01-Boeing Low Speed Wake Surveys

7/21/2019 01-Boeing Low Speed Wake Surveys

1/7

J O U R N A L O F A I R C R A F T

Vol.

31, No. 2,March-April 1994

Quantitative Low-Speed Wake Surveys

G. W.

Brune*

Boeing Comm ercial Airplane

Group, Seattle,

Washington

98124

Theoreticaland practical aspectsof conducting three-dimensional

wake

measurements in large

wind

tunnels

are reviewed

with

em phasison applicationsin low-speed aerodynamics. Such quantitative wake surveys furnish

separatevalues

for thecomponentsof drag

such

as

profile

drag and

induced drag,

b utalso

m easure li t

without

the use of abalance. In addition toglobal

data,

details of the wake flowfield aswell as

spanwise

distributions

of

l i t

and

drag

are

obtained. This article demonstrates

the value of

this measurement technique using

data

from wakemeasurements conducted on a variety of

low-speed

configurations including the

complex high-lift

system of a transport aircraft.

Nom enclature

b = model span

C

D

-

total drag

coefficient

C

D

. =

induced drag coefficient

C

D

- profile drag coefficient

C

L

= total lift coefficient

c = local

wing

chord

c

d

. = wing section induced drag coefficient

c

d)

=

wing section profile drag coefficient

c, =

wing

section lift coefficient

M = Mach number

p

= static pressure

p, =

total pressure

q = dyna mic pressure

Re = Reynolds number

5 = tu nn el cross-sectional area

U

=

axial velocity

component

V, W =

crossflow

velocity components

y,z Cartesian coordinates

in

measuring plane

a = angleofattack

AC

D

= upsweep drag

= axial compon ent of vorticity, Eq. (8)

p = density

a =

source,

Eq. (9)

< I>

= velocity potential,

Eq.

(11)

^

=

stream

function, Eq.

(10)

Subscripts

f t = value pe r

foot

MA C

= meanaerodynamicchord

ref

= reference condition

00

= freestream values

Introduction

Q

UALITATIVErwake surveys employing wake imaging

have verified that most aerodynamic

flows of

interest

are stable.

1

Moreover, theycan be surveyed economicallyin

large

windtunne ls using mechanicaltraversersandpneumatic

probes* Qualitative wake surveys are conducted to visualize

theflowfield, whichis aprerequisiteto abetterunderstanding

of aerodynamic performance.

Quantitative

three-dimensional wake surveys

are a

natura l

extension of wake imaging; They allow separate measure-

ments ofprofile drag, induced drag, an d

lift,

including span-

wise

distributions. How ever, there

are significant

differenc

indata acquisition

and

processing betw een w ake imaging

an

quantitative wake surveys.

The

latter

requires

the use of

pneumatic

probe with multiple holes instead

of

asingle tot

pressure probeto record pressures and velocities whichca

then be

converted into aerodynamic forces. Furthermore

quantitative

wake surveys require very accurate probe pos

tion

m easurem ents since spatial derivativesof flow velociti

mustbe computed duringdatareduction.

Quantitativew ake surveys are ofmu ch value to the aer

dynamicdesign

of

airplanes

for the

following

reasons:

1) Theycan be used as a diagnostic tool during airplan

development to

study

the effect of

configuration changes

o

the

components

of

drag.

2)

Separate measurements of induced drag and profile dra

facilitate

the

prediction

of

flight drag based

on

measuremen

at low

Reyno lds num ber w ind-tunnel test con di tions. This

because induced drag

and

profile drag

are

associated

wi

different

flow

pheno mena w hich must

be

scaled

differently

account for

changing Reynolds num ber.

3)

Separate measurements of the components of drag a

also

ofvalueto thedeveloperof CFDc odes since profile dra

an d induced drag

ar e

usually predicted

with different

aer

dynamic

flow models which must be validated separately.

Thisarticle describes the wake survey technique in use

the

Boeing Aerodynamics Laboratory which

is

based

on th

work

of Maskell

2

an d

Betz.

4

The underlying theory for th

measurement of

induced drag

and

lift

ha d

been published

b

Maskell whoalso conducted an exploratory w ind-tun nel te

confirming the validity of his method. The theory for th

measurement ofprofile drag is that of

Betz.

3

'

4

.

Th ew ake survey methodology also includes certain f eatur

of

the work ofothers. Among them are Wu

5

an dHackett

6

whocontributed to the theoretical fou ndatio n and develope

apractical w ake survey method with emphasiso napplicatio

in automotive engineering.

Severalother experimentalistsreported quanti tative wak

surveys.

Onorato

et

al.

8

conducted w ake measurements b

hind

models of automobiles, but their drag analysis

does

n

utilize

the

simplifications introduce d

by

Maskell

an d

Bet

Chometon and

Laurent

9

performed wake measurements

o

asimple win gtoinvestigatethe relation between induced dra

and

vortexdrag,Weston

10

ofNA SA Langley conducted qua

titativew ake surveys behind w ing half-mode ls based on th

theory

of

Maskell

and Betz. In his

data analysis, Westo

focused on the

role

of

vortex cores,

an d

modified

the

def

nitions

of

profile

drag an d induced drag implementing

11 12


2/7

250

BRUNE: QUANTITATIVE LOW-SPEED

WAKE SURVEYS

Wakes of two-dimensional airfoils have been routinely

measured

f ormanyyearswiththe primary objec tive of getting

accurate profile

drag

data which cannot be obtained

from

balances. Wake

surveys

of three-dimensional

configurations

haveocc asionally

been

conducted

but are not

widelyaccepted

by

design aerodynamicists.

The main

reason

for this is a le-

gitimate

concern about thecost of such wake measurements

which require the measurement of a large number of

data

points.

This ca n indeed be a time consuming and, hence,

expensive process if methods that work so well in

two-di-

mensional wake surveys are

applied

wi thout further refine-

ments.

I n

addit ion,three-dimensionalw a ke

surveys

were

sus-

pected to be inaccurate since the

desired

drag and lift values

are the

com posites

of a large

numbe r

of individual measure-

ments.

This articleaddresses these an d other issues and re-

ports on theprogressmade sinceMaskellconducted the

first

wind-tunnel test

of this kind at the Royal Aircraft Establish-

ment

in the UK some20 yrago.

Theory

Assum ptions

Aerodynamicforcesa recalculated

from

th emeasuredwake

flow data assuming the following:

1)

Wake

flow data

are

measured

in a single

plane

down-

streamof themodel .

This plan e,

locatedat theso-calledwake

survey station

(Fig. 1), is

assumed

to be

perpendicular

to the

wind-tunnel

axis. In

mostwind tunne ls ,

the wake survey

sta-

t ion must be moved veryclose to the model because of

test

section and hardware limitations.

2)

The flow at the

wake survey

station is steady and in-

compressible

w hich limitsthe freestream Machnum ber in the

wind

tunnel

to about0.5.This

does

not

turn

out to be a serious

l imitation,

as

will

be

discussed later.

3) The flow in the empty wind tunne l is a

uniform

free-

stream

parallel to the tunnel axis. Any deviations from

this

ideal wind

tunne l ,

as

well

as instrumentation misalignments,

ar e

assumed

to beaccountedfor bym easurementsat the wake

survey

station with

the

model

and its

support

apparatus re -

moved.

4) The effective

ceiling, floor,

an d side walls of the empty

wind

tunnel , defined

as the geometric

walls modified

by the

displacement

thickness

of the

wallbo undary layers developing

in th e empty

tunne l ,

ar e

such

that the tunnel

freestream

ve-

locity

is everywhere tangent to

these

surfaces.

Note

that the

presence of a

model ,

particularly a

model that

is

large

com-

pared to the

test section

size, will disturb this displacement

surface. Also

notice that

thischoice neglects

the possible ef-

fect of an axialpressure gradient in the empty tunne l

(buoy-

ancy).

5) Viscous

shear stresses at

the wake

survey

station are

neglected.

6)A sw ri t ten , th e equationsdo not account fo rblowingor

suction through the model surface, but could

easily

be mod-

ified.

Com ponents

of Drag

With these assumptions,

an

application

of the

momentum

integral

theorem,employing thecontrolvolume shown in

Fig.

1,

provides

the following equation fo r model drag:

Pt

,-

ds

u

p

c

-T 1

s

Control volume j

^ / lltlliii


3/7

BRUNE: QUANTITATIVE LOW-SPEEDWAKE

SURVEYS

2

Th eeliminationof theu'

termfrom

the induceddrag

equa-

tionis the

most

questionable

aspect

of

Maskell'stheory

since

the distinction between

vortex

drag

and induced

drag disap-

pears.

In princ ipal, theu'termshould remain

part

of induced

drag even

thoug h it is proba blysmallcomparedto vortex

drag

in

many applications.

16

Induced

Drag

According to Maskell, the

remainder

of the induced drag

equation can be

approximated

by

7)

where

the

symbol f

represents the component of wake vor-

ticity

in the direction of the tunnel axis, a is the

crossflow

divergence

o rsource.They are calculated

from

the

measured

V, Wusing

their

definitions

,

is

calculated

from

(U)

dy

2

dz

2

and thefollowing

boundary

condition of no flow

through

the

tunnel

walls:

dn

Notice

that the

first integral

in Eq. (7) is

limited

to the

viscous w akesince vorticity

vanishes

outside.The second term

would stillrequire m easurements throughout the test

section

area, butwakemeasurementsbehind m odels of airplanecon-

figurations have shown that the sourcea is negligibly small

outside the viscous wake. Hence, induced drag can be ap-

proximated

by

0 ,

ds

(12)

Lift

The

momentumintegral

theorem

togetherwith

the control

volume of

Fig.

1 yields the following

equation

fo r

lift:

L

=

p ds - p

ds-

p

WU ds (13)

S3

from the downwash

behind

th e model . The

equation

fo r l

can be cast into the

following form (e.g.,

Refs. 2 and16):

L =

y

ds

+

p

- U )W ds (1

in whichthefirstintegralisexpressedintermsofaxial vortici

which vanishes

outside

the viscous wake

and, hence,

on

requires measurem ents in the

wake .

In most

cases

the secon

integral is

expected

to be small so

thatlift

can be

approximate

by

L~pU^

Instrum entation

(15

Most three-dimensional w akesurveysconductedby

Boein

employ

pneumaticprobes

with

multiple

orifices

mounted o

mechanicaltraversers.A l l wake

surveytestsdescribed

in

th

article

used a single

five-hole

conicalprobe 0.25 in. in dia

(Fig.2), in a nonnulling

mode

f or

fast

data

acquisition. Pneu

maticprobeshave thefollowingadva ntages for testing in larg

low-speed

wind tunnels:

1)

They can accurately and simultan eouslymeasureallthre

components of wake velocity an d total pressure.

2)They provide timeaverageso fdata, therebylimitingth

data

volume

an d data processing time.

3)They

are rugged and not easily

contaminated

by

dirt

the tunnel

circuit.

Data

Reduction

Inthe usualprocedure,the

five-hole

probemeasures tot

pressure

deficit and all

three components

of wake

velocity

alargenumber ofpoints,usuallyinexcessof

10,000.

Handli

thisdatavolume in a

timelyfashion

is themost

difficult

aspe

of the data reduction procedure. Basically, the procedu

consistsof two steps, a review of the data fo rerroneous an

duplicate datasets, and thecalculation of lift an ddrag fro

the final data

set.

Th e

calculation

of

profile drag

using Eq.

(4)

is

straightfo

wardandonlyrequires

integration.

Thecalculationof induc

drag

an d

lift

using

Eqs. (12)

an d

(15)

is

more difficult sin

vorticity

an dsource strength must be computed as interm

diate

results.

Thesecalculations require numerical differe

tiation ofmeasuredcomponents

V

an d W, which ca n easi

lead

to

erroneousvalues

of

induced drag

an d

lift

if not

o

properly. Numericalexperimentation with various schem

showed that accurate vorticity andsource data could be ca

culated by

fitting

cubic

splines

to the measured

crossflow

v

locities.

In

order

to

obtain M

and

< i> from Eqs. (10)

and (11), th

computational domain isextended with uniform

grid

spaci

from thewakesurvey

region

to the

walls

of the windtunne

Wherenecessary,fillets in thecornersof thetest section a

neglected. Values of axial vorticity and source strength a

prescribed

throughout the computationaldomain,w hicha

in generalnonzeroin the wakesurveyregion andzerooutsid

A fast Poisson solver of the FISHPAK library

17

provides s

lutions

fo r

P

and

< I > . Since

the

total num be r

of

grid poin

necessary for the calculation frequentlyexceeds200,000, th

use of asupercomputer isrequired for thisphase of the da

40deg

0.25

in 0


4/7

252

BRUNE: QUANTITATIVE LOW-SPEED

WAKE SURVEYS

reduction. Software for this

purpose

has

been developed

at

Boeing.

Standard

correction methods

18

ar e applied to lift and drag

obtained

from wake surveys

to

account

for the

effects

of

wind-

tunnel walls. Th e effect of

model

support strutsis

accounted

fo r

byincluding

part

of the

modelsupport

wakeduring wake

surveys.

Wake

Survey

Test

Results

Threetestsar e described

ranging

incomplexity from mea-

surements

behinda simplewing to a wing-body-nacellecom-

bination inhigh-lift configuration. All

tests

usedbasically the

same data acquisition system an d data reduction procedure,

bu t

different hardware .

High-Lift Test of TransportAircraft

A

large

half-model of a

twin

engine transport w as

tested

at Mach 0.22 and 1.4 million

chord

Reynolds number in the

Boeing

Transonic

Wind

Tunne l .

The tunnel features an 8- by

12-ft test sectionwithslotted

walls. The

wing

was in

high-lift

configuration with

takeoff

flaps

deployed. The model had a

half-span

of 52 in. and wasinstalled vertically above a hori-

zontal

splitter

plate.

Tw o different

engine

simulations were

employed including

a

flow-through

nacelle and a turbopow-

ered

simulator

(TPS).Thepurposeofthisex periment was to

determine the

feasibility

of

makingqu anti tativewake

surveys

using models of realistichigh-lift configurations.

Wake surveys

were

conducted in a plane two mean aero-

dynamic

chord

lengths (2 4

in.) downstream

of the

inboard

wingtrailingedgewhich

w as as far

down stream

a s

testsection

an d data acquisition hardwarepermitted. Th e boundaries of

the

wake

survey

region

(Fig. 3)werechosen to

capture

wing

an d

nacelle wakes, but did not include the wake behind the

fuselage.

Wake surveys are timeconsuming

since

a

large

number of

data points must

be taken to adequatelydescribe the wake.

In

this

case measurements had to be performed at about15,000

wake points. In

order

to

complete

a wake survey within a

reasonable

time of about 2 h, data

were

recorded while the

probe traversed at a fixed speed.

Preliminary investigations

in which the traversing speed w as varied showed that this

mode

of testingproduced accuratedata up to aprobe speed

of

1

in./s.

Measured

velocities

of the

crossflow

perpendicular to the

tunnel

axis

were converted into

axial vorticity as

described

above.

Such

vorticity

data together with the measured total

pressure deficit

provides much

insight

into

the

structure

of

wing

wakes

(Fig.

4). The wake flows are shown in airplane

view with

the wingtip vortex of the right wing on the right

sideof the plots. The n acelle region of the TPS pow ered mo del

is

visible

on the

left

side of

each

plot.

The

vorticity

data in the wake were used to calculatewing

spanload

as

described

in Ref. 19. The result is

shown

in

Fig.

5 together with inviscid

theoretical predictions

of the panel

code P AN A I R .

20

These

theoreticaldata representa

span wise

l i f t distribution,

scaled

by the

local wing chord

an d

nondi-

mensionalized by the sum of all lift an d side

forces

in the

P

f~

P

foo

0 8

a Total Pressure Contours 0.025

Testsection

Wake survey region

-0.8

- 0.025

-0.1

Fig . 4 Wake

flow

data of transport

high-lift

model with turbo-po

ered

simulator (TPS)

nacelles.

Wake surveytestTPSnacelle

1.6

1.2

C

L

REF

C

REF

0.8

0.4

PANAIR

predictions

Nacelle

region

0 0.2 0.4

0.6

0.8 1.0 1.2

2y/b

Fig . 5 Spanwise wing

loads

of transport

high-lift model

from wa

survey

and

PAN AI Rcode predictions.

outboard

wing

an d nacelle

region. Good

agreement is de

onstrated outboard of the nacelle. The large

differences

the nacelle region are

mainly

due to sideforces,

which

in t

wake

survey

data, could

not be

distinguished from

lift.

Simple Wing Study

The main objectiveof thistestw as to learnmore

about

t

accuracy

a nd

measurement

repeatabilityo f quantitativewa

surveys.

21

I n

this

test,

the

wake

w as

mapped

behind a simp

rectangular wing

model

which

had a span of

6

ft and an u

twisted

NACA 0016 airfoil section. The test was conduct

at the University of Washington

Aeronautical

Laboratory

an 8- by12-ft

low-speed

windtunne l .A ll

m easurements

we

taken at0.18Mach

numbe r

an d

1.27

million

chord

Reynol

number . The model was installed horizontally at the

cent


5/7


6/7

25 4

BRUNE:

QUANTITATIVE

LOW-SPEED

WAKE SURVEYS

M =

0.18 Re

ft

=1.18x10

Upswept

aftbody

7.2 deg

Symmetric

|---

aftbody

-2 2 4

a~deg

Fig .

Drag componentso f symm etric and upswept

aft-body

config-

urations.

30

AC

D

x10

H

-2

-10

737-300Aftbody

M

=

0.18

Re

ft

= 1.18x10

6

Force

data

Uncertainty o f

force

data

Wake survey

Fig .

10 Upsweep

drag

from balance and wake

surveys.

crements

o f

profile drag

a nd

induceddragassociatedwith

the

addition of vortex

gen erators.

Spanwise distributions of profile drag and induced drag

measured in the wake of

this simple rectangular

wing ar e

shown

in

Fig.

8. Here the

span

wise value of induced drag is

the integrand of the induced drag

integral

of Eq. (12). Notice

that this

quant i ty

differs from

the usualdefinition ofspanwise

induceddrag calculated as the

product

o fwingsection lift an d

induced

angle

of attack.

Aft-Body Drag Tests

Wake

surveyswere conductedwithvar iousfuselage models

of

transport

airplanes

in

order

to improve our

understanding

of

aft-body

flowfields

and the

drag

associated

withthem.Con-

traryto

mostmilitary

transports ,civiltransports

feature mod-

erate

aft-body

upsweep

with

a correspondingly smaller con-

tribution

todrag.The vortices shed

from

such aft-bodies

ar e

relatively

w e a k ,

bu t

their

associated

drag must nevertheless

be understood wh en seeking opportunit ies

fo r

airplane drag

reduct ion.

Aft-body dragexperiments

were carr ied

out in the Boeing

Research Wind

Tunnel inSeattle at

0.18

Mach

n u m b e r an d

1.18 million

Reynolds number

per foot. In all tests, the fu-

selage was supported by wing stubs extending through the

tunnel side walls.

The

wingt ips,

in tu rn ,

were

mounted on an

externalbalance, situated below the

test

section. Thisallowed

acomparison ofwakesurveydrag measurementswithbalance

drag.

Parametric studies

investigating the effect of

aft-body length

an d upsweep

angle

on

fuselage drag provided quantitative

data forvortex

drag

and profile drag as

functions

of angle of

attack.

22

As shown in the example of Fig. 9, vortex drag of

Thiskind of drag is defined as the difference indrag betwe

symmetrican d

upswept aft-bodies

at the sametest

condit io

A s seen,

wake drag

iswel l

within

th e

uncertaintyband

of t

force

measurements

providing further

demonstration

for t

accuracy

of

three-dimensional wake

m easurements.

Conclusions

This article describes the wake

survey

methodology deve

opedatBoeingfor thepurposeof measuring the componen

of

drag of lowspeed, high-lift configurat ions. Impor tan t e

men ts of thistechnique

including

mechanical

probe

travers

an d

pneumat ic probe design, re f inemen t

of the

underlyi

theory,

an d data reduction procedures ar e still

under deve

opment at the

present

time.

However ,

the technique has a

ready been successfully applied inseveral

wind-tunnel

te

as shown in

this article.

The fol lowing valuable

features

this measur ing technique should be noted:

1)

The

wake

survey technique providesseparate measu

ments

of

induced

drag, profile drag, an d

lift.

2) Measurement accuracy and data

repeatability

are com

parable

to balance

measurements ,

even though

lift

and dr

data are the

composites

o f a largenumber of

individual

me

surements.

3)

Small increments

in

individual

components of

drag

d

to minor configurat ion changes can be measured accuratel

4) Spanwise distributions of lift can be

obta ined.This

is

value

in

high-lift

aerodynamics since the small

flap

sizes

most high-lift models make it

extremely

difficult to measu

spanlift data using surface pressure taps. However,

all spa

wise

wing

data measured

in wake surveys should be

inte

preted

with caution

since

they

ar e

usually

distorted to som

degreeby wake roll-up, and

hence

ar einfluenced by practic

limitations

on the location of the plane in which th e surv

is conducted.

5) Wake surveys provide spanwise distributions of prof

drag

and induced

drag, which

are of value in diagnosing t

effects

of local changes to the

configuration

geometry.

6 )

Dur ingeach

w ake survey a

large

num ber of velocity a

pressure data arerecordedwhichcan serve as

validation

da

fo r CFD codes in addition to providing lift an d dragdata.

Acknowledgments

I would like to ackno wledge the technical contr ibutions

mypresent an dformer colleagues at Boeing,in part icular ,

Bogataj,

J. Crowder ,T.

Hallstaff,

M. Hudgins, D. Kotk

R. Stoner, and E. Tinoco. I wou ld also like to thank

McMasters,

M. Mack, and K.

Moschetti

for their review an

comments on the draft of this article.

References

Crowder, J . P . , Quick an d

Easy Flow Field Surveys, Astro

nautics an dAeronautics,Vol. 45 ,

Oct.

1980, pp. 38, 39.

2

Maskell , E. C.,

Progress

Towards a Method for the Measur

ment of the Components of the Drag of a Wing of Finite Span

Royal Aircraft Establishment, TR 72232, UK,Dec. 1972.

3

Schlichting, H.,

Determination

ofProfile

Drag,

Boundary-Laye

Theory, 6 th

ed.,

McGraw Hil l, New York,

1968,

Chap. 25, pp.70

711.

4

Betz,

A.,

Ein Verfahren

zu r direkten

Ermit t lung

de s Profi lwi

erstandes, Zeitschrift fur Flugtechnik und

M otorluftschiffahrt,

Vo

16 ,

1925, pp.42-44.

5

W u , J. C.,

Hacket t ,

J.

E.,

and Lilley, D.

E.,

A

General iz

Wake-Integral

Approach fo r

D r ag

Determinat ion inThree-Dime

sional

Flows,

AIAA Paper

79-0279,

Jan .

1979.

6

Hackett,J.E.,and Wu, J.C., DragD eterminationandAnalys


7/7

BRUNE:

QUANTITATIVE LOW-SPEED WAKE SURVEYS

25

ment Through

Wake

Analysis,

Society

of

Automotive Engineers

Paper 840302, Feb. 1984.

9

Chometon,

F., and Laurent, J . ,

Study

of Three-Dimensional

Separated

Flows, RelationBetweenInduced D rag andVortex

Drag,

European Journal

of M echanics,

B/Fluids, Vol.

9, No. 5,

1990,

pp.

437-455.

10

Weston, R. P . , Refine men t of a

Method

for Determining the

Induced and Profi le

D r ag

of a

Finite

Wing from

Detailed

Wake

Measurements, Ph.D.Dissertation, Univ. ofFlorida, Gainesville,

FL,

March

1981.

H

Batchelo r ,

G. K., AxialFlow in Trailing Line Vortices, Journal

of Fluid

M echanics, Vol.

20, Pt. 4,

1964,

pp .

645-653.

12

El-Ramly,

Z.,

Rainb ird ,

W.J. ,and Earl, D.

G.,

Wind

Tunnel

Measurements

of Rolling Mo m ent in a

Swept-Wing Vortex

Wake,

Journal ofAircraft, Vol. 13, No. 12,

1976,

pp .962-967.

13

El-Ramly, Z . M .,and Rainb ird , W.J.,

Effect

of Simulated Jet

Engines on the Flowfield Behind a Swept-Back

Wing, Journal

of

Aircraft, Vol. 14, No. 4,

1977,

pp.

343-349.

14

El-Ramly,Z. M., andRainbird ,W.J ., Computer-Control led

System for the

Investigation

of the Flow Behind Wings, Journal of

Aircraft, Vol. 14, No. 7, 1977, pp.

668-674.

15

El-Ramly,

Z. M., and

Rainb ird ,

W . J.,

Flow

Survey of the

Vortex Wake

Behind

Wings,

Journal

of Aircraft, Vol.

14, No. 11,

1977,

pp.

1102-1108.

16

Van

D a m ,

C .

P.,

Nikfetrat ,K ., Chang, I . C., andVijgen,P . M

H. W.,

Drag

Calculations of

Wings UsingEuler

Methods, A IAA

Paper91-0338, Jan. 1991.

17

Schwarztrauber, P. N., and Sweet, R. A., Efficient Fortran

Subprogram s for theSolutionofSeparableElliptic PartialD ifferent ia

Equations,

Association of Computing M achinery Transactions o

M athematical Software, Vol.

5, No. 3, 1979, pp.

352-364.

18

Rae,

W.

H.,

Jr.,andPope, A.,

Low

Speed Wind

Tunnel Testing

2n d ed , Wiley, Ne wYor k ,

1984.

19

Brune, G. W., andHallstaff, T.

H.,

Wing

Span

Loads of Com

plex High-Lift Systems from

Wake Measurements ,

Journal ofAir

craft, Vol.

22, No. 9,

1985,

pp.

831, 832.

20

Tinoco, E. N . ,

CFD

Applicationsto Complex Configurat ions

A Survey, inApplied ComputationalAerodynamics,V ol. 125, Prog

ress

in

Astronautics

an d

Aeronaut ics ,AIAA,

New Y o rk ,

1990,

pp

559-584.

21

B rune ,

G. W., and

Bogataj,

P . W. ,

Induced

D rag of a Simpl

Wing

from

Wak eMeasurements,

Society

of Automot ive Engineer

Paper 901934,

Oct.

1990.

22

Hallstaff, T. H., and Brune , G. W., An Investigation of Civ

Transport Aft-BodyDrag Using a Three-Dimensional Wak e Surve

Method, AIAA Paper 84-0614, March 1984.

Journal ofGuidance, Control, and Dynamics

Radar

Effecto nSingle Microprocessor

Navigation

G7934

Tanya

Johnson, Ph.D.

WordStar 2.0 / PC

MANDATORY

SUBMITYOUR

MANUSCRIPT

DISKS

Journal of Propulsion and

Power

Hgh Pressure Impact

on

Liquid Propellants

B679

Dr. Jamshid Monadi

Microsoft Word2.0 /

Macintosh

loreduce

pro-

duction c osts and

p r o o f r e a d i n g

time,allauthorsof

journal papers

prepared

with

a

word-processing

program

ar e

required

to

submit

a computer

disk along

wi th

their

final

manuscript.

AIAA

now has

equipmentthat

can convert

virtually any

disk

(3

1

/2-,

5

1

/4-,

or

8-inch) directly

to type,

thus avoid-

ing rekeyboarding and

subsequent

introduction oferrors.

Please retain thediskuntil the

review

process has

been

com pleted

and final revisions have been

incorporated

inyour

paper.

Then

send the Associate Editor all of the

following:

Your final

versionof thedouble-spacedhard copy.

Originalartwork.

Acopyof thereviseddisk

(with

software identified).

Retain the

original

disk.

If your revised

paper

isacceptedfo r

publication,

the

Associate

Editor

will

send the entire

package

justdescribedto the

AIAA

Editorial Department

for copy

editing

and production.

Please note

that

your

paper

may be typeset in thetraditional

mannerifproblems ariseduringtheco nversion.A

problem

ma y

be caused, for

instance,

byusinga

program

within a program

(e.g., special mathematicalenhancements to word-process-

ing

programs). That

potential

problem

may be

avoided

if you

specifically

identify the

enhancement

and the word-process-

ing

program.

Th e fol lowing are

examples

of easily converted

sof tware

programs:

PC orMacintoshT

E

XandLA T

E

X

PC or

Macintosh

Microsoft

Word

PC WordStar

Professional

PC

or

Macintosh F rameMaker

Detailed

formatting

instructions

areava ilable,if

desired.

If you

have anyquestionsor need further information ondiskcon-

version, please telephone:

Richard

Gaskin

AIAA R&D Manager

202/646 7496 American Instituteof

Aeronautics and Astronautics

Documents

01-Boeing Low Speed Wake Surveys