REVIEW OF NASA SUPERCRITICAL AIRFOILS

Richard T. Whitcomb National Aeronautics and Space Administration

Langley Research Center Hampton, Virginia

Abstract

NASA supercr i t ical a i r f o i l s a re characterized by a substant ial ly reduced

curvature of the mid-chord region of the upper surface together with increased

camber near the t r a i l i n g edge. The basic aerodynamic phenomena associated

with the a i r f o i l s and representative wind tunnel r e s u l t s a r e discussed. The

r e su l t s indicate t h a t & e drag r i s e Mach numbers fo r NASA supercr i t ical a i r f o i l s

a re 0.1 higher than fo r comparable NACA 6-series a i r f o i l s . A recent analytic

method f o r predicting the aerodynamic character is t ics of supercr i t ical a i r f o i l s

i s described. The f l i g h t demonstration programs of three applications of

supercr i t ical a i r f o i l s u t i l i z ing the F-8, T-2C and F-111 a s t e s t beds a r e

summarized.

I. Introduction

It is well known t h a t the subsonic cruise speeds of high performance

a i r c r a f t a r e l imited by the onset of the transonic drag r i s e . The use of wing

sweepback delays t h i s onset. However, fo r pract ical amounts of sweepback

(approximately 35') t he onset s t i l l occurs well below the speed of sound

( ~ a c h numbers between 0.80 and 0.85). One method f o r increasing the cruise

speed fur ther is the use of a i r f o i l shapes which delay the drag r i s e .

The first a i r f o i l s developed i n the U. S. A. t o delay the drag r i s e

were the NACA 1 ser ies airfoils!' These a i r f o i l s , designed t o increase the

c r i t i c a l Mach number, t h a t i s , the Mach number at which supersonic flow first

develops loca l ly on the a i r f o i l , have drag r i s e Mach numbers significantly

higher than the ewlier mACA four digit secriea airfoils. Howeyer the

low-speed, high-lifi characteristics of these airfoils are signi#icwtly

poorer than for the earlier drfofls . As a ~ e m t they are uaed only on

high speed propeller blades. The RACA 6-series airfoils aZso proflde

increased c r i t i c d Mach nrmobers with result- jsqpro~ementa in the drag

rise characteristics as compared with those for the h-digit series!' They

result in a md.1 degradation in the low speed c ~ a c t e r i a t i c s . These

airfoils, or their derivatives, were used on most of the first generation

of aubsonic Jet airdrerf% deaigned in the U, 5. A.

The first airfoils designed specifically t o delay drrtg piee by j~~profing

the supercriticd. flow above the upper surface were the l f p e ~ " ai;rPoils Of

Pearcj!' They proyide an isentropic reoompreeaion of the supersonic P l m

ahead of the shock wave. These airfofls result in approximately a .Wd to

.03 d e l a y In the drag ~ f s e with a small degradation of the low speed c W a c t e r -

i s t i c s compared with NACA 6 series airfoils. These airfoils or the* deri:yetiyes

were used on the second generation of subsonic j e t aircref't designed in the U. S. A.

The airfoils to be described herein also are aesigned to improve the

supercriticd flow. They we designed to allow the shock waye to move to

the rear part of the airfoil at the design condition. As a reault they proyide

considerably higher drag rise Mach numbers than prefious airfoils. In the

first work on this approach it was assumed that a slot was requfred to

stabilize the upper surface bounihy layer!4) Later it m a found that vlth

the proper upper surface pressure distribution the boundary layer could be

maintained attached up to the design lkch number without the slot. The

results of the first work on the integral or unslotted airfoil was g i e n

limited distribution in 1967 in a Confidentfal b l e y Working Paper. This

paper has been declass i f ied recent ly and forms t h e bas i s f o r much of t he

discussion included herein. It should be noted, however, t h a t t h e extensive

experimental r e s u l t s obtained since 1967 on refinements and applications

of the NASA supercr i t i ca l a i r f o i l s a r e s t i l l c l a s s i f i ed ,

11. Description and Flow Phenomena a t Design Condition

Description

The evolution of t h e general shape of t he NASA supercr i t i ca l a i r f o i l

i s shown i n f igure 1. I n all cases t he shape i s characterized by substant ia l ly

reduced curvature of t h e middle region of t h e upper surface with a l a rge amount

of camber near t he t r a i l i n g edge. Also the leading edge radius is larger than

previously used and the t r a i l i n g edge closure angle i s very small, It w i l l be

noted t h a t t he or ig ina l in tegra l a i r f o i l had a very t h i n t r a i l i n g edge which

l ed t o s t ruc tura l problems, Therefore t he t r a i l i n g edge was thickened a s

shown a t t he bottom of f igure 1. This change not only improved the s t ruc ture

but a l so the high speed aerodynamic charac te r i s t ics a t k%@ing conditions

with very l i t t l e increase i n t he basic subsonic drag level . The advantages

of thickened t r a i l i n g edges fo r transonic a i r f o i l s i s discussed i n reference

5. The a i r f o i l s used f o r all t h e f l i g h t demonstration programs t o be

described have included t h i s thickened t r a i l i n g edge.

Flow Phenomena a t Desian Condition

A comparison of t h e supercr i t i ca l flow phenomena f o r t he NASA supercr i t i ca l

a i r f o i l and an NACA 6 se r i e s a i r f o i l a t the c ru ise l i f t coeff ic ient i s presented

i n f igure 2. For t h e NACA 6 s e r i e s a i r f o i l , a s shown a t t h e top of t he f igure ,

t h e supersonic flow accelerated t o t he shock wave located near t he mid chord,

causing a strong, extensive shock wave. This wave i s followed immediately

by a subsonic pressure recovery t o t he t r a i l i n g edge. The energy l o s s i n t h e

shock causes some drag increase. Howeyer, the dominant problem i s severe

boundary separation caused by the large, steep t o t a l streamwise pressure

increase, This separation, of course, proiiuces t h e well known abrupt drag

r i s e , buffeting, and s t a b i l i t y problems.

The surface pressure dis t r ibut ion and flow f i e l d shown a t t he bottom

of figure 2 a re representative of those obtainea f o r NASA supercr i t ical a i r f o i l s .

The upper surface pressure and r e l a t e d ~ e l o c i t y dis t r ibut ions a re characterized

by a shock location s ignif icant ly a f t of the midchord, an approximately unifom

supersonic velocity from about the 5% chord s ta t ion t o the shock, a plateau

in the pressure dis t r ibut ion rearward of the shock, a re la t ive ly steep subsonic

pressure recwery on the extreme rearward regionland a t r a i l i n g edge pressure

near ambient. The lower surface has roughly constant negative presaure

coefficients corresponding t o subcri t ical .velocities over the forward region

and a rapid increase i n pressure rearward of the midchord t o a substantially

posit ive pressure forward of the t r a i l i n g edge.

The elimination of t h e flow acceleration on the upper surface ahead of

the shock wave, which r e s u l t s primarily from the reduced curvature of the

midchord region, obviously provides a reduction of t h e Mach number ahead of

the shock fo r a given l i f t coefficient with a resul t ing decrease of the shock

strength, The strength and extent of the shock a t t he design condition can be

reauced below tha t for the pressure dis t r ibut ion shown by shaping the air-

f o i l t o provide a gradual deceleration of the supersonic flow from near the

leadfng edge t o the shock wave. (31, c4" C61 H~wever, as w i l l be discussed ! . . 1. - - a

l a t e r , such a shapemay have an increased drag a t lower Mach numbers. Extensive

experiments indicate tha t the shape associated with t h e design point dis t r ibut ion

shown provides acceptable arag values over the Mach number and lift coefficient

range. Theory and experiments indicate tha t with the pressure dis t r ibut ion

shown and at the s l igh t ly negative angle of a t tack required t o obtain the

design l i f t coefficient t h e ve r t i ca l extent of the supersonic f i e l d decreases

ahead of the shock wave as shown on the l e f t i n f igure 2. This effect i s

s i m i l a r t o that for a i r f o i l s designed specif ical ly t o minimize the extent of

the shock at the design point although i n t h i s case the effect i s somewhat

smaller. The flow f i e l d calculations of reference 6 i l l u s t r a t e

the origin of t h i s effect .

Thepateau i n the pressure dis t r ibut ion rearward of the shock wave

allows a reenergization of the boundary layer by mixing a f t e r it moves through

the severe adverse pressure gradient of the shock and before it moves through

the pressure gradient near the t r a i l i n g edge, A s a resul t , the boundary layer

canmove through a greater t o t a l pressure r i s e without separating. The

importance of t h i s effect w i l l be shown by the experimental data t o be

presented l a t e r . The near-ambient pressure at the t r a i l i n g edge, which

re su l t s from the s m a l l included angle of the t r a i l i n g edge, reduces t o a

minimum the t o t a l pressure r i s e the upper surface boundary layer must t raverse

and thus minimizes the tendancy toward separation.

The maintainence of subcr i t ica l flow over the forward region of the

lower surface eliminates the poss ib i l i ty of a shock wave on tha t surface. The

pressure r i s e of a possible shock wave superimposed on the pronounced pressure

r i s e on the rear portion of t h i s surface would grea t ly increase thetendency,..

for-the-bo~ndCrrg'~layer t e ~ s e p a r a t e . The substant ial ly posi t ive pressure on

the r e a r par t of the lower surface, associated with t h e surface concavity of

t h i s region, allows a s ignif icant reduction i n t h e negative pressure coefficients

and related ve loc i t ies required on the upper surface t o obtain a given l i f t .

This,of course,allows an increase i n the drag r i s e Mach number. The pressure

increase rearward of the midchord i s defined by the Stratford c r i t e r i a . (7 1

The relatively large leading edge radii: of the NASA supercritical

airfoils allow simultaneous reductions of the curvatures of the midchord

regions of both the upper and lower surfaces with resulting rebctions of

the induced velocities. However, experiments indicate that the use.of

relative radii larger than that listed in Table I results in increases of

the low speed drag.

111. Experiments and Aerodynamic Characteristics

Experiments

The Langley 8-Foot Transonic Pressure Tunnel in which the NASA supercritical

airfoils have been developed has solid side walls and thus can be used without

modification to obtain two-dimensional results. A model of an intergral

Cunslotted) supercritical airfoil is shown installed in the tunnel in figure

3. The lift and pitching moment characteristics are obtained by surface

pressure measurements while the.drag.is:derived: from wake surveys. These

measurements also provide substantial information on the flow phenomena in-

volved. Additional information on the flow phenomena is obtained by surface

oil flow studies. (8) The test Reynolds number at Mach numbers near 0.80 is 6 7 x 10 which is substantially less than the flight values for most airplanes.

To simulate full scale Reynolds numbers at least at and near the design

condition the technique described in reference 9 is utilized.

Aerodynamic Characteristics

To provide a general indication of the aerodynamic characteristics of

NASA supercritical airfoils at and off the design condition the experimental

results for the 11%-thick representative airfoil shape defined by Table I

will be presented. The variation of drag with Mach number for the design

lift coefficient of 0.6 is shown in figure 4. Similar variations for an

NACA 64-212 airfoil (lo) and a slotted supercritical airfoil(-4) are shown for

comparison. A l l r e s u l t s a r e corrected t o a condition f o r boundary t r ans i t i on

a t t h e 8% chord s ta t ion. A s indicated by f igure 5 t h e supercr i t i ca l a i r f o i l

i s s t ruc tura l ly equivalent t o a NACA 6-series a i r f o i l of a somewhat greater

thickness-to-chord ~ a t i o . Therefore the data f o r t h e 11%-thick supercr i t i ca l

a i r f o i l a r e compared with the available data f o r a 12% ra the r than a 10%-thick

NACA 6-series a i r f o i l ,

The in tegra l supercr i t i ca l a i r f o i l experiences a small drag increase

s ta r t ing a t a Mach number of about 0.7 and an abrupt drag r i s e associated

with bound- layer separation at M = 0.80. (~ef inements of t h e a i r f o i l shapes

developed since these da ta were obtained have essen t ia l ly eliminated t h e small

drag increase a t a cost of an .01 decrease i n t h e drag r i s e Mach number). For

the approximately comparable NACA 6-series a i r f o i l t h e drag r i s e starts a t

a Mach number of about 0.69. The or ig ina l s lo t t ed supercr i t i ca l a i r f o i l

experiences the drag r i s e a t a Mach number jus t above 0.79, However an

analysis of thickness e f fec t s indicates t h a t a s l o t t e d a i r f o i l 11% thick

would experience a drag r i s e a t about 0.81 o r 0.82. Thus t h e elimination of

t he s l o t had a s m a l l aclverse e f fec t on the drag rise Mach number, The higher

drag l eve l f o r t he s lo t t ed a i r f o i l of course r e s u l t s from t h e added skin

f r i c t i o n associated with t h e s lo t . The d ip i n t h e va r i a t i on of drag with

Mach number a t a Mach number of 0.79 i s due t o an e s sen t i a l elimination of

the shock wave f o r t h i s condition.

The var ia t ion of t h e normal force coeff ic ient f o r separation onset with

Mach number i s shown i n f i gu re 6. It w i l l be noted t h a t t h e supercr i t i ca l

a i r f o i l provides a greater delay i n separation onset compared with t he NACA

a i r f o i l a t t h e higher normal forces than a t t he design condition, It a l so

provides a substant ia l increase i n t he maximum normal force at these higher

Mach numbers. These charac te r i s t ics of supercr i t i ca l a i r f o i l s would r e su l t

i n a substant ia l improvement of t he maneuverability of f i gh te r s a t high

subsonic speeds, The phenomena associated with this effect w i l l be discussed

l a t e r . Because of the increased aft loading on t h e NASA in tegra l supercyitical

a i r f o i l , the pitching moments for a given normal force coefffcient w e

substantially more negative than fo r the NACA 6-series a i r f o i l s (f'igure 71.

However, they a re s ignif icant ly l e s s negative than f o r t h e or iginal s lo t ted

supercr i t ical a i r f o i l . Wind tunnel r e su l t s obtained f o r a swept supercr i t ical

wing, developed f o r the f l i g h t demonstration program t o be discussed later,

indicate tha t the twist required t o obtain the proper span load dis t r ibut ion

r e su l t s i n a posit ive pitching moment which approximately of fse ts the

negative pitching moment associated with the section. A s a r e su l t l i t t l e

or no trim penalty i s incurred, a t l e a s t with such a swept wing.

The variations of drag and pitchingmoment with normal force coefficients

a t representative Mach numbers f o r the 11%-thick representatiye integral

supercr i t ical a i r f o i l a r e presented i n figure 8 f o r reference.

IV. 'Flow Phenomena a t Off-Desian, Subcrit ical , and High L i f t Conditions

The pressure dis t r ibut ions measured on the 11%-thick ~epresen ta t iye

NASA supercr i t ical a i r f o i l defined by Table I provide a general indication of

the flow phenomena associated with NASA supercr i t ica l a i r f o i l s a t off-design,

subcri t ical , and high l i f t conditions. For reference the measured pressure

dis t r ibut ion f o r the design condition of t h i s a i r f o i l i s presented i n f igure 9,

A t a'Mach number jus t below the design value (figure 1 0 ) , t h e shock

location i s s ignif icant ly fa r ther forward than for the design condition and

the flow experiences a reacceleration rearward of t h e shock with a super-

c r i t i c a l peak velocity near the 75% chord s tat ion. This reacceleration

causes a substantially greater and steeper pressure increqse t o the t r e i l i n g

edge as compared with the design condition. T h i s steeper Tepoyery r e s u l t s

i n a small adverse effect on the t r a i l i n g edge pressure recoyexy and drgg.

For unslotted a i r f o i l s designed t o achieye a shockless design condition (4

the reacceleration veloci ty can be suf'ficiently great t o cause a second

") The t o t a l pressure ,rise of t h i s second shock and rearward shock wwe.

the immediately following subsonic pressure recovery may cause sCgnificant

b o u n a ~ y layer separation near the t r a i l i n g edge.

A t subcri t ical Mach numbers (figure 111 the pressure dis t r ibut ion has

a significant peak near the leading edge. The presence of t h i s peak r e s u l t s

i n a small drag increment f o r subcri t ical and s l igh t ly supercrit ic@ conditi.ons.

If an a i r f o i l is shaped t o provide a decellerating supersonic yelocity

dis t r ibut ion on the upper surface at the design condition as discussed e a r l i e r

t h i s subcri t ical peak i s substantially greater than t h a t shown with-a resu l t ing

increase i n the drag f o r the subcr i t ica l and s l igh t ly supercr i t icel eonditions.

The pressure d is t r ibut ion shown i n f igure 12 i s tha t measured a t t he

highMach number corner of the .variation of normal force f o r separation onset

with Mach number shown previously i n figure 6. The shock wave associated

with an upstream Mach number of 1.4, causes a very la rge adverse pressure

graaient. However, t he t r a i l i n g edge pressure recovery and a surface o i l

flow study indicate tha t the boundary layer does not completely sepaxate. The

bulge i n the pressure dis t r ibut ion a f t of the shock wave and the surface o i l

studysinaZciteiamery large separation bubble under the shock which reat taches

near the .75 chord s tat ion. For previous a i r f o i l shapes, such as the NACA

6-series, t he presence of a shock wave associated with an upstream Mach number

of 1.4 causes very severe boundary layer separation. (12 The key t o the

greater s t a b i l i t y of the boundary layer $07 the supercr i t ica l a i H o i l is the

plateau i n the pressure dis t r iPut ipn a f t of the shock waye deqcyihed egrl ier .

For previous a i r f ~ i l s t h e subsonic pressure Tecovery h e a i a t e l y aownstream

of the shock wave opposes boundary layer ~eat tachment . With the plateau on

the supercr i t ical a i r f o i l t h i s adverse effect i s eliminated. It i s of

in te res t t ha t unpublished bounaft~y layer surveys indicate t h a t t he boundary

layer separation developlent under the shock fo r supercr i t ica l a i r f o i l s i s

quite similar t o tha t on a f l a t plate. 0-3 1

'Y. Thick Supercrit ical Air fo i l s

In the prwious discussion the increase i n drag r i s e 'Mach number f o r a

given a i r f o i l thickness-to-chord r a t i o provided by the NASA s u p e r c ~ i t i c a l

a i r f o i l has been emphasizes. However, t he same approach can be us& t o

provide a substantial increase i n section thickness-ratio f o r the same

drag r i s e Mach number. The f i r s t thick supercr i t ica l a i r f o i l was developed

by W. Palmer of the Columbus, Ohio Division of North American-Rockwell

(figure 13). This 17%-thick a i r f o i l has the same drag r i s e Mach number as

a 12$-thick NACA 6-series a i r f o i l a t the same l i f t coefficient.

YI, Theoretical Analysis

Considerable progress has been made during the last three years i n

providing theoret ical methods fo r the design and analysis of two-aimensional

a i r f o i l s at supercr i t ical Mach numbers. No attempt w i l l be made t o cover

a l l t h i s work, instead the method being used a t Langley i n a continuing

ef for t on supercr i t ica l a i r f o i l s w i l l be described.

The i n i t i a l comparisons of theoret ical ly derived pressure dis t r ibut ions

on NASA supercr i t ical a i ~ f o i l s with experimental r e s u l t s indicated 'very poor

agreement. The differences a re associatea with the development of the

boundary layers on these a i r f o i l s , i l l u s t r a t e a by f igure 14.

'The steep pressure r i s e near the t r a i l i n g edge of t h e upper surface causes

t h e boundary layer t o thicken s ignif icant ly . On the lower surface -- -- - - - - -- - - - - -

t he pressure ~ i s e from about the .5 t o t he .9 chords results i n a substant ia l

thickening of t h e boundary layer i n t he cusp while t h e rapid pressure decrease

near t he t r a i l i n g ed@;e causes a pronounced thinning of t h e boundary layer. Each - . - -- - -

of these e f f ec t s contributes t o a substant ia l reduction of t h e e f fec t ive a f t

camber of t he a i r f o i l . It was concluded that f o r NASA supercr i t i ca l a i r f o i l s

any analytic method must include t h e e f f ec t of t he boundary layer.

'Recently an analyt ic method which includes t h e e f f ec t of t h e boundary

layer has been developed a t Langley. ( I4 ) This i t e r a t i v e procedure i s based

on the method of Korn and Garabedian ( I5 ) f o r analyzing t h e external super-

c r i t i c a l f i e ld , which implements a transonic f ini te-difference scheme defined

(16) A similar method was a lso developed by Jameson. by Murman. (17) The

coordinate system, shown i n f igure 15, was suggested by S e l l s C18) and consis ts

of mapping t h e i n t e r i o r of t h e u n i t c i r c l e conformally onto t h e ex te r ior of

t he a i r f o i l with t he point at i n f i n i t y corresponding t o t h e origin. These

flow f i e l d computations a r e made f o r a i r f o i l shapes modified by t h e calculated

displacement thicknesses of t he upper and lower surface boundary layers. The

displacement thicknesses a r e determined by the method of Bradshaw. '19) since

the boundary layer calculations a r e not applicable near t h e t r a i l i n g edge an

empirical correction i s applied f o r t h i s region.

The e f f ec t of including the boundary layer on ana ly t ica l predicted

pressure d i s t r ibu t ions f o r an NASA s u p e r ~ r i t i c a l a i r f o i l i s i l l u s t r a t e d i n

f igure 16. These comparisons a r e fo r l i f t coeff ic ients substant ia l ly greater

than the design value. A t a subcr i t i ca l Mach number, including t h e e f f ec t of

t h e boundary layer causes a moderate change i n t he predicted l i f t . However,

a t a supercr i t i ca l Mach number including the e f f ec t of t h e boundmy layer

r e s u l t s i n substant ia l changes of t h e posit ion of t h e shock wave and the l i f t .

Comparisons of theoret ical pressure dis t r ibut ions obtained by t h i s method

with experimental dis t r ibut ions for a NASA supercr i t ica l a i r f o i l a t a sub-

c r i t i c a l and a supercr i t ical condition a re presented i n figures 17 and

18 respectively. Again these comparisons a re f o r l i f t coeff ic ients substantially

greater than the design value. In both cases the agreement i s quite good.

The difference i n pressures Just rearward of the shock wwe fo r the supercr i t ical

condition (figure 18) i s believed t o be due t o an inadequacy of the external

f i e l d solution i n predicting the pressure r i s e through the shock. Work is

being done t o improve t h e method i n t h i s regard. It should be noted tha t

t he a i r f o i l shapes shown a t the bottom of these f igures include the displace-

ment thicknesses of the upper and lower surface boundary layers.

Y I I . Flight Demonstration Program

Because of the d ras t i ca l ly different nature of the flow over the

NASA supercr i t ical a i r f o i l , there was considerable concern as t o how the

new shape would operate i n actual f l i gh t . Therefore, the several U. S.

government agencies responsible f o r a i r c ra f t , t ha t i s NASA, the A i r Force,

and the Navy, undertook a coordinated, three part f l i g h t demonstration

program. The program was t o evaluate the application of the new a i r f o i l t o a

pwept, long-range~;trranwport wing configuration, a th ick wing, and a variable

sweep f ighter wing. In each case existing mi l i ta ry a i r c r a f t were used a s

t e s t beds. However, i n none of the cases was it intended the t e s t wing would

be applied t o production versions of these a i r c ra f t .

F-8 - The transport supercr i t ical wing configuration was flown on a Navy

F-8 f ighter e i g u r e 19). The basic information concerning t h i s program is

given i n f igure 20. The wing was of simple "boiler plate" construction.

Simple f laps extending from the 408 t o the 80% semispan were used fo r both

l a t e r a l control and increased l i f t fo r lanaing and take off . The sweep

-12-

of t h e midchord was 40'. The a i r f o i l shape outboard approximately t he 40%

semispan s ta t ion was the same as t h a t developed during t h e previously

described two-dimensional investigations. However t h e a i r f o i l shapes f o r

the inboard section yeyes - s i ihstant ia l lyia lBe~eat .to.-acoountr'f OT. Oheilaqge

three-dimensional e f f ec t s i n this region at the near sonic cruiseMach

number. The forward extension of t he leading edge near t h e fuselage a l so

improved the near-sonic three-dimensional flow on t h i s inboard region. The

wing had substant ia l t w i s t .

T-2C - The th ick supercr i t i ca l a i r f o i l was flown on a Navy T-2C t ra iner . A

comparison of a i r c r a f t without and with t he th ick section i s shown i n

f igure 21, The basic information concerning t h i s program i s given 5n

f igure 22. The section shape was obtainea by droo9ing t h e f l a p and ai leron

and then adding balsa wood and f iberg lass t o t h e or ig ina l wing structure.

The a i r f o i l shape was t h e same along the e n t i r e span. Some of t h e r e s u l t s

from t h i s program a r e present i n reference 20.

F-111

The var iable sweep supercr i t i ca l f i gh t e r wing i s being flown on a U. S,

. A i r Force 3'-111 (figure 23). The basic information concerning this program

i s given i n f igure 24. Only t h e var iable sweep panels have been changed

from t h e or ig ina l configuration. The wing panels have been designed f o r

minimum weight and a re equipped with s ing le s lo t t ed t r a i l i n g edge f l a p s

and Kreuger leading edge f laps . The a i r f o i l shapes a r e s imilar t o those

developed two-dimensionally. The panels have subs tan t ia l t w i s t .

a. ' Applications

Following the wind tunnel development of t h e near sonic t ransport wing

configuration usea f o r t h e F-8 f l i g h t demonstration, a complete near-sonic

(20) wee transport configuration, incorporating t h i s wing w a s defined,

U. S. aircraft manufacturers, Boeing, General Dynamics, and Lockheed, under

contract to W A evaluated actual transport aesigns based on thfs configura-

tion. (21 An artist's concept of the General Dynamic's design is shown in

figure 25.

More recently a number of U. S. aircraft manufacturers h m e initiated

new military and commercial airplane designs incorporating NASA supercritical

airfoils. It should be noted that for transport aircraft the principal

interest at present is in using the airfoils to obtain reduced fuel consumption

rather than to obtain increased speed. For a given cruise speed the ai~foils

allow a reduction in wing sweep and/or an increase in section thickness ratio

which permit an increase in wing aspect ratio or a reduction in wing weight.

These changes of course provide a reduction in fuel consumption.

IX. Concluding Bemarks

Over the past ten years extensive wina tunnel investigations of two-

dimensional sections and three-dimensional applications of NASA supercritical

airfoils have been conducted, In addition, two flight demonstration programs

have been completed and another initiated. The results of this research

indicate that the use of these airfoils can successfully provide substantial

improvements of the speed, fuel consumption, or maneuverability of most

aircraft intended for operation at high subsonic speeds. Also, the analytic

methods now becoming available can greatly aid in the design of new operational

aircraft incorporating these airfoils.

1. Stack, John; Tests of Ai r fo i l s Designed t o Delay t h e C q p r e s s i b i l i t y

Burble. NACA !lW 9-76, 1944.

Abbott, Ira He; von Boenhoff, Albert E.; and St ivers , Louis S., Jr.:

Summary of Ai r fo i l Data. NACA 'Report No. 824, 1945

Pearcey, H. H.: The Aerodynamic Design of Section Shapes f o r Swept

Wings. Advances i n Aeronautical Sciences, 701. 3, p. 27.7, Pergamon

Press, 1962.

Whitcomb, Xichard T.; and C l a ~ k , Larry'R,: An Ai r fo i l Shape f o r Eff ic ient

Fl ight a t Supercr i t ical Mach Numbers. NASA TM X-1109, 1965 . Holder, D. W.: The Transonic Tlow Past Two-Dimensional Aerofoils. J. Boy.

Aeronaut. SOC, , vol . 68, no, 644, Aug. 1964, pp. 501-516.

Bauer, F.; Garabeaian, P.; and Korn, D.: Supercr i t ical Wing Sections.

Springer-Verlag, 1972.

Stratford, B, S.: The Prediction of Separation of t h e Turbulent Boundary

Layer, Jo Fluid Mech., vol. 5, pp. 1-16, 1959,

Loving, Donald L.; and Katzoff, S.: The Fluorescent-Oil Film Method and

Other Techniques for Boundary-Layer 'Flow Visualization. NASA Memo

3-17-59L9 1959-

Blackwell, James A., Jr.: Preliminary Study of Effects of 'Reynolds Number

and Boundary-Layer Transit ion Location on Shock-Inaucea Separation.

NASA Tn D-5003, 1969.

Van Dyke, Bfilton D.; ana Wibbert, Gordon A.: High-Speed Aerodynamic

Characterist ics of 12 Thin NACA 6-series Airfoi ls . NACANFI A5F27,

1945.

11. Kacprzynski, J. J.; Ohman, Lo H.; Garabedian, P. 3.; and Korn,D. G;

Analysis of t h e Flgw Past a Shockless L i f t ing A i r fo i l i n Design

and Off-Design Conditions. NRC 'Report LR-554, 19111.

12. Daley, Bernard N.; and Dick, 'Richard S.: Effect of Thickness, Camber,

and Thickness Dis t r ibu t ion on Ai r fo i l Character is t ics a t Mach Numbers

Up t o 1.0. NACA TN 3'607,'1958.

13. Seddon, J.: The Flow Produced by Interact ion of a Turbulent Boundary

Layer With a Normal Shock Wave of Strength Suf f ic ien t t o Cause

Separation. 'R & M No. 3502, Br i t i sh A.B.C., March 1960.

14. Bavitz, Paul C. : An Analysis Method f o r Two-Dimensional Transonic

Y ~ S C O U S F ~ O W , NASA@-% . , 1974.

15. Garabedian, P, 3.; ana Korn, D. G.: Analysis of Transonic Ai r fo i l s .

Comm. on Pure and Applied Math., vol. 24, pp. 841-851, 19111.

16. Murman, E a r l 1 M. ; and Cole, Ju l ian Do : Calculation of Plane Steady

Transonic 'Flows. AIAA J., ~ o l . 9, NO. 1, pp. 114-131, 1971.

17. Jameson, A.: Transonic Flow Calculations f o r A i r fo i l s ana Bodies of

Revolution. GTumman Aero. Corp. 3ep. 390-71-1, 1971.

18. Se l l s , C. C. L.: Plane Subcr i t i ca l Flow Past a L i f t ing Aerofoil,

Proc . Roy Soc . (London), vol. 308A, pp. 377-401, 1968.

19. Bradshaw, P.; Fe r r i s s , D. H.; and Atwell, No P.: Calculation of

Boundary-Layer Development Using t h e Turbulent Energy Equation.

J. ,Fluid Mech., vol. 28, pa r t 3, pp. 593-616, 1967.

20. Ayers, T. G.: Supercr i t i ca l Aerodynamics, Astronautics and Aeronautics,

pp , 32-36, August 1972.

21. Braslow, A. L.; and A l f o ~ d , W. J,: Advanced Subsonic Transport Technology.

Astronautics and Aeronautics, pp. 26-31, August 1972.

TABLE I. - COORDINATES FOR AN 11%-THICK REPRESEWTATIVE NASA SUPERCRITICAL AIRFOIL

4

I

x/c

0.0075 -0125 .0250 0 0375 a 0500 a 0750 .lo00 .1250 .I500 01750 *2000 .2500 .3000 .3500 .4000 .4500 .5000 5500

0 5750 .6000 -6250 .6500 6750

.7000 07250 a7500 7750

.8ooo

.8250

.8500 08750 .goo0 09250 0 9500 9750

1.0000

Upper

0.0176 .0215 .0276 .0316 0 0347 .0394 .0428 .oh55 .0476 .oh93 -0507 .o528 .0540 0547

a 0550 .0548 .0543 -0533 0 0527 0519

-0511 .0501 .0489 .0476 .0460 .0442 .oh22 .0398 -0370 . 0337 .0300 o 0255 .0204 -0144 -0074 -, 0008

P z / c

Lower

-0.0176 - -0216 -. 0281 -. 0324 -. 0358 - .0408 -. 0444 -, 0472 -. 0493 -0 0510 - 0522 -. 0540 -. 0548 -. 0549 -. 0541 -. 0524 -. 0497 -.0455 - -0426 - -0389 - .0342 - .0282 - 0215 -. 0149 -. OOgO - 0036 . 0012 . .0053

.0088

.0114

.0132

.0138

.0131

.0106

.0060 - .0013

\

L. E. radius: 0.0245~