advanced airfoil design empirically based transonic ... · u.5 zero lift pitching moments 39 u.6...

NASA CR-137928

(MASA-CR-13792R) ADVANCED AIPFOIL DESIGN N7"7-20017EMPIRICALLY BASED TRANSONIC AIRCRAFT DRAGBUILDUP TECHNIQUE ^inal Deport(Lockheed-California Co., Burbank.) 80 p "nclasHC A^S/MF A01 CSCL 01A G3/02 1U999

ADVANCED AIRFOIL DESIGN

EMPIRICALLY BASED

TRANSONIC AIRCRAFT-DRAG

BUILDUP TECHNIQUE

FINAL REPORT

by W. D. Morrison, Jr.

January 1976

Prepared Under Contract No. NAS2-8612

for

Ames Research Center

National Aeronautics and Space Administration

by

Lockheed-California Company

Burbank, California

REPRODUCED BY

NATIONAL TECHNICALINFORMATION SERVICE

U S DEPARTMENT OF COMMERCESPRINGFIELD. V*. 22161

https://ntrs.nasa.gov/search.jsp?R=19770013073 2020-06-28T13:18:32+00:00Z

U.S. DEPARTMENT OF COMMERCENational Technical Information Service

N77-20017

ADVANCED AIRFOIL DESIGN EMPIRICALLY BASEDTRANSONIC AIRCRAFT-DRAG BUILDUP TECHNIQUE

W, D, MORRISON

LOCKHEED-CALIFORNIA COMPANYBURBANK, CALIFORNIA

JANUARY 1976

NASA CR-137928


EMPIRICALLY BASED

TRANSONIC AIRCRAFT-DRAG

BUILDUP TECHNIQUE

FINAL REPORT

by W. D. Morrison, Jr.

January 1976

Prepared Under Contract No. NAS2-8612

for

Ames Research Center

National Aeronautics and Space Administration

by

Lockheed-California Company

Burbank, California

I

1. REPORT NO. 2. GOVERNMENT ACCESSION NO.

NASA CR-1379284. TITLE AND SUBTITLE

Advanced Airfoil Design - Empirically Based -Transonic Aircraft Drag Buildup Technique

7. AUTHOR (S)

W. D. Morrison, Jr.

9. PERFORMING ORGANIZATION NAME AND ADDRESSLOCKHEED-CALIFORNIA COMPANYP.O. BOX 551BURBANK, CALIFORNIA 91520 ?

12. SPONSORING AGENCY NAME AND ADDRESSNational Aeronautics and Space AdministrationAmes Research CenterMoffit Field, California

3. RECIPIF.NT'S CATALOG NO.

5. REPORT DATEJanuary 19?6

6. PERFORMING ORG CODE

8. PERFORMING ORG REPORT NO.

LR 2752U10. WORK UNIT NO.

11. CONTRACT OR GRANT NO.

NAS2-861213. TYPE OF REPORT AND PERIOD

COVEREDContractor Report-Final14. SPONSORING AGENCY CODE

15. SUPPLEMENTARY NOTES

16. ABSTRACT

Advances in airfoil section design applicable to aircraft optimized for

transonic cruise offer improvements in the range factor VErt increases in wing

thickness ratios, increases in wing aspect ratio, or reductions in wing sweep

if applied to current transonic aircraft.

To systematically investigate the potential of advanced airfoils in Advance

Preliminary Design studies, empirical relationships have been derived, based

on available wind tunnel test data, through which total drag can be determined

recognizing all major aircraft geometric variables. This technique recognizes

a single design lift coefficient and Mach number for each aircraft. Using this

technique drag polars can be derived for all Mach numbers up to M - c - + 0.05

and lift coefficients -O.Uo to +0.20 from CLDesign

17. KEY WORDS (SUGGESTED BY AUTHORISM

Advanced AirfoilsDrag CorrelationTransonic AerodynamicsSupercritical Airfoils

19. SECURITY CLASSIF.

KA^M'

18. DISTRIBUTION STATEMENT

20. SECURITY CLASSIF. (OF THIS PAGE) 21. NO. OF PAGES 22. PRICE'

UNCLASSIFIED

FOREWORD

The study summarized in this (unclassified final) report (NASA CR-137928)

and the Confidential Appendix (NASA CR-137929K under separate cover, was

performed "by the Lockheed-California Company for the National Aeronautics and

Space Administration, Ames Research Center, under Contract No. NAS2-8612.

Mr. L. J. Williams was the NASA technical monitor. Mr. W. D. Morrison was the

principal investigator. •

111

TABLE OF CONTENTS

Section Page

FOREWORD ii:L

LIST OF FIGURES . vii

LIST OF TABLES ix -

LIST OF SYMBOLS xi

ABSTRACT !

1 INTRODUCTION 1

2 STUDY PREMISES AND OBJECTIVES 2

3 APPROACH TO DATA CORRELATION ^

k DATA CORRELATION/EMPIRICAL RELATIONSHIPS 9

U.I DATA BASE SUMMARY . 9

k.2 MACH AND CT DRAG DIVERGENCE ' 9

Ll

U.3 DESIGN LIFT COEFFICIENT 13

k.k COMPRESSIBILITY AND PRESSURE DRAG 13

ll.U.l Compressibility Drag 5

h.k.2 Pressure Drag 25

U.5 ZERO LIFT PITCHING MOMENTS 39

U.6 BUFFET ONSET ^2

U.T AIRFOIL SECTION - PRESSURE DRAG - FORM FACTOR ^2

5 DRAG BUILDUP PROCEDURES ^5

6 2-D AND 3-D COMPARISON OF COMPRESSIBILITY AND PRESSURE DRAG 55

1 RECOMMENDATIONS

REFERENCES . 59

APPENDIX A , A-l

PBECEDING PAGE BLANK NOT FILMEB

LIST OF FIGURES AND TABLES

Figure ' Page

1 State of the Art and Advanced Airfoil SectionCharacteristics 3

2 Path I of Data Correlation Technique - C Design andM_, . Derivation 5Design

3 Path I of Data Correlation Technique - Drag DivergenceMach Number Derivation 6

U Path II of Data Correlation Technique - IncrementalCompressibility and Pressure Drag Derivation 7

5 State of the Art and Advanced. Airfoil - Flight and WindTunnel Model Data Base Summary H

6 NL Correlation Approach - CL = 0.50 12

7 Mp 2_D vs t/c Correlation - CL = 0.10 ^

8 Mp 2 D vs t/c Correlation - CL = 0.20 15

9 Mp 2_D vs t/c Correlation - CL = 0.30 16

10 IVL vs t/c Correlation - CT = O.UO 17D d—u Li

11 M^ vs t/c Correlation - CL = 0.50 i8

12 MJJ 2 D vs t/c Correlation - CL = 0.60 19

13 Mp 2 D vs t/c Correlation - CL = 0.70 • 20

lit ]yL vs t/c Correlation - C = 0.80 21

15 Correlation of Design Lift Coefficient ^

16 2-D Compressibility and Pressure Drag Variation withReynolds Number 26

17 Incremental Compressibility Drag Variation vithIncremental Mach Number from Mach Design 27

18 Fairing of Incremental Compressibility Drag - Summary 28

PRECEDING PAGE BLANK NOT

LIST OF FIGURES AND TABLES (Continued)

Figure

19

20

21

22

23

2k

25

26

27

28

29

30

31

32

Incremental Pressure Drag Variation with Incremental MachNumber from Mach Design AC = -0.1*0

LiIncremental Pressure Drag Variation with Incremental Mach•Number from Mach Design AC = -0.30

LiIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design AC = -0.20

LiIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design ACT = -0.10LIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design AC = -0.05

LiIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design AC = 0

LIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design AC = +0.05

LJIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design A CL = +0.10

Incremental Pressure Drag Variation with Incremental MachNumber from Mach Design AC = +0.15

LJIncremental Pressure Drag Variation with Incremental MachNumber from Mach Design ACT = +0.20LIFairing of Incremental Pressure Drag - Summary

Zero Lift Pitching Moment Variation with Camber andIncremental Mach Number from Mach Design

Lift Coefficient for Buffet Onset

Conventional, State of the Art, and Advanced Airfoil

Page

29

30

31

32

33

3k

35

36

37

38

Uo

lak3

Section - Ratio of Minimum Drag to Theoretical SkinFriction Drag kk

33 Wing Section Form Factors U6

3l* Body Form Factors kl

35 Variation of Flat Plate Incompressible Skin FrictionCoefficient with Reynolds Number H8

36 Compressibility Correction to Skin Friction Coefficient 50

37 Example Twin Engine - Advanced Transonic AircraftGeometry 51

VI11

LIST OF FIGURES AND TABLES (Continued)

Figure Page

38 Drag Buildup Flov Diagram 53

39 A CDC and A CD Comparison - 3-D Fairing vs 2-D Test Results 57

UO A CD Comparison - 3-D Fairing vs 2-D Test Results 58

Table

I Incremental Mach Number Correction to Drag DivergenceDue to Aspect Ratio and Sweep 10

II MD 2_D M2D 2_D and (M^ 2_D -l) Relationships 22

III • t/c, (t/c)5/3, (t/c)2/3, and (t/c)1/3Relationships 23

IX

LIST OF SYMBOLS

AR

b

c

c"

i,cd

CD

pmin

CDPmin

CDPmin

CDi

CDC

CDp

. Wing aspect ratio

Wing span-tip to wing-body f,

Local Wing Chord

Wing mean aerodynamic chord

Centerline

2-dimensional drag coefficient

3-dimensional drag coefficient

Minimum 2-dimensional pressuredrag coefficient @ M 0.60

Minimum 3-dimensional pressuredrag coefficient @ M 0.60

Zero lift drag coefficient

Induced drag coefficient

Compressibility drag coefficient

Pressure drag coefficient

b2/Sref

ft

ft

ft

dqcD

q Sref

. from TEST DATA

r Y v v vetC X F.F.

ref

CT2/TrAR

Ll

(f) AM , t/c, h/c

(f) AM, ACT , t/cL

L

CLBCLDesign

Cf/Cfincomp.

Skin friction drag coefficient

Incompressible skin friction dragcoefficient

2-dimensional lift coefficient

2-dimensional normal force coefficient

3-dimensional lift coefficient

Lift coefficient for buffet onset

Design lift coefficient

Compressibility correction to skinfriction coefficient

( f ) R N 1

(f) RN

qc"_n_qc

ref

(0.99 M)max

XI

PRECEDING PAGE BLANK NOT

LIST OF SYMBOLS (Continued)

c

cp

°Pcritical

F.F.

F.F.

H

h/c

L/D

A/d

M or MCO

MDesign

MD o nC."—IJ

MT 3-D

A MAR

A M,

.Design

Zero lift pitching moment coefficient

Pressure coefficient

Pressure coefficient = 1.00

s

P/H

Form factor - wing section

Form factor - bodies

Total pressure (static and dynamic)

Wing camber @ ,TOY/|

Lift to drag ratio

Body fineness ratio

Horizontal tail length

Freestream Mach number

Design Mach number

M

q. Sref cPi - Ps

q.f(M)

f(t/c)

lb/ft2

upper uoo

ft

M §(0.99 D max

2-dimensional drag divergence Mach number d C^ = o 10d M

3-dimensional drag divergence Mach number d= Q.10

d M

Correction to divergence Mach number due to aspect ratio

Correction to divergence Mach number due to sweep

AM A M A3-D ~ ( MD 2-D + " "AR

Local static pressure

Freestream static pressure

ratio of static to total pressure

Design

lb/ft'

lb/ft2

"LDES.

Xll

LIST OF SYMBOLS (Continued)

q

RNR

sref

vet

t/c

t/ceff

W

x,y,z

max.

(f)

Dynamic pressure

Reynolds number

Reference wing area - continue basicwing panel leading and trailing edgeto £

Wetted area of airplane component

Wing section thickness ratio

Effective thickness ratio - wing frontalarea divided by wing plan area to wing-body intersection - include gloves

Aircraft weight

Cartesian coordinate system

Maximum value . 1

Function of j

Sweep of basic wing panel quarter chord

lb/ftc

VI

ft'

Ib

deg

.3slug/ff

slug/ft-sec

Xlll


EMPIRICALLY BASED

TRANSONIC AIRCRAFT-DRAG BUILDUP 'TECHNIQUE

By W. D. Morrison, Jr.Lockheed-California Company

SUMMARY

Advances in airfoil section design applicable to aircraft optimized for

transonic cruise offer improvements in the range factor M~, increases in

wing thickness ratios, increases in wing aspect ratio, or reductions in

wing sweep if applied to current transonic aircraft.

,To systematically investigate the potential of advanced airfoils in

Advance Preliminary Design studies, empirical relationships have been derived,

based on available wind tunnel test data, through which total drag can be

determined recognizing all major aircraft geometric variables. This technique

recognizes a single design lift coefficient and Mach number for each aircraft.

Using this technique, drag polars can be derived for all Mach numbers up to

M^ . +0.05 and lift coefficients -O.Uo to +0.20 from CT^esign LDesign

1. INTRODUCTION

In the preliminary design of advanced aircraft there is always the

objective of incorporating into the design the most advanced technologies to

evaluate their potential for future products.

The concept of controlled supersonic flow development used in present

day advanced airfoil design practices has evolved section characteristics

exhibiting improvements over more conventional airfoils for application to

aircraft designed for transonic cruise. The expression controlled supersonic

flow development implies, that as the region of local supersonic flow develops

and grows in extent over the airfoil chord, the shock wave terminating such

a region remains weak. This phenomenon is in contrast to the very strong

upper surface shock associated with more conventional design practices.

A number of prominent investigators have applied descriptive terms to

their advanced airfoil design philosophy, i.e., Dr. R. Whitcomb's super-

critical airfoils, Pearcy's peaky airfoils, and Korn-Garabedian shockless

airfoils. In addition, industry and the universities have developed their

own advanced airfoil design practices and all indicate improvements over

the conventional airfoils. All of these resulting airfoils may be considered

supercritical; however, it has become customary to apply the term supercritical

to those airfoils that in addition to having controlled supersonic flow develop-

ment , also carry a significant amount of aft loading due to an appreciable

lower surface reflex near the trailing edge. Thus, of the above mentioned

advanced airfoil designs, only those developed by Dr. Whitcomb of NASA fit in-

to this more restrictive definition of the term supercritical. i

At the present, limited nonsystematic 2- and 3-dimensional wind tunnel

test data are available from these aforementioned sources. The explicit

methods for the design and quantification of their characteristics reside with

the principal investigators. Only the test results are available.

This study has been undertaken, not in an attempt to devise an advanced

airfoil design procedure, but rather to collect available 2- and 3-dimensional

test data under the generalized concept of "airfoils designed to a controlled

supersonic flow development" and devise correlation techniques which will

permit preliminary design evaluation of the potential of advanced airfoils

for transonic flight applications.

2. STUDY PREMISES AND OBJECTIVES

State of the art and advanced airfoil 2-dimensional section shapes and

approximate design condition pressure coefficients are shown in Figure 1. The

state-of-the-art airfoil shown here represents one of the sections tested during

the development phase of the L-1011. The advanced airfoil shown is representa-

tive of an outboard wing section employed on an advanced L-1011 wind tunnel

model. Both sections are characterized by controlled upper surface supersonic

flow development. However, the advanced airfoil rounder leading edge, flatter

upper surface, and more reflexed trailing edge reduces the leading edge pressure

coefficient peakiness, extends the near sonic flow further aft on the airfoil,

wo•H-PW•H?H0)-POCO'fn0545O

§•H-POOJ

CO

•HO

1TJcCO

<;0)

0)-P£0-PCO

do 'iN3ioidd3oo aanssaud

and produces a more highly aft loaded section; all contributing to a higher

freestream drag divergence Mach number at a somewhat higher lift coefficient.

Application of a similar pressure distribution to a 3-dimentional wing involves

a design process which is complicated, undoubtedly varies between principal

investigators, and to date employs empirical or other approximations

(Reference l). In spite of these complications and probable variations,

consideration was given prior to initiating this correlation in an attempt to

insure a degree of compatibility of definition and identification of parameters

which might aid in the development or validation of theoretical programs.

To this end, the assumption is made that a commonality exists between most

theoretical design programs that a specified design-to pressure distribution,

P/H, over the airfoil is stipulated at the critical or design lift coefficient

and Mach number. This implies that for all advanced airfoil design wind

tunnel models there exists a somewhat common level of local Mach number over

the airfoil at design conditions or for correlation purposes the same level of

pressure drag. The freestream Mach number at which these design conditions

are met can be varied by the geometric parameters of sweep, aspect ratio, and

thickness ratio.

This suggests that the 3-dimensional wind tunnel test results can be

correlated to 2-dimensional equivalence through relationships of design

lift coefficient, design Mach number, model geometry, and a relationship of

the freestream Mach number to the design Mach number.

. 3. APPROACH TO DATA CORRELATION

Following the assumptions previously stated, and guided by the NACA work

in developing data correlation techniques by means of the Transonic Similarity

Rules (Reference 2), a data correlating procedure was evolved and is

descriptively noted on Figures 2, 3, and U.

Two paths of data correlation are shown. Path I involves the deter-

mination of design Mach number, design lift coefficient, and drag divergence

t o>

s,•HW0)

•dCCO

g,•HW0)Q

I

O0)

EH

§•H-P

COrHQ)

OO

CO-PCOPI

O -H-P

M C O

CO 0>PH O

CVJ

0)

'/TWI

CM

O

0)O

8<U•HO

bO03

I•H

O0)

EH

O•H-P

CO

O CO O

•Ha -p-p cdas >O-H<H 0)O Q

H

-Pca

ono>9tiD

Q)

-9

•HCOCO

Oo

05-P

I0>fnOfl

Q)

g<•H

0) OEH -H

§1•H -H-p.. inCO <U•-I Oo;^ bD£H COO fnO O

CO CU•P ?HCO 3Pi w

COH 0)

-P TJ

03fl

W)•H

Mach number. Path II involves determination of the compressibility and

pressure drag.

• Path I: Initial steps require the crossplotting of each wing-bodydata set as drag versus Mach number at constant lift coefficients;then computing M L/D for each data point and replotting as M L/D versusMach number at constant lift coefficients. For maximum range, thelift coefficient and Mach number at which the peak value occurs will,in general, be the airplane cruise or design condition. For practicalreasons, i.e., flatness of the curve and to insure cruise at thehighest speed, an arbitrary value of 0.99 (M L/D) was selected asthe design point for M^ . and CT. Design L_,

Design

Using the same data crossplots of drag coefficient versus Mach numberat constant lift coefficients, the three-dimensional drag divergencecharacteristics are then determined. To these data, AM corrections dueto aspect ratio and sweep are applied to arrive at 2-D equivalent •characteristics. Divergence has been defined as that Mach number ata constant lift coefficient at which the rate of change in drag

. coefficient with Mach number reaches a value of --mD- = 0.10.

At the design C , Mach divergence, and design are synonymous.L

Path II: The basic drag polar, plotted as drag coefficient versuslift coefficient at constant Mach number, is selected for the deter-mination of the incremental compressibility and pressure drag con-

CL2tributions . Idealized induced drag is computed, as ~7rr; e = 1.0,and this quantity is removed from each polar. At the lowest testMach number, at least a AM = 0.30 below design, the minimum pro-file drag is determined as the bucket of the curve and this dragquantity is removed from all polars. Referring back to Path I ofthe data correlation, M_ . and CT are selected and the

' Design L^ .& Designadjusted polars are replotted at a constant AM from M^ . versus

ACT from CT . The drag bucket of each of these polars is de-L -Ll,..Design

fined as the incremental compressibility drag and assumed to vary asa function of AM from M^ . . independent of lift coefficient. TheDesignremaining incremental drag above and below ACT =0, i.e., CT

L LT-

Design,is defined as the pressure drag and is assumed to vary as a function

.esignB

of AM from M_ . at a constant AC from CD ^

TDesign

The above data reduction process was applied to each wing-body data set

and the resulting data correlation is presented in the following sections.

Where appropriate, 2-dimensional data were included.

• • k. DATA CORRELATION/EMPIRICAL RELATIONSHIPS

U.I Data Base Summary

The wing-body wind tunnel models incorporating advanced airfoil design

sections are noted as W through w (see Figure 5); 2-dimensional data as

W through W , . The L-1011 flight test and wind tunnel results, W and W ,

respectively, are included as a state of the art reference. W_ is the

L-1011 wind tunnel model test data incorporating an advanced airfoil section.

Conventional wing design test data "base, not noted on the figure but included

in the correlation as another datum reference, was that obtained from

References 3, U, and 5- W% through W, test data were reported in References

6 through 18, respectively. The remaining references, 19 through 31, are

included as a bibliography of advanced airfoil design tests.

W , W , and W are the wing designs of Mr. L. R. Miranda of the Lockheed-

California Company. W.. embodies supercritical sections designed by Mr. J. A.

Blackwell of the Lockheed-Georgia Company. Wg is the oblique wing of Dr. R. T.

Jones of NASA-Ames with an airfoil section design by Dr. P. Garabedian. W is

a wing-body design by the Boeing Company of Seattle. The remaining wing and wing

body models incorporate the supercritical wing sections of Dr. R. Whitcomb of

NASA-Langley.

The boxed-in numbers simply highlight the minimum and maximum geometric

and design variables associated with this data base.

k.2 Mach and C Drag DivergenceLi

A comparison of conventional, state-of-the-art, and advanced airfoil

design wing section drag divergence characteristics at a lift coefficient of

0.50 is noted on Figure 6. The data points represent either 2-D test results or

3-D data corrected for the effects of aspect ratio and sweep using Table I. As1 an example, for an effective thickness ratio of 11 percent, advanced airfoil design

gains over conventional airfoils are of the order of AM = +0.07- Compared to

state-of-the-art airfoils, these gains are of the order of AM = +0.03 to

+0.0i*. Limiting thickness ratios, minimum and maximum, for incorporating

advanced airfoil design practices have not been reported on to date and

caution should be exercised in extrapolating much beyond the available data.

9

TABLE I. INCREMENTAL MACH NUMBER CORRECTION TO DRAG DIVERGENCEDUE TO ASPECT RATIO AND SWEEP

AR AM A M

1.52.0

2.5

3.0

3.54.0

5-06,0

8.010.0

12.0

20.0

0.097

0.074

0.058

0.047

o.o4o0.035

0.028

0.023

0.018

0.014

0.012

0.008

0

10

1520

25 .

303540

4550

5560

0

0.004

0.0080.0160.028

0.042

0.0570.075

0.0950.115

0.1370.160

10

aM

'DE

SIG

NX^

ineo0*

^r tm

sd

•i MI

(OCOd

^ •»

tv!*•d

inr*r»d

(O

end

[8]'r»lIs*

5d

CO

%d

CO

end

x-

ti

<o >Ao M inin co 9d d d

ro»i8

CO

-PbO•HrHP-4

a?ccUl00s •o i

'asU.U_

Ul

,«

^7

|

5

'««-'

in0

0inCO

mento

i-' '

ino

0

8

inento

rsf-' C

in o0* «!

0 Cin cCO C

in fcen lato* [o

in M4 (N

9 tO

f *(

3 0J CM'M CM

51 co3 <Oa] co

«-'

COen

o

$

sr>

CM

folI1**!Li«J

IcolCM

|tsj|

Oin

end

ixot^

lo 1

111§(0

0s

f-en

CM

CM'

o00to

ffl|d|

1 ol| iri|" ^

iRlcol

S * co m(O O O

.J ,J CN CM

o o o oO O t- T-^™ ^™ ^™ f™

I I I 1

1 1 1 11 1 ) 1

cooH

E>zI

•Ho

CH

•H

< >5

0) «o sCO 1

r^ ra<; d)CO

"d COS pqCO

CO-P -PrH CO<; CH-OI rH

4U <1)-P T3

0

1

in to co

O »- CM CO ^

g" s" af g" g"

D O a

D0) 0)

40 £-P 3CQ EH

ITN

a>rH

11

0.10 0.14 0.18 0.22 0.26 0.30 0.34 0.38

(t/c) 2/3

ADVANCED AIR FOILS

•SHE CONVENTIONAL AIRFOILS 5

Figure 6. IVL Correlation Approach - CL = 0 . 5 0

12

Recognizing that drag divergence Mach number may also "be sensitive to

other first order airfoil geometric variables, additional correlating para-

meters were investigated and are noted on Figure 6. The parameter (Mn o2n - l)2/0 t-—D

versus (t/c) was suggested in Reference 2 and appears to improve the

correlation. Effects of camber are also noted on this figure and reflect

a slight variation in divergence Mach number with increased camber at this

lift coefficient. At lower lift coefficients, the effects of high camber

become more predominant. For -purposes of this study, a linear variation of2 p / *3

(NL_ - l) vs (t/c) , representative of cambers up to &2.2%, is assumed

and this correlation is presented for lift coefficients from 0.10 to 0.80 on

Figures 7 through lU. Tables II and III are included to aid in determination2

of the WL T- and t/c relationships to the chosen parameters (M~0 - l) and0/_D<£-U ud-D

(t/c)2/3.U.3 Design Lift Coefficient

The determination of CL . is the key to this data correlation technique,

Through this definition there is a single optimum polar selected for a given

aircraft geometry.

The initial study premise, that each wing-body wind tunnel data set has

its unique design lift coefficient, implied that certain configuration

relationships would determine'this lift coefficient. The classical definition

of CT (the lift coefficient corresponding to (L/D ) suggested those•"-•optimum e _ max &to

correlating parameters, since CL = f (VeTTAR \fc ~.) On Figure 15 the

CL_, • for the wing-body configurations of this study are noted as a function

of wing aspect ratio. By normalizing those data to a single level of CD =

0.0160 and recognizing section camber as a contributor to CL . , the.us si§nrelationship shown on the left of Figure 15 was determined.

h.k Compressibility and Pressure Drag

An assessment of the magnitude of the various incremental contributors

to total drag is in order prior to review of the following section.

The percentage contribution of the compressibility plus pressure drag

to the total drag of an existing wide-body transport at the design conditions

of M = 0.85 and O.U6 lift coefficient is some Ik percent. This contribution

13

(L.a-za.

oOJ

o

o•H-PCO

OO

o-p

CVJ

CO

W)•rH

15

oen

o

§•H-PCO,-)<D

ouo-pto

PiCM

16

o

oII

o

§•H-P03

f-iOO

w

PiCM

HH

0)

CM

18

oVD

O

II

O

o•H-P

(L)

OO

O

-P

w

PICM

(MrH

Q)

19

Oc-•

O

II1-q

O

§•H-P

0)

!HOO

O

-P

W

CVJ

oo

20

oI

g•H4^>cdiH0)

ouCJ

POJ

21

- \ \a D -

TABLE II. MD 2-D'

V t- ^L.

0.60

0.62

0.6UX /"0.66

0.68

0.700.72

0.7^

0.76

0.78

0.80

0.82

0.8U

0.86(~vO0.88

0.90

0.3600

0.38^OA096OA356n kA?UU . M-Ot.'T

0.^9000.518^0.5^760.57760.608U

0.6^00

0.672^0.70560.73960.77^0.8100

-0.6UOO

-0.6156

-0.590^-0.56^-0.5371

-0.510°PL kRT 6— U . H-OJ-*-1

,-v )ic;oh.-Q.H-y^r\ ) \OO\i_0.'+c-c-H^

-0.3916-0.3600-0.3276-0.29^-0.260U

_0.2256

-0.1900

22

TABLE III . t/c, (t/c)5/3, (t/c)2/3, and (t/c)1/3 RELATIONSHIPS

t/c

O.o40.05

0.06

0.07

0.08

0.090.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.180.190.20

(t/=)5/3

0.004680.006790.009200.011890.014850.01807

0.021550.02526

0.02919

0.033370.037750.04235O.o47l6

0.05218

0.057390.06280

0.06841

(t/c)2/3

0.1170.

0.1357

0.15330.1699

0.18570.2008

0.2154

0.2295

0.24330.2566

0.2696

0.2823

0.2947

0.3068

0.3187

0.3304

0.3419

(t/c)1/3

0.3420

0.36840.39150.4121

0.43090 4- 1-8 1

0 • 4-6 -1-2

0.47910.49320.50660.51930.53130.5429 .

0.55400.5646

0.57490.5848

23

30)•HO

•H<HCH0)oo

£•H1-3

g,•HW0)OCHO

§•H-PCS•-)0)inJHOO

ir\r-l

<D

M•HP4

is essentially equally divided as 7 percent compressibility and 7 percent

pressure. The remaining drag is comprised of 33 percent induced and 53

percent friction, dirtyness , leakage, and interference. As the Mach number

is increased to 0.89, AM = +0.0**, the (AC + ACL, ) contribution increasesDC Dp

to some 30 percent. Reducing the Mach number to M = 0 . 8 0 , A M = 0.05, this

contribution is in the order of 10 percent of total drag.

In evaluating the compressibility plus pressure drag of 2-dimensional or

3-dimensional wing-body test data, consideration must "be given to the test

Reynolds number, location of the boundary layer trip grit, and wind tunnel

blockage. The sensitivity of /ACD + A C n j t o Reynolds number is noted on

Figure 16. The design conditions were approximately Cn = 0.60 at a Mach number

of 0.79. As the test RN is increased, the level of ( A CD + CD ) tends to

reduce or bucket as the design Mach number is approached. These effects will

be noted in the following 3-D correlations and are in the main evidenced in the

ACn_ term.JJp

U . U . I Compressibility Drag. - On Figure 17 ACp is presented as a function

of AM from NL . for the wing-body data sets and the L-1011 state-of-th'e-art

reference flight test and wind tunnel data. At the top of the figure, the

unadjusted compressibility drag shows scatter on the order of 20 counts of5/3

drag, i.e., AC = 0.0020. The correlating factors of ( t /c) and camber

h/c % (lower curve, Figure 17) were those suggested in NACA TR 1253 - Cor-

relation by Transonic Similarity Rules . Up to IVL . the correlation of data.L/C S1 Qfii

appears exceptionally good. Data scatter above M^ . may be attributable toiJQ S1 §il

varying test Reynolds number, test grit location, camber, and section variation

with span, or to the degree of refinement of model following flow visualization

studies of shock buildup across the span. A fairing of these data against a

logorithmic scale is presented on Figure 18.

k.h.2 Pressure Drag. - Pressure drag is presented on Figure 19 through 28

for ACT 's ranging from minus 0.1+0 to plus 0.20. Figure 2k (upper curve)LJpresents the uncorrelated data sets at CL . . Design C for the data sets

ranged from 0.275 to 0.55 and Mach design from 0.73 to 0.97. Approximately

20 counts of data scatter are noted up to design Mach number with increasing

25

0.008

0.006

0.004

0.002

toon

@

SYM RN X10" GRIT

0.60 0.80 0.84

MACH NUMBER-Mc

Figure l6. 2-D Compressibility and Pressure Drag Variation• with Reynolds Number

26

0.008

-0.20 -0.16 -0.12 -0.08 -0.04

AM = Moo-M

0.04 0.08

Figure 1?. Incremental Compressibility Drag Variationwith Incremental Mach Number from Mach Design

27

• ,N T* 3

1 • i'•,

3 On . "31

s o

'!.,

* * x

ii

\

I1

~T~ i_1

1

1

3 s=> o

TT

s^ ^ .

"^ w

jt

^ t

\^.

j— • 5 "^

^-k

-

n .1 _

I. i. ._

i ,i

i I

. . . . . I . I ._o <of- Oo o

T • ~r~

_ _ J _ , ^ . . . _ _ . ^ _ j _ . ^__Lj — I 1

t

.* .\ t. i

i' i ,

.*

\ '_ _. . ,- i

iV

1 '1 "

__ . .t... .1 _ _^. [... t J

1 1 1L>

1. _ .. . k

_ .. . L_ --t - ^I ' ' '

L ' -r ^

_ .1. .^

I I I

1 1 1 1

«* «MO OO O

co

_

o

€N

CO

OCMO

!>>M

CO

M05JHO

>>-P•H

C/S -HUl ,0Q -H

JS O

<I o

H

<HO

a•H?H•HCO

CO

^0)

bO•H

00bv

28

0.008

-0.20 -0.16 .12 -0.08 -0.04

AM=Moo-M

*\04

Figure 19- Incremental Pressure Drag Variation withIncremental Mach Number from Mach DesignACT = -O.kOL

29

0.00.8

O.OOF

0.004

0.002

:5t

0.016

-0.20 -0.16 -0.12 -0.08 0.04

AM = Moo -MDES

0.04 0.08

Figure 20. Incremental Pressure Drag Variation with Incremental Mach Numberfrom Mach Design -ACT = -0.30

L

30

0.008

0.006

-0.20 -O-16 -0.12

AM=Moo-MDES

0.04 0.008

emental Mach Number

31

0.008

0.006

o.Q

U

0.004

0.002

Q.Q

0.016

0.012

CO

> 0.008

0.004

-0.20 -0.16 -0.12 -0.08 -0.04 0.04 0.08

AM = Moo -MDES.


L

32

0.016

0.04 0.08

-MDES.


L

33

0-0.20 -0.16 -0.12 -0.08 -0.04

AM = Moo - MDES

0.04 0.08

Figure 2k. Incremental Pressure Drag Variation with Incremental Mach Numberfrom Mach Design -ACT = 0

L

0.04

O r-

-0.20 -0.16 -0.12 -0.08 -0.04 0.04

MDES.

0.08

Figure 25. Incremental Pressure Drag Variation with Incremental Mach Numberfrom Mach Design -ACT = +0.05

L

35

-0.20 -0.16 0.04-0.12 -0.08 -0.04

AM = Moo - MDES

Figure 2.6. Incremental Pressure Drag Variation with Incremental Mach Numberfrom Mach Design -ACT = +0.10

0.08

36

O C

-0.20 -0.16 -0.12 -0.08 0.04 0.04 0.08

= Moo-MDES

Figure 27. Incremental Pressure Drag Variation with Incremental Mach Numberfrom Mach Design -ACT = +0.15

L

37

0.(K

0.03

QO 0.02

0.01

0.08

? 0.06

a.Q

co^ 0.04

0.02

I.20 -0.16 -0.12 -0.08 -0.04

AM = MOO -MDES

0.04 0.08

Figure 28. Incremental Pressure Drag Variation with Incremental Mach Numberfrom Mach Design -Acr = +0.20

38

scatter above. Again, the correlating factors suggested in NACA TR 1253, i.e.,1/3

( t /c) and camber h/c %, were employed to adjust the data sets for varying

geometries (lower curve, Figure 2 U ) . Again the correlation is improved up

to design Mach number with increasing data scatter above.

Around NL . , grouping of the data pinpoints the desirable reduction inj-'Gsi^npressure drag evidenced from the 2-D tests noted on Figure 16. Figures 19

through 21 and 25 through 28 present both uncorrected and adjusted ACc

for A C ' s ranging from -O.Uo to +0.20. (Note scale changes.) At aLIAC = -O.UO, Figure 19, and AM's above 1YL . the effects of camber do notL » o x Tiesignappear to be sufficiently accounted for by the h/c correction. The deviation

of the W, data may be attributable to lower surface shocks and separation which

was also evidenced in the Mach divergence characteristics of Figure 7 through

lU. It should be pointed out, however, the a AC = -O.UO represents a veryLi

low lift coefficient, i.e., 0 to +0.15, for the majority of the data sets and

is seldom a lift coefficient corresponding to any flight phase of a transport.

Figure 29 summarizes the ACp faired variation with £M for AC , of -0. 0T) J_i S

to +0.20.

U.5 Zero Lift Pitching Moments

Large negative Cm has been associated with advanced airfoil design

practices and raises a concern that this might impose significant trim

penalties.

On Figure 30 the variation of C™ with AM indicates a fairly constant

value up to NL . with some reduction above. The upper curve of Figure 30

indicates at M^ . that C™ correlates'as might be expected with camber.

For preliminary design purposes, the assumption may be made that under

trimmed'conditions and for configurations incorporating aft tails, the wing

must carry an additional lift equal to but opposite in sign to the tail down

load. This increment in lift is AC = -Cm /-=-. At the design C and Mach£tnumber for a 10$ thick airfoil cambered 1.6% with an -=• = 3.0, the wing will

carry approximately 3 counts of trim drag to provide extra AC . The increased

down wash at the tail and resulting angle of the tail lift vector may subtract

from this trim drag; however, this increment would be too difficult to predict

in the normal preliminary design study.

39

CO

o>

3w0)

rHCC-p

O)JnO

<t-tO

bO.s!s

•H05

CM

0)

bo•HP-H

0.1

-0.20 -0.16 -0.12 -0.08 -0.04

AM=MOO-MDES

0.04 0.08

Figure 30. Zero Lift Pitching Moment Variation with Camberand Incremental Mach Number from Mach Design

Ui

h.6 Buffet Onset

For purposes of this discussion, buffet onset is defined as the break in

axial force versus lift coefficient or for those tunnel models employing root

strain gages as the lift coefficient corresponding to a rapid rise in the RMS

root bending moments.

A systematic buffet investigation was conducted by NASA and results were

reported in NASA-TN 5805. The wings of this test series employed 63, 6k, 65,

1+5°, and aspect ratios U to 6. Previous buffet correlation attempts by

Lockheed employing the data of this report had shown a reasonably good

correlation of buffet onset with C^ . . Some buffet data were obtained on

the advanced airfoil designs employed in this study, and a comparison was made

(Figure 31) to compare buffet characteristics of conventional and advanced

airfoil sections.

The variation of the advanced W and W wing/body C Buffet versus AM[ -LU .' Ij

exhibits a vastly different character. W exhibits the same variation with

AM as a conventional airfoil, while W , which is more representative of

actual flight experience, has a very different variation. The reason for

these differences in buffet onset variation are not understood and certainly

additional effort is required in buffet prediction techniques.

h.l Airfoil Section - Pressure Drag - Form Factor

The friction drag buildup process for preliminary design configurations

will generally involve knowledge of both the wing and body form factors as a

function of wing section and body geometry.

c = c x F F Wet

On Figure 32 this form factor has been developed for advanced airfoil

sections and also presents data for a NACA 65 series section for reference.

The parameter F.F = CD /2 C- is simply the 2-dimensional minimum section drag

coefficient divided by twice the flap plate skin friction coefficient at the

test Reynolds number. The factor of 2 accounts for both upper and lower sur-

faces. The data, from top to bottom on Figure 32, is from 2-D tests on a

U2

REF. 5 WING DESIGNATIONS

-0.20 -0.16 -0.12 -0.08 -0.04

I = Moo - MDES_

0.04 0.08

Figure 31. Lift Coefficient for Buffet Onset

1*3

Ill

5a.

5U.

9° 0.5 m

0.5

3 4

REYNOLDS NUMBER~/>Vc~RN/106

M

Figure 32. Conventional State of the Art, and Advanced Airfoil Section -Ratio of. Minimum Drag to Theoretical Skin Friction Drag

conventional NACA 65, 213 a = 0.5 airfoil, 9 percent thickness ratio state-of-

the-art airfoil, and 10 percent and 11 percent thickness ratio advanced air-

foils, respectively. The flagged versus unflagged symbols represent same

model tested in two different facilities. On Figure 33> the average fairing

of C-n /2 C,,, is shown as the form factor versus the section thickness ratio.o /•

The NACA 65 series airfoil results confirm the variation given in the RAS data

sheets and USAF DATCOM. At a thickness ratio of 10 percent the advanced air-

foil appears to carry an approximate 10 percent increased subsonic pressure

drag over the conventional airfoil sections. Subsequent advanced airfoil test

results (data unpublished) of 2nd generation designs are included on Figure 33.

Additional information on 2nd generation airfoils is included in Appendix A.

Figures 3^> 35} and 36, which were not derived as part of this study,

are presented as part of the total drag buildup procedure to be discussed in

a later section.

5. DRAG BUILDUP PROCEDURES

The correlation techniques developed in the previous sections can now

be combined to define a systematic procedure for the total drag buildup of

arbitrary transonic aircraft incorporating advanced airfoil wing sections.

The geometric characteristics of an example twin-engine transonic trans-

port are itemized on Figure 37 and will be used to demonstrate the drag build-

up process. It should be emphasized here that, any interference or compress-

ibility drag of nacelles or tails, and incremental drag due to inlets, antennas,

or other proturbences, is an additive drag element that must be derived from

other sources.

The initial step in the drag buildup procedure, graphically described on

Figure 38, involves the determination of the aircraft design lift coefficient

and design Mach number. The derivation of C^ . involves the determination

of the minimum pressure drag at M = 0.60 at the nominal mission altitude. For

this example 30,000 ft has been selected. Aircraft component drag buildup is

on Figure 38 along with those text figures required for the computation. Using

this computed Cn . , percent wing camber, and wing aspect ratio; CT is* Dpmin' if « > o Design .

• COCO111

wfnO-POCO

go§•H-PG

^0)CO

UD

ooon0)

60•H

1.9

4 6 8 10

FUSELAGE FINENESS RATIO~i/rf

12 14

Figure 3^ Body Form Factors

oo

'•b

52 IX

zoc

0)w

0)•HO•H

0)OO

g•H•PO

•H

0)H

JH--XCO CM

0) <Hfn O

S CMOO -PCj Q)

[ "^ N __ X

COH SHPH 0)

,0-P S03 3

w-c!

g,O•H-PCO•H

I

CO

0)

tiO•H

0)

ocinm

O<

1•HO•H

0OO

§•H-PO

fl•HM03

O-P

§•H•PO(1)

OO

•p•H

•H03W

• fO

VDCO

bO•H

50

CC

HI

O

0I—UL<

AIR

CR

CM

_ S vP to9 °to 8 S w r, §IX CO C> t— ^ CM CO

II II II II II II II

rt- "S U.— - "7Z O • LLJ

a- «• ^ -S ^ ccst < ^ -ii j= -< co

U.111CC

w"h-

LU

CM

I

O2ill

LUCC

2LU

OD.

OU

o q oI co oi o> I

qod

05 I I I CM I

LO in o oo i— toin <o r» i- « r*.•* rx in CM f-; qCM r^ O O d d

oo o o CM oo i-op o h« in in co3 «- o>oo to i-

in<o

^ co cp q in o>r> ^ r* r* ' r^i- CM f t- t- CM

f-l•pIO)O

OftwaCO

EH

O•H

§WS303

Q)

SI

•Htoa

OS

t-ro

bO•H

51

determined. Computation of Mach design involves determination of the

2-dimensional equivalent divergence Mach number for the wing section at

the design lift coefficient. This M_ 2 _ is then corrected for wing aspect

ratio and sweep to obtain the 3-dimensional drag divergence Mach .number, which,

at CT j is equivalent to M^LDesign Design

At this point, the lift coefficient and Mach number have been determined

for best cruise. The total drag polars can now be defined for any Mach-

Altitude condition; however, for purposes of this example buildup, the best

cruise Mach number is chosen. Note that if other than best cruise altitude

is selected for off design polar determination, minimum pressure drag must be

computed based on the Reynolds number and C,, associated with that altitude

Mach number condition. In the final aircraft preliminary design sizing proc-

ess, off design Mach number polars would also be investigated to assure an

airframe-propulsion system match for all mission segments.

The next step in the drag buildup procedure involves the computation of

the minimum pressure drag, the induced drag, compressibility drag, pressure

drag, and trim drag at the design Mach number of 0.85 and altitude of 30>000

ft. These computations are shown on Figure 38 in tabular form. Most of the

steps are self evident. Column (3) is equivalent to the trimmed CT = ¥/ S,,™.^ li q JxEirThe AC due to trim is an additional lift which must be carried on the wing ,

jjto balance the tail down load required to trim the wing pitching moment. For

this example a zero static margin was selected; hence, the required trim is

only that amount necessary to overcome the negative C™ of the wing = -O.OU.

Perhaps, with advancement in active control technology, this trim requirement

on resulting drag can be reduced to zero at the design conditions. Column (6)

is the incremental lift that the wing is experiencing from the design lift

coefficient. The remaining computations are relatively straightforward, with

the possible exception of H/H and (2m . In determining the AC,, , the param-*" IP

eter presented on Figure 29 must be crossplotted versus ACT at AM = 0 toLIallow interpolation of the pressure drag contribution at the AC, represented

Jjby column (6) . The final drag represented by the summation performed for

column (20) must be plotted versus the CT = W/ of column (3)to represent theX^LrX Jj j.S ~

trimmed aircraft polar. For determination of drag polars at other Mach-Altitude

conditions, the same process is followed, i.e., computation of columns (l)

through (20J, respectively.

52

SELECT

AIRCRAFT GEOMETRY

SEE FIGURE 37

1COMPUTE Cn

°PMINM = 0.60 @ 30K

F.F.

FIGS. 33&34

Cfi

FIG. 36

t/cOR i/d RIM X 10° M

ICOMPUTE CLDES|GN

I

1.06

7.0

AR

CLDES =1-06XV0.0150 X 1.16

CLDES= 0.453

AM

COMPUTE MDES|QN

& I TABLES II & III

(t/c)^

[ TABLE I

0.057

35°

Ac/4

9C<1O

O

qo

qo°

0 n01 inO CQ

5 <=>

tauja O

COMPONENT

FUSELAGE

WING

HORIZONTAL

VERTICAL

NACELLE

PYLON

ROUGHNESS & LEAK/!

RN/106

302

41

30

29

25

37

VGE (NOMINAL 6°/

Cfi

0.00175

0.00225

0.00240

0.00240

0.00245

0.00230

,)

F.F.

1.15

1.60

1.31

1.31

1.09

1.28

See NoteSection 4.7

(RN/FT = 1.71 X 106)ACn =C f jX F. F. X !DPMIN Tl

^ET/SREF

2.455

1.765

0.570

0.218

0.191

0.076

JWET X Cf TOTA

SREF Cfi

Cf/cCfi

0.966

Ac0DPMIN

0.0049

0.0061

0.0017

0.0007

0.0005

0.0002

0.0009

LCn =0.0150UPMIN

0

DES

0.45

MDES

0.85

LTRIM

0.100.200.300.400.4350.5000.5500.600

(SELECT)

ACTRIM

0.015

Section 4.5M-0.04

2.7

0

AMPMIN

[email protected]

ACDC

0.067

FIG. 18VS

COL(?)

CL/7TAR

> 0.0006' 0.0021

0.00450.0078

, 0.00920.01210.01450.0172

1.16

0.000380.000330.001 10.00250.00320.00830.01330.0197

IFIG. 29VVS

©

WING

0.1150.2150.3150.4150.4500.5150.5650.615

AC,WING

-0.335-0.235-0.135

0.0350

0.0650.1150.165

-0

0

0.85/30K

(SELECT)

(t/c) 5/3

0.0334

[TABLE in|

(t/c) 1/3

0.5066

[TABLE in]

0.0388 0.588

0.0026 0.00020:0002

0.00060.00150.00190.00490.00780.0116

CD TOTAL0.01820.01970.02250.2670.02850.03440.03970.0426

PLOT VS

COL 7

Figure 38. Drag Buildup FlowDiagram

53

KJLDOU? FRAME /

HOLDOUT FRAME

6. 2-D AND 3-D COMPARISON OF COMPRESSIBILITY AND PRESSURE DRAG

The objective of this section is to establish an equivalence comparison

between 2- and 3-dimensional compressibility and pressure drag which might

permit (l) an assessment of an ultimate potential of advanced airfoil design

practices, (2) indicate some of the-penalties associated with applying 2-D

characteristics to the 3-D wing, and (3) indicate a degree of data sensitivity

to some of the major test variables.

On Figure 39 "the fairing of the 3-dimensional wing-body compressibility

and pressure drag increments; adjusted for the effects of aspect ratio, sweep,

camber, thickness ratio, C^n . and M-. . , using the methods developed in

this report; are compared with 2-dimensional test data for a 10 percent thick-

ness ratio, 1.6U percent camber, advanced airfoil section. The flexibility of

the definition of advanced airfoils; sensitivity of the component drag data to

the test variables; varying design techniques employed by the principal inves-

tigators in arriving at the 3-dimensional wing section, camber, and twist; and

the varying degree of model refinement during testing all contribute to the

data scatter previously evidenced in the 3-d.imensional data. However, the

conservatism in the faired 3-D data relative to the 2-D data appears mainly

attributable to differences in test Reynolds Number, i.e., 3-D wing-body tests

are generally conducted at RN = 2 to 3 million. Additional comparisons are

noted on Figure UO for other AC , . The agreement between 2- and 3-D becomesJLi S

increasingly better at the lower lift coefficient with increasing disagreement

above Design CT.Li

At the present stage of development of advanced airfoil design practices,

it is believed that for preliminary design of aircraft for transonic cruise

applications the potential of advanced airfoils is best represented by the

3-dimensional data fairings of the previous .sections. Additional tests and

data analysis, the subject of the next section, certainly are in order to

sort out the 2-dimensional and 3-d.imensional equivalence differences and in

particular the sensitivity to Reynolds Number.

PRECEDING PAGE BLANK NOT55

7. REG OMMENDATIONS

The advanced airfoil data correlation and drag buildup technique arrived

at in this reporting may assist in determining the potential of advanced air-

foil^ applications; however, there remain major and significant areas of fur-

ther study. These study areas are itemized below:

1. Systematic definition of 2-D design-to criteria and testing toisolate the sensitivity and limitations of the geometric varia-tion on

• design lift coefficient and Mach number

• lift coefficient for buffet onset

• maximum lift coefficient

• zero lift pitching moment

. • minimum pressure drag

2. Determination of the 2- and 3-d.imensional equivalence in the aboveparameters and 3-D design procedures using 2-D data.

3. Systematic 3-D testing of higher aspect ratio wings including buffetonset studies.

h. Continued development of empirical relationships such as those devel-oped in this study extending into maximum lift and pitching momentcorrelation.

5. Empirical correlation of lift, drag and moment characteristics ofhigh-lift devices on wing/body's employing advanced airfoilsections.

6. Systematic wind tunnel investigations to determine the potential ofadvanced airfoil design practices for supersonic cruise applications.

0.006

0.004 p

0.002

AM = Moo

u

0.012

0.010

0.008

9 0.006

0.004

0.002

REFERENCE22-D REF 15, TRANSITION FIXED@ O.OBc, t/c = 10%, h/c = 1.64%

2-D DATA BAND REF. 153-D FAIRING FIG. 18 AND 29

-0.20 -0.16 -0.12 -0.08 -0.04 0.04

Figure 39- Ac and Ac Comparison - 3-D Fairing vs 2-D Test Resultsc p 5T

0.008

0.006

0.004

0.002

EFor t/c=10%h/c=1.64%

-0.20 -0.16 -0.12 -0.08 -0.04

AM = Moo ~

0.04

Figure kO. AC Comparison - 3-D Fairing vs 2-D Test ResultsP

58

REFERENCES

1. Miranda, L. R. : Three-Dimensional Supercritical Wing Design. LR 270U8,May 1975.

2. McDevitt, John B.: A Correlation by Means of Transonic Similarity Rulesof Experimentally Determined Characteristics of a Series of Symmetricaland Cambered Wings of Rectangular Planform. NACA Report 1253.

3. Burdges, Kenneth P.; Blackwell, James A.; and Pounds, Gerald A.: HighReynolds Number Test of a NASA 65, -213, a = 0.5 Airfoil at TransonicSpeeds. NASA CR-2it99 , 1975.

k. Abbott, Ira H.; and Von Doenhoff, Albert E. : Theory of Wing, Sections.

5- Ray, Edward J.; and Taylor, Robert T. : Buffet and Static AerodynamicCharacteristics of Systematic Series of Wings Determined from Subsonic-Wind-Tunnel Study. NASA TN D-5805, 1970.

6. Anon.: L-1011-1 Flight Performance, RB.211-22B Engines. LR 26189,December 1973.

7. Anon.: Transonic Wind Tunnel Tests of the 1/30 Scale L-1011 Airplane,Lockheed Tests Wo. N-227, N-236, N-2^1. Cornell Aeronautical Laboratory,Inc., Report No. AA-U006-W-1, March, June, July 1969.

8. Chudyk, D. W.: Wind Tunnel Test of a 1/30 Scale Model L-1011 AirplaneUtilizing a Supercritical Wing. Calspan Report No. AA-U006-W-29,W.A. T06-53, June 1975.

9. NASA/Lockheed-California Company. Contract #N00019-73-C-OOl*0, 197^.(Report to be published).

10. Blackwell, J. A.; Dansby, T.; Little, B. H. , Jr.; Ryle, D. M. / J r . ;Allison, H. B.: Aerodynamic Design, Test, and Analysis of the Lockheed-Georgia ATT-95 Aircraft. Lockheed-Georgia Company Report LG 72ER OOi+1,1972.

11. Ferris, James C.: Static Aerodynamic Characteristics of a Model with a17-Percent-Thick Supercritical Wing. NASA TMX-2551, 1972.

12. Graham, Lawrence A.; Jones, Robert T. ; and Boltz, Frederick W.: AnExperimental Investigation of the Oblique-Wing and Body Combination atMach Numbers Between 0.60 and l .UO. NASA TMX-62,256, 1973.

59

REFERENCES (Continued)

13. Bartlett, Dennis W.; and Re, Richard J.: Wind Tunnel Investigation ofBasic Aerodynamic Characteristics of a Supercritical-Wing ResearchAirplane Configuration. NASA TMX-2U70, 1972.

lit. Capone, Francis J. : Effect of Various Wing High Lift Devices on theLongitudinal Aerddynamic Characteristics of a Swept-Wing Fighter Modelat Transonic Speeds. NASA TMX-320U, 1975.

15. Burdges, K. P.; Blackwell, J. A., Jr.; and Pounds, G. A.: High ReynoldsNumber Test of a NASA 10% Thick Supercritical Airfoil at TransonicSpeeds. NASA CR-132U68, 1975-

16. Harris, Charles D.: Aerodynamic Characteristics of an Improved 10-Percent-Thick NASA Supercritical Airfoil. NASA TMX-2978, 1971*.

17- Harris, Charles D. ; Blackwell, James A., Jr.: Wind-Tunnel Investigationof Effects of Rear Upper Surface Modification on a NASA SupercriticalAirfoil. TMX-2U5U.; 1972.

18. Harris, Charles D.: Aerodynamic Characteristics of Two NASA SupercriticalAirfoils with Different Maximum Thicknesses. NASA TMX-2532, 1972.

19. Fournier, Paul G.; and Goodson, Kenneth W.: Low Speed AerodynamicCharacteristics of a 1+2 Swept High-Wing Model Having a Double-Slotted'Flap System and a Supercritical Airfoil. NASA TMX-3036, 197*+•

20. Bartlett, Dennis W.; and Harris, Charles D.: Effects of Wing Trailing-Edge Truncation on Aerodynamic Characteristics of a NASA Supercritical-Wing Research Airplane Model. NASA TMX-302U, 197^.

21. Goodson, Kenneth W.: Low Speed Aerodynamic Characteristics of aRectangular, Aspect Ratio-6, Slotted Supercritical Airfoil Wing HavingSeveral High-Lift Flap Systems. NASA TMX-2317, 1971.

22. Harris, Charles D.: Wind Tunnel Investigation of Effects of Trailing-Edge Geometry on a NASA Supercritical Airfoil Section. NASA TMX-2336,1971.

}23. McKinney, Linwood W. •, Herman, Joseph F.; and Boden, Lawrence A.: Effect

of Wing Mounted Nacelles on a h2 Swept Supercritical Wing Configurationat Near-Sonic Speeds. NASA TMX-2951*, 1971*.

2U. Supercritical Wing Technology, - a Progress Report on Flight Evaluation.NASA SP-301, 1972.

60

REFERENCES (Continued)

25. Bartlett, Dennis W.; and Harris, Charles D. : Effects of Wing TrailingEdge Truncation on Aerodynamic Characteristics of NASA Supercritical-Wing Research Airplane Model. NASA TMX-302^ ,

26. Caldwell, A. L.; et al. : Technology Integration for Close SupportAircraft. AFFDL-TR-73-59 , 1973-

27- Harris, Charles D.; and Bartlett, Dennis W.: Wind-Tunnel Investigation ofEffects of Underwing Leading Edge Vortex Generators on a Supercritical-Wing Research Airplane Configuration. NASA TMX-2 71, 1972.

28. Pyle , Jon S.;and Steers, Louis L. : Flight Determined Lift and DragCharacteristics of an F-8 Airplane Modified with a Supercritical WingWith Comparisons to Wind-Tunnel. Results . NASA TMX-3250, 1975-

29. Revell , James D. : Analysis of Transonic Independent Research Data Basedon. Transonic Tests on Airfoils 1 to U Conducted at ARA 8" x 18" 2-DTransonic Wind Tunnel. LR 23162, 1970.

30. Bartlett, Dennis W.: Application of a Supercritical Wing to AnExecutive-Type Jet Transport Model. NASA TMX-3251, October 1975.

61

APPENDIX A

Subsequent to the development of the drag buildup procedures presented

in the body of this report, additional advanced airfoil wing-body wind tunnel

data was made available through NASA Langley. (See Figure A-l. )

Analysis of these data by the previously discussed procedures resulted

in appreciable reduction in the parameters AC and AC with some slight

penalty in drag divergence Mach number.

These new fairings of M^ n, AC , ACn are noted on Figures A-2

through A-7 and are recommended for use as "Advanced Airfoil Design-Potential"

drag buildup.

The more salient features of these advanced airfoils are

• A reduction in the compressibility drag parameter, i.e., drag creepfor all Mach numbers. The fairing of the data on Figure A-3- reflectslevels attained on 2-dimensional sections, i.e., W .

• The pressure drag parameter reflects appreciable reduction in pressuredrag and the Mach number is increased towards Mach design. (SeeFigures A-3 through A-7. )

• Drag divergence Mach numbers are reduced approximately AM = ±over the Advanced Airfoil reported on in the body of this report.(See Figure A-2. )

• The form drag appears to be unchanged. Figure 33 form factors arestill recommended.

• For a wing-body having an effective wing thickness ratio of 10 per-cent, the "Advanced Airfoil Design-Potential" compressibility andpressure drag would be approximately ih drag count lower at M,

and CTr, . than the Advanced Airfoil reported on in the body ofLDesign * .this report.

A-l

COUJQ

COUJQ

o

g.

> UJO 00

oc<

CO

CM to in ino <o en «-r» i*. r*. eqo o o o

s <o § §

in oo«- CO 3 2

00in ooin ooinoi

OJ

om

S - CMin 4- ooo> o> 01 •*r r 0 i-:

A-2

•0.8

-0.6

-0.4

CM

-0.2

9 oCMO

0 —

'O.TOf 0.14 0.18 0.22 0.26 0.30 .0.34 0.38

(t/J 2/3c'eff

Figure A-2. Drag Divergence Mach Number -

A-3

0.016

0.012

CLQ

U

0.008

0.004

OQ

U

0.16

-.0.12o

*"fr+

0.08

0.04!

-0.20 -0.16 -0.12 -0.08 -0.04 0.04 0.08

M - MDES

Figure A-3. Incremental Compressibility and Pressure Drag

A-U

0.016

0.012

0.008

0.004

o<

o 0

0.04

0.03

0.02

0.01

0 -----

-0.20 -0.16 -0.12 -0.08 -0.04 0.04 0.08

Figure A-U. Incremental Pressure Drag, AC = +0.05 and +0.10

A-5

0.04

0.03

0.02

••: •-. A c, =+.20 .

-0.20 -0.16 -0.12 -0.08 -0.04 0.04 0.08

M -MDES

Figure A-5. Incremental Pressure Drag - ACT = +0.15 and 0.20LI

A-6

0.006

o:bo4

0.002

i A CL - .20

o <&

0

0.008

a.Qu

0.004

0.012 •

0.008

0.004

AC, =-.10

e

-0.20 -0.16 -0.12 -0.08 -0.04 0.04 0.08

-MDES

Figure A-6- Incremental Pressure Drag - &C = -0.05, -0.10 and -0.20

A-7

r

0.004

0.002

•• - ----- • AcL=-o.eo : :'-- - - - \ • . • • - -^

: . . ' . . " : • • . « *- - tfS .

' . . . - ' ' . " • ' ' ' • . • • : ! . ::*v: •• ' -- .- . & : . ' • '*,'."& J* L

• • . - . • : : - . • : : - . . : , . "11; • " • ' • • " <£

... - . .„ ..... .. .... . .. ... .._. . . . . . ._ . . . . , . . ............ ..^ ._. ... •-;£:- -.r--;

- .'• • • ' . . ' • . • " . : • -: : : : • • ' } ' ' • • "• • : ' . ' . : • ' • ' > . - ; v. ;.: ::' --; : . "• -.. ..

. ......:::_/ • • • , - . , / • , : :^,-:-1

. . Tr . ' ' ' '". ' " ~ - :

...C'-iL-.-.'-. !'_.'•" _:!. "::--; .jj

• • • _ : • • • : -r • •_ ; • I

:v- : • • ' : ;•" . : . . - - : i ; -.-:..-'.

. . . !. : : . - - . •':. • : • • : . • ; : • : . !

a.ou

0.004

2 0.002

+ • •*••CO

5 0

.U.UU4 ' . . . . . - . - . . - - - . . -- .- . . . . . . . . . ....

- '-'. '• • . • -. '•'. ' : ' , : ; •• . - : ' : • ; . . ' - - ; ' . : ; • : "-.':' ' • ' • • ' • • ' • • ' :" ; .. • ' • • •0.002 •• : ' "" " :'" ' " " . ' ; :' " ". • — . • ." -: .". ". • ~'. -1

• : ' . ' - ' - , - , :^\:- .V,:;.:/.V.:;:\^-L-:;;^V::.:^:^:^.^^

.004 • • - • . .-. . : • . • • • . - . .-•:-.—:-:•..:• — r: :v:p : >- I:-.--—.-:-.-..- :--; •'• ' A f* n on • ' • "

. . . - : ... ' LAUl — "U.OU . . . . ^ . . . . . '

- • • . - - ! . . . . .

: : '• • ' • . . . " : " ' . . . . ' • ' " . . ' : v • ; ' . ' . ' ' . ' . . : ' : . ' ' • : . ' • ; " . : : " " .:'.. . . ' ." ... • : . . ' - . . ; • . : ' , . . • . • • . : ' . . . . : . • . : . • : : . : :' . . : ' : . - . •:': • .. :

•••-.-'-:.:-..- ; :----- :-r: ; ; ;- i~ -••r«:~~i.r'~-^-'~^:-:}—--:~~^-~^^ --<•-

0.002 • ' . - - • - • -=y:--.-- -:-~"~i-r7-::-^r^r^~;— T~~-_~H=T^-r:-r-. r:^rT-r.~ rV-:

•-• - - . - • . . - - • \ : - • • - ! -r~ i - • • • ' - - ; - - . - -

. . . . . . ."

•^f -

" ."

. . „.- ; . ._vi_. ...

:"'•"""'."•.":: :"

.,.:_ ......-.;__.:

^C^.

' . ' • • • - ' . : •;.- ' • -.".••'.' ' . '. ~. " ' ' . "

. . . ; . i - . t

_.:• : . . . - ,_: . ' . . _-.;

:•:- ;.:....-

• i»

* j;••. . : .•-• ;-.-. ::. •]

•~-.— i~-;-.— '

:; -.•'•.:.• i'::-.'!:':li

..-•. j'-u-^-'.

. •: ;:.- -:: : / i : - ; j

o •—-L-

-0.20 -0.16 •0.12 -0.08 -0.04 0.04 0.08

= MOO-MDES

Figure A-7. Incremental Pressure Drag -AC, .= -0.30, -O.: -0.50 and -0.60

A-8

advanced airfoil design empirically based transonic ... · u.5 zero lift pitching moments 39 u.6...

Documents