NASA Technical Memorandum 4673

Surface-Pressure and Flow-Visualization Data

at Mach Number of 1.60 for Three 65 ° Delta

Wings Varying in Leading-Edge Radius and

Camber

S. Naomi McMillin, James E. Byrd, Devendra S. Parmar, Gaudy M. Bezos-O'Connor, Dana K. Forrest,

and Susan Bowen

December 1996

Contents

Summary .......................................................................... 1

Introduction ....................................................................... 1

Symbols .......................................................................... 1

Model Description .................................................................. 2

Wind-Tunnel Test Description ......................................................... 3

Test Techniques .................................................................... 4

Surface-Pressure Measurements ...................................................... 4

Vapor-Screen Technique ............................................................ 5

Painted-Oil-Flow Technique ......................................................... 5

Injected-Oil-Flow Technique ........................................................ 6

Liquid-Crystal Technique ........................................................... 6

Results and Discussion ............................................................... 7

Effect of Angle of Attack ........................................................... 8

Upper surface-pressure coefficient data ............................................... 8

Lower surface-pressure coefficient data .............................................. 9

Vapor-screen data ............................................................... 9

Painted- and injected-oil-flow data ................................................. 9

Liquid-crystal data .............................................................. 9

Effect of Longitudinal Position ...................................................... 10

Flow conicity .................................................................. 10

Rx held constant ............................................................... 10

Effect of Reynolds Number ......................................................... 11

Surface-pressure coefficient data .................................................. 11

Vapor-screen data .............................................................. 12

Painted- and injected-oil-flow data ................................................. 12

Liquid-crystal data ............................................................. 13

Effect of Transition Grit ........................................................... 13

Surface-pressure coefficient data .................................................. 13

Painted- and injected-oil-flow data ................................................ 14

Concluding Remarks ............................................................... 14

Tables ........................................................................... 15

Figures .......................................................................... 56

Appendix A---Analytical Expressions for Cross-Sectional Shapes of Delta Wing Models ........ 156

Appendix B--Determination of Flow Angle ............................................ 157

Appendix C--Description of CD-ROM ................................................ 161

Appendix D--Surface-Pressure Coefficient Data ........................................ 172

References ...................................................................... 262

iii

Summary

An experimental investigation of the effect of

leading-edge radius, camber, Reynolds number, and

boundary-layer state on the incipient separation of a delta

wing at supersonic speeds was conducted at the Langley

Unitary Plan Wind Tunnel. The three delta wing models

examined had a 65 ° swept leading edge and varied in

cross-sectional shape: a sharp wedge, a 20:1 ellipse, and

a 20:1 ellipse with a -9.75 ° circular camber imposed

across the span. The three wings were tested at a Mach

number (M) of 1.60 over a free-stream Reynolds number

(R) range of 1 x 106 to 5 x 106 ft-1. The wings were

tested with and without transition grit applied. Surfacepressure coefficient data were obtained, as well as

flow-visualization data. The flow-visualization techniques employed were the vapor-screen, the paintedoil-flow, the injected-oil-flow, and the liquid-crystal

techniques. The surface-pressure coefficient data and

flow-visualization data are electronically stored on a

CD-ROM that accompanies this report.

The data indicated that by rounding the wing leading

edge or cambering the wing in the spanwise direction,

the onset of leading-edge separation on a delta wing at

supersonic speeds can be raised to a higher angle of

attack than that observed on a sharp-edged delta wing.

Specifically, a 20:1 elliptical cross section increased the

angle of attack at which leading-edge separation begins

by about 2 ° over that observed on a sharp-edged delta

wing. A cambered elliptical wing, which decreased the

local angle of attack at the leading edge by 3.76 °, effectively increased the angle of attack at which leading-edge

separation begins by 1.5 ° over that observed on the

uncambered elliptical wing.

The application of transition grit on the wing or an

increase in R increased the angle of attack at which

leading-edge separation began. Fixing transition or

increasing R causes the boundary-layer transition to

occur closer to the wing apex and leading edge of the

wing. A turbulent boundary layer has more energy than a

laminar boundary layer and will therefore allow the flow

to remain attached at the wing leading edge at higher

angles of attack than is possible with a laminar boundary

layer

Introduction

A standard configuration for supersonic wing design

is that of a highly swept, thin delta wing at moderate

angles of attack. Several researchers have experimentally

investigated and classified the leeside flow over slender

swept wings in supersonic flow. Stanbrook and Squire

(ref. 1) originally classified separated and attached leeside flow regimes by using the similarity parameters

Mach number normal to the leading edge (M N) and angle

of attack normal to the leading edge (CtN). Whitehead

(ref. 2), Szodruch and Ganzer (ref. 3), Szodruch (ref. 4),

Miller and Wood (ref. 5), Seshadri and Narayan (ref. 6),

and Covell and Wesselmann (ref. 7) extended this work

by redefining the separated- and the attached-flow

regimes into smaller regimes containing more complex

flow structures. The flow structures identified over the

leeside of sharp-edged delta wings at supersonic speeds

included attached flow, cross-flow shocks, separation

bubbles, and a complex vortical system of primary and

secondary vortices (ref. 5). The boundaries between the

experimentally derived flow regimes have been identified as functions of M N and ctN.

The aerodynamicist prefers not to be limited to a particular type of flow so that an optimum design may make

use of both attached and separated flows. The boundaries

between separated- and attached-flow regimes are sensitive to changes in wing leading-edge radius, wing thickness, and Reynolds number (refs. 1, 4, 6, and 8). To take

advantage of the sensitivity of the boundaries between

flow regimes, it becomes necessary to understand the

influence of geometrical and flow parameters on the

incipient separation of a delta wing. Incipient separation

is defined as the onset of flow separation at the leading

edge of the wing.

The present wind-tunnel investigation was conducted to establish a database to improve the understanding of incipient separation on delta wings at supersonic

speeds. The effects of leading-edge radius, camber,

Reynolds number, and boundary-layer state on the incipient separation on a 65 ° delta wing at M = 1.60 were

determined. The three delta wing models tested had

a 65 ° swept leading edge and varied in cross-sectional

shape: a sharp wedge, a 20:1 ellipse, and a 20:1 ellipse

with a -9.75 ° circular camber imposed across the span.

The three wings were tested in the Langley Unitary Plan

Wind Tunnel at an M of 1.60, an R range of 1 x 106 to

5 x 106 ft-1, a nominal angle of attack (Ctnom) range of

0 ° to 9 °, and an angle of sideslip (13) of 0 °. The wings

were tested with and without transition grit applied.

Extensive surface-pressure coefficient data were

obtained at two longitudinal stations. Extensive flowvisualization data were obtained to better understand the

flow phenomena associated with incipient separation.

The flow-visualization techniques employed were the

vapor-screen, the painted-oil-flow, the injected-oil-flow,

and the liquid-crystal techniques.

Symbols

AOA angle of attack

b wing reference span, in.
bto

CN

CP#

c

ESP

M

MN

n

P

P,,

q

R

Rx

r

rc

s

s

ro

t

UPWT

x,y,z

O_

_ac

O_att

O_knu

_N

2

wing span with wingtips

removed, in.

normal force coefficient obtained

by integrating surface-pressure

coefficient data

surface-pressure coefficient,

(p - Po_)/q

designation on CD-ROM to denote

pressure orifice number

wing root chord, in.

electronic scanning pressure

free-stream Mach number

component of Mach number normal

to leading edge,

McOSALEJ1 + sin2a tan2ALE

refractive index of a material

local static pressure, lblft 2

free-stream static pressure, lb/ft 2

free-stream dynamic pressure, lb/ft 2

free-stream Reynolds number, ft-1

local Reynolds number based on

distance from apex along centerline

of wing

leading-edge radius, in.

radius of curvature, in.

wing reference area, in 2

arc length, in.

adiabatic wall temperature, °F

stagnation temperature, °F

wing thickness, in.

Langley Unitary Plan Wind Tunnel

Cartesian coordinates where origin is

at apex of wing, in.

corrected angle of attack, deg

angle of attack as measured by

accelerometer, deg

last angle of attack at which attached

flow was observed, deg

pitch of model as set by knuckle, deg

angle of attack normal to leading

edge, deg, tan-l(tan Ct/cOSALE )

nominal angle of attack, deg

angle of attack at which leading-edge

flow separation is first detected, deg

3t

An

0c

0i

A

Subscripts:

LE

l

lam

max

min

TE

turb

u

sideslip angle, deg

display monitor parameter which

controls contrast and brightness of

display

change in angle of attack, deg

z/local semispan

y/local semispan

angle of spanwise camber, deg

angle of wind-tunnel flow, deg

sweep angle, deg

roll angle, deg

leading edge

lower surface of wing

laminar

maximum

minimum

trailing edge

turbulent

upper surface of wing

Tabulated Data Symbols:

ALPHA t_, deg

cP Cp

ETA TI

FLOW ANGLE 07 deg

MACH M

PHI _, deg

PINF p_, lb/ft 2

Q q, lb/ft 2

R/FT R, ft-1

X x, in.

Model Description

A conical 65 ° delta planform at M = 1.60 was chosen

as the baseline geometry. The criteria used to select the

baseline were M u and o_N, which are shown in figure 1.

As angle of attack increases, the 65 ° delta planform

at M= 1.6 traverses the Stanbrook-Squire boundary

(ref. 1)that delineates attached-flow and separated-flow

regimes. The effects of wing leading-edge radius, wing

leading-edge camber, Reynolds number, and boundary

layer (laminar or turbulent) on leading-edge flow separation were expected to be most pronounced in the region

of the Stanbrook-Squire boundary.
Theeffectof wingleading-edgeradiusandwing

camberonleading-edgeflowseparationwasexamined

by varyingthe cross-sectional shapeof the baseline

geometry.Detailsof thethreemodelsexaminedarein

figure2 andtable1.AppendixA containstheanalytical

expressionfor eachof the cross-sectional shapes.

Figure3 showsthe ellipticalmodelinstalledin the

LangleyUnitaryPlanWindTunnel(UPWT).

Thebaselinegeometrywasa 65° deltaplanform

witha ratioof centerlinethicknesstosemispanof 0.10.

Cross-sectional shapewasvariedto obtainthreewing

designs:asharpwing,anellipticalwing,andacambered

wing.Thesharpwinghadawedge-shaped crosssection,

whichis shownin figure2(a).Formachiningpurposes,

thesharpwinghadaleading-edgeradiusof 0.003in.The

ellipticalwing,showninfigure2(b),hada20:1elliptical

crosssection,whichyieldeda leading-edgeradiusto

localsemispanratio(rl(bl2))of 0.0025alongthelength

of theleadingedge.Theellipticalgeometrywasusedas

abaselinecrosssectioninexaminingtheeffectof camber.A spanwisecircular-arccamberwasimposedonthe

ellipticalcrosssectionin thecross-flowplaneto define

thecamberedwing.Theangleofcamber0c is defined as

the spanwise camber angle at the wing leading edge. The

cambered model had an 0c of-9.75 ° (fig. 2(c)).

It should be noted in figure 2 that the wingtips of

each model could be removed. The left side (viewed

upstream from the trailing edge of the model) of the planform shows the wingtips attached and the right side

shows the wingtips removed. The models were built with

removable wingtips for testing in another facility with a

smaller test section than that of the UPWT. The wingtips

were attached for this investigation.

Each model was instrumented with pressure orifices

on both the upper and the lower surfaces. The orifices

were arranged in two spanwise rows at x = 6 in. and

x = 12 in. (measured from the apex along the centerline).

The upper surface-pressure orifices were located on the

right side (viewed upstream from the trailing edge of the

model) of the wing and the lower surface-pressure oririces were located on the left side of the wing. Each orifice on the elliptical and the cambered wings had an inner

diameter of 0.01 in. Each orifice on the sharp wing had

an inner diameter of 0.015 in. All tubing came out the

back of the models as shown in the photographs in

figure 3.

Tables 2, 3, and 4 contain the x and the r I locations

of each pressure orifice, the CP# of each pressure orifice

(the CP# is also used in the pressure-listing file on the

CD-ROM), and the condition of the orifice. On the elliptical and the cambered wings, the pressure orifice locations range from rl = 0.10 to _ = 0.98 at both x stations

on the upper surface. However, because of the thinness

of the sharp wing at the leading edge, the upper surfacepressure orifice locations on the sharp wing range only to

r I = 0.820 for the x = 6 in. station and to rl = 0.899 for the

x = 12 in. station. On the lower surface, the pressure orifice locations range from rl = 0.200 to rl -- 0.95 at both

x stations for the elliptical and the cambered wings. For

the lower surface of the sharp wing, the pressure orifice

locations range to rl = 0.802 for the x = 6 in. station and

rI = 0.901 for thex = 12 in. station.

To minimize any effect of the model support system

on the flow over the upper surface of the delta wing, a

sting was constructed that attached to the trailing edge of

each wing with two bolts. Figure 4 shows the details of

the sting.

An electronic accelerometer measured angle of

attack during pressure data acquisition. The angle of

attack (AOA) sensor was placed in a housing that was

attached to the lower surface of the mounting pad of the

sting. Thus, the AOA sensor was located directly behind

the trailing edge of the delta wing. Because of this location, the AOA sensor was not influenced by sting deflections due to aerodynamic loading. The details of the

AOA housing are shown in figure 5. Figure 3(b) shows

the assembly of the elliptical wing, sting, and AOA housing components.

Wind-Tunnel Test Description

The wind-tunnel test program was conducted in test

section 1 of the UPWT at M = 1.60 over a range of R

from 1 x 106 ft-1 to 5 x 106 ft-1. All data were obtained

at stagnation temperature (T o) of 125°F with the exception of the liquid-crystal data. The liquid-crystal data

were obtained at To= 120°F, 125°F, and 130°F. The

test program was conducted under the following test

conditions:

Mach number

Stagnation

pressure, psf To, °F R, ft -1

1.60 539 125 lxlO 6

1.60 1067 120 2 × 106

1.60 1079 125 2 × 106

1.60 1091 130 2 × 106

1.60 1618 125 3 × 106

1.60 2157 125 4 × 10 6

1.60 2668 120 5 × 106

1.60 2697 125 5 × 106

1.60 2728 130 5 × 106

Reference 9 contains a detailed description of the

wind tunnel and the operating conditions of the wind

tunnel.
Thedew point was maintained sufficiently low during the pressure tests to prevent condensation in the tunnel. However, at R = 5 x 106 ft-1, the dew point was

difficult to control and it rose throughout the run. Eventually, a fog appeared in the test section. To control the

dew point, it became necessary to manually bleed in dry

air. Figure 6 shows the effect of dew point on the

surface-pressure measurements for the cambered wing at

R = 5 x 106 ft-1. Dew point was considered unacceptable

when the generally accepted value (from unpublished

data based on ref. 9) was not met and/or a fog appeared

in the test section.

As discussed in reference 9, flow angularity exists

inside the wind-tunnel test section and is illustrated in

figure 7. To account for this flow angularity, the model

was offset in pitch before data were acquired. This offset

is known as the flow angle 0f where positive flow angulaxity means the flow is deflected upward. A detailed discussion on the determination of the flow angle is

contained in appendix B. The angle of attack correction

due to flow angularity was determined to be 0.4 °. The

corrected angle of attack is referred to as _.

To obtain pressure data, the model was set at 0 = 0°

and the angle of attack was measured with the AOA sensor located directly behind the trailing edge of the wing.

The angle of attack measured with the AOA sensor is

referred to as Sac and is shown in figure 7.

To acquire flow-visualization and liquid-crystal

data, the model was set at _ = 90 °. Because the AOA

sensor could not be used at this roll angle, the angle of

attack was set by using the beta angle system of the wind

tunnel. (The beta angle system sets the sideslip angle of a

model at t_ = 0°.) This arrangement sets the pitch angle at

the tunnel end of the sting instead of at the base of the

model. Thus, sting deflections had to be accounted for

when the angle of attack was set. Sting deflections were

determined by comparing tXac with a corresponding pitch

angle measured at the knuckle etkn u. The knuckle is the

tunnel hardware in which the sting is installed and is

shown in figure 7. Figure 8 shows an example plot of

t_knu and tXac, which were measured on the elliptical wing

without grit at R = 1 x 106 ft-1. The line through the data

points is a least squares fit and was used to determine the

sting deflections. Sting deflections were also obtained at

R= 2 x 106 and 5 x 106ft -1.

Transition grit was used to ensure fully turbulent

flow over the model when the flow was attached at the

wing leading edge. Boundary-layer transition strips of

No. 40 (0.0181-in. diameter) sand grit were applied

0.169 in. perpendicular to the leading edge of the delta

wing on both the upper and the lower surfaces. The grit

was sprinkled on the wing in a strip that was 0.0625 in.

wide. The grit size and location were selected by consulting unpublished data that were based on the methods and

the data in references 10 to 12.

Shown in figure 9 is the location of the grit with

respect to the pressure orifices for each of the three delta

wings. The surface-pressure coefficients at the orifices in

or near the strip of grit are affected by the presence of the

grit (fig. 10). The effect of the grit is more pronounced at

the x = 6 in. station than at the x = 12 in. station. The oririces at the x = 6 in. station are spaced closer together

than at the x= 12 in. station, which can be seen in

figure 9(c). Thus, the effect of the grit covers more of the

orifices at the x = 6 in. station.

For the lower surface, the effect of grit is present

over the entire angle of attack range. However, for the

upper surface, the effect of grit on the surface-pressure

distribution is present only at low angles of attack. This

observation can be explained by noting that for attachedflow cases at low angles of attack, the flow moves

inboard from the wing leading edge to the transition

strip. Whereas, for separated-flow cases at higher angles

of attack, the flow approaches the transition strip from

the other direction as the flow separates at the leading

edge, reattaches inboard of the transition strip, and

moves outboard towards the transition strip as shown in

figure 11 (from ref. 5).

Test Techniques

The rive test techniques used during the test program

were surface-pressure measurements, vapor screens,

painted oil flows, injected oil flows, and encapsulated

liquid crystals.

Surface-Pressure Measurements

Each model had surface-pressure orifices on the

upper and the lower surface with the tubing exiting at the

rear of the model. The tubing was connected to the electronic scanning pressure (ESP) system located outside

the wind-tunnel test section. A valuable feature of the

system is the ability to calibrate the ESP modules at anytime during the test. With this feature, changes in temperature or other environmental features can be taken into

consideration.

The selection of ESP modules was based on the

expected maximum and minimum pressures on the delta

wing over the angle of attack range of 0 ° to 9 °. The following is a table of the expected maximum and minimum

pressures on the upper and the lower surface of the delta

wing forM = 1.60 and TO = 125°F:

4
R, ft-I

1 X 106

2x 106

3x106

4× 106

5x106

Pl, max at

Pl, max at (Cp)t,min = 0.05, PI, maxat

(Cp)l,max= 0.25, (Cp)u,max = 0.05, ( Cp)u.min = -0.45,

psi psi psi

1.276 0.9597 0.1701

2.553 1.921 0.3417

3.828 2.881 0.5118

5.103 3.840 0.6819

6.381 4.801 0.8535

The expected maximum and minimum pressures

were obtained from the computational solutions for

the wind-tunnel model geometries at M= 1.60 and

TO = 125°F. (See ref. 13.)

At the higher Reynolds numbers, the lower surface

would likely experience pressures beyond the range of a

5 psi module; so the 15 psi module was used. The upper

surface would likely experience pressures ranging from

very low values up to 5 psi; therefore, the 5 psi module

was selected. In some instances, the upper surface pressures exceeded the range of the 5 psi module--for example, when the wing was subjected to negative angles of

attack at R= 5 x 106ft -1. These data were discarded.

The 5 psi modules had an accuracy of +0.0025 psi and

the 15 psi module had an accuracy of +0.0075 psi.

When obtaining surface-pressure measurements, the

angle of attack was set and the pressures were allowed to

settle before taking measurements. A study of the effect

of settling time on the pressure measurements was performed. Figure 12 shows surface-pressure coefficient

data taken with a 2 min settling time and with a 7 min

settling time at three points. The measurements obtained

at the different settling times are the same within the

accuracy of the equipment. Based on these results, a settling time of 2 min was allowed between angle of attack

changes.

To obtain the pressure data, an ot sweep from 0° to

9° in 0.5 ° increments was performed. When warranted

by inspection of the on-line pressure plots, a second o_

sweep was performed to obtain data over a selected range

in 0.25 ° increments. These two cx sweeps were used to

determine the repeatability of the pressure data. Figure 13 shows a plot of surface-pressure coefficients with

cx for both _ sweeps. Figure 13 shows that the data

repeatability is satisfactory because the surface-pressure

coefficients obtained during the second o_ sweep follow

the trend of the surface-pressure coefficients from the

first _ sweep.

Vapor-Screen Technique

The vapor-screen technique provides qualitative data

on the flow field above the leeward surface of the model.

Model preparation for the vapor-screen technique consisted of painting one coat of black paint onto the surface

of the model. White dots were painted on the model surface centerline at x = 6 in. and x = 12 in. (the locations of

the rows of pressure orifices). Once tunnel start-up was

complete, water was added in the diffuser downstream of

the test section until a uniform vapor was produced in the

test section.

A 4-W argon-ion laser, which emits a blue-green

light, was used to create the light sheet across the tunnel

test section. Usually, only 2 W of laser power were necessary to produce the desired vapor-screen image. A dual

cylindrical lens was used to spread the laser beam. The

lens assembly was mounted on a support that could rotate

and traverse vertically to the desired orientation. Once a

desired orientation was reached, the laser was fixed in

place and the model was moved to obtain vapor-screen

photographs at various x locations. Still photographs

were obtained with 70-mm film and a camera inside the

test section. The relative locations of the model, light

sheet, and camera are shown in figure 14. Still photographs were obtained at the x = 12 in. station only.

One undesirable characteristic of the vapor-screen

technique is the reflection of the light sheet off the surface of the model. The use of flat black paint on the surface of the model minimizes this reflection, but does not

eliminate it. Another undesirable characteristic of the

vapor-screen technique is that the quality of the vapor is

more difficult to control in the UPWT at lower Mach

numbers such as 1.60. Constant visual monitoring of the

vapor and subsequent adjustment of the water input is

necessary to ensure an evenly distributed vapor in the test

section.

Painted-Oil-Flow Technique

The painted-oil-flow technique provides qualitative

data on the flow characteristics of the surface of the

model. For the painted-oil-flow technique, the model was

painted with one coat of flat black zinc chromate primer.

The model surface was then brushed with a mixture of

90W oil and yellow fluorescent powder. During the tunnel start-up period, the model was kept horizontal to prevent the oil from running. The model was rolled 90 °

(wings vertical) and was illuminated by four ultraviolet

lamps that were mounted on the sidewall door. With selfdeveloping film, photographs of the painted oil flows

were taken through the window by a camera mounted

5
outside the tunnel on the sidewall door. After the model

was positioned, the oil-flow pattern stabilized in approximately 3 to 4 min.

An undesirable characteristic

that only 3 or 4 angles of attack

before the oil had to be replaced.

of this technique was

could be documented

The number of angles

of attack that can be documented in one setup decreases

with increasing Reynolds number.

Injected-Oil-How Technique

The injected-oil-flow technique also provides qualitative data on the flow characteristics of the surface of

the model. The injected-oil-flow technique differs from

the painted-oil-flow technique in that the oil is injected

onto the surface through the pressure orifices. The injection was accomplished by the pressure difference

between the pressure inside the tunnel and the higher

atmospheric pressure outside the tunnel. A peristaltic

pump was also used to inject the oil through the orifices.

Each upper surface orifice tube was connected to a peristaltic pump module located outside the test section. The

oil-flow rate was adjustable as a function of pump speed

for all the orifices simultaneously. The oil-flow rate for

each orifice was adjustable from 0 to approximately

4 ml/min. The source of oil for each peristaltic pump

module was a common container of SAE t0 oil that was

mixed with fluorescent powder.

Maintaining constant flow rates between orifices

was difficult at times. The difficulty was caused by the

fluorescent powder clogging the tubes. The oil and powder mixture had been stirred and filtered beforehand to

eliminate large pieces of powder. However, the nonuniform restrictions of each orifice and the associated tubing

length of 15 fi allowed small pieces of powder to accumulate and clog some of the tubes. The disparity between

orifice flow rates was greater when the pressure difference across the tubes was allowed to be the only motive

force of the oil through the tubes. The peristaltic pump

provided better uniformity in flow rate among orifices.

The model was prepared and illuminated in the same

manner as it was for the painted-oil-flow technique. The

oil flows were photographed with an instrumentation

camera that had a wide angle lens and 70-mm black and

white film. A 30-see exposure time was generally used.

The flow patterns took less than a minute to settle

after a change in tx. When a more significant amount of

time was needed to obtain a desired change in flow conditions, the oil flow could be slowed by clamping the

tubes and removing them from the container of oil and

powder mixture. However, after approximately 2 hr, the

fluorescent powder caused the paint to flake. Nevertheless, the injected-oil-flow technique allowed many

6

more data points to be obtained than could be obtained

with the painted-oil-flow technique. In the paintedoil-flow technique, the oil wore off after 3 to 4 data

points (10o20 min) were obtained. However, as the oil on

the model is being continually replaced in the injectedoil-flow technique, data points could be taken until the

paint started to flake.

Liquid-Crystal Technique

The liquid-crystal technique provides quantitative

data on the flow characteristics of the surface of the

model. This technique records the data visually with

photographs that capture the varying colors of the thermochromic liquid crystals. The thermochromic liquid

crystals used in this technique are materials that demonstrate color changes when their temperature is changed.

Reference 14 discusses the properties of liquid crystals

and how these properties are exploited in measuring temperature. The color of a liquid crystal changes from black

to red to blue as the temperature is increased. As a result

of this feature, these liquid crystals have been used

widely in thermometry and thermography of surfaces.

In their normal state of operation, these liquid crystals are in a viscous fluid state and flow under an applied

shear stress (ref. 15). Thus, the liquid crystals do not bind

rigidly to the model surface that is exposed to a flow of

fluid (ref. 16). To avoid flowing when under shear stress,

microdroplets of these liquid crystals are encapsulated in

polymer shells (ref. 14). A slurry of the capsules in a

water and polymer solution produces a paint that can be

sprayed on the model surface with an air brush. When it

dries on the model surface, the paint leaves a rigid film of

microencapsulated thermochromic liquid-crystal droplets

bound rigidly to the surface yet capable of responding to

the surface temperature (refs. 14 and 17). The density of

the microencapsulated droplets is high enough so that a

dry film (approximately 50-100 btm thick) will provide

the necessary continuous spread of liquid crystals on the

surface. The color pattern on the surface provides information about the temperature distribution on the surface

by referring to the calibration of the liquid crystals. The

calibration is obtained with the methods in references 15

and 17. The commercially available microencapsulated

liquid crystals generally cover a limited temperature

range of =9°F. This limited range allows one to choose a

liquid crystal that is suitable for the desired operation.

To prepare the model for the installation of the liquid

crystals, the model surface was thoroughly cleaned with

acetone and methanol. The model was then given a black

coating compatible with the encapsulated liquid crystals.

The black coating (approximately l0 [am) was deposited

on the model surface by spraying a flat black paint with

an air brush. Unlike many lacquer-based flat black
paints,theblackpaintused for this test was water soluble

and absorbed the light incident on its surface. This

absorption meets the necessary condition that the

observed reflected light is from the liquid-crystal layer

and not from the black coating itself. The paint, being a

good thermal insulator, also provides an adequate thermal insulation layer between the liquid crystal and the

model surface. After the black coating has completely

dried, the encapsulated thermochromic liquid crystal is

spray painted on the black coated model to provide a dry

uniform film that is approximately 50 _tm thick.

In the present experiment, the upper surface of the

model was divided into two parts at the centerline. Each

side was coated with liquid crystals of different operating

ranges of temperature. To gather as much information as

possible with these two ranges of temperature, data were

obtained with three To: 120°F, 125°F, and 130°F. The

temperature range of the liquid crystals was selected

based on the Taw for a flat plate at M= 1.60. (See

ref. 18.) The following is a table of the Taw at each temperature for both a laminar and a turbulent boundary

layer:

To, °F Taw.lam, °F Taw.turb, °F

120 90.6 96.4

125 95.3 101.2

130 100.0 106.0

Based on these values, the right side (viewing

upstream from the trailing edge of the model) was coated

with liquid crystals that had an operating range of 86°F

to 95°F. The left side was coated with liquid crystals that

had an operating range of 95°F to 104°F.

To obtain photographs of the liquid-crystal data, the

model was rolled 90 ° (wingtips vertical) with angle of

attack set by using the beta angle system of the wind tunnel. The model was illuminated by white light lamps

mounted on the sidewall door. The light reflected normal

to the model surface was recorded by still photographs.

An instrumentation camera with a wide angle lens was

mounted outside the tunnel on the sidewall door. Color

photographs were obtained with 70-mm color film. Data

were obtained for the Otnom range of 0° to 9° in 0.5 °

increments. After an angle of attack change, the change

in liquid-crystal color due to changes in surface temperature was virtually instantaneous.

The advantage of using the liquid-crystal technique

is the ability to gain both qualitative and quantitative data

over the entire surface of the model. A possible source of

concern in this technique is the interplay of temperature

on the lower and the upper surfaces because of conduction of heat through _e model. Although the black paint

applied on the model is an insulator, it probably does not

eliminate the heat transfer completely. One disadvantage

of the liquid-crystal technique was that the coating would

start to flake away from the model after being in the flow

stream for 2 to 4 hr. This problem, however, could probably be avoided by using a sturdier oil-based paint.

Results and Discussion

An experimental investigation of incipient separation on supersonic delta wings was conducted. Three 65 °

delta wing models were tested in UPWT at M = 1.60

over an R range of 1 x 106 ft-1 to 5 x 106 ft -1 with and

without transition grit applied to the surface of the models. The three delta wing models had a 65 ° swept leading

edge and varied in cross-sectional shape: a sharp wedge,

a 20:1 ellipse, and a 20:1 ellipse with a -9.75 ° circular

camber imposed across the span. Surface-pressure coefficient, liquid-crystal, and flow-visualization data were

obtained for each model. Table 5 summarizes the different data obtained for each configuration. The _nom

obtained is also listed in table 5. Presented in tables 6

to 11 are indexes of the angles of attack at which data

were obtained during each test technique. The angle of

attack data in tables 6 to 11 have been corrected for

wind-tunnel flow angularity and sting deflections.

All experimental data obtained from the wind-tunnel

test program are on a CD-ROM. The flow-visualization

data are stored on the CD-ROM in digital images.

Appendix C contains a detailed description of the process

used to convert the film negatives or prints to digital

images. Appendix C also contains a description of the

directory structure and the file formats on the CD-ROM,

as well as information on public domain software available to examine the data. The surface-pressure coefficient data are also stored on the CD-ROM in an ASCII

file. The surface-pressure coefficient data have been

summarized and are plotted in appendix D.

Representative results obtained from the experimental investigation are presented here. The discussion is

divided into four sections. The first section discusses the

effect of angle of attack on the development of flow

structures observed over the leeside of the delta wing

models. The second section discusses the effect of longitudinal position on the development of the flow on the

delta wing model. The third and the fourth sections discuss the effect of Reynolds number and transition grit on

the leeside flow of the delta wing models. Surfacepressure coefficient data are presented for all three

wings. However, the majority of the flow-visualization

data presented here are for thc elliptical wing model.
Effect of Angle of Attack

Upper surface-pressure coeJ_icient data. The effect

of angle of attack on the surface-pressure coefficient

distribution (hereafter referred to as pressure distribution) on the upper surface for each wing without grit

at x = 12 in., M = 1.60, and R = 2 x 106 ft-! is presented

in figure 15. For et < 2.22 ° on the elliptical wing (see

fig. 15(b)), the pressure distribution is smooth to the

leading edge. This pressure distribution is typical for an

attached-flow condition at the wing leading edge. However, for tx _>2.22 °, inflections in the pressure distribution over the elliptical wing occur near the leading cdge.

These inflections are indicative of flow separation at the

wing leading edge (referred to hereafter as leading-edge

separation). As tx increases, the inflections develop into a

pressure coefficient distribution typical of a vortex emanating from the wing leading edge (referred to hereafter

as leading-edge vortex).

At the onset of leading-edge separation, a separation

bubble forms at the wing leading edge. A separation bubble emanating from the wing leading edge (referred to

hereafter as a separation bubble) has been defined (refs. 5

and 19) as a leading-edge vortex whose core lies very

close to the wing surface so that the reattachment of the

induced flow onto the wing surface coincides with the

inboard edge of the vortex. As angle of attack increases,

the core of the vortical structure lifts off the surface and

the reattachment line of the induced flow then occurs

slightly inboard of the vortex. Figure 11 (from ref. 5)

shows the basic leading-edge vortex characteristics.

As discussed in reference 5, when the energy of the

flow normal to the leading edge is not sufficient to negotiate the expansion at the leading edge, the flow will separate at the leading edge and form a region of rotational

flow referred to as the primary vortex. The pressure distribution associated with a leading-edge vortex is characterized by a sudden change in the surface-pressure

coefficient that occurs over a small range of r I with the

lower pressures occurring outboard. This characteristic

corresponds to the region where the vortex-induced flow

reattaches inboard of the vortex. On the inboard side of

this reattachment point there is streamwise flow. On the

outboard side of the reattachment point, there is outboard

spanwise flow, which can induce surface velocities that

can decrease the surface pressure relative to the attachedflow pressure distribution (fig. 11).

Figure 16 presents the surface-pressure coefficient

distribution for each wing without grit at common nominal angles of attack for x= 12in., M= 1.60, and

R=2x 106ft -1. All three configurations develop a

leading-edge vortex as angle of attack increases, which is

shown in figures 15 and 16. The data in figure 16 show

that wing cross-sectional shape affects the vortex

strength as indicated by the sudden change in pressure

coefficient near the inboard edge of the vortex. The sharp

wing data in figure 16 show a greater increase in pressure

coefficient occurring over a smaller range of I1 than the

elliptical and the cambered wings for Otnom = 8°. This

greater increase in pressure indicates a stronger vortex

than that observed for the elliptical and the cambered

wings. Of the three wings, the cambered wing has the

smallest change in pressure coefficient over the largest

range of rI. Thus, wing leading-edge radius and wing

camber appear to weaken the leading-edge vortex. However, note that all three configurations have equivalent

values of Cp at the leading edge for O_nom > 8°.

The angle of attack at which leading-edge separation

begins is also dependent upon the cross-sectional shape

of wing. The data in figures 15 and 16 show that the

angle of attack at which the onset of leading-edge separation is first detected O_se p is 2.22 ° for the elliptical wing

and 3.72 ° for the cambered wing. The pressure coefficient distribution inflection that indicates the onset of

leading-edge separation occurs at 0.9 < r I < 1.0. Note

from figures 15 and 16 that the pressure coefficient distribution for the sharp wing ends at r I = 0.9 for the station

at x = 12 in. The pressure coefficient distribution for the

sharp wing for the station at x = 6 in. ends at r I = 0.82.

Therefore, from the data in figures 15 and 16 and the data

for x = 6 in. (not presented here), it is difficult to determine at what tx the onset of leading-edge separation

occurs for the sharp wing. However, Stanbrook and

Squire (ref. 1) observed that increasing wing leadingedge radius increases O_sep. Therefore, leading-edge separation on the sharp wing would be expected to occur at a

lower angle of attack than the elliptical wing.

The cambered wing has a wing leading-edge geometry that effectively lowers the incidence angle of the flow

at the leading edge when compared with the uncambered

wings. The geometrical angle of the cambered wing at

the leading edge is -9.75 ° in the cross-flow plane. This

angle corresponds to 3.76 ° in the streamwise direction.

Thus the effective angle of flow approaching the leading

edge of the elliptical wing is 3.76 ° higher than that

observed for the cambered wing at any given angle of

attack. The data in figure 15 show that the incidence

of Otsep increased only 1.5 ° from the elliptical wing

(Ctsep = 2.22 °) to the cambered wing (tXsep = 3.72°). The

elliptical and the cambered wing data in figure 16 show

that, at the wing centerline, camber had a much smaller

impact on the angle of flow. Thus, the geometrical camber essentially lowers the incidence angle of flow over

the cambered wing with a more pronounced effect at the

wing leading edge.
Lower surface-pressure coefficient data. Figure 17

presents the effect of angle of attack on the lower

surface-pressure coefficient distribution for each wing

without grit at x = 12 in.,M = 1.60, and R = 2 x 106 ft -1.

The data show that for each wing, the flow is attached at

the wing leading edge. The surface-pressure coefficient

is seen to increase with increasing rl and angle of attack.

Vapor-screen data. Presented in figure 18 are vaporscreen photographs for the elliptical win/_ without grit at

x = 12 in., M = 1.60, and R = 2 × 106 ft-'. The effect of

angle of attack on the flow structure is illustrated. The

vapor-screen data do not show any leading-edge vortical

structure until the ot = 3.7 ° condition (fig. 18(0). However, the surface-pressure coefficient data in figure 15(b)

indicate that leading-edge separation is present at

ct = 2.22 °. This inconsistency is related to the glare of the

laser light sheet off the surface of the wind-tunnel model.

At the onset of leading-edge separation (Otsep = 2.22 ° for

the elliptical wing), the leading-edge separation is so

small and close to the surface of the wing that the glare

could obscure the flow structure. At tx = 3.7 ° (fig. 18(f)),

there is an inboard region of separation that has been previously observed with leading-edge vortical flows computationally. (See ref. 19.) This region of separation is

also evident at the _ = 2.7 ° (fig. 18(d)) condition and

could indicate a leading-edge separation that is masked

by the glare of the laser sheet off the wind-tunnel model.

For tx > 3.7 °, the vortical structure of the leadingedge separation is apparent. For each ix> 3.7 ° the

inboard edge of the vortex is within the "q range of the

sudden pressure change in the pressure distribution

(fig. 15).

Painted- and injected-oil-flow data. Figure 19 presents painted-oil-flow photographs for the elliptical wing

without grit at tx = 3.14 °, 4.17 °, 6.26 °, and 8.34 °, M =

1.60, and R = 2 x 106 ft -1. Figure 20 presents injectedoil-flow photographs for the elliptical wing without grit

at M= 1.60, R= 2 x 106 ft-1, and 0° _< ct < 9.39 ° at

approximately 1° increments. The data illustrate the

effect of angle of attack on vortex growth. The injectedoil-flow data in figure 20 indicate attached flow on the

upper surface of the elliptical wing for ct < 2.08 °. For

Otnom = 2 ° and 3° (figs. 19(a), 20(c), and 20(d)), the oil

accumulated along the leading edge of the wing, which

indicates a narrow leading-edge separation bubble. The

injected-oil-flow data (fig. 20(c)) and the surface-pressure coefficient data (fig. 15(b)) indicate similar values

of Ctsep, 2.08 ° and 2.22 °, respectively. In contrast, the

vapor-screen data (fig. 18(0) indicate Otsep = 3.7 °, a

greater angle than those observed in the injected-oil-flow

and surface-pressure coefficient data.

For each Otnom > 4°, the oil-flow patterns indicate a

reattachment line that separates the inboard streamwise

flow and the outboard spanwise flow induced by the

presence of the leading-edge separation. For ot = 4.17 °

(figs. 19(b) and 20(e)), the location of the flow reattachment point corresponds to the location of the inboard

edge of the leading-edge separation bubble, which is

shown in the vapor-screen data (fig. 18(g)). Thus, the

leading-edge separation at t_ = 4.17 ° would be classified

as a leading-edge separation bubble. For each Otnom > 5 °,

the location of the reattachment line as shown in the oilflow data (figs. 19 and 20) falls slightly inboard of the

edge of the leading-edge separation as shown in the corresponding vapor-screen data in figure 18. Thus for

tXnom > 5°, the leading-edge separation is defined as a

classical leading-edge vortex.

For each tx > 4.17 °, the location of the flow reattachment point as shown in the oil-flow data (figs. 19 and 20)

lies in the rl range over which a sudden pressure change

occurs in the corresponding pressure distribution

(fig. 15(b)). Also recall that the vapor-screen data in figure 18 showed that the inboard edge of the primary vortex lies in the same rI range.

Liquid-crystal data. Figure 21 presents liquidcrystal photographs for the elliptical wing without grit

at M= 1.60 and R=2x 106ft -1 for various angles of

attack. The photographs provide quantitative and qualitative data about the flow characteristics of the surface of

the elliptical wing. The color of the liquid crystals is

related to the temperature on the surface of the windtunnel model. Figures 21(k) and 21(1) present the color

band for the temperature range on the right and the left

side of the wing, respectively.

The data in figures 21(a) and 21(b) show that for

ct <_1.03 °, the temperature on the surface increases suddenly along a line roughly parallel to the leading edge of

the wing. At t_ = 2.08 ° (fig. 21(c)) the higher temperature

extends to the leading edge of the wing. This observation

corresponds to the pressure distribution data (fig. 15(b))

and the injected-oil-flow data (fig. 20(c)), which show

values of o_ of 2.22 ° and 2.08 °, respectively. The data in

figures 21(d) to 21(j) for o_ > 3.14 ° also show a distinct

line at which the surface temperature changes dramatically. However, this line is not parallel to the wing leading edge, but extends from the wing apex to the wing

trailing edge. The angle between this line and the leading

edge of the wing increases with increasing angle of

attack. The location of this line corresponds to the flow

reattachment line evident in the corresponding oil-flow

data in figures 19 and 20. This line represents a temperature change on the surface of the model due to reattachment of the leading edge vortical flow to the surface of

the wing. (See figs. 19(d), 20(i), and 21(i) for O_o m = 8%)
Thetemperaturevariationoccurringoverthewingat

Otnom=0°and1.03° (figs.21(a)and21(b))isbelievedto

beanindicationof boundary-layer transition.Whenthe

flowseparatesfromthewingleadingedgeandreattaches

inboard,thetemperatureof thewingsurfaceinboardof

thereattachment line is thatof theturbulentflow at

ot=0°. Thus,theflowinboardof theleading-edgesparationfor ct_>2.08° is believedto havea turbulent

boundary-layer condition.Thetemperatureof thewing

surfaceoutboardof theflowreattachment lineis thatof

thelaminarflowat ct=0°.Alsonotefromthepressure

distributiondatainfigure15(b)thattheflowoutboardof

theflowreattacbment pointisinaproversepressuregradientuntilthepressuredistributionlevelstoalargernegativevalueof Cp than that at the centerline of the wing.

A proverse pressure gradient is a favorable condition for

a laminar boundary layer. Thus, the flow outboard of

the reattachment point is believed to have a laminar

boundary-layer condition.

Effect of Longitudinal Position

Flow conicity. A comparison of the pressure distributions at two longitudinal positions on the model indicates whether the flow over the wing grows conically

down the length of the wing. Figure 22 shows the upper

surface-pressure distribution for each wing at x = 6 in.

and x=12in, for M=1.60 and R=2x106ft -1. The

sharp wing data in figure 22(a) show that the pressure

distributions at x = 6 in. and x = 12 in. are very similar,

thus indicating that the flow over the leeside of the sharp

wing grows conically down the length of the wing.

The elliptical wing data in figure 22(b) show that the

pressure distributions at x = 6 in. and x = 12 in. vary significantly beginning from ct = 2.22 ° (the angle of attack

at which leading-edge separation was first detected in the

pressure data) to, but not including, ct = 5.23 ° (the angle

of attack at which a classical leading-edge vortex was

first detected in the injected-oil-flow data, which is

shown in fig. 20(f)). For 1.23 ° < ot < 5.23 °, the inboard

edge of the leading-edge separation (denoted by a sudden

change in the pressure distribution) occurs at different

ri conditions for the x = 6 in. and x = 12 in. stations,

which indicates that the flow does not grow conically

down the length of the elliptical wing. This observation

corresponds to the painted and the injected-oil-flow data

for 1o < otnorn < 5° (figs. 19(a), 19(b), 20(c), 20(d),

and 20(e)), which show a leading-edge separation bubble

that does not grow conically down the length of the wing.

For ct > 5.23 °, the pressure distributions at the x = 6

in. and x = 12 in. stations (fig. 22(b)) are similar from the

centerline to the flow reattachment point (determined

from the oil-flow data), which indicates that the flow

grows conically down the length of the wing. This obser10

vation corresponds to the injected-oil-flow data for

Ctnom = 5 ° (fig. 20(f)), which show a conical growth of

the leading-edge separation. Outboard of the flow reattachment point for ct = 5.23 °, the pressure distribution

levels to a surface-pressure coefficient that is lower at the

x = 12 in. station than that observed at the x = 6 in. station. This observation indicates that, for angles of attack

just above the ct range of nonconical growth of the flow,

the leading-edge vortex grows conically, but varies

slightly in strength down the length of the wing. For

tx > 5.23 °, the surface-pressure coefficients near the wing

leading edge (fig. 22(b)) are essentially the same at the

two x stations.

The pressure data in figure 22(c) and the flowvisualization data (not presented here) of the cambered

wing show similar trends to the data for the elliptical wing. The flow over the wing is nonconical at

3.18 ° <or< 7.18 °. Recall that Otsep= 3.72 ° for the cambered wing at M = 1.60 and R = 2 x 106 ft-1. The vaporscreen data and oil-flow data for the cambered wing (not

presented here) show that the leading-edge vortex is first

detected at O_nom = 7°.

Figure 23 shows the upper surface-pressure distribution for each wing without grit at x = 6 in. and x = 12 in.

for M = 1.60 and R = 5 x 106 ft-1. For the angle of attack

range where nonconical growth of the flow was observed

at R = 2 x 106 ft-1 for the elliptical wing and the cambered wing, the R = 5 x 106 ft-1 data in figures 23(b)

and 23(c) show that the pressure distributions at x = 6

and 12 in. vary in the rI range from the wing leading edge

to the sudden pressure change that denotes the inboard

edge of the leading-edge separation. However, the variations between the pressure distributions at the x = 6 in.

and x= 12 in. stations are much smaller than was

observed at R=2 x 106ft -1. Thus, Reynolds number

affects the conicity of the flow over the 65 ° swept delta

wing.

R x held constant. The surface-pressure coefficient

data presented in figures 22 and 23 show the effect of

longitudinal position on the wing at a constant R. The

local Reynolds number for each x station Rx changes

when R is held constant. For R = 2 x 106 ft-1 at x = 6 in.,

Rx=l x106 , and at x=12in., Rx=2x106 . Thus, the

nonconical growth of the flow could be attributed to

Reynolds number effects. Figure 24 shows the upper

surface-pressure distributions at x = 6 in. and x = 12 in.

for several wing geometry and constant Rx. The sharp

wing data in figure 24(a) show that the longitudinal position on the wing does not have a profound affect on the

shape of the pressure distribution when R x is held constant. The data in figures 24(b) to 24(d) show that in the

angle of attack range where nonconical growth of the

flow was observed (1.23°< tx < 5.23 ° for the elliptical
wingand3.18° < ct < 7.18 ° for the cambered wing), the

pressure distributions at the two x stations agree well.

This observation indicates that the nonconical growth of

the flow observed on the elliptical and the cambered

wings is partially a function of Rx. The sharp wing and

elliptical wing data in figures 24(a) to 24(c) also show

slightly lower values of Cp across the whole span of the

wing at higher R. This trend was not observed in the

cambered wing data in figure 24(d).

Effect of Reynolds Number

Surface-pressure coefficient data. Data were

obtained over an R range of I x 106 ft-1 to 5 x 106 ft-1 to

determine the effect of Reynolds number on the onset

of leading-edge separation. Figure 25 presents upper

surface-pressure coefficient data obtained at various Rx

conditions on the sharp wing model without grit at

x= 12in. The data in figure 25 were obtained at

M = 1.60 over the angle of attack range of 0° to 9°. The

pressure data in figure 25 show the development of a

leading-edge vortex over the leeside of the sharp wing as

the angle of attack increases. The leading-edge vortex

influences the pressure distribution so that there is a sudden pressure change over a range of 11. The flow reattachment point falls within this range of _i. The pressure

distribution outboard of this rl range levels to a constant

Cp near the wing leading edge. The pressure data in figures 25(b) and 25(c) show that the rl range over which

the sudden pressure change occurs decreases with

increasing Rx and the amount of the sudden pressure

change increases with increasing Rx. These observations

indicate that the strength of the leading-edge vortex

increases with increasing Rx. It should be noted that Rx

appears to have little affect on the Cp near the centerline

or near the leading edge of the sharp wing.

Figure 26 presents upper surface-pressure coefficient

data obtained at various Rx conditions on the elliptical

wing without grit at x=12in., M=1.60, and

0°< ct < 9°. The data in figure 26 show that Reynolds

number has the most effect on the pressure distribution in

the range of 1°< Ctnom < 5° where nonconical growth

of the flow over the upper surface of the elliptical

wing was observed for R = 2 x 106 ft -1 (fig. 22(b)). At

Ctnom = 2.0 °, the pressure distribution at Rx = 1 x 106 has

an inflection near the wing leading edge, which indicates

a leading-edge separation bubble. Because the location

of the inflection in the pressure distribution at ctnom = 3°

has moved more inboard than was observed at

Otnorn = 2.0 °, the leading-edge separation bubble grows

larger with an increase in angle of attack. However, for a

given angle of attack, the location of the inflection in the

pressure distribution moves outboard with increasing Rx.

This characteristic is seen more clearly in the surfacepressure coefficient data in figure 27, which presents the

pressure distributions at Act = 0.25 ° increments for the

elliptical wing. Thus, the leading-edge separation bubble

for 2° <ctnom < 5° on the elliptical wing becomes

smaller with increasing Rx.

As the leading-edge separation bubble weakens with

increasing Reynolds number, the pressure distribution

moves to a distribution more typical of an attached flow

at the wing leading edge (figs. 26(a), 26(b), and 27). As a

result, the surface-pressure coefficient near the leadingedge decreases as Reynolds number increases. The data

in figure 27 show that for Rx= 1 x 106 , the onset

of leading-edge separation was first detected at

ctsep = 1"97°" The data for Rx = 5 x 106 in figure 27 show

that ctsep increases to 2.49 ° where the leading-edge separation is detected by a leveling of the pressure distribution at the leading edge. Thus, ctsep increases with

increasing R x.

The pressure data in figures 26(b) and 26(c) indicate

that increasing the Rx slightly increases the strength of

the leading-edge vortex present over the upper surface of

the elliptical wing at the higher angles of attack

(ctnom > 50) • However, the pressure data in figures 26(b)

and 26(c) also show that the value of Cp near the wing

leading edge is insensitive to Rx.

Figure 28 presents upper surface-pressure coefficient data obtained at various Rx conditions on the cambered wing model without grit at x = 12 in., M = 1.60,

and 0°< ct < 9 °. The cambered wing data in figure 28

show similar trends to those observed in the elliptical

wing data. The pressure data in figure 28 show that

Reynolds number has the most effect on the pressure distribution in the angle of attack range (3°< ctnom < 7°)

where nonconical growth of the flow over the upper

surface of the cambered wing was observed at

R = 2 x 106 ft -1 (fig. 22(c)). As was found on the elliptical wing data, the pressure data for the cambered wing at

3° < Otnom < 7° (fig. 28) show that as Rx increases, the

size of the leading-edge separation bubble decreases and

the surface-pressure coefficient near the leading edge

decreases. Also the angle of attack at which leading-edge

separation begins increases with increasing Rx as shown

in figure 29, which presents the pressure distributions for

the cambered wing at Act = 0.5 ° increments. The pressure data in figure 29 show that the angle of attack at

which leading-edge separation was first detected on the

cambered wing increases from 3.70 ° for Rx= 1 × 106

to 4.20 ° for Rx = 5 x 106.

As seen with the elliptical wing data, the cambered

wing data in figure 28 show that Reynolds number has a

much smaller influence at tY,nom > 7 °, where a leadingedge vortex has formed over the cambered wing. The

pressure data in figure 28 show that as Reynolds number

11
increasesfrom1x 106to5x 106,thesizeoftheleadingedgevortexis unaffected. However,thestrengthof the

vortexincreasesslightlywithincreasingRx. Also the Cp

value near the wing leading edge is unaffected by Rx for

O_nom > 7°.

The R x affects the onset of leading-edge separation

on the leeside of the elliptical and the cambered wings.

One explanation for this observation is the effect of R x

on the boundary layer of the model. With an increase in

Rx, the boundary layer of the model would be expected

to transition from a laminar condition to a turbulent

condition closer to the wing apex and the wing leading

edge. When a boundary layer is turbulent, the flow is

more energetic than when the boundary layer is laminar.

Thus, the closer the turbulent boundary layer is to the

wing leading edge, the more energy the flow requires to

remain attached at the wing leading edge. The onset of

leading-edge separation would occur at a higher angle of

attack.

The sharp wing data were not affected significantly

by increasing Rx. The sharp wing data are available on

the CD-ROM and in appendix D. The sharp wing developed a strong leading-edge separation as soon as angle of

attack was increased from zero. The state of the boundary layer does not appear to affect flow structures that

result from a very strong expansion at the wing leading

edge. A strong expansion at the wing leading edge would

occur for a sharp-edged wing at any angle of attack and

for any wing at high angles of attack.

Vapor-screen data. The effect of Reynolds number

on the flow structure over the cambered wing is illustrated in figure 30, which presents vapor-screen

photographs for the cambered wing without grit at

x = 12 in., O_nom = 5°, M = 1.60, and various Rx. The data

in figure 30 show a leading-edge separation bubble at

Rx = 1 x 106. The separation bubble becomes smaller as

Rx increases until it finally is hidden by the glare of the

laser light sheet off the surface of the model at

Rx = 5 × 106. This observation is supported by the pressure data in figure 28(b). The pressure data show that for

Otnom = 5 °, a leading-edge separation exists at

Rx= 1 x 106, as indicated by a sudden change in the

pressure distribution. The r I location of this sudden

change in pressure corresponds to the inboard edge of the

separation bubble as shown in the vapor-screen data in

figure 30(a). As Rx increases, the separation bubble

becomes smaller, which is indicated by the outboard

movement of the location of inflection in the pressure

distribution near the leading edge (fig. 28(b)).

The effect of Rx on the flow over the cambered wing

at a higher angle of attack is shown in figure 31. This figure presents vapor-screen photographs for the cambered

12

wing without grit at M = 1.60, x = 12 in., Otnom = 8°, and

various Rx. The data in figure 31 show that Rx does not

significantly impact the size of the leading-edge vortex at

Otnom = 8 °. This observation is supported by the surfacepressure coefficient data in figure 28(c).

Painted- and injected-oR-flow data. The paintedand the injected-oil-flow techniques were used to examine the effect of Reynolds number on the flow characteristics of the surface of the wings. Figure 32 presents

painted-oil-flow photographs for the cambered wing

without grit at O_nom = 4°, M = 1.60, and various R. Figure 33 presents the injected-oil-flow photographs for the

same conditions. The oil-flow data in figures 32 and 33

show an accumulation of oil along the leading edge of

the wing at R = 1 × 106 ft-1 for if'nora= 4°. This accumulation is indicative of a leading-edge separation bubble,

which is also evident in the surface-pressure coefficient

data in figures 28 and 29. The data in figures 32 and 33

show that as R increases, the accumulation of oil along

the leading edge becomes thinner, which indicates a

decrease in the size of the separation bubble. Decreasing

separation bubble size with increasing Reynolds number

is also seen in the surface-pressure coefficient data in

figures 28 and 29.

The pressure distribution data for the elliptical and

the cambered wings (figs. 27 and 29) showed that

increasing Reynolds number increased the angle of

attack at which leading-edge separation begins. Recall

that figure 20 presents the injected-oil-flow data for the

elliptical wing without grit at M = 1.60, R = 2 x 106, and

various angles of attack. Figure 34 presents injectedoil-flow photographs for the elliptical wing without grit

at Otnom = 2° and 3 °, M = 1.60, and R = 5 x 106 ft-1. For

Rx = 2 x 106, the oil-flow data in figure 20 show an accumulation of oil along the leading edge (indicating a

leading-edge separation bubble) that first occurs at

= 2.08 ° (O_nom = 2°, fig. 20(C)). However, the

Rx = 5 × 106 data in figure 34 do not show a leadingedge separation bubble occurring until ct = 3.25 °

(O.nom = 3°). This observation corresponds to the pressure data in figure 27, which show that tXsep increased

from 2.22 ° (ff'nom = 2°) to 2.49 ° _Otnom = 2.25 °) as the Rx

increased from 2 x 10°to 5 x 10_'.

The surface-pressure coefficient data in figures 26

and 28 indicated little influence of Reynolds number on

the size of the leading-edge vortex at the higher angles of

attack where a leading-edge vortex was present. Figure 35 presents injected-oil-flow photographs for the

cambered wing without grit at Otnom = 8°, M = 1.60, and

various R. The data show that R does not significantly

affect the position of the flow reattachment point of the

leading-edge vortex. However, the secondary separation
occurringbeneaththeprimaryvortexappearstoweaken

withincreasingReynoldsnumber.

Liquid-crystal data. Liquid-crystal data were

obtained at R = 2 x 106 ft -1 and 5 x 106 ft -1 to examine

the effect of Reynolds number on the flow characteristics

of the leeside surface of the model. The liquid-crystal

data in figure 21 for the elliptical wing at R = 2 x 106ft - 1

first detected the onset of leading-edge separation at

= 2.08 ° (otnom = 2°). Figure 36 presents liquid-crystal

photographs for the elliptical wing at M = 1.60 and

R = 5 × 106 ft-1 for various angles of attack. The data in

figure 36 also showed the onset of leading-edge separation occurring at ot = 2.17 ° (0tnom = 2°). This observation

does not correspond to those made in the surfacepressure coefficient data (fig. 27) and injected-oil-flow

data (fig. 34) as shown in table 12. Table 12 presents the

angle of attack at which leading-edge separation was

detected with the surface-pressure, the injected-oil-flow,

and the liquid-crystal data. Table 12 also shows the last

angle of attack where attached flow was observed O_at t in

each data set. The angle of attack where leading-edge

separation begins falls between O_at t and (Xse p. The data in

table 12 show that the trend of an increase in O_se p with an

increase in Reynolds number is supported by the pressure

and injected-oil-flow data sets. The trend of an increase

in _sep with an increase in Reynolds number is not supported by the liquid-crystal data.

However, the liquid-crystal data did indicate a

smaller leading-edge separation bubble at the

R=5 × 106ft -1 condition than that observed for the

R=2x 106ft -I condition (figs. 21(c) and 36(c) for

Otnom = 2°). This observation is supported by the surfacepressure coefficient data in figure 27, which show a

decrease in the size of the leading-edge separation bubble

with an increase in R x. Because all the data sets indicate

that an increase in Reynolds number decreases the size of

the leading-edge separation bubble for a given angle of

attack, the onset of leading-edge separation occurs at a

higher angle of attack as Reynolds number increases.

This observation could be explained by noting that

increasing the Reynolds number moves the boundarylayer transition location closer to the leading edge. This

explanation is supported by the liquid-crystal data for the

elliptical wing at Otnom = 0 ° and 1° (figs. 21(a), 21(b),

36(a), and 36(b)). The liquid-crystal data show, inboard

of the leading edge, a temperature variation that indicates

boundary-layer transition. However, the temperature

variation for the R = 5 x 106 ft-1 condition occurs much

closer to the leading edge than that observed for the

R = 2 x 106 ft-1 condition. This observation supports the

explanation that boundary-layer condition affects the

onset of leading-edge separation.

Effect of Transition Grit

Surface-pressure coefficient data. Data were

obtained on the three models with and without grit

applied to determine the effect of grit on the onset of

flow separation at the wing leading edge. Figure 37 presents upper surface-pressure coefficient data obtained on

the sharp wing model at x = 12 in. without grit and with

transition grit. The data in figure 37 were obtained at

x = 12 in., M = 1.60, and R x = 2 x 106 over the angle of

attack range of 0 ° to 9 °. The data in figure 37 show that

the application of transition grit appears to have no effect

on the development of the vortex over the leeside of the

sharp wing with increasing angle of attack. This observation is not unexpected as leading-edge separation occurs

on the sharp wing as soon as ct is increased from 0%

Thus, the spanwise flow does not encounter the transition

strip until it has reattached inboard of the wing leading

edge and moves back to the wing leading edge as illustrated in figure 11.

Figure 38 presents a similar set of data for the ellipticai wing with and without grit at x = 12 in., M = 1.60,

and R x= 2 x 106 over the Otnom range of 0° to 9° . For

tXnom > 4% the application of grit appears to have no significant impact on the leading-edge vortex (figs. 38(b)

and 38(c)). For tXnom > 4°, the flow separates at the wing

leading edge, reattaches inboard of the leading edge, and

does not encounter the transition strip. However, at the

angle of attack where leading-edge separation was

first detected on the elliptical wing without grit

(tZsep = 2.22°), grit has an effect on the separation bubble

emanating from the wing leading edge. The separation

bubble influences the upper surface-pressure coefficient

distribution so that an inflection appears in the pressure

distribution at the inboard edge of the separation bubble.

The pressure data in figure 38(a) show that when grit is

applied to the model, the location of the inflection moves

outboard. Also, with the application of the grit to the

model, the pressure distribution moves to a distribution

more typical of an attached flow at the wing leading edge

(fig. 38(a)). As a result, the surface-pressure coefficient

near the leading edge decreases with the application of

grit to the model. These trends indicate a weaker leadingedge separation bubble for the case with grit than was

observed for the case without grit. These features are

seen more clearly in the surface-pressure coefficient data

in figure 39, which presents the pressure distributions for

the elliptical wing in Atz = 0.5 ° increments at x = 12 in.,

M = 1.60, and Rx = 2 x 106.

Figure 40 presents surface-pressure coefficient data

with and without grit for the cambered wing at x = 12 in.,

M = 1.60, and Rx = 2 x 106 over Ctnom range of 0 ° to 9 °.

The effect of transition grit on the cambered wing data

13
was similar to the effect seen in the elliptical wing data

(fig. 38). For or.nom > 6°, the application of grit appears to

have no significant effect on the leading-edge vortex

over the leeside of the cambered wing (figs. 40(b)

and 40(c)). However, at ctnom = 4° (near the angle of

attack where leading-edge separation was first detected

on the cambered wing without grit, tXsep = 3.72°), the

presence of transition grit weakens the leading-edge separation bubble. This observation is more clearly evident

in the surface-pressure coefficient data in figure 41,

which present the pressure distributions for the cambered

wing in increments of Atx = 0.5 ° at x = 12 in., M = 1.60,

andRx=2X 106 .

The surface-pressure coefficient data in figures 38

to 41 indicate that the application of transition grit weakens the leading-edge separation bubble that occurs at low

angles of attack on the elliptical and the cambered wings.

An explanation for this observation is that the transition

grit moves the boundary-layer transition location closer

to the wing leading edge than when transition grit was

not on the model. Because the flow has more energy in a

turbulent boundary layer than in a laminar boundary

layer, the cases with grit remain attached at the wing

leading edge to a higher angle of attack than the cases

without grit. Thus, the cases with grit would have a

weaker separation bubble than the cases without grit for

an angle of attack where both grit conditions yield

leading-edge separation.

Painted- and injected-oil-flow data. The paintedand injected-oil-flow techniques were used to examine

the effect of grit on the flow characteristics of the surface

of each model. Figure 42 presents the painted-oil-flow

photograph for the cambered wing with grit at ¢Xnom = 4 °,

M= 1.60, and R=2x 106ft -1. Figure 43 presents the

injected-oil-flow photograph for the same condition. As

was observed for the case without grit (figs. 32(b)

and 33(b)), the oil-flow data in figures 42 and 43 show an

accumulation of oil along the leading edge of the cambered wing at R = 2 x 106 ft-1 for 0tnom = 4 °. However,

the accumulation of oil on the leading edge is smaller for

the case with grit than that observed for the case without

grit. This observation indicates that the leading-edge separation bubble is weaker for the condition with grit. This

trend is also evident in the surface-pressure coefficient

data in figure 41.

Concluding Remarks

An experimental investigation of the effect of

leading-edge radius, camber, Reynolds number, and

boundary-layer state on the incipient separation of a delta

wing at supersonic speeds was conducted at the Langley

Unitary Plan Wind Tunnel. The three delta wing models

examined had a 65 ° swept leading edge and varied in

cross-sectional shape: a sharp wedge, a 20:1 ellipse, and

a 20:1 ellipse with a -9.75 ° circular camber imposed

across the span. The three wings were tested at a

Mach number of 1.60 over a free-stream Reynolds number range of 1 x 106 to 5 × 106ft -1. The wings were

tested with and without transition grit applied. Surfacepressure coefficient data were obtained, as well as

flow-visualization data. The flow-visualization techniques employed were the vapor-screen, the paintedoil-flow, the injected-oil-flow, and the liquid-crystal

techniques. The surface-pressure coefficient data and

flow-visualization data are electronically stored on a

CD-ROM that accompanies this report.

The data indicated that by rounding the wing leading

edge or cambering the wing in the spanwise direction,

the onset of leading-edge separation on a delta wing at

supersonic speeds occurs at a higher angle of attack than

that observed on a sharp-edged delta wing. Specifically,

the 20:1 elliptical cross section increased the angle of

attack at which leading-edge separation begins by

about 2° over that observed on a sharp-edged delta wing.

The cambered elliptical cross section, which decreased

the local angle of attack at the wing leading edge

by 3.76 °, effectively increased the angle of attack at

which leading-edge separation begins by 1.5 ° over that

observed on the uncambered elliptical cross section. The

data showed that the wing leading-edge radius and/or

camber lowers the incidence angle of the flow over the

wing with a more pronounced effect on the flow at the

wing leading edge.

The application of transition grit on the wing or an

increase in free-stream Reynolds number increased the

angle of attack at which leading-edge separation began.

Fixing transition or increasing free-stream Reynolds

number causes the boundary-layer transition to occur

closer to the wing apex and leading edge of the wing. A

turbulent boundary layer has more energy than a laminar

boundary layer and will therefore allow the flow to

remain attached at the wing leading edge at higher angles

of attack than is possible with a laminar boundary layer.

NASA Langley Research Center

Hampton, VA 23681-0001

December I 1, 1995

14
Table1.GeometricCharacteristics of DeltaWingModels

Overallconstants:

65.00 ALE,deg.......................................................... 0 ATE,deg............................................................. 18.00

c, in ..............................................................

16.7868

bTE, in ..........................................................

bto, in ........................................................... 13.9870

S, in 2 .......................................................... 151.0812

1.8652 Aspect ratio ......................................................

tmax, in ........................................................... 0.8394

Sharp wing:

r, in .................................................................. 0

0c, deg ................................................................ 0

Elliptical wing:

0.0025

r, in .............................................................

0c, deg ................................................................ 0

Cambered wing:

0.0025

r, in .............................................................

0 c, deg ............................................................. 9.75

15
16

x, in.

6

6

6

6

6

Table 2. Pressure Orifice Location, CP#, and Condition for Sharp Wing

Surface

Upper

Upper

Upper

Upper 0.399

Upper 0.499

Upper

Upper

Upper

Upper

6 Upper

6 Upper

6 Upper

6 Upper

6 Upper

6 Upper

Upper

Lower

Lower

Lower

11

0.099

0.199

0.299

0.539

0.579

0.620

0.660

0.699

0.719

0.740

0.759

0.780

0.799

0.820

6 Lower

6 Lower 0.702

6 Lower 0.802

Upper

12 Upper

12 Upper

12 Upper

12

12 Upper

12 Upper

12 Upper

12

0.202

0.402

0.498

0.603

0.100

0.199

0.301

0.349

0.400

0.450

0.500

CP# Condition

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

4

5

6

49

50

51

52

53

54

55

Upper 0.519 56

12 Upper 0.539 57

12 Upper 0.560 58

12 Upper 0.580 59

12 Upper 0.599 60

12

12

0.620

0.639

0.660

Upper

Upper

12 Upper

12 Upper 0.680

12 Upper 0.700

12 Upper 0.720

61

79

66

67

68

69

Plugged
Table 2. Concluded

x, in. Surface

12 Upper

12 Upper

rl CP#

0.740 70

0.760 71

12 Upper 0.780 72

12 Upper 0.800 73

12 Upper 0.820 74

12 Upper 0.840 75

Condition

12 Upper 0.859 76 Plugged

12 Upper 0.879 77

12 Upper 0.899 78

0.201 9

0.401 10

0.451 11

12 Lower

12 Lower

12 Lower

12 Lower 0.501 12

12 Lower 0.551 13

12 Lower 0.601 14

0.651

0.701

15

16

12 Lower

12 Lower

12 Lower 0.751 17

12 Lower 0.800 18 Plugged

12 Lower 0.850 19

12 Lower 0.901 20 Plugged

17
18

in.

Table 3. Pressure Orifice Location, CP#, and Condition for Elliptical Wing

x, Surface

6 Upper

6 Upper

6

6

6

Upper

Upper

Upper

Upper

Upper

Upper

6 Upper

6 Upper

6 Upper

6 Upper

6 Upper

Upper

Upper

Upper

6 Upper

6 Upper

6 Upper

6

6

Upper

Upper

Upper

Upper

Upper

6 Lower

6 Lower

6 Lower

6

6

Lower

Lower

6 Lower

6 Lower

Lower

11

0.099

0.199

0.299

0.400

0.499

0.539

O.579

0.619

0.660

0.700

0.720

0.740

0.759

0.781

0.800

0.820

0.840

0.860

0.880

0.899

0.920

0.939

0.960

0.980

0.200

0.400

0.500

0.600

0.700

0.799

0.850

O.900

6 Lower 0.949

12 Upper 0.100

12 Upper 0.200

12

12

Upper 0.300

Upper 0.350

Upper 0.400

Upper 0.500

Upper 0.520

12

12

12

CP# Condition

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

5O

51

52

53

Plugged from run 22

7

8

9 Plugged

57

58

59

60

61

66

67

54

55 Plugged

56
Table3.Concluded

x, in. Surface

12 Upper

CP#

0.540 68

12 Upper 0.560

12 Upper 0.579

12 Upper 0.599

Upper

12 Upper

12 Upper

12 Upper

12 Upper

12

12 Upper

12 Upper

12 Upper

0.621

0.640

0.660

0.680

0.700

0.720

0.740

0.760

69

70

71

72

73

74

75

76

77

78

79

12 Upper 0.780 80

12 Upper 0.800 81

12 Upper 0.820 82

0.840

0.860

0.879

0.899

0.920

0.940

0.960

0.981

0.200

0.400

0.450

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Lower

12 Lower

12 Lower

12 Lower 0.500

0.550

83

84

85

86

87

88

89

90

12

13

14

15

12 Lower 16

12 Lower 0.600 17

12 Lower 0.650 18

12 Lower 0.700 19

12 Lower 0.750 20

12 Lower 0.800 21

12 Lower 0.850 22

12

12

0.900

0.950

Lower

Lower

Condition

Plugged from run 22

Plugged

23

24 Plugged from run 22

19
Table4.PressureOrificeLocation,CP#,andConditionforCamberedWing

x, in. Surface

6 Upper

6 Upper

6 Upper

Upper

rl CP#

0.099 33

0.199 34

0.299 35

0.400

6 Upper 0.499

6 Upper 0.539

6 Upper 0.579

6

6

6

6

6

Upper

Upper

Upper

Upper

Upper

Upper

Upper

Upper

Upper

Upper

6

6

6 Upper

6 Upper

6 Upper

0.619

0.660

0.700

0.720

0.740

0.759

0.781

0.800

6 Upper

6 Upper 0.939

6 Upper 0.960

6 Upper

6 Lower

6 Lower

6 Lower

6 Lower

Lower

0.820

0.840

0.860

0.880

0.899

0.920

0.980

0.200

0.400

0.500

0.600

0.700

Lower 0.799

6 Lower 0.850

6 Lower 0.900

6 Lower 0.949

Upper

12 Upper

12 Upper

12

12

12

12

Upper

Upper

Upper

12 Upper

0.I00

36

37

38

39

40

41

42

43

44

45

46

47

48

49

5O

51

52

53

54

55

56

i

2

3

4

5

6

7

8

9

57

0.200 58

0.300 59

0.350 60

0.400 61

0.450

0.500

91

66

Condition

Slow leak

Plugged

Plugged

2O
Table4.Concluded

x, in. Surface

12 Upper

12 Upper

12 Upper

12

12

12

Upper

Upper

Upper

1] CP# Condition

0.520 67

O.540 68

12 Upper

12 Upper

12 Upper

12

0.560

0.579

69

70

0.599 71

0.621 72

0.640 73

0.660

0.680

Upper 0.700

12 Upper 0.720

12 Upper 0.740

Upper

Upper

Upper

Upper

Upper

12

12

12

12

12

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Upper

12 Lower

12 Lower

12 Lower

Lower

Lower

Lower

Lower

Lower

Lower

12

12

12

12

12

12

12

0.760

0.780

0.800

0.820

0.840

74

75

76

77

78

79

80

81

82

83

0.860 84

0.879 85

0.899 86

0.920

0.940

0.960

0.981

0.200

0.400

0.450

0.500

0.550

Lower

12 Lower

12 Lower

12 Lower

0.600

0.650

0.700

0.750

0.800

0.850

0.900

0.950

87

88

89

90

12

13

14

15

16

17

18

19

20

21

22

23

24

21
Table5.Summaryof DataforThreeModels

(a)Sharpwingwithoutransitiongrit

R, ft -1

1 x 106

2x 106

5× 106

Run

40

41

42

ro t3_nom, deg

Surface-pressure data

0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.5, 4.0, 4.5, 5.0,

5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0,

7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 4.0,

4.5, 5.0, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5,

9.0

1 x 106

2x 106

2x 106

5× 106

Vapor-screen data

1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 8.5, 9.0

0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 7.0, 8.0, 9.0

Painted-oil-flow data

4.0, 6.0, 8.0

4.0, 6.0, 8.0

Injected-oil-flow data

2 × 106 6.0, 7.0, 8.0, 9.0

5 x 106 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

Liquid-crystal data

2 x 106 120 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

2 × 106 125 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

2 x 106 130 0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5 × 106 120 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5 × 106 125 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5 x 106 130 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

(b) Sharp wing with transition grit a

R, ft-I [ Run [ O_nom,deg

Surface-pressure data

1 x 106 43 0.0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75,

6.0, 6.25, 6.5, 6.75, 7.0, 7.5, 8.0, 8.5, 9.0

2 x 106 44 0.0, 0.5, !.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5,

9.0

5 x 106 45 0.0, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

aVapor-screen data, painted-oil-flow data. injected-oil-flow data, and liquid-crystal data not applicable.

22
Table5.Continued

(c)Ellipticalwingwithoutransitiongrit

 ,ft' I I I

Surface-pressure data

1 x 106 6 0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.5, 4.0, 4.5, 5.0,

5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5, 9.0

2 x 106 7 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0,

7.5, 8.0, 8.5, 9.0

3× 106 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0,

7.5, 8.0, 8.5, 9.0

4x 106 10 0,0.5, 1.0, 1.5,2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5,7.0,

7.5, 8.0, 8.5, 9.0

5 × 106 14 0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 4.0,

4.5, 5.0, 5.5, 5.75, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0

Vapor-screen data

1 x 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

2 × 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5 × 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

Painted-oil-flow data

1 × 106 2.0, 3.0, 4.0, 6.0

2 x 106 3.0, 4.0, 6.0, 8.0

5× 106

I 4.0, 6.0, 8.0

Injected-oil-flow data

2 x 106 [ ] 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5 x 106 I [ 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0

Liquid-crystal dam

2 x 106 120 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

2 x 106 125 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

2x 106

5x 106

5× 106

5x106

130 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

120 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

125 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

130 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

23
R, fl-I Run

1 x 10 6

2X 106

3×106

4× lO6

5× lO 6

22

25

28

32

29

Table 5. Continued

(d) Elliptical wing with transition grit a

¢Xnom, deg

Surface-pressure data

0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75,

6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5 7.0, 7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75,

6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5, 9.0

Vapor-screen data

1 x 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5x 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

Painted-oil-flow data

! x 106 2.0, 3.0, 4.0, 6.0

2 x 106 2.0, 3.0, 4.0, 6.0

Injected-oil-flow data

1 x 106 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

2 x 106 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5 × 106 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

aLiquid-crystal data not applicable.

24
Table5.Continued

(e)Camberedwingwithoutransitiongrit

R, ft -1

1 x 106

2x 106

5x 106

Run

36

34

35

I To I

O_no m, deg

Surface-pressure data

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75, 6.0,

6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0,

7.5, 8.0, 8.5, 9.0

0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75, 6.0,

6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 8.0, 8.5, 9.0

Vapor-screen data

1 x 106

2 x 106

5x 106

0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 9.0

0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 9.0

0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 9.0

Painted-oil-flow data

1 × 106

2x 106

5x 106

I 4.0, 5.0, 6.0, 8.0

4.0, 5.0, 6.0, 8.0

4.0, 6.0

Injected-oil-flow data

1 x 106

2x 106

5xlO 6

2x 106

2× 106

2x 106

5X 106

0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

0, 1.0, 2.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

Liquid-crystal data

i 20 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

125 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

5x 106

130 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

120 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

125 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

25
Table5.Concluded

(f)Camberedwingwithtransitiongrita

R, ft-I [ Run I °_nom, deg

Surface-pressure data

1 x 106 37 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0,

7.25, 7.5, 8.0, 8.5, 9.0

2 x 106 38 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0

5 x 106 39 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0,

7.25, 7.5, 8.0, 8.5, 9.0

Vapor-screen data

1 x 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5

5 x 106 0, 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0,8.0, 9.0

Painted-oil-flow data

2x106 I [ 4.0, 5.0, 6.0, 8.0

Injected-oil-flow data

1 x 106 I

2 X 10 6

5x 10 6

0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

O, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0

aLiquid-crystal data not applicable.

26
Table 6. Corrected Angle of Attack Index of Data for Sharp Wing Without Transition Grit

(a) M = 1.60, R = 1 × 106 ft-1, _ = 0 °, and Of= 0.4 °

Surface-pressure

Otnom, deg point number a

0 849 / 868

0.50 850

1.00

1.50

1.75

2.00

2.25

Surface

pressure

¢x, deg

0.25 / 0.26

0.75

Vapor

screen

¢_, deg

851 1.28 1.1

852 1.75

869 2.03

853

870

2.50 854/871

2.75 872

3.00 855

3.25

856

2.29

2.50

2.76 / 2.74

3.03

3.25

3.75

857 4.25

3.50

3.75

4.00

4.25

4.50 858

4.75

5.00 859

5.25

5.50 860

5.75 873

6.00 861

874

862

875

863

6.25

6.50

6.75

7.00

7.25 876

7.50 864

7.75

865

866

867

4.75

5.30

5.77

6.02

6.26

6.53

6.79

7.01

7.27

7.51

7.76

8.26

2.1

3.1

8.00

8.25

8.50

9.00

aRun 40.

4.1

7.1

9.27 9.1

Painted

oil flow

_, deg

Injected

oil flow Liquid crystal

or, deg o_, deg

27
Otnom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

Table6.Continued

(b)M = 1.60, R = 2 x 106 ft-1, _ = 0°, and Of= 0.4 °

Surface Vapor Painted

Surface-pressure

point number a

pressure

_, deg

877 / 896 0.25 / 0.26

878 0.78

879 1.28

880 1.78

881

882

screen

_, deg

2.25 2.1

2.77

883 3.28

884 3.75

4.27

4.76

5.25

5.78

6.27

885

886

887

888

889

890 6.78

891 7.26

2.6

3.1

3.6

4.1

4.6

5.1

5.6

892

893

894

9.00 895

aRun 41.

7.76

8.27 8.1

8.76

9.28 9.1

oil flow

_, deg

4.17

6.26

8.34

Injected

oil flow

tx, deg

6.26

7.29

8.34

Liquid crystal

or, deg

0

1.03

2.08

3.14

4.17

5.21

6.26

7.29

8.34

9.39 9.39

28
Otnom,deg

Surface-pressure

pointnumbera

0 897/ 916

0.50 898

1.00 899

1.50

1.75

2.00

2.25

2.50

900

917

901

918

902

2.75 919

3.00 903

3.25

3.50

3.75

4.00

4.25

4.50

4.75

920

904

9O5

Table 6. Concluded

(c) M = 1.60, R = 5 x 106 ft-1, _ = 0 °, and Of= 0.4 °

Surface Vapor Painted

pressure screen oil flow

_, deg or, deg a, deg

0.23 / 0.31

0.79

1.28

1.78

2.01

2.29

2.52

2.76

3.00

3.28

3.51

3.76

4.25

906 4.76

5.00 907

5.25

5.50 908

5.75 921

6.00 909

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

5.27

922

910 6.78

923 7.00

911

924

912

913

8.25

8.50

9.00

aRun 42.

4.34

5.75

6.02

6.27 6.51

6.53

7.29

7.52

7.75

8.25

914 8.76

915 9.25

8.68

Injected

oil flow

_, deg

2.17

Liquid crystal

a, deg

0

1.10

2.17

3.25 3.25

4.34 4.34

5.43 5.43

6.51

7.60

8.68

9.75

6.51

7.60

8.68

9.75

29
O_nom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

Table7.CorrectedAngleofAttackIndexofDataforSharpWingWithTransitionGrit

(a)M= 1.60, R = 1 x 106 ft-1, _ = 0% and Of= 0.4 °

Surface-pressure

point number a

937 / 956

938

Surface

pressure

_, deg

0.23 / 0.24

0.78

939 1.26

940 1.78

957

941

958

942

959

943

960

944

945

946

4.75

5.00 947

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

948

961

2.03

2.29

2.49

2.79

3.05

3.24

3.52

3.75

8.00

8.25

8.50

9.00

aRun 43.

4.29

4.76

5.26

5.79

5.99

949 6.25

962 6.51

950/963 6.77/6.77

964

951

952

953

954

955

7.04

7.22

7.79

8.24

8.74

9.27

Vapor

screen

deg

Painted

oil flow

tx, deg

Injected

oil flow

tx, deg

Liquid crysta

t_, deg

3O
Omom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

Surface-pressure

point number a

965 / 985

966

967

968

969

2.50 970

2.75

3.00 971

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 44.

Table 7. Continued

(b) M = 1.60, R = 2 x 106 ft-l, ¢ = 0 °, and Of= 0.4 °

Surface

pressure

a, deg

0.28 / 0.27

0.75

1.29

1.77

2.29

2.74

3.30

972 3.76

973 4.29

974

975

4.76

5.25

976 5.76

977 / 978 6.28 / 6.28

979

980

981

982

983

984

6.77

7.27

7.77

8.26

8.76

9.28

Vapor

screen

ct, deg

Painted

oil flow

a, deg

Injected

oil flow

ct, deg

Liquid crystal

a, deg

31
Otnom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

Table7.Concluded

(c)M = 1.60, R = 5 x 106 ft-1, ¢ = 0 °, and Of= 0.4 °

Surface Vapor Painted

Surface-pressure

point number a

986

987

988

989

pressure

_, deg

991 / 992

0.26

0.78

1.28

2.30

990 3.24

4.25 / 4.25

993 5.29

994

7.00 995

7.25

7.50

7.75

8.00

8.25

8.50

9.00

996

6.24

aRun 45.

7.26

8.30

997 9.29

screen

_, deg

oil flow

_, deg

Injected

oil flow

o_, deg

Liquid crystal

or, deg

32
Table8.CorrectedAngleof Attack Index of Data for Elliptical Wing Without Transition Grit

(a) M = 1.60, R = 1 x 106 ft-1, _ = 0°, and Of= 0.4 °

tZnom, deg

0

0.50

1.00

Surface-pressure

point number a

Surface

pressure

ct, deg

127 / 148 0.23/0.19

128 0.73

129

1.50 130

1.75 149

2.00 131

2.25 150

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

1.23

Vapor

screen

or, deg

0.2

1.2

1.70

1.97

2.17 2.2

2.47

132 2.68 2.7

151 2.94

133 3.19

134 / 135 3.71 / 3.71

136

137

138

139

152

140

6.25 153

6.50 141

6.75 154

142

155

143

144/145

4.18

4.67

Painted

oil flow

ct, deg

2.03

4.2

5.21 5.2

5.70

146

147

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 6.

5.97

6.24

6.45

6.68

6.2

6.96

7.23 7.2

7.43

8.2

9.2

7.72

8.18/8.18

8.69

9.23

4.06

6.12

Injected

oil flow

_, deg

Liquid crystal

or, deg

33
0triom,deg

-4.00

-3.00

Table8.Continued

(b)M = 1.60, R = 1 x 106 ft-1, t_ = 0°, and Of= 0 °

Surface

Surface-pressure

point number a

104

pressure

or, deg

Vapor Painted

-2.00 105

-1.00 106 -0.99

0 107 -0.04

1.00 108 1.02

2.00 109 2.01

3.00 110 2.99

4.00 111 3.99

aRun 4.

screen

o_,deg

oil flow

tx, deg

Injected

oil flow

o_, deg

Liquid crystal

oc, deg

_nom, deg

(c) M= 1.60, R= 1 × 106 ft-l,o = 180°, and Of=O o

Surface-pressure

point number a

Surface

pressure

tx, deg

-4.00 120 -4.00

-3.00 119 -2.98

-2.00 i18 -2.03

-1.00

1.00

2.00

3.00

4.00

117

116

115

114

113

112

aRun 5.

1.03

! .98

3.00

3.99

Vapor

screen

et, deg

Painted

oil flow

o_, deg

Injected

oil flow

_, deg

Liquid crystal

ct, deg

34
Otnom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

Surface-pressure

point number a

Table 8. Continued

(d) M = 1.60, R = 2 x 106 ft-1, * = 0% and 0f = 0.4 °

Surface

pressure

_, deg

157/175 0.19/0.19

158 0.71

159 1.23

160

161

162

163

176

3.75

4.00 164

4.25

4.50

4.75

5.00

5.25

1.75

2.22

2.69

3.24

Vapor

screen

or, deg

2.2

2.7

3.2

3.71 3.7

4.25 4.2

165 4.69

166 5.23

5.50 167

5.75

6.00 168

6.25

6.50 169

6.75

7.00

7.25

7.50

5.70

6.23

6.71

170 7.17

7.71

8.18

5.2

7.75

171

172

173

174

i

8.00

8.25

8.50

9.00

aRun 7.

6.2

7.2

8.2

8.70

9.22 9.2

Painted

oil flow

or, deg

3.14

4.17

6.26

8.34

Injected

oil flow

c_, deg

1.03

2.08

3.14

4.17

5.21

6.26

7.29

8.34

9.39

Liquid crystal

et, deg

1.03

2.08

3.14

4.17

5.21

6.26

7.29

8.34

9.39

35
O_nom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

Table8.Continued

(e) M = 1.60, R = 3 x 106 ft -!, ¢ = 0% and Of= 0.4 °

Surface Vapor Painted

Surface-pressure

point number a

194/213

195

196

197

198

199

200

201

202

203

204

205

206

207

208

7.50 209

7.75

8.00 210

8.25

8.50

9.00

aRun 8.

211

212

pressure

(x, deg

0.20 / 0.23

0.70

1.21

1.72

2.19

2.70

3.19

3.73

4.19

4.70

5.22

5.74

6.23

6.72

7.21

7.73

8.21

8.73

9.18

screen

tx, deg

oil flow

tz, deg

Injected

oil flow

o_, deg

Liquid crystal

tz, deg

36
Table8.Continued

(f)M = 1.60, R = 4 × 106 ft -l, 0 = 0% and Of= 0.4 °

O_.nom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

Surface-pressure

point number a

222 / 241

223

224

225

Surface

pressure

or, deg

0.25 / 0.21

0.73

1.16

1.69

226 2.20

227 2.67

228

229

3.23

3.67

3.75

4.00 230 4.18

4.25

4.50

4.75

5.00

231

232

5.25

5.50 233

4.73

5.17

5.71

234 6.19

5.75

6.00

6.25

6.50

6.75

7.00

235

236

7.25

7.50 237

7.75

238

239

240

8.00

8.25

8.50

9.00

aRun 10.

6.73

7.20

7.71

8.20

8.73

9.21

Vapor

screen

_, deg

Painted

oil flow

or, deg

Injected

oil flow

o_,deg

Liquid crystal

or, deg

37
Table 8. Continued

(g) M = 1.60, R = 5 x 106 f-t-l, _ = 0% and Of= 0.4 °

_nom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

Surface-pressure

point number a

271 / 290

272

273

274

291

275

292

276

293

277

294

3.50 278

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

279

280

281

282

295

283

284

285

286

287

288

289

Surface

pressure

_, deg

0.22 / 0.21

0.67

1.21

1.67

1.96

2.18

2.49

2.68

2.97

3.18

3.49

3.74

4.24

4.65

5.19

5.70

5.96

6.22

6.75

7.16

Vapor

screen

a, deg

2.2

2.7

3.2

3.7

4.2

7.2

7.71

8.21 8.2

9.2

Painted

oil flow

Or,deg

4.34

6.51

Injected

oil flow

_, deg

Liquid crystal

¢X,deg

0

1.10

0

1.10

2.17 2.17

3.25

4.34

5.43

3.25

4.34

5.43

6.51 6.51

7.60 7.60

aRun 14.

8.70

9.22

8.68 8.68 8.68

9.75

38
Otnom, deg

-4.00

Surface-pressure

pointnumbera

-3.00

-2.00

-1.00 265

0 266

1.00 267

Table8.Concluded

(h)M = 1.60, R = 5 × 106 ft-1, d?= 0% and Of = 0 °

Surface Vapor Painted

pressure screen oil flow

or, deg o_,deg tx, deg

-0.97

0.05

1.03

2.00 268 2.05

3.00 269 2.99

4.00 270 3.98

aRun 13.

Injected

oil flow

or, deg

Liquid crystal

cz, deg

(Xnom, deg

-4.00

-3.00

-2.00

(i) M = 1.60, R = 5 × 106 ft -1, ¢ = 180 °, and 0f= 0°

Surface Vapor Painted

Surface-pressure

point number a

pressure

or, deg

- 1.00 247 - 1.06

0 246 -0.04

1.00 245 1.05

2.00 244 2.01

screen

cz, deg

oil flow

tx, deg

3.00 243 2.96 [

4.00 242 4.02 I

aRun 11.

Injected

oil flow

ct, deg

Liquid crystal

or, deg

39
Otnom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

Table9.Corrected Angle of Attack Index of Data for Elliptical Wing With Transition Grit

(a) M = 1.60, R = 1 x 106 ft-1, _ = 0 °, and Of= 0.4 °

Surface Vapor Painted

Surface-pressure

point number a

408 / 427

409

410

411

428

412

pressure

_, deg

0.20 / 0.19

0.71

1.19

screen

_, deg

1.69

1.93

2.21 2.2

429 2.45

413 2.71

430 2.93

3.00 414

3.25 431

3.50 415

3.75

4.00 416

4.25

4.50

4.75

5.00

5.25

5.50

5.75

3.24

3.45

3.65

4.22

4.72

5.19

5.71

5.95

417

418

419

432

6.00 420 6.24

6.25 433 6.46

6.50 421

434

422

435

423

6.74

6.94

7.16

7.47

7.70

424 8.22

425 8.73

426 9.18

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 22.

2.7

3.2

3.7

4.2

5.2

6.2

oil flow

a, deg

2.03

3.05

4.06

6.12

Injected

oil flow

t_, deg

5.0

6.0

7.2 7.0

8.2

9.2

8.0

9.0

Liquid crystal

o_, deg

4O
O_nom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

Surface-pressure

pointnumbera

454/ 473

455

456

457

458

459

46O

461

Table 9. Continued

(b) M = 1.60, R = 2 × 106 ft-1, _ = 0°, and Of= 0.4 °

Surface Vapor Painted

pressure screen oil flow

or, deg or, deg or, deg

0.22 / 0.21

0.71

1.22

1.74

2.22

2.69

3.20

3.71

462 4.18

463 4.69

464

465

466

6.25

6.50 467

6.75

7.00

7.25

7.50

5.21

5.71

7.75

8.00

8.25

8.50

9.00

aRun 25.

6.21

6.74

468 7.16

469 7.69

470

471

472

8.20

2.08

Injected

oil flow

or, deg

3.14 3.0

4.17

6.26

4.0

5.0

6.0

7.0

8.0

9.0

Liquid crystal

_, deg

41
Otnom,deg

-4.00

-3.00

-2.00

Table 9. Continued

(c) M = 1.60, R = 2 x 106 ft -1, _ = 0% and Of= 0 °

Surface-pressure

point number a

436

437

438

Surface

pressure

tx, deg

-4.01

-2.98

-1.98

-1.00 439 -1.00

0 440 0

1.00 441 1.01

2.00 442 2.02

3.00 443 3.04

4.00 444 3.97

aRun 23.

Vapor

screen

_,deg

Pmn_d

oilflow

a,d_

Injected

oil flow

_t, deg

Liquid crystal

ix, deg

tXnom, deg

-4.00

-3.00

Surface-pressure

point number a

(d) M = 1.60, R = 2 x 106 ft-l, _ = 180 °, and Of= 0 °

Surface

pressure

a, deg

453

Vapor

screen

Painted

oil flow

Injected

oil flow

-3.99

452 -2.98

-2.00 451 -1.98

-1.00 450 -!.02

0 449 -0.01

1.00 448 1.00

2.00 447 2.01

3.00 446 3.03

4.00 445 3.99

aRun 24.

iX, deg o_, deg _,deg

Liquid crystal

tx, deg

42
Table9.Continued

(e)M = 1.60, R = 3 x 106 ft-1, 0 = 0% and Of= 0.4 °

Otnom, deg

Surface-pressure

point number a

0 492/511

0.50 493

1.00 494

1.50 495

1.75

2.00 496

2.25

2.50 497

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 28.

498

499

Surface

pressure

a, deg

0.22 / 0.22

0.74

1.21

1.74

2.21

2.69

3.23

3.71

5OO 4.25

501 4.71

5O2

503

504

5O5

506

507

5.21

5.73

6.23

6.69

7.23

7.73

508 8.22

509

510

8.69

9.24

Vapor

screen

(x, deg

Painted

oil flow

(x, deg

Injected

oil flow

(x, deg

Liquid crystal

or, deg

43
O_nom,deg

--4.00

-3.00

-2.00

-1.00

1.00

2.00

3.00

4.00

aRun26.

Table9.Continued

(f)M= 1.60,R= 3 x 106 ft-1, _ = 0o, and 0f= 0o

Surface-pressure

point number a

474

475

476

477

478

479

480

481

482

Surface

pressure

o_,deg

-3.99

-3.00

-2.04

-1.03

0

0.99

1.98

3.00

4.02

Vapor

screen

o_, deg

Painted

oil flow

o_, deg

Injected

oil flow Liquid crystal

_, deg o_,deg

Surface-pressure

O_nom, deg point number a

-4.00 491

-3.00 490

-2.00 489

488

(g) M = 1.60, R = 3 x 106 ft-1, ¢ = 180 °, and Of= 0 °

Surface

pressure

_, deg

-4.01

-3.01

-2.06

-1.00 -1.02

0 487 -0.02

1.00 486 1.04

2.00 485 1.99

3.00

4.00

3.03

4.00

Vapor

screen

Injected

oil flow Liquid crystal

484

483

aRun 27.

Painted

oil flow

o_, deg o_, deg _, deg _, deg

44
Table 9. Continued

(h) M = 1.60, R = 4 x 106 ft-I, d_= 0 °, and Of= 0.4 °

C/_om, deg

0.50

1.00

1.50

1.75

2.00

2.25

2.50

Surface-pressure

point number a

570 / 589

Surface

pressure

ct, deg

0.16/0.20

571 0.75

572 1.17

573 1.73

574 2.23

575 2.76

3.26

577 3.66

2.75

3.00 576

578

3.25

3.50

3.75

4.00

4.25

4.50 588

4.75

5.00 579

5.25

5.50

5.75

58O

581

582

583

584

4.27

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

4.70

5.20

5.76

6.20

6.65

7.25

7.71

585 8.25

586 8.74

9.00 587 9.23

aRun32.

Vapor

screen

cx, deg

Painted

oil flow

or, deg

Injected

oil flow

_x,deg

Liquid crystal

oq deg

45
_om,deg

--4.00

-3.00

Table9. Continued

(i) M = 1.60, R = 4 x 106 ft -1, 0 = 0°, and Of= 0 °

Surface-pressure

point number a

552

553

Surface

pressure

co, deg

-3.98

-2.95

-2.00 554 -2.00

-1.00 555 -1.02

0 556 -0.03

1.00 557 1.06

2.00 558 2.01

3.00 559 3.06

4.00 560 3.99

aRun 30.

Vapor

screen

cz, deg

Painted

oil flow

{X,deg

Injected

oil flow

cz, deg

Liquid crystal

cx, deg

tXnom, deg

-4.00

-3.00

-2.00

(j) M = 1.60, R = 4 x 106 ft-1, _ = 180 °, and Of= 0°

Surface-pressure

point number a

569

568

567

Surface

pressure

_, deg

-4.00

-3.03

-2.02

-1.00 566 -1.04

0 565 0.04

1.00 564 1.04

2.00 563 1.99

3.00 562 2.96

4.00 561 3.98

aRun31.

Vapor

screen

o_,deg

Painted

oil flow

_, deg

Injected

oil flow Liquid crystal

cz, deg o_,deg

46
O_nom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

Surface-pressure

point number a

524 / 543

525

526

Table 9. Concluded

(k) M = 1.60, R = 5 × 106 ft-1, _ = 0 °, and Of= 0.4 °

Surface

pressure

_, deg

0.22 / 0.21

0.70

1.20

527 1.71

544 1.95

528

545

529

546

530

547

531

532

533

2.17

2.47

2.72

2.94

3.20

3.48

3.70

Vapor

screen

_, deg

0.2

1.2

2.2

3.7

4.15 4.2

4.68

534 5.18

535 5.66

548

6.00 536

6.25 549

6.50 537

6.75 550

5.97

6.18

6.45

6.75

6.96

7.20

7.44

7.69

5.2

6.2

538

551

539

54O

541

542

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 29.

7.2

8.23 8.2

8.75

9.25 9.2

Painted

oil flow

_, deg

Injected

oil flow

_, deg

0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Liquid crystal

o_, deg

47
Table10.CorrectedAngleofAttackIndexofDatafor CamberedWingWithoutTransitionGrit

IXnom,deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

Surface-pressure

pointnumbera

683/ 702

684

685

686

687

(a) M = 1.60, R = 1 x 106 ft-1, _ = 0 °, and Of= 0.4 °

Surface Vapor Painted

688

689

690

691

692

693

694

703

695

6.25 704

6.5O 696

6.75 705

7.00

7.25

7.50

697

706

698

7.75

8.00 699

8.25

8.50

9.00

aRun 36.

700

701

pressure

tx, deg

0.21/0.19

0.69

1.18

1.70

2.18

2.71

3.19

3.70

4.21

4.69

5.20

5.69

5.96

6.21

6.44

6.71

6.97

7.19

7.47

7.72

8.21

8.69

9.21

screen

_, deg

2.2

2.7

3.2

3.7

4.2

4.7

5.2

5.7

6.2

6.7

7.2

8.2

9.2

oil flow

tz, deg

Injected

oil flow

o_, deg

0

1.0

2.0

3.0

4.06 4.0

5.09

6.12

8.15

5.0

6.0

7.0

8.0

9.0

Liquid crystal

tz, deg

48
O_om, deg

0

0.50

Surface-pressure

pointnumbera

629/ 648

630

1.00 631

1.50 632

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

Table 10. Continued

(b) M = 1.60, R = 2 x 106 ft-1, 0 = 0°, and Of= 0.4 °

Surface

pressure

_, deg

Vapor

screen

ct, deg

0.21 / 0.20 0.2

0.74

1.19

1.74

633 2.18

634 2.71

635 3.18

636 3.72

637 4.18

4.50 638

4.75

5.00 639

5.25

5.50

5.75

6.00

6.25

6.50

6.75

640

641

642

7.00 643

7.25

7.50 644

7.75

8.00

8.25

8.50

1.2

3.2

3.7

4.2

4.68 4.7

5.17 5.2

5.68

645

6.17

6.68

7.18

7.67

8.17

646 8.70

9.00 647 9.23

aRun34.

Painted

oil flow

or, deg

Injected

oil flow

ct, deg

0

1.0

2.0

4.17 4.0

5.21

6.7

Liquid crystal

or, deg

7.2

8.2

9.2

0

1.03

2.08

3.14

4.17

5.0 5.21

6.0 6.26

7.0 7.29

8.34 8.0 8.34

9.0 9.38

49
Surface-pressure

Otnom,deg pointnumber a

Table10.Continued

(c)M = 1.60, R = 5 x 106 ft -1, _ = 0% and Of= 0.4 °

0 659 / 678

0.50 660

1.00 661

1.50 662

1.75

2.00 663

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

664

Surface

pressure

tx, deg

0.23 / 0.21

0.68

1.21

1.73

2.21

2.69

665 3.21

666

667

668

669

670

679

671

68O

6.50 672

6.75 681

7.00 673

7.25 682

7.50 674

7.75

8.00 675

8.25

8.50 676

9.00 677

aRun35.

Vapor

screen

ct, deg

0.2

1.2

2.2

2.7

3.2

3.69 3.7

4.20 4.2

4.68

5.19

5.71

5.96

6.21

6.47

4.7

5.2

5.7

6.2

6.70

6.96

7.20 7.2

7.47

7.71

8.22 8.2

8.69

9.22

Painted

oil flow

tx, deg

4.34

Injected

oil flow

t_, deg

0

1.0

Liquid crystal

oq deg

0

1.10

2.0 2.17

3.0 3.25

4.0

5.0

4.34

5.43

6.51 6.0 6.51

6.7

7.0

9.2

8.0

9.0

7.60

8.68

9.75

5O
Otnom, deg

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.0O

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 33.

Table 10. Concluded

(d) M = 1.60, R = 5 x 106 fl-l, _ = 0% and 0f= 0.4 ° with an unacceptable dew point setting

Surface-pressure

point number a

Surface

pressure

or, dee

6O5/624

606 0.72

607 1.19

608 1.74

6O9

610

0.20/0.21

2.18

2.72

611 3.22

612

613

614

615

616

625

617

626

618

627

619

628

620

621

3.74

4.15

4.67

5.25

5.67

5.95

6.19

6.45

6.69

6.95

7.24

7.45

7.67

8.17

622 8.68

623 9.25

Vapor

screen

or, deg

Painted

oil flow

cx, dee

Injected

oil flow

or, deg

Liquid crystal

cx, dee

51
O_nom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

Table 11. Angle of Attack Index of Data for Cambered Wing With Transition Grit

(a) M = 1.60, R = l x 106 ft -1, _ = 0°, and Of= 0.4 °

Surface-pressure

point number a

716/735

717

718

719

720

721

722

3.50 723

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

6.75

7.00

7.25

7.50

7.75

8.00

8.25

8.50

9.00

aRun 37.

724

725

726

727

736

Surface

pressure

Ix, deg

0.18/0.24

0.72

1.20

1.70

2.21

2.72

3.20

3.72

Vapor

screen

Ix, deg

0.2

1.2

2.2

2.7

4.21 4.2

4.69

5.20

5.70

5.95

728 6.19

737 6.45

6.69

6.95

7.24

7.46

7.68

8.23

8.70

9.23

729

738

730

739

731

732

733

734

4.7

5.2

5.7

6.2

6.7

Painted

oil flow

Ix, deg

Injected

oil flow

Ix, deg

0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Liquid crystal

Ix, deg

52
Otnom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

Surface-pressure

point number a

740 / 759

741

742

743

744

2.50 745

2.75

3.00 746

3.25

3.50

3.75

4.00

4.25

Table 11. Continued

(b) M = 1.60, R = 2 x 106 ft -1, t_ = 0% and 0f= 0.4 °

Surface Vapor Painted

pressure screen oil flow

or, deg or, deg ct, deg

0.20 / 0.19

0.72

1.19

1.68

2.21

2.69

3.21

747 3.69

748 4.21

4.50 749

4.75

5.00 750

751

752

5.25

5.50

5.75

6.00

6.25

6.50 753

6.75

7.00 754

7.25

4.70

5.21

5.71

6.19

6.72

7.50

7.75

8.00

8.25

7.22

755 7.72

756 8.25

8.50 757 8.70

9.00 758 9.23

aRun 38.

Injected

oil flow

_, deg

1.0

4.17 4.0

5.21

6.26

8.34

7.0

8.0

9.0

Liquid crystal

or, deg

53
Table11.Concluded

(c)M = 1.60, R = 5 × 106 ft -1, (_ = 0% and Of= 0.4 °

O.nom, deg

0

0.50

1.00

1.50

1.75

2.00

2.25

2.50

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

Surface-pressure

point number a

760 / 779

761

Surface

pressure

_, deg

0.18/0.21

0.70

762 1.16

763 1.72

764

765

766

767

768

769

770

771

780

772

781

773

6.75 782

7.00 774

7.25 783

7.50

7.75

8.00

8.25

775

776

8.50 777

9.00 778

aRun 39.

2.21

2.74

3.21

Vapor

screen

or, deg

0.2

1.2

2.2

3.69 3.7

4.21

4.73

5.22

4.2

4.7

5.2

5.72 5.7

5.96

6.23 6.2

6.43

6.69

6.95

7.25

7.46

7.70

8.21

8.71

9.18

6.7

7.2

8.2

9.2

Painted

oil flow

or, deg

Injected

oil flow

or, deg

0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Liquid crysta

o_,deg

54
Table12.Valuesof _attandO_sep From Different Data Sets for Elliptical Wing Without Grit at M = 1.60

R, ft-1

2 x 106

5 × 106

Surface-pressure data

_att, deg

1.75

2.18

(tsep, deg

2.22

2.49

Injected-oil-flow data

t_att, deg _sep, deg

1.03 2.08

2.17 3.25

Liquid-crystal data

_att, deg

1.03

1.10

O_sep,deg

2.08

2.17

55
(zN, deg

20

16

12

(_=8°_

©

©

Separated

flow

©

O

O

Attached

flow

O 65 ° Delta wing

at M = 1.60

Stanbrook-Squire

boundary

0 I I I 1 1

.2 .4 .6 .8 1.0 1.2

M N

Figure 1. Location of 65 ° delta wing at M = !.60 with respect to Stanbrook-Squire boundary at various angles of attack.

56
Removable

wingtip

/

65 °

+X

iii ,, bb I _1

_2.600-_

13.987

16.787

18.000

Figure 2.

I _ +Y

+Z

Screw holes for

sting attachment

(a) Sharp wing.

Two-view sketches of three delta wing models. All dimensions are in inches unless otherwise noted.

57
65 °

\\

,/ /

/

Removable /

wingtip /

/

! I

_26oo_

13.987

16.787

\

\

\

\

\,

18.000

I _ +Y

+z I

Screw holes for

sting attachment

.... _____

(b) Elliptical wing.

Figure 2. Continued.

58
+X

65 °

18.000

Removable

wingtip

P

___7_

.486

I _ +Y

+Z

sting attachment

(c) Cambered wing.

Figure 2. Concluded.

59
(a)Viewofuppersurface.

L-90-04477

(b) Viewof lowersurface. L-90-04479

Figure3. PhotographsofellipticalwingmodelinstalledinLangleyUPWT.

6O
c.D

04

Od

o_

m:

I

0

0 -- -- '

0

O0

t

, T ,_,,/'y:

__-6_

i

1

I

I

I

I

I

I

I

I

0

I

I i i

I :

, i I

8-----

C

-s

0

__ r-

_0

oC_

OEO , . _E

_< -- -- =_

e-,

0

<

0

61
Screw holes for

attachment to sting

1.613

3.991

I I I I_" .......... I r r I

I I _ iI

I t

1.369

.684_ /-- Sized to fit

/ AOA sensor

- .594

t

Figure 5. Details of AOA sensor housing. All linear dimensions are in inches.

62
Acceptable

-.35 -

-.30 -

-.25 -

-.20 --

-.15

Cp -.10 -

-.05 -

0--

.05

.10

.15

or, deg Unacceptable or, deg

dew point dew point

• 0.23 c> 0.20

• 1.21 _ 1.19

• 2.21 _ 2.18

• 3.21 _ 3.22

• 4.20 _ 4.15

• 5.19 _ 5.25

a 6.21 _ 6.19

• 7.20 o 7.24

8.22 _ 8.17

• 9.22 _ 9.25

0

q

(a) Upper surface at x = 6 in.

Figure 6. Effect of dew point on surface-pressure coefficient data for cambered wing without transition grit at M = 1.60

and R = 5 × 106 ft-l.

63
-.05 --

0

k

.05 --

.10

Cp .15 --

.20 -

.25

.30 -

.35

.40

Acceptable

dew point

41,

IL

&

$

6

o_,deg Unacceptable _, deg

dew point

0.23 o 0.20

1.21 [] 1.19

2.21 _ 2.18

3.21 _ 3.22

4.20 _ 4.15

5.19 _ 5.25

6.21 _ 6.19

7.20 o 7.24

8.22 _ 8.17

9.22 c_ 9.25

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure 6. Continued.

64
Acceptable

-.35 -

-.30

-.25 -

-.20 -

-.15 --

Cp -.10

-.05 -

0 -

.05

.10

.15

0

o_,deg Unacceptable e_,deg

dew point dew point

• 0.23 o 0.20

• 1.21 [] 1.19

2.21 O 2.18

• 3.21 _ 3.22

• 4.20 _ 4.15

• 5.19 _ 5.25

• 6.21 c_ 6.19

• 7.20 o 7.24

e 8.22 c_ 8.17

•' 9.22 _ 9.25

T!

(c) Upper surface at x = 12 in.

Figure 6. Continued.

65
Cp

-.05 --

0

.05 --

.10 -

.15

.20

.25

.30

.35

.40

0

Acceptable

dew point

$

M

_, deg Unacceptable o_,deg

dew point

0.23 © 0.20

1.21 [] 1.19

2.21 _ 2.18

3.21 ± 3.22

4.20 _ 4.15

5.19 _ 5.25

6.21 _ 6.19

7.20 _-_ 7.24

8.22 _ 8.17

9.22 _ 9.25

l,,,ll,j,ll,,,I,l,

.1 .2 .3

'l'_'Jl'',lll_lJl,,i,l,,jilltlll

.4 .5 .6 .7 .8 .9 1.0

(d) Lower surface at x = 12 in.

Figure 6. Concluded.

66
Io

Figure 7. Flow angularity, angle of attack, and knuckle assembly.

10

9

6

e_knu' 5

deg

3

0 1 2 3 4 5 6 7 8 9 10

C_ac, deg

Figure 8. Sting deflections for R = 1 x 106 ft-1 and M = 1.60 from data for elliptical wing without transition grit.

67
Section A uppersurface atx = 6in.

F Pressure

Leading .... _ orifice

edge

A

Grit

transition strip

Location of sections on model.

Section A lower surface at x = 6 in.

Section B upper surface at x = 12 in.

Figure 9.

Section B lower surface at x = 12 in.

(a) Sharp wing.

Location of transition grit on model with respect to pressure orifices.

68
Leading

edge

Section A upper surface at x = 6 in.

orifice

-_ • • • • •

Grit transition strip

A

B

Grit

transition strip

Plugged orifice

Section A lower surface at x = 6 in.

Section B upper surface at x = 12 in.

Location of sections on model.

Section B lower surface at x = 12 in.

(b) Elliptical wing.

Figure 9. Continued.

69
Leading

edge

Section A upper surface at x = 6 in.

Plugged orifice

orifice

• • •

Grit transition strip

A

B

Gnt

transition strip

Location of sections on model.

Section A lower surface at x = 6 in.

Section B upper surface at x = 12 in.

Section B lower surface at x = 12 in.

(c) Cambered wing.

Figure 9. Concluded.

7O
-.35 --

p

-.30

-.25 -

-.20 -

-.15

Cp -.10 -

-.05 -

0

.05

.10 -

.15 L I

0

Without grit (x, deg Grit (x, deg

,_, 0.23 • O.18

1.21 • 1.16

_ 2.21 4, 2.21

3.21 • 3.21

4.20 • 4.21

5.19 • 5.22

6.21 • 6.23

,:_ 7.20 • 7.25

i_ 8.22 _ 8.21

9.22 • 9.18

IIll,,,ILllhllllL

.1 .2 .3

I,,, iI,,,,lllllllllll Jill

.4 .5 .6 .7 .8

11

(a) Upper surface at x = 6 in.

Figure 10. Effect of transition grit on surface-pressure coefficient data for cambered wing at M = 1.60 and

R = 5 x 106 ft-1. Shaded area is width and location of transition strip.

71
Cp

-.10 --

-.05

0--

.05 -

.10

.15 --

.20

.25 --

.30

.35 I

0

.40

Without grit (_, deg Grit o_,deg

c_ 0.23 • 0.18

[] 1.21 • 1.16

2.21 • 2.21

± 3.21 • 3.21

4.20 • 4.21

6 5.19 • 5.22

6.21 • 6.23

o 7.20 • 7.25

¢ 8.22 _ 8.21

9.22 a 9.18

q

.9

(b) Lower surface at x = 6 in.

Figure 10. Continued.

72
.15

Without grit e_,deg Grit

_, 0.23 •

[] 1.21 •

2.21 •

A 3.21 •

4.20 •

5.19 •

,_ 6.21 •

_.> 7.20 •

_, 8.22

9.22 ='

_,deg

0.18

1.16

2.21

3.21

4.21

5.22

6.23

7.25

8.21

9.18

11

(c) Upper surface at x = 12 in.

Figure 10. Continued.

73
Cp

-.05 --

0

.05 --

.10

.15

.20

.25

.30 --

.35 -

.40

Without grit _, deg Grit _, deg

_> 0.23 • 0.18

[] 1.21 • 1.16

2.21 • 2.21

3.21 • 3.21

4.20 • 4 21

5.19 • 5:22

6.21 • 6.23 __±

o 7.20 • 7.25

¢_ 8.22 $ 8.21 HI

c_ 9.22 A 9.18 __

_

i = ' ' I ' n n I I + I + _ I a a n n I i r r _ I i n , n I n r _ _ I r n i i I j i _ _ I ,_:=

+ a i

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

n

(d) Lower surface at x = 12 in.

Figure 10. Concluded.

74
y

Vortical flow /

/

Induced flow /

i

/

i

I

),

7" \

Primary vortex

Secondary vortex

- _ nsition strip

J

J

J

J

i

J

s

/

\

Figure 1 I. Sketch of vortex emanating from wing leading edge (from ref. 5).

75
-.3

-.2

-.1

Cp 0

.1

.2

.3 __

C- Surface Settling time x = 6 in.

o Upper 2 min

D Lower 2 rain

_ Upper 7 min ._>,0

Lower 7 min

E3

-.3 -- x= 12in.

-- ,_i _

if>

c_ 0 _s_s_c_, <f_<_;_

.I

.2 -

.3 JJi_I'_''I' J i_lILiIIi,lll fiL_liar _Ij ILjIjiij llilll

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(a) Sharp wing with u'ansidon grit at (_= 4.25 ° and R = .5x ]06 ft-].

Figure ]2. Effect of sett]ing time on surface-pressure coefficient data for delta wing models at M = 1.60.

?6
Cp

-.2

-.1

.1

.2

.3

M

Surface Settling time x = 6 in.

c_ Upper 2 min

[] Lower 2 min

<> Upper 7 min

Cp

%2 --

-.1 -

0

.1

.2

.3

0

tLt,l,,lll,,,llll_,l,,ILl'''_ll'''lll''llll'l'LLII

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Elliptical wing without transition grit at Iz = 3.71° and R = 1 x ]06 ft-1.

Figure 12. Continued.

77
Cp

i

-°_

-.2

-.1

0

.1

.2

.3

Surface Settling time x = 6 in.

© Upper 2 min _,_ ........

Lower 2 min

Upper 7 m!n 0 _

Cp

".3 --

-.2

-.1

0

.1

.2

.3

0

x= 12in. __

':'=ll'lrtJJ=lflJ =,lJlJJr,ll,I, r ==l,_llJijja I, j j, j

•1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(c) Elliptical wing without transition grit at o_= 8.18 ° and R = l x 106 ft-].

Figure 12. Concluded.

78
-.10

-.05

Cp 0

.O5

.10

o First ccsweep

[] Second e_sweep

[]

0

0

x=6in.

0

0

0

0

oE]oNO IBONO

O

O

O

Cp

-.10

-.05

.O5

.10

[]

0 0 0 [] 013 [] D°

x= 12in.

0

0

0

O O1-10 [3 °m OE] O

O O

O

L I i I i I L I i I _ I L I I I i I i 1 i

- 0 1 2 3 4 5 6 7 8 9

tx, deg

(a) The Cp at rl = 0.1 on upper surface of sharp wing without transition grit at M = 1.60 and R = 1 x 106 ft -1.

Figure 13. Repeatability of surface-pressure coefficient data.

10

79
Cp

-.10

-.05

0

.05

.10

o First e_sweep

[] Second ccsweep

x=6in.

[]

0 0

01.- 1ON OE3 0I--10

0

0

0

O I--IO N 0[30 1-10

O

O

O

Cp

-.10

-.05

.05

.10

(b)

[]

0

O IZ] oL_ Oi- I 0[30

O

x= 12in.

0

0

O OS O[z]oNO DO

O

O

O

I I i I i I i I I I I I j 1 , 1 I 1 j I I

0 1 2 3 4 5 6 7 8 9

o_, deg

The Cp at 11= 0.1 on upper surface of elliptical wing with transition grit at M = 1.60 and R = 1 x 10 6 ft -1.

Figure 13. Continued.

I

10

8O
Cp

-.10

-.05

0

.05

.10

F

o First _sweep

Second a sweep

O O

O O

[]

O

O

x=6in.

O

O

O

O

o_oDO D°D°

O

O

O

Cp

-.10

-.05

.05

[]

O O

O

O

x= 12in.

O O O

O

O

oDoDO_ ODO

O

O

O

O

.10 L I , I _ I , I , I l I , I , I , I I I t

- 0 1 2 3 4 5 6 7 8 9

_, deg

(C) The Cp at rl = 0. l on upper surface of cambered wing without transition grit at M = 1.60 and R = 5 x 106 ft-1 .

Figure 13. Concluded.

I

10

81
=25 to 27 I _-/" v\_j

varies with o_ n - _ \

\

x._ Camera lens

orifice location

Figure 14. Approximate locations of model, light sheet, and camera for vapor-screen technique. All linear dimensions

are in inches.

82
Cp

-.40 --

-.35 --

-.30

-.25 -

-.20 --

-.15

-.10 -

-.05

0

.05

.10

.15

_, deg

o 0.25

• 0.78

[] 1.28

• 1.78

,_2 2.25

,O 2.77

.b 3.28

• 3.75

L 4.27

• 4.76

5.25

• 5.78

6.27

• 6.78

_, 7.26

• 7.76

8.27

8.76

c_ 9.28

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

rl

(a) Sharp wing.

Figure 15. Effect of angle of attack on upper surface-pressure coefficient distributions for three delta wings without

transition grit at x = 12 in., M = 1.60, and R = 2 × 106 ft -l .

83
_, deg

© 0.19

• 0.71

[] 1.23

• 1.75

_> 2.22

2.69

3.24

• 3.71

4.25

• 4.69

r_ 5.23

• 5.70

6.23

• 6.71

o 7.17

• 7.71

¢ 8.18

8.70

9.22

q

(b) Elliptical wing.

Figure 15. Continued.

84
-.35 --

-.30 -

-.25

-.20 -

-.15 --

Cp -.10

-.05 -

0

.05 --

.10

.15

0

_,deg

0.21

0.74

1.19

1.74

2.18

2.71

3.18

3.72

4.18

4.68

5.17

5.68

6.17

6.68

7.18

7.67

8.17

8.70

9.23

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(c) Cambered wing.

Figure 15. Concluded.

85
Cp

-.4

-.3

-.2

-.1

.1

0

0

Configuration

o Sharp

Elliptical

Cambered

(x, deg at--

O_nom= 1° (Xnom=2 ° (Znom=30

1.28 2.25 3.28

1.23 2.22 3.24

1.19 2.18 3.18

Gnom 1°

(7.nom = 2°

O_nom =

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

I]

(a) C(nom= ]°, 2°, and 3°.

Figure l 6. Effect of cross-sectional shape on upper surface-pressure coefficient distribution for delta wing without transition grit atx = 12 in., M = i.60, and R = 2 x l0 6 ft -l.

86
Cp

-.4

-.3

-.2

-.1

0

.1

0

o

0

c

D

Configuration cx, deg at--

Otnom = 4° _nom = 5° °tnom= 6°

Sharp 4.27 5.25 6.27

Elliptical 4.25 5.23 6.23

Cam bered 4.18 5.17 6.17

(X.nom =

L;_LliJlllii_tltlnllililill'l'''[l''''kk_'ilt't'l

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(b) (X.nom = 4 °, 5°, and 6°.

Figure 16. Continued.

87
Cp

Configuration

Sharp

Elliptical

Cambered

o_,deg at--

°Cnom= 7° (Xnom = 8° _nom = 9°

7.26 8.27 9.28

7.17 8.18 9.22

7.18 8.17 9.23

0 eCnom = 7 °

0 O_nom= 8°

0 O_nom= 9°

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

1]

(c) (Xnom = 7% 8 °, and 9°

Figure 16. Concluded.

.7 .8 .9 1.0

88
Cp

-.05 -

_

.05

.10

.15

.20

.25

.30

0

(x, deg

_, 0.25

• 0.78

[] 1.28

• 1.78

<_ 2.25

• , 2.77

c, 3.28

• 3.75

_-_ 4.27

• 4.76

5.25

• 5.78

6.27

• 6.78

,_, 7.26

• 7.76

_'. 8.27

O 8.76

c_ 9.28

q

(a) Sharp wing.

Figure 17. Effect of angle of attack on lower surface-pressure coefficient distributions for three delta wings without

transition grit atx = 12 in., M = 1.60, and R = 2 x 106 ft-1.

89
Cp

(b) Elliptical wing.

Figure 17. Continued.

90
Cp

o_,deg

c, 0.21

• 0.74

[] 1.19

• 1.74

2.18

,ql, 2.71

± 3.18

• 3.72

4.18

• 4.68

5.17

• 5.68

6.17

J 6.68

o 7.18

• 7.67

8.17

8.70

c_ 9.23

0

11

(c) Cambered wing.

Figure 17. Concluded.

91
(a) ct = 0.2 °.

(b) ¢z = 1.2 °.

Figure 18. Vapor-screen photographs illustrating vortex growth with angle of attack over leeside of elliptical wing without transition grit at x = 12 in., M = 1.60, and R = 2 x 106 ft-I.

92
(c) Ix = 2.2 °.

(d) Ix = 2.7 °.

Figure 18. Continued.

93
(e) o_= 3.2°.

(0 a = 3.7 °.

Figure 18. Continued.

94
(g) o_= 4.2%

(h) (x = 5.2 °.

Figure 18. Continued.

95
(i) et = 6.2 °.

(j) _ = 7.2 °.

Figure 18. Continued.

96
(k) _ = 8.2 °.

(I) _ = 9.2 °.

Figure 18. Concluded.

97
(a) e¢=3.!4°. (b) o_=4.17°.

(c) o_= 6.26°. (d) o_= 8.34°.

Figure19. Painted-oil-flowphotographsillustrating6vo_exgrowthwithangleof attackonleesideof ellipticalwing withoutransitiongritat M = 1.60 and R = 2 × 10 ft- .

98
(a) ¢z = 0 °.

(b) _ = 1.03 °.

Figure 20. Injected-oil-flow photographs illustrating vortex growth with angle of attack on leeside of elliptical wing

without transition grit at M = 1.60 and R = 2 × 106 ft-1.

99
(c) o_=2.08°.

(d) tx = 3.14 °.

Figure 20. Continued.

100
(e) o_=4.17°.

(f) oc=5.21°.

Figure20.Continued.

101
(g) _ =6.26°.

(h) a = 7.29°.

Figure20.Continued.

102
(i) o_= 8.34°.

(j) cx=9.39°.

Figure20.Concluded.

103
(a) _ = 0°.

(b) ct = 1.03 °.

Figure 21. Liquid-crystal photographs illustrating vortex growth with angle of attack on leeside of elliptical wing without transition grit at M = 1.60, R = 2 × 106 ft-1, and To = 125°F.

104
(c) a = 2.08 °.

(d) et = 3.14 °.

Figure 21. Continued.

105
(e) _ = 4.17 °,

(f) cc = 5.21 °.

Figure 21. Continued.

106
(g) a= 6.26°.

Figure21.Continued.

107
(h) a = 7.29 °.

Figure 21. Continued.

108
(i) a = 8.34 °.

Figure 21. Continued.

109
(j) ot = 9.39 °.

Figure 21. Continued.

II0
o

e

,,-:.

©

G}

.=_

.._

CO

o

..=

_o

..-:.

¢)

G_

0

eO

'F.

.=.

-6

¢0

_=

0

¢q

111
x

r,,,O"O

x

t"-

¢,,,0 "0

x

I4&@9

[] _q S 0 <0

• 4

41! ,0

41! $

4! • _J ¢t4J

41' • dl,,_ 4 4 "Jr 4: •

• " *"_j % i

• • o-_ • • g

1 • i!

i

i :

0__

O_,A tl _

0__

,LJ <:> S <_ <>

/i "

/ ,'

-e_,.

..

.,. . •

I'

_a $o

0

T mt..D

1.0 _"

,,¢

T m

0

0

G)

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121
Cp

-.4

-.3

-.2

-.1

0

.1

0

0

0

[]

Rx o_,deg at--

Or.nom=l° O_nom=2 ° a.nom=3 °

1 x 106 1.28 2.29 3.25

2 x 106 1.28 2.25 3.28

5 x 106 1.28 2.29 3.28

g'nom = 1°

(Xnom = 2 °

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

'q

(a) O_nom = | o, 2o, and 3 °.

Figure 25. Effect of R x on upper surface-pressure coefficient distribution for sharp wing without transition grit at

x= 12 in. andM= 1.60.

122
Cp

-.4

-.3

-.2

-.1

0

.1

0

C)

[]

0

R x (x, deg at--

Gnom = 4° Gnom = 5°

1 x 106 4.25 5.30

2 x 106 4.27 5.25

5 x 106 4.25 5.27

_nom = 6°

6,26

6.27

6.27

O_no m - 4°

O_no m = 5 °

0_no m = 6 °

lllllk,,_i,iilll,,,I,,,,I,,,,l,Jltllllllll''l'''LI

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) (tnom = 4°, 5 °, and 6 °.

Figure 25. Continued.

123
Cp

-.3

-.2

-.1

a x

o 1 x 10 6

2x 10 6

C> 5x 10 6

_nom = 7°

7.27

7.26

7.29

0_, deg at--

(Xnom = 8 °

8.26

8.27

8.25

Gnom = 9°

9.27

9.28

9.25

0 (_nom = 7°

.1

0 O_nom = 8°

0 (Znom = 90

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

q

(c) O_nom = 7°, 8°, and 9°.

Figure 25. Concluded.

.7 .8 .9 1.0

124
Cp

-.4

-.3

-.2

-.1

0

.1

0

L

L

0

a x

1 xlO 6

2x 106

3x 106

4x 10 6

5x 106

ec,deg at--

_nom = 1° OCnom = 2° (Znom = 3 °

1.23 2.17 3.19

1.23 2.22 3.24

1.21 2.19 3.19

1.16 2.20 3.23

1.21 2.18 3.18

OCnom = 1o

F_] '- "

(Znom = 2 °

OCnom =

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

13

(a) tZnom = 1o, 2o, and 3°.

Figure 26. Effect of Rx on upper surface-pressure coefficient distribution for elliptical wing without transition grit at

x=12in, andM=l.60.

125
Cp

Rx o_,deg at--

(Znom = 4° _nom = 5° O_nom = 6°

'_ 1 x 106 4.18 5.21 6.24

".4

[] 2 x 106 4.25 5.23 6.23

3 x 106 4.19 5.22 6.23

'_ 4 x 106 4.18 5.17 6.19

".3

5 x 106 4.24 5.19 6.22

0

0 O_nom = 5°

0 O_nom = 6°

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

q

(b) etnom = 4 °, 5°, and 6 °.

Figure 26. Continued.

.7 .8 .9 1.0

126
Cp

-.4

-.3

-.2

-.1

.1

0

0

o

R x o_, deg at--

=8 ° 9 ° Or,nom = 7 ° Or,nom Or,nom :

1 x 106 7.23 8.18 9.23

2 x 106 7.17 8.18 9.22

3 x 106 7.21 8.21 9.18

4 x 106 7.20 8.20 9.21

5 x 106 7.16 8.21

_nom = 7°

O_nom = 8 °

(_nom = 9°

TI

(c) O_nom = ?o, 8o, and 9°.

Figure 26. Concluded.

127
-.25

-.20

-.15

Cp -.10

-.05

0

.05

0

C)

[]

<>

A

a x _, deg at--

°_nom 1"5° Gnom _ 1.75° O_nom _ 2 °

1 x 106 1.70 1.97 2.17

2 x 106 1.75 2.22

3 x 106 1.72 2.19

4 x 106 1.69 2.20

5 x 106 1.67 1.96 2.18

Or,no m = 1.5 °

1⁄2

/

=

Or,no m = 1.75 °

128
-.25 --

-.20

-.15

Cp -.10

-.05

_

.05 _

0

0

C_

[]

A

R x

1 xlO 6

2x 106

3x 106

4x 106

5x 106

_, deg at--

O(,nom= 2-25° _nom = 2.5° _nom = 2.75°

2.47 2.68 2.94

2.69

2.70

2.67

2.49 2.68 2.97

1⁄2

// x/

O{.nom = 2.25 °

(Xno m = 2.5 °

/

/

0

O_nom = 2.75 °

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) (Znom = 2.25 °, 2.5 °, and 2.75 °.

Figure 27. Concluded.

129
Cp

-.4

-.3

-.2

-.1

0

.1

0

0

0

C,

[]

Rx (z, deg at--

CZnom = 1° _nom = 2° O_nom= 3°

1 x 10 6 1.18 2.18 3.19

2 x 106 1.19 2.18 3.18

5 x 106 1.21 2.21 3.21

Gnom = 1o

(X,no m : 2 °

^/i

I ' ' '11J I _ I J J _ , I t , _, I,,, I I p J , i I j j_L, j,, ,, I j i ,, I i j j i I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(a) Or.nom = 1°, 2°, and 3°.

Figure 28. Effect of Rx on upper surface-pressure coefficient distribution for cambered wing without transition grit at

x = 12 in. and M = 1.60.

130
Cp

-.4

-.3

-.2

-.1

0

.1

0

c_

0

R x o_, deg at--

_nom = 4° °_nom = 5° °_nom = 6°

1 x 106 4.21 5.20 6.21

2 x 10 s 4.18 5.17 6.17

5 x 106 4.20 5.19 6.21

_nom = _- _ - - ....... -

_ O_nom = 6 °

11

(b) Otnom = 4°, 5 °, and 6°.

Figure 28. Continued.

131
Cp

-.4

-.3

-.2

-.1

.1

0

0

[]

Rx _, deg at_

°_nom= 7° °_nom= 8° _nom = 9°

1 x 106 7.19 8.21 9.21

2 x 10 s 7.18 8.17 9.23

5 x 106 7.20 8.22 9.22

O_nom = 7°

....

OCnom = 8 °

O_nom = 9°

''''I''''r''''I'JJLI'_''I',_IIL_L_I,J,,iLJ_,]_j_Li

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(C) OCnom = 7°, 8°, and 9 °.

Figure 28. Concluded.

132
-.25 -

-.20

-.15

-.05

.O5

©

[]

Rx _, deg atn

Or,nom = 3° Or,nom = 3.5 ° (Znom = 4°

1 x 106 3.19 3.70 4.21

2 x 106 3.18 3.72 4.18

5 x 106 3.21 3.69 4.20

O_nom = 3 °

_nom = 3.5°

O_nom = 4 °

,,,,I,,,,I,,,,I,,,,I,,,iI,,,,I,i,iI,,,,I,,,,I,,_,I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

Figure 29. Effect of R x on onset of leading-edge separation for cambered wing without transition grit at x = 12 in. and

M = 1.60.

133
(a) R x=lxlO 6 ands=5.20 °.

(b) Rx=2×106 ands=5.20 °.

Figure 30. Vapor-screen photographs illustrating effect of Rx on flow structure over leeside of cambered wing without

transition grit at x = 12 in., IXnom = 5 °, and M = 1.60.

134
(c) Rx = 5 × 106 and _ = 5.20 °.

Figure 30. Concluded.

135
(a) Rx = 1 x 106 and _ = 8.20 °.

(b) Rx = 2 × 106 and a = 8.20 °.

Figure 31. Vapor-screen photographs illustrating effect of Rx on flow structure over leeside of cambered wing without

transition grit at x = 12 in., Otnom = 8°, and M = 1.60.

136
(c) Rx = 5 x 106 and ct = 8.20 °.

Figure 31. Concluded.

137
(a) R = 1 x 106 ft -1 and _ = 4.06 °. (b) R=2x 106ft -1 andot=4.17 °.

(c) R=5× 106f1-1 ando_=4.34 °.

Figure 32. Painted-oil-flow photographs illustrating effect of Reynolds number on flow structure on leeside of cambered wing without transition grit at Ct_nom = 4 ° and M = 1.60.

138
(a) R = 1 x 106 ft-1 and Ix = 4.00 °.

(b) R = 2 x 106 ft -1 and Ix = 4.00 °.

(c) R = 5 x 106 ft-1 and Ix = 4.00 °.

Figure 33. Injected-oil-flow photographs illustrating effect of Reynolds number on flow structure on teeside of cambered wing without transition grit at Ixnom = 4° and M = 1.60.

139
(a) o_=2.17°.

(b) t_ = 3.25 °.

Figure 34. Injected-oil-flow photographs of leeside of elliptical wing without transition grit at tXnom

M= 1.60, and R = 5 x 106 ft -1. = 2 ° and 3 °,

140
(a) R = 1 × 106 ft -1 and (z = 8.00 °.

(b) R = 2 x 106 ft -1 and (x = 8.00 °.

(c) R = 5 x 106 ft-1 and _ = 8.00 °.

Figure 35. Injected-oil-flow photographs illustrating effect of Reynolds number on flow structure on leeside of cambered wing without transition grit at U.nom = 8° and M = 1.60.

141
(a) _t = 0 °.

(b) ¢x= 1.10 °.

Figure 36. Liquid-crystal photographs illustrating vortex growth with angle of attack on leeside of elliptical wing without transition grit atM= 1.60, R = 5 × 106 ft-1, and To = 125°F.

142
(c) ct = 2.17 °.

(d) a = 3.25 °.

Figure 36. Concluded.

143
Cp

-.4

-.3

-.2

-.1

0

.1

0

0

0

o_, deg at--

Otnom = 1° Otnom = 2° (tnom = 3 °

Without grit 1.28 2.25 3.28

Grit 1.29 2.29 3.30

Otnom = 1o

O_nom = 2°

O_nom = 3 °

11

(a) 0_nom = 1%2°, and 3°.

Figure 37. Effect of transition grit on upper surface-pressure coefficient distribution for sharp wing at x = 12 in.,

M= 1.60, andR= 2 × 106ft -l.

144
Cp

-.4

-.3

-.2

-.1

.1

-- Ci

[]

0

0

0

o_,deg at--

_nom = 4° (Xnom = 5° °Cnom= 6°

Without grit 4.27 5.25 6.27

Grit 4.29 5.25 6.28

(_nom = 4°

O,nom = 5°

O_nom = 6 °

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

ll

(b) (X_om = 4 °, 5 °, and 6°.

Figure 37. Continued.

145
Cp

-.4

-.3

-.2

-.1

0

.1

0

0

0

e_,deg at--

°r'nom = 7° _nom = 6°

c, Without grit 7.26 8.27

[] Grit 7.27 8.26

(Xnom = 9 °

9.28

9.28

O_nom = 7°

Or,no m = 8 °

_nom = 9°

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(C) O_nom = 7°, 8°, and 9°.

Figure 37. Concluded.

146
Cp

-.4

-.3

-.2

-.1

0

.1

0

oc,deg atO_nom= 1° O_nom 2° = 3° = (Znom

,::1 Without grit 1.23 2.22 3.24

[] Grit 1.22 2.22 3.20

Or,nom = 1o

(/,no m = 2 °

0

O_nom = 3°

q

(a) Otnom = l o, 2o, and 3°.

Figure 38. Effect of transition grit on upper surface-pressure coefficient distribution for elliptical wing at x = 12 in.,

M= 1.60, and R=2x 106ft -1.

147
Cp

-.4

-.3

-.2

-.1

0

.1

0

0

[]

_, deg at m

°_nom = 4° _nom = 5° O_nom= 6 °

Without grit 4.25 5.23 6.23

Grit 4.18 5.21 6.21

O_nom = 4 °

_nom = 5°

O_nom = 6°

(b) (:_om = 4°, 5°, and 6 °.

Figure 38. Continued.

148
Cp

-.3

-.2

-.1

-.4 - o

[]

0

0

0

.1

0

oq deg at--

(Znom=7 ° (Znom=8 °

Without grit 7.17 8.18

Grit 7.16 8.20

(Znom = 9°

9.22

9.20

(Zno m = 7 °

)

0t,nom = 8 °

,/

(Zno m = 9 °

(c) (Znom = 7°, 8°, and 9 °.

Figure 38. Concluded.

149
-.25

-.20

-.15

Cp -.10

-.05

0

.O5

0

o_,deg atm

_nom = 1.5 ° O_nom = 2 ° OCnom = 2.5 °

c, Without grit 1.75 2.22 2.69

Grit 1.74 2.22 2.69

i

[ ) /

(_nom = 1.5 °

_nom = 2°

' iI

i!_ /

o

O_nom = 2.5 °

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

Figure 39. Effect of transition grit on onset of leading-edge separation for elliptical wing at x = 12 in., M = ] .60, and

R=2x ]06fi -].

150
Cp

-.4

-.3

-.2

-.1

.1

0

0

-- O

o_,deg at--

ff'nom= 1° O_nom = 2° (Znom = 3°

Without grit 1.19 2.18 3.18

Grit 1.19 2.21 3.21

if'nora= I o - -_3_

Or,nom = 2°

CZnom = 3° - -- -

11

(a) t:tnom = 1o, 2o, and 3°.

Figure 40. Effect of transition grit on upper surface-pressure coefficient distribution for cambered wing at x = 12 in.,

M=1.60, and R=2x106ft -1.

151
Cp

-.4

-.3

-.2

-.1

0

.1

0

0

0

-- 0

[]

Without grit

Grit

o_,deg at--

O_nom = 4 ° (Znom : 5° _nom = 6°

4.18 5.17 6.17

4.21 5.21 6.19

O_nom = 4 °

O_nom = 5°

Of,nom = 6°

J I J 4 I I I I J I _ _ I I I I I I I t I I _ I I i i i i i j j j i [ i i i i [ i i j i ] _ I _ i t

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) (/.nom ----4 °, 5°, and 6°.

Figure 40. Continued.

152
Cp

-.4

-.3

-.2

-.1

.1

0

0

_ ©

(_, deg at--

O_nom=7 ° O_nom=8 ° OCnom=9 °

Without grit 7.18 8.17 9.23

Grit 7.22 8.25 9.23

(X,nom = 7°

IXnom = 8°

O_nom -- 9°

1]

(C) Otnom = 7°, 8°, and 9°.

Figure 40. Concluded.

153
-.25

-.20

-.15

-.05

0

.05

o_,deg at--

(Znom = 3° _nom = 3.5° C(nom = 4 °

c_ Without grit 3.18 3.72 4.18

[] Grit 3.21 3.69 4.21

O_nom : 3°

O_nom = 3.5 °

J

( J

_nom = 4°

Ll''J''''li_EJJJIril'_ltlll,l_li,j,_lllijliI,j,it

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

Figure 4]. Effect of transition grit on onset of leading-eclg¢ separation for cambered wing at x = |2 in., M = |.60, and R=2x 106ft -l.

154
Figure 42. Painted-oil-flow photograph of leeside of cambered wing with transition grit at t_ = 4.17 °, M = 1.60, and

R=2× 106ft -1.

Figure 43. Injected-oil-flow photograph of leeside of cambered wing with transition grit at ot = 4.00 °, M = 1.60, and

R=2xl06ft -1.

155
Appendix A

Analytical Expressions for Cross-Sectional

Shapes of Delta Wing Models

The three cross-sectional shapes that were tested can

be expressed analytically. The equations given in this

appendix are in terms of y and z normalized by the local

semispan (r I and _, respectively). The equation defining

the sharp cross-sectional shape is as follows for the upper

surface:

= 0.05 - 0.05r I (A1)

for the lower surface

= - 0.05 + 0.05r I (A2)

The equation defining a 20:1 ellipse is as follows for

the upper surface:

= 0.05 _/1 - rl 2 (A3)

for the lower surface:

= -0.05 _/1 - r 12 (A4)

To obtain a conical cambered geometry, a spanwise

circular-arc camber was imposed on the elliptical crosssection geometry in the cross-flow plane. The equation

for a circular arc with the center at y = 0, z = Zl is as

follows:

z = z 1 + _/(rc )2-y2

where ro the radius of curvature, is

(A5)

rc = s/O c (A6)

where s is the arc length and 0c is the angle of camber

in radians. A given condition is that at y = 0, z would

equal 0. Therefore, zi would equal rc. Thus, the equation

for the camber line is

z = Occ s + J/_cc )2 -Y 2 (A7)

Instead of the arc length, the semispan b/2 was used

in generating the cambered geometry. Thus, the equation

for the camber line is as follows:

(b/2) [(b/2"_ 2

z - 0c +_\ 0c )-y (A8)

The equation defining the camber line in terms oft I and

is as follows:

1 J/_ 2

= --+ -(rl) 2

0c

(A9)

The angle of camber selected was -10 °. The cambered cross-section equations are derived by adding the

camber line equation (eq. (A9)) to the elliptical crosssection equations (eqs. (A3) and (A4)). The equations for

the cambered cross section in terms of rI and _ are as follows for the upper surface:

= O.05,V_ - 1]2 - 5.72958 + J32.8281 - 1"12 (AlO)

for the lower surface:

= (-0.05)4q - 1"12- 5.72958 + _32.8281 - rl 2 (A11)

As stated before, the arc length was set equal to the

semispan. However, the arc length of the camber line

would be greater than the semispan. The angle of camber

0c can be corrected by taking the derivative of the camber line equation (eq. (A5)) with respect to z. Solving for

_y/_z yields

_y _ Z-Zl 1

_z y tan ( 0c)

(A12)

The angle of camber can be determined by using the

known values of y and z at the end of the camber line.

At the trailing edge, the following conditions apply:

y = 8.3935, z = -0.7381, and z! = 48.0912. The correct

angle of camber is -9.75 °.

156
Appendix B

Determination of Flow Angle

The flow angularity that exists in both test sections

of UPWT is described in reference 9 and is illustrated in

figure 7. A positive flow angularity indicates that the

flow is deflected upward in the test section. The data in

reference 9 were used to develop unpublished flow angularity charts for each test section over a range of Mach

numbers and Reynolds number. However, in actual practice, the flow angle is determined by obtaining force or

pressure data with the model upright (_ = 0°) and

inverted (_ = 180 °) at several angles of attack. The data

for both upright and inverted runs are plotted with angle

of attack. A straight line is faired through the data for

each run with emphasis on -2 ° < c_ < 2 °. The increment

between the two faired lines is twice the flow angle 0p

In this study, two approaches were used to determine

0f. In the first approach, individual pressure measurements were used to calculate 0p In the second approach,

all pressure data at each x station were integrated

to determine C N. The C N was then used to calculate Of.

The pressure data in this study were obtained on the

elliptical wing at M-1.60 and R=I x106 , 2x106 ,

3 x 106, 4 x 106, and 5 x 106 ft -1. The R = 1 x 106 and

5 x 106 ft-1 data were obtained without transition grit on

the elliptical wing. TheR=2×106 , 3×106 , and

4× 106ft -1 data were obtained with transition grit

inboard of the leading edge of the elliptical wing.

Figure B 1 gives an example of the method for determining Of with individual pressure measurements. Figure B 1 shows the measured pressure coefficient from the

orifice A on the lower surface at x = 6 in. and r I = 0.20

plotted with angle of attack at _=0 ° and 180 ° for

R = 1 × 106 ft-1. Also shown are the faired lines for both

the upright and the inverted runs. The increment between

the two faired lines is twice the flow angle, Of. Table B 1

shows 0fdetermined with this approach for six individual

orifices at M= 1.60 and R=I × 106 , 2× 106 , 3× 106 ,

4 × 106, and 5 × 106 ft-1. Three pressure orifices were

located at the forward station (x = 6 in.) and three were

located at the aft station (x = 12 in.). At each station, one

pressure orifice was located on the lower surface and

two pressure orifices were located on the upper surface.

The data in table B1 show that flow angle is dependent upon chordwise location. The flow angle decreases

about 0.25 ° between x = 6 in. to x = 12 in. at the lower

Reynolds numbers. The data at x = 12 in. indicate a

dependency on Reynolds number, which results in flow

angle increases with increasing Reynolds number. Also

note that the variation of Of with x becomes smaller with

an increase in Reynolds number.

Figure B2 shows an example of the second approach

for determining 0f. This approach uses C N, which is calculated by integrating all the measured pressures at a

given x station. Figure B2 shows the calculated values

of C N plotted with angle of attack for x = 6 in. and _ = 0 °

and 180 ° at R = 1 × 106 ft-1. Also shown are the faired

lines for both the upright and the inverted runs. The

increment between the two faired lines is twice the flow

angle, Of. Table B2 shows Of determined with this

approach for x=6 and 12 in. at M=1.60 and R =

1×106 ,2×106 ,3×106 ,4x106 , and5×106ft -l.Table

B2 shows that the trends in the 0fdata are similar to those

observed in the 0fdata obtained from individual pressure

measurements. However, the change in Of with a variation in x or Reynolds number is approximately 0.1 ° or

less, which is smaller than that observed in the Of data

obtained from individual pressure measurements.

The two approaches for determining Of yielded similar trends in 0f with respect to x and Reynolds number.

Reference 9 documents a dependency of flow angle on

x location in the test section. However, the variation of

flow angle with x is very slight in the region of test section where the model is located. Reference 9 does not

document a dependency of 0f on Reynolds number. The

approach using the calculated force data yielded smaller

variations in 0f with changes in x or Reynolds number

than the approach using individual pressure measurements. The usual choice in determining flow angle at

UPWT is force data. Because of these two observations,

the calculated force data were used to determine 0f. The

data in table B2 were averaged so that the flow angle that

was applied to all data was 0.4 °.

157
Table B 1. Flow Angles From Individual Pressure Measurements

Location

Orifice Surface x, in.

A Lower 6

B Upper 6

C Upper 6

D Lower 12

E Upper 12

F Upper 12

n

0.2

0.1

0.2

0.2

0.1

0.2

0y_deg at R, ft -l, of--

1 x 106 2 x 106 3 x 106 4 x 106 5 x 106

0.50 0.50 0.45 0.48 0.35

0.45 0.45 0.45 0.45 0.52

0.50 0.45 0.46 0.46 0.58

0.20 0.28 0.30 0.35 0.40

0.22 0.30 0.35 0.38 0.40

0.22 0.25 0.33 0.40 0.40

Table B2. Flow Angles From Integrated Force Data

Of, deg at R, ft-1, of---

x, in. 1x106 2x106 3x106 4x106 5x106

6 0.45 0.45 0.40

12 0.30 0.35 0.38

0.40 0.38

0.42 0.40

158
Cp

_,deg

0 (upright)

180.0 (inve_ed)

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[[tlll[llllllJllllllllllll I J

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IIIIIIIIIIII1[1111[1111111 I I

IIIIIIIIIIl[llllllilllllll I I

illllillilliillltilllllili I I

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-.08 iillllilillilillllillllilli I I

-5 -3 -2 -1 0

• Least square fit

-4 1 2 3 4 5

O_ac,deg

Figure B I. Example of method used to determine 0f with individual pressure data from orifice A (lower surface,

x = 6 in., 11= 0.2) on elliptical wing without grit at R = 1 × 106 ft-1.

159
¢, deg

• 0 (upright) Least square fit

• 180.0 (inverted)

ON

.20

_________________________________________________________I_i_____________i___I____I Ji

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_____________________i___________________]_________________i_______j___1T______Z__I !

__8________________________________________________________________L4__________r____I :i

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__i______i__ t

_____________________i___________________________________/_T______21_]____________I

_4______2r____ Ill

_____________________________________________________H1______L__4_______________I t 1

____j__W____ I I 1

0 _______________________________________________d_______/_________________________

_j________j_]j___________]____j_______________j.h'_1'1.j____L_d_j_____i____]__r______j__1 i

______._..i2f____ i

_[_]_j_j_j_]_]__j_j__]_]_j_]_j_jj_ [

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IllJllll_lJlJlllllJl]Jtll _]_]_]_I_Iji_j_IIj_ij_jj_j_I_[Ij_j_jj_i_]_i_j_]_i_I_j]_I_ij II]lJJllllJllllJ[llll]lllllllllttlltlllll]llllllJllllJl / i I

____j___]_________I_I___I__]__i_]____II__i___i___j_i__I____j__Ij____jj__i_______j___ I I l

-4 -3 -2 -1 0 1 2 3 4 5

O_ac,deg

Figure B2. Example of method to determine Of with CN obtained by integrating pressure data at x = 6 in. on elliptical

wing without grit at R = 1 x 10 6 ft -1.

160
Appendix C

Description of CD-ROM

This appendix gives a description of the process used

to transfer the experimental data recorded with photography into digital form. The digital data are stored on a

CD-ROM disc that conforms to the ISO 9660 standard.

Scanning

The four flow-visualization techniques used to

obtain data on the three delta wing models were the

vapor-screen, painted-oil-flow, injected-oil-flow, and

liquid-crystal techniques. The flow-visualization data

were obtained by photography. The photographic images

were digitized by using two standard charge coupled

device (CCD) based scanners. Scanning resolution was

selected to balance the need to represent the detailed flow

field information and the requirement that all images

would be distributed on one 650 MB CD-ROM disc.

Table C 1 summarizes the scanning process. The scanned

images were stored in the TIFF format.

The vapor-screen data were digitized by scanning

the 70-mm negatives with a flatbed scanner capable of

scanning color images. The flatbed scanner has a resolution of 600 dots/in. (dpi) and uses a three-color fluorescent lamp system and a CCD image sensor. This

equipment generates an image that has 8 bits per channel.

The image size varies, but is usually 720 columns by

504 rows. To scan the negatives, it was necessary to

specify their contrast level to achieve an accurate image.

The flatbed scanner is limited to three contrast settings. For some of the images, it was not possible to

obtain optimal contrast because of the discrete nature of

the contrast levels and the large variations in opacity of

the negatives. When a suboptimal result was obtained,

the image was automatically scaled to effectively

increase the contrast. To determine those scans that were

suboptimal, a region of the image that should have been

gray level zero, or black, was probed. If the region was

not reading an average gray level less than 30, the image

was linearly scaled, with common data analysis software,

between the average region value and the maximum

image brightness value of 255. The integrity of each

image was visually verified after scaling by comparison

with photographic prints.

In addition to adjusting the contrast, two other corrections for the scanned vapor-screen technique images

were necessary. The first correction was to invert the

scanned image so that the final product was similar to a

photographic print. This correction was done with common data analysis software. The second correction was

to remove artifact lines---bright scan lines that propagated along the vertical, or subscan, direction in the

scanned images. A procedure was developed that would

detect an artifact line and replace it with a line equal to

the average of the scan lines to the left and the right of

the artifact line. Proper removal of these artifact lines

was verified after processing was completed.

The liquid-crystal images were digitized by scanning

the 70-mm negatives with a tabletop scanner which can

scan color images. This tabletop scanner probes with a

triband phosphor fluorescent lamp and measures the data

with a 6000 element linear CCD array. The scanner was

driven from a commercial image manipulation software

package on a Macintosh computer system. Twenty-fourbit (three color planes of eight bits per plane) images

were produced and the images on the CD-ROM are

24 bits as well. The negatives were scanned at 350 dpi

resolution, which produced images that are 637 columns

by 619 rows. The scanning software was used to convert

the negative scan into a positive image by sensing and

removing the orange mask present in color negatives.

The 70-mm negatives of the injected-oil-flow technique and the 4 in. by 5 in. positives of the paintedoil-flow technique were also scanned by the tabletop

color scanner with a 6000 element linear CCD array.

Both sets of images were scanned at 350 dpi resolution

with the scanner producing 8-bit gray scale images.

Again, the scanning software generated a positive from

negatives of the injected-oil-flow technique by inverting

the image. The size of all the injected-oil-flow images is

619 pixels x 637 pixels, while the painted-oil-flow image

size is 622 pixels x 520 pixeis.

Image Display

The digitized images were carefully reviewed after

scanning. The gray levels in the scanned digital images

accurately represent the flow-field information in the traditional positive prints. However, each monitor and

printing device has a unique way of presenting the same

digital gray level information. A sample image is given

in figure C1 to illustrate this point. The image in figure Cl(a) is displayed on a monitor that has a display

_'= 1.0, while the image in figure Cl(b) is displayed on a

monitor with _/= 1.7. The parameter _' is a measure of the

contrast response of the display; _' values greater or less

than 1.0 will expand or compress the dark or bright end

of the display range. Generally, _' values are different for

each system and monitor, so image displays between

monitors are not consistent even though the same digital

image file is used. References 20-22 discuss the standardization of monitors so that image display is consistent between computer systems. It is suggested that

an image display be adjusted so the model surface is

essentially all black and there is a visible transition

between the model and the flow field.

161
The above observations are also true with printers.

Printers vary in the number of gray levels they can produce and the maximum resolution that can be printed.

These two factors determine the fidelity of the image and

adjustments may be needed to obtain a realistic print of

the digital images.

In addition to being aware of system, printer, and

monitor variations, there is another factor to consider

when displaying 24-bit images on monitors that do not

have full color capability. Ideally, the liquid-crystal

images would be displayed on a monitor capable of displaying 24-bit images. Otherwise, the image must be

quantized from 24 to 8 bits before displaying. Quantization is a procedure that will produce a pseudocolored

image with 8 bits of data that have coloring similar to the

24-bit image. There are many different quantization

schemes and some image display software packages will

have a quantization code that is used automatically. The

color range in the image is usually an input into a quantization algorithm. Therefore, it is suggested that the calibration images (the images containing the temperature

scales to the colors viewed in the data images) be pasted

into a data image file before quantization. If the flowfield image and the calibration images are quantized

independently, comparisons of colors in the quantized

data image to colors in the quantized calibration images

may be invalid. References 23 to 24 contain more

detailed discussion of quantization methods.

The CD-ROM

The CD-ROM distributed with this paper conforms

to the ISO 9660 standard. Included on the CD are the

images mentioned in the scanning section, a table of

pressure data, and a description of header size and image

dimensions for each TIFF image file. The remainder of

this section will discuss the directory structure, image

file format, image format conversion, and available software for three commonly used computer systems: UNIX,

PC with DOS, and Macintosh.

The root directory of the CD-ROM contains three

directories: PRESSDAT, IMAGES, and FILEINFO. The

README file in each directory provides information on

the contents of that directory. A schematic of the directory hierarchy is given in figure C2 and table C2 contains

a brief description of each directory.

Appendix D gives a detailed description of the variables found in each pressure file and a summary of

the pressure data. Figure C3(b) shows a listing of all

pressures and flow conditions for each data point.

The pressure-listing file name on the CD-ROM is

PRESS.LST. The pressure-listing data identifies each

pressure measurement by the variable name CP#

(tables 2 to 4). The pressure-listing file does not contain

the location of each pressure. Tables 2 to 4 contain the

location on the wing and the corresponding CP# for each

pressure measurement. Thus, for plotting purposes, the

pressure-listing data must be used with a curve definition

file that gives the location for each pressure. Figure C4

shows a portion of the curve definition file, which is

named CURDEF on the CD-ROM. The first curve

defined in .qgure C4 is identified as curve "ellul a" and is

the pressure distribution on the upper surface of the elliptical wing at x = 6 in. for runs 4-21. The r I location for

each pressure measurement is given in the "xlist" section

and the corresponding variable name for each pressure

measurement from the pressure-listing file is given in the

"ylist" section.

Image files and formats. The image files in the

IMAGES directory are stored in a directory hierarchy

that indicates the wing type, transition grit application,

the flow-visualization technique, R, and To. The directory hierarchy is given in figure C2. A brief description

of each directory is given in table C2. The file name for

each image indicates the previously mentioned conditions as well as the angle of attack, while adhering to the

DOS 8.3 file naming convention. Table C4 contains a

description of the file name convention that was used on

the CD-ROM.

Images are stored in the tagged image file format

(TIFF). The TIFF files on this CD have some finite

amount of supplemental information stored at the beginning of the file (often called a header) followed by the

image information stored in sequential rows. If software

that reads either one of these formats is unavailable, it is

possible to read the TIFF images as raw data into most

image display software packages. To read an image as

raw data, the length of the header and the number of rows

and columns in the image must be known. For all of

the TIFF files, this information is provided in the file,

FILESIZE.TXT under the FILEINFO directory.

Pressure datafilesandf°rmats'The files in the

PRESSDAT directory are stored as ASCII files. Figure C3 shows the two formats in which the pressure data

are given. Figure C3(a) shows a table format where, for a

given condition, each pressure measurement is listed

with its location on the wing. Table C3 contains the file

name convention for the tabulated pressure data files.

The calibration images (the images containing the

temperature scales to the colors viewed in the data

images) for the liquid-crystal data are contained in the

root directory. The file names are LEFTCB and

RIGHTCB referring, respectively, to the left and right

side of the wing when looking upstream of the model

from the trailing edge.

162
UNIX workstation systems. There are many conversion and display routines written for UNIX workstations.

Below is a listing of software that can be used to convert and display the TIFF images. The software is available by anonymous file transfer. The FTP directories

listed are the current locations, but they are subject to

change. Restrictions on the use and licensing for any

of the software may be obtained from the associated

documentation.

Conversion:

Software: imtools

Developer: San Diego Supercomputing Center

(SDSC)

FI'P site: ftp.sdsc.edu

Directory location: pub/sdsc/graphics/imtools

Description: Software that will read and write a

variety of formats. The software, at this

writing, only runs on UNIX based machines,

but will write and read some typical PC and

Macintosh formats.

Software: pbmplus

Developer: Jef Poskanzer

FI'P site: ftp.x.org

Directory location: R5contrib

Description: Software that will read and write a

variety of formats.

Display:

Software: ImageMagick

Developer: John Cristy, E. I. du Pont

de Nemours and Company, Incorporated

F'I'P site: export.lcs.mit.edu

Directory location: contrib/applications/

ImageMagick

Software: xv version 2.21

Developer: John Bradley, Grasp Laboratory at

U. Penn.

FTP site: edhs I .gsfc.nasa.gov

Directory location: pub/freeware/unix/src/xv

Description: Software to display images on X

compatible windowing environments. This

software also has built-in quantization code

and provides some flexibility on the method

used to quantize 24-bit images.

PC with DOS systems. There are many conversion

and display routines written in DOS for PC or PCcompatible systems using DOS. Listed below are a package, pbmplus, that can convert images and a package,

imdisp, that can be used to display images. These are

available by anonymous file transfer (FTP) at the sites

given in each package description. The FTP directories

listed are the current locations, but they are subject to

change. Restrictions on the use and licensing for any of

the software may be obtained from the associated

documentation.

Conversion:

Software: pbmplus

Developer: Jef Poskanzer

b-q'P site: wuarchive.wustl.edu

Directory location: SimTel/msdos/graphics

Description: Image format conversion tools that

read and write a large variety of image

formats.

Display:

Software: imdisp

Developer: Jet Propulsion Laboratory (JPL)

FTP site: oak.oakland.edu

Directory location: simtel/msdos/graphics

Description: Written at JPL to display planetary

data. It provides support for a very large

variety of PC graphics cards (EGA, CGA,

and VGA). The software will read and write

out the special image formats used to

distribute planetary data; however, the TIFF

images can be read in as raw data with the

header and size information as previously

discussed. The package also provides some

limited image processing and enhancement

capabilities.

Macintosh systems. There are several display packages for the Macintosh systems that also have extensive

image processing capabilities. Some of these packages

are listed below along with anonymous file transfer sites

from which the user can download the binaries for each

package. Most of the packages listed have additional output formats and can also serve as conversion software.

The FTP directories listed are the current locations, but

they are subject to change. Restrictions on the use and

licensing of any of the software may be obtained from

the associated documentation.

163
Software:NIHImage

Developer: NIH

FrP site: zippy.nimh.nih.gov

Directory location: pub/nih-image

Description: This is a general purpose image

processing package for the Macintosh. It can

read 8-bit images only.

Software: JPEGView 3.3

Developer: Aaron Giles, Cornell University

P'TP site: edhsl .gsfc.nasa.gov

Description: Can read and display (if hardware

is capable) 24-bit and 8-bit TIFF files

Directory location: pub/freeware/mac

Table C 1. Scanning Summary

Flow-visualization

technique

Vapor screen

Liquid crystal

Painted oil flow

Injected oil flow

Film type

70-mm black and

white negatives

70-mm color

negatives

4 in. by 5 in. selfdeveloping film

70-mm black and

white negatives

Scanning resolution,

dpi

600

350

350

350

Image size (pixels)

Columns

Variable

673

622

619

Rows

Variable

619

520

637

Pixel depth, bits

24

164
TableC2.Descriptionof DirectoriesonCD-ROM

Directory Description

IMAGES.INF Directorycontaininginformationonimages.

PRESSDAT Directorycontainingpressuredata.

IMAGES Directorycontainingallscannedimages.

SNWING Subdirectorycontainingallscannedimagesforsharpwingwithoutransitiongrit.

ENWING Subdirectorycontainingallscannedimagesforellipticalwingwithoutransitiongrit.

EYWING Subdirectorycontainingallscannedimagesforellipticalwingwithtransitiongrit.

CNWING Subdirectorycontainingallscannedimagesforcamberedwingwithoutransitiongrit.

CYWING Subdirectorycontainingall scannedimagesforcamberedwingwithtransitiongrit.

IMAGES/??WlNG/ Subdirectorycontainingall vapor-screen imagesforconfigurationassociatedwith

V_SCREEN IMAGES/??WINGdirectory(where??WINGisSNWING,ENWING,EYWING,

CNWING,orCYWlNGdirectory).

IMAGES/??WING/ Subdirectorycontainingallinjected-oil-flowimagesforconfigurationassociatedwith

I_OILFLO IMAGES/??WlNGdirectory.

IMAGES/??WlNG/ Subdirectorycontainingallpainted-oil-flowimagesforconfigurationassociatedwith

P_OILFLO IMAGES/??WINGdirectory.

IMAGES/??WING/ Subdirectorycontainingallliquid-crystal imagesforconfigurationassociatedwith

LIQ_CRY IMAGES/??WlNGdirectory.

IMAGES/??WlNG/ SubdirectorycontainingdataatR = 1 x 106 ft-1 associated with IMAGES/??WlNG/*_*

*_*/R1 directory (where *_* is V_SCREEN, I_OIFLO, P_OILFLO, or LIQ_CRY directory).

IMAGES/??WING/ Subdirectory containing data at R = 2 x 106 ft-1 associated with IMAGES/??WlNG/*_*

*_*/R2 directory.

IMAGES/??WING/ Subdirectory containing data at R = 5 × 106 r-t associated with IMAGES/??WlNG/*_*

*_*/R5 directory.

IMAGES/??WING/ Subdirectory containing liquid-crystal data at TO = 120°E Configuration and free-stream

LIQ_CRY/R#/T120 Reynolds number condition is that associated with IMAGES/??WING/LIQ_CRY/R#

directory (where R# is RI, R2, or R5 directory).

IMAGES/??WING/ Subdirectory containing liquid-crystal data at TO = 125°F. Configuration and free-stream

LIQ_CRY/R#/T125 Reynolds number condition is that associated with IMAGES/??WING/Liq_cry/R#

directory.

IMAGES/??WING/ Subdirectory containing liquid-crystal data at TO = 130°F. Configuration and free-stream

LIQ_CRY/R#/T130 Reynolds number condition is that associated with IMAGES/??WlNG/Liq_cry/R#

directory.

165
TableC3.DescriptionofTabulatedPressureDataFileNameson CD-ROM

[Tabulated Pressure File Name - 1 2 PRESS. TAB]

File name characters Description

1 - Model geometry S ... Sharp wing

E ... Elliptical wing

C ... Cambered wing

2 - Grit N ... No transition grit applied

Y ... Transition grit applied

Example: ENPRESS.TAB File for all pressures for elliptical wing with no transition grit

Table C4. Description of Image File Names on CD-ROM

[Image File Name - 1 2 3 4 T 5 __. A 6_ ]

File name characters

i - Model geometry

2 - Grit

3 - Flow visualization technique

4 - Freestream Reynolds number

T5 -T O

A _6_ - Otnom

Example: ENV2TI25.A50

Description

S ... Sharp wing

E ... Elliptical wing

C ... Cambered wing

N ... No transition grit applied

Y ... Transition grit applied

V ,..Vapor screen

P ... Painted oil flow

I ... Injected oil flow

L ... Liquid crystal

1 ...R= 1 x 106ft -l

2...R=2×106ft -l

5...R=5xi06ft -1

T120 ... TO = 120°F

T125 ... TO = 125°F

T130 ... To= 130°F

A00 ... O_nom = 0 °

A10 ... Otnom = 1.0 °

A15 ... 13_nom = 1.5 °

A90 ... 0triom = 9.0 °

Image file for vapor-screen photograph of elliptical wing without grit at R = 2 x 106 ft-1, To = 125 °F, and Otnom = 5.0 °. All

image data were obtained at x = 12 in.

166
(a) 7= 1.0.

(b) _'=1.7.

FigureC1.Comparisonofsameimagefromdifferentdisplaysystems.

167
--j

rrw

w (.,.,.,3

,-_1m

I1"

13..u

--!'-

7-

Z

C,.,'.'3 Z

1,11

pr_l

,731

00

I.,IJ nnnoo• I I 0 0 0

u'im Z Z

I.IJ nnnoo e,

0

_5

O,4

I-, nZW0

O)

0,,,I

I,,- Z

i!1I ©

rj0

o_£0E

c,¢)

r4

168
MACH= 1.60 Q=227.6 PINF= 127.0 R/FT=I.00

PHI = -0.08 FLOW ANGLE = 0.40

X/C = 0.333, UPPER SURFACE

ETA CP ETA CP ETA

0.099 0.0718 0.579 0.0749 0.759

0.199 0.0701 0.619 0.0767 0.781

0.299 0.0692 0.660 0.0784 0.800

0.400 0.0709 0.700 0.0811 0.820

0.499 0.0727 0.720 0.0824 0.840

0.539 0.0740 0.740 0.0842 0.860

CP

0.0859

0.0890

0.0899

0.0925

0.0943

0.0983

ETA CP

0.880 0.1027

0.899 0.1084

0.920 0.1155

0.939 0.1252

0.980 0.1670

X/C = 0.333, LOWER SURFACE

ETA CP ETA CP

0.200 0.0031 0.500 -0.0009

0.400 0.0017 0.600 -0.0031

ETA CP ETA CP

0.700 0.0009 0.850 -0.0547

0.799 -0.0516 0.900 -0.0626

X/C = 0.667, UPPER SURFACE

ETA CP ETA CP

0.100 0.0679 0.540 0.0749

0.200 0.0679 0.560 0.0749

0.300 0.0679 0.579 0.0753

0.350 0.0683 0.599 0.0767

0.400 0.0692 0.621 0.0771

0.450 0.0705 0.640 0.0780

0.500 0.0767 0.660 0.0784

0.520 0.0753 0.680 0.0802

ETA CP

0.700 0.0811

0.720 0.0820

0.740 0.0837

0.760 0.0846

0.780 0.0868

0.800 0.0894

0.820 0.0921

0.840 0.0956

ETA CP

0.860 0.0991

0.879 0.1044

0.899 0.1102

0.920 0.1185

0.940 0.1287

0.960 0.1423

0.981 0.1754

X/C = 0.667, LOWER SURFACE

ETA CP ETA CP

0.200 -0.0049 0.550 -0.0084

0.400 -0.0027 0.600 -0.0093

0.450 -0.0036 0.650 -0.0146

ETA CP ETA CP

0.700 -0.0146 0.850 -0.0221

0.750 -0.0159 0.900 -0.0847

0.800 -0.0207 0.950 -0.1045

(a) Table format.

Figure C3. Formats in which surface-pressure coefficient data are stored on CD-ROM.

169
RUN POINT MACH

PINF CP1 CP2

CP6 CP7 CP8

CP12 CP13 CP14

CP18 CP19 CP20

CP24 CP33 CP34

CP38 CP39 CP40

CP44 CP45 CP46

CP50 CP51 CP52

CP56 CP57 CP58

CP66 CP67 CP68

CP72 CP73 CP74

CP78 CP79 CP80

CP84 CP85 CP86

CP90 CP91

0.40000E+01 0.10400E+03 0.16000E+01

0.12661E+03 0.30589E-02 0.17365E-02

-0.51596E-01 -0.54681E-01 -0.62615E-01

-0.48749E-02 -0.26711E-02 -0.35526E-02

-0.14572E-01 -0.14572E-01 -0.15894E-01

-0.10449E+00 0.71818E-01 0.70055E-01

0.74022E-01 0.74904E-01 0.76667E-01

0.84160E-01 0.85923E-01 0.89008E-01

0.98264E-01 0.10267E+00 0.10840E+00

0.16702E+00 0.67851E-01 0.67851E-01

0.76667E-01 0.75344E-01 0.74904E-01

0.77107E-01 0.77989E-01 0.78430E-01

0.83719E-01 0.84601E-01 0.86804E-01

0.99146E-01 0.10443E+00 0.11016E+00

0.17540E+00 0.70496E-01

0.40000E+01 0.10500E+03 0.16000E+01

0.12657E+03 0.15113E-01 0.13790E-01

0.56379E-03 -0.47268E-02 -0.12663E-01

Q ALPHA R/FT

CP3 CP4 CP5

CP9 CP10 CP11

CP15 CP16 CP17

CP21 CP22 CP23

CP35 CP36 CP37

CP41 CP42 CP43

CP47 CP48 CP49

CP53 CP54 CP55

CP59 CP60 CP61

CP69 CP70 CP71

CP75 CP76 CP77

CP81 CP82 CP83

CP87 CP88 CP89

0.22688E+03 -0.30213E+01 0.99229E+00

-0.90805E-03 -0.31119E-02 0.85502E-03

0.99999E+01 -0.62174E-01 -0.53157E-02

0.99999E+01 -0.84011E-02 -0.92826E-02

-0.20743 E-01 -0.22065 E-01 -0.84653 E-01

0.69174E-01 0.70937E-01 0.72700E-01

0.78430E-01 0.81074E-01 0.82397E-01

0.89890E-01 0.92534E-01 0.94297E-01

0.11545E+00 0.12515E+00 0.99999E+01

0.67851E-01 0.68292E-01 0.69174E-01

0.74904E-01 0.75344E-01 0.76667E-01

0.80193E-01 0.81074E-01 0.81956E-01

0.89449E-01 0.92093E-01 0.95620E-01

0.11854E+00 0.12868E+00 0.14234E+00

0.22682E+03 -0.20316E+01

0.12027E-01 0.10263E-01

0.99999E+01 -0.10899E-01

(b) Pressure listing format.

Figure C3. Concluded.

0.99514E+00

0.76179E-02

0.45317E-02

170
_t

* Curve Definition File

* Elliptic wing for Runs 4-21, upper surface, x=6"

curve ellula

xlist

0.099 0.199 0.299 0.4 0.499 0.539 0.579 0.619

0.66 0.7 0.72 0.74 0.759 0.781 0.8 0.82

0.84 0.86 0.88 0.899 0.92 0.939 0.98

ylist

CP33 CP34 CP35 CP36 CP37 CP38 CP39 CP40

CP41 CP42 CP43 CP44 CP45 CP46 CP47 CP48

CP49 CP50 CP51 CP52 CP53 CP54 CP56

* Elliptic wing for runs 22-32, upper surface, x=6"

curve ellul b

xlist

0.099 0.199 0.299 0.4 0.499 0.539 0.579 0.619

0.66 0.7 0.72 0.74 0.759 0.781 0.8 0.82

0.84 0.86 0.88 0.92 0.939 0.98

ylist

CP33 CP34 CP35 CP36 CP37 CP38 CP39 CP40

CP41 CP42 CP43 CP44 CP45 CP46 CP47 CP48

CP49 CP50 CP51 CP53 CP54 CP56

Figure C4. Example of curve definition file for pressure data.

171
Appendix D

Surface-Pressure Coefficient Data

The surface-pressure coefficient data (referred to

hereafter as pressure data) are referenced to the freestream dynamic pressure q. The pressure data are presented in figures D1 to D22. The pressure data for each

row of orifices on the upper and the lower surface are

presented for each configuration. For example, figure D1

presents the surface-pressure coefficient data for the

sharp wing without grit at R = 1 x 106 ft-1 and angles of

attack from 0.25 ° to 9.27 ° in approximately 0.5 ° increments. Table D1 presents an index to the data and the

wind-tunnel conditions for each figure.

The surface-pressure coefficient data are also presented on the CD-ROM in a simple pressure-listing format and a table format. The pressure-listing format

presents a row of pressures for each data point. For plotring purposes, the pressure-listing file must be used with

a curve definition file, which gives the location of each

pressure for a given run. The curve definition file is also

located on the CD-ROM. The pressure data are also

stored on the CD-ROM in table format where, for a given

condition, each pressure measurement is listed with its

location on the wing. Appendix C contains the details on

the pressure data files and CD-ROM. Table D1 presents,

for each run, the test conditions and the CD-ROM file

that contains the tabulated pressure data. Tables 6 to 1 l

contain a point and tx index to the pressure data. All

surface-pressure coefficient data were taken at _3= 0 ° and

T O= 125°F.

172
Table D1. Index to Figures D1 to D22 and Tabulated Data at M = 1.60 and TO= 125°F on CD-ROM

Pressure data table R, 0f, ¢,

Figure file name Configuration Run million/ft deg deg

D 1 SNPRESS.TAB Sharp wing without grit 40 1 0.4 0

D2 SNPRESS.TAB Sharp wing without grit 41 2 0.4 0

D3 SNPRESS.TAB Sharp wing without grit 42 5 0.4 0

D4

D5

SYPRESS.TAB

SYPRESS.TAB

D6 SYPRESS.TAB

ENPRESS.TAB

ENPRESS.TAB

Sharp wing with grit

Sharp wing with grit

43

Elliptical wing without grit

0.4

44 2 0.4 0

Sharp wing with grit 45 5 0.4 0

Elliptical wing without grit 4a 1 0 0

5a 1 0 180.0

D7 ENPRESS.TAB Elliptical wing without grit 6 1 0.4 0

D8 ENPRESS.TAB Elliptical wing without grit 7 2 0.4 0

D9 ENPRESS.TAB Elliptical wing without grit 8 3 0.4 0

DI0 ENPRESS.TAB

ENPRESS.TAB

ENPRESS.TAB

D 11 ENPRESS.TAB

Elliptical wing without grit

Elliptical wing without grit

Elliptical wing without grit

Elliptical wing without grit

D12 EYPRESS.TAB

10 4 0.4 0

13a 5 0 0

11a 5 0 180.0

14 5 0.4 0

Elliptical wing with grit 22 1 0.4 0

EYPRESS.TAB Elliptical wing with grit 23 a 2 0 0

EYPRESS.TAB Elliptical wing with grit 24 a 2 0 180.0

D13 EYPRESS.TAB Elliptical wing with grit 25 2 0.4 0

EYPRESS.TAB Elliptical wing with grit 26 a 3 0 0

EYPRESS.TAB Elliptical wing with grit 27 a 3 0 180.0

D 14 EYPRESS.TAB Elliptical wing with grit 28 3 0.4 0

EYPRESS.TAB Elliptical wing with grit 30 a 4 0 0

EYPRESS.TAB Elliptical wing with grit 31 a 4 0 180.0

D 15 EYPRESS.TAB Elliptical wing with grit

D 16 EYPRESS.TAB Elliptical wing with grit

D 17 CNPRESS.TAB Cambered wing without grit

D I 8 CNPRESS.TAB Cambered wing without grit

CNPRESS.TAB Cambered wing without grit

(Unacceptable dew point)

D 19 CNPRESS.TAB Cambered wing without grit

D20 CYPRESS.TAB Cambered wing with grit

D21 CYPRESS.TAB Cambered wing with grit

D22 CYPRESS.TAB Cambered wing with grit

32 4 0.4 0

29 5 0.4 0

36 1 0.4 0

34 2 0.4 0

33 5 0.4 0

35 5 0.4 0

37 1 0.4 0

38 2 0.4 0

39 5 0.4 0

aData used in determining 0f.

173
-.35 --

-.30 -

-.25 -

-.20 -

-.15 --

Cp -.10 --

-.05

0

.05 -

.10

.15

_,deg Point

o 0.25 849

• 0.75 850

[] 1.28 851

• 1.75 852

2.29 853

2.76 854

3.25 855

• 3.75 856

4.25 857

• 4.75 858

5.30 859

• 5.77 860

6.26 861

• 6.79 862

7.27 863

• 7.76 864

¢ 8.26 865

$ 8.75 866

9.27 867

/

lllllllLILlllll''''l''''l_Llll''''l''l'l''''l'_''l

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(a) Upper surface at x = 6 in.

Figure D1. Surface-pressure coefficient data for sharp wing without transition grit at M = 1.60 and R = l x l06 ft-1 for

run 40.

174
m

.05 --

.10 -

.15 -

Cp .20 -

.25

.30

.35

.40

[]

4

L

_,deg Point _,deg Point

0.25 849 _ 5.30 859

0.75 850 • 5.77 860

1.28 851 a 6.26 861

1.75 852 • 6.79 862

2.29 853 o 7.27 863

2.76 854 • 7.76 864

3.25 855 _ 8.26 865

3.75 856 _ 8.75 866

4.25 857 _ 9.27 867

4.75 858

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) Lower surface at x = 6 in.

Figure DI. Continued.

175
-.40 --

_,deg Point

o 0.25 849

• 0.75 850

[] 1.28 851

• 1.75 852

2.29 853

2.76 854

A 3.25 855

• 3.75 856

4.25 857

• 4.75 858

L 5.30 859

• 5.77 860

6.26 861

• 6.79 862

O 7.27 863

• 7.76 864

_:_ 8.26 865

8.75 866

9.27 867

A

0

(c) Upper surface at x = 12 in.

Figure DI. Continued.

176
D

.05 -

.10 -

.15 -

Cp .20

.25

.30

.35

.40

o

[]

A

_,deg Point _,deg Point

0.25 849 _ 5.30 859

0.75 850 • 5.77 860

1.28 851 _ 6.26 861

1.75 852 • 6.79 862

2.29 853 Q 7.27 863

2.76 854 • 7.76 864

3.25 855 _ 8.26 865

3.75 856 _ 8.75 866

4.25 857 _ 9.27 867

4.75 858

------- _

0 © 0 0 - •

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(d) Lower surface at x = 12 in.

Figure D1. Concluded.

177
-.40 --

-.35 --

-.30 -

-.25 -

-.20 -

Cp -.15 -

-.10 -

-.05 -

0 -

.05 -

.10 -

.15

_,deg Point

0.25 877

0.78 878

1.28 879

1.78 880

2.25 881

2.77 882

3.28 883

3.75 884

4.27 885

4.76 886

5.25 887

5.78 888

6.27 889

6.78 890

7.26 891

7.76 892

8.27 893

8.76 894

9.28 895

/

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(a) Upper surface at x = 6 in.

Figure D2. Surface-pressure coefficient data for sharp wing without transition grit at M = 1.60 and R = 2 x 106 ft -1 for

run 41.

178
b

.05

.10

.15

Cp .2O

.25

.30

.35

.40

0

[]

A

_,deg Point _,deg Point

0.25 877 _ 5.25 887

0.78 878 • 5.78 888

1.28 879 _ 6.27 889

1.78 880 • 6.78 890

2.25 881 © 7.26 891

2.77 882 • 7.76 892

3.28 883 ¢ 8.27 893

3.75 884 O 8.76 894

4.27 885 _ 9.28 895

4.76 886

L

0

(b) Lower surface at x = 6 in.

Figure D2. Continued.

179
-.40 --

_,deg Point

o 0.25 877

• 0.78 878

[] 1.28 879

• 1.78 880

2.25 881

2.77 882

3.28 883

• 3.75 884

4.27 885

• 4.76 886

5.25 887

• 5.78 888

6.27 889

• 6.78 890

7.26 891

• 7.76 892

8.27 893

i 8.76 894

9.28 895

0

(c) Upper surface at x = 12 in.

Figure D2. Continued.

180
__

.05

.10

.15

Cp .20

.25

.30

.35

.40

C_

[]

1⁄2

_,deg Point _,deg Point

0.25 877 _ 5.25 887

0.78 878 • 5.78 888

1.28 879 _ 6.27 889

1.78 880 • 6.78 890

2.25 881 o 7.26 891

2.77 882 • 7.76 892

3.28 883 0 8.27 893

3.75 884 t 8.76 894

4.27 885 _ 9.28 895

4.76 886

0

(d) Lower surface at x = 12 in.

Figure D2. Concluded.

181
-.45 --

Cp

-.40

-.35

-.30

-.25

-.20

-.15

-.10

-.05

0

.05

.10

.15

_,deg Point

o 0.23 897

• 0.79 898

[] 1.28 899

• 1.78 900

0 2.29 901

i 2.76 902

3.28 903

• 3.76 904

4.25 905

• 4.76 906

5.27 907

• 5.75 908

6.27 909

• 6.78 910

© 7.29 911

• 7.75 912

0 8.25 913

t 8.76 914

9.25 915

I I

0

iillll,t,,,,I,,,,I,lllliilillillllllllllillJlJll

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

1]

(a) Upper surface at x = 6 in.

Figure D3. Surface-pressure coefficient data for sharp wing without transition grit at M = 1.60 and R = 5 x 106 ft-1 for

run 42.

182
C_

[]

t

_,deg Point _,deg Point

0.23 897 _ 5.27 907

0.79 898 • 5.75 908

1.28 899 _ 6.27 909

1.78 900 • 6.78 910

2.29 901 o 7.29 911

2.76 902 • 7.75 912

3.28 903 ,_ 8.25 913

3.76 904 _ 8.76 914

4.25 905 _ 9.25 915

4.76 906

B

.05

.10 --

.15 --

Cp .20

.25 -

.30 -

.35

.40

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) Lower surface at x = 6 in.

Figure D3. Continued.

183
-.45 -

-.40 -

-.35 -

-.30 -

-.25 -

-.20 --

Cp

-.15

-.10

-.05

0

.05 -

.10 -

.15 _l

0

e_,deg Point

c_ 0.23 897

• 0.79 898

[] 1.28 899

• 1.78 900

2.29 901

2.76 902

3.28 903

• 3.76 904

4.25 905

• 4.76 906

L, 5.27 907

• 5.75 908

6.27 909

• 6.78 910

q, 7.29 911

• 7.75 912

,_ 8.25 913

t 8.76 914

9.25 915

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(c) Upper surface at x = 12 in.

Figure D3. Continued.

184
__

.05

.10

.15 --

p

Cp .20 --

.25 -

.30

.35

.40

©

[]

_,deg Point _,deg Point

0.23 897 _ 5.27 907

0.79 898 • 5.75 908

1.28 899 _ 6.27 909

1.78 900 • 6.78 910

2.29 901 _ 7.29 911

2.76 902 • 7.75 912

3.28 903 0 8.25 913

3.76 904 _ 8.76 914

4.25 905 _ 9.25 915

4.76 906

0

q

(d) Lower surface at x = 12 in.

Figure D3. Concluded.

185
-.40 -

-.35

-.30

-.25

-.20

Cp -.15

-.10

-.05

0

.05

.10

.15

co,deg Point

o 0.23 937

• 0.78 938

[] 1.26 939

• 1.78 940

2.29 941

_I, 2.79 942

c_ 3.24 943

• 3.75 944

L 4.29 945

• 4.76 946

L 5.26 947

b 5.79 948

6.25 949

• 6.77 950

_.,' 7.22 951

• 7.79 952

_i 8.24 953

8.74 954

9.27 955

/

0

(a) Upper surface at x = 6 in.

Figure D4. Surface-pressure coefficient data for sharp wing with transition grit at M = 1.60 and R = 1 x 106 ft -1 for

run 43.

186
B

o

[]

<>

_,deg Point _,deg Point

0.23 937 _ 5.26 947

0.78 938 • 5.79 948

1.26 939 _ 6.25 949

1.78 940 • 6.77 950

2.29 941 o 7.22 951

2.79 942 • 7.79 952

3.24 943 0 8.24 953

3.75 944 t 8.74 954

4.29 945 _ 9.27 955

4.76 946

.05

.10

.15

Cp .2O

.25

.30

.35

.40

----------- •

A

"C5

-IllllJIIIIl_l,,,,I,,,,lllllllllll_,l_,,,I,,,,I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) Lower surface at x = 6 in.

Figure D4. Continued.

187
-.40 --

-.35

-.30 -

-.25 -

-.20 -

Cp -.15 -

-.10 -

-.05 -

0 -

.05 -

.10 --

.15

0

_,deg Point

c_ 0.23 937

• 0.78 938

[] 1.26 939

• 1.78 940

2.29 941

2.79 942

± 3.24 943

• 3.75 944

4.29 945

• 4.76 946

5.26 947

• 5.79 948

6.25 949

• 6.77 950

_ 7.22 951

• 7.79 952

¢, 8.24 953

t 8.74 954

9.27 955

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(c) Upper surface at x = 12 in.

Figure D4. Continued.

188
©

[]

A

_,deg Point _,deg Point

0.23 937 _ 5.26 947

0.78 938 h 5.79 948

1.26 939 _ 6.25 949

1.78 940 • 6.77 950

2.29 941 <_ 7.22 951

2.79 942 • 7.79 952

3.24 943 ¢ 8.24 953

3.75 944 O 8.74 954

4.29 945 _ 9.27 955

4.76 946

m

.05

.10

.15 --

Cp .20

.25 -

.30 -

.35

.40

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

1]

(d) Lower surface at x = 12 in.

Figure D4. Concluded.

189
Cp

-.40 -

-.35

-.30

-.25

-.20

-.15

-.10

-.05

0

.05

.10

.15

_,deg Point

o 0.28 965

• 0.75 966

[] 1.29 967

• 1.77 968

0 2.29 969

• 2.74 970

± 3.30 971

• 3.76 972

4.29 973

L 4.76 974

5.25 975

• 5.76 976

6.28 977

• 6.77 979

o 7.27 980

• 7.77 981

0 8.26 982

O 8.76 983

9.28 984

/

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(a) Upper surface at x = 6 in.

Figure D5. Surface-pressure coefficient data for sharp wing with transition grit at M = 1.60 and R = 2 × 106 ft -1 for

run 44.

190
[]

L_

_,deg Point _,deg Point

0.28 965 _ 5.25 975

0.75 966 • 5.76 976

1.29 967 _ 6.28 977

1.77 968 • 6.77 979

2.29 969 o 7.27 980

2.74 970 • 7.77 981

3.30 971 0 8.26 982

3.76 972 _ 8.76 983

4.29 973 _ 9.28 984

4.76 974

__

.05

.10 --

.15 -

Cp .2O -

.25

.30

.35

i

.40 ,,

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) Lower surface at x = 6 in.

Figure D5. Continued.

191
-.40 -

-.35 -

-.30 -

-.25 -

-.20 -

Cp -.15 --

-.10 --

-.05

0

.05

.10 -

.15

_, deg Point

© 0.28 965

• 0.75 966

[] 1.29 967

• 1.77 968

2.29 969

4, 2.74 970

E_ 3.30 971

• 3.76 972

i_ 4.29 973

• 4.76 974

5.25 975

• 5.76 976

cJ 6.28 977

• 6.77 979

,_ 7.27 980

• 7.77 981

_ 8.26 982

¢ 8.76 983

_ 9.28 984

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(c) Upper surface at x = 12 in.

Figure D5. Continued.

192
[]

A

_,deg Point _,deg Point

0.28 965 _ 5.25 975

0.75 966 • 5.76 976

1.29 967 _ 6.28 977

1.77 968 • 6.77 979

2.29 969 o 7.27 980

2.74 970 • 7.77 981

3.30 971 ¢, 8.26 982

3.76 972 O 8.76 983

4.29 973 _ 9.28 984

4.76 974

0

.05

.10

.15

Cp .2O

.25

.30

.35

!

.40

0

q

(d) Lower surface at x = 12 in.

Figure D5. Concluded.

193
-.45 --

Cp

-.40

-.35

-.30

-.25

-.20

-.15

-.10

-.05

0

.05

.10

.15

m

_, deg Point

_ 0.26

• 0.78

[] 1.28

2.30

3.24

4.25

5.29

6.24

'_ 7.26

0 8.30

9.29

986

987

988

989

990

0

,,,l,ll_llllllllLIlll,,I,,,,I,,,ilLlllllJlll''''l

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(a) Upper surface at x = 6 in.

Figure D6. Surface-pressure coefficient data for sharp wing with transition grit at M = 1.60 and R = 5 x 106 ft-I for

run 45.

194
__

.05

.10 --

.15 --

Cp .20 -

.25 -

.30

.35

.40

0

o_,deg Point

o 0.26 986

• 0.78 987

[] 1.28 988

? 2.30 989

3.24 990

4.25 991

5.29 993

6.24 994

o 7.26 995

<? 8.30 996

c_ 9.29 997

?-- A _O

L- 1__ 1__ _ _A

© -_ E3

_3

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure D6. Continued.

195
_,deg Point

o 0.26 986

• 0.78 987

[] 1.28 988

O. 2.30 989

£ 3.24 990

4.25 991

5.29 993

6.24 994

o 7.26 995

,3, 8.30 996

9.29 997

0

q

(c) Upper surface at x = 12 in.

Figure D6. Continued.

196
__

.05 --

.10 --

.15 -

Cp .20

.25

.30

.35

.40

_,deg Point

o 0.26 986

• 0.78 987

[] 1.28 988

2.30 989

3.24 990

L 4.25 991

5.29 993

6.24 994

o 7.26 995

0 8.30 996

9.29 997

-JJlllJllLliJlll''''l''''l''''lill ltJl,l,,,,I,,ILI

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(d) Lower surface at x = 12 in.

Figure D6. Concluded.

197
-.35 --

(z, deg Point

o 0.23 127

• 0.73 128

[] 1.23 129

• 1.70 130

2.17 131

2.68 132

3.19 133

• 3.71 134

4.18 136

• 4.67 137

5.21 138

• 5.70 139

6.24 140

• 6.68 141

4, 7.23 142

• 7.72 143

C, 8.18 144

8.69 146

c_ 9.23 147

©

0

(a) Upper surface at x = 6 in.

Figure DT. Surface-pressure coefficient data for elliptical wing without transition grit at M = 1.60 and R = 1 x 106 ft-n

for run 6.

198
__

.05 --

.10 -

.15 -

Cp .20 -

.25

L

.30 --

.35 --

.40

0

C)

[]

&

_, deg Point _, deg Point

0.23 127 _ 5.21 138

0.73 128 • 5.70 139

1.23 129 _ 6.24 140

1.70 130 • 6.68 141

2.17 131 o 7.23 142

2.68 132 • 7.72 143

3.19 133 _, 8.18 144

3.71 134 + 8.69 146

4.18 136 _ 9.23 147

4.67 137

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure D7. Continued.

199
Cp

e_,deg Point

o 0.23 127

• 0.73 128

[] 1.23 129

• 1.70 130

O 2.17 131

• 2.68 132

A 3.19 133

• 3.71 134

4.18 136

_, 4.67 137

L 5.21 138

• 5.70 139

u 6.24 140

• 6.68 141

_' 7.23 142

• 7.72 143

(' 8.18 144

8.69 146

C_ 9.23 147

(c) Upper surface at x = 12 in.

Figure DT. Continued.

2OO
[]

4

A

e_,deg Point _, deg Point

0.23 127 _ 5.21 138

0.73 128 • 5.70 139

1.23 129 _ 6.24 140

1.70 130 • 6.68 141

2.17 131 o 7.23 142

2.68 132 • 7.72 143

3.19 133 (> 8.18 144

3.71 134 _ 8.69 146

4.18 136 _ 9.23 147

4.67 137

q

(d) Lower surface atx = 12 in.

Figure DT. Concluded.

201
Cp

-.35 -

-.30

-.25

-.20

-.15

-.10

-.05

0

.05

.10

_, deg Point

o 0.19 157

• 0.71 158

[] 1.23 159

• 1.75 160

0 2.22 161

_I, 2.69 162

3.24 163

• 3.71 176

4.25 164

L 4.69 165

5.23 166

• 5.70 167

cJ 6.23 168

a 6.71 169

o 7.17 170

• 7.71 171

,7 8.18 172

$ 8.70 173

c_ 9.22 174

.15 ,, , , I , , , , I , , , , I, ,, , I , , , , I , , , , I, ,, , I , , , , I , , , , I , , , , I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(a) Upper surface at x = 6 in.

Figure D8. Surface-pressure coefficient data for elliptical wing without transition grit at M = 1.60 and R = 2 x 106 ft-l

for run 7.

202
0

[]

L

e_,deg Point _, deg Point

O.19 157 _ 5.23 166

0.71 158 • 5.70 167

1.23 159 6 6.23 168

1.75 160 • 6.71 169

2.22 161 ¢' 7.17 170

2.69 162 • 7.71 171

3.24 163 ¢ 8.18 172

3.71 176 t 8.70 173

4.25 164 _ 9.22 174

4.69 165

-q

(b) Lower surface at x = 6 in.

Figure D8. Continued.

2O3
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

.05

.10

.15

o_,deg Point

,3 0.19 157

• 0.71 158

[] 1.23 159

• 1.75 160

_ 2.22 161

2.69 162

± 3.24 163

• 3.71 176

4.25 164

• 4.69 165

5.23 166

• 5.70 167

cJ 6.23 168

a 6.71 169

_ 7.17 170

• 7.71 171

,_., 8.18 172

8.70 173

9.22 174

t

0

(c) Upper surface at x = 12 in.

Figure D8. Continued.

204
__

C_

[]

_, deg Point o_,deg Point

0.19 157 _ 5.23 166

0.71 158 h 5.70 167

1.23 159 c_ 6.23 168

1.75 160 m 6.71 169

2.22 161 _ 7.17 170

2.69 162 • 7.71 171

3.24 163 _ 8.18 172

3.71 176 _ 8.70 173

4.25 164 c_ 9.22 174

4.69 165

.05

.10

.15

Cp .20

.25

.30

.35

.40

L_

0

13

(d) Lower surface at x = 12 in.

Figure D8. Concluded.

205
Cp

-.35 --

-.30 -

-.25 -

-.20 -

-.15 -

-.10

-.05

0

.05

.10

.15

c_,deg Point

© 0.20 194

• 0.70 195

[] 1.21 196

• 1.72 197

<> 2.19 198

41, 2.70 199

3.19 200

• 3.73 201

4.19 202

• 4.70 203

5.22 204

• 5.74 205

6.23 206

• 6.72 207

,_, 7.21 208

• 7.73 209

¢, 8.21 210

$ 8.73 211

c_ 9.18 212

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

1]

(a) Upper surface at x = 6 in.

Figure D9. Surface-pressure coefficient data for e]]iptica] wing without transition _t at M -- ].60 and R = 3 x ]06 ft-!

for run 8.

206
©

[]

0

L_

_,deg Point _,deg Point

0.20 194 _ 5.22 204

0.70 195 • 5.74 205

1.21 196 _ 6.23 206

1.72 197 • 6.72 207

2.19 198 o 7.21 208

2.70 199 • 7.73 209

3.19 200 0 8.21 210

3.73 201 O 8.73 211

4.19 202 _ 9.18 212

4.70 203

__

.05

.10

.15

Cp .20

.25

.30

.35

.40

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure D9. Continued.

207
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

0

.05

.10

.15

(z, deg Point

o 0.20 194

• 0.70 195

[] 1.21 196

• 1.72 197

<> 2.19 198

2.70 199

A 3.19 200

• 3.73 201

4.19 202

• 4.70 203

L 5.22 204

• 5.74 205

6.23 206

• 6.72 207

o 7.21 208

• 7.73 209

0 8.21 210

8.73 211

9.18 212

ooeoooooo °e

(c) Upper surface at x = 12 in.

Figure D9. Continued.

208
o_,deg Point o_,deg Point

_:_ 0.20 194 _ 5.22 204

• 0.70 195 • 5.74 205

1.21 196 _ 6.23 206

• 1.72 197 • 6.72 207

2.19 198 _ 7.21 208

• 2.70 199 • 7.73 209

3.19 200 _ 8.21 210

• 3.73 201 $ 8.73 211

4.19 202 _ 9.18 212

• 4.70 203

q

(d) Lower surface at x = 12 in.

Figure D9. Concluded.

209
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

.05

.10

_,deg Point

© 0.25 222

• 0.73 223

[] 1.16 224

• 1.69 225

2.20 226

2.67 227

3.23 228

• 3.67 229

4.18 230

• 4.73 231

5.17 232

• 5.71 233

6.19 234

• 6.73 235

o 7.20 236

• 7.71 237

8.20 238

0 8.73 239

9.21 240

m

w

.15 i i i i I i i i i I i i i i l, , , , I _ i i J I i i I I I I I I I 11 I I , I , , , , I , , I, I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(a) Upper surface at x = 6 in.

Figure D10. Surface-pressure coefficient data for elliptical wing without transition grit at M = 1.60 and R = 4 x 106ft-I

for run 10.

210
C_)

[]

F_

o_,deg Point oc,deg Point

0.25 222 _ 5.17 232

0.73 223 • 5.71 233

1.16 224 c 6.19 234

1.69 225 • 6.73 235

2.20 226 © 7.20 236

2.67 227 • 7.71 237

3.23 228 _ 8.20 238

3.67 229 _ 8.73 239

4.18 230 _ 9.21 240

4.73 231

__

.05

.10

.15

Cp .20

.25

.30

.35

.40

0

(b) Lower surface at x = 6 in.

Figure D10. Continued.

211
-.40 --

-.35 -

-.30 -

-.25 --

-.20 --

p

Cp-.15 -

-.10 -

-.05

0

.05

.10

.15

cx, deg Point

c, 0.25 222

• 0.73 223

[] 1.16 224

• 1.69 225

2.20 226

<I, 2.67 227

3.23 228

• 3.67 229

L 4.18 230

• 4.73 231

r_ 5.17 232

• 5.71 233

6.19 234

• 6.73 235

'_, 7.20 236

• 7.71 237

',7 8.20 238

t 8.73 239

c_ 9.21 240

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(c) Upper surface at x = 12 in.

Figure DI0. Continued.

212
__

C)

[]

±

oc,deg Point o_,deg Point

0.25 222 L 5.17 232

0.73 223 • 5.71 233

1.16 224 _ 6.19 234

1.69 225 • 6.73 235

2.20 226 o 7.20 236

2.67 227 • 7.71 237

3.23 228 0 8.20 238

3.67 229 t 8.73 239

4.18 230 _ 9.21 240

4.73 231

.05

.10

.15

Cp .2O

.25

.30

.35

.4O

0

(d) Lower surface at x = 12 in.

Figure D10. Concluded.

213
-.40 --

-.35 --

-.30

-.25

-.20

Cp -.15 -

-.10 -

-.05 -

0 -

.05

.10

.15

_,deg Point

© 0.22 271

• 0.67 272

[] 1.21 273

• 1.67 274

2.18 275

2.68 276

3.18 277

• 3.74 278

4.24 279

• 4.65 280

5.19 281

• 5.70 282

6.22 283

• 6.75 284

,_ 7.16 285

• 7.71 286

8.21 287

t 8.70 288

9.22 289

re-<> <>

/

-LIII! j,,,I,,,,l_,_lll iI I_t Jllllllll III I,,,,I,,,_1

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(a) Upper surfaceat x = 6 in.

Figure D! ]. Surface-pressure coefficient data for ¢l|iptica] wing without transitiongrit at M = ].60 and R = 5 x ]06 ft-1

for run 14.

214
0

.05

.10

.15

Cp .20

.25

.30

.35

.40

_,deg Point

o 0.22 271

• 0.67 272

[] 1.21 273

• 1.67 274

2.18 275

2.68 276

3.18 277

• 3.74 278

4.24 279

• 4.65 280

_,deg Point

5.19 281

• 5.70 282

a 6.22 283

• 6.75 284

7.16 285

• 7.71 286

8.21 287

I 8.70 288

9.22 289

0

11

(b) Lower surface at x = 6 in.

Figure D1 l. Continued.

215
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

0

.05

.10

.15

_,deg Point

© 0.22 271

• 0.67 272

[] 1.21 273

• 1.67 274

2.18 275

2.68 276

c 3.18 277

• 3.74 278

4.24 279

L 4.65 280

5.19 281

• 5.70 282

6.22 283

• 6.75 284

7.16 285

• 7.71 286

8.21 287

t 8.70 288

9.22 289

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(c) Upper surface atx = 12 in.

Figure DI 1. Continued.

216
O m

o_, deg Point _, deg Point

,_ 0.22 271 _ 5.19 281

• 0.67 272 • 5.70 282

[] 1.21 273 _ 6.22 283

• 1.67 274 • 6.75 284

#_> 2.18 275 o 7.16 285

2.68 276 • 7.71 286

3.18 277 0 8.21 287

• 3.74 278 O 8.70 288

L 4.24 279 _ 9.22 289

• 4.65 280

.05

.10

.15

Cp .20

.25

.30

.35

.40

0

13

(d) Lower surface at x = 12 in.

Figure D11. Concluded.

217
Cp

-.35 --

-.30

-.25

-.20

-.15

-.10

-.05 -

0 -

.o5

.10 -

.15

o_,deg Point

c_ 0.20 408

• 0.71 409

[] 1.19 410

• 1.69 411

<_ 2.21 412

• 2.71 413

A 3.24 414

• 3.65 415

4.22 416

• 4.72 417

5.19 418

h 5.71 419

c_ 6.24 420

• 6.74 421

_ 7.16 422

• 7.70 423

,_'., 8.22 424

t 8.73 425

c_ 9.18 426

/

,,,IL,,ijlLltll,,,,l,,,,l_,_l,llll,ll,ll_l,l,,,,I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(a) Upper surface at x = 6 in.

Figure DI2. Surface-pressure coefficient data for elliptical wing with transition grit at M = 1.60 and R = l x 106 ft-l for

run 22.

218
0

[]

(_, deg Point (_, deg Point

0.20 408 _ 5.19 418

0.71 409 • 5.71 419

1.1 9 410 c_ 6.24 420

1.69 411 • 6.74 421

2.21 412 o 7.16 422

2.71 413 • 7.70 423

3.24 414 ¢ 8.22 424

3.65 415 i 8.73 425

4.22 416 (_ 9.18 426

4.72 417

0

.05

.10

.15

Cp .20

.25

.30

.35

.40

0 •1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

1]

(b) Lower surface at x = 6 in.

Figure D12. Continued.

219
Cp

-.35 -

-.30 -

-.25 -

-.20 -

-.15 -

-.10 -

-.05 -

0 -

.05 --

.10 --

.15

(z, deg Point

,3 0.20 408

• 0.71 409

[] 1.19 410

• 1.69 411

2.21 412

_I, 2.71 413

± 3.24 414

• 3.65 415

4.22 416

• 4.72 417

5.19 418

h 5.71 419

6.24 420

• 6.74 421

_ 7.16 422

• 7.70 423

_ 8.22 424

o 8.73 425

c_ 9.18 426

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(c) Upper surface atx = 12 in.

Figure D12. Continued.

220
[]

A

r_

co,deg Point c_,deg Point

0.20 408 _ 5.19 418

0.71 409 • 5.71 419

1.19 410 _ 6.24 420

1.69 411 • 6.74 421

2.21 412 o 7.16 422

2.71 413 • 7.70 423

3.24 414 _ 8.22 424

3.65 415 # 8.73 425

4.22 416 _ 9.18 426

4.72 417

TI

(d) Lower surface at x = 12 in.

Figure D 12. Concluded.

221
Cp

-.35 --

-.30 --

-.25 -

-.20

-.15 -

-.10 -

-.05 -

o -

.o5

.10

.15

e_,deg Point

_, 0.22 454

• 0.71 455

[] 1.22 456

• 1.74 457

2.22 458

• 2.69 459

3.20 460

• 3.71 461

L 4.18 462

• 4.69 463

5.21 464

• 5.71 465

L_ 6.21 466

a 6.74 467

_ 7.16 468

• 7.69 469

_', 8.20 470

8.72 471

c_ 9.20 472

m

B

m

-FIIIII

0 .1

IhL[I,,,t,,_,l,lLIlIJ_Ll',,'l'''_l''_ll''''l

.2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(a) Upper surface at x = 6 in.

Figure D13. Surface-pressure coefficient data for elliptical wing with transition grit at M = 1.60 and R = 2 x 106 ft-1 for

run 25.

222
0

.05

.10

.15

Cp .20

.25

.30

.35

.40

0

[]

A

_,deg Point _,deg Point

0.22 454 _ 5.21 464

0.71 455 • 5.71 465

1.22 456 c 6.21 466

1.74 457 • 6.74 467

2.22 458 o 7.16 468

2.69 459 • 7.69 469

3.20 460 ¢ 8.20 470

3.71 461 t 8.72 471

4.18 462 _ 9.20 472

4.69 463

b

0

q

(b) Lower surface at x = 6 in.

Figure DI 3. Continued.

223
-.40 -

-.35

-.30

-.25

-.20

Cp -.15

-.10

-.05

0

.05

.10

.15

(x, deg Point

¢_ 0.22 454

• 0.71 455

[] 1.22 456

• 1.74 457

<_ 2.22 458

4 2.69 459

,_ 3.20 460

• 3.71 461

4.18 462

• 4.69 463

L 5.21 464

• 5.71 465

6.21 466

• 6.74 467

¢_ 7.16 468

• 7.69 469

¢' 8.20 470

# 8.72 471

c_ 9.20 472

0

(c) Upper surface at x = 12 in.

Figure D13. Continued.

224
__

.05 -

.10 -

.15

Cp .20

.25

L

.30 --

.35 -

.40

0

[]

_,deg Point _,deg Point

0.22 454 _ 5.21 464

0.71 455 • 5.71 465

1.22 456 _ 6.21 466

1.74 457 • 6.74 467

2.22 458 Q 7.16 468

2.69 459 • 7.69 469

3.20 460 ¢ 8.20 470

3.71 461 i 8.72 471

4.18 462 _ 9.20 472

4.69 463

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(d) Lower surface at x = 12 in.

Figure DI3. Concluded.

225
Cp

-.35 -

-.30

-.25

-.20

-.15

-.10

-.05

0

.05

.10

.15

_,deg Point

© 0.22 492

• 0.74 493

[] 1.21 494

• 1.74 495

2.21 496

• 2.69 497

3.23 498

• 3.71 499

4.25 500

• 4.71 501

5.21 502

• 5.73 503

6.23 504

• 6.69 505

o 7.23 506

• 7.73 507

_ 8.22 508

i 8.69 509

9.24 510

/ /i_i-i"

/ /

0

(a) Upper surface at x = 6 in.

Figure D14. Surface-pressure coefficient data for elliptical wing with transition grit at M = 1.60 and R = 3 x 106 ft-I for

run 28.

226
0

[]

<>

S

L

a, deg Point _,deg Point

0.22 492 _ 5.21 502

0.74 493 • 5.73 503

1.21 494 _ 6.23 504

1.74 495 • 6.69 505

2.21 496 © 7.23 506

2.69 497 • 7.73 507

3.23 498 C_ 8.22 508

3.71 499 + 8.69 509

4.25 500 _ 9.24 510

4.71 501

__

.05

.10

.15

Cp .20

.25

.30

.35

.40

0

b

•1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure DI4. Continued.

227
-.40 --

-.35

-.30

-.25

-.20

-.10

-.05

0

.05

.10

.15

o_,deg Point

_:_ 0.22 492

• 0.74 493

[] 1.21 494

• 1.74 495

<3 2.21 496

4, 2.69 497

3.23 498

• 3.71 499

4.25 500

• 4.71 501

5.21 502

• 5.73 503

6.23 504

m 6.69 505

_ 7.23 506

• 7.73 507

:_ 8.22 508

# 8.69 509

_ 9.24 510

[]

0

(c) Upper surface at x = 12 in.

Figure D 14. Continued.

228
.05 --

.10 --

.15 -

Cp .2O -

.25 -

.30

.35 --

.40

0

C'

[]

_,deg Point _,deg Point

0.22 492 _ 5.21 502

0.74 493 • 5.73 503

1.21 494 _ 6.23 504

1.74 495 • 6.69 505

2.21 496 o 7.23 506

2.69 497 • 7.73 507

3.23 498 _ 8.22 508

3.71 499 _ 8.69 509

4.25 500 _ 9.24 510

4.71 501

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(d) Lower surface at x = 12 in.

Figure D! 4. Concluded.

229
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

0

.05

.10

.15

_, deg Point

c, O.16 570

• 0.75 571

[] 1.17 572

• 1.73 573

2.23 574

41, 2.76 575

3.26 576

• 3.66 577

4.27 578

• 4.70 588

5.20 579

• 5.76 580

6.20 581

• 6.65 582

7.25 583

• 7.71 584

¢ 8.25 585

O 8.74 586

c_ 9.23 587

k

0

(a) Upper surface at x = 6 in.

Figure DI5. Surface-pressure coefficient data for elliptical wing with transition grit at M = 1.60 and R = 4 × 106 ft-] for

run 32.

230
__

.05 -

.10

.15

Cp .20

.25 --

.30 -

.35 -

.40

[]

t

(_, deg Point c_,deg Point

O.16 570 _ 5.20 579

0.75 571 • 5.76 580

1.17 572 c_ 6.20 581

1.73 573 • 6.65 582

2.23 574 o 7.25 583

2.76 575 • 7.71 584

3.26 576 _., 8.25 585

3.66 577 + 8.74 586

4.27 578 _ 9.23 587

4.70 588

O

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure D 15. Continued.

231
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

0

.05

.10

.15

ec,deg

0.16

0.75

1.17

1.73

2.23

2.76

3.26

3.66

4.27

4.70

5.20

5.76

6.20

6.65

7.25

7.71

8.25

8.74

9.23

Point

570

571

572

573

574

575

576

577

578

588

579

580

581

582

583

584

585

586

587

/

[]

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(c) Upper surface at x = 12 in.

Figure D 15. Continued.

232
C)

[]

A

_,deg Point _,deg Point

0.16 570 h 5.20 579

0.75 571 h 5.76 580

1.17 572 _ 6.20 581

1.73 573 • 6.65 582

2.23 574 o 7.25 583

2.76 575 • 7.71 584

3.26 576 ¢ 8.25 585

3.66 577 t 8.74 586

4.27 578 _ 9.23 587

4.70 588

q

(d) Lower surface at x = 12 in.

Figure D 15. Concluded.

233
-.40 --

-.35 --

-.30 -

-.25

-.20

Cp -.15 -

-.10 -

-.05

0

.05

.10

.15

0

(z, deg Point

o 0.22 524

• 0.70 525

[] 1.20 526

• 1.71 527

2.17 528

41, 2.72 529

3.20 530

• 3.70 531

4.15 532

• 4.68 533

5.18 534

• 5.65 535

cJ 6.18 536

• 6.75 537

_ 7.20 538

• 7.69 539

¢, 8.23 540

t 8.75 541

c_ 9.25 542

/

, lI,Lll[lll ll,,,I,,LIl,,t lllL'llllllLLl'l''L'l

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(a) Upper surface at x = 6 in.

Figure D16. Surface-pressure coefficient data for elliptical wing with transition grit at M = 1.60 and R = 5 x 106it-] for

run 29.

234
[]

t

A

_,deg Point _,deg Point

0.22 524 _ 5.18 534

0.70 525 • 5.65 535

1.20 526 _ 6.18 536

1.71 527 • 6.75 537

2.17 528 o 7.20 538

2.72 529 • 7.69 539

3.20 530 _ 8.23 540

3.70 531 _ 8.75 541

4.15 532 _ 9.25 542

4.68 533

(b) Lower surface at x = 6 in.

Figure D16. Continued.

235
-.40 -

-.35

-.30

-.25

-.20

-.10

-.05

0

.05

.10

.15

_,deg Point

¢_ 0.22 524

• 0.70 525

[] 1.20 526

• 1.71 527

2.17 528

2.72 529

3.20 530

• 3.70 531

4.15 532

• 4.68 533

5.18 534

• 5.65 535

6.18 536

• 6.75 537

*_ 7.20 538

• 7.69 539

C_ 8.23 540

t 8.75 541

9.25 542

[]

0

(c) Upper surface at x = 12 in.

Figure D16. Continued.

236
__

.05 --

.10 --

.15 -

Cp .20

.25

.30

.35

.40

C)

±

_,deg Point _,deg Point

0.22 524 _ 5.18 534

0.70 525 h 5.65 535

1.20 526 _ 6.18 536

1.71 527 a 6.75 537

2.17 528 o 7.20 538

2.72 529 • 7.69 539

3.20 530 ¢ 8.23 540

3.70 531 t 8.75 541

4.15 532 _ 9.25 542

4.68 533

-,,,, I, till I, I, I_,_, I,,,, I, i, j I i iLll j,,, I,,,, I,,,, I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(d) Lower surface at x = 12 in.

Figure DI 6. Concluded.

237
Cp

-.35 -

-.30

-.25

-.20

-.15

-.10

-.05

0

.05

.10

.15

_, deg Point

o 0.21 683

• 0.69 684

[] 1.18 685

• 1.70 686

© 2.18 687

t 2.71 688

± 3.19 689

• 3.70 690

4.21 691

• 4.69 692

5.20 693

• 5.69 694

_ 6.21 695

• 6.71 696

7.19 697

• 7.72 698

_;, 8.21 699

t 8.69 700

_ 9.21 701

/

/

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

TI

(a) Upper surface at x = 6 in.

Figure DI?. Surface-pressure coefficient data for cambered wing without transition grit at M= 1.60 and

R= ! x 106ft -I for run 36.

238
.05 --

.10 --

.15

Cp .20 -

.25 -

.30

.35

.40

C)

A

c_,deg Point e_,deg Point

0.21 683 _ 5.20 693

0.69 684 • 5.69 694

1.18 685 _ 6.21 695

1.70 686 • 6.71 696

2.18 687 o 7.19 697

2.71 688 • 7.72 698

3.19 689 _'>{' 8.21 699

3.70 690 _ 8.69 700

4.21 691 c_ 9.21 701

4.69 692

0 _ G " Ik

,q,. OC' p\ I

-I.\¢\ o

0 •1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(b) Lower surface at x = 6 in.

Figure D17. Continued.

239
Cp

-.35 --

_, deg Point

o 0.21 683

• 0.69 684

[] 1.18 685

• 1.70 686

<_ 2.18 687

41, 2.71 688

3.19 689

• 3.70 690

4.21 691

• 4.69 692

5.20 693

h 5.69 694

c_ 6.21 695

• 6.71 696

7.19 697

• 7.72 698

_, 8.21 699

$ 8.69 700

9.21 701

0

(c) Upper surface at x = 12 in.

Figure DIT. Continued.

24O
[]

A

_,deg

0.21

0.69

1.18

1.70

2.18

2.71

3.19

3.70

4.21

4.69

Point

683

684

685

686

687

688

689

690

691

692

_,deg Point

5.20 693

• 5.69 694

6.21 695

• 6.71 696

o 7.19 697

• 7.72 698

0 8.21 699

8.69 700

9.21 701

__

.05

0

(d) Lower surface at x = 12 in.

Figure D17. Concluded.

241
Cp

-.35 --

-.30 --

-.25

-.20

-.15

-.10

-.05

o

.05

.10

.15

0

_,deg Point

c, 0.21 629

• 0.74 630

[] 1.19 631

• 1.74 632

2.18 633

2.71 634

3.18 635

• 3.72 636

4.18 637

• 4.68 638

L 5.17 639

h 5.68 640

6.17 641

• 6.68 642

o 7.18 643

• 7.67 644

¢ 8.17 645

8.70 646

9.23 647

/

IIIIIIIIIIILL,I,,,,I,,,,I,,,,I,,,,I,,,,I,,,,I,,,,I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

T!

(a) Upper surface at x = 6 in.

Figure D18. Surface-pressure coefficient data for cambered wing without transition grit at M= 1.60 and

R = 2 x 106 ft-1 for run 34.

242
Cp

-.05

0

.05

.10

.15

.20

.25

.30

.35

.40

m

b

0

0

[]

A

L

_,deg Point _,deg Point

0.21 629 L 5.17 639

0.74 630 • 5.68 640

1.19 631 a 6.17 641

1.74 632 • 6.68 642

2.18 633 o 7.18 643

2.71 634 • 7.67 644

3.18 635 0 8.17 645

3.72 636 _ 8.70 646

4.18 637 _ 9.23 647

4.68 638

(

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) Lower surface at x = 6 in.

Figure D18. Continued.

243
Cp

-.35 -

-.30

-.25

_, deg Point

,_ 0.21 629

• 0.74 630

[] 1.19 631

• 1.74 632

_> 2.18 633

¢, 2.71 634

3.18 635

• 3.72 636

4.18 637

• 4.68 638

5.17 639

• 5.68 640

_J 6.17 641

• 6.68 642

7.18 643

• 7.67 644

'._ 8.17 645

t 8.70 646

c_ 9.23 647

0

q

(c) Upper surface at x = 12 in.

Figure DI 8. Continued.

244
Cp

-.05

0

.05

.10

.15

.20

.25

.30

.35

.40

t

b

w

o_,deg Point (_, deg Point

c, 0.21 629 _ 5.17 639

• 0.74 630 • 5.68 640

[] 1.19 631 _ 6.17 641

• 1.74 632 • 6.68 642

_ 2.18 633 o 7.18 643

4, 2.71 634 • 7.67 644

± 3.18 635 _ 8.17 645

• 3.72 636 _ 8.70 646

4.18 637 _ 9.23 647

• 4.68 638

--I I I I J I I 1 L l 1 I I I I I I I I I I I I I I I I I I 1 I I I 1 ] I I I I I _ I I I l I i I i I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(d) Lower surface at x = 12 in.

Figure D 18. Concluded.

245
-.35 --

_,deg Point

© 0.23 659

• 0.68 660

[] 1.21 661

• 1.73 662

2.21 663

2.69 664

± 3.21 665

• 3.69 666

4.20 667

• 4.68 668

L 5.19 669

• 5.71 670

6.21 671

• 6.70 672

_ 7.20 673

• 7.71 674

_ 8.22 675

8.69 676

9.22 677

/

1⁄2

/

(a) Upper surface at x = 6 in.

Figure DI9. Surface-pressure coefficient data for cambered wing without transition grit at M--1.60 and

R = 5 x 106 ft-1 for run 35.

246
Cp

-.05 --

0 --

.05 -

.10

.15

.20 --

.25 --

.30 -

.35 -

.40

_,deg Point

¢_ 0.23 659

• 0.68 660

[] 1.21 661

• 1.73 662

'_ 2.21 663

2.69 664

± 3.21 665

• 3.69 666

h 4.20 667

• 4.68 668

_,deg Point

5.19 669

• 5.71 670

6.21 671

• 6.70 672

7.20 673

• 7.71 674

,_ 8.22 675

$ 8.69 676

9.22 677

©

0

''''l'llllt,,,l_,,,lIKill_l,jl,,I,l,_l_,llI,Jl,I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(b) Lower surface at x = 6 in.

Figure DI9. Continued.

247
Cp

-.35 --

-.30 -

-.25 -

-.20 -

-.15 -

-.10 -

-.05 -

0 -

.05

.10 -

.15

_,deg Point

c_ 0.23 659

• 0.68 660

[] 1.21 661

• 1.73 662

2.21 663

• 2.69 664

3.21 665

• 3.69 666

4.20 667

• 4.68 668

L 5.19 669

h 5.71 670

6.21 671

• 6.70 672

o 7.20 673

• 7.71 674

,i_ 8.22 675

# 8.69 676

9.22 677

k

1⁄2

(c) Upper surface at x = 12 in.

Figure D 19. Continued.

248
Cp

-.05 -

0

.05 --

.10 --

.15 --

.20 -

.25 -

.30

.35

.40

0

C_

_,deg

0.23

0.68

1.21

1.73

2.21

2.69

3.21

3.69

4.20

4.68

Point

659

660

661

662

663

664

665

666

667

668

D

0

C_

_,deg

5.19

5.71

6.21

6.70

7.20

7.71

8.22

8.69

9.22

Point

669

670

671

672

673

674

675

676

677

i

J_

i

©.

9-

0

,,,,J,,,,I,ii,ll,,,l,,,,I,,,,I,,,,l,,,,l,,,jll,,,I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(d) Lower surface at x = 12 in.

Figure DI 9. Concluded.

249
-.30 -

-.25

-.20

-.15

Cp -.10

-.05

0

.05

.10

.15

(_, deg Point

o 0.18 716

• 0.72 717

[] 1.20 718

• 1.70 719

0 2.21 720

41, 2.72 721

3.20 722

• 3.72 723

4.21 724

• 4.69 725

5.20 726

h 5.70 727

a 6.19 728

• 6.69 729

o 7.24 730

• 7.68 731

0 8.23 732

O 8.70 733

c_ 9.23 734

/

/

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(a) Upper surface at x = 6 in.

Figure D20. Surface-pressure coefficient data for cambered wing with transition grit at M = 1.60 and R = l x 106 ft -1

for run 37.

250
Cp

-.10 -

-.05

0

.05 --

.10 --

.15 -

.20 -

.25 -

.30

.35

.40 i J

0

C_

[]

4'

(z, deg Point o_,deg Point

0.18 716 _ 5.20 726

0.72 717 • 5.70 727

1.20 718 cJ 6.19 728

1.70 719 • 6.69 729

2.21 720 o 7.24 730

2.72 721 • 7.68 731

3.20 722 ¢ 8.23 732

3.72 723 $ 8.70 733

4.21 724 _ 9.23 734

4.69 725

©

q

(b) Lower surface at x = 6 in.

Figure D20. Continued.

251
Cp

-.35 -

-.30

-.25

-.2o

-.15

-.lO

-.05

o

.05

.10

.15

oc,deg Point

'::, O.18 716

• 0.72 717

[] 1.20 718

• 1.70 719

2.21 720

4, 2.72 721

3.20 722

• 3.72 723

4.21 724

• 4.69 725

5.20 726

• 5.70 727

6.19 728

• 6.69 729

7.24 730

• 7.68 731

¢ 8.23 732

l 8.70 733

c_ 9.23 734

/

1⁄2

[]

%

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(c) Upper surface at x = 12 in.

Figure D20. Continued.

252
-.05 --

oc,deg Point

c, 0.18 716

• 0.72 717

[] 1.20 718

• 1.70 719

2.21 720

,_ 2.72 721

A 3.20 722

• 3.72 723

L 4.21 724

• 4.69 725

o_,deg Point

r_ 5.20 726

• 5.70 727

6.19 728

• 6.69 729

o 7.24 730

• 7.68 731

:_ 8.23 732

O 8.70 733

c_ 9.23 734

©

11

(d) Lower surface at x = 12 in.

Figure D20. Concluded.

253
Cp

-.35 -

-.30 -

-.25 -

-.20 -

-.15 -

-.10 -

-.05 -

0 -

.05

.10 -

.15

_,deg Point

o 0.20 740

• 0.72 741

[] 1.19 742

• 1.68 743

2.21 744

2.69 745

A 3.21 746

• 3.69 747

4.21 748

• 4.70 749

5.21 750

• 5.71 751

D 6.19 752

• 6.72 753

,_ 7.22 754

• 7.72 755

.3 8.25 756

0 8.70 757

9.23 758

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(a) Upper surface at x = 6 in.

Figure D2I. Surface-pressure coefficient data for cambered wing with transition grit at M = 1.60 and R = 2 x 106 ft-1

for run 38.

254
Cp

_,deg Point _,deg Point

0.20 740 L 5.21 750

0.72 741 • 5.71 751

1.19 742 _ 6.19 752

1.68 743 • 6.72 753

2.21 744 o 7.22 754

2.69 745 • 7.72 755

3.21 746 _ 8.25 756

3.69 747 t 8.70 757

4.21 748 _ 9.23 758

4.70 749

q

(b) Lower surface at x = 6 in.

Figure D2I. Continued.

255
Cp

o_,deg

0.20

0.72

1.19

1.68

2.21

2.69

3.21

3.69

4.21

4.70

5.21

5.71

6.19

6.72

7.22

7.72

8.25

8.70

9.23

Point

740

741

742

743

744

745

746

747

748

749

750

751

752

753

754

755

756

757

758

[]

©

(c) Upper surface at x = 12 in.

Figure D21. Continued.

256
-.05 -

0

.05

.10

Cp .15 --

.20 --

.25 -

.30

.35

.40

0

CI

[]

±

c_,deg Point

0.20 740

0.72 741

1.19 742

1.68 743

2.21 744

2.69 745

3.21 746

3.69 747

4.21 748

4.70 749

e_, deg Point

6 5.21 750

• 5.71 751

a 6.19 752

m 6.72 753

<_ 7.22 754

• 7.72 755

¢_ 8.25 756

8.70 757

9.23 758

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(d) Lower surface at x = 12 in.

Figure D21. Concluded.

257
Cp

-.35

-.30

-.25

-.20

-.15

-.10

o_,deg Point

o O.18 760

• 0.70 761

[] 1.16 762

• 1.72 763

<_ 2.21 764

• 2.74 765

3.21 766

• 3.69 767

4.21 768

• 4.73 769

5.22 770

• 5.72 771

cJ 6.23 772

• 6.69 773

_ 7.25 774

• 7.70 775

_ 8.21 776

$ 8.71 777

c_ 9.18 778

-.05

0

.05

.10

\

.15

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(a) Upper surface at x = 6 in.

Figure D22. Surface-pressure coefficient data for cambered wing with transition grit at M = 1.60 and R = 5 x 106 ft -1

for run 39.

258
Cp

-.10

-.05

0

.05

.10

.15

.20

.25

.30

.35

.40

e_,deg Point

© 0.18 760

• 0.70 761

[] 1.16 762

• 1.72 763

2.21 764

4, 2.74 765

A 3.21 766

• 3.69 767

4.21 768

• 4.73 769

_,deg Point

6 5.22 770

• 5.72 771

6.23 772

• 6.69 773

o 7.25 774

• 7.70 775

8.21 776

8.71 777

9.18 778

I

D

m

©

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

11

(b) Lower surface at x = 6 in.

Figure D22. Continued.

259
Cp

-.35 --

-.30 _-

-.25

L

r-

-.20

-.15

-.10

-.05

0

.05

.10

.15

_, deg Point

_ O.18 760

• 0.70 761

[] 1.16 762

• 1.72 763

2.21 764

2.74 765

3.21 766

• 3.69 767

4.21 768

• 4.73 769

5.22 770

• 5.72 771

_ 6.23 772

• 6.69 773

_ 7.25 774

• 7.70 775

8.21 776

8.71 777

_ 9.18 778

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

(c) Upper surface at x = 12 in.

Figure D22. Continued.

260
-.05 -

0

.05 --

.10 b

Cp .15

.20 -

.25 -

.30

.35

.40

0

(z, deg Point

o O.18 760

• 0.70 761

[] 1.16 762

• 1.72 763

0 2.21 764

2.74 765

± 3.21 766

• 3.69 767

4.21 768

• 4.73 769

LG

A

I

0

t

o_,deg Point

5.22 770

• 5.72 771

6.23 772

• 6.69 773

o 7.25 774

• 7.70 775

0 8.21 776

8.71 777

a 9.18 778

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

q

(d) Lower surface at x = 12 in.

Figure D22. Concluded.

261
References

1. Stanbrook, A.; and Squire, L. C.: Possible Types of Flow

at Swept Leading Edges. Aeronaut. Q., vol. XV, pt. 1,

Feb. 1964, pp. 72-82.

2. Whitehead, A. H.: Lee-Surface Vortex Effects Over Configurations in Hypersonic Flow. AIAA-72-77, 1972.

3. Szodruch, Joachim; and Ganzer, Uwe: On the Lee-Side Flow

Over Delta Wings at High Angle of Attack. High Angle of

Attack Aerodynamics, AGARD-CP-247, 1979, pp. 21-1-21-7.

4. Szodrucb, Joachim: Lee Side Flow for Slender Delta Wings of

Finite Thickness. NASA TM-75753, 1980.

5. Miller, David S.; and Wood, Richard M.: Lee-Side Flow Over

Delta Wings at Supersonic Speeds. NASA TP-2430, 1985.

6. Seshadri, S. N.; and Narayan, K. Y.: Lee-Surface Flow Over

Delta Wings at Supersonic Speeds. TM AE 8610, National

Aeronautical Lab. (Bangalore, India), Sept. 1986.

7. Covell, Peter F.; and Wesselmann, Gary E: Flow-Field Characteristics and Normal-Force Correlations for Delta Wings

From Mach 2.4 to 4.6. AIAA-89-0026, Jan. 1989.

8. Szodruch, Joachim G.: Leeward Flow Over Delta Wings at

Supersonic Speeds. NASA TM-81187, 1980.

9. Jackson, C. M., Jr.: Description and Calibration of the

Langley Unitary Plan Wind Tunnel. NASA TP-1905, 1981.

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

for Determination of Critical Height of Distributed Roughness

Particles for Boundary-Layer Transition at Mach Numbers

From 0 to 5. NACA TN-4363, 1958.

11. Braslow, Albert L.; Hicks, Raymond M.; and Harris,

Roy V., Jr.: Use of Grit-Type Boundary-Layer-Transition Trips

on Wind-Tunnel Models. NASA TN D-3579, 1966.

12. Stallings, Robert L., Jr.; and Lamb, Milton: Effects of Roughness Size on the Position of Boundary-Layer Transition and on

the Aerodynamic Characteristics of a 55 ° Swept Delta Wing at

Supersonic Speeds. NASA TP- 1027, !977.

13. McMillin, S. N.; Pittman, James L.; and Thomas, James L.:

Computational Study of Incipient Leading-Edge Separation on

a Supersonic Delta Wing. J. Aircr. vol. 29, Mar.-Apr. 1992,

pp. 203-209.

14. Gray, G. W., ed.: Thermotropic Liquid Crystals. Critical

Reports on Applied Chemistry, Volume 22, John Wiley &

Sons, Inc., 1987.

15. Holmes, Bruce J.; Gall, Peter D., Croom, Cynthia C.; Manuel,

Gregory S.; and Kelliher, Warren C.: A New Method for Laminar Boundary Layer Transition Visualization in Flight--Color

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16. Parrnar, D. S.; Singh, Jag J.; and Eftekhari, Abe: A Shear Sensitive Monomer-Polymer Liquid Crystal System for Wind

Tunnel Applications. Rev. Sci. Inst. vol. 63, Jan. 1992,

pp. 225-229.

17. Ireland, P. T.; and Jones, T. V.: Response Time of a Surface Thermometer Employing Encapsulated Thermochromic

Liquid Crystals. J. Phys. E: Sci. lnstrum., vol. 20, no. 10,

Oct. 1987, pp. 1195-1199.

18. Schlichting, Hermann (J. Kestin, transl.): Boundary-Layer

Theory. Seventh ed., McGraw-Hill Book Co., 1979.

19. McMillin, S. Naomi; Thomas, James L.; and Murman,

Earll M.: Navier-Stokes and Euler Solutions for Lee-Side

Flows Over Supersonic Delta Wings--A Correlation With

Experiment. NASA TP-3035, 1990.

20. Cromartie, Robert C.; Johnston, R. Eugene; Pizer, Stephen M.;

and Rogers, Diane: Standardization of Electronic Display

Devices Based on Human Perception. TR88-002, Univ. of

North Carolina, 1988.

21. Johnston, R. E.; Zimmerman, J. B.; Rogers, D. C.; and Pizer,

S.M.: Preceptual Standardization. SPIE, vol. 236, 1985,

pp. 44-50.

22. Pizer, S. M.; Johnsont, R. E.; Zimmerman, J. B.; and Chan,

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A. J. Duerinckx, ed., SPIE, voi. 318, Jan. 1982, pp. 223-230.

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Printing on Limited Color Output Devices. Comput. & Graph.,

vol. 15, no. 4, 1991, pp. 561-567,

24. Pearson, D. E.: Transmission and Display of Pictorial Information. John Wiley & Sons, Inc., 1975.

262

FormAoprov_

REPORT DOCUMENTATION PAGE OMBNo.0704-0188

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

December 1996 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Surface-Pressure and Flow-Visualization Data at Mach Number of 1.60

for Three 65 ° Delta Wings Varying in Leading-Edge Radius and Camber WU 505-59-53-05

6. AUTHOR(S)

S. Naomi McMillin, James E. Byrd, Devendra S. Parmar,

Gaudy M. Bezos-O'Connor, Dana K. Forrest, and Susan Bowen

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS{ES)

NASA Langley Research Center

Hampton, VA 23681-0001

9. SPONSORING/MONITORINGAENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

8. PERFORMING ORGANIZATION

REPORT NUMBER

L-17443

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4673

11.SUPPLEMENTARYNOTES

McMillin, Bezos-O'Connor, and Forrest: Langley Research Center, Hampton, VA; Byrd: Lockheed Engineering &

Sciences Company, Hampton, VA; Parmar: Old Dominion University, Norfolk, VA; Bowen: Computer Sciences

Corporation, Hampton, VA.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 02

Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

An experimental investigation of the effect of leading-edge radius, camber, Reynolds number, and boundary-layer

state on the incipient separation of a delta wing at supersonic speeds was conducted at the Langley Unitary Plan

Wind Tunnel at Mach number of 1.60 over a free-stream Reynolds number range of 1 x 106 to 5 x 106 ft-1. The

three delta wing models examined had a 65 ° swept leading edge and varied in cross-sectional shape: a sharp wedge,

a 20:1 ellipse, and a 20:1 ellipse with a -9.750 circular camber imposed across the span. The wings were tested

with and without transition grit applied. Surface-pressure coefficient data and flow-visualization data are electronically stored on a CD-ROM. The data indicated that by rounding the wing leading edge or cambering the wing in the

spanwise direction, the onset of leading-edge separation on a delta wing can be raised to a higher angle of attack

than that observed on a sharp-edged delta wing. The data also showed that the onset of leading-edge separation can

be raised to a higher angle of attack by forcing boundary-layer transition to occur closer to the wing leading edge

by the application of grit or the increase in free-stream Reynolds number.

14. SUBJECT TERMS

Delta wings; Supersonic; Vortical flows; Leading-edge separation; Leeside flows

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