Amer, Kenneth B

English

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RESEARCH MEMORANDUM 
https://ntrs.nasa.gov/search.jsp?R=19930085469 2020-06-17T14:51:46+00:00Z
S n  LAW TO DRAG DATA OF NACA 6- WINGS 
By Kenneth B . h e r  
In order to detemnine  the  usefulness  of one part  of Ton I&&' s 
two-dimensional  transonic  similarity law as a means of  correlating  and 
extrapolating  transonic  wing  data,  the law is.applied to drag data  of 
three  different  thickness  wings  having NACA 6-eries aectfons a d  
aspect  ratios  of 7.6 in the lhch number range *om 0.85 to 1.15. This 
L. portion of the law ststes that, for tw&imensiozlEtl airfoils of the 
1d02cDp 
sazw family in the tramonlc range at zero lift,  the  parameter 
(t/c) 513 
is only a function of the  parameter 
law *om the  potential-flow  equation ass- thin, two-dimamional 
bodies  with  local  velocities  not  much  different  from  sonic.  The  corre- 
lation of t h e  data  is  satisfactory,  being  somewbat  better  in  the  subsonfc 
range than in the supersmic range. The presence  of a st-ation  ppint, 
the  probable  presence of eepaxation  at  high  subsonic  speeds, and a finite 
aspect  ratfo  of 7.6, all of  which were not  considered in the  derivation 
of the law, did  not  appreciably  affect  the  degree  of  correlation. The 
presence of a boundary l ayer ,  which also was no5 considered in the 
derivation,  was  adequately  accounted f o r  by  assuming a reasonable  value 
of skin-friction drag coefficient. 
M, "1 Von K&& derived  thie 
(t/c)2/3' 
INTRODUCTION 
A reliable means of  correlating  and  extrapolating  transonic .Ri g 
data  would be extremely  useful. Dr. Theodore von K&m& has  developed 
theoretically f'rm the  potential-flaw  equation a two-dimensional  transonic 
similarity law f o r  thin  bodies  with  local  velocities only slightly 
diFferent from sonic. One part  of  this law states that for el1 thin tw- 
dimensional  airfoils  of  the stme family in the transonic  range  at zero 
2 - NACA RM No. L8F24 
lift,  the  parameter 
(t/c> 5 / 3  
is only a function  of  the 
parameter M, - Derivations  of  the  law are preserked  in  referenzes 1 
(t/c) 213 
ana 2. 
So far a8 is kown, the  only data available to  determFne  the uaef’ul” 
ne88 of this part of the l a w  -re  obtained  by  the freely-famng-body 
method and  presented in references 3 $0 5 .  Drag data in the  Mach nmber 
range from 0.85 to 1.15 are  presented in these references  for wins having 
aapecC ratios of 7.6 and 5.1 and three NACA 65-serim airfoil  sectiona, 
the 65-036, t he  65-009, and  the 651-0012. The egnolda nuniber of these testa, 
based  on t h e  chord, varied from about I x to about 5 X lo6 for  each 
wing. 
The derivation  of  the  similarity l a w  does not  take  into  account all 
details  of  the flaw about  these pmticulm wings. The derivation does 
not  account for the  fact  that he wings we of.finite span having  stag- 
nation  points, boundary layera, and probably some separation  at  hi& 
subsonlc ~peedB, have local  velocities w e l l  above sonic  at  the  higher 
transonic  Mach  numbers,  and  (although  the  airfoil  s6ctione. are of the 
same series)  their  thickness  dis,tributione ar  not exactly  proportional. 
In  this  paper, the  law  is  applied  to the available  data to determine 
the degree of  correlation  proCiuce!L by the law and to  indicate  which of 
the  unaccounted  for  factors in the flm. about the wings affected  the 
degree of  correlation  appreciably. 
CD total drag coefficient based on exposed p lan  area 
cDf  friction dra,g coefficient 
cDP pressure drag coefficient 
M, fiee-atream  Mach number 
t/c airfoil  thickness  ratio 
8 
NACA RM No. LBF24 3 
. 
RESULTS AND DISCUSSION 
Y 
The pressure drag parameter was calculated for the various 
(t  /c) 5/3
wings f r o m  the  continuous  curves of CD  against of references 3 to 5 
at  equal  increments of the  parameter M, "1 . Because  of  the  lack  of 
( t /c> 213 
any reliable  friction drag data in the  transonic  range, a friction dreg 
coefficient  of 0.006 was assumed far all  wing^. The  parameters for the 
three wiqp having an aspect  ratio  of 7.6 are  plotted in figure 1. m e  
daha are plotted aa individual  points  rather  than  as  continuous  curves 
for  clarity. 
In order  to  gain a quantitative  idea  of  what the deviations  shown 
in figure 1 mean in terms  'of drag coefficient and Mach  number,  the  faired 
curve  of  figure 1 waa used to  recompute a c m e  of C D ~  against M, for 
each  wing. Ln figure 2 these  curves a r e  ccanpared vith curves  of 
against M, computed frcm the  reference  data.  The eqerimental 
uncertainty in Mach  number  is  about w.01. At  the  highest  Mach  numbers 
tested,  the  experimental  uncertainty in Q) is  about a.0025 for  the 
12"percent"thick wing and about * .OOO5 for  the. hercent- and +percent- 
thick wings. The  uncertainties in drag coefficient  increase  somewhat 
as M, is  reduced.  The  uncertainty  in the a s m d  value  of C D ~  is 
probably  within  about %.OOl. Thus, the two curves  for  the hercent- 
and g-percent-thick a s  differ in the  subsonic  range  by less than  the 
maximm possible  uncertainties in the  experimental  data and skin-friction 
drag  coefficient.  The  difference  between  the two curves  for  the  12"percent- 
thick  wing  exceeds this uncertainty  slightly  at  about Mo = 0.98 because 
of  the  hump in the  experimental c v e .  *The difference  between  the  two 
curves  for  each w i n g  in the  supersonic  range is less than twice  the sum of 
the  experimental  uncertainty and the uncertain3 in the assumed value 
c% 
of %f* 
Apparently, In the  Elupersonic  range,  the similarity law does not 
entirely  correlate the effect of variations in thickness  ratio, and there 
is a consistent  variation  in  the drag parazneter  with thichess ratio. In 
figure 3 this  trend  is  compared with the  calculated  variations in drag 
parameter  for  circul-c  airfoils  of  the same thichess ratios  at  hi&er 
Mach  numbers  where  the  supersonic tspe of flow pattern is wholly established. 
The  circul-ceirfoil &ag coefficients  were  calculated  from  the  formula 
(formda 9.23, reference 6 )  
4 - NACA RM No. L8F24 
For the 12-percenMhick a i r f o i l  a t  a low supersonic Mach number, t h i s  
formula checked within a few percent a more accurate  calculation baaed 
on exact shock-xpansion relatione.  The plo ts  for these circular-rlrc 
a i r f o i l s  start at approximateu the Mach nmbers at which the shock 
waves became attached t o  the leading edges. These Mach numbers are 
about 1 . 3  for  the  hercent - th ick  a i r fo i l ,  1.4 f o r  the Wercent-thick 
a i r fo i l ,  and 1.6 for the 12-percent"thick airfoil.  
Flgure 3 shms that there is a ~pread of about 25 percent in the 
supersonic drag pmameters'for the c i r c u l n c   a i r f o i l s ,  which is due t o  
the f ac t  t h a t  the similari ty l a w  does not f i t  the actual flow conditions 
since the local  veloci t ies  axe not neazceonic. This spread is i n  the same 
direct ion as the spread of the experimantal drag parameters on the super- 
sonic side of the traneonic region. Therefore, the trend of the drag 
parameters with the thickness EIhm in   t he  experFmenta1 data indicate8 that, 
because the local  veloci t ies  are no longer ne-onic, the eimilari ty l a w  
correlates 1088 w e l l  a8 theMach number Fncreases above 1.0, and there is 
a gradual  transit ion  to the theoret ical   var ia t ion of the drag parameter 
with thickness  ra t io  in  the wholly supersonic regime of  flow. It appears 
tha t  an empirical  correction for this trend could be developed. 
The satisfactory correlation obtained by the m e  of the similarity 
l a w  indicates that the fac tors   in  the flow field not accounted for by 
the theory (other than the presence of local  veloci t ies  w e l l  above sonic 
at the higher Mach numbem) did not affect appreciably the degree of 
correlation; that is, the presence of a stagnation point, the probable 
presence of separation at high subsonic speeds, the  f in i te  aspec t  ra t io  
of 7.6, and the slight nonpraportionality of the thichess  dis t r ibut ion8 
did not appreciably af'fect the degree of correlation. The presence of a 
boundary layer was adequately accounted fo r  by a~tsuming a reuonable  
value of 8kin"friCtiOn coefficient.  
Limited data f o r  wings having aspect ratios of 5.1 are presented 
i n  figure 4. The data for the 9-ercent- and 12"percent-thick a i r f o i l s  
show a greater spread in the supersonic range than the corresponding 
u t a  of aspect  ra t io  7..6. These data indicate the des i rab i l i ty  of 
further investigation of the degree of correlation of low-a8pect-ratio 
data obtainable with V a n  K6rmsh' 8 similarity l a w .  
Application of one par t  of Von Kthrah 'e  two-dimensional. transonic 
similari ty law t o  d ~ w  data of W-6 having NACA 6 ~ 0 6 ,  65-009, 
and 651-0012 profi les  and a_spect r a t io s  of 7.6 i n  the Mach number range 
from 0.85 to 1.15 shows sat isfactory correlat ion which is somewhat 
be t te r  In the subsonic.range than in the supersonic range. The presence 
of a stagmtion point, the probable presence of separation at high 
. 
subsonic speed, and a f in i t e   a spec t   r a t io  of 7.6, all Q f  which were not 
considered i n  the derivation Df the law,  did not appreciably affect the 
degree of correlation. The presence of a boundmy layer, which also was 
not considered in the derivation, was  adequately accounted f o r  by assuming 
a reasonable value of skh-fr ic t ion drag coefficient.  
Langley Aeronautical  Laboratory 
National Advisory Cammittee f o r  Aeronautics 
Langley Field, Va. 
3. Mathews, Chaxles W., and Thompson, JimRogers: Drag Measurements at 
Transonic Speeda of NACA 634309 Air fo i l s  Mounted on a Freely 
Fal l ing Body t o  Determine the Effects of Sweepback and ABpect Ratio. 
MACA RM No I&08c, 1947. 
4. Thompson, Jim Rogers, and Marechner, Bernard. W.: Comparative D r a g  
Measurements at Tran80ni~ Speeds of an NACA 65-006 Air fo i l  and a 
Symmetrical Circ-c Airfoi l .  MACA RM NO. L6J30, 1947. 
5.  Thompson, Jim Rogers, and Mathewa, Charlea W. : Measurements of the 
Effects of Thicknesa Ratio and Aspect Ratio on the D r a g  of 
R e c t a n g u l d l m 4 i ' o m  A i r f o i l e  a t  Transonic Speeds. NACA FM 
No. LP08, 1947. 
6 .  Liepmann, Hans Wolfgang, and Puckett, Allen E.: Introduction t o  
Aerodynamics of a Compressible Fluid. John Wiley Sons, k c . ,  
1947 
. . .  . . . . 
- 
-. 8 0 .4 .6 
Mgure 1.- Transonic drag data (with CQ assumed = 0.008) for three m s  h a w  an NACA 66-series 
section and an aspect ratlo of 7.6 plotted according to Von K & d n 9 s  two-dimensional transonic 
similaritg law. _I 
. .  . . . .  . 
.. . . . . . . .  - . . . . . . . . . . .  
I 
. . . . . . . . . . . . . . . .  
c . ! 
“Expertmen fuJ . 
---Replot o f  
datu 
fared curve 
of fyure 1 
Mach number 
Figure 2.- Comparison between measured drag coefflcients (with C 9  assumed = 0.006) and pressure drag 
coefficients obtained from faired curve of figure 1. Aspect ratio of wings is 7.0. -
. .  
.~ .. ... . . .. . . 
Flgure 3.- Comparison between the measured effect of thickness ratio on wings having NACA 65-series 
sections and aspect raws of 7.6 in the transonic range and its calculated effect on circular-arc Moa 
sections in the supersonic range. -
. 
. .... 
4 
3 
2 
. . . . . . .  . . . . I 
4 
Figure 4.- Transonic drag data (with Cq asumed = 0.00s) for two wlngs havlng an NACA 66-series 
section and an aspect ratio of 5.1 plotted according to Von &'s two-dimensional transonic 
similarity law. -
. .. . 
C 
P 


Application of one part of Von Karman's two-dimensional transonic similarity law to drag data of NACA 65-series wings

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