ’

-. 02 .00646 -. 0096

2.03 .00685 .2291 .0016 33.44 4.08 .00737 .4682 .0019 63.52 6.06 .00789 .6843 .0052 86.70 8.12 .00865 .9171 .0070 105.98 10.18 .01357 1.1439 .0112 84.27 11.23 .02008 1.2171 .0259 60.61 .0322 42.81 12.12 .02867 1.2274 13.30 -09164 1.1671 .0048 12.74 .15857 1.1641 -.0434 7.34 14.24

15.18 .19763 1.1281 -. 0670 5.71

R = 8.90 x lo6 a , deg.

t/d Cd ce cm .0003 -66.06

-4.27 .00718 -. 4743

-2.01 .00755 -. 2377 .0017 -31.48

28.58 1.95 .00780 .2229 .0021 3.92 -00800 .4604 .0009 57.55 .00798 .6971 .0027 87.36 5.94 8.03 .00975 .9135 -0007 93.69 10.81 .01785 1.2265 .0233 68.71 40.58 12.21 .03055 1.2398 .0294 13.26 .05821 1.2466 .0190 21.42 13.99 .72320 1.2193 .0228 1.69

Table VI. Force Coefficients at M = 0.05 for Transition Fixed With No. 60-W Grit

R = 0.70 x lo6 a, deg.

Cd ce cm

-. 0055 -31.29

-4.03 .01121 -. 3507

-1.98 -00857 -.1716 -. 0050 -20.03

-00 -00872 -. 0094 -. 0003 -1.08

2.00 .00847 -1545 .0032 18.24 4.00 .01080 .3283 .0070 30.39 6.06 .01237 .5327 .0025 43.07 8.12 .01450 .6878 .0086 47.43 10.15 43.34 .01853 .8030 .0171 11.12 .02147 -8495 .0200 39.56 12.18 -02716 .8957 .0233 32.98

13.19 .08334 .8918 -. 0089 10.70

14.10 .15345 .9391 -.0479 6.12

15.32 .16754 .8626 -. 0580 5.15

16.03 .21721 -7506 -. 0669 3.46

17.29 .23011 .9005 -.0762 3.91

18.15 .23479 .9382 -. 0672 4.00

Table VII. Force Coefficients at M = 0.15 for Transition Fixed With No. 60-W Grit

R = 2.00 x lo6 a, deg.

t/d ' d -.4300 -.0041 -35.44 -4.16 .01213 -2.14 .01080 -.2271 -.0022 -21.03

-. 03 .01091 -.0102 -.0005 -.93

.oo .OllOO -.0060 -.0001 -.54 1.97 .01084 .1970 .0017 18.17 36.63 4.14 .01152 -4219 .0039 5.98 .01336 .6084 .0063 45.54 .01631 .8123 .0098 49.82 8.10 10.04 .02093 .9789 .0143 46.78 .02497 1.0644 .0170 42.63 11.22 12.25 .02921 1.1276 .0194 38.60 13.15 .03599 1.1647 .0221 32.36 .21056 -9020 -.0828 4.28 14.15 15.17 .23758 .9025 -.0939 3.80 R = 4.00 x lo6 -39.42 -4.07 .01099 -.4332 -.0032 -2.06 .00952 -.2243 -.0016 -23.55 .oo .00954 -.0075 -.0003 -.78

.02 .00952 -. 0052 -. 0003 -.54

.2130 .0011 21.48 2.08 .00991 3.93 .01015 .4102 .0024 40.42 5.99 .01119 -6256 .0044 55.90 8.06 .01448 .8262 .0088 57.04 10.04 .01939 1.0068 -0121 51.91 1.0844 .0152 48.26 11.04 .02247 12.06 .02668 1.1518 -0183 43.17 13.18 .03355 1.2003 .0222 35.78 14.26 .04445 1.2068 .0249 27.15 15.03 .22424 .9101 -.0845 4.06 R = 6.00 x lo6

-4.15 .01048 -. 4455 -. 0022 -42.53

,00905 -.2321 -. 0011 -25.64

-2.13

.oo .00895 -. 0043 -. 0002 -.48

2.06 .00945 .2145 .0008 22.69 4.06 .00976 -4296 .0020 44.04 6.01 .01116 .6359 .0037 56.99 -0066 59.43 8.03 .01406 .8354 10.12 -01928 1.0209 .0112 52.96 .02188 .0146 50.28 11.17 1.1002 12.05 .02551 1.1585 .0177 45.42 * 03200 .0221 37.76 13.24 1.2083 14.02 .03891 1.2169 .0246 31.27

-. 0828 4.34

15.06 .21816 .9470 16.16 .25187 -8884 -.0940 3.53

Table VII. Concluded

R = 8.95 x lo6 a, deg.

e/ d

Cd =e c , -4.09 .01008 -.4498 -.0020 -44.62 -2.05 .00867 -.2331 -.0007 -26.88

-. 0002

-.01 -00862 -. 0107 -1.24

.Ol .00847 -. 0093 .oooo -1.10

2.03 .00905 -2100 -0005 23.21 4.03 -00926 -4262 .0015 46.04 6.12 -01048 .6467 .0042 61.71 8.05 .01340 .a438 .0059 62.97 10.09 .01840 1.0279 .0107 55.85 .0141 52.61 11.15 .02110 1.1102 12.26 .02538 1.1800 .0181 46.49 13.18 .03068 1.2209 .0214 39.79 14.17 .03814 1.2289 .0243 32.22 15.08 .21771 .7151 .0767 3.28

16.27 .25842 .9974 -. 1008 3.86

R = 12.10 x 106

-4.07 .01004 -.4506 -. 0016 -44.86

-2.01 .00834 -.2310 -. 0004 -27.70

.01 .00842 -. 0088 .OOOl -1.04

-.29

.08 .00827 -.0024 -. 0001

2.01 .00882 ,2074 .0006 23.51 4.01 .00917 .4262 -0013 46.46 6.13 .01036 -6514 .0034 62.85 8.07 .01286 .8474 -0060 65.90 10.26 .01845 1.0438 .0116 56.57 11.23 .02131 1.1209 .0139 52.61 .1128 42.10 12.37 .02305 .9704 c

Table VIII. Force Coefficients at M = 0.30 for Transition Fixed With No. 60-W Grit

R = 4.00 x lo6 a, deg.

L/ d

Cd Cm

-4.18 .01124 -. 4607 -. 0040 -40.99

-2.14 .00969 -.2421 -. 0021 -24.98

-. 04 .00964 -. 0100 -. 0004 -1.04

-. 03 -00967 -. 0112 -. 0004 -1.16

2.03 -00986 .2171 .0013 22.02 4.03 .01049 -4365 .0033 41.59 6.03 .01203 .6515 -0061 54.18 8.09 .01534 .8647 .0106 56.36 10.09 .02138 1.0389 -0170 48.60 11.58 .02910 1.1333 .0232 38.94

12.26 -11061 .9854 -. 0357 8.91

13.04 -18059 .9263 -. 0596 5.13

R = 6.00 x lo6

-4.20 .01067 -. 4719 -. 0033 -44.21

-2.01 .00914 -.2313 -. 0014 -25.31

-. 04 .00921 -. 0115 -. 0003 -1.25

.Ol .00925 -. 0060 -. 0003 -.65

1.92 .00947 .2075 .OOlO 21.92 4.05 .00999 .4456 .0028 44.58 6.00 .01144 .6588 .0053 57.61 8.02 .01458 .8673 .0096 59.50 10.11 .02073 1.0546 .0167 50.87 11-09 .02524 1.1243 .0210 44.54 35.86 12.17 .03259 1.1685 .0257

13.07 .17991 .9609 -. 0638 5.34

14.03 .20761 .9278 -. 0690 4.47

R = 8.95 x lo6

-4.26 .01040 -.4872 -. 0028 -46.85

-2.19 .00880 -. 2562 -. 0012 -29.12

-. 01 .00860 -. 0084 -. 0002 -.97

.oo -00863 -.0063 -. 0001 -.73

2.08 .00927 .2285 -0008 24.66 3.94 .00956 .4379 .0023 45.81 6.18 .01117 .6859 .0053 61.41 8.21 .01450 .8984 .OlOO 61.98 10.08 .02016 1.0672 .0167 52.93 11.27 .02559 1.1490 .0217 44.90 12.12 .03171 1.1816 .0263 37.26 -.0710 5.25 13.31 .18204 .9565

14.21 .21204 .9134 -. 0724 4.31

R = 12.00 x lo6

-4.07 -01004 -.4707 -. 0022 -46.87

-1.96 .00851 -. 2351 -. 0009 -27.62

-.02 .00826 -. 0112 -.0001 -1.35

-00 .00838 -. 0088 .oooo -1.05

2.05 .00893 .2237 * 0010 25.04 4.03 .00939 .4511 .0023 48.05 6.04 -01070 .6724 .0048 62.86 8.15 .01377 .8957 .0095 65.02 11.38 .02580 1.1595 .0228 44.94 12.23 .03140 1.1906 .0263 37.92

13.12 .16692 .9603 -. 0588 5.75

Table IX. Force Coefficients at M = 0.15 for Transition Fixed With No. 80-W Grit

E R = 2.00 x lo6 a, deg.

Y d

Cd CL cm

-4.03 ,01006 -.4205 -. 0018 -41.80

-2.03 .00973 -.2159 -. 0007 -22.19

.oo .00992 -.0037 -.0002 -.38

.02 .00995 -. 0025 .0002 -.25

1.99 -00979 .2060 .OOlO 21.04 4.01 .01033 .4187 * 0019 40.54 6.11 .01068 .0040 .6374 59.70 8.08 .01286 .8214 .0067 63.85 10.24 .01552 1.0261 .0112 66.12 11.15 .01615 1.1118 -0135 68.86 12.25 .01807 1.2013 .0160 66.47 13.17 .01963 1.2654 .0176 64.47 14.18 -02360 1.3308 .0208 56.39 15.16 .02910 1.3748 .0238 47.24 16.02 .22889 1.0732 -.0815 4.69 16.99 .24907 1.0919 -.0838 4.38 R = 3.99 x lo6 -4.03 .00930 -.4319 -.0008 -46.47 -26.74 -2.08 .00852 -.2279 -.0002 -.05 .00874 -.0118 .0001 -1.36

-04 .00864 -.0037 -.0001 -. 43

2.03 ,00865 .2105 .0003 24.33 4.06 ,00872 .4300 .0009 49.31 6.13 .00917 .6498 .0020 70.87 8.17 .01120 .a631 .004i 77.10 10.19 .01288 1.0643 .0069 82.66 11.15 .01372 1.1559 .0084 84.25 12.12 .01401 1.2413 .0103 88.59 13.23 83.58 .01597 1.3349 .0131 14.20 .01853 1.4103 .0159 76.10 15.27 .02115 1.4818 .0199 70.06 16.15 .02498 1.5287 .0229 61.20 17.26 .03039 1.5692 .0267 51.64 18.03 ,25362 .9899 -.0868 3.90 19.08 .28752 .9033 -.1123 3.14 R = 5.95 x lo6

-4.04 .00871 -. 4417 -. 0003 -50.74

-2.14 .00800 -.2385 .OOOl -29.79

-. 05 -00809 -.0126 .OOOl -1.55

2.05 .00816 .2125 -0003 26.05 4.04 .00823 -4316 .0005 52.46 6.09 .00885 .6546 .0012 74.00 8.30 .01050 .8872 -0031 84.47 10.12 .01201 1.0707 .0052 89.19 11.13 .01239 1.1685 .0069 94.33 12.12 .01332 1.2605 .0089 94.64 13.08 -01503 1.3455 .Olll 89.51 14.22 -01625 1.4365 .0145 88.40 79.64 15.26 .01900 1.5129 -0178 16.30 .02218 1.5739 I .0216 70.95 17.13 .02560 1.6116 .0253 62.95

18.02 .18785 .9967 -. 0681 5.31

19.08 .27292 1.1358 -. 0989 4.16

Table X. Force Coefficients at M = 0.30 for Transition Fixed With No. 80 Grit

R = 4.00 x lo6 a, deg.

L/d Cd ce cm .

-4.16 .00958 -. 4637 -. 0012 -48.40

-2 * 10 -00869 -. 2379 -. 0005 -27.38

. 00 .00876 -. 0043 .oooo -.49

.Ol .00874 -. 0045 .OOOl -.52

2.13 .00879 -2338 .0007 26.61 4.10 .00888 .4546 .0015 51.17 6.02 .00947 .6661 .0032 70.37 .go38 .0069 8.22 .01156 78.20 10.20 .01424 1.1102 .0116 77.95 11.18 .01541 1.2050 .0144 78.19 12.22 -01775 1.2899 .0174 72.66 13.29 .02341 1.3474 .0239 57.56 14.21 .03608 1.3485 .0286 37.38 15.03 -19522 1.1712 -.0647 6.00

.24735 1.1447 -. 0903 4.63

16.06

17.37 .26673 1.1407 -. 0835 4.28

R = 6.00 x lo6 -.4746 -.0007 -53.87 -4.17 .00881 -2.04 .00810 -.2377 -.0002 -29.36 .oo .00824 -.0058 .0001 -.70 .04 .00826 -.0023 .OOOO -.28 2.06 .00828 .2285 -0002 27.59 .4527 .0008 4.02 .00832 54.40 6.14 .00913 .6895 .0025 75.54 8.11 .01060 .9065 .0053 85.52 10.12 -01420 1.1231 .0096 79.10 11.13 .01598 1.2230 .0121 76.54 12.09 .01605 1.3117 .0161 81.75 13.40 .02360 1.3900 .0236 58.90 14.31 .03430 1.3824 .0296 40.30 15.08 .14073 1.2059 -.0485 8.57 .20900 1.1508 -.0893 5.51 16.12

Table XI. Force Coefficients at M = 0.15 for Transition Fixed With No. 120 Grit

R = 3.95 x 106 or, deg.

t/d =d ct cm

-4.13 .00924 -. 4508 -. 0009 -48.80

-2.00 .00857 -. 0003 -26.26

-. 2251

.03 .00865 -. 0080 -. 0001 -.93

.05 -00874 -. 0048 .oooo -.55

2.09 .00867 .2165 .0003 24.98 4.09 .00872 .4336 .0009 49.75 6.05 .00924 -0020 69.80 8.19 .OllOO -8703 -0040 79.13 10.08 -01272 1.0623 83.54 .0067 11.25 .01334 1.1722 .0083 87.88 12.29 .01396 1.2659 .0106 90.67 13.37 .01592 1.3583 .0135 85.35 14.31 .01749 1.4309 .0163 81.82 15.14 .02078 1.4934 .0191 71.88 16.25 .02443 1.5528 .0232 63.55 17.29 .03095 1.5919 .0266 51.43

18.05 .25330 1.0423 -. 1002 4.11

19.25 .28423 .9771 -. 0838 3.44

R = 6.00 x lo6 -4.01 .ooa43 -.4466 -.0001 -52.98 -2.12 .00789 -.2425 .0002 -30.72 -.01 .00811 -.0120 .0001 -1.48 .Ol .00804 -.0122 .0008 -1.52 2.15 ,00823 .2236 .0004 27.18 4.11 .00879 .4397 .0004 50.03 6.01 .00842 .6487 .0011 77.00 8.08 .00995 .8701 .0026 87.47 10.10 .01175 1.0775 .0049 91.73 11.23 .01248 1.1849 .0069 94.97 12.13 .01282 1.2720 .0082 99.21 13.26 .01408 1.3699 .0109 97.29 14.30 .01628 1.4571 .0143 89.51 15.27 .01790 1.5280 .0175 85.39 16.16 .02093 1.5838 .0208 75.68 17.24 .02519 1.6347 -0251 64.90 18.18 .25194 1.1886 -.0910 4.72

19.25 .28015 1.1888 -. 0931 4.24

R = 8.90 x lo6

-3.99 -00806 -. 4503 .0007 -55.89

-2.01 .00745 -.2339 .0005 -31.40

-.01 .00761 -. 0138 .OOOl -1.81

1.97 .00776 -2050 .OOOl 26.40

4.01 .00765 .4329 -. 0001 56.58

6.13 .00823 -6659 .0007 80.91 8.21 .00929 .8920 .0019 96.01

io. oa . oiioa 1.0852 .0038 97.92

11.11 .01169 1.1871 .0056 101.53 12.12 .01249 1.2839 .0073 102.80 13.16 .01350 1.3754 -0098 101.90 14.24 .01499 1.4664 .0120 97.80 15.54 .01814 1.5663 .0164 86.35 16.30 .02003 1.6172 -0190 80.72 17.21 -02266 1.6627 .0226 73.37 18.38 .02685 1.7026 .0270 63.41

-. 0900 4.56

19.53 .28685 1.3083

20.35 .30408 1.3512 -. 1132 4.44

Table XII. Force Coefficients at M = 0.30 for Transition Fixed With No. 120 Grit

R = 3.90 x lo6 a, deg.

v d

Cd CL cm

-4.06 .00936 -. 4610 -. 0011 -49.23

-1.93 .00853 -.2252 -. 0004 -26.41

.Ol .00881 -. 0073 .oooo -.83

.05 .00874 -. 0044 -. 50

.OOOl 2.05 .00876 .2205 .0007 25.18 4.13 .00889 .4565 .0015 51.37 6.09 .00952 .6745 .0033 70.89 8.19 .01160 .9025 .0067 77.79 10.17 .01397 1.1102 .0114 79.46 11.15 .01502 1.2047 .0141 80.20 12.15 .01702 1.2880 .0169 75.68 13.21 -02194 1.3482 .0231 61.45 14.11 .03255 1.3517 .0276 41.53

15.12 .16052 1.1447 -. 0590 7.13

16.07 -25551 -8559 -. 1171 3.35

R = 5.95 x lo6 -4.02 .00876 -.4646 -.0004 -53 * 02 -2.08 .00799 -.2472 .OOOO -30.93 .02 -00823 -.0088 -0001 -1.07 .03 -00825 -.0064 .0001 -.78 1.99 .00824 .2168 .0003 26.32 4.06 .00835 -4544 -0009 54.42 6.21 .00903 -6975 .0024 77.27 8.29 .01069 .9270 -0054 86.70 10.21 .01290 1.1345 -0096 87.96 11.11 .01380 1.2247 .0119 88.77 12.22 .01591 1.3268 .0162 83.40 13.23 .02009 1.3908 .0220 69.23 14.32 .03175 1.3941 .0289 43.91 15.18 .14253 1.2873 -.0635 9.03 16.02 .20164 1.1514 -.OB43 5.71 R = 8.90 x lo6 -4.07 .00834 -.4784 .0001 -57.40 -2.11 .00757 -.2557 .0005 -33.77 .Ol -00766 -.0101 .0002 -1.32 .05 .00765 -.0052 -0003 -.69 2.22 .00785 -2459 .0001 31.33 4.15 .00778 .4691 .0004 60.29 6.29 .00843 .7238 -.0012 85.87 8.13 .00976 .9263 .0042 94.91 10.16 -01204 1.1468 .0081 95.22 96.36 11.10 .01290 1.2435 .0107 12.31 .01496 1.3570 .0159 90.70 13.47 -02043 1.4266 .0236 69.83 14.29 .03011 1.4195 .0303 47.15 9.05 15.29 .14155 1.2813 -.0358 16.20 .20968 1.2531 -.OB94 5.98 17.08 .23815 1.1755 -.OB53 4.94

Table XIII. Force Coefficients at M = 0.15 for Transition Fixed With No. 180 Grit

R = 5.95 x lo6 CY, deg.

t/d

Cd 9 cm

-3.99 .00871 -.4363 -. 0004 -50.11

-1.98 .00792 -.2213 * 0000 -27.93

-.03 ,00803 -. 0115 .oooo -1.44

-04 -00811 -. 0013 .0002 -.15

2.00 .00814 .2 113 .OOOl 25.97 4.06 .00814 .4365 .0003 53.59 6.09 .00851 .6558 .OOll 77.10 8.09 .00985 -8689 .0027 88.24 10.18 .01165 1.0809 .0050 92.80 11.13 .01247 1.1731 .0064 94.07 12.10 -01299 1.2644 .0082 97.35 13.31 .01408 1.3676 .Olll 97.16 14.08 .01533 1.4316 -0133 93.38 15.24 .01870 1.5169 .0173 81.14 16.33 .02186 1.5855 .0213 72.53 17.13 -02513 .0247 64-54 1.6219 18.21 .25899 1.0104 -.lo70 3.90

19.27 .43446 1.0664 -. 0693 2.45

R = 8.95 x lo6 -4.07 -00843 -.4550 .0004 -53.99 -2.11 .00753 -.2428 .0005 -32.26 .03

.00765 -. 0052 0001 -.68

2.04 .00793 .2150 -. 0001 27.10

4.06 .00780 .4410 -. 0001 56.52

6.12 ,00808 .6655 .0004 82.41 8.15 .00929 .8868 .0014 95.48 10.16 -01147 1.0947 .0037 95.48 11-10 .01173 1.1852 .0051 101.03 12.11 .01218 1.2813 .0071 105.17 13.11 -01316 1.3716 .0091 104.21 14.36 .01511 1.4750 .0128 97.63 15.31 .01722 1.5487 .0163 89.93 16.46 .02025 1.6187 .0193 79.92 17.33 .02220 1.6611 .0238 74.83

18.59 .25066 1.1825 -. 0461 4.72

19.22 .26933 1.2901 -. 1036 4.79

R = 11.95 x lo6

-4.05 .00810 -. 4594 .0008 -56.70

-1.98 .00719 -. 2337 .0007 -32.50

- 0 1 .00736 -.0121 .0003 -1.65

.03 .00726 -. 0097 .0003 -1.34

2.07 -00763 .2183 .OOOl 28.60 4.09

.00746 ,4437 -. 0002 59.45

6.01 .00768 -6571 .0003 85.60 8.03 .00907 .8777 .0011 96.81 10.12 .01092 1.0983 .0032 100.60 11.27 .01126 .0047 1.2150 107.93 12.12 .01175 1.2954 .0062 110.26 13.24 .01376 1.3965 .0093 101.48 14.16 .01491 1.4736 .0117 98.83 15.15 .01683 1.5514 .0143 92.20 16.27 .01996 1.6212 .0190 81.23 17.28 1.6693 .0236 .02378 70.18 18.18 .23217 1.3948 -.1218 6.01

Table XIV. Force Coefficients at M = 0.30 for Transition Fixed With No. 180 Grit

R = 5.95 x lo6 Q, deg.

t/ d cd CL c,

-4.04 .00891 -. 4610 -. 0007 -51.74

-2.03 .00800 -. 2363 -. 0002 -29.53

.oo -00816 -. 0045 -.0001 -.56

28.36 2.09 .00819 .2321 .0002 4.00 .00826 .4508 .0007 54.55 6.13 .00893 .6906 -0023 77.30 8.08 .01043 .9074 .0050 87.01 10.23 .01303 1.1359 -0095 87.16 88.56 11.10 -01382 I . . 2241 * 0119 12.34 .01633 1.3354 .0170 81.79 .02069 66.19 13.23 1.3693 .0203 14.15 .03180 1.3815 .0287 43.44 -14715 1.2390 -.0308 8.42 15.06

16.09 .2033% 1.2505 -. 1093 6.15

R = 8.85 x lo6 .00856 -.4753 -.0003 -55.52 -4.11 -2.06 .00769 -.2430 .0002 -31.60 .00767 -.0094 .0001 -1.23 -.02 -1.17 -.02 -00765 -.0090 .0001 2.04 .00793 .2282 .0002 28.79 59.91 4.07 .00774 .4638 .0003 6.04 .00828 .6909 .0016 83.48 96.73 8.12 .00959 .9276 -0042 10.09 .01175 1.1582 .a125 98.54 1.2515 .0110 96.71 11.17 .01294 12.16 -01456 1.3433 .0151 92.26 .01886 1.4155 .0220 75.05 13.17 14.12 .02817 1.4173 .0295 50.31 15.35 .15957 1.2265 -.0315 7.69 5.78 16.30 .21003 1.2134 -.0704 R = 11-90 x lo6 -4.04 .00811 -.4714 -.0004 -58.14 -1.94 .00738 -.2358 .0006 -31.94 -.05 .00737 -.0144 -0001 -1.96 -1.72 -.03 .00732 -.0126 -0004 -00 .00737 -.0102 .0005 -1.38 29.59 2.03 .00774 .2290 .0001 4.08 .00755 .4714 .0002 62.47 .00798 .6956 .0014 87.19 6.01 8.06 .00910 -9285 .0036 102.05 10.24 .01148 1.1684 .0077 101.77 11.18 .01250 1.2678 .0106 101.46 -01417 1.3711 -0152 96.77 12.28 13 34 .01971 1.4250 .0250 72.31 .03165 1.4225 -0321 44.95 14.35 8.08 15.27 .16237 1.3117 -.0581 I Tunnel sidewall b t,.

_t A Airflow

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a

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a

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N3

R

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* 12

.12 .11 ce,, .1 .09 .1 -15 .2 .25 .3 .35 .4

M

(a) Variation with Mach number.

M .13 -6- .15 --p- .2 -4- .25

* .3

.12

-+-- .36

.11

ce, a

.1 .09 0 5 15 x l @

R

(b) Variation with Reynolds number.

Figure 17. Variation of lift-curve slope with Mach number and Reynolds number for free-transition case.

.13 I .12 .11 ce,, .1 -09

0 5 10 15 x 1 0 6

R

(a) Free transition.

+ #60-W

-13 -e- # E O

+ #120

+ #le0 .12 .ll ce,, .1 .09 15 x106 0 5 10

R

(b) Fixed transition.

Figure 18. Variation of lift-curve slope with Reynolds number for free and k e d transition at M = 0.15.

.13 .12 .11 ceJa .1

+--_____c__-

I

! I

.09

0 5 10 15 x lo6

R

(a) Free transition.

.13 -El- #6O-W

- #BO

+ #l20

--e- #I80

.12

I I

.ll ceJm

I

.1

I I

.09

5 10 15 xla6

R

(b) Fixed transition.

Figure 19. Variation of lift-curve slope with Reynolds number for free and fixed transition at M = 0.30.

.13 Experiment

- Stevens

-- Eppler

.12

.ll

‘[,a .1 .09 .1 .15 .2 .25 .3 3 5 .4

M

(a) R = 4 x lo6

D Experiment .13

- Stevens

-- Eppler

.12 .ll

‘t,a

.1 .09 .1 .15 .2 .25 .3 3 5 .4

M

(b) R = 12 x lo6.

Figure 20. Theoretical and experimental lift-curve slopes as function of Mach number for free-transition case.

Experiment .13

- Stevens

-- Eppler

.12 .11 ce,, .1 .09

0 5 10 15 x lo6

R

(a) M = 0.15.

.13 Experiment

I I

- Stevens

--

Eppler .12 .ll

ce, a