Effects of specific types of surface roughness on boundary-layer transition

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Title:
Effects of specific types of surface roughness on boundary-layer transition
Alternate Title:
NACA wartime reports
Physical Description:
23, 20 p. : ill. ; 28 cm.
Language:
English
Creator:
Loftin, Laurence K
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Aerofoils   ( lcsh )
Reynolds number   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Tests were conducted with two typical low-drag airfoils of 90-inch chord to determine the effects of surface projections, grooves, and sanding scratches on boundary-layer transition. The Reynolds number at which a spanwise row of cylindrical projections would cause premature transition was determined for a range of Reynolds number from approximately 3 x 10⁶ to 10 x 10⁶. Data were obtained for projections of various sizes and chordwise locations on both low-drag airfoils. The results were analyzed on the assumption that the critical airfoil Reynolds number for a given projection was a function only of the local-flow conditions around the projection. This assumption neglected possible effects of tunnel turbulence, pressure gradient, boundary-layer Reynolds number, and the original extent of the laminar flow. The data correlated on the basis of this assumption within a range of critical airfoil Reynolds number of ±0.5 x 10⁶ and within a range of projection height of ±0.002 inch. The tests of surface grooves and sanding scratches indicated that, for the range of Reynolds number investigated, the laminar boundary layer was much less sensitive to surface grooves and sanding scratches than to projections above the surface.
Bibliography:
Includes bibliographic references (p. 18-19).
Statement of Responsibility:
by Laurence K. Loftin, Jr.
General Note:
"Report no. L-48."
General Note:
"Originally issued February 1946 as Advance Confidential Report L5J29a."
General Note:
"Report date February 1946."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003616147
oclc - 71295711
sobekcm - AA00006245_00001
System ID:
AA00006245:00001

Full Text

l~ci


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WA RTI l M REPORT
ORIGINALLY ISSUED
February 1946 as
Advance Confidential Report L5J29a

EFFECTS OF SPECIFIC TYPES OF SURFACE ROUIDGESS
ON BOUNDARY-LAYER TRANSITION
By Laurence K. Loftin, Jr.


1
Langley Memorial Aeronautical
Langley Field, Va.


Laboratory


*""'i:.. .- .. ... ..


.. ." "
v*-eX
S' .,e ,. ,.
A.


WASHINGTON
NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.


L 48


K.i sL.. i..;; i... t ..


DOCUMENTS DEPARTMENT


/,




I




-i 2
MACA ACR No. L5J29a I /

:JATIO_;AL ADVISORY COi':TT'E FOR A- O-CIR.-. jC


A~DV ,, CO ::D IAL I.PORT


EFFECTS OF SPECIFIC TYPiS OF SURFACE RO'.GHW'SS

ON BOUNJkDAY-LAYSR TrA;!3SITIO:

ny Laurence K. Loftin, Jr.


S I: ARY


Tests .',ere conducted '::ith tvo typical low-drag air-
foils of .O-inch chord to determine the effects of surface
projections, grooves, and sandinc scratches on boundary-
layer transition. The Reynolds number at which a s-an'..ise
reo- of cylindrical projections w*.ould cause pre:.iaturo
transition was determined for a range of Reynolds number
fro-n approximately 5 x 10 to 10 x 10. Data :ere
obtained for projections of various sizes and clord":ise
locations on both. lov:-drag airfoils. Th. results were
analyzed on the assumption that the critical airfoil
ReI-nolds number for a Liven projection .:as a fuilction
only cf the local-flow conditions around the projection.
This Fssulption neglec:ted possible effects cf tun:;el tur-
bulence, pressure gradient, boundary-layer Reynolds
number, and the crifin;al -:.tent of the la:.i.nar flow. The
data correlated on the basis of thick assur:tion a'ithin a
range of critical airfoil Reynolds number of 0.5 x 10
and within a range of projection eight of C.00'2 inch.
The tests of surface grooves and sanding scratches indi-
cated that, for the range cf Re-:niolds ou.nber investigated,
the laminar boundary layer :*as ;muc-h less sensitive to
surface rrooves and sanding scratches than to projections
above the surface.


INTRODTJCTIONi


The development of the 5ACA low-drag airfoils has
aroused a greatt deal of interest in the problem of deter-
mining the amount of surface roughness necessary to lause
pre.nature boundary-layer transition from laninar to tur-
bulent flow. A considerable amount of data has been
published (references 1 ?r-n 2-) pcvtaining to th: effects








NACA ACR i;o. L5J2Qa


on airfoil characteristics of the application of carbo-
rundum grains to airfoil surfaces. Little data have been
published, however, concerning the Reynolds number at
which surface projections of a given size and chordwise
location would cause premature transition. Fa"T has con-
ducted tests to determine the allowable size of three
forms of surface ridge flat, arch, and wire located
at various positions on low-drag airfoils (references 5
and 4) and later extended the work to include the effect
of smooth bulges and hollows (reference 5). Tani, Hama,
and Mituisi (reference 6) have investigated the effect of
spanwise wires on premature transition.

The purpose of the present investigation was to
determine the Reynolds nu-, .er at which surface projections
of a given type but of various sizes and chordwise loca-
tions would cause premature transition and, if possible,
to establish a general relation between the projection
size and critical Reynolds number. An attempt was also
made to determine the effects of sanding scratches and
imperfect sheet-metal butt joints.

The tests of this investigation were conducted in
the Langley two-dimensional low-turbulence tunnel. Two
typical low-drag airfoils were tested and data were
obtained for various combinations of projection size and
chordwise location through a range of Reynolds number
from approximately 3 x 106 to 10 x 106. Data were also
obtained with the airfoil surfaces finished with various
grades of sandpaper and carborundum paper. The imperfect
sheet-metal butt joints were simulated by grooves cut
into the surface. Tests were made with spanwise grooves
of various sizes and chordwise locations.

Although the projections tested simulated no definite
type of roughness, the results of this investigation
should prove useful as an indication of the order of mag-
nitude of the individual specks that may be tolerated on
a low-drag airfoil of given chord and pressure distri-
bution. T::e Reynolds numbers of these tests were low
compared with usual flight values; however, application
of the analysis to the prediction of allowable projection
sizes at higher Reynolds numbers appears reasonable, par-
ticularly for projections on the forward part of the
airfoil.


CC I DEN. : IAL


CO IDE'IAL








'A: AD3. 1:. Lj29a CC':'DE:.TIAL 3


SET7,CLS A:D COE'FICIZl.TS


c. airfoil section drsa coefficient

y distance normal to surface of lo,'.-drag airfoil

S bcun.'.rd;:-layer_ thicc'ness, defin.-ri as t!lat distance

normal to the surface at which = -

1; h-.-iht of nrc action

d diameter of projection

c chord of ln':.-dr.rz airfoil

j stancee frnom airfcil leading e'l,-e me-asxred alon.i
chord line

s distancee from atifcil leading edge mlieasur.ae along
surl 1' .ce

Ti, free-streaam velocity

cI local velocity just *:.tsit,7 i tou'ndr 1- le:'

u local veloc ltAy 'n-ide boun-dry a: 1er

Uk local v.locit- inside bou nirrl' l' er at to, of a
projection

qo free-strea:n dyrnam.ic npressiure

p local static ?r assure

V; local total pressure just outside boundary layer

II0 "'rce-streamn total pressure

h local total pressure inside boundary layer

o -e\
S pressure coefficient (o r'
Scoeffiieo

', coefficient of kinematic viscosity.


C ON F IE'ENT IAL








4 CC'TID; TIAL T..1CA AC(. "o. L5T2 a


R airfoil Reynolds number; based on chord of low-draj

airfoil and free-stream velocity --

R' Reynolds number per unit length; bas,. on velocity
just outside bounair-ry. layer ()

RF boundary-layer Reynolds number; based on boundary-
layer thickness and 1rcal velocity just outside
boundary layer (R'6)

Rk projection Reynolds number; based on hLiJht of pro-
jection ri'n velocity in boundary layer at top of

projection (--)

Rx Reynolds number bas3d on distance x and local
velocity just outside boundary layer at
position x (R'x)


T boundary-layer transition parameter


A constant for any1 chordwi*c, location of
(cT ;2/3
projection CU C

Subscripnt

cr indicates conditions just -:.fore transition from
laminar to turbulent flo':.


TEST TIET_ OLDS


Models.- The tests were conducted in the L.ranley
two-dimensional low-turbulence tunnel. The test section
of this tunnel measures 3 by 7.5 feet and when mounted
the models completely spanned the 5-foot dimension.

T--sts were ccreiducted with two typical laminar-flow
airfoils which hereinafter will be referred to as low-
drag airfoil 1 and low-drag airfoil 2. On both airfoils


C OT7 !i: TI AL








IACA AC i No. L5J29a


the position of rn.inuiou. pressure was at 0.7c; however,
the pressure gradient was r.:ore favorable on low--drag air-
foil 1 than on low-drag airfoil 2. Low-drag airfoil 1
was cambered for an ideal lift coefficient of 0.2 with a
r.ean line of the typ- a = 0.7; low-drag airfoil 2 was a
sy-nmetrical section. Lxperirental pressur-e distributions
are presented for the two airfoils at the given test con-
ditions in figures 1 and 2. Th3 models were constructed
of wood and were painted and sanded ;o have aerodynam i-
cally smooth finishes. Zach r.odcl had a chord of
90 inches.

Tests.- The projections were cylindrical and con-
sisted of headless nails driven p-rp6enQ-icular into the
surface until the desired height was attained. The pro-
jection heights were determined with an Ames dial gage.
Tests 'were performed w-lth one sparnis13 row of projections
of constant size located at the desired chordwise station
on the upper surface of the airfoil; the spanwise spacing
was 3 inches in all tests. Projections of 0.055-inch
diameter and various heights w3re employed in the tests;
check tests %.ere conducted with projections of 3.l15-t.nch
diaa.eter. -he various combinations of projection size
and chord-ise location tested with low-drar airfo-ls 1
and 2 are nipesented in table I. Drag data were obtained
for airfoil Reynolds ni:umners varyir? from a:.proxi-
mately 3 x 100 to 10 x 10u for the airfoils with smooth
surfaces and with each conrbiiat.Ion of projection size
and location. The dra- measurements 'w.ere made at a
single spanuwse location by the .akaz-urvey retihod, a
cort.plete description of vhi'ch appears in refere'.nce. 1.
For each projections cctbination, the :.eynolds num-ber at
which the drag coefficient showed a definite increase
over that o0 the smooth airfoil :a.s considered to be the
critical Reynolds number. The dr.a data wo.-re often Incon-
clusive, particularly when the projections were located
at lar-e distances behind the leading. edge. In these
instances the boundary-layer transition parameter (refer-
ence 7) was determined from measure,-.ents of the velocity
profile in the boundary layer. These neasuirements were
made with a rac:: of total-pressure tubes (-eference 7)
located 2 inches behind the projectio.;s. The iReynolds
number at which the boundary-layc-.r transition parameter
showed a definite increase was considered the critical
value. The drag of the airfoil without projections was
determined at frequent intervals to insure that all drag
increments were caused by the projections and not some
other surface imperfection.


COCFIDEYTIAL


CC' FIDLT IAL








NACA ACd :Io. L5J29a


Imperfect sheet-metal butt joints were simulated by
grooves of several sizes cut into the surface of low-drag
airfoil 1. The various combinations of groove size and
configuration that were tested are presented in table II.
Grooves of X-plan form are illustrated in figure 3. The
procedure followed in performing the tests of the airfoil
with grooves was the same as that for the airfoils with
projections.

The various grades of sandpaper and carborundum
pa'er used for determining the effects of sanding scratches
on transition are indicated in table III. ilot only were
various grades of abrasive used to determine the effects
of sanding but the direction of sanding relative to the
air stream .vas also varied. Enlarged photographs of sur-
face areas sanded with circular and cross-hatched strokes
are shown in figure 4. The method for applying the rough-
ness is shown in figure 5. The roughness area was pro-
gressively increased from a strip from 0.7c to 0.5c to
include the part of the airfoil between 0.7c and the
leading edge. Drag data were taken through the range of
Reynolds number after each area was sanded.


RE S ULTS


Projections.- The results of the investigation of
the effects of surface projections on transition are pre-
sented in figures 6 to 10. The variation of section drag
coefficient with airfoil Reynolds number for the two low-
drsp airfoils with smooth surfaces is given in figure 6.
The increase in d:'ag coefficient for low-drag airfoil 2
at the higher airfoil Reynolds numbers is believed to
have been caused by the increase in air-stream turbulence
with Reynolds nuInber. The drag of low-drag airfoil 1 was
not affected by the increasing air-stream turbulence
because of the more favorable pressure gradient of this
airfoil. The results of the analysis given later in the
discussion appear to indicate that the turbulence of the
air stream had only a secondary effect on the Reynolds
nrundoCr at which the projections caused premature
transition.

The increments of dra;: induced by projections of
various sizes and chord'.ise locations are plotted against
airfoil Reynolds number in figures 7 and 8. The boundary-
layer transition parameter (reference 7) is plotted as a
function of airfoil Re nolds number in figures 9 and 10.


CONFI DE r T AL


COTF7TDE ITIAL








!ACA AC1r. AC L' J.9a C .'iDECi;T.M L 7


Surf-ac; grooves -ind. .rndi-l sc'ra.tches.- The results
of the in"-' ti'.-to&.t ..f 'che fi'' -rt .t f s;E',h "c t-e.r..' .-
end sandin- s!r-.tches on 'zrcnsi: ion rccetn.r -till- tie
test conditions at wh ilc-h the results :-.ere obtaiind are
presented in tables IM and III, resT.ectiv-ly.


DISC'.LSIO '' Pi.D A.-.'L T:S


Projecttions.- 's has already buen indicated, the
airfoil Rei,.olds rurnbcr at ;::icl. either the ira- injree:.ent
or boundary-layer transition paioraeter sho'.s a definite
incre.se is consider-ed to be the critical .eynolds numtesr
at 4hich preT.attre trr::nsition oc-curs. Tie ,Eccu-acy with
which an inic:rense in either of these parame-nters est -b-
lishes the critical i;.-polds nu:.iber is indic-txred in fig-
ur-s 7(c) to 7f' Several va'l.ues ol the critical
ReynoJds nurttib:er. were ottaincd "Jith each si:.e of projection
at 0.20c on lo'.-dra- airfoil 1. Tn.c values of the
critical RcynolsQ niu,:ier obtained w'it, ac!h conflgurat ion
genera;lly ar- withn 1 x Althcuih Leter .-,r w'i:: 1n
ri.:'lt be considered s sirable, the results presented are
thou.'ht to rive a jood indication of uhe order of rnmari-
tude of the Reynolds numberi at .;:-_hichi pre.iatire transition
may Ole expected w-ith .roje.:tions of a g lv'-n size: and
location.

The -eneral eff.:. ts of :2.roj-ctjion siz. and 3.ccation
on transition a-e in-i,'cated L;' the e::peri.iental curves.
As .ni-ht be ex-emcted, the arltical airfoil ,eynjolds nunber
et a specified chord- ise sc.:tion decreases vwith incvreasin-
projection height and Ciamet r. As project icns of t- given
sizo are. moved toward the leading efi6, the cri..cal
Re-nolds nur-ber d.ecr,~ ses until th.- ,rocjec icons al...~st
reach the stagnation point ani then 'egine to increuae.
rie lower critical Reynolds numbers for p'rojections of
given height at C.65"c cs compareid wth -. those for projec-
tions of the sar:e height at 0.50c (fi.-s. 7 and -) may be
due to the combined effects of a zero or slightly unfa-
vorable pressure gradient and larder values of the
boundar-y-layer Heynolds number. The results obtained
with projections near the stagnation pcint are explained
by the low velocity over the surface and the steep
velocity Gradient at the sta.nation oc.oint. The increase
in critical Reynolds rnumnbor as nroj- ntions are placed
near the stagnation point should not, however, be taken


CC. FIDE-;TIAL



































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:[ACI ACRL I'o. L5J2P a


span.vise ro-.i across the ai-'rfoil did n':t hav:- exactly the
same h-,eiht and shape and therefore the same critical
Reynolds number. In any case, the sharp rise ii drag
seems characteristic of the projections tesctd.

An attenpt was mT.ade to correlate, the critical airfoil
Rcy.nols nutilbers at which the projections caused prema-
ture transition with local-flow conditions around the
projection (reference 10). In such an analysis of the
results, certain var ables are neglected, r rch as tunnel
turbulence, ..re- si-re "radi3nt, bo .ndrry-lay.:l .-- ynolds
number, and th :ri' -inal e-xtnt of 1.u aLe- flcew, except
insofar as 'h':s '.l. -ibles affect loy l-f>. conditions.

Simi lar it:- of 1 >".l-flVo conIlt i .'. a':c'.tt rejectionsns
in similar fieli' L'-f 'lov is o-:bcaz:-.ed if tL.e projections
are ,eo,.,etr;ca-ll L ".llar and if the :-;Troids numfoer of
the flow about the pr-o.cctions is the Za::.e. In the fol-
lowinr anal;-,is, '.:. c pr:ojectiLc.- are ta'-en to be suffi-
clit l, srr.ma: tc ;a;:5 cu/,i in the a':-en-e of the pro-
jection es_-tse-tislly -ostant fro-! the .'v.ri'sc. to a height
equal to the heil-.t of the projection. Cylindrical pro-
jections are geometrically si-.ilar if their iin-ness
ratios d/i: are the sae.:e. For each vailu. o01 / the
locsl-flo.v pattern is therefore co::pletely ,.'.terr.lined by
thel Re:-,rolds number oi the fio-' 0.Lcub t' :h p-.rjection.
The Rcrnolls numob'r 3f thl. flow about the projection lR
ulI k
was taI:tn to be --. Tlhe critical nrojEct'on Reynolds
number RF, was calculated iromt the- experimental data
corresponding to the critical airfcil Reynolds nuraber as
indicated by the curves of figures 7 to 10. The Blasius
relation for 5u/6y expressed in terms of the boundary-
layer thickness vns e..2ployed for calculating uk. The
variat.c.n. of the Lcundary-layer thickness with chordwise
position at "eynolds nznbars cf 3 10 and 6 x 10 is
Clven in fir-ure 11 for low-drag airfoils 1 and 2. T'h
boundary-layer thicknesses were calculated b'y means of
equation (31) of appendix 3. The final equation for the
critical projection Rey.nolds number is as follows:

2
Ri = 0.74/-- Rt (1)
"-cr k6cr/ cr


C ONF IL, 'IT L!.L


CO:rIDEIITIAL










COITF1DLrTIAL '/.CA ACR !To. L5J29a


The derivation of equation (1) is given in appendix A
and the method of reducing the experimental data to
obtain Rker is outlined in appendix B.

Values of r are plotted against the corre-
V kcr
spending values of the projection fineness ratio d/k in
figre 12. In this figure N R-_k was used as a variable
rather than Rkr because v/Tkcr is directly propor-
cr v-cr
tional to the critical projection height.

The considerable scatter of the points shown in
figure 12 ap--ars to be unsystematic. The scatter may
have L-een caused primarily either by the neglect of some
of the variables previously mentioned or by ex-erimental
inaccuracies in determining the critical airfoil Reynolds
number for a given projection. Check tests of the
critical Reynolds number have been shown to differ by
approximately 1 x 10 In order to indicate the practical
significance of the scatter of the data shown in figure 12,
curves of projection height against critical airfoil
Reynolds number have been calculated from the faired curve
of figure 12 by means of the relation presented in
appendix C. The comparison of the experimental points
with the calculated curves (figs. 13 and !4) shows that
virtually all the experimental points of the critical
Reynolds number can be made to agree with the calculated
curves by shifting the points not more than 0.5 x 10 on
the Reynolds number scale and not more than 0.002 inch
on the height scale. The results therefore indicate that,
with the exception of the points obtained for projections
close to the stagnation point, the effects of small pro-
jections on transition can be correlated with local-flow
conditions within the limits of experimental error in
this investigation.

The data from which \R was correlated with d/k
were taken at Reynolds numbers from approximately 3 x 106
to 10 x 106. It is reasonable to believe, however, that
the correlation would be valid at higher Reynolds nu.1:ters.
A consideration of the parameters describing the boundary
laysr indicates that conditions near the leading edge at
high Reynolds numbers are equivalent to conditions farther
back at low Re-uiolds nur.mb~rs. The analysis pre~sernted is
then particularly applicable -when small vlueLSs of x/c


COC, IDE:I AL








EIACA ACR fo. L5J29a


are considered with relation to high eynolds n-u-.bers.
Inasmuch as all tests were made with one soanwise row of
cylindrical projections, the critical Reynolds number may
be somewhat optimistic for projections likely to occur in
practice because of variations in the shape of the reo-
jections from the type investigated and possible combined
effects of a nunter of projections at various chordwise
locations. It should also be noted that the analysis was
based on data in which the height of the projection was
small compared to the boundary-layer thickness and can be
expected to apoly only when this condition is fulfilled.

Page has presented the results of experiments con-
ducted for the purpose of deterininin a criterion for the
critical height of either a single arch or a flat ridge
located in a spanwise direction at various chordwise
positions on a low-drag airfoil (reference 3) and a flat
plate (reference 4). The criterion as determined from
the airfoil tests was presented in the form of a corre-
lation of Rk with k/c, here c is the airfoil
cr
chord and k the ridge height. The values of .
cr
determined from the flat-plate tests were correlated
wjth : /L, where L is the original length of lamrinar
flow. Although the drag data presented in reference 5
show that the critical Reynolds number is somewhat
dependent upon the design length of laminar flow, the
values of Rkc determined from these two investigations
were plotted in figure 15 as a function of d/k, where d,
in this case, was taken to be the ridge width. '1he
parameter d/k is similar to the projection fineness
ratio in that it describes the forrm or geometry of the
boundary-layer disturbance. The val-es of VR
obtained from tests made with projections and ridges are
not strictly comparable, since ridges represent a two-
dimensional disturbance and projections are th'ec-
dimensional. Values of Rkcr obtained from th'- inves-
tigation of three-dimensional projections r-re, however,
also included in figure 1i and show the similarity between
the results obtained with the two distinctive types of
disturbance. Although the values of Rkcr obtained
with the two types of disturbance do not form a con-
tinuous curve, they are of the same order of magnitude.


CONFIDENTIAL


CONFIDETI AL








TTAJA ACR No. L5J29a


In order to check Fage's results, a strip of "Scotch"
cellulose tape simulating a spanwise ridge was applied to
low-drag airfoil 1. Two thicknesses were employed and
the results, which are plotted in figure 15, are in fair
agreement with rage's results. "age also made tests with
a spanwise wire located at various chordwise positions
(reference 75). Wires of three diameters were tested; the
value of d/1 was, of course, 1 in all cases. The values
of Vcr obtained were 13.1, 15.5, and 8.6. Tani, T .::a,
and : ttuisi (reference 6) conducted similar tests with
wires located on an airfoil and a flat plate. The values
of F1cr were 13 for a flat plate and 15 for an airfoil.

Surface grooves and sanding scratches.- The results
of the investigation of the effects of surface grooves
and sanding scratches indicate that within the range of
Reynolds number from 3 x 10 to 10 x 10 at which these
tests were conducted, the boundary layer is relatively
insensitive to surface scratches. Only deep X-plan-form
grooves located near the ledi ,g edge caused premature
transition (table II). No definite indications of pre-
mature transition were noticed with any of the types of
sanded surface. The drag was soi. 'hat hiht. -I.en the
1
surface was finished with TTo. 1- -nd.pae.r, but there
2
was no definite break in the drag curve. It is thought
that at higher Reynolds numbers than those at which the
tests were made the t;-)e of sanded surface would show a
more definite effect upon transition. A comparison of
the results obtained with various types of surface imp.er-
fections indicates clearly that, within a given rfnge of
Reynolds number, the laminar boundary layer is much more
sensitive to surface projections than to inS entations in
the surface.


C ONCLTS I OIS


From tests cc!~ducted with two typical low-drag air-
foils of 90-inch chord to determiino the effects of surface
projections, grooves, and sanding scratches on bou.rndtry-
layer transition, the following conclusions were reached:

1. The Reynolds number at which one row of spanwise
projections causes prezmrature transition is primarily a


C CO'rI DL:r IAL


CC:iIDEIITIAL










ITAC.A ACT' No. L5J29a CC'TIDEN TAL 1x


function of the projection geo-netry and the R?;e ynolds
r1.nmbr based on the height of :h'-~ projection and ti-ie
velocity at the top of the projection, provided the
height of the projection is small co.;pared *.ith: the
bou.nd&.r--laYver thickness.

2. The laminar boundary layer is more sensitive to
surface projections than co surface -roovec or car.dini
scratches.


Langley Tem:iorial ..eron:.'utical La':ori or.'y
national Advisory Co..imittee for aeronautics s
Lan;ley Field, Ia.


C OUI DNT AL









14 CO0 TDENTIAL IACA ACR :Io. L5J29a


APPL-D IX A
,/ k2
DR-IVATIOI: OF Rk = 0.76 T--) Rgc
er 0r/ or


The parameter Rk may be thought of as a Reynolds
number based on the projection height and the boundary-
layer velocity at the top of the projection; that is,
uk
Rk =

For small values of y, the velocity u in the laminar
boj-indary layer may be expressed as a linear function
of y by
du
u =y


then
Sdu
Uk = k

so that
k2 du
Rk dy

In order that Rk may be more easily calculated,
the Dlasius relation (reference 11) for the slope of the
laminar boundary-layer velocity profile is introduced


u = 0.3352 (A2)
dy x A

The substitution of equation (A2) into the expression for
the projection Reynolds number gives


Rk = k20.2 (A5)
V ~x


C C:F i Di':7'AL








NACA ACEP. o. L5J29a


The Blasius expression
layer thickness, which
to the wing. surface at


(reference
is defined
u
whichh =
U


11) for tie boundary-
as the distance normal
0.707, is


2 5x
-


Since in equation (AS)


x .


eIuation (AS) may be .written as

k2
k = 0.7 6 '-


but


U


therefore


rp. = o.76L,-,-'
6


If the numerator and denominator are multiolied by 5
2
Rk = 0.76h ) (-

If 6 is taken as the boundary-layer thick:ncss just
before transition from laminar to tarliblent flour, then
i:6 is tLhs critical boundary-layer Rer-:olds number and
equation (AL) may be written as follows:

S.72
p Cr 0.76L.-. -) Rg (A
"ker 'cr'. Oc


1)


,)


CONFIDENTIAL


CO-FIDENT.IAL








'ACA ACR No. L5J2Qa


APPLEDIX B


DETB1C -'I NATIONN OF Rk, FROM EXPERI'.E!;IAL DATA


From equation (A5), it is seen that the values of R6
and 5 whric' correspond to the airfoil Reynolds number at
transition must be calculated. A suitable equation for 6
is obtained by assuming a Blasius velocity distribution
and integrating the von Kir:nan momentum relation. The
following equation results (reference 12):



U \ J \Uo7) c

A more convenient relation is obtained if equation (El)
is multiplied by R'


.2 p/Uo8.17 is/c 8.17 s
R r)2 = 5.0- 0 d- (B2)
i ,so \Uo

The numerical value of equation (D2) is a constant for
any chordwise position and need be calculated only once
for each position at which tests are being conducted.
The critical values of 6 and Rg may be calculated
from equation (B2) when the critical Reynolds number Rcr
has been experimentally determined. By definition,
U
R -
but
Uoc
"cr
therefore,
U
R' = --Rcr (B3)
Uc

The boundary-lay,-_r- thLickness is then obtained by dividing
t:le square root of R', as determin-d from equation (35),
into the constant 6/,'. In order to obtain R3, it is
only necessary to multiply 6 by R'. All the variables
in equation (A5) are now known, and Rkcr may be calculated.


COTIFIDE T IAL


CO ILr IDE NT IAL









I;ACA ACR iTo. L5J29a


DERIVATIOi1 OF


C CI IDE iIAL


AFPPEJlDIX C


/'- .555

Rcr


Si'-ce


2
or r r U r


then


R2

!,2C .7 l4


p,r
- 11


If both sides of equation (E11 arc mn.ltiplled

by 6or 'rc?/12 ) 3/2
bi


"2 r v c/2 R
V cr kcr
D.7. 64 1-


poto o t
b:ut o' r is
pc.3,_ticn so thiat


- /-j


o- r
r cr


5/2c /2
C.


= 3/2
o'r


constant for an-y riven chordwisJ


2/3

cr \ /..,
^=\J.


vjh coe


, o .'.
TJ 0.7o../


COITFIDE lTIAL


(Cl)


(3u
u


/ r-- 33\

- \ 1 :









18 COIIDE;TIAL I!ACA ACI No. L5J29a


RLE'ZhENCES

1. Abbott, Ira H., von Doenhoff, Albert E., and Stivers,
Louis ., Jr.: Summary of Airfoil Data. NACA
ACR No. L5005, 1945.

2. Abbott, .rank T., Jr., and Turner, Harold R.,' Jr.:
The Effects of Roughness at High Reynolds Numbers
on the Lift and Drag Ch.:asct eristics of Three Thick
Airfoils. I..CA ACER .,. L-L21, 19$4.

5. Fage, A.: The Effect of Harrow Spanwise Surface
Ridges on the Drag of a La!-inapr-Flow Aerofoil.
5950, Ae. 2019, British A.P.C., July 13, 191,2.

4. Fage, A.* The Effect of i!arrow Spanwise Surface
Riges on the Drag of a Laminar-Flow Aerofoil.
6126, Ae. 2019a, British A.R.C., Sept. 22, 1942.

5. Fage, A.: The Smallest Size of a Surface Bulge, a
Ridge or Hollow, Which Affects the Drag of a
Laminar-Flow Aerofoil. 6i45, Ae. 2148, British
A.R.C., Jan. 22, 1943.

6. Tan., Itiro, Hama, Ryosuke, and Mituisi, Satosi: On
the Permissible Rouighness in the Laminar Boi.nd'ry
Layer. Rep. 'o. 199 (vol. XV, 13), Aero. Res.
Inst., To:..yo Imperial Tniv., Oct. 1940.

7. von Dosnhoff, Albert E.: Investigation of the Boundary
Layer about a S-r. metrical Airfoil in a Wind Tannel
of Low Turbulence. L".C. ACR, Aug. 1940.

8. SciLubauer, G. B., and Skramstad, H. K.: Laminar-
Boundary-Layer Oscillations and Transition on a
Flat Plate. NACA ACR, April 195.

9. Tollmien, *;. The Production of '_':'u -ul ncr. AV.CA
T: *,!. 60o 1931.

10. Schiller, L.: Stromung in Rohren. Handbuch der
x-.olimentai:liv;ik Bd. IV, 4. -eil, Hydro- und
Aero';dna,]il.; Lidvrig Schiller, 3Irsg.; Akad.
Verl'.,,-gesellschaft m. b. 1. (LeirZig), 1952, p. 191.


C C '7T DE' T TAL









NACA ACR No. L5J29a


11. Frndtl, L.: Thae ;echanics of Viscous Tluids. The
lit Plate. Vol. III cf A.-i otAn-,l..ic fheory,
.iv. sec. I.L, V. c. -ur..nrd, co., Julius
--rringer (TBerlin), 1Q55, pp. j4-QO.

12. Jacobs, E. N., and von DoerL-inhof, E.: Fcrmr.1l3
for Use in floundLary-LaC.e Calculations on Low-
rM,., :.'ings. .i. AC -., A'i '19 1.


COn FTENr T IAL


:,; I TIAL






I:ACA ACR No. L5J29a


TAELZ I

CO!I:ATIONS OF SIZE AND CHORD.N'ISL LOCATION OF PROJECTIONS

TESTED WITH LOV-DRAG AIRFOILS 1 AND 2

Low-drag airfoil 1 Low-drag airfoil 2
Chordvise Diam. Height Chordwise Diam. i Height
location (in.) (in.) location (in.) (in.)


0.o0)
.o
.08


0.005
.010
.015


0.20c 0.035 0.009
.20c .035 .05
.20c .055 .020
.20c .055 .025
.20c .0j .025


0.010
.015
.020
.025


0.010
.015
.025
.050
.QLtO


0.05c
.05c
.05c
.050


0.20c
.20c
.20c
.20c
.20c
.20c
.20c
.20c
.20c
.20c


0.20c
.20c
.20c
.20c
.20c
.20c
.20c
.20c
.20c


.o3515
0.055
.035
.035
.055


0.055
.035
.035
.035
.055
.055
.055
.035
055
.05


I-- --- t-+ t-- 1-


0.015
.015
.015
.015
.015
.015
.015
.015
.015


0.010

.020
.025
.050


0.010
.011
.012
.015
.020
.025

.035
.040
050


0.015

.016
.018
.019
.021
.025
.25


o.650 0o.o5 o.01o o.50c 0.055 o.oo2
.650 .055 .015 .50c .055 .c25
.65c .055 .020 .50c .c35. .030
.65c .055 .025 .50c .055 1 .'5
.650 .055 .000 .50c .035 .
.65c .055 .05 .50c .055 .050
.65' .055 .oo i
.65c .035 .c!5 -5

'ATICl'.L ADVISORY
CC :::I"-TT FOR ,-.LONAUTiICS


CO0iiFIDEiiTIAL


0.0007c
.0007c
.0007c

0.058c
.058c
.058c


0.055
.055
.055


0.055
.055
.035
.o 355


o.55c
.35c
.35c
.35e


0.50c
.50c
.50c
.50c
.55c
.50c


0.035
.055
.055
.055


0.055
.055
.055
.055
.055


I


CO!TFIDE'T IAL








PIACA AC- io. LSJ2' a COrFFIDEi'.TIL 21

TABLE I I

F2?QCTS OF 'P -SURFAC. GRO' '.S 0; DR.'G' CrEAACTLF ISTTCS

OF LOi-DR.iO AIPFOIL 1



ircove description ,FLemarks I
----- -------I--C---__-_-- --
Sp"an ise :r-ve -ro ve 0. 0 J.i. io ."-)-asu.r:,ble increase in
deep n id 0.00C5 i,. wide Idrag o'er that of s:nooth
at .20,c wi 'n;g for- ranie of ;eyniolds
n .u.be from 5 10
to 10.7 >' 10

3nan,.'jise r'oc've 0 L,,'3 in.
deep and 0.010 .n. v.ie Do.
at .'C:c

j ,Spanw.i.se grooves O.l-'.. in.
deep and C0.0 10 in. ',ide Do.
E..t .C0Cc and C.ic.: .
--~ .--- 2-n.
Span-"nie gr-oves 0.0 in.
deen and 0.0'10 in. wide Do.
at .20c, i.-. %f c,
and 0.0c 1

Span.wise r-oove e. 00I in.
deep and O.C'l in. "'ide Do.
at ".05 :,c

Spant'ise .rccve ,J.CO. in.
deep an'd c.021 in. .'ide i Do.
at 0.C053
-- I----- --_ -
Grooves 0 .C ini. deep Premratiure transition indi-
and U.C') i. 'ide in c-,ted .;:- sudden increase
X:-plan; form at ir. dra- at a Reynolds
approx. ,.,0, :j ua. er of 6.5 x 1C6
(see fi f)


:JIIOL .AL ADVISORY
COa'.:ITTTi FOR -A Ci:A TICS


CO FIDEITIAL








NACA ACR No. L5J29a


TABLE III


S'r::0.F.Y OP DRAG RES'TjTS FROM TrLSTS OF LOSJ-DRAG AIRFOIL 1

FI-TIST D .'ITI! VARIOUS GRADES OF S~FDPAPZER

A iD CARBORUITDTM. PAPLR

All tests were tradee of low-drag airfoil 1 at Feynolds
numbers from approximately 5 x 106 to 10.57 x 10o6


Abrasive


No. 320
carborundum
paper



No. 520
carborundum
paper


Ch ord-: ise
extent of
roughness


0.7c to 0.Oc


Sanding
strokes


Parallel to


sanrea in windc
steps as direction
indicated ini
figure 5

-----do------ perpendicular
Sto wind
direction


Effect on
drag


No measurable
increase in
drag over
that of
smooth wing

Do.


------F------, -_ ------------------
No. 520 ----do------ 145 to wind Do.
carborundum direction
?, per

No. 280 -----do------ Parallel to Do.
carboru-.-,di.u i wind
p,alper direction


No. 280
carborundum
paper

No. 260
carborundum
paper


-----do------ Perpendicular
to wind
direction


Complete
surface


lErratic


Do.


Do.


NATIONAL ADVISORY
COC' ;ITTL. FOR A.-.OIAUTICS


CCO i-, .-mTIAL


------~----------i -----~- ------------C------


i ___t__-- ~ -- t-


~------ I--~L----


CONFIDENTIAL


!
I
I








IACA AC;?, 'o. L5729a


TABLE III Concluded


SUMrM."RY OF DRAG RESULTS FRO"' TESTS Concluded


Abrasive


-4-------


To0. Cl i Com rlete
carborundum surface


ise Sanding
of strokes
eSS
__I


i-rratic
I


paper



--. 120 d----do------ Cross-hatched
carborundum i (see fig. 4)
paper
-- .-- --i-* ___-
No. 120 -----do------ Circular
carborundm I (see fig. 4)
paper


1
To. 12

sandpaper


0.7c to 0.5c IPerpndicular
to wind
direction


----------
1 I
No. 1 .-----o------ Erratic

sandpaper .


NATIONAL ADVISORY
COMMITTEE FOP; AERONAUTICS


CONFIDEIT IAL


r
.
l


CO DNFID ;-;TIAL


Effect on
drag

--Hi

:o r.ieasura.ble
increase in
drag over
that of
smooth wing

Do.



Do.




Drag slightly
high at
Reynolds
number of

10.57 x 10

Do.

___J











NACA ACR No. L5J29a Fig.l














2.0 ,
I CONFIDENTIAL

o tUpper surface i-
+ wratr surface















%4 1.0














.2 COMMITTEE F06-A--MA S UT-




S1.. .2 .3 .5 .6 .8 .9 2.0
Chordwise station, z/o
Figure 1 .- Preasure distribution of low-drag airfoil 1 at a lift
coerricient of 0.347.
.8 ---- ---------------





NATIONAL ADVISORY



CONFIDENTIAL
0 .1 .2 .5 .J .5 .6 .7 .8 .9 1.0
Chordwise station, z/o
Figure 1 .- Pressure distribution or low-drag airfoil 1 at a lift
coerficient of 0.h7.








NACA ACR No. L5J29a


o Upper surface
+ Lower surface


CONFIDENTIAL I


-4






















NATIONAL ADVISORY
COMMITTEE FOR AIONAUTICS


CONFIDENTIAL
L I I I
) .1 .2 .3 .4 .5 .6 .7 .8 .9 z
Chordwiae station, x/o
Figure 2 .- Pressure distribution of low-drag airfoil 2 at a lift
coefficient of 0.


2W.


1.8



1.6



1.4



1.2



S1.0

0
0

5 .8


.6



.4



.2



0


Fig. 2







NACA ACR No. L5J29a Fig. 3
















o

S0
_j o0

O
0 w


0 0






0
o I a











(i
S o
s
o


0 it












S00
-4.



Id
1r-l
\ I < "
\~ 1 i-t
\ s l^

\ ^ I! :!
^^ .^r> B *f
^,^^ ^ ^
>C ^ Is
X s il .











NACA ACR No. L5J29a Fig. 4a,b


us







0 0












i a
to :


C,






o0
4-3















4 z-I
z


2 O


2 4O *
oO







0 a
544
0

4 3

10 0


C) N












NACA ACR No. L5J29a Fig. 5













a a










OUt

44 o

0o
O $




I oo

0






on
z





PO
0- E4

O4




0









Fig. 6 NACA ACR No. L5J29a





x
0


0a 0


z zO
OS *








r. *



za
z 0
z 0 *
tZ id I







-- a P
A el
-- -- --- -- _|- 0 '










o'






e+ r- *
----- ---- o


NO 0


\ 00 ^"




g \^ -i -
2 1 Z '4


PO 'aeoTOjjQOo Swap Unoroeg








NACA ACR No. L5J29a


.006
C

o o.oB
005 (in.)J
.06
.oo4 06 .o4






.001

0--
3.0 4.0 5.0 6.0 7.0 8.0 9.0

Reynolds number, R

1o (a) Projectionl of 0.035-inch diameter at 0.0007c.
aO


Fig. 7a-c



AL







..


.006- -
k
(in.)
.005o- 0.015
.010
.004-- .005


.00?


5.0 4.0 5.0 6.0 7.0 8.0 9 10.0o 1l. x 106

Reynolds number, R

(b) Projections of 0.035-inch diameter at 0.0580.


.006
Teat

.005- + 2
7 NATIONAL ADVISORY
.004 C-- ITTEE FI *, AMITICS




-n fl -
nn -- -- -- -- -- -- i -- / -


.001


4.0 5.0 6.0 7.0 8.0 9.0 10.0
Reynolds number, R
(c) Projections of 0.055-inch diameter and
0.009-inch height at 0.200.
Figure 7 .- Increment of section drag coefficient as a function of
Reynolds number for projections of various mimes and cbordwise
locations on low-drag airfoil 1.


1]


.0 x 106


CONFIDENTIAL


-a


o









Fig. 7d-f


.00 o I I I
Teat CONFIDENTIAL
o 1 ____
.ook - -
.005 --- -
+ 2



4003 L+




.001
.00 -__ ___



C' -^ -^ -- -


S 3.0


NACA ACR No. L5J29a


5.0 6.0 7.0 8.0 9.0 10.0 l1.ox 106
Reynolds number, R

(d) Projections of 0.035-inch diameter and
0.015-inch height at O.20e.


. U U b I 1 -

.005- Teat
e 1
+ 2
.00 --------- -- ------




.002 --

.001


3.o 4.0 5.0 6.0 7.0 8.o 9.0 10.0 11.


Reynolds number, R

(e) Projections of 0.035-inch diameter and
0.020-inch height at 0.20c.


5.0 6.0 7.0 8.0
Reynolds number, R


0 x 106


(f) Projections of 0.055-inch diameter at 0.20c.


F-ijre 7 .- Continued.


k Test
(in.)
o 0.025 1
+ .025 2
x .-02




NATIONAL ADVISORY
COMMITTEE FOA AIONAUTICS


CONFIDENTIAL
I I I


-1 .I......... 4 4.. J -


I I.


h


I t


9.0 10.0 11.0 106










NACA ACR No. L5J29a


.oo6


.005

.005

.003


.002


.001

0
3


Fig. 7g-i


k CONFIDENTIAL
(in.)
o 0.010
.015












.0 L.0 5.0 6.0 7.0 8.0 9.0 10.0 11.


Reynolds number, R

Projections of 0.035-inoh diameter at 0.55o.


5.0 6.0 7.0 8.0 9.0

Reynolas number, R

Projections of 0.055-inch diameter at 0.35c.


5.0 6.o 7.0 8.0 9.0
heynoiis rumLer, R

Projections or 0.0O5j-nch diameter at 0.50o.

Concluded.


10.0 11.0 x 10


,0 x 106


- k I-
(in.)
o 0.020
- *- --"02 -__-






__ __ < __ / __ __ __ __ __ __ __ __ q


.006


.005




.002



.001



0
5


0


.oo6
.006


.005




.003

.002


.001

0
5


lin.)
- e 0.010-
+ .015
S .02






NATIONAL ADVISORY
CONFIDENTIAL COMMITTEE FOR AERONAUTICS



~ ~~~ ~ ~~~~~~~~~~~ f^~ ~ ^^^^^^^^ 1 ^ ** o^ ~^^


.0


(1)

Figure 7.-


K


f~ IfLI I I i i [[-1 i:I I


-
.


10.0 11.0 x 10b


J










Fig. 8a-c


5.0 6.0 7.0 8.0 9.0
Reynolds number, R
Projections of 0.035-inch diameter at 0.05e.


NACA ACR No. L5J29a


11.0 x 10























11.0 i 06
--


Reynolds number, R

(b) Projections of 0.035-inch diameter at 0.20c.


k I
(in.) CONFIDENTIAL
o 0.025-
* .025
* .021 ___
.021
t .019
0 .018
A .016
& .016---------------------__
V 015 --- NATIONAL ADVISORY
S .01g COMMITTEE FM AELMAUTICS
.. .01


SI.


IJ247d~7


. 0 x 106


Reynolds number, R
(c) Projections of 0.015-inch diameter at 0.20c.
Figure 8 .- Increment of section drag coefficient as a function of
Reyn.:,is number for projections of various sizes and chordwise
locations on low-drag alrfoll 2.


Sk) CONFIDENTIAL
(in.)
15 -- o 0.015
+ .010









0 -
--

I5 -- -- --I= = B -- -- -

e -- -


5.0



0
44

4'.oo6
<-I
. .006
-
o

0
0 .004






0 .002 -
a

*
S.001 -
OL
g .001


0
a
1-4


.006
.oo6

.005

.004


.005

.002


.001


'"" "'


r


.


- 1









NACA ACR No. L5J29a


.5

-1.


.3

.2
.2




0




I
I





.24


m



.1


0


Fig. 9a,b


2.0 5.0 4.0 5.0 6.0
Rern:.lds rn moer, R
(a) Projections of 0.055-inch diameter at 0.50c.


i In.)

0 .040
.035
-- .030-
o .025
A .020
015 --
P .010


CONFIDENTIAL
f I


NATIONAL ADVISORY
coNNiTTEE FO ALMONAUTICS


2.0 5.0 4.0 5.0 6.0 7.0
Reynolds number, R
(b) Projectlons of 0.03-lnch diameter at 0.65c.
Figure 9 .- Boundary-layer tranaltion parameter as a function of
Reynolds number for low-drag airfoil 1 with projections of
various sizes and chordriae locations.


.r t


8.o 9.o0x 0


S (n.) CONFIDENTIAL
-- 0 0.0h0 --
+ .030 o
.025

IJ i ==--- -


..O 8.0 X00


"''''"'"'


1.0









Fig. lOa-c


NACA ACR No. L5J29a


1.0 2.0


4.0 5.0 6.0


7.0 8.0


Reynolds number, R
(a) Projections of 0.035-inch diameter at 0.05c.



k
(in.
o O.0o
--+ .035--
Z .030
S .021


1.0 2.0


3.0 4.0 5.0


6.0 7.0


8.0


-.Ox 106
0.ox 206


Reynolds number, R
(b) Projections of 0.035-inch diameter at 0.20c.



k
(in.)
0 0.050
+ 0' ---
= .035
El .030
.020

NATIONAL ADVISORY
CONNITTEE FOI AERONAUTICS

CONFIDENTIAL

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0x 1
Reynolds number, R
(c) Projections of 0.035-inch diameter at 0.50c.

Figure 10 .- Boundary-layer transition parameter as a function of
Reyricids number for low-drag airfoil 2 with projections of
various sizes and chordwise locations.


CONFIDENTIAL

(in.
S0 0.030
+ .025
x .020


5-.

S.6

5

9 .64




S.2


[.1
0

i


06










NACA ACR No. L5J29a


0N
o o0 0


*u g '8oSemg(oq .zjeT-Lzmpunog


Fig. 11


Lir b










0-


U -4 #-4
a










al. 0



0- O
.aI
-4 3











0 o









to







0-4 C
a 4 3-0
*P 0)








-i4



> a
a eo
o C
S >**
X;(>k
' en
*^ *VS













I (0 a
* 0) r-
o c






(mm
Ix.-








Fig. 12 NACA ACR No. L5J29a







0 -

,4 oc
O .. 0 I #1 .1 5
Q0 O Q- O


0 0 C 4

a a 2 1

(< 0 1 d& Z

SI 00ri
S0 0 -
S0 0
04+E 4[ .4 Al





+_ 0
Ow t


--2
W 0 0
SUa


--- --- --- --f --- -- ----- *(4

a- T-- *4



*o k
0 -'-4
O + Or0






--- -- I
0




0 0 0 0
0 0 0
P\ N H

Nu 'to~ovj jequinu sptou~eU jsLBT-LjvUDunoS
-- i -- f .








NACA ACR No. L5J29a


0 1.0 2.0 5.0 4.0 5.0 6.0 7.0


Critical Reynolds number, Rcr

(a) Projections at 0.0007c.


CONFIDENTIAL


0





----- Calculated
0 Experimental
\srzrz


8.0 9.0 10.ox 10


.U(

.06
6 --C-- calculated
+ Experimental
.05 -

S .04 -- -
-I04
-0 3
.: .05 -------- -- -- -- -- -
c \ NATIONAL ADVISORY
So COMMITTEE FOR AERONAUTICS
.02
0


CONFIDENTIAL
0 x 1 0 6
0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.3 10.0 x1o6
Critical Reynolds number, Rcr

(b) Projections at 0.058c.
Figure 13 .- Calculated and experimental values of maximum allowable
projection height as a function of Reynolds number for projections
of 0.055-inch diameter at various chordwise locations on a 90-inch-
chord model of low-drag airfoil 1.


"


Fig. 13a,b







NACA ACR No. L5J29a


1.0 2.0 3.0 4.0 5.0
Critical Reynolds


6.0 7.0 8.0
number, Rcr


9.0 l0.OX 10


) Projections at 0.20c.


.uo -
-- Calculated
B Experimental
.05


.04


03 -
SNATIONAL ADVISORY
L CONNITTEE FOR AERONAUTICS
.02 a_



CONFIDENTIAL
0 --I 1 I- 1 6
0 1.0 2.0 5.0 4.0 5.0 6.0 7.0 8.0 9.0 l0.ox 10
Critical Reynolds number, Rcr


(d) Projections at 0,35c.


I I I
CONFIDENTIAL

S----Calculated
K Experimental









I


Fig. 13c,d


6








NACA ACR No. L5J29a


Fig. 13e,f


CONFIDENT AL

--Calculated
0 Experimental














0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 l0.x 106
Critical Reynolds number, Rcr


(e) Projections at 0.50c.


1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Critical Reynolds number, Rcr


L


9.0 10.0 x 10


(f) Projections at 0.65c.


Figure 13 .- Concluded.


.04



4.3
* .02
0
a .02
.01

0


-Calculated
A Experimental



_---a ---I--I]IL I-
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS







CONFIDENTIAL
-. l l-








NACA ACR No. L5J29a


.02


.01


n


.06


.05


.04


.05


.02


.01

n


o i.o 2.0 5.0 4.0 5.0 6.0 7.0 8.0 9.0 1
Critical Reynolds number, Rcr
(a) Projections 0.055 inch in diameter at 0.05c.


0.0 x 106


0 1.0 2.0 5.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 x106
Critical Reynolds number, Rcr


(b) Projections 0.055 inch in diameter at 0.20c.
FIijre 14 .- Calculated and experimental values of maximum allowable
projection height as a function of Reynolds number for projections
at various chordwise locations on a 90-inch-chord model of low-drae
airfoil 2.


I I I
CONFIDENTIAL

---Calculated
o Experimental






0



0


--Calculated
\ + Experimental






NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS




CONFIDENTIAL


w


Fig. 14a,b


-


V








NACA ACR No. L5J29a


1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Critical Reynolds number, Rcr


9.0 10.0x 10


(c) Projections 0.015 inch in diameter at 0.20c.


0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 11
Critical Reynolds number, Rcr
(d) Projections 0.035 inch in diameter at 0.50c.


Figure 14 .- Concluded.


CONFIDENTIAL

-Calculated
u Experimental


\,-

\ s


--Calculated
0 Experimental



NATIONAL ADVISORY
COMMITTEE FOI AEOIIAUTICS







CONFIDENTIAL
S I I


0.0 x 106


f


Fig. 14c,d













Fig. 15 NACA ACR No. L5J29a





o
0


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0 0.
._
E -
0U 0














UN
*40. + *

N 4- 0

































oo
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0
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z 4z
L o( o, ( wr ca 0



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0 x0



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d Cd 0B *-
ss 00



a 'S.
ni 4-
NH S t.00.4?

c s.
















--,--


0 0 0 0

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UNIVERSITY OF FLORIDA
I11 11 l 111 lllll1n
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