Section properties of a series of airfoils suitable for propeller design (Airplane Branch report)

              Auburn University L ih1 <rnes
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File D 52.338/ 138 MAT:g~IE"!;IVI VISION REPORT, SERIAL No. 13768
_,
AIR CORPS INFORMATION · CIRCULAR
PUBLISHED BY THE CHIEF OF THE AIR CORPS, WASHINGTON, D. C.
Vol. VI November I, 1927 No. 597
SECTION PROPERTIES OF A SERIES OF AIRFOILS
SUITABLE FOR PROPELLER DESIGN
• alph Brown Draughon
LIBRARY
MAY 2 8 2013
Non·Depoitory
Auburn University
(AIRPLANE BRANCH REPORT)
Prepared by Frank W. Caldwell
Materiel Division, Air Corps
Wright Field, Dayton, Ohio
March 18, 1927
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON
1928
CERTIPICATE : By direction of the Secretary of War the matter contained
herein is published as administrative information and is req uired for the proper
transaction of the public business. •
(n )
SECTION PROPERTIES OF A SERIES OF AIRFOILS
SUIT ABLE FOR PROPELLER DESIGN
The section properties of a series of sections some­what
imilar to the Clark Y section were desired in
order to facilitate the use of these sections in pro­peller
design.
These sections are a ll based on the same meclian
line, the camber ratio being in creased by eq ual incre­ments
above and below the median lin e.
The chord is taken as a line joining the two ends of
the median line.
The area of the sections was determined by means
of the p lanimeter wheel on the integrating machine.
The statical moment about two axes was found
from the moment wheel on the integrating machine
and the po ition of the center of gravity determined by
dividing the statical moment by the a rea.
A new set of axes t hrough the center of grav ity
parallel and perpendicular to the chord line was taken
and the moments of inertia about these two axes
found from the integrating machine.
As the precision of t he machine is unsati factory
for the moment of inertia about the axis parallel to the
chord, this value was checked by determining the
moment of inertia per inch of chord , plotting this
against the chord and finding the area under the curve.
The products of inertia were determ ined by finding
the products per iuch of chord, plotting thi value
against the chord and agn in finding the area under the
curve.
The moment of inertia about the minor and major
axes · and the angle between the chord and the minor
axis were found from the equation given below:
K
(1) tan 2 a = Iy- I x
(2) Find a .
(3) I miu= (IY sin2 a)+ (I . cos2 a) - (2 K sin a cos a ).
( 4) Ima;= (IY cos2 a)+ (I . sin2 a)+ (2 K cos a sin a) .
Find I minor (5) and I major (6).
The angle between the minor ax is and the chord is
substantially zern for the purpose of design. It varies
from 0.1° for t he th in sections to nearly 0.3° for the
thick sections. An average value of 0.2° may be taken
if desired when the ch ord is taken as a line joining the
two ends of t he median line.
. Area of the section may be taken as Area = 0.7245
hX t.
The height of the center of gravity above t he chord
may be taken as h0 = 0.0255 b.
The distance of the center of gravity from t he
leading edge may be taken as b0 = 0.4405 X b.
The moment of iner t ia about the major axis may be
taken as I mai= 0.0417 b3 t.
The moment of inertia about the minor axis may be
taken as Imin= 0.0454 b t3.
For the thinner sections of a lower camber than 0.12
t he chord was kept a stra igh t line for the greater part
of t he distance, the ordinates being obtained as shown
in Figure 1.
For t hese thinner sections t he following formula
will give the section properties.
The a ngle between the rn inor axis and t he chord may
be taken as a = 15.20X t/ b.
The a rea of the section may be taken as A=0.7245
bX I.
The height of the center of gravity above the chord
a = angle between chord and minor axis. may be taken as h.= 0. 416 t.
I= maximum thickness. The distance of the center of gravity from t he leading
K = products of in er tia. edge may be taken as b0 = 0.4405 b.
Jy=moment of inertia about perpendicular The moment of inertia about the major axis may be
to c·hord th rough center of gravity. taken as I m.; = 0.0418 b3 t.
I. = moment of inertia about a line parallel to The moment of inertia about the minor axis may be
the chord and through the center of gravity. taken as I m, 0 = 0.0454 bt3•
(1)
2
~--d-fb_ _ _ , __ _0 _ _1 _-0_25_ __.0_ 5_0_ __o _.i _ __o_ .2_ ___o._ 3_1 __0._ 4_
1
__0._ 5_ __o. 6_1 __0_ .1_ ___o._ 8_ __o_ .9_ _\ _rad. ~_t_i_e
h/t ___ ________ o.2992 o.549 o. 6625 o.8055 o.957 o.995 o.983 o.928 o.829 o.6835 o. 52l o.3375 \ o.ffi96
h1/t_ __ ___ __ -- - - --- -- --- . 1281 . ffill . 0384 . 0085 -- - - -- ---i-- ---- ---1-- ------- -- ---- --- .- -- -- ----- -- -- ------- --------,-- ---- ----
i----------~hc----------""1-
Area= 0. 72-L5 bX t.
b, = 0. 4405 b.
h, = 0. 416 t.
= 15. 20X t/ b.
h
.(;.
l w oj . = 0. 1}!18 b't.
l mio.=0. 0454 bt3.
t = maximum thickness.
~' JG . 1.- Diruensions and section properties for propeller airfoils or Lhe Clark l\l"oclifled Series. Cambers less than 0.12
d/b 0. 025 1~ 0. 075
a/b_ -- - -- - 0.000 I o. 0!05 o. 0145
h1/l = h2L - . 2l75 . 2966 . 34.85
----------be
d
Area=O. 7245 bX I.
b, = 0. 4405 b.
"· = 0. 0255 b.
_o. ~~~1-~ -
o. 0175 o. 0275 o. 032 I o. 0335
. 3885 . 476 . 500 . 4945
8 £.AOe WIOT!i(b}
= 0. 2° angle between minor axis and chord .
0. 5
0.033
. 4641
0.6 1 0.7 i 0. 8
- --- ---- ----
0. 0295 0. 024
. 416 .342
I
I.o•I· = 0. 0418 b•t
lwho . = 0. 0454 bt3
0. 017
. 260
I = maximum thickness.
0. 9
0. 0085
.169
FIG . 2.-Dimensions and section properties for propeller airfoils of the Smith Series. Cambers greater tban 0.12
racl. att e
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10
AREAS AND CENTER OF GRAVITY LOCATION BY INTEGRATING MACHINE
Clark Y aiifoil- 0.08 camber
Area of entire section (A):
First reading ____________ ______ ________ --
Second reading ______ _________________ _ --
Average __ __________________________ _ 1156
1156X (f = 0.02) = 23 .10
Moment of entire section (M):
First read ing _________________________ _
'econd reading __ _____________________ _
Average__ ___________________________ 375
375X 0.04 = 15
h.=;~:~~= 0 .668 = (d istance above reference l ine)
ection to left of center of gravity: Section to right of center of gravity:
A M A' M'
First reading _____________________ 698 9810 F irst reading ____________________ 460 045
Second reading ___________________ 699 9 10 Second reading _________________ 468 042
Average ___________________ ~ ___ 698 9810 Average______ ________________ 464 043. 5
A= 698 X 0.02 = 13. 96 A' = 464X 0.02= 9. 28
M= 10000- 9810= 190 i\1' = 43.5 X 0.04 = 1. 74
190X 0.04 = 7. 60
AX 4 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 55. 84 A' X 4 =---------------------------------- 37. 12
lVI =------------------------------------- 7. 60 M' =------------------------------------ 1. 74
(AX 4)+ M=----------------------- 63. 44 (A' X 4) - M' = ______________________ 35. 38
(AX 4) + M = _____________________________ 63. 44 A= ______________________________________ 13. 96
(A' X 4) - M' =--- _________________________ 35. 38 A' = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 9. 28
B = __________________ . _ _ _ _ _ _ _ _ _ _ _ 28. 06 A+ A' =-------- ____________________ 23. 24
_ B _ _ 2 .06_
A+ A' - 23.24- 1 .9~ 06 10- l.206=8.794 = di stance of center of gravity from leading edge
Clark Y airf oil-0.12 camber
Area of entire section (A):
F irnt reading __ ________________________ 1 740
Second reading ________________________ 1734
Average __ __ _______________ __ ________ 1737
l 737X (f= 0.02) = 34.74
Moment of entire section (M):
First reading ___ ________ _____ ____ _____ 862
Second reading ____________ ______ _____ 861
Average____________________________ 61. 5
861.5 x 0.04= 34.46
34.'16
h.=3-!.74 = 0.9925
Section to left of center of gravity : Section to right of center of gravity:
A i\1 A' M'
First Reading ___________________ 1040 9720 First read ing _______ ___ _________ __ 702 48
Second reading __________________ 1040 9716 Second reading ________________ ·-__ 697 4 7
Average _________________ _____ 1040 9718 Average ___________ ____________ 700 4~ 5
A= 1040X 0.02 = 20.80 A' = 700 X 0.02 = 14
M = l0000 - 971 = 2 2 M' = 475 X 0.04= 1.90
282X 0.04 = 11.28
AX 4 = ___________________________ __ ___ __ 83. 20 A' X 4 =---------- - ----------------------- 56. 00
lVI = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 11. 28 l\11 I = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. 90
(AX 4)+ M=---- - ------------------ 94. 48 (A' X 4)- M' = ---------------------- 54. 10
(AX 4)+ M = __ ___________________________ 94. 4 A= __________________________________ ____ 20. 80
(A' X 4)- M' =--------------------------- 54. 10 A' =------------------------------------- l ~ 00
B= ----------- --- ___________________ 40. 38 A+ A' = _____ __________________ ____ 34. 80
B 40.38
A+ A' = 34.80= 1.16
10- l. 16=8.84= distance of center of gravity from leading edge
11
Clark Y aiijoil-0.14 camber
Area of entire section (A):
First reading_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2008
Second reading ____ ____________________ 2008
Average _ ___________________________ 2008
2008X !j = 0.02) = 40.16
Section to left of center of gra vity : A M
First reading __________________ 1213 9693
· Second reading ____ : ____________ 1211 9694
Average ____________________ 1212 9693. 5
A= 1212X 0.02 = 24.24
M = 10000- 9693.5= 306.5
3065 x 0.04 = 12.26
AX 4 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 96. 96
11 = -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12. 26
(AX 4)+ M=--------------------- 109. 220
(AX 4)+ M = _____ ______________ ________ 109. 22
(A'X 4)- M' = ----------------··-------- 60. 984
Moment of entire section (M):
First reading __________________________ 1005
Second reading_________________________ 1003
Average ____________________________ 1004
1004X (f= 0.04) = 40.16
Section to right of center of gravity: A'
First reading ____ ____________ ___ 815
Second reading _________________ 810
M'
1005
1007
Average _____________________ 812. 5 1006
A'=812. 5X 0.02 = 16.25
M' = 1006X 0.04 = 4.016
A' X 4= __ - ___ --- ___ __ _________ __ ________ 65. 00
M' =- -- ------ - ---------- - -------------- 4. 016
(A' X 4) - M' = --- ------ - ---- _______ 60. 984
A= - _ - - _ - __ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 24. 24
A' =------------------------------------ 1~ 25
B= _ _ _ __ _ __ ___ _ _ _ _ _ _ _ __ _ _ _ __ _ 48. 236 A+ A' = __________________________ 40. 49
B 48.236
A+ A' = 40.49 = l.l92
10- l.192 =8.808=distance of center of gravity from leading edge
Clark Y airfoil- 0.16 camber
Area of entire section (A): Moment of entire section (M):
First reading ___ _______________________ 2300 First reading __________________________ 1163
Second reading _____________________ . ___ 2296 Second reading ________________________ 1150
Average ____________________________ 2298 Average _ ___________________________ 1156
2298X (f= 0.02) = 45.96 1156X (f = 0.04) = 46.24
46.24
h.= 45.96=1.008
Section to left of center of gravity: ·
A
First reading _____ _____________ 1385
Second reading ________________ 1390
M
9644
9633
Average ____________________ 1387. 8 9638
A= 1387. 8 X O. 02 = 27. 75
M = 10000- 9638 = 362
362X O. 04= 14. 48
AX 4= _____________________ ________ ____ 111. 00
M = __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 14. 48
(AX 4) + M =-- ___ _________________ 125. 48
(AX 4) + M = __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 125. 48
(A' x 4) - MI= - - - - - - - - - - - - - - - - - - - - - - - - - - 70. 98
Section to right of center of gravity:
A'
First reading _ _______________ __ 924
Second reading ________________ 922
Average ____________________ 923
A' = 923 X O. 02 = 18. 46
M' = 071.5 X O. 04 = 2. 860
M'
073
070
071. 5
A' X 4 =---------------------------·------ 73. 84
11' = - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. 86
70. 98
A=____________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 27. 7 5
A' =- -- ---------------------------------- 1& 46
B =---------- -------------------- 54. 50 A+ A' =--------------------------- 46. 21
B 54.50
A+ A'=46.21=1.l8
10- l.18=8.82=distance of center of gravity from leading edge
12
Clark Y airfoil-0.20 camber
Area of entire section (A) :
First reading___ __________ ___ ________ 2885
Second reading_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2888
Average____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2886. 5
2886. 5X (f= O. 02)=57. 72
Moment of entire section (M) :
First reading ________________________ 1440
Second reading ___ __________________ _ 1443
Average __ ____ ____________________ 1441. 5
1441. 5X (f= 0. 04)=57. 64
57 .64
h.= 57.72=0.999
Section to left of center of gravity:
A
First reading _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 17 40
Second reading _____ ______ ___ 1743
M
9520
9523
Average _ _________________ 1741. 5 9521. 5
A= 1741. 5X O. 02 = 34. 83
M= l0000 - 9521. 5 = 478. 5
478. 5X O. 04 = 19. 14
AX 4= _ ------------ - ___________________ 139. 32
M=------------------------------------ 19. 14
(AX 4)+M=-------- --------·------ 158. 46
(AX 4) + M = ___ _________ ___ ------------- 158. 46
(A' X 4)-M _______ ________ __ ____________ 89. 16
, ection to righ t of center of gravity :
A'
First reading__ ___ _______________ 1155
Second reading _______ -__________ 1160
M'
0 6
086
Average_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 115 7. 5 086
A' = 1157. 5X O. 02 = 23. 15
M' = 086 X O. 04 = 3. 44
A' X 4=- - - ----------- -------------------- 92. 60
M' = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 3. 44
(A' X 4)- M' =---------------------- 89. 16
A=________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 34. 3
A' =------------------------------------- 23. 15
B =------------------------------ 69. 30 A+ A' =---------------------------- 57. 98
B 69.30
A+A'=57.9 = l.l97
10 - 1.197= .803 = distance of center of gravity from leading edge
Clark Y aiifoil- 0 .24 camber
Area of entire section (A):
First reading__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 3460
Second reading _ __ __ _____ ____________ 3459
Average______ _____________________ 3459. 5
A= 3459.5X (f = 0.02) = 69.19
Moment of entire section (M ):
First reading __ ____________ __________ __ 1750
Second reading ________________________ 1748
Average __ ____ _____________________ __ 1749
M = 1749X (f= 0.02) = 69.96
69.96
h.= 59,19=1.0l
Section to left of center of gravity:
A
First reading _____________ _____ 2080
Second reading ___ ________ _____ 2082
Average _____________________ 2081
A= 2081 X 0.02 = 41.62
M = 10000- 9446= 554
554X 0.04 = 22.16
M
9442
9450
9446
AX 4= __ _________________ --------- _____ 166. 48
M=--- - ----- -- - --------- -- ------------- 22. 16
(AX 4)+ M =---------------------- 188. 64
(AX 4) + M = ____ _____ - ------ -- __________ 188. 64
(A' X 4) - M' = __________________________ 106. 58
Section to righ t of center of gravity:
A'
Fi rst reading ____________ __ ___ 1384
Second reading___ _____________ 1385
M'
0106
0100
Average____________________ 1384. 5 0104. 5
A' = 1384. 5X 0.02 = 27.69
M' = 0104. 5X 0.04 = 4.l 0
A' X 4 = - - - --- - -- ------- --------- -------- 110. 76
l\i[ ' = - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. 18
(A' X 4)- M'=------ --------- ------ 106. 58
A=----------------------------------- -- 41. 62
A' =-- - - ---------------------------- -- -- 27. 69
B = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 82. 06 A+ A' = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 69. 31
B 82.06
A+ A'=69.31= 1.l 5
10- 1.1 5 = 8. 15= distance of center of gravity frorn leading edge
13
Clark Y airfoil- 0.32 camber
Area of entire section (A) : Moment of entire section (M) :
First reading ________________________ 4630 First reading _ _______________ _____ ___ 2277
Second reading ___________ ____________ 4625
Average _________________ ___ __ ____ _ 4627. 5
A ~ 4627.5 X (f= 0.02) = 92.55
Second reading ______________________ 2280
Average___________________________ 2278. 5
M = 2278.5X 0.04 = 91.14
91.14
h. = 92.55= 0.985
Section to left of center of gravit,y: Section to right of cen ter of gravity :
A M A' M'
First reading __________________ 2780 9252 First reading___ ______ ___________ 1862 0153
Second reading__ ___ _____________ 2782 924 7 Second r eading _____ ________ ___ 1858 0158
Average _ ________ _______ ____ 2781 9249. 5 Average ____________________ 1860 0155. 5
A= 2781 X 0.02 = 55. 62 A' = 1860X 0.02 = 37. 20
M= 10000 - 9249.5= 750. 5 M' = 0155.5X 0.04 = 6. 22
750.5X 0.04 = 30. 02
AX 4= _________ ________________________ 222. 48 A' x 4=_ - -- -- - - - - - - - - - - - - -- - - - - - - - - - - - - - 148. 80
M = __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 30. 02 MI = - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 6. 22
(AX 4)+ M=---------------------- 252. 50
(AX 4)+ M =---- ----------------------- - 252. 50
(A' X 4)- M' =--- - -------------- - - - 142. 58
(A' X 4) - M' = ________ ___ ________ _____ __ 142. 58
A=---------------------------- -- - - ----- 5~ 62
A'=-------------------------- --- - - ---- - 3~ 20
B = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 109. 92 A+ A' = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 92. 82
B 109.92
A+ A'= 92.82 = l. l 83
10- l.183 = 8.817 = distancc of center of gravity from leading edge
Distance of center of gravity from leading edge
Camber
Forward
from 10"
ordinate
Forward
from 10"
Camber ordinate
0.08 __________________ ____ ___ _______ ____ _ 1. 206
1. 160
1. 192
Q24 _______________________________________ 1. 185
.12 ___________ ___ ____ ____ _______ ________ _ .32 __________________ _________________ ____ 1. 183
.14 ________ __ ____ ! _____ _ ________ _ _______ _
.16 ________________ ____________ ______ ___ _ 1. 180
.20 ___________________ ____ _______________ _ 1. 197
8.~03=1.188
I
10.00 - l.188 = 8.812 = average distance from leading edge
IMAJOa- COMPUTATION OF MOMENT OF INERTIA ABOUT MAJOR AXIS
Imai = (Iycos2a) + (I,sin2a) + (2E: cosasina)
0.08 CAMBER
Imai= 534 x 0.998+ 3.861! X 0.00002209 + 5.04 x 0.999X 0.00474= 532.5+ 0.000085 + 0.02382= 532.5
0.12 CAMBER
Imai = 795.4X 0.998+ 12.73 x 0.00002462+ 7 .76 x 0.999X 0.00496= 794.5 + 0.0003165+ 0.0385 = 794.5
0. 14 CAMBER
Imai= 924.6X l.O+ 19.88X 0.00000755 + 4.96 X l.OX 0.002745= 924.6+ 0.0001.5+ 0.01362= 924.6
0. 16 CAMBER
Im.;= 1104.5X 0.998+29.024X 0.0000411 + 13.80X 0.999X 0.006415= 1102 + 0.001193 + 0.0885= 1102.1
8. 303
14
0.20 CAMBER
Ima;= 1329.5X 0.998+ 56.40X 0.0001063+ 26.24X 0.999 x 0.01031 = 1325+0.006+ 0.2705= 1325.3
0.24 CAMBEU
I ma;= 1585.6X 0.998+93.84X 0.0000955+ 29.20X 0.999X 0.009772= 1582+0.00935+0.285= 1582.3
0.32 CAMBEH
Ima;=2114X 0.998+ 227 .04X 0.0000831+ 34.40X 0.999 x 0.009115 = 2108+ 0.01888+ 0.3135= 2108.3
Camber
ratio
Ima; b3t- for 0. 08 _________________________ _
. 12 ________________________ _ _
. 14 _________________________ _
. 16 __ _______________________ _
. 20 _______ ___________ _____ __ Factor for I maior
Camber
K ratio K
0. 0418
. 0416
. 0415
. 0433
. 0416
Irua;b3t- for 0. 24 ______________________ ____ 0. 0414
. 32_______________ ___ ________ . 0414
Average __ ____________ __ ·• 0418
Imai = 0.0418 b3t
IMINOn- COMPUTATION OF MOMENT OF INERTIA ABOUT MINOR AXIS
Imio = (lysin2a ) + (l 1 cos2a ) - (2K sinacosa )
0.08 CAMBER
Imio= (534X 0.00002209) + (3.864X 0.998)- (5.04X 0.00474X 0.999) = 0.00117 + 3.86 - 0.02382= 3. 37
0.12 CAMBER
Imio= (795.4X 0.00002462) + (12.732X 0.998) - (7.76X 0.00496X 0.999) = 0.00196+ 12.71 - 0.03845= 12.67
0.14 CAMBER
Imio= (924.6X 0.00000755) + (19.88X 1.0)- (4.96X 0.002745X 1.0) = 0.00698+ 19. 8 - 0.01362= 19. 7
0.16 CAMBEH
Im1n = (1104.5X 0.0000411) + (29.024X 0.998)- (13.80X 0.006415X 0.999) = 0.0455 + 30.022- 0.0 85 = 29.98
0.20 CAMBER .
Imin= (1329.5X 0.0001063) + (56.40X 0.998) - (26 .24X 0.01031 x 0.999) = 0.1412+ 56.30-0.2705=56.l 7
0.24 CAMBEH
l wiu = (1585.6 X 0.0000955) + (93.84 X 0.998) - (29.20X 0.009772X 0.999) = 0.1512+ 93.65 - 0.2852= 93.52
0.32 CAMBEH
I min= (2114 X 0.0000831) + (227 .04 X 0.998) - (34.40X 0.009115 X 0.999) = 0.1757 + 226.4- 0.3135- 226.3
Factor for I mi n or
Im i 0 = k2bt3
Camber Camber
ratio k1 rat io k2
I mio bt3-for 0. 08- ---- ----- - ------ -- -- - --- - 0. 0475 Im in bt3- for 0. 24·--- - ----- - ---------------- 0. 0430
. 12___ ____ _____________ ____ __ . 0464 . 32__ ____ ______ ______________ . 0438
. 14 _ - - - - - - - - - - - - - - - - - - - - - - - - - . 0458
. 16____ ____ _____ ________ ____ _ . 0464 Average_ ___ ___ __________ . 0453
. 20 _ - - - - - - - - - - - - - - - - : - - - - - - - - . 0446
Imin=0.0453 bt3
15
MOMENT OF INERTIA BY INTEGRATI G MACHINE
Clark Y aiijoil- 0.08 camber
Area = a:
First reading ___ ________ ____ ________ ___ 1147
Second reading ____ ___ ___ ___________ ___ 1145
tatical inoment=m:
First reading ____ ____ __ ___ · _______ _____ 9988
econd reading ______ _______ ___ __ _____ _ 9985
l\ loment of inertia=i:
First reading ______ _______ _____________ 3688
Second reading ______ ____ _ -__ ___ ________ 3688
Left section:
First reading ___________ ____ _
Second reading _____________ _
AreaX42= 609 X 0.02X 16= 195
Ml= 0.32X 609-127.4 = 67. 6
a m i
61 028 1274
608 028 1277
a x 0.02= 1146 x 0.02= 22.92
10000 - 9988 = 0. 0012}check of error in center of
10000 - 9985 = 0, 0015 gravity location.
i = 0.32 X a-1i0= 0.32X 1146= 366.5-368.8=:- 2.3.
(precision of machine insufficiently accurate) .
Ml=-2 .. 3
Ri gh t section: a m i
First reading __ ·------------c-- -- 558 90 852
Second reading ____________ ____ 555 90 848
Area X 42= 557 X 0.02 X 16 = 178.2= __ __ _____ _ ·178. 2
93. 2
l\ll = 0.32X 557-85=93.2= _______________ _ 195. O
67. 6
!y= - - - -- - - - - - ----- - - - - --- - ---- - -- - 534. 0
Clark Y aiijoil-0.12 camber
Area=a:
First reading ______ ___ ___________ - ----_ 1750
Second reading __ _____ ____ _________ ____ 1730
Statical moment= m:
First reading_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0005
Second reading _____ ____ __________ ___ __ 9998
Moment of iner t ia=i:
First reading _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5448
Second reading __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5440
Left section:
First reading ______ _______ . __
Second reading ____ _____ ____ _
AreaX 42= 910X 0.02 X 16= 291.2
Ml=0.32X 910- 190.8= 100.4
a m
910 021
910 023
i
191
1905
Area X 0.02 = 1740X 0.02= 34.80
10000- 0005 = 9995}check of error in center of gravity
10000 - 9998 = 0002 location.
Moment of inertia = 0.32 X area - 1i
0
=0.32 X 1740-
544. 0=556.5-544.0 = 12.5
Ml= l2.5
Right section :
First reading _____ ___________ _
Second reading _ __________ __ _
AreaX 42= 828 X 0.02X 16= 264.8
a m
829 885
827 877
i
1252
1264-
Ml= 0.32X 828 - 125.8 = 139.0= _________ ___ 264. 8
139. 0
291. 2
100. 4-
Iy = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 795. 4
('lark Y oi1joi l- O.J J, camber
MINOR AXI S
Area=a:
First reading ____ ___ __ ______ ______ ___ __ 2009
Second reading __ _____ ____ __________ ___ 2010
Statical moment=m:
First reading _____ _____ __ _______ _______ 0005
Second reading _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0007
Moment of inertia =i:
First reading _______ _______ __________ _ 628. 5
Second reading ______________________ _ 628. 7
Left section: a in i
First reading __ ___________ 1050 0035 219. 1
Second reading __ _________ 1048 0037 218. 8
AreaX 42= 1049X 0.02X 16 = 336
Ml= 0.32X 1019-Z19,0 = 117
AreaX 0.02 = 40.18.
10000 - 0005 = 9995}check of error in center of gravity
10000 - 0007 = 9993 location.
Moment of inertia = 0. 32 Xarea- 1~ = 0. 32 X 2009 -
628.6 = 643. - 628.6 = 15.2
Ml= 15.2
Right section:
First reading __ __ _____ _____ _
Secoud reading _____ ____ ___ _
a m
069 862
972 862
AreaX 42= 9705 X 0.02X 16= 310.5
l\il = 0.32x 970.5-149.4 = 161.1 =- - -- - --- - --
i
148. 5
149. 4
310. 5
161. 1
336. 0
117. 0
Ir= - - _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 924. 6
16
Clark Y airfoil-0.16 camber
Area= a:
First reading ______ ___ ______________ ___ 2300
Second reading ____ ______ _______ -· _ _ _ _ _ 2304
Statical moment = m:
First reading _____ ______ _______________ 9968
Second reading __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 9963
Moment of inertiil. = i:
First reading ______ ___ _____ ___ _________ 7130
Second reading ________________________ 7134
Left section : a m i
First reading __ - ---------- 1210 9336 224. 0
Second reading ___________ 1214 9338 225. 2
Area X 42= 1212 X 0.02 X 16= 388.2
Ml= 0.32 X 1212-224.6= 163.6
Area X 0.02=46.05.
10000 - 9968 = 0032}check of error in center of gravity
10000 - 9963 = 0037 ·iocation.
Moment of inertia = 0.32X area-1 i
0 = 0.32X 2302-
713.2 = 737-713.2 = 23.8
Ml= 23.8
Right section :
First reading _______________ _
Second reading ____________ _
AreaX 42= 1105X 0.02 X 16= 354.0
a m
1103 644
1107 635
Ml = 0.32 X 1105 - 155.3 = 198. 7 = __________ _
1564
1542
354. 0
198. 7
388. 2
163. 6
ly= - - - - - - -- - - - - -- -- - - . - - - -- -- - - - - 1104. 5
Clark Y airfoil--0.20 camber
Area = a:
First reading _________________ ~ _______ _ 2882
Second reading ___ __ __ __ _____ ___ _______ 2887
Statical moment = m:
First reading __ ------------------------ 0005
Second reading ________________ ________ 0022
Moment of inertia = i:
First reacting _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 8722
Second reading ____ ______________ ______ 8730
Section to left of center of gravity:
First reading __ ______ ___ ___ _
Second reading ____________ _
AreaX 42= 1516.5 X 0.02X 16= 485
Mt= 0.32 X 1516.5-317.65= 167.35
a m i
1518 032 3175
1515 030 3178
Area X 0.02 = 2884.5 = 57 .68
10000 - 0005 = 9995}check of error in center of gravity
10000 - 0022 = 9978 location.
Moment of inertia = 0.32X a rea- 1i0 = 0.32 X 2284.5
- 872.5 = 924.5-872.5 = 52
Ml= 52
Section to right of center of gravity: a
First reading ___ ____ ________ 1382
Second reading ____________ _ 1386
Area X 42= 1384 X 0.02X 16= 443.5
m i
774 2095
775 2102
MI= 0.32X 1384-209.85 = 233.65= ______ _ 443. 5
233. 65
485. 0
167. 35
!y = - - - - - - - - - - - - - - - - - - - : _ - - - - - - - - 1329. 50
Clark Y airfoil--0.24 camber
Area=a:
First reading ____ ___ ____ _______________ 3454
Second reading _____ ___ _________ ___ ____ 3455
Statical moment:=m:
Fir treading ____ ________ __ ____________ 9947
Second reading ____ --- - ----------- -- -- - 9942
Moment of inertia = i:
First reading __ __ ___________________ _ 101500
Second reading ____ __________________ 101360
Section to left of center of gravity:
First reading __ ____________ _
Second reading ____ ______ __ _
AreaX 42= 1809 X 0.02 X 16 = 579
Ml= 0.32X 1809-379.5 = 200
a m
1809 058 3795
1809 056 3796
a X 0.02 = 3455 X 0.02 = 69.1 .
10000 - 9947 = 0053}check of error in center of gravity
10000 - 9942 = 0058 location.
i= 0.32X a-
1
i
0
= 0.32X 3455 = 1106 - 1014.2= 91.8
Ml= 91.
Section to right of center of gravity : a m
First reading __ ______ _______ 1653 751
Second reading __ ________ ___ 1657 749
AreaX 42= 1655X 0.02 X 16= 530
MI = 0.32X 1655 - 253.4 = 276.6= ____ _____ _
i
2535
2533
530. 0
276. 6
579. 0
200. 0
Iy = ____________ • _____ • _______ __ • - 1585. 6
17
Clark Y airfoil-0.32 camber
Area=a:
First reading _________ ____ _______ ______ 4617
Second reading _____________ · ___________ 4615
Statical moment.= m:
First reading ___ ____________ _________ __ 0073
Second reading ____ ___ ____ ___________ __ 0074
Moment of inertia=i:
First reading _________________________ 12560
Second reading ________________ _______ 12565
Left section: a
First reading ________________ 2410
Second reading _____ _______ __ 2415
AreaX 42 = 2412 X 0.02X 16 = 772
MI = 0.32 X 2412 - 507 .5 = 264
m
08
08
i
5078
5073
AreaX 0.02 = 4616 X 0.02 = 92.32
10000 - 0073 = 9927}check in error of center of gravity
10000 - 0074 = 9926 location
• Moment of inertia = 0.32X area-
1
i
0
= 0.32X 4616-
1256 = 1479 - 1256 = 223
MI= 223
Right section: a m
First reading ______________ 2210 9662
Second reading ___ _________ 2211 9661
AreaX 42= 2210X 0.02 X 16= _____ _______ __ _
MI = 0.32 X 2210-337.5= _____________ ___ _
i
3381
3369
707. 5
370. 5
772. 0
264. 0
Iy = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2114. O
MOMENT OF INERTIA ABOUT MINOR AXIS BY PLANIMETER METHOD
CLARK Y AIRFOIJ,-Q.08 CAMBER CLARK Y AIRFOIL-0.16 CAMBER
A B A B
y y X1-X2
8. 8------ --- ----- -- ---------- ---- - ----- ---------- ---------- ------- -- -
8______ __ -0. 50 0. 86 0. 0616 0. 0625 0.1241 0.10(j8
7).1!_ ___ __ -.39 J.05 .0919 .0380 .1299 .1 363
7_ _______ -.29 1.19 . 1180 .02102 . 1390 . l653
6________ -. 13 I. 39 . l610 . 00422 . 1652 . 230
4_ _______ +. 07 1.57 .2055 .00l222 .2067 .3248
2________ + . 18 l.60 .2l35 .00 l .2216 .3542
o___ _____ +. 09 J. 55 . 200 .002022 . 2020 .3132
-2____ __ +.16 l.44 . 1727 .00640 .1791 . 2580
- 4____ __ +. 04 l. 24 . 1282 . 00040 . 1286 .1593
-6______ - . 15 . 99 . 08165 . 00562 . 0872 . 0864
-7______ -. 25 .85 . 06015 . 01562 . 07577 . 0644
-7Y,__ __ -.30 . 78 .0507 . 0225 . 0732 .057l
-8____ __ -.35 . 1t . 0420 .03065 . 0126 . 0516
-8).1!____ -.41 .63 .0331 .0420 . 0761 . 0473
-9______ - . 48 .56 .02612 . 0576 .0837 .0169
8. 83 _____ ---------- -- ----- --- ------ --- - ---------- ----- - ---- ----------
8Y,______ -0. 87 1.11 0.1027 0. 1892 0: 2919 0. 324
8________ - . 67 1. 75 . 255 . 1122 . 3672 . 6425
7Y,______ - .51 2.13 .3785 .0650 .4435 . 945
'-- -- - - -- - . 36 2. 38 . 4715 . 0324 . 5039 l. l99
6___ __ ___ - .14 2. 74 . 626 . 00490 . 6309 1. 73
4________ +. 17 3.13 .8165 .007225 :8237 2. 575
2________ +.28 3. 18 .8425 . 01963 .8621 2.742
o________ +. 30 3. 08 . 7915 . 0225 . 8140 2. 52
-2___ ___ +. 24 2.86 . 682 .0144 .6964 1. 992
- 4______ +. 05 2. 47 . 509 . 000625 . 5096 1. 26
-6______ +. 23 1. 97 . 3235 . 01323 . 3367 . 664
-8______ -.54 1.43 .1703 . 0728 .2431° .3475
-9___ __ _ - . 68 1. 14 . 1083 . 1156 . 2239 . 255
-9).1!____ - . 7 . 98 . 80 . 1521 . 9521 . 09335
-11.17 __ - ------ --- ---------- ---------- ---------- ---------- ----------
CLARK Y AlRFOIL-0.12 CAMBER CLARK Y AIRFOIL-0.20 CAMBER
I I
t~~ ::::r-=-=0:00- ---- i:30-- --0:141--- -0:1089 ___ ---0:2499- -- 0.-3246-
1y.______ -. 50 l. 5 .208 .0625 .2705 .4275
7_ _______ -.37 1. 79 . 2672 .03425 .3014 .540
8. 2 __ __ ---- -- ----!---------- ---------- ----- --- -- ______ ____ ! _______ __ _
8).1!_ _____ - 0.83 1 1.33 0.1473 0.1723 0.3196 0 . 42~
8______ __ - . 64 2. 14 . 382 . lCJ?..A • 4844 1. 031
7).1!_ __ ___ -. 48 2.62 .572 . 0576 .6336 1.66
7________ -.35 2. 97 .736 . 03062 . 7666 2.278
6 ____ ___ _ , -. 13 2.09 . 3642 . 00422 .3684 . 771 6-------- - .09 3. 47 1.0025 .02022 1.0227 3.555
4_ _______ , +. 15 2.35 . 461 .005625 . 4666 1.097 4________ +. 20 3.92 1.28 .010 1.29 5.06
2_____ ___ +.29 2.39 .476 .Cl"2JO .4970 1.189 2------- - +. 30 4. 00 L 333 . 0225 l. 3555 5. 425
o________ +. 34 2. 32 . 448 . 02888 . 4768 r. 108
=L::::r :U~ i: ~ :~~~g : &\~~5 : g~~ :~85
-6----- - - . 20 L 48 . l 25 . 01 .1925 . 285
-7__ ____ -.34 J.28 .1365 .02888 . 1653 .2115
-8______ - . 47 i. 01 . 0954 . 05520 .1506 . 161
=g~::::1 =: ~ :~ :~~ : n~ : m~ :~ro~
-11.15--1---- ---- -- ---- ----- - ---------- -- -------- ---------- ---- - -----
o________ +. 32 3. 86 1. 242 . 0256 1. 2676 4. 89"
-2 _____ ------- -- - 3. 56 1. 056 L 056 3. 76
- 4______ -.02 1 3.08 . 7915 .0001 . 7916 2. 44
-6--- --- - .18 2. 48 .513 .0081 .5211 1.292
-8______ -.4.9 1 I. 79 . 267 .060 . 327 .5855
-9____ __ -.64 J.4.2 . 168 . 1023 . 2703 .3842
-9Y.---- -. 74 ]. 24 . 1282 . 1369 . 2651 . 3~~
-10_____ -.83 1.05 . 0919 .1723 .2642 . 2uo
- 11.18 __ --- ------- ,---------- ---------- ---------- -- ------- - ----- -----
CLARK Y AlRFOIL-0.1.4 CAMBER
CLARK Y AIRFOIL-0.24 CAMBER
8.8!_ ____ 1 ________ __ ------ ---- __ __ __ __ __ ! ________ __ ! __________ ----------
8Y, ______ - 0.82 l.18 0.116 0.168 0.284 0. 335
8______ __ -.66 1.52 . 1925 .109 . 3015 .458
7).1! __ ____ - .50 1.84 . 282 .0625 .3445 .634
7__ ______ - . 36 2. 08 . 3605 . 03238 . 3928 . 817
6-------- -.13 2. 37 . 468 . 00422 . 4722 1.12
4________ +. 15 2. 68 . .599 . 00640 . 6054 1. 622
2___ _____ +.30 2. 80 .654 . 0225 .6765 1. 894
o________ +. 33 2. 71 . 6125 . 02722 . 6397 1. 732
-2______ +.28 2.52 .530 . 01962 .5496 1. 385
-4______ +. 09 2.17 . 3926 .002022 .3946 . 857
-6____ __ - .16 l. 74 . 2605 . 00640 . 2869 . 50
- 8------ -. 47 L 25 . l302 . 05525 . 1854 . 232
-9______ -.64 .98 .08 .1025 . 1825 . 1788
-9).1!____ -. 71 . 85 . 06015 . l26 . 1861 . 1- 2
-11. 19 __ ---------- ------ --- - ------- --- --- - --- --- -- - - - ----- ----------
8. 83 _____ -- -- ______ !___ -------1---------- _________ _! __________ ----- -- ---
8Y2-- --- - -0. 86 1. 58 0. 208 0. 1849 0. 3929 0. 6207
8___ _____ - . 67 2. 55 .542 . 1123 . 6543 1.667
7y.____ __ -. 51 3. 13 .816 .065 .881 2. 76
7_ __ _____ -.39 3.55 1.05 .0380 J.038 3.685
6________ -.14 4.14 1.429 . 00490 1.4339 5.94
4__ ______ +. 12 4.70 1.84 . 00360 J.8436 8. 675
2___ ___ __ +. 25 4.77 l.898 . 01 562 1.9136 9.15
0 -- --- -- +. 28 4. 64 1. 791 . 01961 1. 8106 8. 40 -2____ __ + .18 4. 26 1. 512 . 0081 J. 5201 6. 49
-4______ - . 01 3. 71 1.147 . 000025 L 1470 4. 255
- 6__ __ __ - . 26 2. 98 . 740 . 0169 . 7569 2. 255
-8______ -. 55 2. 15 .3855 .0756 .4611 .9925
-9__ ____ -.71 1.71 .244 .126 .370 .6325
-9Y,____ -. 78 1. 48 . 1827 . 152 . 3347 . 496
- 10_____ -.87 1.25 . 1302 .192 . 3194 . 3995
I -- 1L1O.Y r,n_ ____ _____-_.9__3_ ______1._0__2_ _____.0__86_6_ __ ___.2__16__2 _____ __._3_0_2_8_ ______._3_0_9_ _
18
CLARK Y AIRFOIL-0.32 CAMBER
[Reference line~ inch above line connecting center of I. e. and t. e.]
A B
y
--- - --- --- ------ ---
8. 82 ___ __ ---------- ---------- ----- - - - -- - - - - --- -- - - - - --- - --- ----- - ----
8~--- --- -0. 82 2. 08 0. 3606 0. 168 0. 5286 l. 099
8- -- - ---- -. 52 3. 44 . 985 . 0675 L 0525 3. 622
7~ - - - --- -. 38 4. 20 1. 47 . 0061 I. 5061 6. 225
7__ ______ - . 24 4. 76 1 89 . 01442 I. 9044 9. 08
fj______ __ -.00 5.57 2. 6 .000225 2.5862 14.41
4___ ___ __ +.24 6.24 3. 24 . 01442 3.2544 20.3
2___ __ ___ +. 3,5 6. 37 3. 385 . 03062 3. 4J56 21. 75 o____ ____ +. 37 6. 19 3. 185 . 03422 3. 2192 rn. g
- 2______ +. 29 5. il 2. 715 . 02l0t 2. 7360 15. 61
- 4_ _____ +. ll 4. 93 2. 025 . 003022 2. 0280 10. 0 -fi______ - . l.5 3. 95 l. 30 . 005625 1. 3056 5. 155
-. 4.2 2. 86 . 6815 . 0441 . 7256 2. 076
- 9______ -.633 2.227 . 414 . 1002 .5142 1.145
- 9~ - - - - -.68 J.9 .3268 . 1156 .4424 .876
- JO_____ -. 77 1. 67 . 2785 . 1482 . 4267 . 714
- 10~ - - - -. 85 ]. 37 . J564. . 1806 . 3370 . 4615
-JL J9. + --------T·-------- ---- - --- -- - --- - ---- - - --- - ----- - ---------
PRODUCTS OF INERTIA
CLARK Y AIRFOIL-o.08 CAMBER
x1 t-x22
x2 x12 x12 x1 2-x22 -
2
- v
----·l------1--- 1--- --- - -
t~:::::~:::: ---o~is- ---o~68·j--o~:i24--- ---o~46i-- -=o:i:is-- --=o~55i5
1~---------- . 33 . 72 . 109 . 518 - . 409 I -1. 431
7 ___________ .45 .74 . 2022 .5475 -.3453 -1.208
6------------ . 63 . 76 . 3968 . 5775 -.1807 -. 542 4____________ .82 . 75 .672 .562 +.110 +.220
2___ _________ . 89 . 7J . 792 . 501 + . 288 +. 288
o______ ___ ___ . 87 . 68 . 756 . 462 +. 294
-2__________ . 80 . 6 ~ . 64 . 409 +. 231 -4__________ . 64 . 60 . 41 . 36 +. 050
-6__________ . 42 . 57 . 1763 . 325 -.1487
-7__________ .30 .55 .09 . 3022 - . 2122
-7~-------- . 24 . 54 . 0576 . 2912 -. 2336
-8__ ______ __ .18 . 53 . 0324 . 281 -. 2486
-8 1~------ - - • 1 l . 52 . 0121 . 270 -. 2579
-9__ ______ __ . 04 . 52 . 016 . 270 -. 254.
CLARK Y ACRFOIL-o.12 CAMBER
-.231
-.100
+.446
+. 744
+. 76
+. 9955
+1.096
+ 1. 142
8.84 ___ __ ___ _ -------- ------ -- -- - - - - --- - -- - ---- - -- - - -- - -- - -- - - ---- - -- -
8____ ________ 0. 32 0. 9 0. 1023 0. 96 -0. 8577 -3. 432
7~-- - --- - - - - . 54 I. 04 . 29 15 ]. 082 - . 7905 - 2. 962
7________ ___ _ . 7l ]. 08 . 501 I. 168 - . 66'1 -2. 322
6- --- ---- -- -- . 98 I. ll . 96 L 232 - . 272 -. 816
4_____ ____ ___ 1. 25 1.10 I. 562 I. 210 +. 352 +. 701
2____________ l. 34 1. 05 I. 795 J.1()'2 + . 693 +. 693
o____________ 1. 33 . 99 1. 7C'8 . 98 +. 788
- 2___ _______ 1.19 . 94 I. 417 . 883 +. 534 -. 534
- 4_____ _____ .96 .89 .92'2 .792 +.130 -.260
-6__ __ ______ . 64 . 84 . 4095 . 705 -. 2955 +. 887
-7_____ _____ .47 . 81 . 2203 . 656 -. 4352 +i. 523
-8- ---- - -- -- . 30 . 77 . 09 . 593 -. 503 +2. Ol - ~-- - - -- -- 1 .20 .76 .M .5775 -.5375 +2.282
=ki5~~:::: ----~~~- ----~'.\--~~'.----1·---~~~- --=~~~~~- __ ::~~~~-
C LARK Y AIRFOIL-0.14 CAM BER
8.81. ___ _____ ______ __ ____ __ __ 1 ____ _______ ___ ______ I ____ . ______________ I
8~~ ---- - -- --- 0.18 1. 0 0. 0324 l. 0 -0. 9676 -4. ll
8____________ .43 1.09 .1848 l.188 -1.0032 -4.0l
7 ~- ------ - -- .67 l.17 .4485 1.368 -.9195 -3. 45
7__ _______ ___ .86 1.22 .739 l.488 - . 749 -2. 622
6- - ----- - ---- ' l. J2 l. 25 l. 253 l. 562 -. 309 -. 928
4---------- - - I. 4.2 I. 26 2. 015 L 588 +. 427 +. 855
2____ ___ __ __ _ I. 55 I. 25 2. 402 I. 562 +. 840 +. 840
o _____ __ _____ i.52 1.19 2.31 t.4J6 +.894
-2___ __ _____ 1.40 1. 12 J.96 1. 253 +. 707 -.707
-4-- -- - --- - -1 I. !3 l. 04 I. 276 ]. 082 +. 194 -. 388
-6__________ . 19 . 95 . 624 . 9025 -. 2785 +. 837
-8---------- . 39 . 86 . 152 . 140 - . 588 +2. 35
-9----------i .17 . 81 . 0289 . 656 -. 6271 +2. 82
=i~i9~::::: ----~~'.- ----~'.~- ---~~=--- ----~~-- --=~~-- __ ::~~~-- 1
CJ, ARK Y AIRFOIT.- 0.16 CAMBER
:n
8.83 ___ __ ____ ------ - - -------- - ------ --- ---------- ---------- -- - ----- · -
gt~---- - - ---- 0. 12 0. 99 0. 0144 0. 98 -0. 9656 - 4. lO!i
g__ ___ ____ ___ . 54 l. 21 . 2915 I. 4f>4 -!. 1725 -4. 69!\
7 ~---- -- - - -- .81 1.32 .656 1.742 -1.086 - 4.07
7 __________ _ , 1. 01 l. 37 I. 02 l. 877 - . 857 -2. 991i
6--- --------- · 1.30 1.44 1.69 2.072 - .382 - l.14fi
4___________ _ 1.65 1.48 2. 72 2. 190 + .53 + 1.0t;
2___ ______ ___ I. 73 I. 45 2. 992 2. lO +. 892 +. 892
0 ___ ____ ___ __
1
I.69 1.39 2. 855 1.932 +.923
-2__ ____ ____ 1.55 1.31 2.40 I. 715 + .685 -.68.5
-4 ____ __ ____ I. 2fi I. 21 I. 587 J. 46.3 +. 124 -. 248
-6__________ . 87 I. 10 . 756 I. 210 __ 454 I + 1. 3n2
- ----- -- --- . 45 . 9 . 2022 . 96 -. 7578 +3. 03
-9__________ . 23 . 91 . 05295 . 275 -. 7746 +3. ~8.5
-9' ~--- - ---- . JO . 88 . 010 . 774 -. 764 +3. 62.'i
-ll.17. _____ --- -- - - - --------1---------- ---------- -------- --1··--- -----
CLARK Y AIRFOilr-0.20 CAMBER
o__ ___ _______ 2. 09 1. 11 4. 37 3. 133 1. 231
2____ ____ ____ 2.15 I. 85 4. 62 3. 42 I. 20 1. 20
4__________ __ 2.06 1.86 4.25 3.46 . 79 1.58
6------------ I. 69 I. 78 2. 855 3. 168 -. 313 -. 94
7 ___________ 1. 31 L 66 I. 715 2. 755 -l. 040 -3. 64
1~-- - --- - --- !. 07 1. 55 L 145 2. 402 -1. 257 -4. 71
8 ________ ____ .75 J.39 .562 1.932 -1.370 -5.475
~ --------- . 25 I. 08 . 06255 1.167 -1.1045 -4. 70
8. 2 _______ _ -- Q__ __ ____ ____ -- ---- -------- ------ ---- - -- -- ----- - -- --- -- - - ----- - --- - 2. 09 I. 77 4. 37 3. 133 I. 237
- 2- -- --- ---- L 78 L 78 3.168 3. 168 0
-4---- - - - - -- L 53 L 55 2. 34 2. 40 -. 06 + . 12
-6-------- -- 1.15 I. 33 I. 322 I. 768 -. 446 + L 338
-8__________ .65 1.14 .4.22 1.30 -.878 +3.51
-9______ ____ . 39 I. 03 . 152 1. 06 - . 908 +2. 068
-9 ~- - -- -- -- .25 .99 .0625 .98 -.9175 +4.36
- 10_____ ____ . 11 .94 .OJ2l .883 -.8709 +4.36
-J l.18. - ----1··------ --------,----------1---- ------ -- -- ------1----------
CLARK Y AIRFOl L-o.24 CAMBER
Q_____ _____ __ 2. 46 2. JS 6. 05 4. 755 1 1. 29.'i 0. 0
2- - - - --- ---- - 2. 51 2. 26 6. 30 5.110 I. 19 L 19
4___ _________ 2. 4J 2. 29 5. 1 5. 25 . 56 1.12
6- - - -- ------- 2. 00 2.14 4. 00 4. , -. 58 - L 74
7 ___________ L 58 I. 97 2. 495 3. -L 38.5 -4. 845
7 ~-- - -- - - - -- I. 31 L 2 I. 7!i; 3. 31~ -l. 607 -6. 025'
- --- -- - - ---- . 94 !.6J . 884 2.59 - 1. 706 -6.825
8''1!- -- -- - - --- . 36 I. 2'2 . 1295 ]. 4 - 1. 3585 -5. 765
t~::::::::: ::::=::: :::::::: :::::::::: ::::::::::i:::::::::: :::::::::: -2__________ 2. 22 2. 04 4. 93 4. 16 +. 77 . 77
- 4__ ____ ____ 1.85 l.86 3.4.2 3. 46 -. 04 -.08
-6------- --- 1. 36 1. 62 1. 78 2. 622 - . 842 +2. 522
. 80 I. 35 . 64 I. 22 -1.182 +4. 73
- 9__ _____ ___ .50 l.2J .25 1.463 -1.213 +5. 46
-9~-- - - --- - . 3;, 1.13 . l 221i L 21 -t. J555 +5. 49
-JO_____ __ __ . 19 !. 06 . 036J I. 123 -1. 0869 +5. 43
-10.5____ ___ . 03 .99 . 025 .98 - . 955 +5.0J!i
-10.6 _______ - - ------ ---- ---- ---- ---- -- -- --- ----- -- -- - -- --- -- ----- - --
-11 .19 _____ _ - - - - - --- -- ---- -- -- -- -- -- -- ---- --- -- - - - -- - ----- - - - -- ---- -
CLARK Y ArRFOIL-o.32 CAMBER
[Reference line ~ inch above line connecting center or I.e. and t. e.J
I
I I I I
M~::: :: :::: __ o_fi:i __ ---1.-45· --o.-:iiioo-- --·z:10·-- ·:.:1.-ioo.i- ··:.:1.·25··
8- - ----- - -- - - J 46 I. 98 2. 13 3. 92 -1. 19 -7.16
7~--- - --- -- - I 91 2. 29 3. 65 5. 25 -I 60 -6. 0
7 __ ______ __ _ 1 2. 26 2. 50 5. 11 6 25 -l 14 -3. 99
6- - --------- - 2. 77 2. 0 7. 68 7. 85 -0. 17 - . . 510
4- ---- ----- -- 3. 24 3 o 10.5 9.o + 1. so +3. o
2-- ---------- 3. 36 3. Ol II. 3 9 07 +2. 23 +2. 23
0---------- -- 3. 28 2. 9J JO. 76 8. 47 +2. 29
-2 ___ ______ 1 3 00 2. 71 9. 0 7. 35 + 1 65 - 1. 65
-4---------- 2. 52 2. 4'. 6. 35 5. 81 +. 54 -L 08
-6 _________
1
I. 90 I 2. 05 3. 6J 4. 2J -. 60 +1. 80
-8--- - --- - -- 1.22_ J.64 t.4 _ 2. 69 -1.202 +4.81
-9___ ____ ___ . 191 1.43 .630 2.042 -1.407 +6.34
-9~ -- --- - - - . 65 1. 33 . 4222 I. 768 -1. 3458 +6. 39
-10 _ __ ____ _ , .45 i.22 .zo22 t.49 -1.2818 +6.44
=~?~k: ::::1- - -~~~-+-- '.~'.\---~~:~-- ___'.~ ::i'. __ _:- :'.~'.~~- __::~ ~'.'. __
19
ANGLE BETWEEN THE MINOR AXIS AND CHORD
0.08 CAMBER
t 2 K 2.52 2.52 000474 a=162.5'=8.25'
an a=Iy-I,=534-3. 64=530.136= ·
0.12 CAMBER
3.880 3.880
795.4-12.732 782.668= 0·00496
For camber ratios less than 0.12
0.14 CAMBER
2.48 2.48 0 02
924.6-19.88 904.72= .o 745
0.16 CAMBER
a=-1z7'= .5'
a= l5.2 X t/b
9 5'
a = 2 = 4.75'
1104.~:~9.024 10~5~~76 °·006415
0.20 CAMBER
13.12 13.12 0 0 031 ~= 352.5' = 17.75'
1329.5- 56.-!0= :i273.l = . 1 ~
0.24 CAMBEH
14.60 14.60 0009772 ~=332.5'=16.75'
1585.6-93. 4=1491.76= . ~
0.32 CAMBER
17.20 17.20 O O 9 a=31
2
.51 = l 5.75,
2114-227.04 1886.96= . 0 ll5
For camber ratios greater than 0.12 a=0.2°
/ ~._8~t.348
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SMITH 5ER.JE:i
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FIG. 22
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.32 CAMBER
SMITH SEE/ES
FIG. 23
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