Tables and charts for the evaluation of profile drag from wake surveys at high subsonic speeds

) 1
lVAC A-L" IC"


RB No. L5Fl5a


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WAR' iTI ME IRE PORT
ORIGINALLY ISSUED
July 1945 as
Restricted Bulletin L5F15a

TABLES AND CHARTS FOR THE EVALUATION OF
PROFILE DRAG FROM WAKE SURVEYS AT
HIGH SUBSONIC SPEEDS
By Myron J. Block and. S. Katzoff

Langley Memorial Aeronautical Laboratory
Langley Field, Va.







NACA


WASHINGTON
NACA WARTIME REPORTS are reprints of papersoriginally 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 107


DOCUMENTS DEPART MiNl I


A
:...... .. ...=. ... ... .... .. ..... .




Yr



















































I..







NACA RB N.o. L5?15a

NATIONAL ADVISORY COMMIrTTEE FOR AEROFAUTICS


RESTRICTED BULLETIN

TABLES AND Ch .RTS FOR TPE EVALUATION OF

PR07TLE DRAG 7ROM '.VAKE SIRVEY nT

HIGH SU?.T)NiIC SPEEDS

By 'Tyrron J. Block and S. Katzoff


SUMMARY


Tables and charts for the evaluation of profile drag
from ;wake surveys at h-igh subsonic speeds are presented.
These tables and charts are for use with two methods of
evaluation, an exact method that may be applied to wakes
of any sr.ape and a simple approximate method that may be
aoplied when the variation of total-pressure loss across
the wake has the typical form (resembling a cycle of a
cosine-squared curve).


INTRODUCTION


As an aid in the determination of profile drag from
wake surveys at high subsonic speeds, tables and charts
have been prepared to minimize the computational labor
involved. These tables and charts are presented herein,
together with a brief discussion of their application.
The data are for both the approximate method of refer-
ence 1, which simply applies a correction factor to the
integral of the total-pressure loss across the wake, and
the exact ooint-by-point method, for use when the distri-
bution of total-pressure loss across the wake does not
follow the typical pattern. The data for both methods
are for Mach numbers up to 1.0.


? Y,"BOLS


c chord


d drag per unit span










2 il.-Cr RB ND. L5F15a


cdo section profile-drag coefficient Qpd-o2)

F factor for evaluation of drag coefficient by
approximate method

H total pressure

M :iach number

p static pressure

V velocity

w thickness of wake

y distance across wake

p density

Subscripts:

o free stream

1 at plane of measurement

max maximum


THEORY AID METHOD


The basic theory of the use of wake surveys for the
measurement of wing profile drag has been largely dis-
cussed in previous literature (for example, reference 2).
No further discussion of the equations used will there-
fore be given, except to note that the ratio of specific
heats for air was taken as 1.40.L Theoretical and experi-
mental studies have confirmed that the basic assu.motions -
for example, that essentially streamline flow exists in
the wake inv.'nstream of the measuring station :nd that
the stagnation teroperature in the wake is the same as in
the free stream are accurate or are satisfactory .oproxi-
mations to the actual conditions. Zrrors are more likely
to arise from sources of a less fun',._A;ental nature, such
as from cross flows of the wing boundary layer, which
may confuse the relation between the wake at a certain
span.riise station and the profile Crag of the wing at that










NACA RB .Ho. L5FP5a


station, or fr>m so high a decree of turbulence in the
wake (as behind a flap) that both the method and the
pressure readings are invalid.


CHARTS AND TABLES FOR POINT-BY-POINT CALCULATIONS


The flight Mach number MI and the flight impact
pressure Ho P0 are assumed to be known, in addition
to the values of total-pressure deficiency Ho H1 and
of static-oressure rise pl Po at points in the wake.
Table I and figure 1 give the factor

d (cdo) Ho H1
dy / Ho Po

or

Drag per unit span per unit thickness of wake/ H HI
1 2 k Ho PO
EPoVo

Ho HI P1 Po
as a function of M, and 0. Multiplying
Ho Po Ho Po
this factor by the fractional loss of impact pressure at
Ho Hl
a point in the wake H0 gives the value of ccdo,
Ho Po
which corresponds to unit thickness of wake at that point.
Integration of this value across the wake gives ccod
for the section.

The values given herein were computed in some detail
for Mo = 0, 0.2, 0.4, 0.6, 0.8, and 1.0, and for
pl PO
H0 = -0.1, 0, 0.1, and 0.2. The.values for other
Ho PO
Mach numbers and pressure ratios were found-by interpo-
lation and numerous calculated checks were made. The
factors are accurate within 0.002.









AIrIC RB No. L5Fl5a


CHARTS FOR APPROXIMATE METHOD


\?ien the distribution of total-pressure loss across
the wake follows the typical pattern, profile drag can
be obtained with good accuracy by a relatively simple
method (reference 1). In this method, the drag is deter-
mined directly from the product of the integral of total-
1Ho H1
pressure loss across the wake f ---H dy and a fac-
SHo P
tor F, which is a function of the maximum total-pressure
loss in the wake, the average static pressure in the wake,
and the flight Mach number; thus,


/ccd Ho y

w


where F is a function of -----,
Poa0 Ho P0
max
and JM. In practice the integral is obtained either by
use of an integrating manometer or by actual integration
of point-by-point measurements of Ho H1 in the wake.

Values of F are plotted in figure 2. The values
were computed by assuming that the total-pressure loss
across the wake had a cosine-squared distribution

Ho H1 H HI 2 AYl w w
Ho -o cos Po w 2 = =
max

and by dividing the value of ccao, as computed by the
P Ho H1
point-by-point method, by the value of jHo l dyl"
H Ho ~ Po
Figure 2, which gives P directly for Each numbers
from 0 to 1.0, is considerably more convenient to use than
the data of reference 1, which gives F directly only
for Mo = 0 and includes a table of corrections for
values of Mo other than zero. It should be pointed








NACA R3 No. L5F15a 5


out further that the correction table of reference 1
contains some systematic errors that are appreciable at
high W'ach numbers. The results presented herein are
considered accurate (for an exact cosine-squared profile)
to about 0.2 percent.

Although this simplified procedure can greatly
expedite the computation of wing profile drag, its appli-
cation definitely requires that the wake profile bear a
reasonable resemblance to the assumed cosine-squared
profile, especially for wakes with large values of
(H -- H Even with an appreciable deformity from
o P/max
the usual profile, however, the error in the use of this
method will hardly exceed 2 percent. As in the case of
a shock where the wake profile shows a relatively narrow
peak superimposed on a broad base (fig. 5), the error,
however, may easily become excessive. When point-by-
point measurements in the wake are available, accuracy
can be retained in such a case by considering the wake
in two parts, as indicated in figure 5; each part shows
a satisfactory approximation to a cosine-squared profile
but each has a different value of 0--
Ho po
max


RELATED CHARTS


Another paper (reference 3) has been prepared that
gives results related to those given in the present paper.
In reference 3, charts are given of the ratio of F for
compressible flow to P for incompressible flow for Mach
numbers to 1.0, for values of P1 Pc from -0.4 to 0.1,
Ho Po

and for values of .( from 0 to 0.7. A sepa-
m- PO/ax
rate chart is given of F for incompressible flow.


Langley Memorial Aeronauti-cal Laboratory
National Advisory Committee for Aeronautics
Langley Field4 Va.








NACA RB No. L5F15a


REEFERE.:CCS

1. Silverstein, A., and Katzoff, S.: A Simplified !M.ethod
for Deter, iin. I ing Profile Drag in Plight. Jour.
Aero. Sci., vol. 7, no. 7, May 1940, pp. 295-501.

2. Davis, WValsce F.: Comparison of Various !ethods for
Cor:puting Drf- fr-r. ",a.':e Surveys. -iACA ARR, Jan.
1945.
5. Heaslet, Max A.: Theoretical Investigation of Methods
for Cor..u. ting Drag from "Vake Surveys at High Sub-
sonic Speeds. 'MACA ARR No. 5C21, 1915.





The authors wish to cell attention to the following
related paper:

Baals, Donald D., and ':ourhais, Yary J.: Nlu.ierical Evalu-
ation of the t.7ake-Survey -quations for Subsonic Flow
Including the Effect of Energy Addition. ::ACA AR.'
-o. L5H2S7, 1945

which has appeared since publication of the present bulletin.
The tables and charts of this related paper, which is
concerned only with the point-by-point method, are for use
not only with flows of constant total energy, as in normal
wakes, but also .2'th flows of increase i total energy, as
in wakes of pro,-llers and jet-propulsion units. Total-
r.r-soure and static-pressure coefficients are b:.zed zn

-PoV2 instead of on H p as in the present bulletin.
7PO o PO











NACA RB No. L5F15a




TABLE I.- VALUES OF E -I to FOR EVALUATION

or PROiLZ IRAG PFRCM WAKE suRVEY


-, = 0


Po .
B ,o -0100 -o.loo0-0.075 -0.050 -0.025 o 0.025 0.050 0.075 0.100 0.125 0.150 0.175 oG2oo
so I I


025
.050
075,
.100
.125
.150
175
.200
225
.250
.275
300
V5oo

550
.575
1oo00
.1L25
.1.50
4175
.500
525
550
.575
.600
.625
.650
675
700
725
.750
.775
.800
.825
.B50
.875
.900
.925
.950
975
1.000


1.048
1 L0b3
1.058
1.052
1.026
1.020
1.01L
1.008


995
.988
981
.971.
.967

959
.951
91.5
.955
.926
.917
.908
.8981
.888
.877
.866
.855
.8.3
.850
.817
.803
.789
.773
.757
.71.0
.721
.701
.679
657
655
.610
.632


1.012
1.006
1.000
.995
.987
.980
.973
.966

.959
.951
.943
-935
.927
.919
.910
.901
.891
.881
.871
.860
8149
.837
.825
.812
.799
.785
.770

.754
.737
.719
.699
.678
.655
.631
.604
.572
.536
.496


.386
.316


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS




































Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/tableschar-stor eOiang









NACA RB No. L5F15a


d(co) H/.o Jl
TABLE I.- VALUS .0P FOR EVALUATION
O PROIL A ROM WAE SURVEY Po ntod
0? PROFILE riu. FUCE *AIEX SURVEY coatimnu.


us 0.1
Pl Po
Bo PO -0.100 -0.075 -0o.o050 -0.025 0 0.025 0.050 0.075 0.100 0.125 o.150 0.175 0.200
HO PO

o 1.042 1.029 1.018 1.005 0.993 0.981 0.968 0.956 0.945 0.951 0.917 0.904 0.890
.025 1.037 1.024 1.013 .999 .987 .974 .961 .949 .936 .923 .910 .896 .882
.050 1.031 1.018 1.007 .994 .980 .968 .'955 .942 .929 .915 .902 .887 .873
075 1.025 1.013 1.001 .988 .973 .962 .948 .935 .921 .908 .894 ,879 .864
.100 1.019 1.007 .994 .981 .967 .954 .941 .927 .914 .899 .885 .870 .855
.225 1 014 1.001 .988 .975 .961 .947 .933 .919 .905 .890 .876 .860 .845
50 1.oo08 .996 .982 .969 .954 .940 .925 .911 .896 .881 .867 .851 .835
.175 1.002 .989 .975 .962 .947 .932 .918 .903 .888 .873 .858 .842 .825
.200 .995 .981 .968 .954 .939 .925 .910 .894 .879 .865 .848 .832 .815
.225 .989 .975 .961 .947 .931 .916 .901 .886 .871 .854 .838 .821 .804
.250 983 .969 .954 .939 .923 .908 .893 .877 .862 .845 .828 .810 .792
.275 .976 .963 .946 .932 .915 .899 .883 .867 .852 .833 .817 .799 .780
3oo 969 .955 .958 .923 .906 .890 .874 .857 .841 .823 .805 .787 .768
.525 962 .947 .950 .914 .898 .881 .864 .847 .829 .812 .795 .774 .755
-350 .955 .939 .922 -905 .889 .871 .853 .836 .818 .799 -780 .761 .741
.375 .947 .930 .915 .896 .879 .861 .843 .824 .806 .786 .767 .747 .727
.400 .939 .921 .904 .887 .870 .850 .853 .812 .793 .775 .753 .752 .712
.425 .931 .913 .895 -877 .860 .840 .821 .801 .781 .760 .739 .718 .695
.450 .925 .905 .886 .868 .849 .829 .809 .789 .768 .747 .725 .702 .679
475 .915 .895 .876 .857 .838 .818 .797 .776 .754 .732 .709 .685 .661
.500 .906 .886 .8A6 .846 .8a6 .805 .784 .76a .740 .716 .692 .666 .42
.525 896 .876 .855 .835 .814 .792 .770 .747 .724 .699 .674 .647 .620
.550 .886 .866 .844 .824 .801 .779 .756 -.72 .707 .680 .654 .627 .598
.575 .875 .855 .852 .811 .788 .764 .740 .715 .689 .661 .653 .604 .574
.600 .864 .844 .820 .797 -773 .749 -724 .697 .671 .640 .611 .580 .548
.625 .853 .851 .807 .783 .758 .732 .706 .677 .650 .619 .586 .556 .520
.650 .841 .818 .794 .769 .7k2 .715 .686 .657 .628 .595 .5.0 .525 .488
.675 .829 .804 .779 .752 .725 .696 .666 .635 .604 .570 .551 .493 .450
.700 .815 .789 .763 .734 .706 .676 .644 .612 .577 .540 .500 .457 .409
.725 .802 .775 .747 .716 .686 .654 .620 .586 .549 .508 .464 .415 .362
.750 .788 .759 .729 .697 .665 .651 .594 -557 .515 .472 .422 .367 .298
.775 .773 .743 .710 .676 .643 .604 .565 .525 .479 .450 .372 .304 .21)
.800 .7S7 .725 .691 .65i .618 .577 .53h .688 .457 .378 .310 .218 0


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS










NACA RB No. L5Fl5a


d(coda) /E6* 1
TABLE I.- VALUES OP -dy (O O/ R EVALUATION

OP PROFILE DRAG PRCO WAXE SURVEY Continued


M, = 0.2
-IPI PO

Bo B -0.100 -0.075 -0.050 -0.025 0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200


0
.025
.050
.075
.100
.125
.150
.175
.200
.225
.250
*275
.300
.325
.350
.550
. 75
.1oo00
.1425
.450
.475
.500
.525
.559
.575
.600
.625
.650
.675
.700
.725
.750
.775
.800
.825
.850
.875
.900
.925
.950
.975
1.000


.501 .213
.218 0


NATIONAL ADVISORY
COMITTRE FOR AERONAUTICS









NACA RB No. L5F15a



TABLE I.- VALUSo -O / FOR ,VALVRTION

or Pr'iLs wtas FR M waI saiRV Continued


No x 0.5
S P C" o
10p -o -o.1ou -o.o07 -0.050 -0.025 0 0.025 0. 075 0.100 o.a5S 0.150 0.175 0.200
B__ O_.


NATIONAL ADVISORY
COMMITT FOR AERONAUTICS










NACA RB No. L5F15a


d(<*do) /RO HI
TABLE 1. VALUM O / OR iVALcATION
OPy / PROP R ConnuO
OP PnoPrzL M&O FoR WA*u HUIVlT continauo


Mo = *

o Po
-0 PO -o o00 -0.075 -0.050 -0.025 0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
ra pa_ _______.


0.965
.959
.956
.951
.947
.942
.957
.951
.926
.921
.916
.909
.905
.897
.891
.884
.878
.871
.863
.856
.848
.840
.852
.825
.813
.802
.791
.779
.766
.753
.728
.723
.707
.689
.671
.6148
.625
.599
.571
.5142
.5147


.350 .247
.260 o


0.901 0.89010.879 0.868 0.857 0.845


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS









NACA RB No. L5F15a


d(col6) /Ho P L
TABLE .- VALUES OF --P-/ -- FOR IVALUh.TIo
dy j o Po
OF 1IOPIL2 MtAO PKE WAKE SURVVT Continued


"o = 0.5
Po Po
B e'. -0.100 -0.075 -0.050 -0.025 0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
Ho Po _

a 0.9532 0.925 0.915 0.906 D.898 0.888 0.878 0.870 0.860 0.850 0.840 0.829 0.817
.025 .929 .921 .912 .903 .894 .884 .874 .865 .855 84 .854 .8 .825 811
050 .926 .917 .908 .899 .890 .880 .870 .860 .850 .858 .828 .817 .805
.075 .925 .915 .904 .895 .886 .875 .865 .854 .844 .832 .822 .809 .798
.100 .920 .909 .900 .890 .882 .870 .86o .848 .858 .827 .816 .805 .791
.125 .916 .905 .896 .885 .877 .86M .855 .842 .832 .820o .809 .797 .784
.150 .912 .902 .892 .881 .872 .860 .850 .857 .826 .814 .802 .790 .776
.175 .908 .898 .888 .877 .867 .856 .844 .852 .820 .809 .795 .783 .768
.200 .904 .895 .884 .873 .862 .851 .838 .827 .814 .802 .788 .775 .760
.225 .goo .890 .879 .868 .857 .846 .832 .821 .807 .794 .780 .767 .751
.250 .896 .886 .874 .863 .851 .859 .825 .814 .799 .786 .772 .757 .74,2
275 .891 .880 .869 .857 .845 .8352 .818 .806 .791 .777 .765 .747 .7355
.oo00 .887 .875 .865 .850 .859 .824 .811 .797 .783 .768 .754 .738 .723
.525 .882 .870 .857 .814 .832 .818 .8o4 .789 .774 .761 .744 .729 .712
.550 .878 .865 .851 .859 .825 .811 .796 .782 .765 .752 .734 .718 .700
575 .873 .859 84,5 .832 .818 .805 .788 .773 .756 .741 .723 .707 .688
.Loo .867 .853 .859 .824 .811 .795 .780 .74 .746 .731 .712 .696 .675
.125 .861 .847 .833 .818 .803 .787 .771 .753 .735 .718 .699 .682 .662
1.50 .855 .841 .826 .811 .795 .779 .762 .741 .724 .706 .686 .667 .64E8
.L75 .849 .834 .818 .80o .786 .769 .751 .732 .713 .693 .675 .652 .651
.500 .845 .827 .810 .795 .777 .759 .740 .722 .701 .680 .659 .637 .614
525 .856 .819 .802 .786 .768 .748 .729 .709 .688 .667 .644 .621 .596
.550 .829 .812 .794 .776 .758 .738 .716 .696 .674 .652 .628 .6o0 .576
.575 .822 .804 .785 .765 .747 .726 .704 .682 .657 .64 .609 .58 .584 555
600 .814 .795 .775 .755 .755 .712 .690 .667 .640 .616 .588 .561 .531
.625 .805 .784 .764 .745 .722 .699 .674 .649 .623 .596 .567 .536 .505
650 .796 .774 .753 .751 .708 .684 .658 .633 .6o04 .576 .543 .511 .475
.675 .786 .765 .741 .717 .692 .667 .640 .615 .583 .552 .518 .482 .440o
.700 .775 .751 .72B .705 .676 .650 .622 .592 .56o .525 .487 .447 01
.725 .764 .738 .715 .686 .659 .631 .601 .568 .533 .496 .454 .407 .355
.750 .755 .725 .699 .669 .641 .609 -579 .541 .502 .461 .413 .360 .292
.775 .740 .712 .685 .652 .621 .587 .553 .512 .469 .419 .566 .298 .211
.8oo .727 .698 .666 .654 .599 .562 .522 .77 .428 .572 .505 .215 0
.825 .712 .681 .647 .611 .574 .552 .487 .580 .312 .220 0
.850 .696 .665 .626 .587 .546 .499 .448 .388 .519 .225 0
.875 .679 .641 .602 .557 .512 .459 .597 .328 .232 0
.900 .662 .619 .575 .524 .472 .410 .337 .259 0
925 .642 .594 .545 .487 .424 .550 .247 0
.950 .620 .566 .506 .159 .565 .259 o
.V75 .600 .559 .468 .376 .273 0
1.000 .650 .547 .447 .517 0


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS











NACA RB No. L5F15a


TABLE I. VALUES O? No OR F EVAL UAzTIO
d Bo Po ue
OP PROFILE DRAG PROM WAKE 3RVEY Continued


P Io = 0.6

H ,- Po
S "1 -0.10 0 -o 075 -o.o0 -o.O5 o 0 .025 0.050 0.075 o 100 o.125 0.15 o 175 0.200
no Po "


.025
.050
.075
.100
125
.150
.175
.200
.225
.250
.275
.500
.525
550
.575
.Loo
.L25
.150
..75
.500
.525
.550
.575
.600
.625
.650
.675
.700
.725
.750
.775
.800
.625
.850

.875
.900
.925

.950
975
1.000


0.877
.875
.872
.869
.867

.864
.861
.858
.855
852
.848
.81.5
.8)1
.857
.852
.827
8.623
.818
812
.806
.o00

.791
.787
779
.772
.761
755
.7.5
755
.725
.712
.698
.6B4
.670
.654
.635
.61.1
569

565
.557
.547


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS










NACA RB No. L5Fl5a 14



(cdo>)/Ho 81
TABLE I.- VALUES OPF o / 1F/OR EVALUATION

OF PROFILE DRAO PROM WAKE SURVEY Continued


.o = 0.7
PI P,
H"- p0
s. -o0.100 0.075 -0.050 -0.025 0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
Ho Po 1 -0 0 0 0.5


NATIONAL ADVISORY
CCEMITTEE FOR AERONAUTICS











NACA RB No. L5Fl5a



d(cco) /Ho BI
TABLE I.- VALUES OP --"/. FOR EVALUATION

OP PROFILE DRAG PROM WARE SURVEY Continued



Mi 0.8

-0 P-o

E-. 8 -0.100o -0.075 -0.050 -0.025 0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
Eo Po


.025
.050
.075
.100
.125
.150
. 175
.200
.225
.250
.275
.500
.325
S550

.375
.I400
.L25
.450
.1.75
.500
.525
.550
.575
.600
.625
.650
.675
.700
.725
.750
.775
.800
825
.850
.875
.900
.925
.950
.975
1 000


.375 .271
.320 0


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS










NACA RB No. L5F15a


d(eoq) /ao 1
TABL I.- VALUES O FOR EVALUATION

OP PROFILE 1AG ROM WAZZ SURVE! Continued


go = 0.9


B II
Ho p'. -0.100 -0.075 -0.050 -0.025 0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200
E0 0 *.


.025
.050
075
.100
.125
.150
.175
.200


.250
275
300
.525
.350
575
.4i00
.L25
.L.50
.175
.500
.525
.550
.575
600
.625
.650
.675
. .700
.725
.750
.775
.8oo
.825
.850
.875
.900
.925
.950
.975
1.000


0.724
.724
.724
.724
.723
.723
.722
.722
.722
.722
.720
.720
.719
.718
.716
.714
.712
.710
.708
.706
.703
.699
.696
.693
.688
.6846
.679
.674
.667
.660
.653
.644
.635
.624
.611
.596
.581
.563
.542
.523
.545


.427 .353 .254
.373 .272 0
.321 0


1sATI OAL ADVI1aoR
COMIITT FOR 0AIRONAMTICS


.25 .232
.24210o










NACA RB No. L5F15a




TABLE I.- VALUES OF -- / Po FOR EVALUATION
dy / Ho P0o

OP PROFILE IDAO PROM WAKE SURVEY Concluded


mo = 1.0


Z Pi Po

E6 p0

so -Po


.025
.050
.075
.100
.125
.150
.175
.200
.225
.250
.275
.300
.325
.350
.375
.400
.425
.450
.475
.500
.525
.550
.575
.600
.625
.650
.675
.700
.725
.750
.775
.800
.825
.850
-875
.9oo
.925
.950
.975
1.000


-0.100



0.669
.670
.671
.671
.672
.674
.674
.675
.675
.675
.675
.675
.675
.675
.675
.675
.674
.674
.673
.672
.671
.669
.667
.665
.664
.661
.658
.655
.652
.648
.644
.638
.633
.625
.618
.609o
.600!
.590;
.580,
.572
.619


-0.075 -



0.672
.672
.673
.672
.673
.674
.674
.674
.673
.674
.673
.673
.673
.673
.673
.672
.670
.670
.669
.666
.665
.662
.660
.657
.655
.652
.648
.645
.640
.6351
.628
.621
.614
.604!
.5953
.581
.567
.553
.555
.518


.0.050


-0.025 0 0.025



0.674 D.673 0.673
.674 .673 .673
.674 .675 .673
.672 .672 .672
.672 .672 .671
.672 .671 .669
.672 .671 .668
.672 .670 .668
.672 .670 .667
.672 .669 .667
.670 .668 .665
.670 .666 .663
.669 .665 .661
.667 .663 .659
.666 .662 .657
.665 .660 .654
.662 .657 .651
.660 .655 .648
.658 .652 .644
.655 .648 .640
.652 .645 .635
.648 .64o .630
.645 .636 .624
.649 .651 .619
.656 .625 .613
.630 .620 .605
.625 .613 .597
.619 .605 .587
.611 '.595 .576
.603 .585 .563
.593, .573 .550
.582 .560 .535
.569 .544 .517
.595 .525 .493
.535 .502 .466
.515 .479 .432
.490 .443 .390
La7 .40o7 .336
.420 352 .253
.372 .270 0
-322 0


0.050 0.075 o.10oo0



0.672 0.671 0.669
.672 .670 .668


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


0.1751


0.662


0.125 0.150



0.667 0.665
.666 .663
.665 .662
.663 .660
.662 .658
.660 .655
.657 .655
.655 .650
.651 .646
.648 .643
.646 .640
.645 .636
.659 .651
.635 .627
.650 .621
.625 .616
.620 .610
.614 .603
.608 .596
.601 .588
.592 .578
.583 .567
.573 .556
.562 .543
.549 .528
.555 .512
.520 .493
.500 .471
.477 .447
.454 .418
.427 .385
.394 .ML6
.353 .292
.298 .213
.218 0
0 1


0.200



0.659
.658
.655
.652
.649
.646
.645
.658
.635
.650
.626
.620
.615
.609
.602
.595
.587
.579
.569
.558
.547
.534
.519
.50?
.484
.461

.455
.405
.370


.280
.204
0








NACA RB No. L5F15a


ktElt:i -:-


-:--- -r !- s f i r : : i I__, -i_ T--1 -7 7-- _
4F FIF.: Iq a~-. :.il 1 .:i i l ~ ,. .
:.--- t+ -r~ i1;-t. t .-; -'- -:.--- :.t, -:I i -! 1 l: I t-1 .: :l: i t-t.:: -. : -i-.,. W :


-i- .-- "i __










----*AT.O _,15-:1
----- coNr r u -






















: -.' ^i ure r a 'r fur ev tda cr. c f c ofl l- ri fr ru -iir Fir ec r..a,. r F .:il j c as l retr~j] _
i_ U T T
Or r

















i~~~ -V ---


--I--: --t I -


II .. ... L:A .-


.o~TE r-- -~ ~ yc -- t A



14 V- _4 .........

ure i -,ir s f rf r o i a a r I' t -


Fig. la








NACA RB No. L5F15a


*4--- hr I -I-


I -- 1 4-1 -[ 1 L 1- 4-


== -- -~ ~ ~~~~----- --- --- ---^ S l- S .':!a* L -

=i-^ *". ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -- ------ -i^ a c a ^ -^ ^ ^- :; i ... -



-- ------- -- --- -
I \
:-: ^ -3 ----;-- -^r -.-- ---.^ E Sg si e is i^ S ea l sat S ,!; l
i~ :, ,

33 :I m

fE --,z



1 We
.z 4f: .~ IF.


.I- s
-1, -7 : -404iA,
-^^^Ls~~~~.-! i=...2:~gil i~ 1 ._-^ ^.; p ^ |











^^^^'^^ ^^Z^ *^ __:;; NATIONAL ADVISORY ^ s._''~ ^:-S "^\ *- -3 -3 LL
A -- --- -
-. 7
--a=- z~:i-- Ar.


C i IJ nue. 1.


4iz1jL~Izh41ju1


i;~ih~'i44f4izIzz~


4--44


- ;- : -- -- -- -- I I --- "r -


- i
,1- .=--


Fig. lb


il


.:PT IL- -^444-tq


^r-- l- j,- I-,-'-;-P HFp--


r L I L-41


-
E- 1-


h-r^


ffls


--I- l.' .!


LL "-- [;












FplH


V


NACA RB No. L5F15a


_ _..,_ I I_-L_-_ i IIt._L -L-


I
A _L AVI






A i iI I .. .. .I
I I







. --! -' ''. i 3 \ -! i -







I I (I __ I -
I i i







liii


Fig. ic







NACA RB No. L5F15a


--- --- T ---- -- --- -- I jT 14












aI
[VT



















---H 4 I i






.-- ---- --
S-H- --J- _-__+_ ~ '-__- __^- + -, -4------- -- i









=71



Z- F I ', ir _
1 = 31-: -I ; ---^-- f- ^ ^^-m ,-E wfownc ;


Fig. Id







NACA RB No. L5Fl5a


I I I i I F I -I ,
" I-. ..-, 4. .. ..[ .. .. .., .. .. .. .. -T I... .i..... .. ,_


_ ... ..... ...........I ...


..~ n": _.~-~ i i I :-' 7 T{71 I 17'7 4 ,,


II -.42^ ^ """^^^^"!^^:^!





~in
:i I!, I l i. i






-i i. N
_ --.-- -- .--- .. .. .. .. ... i-- ; .- .... i --- .- -* ... 1- -- l- -t --_.. ..... ^ _1- l -- _



'I I _


,t -A





L p- ____ Ill F___ -p I^X ^ ^L. _
.- I i i : : I O, | i G -
. .... ; ........ ---- --I .... -- --- ---:--- --- -- 1 ......- '~~ T






___T_ _7 ___
I I i I ---- i


C^m^^[ ,-T.-----
.*: .z.__ L.j. __ : _,t I ,_ \Y_ ..___._..__..__ _._.
,''- i, '.. ; I i '~ l ^" i'
"- -- .. -,- ..jf -._ 54 I '. ''- }I i coIi E /M tloi~ic |. 1- I .-

~Z ,^!_ .>_ 1 'J ~;__ -L .. _,- :I. f~ ---1


___ ---- _. ": ./. .. .. I-;.. j--..I _,.,, __"-___ Fi 1- ,"4 : I*- 1 -- ;-- *


Fig. le








NACA RB No. L5F15a


-4O T A-I U .IJT '.
A--" I















I NATIONAL ADVISORY -
-i-















,- NTIN A -LI OI
_~__ .~i~ ---~^ J ~ ^F ^ ^ "'i ~ r--- ~'i F ~'J p ^


*1'I-t CTL


1 '* I '4i i f I


P 'i-Jr


I I I I I i I


- I


-I--- ~i'.r.- I


.1 F:I


- 1 ,


Fig. If







NACA RB No. L5F15a


Fig. ig


--- ---- [+
....... .................... -. .,- ----- -- -.- -



.... ..... !!

IE ^ : E :=---- ---- --- ---:i


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




l -44-_--



..-...: fl -- -.........

---1 __ .i. ,





NATIONAL AOVSOV .. I
... T .- ---Mi ---I ... .. -i~ n c ; 1---1 -,.-- 1 | .--









CONMfI FOR AIDOAlI CS
T-I
-41


~1~


I H
l 1 '


I I /-. 4-+ i t -


' -I-- -.i [ -


LKiIL~ -


I I II I1'
l i-id -i-- -I- II i- t--- ....I....


P441-7..


I I I I r I !


g,191,!ll lll


--H-I






NACA RB No. L5Fl5a


I:. l i ,i / I : L : l I, / /II


._ ..-_.- ..- ---.- --- --- .---i- 1.-- -_ ____ l_




f /i, 1 : i ,1 ... .
-. ] ,-- T ,k / F I I I l i / l


i-- .. --- '. i ___ t. J '.__ -- -- -





11 4 _ZFK
.- I--- : P-I- ; -: -: --. i--t- l:! J-, ---l--:-- ----


:r_ _[ ____ ___.f.. JL : l~ 4 .:_.__ L2,-_- ..4 _t ...... __,


I z::_.t-!j i 1: ^^i/ :iit^^ ^lJ.: .-^-^1^^l1
i-- ---- ---- -- ....-- -- 1 ---- --T -- ----i-- -











L 44q
-I i I ''NAT I IONAL AD SOR I

CDNlrfl FOG A1ERO.ALI-CS4
-I-.1 ... .. -- -l -- -I -


[__j ^ 1 ; -- ,- -. -- -,-J- j..-i- ---F- -- -- t- -------- -------


-717 ~L7Lfl7~ rfl
- 71ZL11L1L I
~ 4L ~
I *. i i1
I II
L~I I
I ,I


- -l 1--- T


T1 -47 K


L L
- "i


Fig. lh







NACA RB No. L5F15a


L ._ I
-- ---- -- -- -









LH
-'-S^^^^^- -iSI^F^^^jj








N-- r-M .. I rog M10.A,.,C [
E-j L --r I- ~-
4 r -










_ -^~ ~~~--:--4 -_ _Z Z XL-1' -Aj F
: 1-T= : I-!







4- : 1= A- -I, i I I T\
---i^^=^r^^^4^-t::-::
I-IL





kk
__t NATIONAL ADW*SORY

I-P I- J- 1- 7.,lurw _
-1 t


S1


- r r i.- .c.rt ruej
SI-- i f T )_ --It _-
I- I T : ...F, .:
'-T-,: f : .'.; -'


zl'Fi'F4+LV


--H'


I ilThrhzltz&izH


4- -J-1


+ t+4 I' H-4 Vi


- .. .- r i nI I l. L I-


FI|'


I i [ T I I T p- --I- -. i--. f I d-.- i


p


I i I I I


] : L L I I I i l I r l i I [


I


FIII I


,1 : -. M
" !., nr


ilI


-
fi t t i l i f t


Fig. li








NACA RB No. L5F15a


,I i I 1
-4 1 1 1 i ] i ]


-LjI-'


IA
I .. I-1 !



- ---- -- -- -



F -






444'








I TI V
_,_i"L--77
J4---









V V I--- 1--


I -I I I i I I L 3-- 1


- 4 L---


4- J...-I


I ~ ~ ~ ~~~ .i~ l l .'i l ~ .1 T .


' I- 1.* 1L -


Fig. 1j












'_'_ --_ L ijl..... ,i _T_;" ~ ~ ~ "''~ T '' ~~ I ; i i _
t- t ,- -- r.- --- -4- "- L----I --- -- ---- i'- t-- : ... -- -



^^^^ =^^ ^^^ ^4:=^- --TJ-

I I I! F -J I '
JIJI1iITI 1VI T-









I T



t N7 INALADVSOR T V J
A_^^ 1- 41^Z~ ^^ i^^Izz^^~~''T __ "~','"
'',-2



-i --+7








._.1_i -_J__ _- .. __!.______L'..j .,' .._ __
- --- -_ __ '__ I i ,_ __ >L D t f, ; '. T 1 ,' .... r -. .
| I | "![ IM ,--- $ n F--_ --. .. -- ...



r-K ^ r -- K i- -- -.- ..
l i 1i i F '__ __1. .I l I __l L I. .. ...L l l 1

I '- i
WNIM i I ,- I TC ', l M.*TC I iI ,
1 i. .1 '~i 4rj


_. __.. '__i L_ -__ --4- ; I1 t l


q *
I I
11:1~1


A-r
' I 'l I ,' I I i i .i-. ,
' i i I : / .i- i I I
... .' .. l i.. l- ------f. .. i '-


i-i I 71-


t 7i.


NACA RB No. L5F15a


Fig. 1k


WL :I~ ~'
1:>


i #


I







NACA RB No. L5Fi5a


i -


pT



---


21:


I--


:t 1 IA i/ i I l iL


I- C



-------Ai


.f...iP......
-1 E


1 4



S! I!
| ~ T
-- -__ r I








t:p IH ,5H J ,'Pf ::,


4 1

I-
__ I

I I


- I


Fig. 2a




41-








.- i

r I
G






El
a. i
>-, : -"








I



-. LC
3











C-,
r----
i










:I"
i i v













Wr
L._-








3


_







NACA RB No. L5Fl5a


- -7---

4 44


0 0

CL =
]


-- --_ a

















_" -- d "IH 'P v I
t_ V
fI




















'_ .. I = H
:_ :1 I


__-r


_LLI 1


I 0 0 -
IV..:j ^ -* ;:. ^ *-: -


- :r-. i


Fig. 2b


i i l I
ii, i
! : :
" I I-






NACA RB No. L5Fl5a


.- -7




















--ley

4o -1-
..... ..
___I -- I- -- -
--







- ~ ~ ~~~~----l l i| ---
L1tLitr.T

m ~


Fig. 2c







NACA RB No. L5F15a


0
__I --_--. _-:
- -
: ,- ~ ~ ~ *' 4
^ ^ i 2
--^^-^t^ --- 2


----f- f---F [ i


A ~" ~ ~ -- --



Il*- -- ---1- ---- -- -- --- -- -
B. 1 J _


--* ^-L ~jr~~~i --,---- --- -t-----^--I-

o c --z z -- -r ----
lE-0






I1 -- .
'



-

"- ----- .-
:-t

:,_ ._- -- -

..T iJ-/.


I-


7171 171MM II-W -


Kii7 ~


i-i TT ---- .-
1I


r7r
TI
I_ -

I -_
i 3L _


7...


Fig. 2d


11 I f I I II


i i ; 1 1 1 1 1


4


: : i .


1 7 i T I I


I I I I I


I 1 I I






NACA RB No. L5F15a


H-K


3A


_ _ _
4
_ -_ -/ I ._ .z
0 r
- -- -- .^ _


Li-


I -
!L.. '1-ii-tL


II I v 4
-_ [ ~
o -



--
S-



_j _







ITI

SIE IA4 .' ''i~


V


K ~~I I-~. I I I L
E H--ii, id .... ---
__ _H -* I -- H -/ -- -- -- -- _-


,-^--


L I

^-iT


r rp
.T T 7 Fi


Fig. 2e








NACA RB No. L5F15a


it lF >1


t:- L-
. M

W-4
I.4?, i fe il ^ r'
?* ~ ~ ~ ~ ~ ~ ~ ~ / ](^ nfp r+ST Ti' I""-.-"


1 1. 1


I-. I


Tf i- --4 1 : -
-- ,------- [-. -

,:, V. -.

-, i -ir '
'.TIE' ',E r....11 i -:
Y. t -- TiI

l t ,,, .^ -... i ,: : .;,-




2
-. -- J*-- f 4 -K -






















I
S: : p r ;: :gp : -
















.... ,f -


Fig. 2f


tA- V -







NACA RB No. L5F15a


I z:IzI11 IZIZVEI
I--~~ ~~ -- I-i T- -~f T_ __ F ._.___


-4-_--LA





I,1
===^^7^


----- I-i j- -- -- -- --
















___ ,__ I -{I H j I _
...~ -- --
o





7--







I 4- -1 -
E~IE9EEIE 4T ii


II


Fig. 2g








NACA RB No. L5Fl5a


Fig. 2h


-- ----- -- t------- -4
-----.--- --



1 7 w-
::___ LjZ-j --4_ _


T-: V. ~ 71 V -.


O IC

.1=


I.
I


B __
~


V : -- -



,~ii- 7_














^ +-- ^ ^ ^ ^ "" "r ^ ^ ^ ^ ^',
-i :..--.- 4 -.-. -.
-- ....


--T_






---- --- ---
-- -.+jIL 1- 'l"







-- -- :



t-7-1
... .. .
--, .-
-- -'---
I + --




-- --""""" +-'-' --" --l
4- A ---&4-4-i-

--" "- i I F-H
~~~*1 ~ -"-~-"--I'-H i-"'--


i~ ~ ~ ~ ~ I il . i i i I I .


-tn' T --' L' ; --'-4





NACA RB No. L5F15a


EL131IIBAIEE1JEEE~ILEEFE


ThTh

7:2>


A--t


Fig. 2i


- -- _









-------------- -----
ci
- 1

_ p H----- o ,-/








NACA RB No. L5Fl5a


L.- ,I .. a

.* 1. 7- C -

lt
-- I
F o4
ol U


C-1--! l-

'i ^ --L A^ -- -


.- .$4 n],,', ". ',t 4-, :4 .; "'.: + -, -4- -. ; 1 -4-


I21.


m- --E_ v,- I






-b






2-
) Ii y ii"'.



S-T






S- "p-





". -- -1


SJ



1-7A



d HIT


Fig. 2i


.n . . ,


II1111111


4 -r, ,..







NACA RB No. L5Fl5a


-H__ _L


7-


S,

I 1 11 I


-H


4-

1-


-IT
I10


7-"


- j
0+


-I- -


a


-m






C-
.1-
* I--
rj
.x.
0
U


--.1

I- ___

* I


-F----


--t-- I-- -- --

+









.... .... H _
m I I I-,






















i i i L 7
' 4- _./.-- _,_-,- -- -:--4- ------



El










1". -l A sI-k .--77
-- j --I---.-.-. -


Fig. 2k


I !


-T-
4- -7-7


t-
4
-a









Fig. 3


NACA RB No. L5Fl5a










Cdo




0

z 0
Zua 44 O



E o




00 o4


+-4




O N
wO





Cd

*4


S.,-1 -t
+v 0
cd .,-4








.Cd.




0 0
OOc








NACA RB No. L5Fl5a Fig. 3













0'

0 0


ca3

E4 4










.O
S o







C-
0 >










-4 rC

*4
OO "s^*









UNIVERSITY OF FLORIDA


3 1262 08104 983 4































































I'i