Experimental investigation of the effects of viscosity on the drag of bodies of revolution at a Mach number of 1.5


Material Information

Experimental investigation of the effects of viscosity on the drag of bodies of revolution at a Mach number of 1.5
Series Title:
Physical Description:
31 p., 28 leaves : ill. ; 28 cm.
Chapman, Dean R
Perkins, Edward W
Ames Research Center
United States -- National Advisory Committee for Aeronautics
Place of Publication:
Washington, D.C
Publication Date:


Subjects / Keywords:
Body of revolution   ( lcsh )
Drag (Aerodynamics)   ( lcsh )
Aerodynamics -- Research   ( lcsh )
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )


Summary: Tests were conducted to determine the effects of viscosity on the drag and base pressure characteristics of various bodies of revolution at a Mach number of 1.5. The models were tested both with smooth surfaces and with roughness added to evaluate the effects of Reynolds number for both laminar and turbulent boundary layers. The principal geometric variables investigated were after-body shape and length-diameter ratio. For most models, force tests and base pressure measurements were made over a range of Reynolds numbers, based on model length, from 0.6 million to 5.0 millions. Schlieren photographs were used to analyze the effects of viscosity on flow separation and shock-wave configuration near the base and to verify the condition of the boundary layer as deduced from force tests. The results are discussed and compared with theoretical calculations.
Includes bibliographic references (p. 30-31).
Statement of Responsibility:
by Dean R. Chapman and Edward W. Perkins.
General Note:
"Report date April 3, 1947.."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003810752
oclc - 135208262
sobekcm - AA00006237_00001
System ID:

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PE3ZEACE i.EM3,.j- 'UM




By Dean E. Chapman cnd Edword V. P:rkins

Tests were conducted to determine the -*:ffects of viscosity
on the drag and base pressure cheractorc'ietics of various b.dic- of
revolution at a Mach number of 1.5. The modola wore tested 'bDth
with smooth surfaces and with roughness ai:t.od to ovT.luete the
effe-cts of Roynnclds number fcr both lamin:'n: and turbulent b:'-und jry
laye,-rs. The principal geometric variables inves-tlg-atte were after-
body shape and length-dimincc:-r ratio. 'Fr most mind-1ls, f'-,'rcL tests
and base pressure rac-asur iments w.re. miad? over a range of poyrrl si
numbers, based on model length, frJm 0.C million to 5.0 millions.
Schlicron photographs wort used to analyze the effects of viscosity
cn flow separation and shock-wave cnf'iguraticn near the base and
to verify the condition of thi boundary layer as deduc:d from force
tcst3. ThIc results are:. discussed and compared with theor.tical

Tb.he -esults show th"t viscosity effects are large and deacnd
to a great d.groD on the body Lsh.c. Thie effects differ. gro-.tl for
laminaar and turbulr.nt flow in the boundary layer, and within e:ac
regime depend upon the Roynolds number of the flow. Lominar flow
was found uu to a Reynclds number of 6.5 millions and may possibly
exist to higher values.

The flow over th5 ofterbody and the shock-wE.vo configuration
near the base are shown to be very much diff:ront for la i:ncr than
for turbulent flow in the boundary layer. Th'- base pi-esure is much
higher with the turbulent layor than with the laminar layer, result-
ing in a negative base dr:.g in some cases. Tho total drag c'ibracter--
istics at a given Peynolds number are affected c,-nsiderably by the
transition to turbulent flow. The fore drag of bodies without boat
tailing or of boat-tailed bodies for which the effects of flow
separation are negligible can be calculoatd by adding the ckin-
friction drag based upon the ascumptiion of th,! low-speed friction
characteristics to the theoretical wave drag.


2 COFOTITTDEF-L 'AC,. R3: I;c. .7.'31

For laminar flow in th.: boundc.;-- 1-.c-"r t.:o :.'fr:ctz o' v-r'ink
the Reynolds number were fu,'nd to be la: _e, p:'._.x:'"matpl dc-:bllng
the base da-CE in man: cases and increasing the t. tal drg debut
20 percent over the Reynolds number renge inves-tl~sed _r''
turbulent flow in the b-'undary layer, the effects cf va.-.;.pn tlhe
Reynolds number usually changed the base drag and total drra coe.?C
clients ccnslderblyr.


The effects of viscosity on the aer-dyrnamic characterist-cs
of bodies moving at low subsonic speeds have been kn'-wwni fto man-
years and have been evaluated by numerous investing tcrs. T.
effects of viscosity at transonic speeds have be.r. Invest .,ated
only recently, and relatively large effects on t:,e fl:w ove-" -r-
foils are reported o;- Acho:ret (referer.2e 1) and Lpspann (-eftrence 2).
Alth:c.ugh the relative t-i,'oni'rhnesa of the-sz two inV,!E'tigatlons has
furnished a *'ood start toward a satisfactory evaluation and under-
strndilng of thE. effects of visc :osity in transonic flow fdld. -till
very little is known about the effects at purely supersonic spe-'ds.

The experiments reported in references 3, 4, and 5 have succs3eed
in evaluatilrn the mancntude of the skin friction for supersonic flows
in pipes and on curved surfaces. Reference 6 contains a small
amount of data on the effects of Reynolds number on the drag of a
sphere and a circular cylinder; however, these data are not appli-
cable to eerjd;.'nrmic shapes which are practical for supciscni? fr ght.

It has been gen.r-rally assumed that the effects of viscosity are
small rnd need be ccnidc'r-.d only when dtnrmninn-.- the magnitude; of
skin friction. In repviewing past data for the effects of visccsity
it was found that in many reports, such as references 7 and b, the
model size was not stated, th.orc-by rand-'.ing the calculation of
Ren-ilds number.- qu'te difficult.

Proelminar:r tests in the Ames 1- by 3-coot supTssojni0 wind
tunnel No. 1, which is a variabl-prorss-.Lre tunnel, showed a r.latlvcly
large effect of Roynolds number on the drag of bodiics of revolution.
Th-3 results of this cursory -nvostigation wore not ro,.o ;td' b~c.-aus-
the magnitude of suppo-rt int.-rforence was not known cnd because
certain inaccuracies in the balance measurements wore kncw-, to x.i:st
in the data tak.-n at low tunnel pr-'ss3ur':s. An invosti:,otic n of w.nj-
body interaction at supe rsonic sp,:ed. has been ccndj.ct.d subsquontly
and the results presented in r-foronco 9. Bc'e-use .if th,- supnrrt
interference and the boln:e inaccuracies nrtcd at low pros33ur'S.
the dr.ts pr,:esntcd ther.ein of t,.r .lffoct of RP.ynolds numibr on th;'
drag of smooth bodies are not sufficinr.tl:, accurate thr'u-iout
the r nGo of E;,T:nolds numbers for direct applicaton to tho conditions
cf froo flight.



Since the effects of viscosity already were known to be
relatively large at the :-utset of t*his investigation, the purpose
of the present research was made twofold. The primary puriji:se was
to develop an understanding of the mechanism by which viscosity
alters the theoretical inviscid flow over bodies of revolution at
supersonic speeds, and the secondary purpose to determine the magni-
tude of these effects for the particular bodies investicatc.d.


Vind Tunnel and Instrumentation

A general description of the wind tunnel and the principal
instrumentation used can be found in reference 9. Included therein
is a description of the schlieren apparatus, which forms an integral
part of the wind-tunnel cqulpment, and the strain-gage balance system
employed for measuring aerodynamic forces. In order to obtain
accurate data at low as well as high tunnel pressures, a more sensi-
tive dra- gage was used in the present investigation thbn in the
investigation of reference 9; however, all other details of th;
balance system cre the same. For the purposua of ti.e present
investigation, it is p.Jrtinont to add that the tunnel is equipped
with three turbulence-reducing scrosns located in the settling

The tunnel total pressure, the static reference pressure in
the test s-ctien, and the pressure in the air cher.bc.r of the balan.:ce
housing wore obsercvd on a mercury manometer. Because the differ-
once b. twoon the base pressure and the static rc-foronce pressure in
th.: tit suction is ordinarily too small (only 0.5 cm of mercury at
low tunnel pressures) to be accurately road from a. orcury.manomoter,
a supplementary manometer using a fluid of lower specific gravity :
was employed. Dibutyl phthalate, havn- a specific gravit;,- of
approximately 1.05 at rom temperatures, was used as an :ndicating
fluid in this manometer instead of the conventional light mcannmeter
fluids, such as water and alcohol, because of its lower vapcL: pres-
sure and its property of releasing little or no dissolved air when
exposed to very low pressures.

Models and Suppcrts

Photographs of the models, which were made of aluminum alloy,
are shown in fires 1 and 2, and their dimensions are given in
figure 3. Models 1, 2, and 3 were each formed of a 10-caliber ogive
nose followed by a short cylindrical section; they differ from one
another only in the amount of bcar tailing. The shape of the olve
was not varied in this investigation because the flow over it is not
affected appreciably by viscosity. Models 4, 5, and 6, which differ



4 CL'iJrF 'EI'TL'JL IL.C PM4 l.o, ..31*

from one another only in thickness ratio, were formed by: pr.abot-l-
arcs with the vortex at the position of maximum tihk.--s. F:
convenience, some of thi.- more important geometric prp..rt:i- t .f
models 1 t;r'.iurt. 6 are listed in the following table:

Nose Area- L :. Base-
Model Frontal half volume diameter area
area, anglo ratio Li- ratio
A(sq in) e(dog) A/(V)2/s L,/D A/A
1 1.227 18.2 0.302 7.0 1.00
2 1.227 18.2 .309 7.0 .5.8
3 1.227 18.2 .318 7.0 .348
4 .866 11 3 8.8 .191
5 1.758 15.9 .32 6.2 .186
6 3.426 21.8 .479 4.4 .187

In addition to the above-montionod models, several other bodies
were tested for certain specific purposes. Thus, models 7 and 8
woro made unusually 1-ng so that the skin friction would be a. :..
portion of the messi-ed drag, thereby enabling the condition of the
boundary layer to be deduced from force tests. Various substitute
c.gives, shown in figure 2(a), were made interchangeable with the
smooth ocZ-ve that is shown attached to the -ylindrical a'fte'brod;. c
model 8. Th3-,e- ogives were provided with different t;..Les and
amounts of roughness and could be tested either alone or with the
lcrnp cylindrical aftr.b:1dy attached. When the gives were tested
alone, a shroud of the same diameter as the ogive was used to
replace the cylindrical afterbody. MJ'del 9, a bfd.y.- with a conical
nose, and l.'del 10, a splere, were tested in order to compare the
results of the present investigation with existing theoretical
calculations and with-the results of other exper~e-'im:nt-:l investl;s-
tions. Il.:,dils 11, 12, 13, and 14 were constr.,-ctr,.e to determine the
effects of the length--diameter ratio for a fixed shape of aftei'bhdy.
In all cases when a smooth surface was desired, the models were
polished before testing to obtain a surface as free from scratches
and machining marks as possible.

The models were supported in two different -.*-". : by a rear
support and by a side support, as shown in f".:; v.: 4, 5, and 3. The
rear .;_..pc't used in the :i.jori'.- of the cases consists ci' a, s.n.
which .1i1,.':.t t? -. model and attaches to the balance beam. A thin
steel shroud encloses the sti.n :-rnd t,':-b.' li:.r't.tes the aero-
dynamic tare forces. Use ':2 the rear S'.; :,.' allows force it., base
ei.;: ,;:i',:. data, and schlieren pr : t ~:-ro,.1: to be taken simultaneously.
Th. side ?i;.ppoj-t which attaches to the lower side -.. the ..:ik.'1
consists ..f a 6-percent-Lh'c'-: airfoil of tra-: ~-e'i: s.-.r.:nts
and 70 .Tiw tt..-. onl.: a.t -the;l 1.:3adir and trailing .a-:i Thc



side support was used to dotormine the effects of the axial variation
in test-section static pressure on base pressure, and, in conjunc-
tion with a dummy r. ar support, to evaluate the effectss of support
int-rfcrerncs. Base pressure data and schlieren ph.,'t' ,'aphs can be
obtained when the side support is used.

Test Methods

The tests w-re conducted at zero anglo of attack in a flixd
nozzle designed to provide a uniform Mach number of approximately
1.5 in the tost section. For the positions occupied by the different
models, the frc.-stream Mach number actually varied from 1.49 to
1.51. This is somewhat lower than the Mach number of the tests
reported in reference 9, which were conducted farth,::r da:.matronc in
the test section.

Before ar d after each run precautions wore taken to test the
pressure lines for leak-s and the balance system for friction or
zero shift. Each run we.s mad. by starting the tunnel at a low
pressure, usually 3 pounds per square inch absolute, and taking
data at different levels of tunnel stagnation pressure up to a
maximum of 25 pounds per square inch absolute. Bccaus..- of the lag
in the manometer system, approximately 15 minutes at low pr:ssurcs
and 5 minutes at high pressures wore allowed for conditions to
come to -quilibrium. The over-all variation in Reynolds number
based on body length ranged from about 60,000 to 9.4 millions. The
specific humidity of the air usually was maintained below 0.0001
pound of water per pound of dry air, and in all cases was below

In general, coach body was tested with a polished surfa'c and
then later with roughness added to fix transition. As illustrated
in figure 2(a), several different methods of fixing transition on
a body in a supersonic stream wore tried. The usual carborundum
method employed in subsonic research was not used bcciiuse of the
danger of blowing carborundum p.rticl:s into the tunnel-drive
compressors. The method finally adopted was to cement a 1/8-inch-
wide band of particles of table salt around the body. This method
proved successful at all but the very low Roynolds numb-rs. On
models 1, 2, 3, and 12 roughness was located one-ighth inch down-
stream of the beginning of the cylindric'-l section. On models 4,
5, and 6 the roughness was placed 4.5 inches from the nose and on
model 8 one--ighth inch upstream of the beginning of th,:: 7ylindiical
aftorbody. Models 7, 9, 10, 11, 13, and 14 were tested in the smooth
condition only.


6 COFENTIl .CA ::0 .7.31


iedivtion of L.'ta

The force data. 5n-ludd. in this rccr:t '..-- b.c r-e.cd t-
the usual coefficient form through division by the p;:-d.:. -f the-
f-j-stream d,-ncr.ic pressure and the f-'cntal area o:f th! b U';.
If it is desired to refer lTh.se coefficients to (-IlvJ...) t;-
nocessary conversion factors can b: found. in the t-bl.- ofI t.;-
geometric p.-:p-rtieo of tLc- ilodjls includedd in th- s.rtin .n
models and supports In each case, conditions just ?h..'- .f t':.,
nose of a model are taken as the fruo-stroam condit-ins.

The measurements of the ur.essur;- on tho base of o,.. !.,;:. i
are ref -.i -. to freo stream static pressure and mai- ." :n- -n"l. aJ
t~rn':.h division by t..! free-stroam dynamic pi -s-.;-. T. t..
base pressure coefficient is calculated from the :-quawt n


Pg base pressure coL.ff Lcient

PB pressure ac't'n., on the base

P1 f..-- team static pressure

q1 fr..-'2-.st..-t :.vcl d -r.u c pressure

-The dynamic pressure is c--jcul:tAd from the isent)i', ... .
ships. A small cxp .r:m.i-ntally det.:i.L:nAd correcti:.n is .ppli.:i
for the loss in total pressur-, duo to condensation f- wat-.r va-:;r
in the nozzle. T!:, R.-.ynolds number is Lbszd upo- t-. b.d;.: ln'U..
and is calculated from the isontropic r:lat jns'.i,.: ,i'.,-
Sutililand's formula for tbo vri:t .n. vi'scosi-L' witi t:-
tomperaturo :f the air.

It is convenient to consider th... frc. due to tLeo bas:. pr3ss
as a s.. .r..rst,- .:ompn.nt of th-- t-tl i'g Acc:.rd:lnjl:', t- bLsa.
drac is r.f rr.A to th-. frontal are-, snd in c.-;'i-'.:..-nt f.oi is
"i von by

%C = PB (
i" B P 'A




CDIB base. dr--O cc:fficiient

A3 area of base

A fr:ntal c2ea *:f the body

The fore dral is defined as the sum of all .drag forces that
act on the b:,d,' surface forward of the base. Hence, t3.e fore _l-:i
coefficient is given by

F = CD CrB (3)

wh.i' Cp is the trtal drag ccefficient and 1 .F the fore drag
coeff'.cient. The c':ncept of fore drag coefficient is u'efl.il for
se-veral reasons. It is the fore dr-ag that is of direct importance
t- the practical designeir when the pressure acting on the base of
a bcdy is altered by jet of Eises from a power plant. Considerll.n
the fcre 'ira a.s an independent c-.monent of the total drag :-'?atl1
srmplifies the drha anl.ysis of a given bo;r,. Finally, the fore
draC, as will be exy^lineli later, is not affected appreciably by
interference cf ti:e :ear supports used in the investigation.

Since the nozzle calibration with no model present showed that
the ctatic pressure el-'ng the axis of the test section is not
cnrjstant (fig. 7), tl-.e measured coefficients have been corrected
fC thie in:renent of dr. or pressure resulting from the axial
-'essulre c-adient. -, detailed discussion of this cc:.rect'on is
presented in appendi-:- A and the experimental justification shown
in figu-res and .7


The table which follows list.3 the total uncertainty that
would be int-oduced into each coefficient in the majority cf the
results if all of the possible errors that are known to exist in
the measurement o' tle forces and p:-ssries and the determination
of free-stresam lich number and gradient corrections were to accumulate,
Actually the errors may be expected to be partially c mpensating, so
the probable in.ccui acy is about half tl.at given in the table, T::L
sources and estimated magnitudes of the pr-bable .?irr:rs3 invol'.-d are
considered at zre te" length in appendix B. T'.e values in the
following tabl- are for the lowest and highest t.r:nrl pri-?ru'es and
vary lineariy in between The table does not applyy to data that are
presented in figures 12(b), 16, 17 and for mcdeis 4, 5, and 6 in


NACA R, f?:_. !.".-31-

figures 2'(a) 2nd(a) aT) .Lr the- possible variation in tlh. ral,-nc:
callbret i:n constant -_,? increase the limits 2 cr: dils:.sd
in appnd'.: B.

Maximum value of im value value of
( efficientt error at lowest pressure c-:ro-T' t h!1'..,at *.r.;Zi-
Total d:-- (2.I- plus 0.004) + (I.r! plus 0.004)
Fore dr?.- (1..' plus O.COh) (0.' p1u 0. .)
3Baf .r ssur.: (0.-1 plus 0.005) (0.." plus 0.':5)
Base drag [0,.8 plus 0.005(;.-,/A)] [0.. pls (A/A)

EL'ects of Suppocrct Intorference

.'_-'.lous to the r.s'-nt investigation an extensive sjrios of
tests was c:'nd":t:J to determine Thc bL;' shapo and .?'.:p-'t combina--
tions necessary to eliminate or evaluate the support interferoncc,
BEs:d upon the results obtainrid, a summary of vwh:;:i- -.p..'rsE in
-pp.-ndix C, it is believed that all the droe d-ta., presented herein
for the models tested in the smooth condition is free from support
interference effects with the exception of the data shown in fil.ie
30. Fcr the models tested with r'ui.ness, the fore ira:. data are
free from interference effects, but an uncertainty in the base
pressure ccefficient exists which nsy vary from a mn'.nr.m of 0O.005
to a maximum of 00.015 for the different bodies. As a result, i2e
base drag coefficients and total dra.- .:e:ficients for the same
test conditions are subject to a c:rrespond.ing small uncert.qint.:.

Schlieren Ph to raphs

Since much of the basic information contained in this report
is obtained from schlieren pbct_-.r'ap:'s, a somewhat detailed explana-
tion of their int-rpretation is in order. A typ~:icl schlieren
photograph taken with the knife edge vertical is shown in figure 1C.
The various features of the flow are -deagneted in this photograph
which shows the entire field of view cf the sihlieren appciratus.
Other items, such as the natural -ralients inherent in the glass
and the horizontal and vertical reference wires amounted outside of
the tunnel are also apparent in this 9nd other phiotot.rr-phs presented
in the report. The horizontal streal:s that appear on some ct' ;he
schlieren photcraphs are a, result of oil in the tunnel cic--uit
due to temporarily faulty gaskltirn in one of the main drive
compressors. T;e mottled appearance of the background is believe'
to result frcr the varying density grRdients in the boundcry layer
flow on the glass windows.

The schlieren photographs were taken with the knife edge both
horizontal and vertical. Density grraiF:nts nDmrsl to the stream


NACA P.I No. A7A31a

direction are detected with the knife edge horizontal) whereas those
parallel t- the stream direction are detected with the -ni.'fe -J
vertical. F:.i the horizontal orientation the i:.ife edge was pl c-
so thet increasing density -rcdients in a d:_.rr1;-.i.L direction .: ;p;.r
as white- .:]?eas on the photoraphs. For the vertical orientation
the knife ed- was plcrred (except for the pi-tr-aph in fig. 10 and
the sph:-re p:i oL.c;raphs in fig. 20) so that incre-,lr-n' density
gradients in the downstream direction appear as -white areas.

Tho critical C -lciulations

Alth;ouih .t -present no theoretical method is available for
calculatin- t!-- jase pressure and hence the total drag of a h-b ,
sove:al neth cds are available which provide an excellent theoretical
stand-ard. t. w;ichi the experimental measurements of fore drag can be
compared. In this re:-port the theoretical fore ?rx5 is considered
to bc; t.,: sum of the theoretical wave drag for an inviscid flow and
tho .3skin-fricti.n drag corresponding to the t-p;t- of boundary layer
ti-:t exists r.n thl. body.

'-. tj.-icsl MIchi net and the corresponding pressure distribution
for t'hl th;:ret.c .1 inviscid flT-.r over one of the boat-tailed bodies
testo:d in this investigation is shown in figure 11. For 'ur;p:'.,. of
c ,mprisnr! the pre soi-e distribution as calculated by the liner
thei-r:- f :n Kaman and ..r. is included as is the pressure
coeffici nt a t t nc nose of a cone, the included ronl- of which is
equl t th: cr.'lc between the surface tangents at the nose of the
c.gv... This 1 tt,:.r is obtained by the meth;i of references 10 and 11.

Th- wayv.: io'og for m?.rny of the bc.diULs tested was calculated by
th.- mcthl-d of characteristics for rotationally symmetric supersonic
flow %s ,viv:;n in r:. foroncos 12 and 13. In accordance with the
the.ci ticm1 rosuiits of reference 14, the fluid rotation produc:-i by
the. very small curvature of the head shock wave was neglected. This
proc.dur: is justified expcr.imntally in reforonco 8, w tre the
thi-or.?tic.l calculation using th.; method of characteristics as
pr..sont;'d in r'.:'-renco 12 ore shown to be in excellent agreement
with thr. c m:csur--c pressure distributions forogivos with ',ln ndrical

Th-_ calculation of the skin-friction drag in any given case
requires a kno.wlcdg- of the condition of the boundary layer. In the
cases for which the sc:liciren photographs and the force tests indi
cated t!:-t thi entire boundary layer was lonhinr, the curve of
th. core.tical fcor-. drag used for comparison with the experimental
results was obtained by adding to the wave i-:.g a t"'.:-or.'tical
skin-fr-iction drag calculated by using the low-speed sir,-f-ictiorn
co.fficcnts fcr laminar boundary l;,-yr flow at the Roynolds number



10 COMrfDEITIJ. NAC.A :-_M i. A-.. 3L

based on the full length of the m-.del. Ti':n r -.':d'::'e, wic 1 in
accordance with reference 3, g ves the oqaation

S= ACfi,(rA) (/))


CDf sk:'n-fr''*tion dr'a co?2f:":'ient for the model at the
Reynolds niur'.Cr, r.e, based on the full length of
the model

Cfram low- z.ped skin-friction coefficient for laminar bo.nc.i.'-
layer flow at Re

AF wetted area of the macie1 forward. of the base

A frontal area of the model

F'.r the -dels with r'ug..nes. added it was assumed that t!e
disturbance of the boundary layer resulting from the salt lI-ndl was
sufficient to cause transition to a. turbulent bc'.nd-.cy 1-:.-r to
occur at the band. The theoretical skin--friction -::: was th'.r.
obtained by means of the equation

"Lf = C4lam ) + f Aturb ~ C turb (Alm


Cflam low-speed skin-friction coefficient for laminar bi.undr,-
l:ye- flow at the effective Reynolds numbr-,, Re', bDuse'.
on the length of the mnr-?l from the nose to the -:.ont
where the salt band was --isliod

Alam wetted area of thft portion of the 7r-~irli frvwi-^A .:I the
salt band

Cfturb low-speed skir--friction coefficient for turbulent b.dry-
layer flow at the P.ei.lida rn'- L:r 7., based on the full
lenr,gth. the :r.adel

Chturb lzw--spied skin-friction coefficient for turbulent 'c undari-
la'ye_ flow at th3 effective R.enmlds number:. F."


NACA PJ.l I'To. A7A31a

This meth-'d of calculation -rr-eurmez that the fT.:.i ro""':;;r-s: was
of such a nature as to cause the turbulent b:jund'ir, layer :;'lw
dcwnstream of the print where the roughness was addslle to be the
same as would have existed had the boundar..--layer flow hecr
turbulent all the way from the nose of the bod.d.

D:3CUS3 I;i

Flow Characteristics

Be-fore analyzing the effects of viscosity on the drag of the
bodies of revolution, it is convenient to consider qualitatively
the effects on the general characteristics of the observed -low.
In s- doing it is adv.-nta.eouz to consider first the condition cf
te t:unda sr layer characterized by whether it is laminar or tr--
blent and then the effect of variation in Reynolds number on flow
sep?-rat-:n for each typo 'f.- boundary l-yer-. Once the effects, on
flew ser aration, of the Reynolds number- and the condition of t'e
bcunda-s.: layer are known, the observed effects on the shock-wave
configuation at the base of the model are easily explained.
Likewise, once the effects on flow separation and sijock--w;ve
confi-iur-ticn are Inclri, the resulting effects of viscosity on
the fcr": drag, base da-rg, and total drag are easily understood.

Cr.dition of the boundary layer.- Since results !:.bs-vod at
transon-i c speed s F:'fo- rnces 1 and 2) have shown that tL.-: -n-'al
flow pattern about a, body depends to a marked degree on the t;-,.
of boundary layer present, it is possible that the boundary- 1c.:,-.
flow at supersonic speeds also may be of primary importance in
dt.-tJrmininj, the over-all aerodynamic characteristics of a. b:-.
Cocnse-quently, the determination of the extent of the laminar
boundary; layer under normal test conditions is of -fudanental

In an attcmot to determine the highest Ec-nn:lds n-maLnb: at which
lamina' flow exists on models tested in this investi ltiLn, a
relatively long polished body (model 7) was tested from a low
pressure up to the highest tunnel pressure obtainable. In this
case, the diameter of the sh:-ud which encloses the rear E.n.-'t
sting was made the same as the- diameter of the body. T'.- fore
drag n-asurcmcnnt on this model are shown in figure 12(a). Snc---
th: skin friction is a relatively large portion of the measured
for.: dr-ag, the condition of the boundary layer can be da:'.:!i fr-.
these force tests. Th1 data iniicntj that tC: boundary layor on
this body is still laminar up to the hi-h:-st obtainable _c:.-.:ld
number cf 6.5 millions. Thc computed fore dr-s data used for
ccmparison are obtain ;,d by adding a laminar or t.u:ri.l:nt skin-
frictin co'fficic-.t bas:d on low-speed characteristics to t':

!*'r',?F -1,E!'T !.L


experimental wave dr.- of the cgi-'-l nose. This letter is dotormincd
by subtract.ing frm the fore i-s a data :D SIn"lo 16 Cr.- Ic. s-s ..d
laminar s: in-f;r'ctin cc ffici:nts for the smooth c-iv. at t:.,
h.:.rj Reynolds numbers where the error, result'n :'fo tie .ss'zp-
tion of the low-speed cc;fficcint3, is a. smli percent of the
d:duic.d wave d;-''. Schlioren phot-gra;.hs frL'i.r which the condition
of the boundary layor maa," be obs.rv.:d arc i.o'.mn in figur-. 13. They
confirm the previous f'ndini by showing that transition does not
occur on the body, but begins a short distance doKnstr-cn 'r-':
the base of the model, as indicated by arrow 1 in tl.: p:.-t -ral:..

A close examination of the iph, .toGr'aph in fir:roe 13 reveals
that the 1-oJinn ng of transition (arrow 1) is located at tc., same
point on the supiiF'rt c':rcud. as the waves (arrows 2 and 3) which
originate from a disturbance of the boundary layer. It was found
by measuremonts on the schl:lron phVtog:c'p:1s that the point of
or'.in of those waves on the shroud and the intersection with the
shroud of the bow wave, which has been reflected by the test -- t. on
side walls, coincide. This su.z;- ts tbht transition on the s1 :-.'1.
is being brought about p:-~aotu.rcly by the a, ficct... b':r waves. ,.l-
tional evidence that.thi.: is not natural t-3an'ition is obtained in
notin- from figure 13 Lthat the point where transition bZI-'.ns d.
not move with a. change in .I:. .l, nbr. l t modol were i:-nr
than a critical length, whic:i is about 11 inches for the conditions
of the pi'.s:-nt tests, tU sa. reflected waves would strike the m:71,d
somewhere on the aft.-;bod;' and premature transition would i- ::xrctod
to affect the results. F"i urc. 12(b) shows the results of tho
measurements of fore drag on a, 16.7-inch b:.7,d (model 8), is!ich is
considerably longer t:hn the critical length. I.. force dc t
confirm the above conjocturo by clearly indlcotIn a partially
turbulent boundary I;'- on the body oven at Roynolds numbers as
low as 2 millions. The schlieron photz-:.--?hi of the flow over this
body are presented in figure 14. It is soon thEt, in this case also,
the transition to turbulent flow (arrow 1) is ic2t.,d 't th] some
point as th- waves (arrows 2 .nd 3) originating t':-m the di'turb':*c:
of the bound~irjy 1 ;.. by the r:'floctod bow wave. Similarly, an
additional small wave (arrow 4) can be traced b-inc': to a d:stu-'bnc.
of the boundary Ic, causedby a sh.ck wave originating from a
vory slightly imp.:-rfoct fit of the sla-ss windows in the sid..' w.ll- .

Alth'-ugh the main:e'it possible extent of laminar flow that m2;
be -:ajct.i on bodis of revolution cannot be d, t r.-in.d on the
basis of the present tests because of this Jint-rf.rk.n:- from the
reflected shock waves, the f-'r-ie~rng results show thl.. t, nd.r the
conditions cf those tests, a -mi'n3or bo-undor; l';r ;rists over th.
entire surface of a smooth model about 11 inches l1n3 up to at l .-st
6.5 millions REynolds ntur,.b.r.

In cnrmprison to th.: values n:.inr.llrj enrr''ut..l.i 4it subsoDnic
speeds, a R::.nlds number of 6.5 m31iiimne at fl-jt '.-),crs tc b,:

NACA: 71.[ T.11 .ATA31A

c('o -T'...1-.T=I'L

NACA RM No. A7A31a

somcwhst hiCih for maintenance of lamino:r flow over a b;od.r, unless
favorable pressure gradients exist over tho entire length of that
body. The pressure distribution over madel 7, shown in flj'-r: 15,
has been dotormined by superimposing the pressure distribution which
exists along the :xis of the nozzle with no model pros':nt upon the
thc: -cLical prossuro distribution calculated for model 7 by the
mia:-tod of characteristics. The resulting pressure distribution shows
that the pressure gradient is favorable over the ogivo, but is
actually adverse over the cylindrical aftorbody. This suggests
that the stability of the laminar boundary layer at a Mach number of
1.5 may b: considerably greater than at low Mach numbers.

An increase in the stability of the laminar boundary layer with
an increase in Mach number has been indicated previously by the
theoretical work of references 15 and 16, and is confirmed experi-
mentally for subsonic flows by the results of references 6 and 17
as well as by the experimental data given for airfoils in reference
15. Some of the experimental research carried out in Germany are
in disagreement with these results. In fact, part IV of reference
1l reports that the schlieren observations made in the supersonic
wind tunnels at Kochel indicated that the Reynolds number of transi-
tion to turbulent flow on cones was even less than the value for
an incompressible flow with no pressure gradient. On the basis of
the description of the Kochel wind tunnels given in part I of
reference 18, it appears that because of several factors the condi-
tions of flow therein are somewhat adverse to the formation of
laminar boundary layers as extensive as those that would exist in
free flight. One of the more important of these factors is
believed to be the large number of shock waves which originate
from imperfections in the nozzle walls and disturb the boundary
layer over the body. These shock waves ordinarily number about 15
and are readily visible in various schlieren photographs. (See
reference 21, for example.)

In order to cause the laminar boundary layer to become tur-
bulent in this investigation, an artifice such as adding rou2hness
was necessary. In a supersonic stream, however, the addition of
roughness to a body also will increase the wave drag of that body.
The magnitude of the wave drag due to roughness was determined by
testing with full diameter shrouding and no afterbody attached,
first the smooth ogive, and then the ogives with various amounts
and kinds of roughness added (fig, 2(a)).

The corresponding fore drag measurements are shown in figure 16.
These data illustrate that little additional drag is attributable to
roughness at the low Reynolds numbers where the boundary layer is
relatively thick, but that an appreciable amount of wave drag is
attributable to it at the higher Peynolds numbers. For all subsequent
results presented, the amount of drag caused by the artificial
roughness is subtracted from the measured iata taken for the bodies



14 C OnF IT'MITT L NACA ?7 :l. A .:-

tested with transition fixed. In .-":r- to calculate the amount of
drag caused by the roi hr.n s for "mod.-ls of diasaeters different ...:
the ogives tested, it was assumed that for any model tLe :r.._"?-e-.t
in d.r7- coefficient attributable to -th,- di.L of thy .-t.ificial
ro'u-.-ness was inv;rsl,.. prcpc:_tional to tho diameter cf the .-:
at the station at which the r.t,-iness was aeplied.

The fore drag measurements of model 8, which: consists of a
cylindrical afterbcdiy with an.: one of the interchanreable c l-ec
directly attacLed, are presented in figure 17. TreZe deta~, D-..I
which the dros, increment due to the adied rc'igriess has ;enr sub-
tracted as noted previously, show that the '.-rees of r:v;l.r?.
prod'iced by sand -jlating the surface of the C. ive is ins.,Iff :"ent
to cause transition at low ?eynolds numbers; whereas, the ri .: ss
produced by the 3/16-inch- or the 3/i-ir.nh--wide' salt band caused
transition at all .e:.'nlds numbers.

A vivid illust!.-rtion of the turbulent character of the boundary
layer on those bodies with :r-u.hness addedd is given by the schlieren
phct;'i,'ra;'5s in fl'::v-e 1. The b' .ndary layer is best seen in the
phc.to-.-.'. taken with the knife edge horizontal. A -:-.jp-'son of
these pio.- L: '' z witi. those of laminar boundary :l.;e-s (fi'. -.*,
for example) illustr-tes how the condition of the b 'Lundr'r layer is
ppuarent f'-:re schlieren ph.t~gr'ahs.

The results at t-snzonic speeds r-'eported in references 1 and 2
have s:'.; wrn that the same :chnges in prezs'ire distribution arnd 'hoc'-
wave configuration 'r:u b:t about by transition i to inherent
bcundary-layer instability at biTh Reynolds numbers can also be
br'.-u.lt about at those speeds by any cf several means. T !.- artifices
..sed in references 1 and 2 included fine-grain ruli.nes., f -
stream turbulence, and a" single large dist.u-bance; the result:n:
aerodynamic effects were the same, provided in each case the the ..'.r:7
layer was ch~i.ned from laminar to turb'l.-.nt. ,cne.,ently, no
matter what causes the bound-ry layer to become turbulent in "':.
flight, it seems l'k:-ly thot, excl'..dinc poz-;:.ble snall d ?fff rera.
in s:irn f-.-ict crn, the resulting ef-ects on the c.:..r.c.l.c 0'..'sc~tr-
istics of th- bo.dy will be very r.narly the same as if the b.'..cr"
layerwore mrde turbulent by rcughness alone, as is the case in t!e
experiments -~-nducted in this investigation.

Flow -eSnration.- Changes in flow separation brought ab:,ut by
chan:inr, tle b:,ndq-r- layer flow fr:,r laminar to tur-bulent alter
the effective shape of the bc.dy, the shock-wave configurati'-n, and
also the dra.'. It is therefore essential to consider the effects
on flow separation of b-th the '--nd.ttion of the bo'undary: la'.-. and
the Reynolds number.

Tie location and degree of separation cf the la.a'nr-: boundary
layer for the b-'at tailed bodies tested in the sm:.;th rc-ndition


T:AC;. F.I.1 P .- .AL31a

varied n-ti.esbly w'.th the Beynolds numbe- of f'1 w. ITh schlieren
photo'gaphs -f Model 6 in figure 19 are typical o this e.'ect.
Additional p!:Ltojr';ph-, presented in figure 20, illustrate the
same open.omena in the flow over models 2, 3, and 10, each at two
different .e.ynclds numbers. In each case, as the Eeynl'ds number
of the flow is increased, the separation de:-reses, the convergence
rf the wa-ke increases, and the trailing shock wave moves forw rd.

3epraration of an apparently laminar boundary layer has been
pointed out previously by Ferri in reference 19 for the two-
dimensional suner3onic flow over the surface cf curved a-ifoiizl
Tha schlieren photcgrap'hs therein indicate that a shock wave forms
at the point of laminar separation. On the other h:nd, the schlieren
pictures of the flow fields for the bodies -f revolution tested in
the present investigation, show no definite shock wave a':o,,- n:-inr
separation except for the sphere (fig. 20) in which case the shock
wave is very weak indeed. It may be concluded, te- before, that a
separation of the laminar boundary layer is not necessarily
accompanied by a shock wave at supersonic speels. The same con
clusion for transonic flows has been drawn in reference 2.

It might be surmised that the trailing shock wave situated some
distance downstream of the separation point is interacting with or,
perhaps, even causing the flow separation by virtue of pressure
disturbances propagated upstream thrzo.',h the subsonic portion of
the wake and boundary layer. Some indication that this is not the
case is given by the schlieren photographs in figures 19 and 20. It
can be seen from these photograp.'hs that the trailing shock wave
moves upstream and the point of separation moves downstream as the
Re:ynlds number is inc-eased. It would logically be expected th'r
this decrease in the distance between the shock wave and the se'paira-
tion point would intensify any pcss'ble interaction between these two
elements. The photographs show, however, that the degree :.f separa-
tion actually decreases as the trailing shock wave moves u,,t'aesm.
This suggests that the trailing shock wave does not have much
influence *:n the laminar separation. Additional evidence which
corroborates this conjecture was noted in the course of t-h investiga-
tion of support interference, wherein it was found that if the
diameter of the support behind models 2 and 3 was increased, the
trailing s.ck wave moved forward, but the base pressure and laminar
separation did not change. On this basis it appears likely that the
cause of the laminar separaticn is not associated with a shock wave,
but with othar.- phenomena.

In order to analyze more closely the details of the flow
sC-par'ation, the pressure distribution along the streamline just
outside of the sp:nra2ted b'urndary levye- was calculated for several
flow conditions over models 3 and 6. The calculations were made
using the method of characteristics, and obtaining the cornt;.'r-
of the streamline just outside the separated boundary layer 1rcom
enlargements of the schlieren ph:-t=graphs. Typical results frc-i




these calculations for model 3 are presented ir. : ;ure 21 It i7
seen that the pressure on the outside of thl b,;.ndar;: layer i
approximately constant, dcwnst:-am of the ;::int o 'e 'JraLir:'n, s3
is ~ -.ara-Ateristic Elcn.g- the bo:.undc--y of a ead -w:te-- re in. The
pressure along the line of seoparat'on can be :. ted to be z.-. x--
mately equal to that in th! dead irter -egiro, end ien:c, eq'. l to
the base pressure. A cmr.:-.rison of the calculated values of the
average ra -.-u.'e in the de-?e-water -re.i:n with the ma.9-':r-d values
of the base pressure for several cr.nd-itions :f flow over models 3
and 6 is given in the fcll.wing table:

Calculated e s're
\. e--:: :i. coeffi- L--..-
cient of dead. r. -:''e
Model Fe-.:,n :.is number water ". :,ion coeffi -ie'.t

3 0.6 x 106 -0.06 -0.:
3 2.0 x 1I -.11 -.12
6 .6 x 10 -.10 -.11
6 1.5 x 10a -13 -.13

The pr'eceding results indicate that for lamlnar flow the base pressure,
at least for boatt--t"-'ld bodies, is det:rm'n:d 3bj t:.. degree of
separa-t: n which occurs forward of the base. This rlug:,:s that,
if a means can be found, to control the separation, the base prj';su:.-
also can be controlled.

The theoretical pressure distributions on models 4 and 5 are
similar to the r..: .sre distribution on model 6, whTi'h is s-:. :fn in
figure ?'. In each case, the leminar s.p'.rti-on bL.eiv.:-d in tih:
schlloren ph, to r,-oA-,t is located at a point ;uptr.::'i .:.f which the
pressure decreases -*::ntlnu'-_lly .alcng the di:'r:ction of fl':w. For
subsonic flow this condition ordclnrily wui.lld be ten;ued favorble.
and s.:.' ction would not be expected. It thus cap.i'irs that thli
separation ohenr.inml observed are of a diffcr-.nit nature f'rc- tih.;sc.
which commonly result from a retardation of the flu.'.d partl't.s in
the- b.:undiar;' layer. Fiurthr? research on this subj-ct is n.oase.3ry
in rord-,er to gain a satisfactory understanding of the observed results.

The :find'.n; of p:'. ious investigations in l.w ope>d flows
indicate that if a b-,undajry layer wh'.ch is normally lkni2n'na over
the aftcrb.ody is made turbulent by either natural or artificial
means, the resistance to separation is '.n.-rcased ,r~atl:. Thr.- t.-sts
on models 2, 3, 4, 5, and 6 with roughness addjd sho-w clc-1-l. tiat
this is also the case in supo.-.s.nic flows The two schlior -n
photographs presented in figure 23 were t-akcn of mid.l t with and
without r~,ughnl.ss added and aro typic)ol of this ff--'-. A -oap:r-
son of the two phhotogr-phs shows that, without rou'3nus: ad-',
s'-parqt ti.n occurs near the p-int of maxim:.sL thLckn.ss, but if
transition is fix'ed ahead of this point su.-' spcrat.i n n: l rngcr


:;A,?. 1 FfM ro. ATl.:.7?: _,I __TLqL 1T

S.-T.:-.i. -'n 'ra tio It is to be ::::.:-ted that the changes
in fl w soperation duo to ch-ngcs in the condition of the o-;-.nd'y
1;-.: an;nd in the Roynolds number of the flow will brinr.- *' -..t c'::..nj:-s
in t:.; slhc-uwave c:r-nf.u'ation at the base .' a bd. IT'. schlieron
e"-:t-.:^ rj:.s of fi:.ur.s 19 ornd 20, which show how the laminar >.;..:_a-
t"'.n i:'-oases and the cinv.~r':nc'. of the wake increases as the
R-;.-r:lds number is inrr. si-, also show that those phi.n-.rr-n ere
Sc:L.::.nlod by a forward motion of the trailing shock wave. In
:. n.-j-, as long as the boundary layer is laminar, the trrell!n,:
.-::.k ,-:vo moves forward as the Reynolds number increases, ;. Lo no
inoj:; ch:r.:-, in the shock-wave confij':-r1ti.nr takes place.

i.: shock-wave c:nfig:i.u-tion with a. turbulent boundary leyor,
!h ::w..:.r, is very much different from the ccrnfiguration with a
1:m.'.r,"r layer, as is illustrated by the schlioron phot -.-.phs of
.-1 shown in figure 23. Such cc'-f rationin -':.; du2 to
tP.: t-2nsition to turbulent boundary-layer flow correlate quite
':11 with t'E. angleo that the t:rncjnt to the a. 'K'ace just ;:h.:-.
:f tl.e base makes with the axis of synmetry. Figure 24 3bi.'.,s the
F:'.Enr:.; in shock-wave configuration for models 1 through 6 r--:j- e..
-ir: _'de of inr-,ras:lng angle P. It is seen that, on the boat-
tllecd bodies with a small ?nJle 0, the transition to a turbulent
b :..uar;n-: -.e:- is accompanied by the appearance of a weak shock
w:-. or:'i t-ng at the base of the body (r. d,_ei 4 and 2). For
bodies with larger boat -tail angles (model 5) the strength of this
wsve, hereafter termed the "base shock wave," increases until it is
approxL-:iatly as strong as the c.r..inal trailing shock wave. For
ev-in la-:-er boat--tail anglles, the base shock wave becomes more
d.ist'n.t, and eventually is the only appreciable shock wave exist-
in' news" the base of the body (models 3 and 6). In such a. case,
t:.e .nrpressi :n through the base shock wave occurs forward of the
base. This, as will be shown later, greatly increases the base
pressir'-e and decreases the base d-rag-. Sin're the change in shock-
w:ve configuration caused by the addition of roughness is due to
t -.e -reater resistance to flow separation of the turbullent boundary
l-y'er, ;i may be ee-e::ted that the above shock-wave configurations
f.'-r L.'ie tur'bul-ent boundary layer will be obtained regardless of the
cause "' transition.

comparedd to the phenomena observe.d with'a laminar boundary layer
(fi:. 1?), changes in the Reynolds number for a bod; with a turbulent
b,.undry;. layer do not alter the shock wave configuration to any
3si_-niflcant extent, because tiL turbulent la;.:-, even at low
Reayn: ls numbers, ordinarily does not soparote. This fact is evident
in figure 25, '.hl".ch shows the schlieren phot...Jmrahs of model 3 at
different Reynolds numbers with rc'u:Tlner, added. No sapo:rznt change
in the flow characteristics takes place as the Reynolds number is
in-r'r-asid. With a turbulent t-ound-ry layer, thhrefore, the effect
on base drag of varying the Reynolds number may be expected to be
much less than with a laminar layer.


b10 C ;.-' .i l- :.L !..... RIM No. A7A1'.a

Analysis of the Dr,-s- -,ts

The qualitative effects of viscosity on flow separation and on
shock-wave confi-'-.ro tin, which have been :.:.u3ssd in the prsedLng,
sect:ins, provide the pL;.:3lsl basis for understanding the off e*ts
.. v:;.:.' n. the Reynolds nu:ib-. and :1h!ancing the condition of the
boundary layer on the cdAr' f coefficients of the vrrious bodies tesLtd.

Fore drag.- The fore d*-as; coefficients of mod3is 1 thri' :u 6
with laminar flow in the boundary layer are shown in figure 2C(a)
as a, f.un"-tion of the Reynolds number. These data. show that, over
the Reyrn-.ld, number range covered in t er tests, thr fore drag of
model 1 decreases about 2C' -': .ent, while tl.j t of model 6 increases
about 15 percent. The fore drag of the othe- bodies does not change
ap-' iably.

The reason the effects of Reynolds number vary considerably
with different body olapes is clearly illustrated by a comparison
of the measured fore drags with the theoretical fore drags. In
figure 27(a) the theoretical and measured values of fore drag are
compared for model 1, which has no beat tailing, snd for model 3,
which is typical of the boat-tailed models. From this c:,.r~.rison,
it is seen that, as previously noted for other m -.22ls without boat
toilln:-, the ti,:o;etical and experimental fore drago: for model 1 are
in good c-reecment. The decrease in fore drt with increasing Reynolds
number for the bodies without boat tailing is duo entirely to the
decrease in skin-friction cc.,~7ficient. For model 3, which has
conrl.d.:rable boat tailing, the curves of figure 27(a) show that the
theoretical and experimental fore drags agree only at 1-igh -r:ynolds
numbers. At the low Reynolds numb-ers the measured fore drags are
lower than the. theoretical values because of the separation of the
laminar bounder y layer as previousl-r illustrated by tio schlieren
pLh-tcgrsphs in figures 19 and 20. With Esp i-rtion, the flow over the
boat tail does not follow the contour of the boi;d, and the pressure
in the acc .mpqrnyiT.ri dead-water roji:n is lihc-r than it would be if
the sL-o ratl:n did not occur (fig. 21). This makrcs the actual
fore drag lower than the theoretical value for a flow without separa-
tion. At tli. hi-r RE:;Tnlds numbers, th- separation is rn"-lillble
and t.j flow closely follows the contour of the tLcdd; hence, t:-
theoretical and exp:q:i:.cnt-al fore dras-.i agree. The rJason f:,r the
1::-'"-'ri m.t.l: constant for.- iragz of models 2, 3, 4, and 5, th:.r., ore,
is that the chan7..s duo to skin friction and flow scparat-on are
compensating. For m;dul 6 with a smooth suirfco, the fore dra&
shown in f..uri'- 26(a) rises rather rap:dl;r at low Reynolds numbers
because the separation effects for this relat:.vjly thick body
(:.'i. 19) more th'.n comp-mna-tc for tbh ch-angf, in skin friction due
to th. variation of the .-;,ynolds ni.nbe:..

Figuro 2(b), which shows thj f.-.rc dragf coeff cients :.f model 1
t;.-u.'.ch 6 with r'uhns..s :'dd.-d, indic-2tus th.-t tlhe for drsa for all
the bod.Ls docroases as the Pc.yn Ide numnb.r incroass ab;ve a


NACA F.I T:o. AT7-.31l

Roynolds number of 1.75 millions. This is to be exp:ctod, since with
the change to turbulent boundary layer and c:ns-quicnt climnnation -f
sparatio-n, the only factor roncininC to influence the fore drc i
c'.cff'.'ic-nts is th- decrease of skin-frlction coefficients with
incro:ss in Roynolds number. Below a Reynolds number of 1.75 millions,
however, thu fore; drag of all the mod.-ls cxc'pt model 1 increases
with increasing Roynolds number. The cause of this sl:-w'i:.t puzzling
bchl!vi :r is apparent upon closer examination of the data.

Fi.-u-e 27(b) shows a comparison of the theoretical fcore draogs
with the experimental values for models 1 and 3 with roughness
added. The theoretical value for skin-friction drag was calculated
assuming. laminar flow up to the location of the roughness, and
turbulent flow behind it. This value of drag was added to the
theoreti-al wave drag to obtain the theoretical fore .;.ag. It is
seen from f'.gure 27(b) that for Lodel 1 the curves of theoretical
and experimental fore dra_ have the previously indicated trend of
decreasing drag with increasing Reynolds nuimbor over the entire range.
.-nwever, for model 3, which is typical of the boat-tailed bodies,
the measured fore drag at low Reynolds numbers falls considerably
belcw the theoretical value in the manner previously noted. The
reason for this is evident from an examination of the schlieren
phcto7g-aphs shown in figure 28, which were taken of the flow over
models 3 and 6 with roughness added. They show that at the low
R:e.,nold- numbers a flow separation similar to that observed for an
undisturbed laminar boundary layer (fig. 19) is evident, and the
resulting shock-wave configuration is characteristic cf the config-
uration for a laminar boundary layer rather than that for a turbu-
lent boundary layer. It appears that, at the low Reynolds numbers,
the amount of roughness added does not cause transition far enough
upstream of the point for laminar separation so that the free
stream can p-zvv.ide the bcundary layer with the necessary additional
momentum to prevent separc tion. Ih portions of the Ira;, curves
in which the desired transition was not realized are shown dotted
over the region in which sepa~rtion was app-arent from the schlieren
pictures. For model 1, the schlieren phcto rai.phs shi:wed that at
the low Reynolds numbers the amount of roughness added was suffi-
cient to effect transition some distance ahead of the base, although
not immediately aft of the roughness.

The agreement between the experimental and the th-or-tical
results obtained by the use of equations (4) and (5) indicates that,
aL a Mach number of 1.5 and in the range of Rernolds numbers
covered by this investigation, the familiar low-speed skin-friction
coefficients can be used to estimate drag due to skin friction at
supersonic speeds. This confirms the results of references 3, 4,
and ) and extends their application to the evaluaticn of skin-friction
drag for supersonic flow on bodies of revolution.



20 C,.:T_ L:;TIAL NACA 7 i No. A7.J31a

A comnnrison of the curves of figures ."(a) and '6(b) shows
that for a given body at a givenn value of the Ielno!lds number the.
fore drag with r. uihne.:s added is consistently higher than tL-.
corres-' 4.d1in,-; fore drag of the -:: tl, s..-'.faced body. In the
general case, this over-all increase in fore drag is ett'ib .table
both to the increase in the skin-friction drag of the body and to
the elimination of -E,,:ration with consequent increase in the
pressure drag of the boat tail. F:r model 1, which has no boat
t:illn.-, the increase in skin friction is the sole factor contribut-
ing to the increase in fore drag.

I,- r.rs u-e and bose drac.- Figure 29(a) shows the bc.Se
pressure coefficients plotted as a function of the e-'rnclds n'.:.ibe
for models 1 through 6, each with a. smooth surface. It is evident
from the data in this figure that the effects of ?e;,nrlds number on
base pressure for a body with a laminar boundary layer are quite large.
In the :.rn:e of Reyrn:li' nr.uabern cov-.-c.i, the base pressure coeffi-
cient of model 1 increases about 60 percent, and the ,:'.,efficPjents of
models 2, 3, and 4 more than dc.;.bl_. The t"!.':..r bodies, models 5
and 6, do not exhibit such l~,.-:. chlan.-c in base 'ejsurs clocfficient,
for the coefficients apparently reach a maximum at a relatively low
F.-:ynolds numblir, and then decrease with further increase in the
- ;..rnA.: number.

The base pressure coefficients for models 1 thro.i.h 6 with
roughness added are shown in figure 29(b). Here a.-in, the- portions
of the curves which e1 respo.n. to the low er--n-li number rein
wherein t:ra'nsiion did not occur far enough upstream to prevent
separation are shown as dotted lines. Model 1 exhibits the lowest
b-se pressure and model 6 the ;ehest; in this latter case the base
pressure is even higher than the free-stream static pressure. The
physical reason for t":.s is evident from the schlieren pihot-.-raph
at the bottom of f:i:..e 23, which shows that a compression throughh
the sh .ck wave occurs just ahead of the boase of model 6. Except
for the large c''en.es in pressure coefficient at low e;e'ncllis
nri:i-,eri's where the desired transition was not effc.'tei, the variation
of base pressure coefficient with Reynolds number is relnt'iv3.-r
small for the bodies with ro..ghnes3s added.

From a comparison of the curves for the brdiles with ro.ugh.n-ss
3.i.ed .to the corrs;'r-.n'n -i curves for the smooth-surfaced bodies,
it is evident that a, l:rle cha-n3e in the base pressure zcefficient
is attributable to the cihnge in the condition of the boundary
layer. In rnerml, the base pressures :for 1:dles with rougl-ness
aided are ccnsiirabl/y :1 l-er than the correspndn base pr-esses
for the smooth-surfec,-:d bodies. In the case tf ,he-boat-tailed
-bodies the rhsl-l reason for this increase in the base pres-ure
is the ap..sr-nc, of t:.o base shock wave, as shown in figure 24.
Fc,: mod-rl 1, which has no boat tailing, the .lx-.inj a'--ti:n and
.'re-tor thickness of the turbulent boundary layer are probably

'~~'_T~~lrZ :TL'JI

.-'.CA .=. ::c A7..1l C 'Z mTAL 21

responsibiD for the ..b.erved increase.

The foregoin, data show that th;e effec t- .f : *n'l~3 number srnd
crnilt.liln of the l. unda-'r layer on the base pressure of a 1: ?' movirn-'
it 5.ies-, Dni speels daee-.r consid.ei',rbly.u pc.n the Z n,.- of the afte -
b'.d,. ITn crdr to ascertain whether the effects of viscosity also
dLpe-nd uwpn the len.-th-di..neter ratio for a fixed sl.. ie of after: b:id
s:me m-,io 13 of different length diameter ratios were tested and the
dcts ipr3: t.ed in figures 30(a) and 3.'(b) which show the variation
nf b':3 pressure coefficient with aeynolds number. iie data present.id
in this figure are not free of support interference. From these
data it is apparent that the effects of viscosity on the base pressure
incr-ase with the longth-diameter ratio of the cdy;'. It is to be noted
thnt thj b ?- pressure in crcsc as the lonjt'. diameter ratio
irc-aesz7. This is somewhat at variance with the results of
:''ference 2C (also rcpcrted in reference 18), which showed an effect,
bot not a systematic one, of lenitth-diameter ratio on the base
prszuru of br.dies without boat tailln,g.

The base drag oc.efficient can be obtained fr-r. the base pressure
coifficicnt of the models by using. equation (2). T:,: base drag
co-efi'cients for the smooth --surfaced bod--s are presented in figurec-.
31(a) and fc- the bodies with roughness added in figure 31(b). l.
,curves are, of course, similar to the c:i':esp.nd'nn curves of base
pressure coefficient given in fi u:-'cs 29(a) and 29(b). In this
form the ordinates can be added directly to the fore drag coeffi-
cients of figure 26 to obtain the total drag c.-;fficient of a given
bod;. It is seen that the contribution of the base pressure to the
tc-tal drag is very small for models with large amounts of boat
tailing, such as model 3, 4, 5, and 6.

Total dras.-- The total d-.7 c'oefficients for models 1 through 6
with smo:th surfaces are shown in f.'.V--e 32(a) as a function of
Pe.-lis nutbecr. These data show that the drag .:.coff-cients of
both models 1 and 2 with a laminar boundary layer increase a little
over 2C pe_-cc-t from the lowest to the high-,st value of Reynolds
numib.-r obtained in the tests. The other models exhibit sc:~ii,;
suall-er changc.s. The data presented in figures 26 and 31 indicate
th-t the prin.lipal effect controlling the variation of total drag
with Reyl.-nlds nur.ber for laminar flow in the b -urndary- layer is the
effect of Reynolds number on the base drag of the bodies. For the
speccil cas of highly boat-tailed bodies, however, this effect is
of little, relative inportanc.:, because the base drag is a small part
of the t-tal draq. In such cases, the over-all variation of drag
cocfficiL-nt is due almost entirely to the variation of fore dr.rg
with _Rc\nolds number.

Fig.uru 32(b) shows the total dra, coefficients plotted as a.
furction of the ?e;ynml.s number for models 1 t-rouh- 6 with rough-
noss add:-d. Again, the portions of thu curves that are shown dotted


NACA PM No. AT.31l

represent the Reynolds number region in which the amount of :-ouglness
added is insufficient to cause transition far enough lupstre-im so that
s_--a'a--tion is prevented. All the curves have appr'x::-latelJr the same
trand, t', over-all effect on the drag :-fficiaetsbeln, about 15
.:-,. -nt or less for the various bodies.

A -:-mprilson of the curves of total drag for bodies with rough-
ness added to the corresponding curves for bodies with smooth surfaces
shows an interesting phh-n'uenn.. At the higher Reynolds numbers the
drag of models 1 and 6 is actually dec-e.az-d slightly by the addition
of roughness, in spite of the cc,:res,. morning increase in skin-fri -t.:n
drag. 7The reason is, of course, that the base drags are very much
lower for the turbulent boundary layer than for the laminar. The
drag c: -ffLcients of the other bodies (models 2, 3, 4, and 5) are
somewhat :lT:;:*r with r-'j:ghr:ss added, because the increase in friction
drag of the ti.u-bilnt boundary layer is greater than the decrease in
base dreg.

I'. importance of always considering both the .-In:.1J:,1 number of
the flow and c -nd'.tion of the boundary layer is illustrated by the
total drag characteristics of model 2. For example, if model 2 were
tested with a turbulent boundary layer at a ::-ynolds number of 2
millions, the d':.. would be about 35 percent higher than if tested.
with a laminar b'.'unry layer at a, E -.:T:l4 number of one-half
million. Alt::.:.h discrepancies as large as these have not been
reported as yet in the drag data from different supersonic wind
tunnels, certain consistent differences, v.Lr;-:n f':m about 5 to 25
percent, have been reported (reference 21) in the drag data of
similar projectiles tested in the Gottingen and the Kochol tunnels.
AlthcuL'.- in r forence 21 the disci_:p-.n.:Les between t:.. two tunnels
wore attributed Tr.l-r to the variation in :l::n friction with Reynolds
number, it appears from the results of the present investigation
that such disci ~:.ncies are attributable ixpi:.:.rily to differences
in flow separation and base pressure.

A comparison of the effects of viscosity for pointed b.ices
with the effects for a blunt body shows clearly t. t body s:c--
must be considered, and that conclusions about viscosity :-ffects
based upon tests of blunt bodies i'.-- be ccm.ll:.tely Irnpplic.itl3
to the aerodynamic shapes which are suitable for supersonic flight.
For example, in the case of a z:.h'-r: at 1.5 Mach number wit, an over-
all Reynolds number variation of from 7.5 x 104 to 9.0 X 10", the
agreement between the drx--. data from G-tt:n.r-r (r-erence 7),
Poonomundo (r feronc- 21), and-the p.r s;-nt wind tunnel is within 1
percent of tr.- values measured for fr :-i.1ght referencess 7 and 22).
It is ovidont that the ::ffacts of viscosity on Lthe-. drag of a sphcie-
are quite different from the :ffocts on the pointed bodies tested
in this inv:-sti -:tion.



C 17 rP .TLT

C 01 'I U.jU, i; 7,

The cor.clusions which follow apply for a Mach n'ib.b-r D 1.5 and
at R-:-.oli. numbers ba.:-d unon model length ui! to about 5 millions
for bodi-::- revolution similar to the ones tested.

1. Th- effects of viscosity differ grealy for laminar and
turwl-.: :'low in the boLunT r:-" layer, and within each r:-li.: e >:.n
v-:; -h. i--nolds number of the flow and the shape of the body.

2. L-inar flow was found on the smooth bci- e up' to a Ieyr..,ids
nrn.ber _' 6.5 millions and may possibly exist to -:gr.:drlr..r higher
al--;1> ..

SA cc.-marison between the test results for laminar and. for
tulu--.l..- .'low in the boundary layer at a fixed value .' the Reynolds
r-i .-:w:- that:

I ) The. resistance to separation with turbulent flow in the
b-undary layer is much greater.

(b) Th= shock-wave confiMu-i'atlon near the base depends upon)
he ..;,.-o of the boundary-layer flow and the relative
d--.r .: of boat tp.l~;,r.

(') The fore drag c--.fiicients with turbulent boundary
i:.yer ordinarily are hl_-h-er.

id) The b'aSe pressure is much higher vith the .u'bul-
boundary layer.

(e) The total drar is usually higher with the turbulent
boundary layer.

4. For laminar flow in the boundary 1...;'rr the following
Eff -- e w-rl- found:

(s.) Th;- laminar boundary layer separates for.:ari of the
bc..ae on all boat-tailed bodies tes ed, and the
pcc-.tion of separation varies noticeably with rTynL-lds
number. Laminar separation is not necessarily
accor,:.ni*ed by a shock wave originat:ln from Ihe
,: int of separation. On many of the models the
z--ar ion is located in a region upstream of vi:hich
;.h! treasure continually decreases in zhe direction
of the flow.

(b) The trailing shock wave moves forward slightly as the
RFynolds r.ur.F-er is increased, but no :~r.i 'icant .hCg:-
ta'2es place in the shock-wave configuration near the


. C .' TT I A 7,'1 1,
n,.'-.C.. ri A'. .-. ;', -

SKAA iM No. ATA312

(c) With increasing R.ynolds numbers, the fare ._. ..: i-
cionts increase for highly boat--t- I.l .i bodies and
decrease for bodies without boat trll!n-. ::- modor-
atoly boat-teilod bodies the variation of the fore
drag c-.ffclont with 7.;:n:lci. number is rolativ'lyr

(d) -i: base pressure of the bcbct--t 11ii bodies is
controlled byj the laminar soparaticn end o:. n-
: Z.: .d; with Reynolds number. :. ':d.s with
tho same _ft lrb-;. shape, the ba'. prossuro else
SJnrd.: upon the 1-ntL d-iaotor retio to tb: -i.

(o) t!-l dr.g varies conside o-Iblj with BRynolds n-.:i.-',
.-nrg more ti-n 20 percent for savoral fi thu

5. F7- tui.l. nt flow in the bciund-r. la-er theo following .lfocts
wour found:

(.) -5: --:'. tLon doo3 not ordinarily. occur.

(b) Tho shock-wavo v :-.fri iguration noar tho baseo ".3 not
c',-n' noticeably as tl.-, Rynolds nurbor c'.-'.-s.

(c) Tho foro drag j.f.icionts decrease sli hitly as the
F -n: 1is number is increased.

(d) lih base pressure changes vory little with c.':n lri
E.ynolds number.

(c) The total drag docroa.sos as t:-- Rcynolds number is
incr. i'.

Aros .:. :r- ..t ical L'.: -,-tory,
1a.tf.tonal Advisory Committco fo:-- Aronautics,
.i-f-ett Field, Crli.


c, 'i- --"T-! L

NACA i:; .-. /'".?-1- *C;L _-'.-T-T-.L 29



Since tie static pressure with no m:liel present varied along tle
a x:. of ths test section as shcwn in figure 7, it was necessary to
r.ppl. a correztijn to the meassured 7efficients to account for the
:i;'rc.ment in drag or pressure resulting from this axial pressure
C-'d.."ent. A.lthc.uh the axial variation of test-section static
ore2surs is not m:'nctonic, the pressures at tIh downstream end of
tl] tLest section are uniformly lower than the pressures of the up-
st-ream end where the nose of the .rm:dels are ordinarily placed. This
r'.tr.3 that ti:e c tul1 preserre exerted at a. "'Iven point on a body
is wer th n it .r.uld be if the embient pressure gradient were zero
es it is In free fli,.t. The gr.dier.t corrections are calculated on
ti:e assumption that the magnitude of the pressure exerted at an
airbltr-';- point sn t'e body in the tunnel is lower than it would
be if no gradient were present by an increment ecual to tle amount
whi:h t'e static pressure d.crcases (with no model present) from
t.ze : .siti;n cf tihe model nose to the position of the arbitrary
p:'.nt. It :.3 not necessary to include the c:,lr-es~onding axial
va-iat.icn of dynamic pressure in the corrections since it varies
cnl .: :- '.? per'.ent from the mean test-section value used in all
.;lculot:'.cns. The corrections to the measured .:.Cefficients of model
1 li- ztei 2... inr:ies downstream from the reference pressure orifice,
fr e.xajmle, :unt to +0.012 in fore dsSe efficient and -0.02'
in bao.e dra'3 ,-:ceffi.lent; the corresponding pir:er.ntaes of the
U.nc,: ire.ectc- cce 21-cients of fore drag and base r-c;;u.-'e are 12 and
1^, r: .:-? tlv;c '.

_.e.-'.sc the .gradient correction is relatively I:.--e in the
pr.'-sent te3st3 .and apparently has not been ep':'l'-.i in the past to
su.:e-cr,,ic win4-tu.nel data, an experimental justification of such
thcor:ticl co;:.lceticns is in order. The validity; of the corrections
as epplied t.. fore d Lra.is confirmed by tests on model 9, which
.cc'rssts cf .. .cnicil nose with a 200 included angle and a short
cylind.rical olftcrbc~ ..i. The theoretical fore drag of this bridj, which
is eqi.ual to th:- s31 of the wave and friction drags, can be assill,
c-lculot.,Id -s function of Reynolds number. The wave d-:n.- of the
cor.i:al ncse is :lven accurately by the experimentally confirmed
calculat.'.cns of T';.l.r and Maccoll (references 10 and 11). The
fictional drIe ca-n be calculated using the l:w--sn-cd laminar skin-
fr-ict' n c:cifficie-nts in accO:,i-dance with references 3 and 11, since
the bounder.; layer was completely laminar over this model. A com-
ea:-is:n of the corrected and uncorrected fore d-c:s with the theo-
rc-tic-al fc.re' d-ar is shown in fi:,- re 8. The corrected fore ir-
coefficients are seen to be in good :r. oem-cnt with tho theoretical
values, whrceas the. uncorrected data fcll below the wave L--': at
hi*:. tunnel pressures. .This latter condition, of course, represents
an impossible situation for a body without boat tailing.


v:,: ""La T

In order to check e;oi':lientallj the validity :,f the corrections
as applied to the measured base p_ esI..re, .ic'.;l 1 was tested on the
side support t a :'ve different p:.itions 2lL the axis of the test
section. 35 .auc, the support s;-.:te r.mr-ne d fixed relative to th:
body, the interference of the support is the same in each case, hcr.co,
any d'sc*,:-,--.}n? ies in the measured base pressures at the various
p-r'tions are a.ttif'Ltt.bls only to the pressure gradient al-nr t.1-
tunnel axis. iuire 9 shows that the uncorrected base pressure data
talen at the five different p-sltions differ c' about -'L percent, but
the corrtsj.:i : five sets of corrected data fall within about 1.5
percent of their mean, thus crnf'rming the validity cf the c.-rrc-zt`ion.


T-.c.-. M UD. .-..A..11

,AC.A FM Nc A7A31a

A.IZ7:.Z:. B

-R ,Ig.- ;.; OF i,--'TA

.5 ac,.-.:". f the rez.zlts pre3ented can be estl:iac'.d b;
ccicr.'-cing thoe ?:.slle errors that are known to be involved in
th;- mea u-oment .-f the forces and press''ec, and in the dcote-'in;c--
tion c.f tie f:--..st'eam Mach number and grad." nt corrections.

T1?. f:-'rc. msurements are subject to errcrs frcm s:.-fts in
th:- bcl_-nco. zer !ue to temperature effects, and also from a shift
In th.- cLlibraTlcn constant. The zero shift, which is less th;an 1
o. -'c;nt of the fi.rce data at low pressures and less than 0.2
p-rcent at LTi,.h p.'e-sures, was checked periodically by running the
t.;:nnl tthr'-,u the- complete temp:i-atiur range with no force acpliad
t. t:-e b>lanc:-. In the majority of cases the variation of the
balance calibratt:n constant, which was checked before and after
ech: se'Cies of tests, permitted a possible deviation of 0.3 p r:'ent
in the force dat2. All data presented in fi-f'.-res 12(b), 16, 17, and
1 .e a -ca f'-r models 4,.5, and 6 in fic:re.- 26(a) and 32(a) were
:L..ne.d idurin a period between two consecutive balance calibrations
for which' t:he c-nszant differed by 6.4 pe_'cent. A comparison of the
der~i obtained during this period with theoretical results and with the
-esults of subsecuont reruns of some of the same models indicates
t!h'-t the .'i'-ne In balance calibration occurred before e the data in
qLuesti:; \/ere obcsined. The results in the aforementioned figures
were tlhecrfce cc'nruted on the basis of the later calibration. It
is estimated that the maximum error in the balance calibration
ccn-r!tear for th.esCe results is at worst no Cgre-ter than +0.3 to
-7. pe. ...s.L.

The pres3uc-e datt, including the dynamic pressure, are 3Ubject
to szall errors resulting f-ron p-:z'Ible inexact readings of the
..e'-;1ury mnc.neterz. 'Te base pressure data are also "':.>.ct to an
additi-.'nnal err: r resultin.-n from the small variation in the specific
grav't;:' of the dibutyl phthalate indicating fluid. At the most,
the2e sa;u-ces can cause an error in the total and fore drag .:effi-
cients of about '.3 percent, and in the base dr-a coefficient of
Eb:.uT =1.' percent. The error in dynamic pressure due to the
unc:ertainty in the free-stream Mach njuber is nell1ibile, since the
isentr:pic relati-on for the dynamic p:-essure as a function of Mach
n'aber Is near a maximum at a Mach number of 1.5. For slender bodies
cf re-.vlutlon the variation of the force coefficients with Miach
number is quite small; hence, errors resulting from the variation of
free-stream Mach number from 1.49 to 1.51 are neglijibl3.

LCn the basis cf the data presented in figures 8 and 9, it is
estimated that f:rr all tunnel pressures the uncertainty in the
gradient corrections to total drog, fore drag, and base prc3essu'e
coefficienx.s can cause at the most an error in these coefficients



2?. Cx DE]'TiL-L I.ACL i .R -.7-.?.1

of 0.004, 0.004,aOnd O.C,-':, I-:-;c-,tively. It .::-;ild be nrt-ed
that in the table on p.'eci- ln, n-:3,resent in the se--tion on results,
this source of error, which is independent cof tunnel pressure, is
expressed as an increment and not as a pier-'etage of the i,- '..ie.
-". :'icient.

envious ir.v';-stir,2t'Lons have shown that an uncertainty :.-;- be
introduced in se'.'s':nic wind-tunnel dIita -'f the ilj'ty of the
tunnel air is '.-bhih. To determine the effects of this var.i3le
in the :--s,:nt investigation, tl}. specific i .nility was varied from
the lowest values (app':rxiaitely O.OC''i) to values appr:xirmt-li
20 times those normally encountered in the tests. TrIa. and base
pressure measurements were taken on a body with a conical bead 'ind also
on a -:..ere. The results showed no appreciable effect of humidity
over a range much greater than thit encountered in the prn.-.;:-.t tests,
provit ., the variation in test-section d. nC..': pressure with the
in.'.-: in .luni1i ty was tLa'n into account in tf reduction .' t:..
data. It is ba.li-,ved, t.l:r.fore, that the precision F t.-: resilIts
presented in this report is un'ffuct,1 by tunidit,-.


I;A':A .: !'. 7A31'7 :.T 29

EFFECT OF SU,.'?T ''? .-L7",

:.". nowl,:. of the c:fects of 3upp,:rt -nt.:ie'erence .i:.n the
d:to .in question is essential to an underst:.nd.in of its a'.pi':l-,
bil'ty to fr:: flight conditions. Previous to the present inveati--
rt'In an extensive series of tests were conducted to dctermino the
b: .:y Ci:,:pe and supp':rt combinations necessary to evaluate the support
int:rfe: ence.

In gcne-ral, it was found that for the models tested in the smooth
condition laminarr boundary layer) the effect :f the rear sup'l.'ts
used in th;- present investigation was negligible in all r s,'cts for
t;h b. :Lt-t'ilcd models 2 and 3 and was appreciable only in the bese
pr;-....... measurements for model 1. On the basis of these results
it 1. believed that the rear supports used for the other highly boat-
tail:-d bodies (mrd.-1is 4, 5, and 6) have a nr _,l "'le. oiffct on the
dr--: :f the model. For model 1 combinations of rear supp.:rt and side
s,.rpprt,-t were used to evaluate the effect of the rear support on the
bz.:- -''essure. The evaluation was made on the assumption of no
w.-s!l interference between the rear support and side support, and
\ra: cracked by the use of two different combinations of side support
nd _-:e'".r support. The data indicate that the assumption is justified
wi;.-:ln th-; limits of the e.:e:r--'i..ntal accuracy and that the corrected,
int rf:eence-free base pressures deduced by this method differ only
siigiLlr .y :.r- those measured with the side s.ppcrt alone.

For the b:dl.:s with roughness added (producing a turbulent
bc-Ori'.Uty- layer) a clplote investigation of the support interference
w-s net made; consequently, a d-finite quantitative evaluation of
thr irnt:rfeornce effects for each body in this condition cannot be
given. From the data that were obtained it has been found that the
f-:r.: L-'ag is unaffected by the presence of the supports used in the
pr:.s-nt investi7 tion, but that a small amount of interference is
c-vid.-nt in the base pressure, coefficient which may vary from a
mlr.nuLnjm f 0.005 to a maximum of -0,015 for the different bodies.
This uncertainty in the base pressure coefficient results in a cor-
:repond n,'l.ri small uncertainty in the base drag coefficient srn in
th,. t:t.l dri:- c-. T'ficiont.


30 L:.J ,r7TL'.L "'A .-. IT..7A31.

1. Aclxret, J., "Fli..:-nn, F., and Rott, N.: Invost.'ati..s -f
Compression Shocks and Boundary Ln .,.-. in Gases Mnovn_- at 'F _
Spood. IACA TV No. 1113, 1947.

2. i.' i.nn, H.W.: _-urti Investigations :- the Interaction of
Boundary Layor and S:-:ckr Wavos in Transonic Flow. Jour. Aero.
-., vol. 13, no. 12, Dcc. 1946.

3. Thoodorson, ..'ro, eand F:-. -..:r, Arthur: -.:.::,-:imonts on 1I'-;
of 5:-.'lving Disks, Cylindors and Ptre'amin ERods at 1i,-, Seeods.
NACA IAC No. L4F16, 1944.

4. Koonan, Joseph H., and I"..km.nn, Lrn::t P.: ri-lction in Fl--.: at
.i.-' sonic and Subsonic Velocities. NACA TN I': 963, 1945.

5. Frosoll, W.: Flow in Smooth Straight Pip:: aat Volocitios t'bove
and l.:-w ;.nd Velocity. .:.. M No, 1

6. F _ri, Antonio: Influenza daol i'.~x: : d I:'. -:1iz ai G.'-nc'.
iNumcri di Mach. Atti di Guidonia No. 67 j, 1942.

7 Walchnor, 0.: Systematische Goschca~s: .: .-:-' "-.n Inl':i:.l
Lilionthal-G :-. 11ch .ft fur Luft2ph-' tfc.: o 3-. : 1I,
Toil 1, Oct. 1941

6. Bach, F.: Druckverteilungsmossungen an(; _-. :d. ill r.
Deutscho Luft: VL h''frschung, .i-i 6'i 7, Mar. 1945

9. Van r:- -, Milton D.: A.-.-. i. ChL:-..:t.ristics Including
Scale if:oc t of Several W-lr. and Bodi. Alone and in Combina
tion at a Mach .tmbor of 1.53. NACA Ri. No. A6K22, 1946.

10. Maccoll, J.W.: Tho Conical .c-: Wvoe F:..t~'- by a Cone Mov-inc
at a High J; ....i Proc. cf theo .:;al Soc. of L.nd.:n, sur. A,
vol. 159, Apr. 1, 1,'

11. Taylor, G.I and i.:.-coll, J.W.: Th- Air fr-r.3 a:'o on a Cono
Movin- at TT4h Spoods, Proc. of the Royal Soc. of LI.nd:n,
ser. A, vol 139, F.b. 1, 1933

12. Sauer, R.: Method of Characteristics for Three-Dimensricnal
Axially Symmretrical Supersonic Flows. NACA TM No. 1133, 1947.


ir.'! m1 No. A,".'.31a C0HFi-I:"'LAL 31
J .. ., .. B .o. .....31a

13. S., R.: Thoorotlscho Erl 'i:-r--. in die Gesdyna.mk. B.: iJn,
Spr inc.- ', 1 ~3 (Reprinted '.. L: A'i ds L1.'3., '.nn .-'"b -, Mich.,

14. T~-llncin, W., and 'e..for, M.: Retati .zc: Inl.. t'.scho3
Uborschallstrmun'ac: n Lil i-ntl21-Gosellschaft fur
1.--ftfh--Ahtforschung, r..-'.ct 139, Toil 2, Oct., 1,7-1.

15. -ll11. n, E. Julian, and ;i;tzborg, Gerald E.: The Effect cf
Comprossibility on the Growth of the Leminar Boundary Lay:
on Low-Dr?. Wings and Bcri:.-.z. l.CA ACR, Jan. 1943.

16. Loc, Lostor, and Lin, Chia Chiao: Invostigation of the
Stability of the Laminar B.irndre--y Layor in a Compressiblo
Fluid. KACA TM 11. 1115, 1946.

17. H.t, H.: 3c:hl nd. vind_:.its.-m:s'-in:nr an Rund-und
Profilst'rns.:n versche li-- n.:r Durchnmossor. Lilienthal-
Gosollschaft fur Luftfa]-:tfco.'?:-h-ing,:n, Boricht 156, Oct. 1942.

18. -Cw-:., P.p.: Note on the Apparatus and Work of the W.V.A.
-:rs onc Institute at Kochol, S. Germany. Pert I, (?1. I7i EC0. 1711)
Oct. 19U5, and Part IT, ('s :;:.. 1742) Jan. 1946. (British/U.S.

19. 7 A:.-. Antonio: Experimental Results with Airfoils Tested in
tho High-Speod. Tunn. e at Gr i'.nin. NACA TM No. 946, 1940.

20. Er ar.n, S.: Widorstandsbos.timnumg Von Kogoln und Kugoln
aus de.r Druckvortoilung boi Urb.-,s: 2,-'lloschwi r. -. ;]:it.
Lilionthal-G: s.11sh i:t fur Luftfahi'tforschunegn, Boricht 139,
Toil 2, Oct. 1941.

21. Lehnort, R.: Systomatischo :'. jur. .:-n an noun .; n-.achon
Goschossfo-non im Vorgloich zu T- S:.'.ngr:n dor AVA-Gottingon.
Lilionthal -Gosollschaft fur Luf fsBhrtf ':.r.?h'T.:r:, Bericht 139,
Toil 2, 1-'-1.

22. ,hsrt .r., A.C., and Thomas, R.N.: TIh: Aorodynamic P.. formanco
of Small Sph.rc.s from Subso3-rn:. to High Supersonic Velocities.
Jour. Acro. Sci., vol. 12, no. 4, Oct. 1945.


[ACA RM No. A7A31 a


Ki ? b

.'. ..

., .. *1
'::::.-; :". .
";. .. '.;.;'.~ i ... "

: .: : i.. HH .

^~~~~~r '****^^^^ ^^^ ^ B
.- i *";? ..
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..... 1i.t
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.. .:. "i.:

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.. ..... .--..."..'.. -

~~~~~:. ~.F.,j ;.' ..,:... .


Figui'e 1




... ... ..
:. :.;, :.. ,, -.::

:NACA RM No. A7A31 a


Figure 2a

(a) Models used for boundary-layer tests and for comparison tests with other investigation.

FIGULE 2.-Special-purpose models.

,NACA RM No. A7A31 a

(hI Models used to evaluate effect of length-diameter ratio on chase pressuIe.

FIGURE 2.-Concluded.


Figiire 2b













ui L 1 w i
0 0000
2 22





Fig. a


- Nr w

2 E

7* N
-> >

SIACA RM No. A7A31 a

A,"/,WS ..*.


FIGURE 4.-Sichematic diagram of mo.l-.l installation v'.it, rear suLppor))t and Idrag gage.


Figure 4



NACA RM No. A7A31a

FIGURE 5.-Schematic diagram of model installed with side support.

Figure 5


NACA RM No. A7A31 a

(hi Side support.

FIGURE 6.-Typical model installations.

Figure 6

B..: I




Ii---(- -4d



4 0

0 0

I a


-- -- -- -^ > o -- ^
- __ __ _^ : __ _
l> < ^

o 35 to o

aD 040 100 do f
i.l4 t.4. 0a --

E et C X ^

a rp w 3 4

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0 0 0 0 0 0 0
1- CD 1 m 1 O1

b/"d-d 'e.nsneeed eoueozoej o pezeoez eajnesezd oTlse v o uaTOTEPeo


Figs. 7,8



a o

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.4 0

o o

atm" aM

.4 O.4

o O

*t 04'

+j o v
4.. 04'




C a


* .
Q 0







NACA RU No. A7A31a


Model 1

Reynolds number, Re, millions

Figure 9.- Comparison of base pressure coefficients'on
model 1 measured at various positions along
the tunnel axis, with and without corrections applied
for the variation of test-section static pressure.








Fig. 9

NACA RM No. A7A31 a


I HOC f. '.'ES


Figure 10



"- TURBULENT .'..-



FIGURE 10.-Typical schlieren photograph.

NAOA RM No. A7A31a

Fig. 11



.32 r,, FOP iN 1-2 CONE,












IAOA RM No. AT731a

ni. is



-10 ---14--4- 0
,o a

0 4
0D_ _J, -^ -- 53

Is43 o /
00 "a- .
4 4

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I -- I 1 -- -- I -- -- I -- -- I -- he ft, c

LOD 'Y8u 3rOT;J oo s zx *zoj


*NACA RM No. A7A31 a

Re=3.7 x 106.

Re=6.5 x 106.

FICURE 13.-Schlieren photographs showing laminar flow over the cylindrical afterbody of model 7 at two
values of the Reynolds number. Knife edge horizontal.


Figure 13

NACA RM No. A7A31 a


(a) Knife edge vertical.

(b) Knife edge horizontal.

FICrRE 14.-Schlieren photograph showing premature transition on the cylinder afterbody of model 8.
Reynolds number 9.35 million.


Figure 14

IAOA RM No. A7A31&



0 0 w

_ a ^ -- g :

A --,a so.
I ,
SO O f 0
0 '. TT o I / l^e I kM

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. I

I 1

O l
I l


0 0 0 0 0 0
!I Cl
Tb/Td d d 0n9ttjO eG.rnsseZe d

rigm. 15,16


NACA RM No. A7A31a


/Roughness added

6.7 'Shroud


Experimental wave drag
plue turbulent friction

'Experimental wave drag
-~-I--- plus laminar friction
'Experimental wave drag

o Smooth surface_
0 1/4 inch knurled band
S--Ogive completely sandblasted
a 3/8 inch salt.band
v 3/16 inch salt band-

2 4 6 8 10 11
Reynolds number, Re, millions

Figure 17.- Variation of fore drag coefficient
with Reynolds number for model 8
with various amounts of roughness.



N. 20


o .08



Fig. 17



(a) Knife edge vertical.

rr;;.: .:"".. iSH- ^"c ".... ..^i

(b) Knife edge horizontal.

FIGURE 18.-Schlieren photographs of model 8 with transition fixed. Reynolds number 7.2 million.


Figure 18









Re=-.i.hS x Hr. Re=0.87 x 106.

Re 1.1 x 1 .-. Re=1.4 x 10G.

'IGURE 19.-Schlieren photographs showing the effect of Reynolds number on laminar separation for
nmolel 6. Knife edge vertical.



NACA RM No. A7A31 a

re=ti.7,i lii .

Re=3.8 x 100.

Model 2

Re= 1.2 x 11-.

Re=3.8 x 10g.

Model 3

Re=0.1u x 1U".

Re=0.45 x 106.

Model 10

FIGURE 20.-Schlieren photographs showing the effect of Reynolds number on laminar separation for
models 2. 3, and 10. Knife edge vertical.


Figure 20

- --- ---------- ---

NAOA RM No. A7A31a

Figs. 21,22









__ (



Tb/Td d 'ue0ToT jjoo eznaeedez

Tb/Td d 'unaTOT;;jOoo aZnseez




NACA RM No. A7A31a

iI I


(a) Laminar boundary layer, Re=0.87 x 106.


(b) Turbulent boundary layer, Re=0.87 x 106.
IGURE 23.-Schlieren photographs of model 6 illustrating the effect on flow separation of the condition
of the boundary layer.

Figure 2:

NACA RM No. A7A31 a

Model 1
Re=3.8 x 10".

Model 4
Re 4.0 x 10'.

Model 2
Re=3.8 x 10'.

Model 5
Re-2.7 x 10".
3=t l 12.13 .

Model 3
Re=3.8 x 10'.

Model 6
Re-1.1 x 10.
9=16.75 .

Laminar. Turbulent.

FIGURE 24.-Schlieren photographs showing the effect of turbulent boundary layer on shock-wave con-
figuration at base of models 1, 2, 3, 4, 5, and 6. Knife edge vertical.


Figures 24


NACA RM No. A7A31 a

Re-1.2 x 10'.

Re=2.6 x 100.


Re -. l1p. Re=5.1x 106.

FIGURE 25.-Schlieren photographs showing the absence of any effect of Reynolds number on the flow over
the afterbody of model 3 with roughness added. Knife edge vertical.


Figure 27)

NACA RM No. A7A31a


CT d


or e


1 I r I ** 1- I



S = 5

Fi- a6


a )

-_ _-___-_ _L__4

1 Lm

\\ o
--- -------







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0 0

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r -

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a 0a


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a a
t -i

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a .40
oo a

0 cg

(M 0

0 )

I1 -(

1 ;

IACA RM No. A7A31a


JaO 'Ue TOT$J;joo sXp OaoI

a0c '!t=UOT;3SOQ B2zp *iog


Fig. 27


a "








NACA RM No. A7A31 a

Model P. Re='I.I2 x 1l".

IGLURE 28.-Schlieren photographs at low Rey nolds numbers of models : and 6 with roughness added.
Knife edge vertical.


Figure 28

Mod, el :-'.. n1=1,..s 11. .


NAOA RM lo. A7A31a

0 1 2 3 4 5 0 1 2 3 4 5
Reynolds number, Re, millions Reynolds number, Re, millions
Figure 29.- Variation of base pressure coefficient with Reynolds number for models 1, 2, 3,
4, 5, and 6 in the smooth condition and with roughness added.

-- ~ ~ ~ ~ ~ ~ 0 ^ -- ^-^-^Z- ~ ------ --- -- -- ---- --


a-"-- -- -- -- 1 1 1 1 1 1 11--- -- -



(a) 8mootn condition (b) Rouhness added
I I II I I I I__ _

0 1 2 3
Reynolds number,

Re, millions

1 2 3 4
Reynolds number, be, millions

figure 30.- Variation of base pressure coefficient with Reynolds number for bodies without
boat-tailing but with different length-diameter ratioe.

.0 Model 11 L/D 4.34.
0 12 5.00
0 13 6.00-
S" 1 7.00
v 14 9.00

Figs. 29,30

O Mode
A "

- 5.0


.24 r- -- 1

Note: Flagged eymoole denote reruns

S: |/ i I -
10^ -- -- ----
0 __model 1 -

m 04

(a) Smootn condition (b) Roughness added
0 L 2 a 4 5 0 1 a 3 4 5
Reynolds number, Re, millions Reynolds number, Re, millions
Figure 31.- Variation of base drag coefficient with Reynolds number for models 1, 21, 3, 4, 5
and 6 In smooth condition and with |oughnee added

0- -- -s--' -" o-- --""- ----' ----

o ,

(a)I I (b Rougne added nA 1

0 1 a2 4 5 0 1 3 4 5
Reynolds number, Re, millions Reynolds number, Re, millions
Figure 32.- Variation of total-drag coefficient with Reynolds number for models 1, 8, 3, 4, 5
and 6 in the smooth condition and with roughness added.

Fige. 31,38

NACA RM No. A'Aola


1-: -6

3 262 81C 5 580

TP t T',' ,,l 'Y"t,

7 ''7

:'l Q,

'TT *4,VjL

,t ITT



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o Jo 44


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