An Empirical Method for the Prediction of Airplane Drag Divergence Mach Number

37 Pages·2016·2.81 MB·English

by  Roger P. Johnson

U.S. AIR TORCE

PROJECT RAND

RESEARCH MEMORANDUM

AN SUFTEIGAL YSTHOD FOR THe PIODTOTION OF
ATAPLANE DRAG DTVERGENGE MATS TUMLSR.

Ry Pe Sokinson
ma-1168
ASTTA Document Wumber AD 85834

2 Avgust 1953

datigned a

work pores Bacance Ht may be asponded, raited, oe withdrawn

ine, petmsion Yo quale or repradace must be obtained! from BAAD,
‘The vows, fancluscn, ave recemrventations anaitsed herln da aah cee
{aly atoe the offical wows or poles of the Unled Sloss Air sore,

DISTRIBUTION RESTRICTIONS.

s le RA n 1) enaoetne
HM1188 penes
aries

sions

‘The problew of presiction of airplane érag divergence Wich ruber
war investigeted and an expirtcally dotermined exprension mes oMte‘ned
‘that 42 applicable to clean airplane configurations whoae wing sages
Ide Within: the general Limita of 0° to 47° sueephank, sapeet racdoe of
2 to 10, and thickuess ratioe of k per cant to 12 per cent, Suhacrtow

type aixfoll sections are inplia

0 the Fkselages ere of the eozvor=
‘onal convex shape, Gosperieon of tha pradtcted veltna with exports
mental and aircraft mancfacturare! perfornence erticate val:ce inticates
‘that the accuracy nf ta method 1s within £ 2 par emt, Sceh special
profilems ao the prediction of tha effect on drag diverpecce ach aurhar
of thiokened wing root air intake configurations and large Anterference

effvcls of certain nacelle locations are beyond the seapa of thts rarer,
Rees
cSt
ate

ast oF CONT

Sonar.
‘table of Contents, 4“
SUDOL Ss vere at

TOLVOELODeegeegee

Tefinition of Drag Divergence Mach Bember.

Scope and Linitstions...

Henlte,

Diseuasion of HeUhods Used.

Discussion of Dabs Used,

References,

eee Wt

Table Teese

Figure Leseees

Pigare eves

Figure ee

Figure
Figure

Figura

"igure
RMA

4

8
yp

a my fie ab

A tty {404 (0)}

3 Wap Lope (t/onadh

2 Wap fog.)
eh}

weeliag
81-53
13>

snot

gross wing area

cup span
axa: ody damster

aspect ratic, 8/5

sroogback angle of winy qverter-chard line

Yotoknoes ratio of wing elrfotl soetion parsllel
to emier-Lina (constant value spamtiee)

wing span to body dlaneter ratio
wing taper ratio, 44p chord to root ebord

design Lift coaffieient of ainfo!l section
parablal to center-Line, indox of eanber

Lite coaffictent based on grees wing arma
drag coaffiodent based on yrose wing arma

Mach: number
ac
drag divergence Wach omber, Mat wileh yy] = 9.3,

G,, = const,

1
My Sneromsnt providing prinary effect of ® and A
incronant providing priumy effect of t/e

2»
Nyy Increnent providing prizary effect of O,
Yop Hneronent proriding effect oF 2,

Dweemback angle correction factor on t/e tera

Ioan, (Gp (ele, Alp

mnse

iaetiee
Bales
he

NTR QLvOTTO

Generalized performance

tudios of aircraft necessitate = knowledge of
drag divergence Mach munber fe

‘any configuration considered. Thin Imoxtedge
te important to both the high speed cruise of subsonic atrerart and to the

aubnonte cruise of supersonic aircraft, Given a drag divengenee Mach nunber,

zoe

one needs to know whet con?igurations ars per: for, given an eirpiane
‘configuration, what 19 te drag divergence Mach muuber?
This pazer presents = method of eotimling the drug divergence Nach

number for a variety of sing-body combinations,
wet1es
1-53

DEEDITIOY oF nak DIYERERICE Wi

arnsly

‘The drag divergence Mach nunbep is defined a9 the Hach number at vhich

Os1, The Ss Allustrated in the accompanying skateh.
const.
L

ST LE store na unnarrae |

‘Tho data used in the preparation of thts paper were obtained from wind

tunnel model t

8, fron rocket-propelled model teste, from full-scale airplane

Tight testa, and fron airerar

snafactuverst performance estimates for air
planes,

he rang:

of the primary wing geonstry pi

renetars, aspect ratio, swssp-

back anzle, and thickness

So, for which this netood fa applisabla are given
by the dached-line palzgma enclosing the points plotted on Figs, Lt, 18, and

JC. Mack point reprasants a configuration that was included in the data analysed.
34 can be aven that the configuration geonetriss indicated by these plots guits

completely include tha spectrum of parameter conbinstiona af currant interest

to the designer, In addition to the wing geometry parsneters given azove,

design Lift coofficlent of the airfoil eection, cy , and airplane Lift
zi

coeffletent, @,, were included in the analysis of the data end the resulting
emplrieal Won sredietion method,
Aizplane configuration paraneters not ascounted for explicitly in the

preceding section a1

subject to the following Lattetions:
Bie118s

ie11e8
Belot3

As Wig taper ratio, 224.6
By Subsonke aivrfol? sections are siudler to the NACA G4A- or é5-sertes
3, Wing thickness watio fo constant spamise

As Wing span to body mazimm diameter retio, b/d 24

5. Bady shape ab the wing functure ie eonvex or cylinantesl, and ving

4s positioned near the maxinun body disnelor

Jn uddition to those rostrjetions on the shove mentioned parmeters

At should

noted thet the method developed in this paper 4e epplicabie
to clean sirplane configurstions of the wing-body-tail type. Additional
or umtusl componente whose effects are large enough to govern the tntial
mag rise of the configuration vill tovalidcte the use of theoe resulta,
Bxaxplas of theee componsats are hesvily thickened Sabosnd wing panale to
Frovide engine air intalos in the wing Jaading edge at the wine-fuselepe
Junchire and an asnedynanicdlly unfarorsbla porstioning of engine nacelies
Pylon-nounted or at the wing-fuselega juncture,

RESULTS
‘Te aupirical equations given below slong With the data supplied by

Figs. 2 end 3 permit the celoulution of érag divergence Mach muttber for

configurations within the Linkte specified above,

Moy 7 ARE Alyy RAP + Ay [Ales CA} + ing (Opyit/er ] + yy {ey}, 2)
whore

Aly {a} $0 etvun by Pg. 2, a

My {t/e, (a)} = 1.375 (.08 = te) cos ty @

Ahoy, (yp elernl} «= oy [.05 + & [9 (4/er04)] » ay
with x (1) atven by Figs 3,

D5

on [e,}* 8)
enes

‘Thie may be expanded to +
Nyy T e820 + ayy {Wy A} #26975 (.094/c) com se oy[.0%+ & {a} (b/e ~ 01]
~ 056,

(6)

ag!
‘The baste Talus, 828, was arrived at fron a study of pest

on data,
‘tae Value, Mop * +828, corresponds to an inzinite nepect ratio, unewept wine
vellh etght por cent thick eymatric airfoll sections at sapo Lifts

Alyy {Hs A} do given in the form of empl

cally derived curves
(Pigs 2} ap @ functton of sweapback angle for constant values of appest raviog

‘The coiplex neture of the varlation’of the curves prevents the writing of a

simple analytic expression for this inerenent.

Ap {tfa, tA} von be writter

siytienlly, Tia incraeent: peinarty
ropraomts tho effect of thickness ratio, bit thts effect t2 somarhat anpentant
on the aweerback anal.
Alyy {Opp (t/es AD) 4 with the vee of the eveepbick factor K (2) given
by Figs 3, csi eleo ba written 4p snnlytie fort. This dneceent ples the
affect of variation of Lift ooetficient which 4 in turn dependent on thiclaiess
rato and sweoybsck ance,
Atyy fez} rove a tat eprosinction to the effect vicg ower
and te expressed in terms of the design Lift coefficient of the wing <lnfoix
sections
To iMiustrate the exlelation procedine, tgp values will be determined
by Ute method for a wing-body configuration thet wes the subject of a transon-
de vind tunel investigation, Hefi 27. The pertinent piysics] charscteristies
of thie model ares

R= 3s Ae 35, HACK 654004 ALefo1 Section {apprex.),
The determination of the severel incranente of My, $4 elven below:
iy, {R, A} = 4100 as given by Figs 2,
gy {t/ey A} 1375 (408 ~ tfc) coe +
= 1.375 (.08 = .08) (.328)

= 4.045,

Any [yy tes a» ty [.05 + x (a} (to ~ 043]

(.08 = 043}

$0, =,015, and =.030 for O, =0, 3, and
«6 respectively,

aid

‘The Nyy eatinetes sre obtained by adding these increments to the baste

value, a8 follows:

qe
ate My ae
Ay, fa, a} ace Bt) 100
Athy (Ue 4} 015 045 ous
Alyy (Op t/er A) = .030
on, = 019
\ Bw
orl,
an
"tata
ot cont sifferance 3 a @ |

For this sample calculation the per cant difference: betwaan the astinated

, Mypts and

© experimental Ho's are well within the sxperiatentel errore