fPr W'' L"I'.
ACR No. L4E10O
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
ARTIME RIE PO
SMay 1944 as
Advance Confidential Report L4E10
iERSTIATION OF PRESSURES ON COCKPIT CANOPIES, GUN
1,. TURRETS, BLISTERS, AND SIMILAR PROTUBERANCES
By Ray H. Wright
Langley Memorial Aeronautical Laboratory
Langley Field, Va.
CA WARTIME REPORTS are reprints of papers originally las
ae research results to an authorized group requiring them f
aulf hbed under a security status but are now unclassified. So
al. edited, AU have been reproduced without change in ord
S 2~i:n~w ,:.:.**.~..1r;, :'6~'~:L'..
ued to provide rapid distribution of
or the war effort. They were pre-
me of these reports were not tech-
er to expedite general distribution.
DOCUMENTS DEPARTMENT ,
i ;'. ":,I.. "
i, -'". P
* EN -
* iii, ".
F ,:'. ..
j ..: N.
Q 0 .
NACA ACR ITo. LiJFlO
NATIONAL ADVISORY COMMITTEE FOR PEROI.AUTT S
ADVAiJ.C!. C 1 'T D .TI AL FORT
ESTT'ATIriIl OF PRESSURES 0' COC'TTT CFT ES,
TURrETS, LITSTEFPE, ATID S'Th.LAP ')nT"T3E;Tf.A"CE
By e.ay H. Wright
ST T .iA 1 '..
Methods are des ribed for ?st "-st'.rn.: crressur,:- di' -
tribut-,.,ns no er protu')er-&nce..3 sach ,s acoc', t I3a1o. es,
gun turrets, blisters, sco 'n:s, s['T!; ?., s.
These meth:!-r-c are ac:.led to thas est'l-iati on of the :-res-
sure distributions over sph ricaI-ceg.neit and failed
gun turrets and o'.'er there nrotLuberanes o, the
BrewsLer S 2A- a1s ri.jnc. Th e efiie.t of comrrsessib ili 1 t,
interferen-ce, and fl.o sena'-ati n are ,J.-.s.cused., It is
shown that by a corbL'. ati.n or -:t r rerrct il dvta vi' th
theoretical methods; liritirnc r:.s:u..rs for use in :"ter-
mining r'aximurm losiOs ~,n in r.any r!-,ases Lie srti sf1s ct cril y
estimated. "Lic.' s str.ti.c exIcr.mc itati n is ne-'.ded,
however, to -rinor .ve the r-ccuracy of est j rat i:.
Th: purnos.o of the pr-:sent r':-or't is to dz:s.r'oib
methods by 'which pressures .rid .:.*.nce loads on 'tr.otu.-r-
ances, such as co ;-ir c.a op.es, iUn -tuirrets, bl ters,
scoos and ighti-ng domes, m-y be r1o-r ; ntim-...
In particular r, t}: poss'bl -1itC1 of det rri 'in,; li"iti:.
values of the ',r-us.-re co, ffcc-ont values which cannot
be exceeded in o:'acti:e is oem '7Inst"i'.
The invest, ati :,n was initiated ;, a re'u:--st from
the &ureeu of Aeronauties, ,pvy Denartr'rt, for hai
data on pun turrots. U:. qplictle e-.erl'rnta. d.ta
viere available an., as the I'AA testi..- facilities 'were
already cov-mitte.d to other .nvesti.-art:-ns, it was decided
to estinrate the limiting loads.
Methods generally useful in the estimastinn of lo:.ds
on protuberances are described in the present report,
These methods are aoplied and, where )oss.t.ble, the
2 CONFIDENTIAL NACA ACR No. LrEIO
results are compared with experimental data. The
methods are necessarily only approximate. Even if the
potential flow could be exactly calculated, the actual
flow vromId likely depart so widely from the calculated
flov as to reader the results invalid. The exercise
of judgment, based on experience, and the use of experi-
ment in evaluating the effects of boundary layer, separa-
tion, compressilbi1ty, interference, and departure of
the shape fro- th'it for which pressures can be com..uted
are necessary in oreer to arrive at useful results.
Although little opportunity for systemrtlc exreri-
l-entation is likely gt rresert, the study presented
herein is be!r. as? ]-ted to turret shaocs on particular
sirFlane moccl]s oeing investigateed at LI4AL with a view
toward improv.rin the methods of estimation of pressures.
p p pressure
V veloc. ty
P rnsss d&rsity
q dynamic pressure, free stream unless otherwise
P pressure cnefficier.t
M. I.lach number, free stream unless otherwise stated
&V velocity increment
.0/V0 vclozit.y-increTrnt coefficient
V/V0 velocity coefficient ] +
Y ratio of specific heat at constant pressure to
specific heat at constant volume (-
x,y Cartesian coord!natEs
NACA ACR No. lOE10
Z,t complex variables
i incomoressible or lo-:v speed
o in undisturbed stream
Other s;7rrtbol are ir.trd-u:ced and defined as needed.
Insofar Es 'oEsible, the notations of the references are
retained in the o-,rsent report. For tiLs reason, more
thr.n one quanT'ty .isy be' des' asted by ':l-e sa..e s:-.'rbol
or one qusnt 'y. may be deslgnnted by more t a- 1. one
E'fTnDS 7rp1 *,.ALCU.LA'TTI."'. 0F1 V g-C:Ts
Althou:zn thr -ir3l'-ne w'-th its c on .-,, t,.urret.,
blisters, and other pro'.'ier.nrices is a complicated
three-d inmens-onal form about vwhicl even the potential
flow cannot now be corruted, an esti.rs.te of thle pressures
on the orotuberane. can be obtain.?d. the airp:ln 1 n.
presents the ',:-neral e:-)c eran-e 'f Pa Wi.Ln.., fisE]C :e,
and tail wi tn the nrotuberancev s'-i.,roo3.-o. LhesE-
protuberances ar.' usi:ally of snall lenth r:-l:tive to
the length of the fuselage o' to the cho-'4 th-e ,:ing
and are v,-ry often qt..ite thick in -elat'on. to their
length. Th. oad.. oer tts_3 r rotu'beran3 strher.'er
are assumed to be dttermLncd larrt.:l ty the s pes of
the protuberances ari. t) be :r.odifiedr by the interfe.r-nce
of the wing and fuseleea. As an aoproximstlon that is
usually vrlid t''r.?1.3. the .'ror.tbera&ie i3 2ccated near
the nose or int the. wake 'f tre tody, the total velocity
V is assured to be equal t3 'the s.It of the veloci, r"
over the protuberanece vw.thout i nterferenic and the
induced velocity increment Y7 due to th-. interfering
bodies or, in coefficient forwm.,
nc interfere /V\ /
o V )rrotuberanco alone interfneence
U4 COIFITDEN TIAL NACA ACR No. LiElO
Methods of determining the velocity increment due to
interf-rence are r.iven in the appendix of reference 1.
Tn rany cases, the interference is sufficiently small
that it may be neglettcd.
It is ornvenient and sufficiently accurate to apply
the o,'-pressibility correction to the pressuree coeffi-
cient .p tim'ijted for incc.m-prrss.ibl2 flo'.
i = 1 (2)
whe re I' /.', is the value of equation (]1 for incom-
pres]l ble flow. The pressure *.orfficier.t for c.-m-
nressijle flv. is the., obtair.ed fro- aen approximation
given oy," Frardtl in referee:' 2 as
where i.B is the stream l%,.'L nur'oer. An approximation
that in : ;.e.ific t..starces has 'be.-n fo md to describe
exFeri rnental result ts more accurat,-:I,' than r'randtl's
nethon has bcen A,,ven by von K.arnmn in reference 5 as
Equstior (5) is s,'ffi 3 ntlyv scf 1urat however, for the
est'iiati cns des*r!iPed here in.
Three r esur istriL .ut1 ns o obtained up to this
point t apply in 'ot n-tia- flow. The effects of departure
from 'otcntCal Ilov, w h'-.h iclu.!e develo\rm nt of the
boundary 1 -a ;er on the .srface forvErd of the protuber-
ance, screariat'in -. tlhe f]"i, 1*h.L.ih 2oLrs r-eularly on
th,- r'ar of blunt boz>s aind int:er- t',n of these
Stffcts with c.'-p'res's i ;i lit; "tust now b-) e;stirrm ted. Al-
thou.., thu: b- ni vi laye r and thE r. o nt and cYistence of
s tar.ation -iFht c, ca].lul at(. at at ist for low creeds,
b-' t'? m.tno.ns r e. reUn.::- anO (,ith modification
CO'FT DLNTI AL
NACA ACR To, JtjFlO
of the romentum c.lust'on fxr the three-dim.rensi onal flow),
*n.i rrme th,-.d I s know-: f o-' coa 1,'1l 9 tin.., the r-o re r .or 7 C.: *
rress.ires nor is iny theory available for *stimattl.rji
the con-,pre 3 sibi 1 ty interaction. Fr-,n t"-. r.',ea rn
e:',er'inenta.l csal evai -bl'e, tn sr-. ef.fr;ts can be it
least qualitative, l e-strriater'.. (thes d stt re
presented and discussed. in fhe section er.title'd
"Angplicotions.") In brief, the .,r.-cedure is 1s follows:
'1) Est mate the' veloc- t'-seffit i ent di stri-
bution for lnco.npres u'.] e .te.tisl flow ove:- th ro-
ft) 1.t r'.t... t-' int2"f' r : C- -,- cit. coe -
fici snts for. i cor:.r-..: l :.*c.tet i; flow.'
( ) A.'0 tl'.- o- ff:"' -. ts3 o' i".ln.,A st s (1)
and '2) as n equ'-t-i, n fl L)
(4) e us' n'" f sL'-o ( c. r te th .re re
coefficients for irc.i.niresstbls flow 'equation '.-')
i5) A'jply t zoi.pre.sibil i;, corre ti.on
(equation (7) or iL,):
( 76) E-ti.r te- the effe'ts of deoa-t'_re f r.cr
rotent ial flow
Tir practice, ss n.e),es- in the e::- C'.lev- -- ro i iation
of this .rocedurc. n'- ;' be neoessar .
The rest of" this sector, s ccn.er.:'d ir-:rel-- with
the determination of the ve.ocit d istribiti.-.n vtith
potential flow over soec fic ocotuL er e.nce sh t.s .. thut
Snterfe r ence.
Protuberances often near as bodjes that ?rec
aporoximatel.y half :.,: :.:y mrr', tricI fi f or.iins c, ,t b;, an infinite
plane as indcoc tod in i,'ire 1. The fio.v .-it"iI't the
interfer-ence is then thle oit '.cal.-, a)8 -ox i .m te to the
c.orr'sa. ondirr half of tnat o'-er tlc nr:.l ?te body.. In
many cases the half'-bx3-i 3 ,rcech-s t"-, t'. n-,'l .m e.ional
form fsairfo]il); for '.Shch the or- srur distribution is
alf;avs calculable: then, as the ,prcs s.3Uire chir.g.cs are
larger in the two-ci'nm.-sionl thrn :n the three-
dimensional case, it Is *3.oserv3tiv? to c )nsider the
CO~TPI DN'.TT T
NACA ACR No. I4TF.
flow t.'o dimensionril. In other cases the shapes nay
a,)P"ro1xin.te simole three-dimensional firms', such as
s,)'.ertes and nrolate or oblate s)hIroids for which the
f'lcv is '-:no'."n, aend the corr3sponl.i.r:s Dressure, distribu-
t'.ons may be essu'::.ed.
[f the form of the body or half-oody is such that
the flow' cai.not be directly calculated, it mnay bz ':pproj.-
mated o- var'oos ricvizes. .f the shapes of ihe front
and r3ar e'.t's of a or..tuberance are; different, i;nn.uch
as the flow u .r onz- l.-, 1. i often little affected by
that over the other, it un;y be nossibl2, to computer the
prs-.asure distri-but,nrs ovor front and reor ed: .gs sppa-
rately arnd to join ti-; distri"uti -ns at the c-nter.
In scene case & s'r-,ie jody, for which the flow
in thr a d.m :rs .i ciw n Le c. iculite a;, o- -. mod' ied
by F, two,-dimen.s onl T..t3..d to aoE'toximate a iv.n
shape. Such a rni fl ct n '..eoen'lis u-or. the ussur-ption
tihst a swell local ch'1.,e in t e radiu3 of a Uody of
revolut'rn. p or'uc: s a Io- E.I L-o-dim;nrsioniirl effect.
As the rHclu: r .',f c':e L:y of revluten bO..sfa
larger, this .ssu.,0tt .i. bec rnjs .nore nearly correct.
For exxt.-le, 1th, .: e s r'.2. .r'.r 1- the I 'n of' an coen en- ino
c .)i]. lnc on-.roL'.c': the o'.-ssures ov3e'r an a.' rfoL' with the
coOlili 2h',e nf t;-,e li,: end ".,' th tIhe sar:.e effective
an--le of atto.-. Arn -::T I,,- of an oblate sohertld
i.)r li fie, Io tD .ro`fT'- 1 he- -sh.l -. cf thlt 'c.xson toirrct on
the r-.rce.!ster S'L2A-1 Dirolsqne 1 s xi ven in the section
T. o-DT in-r. i onl Shoes
Arbitrar-r foris.- The t,:-.',-dim signal potential
flow post sy-.tr'caJ ,roi 1 le- that correco-)nd to !given
hslf-ftod os c'.r, t obtain .n'-d b:y the mtl thod of Theodor-sen
and& 'rri cl' f refer:nce :. Tri mwn casr=s, however,
le.-'s lr, ori.'ous n.-thods 'iff icc. Thc granhlcal miethod
of Jcnes rind ",hen f,'eference 71 is well suited to the
co.nrutat:,.-n of flte. tisl I ow v'.'er Lus.
For'is for vh:ih not.er.til i lof' is known. In certain
cases, ft. 6,::-tm F-l--T' .? rct .F'be "ance a:- oache that of
some tA'o-&d Sm.nslnal orf1le '.r wi'.ch the pressure
d 1itr'l.'itton o"" correes ,ndQ n ~; -.elo-.1ry distri ution is
already kz.ovn rd '-'n rbe a'pt".e v.'1thout much furt,.er
co;nr-iut. t't.n. Thre. such s nr)le or,-fi.les are the
ini-r, it.ely lon,, ci2n1lar cylini-der, the ellipse, and the
GCO 'i DYTTI AT,
NACA .tCP No. LTi710 CO ITDL''TTAL 7
double-cir.'cul r--nc ornf le. Fir- the circ,... r c'yl in,'er
movinT rormal to ; tE a:-i?, t.e v 1oclt.y ris ributic.r
'ith notent '.: 1 flow is ,. v en by
V = :V o sin e (5)
where 0 is the o lc,-' rn;nle me.-,c: rel fror t'lhe stream
direction ..Ad V: is the f." war* d or stret-,r 1103.t .
Thr v'1 0oc ty diQt-' but' or. a:'-.t the el 't i
cyl!ini.eT v'nr -:r. -111 to it: .i or ..i i n.-
07 Zashi in r.efi reice cr2j ri-;, ;-:-ei e:: s .d n t ,- .'r'm
r 7: ,j I' + ( '
a s .mili?.or :i s
b s rrmiinr.or -.I s
x l sta.n.:oc :. rg cn r s: :1 :rIs C:l -:a :r'
ThF forrar-.i r.ort, n r of a :.,-. tr i "l I f -LL L 'r :.e
w th .zero lift c ni often be nr: ':r-in r' L 1-n 3.'t e
as 1n igur"e 1 1l. 'f '. t -? .' :ti.c? rr.":
the n -- st ': i h -l 'i? ,.xi r'.. or :,.st: :3 a: .:3' rs,
th e -1 1 -' n c1,,l ,ir a ll.,, b ...et ?r..:i t d ,r I
2. A 7
The veloc it:- r" s- r-'t. on ,v 1 f:.'-."rd .rt : f
the Ji. .oi. r.Sy thr n br t:-.';: t : E .,-' ..: :', t ..e
.Ain th :r v r:r : tf.1i s.t.i, i2 ; t. d.o'u lL -- .' r-
arc s;rT- et. 1 c i. ft f "'io.i h. :- Jn o.v;:' r
surface or.fill s aTe ires 11 It? r..:r.? i2 -.- % -
Co' -!D:- 'TTI T?
8 CONFIDENTIAL NACA ACR No. LE.10O
conformal transforratton into a circle is given by
Gli.uert in refers", "-. The velocity distributions,
-obt.ine 1 y notentlpl theory, are given for different
th'.ckneases by th: trolid llnes in figure 2.
Thin bodies by s!one method.- A simnnle anproxirate
two-dThrsfn.l a eT Thod Th-aT ha oroved extremely useful
has been included in a publication by 9oldstein (ref-
erenrce 10). This Tethijd, which g.ivss ti.e veioci.ty
distriou.tion a-r in int-itral funrctI*'n of the slope of a
symretr.ical orcfile, ma;., be c:411ad the "sloi' method."
For the dertvrtlon of the slope method, the following
two si.fnnlifyj r. 7 2ssu.t.oL.s nrec narecssqry:
(1) T.i' rrofile .s sL'ff i intly thin that the
vclocit., is ov.h c-cre v-r; di.C'ii r..nt from store am
(2) Tho slo-"- of the profile is suv-rywhere small
There assunmotions oreclvue the existence of etsgnation
The s~nrctric'al or-file rmny bo assumed to be
re-resented by a dl rtr' .)ut' n of sources d),/dx along
tne chord The- velor'ity Hicrenent f(&V) at any
pci.nt (xon.t) *.p t-he profile (fij. 5) due tp the
source eler ent dx -it x is
A(Av.) = (7)
Because the nrof.le is thin, the velocity at (xo,y-,)
cinr.ot bLe very differ-.nt fi o,- the veloc" t- at x,,; thus,
a(AV) O -__2r. (8)
CO TID- ITTIAL
NACA ACR No. T4lElO COIT0ID.TIAL 9
TThe total induced velocity therefore is
rr (7y, ')
For unit len,_th of the profile, the cross secti n
at x is 2;y 9ad, with 7 = V.), the volum,,e flow is
apoproximatel: eiLiql to 2Vov The volur.e flow through
any cross section, however, must ibe e i.-l t.: the total
output of t.:. sou,.ces unstr,-ea. a.d, t.,erefore,
With sutstit..tTon of the value ..' d,/.ix f:'oir, eq a-
tion lOC) i: equatio -L ), the .cneffi cent of the indued
/V 1.. dx
.' / 9X y,
"h u C j5
The inter-ra'iid .-i c'-qu tion (1 ) -ar be eF-) r S? i r.
tri gonomretrLc forr: bit, for rhs nrses.t Ui'j2Es, thre
algebraic :-7.res'. ,n i .- r tair.ed. The v- loc it r
coefficient is 4, -'n c:
S= I + --- le )
T.f the slo-'j dy/'-ix in. knorn as an al., ,.bra-iL;
function of x, the vclor:2. L t',' d'i'tricuti.on c.,ri uv-_uallv
b'- obtained vithout much trouble lc a function of x .
The integ.rand :.n tquiti.a '11) a arircahis -..i intty
or b.eccmes Indster-r.in'tc at x >.,, but t'. integral
C' *ITIF TD.TI ALr
NACA ACR No. iC410
is usually fI.nte; thn innfi'n'te positive and neg-".tve
strio. can.el f the Integral approaches infinity at
Spv1 aen ':.'Mi.t x,,, a finit integral that yleld.s a
vol.o-i. -T ncrement wi.lch approximately egreer with the
vctuial flon can nuually be obtained for a slightl-
different v-lu9 of xx.
ihe sl--.pe method is mere useful than might be
supposed frir the restrictions .m.posed in the der'va-
t,'on. Although the results are not ex.r.ct, thej provide
a reasonably g)d4 eoproimation even for relatively
thick forns, eso.ci alli; over rei-ons of the orof3le
having small slo c. The -ethod is not aoplicaole in
the vc :1nty of a st 'tat'on ..int or ..:h-rc the
Flooe Cdy/ i. lare. This d'ffic ltt ma.7, however,
be ci r', v r nted. I'-ny nrotuber..iLc. ChPl es "nvDlve no
very l ir v values nf n .' /dx arn reqUire no -!t.agnation
point. Tf a t.'.r.naton onlnt does occur, t"le vlo'o.ty
distritutior- over the rest of the profile at somr
distance from thr. nc s nPay be Dax',oxini.ted jroviiled. the
round-oa n c- or coil, 'hlih. -i-vo..ves l .finiCte? lone,
:.s exterd l 'n a c':-) cr ot.eilelse is sli '.i tly altered
to prcvLant veir-; -tr,2 v.nla-' of r '/d.:
A re-scrnabl-': SaE .: st c volci ..ty .n.iputat o en can be
made 1f the sloo:. rre tr d '-3 lt.0-:'.- not t to the given
"rofit 1. b'ut to ti,-'. shEt .- ojutain. Es the anamonts j.y
b Wh. c t.-e ord r.at "' rf i'. i /e'! 'fil :- cx ed those
of a .sir'11e profile, vrch as .ii3.se or Ju$.,owski air-
f,-il, for :'hi-.h t'.e velocity distrit-.iLon i? known. The
vclo-ity inacre.e.:t. a-,e slmnly n3perPosed; that is, the
required vel.oclit, distributl .n is the sum of the velocity
.ettrtbuttr.n on the ,".imil ar orofle and the incrOement .V
found .fcr the d fer-'rtce sn-pe. '.hr' e-dimensi- nSal
sh'.-.nes ri n7 be sl-.hti: rodi.l"ed 'n the same way.
r'Ven r'rotuler'ane ,rofile ..haces can often be
asrT r .'.ated b t !. jaxta.-I t1- Tn of s er.ehs -)f zIcs
for which thic slor es are -river. a, relritively si.npile
alga:,'raic fu!:ct'.'.is :or xe-: rp.).Le, c rc'ular, ellipti3,
and rir.bol .c T'fe ... duaei-e 1 oci t7 oeffi.-
clent &AV/.1, '.'- then he nobtsin-7d fror eqastion (11)
b; direct *-. tegr'.tion. r.liz r.ced.ir ds anproxi-
m"ately correct v,0lo03t:' distributions even th',ugh the
curvature it the .'ur.t'.onn.s r:y 0e dis.IcotInuous. The
slooe should obvi.us.v be rude continuous; that is, the
arcs ab.uld hal;s the s'r-e -loD.- aj th ju-icture.
COrTDT "FTT AT.,
NA A ACR No. 1).! TI.
A r rotubcr-ance ornifi 1 maiy have the approximate -hape.
of a smicl.? imlole ar, such as the i- rcular arc, in vihich
case the velocltj distribution 13is easily calculasLpd.
Thus, in figure L,
-- = tan 6
x = r sin @
,- = r cos 9 ,-9
and equation (11) becomes
sin 0 dO
sin 9 sin 0H
sin e .in a
Integration nd si.ibstit.utMon of the limits gi-ve
ssin i tan -+ co a 1\
AV 1 n_
V 7T291+ tan 1Fe (1- lb)
o sin 9, tan --- Ons 9 + 1
t 1 /
I sin 9o tan -+' cs +
for the velocity di str'bution -as a f.function of 6,
CO FIDL 1- TI I-
1 1 p 91
=- de + sin 9
NACA ACR No. LrEl0
From figure L,
8, = sin -
6 = sin
= r2 _- r h)-
r = -j.
from w}. ch
9! = s'n-1
1 + C
Substitution cf equations (1i1.) and (15Y) In equation (13b)
gives the Indu.;e1-vel-city coeffi.cient AVP/' as a
function of the chorl -osition xo/c and of the thick-
nees ratio C-, Tv:hEre xo/3 is measured from the center
as shourn. The velocity inzrements for circuler-arc
profiles r-a.ing in thic-nres9 ratio from D.1 to 3.5 are
shcwrn ir figL.re 2, in whi:h the results of the slope
method are -omrrarer' with tn? res-ilts o)f the accurate
conforral-transfor- action methc.c. In figure 2, x/c is
measured from tn- end of the ir..'ile rather than from the
NACA A C. Tc. 11.710
center. Up to a thic-'-es? ratio of 0.2, the slopr.
method CiveF L. fair sp roxir-ation of the velocity, dis-
tributions over circula. arcs. As was to be expDcted,
the error is greater in regions of greater slope. The
velocities at the center of the profile, v.here the
slope is zero, are appro-:1r.at.] y correct even fcr the
Iletbods availb-tle for the calculation of flo,.ws- in
three dir.en ions are ler-& gec.er.al + hn tic-. corCre'po.dingi
two-dimensional :-ethod" because, e:'C'e i thtf s..r i-'6 l
case of the e li.:,.cid ".' th three u.e -). ] z7 t ,y
apply onl, to bo .s poss.es :i.ng a:,1i l s'r.i*).r1:,, th.t iS,
tn bodies of revolution. ;'i.;7.prot.uberavice: are
approximately axi'lly s:-rne trial, however, ard tihe
three-direnssioral theory rr.a/' grove useful ir: esti.1, ti:ng
velocityT and corresp.oidir nr essiie di.tibu tionz i-
The sph-re.- The Zit-mple.t bod;. of revolution is tae
sphere, for which the velo.'.: r di? trib'hit n is givEr Ib
-= o.-? in 0 (16'
where the anrle 3 i- r:'easurc-d alonr an.- m'.- r dian
ste.rtinf fror the stream or flight di.-eetion.
The o') lte "Dph-r.id.- A todI of revoljticn r' r, F cling
a guun turret ? t'er oblate spher3 .'.. o:bti'n r!ed .y "c 1 v1ing
the ellipse about Its n'".nor axisr. '.Motion .n the direc-
tlon of a ma 'or a.:-s :f the E llinse as 'shown in f i ire 5
correspond t-oC thr'L o- the -C'LU turret. T' r, o t, al
is given by Larn.b referencee 11) in tecre of Ith el-litic-
cylindrical coo.-1irates pi., and w, At the anrface
of the cblate spheroid, = :o and r iz give, by
where a and b are the set.ir.a i-r n.d renir i.'nor Exe ,
respectivel-y, of the corres:,ondin( ellip.Fe. F'roan the
COFIl E-ITT/ .L
NACA ACE No. LIO10
potential, the v-lccitv distributions at the
re-ative to th.e bod; uay be derived.
Around the rim in the TL-plane (line 1, fig. E)
= L sin (w
to + 2 to(o + 1)cot-1 -o
ind w is t'P rrncr-le v.'th the plane containing thr direc-
tion .of flow and '.he nDoar alis as shnwn in figure and
ir related to t'-e dist:.ce alonr: the Y-aris i!easured
from the center b:'
y/a = cos )
The velocit'r over the tnp in the XY)-plnne (line 2,
fig. 5) is
f + +
V \a I
The velocitT vcrosF the Mieridian
X)-plane (line .) is
\' v r/2
lyinrr in the
which, for a gFven t.'-:ness rrati b/a, is constant;
CO TTI DE"TT 'L
NACA ACR No. LIE10
that is, the velocity at the surface across the meridian
perpendicular to the motion of an oblate spheroid moving
normal to its polar axis is constant. Although velocity
distributions along other lies on the surface may be
obtained, those given by equations (18), (20), and (21)
are of greatest interest and are most simply derived.
The prolate spheroid.- A related body, for which
the velocity distribution is more easily obtained than
for the oblate spheroid, is the prola-.te spheroid moving
parallel to its polar axis. The velocity distribution
at the surface along any meridian as given by Zahm
(reference 8) may oe expressed as
V (1 + ka) (22)
o x2 b x2
a Y + ( a (a
loge e 2e
a 1 + e 2e
1 e 1 e2
where the eccentricity
e = (T
and a and b are the semimajor and semiminor axes of
the corresponding ellipse. The equivalent prolate spheroid
can be employed to approximate the forward portion of
a body of revolution in exactly the same way in which
the ellipse was used to approximate the forward portion
of a symmetrical airfoil. (See fig. 1.) The velocity
distribution over the forward portion of the body of
revolution may then be considered the same as that over
the corresponding portion of Lhe equivalent prolate spheroid.
NACA ACR No. L4E1O
Bory of revolution represented by axial source
ditrirton.. TLi-: elo "city .distr.ibution 8aout a body of
revol'tlon w'th flow oirallel to the Paxs can be obtained
by the iiMethod of ":on-k'rm. an (reference 1), provides the
body can be r eprzsented by a distribution of sources and
sinks :.1cYrr Lte sxis. This method is useful for a very
r',:ul:]r body for which the shaDe of the reridiar. profile
-an ce ',iven by only a few ordinates. If the Treridian
prfile is irregular, the Tethod ir tedious ar.d perhaps
Imrnossible. It Ls described in detail in reference 12.
od-y of revoilit in recrp'sented by doublet distri-
oution aton, 7yi ; ..r- a to flo w.- The circule.r .cylinder
projeceLr, from a lanT surface A-A (fig. 6) is considered
a halfl-body of "i-c h ihe other h-ilf Is rhown by dashed
lines. At the plane of sy -etry A-A, the velocity
:r,..st lie rarl:-l to thr plunr an tan',ential to the
surfac-' cf thrn cyli 'nder. At other plinres, crosl
vcloc!ties o'cur fr.d reduce the r:,' 's; the :rTaximun
veloc'iy changes consiuerntly occur st the plane A-A,
;eit f-sLL'ly o.'er t- share. irners at the ends for
which th-e velocity distribut.cens cannot be comp.ted.
By a r:t.lod describhc- o von I'.a'r-.."i (reference 12), the
part of the C.c.la- .3 occu.yd o' the cylAl.er .s
co-.vered v- ith. d. 'icl -t of' -. '..t .c-r rnit l=inoth equal
to tr'at obta'r.s- .: thn yltiider 're infinite in length.
The erncir of the c. 5i-J..:r 2orrespo)ns ir-.. to rt.s Tjathe-
mtical ,,v'ce 9sr ru.-deid r?ether then -lsne bs shovn;
th. irifluen-c of t're rou.ndel cndrs .n the velocity dis-
trl',.tior. *it the ,'ar?- A-f rorust z- Es-all, hDwever, and
the cndq of actuall g._n turrets ar: !=r-n lik-ly to 'be
rox.;nded than p!en =. T'.e -.russur. distributions in
pl ..nes parallel tL the u. ane A-A g.- neraIly ane sim illar,
but thr r~. k. are lov.sr ss th'. eind of t!"e cvl.ir-der Is
a;.-,.roa ,i ex,?cpt thvt, in thc. r. -.ion of snall radius
o:[ e.',r-vatur? nea.- a blunt -:nd, high poeks mr-y ozcurr.
The velocity at the ~u.rf'ce cf the cylinder in the
plEne A-A is
(1 + cos 9) sin $ (25)
where is t }e .,nlr aile measured from the plane
containrng the flov: dirccti-n rnd Lte polar axis, 0 is
C '.)TF I DE 'WTI AL,
IlACA ACF Nt'. LLE lO
the an, ] e shown in figure 6 for v'hich
o 9 = -
/ r + 72
r is the radius of the cylinder, and Z Is the length
of its orjjection fro.r the surface. An exzr',:le 1fr
which r is not constant is treated l1:ter. TIn-: method
is described in reference 12.
..ody of revolut'on by r'eiod ocf 31A. A. n th- d
hes rc.eentyv be de7 l-ootid .y "api- "ef rerce 13) by
which the no t.ent 'l fLou shout : b -iy -f revolJ.t '
miovin; in the d'ri section of "ts nlar ) o. I. mI,. be cs3 u-
lated to any iesIred. de ree of Ar prox :,at ,y this
method, tne flo-7 "s 3otsined vwith crt'iogonal -j urv linear
coordirnates for "'f-'h su.rfac of h"c ny><. tsf is s
a constant. 'L e cr ,.'or tei nate s-. tc1, v'si r: is di ifer'2r.t
for each bod', is ojta'a-ed n i:amns of ths confo .al.
z = Z + C + -- + + ... (2L.)
which tran-,sforms th-e ?irles n = Constant n.d the
n -i i
radisi lin=s s = C.nsstant in th-e la:"e 1 = P-
into C.he corres jodin I- orthogocrial coordinated lin-es in-
the z--!ane, v-.e:e q = 0 is th-- ;.oi1crin : i,. of
the bocy of rc vo 'tioln. Tnh. pot-_nt a l is n .- :v-. a
s2 ri of t.-rn.s in'ol ng th'. L .nrd.t fun cions F
and an-d the constants P .'.n .*.en .g i n the ser les
ii. e u1tion t-' ).
The d r, ovation .-f the nc :.e'Lzar;, f 'icti jr.s h es be
extended in ref3rfnce 15 only far -noi 1t-. 10 t- ccowit
of the ter.r. a," Z- in equ't 'on ._ ). If ndd,. t n-l
terms are necessa.3, to des .rtbe the ie.ri.rda.-i profile to
a suffiiie.:t degree f Prox] mat ._!i, the Lor resoLc'i
functions :-uct 'e ,.erived. Th-e ',,eth:xd of J.i S vatirn
is described in drateil in rf-ference 13. F'".er t-ri:ms of
e',uvt lt.i (2.'.) arc required as the profile i, r.ore rerinrir
and more nearly q '..,',.ates t'r. -llL "e. Pcr irreg'.u r
CO" FI DT.'TAIT
NACA ACR No. L4E10
bodies, additional terms are required and the labor
necessary to calculate the flow is greatly increased.
The practical utility of the method is therefore much
greater for regular bodies such as airship shapes,
fuselages, or nacelles than for irregular shapes.
For such regular bodies, the labor required is not
Approximate thin body.- A thin-body method appli-
cable to bodies of revolution and corresponding to the
slope method in two dimensions has been suggested by
Munk (reference iL, p. 269). An attempt to use this
method indicated that, with usual fineness ratios
(less than 10), the accuracy was insufficient for
estimating induced velocities over protuberances.
proximatee body of revolution for use with method
of Kaplan.- If the transformation (21.) is known (it can
always be obtained by the method given in reference 6)
and if the given meridian profile can be sufficiently
well approximated by the first three or four terms of
this transformation, the flow about a body of revolution
moving in the direction of the polar axis rmay be cal-
culated by Vaolan's method with no more labor than is
required by the thin-urofile method. The potential
flow thus calculated is the potential flow about the body
that corresponds to the terms retained in equation (24).
If the given body of revolution does not depart too
greatly from an clliose, the required transformation
may be approximated by a method of superposition.
The series of equation (-24) can be written in the
z = x + ly
a2 EIa (cfa Cp93a
= Z + a- + 2 -- ... (25)
Z 1 Z z2 Z5
= + iT
P = (1 + E)a
CO NFID NTIAL
NACA ACR No. rhrlO CONFIDENTIAL 19
and a is a constant depending on the size of the body.
On the profile (r] = 0), equation (25) becomes
x + iy = (1 + E)a(cost -i sin ) + --- (cos + i sin E)
o 0 1 + --
+ c la(cos ( + i sI.n )
E2 acos 2, + 1 sin 22)
cza'cos Uc + i sin (5) (26)
The first two terms of equation (26) give the
1 + E + -- cos s
a + "
+ -- s in
a I + I
and the remaining terms give
--'= c: c! Cs 3' e2 cos 2 ez 0os 5 ...|
a L E2 co -s f
= El sn !- E sn 2r E sin 53 ..
The coefficients C'q E, and C, maj be so determined
as to yield a slight modification of the ellipse
approximating a jiven meridian Drofile. ror a small
modification of the ordinates, the absclssa x/a is
only slightly changed and, as an approximation, the
required modification Ay/a may therefore be determined
at the values of x/a for the ellipse. The ellipse to
be used as a basis for the approximation should be so
CO NF I DENTT AL
20 CONFIDENTIAL MACA ACR No. LE10O
chosen that the required zrod!fication is as small as
possibl-. The vlve of corraspondtng to a given
thickness ratio 3//, when b is the minor axis and A
the mnjor axis, is obtained from equation (27). Thus,
1 + c- -----
1 + c
1 + + --
1 + E
and solution for rc gves
< = 1 7!29)
An eear-le will clarif:y the method.
In figure' 7(a) is Ehorn i meridian profile to be
ao')roxim.ated. The ellipse w "th e = 0.?, also sho,-wn
in figure 7, S' determined to be a satisfactory basic
r.rof~le for the a:oro>.i'ation. The required modifi cation
of the ellI os i' s *h\shown in figure 7(e). For convenience
in ti-Is modificati.n, the values of -0.1 sin ,
-0.1 sin 2", and -'.1 gin 5. are plottrcd against x/a
as cc.r-,uted frr. equation (27). Tt is seen frorm- fIg-
ores 7(D) to 7(d) with eqluation (23' that cE changes
the thikc'ess of the -.rDf!le while the symmetry is re-
ta" ned, c-2 ruciu.,.' an asy.r.ctry forward and rearward,
anr c z increases the ordinate at Lhe ends while the
center is deoress.,d. Tn:.sn-.uch as the main adjustment
required Is the !ntroductlon of asymmetry (fig. 7(e)),
cE2 irust be given s'rmie value. It is seen that a value
of 2 = 0.1 accounts for a large part of the modifica-
tion required. Further adjustment requires the eleva-
tion of both enCd: wnilc the center remains unaffected.
CONFIDE NTI AL
NACA ACE No. LLElO CONFIDEiNTIAL 21
If one-half the elevation is accomplished with c and
one-half with e the desired modification is achieved.
Because the required elevation Ay/a is -0.05, the
values of these coefficients are
c1 = 0.025
E = D.325
The resulting coordinates from equations (27) and (28),
shown as the first approximation in figure 7(a), are
S= (1.2 + -- 0.02 cos 0.1 cos 2E 0.025 cos 3
a 1.2 -
= -(.2 + 0.325 sin 0.1 sin 2( 0.025 sin 7.
a 1.2 -
The failure of the first apnroximation near the nose
of the ,iven profile is due largely to the reduction
in x/a produced by c2. It is further evident that
the forward nart of the profile is more nearly aporoxi-
mated if the value of E2 is reduc-ed from 3.10 to 0.07
and if the effect of 2 in reduc.irng the value of x/a
at the nose is neutralized by giving c1 the value O.07a.
The resulting, profile, which is a satisfactory approxi-
mation to the giver, orofile, is shion as the second
approximation in figure 7(a). A still better approxi-
mation is obtained if the vadi-e of ci is increased
to 0.lOa. The whole forward part of the given profile
is then very closely anproxiniated, and substitution of
c = 0.20 E2 = 0.07
E = ez = 0.025 cI = O.lOa
NACA ACR No. LlE10
in equation (25) r.'.ves the required traneforination
0.r'fa2 0.130,a- O.OL)2a_
z = + 3.1a + ---- ------ -.OL
Z Z2 Z5
from which the flov may be calculated without great
difficulty b): the eth.) of reference 13.
Alth:urh tre -,-or:-A.wrata method yields the potential
flow su.ut a sh,.'- s..st J"flferent frorr the given pro-
file, it is t:.3',-eral quite rstisf!.ctory for use in
estimatir: lor.. a t ap. r orm.ate shaoe is likely to
show sl.irht bi'u ns 'her-e none oC nr. the govern orofile,
but tn. es'iin-' r "resure d'strlbution is )orservative
in tb'qt it an:.ws i:;'rs;-r nr .: ure rationsios then would
be ol.t -ired for a ,i.ore re-.i.i.Lr o-ofile. On account of
.mran'facturrin irre gL..itjie,, the's conservstismr ma-, be
desira'j-L. nv:- thr r-'-r o'. E- body, m.orev-r, the
actual fior alwayss :-:rts ar-.e- .3 less from t.e ooten-
tial f?.ov arid '11-tl .i.:*s ir, .3'uracy7 n.:. therefore be
expected frro- an; .zisl lil-.re of the atprr:.lnmacion in
that region. T-.z? ret':c .-'- e'..] oye. sho.Id not be
ascu.edi tre ?.-.me I.s a 'it l hsr-nonic analysis.
COrres.3cr-'itn., b-'ics in two- and t, ;ree-d r;e.onnl
fl ov-s.- s .' T Th :I T 'Ti1 -_on bo- t v. -
dimnesinal PLh-.3 is .cn:rn, h r3';h estir.etio. of the
veloctr distri 0o1in nbcut ty.e bocy of revolution of
which it is the m rid 1an or:ifile m1'y be obta tried from
the rsn of velo3 ties in thi e-dlmensl..ral flow tc
those in ftlw-r lr.?:n.ioia&.l fl.': ebault corres roonl.in;: tbii..s.
The velo.31ty dlstr'but lns about the corresnor.ning bodies -
elliptlcal o1'rin.e.rs and or-olate o.herjic:s with motion
psralle' to the :r.ajor i;.Fs r.ve been cu c'alated L.
eqv.torf l r ) .nr (2 respe tivel;, a--:d ha--e been
plc'tte.' for c-.n.:,3 Ison Ir. fi-ure L ) SIrm. arli, in
figure C[ b), the It ,', t',, rtric ti'i.ons obtqLred for
aprovo2r(itely ct-'c rlar-nare :odces of rev-lution by the
C. thod of a '.en r.:.e o:. -' .i t 'the ve o1 ty dic-
tributions ov',-.t ne iresour.'in-r t '-.irienea icnal
sha Pe Tn i -Urr :" is th. -.st::-.ce fror: che
nose of the brd- :r.d 1 i4: 4t length.
D. vision f u-':..n -., by eu t.'tcn (o) -ivCes for
the ell:'':s? a-,d arol t., soh rnid
CC !T DE:TT AL
CO NTPIL ENTIAL
NACA ACR No. LLF10
VSD 1 + ka
V2D 1 +-
where 3D indicates three-dimensional flow and 2D two-
dimensional flow about corresponding bodies. Tnasmuch
as kg is a function of the thickness ratio b/a of the
corresponding ellipse, equation (30) shows trat the
velocity distribution about a prolte spheroid is a
ccnl-tsa,t times the velocity distribution about the
ellipse which is its meridian profile. The constant
V2D given by equation (50) is plotted in figure ) as a
function of the thickness ratio d/Z. This relation
suggests the pnssioility of usir.n the corresponding two-
dinensi)nal 3hape to des'ipn a body of revolution
sir..ilar to the prelate suheroid with a gI ';en velocity
dis tri b.ition.
The velocity ratio -- is not -enerally constant
along the length, however, as ray be seen from fig-
ure 9(b). Ini particular, the velocity over the tail
of a three-dimensional body dpoerts less from streak
velocity than the velo-ity ov.:r the tail of the corre-
sponding airfoil: the ratio therefore increases
and exceeds unity as the trailing edge is so:jroached.
Tt is nevertheless reasonable to saopose that figure c
could be used to estimate the velocities on bodies of
revolutiLon over tne parts of the meridian profile that
are roughly elliot'cal in sh-.:e. The following methods
are suggested as alternative.:
(1) Fit an equivalent elliose to the profile as
in figure 1. 'With the thickness rsti- fi this ellipse,
find the corresponding velocity ratio from fig-
NACA AC No. L)4E10
(2) Assume that the corresoonding ellipse is the
one which has the sa rre peak velocity as occurs on the
profile. Prom equation (6), the corre0oondiz.E th'.ck-
nesc rFtic d/,,Z or b/a then is
t -=b- 1 (31)
which witP figure gives the velocity ratio 7-.
As a tes& of the meth-od, the velocity ratios
---, wh:ch "ere constant alon,- tnc length for the
elliptical profile: tjt gc'.n:erally wvriable, were com-
put.ed for several :,airs of correspondin:.p, -haoes. The
variation along the length I is given in figure 10,
in which the values of for the equivalent ellipses
obtained by 'r,ethod (l) are s'ihon for co-nmri son.
'ethod '2) would l-.ve quite similar val-i.e.. or bodies
of revolution vwit., reri-i "an profiless rouahl7 similar to
tnose for which t-ih values of -re Ia-own, these
values mir b.e used to obt.tin velocity estimates rnmre
nearly cox rect than can be obtained by ase of the
elliptical profiles alone. Relations similar to equa-
tion (30) can also be obtained for the o'.,late soheroid,
tut th-!.r- an)nlicatinr is less benara! than for the
The elli-iscid v-ith three nr.eqa.l a::es.- A .;ro-
tuberance shane nor' rossessin:. axia] sy;a'netry a
flatten-.d blister, frr instance m-'y be anproxImated by
an ellipsold wvth three unequal axes. The necessary
elliition!F c ordinates and the potaItial. are g ven .:nd
exalIinod in reference 1j. on psges 25-13-'2. The mathe-
,m.atical :o.xrlnxity is such that, in mianj cases, a less
accurate a.pzroxicmat'cn by meins of the simpler body of
revolution is -"r.:-ferred.
ITACA ACR No. L.FIO
Estimation by Comparison
Comparison of the shace for which pressures are
required with a somewhat similar shaoe for which the
pressure distribution has been experimentally deter-
mined should prove very satisfactory if sufficiently
extensive sstematic experimentation had been com-
pleted- for the most part, hnv.ev.r", only s-attered
data are available.
The only existing syster:atic investigation of pres-
sure distributions over protuberances at high speeds is
that for windshields and cockpit canopies given in ref-
erence 1. If a given shape arioxi 'sat.s -ne of the
shapes tested, the corresponding pressure distribution
may be assumed. If a shape lies between t'wo of those?
tested, its press-ue distribution may also be assuned
to lie between the to measured, rYovided no critical
change in flow occurs for exam-l-e, separation or com-
pressibility burble,. Tf the -anony has no tail of its
ownbut is fired directly into the fuselage (as in the
case of the P-LO airplane), the -pressure distribution over
the forward part may be assumed independent of that over
the tail and may be faired into that for the fuselage.
In comparing canopies, the angle between the nose section
and the hood is assumed an important variable because,
for the small radii of curvature often found at the junc-
ture between these two sections, the theoretical ores-
sures, which are large negatively, are not attained; it
therefore seems reason-.ble to suppose that the peal-
negative pressure coefficients are determined largely
by the angle through which the stream must turn. These
assumptions have not been thoroughly and systematically
tested but, when applied to the estimation of the pres-
sure distribution about the coceM,!it canopy of the F-lOD
airplane, gave results in substantial agreement with
measurements subsequently obtained in the M.ACA S-foot
high-speed tunnel unpublishedd).
The results of experiment may also be used to esti-
mate the difference in pressure distributions between
nearly similar bodies when the theoretical pressure distri-
bution can be calculated for one of the bodies. Few data
suitable for this pur;-ose are available, however.
NACA ACR No. LU-E10
Experimental data used for comparison may include
interference and cor-prossibility effects: in this case,
the difference in these effects must be estimated and a
suitable adjustment applied.
In this section of the present report, certain of
the methods described in the preceding section are applied
to the estimation of pressures over various protaberances,
for some of vwhih experimental pressure distributions are
available for comparison. These and other experimental
data are analyzed to determine how the methods should be
applied and what modifications and adjustments are re-
quired to bring the estimated pressures into agreement
with the experimental values.
-aRrtin turret.- complete low-speed pressure-
distribution data for the "artin turret cn a model of
the North American B-25 fuselage are given in refer-
ence 15. The location of this turret on the fuselage
is showrr in figure 11(i). The pressure distributions
are compared in figure 12 with the calculated values
for the sphere and for the oblate spheroid with thick-
ness ratio b/a = 0.67.
The theoretical estimation of the velocity dis-
tribution about this turret is oarticularly simple.
The shape is that of a body of revolution almost ellip-
tical in cross section end may therefore be represented
by an oblate spheroid moving normal to its oolar axis.
The formulas for the velocity distribution over the top
of the body in the direction of motion, across the top
of the tody in a :lane peroundicular to the direction
of motion, and aroundd the rim of such a body are given
in the se-tion entitled "Metnods." The interference
from the fuselage should be small and, except for oound-
ary layer and separation effects, tha agreement between
estimated and nmeasur3d values should therefore be good.
7igur! 12 shows that the estimated negative pressure
peak, n particular, is alirost exactly' the same as the
value obtained fror the measured pressures. Over the
top of the turr3t In a .lane oero. ndlcular to the direc-
tion of motion, the theory indicates a constant pressure
NACA ACR No. LhElO
and the measured values show al-rost constant pressure.
Failure to reach stagnation pressure in front of the
turret is due to the boundary layer developed over the
fuselage; behind the turret, where the pressure coeffi-
cient approaches ze.-o, stagnation pressure Is not
attained owing to separation.
Inasmuch as the pressures we-re measured at low speeds,
no allowance has been made for compressibility effects.
A rough estimation could be obtained by multiplying all
pressure coefficients F by the factor
Turret A.- The two locations.of turret A on the
fuselage ar- shown In figure 11(o). Its shape and
di.r.ens'ons are given in figure 15. Pressure measure-
ments on this turret are given in reference t16 and are
plotted for comparison v.ith estimated values in fig-
ure i1.. Turret A is a spherical segment in form and
is large comp.ar2d with +he fuselage, having only slightly
smaller radius than tht fusege radius. About a
third of the radius is projected above the fuselage.
The turret is located back on the fuselage where the
interference cannot b.' large. TI cons deration nf this
geometrical configuration, "t is esti'rated that the
pressure peal's cannot be greater in absolute valu: than
would occur on thc sphere and that, because '.f tht-
interference of the fuselage and the development of the
boundary layer along its surface, tha peaks nre probably
lower. The change with M.ach number u. to = 0.70 is
assured insufficient to cause the prcssvre coefficients
to exceed in abs-ilute val ie thos.e- calculated for th,-
sphere by the potential theory. The tLeoretical pres-
sure distribution for the sphere, as obtained from
equation (16) with equation (2), is shown as the solid
line in figure iL.
A velocity distribution of approximately the correct
shape but w.th peaks higher than actually occur is obtained
by applying the two-dimensional theory to the circular
arcs over the top and side of the turret. The distri-
bution of induced velocities, from which the pressure
distribution is calculated by equations (2) and (12),
can be obtained by interpolation for the proper thick-
ness in figure 2. In this nase, the velocity incre-
ments corresponding to the more accurate method of
ITACA ACn N:%. LE10O
conformrl transformation from a circle are used. The
pressure distributic.is obtained by this method for the
L5-percent-tlick circular arc on the top and for the
approximately 27-nercent-thick circular arc on the side
are shovrT in figure 1L.
The pressure on the rear of the body departs from
the estimated values but, without the experimental data
shown, the limits could hardly be fixed more closely
than -0.h5 for the circular cylinder (from unpublished
data obtained in the 'ACA 3-foot high-speed tunnel) and
0..6 for the sohere (reference 17); however, a value close
to zero would seem likely.
Turret B.- Turret B is described in reference 16.
Its loca-ton cn the fuselage is shown in figure 11(c)
and the shape and dlm3nsions are oiven in figure 15.
A pressure distribution over the central profile (line 1,
fig. 15), with peaks larger than are expected in prac-
tice, may be comnnuted by the t'ro-dimensional slooe
method. The integral indicated in equation (11) is
made up of three narts, designated integrals I, II,
and ITI, that corresoond tU the three divisions of the
profile shown in figure 16. The integral I extending
frcm x = 3 to x = 2.03 inches is obtained from equa-
tion (1) with the upper limit equal to 0 and the lower
limit equal to G-. Tntegration and substitution of
C-' IT DE TTI AL
NACA AC' fro. TE1, CONFIDErITIAL
c c + r
,-4* 0) I
':' r 0 r--
r- a) -1
C --, I r
; 44-1 J
C 0o I D NTI A .
30 CCNFIDENTIAL ITACA ACR No. L4E1O
-4- "-,j ,- I
II1 + 1 N rj
11 '4 'J .
Se 0 0 _
-- -' r .,
-i) C' 0 |
CO 4 |
X' ,- -
rco ,, .
C 0 -- ---
>l I II
0 CO 0
C) o r-1
-D '0 C .
04- CC 4C3
e on ct -
.4-' u-i (p
o0 CL *- '
OO c 3
COIID 'T-'T AT
NACA ACR FNo. T.4EIo Cr'NFIDENTTAL 51
The integral ITT from x = L.79 inches to
x = 3.16 inches as obt:rined from equati.rlr I11) viith uoper
and lower limits of 3.16 and 4.79, respecti""aly, and -'ith
dy/dx = -O0.S3Lq Is
Then, for : < 6.1. inches,
4- TI + ITT
and, for x > 6.L6 inches,
I- = T(a) + IT + ITT
Calculated values ha-e been converted to pressure coef-
ficients, and th.e resulting di tri buti.n has been
plotted as the solid 1ine irn f.-ure 10. The cocffi-
ciei'-E t.:-n octair nel nrre c-,onsidered linitinf values
and i-- a. ue.' h.::f f '.! e-tlr h.,-h in a-ts i te vlue to
elliw 1 c-oi )rssi.o'i" t: effects u-) to a "ach number
of 2.73 ind remain concerv;-tive.
From the calculated tv.'o-dirlensi-nml veloci t:. dis-
tribution, the velo,.t.ies abo it the corresnoond:in. body
of revol't.on w-r-e e imat ed b'" the r-.tij of velocities
in three-dimensionri fl t.i to those in twv.-..irr.ensional
flow as ,ven for ellil-ses and nrolate sbiherols.c in
fi, ._ure 9. Th 2or.e.32andJ -nuTIg ,jresszui coefficients
ar? ThoAn as the dashed -urve in fi.'ure 16. The shape
of this turret is batveen the two-dii.ens ioni! ha:,e and
the body of revolution and, c'nseq.iitly, h.e measured
pressures lie betweEn the estimated values for the pro-
file and the values estimated for the body of revolution.
Cockoit canopy nd gun turret -,n Erewster SB2A-1 air-
plane.- Thie s apes an. lo3l a lons of the- cockF it canony
and gun turrets on the fuselage of the E.rewster SB2A-1
airplane are shown in figure 17. Two alternative gun
turrets have been suggested for this air.ilane. The top
KACA ACR No. L4EIC.
shane of the "axson turret approxjr ates an oblate
spheroid moving normal to the polar axis. The other
turret is spherical in shane. The tneoret4cal velocity
distributions are computed first for the turret shapes
alone without interference. The meridian profile of
the 'axson turret is shown -,ith pertinert dimensions in
figure 1S. Tnas.r.uch' as the shape Is symmetrical, the
pressure distribution is s-ymmretrical from front to back
and only one-half the half profile neeO be considered.
The axes of figure I1 are arranged to correspond with
those of fi'gura r. The turret profile is seen to be
only slightly different front the ellipse with thickness
ratio b/a = 0.67. The difference is shown as the
short-dash line plotted along the y-ax!s. This dif-
ference can te approx!msted by a circular arc; and the
turret profile shapo thus -can be more nearly aporoximated
by adding to the ellipse in the region indicated the
half thickness of the double circular arc of thickness
ratio t = 0. 1L. The corresponding velocity ratio VVIo
is obtained by directly superposing the increments aV/Vo,
as found for the circular arc b. interpolation in fig-
ure 2, on the values ( =- over the elliptical oro-
file r.f the oblate snheroid. ""ith b/a = 0.67, equa-
tion (17) gives [.3 = D.91 end the velocity ratio over
the elliotical section in the xy-plane is given by
equation (20) for values of *,. The cormoutation form
is indicated in the
i V/V for
9 ,/a Ioblate
0 t1.00, 0 0
.23 .98 .LO 0
.O .71 1.1 .1'
t. 1 6o 1.24 .1.
^o0 -.1,. 1. 2 .ot
oo I.51 1.5o o
1.00 0 1.0 3
CC .J- T77 NTT AI
NACA ACR No. ..10 COVNFIDFNTTL 55
The velocity increments AV/Vo obtained by the twvo-
dimensional method are likely to be somewhat large, and
some small adjustment in the corresoonein pressure coef-
ficients must therefore be made. The pressure coefft-
cients with these and other adjustments to be discussed
later are plotted along the turret line 1, fig. 19).
Around the circular rim of the turret, velocities
somewhat higher than those aoaut the rin. of the oblate
spheroid may be expected beca.Ase cf the departure of the
turret from the true spheroiral shi.ne and because of
interference from the cylindrical sides of the turret
extending down onto the fuselage. For use in the esti-
mation, the velocit-y :.rrundr the A1.rm of the oblate
spheroid is computed. 'i,,ith ) 0. 1, the velocity
distribution ('1/ 0) is obtained from equation (1.)
as a function of (L and is sho'."n in the following
y/a = cosw V/r. -
(deg) i \o
0 1.0' 0 1.00
10 .98 .211
20 .9. .L7 .73
50 .37 .52
,) .77 .. : .21
5C .64 1.06 -.12
6Q .50 1.29 -.ILL
o .17 .7 -.3
9c o 1.5 -.7
Again because of symmetry, this pressure distribution
holds for negative values of y/a:. that is, for w
between 99 and l!08.
For the soherical turret, shown .; profile i-,
figure 23, the theoretical velocity distribution over the
merid sn lying in the olane with the forward velocity was
calculated from equation (16), and the pressure coeffi-
cients were obtained 'y equation '2'. The values of y/a
are obtained from y/a = cos 0, vrhere again y is taken
in the direction of motion.
C3FI 'J TA. 'T A'
NACA ACP. No. L4ElO
For the cockpit canopy, the pressures over the nose
and the general pressure distribution forward of sta-
tion 121 'figs. 17, 1, and 29) were estimated from the
data for the -L.-5 windshield given in figure 22 of ref-
erence 1. The an'le between the nose piece and the
hood v'as 4c' for the SB2A-1 windshield as compared with
4'.S for the O3--5c win.dshield; otherwise, the two wind-
shields appeared similar. The data for a Vach rumber
of about 0.70 were used, but the negative pressure peak
was elevated slightly to allow- for conservatism in regard
to the somewhat sharper nnse angle of the SB2A-1 wind-
shield. The use o2 this pressure distribution involves
the assum: tion that the difference between wing and fuse-
lase interference in th- two cases -airnlane and model
tested) ir negligible. This assumption is reasonable
because the wing and. fussalge cann-t differ greatly in
the two cases and because the interference velocities
are relatively small.
The burin in the oressure-distribution curve about
station L2 is intended to represent the slight discon-
tinult;, at the rear of the sliding natch cover. The
dimensional data available do not -errit the exact
determination of the shaipe of the offset and, even if
the share werae known, the calculated pressure distribution
would be of questi'ratle accuracy. The magnitude of the
bwiu above thu general pressure distribution was taken
instead from the recu.lts of tests of a cockoit canopy
similar to tiat of the S32A-1 airplane.
The theoretical pressure distributions for the
turret shapes are modified by interference, for which
certain assumotions must be made. The turret is too
close to the canooy and too large in relation to it for
a read%. estimate to he made of the effect of the canopy
on the turret oresrures: because the canopy is situated
entirely ahead of the turret, however, the assumption can
safely be mrade that the nnly effect of the canopy is to
lo',er the velocities ov-r the turret. The shope of the
f.,s-la., in thc r.s.rion of the turret is such that the
incLucad veloeities must be small a:ud in addition it may
b.- Ess:m.rvd th!it, because tre -'in.f is ahead of and not very
close to the turret, tno induced velocities due to the
wing tend to be canceled by the: induced velocities from
the canopy. Tnat thee assumptions are reasonable is
indicated by figure .2 of reference 1, in which the pres-
sure coefficler.ts bclhind the windshield rith the tail
an in! the presence of 'K.Lng a:.d fuselage approach zero.
If the ccnopy of the S32A-1 airplane were faired out
with a sirilir tail in the rea.r, minreover, the turret
CCI:JFTO NTT AT.
NACA ACR No. LLElO
would appear very similar to the half-sphere or half-
spheroid on the tail. The flow over the part of the
gun turret not thereby covered should be affected only
slightly by extending the canopy straight back to the
turret. The pressures over the top (line 1, figs. 19
and 20) have accordingly been taken as those over the
modified spheroid and sphere, respectively, for which
the theoretical distributions are given in the first part
of this section.
Over the section indicated by line 3 in fig-
ures 17, 19, and 20, either turret contour is charac-
terized by a circular-arc profile of about 50-percent
thickness ratio superposed on the surface of the fuse-
lage. Figure 2 gives the velocity distribution, which
may be used with equation (2) to calculate the pres-
Over the rim (line 2, figs. 17, 19, and 20), the
velocities must lie somewhere between those over the
side (line 5) and those over the top (line 1). They
are therefore taken to lie between the theoretical
velocities over the rim of the oblate srheroid and
those estimated for line 7, and the peak is assumed to
be about the same as the theoretical peak for the
sphere. The resulting curve Is quite similar to that
for the sphere and is taken to be the same for both
The pressures at line L. must be determined -largely
by guess, because the contour itself is only slightly
disturbed by the presence of the gun turret. The dis-
turbance at line 5 must influence the velocities, however,
and it therefore seemed reasonable to assume induced
velocities one-half those at line 5. The corresponding
pressure coefficients have been so calculated.
Behind the turret, because of separation, complete
pressure recovery as indicated by the theoretical dis-
tributions is not attained. The pressure recovery
shown in figures 19 and 20 Is based on the tests of
reference 15. The pressures on the rear of the circu-
lar cylinder and on the rear of the sphere are shown
for comparison in figures ]Q and 20C and art considered
limiting values for low and moderate Mach numbers.
ro adjustment of the pressure peaks has been made
for the effect of compressibility because, for such
blunt bodies, at least up to a Mach number of 0.70, the
F".CA A.CR No. LLE10
conservatism of the nethods used is assumed sufficient
to cover the changes. Compressibility may, however,
cause the separation noint to move forward and uhus lower
the regat've peas arind decrease the pressure oshind the
turrets. The negative pressure p3al:s therefore ra-; be
brandened backward, and some account of this effect has
been tak:-n in broadening the peaks in figures 1' and 20.
Tn no ca-e, however, at least up to a '"ash nu:nber of 0.70,
can the pressuree on the rear of the turret decrease below
the negative pressure oeak that v:ould be obtained in
potential flow at the sane r'ach number. The negative
pressure :.eal' in figures l and 20 is th'.s indicated as
the limit of the oressure or. the rear of the turrets.
The development of the b-urdery layer over the
canory ahead of the turr';t and separation in the rear
tend to prevent either positive or negative pea&-s in the
pressure c1istributiin from being as great as predicted;
in this respect, the estiration is therefore connservative.
Average vRlaes of pressures obtained over the gun
turret of thI 3rewster X3b2A-l tirnlane in flight at
soaedfs below 22; miles ,o-r hour unpublishedd) are ore-
sented for comparison in figure 1. F)r obtainincr
loads, the estimation c-mPriares satisfactorily with the
measured values though, for the to) of the turret, it
aPoears to be unconservative. Frni.. the data available,
however, the turret on the XS32A-1 airplane appears to
pr,-.ject h.hher above the canopy than was assumed in the
estimations and larger pressure peaks miriht therefore
be expected. The irregularities in the measured pres-
sure distribution may be caused by the ribs and other
irregularities on the surface. Severe separation is
indicated behind this turret, where the pressure recovery
is little greater than that behind the circular cylinder.
Lower qun turret on Douglas XS3-2D-1 airilane,- As
a furt-Ter exam--Te that involves the method f ditribu-
tion of doublets along the axis of a body of revolution
movin, normal to Its axis, tne pressure distribution
ove:r the lower gun turret of the Douglas XS3-2E-1 air-
'lane is estimated. The form and location of this gun
turret are shown in figure 21. The pressure distribu-
tion over the central orofile (line 1, figs. 21 and 22)
is obtained and the distributions over other lines from
front to back cre assumed.to ba. quite similar. -or a
shave that does not differ too greatly from a body of
revolution, this ass': motion is reasonable and has in
other cases been found to agree wll with experiment.
(S.,- reference 1, for instance.)
C"N IDENTT AT
N.",CA ACR To. LLE1 C
The turret was divided for comroutational ourooses
into front and rear Jarts. The pressures were assumed
to be the sqme as if the turret were a half-tody on a
plane containing th3 surface of the fuselage imme-..diately
forward of and to the rear of the turret, with a stream
velocity parsels1 to the olenc. As sho3mP in figure 25,
the forward part of the turret profMl.- can be opproxi-
mated bS an arc of the parabola-
o 0.7 x1 -
Vith substitution of the slooe
-/- = l.7Lh 1.L,..C-
d( x/c) c
in equation (11), th'- velocity ,-istribution
A V 1 "o
1.L38 3.7L. 1.,l8 10le '--- --
shown in figure 25 s easily obtained.
The rear of the turret was apor..xi.mated by a
quarter-body of revolution v'ith polar axis normal to
the stream in the horizontal direction and with symmetry
to the rirht and to the left. Velocity distribution
was cor.uted by the method of distri'--.uting doublets
along the polar axis normal to the flow. (See ref-
erence 12.1 The cross section normal to the stream,
the central profile that is the ap.oroxiration to the rear
part of line 1 along the stream direction, and the re-
quired dirensions are shown in figure 2L. The doublets
of constant strength are indicated oy the short, heavy
lines along the axis; and, from equation (5) of refer-
ence 12, the potential for one doublet is
= i- (cos 9" cos 9') cos '
COr' FT DNTTrTiL
NACA ACF. N.. LhElO
By symmetry, the velocity on the surface at 1 = 0 must
lie along the central profile (fig. 24(b)) in the plane
of the stream velocity. Because the largest and smallest
velocities on the body occur along this profile,this distri-
bution is of greatest interest. The velocity due to
one doublet, the i doublet, is
AV = L _o = .~ (cos ei" cos 98,) sin
S ro ~6 hrorr
Reference 12 shows that as an approximation the doublet
intensity VI can be written
91 = 2Tr i2V
The velocity increments AVi are parallel and, with the
substitution for .i, can be added to give
AV_ 1 sin
Vo 2 \r) (cos ei' cos ei ) sin
The component of the stream velocity V, in the direction
of the profile is Vo sin $ and the total velocity is
= 1 + 43-) (cos 01' cos Qi" sin #
From the dimensions given in figure 24, the com-
putation of AV/Vo is indicated as follows:
NACA ACR No, L 0FlO
The velocity is therefore
(- + sin = 1.-9 sin 9
which seems reasonable in comn'-rison v.ith the value
1.5 sin $ for the sohere. The nosttion along the
stream direction x at which the velocity occurs is
obtained with sin 9.
From the velocity distributions thus calculated
for the front and rear portionss of the turret, the
corres9ondinz pressure distributions were obtained by
equation (2) and were then joined at the center to give
the solid line in figure 22. S'-me adjustment of pres-
sures was necessary to effect this junction.
For the turret in the guns-asear. osc'iDn, the
pressure distribution over the cylindrical surface
(line 2, fig. 21) was estimated by assurming a circular
cylinder projecting, from a wall. The dimensions are
such that cos G = ).).52. Substitat:on of this value
in equation (25) gives the velocity on the surface of
the cylindrical gun t .-rret near the fuselg-e. The
pressures are thereby determined and are shown as the
dashed line in figure 22.
NACA ACP No. L4ElO
The remarks concerning the effects of interference,
boundary layer, and separation on the SB2A-1 turret also
apoly to the XSB-2D-1 turret. For the reasons discussed
in reference to the SB2A-1 airplane, no compressibility
correction has been applied. The turret does not project
from the fuselage so far as was ess'uned in the calcula-
tions. Focr this rea-son, the estimated pressures should
be more conservative than woald otherwise have been the
case. !n exoerSmentsl data are available for comparison.
Analysis and Discussion
The agreement oetv.men estimrnted and measured pres-
sures generally is better than had been expected and it
&?ooe?rs that, if allo-ance is made for the effects of
interference and separation, calculations based on the
poter-tial-flow theory J-ve a satlsfactor- indication of
tho rmiximwur loads. The qgreenert is good for the martinn
and !,'axson turrets, v'iisn approach forms for which the
potential flow can be accurately calculated. In other
cases, the ac".,al oressures way denart widely from the
theoretical values. Tna reasons for this divergence
from the calculated values which are connected with
departure of the shares from those assumed, with com-
oressibility effects, rvth interference, and ,ith sepa-
ration and other boundary-layer effects are now dis-
cussed. The experimental data available are analyzed
and comrnared w,.th theoretical values to deterimne, at
least qualitat-vely, the modifications that should be
made to calculated pressure distributions in order to
aoroxi-ate more closely the actual values. The appli-
cation of pressure distributions to the estimation of
loads is briefly considered. The following additional
figures are introduced-:
Pressure data obtained in the NTACA S-foot high-
speed tunnel 'unpublished) on approximately hemispherical
turrets at different locations on a fuselage are shown
in figure 25. The orifices at which these pressure data
were obtained were located at the tops of turrets C, D,
and E anid at Ql-.e side of turret C, where velocities
approaching the maximum should occur. The variation of
-rezsure coefficient P with stream "ac91 number M!
is compared with the heoretical variation given by the
factor / _2". In figures 25 to 27, the curve of
critical pressure Doefficient Pcr that is, the
I,.kCA ACP No. LrE10
pressure coeffiident corres"ondinp- outside the bounc.sr-;
Plyer to thie attinr.r.ent of the lo-al speed of sound -
is shown to indicate the critical speecs of the turrets.
The critical Mach nu;.mber '.1 Is the I'ach num-ber at
which the pressure-coefficient curve intersects the
Figure 26 shows a comparison between the pressures
at the top of two spherical-se,iment turrets A and E, both
in the forward location of turret A as shownr: in figure 11ib)
and projecting different portions of the radius above the
fuselage. These pressures are conrmared. w'th the th?o-
retical pressures for the sphere including the variation
with Mach number i.veln by the factor 1
A com r arison is given ir, fLcure 27 between i-res-
sure coefficients at various pos'. tons on the fired
turret 2. of referenc- 16 and those .:n a tnci-ker faired
turret F, both in the locsti-.n of turret 3 shown-i in
figure llc). The vr.riauton -."' Lh ..ach number is sho,',n
and co opared with the theoretic'-.,l aviationn.
Figure 2'3, for -"hich the data a-r,. taken from ref-
erence 1, shc:r.s the pressure change ', -th ;.:ach number at
four different points on wirdshiilds rerresrtVnp bodies
of three different types; the 5-1-1, which has blant
tail; the 7-5-', which is characterized by a sharp
corner at the nose and ty a lonj, faired t-il; and the
X-1, which is well strea:-nl ined.
Departure frcm for.s for "'h:ch potential flow can
be calculated.j- The shape of a protuberance is usually
such that the potent l flow cannot be exactly computed.
ExperimenL is therefore needed to determine the effect
of -*.stevatic departure frcm forns for which the poten-
tial flox is calculable, such as variation in segment of
a sphere from the half-body or variation in thickness of
a body. The effect of these variations is indicated in
figures 26 and 27. The pressures vary qualitatively as
might have been expected; that is, larger peaks are
obtained for thicker bodies. The data are insufficient,
however, to define any quantitative relations.
CONF DEITTT AL
NACA ACR No. L4EIO
Figures 25 and 26 Indicate that, unless considerable inter-
ference is present, the limiting pressure on a spherical
segment less than a hemisphere may be taken as that on
CoinressLilIty;. The effect of comaressibility on
the pressure &oefT-f'7ents over protuberances cannot be
accurately estiu'at-3d although a qualitative estimate of
the nature of the change of pressure with 'ach numoer
may ce obtained. "Th theoretical variation shorn in
equations (5) and QL) and derived in referenceso2 and 3,
respectively, strictly applies only to potential flow.
The actual variation -ay be greater or lose than the
theoretical v.ariat'on and ra.; even be ooposite in siLn.
For protuberances, !'hich ti re usually influenced by
bo'"nd.ar-layer developmr-nt forward of the protuberance
and by sep:aration of tje flow, the theory is less uze-
ful than for a.rfo'ls, for which the flow generally
aroroaches more ne.rl the potential. As snown in fig-
ures 1i, 16, and 25 to 21.3, the peak negative pressures
general% increase rith "ach number more rapidly on well-
faired bodies located on the forward part of the wing or
fuselan than on blunt bodies located near the tail. A
detailed eyannation of the exnerrimental data available
indicates how and why the roes'sure coefficients in dif-
ferent positions on protuberances char,1e with e'ach number.
On the low-cambered turret A of figure l4, the peak
pressures change with '"ach number anzrroxir;ately as pre-
dicted b:T the ,qlauert-Prandtl theor'-. At the rear of
such a body, the oressures decrease because of an increase
in severity of seoarsti.in a comprecssibility effect that
has beer observed in other tests (unpublished). The
compressibility effects on the faired. turret a of fig-
ur.-- 1a are, similar to those on turret A, except that for
turret "' the positive pressuar coefficient at the rear,
which should theoretically have increased, was maintained
constant by the slight separation of the flow or
thickenhing of the bcrndary layer. The effective change
in shaac c f the form was apparently sufficient to cause
a slight c'ecrease in the negative pressure coefficient
at th.e 5-inch station.
Fi ure 25 shows different com--ressibility effects
on the -~essires at tr- *-op and side of approximately
hericoh'erical turrets that deorend on interference and
the bounDriry-layer c(evalopment ahead of the turret.
CONP FNT T AL
CONFI DE:TI iJ.
TNACA ACR Fo. LLEFI"'
Turret C is subject t considerable interference front. the
windshield ju3t downstrearii. This interference dec re-ses
the "elocities and nrevenc? th.= increase 1i. ne-ativa
pressure e coEfficient v ith "ach nrurrber that would other-
wise occur. Turret L, on the other hand, is placed in
a region in which the inteeferenc m- be xoec ted to
increase the veploctit s 6 am the incrcass vith :'ach
number of the top negative pre.;sure c.-effci-ent 9poroxi-
mates the th oreticl] inreasz up to tre critical snctd,
after which it increas-es shar i:: fhr :a s.):rt ",. nul-Mnber
range. Turret E, whichc h is lo-.ted far bock on ti-1e fuse-
lage and therefore subject to c.ns i.rsa:, interier-c-.ce
from the boundary I ,-er, shcws sm-1 1 2.hsn:1. in th,. ares -
sure coefficient wLIh p'ah r! number.
The turrets of f gure 26 were located in r:,ion
in which the boundary layer on the-.f.selage must ha:'r
been very thin. TIn ad-11tion, considerable inLeferrence
was possible; the possible effect of interference i'
increasing the change of :.ressur'e ceffent ':,ith -ach
number is discussed in reference 1. The neak nPe.at-L.ve
pressure coefficient on the appro 'x. matel-:: hersph.r- c.l
turret D increased ,;ith "ach nur.be-: about ac 2 ord-in. to
theory un to the c-] tical speed and -,ore r;soidly there-
after. The incre se on the lower-cotr'bered turret A
approximates the theoretical increase.
The comoressib'iity effect on the pressuress of
turret 3 has already- been noted in figure 27. The
variation of the roakt native c.re-sur_ .oefficients
ac.oears to asree closely vith the the. retical vri nation.
For the thicker turret -, the .eoar-t ion should be more
severe; this fpct is probably be rtlSs n that the ores-
sure coefficient at the to in.-rea':-s less ra-aidly with
r'rach number than the the-ry iandicates. Farther back
on the turret, the chan-ge in efifetive shee due to
separation produces a large decreass- in negative .res-
sure coefficient as the I'ach number is increased.
Tbs effect of ?omorcssibllit: .-,n pressuree coeff:-
ci nts at points on bo.-_ics of three different t.,ces
(from reference 1) is shown in fijuar 23. T'or the
well-streamlined X-I body, the pressures at oIrnts b
and d agree with the theoretical change vith "ach
number: at point a, t'.e peak increases more rapidly
than the theoretical values; and, at point c, the
effect of thickening boundary layer in decreasing. the
pressure is seen. On the 7-5-L body which has a
COU' TDFNTT Al.
00 FTiDE TLT,
NnCA '.CR No. L4E1O
well-faired tail end a sharp corner between the wind-
shield and the hood, the pressure at point d agrees
with Lhe theoretical variation, the pressure at noint c
show., the effect of thickening boundary layer, and the
negative pressure coefficients at points a and b a short
distance behind Lhe ooint of separation decrease before
they -rErt to r'se wiNh 'ach number. On the 3-1-1
body, whi'h has a blunt tail, the pressures at pointss b
and 1 change about as theoretically predicted, the pres-
sure at -Dint a sorrewhat aherd of the separation point
fails for the most po"'t to decrease as fast as indicated
by the theory, one the nres-ure at poInt c on thu tail
-:ecreases greatly behind the ":oint at which separation
The effect on pressure coefficients of change in
"'ach number is seen to be different for different
points and for diffe-ent bodies. For roughly similar
shares In similar locations, the ccrres-.onding varia-
tions with Vach number may be assumed.
The effect of compressibility cn the pressures
over a orotuberance obv3.-.usly deends on the Feynolds
number of the ,ro-uberance anc of the body on which it
is placed, inasmuch as the type of flow must be a func-
tion of the reynolds number. Comr.ressibility effects
also depend cn the relative size of the protuberance in
relation to the body -n which it ".s placed, because
interference and boundary-layer effects are different
for different relative dimensions.
From the experimental data, the following principles
that are useful in a qualitative estimation of the change
of pressure coefficient with "'ach number may be derived:
'1) Over the greater part of well-faired bodies
that are not too thicv and are relatively free from
boundary-layer and velocity interference from other
bodies, the theoretical change of pressure coefficient
with ;"ach number may be assir.ed. The factor
1 expresses the change with sufficient accuracy.
The negative pressure peaks may be assumed ts increase
somewhat more rapidly than this factor indicates.
1';\CA ACR To. LTL, 0O
(2) Separation of the flow, which re ulsrl., occurs
from the rear of blunt forms such as the sDhere and
the circular cylinder and to a less degree fror less
blunt bodies, Is likely to becoi..e more severe with in-
crease in I'ach number. The res.'ltinyg change in the
effective sha)e of the body ma-.y roriuce an increase (as
compared with the tn nreteal decrease of the -:ressure
coefficients near the be.;ining of the se'arat-d rei.ion
and a decrease m.ore-nregati.ve proesseire o.effic Lents
near the tail. Fvu n on mo derately thin faired bodies,
som-thing of this effect may a:,..-ear" whereas, on tod es
with short tails, a larae decr.a&se in the negative ores-
sure coefficients just forward of the tail and a con-
siderable increase in the negative Dressure coeffi-,ents
at the rear may oscur.
(3) Tnterference that increases the veloc'Lties is
likely to cause a further in-rease in negative pressure e
coefficiernts 'i th "ach number, whereas interference
that decreases the veocities "- liely: to ha-,e -he
(1.) Tf any considerable a.rt of the protuberance
lies within the bouncdsry layer nrodI ced on the body for-
ward of the procubera-nce, the chobtn: in pressure coeffi-
cient ,with Vach number is likely" t, be different fror
the change that would oc:ur if no boundary layer existed.
The pressure peaaks may be smaller and seOaratin effects
ma'.a be introduced.
(5) If a critical Reynolds num.iber occurs ,'ithi_-.
the !,ach number rsn-.e or if a considerable cha-nge in
pressure coefficient with Peynolds number is otherwise
to be expected, the resulting effect on the change in
pressure coefficient with ?ach number musL be accounted
The foregoing discussion hilds for "'ach n;unbers
less than the critical. Above the critical "'sch
number, still less is known about the pressures to be
expected. outside the region of suersonic -speeds, the
pressure change is much the same as at subcritical ;"ach
numbers. The supersonic region commonly coreads rear-
ward as the '"ach nume..?r is increased, and the negative
pressure oeak usually increases and broadens toward the
rear. As the shoc'c- wave develops with its large un-
favorable pressure gradient, seoration is likely to
occur and produce the pressure changes already discussed.
COF'T DENTI AL
h16 CONFIDENTIAL NACA ACRT No. LL-E10
The negative pressure coefficients cannot in any case
continue indefinitely to increase with 1iech number, and
a tendency to decrease at the highest Mach numbers is
already apparent Ir. sare of the curves in figures 25
and 26. An absolute Jliilt imposed by the condition
that the local static pressure be zero is given oy
(-P)ma The experimental data available indi-
cate a limit less then given by this relation. Up to
a iach numoer of C0.70, however, the changes in pressure
coefficients likely to be encountered on protuberances
may be estimated by the methods herein presented.
Tn order to estimate with quantitative accuracy
the effect of compresslbility on the pressure distribu-
tions over protubersices, extensive systematic experi-
mentation Is necessary.
Interference.- ror cases in which the interference
cannot eV expressed by slmnly adding in the induced
velocities due to the interferin-, bodies, an estiratton
at least qualitatively correct may still be obtained.
It is reasonably certain, for instance, that a canopy
in front of a .un turret can have only the effect of
reducing the velocities and thereby the pressure peaks.
Figure 25 illustrates the difference in Znter-
ference effects for turrets in different locations on
the fuselage &nd for different angles of attack of the
wing and fuselage. Turret C is subject to a reduction
in velocity due to the hump in the fuselage immediately
behind it and, -n addition, the accompanying unfavorable
pressure gradient ray be expected to precipitate earlier
separation than would otherwise occur. As seen in fig-
ure 25, the negative pressure coeflfiients on the top
of turret C were much v-aller than on turret D, which
was located in a region of .increased velocity due to
both wing and fuselage. Turret E is so located that
the velocity interference should be small but, with
most of the fuselage forward of the turret, the boundary-
layer interference must have been considerable. The
negative pressure coefficients are only moderately large.
The change in pressure coefficient with angle of attack
is aopreciable. A rough estimate of the interference
could be obtained by adding the induced velocities due
to the win;g and fuselage as in reference 1.
'-ACA, ACR N0o. T, 10
The velocity interference on the central part of -
fuselage commonly amounts to about = 0.10. A rouh'
estimate of the induced velocity'. c.An 'e obtained b-
fitting an equivalent prolate spheroid to the fuselage
as described in the section entitled "reth:c's" an.d in
The wing -. s approximate ely a two-d.i nsional form
and thus may cause relatively large tu.terferi-n-
velocities, If a protuberance is located n.esr the
velocity peak on a *...tng, tl.erefore, tnc. ress,'res m:.- be
widely different fr'.-.i those on the sra ,r,'tu,.bartnce not
subject to the interference: in pddit.i-'n, 4Lhe c.aroe in
pressure with change in 'ach number or vin_ an le of
attack mra:. be large.
Tt may be necessLry in some cascs to determine the
interference effect of a nrotubOerasnce on tha loads over
surrounding surfaces. The induced velo Lties -enerally
decrease very raidly wit 'h inrease i.n distance fr Mi the
surface. The decrease of the 'e:--- velo ity incre:rent
is shown for a win' and for oro.-late stero-ids in fi:-
ures 56 and 57, reso,.,tively:, of reference 1. The
methods given in the &p-.pen'-x of' Teference 1 can te
used to estimate the interference die to a orot.iberance.
If an equivalent orolate soheri-'1 can b,- fitted to the
protuberance, the maximum. interfere.nme %elocities can
be estimated fro,.r figure '7 of' ref" r'-,ce 1. If f'ore
detailed information is needed, however, a veloicTy-
contour chart sucl as that of figure .r of r.eer- nc: 1
can De cre:ared for a 'od-y r.rox.in trinl the orotube-
rance in shane. For simp)Ic haoes, such as thc sphere
or oblate soheroid, vv:lo'i.tty: c--),tour.s r '.ss-il., obtained
from the potential theory. A':itt'L nal exoerirnnt is
needed to permit very accurate cstimstcs of the effects
Surface Irregul.ariti3s.- The the-retical pressure e
distributions are calculated for smnth bodies, but in
practice the surface is usually oro'-er. by ribs, joints,
waves, or other irregularities; as a result, oea'.-s and
valleys appear in the pressure-districution curve.
Such an irregular )pressure distribution is Liven by the
experimental data shown in figure 1'. The irost obvious
surface irregularities in this case were the ribs of the
turret. Estimated ,c.ressure distributions should be
made sufficiently conservative to allow for the effects
of these irregularities.
FACA ACP No. LLE10
Separation and Dress'ire behind a protuberance.-
ost prcEFT eran-c are sufTfcTlen-ly -Etat tHef tail
that the flow fails to some extent to follow the sur-
face. Thic sen&rstion of the flow is aggravated by
the boundarN layer develoood on the surface forward
cf the protuber-ance "iith the result that separation
becomes more severe as the protuberance is placed far-
ther beck from the noe of the fuselage or other body
on which i.t is s!tuat--d.
Although separation dops not usually increase the
severity of the leads, it greatly increases the drag
of the protuberance and shov.ld therefore be prevented
by a firing if conveniently nissible. In the case
of gun turrets, a r.3thod that might be used while the
advantages of 3vr.me'rical turrets are retained i, to
install r:trsctable fairinns behind the turrets. The
effect of fairing on separation is sh.wn in a coim-
,arison of the ":xper'"icntal data given In figures 12,
.l, 16, and 1). The use of faired turrets appears to
give little advanteae over symmretrical turrets unless
the fairing is suffic'ert to orwvent anr.y considerable
separation. If the flow becomes unsyr.- retrical when
the turret is rotated from the stowed position, local
loads may be substantially Increased. If sharp
corners are thus exoosed, the pressur-s may be impos-
sible to estimate and the neak negative pressures may
become very high.
At share outside corners, the flw se-arates either
completely or swith a bubble sbout which the flow later
closes in. A method of estimatingM the pressures near
sharn corners has been sug-ested in the section entitled
"Estimation by Comoarlson." Tt is point3d out in ref-
erence 1 .n ages 12 and 15 that outside corners with
radii of curvstures leEs than a-'nrxiu-atel- 25 percent
of the height of the orotuberance may be considered
Separation changes the eff)ctiv': shape of a body
In such a ,-,ay that th.. pressure nea'-s influenced by the
se~'artion are reduced and the oressure on the rear of
the original form is decreased. At the roar cf the
fsir.=d turnet of fir..re 16. therefore, the pressure
coefficient is posi ie; whereas, on the rear of the
more severe turret Df figure li,, for which a greater
pressure recovery; is irdicated, se,'aration has reduced
the pressure coeffic ent to zero. behind the still
C'Or TDFNTT AT
CONF IDFITTA. T,
FACA ACR No. LL.ElO
more severe forms of figuress 12 and '1, the pressure
coefficients at the rear are naga&tive. Frori, t.-ese
exoerimental data and irom the kCnown vpales of the
pressure coefficient on the rear atf spheres ar.- cir--
cular cylinders, a rough eatimare c.f the Drcssires
behind protuberances cerr be madre; but it 1- evident
that, in order to judge accurately whether sepa-ation
will occur and vbat -.iressures will then exist, much
systematic experimenio'tion is required.
The effect of iorpressibility in rrcipitating or
increasing the severity of separation has already been
Estimation of loids.- From the pressure distribu-
tions, estimated or measured, the lo.Id.s can be determined
provided the internal lressuras are known. The
internal-pressure coefficient may be :osL.ive if the pro-
tuberence is vented to a high-oress're region, as about
the nose or tall of the fuselage, but Is more likel- to
be negative because leaks regul.arly occur to the low-
pressure region "'n which a prj:tuoera.ice is usually
placed, such as leaks around the sliding canopy, through
other craci's, or through holes .n the surface. Because
the external pressures var-; with an-le of -ttack or the
positions of the leaks change with ancle of ;.un turret,
the internal pressures also var:-. Since negative
pressure coefficients uo to P = -O.LC often accur on
a fuselage similar n-e .~ures m:n be expected in.'ide
canopies or guai turre.s. In low-s -ed t& ts of the
GrunTr.an XTBF-1 airnlare unpublishedi), for example,
internal-pressure 3oefficients of -0.15 were found in
the canony vhil e, in the .'mmetr-.cal s''rt 'n turret
tested., t.h orcssur:- co-fficient varied fror -0.02
to -0.11 depending on the angular position of the
turret and angle of attack of the airplane: similarly,
in the unsyrmmretrical Grumman turret with which the air-
plane was originally equipped, the internal-pressure
coefficient varied between 0 and -0.06. For the
Brewster XSB2A-1 air)lano in flight funoublished),
internal pressures in the gun turret varied from
P = -0.20 to P = -0.32- inside the ccckoit canopy of
the SP2A-)4 airplane, very low pressure coefficients of
-0.530 to -0.LO were found. Because of differences in
leakage, the internal oressures are likely to be differ-
ent from time to tire, even for the same airplane, unless the
SCO NF IDENTI AL
NACA ACP No. LLElO
enclosures are sealed. It is evident that, because of
low internal prsssureq, jettison may be impossible even
if a orotuberance is dei.ignind to be released. An
increase of internal pressure could be realized by
venting to the tail of the fuselage.
1. By the meth'bs given in the present report,
pressure distributions can be estimated for use in cal-
2. Tf allowance ir trade for the effects of inter-
ference and separation, calculations based on the
ootential-flov: theory give a satisfactory indication of
the maximum pressures to be expected.
5. For shares abnut which the potential flow.' is
not exactly calculate, the pressures may be estimated
by various ionroxirrate methods presented or by coan-
oarison v ith exoer'mrent.
J. Com-'ress'iblit v and interfer-rice effects and
the effects -f deoarture from potential flow, including
seoara*ion, can be estimated by a combination of
theoretical methods presented and by comparison with
5. In order to estimate the loads, the pressure
inside the body as well as t.he external-oressure dis-
tribut or Ii'.st be known.
6. hurtrer erperirental investigation is needed to
determine the effects of interference, zompressibility,
separation, nrid systeirmtic ch--nges in form.
Lan-ley remor ral Aeronautical Laboratory,
nationall Advisory Corrmittee for Aeronautics,
Tangle.; Field, Va.
TTACA ACR No. LLFlO
REFERE ':CE S
1. Delano, James 3. and Vright, Ray H. : Investigation
of rras and pressure Distribution of '.indshi.lIds
at Eigh Speeds. i!ACA ARE, Jan. 19L2,
2. Frandtl, I.: General Considerations on thE Flow of
Compressible Fluids. NACA Tk.. Io. S., 1956.
5. von FKarmarn, Th. : Compressibility Effects in
Aercdynaymics. Jour. A-ro. 3Ei. vol. 8, no. 9,
.Tuly 19)1,, pp. 537-556.
L. von Doenhoff, i:- ert E. : A :.!-thod of Fa[cdly Esti-
mating the Fosition of the Larinar Separation
Point. TA>A T. No. 671, lQ3i
5. von Doenhoff, Albert F-. and .- terv'n, Neal:
Determination of Li.',ner.cl Eel'ati ons for the 3B--havior
of Turoulecnt boundary L.yers. i!ACA PCR i1o. 301,
6. Theodorsen, T., and C-arricI':, I.E.. 'General potential
Theory of Arbitrary r'"I-,: Sections. NCA Rep. I:o. l2,
7. Jones, Robert T. and Cohen, DWris; A Gra.hicnl
Yiethod of DeLermni1ng Pressure Distribbution in
Two-Dimensional Fl'7v. V' ,CA Re.. o-,. 722, Il-l.
8. Zahn. A.F.. Flow and Drag I-rmulas for Simule
Qundric?. IJAC.. Pep. Pi. 253, 1927.
9, C-laniert, H.: A Ceneralised Tyue- of Joukowski Aerofoil.
P. & r. No. 911, British .. R.C. ].12L..
10. 33ldstein, S.: A Theory of -.erofoils of Small
Thickness. Fart T. Velocity Distributions for
Syrrmetrical .erofoils. 58dL, .e. 1976 ('revised),
British ... .C., M'ay 1 4, 1 .
11. Lamb, Horace: Hydrodynamics. Sixth ed.,Cafribridge
Univ. Press, 19532, pars. 107 and 10, pp. 1'2-14.6
12. von F'rr'ia'n, Th. : Calculation of pressure Distri-
oution on '.irship Hulls. P3A. TM 1;;o. 574, 190.
COITT DENTI AL
NACA ACR No. LElO
15. 1Kaplsn, Carl: On a New Method for Calculating the
lotentlal F)ow past a Body of Revolution. NACA
ARR, July 19Lo2.
1L. Munk, p.ax M.- Fluid mechanics, Pt. II. Vol. I of
/..rdim.nemi T'.eory, div. C, W. F. Durand, ed.,
Juli..: 2,-'nger (Berlin), I09 -.
Fluid ;;,oLjon with Axial Syr-metry, ch. V, sec. 6,
p. _( .
Ellipsold with Three Unequal Axes, ch. VIII,
ses.-. 1-5, pp. 293-502.
15. Yonur., D. "'., and Devis, E. L.: Drag and Pressure
Dist i-itr.tn of Gun Turrets on a Model of the
B-25 Tuselage. Five-Foot "ind Tunnel Test No. 30C.
A.C.T.P. 1o. 1753, ..aterlel Command, Army Air
Forces, A,.ril 10, 19i2.
16. 2atts)n, Axel T.: Tests of a Large Spherical Turret
and a Podfo_ ed Turret on a Typical Bomber Fuselage.
IVO.CA nRR, Oct. 1Qi2.
17. Fluid "ntion Panel of the Aeronautical Research
Co-m.1-tee and Others: Modern Developments in
ludl, Dynernics. 'Vols. I and II. S. Goldstein,
ed., Oxford 6t the Clarendon Press, 1938.
NAfA ACR No. L4E10
t 1 -
NACA ACR Nc. L4F10
oA/IV '.4et8J:eo:.o wau!-4oooe
NACA ACR No. L4F10
Vo \_S 0lpe dx
--Souce disribwtion Calong a x
/oe dy NATIONAL ADVISORY
dx. COMMITTEE FOR AERONAUTICS.
Fi'gure 3.- Slope method for
Figure 4.- Circular-arc profile .
veloc'ify c/lcula fi/n
COMMITTEE FOR AERONAUTICS.
NACA ACR No. L4E10 Fig. 5
I 5 -
/ \ \ ^ (Uo
D <"* Xb -
^ 1 -
NACA ACR No. L4E10
-Po laP r
COMMITTEE FOR AERONAUTICS.
Figutr 6,- Circular cly/inder of fi,'ife
,from 7 s a rfqce.
. Fig. 6
I I \
! I i
NACA ACR No. L4EIO
(b) o./ sin h
I~ ~ ~ ~ ~~~4 --- ---- -- ^-^- -- --- -- --- --*- -
(C) -0.I 6in 2 f -
(d) -0./I in 3 .-
AmountL ao be odded to eclipse
0 ----- 0.i Sin 2 | |1 I I 1 I
f | ,CONFIDENTIAL
l I ] I .. .. .. .
I __ I
NA IINAL ADVISORY
COMMITTEE FOR AERONAUTICS.
#* .8 /.2. /. 2.0 2.4
-/.6 -1.2 -8 -. O0
Figure 7. Deferminaf'lon of Ohe complex functi'oi for Mhe
coaormna/o/ freisfaorma'ion of a circle infto a profi//e pproxii/ing
the meridian section of a body of revol/rOtn- -
CONFIDENTIAL I -
- ----Fir.s* approximation
econcd cpproxi/m ftibn
I I I i i I I I
n n. .
NACA ACR No. L4F10
2.0- t CONFIDENTrAL t
0.1 = -..-- -0.4^ZI
1.6 3, -- -, "
4------ Three d,'mensionr/l
0.4 (-- ) Ellipficql cylinder3 and rneridian iro file- -
of prolate Spheroid,5.
o I I_ _ii _I___ ___
1.6 .4 1 1.
1I IV NATIONAL ADVISORY
-"Two dmens ional "
--- -' --Three d imenSionc Il
.4 -(b) Approximale circular-arc syrnmefrical airfo;/15
ar meridian profiles of bodies oP revolution -
.. I, ,,_I I I IL ,II I U IU NLd f iAL L
0 ./ .2 .3 .4 .5 .6 .7 .8 .9
F'i0ure 8.- Corparisonr of calcu/loaed ve/oci/y
aisfributions over #two dimensional shapes wifh
those over -the correspondcti' bodies of revolution.
NACA ACR No. L4E10
( ^ )
I I ~ I I I
COMMITTEE FOR AERONAUTICS.
Figure 9.- Ratio oa velocities on
probate spheroic/s *o those on
correspoinacig. ellipi'c cy/'nder's.
1\11 III I Ill
NACA ACR No. L4E10
(a) Circular- arc profiles.
(b) Joukowaki approximately symmrefrical profile;
S=0.277 (reference 13) .
uI Lmiarnir-flaow profT/e
I I I I I l
EWuivalen', e //ipse ,'
r" d /1 = 0.37 --
/ / NATxONAL ADVISORY
COMMITTEE FOR AERONAUTICS.
,. ri^r. ._____
_(c) Lamia- fa pro file. t =.6
./ .2 .3 .4 .6 .6 .7 .8 .9 '.o
Ftywre /0o.-- V/at'afion of /he ratio of ve/ocifies it,
three -dirnersionaia to those ifp two-dcimei.sional flow
over sever/l bodies drcd +heir eyui'valenrt ellipses.
NACA ACR No. L4E10
(a) Mar in 6u.rret.
(b) Turret A in tivo loccxltons.
z/? = 0.590
(c) Tu rre- B3.
COMMITTEE FOR AERONAUTICS.
furre- and #urreit A aon B
on fs e /age.
X/1 = O. S90
NACA ACR No. L4F10
Af o- f Err t CONFIDENTIAL
6/ = O. 0.67
o Around rism, line /.
+ Over central meridian -
In direction of 1fl/o".
x Over cen-ra/ meridan -
norm/al o direction
of f/oV, line 3.
Figure 12.- C-.znpQrisoin of mea sured pressures on
the AR/ar-fi' tfrr-e r referencee /5) tvifh calculated values
on @n equival/ena oblate sphero;id and on a sphere.
NACA ACR No. L4E10
COMMITTEE FOR AERONAUTICS.
' Turret A det//As.
NACA ACR No. L4E10
L/'ne / (Cbp)
,'ne / (Ao). CONFIDENTIAL
Line 2 (s/e). -'",,
/ Theory for
-1.2 ----- sphere
/ \ /- Circular Orc,
F Circula/r arc,_
/ \ o over s$ie.
1 JMeasured oft___
-4 x 1 28.6" fuse/oge
s ation, lie I /f (op).
I o o. 22
1.2. Measured of 67.8
L.2 fuselage station .
Line I (top) At Line 2 (side)
1I6IA NATIONAL ADVISORY
I IU~NE IIAL COMaMITTEE FO EoWM cs
0 z. 4-. 6 8 /0 12
Distance from edge, in-
Fl'gure /14.- Comparison of measured pressures
on turret A of reference /6 vwo'v# theoretico/
pressures on sphere and circular arcs. a = J".
NACA ACR No. L4E10
Re/c five w-ind_
COMMITTEE FOR AERONAUTICS.
D de' /5- -s.
NACA ACR No. L4E10
. /= -0.3319
J1 I 2ZZT
-- /.2 .\ -
o / I o
-oA Meo5aswrdc/ at 67.8 ,1-
fu.se/loe afa-ion, c=3. '
46 Top S lde
n. orifices orifices NATIONAL ADVISORY
o 0. 22 COMMITTEE FO AERONAUTICS
\ _-+ .67 a ]CONFIDENTIAL _
Calculoated by slope method -wo dim enaionaI.
-- -- Estimafed for body of revo/utiorpi from
fwo-dcriensiomna/ ve/ocify disbribuifon.
I l I I I I I I I I I 1 I l I
0 / 2 3
4 5 6 7 a
/ecft'np9 edge., r.
Figure 16.- Comparison of es /,'faecf Wii;
meoasuredc pressures over tc'rret B owT
reference /6 .
NACA ACR No. L4E10
I i 9 j
-- D- \
---- \- c
*_i qj qj^^^ ^
^ "> -
S J i,-
NACA ACR No. L4E10
NACA ACR No. L4E10 Fig. 19
/~~ i, -^ s
\ i '1 ^ra
^~I Ub a 5/
:3 /:z %6l Sas
gnA u OM
o .1 ^ --"^j .--.^ o
-I ^^ ["00
s i oit
^ // '
1r g Ii I
l '-'/o '*SA
^ t ^-^ <"-Coi
NACA ACR No. L4E10 Fig. 20
.NACA ACR No. L4E1O
NACA ACR No. L4E10
LJ /1" T
/I -_________ _____________
---- op of turrets lind e /.
j-----cli'ndrical side of ft
^ -* z- *-..
n i guns a eom position,
COMMITTEE F0A AERONAUTICS.
Figure 22.- Esdimated pressure distribution
about lowerr gun turrer of Doug/os XSB-2D-/
airp/one. /v7l = 0.70.
NACA ACR No. L4E10 Fig. 23
\ 0 0
\o ---- I- -
\ 0 __
S\ 0 0
C. 0 4 0.? |
/ -I- ----N
S----- --- I
a-< 1 1 1 _ogo
NACA ACR No. L4E10
NACA ACR No. L4E10
Alach number, M
Figure5.- Pressures on similar yvn furrets in different locations
on the fuselage.
NACA ACR No. L4E10
- 1.0 -- -- I -
__ __ _
e- Turret A freaerence /6J.
' ^ + Turret D (unpublished dato).
Theory for- sphere P = '--
-.2--- --- -
C CUFIDE,'nTIAL NATIONAL ADVISORY
i I COMMITTEE F AFAomAUtICs
. / .2 .3 .4 -
M-ach number, /.
Figure 26.-- Pressures on top of two spherical
turrets shoAwing effect of re/otive project t-ion
above Mhe fuselage. Both turrets located ao
24.9 perce-et fuselage length from nose. tt = 3".
NACA ACR No. L4E10
.2 .---------- --------------
Tu etr -NATIONAL ADVISORY
COMMITTEE Fu AErONAUTICS
.4 -o -- F, near top (frome unpublished data)
+ F, near back
-x ---- f a fop (reference 16) -
.6 -- 8. at sio.de |
S- ... -- at x/1 = 0.61 CONFIDENTIAL
0 .1 .2 .3 .4 .5 .6 .7 .8
Mach number, 14
Figure 27.- Comparison of pressures on two .sream/ine
furreft.s of different thfickness ratio .shovvrng
different compressibili ty effect-s.
NACA ACR No. L4E10
7- 3- 4
<- d j-b c
I CONFIDENTIAL j
I. .2. 3 .4 .5 .6 .7 .8
A4Qch number, A-I
Figure 28. Pressure change wvd/ Acach Imrnber
at points on -three windashields from reference /.
Point- locations and corresponding pressures are
indicate.f by the /lefters a b c anc cf.
UNIVERSITY OF FLORIDA
I, 'L Ii' UWLY