Effect of cellule arrangement on the rate of autorotation calculated by the "strip" method (Airplane Branch report)

              NO • G
Auburn University Lihrnries
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3 1706 025 851 43 2 J
File D 52.151 /55
AIR CORPS INFORMATION CIRCULAR
PUBLISHED BY THE CHIEF OF THE AIR CORPS, WASHINGTON, D. C.
Vol. VII February 1, 1928 No. 609
EFFECT OF CELLULE ARRANGEMENT ON THE RATE
OF AUTOROTATION CALCULATED BY
THE "STRIP" METHOD
(AIRPLANE BRANCH REPORT)
Prepared by H. A. Sutton
Materiel Division, Air Corps
Wright Field, Dayton, Ohio
July 7, 1927 Ralph Brown Draughon
LIBRARY
UNITED STATES
GOVERNMENT PRINTING_OFFICE
WASHINGTON
1928
JUN 1 0 2013
Non·Depoitory
Auburn University
CERTIFICATE : By d iTection of the Secretary of vVar the matter contained
herein is published as administrative info rmation and is required for the proper
transaction of the public business.
(n )
EFFECT OF CELLULE ARRANGEMENT ON RA TE OF AUTO~
ROT A TION CALCULATED BY THE "STRIP" METHOD
This investigation was mad ~ to determine the effect
of changes in tagger and weepback on the lift and
drag characteristics and on the rates of autorotation
calculated by the "strip " method for a model of the
0 - 2E airplane. The study was extended to in clude
the 0 - 1 airplane model and several wing cellules. It
was hoped that the investigation would throw some
light on the effect of cellule arrangement on spinning
characteristics of airplanes.
DESCRIPTION OF MODELS
The 0 -2El was an observation type, single-engined
airplane with a single bay nonstaggered wing cellule.
It was a modification of the 0-2C design, in which the
principal changes were an increa 1e in span of 6 feet,
the installation of d ifferential ailerons which could be
used as flaps, chan_ge in t he gasoline location from wing
tanks to a fuselage tank, and an increase in the ize of
all ta.ii surfaces. This model was modified by sweeping
back the lower wing 5° and moving the upper wing
forward 8 inches, maintaining the same balance loca­tion
as in the 0-2El. The model so modified was
designated as the 0 - 2E2.
The sweepback was increased to 9° and t he stagger
at the center section was increased to 12 inches. This
model was designated as the 0 - 2E3. A model of the
0-1 airplane was also included in the investigation .
Sketches of the above models, showing principal char­acteristics,
are included in this report. (See figs. 1, 2,
3, and 4.)
METHOD OF TESTING
The models wne mounted in the ,) -foot wind tunnel
on the N. P . Ii. type balance by means of a wing tip
spindle. Measurements of lift, drag, and pitching
moment were made in the usual manner through a range
of angle of attack from 0° to 90° in all cases an<l from
-20° to + 120° in a few tests. A}l tests were made
with an air speed of 40 miles per hour at the model.
Results were not corrected for speed effect, scale effect,
or wall interference. The accuracy was slightly lower
than that maintained in tests to be used for calculating
performance qualities, but was considered ample for
the purpose of this investigation.
D'I SCUSSION OF RESULTS
In consider ing the results of this study, it must be
borne in mind that the calculations are based on very
approximate assumptions, some of which are known to
be untrue, and many important factors are neglected.
Relative variation of the aerodynamic forces of lift and
drag on the airplane ar e, however, the fundamental
(1)
cau e of tail spitis or autorotation. Sit1Ce previous
studies have shown that the method of investigation
used in this study checks reasonably well with model
a utorotation tests in the wind tunnel, it was advisable
that an investigation be made of a eries of models
havit1g consistent variations of wing cellule arrange­ment.
Any consistent variation t hus disclosed in the
calcu lated autorotation might be of considerable impor­tance
in indicating solut ion of the problem of control-ling,
by suitable design, the spinning characteristics of
an airplane.
The investigat ion of a simple criterion (p. 5) indi­cating
the angular range through which autorotation
might be expected, revealed very little change due to
variations of stagger and sweepback. In all cases
autorotation begins at about the burble angle. The
low angle region extends from this point to about 30°.
From 30° to about 50° this criterion indicates absence
of any tendency toward autorotation. Another region
of autorotation is indicated from about 50° to 90°.
The model with an unstaggered cellule showed a con­siderably
larger range of a ngular region of autorotation
than any of the staggered models. Increase in stagger
and sweepback indicated a consistent small decrease
in the angular region of autorotation and a greater
separation between the low and high angle regions. In
general the criterion indicated that the calculated
rotation would show a reduction in angular range of
autorotation for the series of models with increasing
stagger and sweepback.
The air force vectors were plotted for all tests to
furnish a collected picture of changes in r elation of the
air forces for different cell ule arrangements. The
center of p ressure position does not enter into autoro­tation
calculation made by t he strip method, but is of
value in a consideration of the spinning attitude.
Although the center of pre ure position as found in
these tests would probably not be true in a spin, the
relative vl!.riation in the d ifferent models could be
relied upon as a first approximation.
All autorotation calculations were made about a
center of rotation assumed at the center of the span.
In gei1eral two regions and rates are shown indicating
that at some angles there may be two rates at which
:tutorotation could occur. With exception of the
0 - 2El model there is little difference in the calculated
a utorotation of the four models. (See fig. 5.) The
0 - 2El indicates a steadily increasing speed with
increase in angle through the range investigated.
Calculations made from wing cellule tests without
fuselage show (see fig. 6) increasing speed with increas­ing
angle similar to the 0 - 2El model results.
I
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Movement of the center of _rotation along the "Y"
axis from the center of the span changes the character
of the rotating moment curves considerably.
Flight tests have shown that the method of investi
gation and results secured in th.is report are not pro­ductive
of any result which can be used at p resent in
predicting the spinning characteristics of an airplane.
In view of the large number of assmnptions which have
been made in this study and in previous similar
calculations and model autorotation tests, it is not
unu sual that the results should have little relation to
the action of a full scale airplane not bound by these
as urned conditions. A serious di crepancy is that
the calculation indicated that an increase in angle of
attack would assist in recovery from a spin except in
the case of the 0-2El, while a reduction in angle of
attack below the burble point has been the only effec­t
ive method of stopping a spin. Flight te ts also
proved that the rate of rotation and attitude of an
airplane in a spin can be varied through large ranges by
changing the load distributiop. A calculation of
autorotation characteristics by the method used in this
study can not, therefore, be expected to yield any
information which will be generally applicable to a
spinning airplane.
Descriptions of flight te.sts on the 0-1, 0 - 2El, and
0 - 2E4 airplanes are given in Materiel Division
Reports No. 2770, A. D. M. 884, and D 52.l Douglas-67
CONCLUSIONS
1. An increase in stagger and sweepback resulted in
increases in both maximum lift and drag.
5
2. Although changes in stagger and sweepback
resulted in small changes in the calculated autorotation,
the differences were small and the conclusion that
stagger is beneficial in reducing the angular range,
through which forces tending to produce autorotation
occur, is subject to misinterpretation unless all pertinent
assumptions are considered.
3. Results obtained by the" strip method" of analyz­ing
autorotation are r elatively u nimportant, in pre­dicting
spinning characteristics of airplanes, because of
the erroneous assumptions made and the factors of
great importance which arc neglected .
4. The development of a satisfactor y t heoretical
ba ·is upon which to p redict spinn ing charact.cristics i
dependent on the accumulation of sufficient fact
regarding tail spins by means of flight testin g.
CRITERION FOR DETERMINATION OF REGION
OF AUTOROTATION
In a discussion of the autorotation of an aerofoil
co11tained in Reports and Memorauda No. 595 by t he
British Advisory Committee for Aeronautics and in
T echnical Memorandum No. 380 by the National
Advisory Committee for Aeronautics, the following
criterion for determining the region in which auto­rotation
may be expected is given.
Taking a in degrees, the region of autorotation is
determined by the condition that 180/7r(dKy/da) +
K,<O and the limits of ao and a1 are obtained by
equating this expression to zero. K, is always positive
and the general form of K>' is that it rises rapidly from
a= 0 to a maximum at the crit ical angle and than falls
off at a decreasing rate to zero at or about a= 90.
Autorotation will occur provided that the ncgati ve
slope of Ky above the stalling angle is sufficiently great
to outweigh the value of I(.. The lower limit ao will
be nearly equal to the critical angle. The upper
limit is determined by the rate at which the drag
coefficient increases and the negative lope of the lift
coefficient decreases.
The values obtained by applying this criterion to the
wind tunnel r e ults for the 0 - 2El , 0-2E2, 0-2E3,
and 0 - 1 models arc plotted in Figure 1. Two regions
of a uto rotation arc indicated-one from abo ut t he
cri t ical angle to between 24° and 30°, and the other
between 50° and 90°. A fairly consistant small reduc­t
ion in t he angular range of autorotation is indicated as
the stagger is increased.
The region of a utorotation a calculated by the strip
method agrees reasonably well with the above criterion
except in the case of the 0-2El.
METHOD OF CALCULATING THE RATE OF
AUTOROTATION
A summation of the vertical and horizontal compo­nents
of t he lift and drag forces, as measured on the
model in the wind tunnel, is made for several assumed
conditions of spinning. From a summation of the ver­t
ical components the vertical velocity i determined.
A summation of the moment of the vert ical and hori­zontal
forces about the center of gravity gives the rate
of rotation abo ut the two axes, provided all damping is
neglected.
In these calculations the airplane is assumed to be
spinning to the left . Forces and moments are calcu­lated
for the following assumed condiiions:
Angle of attack at the center of rotation,
Ratio of horizontal velocity of the outer wing tip
to t he vertical velocity, and
Center of rotation.
Figure 8 shows the force acting on a wing rotating
to the left with a horizontal velocity, Vn" at the right
wing t ip and settling with a vertical velocity, Vv. The
angle of attack at the center of rotation i ao. At the
wing t ip which i moYing forward with re pect to the
center of rotation the angle of attack is diminished from
ao by an amount Ll.a1 = Ta n- 1 V n1/Vv. At the wing
tip \\·hich is moYing rearn·ard \dth respect to the center
of rotation t he angle of attack is increased from ao by
an amount Ll.a2 = Tan- 1 Vn2/Vv. If the center of r ota­t
ion is at the center of t he span VR1=VR2 and Ll.a1 = Ll.az.
The air forces are resolved into their vertical and hori­zontal
components. Kv and l.\n, wh.ich determine the
settling and rotational velocit ies respectivel.''-
For each value of ao assumed, Kv and Kn arc cal­culated
for several values of .".a. Tan LI.a is assumed to
vary linearly along the span. A true angle of attack
can thus be determined for each point along the span.
For an increment of area Ll.s, the increment of vertical
force is Ll.Fv=Kv VE2 Ll.s = Kv Vv2 Sec2 Ll.a·Ll.s. A um­mation
along the span give the total for the airplane.
The vertical velocity downward is found from the rela-t
ion Vv = .Jiv·
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'Th ts tip moves forward wz'th
r espect to center of rotation.
ao -LJ«, is true angle of attack.
Kv=J(y5tn.LJcx+Kx Co~.Ll a
/(R =Ky Cos. LJcx-f(x .5tn. LJ a-
CKo,;:Anq/e ofottock otcellterof rotmi ·
VR= Velocity due to rotatwn
Vv= Verftcaf ve!ocdy ·
V£=VvSect::Jcxeffectl'veor resultant
velocity
Li a= Cf7a(lqe tn anq!e of ollack from
0<0 of pouits awoyfrom center of
rotatz on due to 0-?
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For an increment of area As, located at a di tance 1,
from the center of the span the increment of rotating
moment about a horizontal axis is AMnv= Kvl Vv2 Sec2
!!.a · A<: A summation along the span gives the total rotat­ing
moment about the horizontal axis. Moments which
tend to raise the inner wing are considered negative.
0-2E1, Dwg. X - 150214, with stagger and sweepback
removed-Lift and drag on 1/24 scale model tested in
McCook Field 5-foot wind tunnel at 40 m. p. h. ·
For an increment of area As, located at a distance 1,
from the center of the span, the increment of rotating
moment about a vertical axis is AMna=Knl Sec2 !!.a·
Vv2 !!.s. A summation along the span gives the total
rotating moment about the vertical axis. Moments
tending to rotate the airplane in the direction of the
spin are considered positive.
The rotating moments thus determined are plotted
against the rate of rotation. Since damping moments
have been neglected t he points at which these moment
curves cross t he zero moment axis will give rotational
speeds at which the airplane would maintain rotation,
or autorotate.
Angle
or at-tack,
degrees
-6
4
2
0
+2
4
6
8
10
12
14
16
20
24
26
28
K, K,
-0. 000381 +o. 0001 6
+. 000039 . 000157
. 000-131 . 000147
. 000832 .000148
. OO!l82 . 000163
. 001543 . 000186
. 001876 . 000217
. 002202 . 000256
. 002523 .000305
. 002731 . 000381
. 002878 . 000460
.002700 . 000656
. 002629 • 000948
• 002520 . 001237
• OQ?A60 . 001363
. 002430 • 001475
Angle
of at- tack, K, K.
degrees
30 + o. 002360 +o. 001519
32 . 002358 . 00169
36 . 002282 . 001873
40 . 002197 .002027
44 . 002097 . 002198
48 . 001972 . 002360
52 . 001814 . 002458
56 . 001623 . 002510
60 . 001400 . 002541
64 . 001190 . 002505
68 . 000944 • 002355
72 • 000798 . 002318
76 . 000671 . 002379
80 . 000523 . 002425
84 . 000369 .002464
88 . 000199 . 002505
Autorotation calculation for 0- 2E, Drawing X - 150214, with stagger and sweeiiback removed
Aa 13+ Aa K, K x I
--
0 + 13 +o. 00283 0. 000 12
5 18 . 00267 . 00079
10 23 . 00255 . 001l7
15 28 . 00243 .00148
20 33 . 00234 . 00174
- --
13-Aa
---
0 + 13 +. 00283 . 00042
5 18 . 002202 . 00026
10 3 . 00137 . 000175
15 -2 +. 00043 •. 000147
20 7 -. 00055 . 000210
15+Aa I
---
0 15 +o. 00219 I +o. 00052
5 20 . 00263 . 00095
10 25 . 00250 . 00130
15 30 . 00239 . 00158
20 35 . 00230 .00183
25 40 . 00220 . 00203
30 45 . 00206 . 00224
---
15-L\a
---
0 +is +. 00279 +. 00052
5 10 . 00252 . 00031
10 5 . 00171 . 00020
15 0 +. 00083 .00015
20 -5 -. 00013 . 00017
25 10 .00105 . 00036
30 15 .00126 . 00058
I
Calculation of Kv and Ka
ao = l3 degrees
K, Sin Aa Kx Cos Aa Kv
---
0 0. 00042 +o. 00012
. 000233 . 0007 7 . 000554
. 000443 . 00ll52 . 000709
. 000629 . 001430 . 000801
. 000800 . 001636 . 000836
0 . 00042 +. 00042
. 000192 . 000259 . 000!51
. 000238 . 000172 . 000410
.000111 . 000142 . 000253
.00018 . 000197 . 000009
ao= 15 degrees
0 0. 00052 +o. ooos2
. 000229 . 0009-!6 .0007 17
. 000434 . 00128 . 000846
.00061 . 001527 .000909
. 000786" .00172 . 000934
. 000930 .00184 . 000910
. 001030 .00 194 . 000910
0 .0001\2 +. 00052
. 000219 . 00031JlJ . 000528
. 000297 . 000197 . 000-19-1
.000211\ . 000145 . 000360
. 000044 . 000160 +. 000116
. OOOl4~ . 000326 -. 000118
. 000630 I . 000502 -. 000128
I
K, Cos Aa Kx Sin Aa Ka
o. 00283 0 -0. 00283
. 00266 . 000069 . 00273
. 00251 . 000203 . 00271
. 00235 . 000383 . 00273
.00220 . 000595 • 002795
. 00283 0 +.00283
. 002192 . 000023 .00217
.00135 . 0000304 . 00132
. 000!16 . 000038 +. 0003
. 000517 . 0000718 - . 000589
0. 00279 0 -0. 00279
. 00262 • 000083 . 002i0
. 00246 . 000226 . 00269
.00231 . 000109 . 00272
.0021~ .000626 . 00279
. 001994 . 000858 . 00285
. 001784 . 00112 . 00290
. 00279 0 +. 00279
. 00251 . 000027 . 00248
. 001684 . 000035 .00161\
. 000801 . 000039 +.00076
. 000122 . 0000.'iS -. 00018
. 000951 . 000152 . 00110
.00109 . 000290 .00138
.0028 /\
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) .,. ..::J \
nf' 1() I ,,v; () - 9fr1 \
I I/ !' '(J •' ' ,, 't l'f •. IL - .I ~
I I - /)/) n.R ~
I " j J -c---,__
()(, hr,:; I I I /fr " I I w "--
(]() f'Jd I I / '\
'-
// "' ' +nr /19 J ..... ~ ( "!\..
'~ ~ -- ,
I /
a I /v l..1r '(')/ , , n ; ~ ' I
I /v
..,
711". /l? s• /; Do ,o 10 0 1 , IJ " ~')· v_i o ' 50 .t.O" ..:: .i:;o :. a· ' 'i')o t ;(Jo t ~")'· . o· :5 0 o· } .'i 0
]'10. 12
L
L
I
')Ve
)5"/._ o '
L co
25
l
I
50 YJVE'
''°'3o~
L :D
10°
v~,,....__501 /,)
VE,A_"-10•1
/ ~.5·._J
12
Liff ond droo. vectors
0-ZEI !1odel wi-lhollt sta99er:
or sweepback «o = 35° .
A ex,= 15° 0 rrueL of off. =ZO
Lla'i =25°
Tnu:Lofa#.=10°
Aa1=30°
TrueLafalt =5°
Llcx1 =35° 0 Tn;etotatl =O
L1 a't =40°
True L ala#:::: - 5°
da't =45°
TrueL ofall=-10°
L) ex, = 10°
TrueLofalt. = 45°
L}C(,::::15°
True L of alt= 50 °
Ll d/ :::::zo 0
Tr11e/ofatf ==.55°
LJa'1=Z5°
. TrueLotall: :::: (j() 0
Ad1::::J0°
TrJLe /at all =-<O 5 °
Lld1=35°
True/ at all= 70 °
FIG. 13
13
nm - - .,,_ ~~.b rr t? v,,. : .... 1., · .... ,_jt., .( f-,/
l/J .., 1 ~ 17' , __ , - .+ ~ ~
, __
ei.. ,__ - -- ~ _, / -~
-
In<
t-- t--~
r-- 1--~ - r-..~ ...... 1-,
~ ""; ,_ ~ , ,,~ -
Int
-i-- r-- -r-..... .:: ........ "- ' ~J; O I. .,, !".:..._
-t ~ L-- -- --t-- f'::..._ l'l!>-!:la;
r--1--t-- .............. I'-...._
/( IJ . -~~ ~ i.-· r---... [..., o I'-. 11~ " Jl5 ,...__ -· :;-::: i--.... ~15" 4w I'-.. ~15-
/ Irr - "'-' ""' :r, I'--- 3.?£ IA~
>111
FIG.H
1? . .s-'• - ·- 1..c-
._. _
- '-~
ti. _,- -J- ,,,
nH ~-
'7 " ''
,;_, .., __
.J_ ,
15 LI :<,
. J
........ - -- .,.. Ar " r-...... - -.....
n,\? "" " "t-... A5 -4 oc,
" "- " .........
-....., " " !".....
' I"'- -....., "'
,,, , !'... " ' ~ - ~ ' Ii'.. " ' " f'.... .;. "' 'r..... ""- '""-
~ ~ '\ ...
IJC n . •o• Ii;• ['.. . ,,,. ~~· f"-. ·I n ' <!<:•
..... r......
1-0 ,!!;•
- " . er I". f"-.
- ....... '"t-... -.....,...
" !'-.... " t-... 1"' "' ~
n.it
'r--... 1--
~--
111'1 ? 4'1~ lz.
_i.--
I '2< ,.._ -.
'?• '.L 1~ - - '
/I ll~ 1 ... ·~ '
FIG. 15
14
A utorotation calcu!ation for 0-2E1, Drawing X - 150214, with stagger and sweepback removed-Continued
Calculation of Kv and KR
ao=25 degrees
f>a I 25+ t>a I K , K , K , Sin l>a K, Cos t>a l_Kv K,. C os f>a Kx Sin 6a KR - i- -- --
~ 25 +o. 00250 + o. 00130 0 0. 001 30 + o. 00130 0. 00250 0 -0. 002~0
5 30 . 00239 .00158 . 000208 . 001 57 . 00136 . 00238 . 0001 38 . 00252
JO 35 . 002:JO . 001 83 . 000399 .001 0 .00140 . 002266 . 00031 . 00258
15 40 . 00~20 . 00203 . 000570 . 00196 . 00139 . 002126 . 000526 . 00265
20 4!i . 00206 . 00224 . OOOi().J .00210 .00140 . 001936 . 000766 . 00270
2!i 50 . oorno .00211 . 000803 . 0021 , 5 .00138 . 001722 .00101 . 002i4
30 55 . 001(i8 . 00250 . 000810 .0021r.G .00138 .001 l!i5 . 001 250 . 00270
35 GO . 00140 . 0025-1 . 000ii03 . 0020l>l • ()()l~ . 001147 . 001455 . 00260
---
2f>-..1a
---
0 +25 +. 00250 + . 00130 0 .00130 +. 001 :io . 00250 0 +.00250
.1 20 . 00203 .00095 . 000229 . ()()()1117 .00118 . 00262 . 00008,3 . 002fi4
10 15 . 00279 . 00052 . 000484 . 000512 . 00100 . 00275 . 000090 . 00266
15 10 . 002.12 .00031 . 000652 . 000290 . 00095 '00243 . 0000 0 . 00235
20 5 . 00 171 . 00020 . 000585 . 000188 . 00077 .OOtr,07 . 000068 .001 51
25 0 +. 00083 .00015 . 000351 .000136 . 00049 . 000752 I . 000063 +. 00069
30 -5 - . 00013 . 00017 . 000065 . 000147 + . 00008 '000113 . 000085 -. 00019
35 10 . 00090 . 00030 . 000.116 . 000246 -. 00027 . 000737 . 000172 . 00091
ao=35 degrees
35+t>a
---
0 35 + o. 00230 0. 00183 0 o. 001 83 +0.00183 0. 00230 0 -0. 00230
5 40 . 00220 . 00203 . 000192 . 00202 . 00183 \ . 00219 . 000177 . 00237
10 45 . 00206 . 00224 . 000357 . 00221 . 00185 . 00203 . 000389 . 002 l2
15 50 .00190 . 00241 . 000492 . 00233 .00184 . 001835 . 000624 . 00246
20 55 . 00168 . 00250 . 000575 . 00235 . 00178 . 00158 . 000855 . 00243
25 60 . 00140 . 00254 . 000592 . 00230 . 00171 .00127 . 001073 . 00234
30 65 . 00113 . 00248 . 000565 . 00215 . 00159 . 000979 . 001240 . 00222
35 70 . 00087 . 00233 . 000499 . 001908 . 00141 . 000712 . 001337 . 00205
40 75 . 00070 . 00236 . 000450 . 001 08 . 00136 . 000536 . 001 517 . 00205
45 80 . 00053 . 00242 . 000375 . 001710 . 00133 . 000375 . 001710 . 00208
ao=35 d egrees
· 35-.1a I I I
0 35 + o. 00230 + 0. 00183 0 0. 00183 +o. 00133 0. 002300 0 +o. 00230
5 30 . 00239 . 00158 . 000208 . 001575 . 00178 . 002380 . 000138 . 00224
10 25 . 00250 . 00130 . 000434 . 001280 . 00171 . 002462 . 000226 . 00224
15 20 . 00263 . 00095 . 000680 . 000918 . 00160 . 002540 .000246 . 00229
20 15 . 00279 . 00052 . 000954 . 000189 . 00144 . 002622 . 000178 . 00244
25 JO . 00252 . 00031 . 001065 . 000281 . 00137 . 002283 . 000131 . 00215
30 5 . 00171 . 00020 . 000855 . 000173 . 00105 .0014 2 . 000100 .00138
35 0 + . 00083 .00015 . OOOl76 . 000123 . 00063 . OOOf>BO . OOOOS6 +. 00059
40 -5 -. 00013 . 000 17 . 0000835 . 000130 +. 00005 . 00009<J6 . 000109 -. 00021
45 JO . 00090 . 00030 . 000636 . 000212 -. 00().Jl . 000636 . 000212 . 00085
ao = 45 d egrees
45+t>a
---
0 45 + 0.00206 + o. 00224 0 0. 00224 + o. 00224 o. 002060 0 -0. C0200
5 50 . 00190 . 00241 . 000166 . 00240 . 002".3 . 001893 . 000210 . 00210
10 55 .0016 . 00250 . 000291 . 002462 . 00217 . 001655 . 000434 . 00209
15 60 . 00140 . 00254 . 000362 . 0024 53 . 00209 . 001352 . 000657 . 00201
20 65 . 00113 . 00248 . 000386 . 002330 . 00194 . 001062 . 000848 .00191
25 70 . 00087 . 00233 . 000368 . 002112 . 00174 . 0007 9 . 0009 5 . 00177
30 75 .00070 . 00236 . 000350 . 0020-14 . 00169 . 000606 .0011 0 . 00179
35 80 . 00053 . 00242 . 000304 . 001982 . 00168 . OOQ.134 . 001 . 00182
40 I 85 . 00033 . 00248 . 000212 . 001900 .00169 . 000253 . 001 59~ . 001 5
45 90 . 00012 . 00252 . 000085 . 001782 . 00170 . 000850 . 001782 . 00187
ao=45 degrees
45-f>a I ---
0 45 + o. 00206 +0.00224 0 0. 002240 + o. 00224 0. 002060 0 +o. 00206
5 40 . 00220 . 00203 . 000192 . 002023 . OOZ21 . 002192 . 000177 . 00201
10 35 . 00230 .00183 . 000399 . 001803 .00220 .002267 .00031 . 00195
15 30 . 00239 . 00158 . 000618 . 001 526 . 00214 . 002308 . 000409 .00190
20 25 . 00250 . 001 30 . 000855 . 001222 . 00208 . 002350 . 000145 .00190
25 20 .00263 . 00095 . 001112 . 000 61 . 00197 . 002385 . 000401 . 00198
30 15 . 00279 . 00052 . 001395 . 000450 . 00184 .002417 . 000260 . 00210
35 10 . 00252 . 00031 . 001445 . 000254 . 00170 . 002064 . 00017 . 00189
40 5 . 00171 . 00020 . 001099 . 000153 . 00125
I
. 001310 . 000129 . 00118
45 0 . 00083 . 00015 .000586 . 000106 . 00069 . 000586 • 000106 . 00048
15
Calculation of vertical force and rotating moments for 0 - 2E1 model
(Center or rotation at centor or span)
no= 15 degrees. .1a1 = 2 degrees
Sec1Ua I Kv Kv Sec•
!\a: · At
---------- ----1-----1-----
~'. ~~1' KR Kan~.s;~· j
22.84
20 . . 56
15. 98
11. 42
6. 5
2. 28
0
2. 28
6. 85
I I. 42
15. 9~
20. 50
22. 81
22. 84
20. 56
15. 98
II. 42
6. 85
2. 28
0
2. 28
6. 85
II. 42
15. 98
20. 56
22. 84
22.84
20. 56
15. 98
II. 42
6.85
2. 28
0
2. 28
6. 85
II. 42
15. 98
20. 56
22. 84
22. 84
20. 56
15. 98
II. 42
6. 85
2. 28
0
2. 28
6. 85
ll . 42
15. 98
20. 56
22.84
22. 84
20. 56
15. 98
JI. 42
6. 85
2. 28
0
2. 28
6. 85
11. 42
15. 98
20. 56
22.84
0
41. 8
51. 8
51. 8
·'1. 8
42. 8
0
42. 8
51.
51. 8
51. 8
41. 8
0
0
41. 8
51. 8
51. 8
51. 8
42.8
0
42. 8
51. s
51. 8
51.
~!. 8
0
0
41. 8
[1 1. 8
51. 8
51.8
42. 8
0
42.8
51. 8
51. 8
51.8
41. 8
0
0
41. 8
51. 8
51. 8
51.8
42. 8
0
42. 8
51. 8
51. 8
51. 8
41. 8
0
0
41. 8
51. 8
51.8
51. 8
42.8
0
42. 8
51.8
51. 8
51. 8
41. 8
0
98091-28--3
---=0:~~r-- -_:0:~~tf · --=n~rl
. 33i . 002i6 I. 632
2 0 ------------ -----·--·-----
1 4 1.001 + o. 00001 + o. 0255
I 24 1.000 . 00059 . 0306
I 0 J.000 . 0005i . 0295
0 36 J.000 . 00055 . 028:\ . 195 . 00277 . 983
0 12 1.000 . 00052 . 0222 --·---------- . 00278 . 271
0 12 1.000 . 00052 .0222 ----------- +. 00279 +.272
0 36 1.000 . 00052 . 0269 +. 184 . 002i8 . 9 5
I 0 J.000 . 00052 . 0269 . 30i . 002i8 I. 643
I 24 J.000 . ()()(}[12 . 0269 . 430 . 0027i 2. 292
I 48 1.001 . 00052 . 0217 . 446 . 002i5 2. 362 ----
---- -- ---- ------------- +. 2609 -. li8 -----------·-! +.033
a:o= l5 degrees. .6.a1=5 degrees
i ~ ---n~r --:~0:·~-- -·-+0:-8rJ·- ---=0]ll5-- --=0:-~~tf ---=r~rJ
2 30 I. 002 . 00064 . 0332 . 3i9 . 002i3 I. 615
i 30 1. 001 . 00000 . 0313 . 2145 . 002n . 9n
0 30 I. 000 . 00054 . 0231 . 052i . 002i7 . 2i0
0 30
I 30
2 30
3 30
4 30
5 0
15 0
13 33
JO 3i
38
35
32
1 32
4 3.5
7 38
JO 37
rn 33
.15 0
5 0
4 30
3 30
2 30
l 30
0 30
0 30
I 30
2 30
3 30
4 30
5 0
I. 000 . 000:\2 . 0222 +. 0506
I. 001 . 00052 . 0269 . 1843
I. 002 . 00052 . 0269 . 30i
1.004 . 00052 . 02i0 . 4315
1.007 . 00052 . 021 . 448
---------- ------------- ------------- -------------
+. 27i7 -.405
a o= 15 degrees. .1a1=15 degrc~s
---- -- --- - ------------ - ------------- -------------
I. 059 + o. 00089 + o. 0349 -0.810
1. 035 . 00085 . 0455 . 72i
J.018 . 000i9 . ()416 . 4i5
I. 007 . 00072 . 03i5 . 257
1.001 . 00060 . 0259 . 059
1.001 . 00052 . 0222 +. 051
I. OOi . 00052 . 0271 . 186
I. 018 . 00051 .0269 . 30i
J.035 . 000!8 . 0257 . 4Jl
1.059 . 000-10 . Oli7 . 364
-- -- ------ ------------- ------------- ----------- --
+. 3095 -1. 009
ao=25 degrees . .1a1=5 degrees
----- ------ - ----------- ------------- --------- ----
1. 007 +o. 00131 + o. osn -1.186
1.004 . 00135 . Oi02 J.122
1.002 . 00134 .0696 . 795
I. 001 .00132 .0685 .469
1.000 . 00131 . 0556 -------------
1.000 . 00130 . 0556 -------------
1. 001 . 00127 . 0659 +.451
1.002 .00125 . 0648 . 740
J . 004 . 00123 . 0639 I. 022
1. 007 .00120 . 0505 1. 038
+. 6223 I -. 321
ao= 25 degrees. .'.\a1 = 15 degrees
+. 00278 +.271
. 002ii .983
. 00272 I. 610
. 00264 2. llO
. 00254 2. 198
------------- ----------·
- . 281
--- ---------- ----------- -
-0.002i0 - 2. 458
. 00268 2. 292
. 002f>8 I. 613
. 002i0 . 964
. 00275 . 268
+. 002i5 + . 2
. 00253 . 904
. 00212 I. 27,;
. 00153 I. 310
.00100 . . 910
------------- -----------.
- 2. 928
------------- ------------
-0. 00252 - 2.180
.002'11 2. 084
. 00250 I. 4 l
. 00250
. 00250 • 244
+. 00250 +. 244
. 00250
. 00250 1. 481
. 00251 2. 084
. 00252 2.180
15 0 ------------ ----------- ---------- --- ------------- ------------- ------------
13 33 1.059 +0.00140 +0. 0618 - l.2i0 -0.00263 - 2. 390
JO 37 I. 035 . 00140 . 0751 I. 200 . 00259 2. 217
7 38 I. 018 . 00139 . 0730 . 833 . 00254 I. 528
4 35 I. 007 . 00136 . 0710 . 486 . 00252 . 901
I 32 I. 001 . 00133 . 0569 . 130 . 00250 . 244 --Tl"-- T~r-- ---~~!~-.- ------~~~r -----+]~-- ---+~~~~r ----~:-*CI
l 0 37 1. 035 . 00099 . 0528 . 844 . 00267 2. 290
13 33 I. 059 . 0009i . 04.29 . 882 . 00251 2. 280 I
15 0 -------- --- - ----------- --- - --------- ----- - ------- - --- --------- ------------
+. 6080 -. 988 +. 010
16
Calculation of vertical force and rotating moments for 0-2EJ model-Continued
da
(Center of rotation at center of span)
a o=25 degrees. da1=25 degrees
Sec•aa Kv Kv Sec•
lla•.6.r
Kv Sec•
da·drl
Knl Sec'
.cla·!lr
- ------------1-----1----1-----1-----1-----1
22. 84 0 25 0 --------- - ------- --- --- ---- --- --- --- --- -- ---- ---- ----------- -- --------- ---
20. 56 41. 8 22 46 1.177 +o. 00140 +o. 0689 -1.416 -0. 00273 -2. 758
15. 98 51. 8 18 4 l.107 . 00140 .0803 I. 283 . 00268 2. 455
11.42 51. 8 13 7 1.053 .00140 . 0763 . 871 . 00262 l. 631
6.85 51. 8 7 58 J.020 . 00139 . 0735 . 504 .00255 . 922
2. 28 42. 8 2 40 l.002 . 00134 . 0574 . 131 .00250 . 244
0 0 ---- -- --- - --- --- ---- --- ----- ----- ------------- --- ---------- ---- --------- ------------
2. 28 42.8 2 40 1.002 . 00125 .0536 +.122 +. 00250 + . 244
6.85 51. 8 7 58 1.020 .00106 .0560 . 384 . 00263 . 951
11. 42 51.8 13 7 1.053 . 00097 . 0529 . 604 . 00255 1.587
15. 98 51. 8 18 4 1.107 . 00087 . 0498 . 796 .00185 1. 693
20.56 41. 8 22 46 I. 177 .00063 . 0310 . 637 . 00107 1.081
22. 84 0 25 0 ------- --- ------------- -- -------- --- ---- -- ------- -------------------- -----
+. 5997 -1.662 -2. 454
a o=35 degrees. da1=5 degrees
22.84 0 5 0 --+ii.-00185-- ---+ii:ii778-- ----~ i : 600 - - ---- -- ------- ----------- -
20.56 41. 8 4 30 1. 007 -0. 00235 -2. 030
15. 98 51. 8 3 30 1.004 . 00185 .0961 l. 536 .00235 I. 953
11. 42 51. 8 2 30 1.002 . 00185 .0960 1. 097 . 00233 I. 383
6. 85 51. 8 1 30 1.001 .00185 .0958 . 656 .00232 . 824
2. 28 42. 8 0 30 1.000 .00185 . 0792 ------ ------- . 00230 . 224
0 0 ----- ----- ---------- --- -------- -- ----- --- ----- ------ --- ---- ------------- ---- --------
2. 28 42. 8 0 30 1.000 . 00184 . 0792 ---- --------- +. 00229 +. 223
6. 85 51.8 I 30 1.001 .00182 . 0944 +.647 . 00228 . 810
11. 42 51.8 2 30 1.002 .00181 . 0939 1.072 . 00227 1. 346
15. 98 51.8 3 30 1.004 .00180 .0936 1. 496 . 00226 I. 877
20.56 41. 8 4 30 1.007 .00178 . 0749 1.540 .00225 1. 945
22. 84 0 5 0 ---------- --------- --- - ------------ - ------------- --- -- -------- --------- ---
+ . 8809 - . 134 -.213
ae=35 degrees. aa1=15 degrees
22. 84 0 15 0 ---1:059-- --+0.-00183-- --- ---------- ----- -------- --- -------- -- ------------
20.56 41. 8 13 33 +0.0810 - 1.665 -0. 00244 -2.218
15.98 51.8 IO 37 I. 035 .00185 .0991 I. 583 . 00242 2. 071
11.42 51. 8 7 38 1.018 . 00185 .0975 1. 113 . 00239 1. 440
6.85 51.8 4 35 1.007 .00185 . 0965 . 661 . 00235 .839
2. 28 42. 8 l 32 1. 001 . 00185 . 0792 .180 . 00232 . 226
0 0 ------ ---- -------- -- -- --- -- ------ ---- -- ------- -- ----------- ------------- --- ---------
2. 28 42. 8 l 32 1.001 .00182 . 0779 +. l7i +.00228 +.222
6. 85 5L 8 4 35 I. 007 . 00178 .0928 . 635 . 00225 . 804
IL 42 51. 8 7 38 1.018 . 00175 . 0922 1.053 . 00223 1. 343
15. 98 51. 8 JO 37 1.035 .00170 . 0912 1.457 . 00233 1.910
20.56 41. 8 13 33 1.059 .00163 .0721 1. 482 . 00227 2. 064
22.84 0 15 0 -------- -- ---- ---- ----- ------------- ------------ - ---- --------- ------------
+. 8795 -.398 -.451
ao=35 degrees. da1 =25 degrees
' I 22. 84 0 25 0 ---------- ----------- -- --------- -- -- ------ ---- --- ------------- ------------
20.56 41. 8 22 4.5 1. 175 +o. 00115 +o. 0859 -!. 765 -0. 00240 -2. 420
15. 98 51.8 18 4 1. 106 .00180 . 1031 I. 647 . 00245 2. 242
IL 42 51.8 13 8 1.053 . 00183 . 1000 1.142 . 00244 1. 518
6.85 51.8 7 58 1.020 .00185 .0977 . 669 . 00240 .868
2. 28 42. 8 2 40 1.002 .00185 . 0793 .181 . 00233 . 278
0 0 ----- -- --- ---------- - -- ---------- ------------- ------------- ----- -------- ---- --------
2. 28 42. 8 2 40 1.002 .00180 . 0771 +. 176 +. 00227 + . 222
6. 85 51. 8 7 58 1.020 .00174 . 0920 . 630 . 00223 . 807
11. 42 51. 8 13 8 1.053 .00165 .0900 1.027 . 00227 1. 412
15. 98 51. 8 18 4 1.106 . 00150 .0859 I. 372 . 00239 2. 187
20. 56 41. 8 22 45 1.175 . 00143 .0702 1. 443 . 00234 2. 360
22. 84 0 25 0 ---- ---- -- ------------- ---- ----- ---- ------------- --- ---------- ------------
+.8812 - . 756 -.338
•
17
Ca ~ cu!ation of vertical force and rotating moments Joi· 0 - 2E1 model-Continued
Aa
(Center of rotation at center of span)
a o=35 degrees. Aa 1=35 degrees
Sec2L\.a K v Kv See'
Ila L\.s
K v Sec'
Aa·~• I
- - - -----------1-- ----1----- ----- ----- ----
22.84 0 35 0 ------- - -- ------------- ------------- --- - --------- - - - - ---- - ---- ------------
20. 56 41. 8 32 12 l. 397 + o. 00152 + o. 0887 - 1. 823 - 0. 00212 .-2. 545
15. 98 51. 8 26 6 I. 242 . 00168 . 1080 l. 726 . 00230 2. 361
II . 42 51. 8 19 16 I. 122 .00180 . 1045 J.193 . 00245 1. 625
6. 85 51. 8 II 52 I. 044 . 00185 .1000 . 685 . 00243 .899
2. 28 42.8 4 0 1. 003 . 00185 . 0794 . 181 . 00235 . 230
0 0 ---------- ---------- - - ----------- ---- -- ------ - -------- - --- - ---- --------- --- - --------
2. 28 42. 8 4 0 1. 003 . 00180 . 0773 +. 176 +. 00225 +. 220
6. 85 51. 8 II 52 1. 044 . 00167 .0903 . 581 . 00225 . 833
ll. 42 51. 8 19 16 l. 122 . 00146 . 0849 . 970 . 00243 l. 611
15. 98 51. 8 26 6 L 242 . 00130 . 0837 I. 337 . 00198 2. 035
20. 56 41. 8 32 12 L. 397 . 00088 . 0513 I. 054 . 00105 ' l. 259
22. 84 0 35 0 ---------- --------- - ---- ---------- - -- ------------- --- -------- - - ------------
+. 8681 -l.490 -1. 702
a o=45 degrees. Aa1= 15 degrees
22. 84 0 15 0 ---------- ------------- ----- - ------ - --- - --------- ----- - ------- ------------
20. 56 41. 8 13 33 I. 059 + o. 00210 + o. 0936 - 1. 925 - 0. 00204 - 1. 855
15. 98 51. 8 IO 37 1. 035 . 00216 . 11 57 I. 848 . 00208 !. 782
11. 42 51. 8 38 1. 018 . 00220 . 11 59 I. 324 . 00209 !. 258
6. 85 51. 8 35 1. 007 . 00222 . 1158 . 793 . 00209 . 746
2. 28 42. 32 1.001 . 00223 . 0955 . 218 . 00207 . 202
0 0 ------ - - - - ------ - --- ------- ------ - ---- - -- - --- - ------------- ------------ - --
2. 28 42. 8 I 32 l. 001 . 0022"J . 09fi5 + . 218 +. 00205 +.200
0. 85 51. 8 4 35 l. 007 . 00222 . 1158 . 793 . 00202 . 722
IJ.42 51. 8 7 38 I. 018 . 00220 I . 11 59 !. 324 . 00198 I. 192
15. 98 51. 8 JO 37 L 035 . 00210 .i 157 !. 848 . 00195 L. &70
20. 56 41. 8 13 33 J. 059 . 00215 . 0936 J. 925 . 00192 I. 745
22.84 0 15 0 --- ------- -------- ------------------ ------------- ------ - ------ ------------
I + L 0£30 -. 314
a o= 45 degrees. Aa1=25 degrees
22. 84 o I 25 o 20. 56 41 8 22 46~ -- --1.-111· --·+0·00183· ---· +a·oooo· ----·:..:1·850· - - · :..: 0:001~2 - -·- :..:1 -838--
15. 98 51 8 18 4 J 107 00200 1147 I. 833 . 00195 I. 786
11.42 51. 8 1 13 7 J 053 . 00212 .1156 1. 320 . 00205 l.274
6.85 51 8 7 58 J.020 .00218 . 11 .)2 -- · ----- - ---- . 00210 . 759
2. 28 42.8 2 10 J 002 00222 .0951 ------------- .00208 .203
0 0 ----- - ---- ---------- ---- - - - ------ -------- - ---- --- ---- -- --·- ------------ - ------------
2. 28 42.8 2 40 1. 002 .00222 .0951 ------ ------- +.00203 +. 198
o.8.; 5J. 8 1 58 J.020 .00218 . 11.>2 ____________ .00198 .111
11.42 51. 8 13 7 J. 053 .00215 . 1172 + J. 338 . 00192 1.196
15. 98 51. 8 18 4 1. 107 . 00210 . 1204 1. 924 . 00190 1. 740
20. 56 41. S 22 46 1. I 77 . 00202 . 0993 2. 040 . 00193 L 952
22. 84 0 25 0 - - ·-···· · · ·----------·· --··- - ------- · · · · ·---·--·- · · - ···-----·- -·-·--------
22. 84
20.56
15.98
11. 42
6. 85
2. 28
0
2. 28
6. 85
11. 42
15. 98
20. 56
22. 84
22. 84
20. 56
15. 98
11. 42
6. 85
2. 28
0
2. 28
6. 85
I I. 42
15. 98
20. 50
22. 84
0
41. 8
51. 8
51. 8
51. 8
42. 8
0
42. 8
51. 8
51. 8
51. 8
41. 8
0
0
41. 8
51. 8
51. 8
51. 8
42. 8
0
42. 8
51. 8
51. 8
51. 8
41. 8
0
35 0
32 12
26 6
19 l6
11 52
4 0
+ 1. Oii8 +.299 -.057
a o=45 degrees. Aa1=35 degrees
- I I -- T~!C --+0:~:~-- -·· +0:cnrr- 1··-· :..:n~r ··:..:0.-~l~r- -·· :..:n~--
1. 122 . 00197 .1145 I. 308 . 00192 !. 274
I. 044 . 00215 .1103 ---·--------- . 00207 . 767
I. 003 . 00222 . 0952 ------------- . 00208 . 203
···4··a· -- ·--1.-oo:i-- -----~ 00222·· -----·.·0952-- ::::::::::::: ---+.-00202-- ---·+:198--
11 52 !. 044 . 00215 . 1163 ------------- . 00193 . 715
19 16 1.1 22 .00210 .1220 I + 1.393 . 00190 1. 261
26 6 !. 242 . 00195 . 1255 2. 006 . 00202 2. 078
32 12 l. 397 . 00177 --. 1033 2. 125 . 00210 2. 520
35 0 ----- - ---- ------------- ---------- - -- ---------- - ·- ----------·-· ------------
+1. 0974 I +. 428 +. 548 .
ao= 45 degrees. Aa1= 45 degrees
45 0 ----- ------------- ------------- ------------- ···:..:2:874-- 41 59 J. 808 + o. 00110 + o. 1284 -2. 640 - 0. 00185
35 0 1. 491 . 00168 . 1296 ------------- . 00182 2. 245
26 34 !. 251 . 00173 . 1121 !. 280 .00177 J.309
16 42 1.090 . 00180 .1016 . 6955 . 00197 . 762
5 42 !. QlO . 00220 . 0950 - - ----------- . 00210 . 207
--------- - ----- .. ---- ----------- -- ------------- ------------- ------------- ---- +.-197·· 5 42 !. 010 . 00220 . 0950 ---------- --- +. 00200
16 42 1.090 . 00213 .1202 +.823 . 00199 . 769
26 34 !. 251 .00194 . 1256 1. 434 . 00204 1. 509
35 0 1. 491 . 00168 .1296 ------------- . 00189 2. 332
41 59 1.808 . 00102 . 0757 1. 556 . 00090 1. 397
45 0 --- ------- ------------- ------------ - --------- ---- ------------- --- ---------
+ 1. 1128 -.802 -1.193
I
18
Summary of results for 0-2E1 without stagger or sweepback
(Center of rotation at center of span)
a o 15 15 15 25 25 25 35 35 35
Aa1 2 5 15 5 15 25 5 15 25
Fv 0. 2609 0. 2777 0. 3095 0. 6223 0. 6080 0. 5997 0. 8809 0. 8795 0. 8812
Vv 196 190 180 127 128 i29 107 107 107
'l' 21. 0 8. 62 2. 97 12. 9 4.17 2.38 15. 37 5. 01 2. 89
w . 299 . 740 2. 12 . 487 1.51 2. 64 .409 I. 25 2. 17
AT 4940 1970 643 1970 643 369 1970 643 369
Mnv
VV2 - . 178 -.405 -1. 009 -.321 - . 9 -!. 662 -. 134 -.398 - . 756
MRv -3, 187 -6, JO -15, 220 -2, 410 -7, 590 - 12, 950 -710 -2, 114 - 4,000
MRH +. 029 -. 281 -2. 928 0 + .010 - 2. 454 - . 213 -.451 -.338 VY'
MRH +591 -4, 725 - 44, 160 0 +n -19, 100 - 1, 128 -239 - 179
a o 35 45 45 45 45 W = 4668 lb.
Aa1 35 15 25 35 45 I. 467 :., ~ V v in ft ./sec.
T=2 .. X22.84
VvTan.6.a:1 Sec. Fv o. 868 1 I. 073 I. 078 l. 097 l. 1128 w=2. ./ T= R ad./Sec. V v 107 97 96. 5 96 95 AT=TVv=Altitude lost per t urn in rt . T l. 905 5. 54 3.19 2. 14 I. 51 Mnv=Rotating moment abou t horizon tal w 3. 30 l. 134 l. 97 2. 94 4. 16 axis in lb. rt .
AT 246 643 369 246 172 Mnn=Rotating moment about vertical axis Mav
- l.490 0 +. 299 +.42 - . 802 in lb. ft. V;i
Mnv - 8,010 0 + J,294 +1,821 - 3, 366
MRn -!. 702 -.314 -.057 +.548 -1.193 Vv•
Man -9, 150 - 1,366 -251 +2, 330 -5, 010
Lift and drag on 1 /24 scale model of 0- 2E2 tested in McCook Field 5-foot wind tunnel at 40 m. p. h.
Angle of
attack,
degree
-6
-4
- 2
0
+2
4
6
8
10
12
14
15
16
20
24
28
Aa 15+ Aa K,
---
0 +15 0. 00305
5 20 . 00266
10 25 . 00253
15 30 . 00252
20 35 . 00241
25 40 . 00232
---
15-Aa
---
0 15 . 00300
5 10 .00261
10 5 .00180
15 0 . 00091
20 - 5 - . 00016
25 -10 -. 00080
K, K,
Angle of
attack,
degree
K ,
-0. 000339 -0. 000184 32 . 002505
+ . 0000974 . 000156 36 . 002382
. 000513 . 000145 40 . 002318
. 000906 . 000150 44 . 002243
. 001267 . 000165 48 . 002148
. 001629 .000191 52 . 002003
. 001967 . 000226 56 . 001833
. 002297 . 000267 60 . 001633
. 002612 . 000316 64 . 001432
. 002906 . 000374 68 . 001207
. 003034 . 000439 72 . 000981
. 003052 . 0004.83 76 . 000756
. 002915 . 000616 80 . 000544
. 002665 . 000973 84 . 000368
. 002538 . 001268 88 . 000206
. 002507 . 001505
A utorotation calculation for 0 -2E2 model
K ,
0. 00050
. 00097
. 00132
. 00163
. 00190
. 00215
. 00050
. 00032
.00021
.00015
-. 00016
.00021
Calculation of K v and Kn
ao= 15 degrees
K ySi n.6.a K , CosAa Kv
0 0. 00050 +o. 00050
. 000232 . 000966 . 000734
. 000439 . 00132 . 000881
. 000652 . 001585 . 000933
. 000824 . 001786 . 000962
. 000979 . 001948 . 000969
0 . 00050 . 00050
. 000227 . 000319 .000546
. 000312 . 000207 . 000519
. 000236 . 000145 . 000381
-. 0000547 . 0001504 +. 000096
- . 000338 . 0001902 -. 000148
K,
. 001750
. 001948
. 002153
. 002349
. 002550
. 002698
. 002811
. 002916
. 002952
. 002955
. 002955
. 002880
. 002708
. 002575
. 002508
K,CosAa K1Sin6.a Ka
0. 00305 0 - 0. 00305
. 00265 . 0000845 . 00273
. 00249 . 000229 . 00272
. 00243 . 000422 . 00285
. 00226 . 00065 . 00291
. 00210 . 000908 . 00301
. 00050 0 +. 00305
. 00260 . 0000279 . 00257
. 001773 . 0000364 . 00174
. 000879 . 0000388 +. 000840
- . 0001504 . 0000547 -.000205
- . 000725 . 0000887 - . 000814
M
~ ./'1
f01DIJn
1101100
I \
17n, Oil/
M
.J 'y
~11
+
11111117/'J
70 r')(J/
!qQ, 7()(J
~ ,
-
.
/)
19
p_l fm zn) t "
I" 1£1
' I\.
\ '
' \
\
' '\
\
_Jo ll
~r--
-....r---. _ -r-- r-....__
'\.
J \"=o
,, ,;f .JI I
)
I v
v
v
I /
Fm. l6
tJ.a 20+ tJ.a K,
--
0 20 0. 00266
5 25 . 00253
IO 30 . 00252
LS 35 . 00241
20 40 . 00232
25 45 . 00222
30 50 . 00207
---
20-tJ.a
- --
0 20 . 00266
5 15 . 00305
10 IO . 00261
15 5 . 00180
20 0 .00091
25 -5 -. 00016
30 -10 -. 00080
25+tJ.a
---
0 25 0. 00253
5 30 .00252
10 35 . .0024 l
15 40 . 00232
20 45 25 50 ~~
30 55 . 00 187
35 60 . 00163
- --
25-.6.a
- --
0 25 +. 00253
5 20 . 00266
IO 15 .00305
15 JO . 00261
20 5 . 00 180
25 0 . 00091
30 - 5 - . 00016
35 -JO - . 00080
30+tJ.a ----
0 30 o. 00252
5 35 . 0024 1
JO 40 . 00232
15 45 . 00222
20 50 . 00207
25 55 . 00187
30 60 . 00163
35 65 . 00 137 ---
30-tJ.a
----
0 30 . 00252
5 25 . 00253
10 20 . 00266
15 15 . 00305
20 10 .00261
25 5 . 00180
30 0 +.00091
35 - 5 - . 00016
20
A utorotation calculation for 0-2E2 model- Continued
K,
0. 00097
. 001 32
.00163
. 00190
.002 15
. 00240
. 00262
. 00097
. 00050
. 00032
.00021
.000 15
.00016
.00021
0. 00132
. 00163
. 00190
. 00215
. 00240
.. 00262
. 00279
. 00291
. 001 32
. 00097
. 00050
. 00032
. 00021
.00015
. 00016
. 00021
0. 00163
.00190
. 00215
. 00240
. 00262
. 00279
. 00291
. 00295
.00163
.00132
. 00097
. 00050
. 00032
.00021
. 00015
. 00016
Calculation of Kv and KR
ao=20 degrees
KySinlla K ,CostJ.a Kv
0 0. 00097 + o. 00097
. 0002'1 1 . 00131 .00109
. 000437 . 001 60 . 00116
. 000624 . 001835 . 001 21
. 000793 . 00202 . 00123
. 000937 . 00217 . 00123
. 001035 . 00227 . 00124
0 . 00097 +. 00097
. 000266 . 000498 . 000764
. 000453 . 000315 . 000768
. 000466 . 000203 . 000669
.00031 1 . 000141 . 000452
-. 0000675 . 000145 +. 000078
-. 000400 -. 000182 -. 000218
a o=25 degrees
0 0. 00132 + o. 00132
. 0002198 . 001 62 . 00140
.0004 18 . 00187 . 00145
. 000600 . 00208 . 0014
. 000759 . 00226 . 00150
. 000875 . 00237 . 00150
. 00093.5 . 00241 . 00148
. 000935 . 00238 . 00145
0 . 001 32 +. 001 32
. 000232 . 000966 . 001 198
. 000529 . 000492 . 00102
. 000675 . 000309 . 00098
. 000616 . 000197 . 00081
. 000384 . 000136 . 00052
-. 000080 . 0001385 +. 00058
-. 000459 . 000172 - . 000287
a o=30 degrees
0 0. 00163 + o. 00163
. 00021 .00189 . 00168
. 000403 . 00212 . 00172
. 000574 . 00232 . 00175
. 000708 . 00246 . 00175
. 000790 . 00253 . 00174
. 000815 . 00252 . 00171
. 000788 . 00242 . 00163
0 . 00163 +. 00163
. 000221 . 001315 . 00153
. 000462 . 000955 . 00142
. 000789 . 000483 . 00127
. 000892 . 000301 .00119
. 000760
I
. 000190 . 00095
+. 000455 . 000130 +. 000585
-. 0000918 . 000131 -. 000039
K , CostJ.a
0. 00266
. 00252
. 00248
. 00233
. 00218
. 00201
. 001792
. 00266
. 00304
. 00257
. 00174
. 000855
- . 000145
-. 000693
o. 00253
. 00251
. 00237
. 00224
. 00209
. 001875
. 00162
. 001335
. 00253
. 00265
. 00300
. 00252
. 00 169
. 000824
- . 000139
- . 000655
0. 00252
. 00240
. 00228
. 00214
. 001945
. 00169
. 00141
. 00112
. 00252
. 00252
. 00262
. 00295
. 00245
. 00163
+. 000788
-. 000131
K .Sin!la Kil
0 - 0. 00266
. 0001142 - . 00263
. 000283 . 00276
. 000492 . 00282
. 000735 . 00291
. 001014 . 00302
. 001310 . 00310
0 +. 00266
. 0000436 . 00300
. 0000555 . 00252
. 0000544 . 00169
. 0000513 +. 000804
. 0000676 -. 000213
. 0001050 -. 000798
0 -0. 00253
. 000142 . 00265
. 00033 . 00270
. 000556 . 00280
. 00082 . 00291
. 00ll06 . 00298
. 00139 .00301
. 00167 . 00300
0 +. 00253
. 0000845 . 00257
. 0000868 . 00291
. 0000828 . 00244
. 00007 18 . 00162
. 0000634 +. 000261
. 000080 - . 000219
. 000120 - . 000775
I
0
I
-0. 00252
. 000166 . 00257
. 000373 . 00265
. 000621 . 00276
. 00895 . 00284
. 001179 . 00287
. 001455
I . 00286
. OOJ692 . 00281
0 + .00252
. 000115 . 00241
. 0001 68 . 00245
. 000129 I . 00282
. 0001094 . 00234
. 0000887 . 00154
. 000075 I +. 0007 13
. 0000918 -. 000223
21
.. n. ,~ ? ~--
,.,
) I - ·- - --·
!(,. - ~ .... ~ ..
" 2< •L ... - ,_ -
- .,.. IM," . .,
,,,,,. J \: ""~' -- -...._
7 ' k ./ ........ ........_
,,,,,,,, I
___ ,
~-- 7 ---, ~
n '"" I ,,/' '~
I
___ ,.,
.........
" ,, I / .........
I v ......... ,
"' ',,, , ,...v ...........
I / !"'-. ...
A• IA• / 'r-....
I J .........
,,,, i,,,, I .y .........
J _c.-....... ..... , 1~
h I .....
M I,,) A~ ~1. ,,it_ <I~ ht. ,.. OA
I
..,
.I -.•. . . ,i,,• 1k0 'O. .iis-· ~11· ~I~ .. ;;• .. .ri;• tn• .M• <O" ,;~· ·to· r•~ iro· ~If· " FIG. 17
, -I
~~- ·~
AA " ,_,
/l ? ? "- . .
-~ -·
•
Mi- ~- -........ - -- -- ,, "' "'"" -~ lu -
~ --- --- L~ r--.. ....
,,,,, -i-. ,. ....... ..4..._~ - - !"-... -- r--.. ... , ..............
-~ ,, . .,._
_Lo..-- ---..... r--.. '~
... , ~ - ....... r- -- ~r--., i'... ..........
~ i'"-o ;;;;;:, il ,. ,,, . J 15'" ~ ~ .. · ........ .,,. ............. !'-... ,,,.., 11;•
.a~ -~ •5• 1.:2« ...._ ~ ..... Jo• Ida , .
.
4.:J 4·~ -~~! ,_
,, 1
FIG. 18
; ..
lla 35+Aa
-- .,
0 35
5 40
lO 45
15 50
20 ' L55
25 60
30 65
' 35 70
40 . 75
45 80
-~-
35-'Aa
---
0 35
5 30
10 25
f5 20
20 15
25 JO
30 5
35 0
40 -5
45 - 10
----
45+ Aa ----
0 . 45 '
5 50
10 ' 55
15 20 ·- ~~g .
25 70
30 75
35 80
40 85
45 90 ---
45-Aa
----
0 45
5 40
10 35
15 30
20 25
25 20
30 15
35 JO
40 5
45 0
22
A utorotation calculation for 0-2E2 model-Continued
K, I K,
-"
o. 00241 I : 00232 o: ~~~g ..
. 00222
I
'00240 .
. 00207 . 00262
. 00187 . 00~79 .
'00163 . 00291
' 00137 . 00295
. 00110 . 00295
. 00080 . 00290 -
. 00054
I
. 00271
. 00241 . 00190
. 0()252 . 00163
'00253 -. . 00132
'00266 . 00097
' 00305 . 00050
\ '\10261 • 00032
.00180 .00021
+. 00091 . 00015
-. 00016 . 00016
-. 00080 . 00021
'
•' -.1 ·: 'I
0. OQ222 0. 00240
. 00207 . 00262
. 06187 . 00279
.. OQ,163 .00291
. 00137 . 00295
. 00110 . 002\j5
. 00080 . 00290
. 00054 . 00~71
. 00033 . 00255
. 00011 . 00250
. 00222 . 00240
. 00232 . 00215
. 00241 . 00190
. 00252 . 00163
. 00253 . 00132
. 00266 . 00097
. 00305 . 00050
. 00261 . 00032
.00180 .00021
' 00091 . 00015
Ca lculation of K v and Kii
ao=35 degrees
K,SinAa K ,CosAa ' Kv -
;0 " o. 00190 ' +o. 00100
. 000202 .'00214 ' .. . 1lol94
... 000385 ' 00236 .~198
.. 000536 .,002~ ' 1!!9
'. 000639 ' ..()()2 '00198
. 000689 ' 00263 . 00194
. 000685 . 00255 . 00187
. 000631 '00241 ' 00178
' 000514 . 00222 . 00171
. ooo;i82 . 001916 :·00153
'
0 :·00190 +.00190
. 000220 . 00162 . 00184
. 000439 : 00130 . 00174
. ood688 . 000937 . 00 162
. 001042 . 00047 . 00151
. 001103 · :~2 · . 00?39
. 00090 . 00108 +. 000522 . 000123 ' >. 00065
-. 0001029 .0001225 +. 00002
-. 000565 . 000,14, 84 . -. 00,0 .4. 2
&o;. 45' degrees
·1
0 I 0. 00240 +0~ 00240
. po<lJ805; .,00261 .00~3
. 0003246 ' . 00275 : 00243
. 0004217 . 00281 '00239
. 0004685 . 00277 . 00230
. 000465 . 00267 .00221
. 000400 . 00251 . 00211
. 00031 . 00222 . 00191
. 000212 . 00195 ' 00174
. 0000777 '00177 . 00169
0 ' 00240 +. 00240
. 000202 ' 00214 . 00234
. 000418 . 00187 . 00229
. 000652 . 001574 '00223
'000865 . 00124 ' 00210
. 001124 ' 000879 . 00200
. 001 525 . 000433 .00196
. 001497 ' 000262 . 00176
. 001 157 . 000161 . 00132
. 000643 . 000106 . 00075
: K,CosAa
0. 00241
. ~l !c - . 00219
r.
.00~
.00!76
. 00148
'001186 '
·. ' 000901 . 000613
. 0003815 .,
. 00241
. 00251
. 00249
~00257
. 00287
l . 00236
. 001558
+. 000745
-. 0001225
-. 000565
' ' . ..
. , .... ..
0. 002'22
. 00206
. 00184
. 001575
. 001288
. 000997
. 000693
. 000442
. 000253
. 0000778
. 00222
. 00231
. 00237
. 002434
. 002380
. 00241
. 00264
. 00214
. 00138
' 000643
I Ki:Sin6a
I
0
. OOQ,187
'000417
;~~
. 001230
' 001474
' 001692
. 001864
. 001915
0
' o00142
. 000229
' 000251
· •. OOOlil
•". (jpf!l35
,\
• 000105
.il000860
' 0001028
. li001484
.~
" ' .
0 "'l
. 000228
.©0484
.1000753
. 001008
. 001246
. 001450
. 001555
. 001640
. 001766
0
. 0001875
. 000330
. 000422
. 0004515
. 000410
. 00025
. 0001835
. 000135
. 000106
Calculation of vertical force and rotating moments for 0 -2E2 model
As
(Center of rota tion at center of span)
ao= 15 degrees . Aa1 = 2 degrees
Sec?fia Kv Kv Sec26atu Kai Sec•
' .dads
------,------- -----1------1----- -----1-~--- 1
22.84 0 2 0 -· +o~ ooo.59-- ------------- -- --- -- ------ 20. 56 41. 8 I 48 I. 001 0. 02467 - 0. 5070 ·· :.:o~oo2iii -- ::I::::::::
15. 98 51. 8 I 24 J.000 .'00057 ' 02951 . 471 5 -. 00295 ------------ 11. 42 51. 8 I 0 1.000 . 00055 . 02848 . 3250 -. 00297 --- --- ------ 6.85 51. 8 0 36 I. 000 .'00053 . 02744 1880 -. 00300 -- - --------- 2. 28 4~. 8 0 12 1.000 .00051 . 021 82 ' 0497 -. 00303 ------------ 0 0 0 ---------- ---- --------- ------------- ------------- ------------- ---------- -- 2. 28 42. 8 0 12 1.000 . 00050 . 02140 +. 0488 + . 00303 ------------ 6. 85 51. 8 0 36 1. 000 .00051 . 02642 . 1810 +. 00300 ----------- - 11. 42 51.8 l 0 1.000 .00051 '02642 . 3018 +. 00297 ------------ 15. 98 51.8 I 24 1.000 ' 00052 . 02692 . 4300 +.00295 ------------ 20.56 41. 8 l 48 I. 001 '00052 . 02175 . 44i0 +.00291 - --~- -------
22. 84 0, , 2 0 ---------- --- -- ------- - +. 25483 -. 1326 ------------- -- o
Ka
-0. 00241
. 00250 , . 00261
I . 00268
. 00271
. 00271
. 00266
! . 00259
. 00248
. 00230
l
+. 00241
. 00237
. 00226
. 00232
- . 00270 . 00223
. 00145
+. 00066
-. 000225
-. 00071
:
-0. 00222
. 00228
. 00232
. 00233
. 00230
' . 00224
. 00214
. 001997
. 00189
. 00184
+ . 00222
. 00212
. 00204
. 00201
. 00193
. 00200
. 00239
. 00196
. 00125
. 000537
\
23
Calculation of vertical force and rotating moments for 0 -2E2 model- Continued
(Center of rotation at center of span)
ao= l5 degrees. da=5 degrees
ds Sec•aa Kv Kv Sec•aads Kv Sec•
dadsl Kn Knl Sec•
Aa6s
- - - ------- --- - -----1- - - - - l·-----1-----·l-----1
22. 84 0 5 0 ---------- ------------- ----------- -- ------------- --- ----- ----- ------------
20. 56 41.8 4 30 1.007 +-0. 00072 0. 0303 -0. 623 - 0. 00275 - 2. 378
15. 98 51.8 3 30 1.004 . 00067 . 03482 . 557 -. 002 1 - 2. 333
11. 42 51. 8 2 30 l. 002 . 00062 . 03218 . 3672 - . 00287 - J.702
6. 85 51.8 1 30 1. 001 . 00058 . 03007 . 2060 -. 00293 - l.041
2. 28 42. 8 0 30 l. 000 . 000525 . 02247 . 0512 - . 00301 -. 29
0 0 0 ----- ----- -------- -- - -- -- --- ---- -- -- --- ---------- ----- ----- -- - ------ ------
2. 28 42.8 0 30 1.000 . 00051 . 02182 +. 0497 + . 00301 +. 2938
6. 85 51.8 l 30 1.001 . 00052 . 02696 .1845 +. 00293 + L04J
11.42 51. 8 2 30 1. 002 . 00053 . 02750 . 314 +. 00285 + 1. 689
15. 98 51. 8 3 30 1.004 . 00053 . 02756 . 4405 +. 00275 + 2. 284
20. 56 41. 8 4 30 1.007 . 00054 . 02271 . 4667 +.00262 +2. 265
22.84 0 5 0 ---------- ------------- +. 27639 -. 349 ------ ------- -. 175
ao= 15 degrees. da= l5 degrees
--- - - I
22.84 0 15 0 ---------- ------------- ------------- ------------- ----- -------- ------------ 20. 56 41.8 13 33 1. 059 + o. 000925 0. 04095 - 0. 842 - 0. 00282 - 2. 564
15. 98 51. 8 10 37 I. 035 . 00089 . 04770 . 762 -. 00272 - 2. 330
11.42 51. 8 7 38 I. 018 . 00082 . 04320 . 493 -. 00268 - l.61a
6.85 51.8 4 3.5 I. 007 . 00071 . 0370 . 2532 -. 00275 -. 982
2. 28 42. 8 1 32 1.001 .00058 . 02482 . 0566 -. 00293 -. 286
0 0 0 -- -------- ---- -------- - ----- --- -- --- ----- ----- --- ----- -------- ------- ----- 2. 28 42.8 1 32 1. 001 . 00052 . 02482 +. 0566 +. 00293 + . 286
6.85 51.8 4 35 J.007 . 00054 . 02814 . 1926 +. 00262 . 936
l I. 42 51. 8 7 38 I. 018 . 00051 . 02846 . 325 +. 00217 1. 306
15. 98 51. 8 10 37 1. 035 .00050 . 02680 .4.28 +. 00162 J. 388
20.56 41. 8 13 33 I. 059 . 00044 . 01947 . 4002 +. 00109 • 992
22. 84 0 15 0 ---------- ------------- + . 32136 - 1.004 -- -------- --- -2. 67
ao=20 degrees da1=5 degrees
22.84 0 5 0 --------- - --+0:00108-- ----0:0455 ___ -- -:.:0:936--- --:.:0:00262-- ---------- -- 20. 56 41. 8 4 30 1. 007 -2. 265
15. 98 51.8 3 30 1.004 . 00106 . 0551 .881 - . 00262 - 2.177
11.42 51. 8 2 30 1.002 . 00103 .0535 . 611 - . 00262 - 1. 553
6.85 51. 8 1 30 1. 001 .00100 . 0518 • 3546 - . 00263 -. 934
2. 28 42. 8 0 30 1.000 .00098 .0419 . 0955 -. 00266 -. 2596
0 0 0 ------- --- ------------- ------------- ------------- --- ---- -- ---- ------------ 2. 28 42.8 0 30 1.000 .00093 . 0398 +. 0907 +. 00270 +. 2635
6.85 51.8 1 30 1. 001 .00087 . 0451 . 30 + . 00279 . 991
11.42 51. 8 2 30 1. 002 . 00083 . 0431 . 492 +. 00291 I. 723
15. 98 51. 8 3 30 1.004 . 00080 . 0416 . 665 +. 00300 2. 495
20. 56 41.8 4 30 I. 007 . 00078 . 03282 . 675 +. 00301 2. 603
22. 84 0 [j .. o ----- ----- ------------- +. 4502 - . 6466 ------------- +. 9
ao= 20 degrees. aa = 15 degrees
22. 84 0 15 0 ---------- ------------- ------------- ____________ !__==-~---~-
20. 56 41. 8 13 33 I. 059 + o. 00120 o. 0531 - 1.092 I - 0. 00280 -2. 550
15. 98 51. 10 37 J. 035 . 00117 . 0627 l.002 -. 00277 -2. 372
11.42 51. 8 7 38 1.018 . 00113 . 0596 . 680 - .00268 - 1. 612
6. 85 51. 8 4 35 J.007 . 00108 . 0564 . 386 - . 00263 -.940
2. 28 42. 8 1 32 1. 001 .00100 . 0428 . 0976 -. 00263 - . 2.57
0 0 0 ---------- _________ .. ___ ------------- ------------- ------------- ------------ 2. 28 4.2.8 l 32 1. 001 . 00087 . 0372 + . 0848 +. 00293 +. 286
6. 85 51. 8 4 35 1. 007 . 00078 • 0407 . 279 +. 00301 I. 075
11. 42 51. 8 7 38 1. 018 . 00075 .0395 . 451 +. 00282 l. 697
15. 98 51. 8 10 37 1. 035 . 00075 . 0402 . 64:1 +. 00244 2. 090
I
20. 56 41. 8 13 33 I. 059 . 00070 . 0310 . 637 +. 00195 1. 775
22.84 0 15 0 ---------- ------------ - +. 4632 - 1.1628 ------------- -.80
a o=20 degrees. da=25 degrees
22. 84 0 25 0
20. 56 41.8 22 46
15. 98 51.8 18 4
---1:111·- --:i=o:oo123·- l----o:ooao-- - ---:.:1:295· -- --:.:0:002iiii _J_:.:2:992· --
1. 107 . 00123 . 0706 1.128 -. 00290 - 2. 659
11. 42 51.8 13 7 1. 053 .. 00120 . 0654 . 747 - . 00280 - 1. 743
6. 85 51.8 7 58 1. 020 . 00115 . 0607 . 415 - . 00268 -. 970
2.28 42. 8 2 40 1. 002 . 00103 . 0442 .1007 -. 00285 -. 278
0 0 0 ---- --- --- ------------- ---- --------- -------- ---- -'-------- ----- ------------ 2. 28 42.8 2 40
6.85 51. 8 7 58
!. 002 . 00083 . 0356 + . 0812 +. 00300 +. 293
1. 020 . 00075 . 0396 . 271 + . 00278 I. 006
11. 42 51. 8 13 7
15. 98 51.8 18 4
20. 56 41.8 22 46
22. 84 0 25 0
1. 053 . 00072 . 0392 . 447 +. 00200 1. 245
1.107 . 00055 . 0315 . 503 +. 00115 l. 054
---~~~:: _ -----~~--1 +: ::: -2: :: ---~~~~:__ -4: :~
98091-28-4
..
24
Calwlation of vertical force and rotating moments for 0 -2E2 model-Continued
(Center of rotation at center of span)
---1---
22. 84
20. 56
15. 98
J 1.42
6. 85
2. 28
0
2. 28
6. 85
11. 42
15. 98
20. 56
22.
22.
20.
15.
11.
6.
2.
0
2.
6.
11.
15.
20.
22.
4
·I
56
98
42
85
28
28
85
42
98
56
84
22. 84
20.56
J5. 98
11. 42
6. 85
2.28
0
2. 28
6.85
J]. 42
J5. 98
20. 56
22.84
22. 84
20. 56
15. 9
l I. 42
6.85
2. 28
0
2. 28
6.85
11. 42
15. 98
20. 56
22. 84
22. 84
20. 56
15. 98
11. 42
6. 85
2. 28
0
2.28
6. 85
Jl.42
15. 98
20. 56
22.84
0
41. 8
51. 8
51. 8
51.8
42. 8
0
42.8
51. 8
51. 8
51. 8
41. 8
0
0
41. 8
51.~
5.1. 8
51. 8
42. 8
0
4.2. 8
51.8
51.
5 1. 8
41. 8
0
0
41. 8
51. 8
51.8
51. 8
42. 8
0
42.8
51. 8
51.8
51.8
41. 8
0
0
41. 8
51.
51. 8
51. 8
42. 8
0
42. 8
51. 8
51. 8
51. 8
41. 8
0
0
41. 8
51. 8
51.8
5l.8
42.8
0
42. 8
51. 8
51. 8
51. 8
41. 8
0
a o=25 degrees. Aa1=5 degrees
Aa Sec•Aa I Kv KvSec'
AaA,J
- - -
I
5 0
4 30
3 30
2 30
1 30
0 30
0
0 30
J 30
2 30
3 30
4 30
,/j 0
15 0
13 33
JO 37
7 3
4 35
1 32
0
1 32
4 35
7 38
10 37
13 33
J5 0
25 0
22 46
JS 4
13 7
7 58
2 40
0
2 40
7 58
13 7
18 4
22 46
25 0
l. 007
J.004
l. 002
]. 001
]. 000
+o. 00140
.OOJ38
. 00137
. 00135
. 00133
0. 0589
. 0718
. 0711
. 0700
. 0569
- 1.211
I. 148
.812
. 479
.1297
-0. 00289 -2. 500
-. 00287 -2. 386
- .00285 - J.689
-. 00283 - 1.006
-. 00280 -.273
-T~--1-----:-~~~-- -----:-~--- ---+~Hr-- --t~tT
i. 004 . 00123 I . 0640 J. 023 +. 00250
+.244
.878
1.47
2.080
2. 215
-. 967
l 007 00120 0505 l. 038 +. 00256 . ---~-----i-----~- -- __ -l'-+--: -63_01 _, ___ 3_ -9 5_9_ ____________ -I
ao=25 degrees. Aa=l5 degrees
--------- ------------ -------------I- - ---- - ------ ----- ------ -- I- ----------- 1.059 +o. 00148 0. 0655 - 1.347 - 0. 00277 -2. 520
J. 035 . 00146 . 0783 I. 252 - . 00271
I
-2. 320
J. 018 . 00143 . 0754 . 861 -.00268 - 1. 614
1.007 . 00140 .0730 .500 -.00264 -. 943
I. 001 . 00135 . 0578 .132 -. 00257 -.251
------ ---1-- ---------- ------------- ------------- -------- ---- - ------------ I. 001 .00128 .054 +. 125 + . 00247 +. 241
1. 007 .00120 . 0626
I
. 428 +.00256 . 915
l.018 . oono .0580 . 662 +. 00285 l. 716
l. 035 . 00101 . 05'l2 . 866 +. 00289 2. 474
1.059 . 00098 .0434 . 892 +. 00263 2. 392
--- ------ ------ -- ----- +. 6230 I -1.119 1------------- +.090
ao=25 degrees. 6a=25 degrees
---------- ------------- --------- ---- ---------- --- ------- -- -- -- ---- -------- l.177 +o. 00150 0. 0738 -1. 517 -0. 00295 -2.9 5
l. 107 . 00150 . 0860 ]. 374 -.00287 -2. 630
I. 053 . 00148 . 0807 . 922 -.00275 - ]. 7J4
l. 020 . 00143 . 0755 . 517 -.00269 -.973
]. 002 . 00137 . 0587 .134 -. 00260 -. 254
----------!------ ------- ------------- ------- ------ -- ---------- - --- --------- 1.002 .00125 . 0536 +. 122 +. 00248 +.242
]. 020 . 00110 . 0581 . 398 +. :l8288 J.042
]. 053 . 00098 . 0534 . 610 +. 270 ]. 681
]. 107 . 00089 . 0510 . 815 +.00195 ]. 787
1.177 . 00066 . 0325 .668 + . 00113 1. 143
---------- ------------- +.6233 -l.851 ------------- -2.661
ao=30 degrees. Aa=5 degrees
.5 0 ! __________ ---- -------- ____________ _!_ _________________________ , _________ J
4 30 1. 001 + o. 001 o. 0;01 - 1. 4~ -o. 002~1 -2. 222
1
3 30 1. 004 . 001~ . 087~ I I. 391 -. 002a~ -2. JJS
2 30 I. 001 . 00161 . 0 61 . 990 -. 0025a -l. 524
1 30 1.001 .00165 . 0856 .586 -.00253 -.898
0 30 l. 000 . 0016.J . 0702 . .160 -. 00252 - . 246 8 30 1. 000 . 00163 ------.-669 ___ -----+.-159 - ---+:00250- - ---- +:244--
J 30 l.OOL .00160 .0829 .568 +.00-247 .877
2 30 I. 002 . 001- . 0820 . 936 +. 00245 I. 465
3 30 1.004 .00156 .0811 1.296 +.00242 2.010
4 30 J.007 .0015'l .0648 J.332 +.00242 2.097
0 +. 7812 -. 296 -.320
a o=30 degrees. Aa=lO degrees
ig ? --1.-025-· --+0:0017'.i-- -----0:0737-- /----:..::1:515-- --:..::0:00258 _ _1___ :..::2:270--
7 2 1. OJ5 . 00170 . 0894 1. 428 -. 00253 -2.126
5 2 1. 008 . 00169 . 0882 l. 006 -. 00250 -1. 490
3 2 l. 002 . 0016i . 0867 . 594 - . 00246 -. 874
6 0 ]. 000 -----~~=~-- - ---- -~~:~~- - - ------~=~=-- ___:-: ~:xi~~- -'----:-:~~: _ l 0 l. 000 . 00J62 . 0693 +. J58 +. 00248 I +. 242
3 2 1. 002 . 00157 . 0815 . 558 +. 00243 . 864
5 2 l. 008 . 00153 . 0799 . 912 +. 00241 l. 436
7 2 1. 015 . 00149 . 0783 1. 251 +. 00241 I 2. 024
1: ~ ---~~~:: _ -----~:~::__ +: ~~: ~: :: ---~~::~-- ~::
25
Caiculation of vertical force and rotating moments for 0-2E2 model- Continued
(Center of rota tion a t cen ter of span)
a o= 30 degrees. Aa= 15 d egrees
I I I A< I Aa Sec•Aa K v K v Sec•AaA' K v Sec•
A a Ari - -01- 22. 84 15 0 ---- - - -- - - - ---- - ---- - -- ---- - ----- - -- - ----- - - - - --- ----- --- ----- -- -- ----- - --
20. 56 41. 8 13 33
15. 98 51. 8 JO 37
ll.42 51. 8 7 38
6. 85 51. 8 4 35
2.28 42.8 l 32
0 0 0
2. 28 42. 8 1 32
6. 85 51. 8 . 4 35
ll.42 51. 8 7 38
15. 98 51. 8 10 37
20.56 41. 8 13 33
22. 84 0 15 0
22. 84 0 25 0
20. 56 41.8 22 46
15. 98 51. 8 18 4
11.42 51. 8 13 7
6.85 51. 8 7 58
2. 28 42. 8 2 40
0 0 0
2. 28 42. 8 2 40
6.85 51. 8 7 58
11. 42 51. 8 13 7
15. 98 51. 8 18 4
20. 56 41.8 22 46
22. 84 0 25 0
22. 84 0 15 0
20. 56 41. 8 13 33
15. 98 51. 8 10 37
11. 42 51. 8 7 38
6.85 51. 8 4 35
2. 28 42. 8 1 32
0 0 0
2. 28 42. 8 1 32
6. 85 51. 8 4 35
11. 42 51. 8 7 38
15. 98 51. 8 10 37
20.56 41. 8 13 33
22. 84 0 15 0
22. 84 0 25 0
20. 56 41. 8 22 46
15. 98 51. 8 JS 4
11. 4~ 51. 8 13 7
6. 85 51. 8 7 58
2.28 4.2. 8 2 40
0 0 0
2. 28 42. 8 2 40
6. 85 51. 8 7 58
11. 42 51. 8 13 7
15. 98 51. 8 18 4
20. 56 41. 8 22 46
22. 84 25 0
22. 84 0 35 0
20. 56 41. 8 32 12
15. 98 51. 8 26 6
11. 42 51. 8 19 16
6. 85 51. 8 11 52
2. 28 42. 8 4 0
0 0 0
2. 28 42. 8 4 0
6. 85 51. 8 11 52
11. 42 51. 8 19 16
15. 98 51. 8 26 6
20. 56 41. 8 32 12
22. 84 0 35 0
1. 059
l. 035
1.018
J.007
l. 001
]. 001
]. 007
l. 018
1.035
l.059
--------- -
+ o. 00115
. 00172
. 001 71
. 00168
. 00165
. 00160
. 00154
. 00148
. 00140
. 00132
---- --- -- ----
0. 0775
. 0922
.0902
. 0876
. 0707
.0685
. 0804
. 0781
. 0751
. 0584
+ . 7787
a o=30 degrees . Aa = 25 d egrees
- 1. 593
1. 474
1. 030
.600
. 161
+ . 156
. 550
. 892
1.200
1. 200
-. 860
- 0. 00270
- . 00205
- . 00260
-. 00257
- . 00253
+. 00248
+ . 00241
+. 00242
+. 00250
+. 00282
-------------
-2. 458
- 2. 270
- 1.566
- .918
-. 247
+. 242
.861
1.457
2. 142
2. 566
-. 191
. I
--Tm-- --+0:-~Hr -----0:~--1----~F~f --~j:~~f ---=r~r
1. 053 . 00175 . 0954 l. 089 - . 00269 - 1. 615
l. 020 . 00172 . 0909 . 623 -. 00261 - . 944
1. 002 . 00167 . 0716 .163 - . 00255 - . 249
J.002 . 00158 .0678 +. 155 +. 00245 + .240
). 020 . 00147 . 0777 . 532 +. 00242 . 875
l. 053 . 00133 . 0725 . 828 +. 00280 ]. 743
1.l07 . 00122 . 0700 1. 119 + .00260 2.382
1. 177 . 00108 . 0531 1. 092 +. 00190 1. 921
---------- ------ ------- +. 7856 - 1. 529 --------- ---- -1.147
a o=35 d egrees. Aa= 15 degrees
---------- --- - - -- -- ---- -- ----------- -- ----- -- ---- --- ---------- ------------
1. 059 + o. 00199 0. 0881 - 1. 811 - 0. 00266 -2. 418
1. 035 • 00198 .1062 1. 697 - . 00261 -2. 236
1. 018 . 00197 . 1039 1. 187 -. 00255 - 1.535
l.007 . 00194 . 1012 . 693 - . 00249 - . 890
1. 001 . 00192 . 0823 . 188 - . 002-13 - . 237
------- -- - ------------- - -------- ---- ------------- ----- ---- ---- --- ----- ----
1. 001 . 00188 . 0805 +. 184 +. 00240 +. 234
1. 007 . 00183 . 0955 . 654 +. 00237 . 847
1.018 . 00178 . 0939 1.072 + . 00233 1. 403
1. 035 . 00171 . 0917 l. 466 +. 00227 1. 944
1. 059 . 00165 . 0730 1. 501 +. 0022S 2. 072
----- ----- ------- --- -- - +. 9163 -.699 ---- --- ------ -.816
-
ao = 35 d egrees. Aa= 25 d egrees
---1~171--l--+ii.-00195-- - I
------------- ------------- -------- ----- ------- -----
0. 0960 - 1. 973 - 0. 00271 - 2. 738
1. 107 . 00199 . 1141 1. 823 -. 00270 - 2.473
1. 053 . 00199 . 1086 1. 240 - . 00265 - 1.651
!. 020 . 00197 . 1041 . 713 -. 00255 - .923
1.002 . 00192 . 0823 . 188 - . 00245 -. 239
---------- --- ---------- ------------- -------- - ---- -- ----------- ------------
!. 002 . 00187 .0802 +. 183 +. 00239 +. 233
1. 020 . 00178 . 0940 .644 + . 00232 .840
1. 053 . 00165 . 0900 J.028 +. 00228 l. 420
1.107 . 00155 .0889 1. 421 +. 00260 2. 382
1.177 . 00145 . 0714 1. 468 + . 00250 2. 5'.l7 ----
-------- -- ----- ---- ---- + . 9296 - 1.193 ------------- -.622
a o=35 d egrees. Aa = 35 d egrees
____ ______ !_ __ ____ ______ ---------- --- ------------- --------- ---- ------------
!. 397 + 0. 00183 0. 1069 - 2. 196 -0. 00263 -3.155
!. 242 . 00192 . 1235 1. 974 - . 00270 - 2. 774
1.122 . 00198 . 1150 1. 313 -. 00270 - 1. 792
1. 044 • 00198 . 1071 . 733 - . 00263 - . 975
1. 003 . 00193 . 0828 .189 - . 00248 - . 243
---------- -------- ----- ----- -------- -- - ----- - ---- ------------- ------------
!. 003 • 00185 .0794 +. 181 +. 00238 +. 233
1. 044 . 00168 .0908 . 622 + .00229 + .849
1.122 . 00152 .0884 1. 009 + . 00268 1. 778
1.242 . 00133 . 0855 1. 366 +. 00207 2. 127
1. 397 • 00090 . 0525 1. 079 + . 00110 1. 320
------ ---- -- -------- --- + . 9319 -2. 148 -------- -- --- -1. 632
26
Calculatfon of vertical force and rotating moments for 0-2E2 model-Continued
(Center of rotation at center or span)
ao=45 degrees . da=l5 degrees
I
KvSec• Knl Sec'
1 a, aa Sec'lla Kv Kv Sec•aaa, aaa,J Kn aaa,
-::-·-o--I~ =------------- __________________________________________________ _ 20. 56 41. 13 33 1. 059 + o. 0024.0 0. 1062 -2.181 -0. 00233 - 2. 120
15. 98 51. 8 10 37 l. 035 . 00243 .1303 2. 082 -. 00232 - 1. 987
j I. 42 51. 8 7 38 1. 018 .00244 .1286 l. 468 -. 00232 -1.397
6. 85 51. 8 4 35 1.007 . 00243 . 1267 .868 - . 00228 - . 814
2. 28 42. 8 l 32 1. 001 . 00242 . 1037 . 236 - . 00225 - . 220
0 0 0
2.28 42. 8 1 32 1. 001 . 00238 . 1020 +. 233 +. 00218 + . 213
6. 85 51. 8 4. 35 l.007 . 00234 . 1220 . 836 +.00212 . 757
11.4.2 51. 8 7 38 l.018 . 00231 . 1217 1. 389 +. 00207 1. 246
15. 98 51. 8 10 37 l.035 . 00229 . 1227 1.962 + . 00203 1. 738
20.56 4.l.8 13 33 l.059 . 00225 .0996 2. 04.8 +. 00201 l.828
22. 84 0 15 0 -------- -- ------------- + J.1635 -.367 ------ ------- - . 756
a o=45 degrees . da = 25 degrees
-;;:T-o
20. 56 41.
15. 98 51.8
11.4.2 51. 8
~i 4~ \--Tm-- --+0:~~f -----0:Hff-----=n~r --=~:~r ---=r~x-
13 8 1. 053 . 0024.0 . 1308 1. 4.93 - . 00'.233 - I. 452
6. 85 51.8
2. 28 42. 8
0 0
2. 28 42. 8
6. 85 51. 8
11. 4.2 51. 8
15. 98 51. 8
20.56 41.8
22. 84. 0
22.84 0 I
20. 56 41.
15. 9 51. 8
11. 42 51.8
6. 85 51. 8 2. 28 4.2. 8 I
0 0
2. 28 42. 8
6. 85 51.8
11.42 51.8
15. 98 51.
20.56 41. 8
22. 4 0 I
22. 84 0
20. 56 41. 8
15. 98 51. 8
11. 42 51. 8
6. 5 51. 8
2. 28 42. 8
0 0
2. 28 42. 8
6.85 51.8
11. 42 51.8
15. 98 51. 8
20. 56 41. 8
22. 84 0
7 58 l. 020 . 00245 . 1294 . 887 -. 00232 -. 840
2 40 1. 002 . 0024.2 . I 037 . 236 - . 00225 - . 220
0
2 40
7 58
13 8
18 4
22 45
25
30 0
27 27
22 0
16 6
9 50
3 18
0
3 18
9 50
16 6
22 0
27 27
30 0
35 0
32 12
26 6
19 16
11 52
4 0
0
4 0
11 52
19 16
26 6
32 12
35 0
I. 002 . 00237
I . 020 . 00230
I
u~ :~~
l. 175 . 00204
---------- -------------
.1016
. 1215
. 1232
. 1243
. 1002
+ 1. 1792
+. 232
. 832
1.406
l. 987
2. 060
-. 531
a o=45 degrees. lla = 30 degrees
--- ------ - -- - --- - ------ --- ---------- --- - - - - - - - - --
1. 273 + 0. 00217 0. 1154 - 2.372
l. 163 . 002"25 . 1355 2. 165
1.083 . 00237 .1329 1. 517
l. 030 .'00244 . 1302 . 892
1. 003 . 0024.3 . 1042 . 237
----- ----- ------------- -- ----------- ------------- 1.003 . 002'J6 .1012 +. 231
1. 030 . 00230 .1227 . 841
l. 083 . 00223 .1251 1. 427
1.163 . 00205 .1235 1. 973
l. 273 . 0019 .1053 2.164
---------- -- ---- ---- --- + 1.1960 -. 54.7
a o=45 degrees . lla= 35 degrees
---------- ------------- -- ---------- ------------- J. 397 + o. 0020-1 0. 11 91 - 2. 448
I. 242 . 00219 . 1409 2. 252
1.122 . 00232 . 1348 I. 539
1.044 .00242 . 1308 .896
1.003 . OQ243 . 1()43 . 238
---------- -- ----------- ·- ---------- ------- ------ J.003 . 00235 . 1008 + . 230
], 044 . 00228 . 1233 . 845
1.122 . 00212 . 1232 1. 406
I. 242 .00199 . 1280 2. 047 '
I. 397 . 00190 . 1109 2. 280
---------- ------------- + L.2161 -. 565
-
+ . 00216 +. 00206
+. 00201
+. 00198
+. 001925
---------- ---!
-- ---------- -
-0. 00219
- . 00227
- . 00232
-. 00232
- . 00227
---+--.- -- ----- 00215
+. 00204.
+. 00200
+. 00192
+. 00220
----- --------
-- -----------
-0. 00208
-. 00222
- . 00232
- . 00232
-. 00227
-------------
+ . 00213
+. 00202
+. 00195
+. 00207
+. 00229
-------------
+. 211
. 746
.I. 252
I. 12
I. 943
-. 961
----- ---- --- - 2. 394
- 2. 187
- J.487
-. 848
-. 222
------------
+ . 210
. 746
1.282
I. 850
2. 407
----
-. 743
------------
- 2.496
- 2. 282
- 1.540
-. 859
- . 222
------------
+. 208
. 748
I. 294
2. 128
2. 750
- . 271
.,
ao
Fv
Vv
T
w
AT
MRR
VV2
Mae
Mav
V;2
Mav
ao
27
Calc'Ulation of vertical force and rotating moments for 0-2E2 model- Continued
(Center of rotation at center of spau)
---
2"2. 84
20. 56
15. 98
11. 42
6. 5
2. 28
0
2. 28
6.85
11. 42
15. 98
20.56
22. 84
15
2
0. 2548
198. 3
20. 73
.303
4, ll5
0
0
- . 1326
-2, 430
30
10
l!.r
---
0
41. 8
51. 8
51. 8
51. 8
42.
0
42.8
51. 8
51.8
51. 8
41. 8
0
15
0. 2764
190. 5
8.6
. 73
1, 638
-. li5
- 2, 955
-.349
-5, 890
30
15
ao=45 degrees. ti.a=45 degrees
ti.a K v KvSec•
ti.al!.rl
KRI Sec'
---
IKv Sec2L\aL\r
----1-----·i-----1-----1----- -----
45 0
41 59
35 0
26 34
16 42
5 42
0
5 42
16 42
26 34
35 0
41 59
1.808
1.491
1. 251
1.090
1. 010
1.010
1.090
I. 251
1. 491
1.808
+ o. 00112
. 00192
.00218
. 00237
. 00294
. 00237
. 00220
. 00 199
. 00176
. oouo
0. 1300
. 1483
. 1412
. 1338
. 1270
.1024
. 1242
.1289
. 1360
.0831
- 2. 672
2. 370
I. 612
. 917
. 290
+.234
. 851
I. 471
2.173
1. 708
- 0. 00185 -2.872
- . 00200 -3.018
-. 00221 -1. 635
-. 00233 -.902
-. 00230 -. 227
+. 00210 +. 207
+. 00200 +. i74
+. 002.10 I. 555
+. 00196 2. 958
+. 00096 1.491
45 0 ---------- -------------! + 1. 2549 - 1. 424 ------------- - 1. 669
Summary of results for 0-2E2 model
(Center of rotation at center of span)
15
15
0. 3214
176. 7
3. 03
2. 073
535
-2. 867
-41, 600
-1.004
I - 14,580
30
25
35
15
20
5
0. 4502
149. 3
11. 00
. 571
1, 642
+. 8869
+9, 200
-. 6466
-6, 710
35
25
20
15
I
I
I
o. 4632 I 147. 2
3. 64 I 1. 725
536
-.808
-8, 140
- 1.163
-11, 720
35
35
20
25
0.4631
147. 2
2. 09
3. 00
308
- 4. 791
- 48, 260
- 2. 117
-21, 310
45
15
25
5
0. 6301
126. 2
12. 98
.483
1, 638
-.967
- 7, 160
- .3959
-2, 934
45
25
25
15
25
25
30
5
--------·1-----1
o. 6230
127. 0
4. 22
1.488
536
+. ooo
+675
- 1.119
- ,390
45
30
0. 6233
127. 0
2.425
2. 59
308
- 2. 661
- 19, 930
- 1.851
-13, 870
0. 7812
113. 5
14. 46
.434
l , 642
-.320
-1, 913
-. 296
-1, 770
I
I
45 1 45
35 I 45
--~-~--oi-i-~9-45- __o i_i~~-~- 1--0-ir- r-.6 1- -1--0-ii_hl_~-1--o-i &-2i-9. g- 1--o-i&i3_1~-1--1-. 9-l-~. ~-1--1-. ~-~-93 -~ - 1---\-i :_9? _ --l.-~-16-~-ll I. ~ii
T 7. 29 4. 72 2. 72 5. 12 2. 96 l. 975 5. 77 3. 34 2. 71 2. 25 1. 601
w . 862 I. 33 2. 31. I. 227 2. 12 3. 18 1. 088 J. 88 2. 32 2. 83 I 3. 915
h ~ ~ D ~ D D ~ D m m ~
MRH -.283 -. 191 - 1.147 - 16 -.622 - 1. 632 - .756 -.961 -.743 -.271 -1.669
~
Mnu - 2, 206 - 1, 146 -6,820 - 4, 160 -3,123 -8, 180 -3,034 -3,800 -2,900 - l,OH -6,210
MV-;a;v> -.548 -.860 - 1.527 -.699 - 1.193 - 2. 148 -.367 -.531 -.547 - . 565 -.424
MRv - 4,270 -5, 160 -9.070 -3,563 -5,990 - 10, 760 - 1,472 -2, LOO -2, 135 - 2, 170 -1.578
Lift and drag on .t /24 scale model of 0-2E.'J model tested in McCook Fi ~ld 5-foot wind tunnel at 40 m. p. h.
Angle I I Augle I
I
of attack, K, K, of attack, K, K,
degrees degrees
-20 -0. 001272 o. 000781 44 o. 002338 0. 00241
16 . 001267 . 000629 48 • 002228 . 002612
12 • 001228 . 000453 52 . 002058 • 002757
8 - . 000834 . 000252 56 • 001890 . 002899
4 +. 000019 . 000157 60 . 001692 . 003011
2 . 000462 . 000148 64 . 001506 . 003102
0 . 000872 . 000156 68 . 001302 • 003198
2 . 001238 .-000171 ;~ ·~ . 001067 . 003193
4 . 001618 . 000196 • 000823 . 003112
6 . 001958 . 000232 80 . 000587 . 003012
8 .002255 .000~0 84 . 000385 . 002907
10 .002642 . 000328 88 . 000189 . 002720
12 . 002927 . 000386 92 +. 000019 . 002568
14 .OOD4 . 000446 96 -. 000141 . 002469
16 . 002973 . 000624 100 . 000286 . 002359
20 . 002653 . 001000 104 • 000430 . 002296
• 24 . 002548 . 001292 108 . 000586 . 002258
28 . 00-2580 . 001542 112 . 000722 • 002187
32 . 002608 . 001784 116 - . 000851 • 002073
36 . 002473 . 001988 120 . 000961 . 001967
40 • ()()?.A09 . 002206
28
~ t --..J ·- r..-.. .... ,_ . , ·~
r ~
IX 1-.....
F io. 19
JJ ~ . ,[ ' •- ~,,A ~ , r? I /)
:t ... ['...
/ ·" ' 0 ~
' ~L-- ' ' ~ -"" :5
I\. I\.
MM ' "\ ~ 0
\
3 '"~ I\
I\ I\
''" ~"' \ ·,-; I\
r- '"' I~
IM
0 I: ,,
""' s•
;;. .,, ... r--
-~ r;;: ,,..._ ,..
~· . ....._-,._ .
loA .IM ~ ......
~n
I?
w -- v ' ,_ ,_
II I/ ,,., • ~i..
J
I
0
0 t> ;I:) ~ 15 ~o !<!> 0
F10. 20
..
29
Aulorolalion calculation for 0 -2E3 model
Calculation or Kv and KR
ao = 15 degrees
Aa 15+Aa K ,
l_K, _
K, Sin Aa K, Cos Aa Kv K, Cos Aa K. Sin Aa KR
0 J5 o. 00307 0. 00053 0 0. 00053 I +o. 00053 o. 00307 0 -. 00307
5 20 . 00265 .00100 . 000231 . 0009()6 . 000765 . 00264 . 0000872 . 00273
10 25 . 00255 .00136 . 000442 . 00134 . 00090 . 00251 . 000236 15 . 002i'l6 30 . 00261 . 00166 . 0006i."'1 . 001604 . 000929 . 00252 . 0004296 . 00295
20 35 .00250 . 00194 . 000855 .001 22 . 000967 . 002317 . 000653 . 00300
25 40 . 00241 . 00221 . 0010J8 . 00200 . 00098 . 002J82 . 000933 . 00311
15-Aa
0 J5 . 00307 .00053 0 . 00053 +. 00053 . 00307 0 +. 00307
5 JO . 00264 . 00033 . 00023b . 00032Y . 000559 . 00263 . 0000288 . 00260
10 5 . 0017 . 00021 . 000309 . 000207 . 000516 . 001753 . 00003645 . 00172
J5 0 +. 00087 .00015 + . 000225 . 000145 +. 000370 +. 000840 . 00003883 +. 000801
20 -5 -. 00020 . 00017 -. 0000684 I . 0001598 +. 0000914 -. 0001877 . 0000581 -. 000246
25 - LO -. OOlLO . 00034 -. 00046.5 . ()()().308 I -. 000157 - . 000996 . 0001435 -. 001139
ao = 20 degrees
-
20+Aa
0 20 o. 00265 0. 00100 0 o. 00100 + o. 00100 0. 002fi5 0 -0. 00265
5 25 . 00255 . 00136 . 000222 . 001355 . 001133 . 00254 . 0001186 . 00266
10 30 . 00261 . 00166 . 000453 . 001636 . 001183 . 00257 . 000288 . 002 6
15 35 . 00250 .OOJ94 . 000647 . 001 73 .OO!'lJ . 002415 . 000502 . 00292
20 40 . 00241 . 00221 . 000824 . 002078 . 00125 . 002260 . 000756 . 00302
25 45 . 00231 . 00248 . 000975 . 002247 . 00127 . 002091 . 001047 . 00314 30 50 . 00215 . 00270 . 001075 . 00234 . 00127 . 001862 . 001350 . 00321
20-Aa
0 20 . 00265 .00100 0 . 00100 +. 00100 . 00265 0 +. 00265 5 15 . 00307 . 00053 . 000268 . 000528 . 000796 . 00306 . 0000462 . 00301
10 10 . 00264 . 00033 . 000458 . 000325 . 000783 . 00260 . 0000573 . 00254 15 5 . 00178 . 00021 I . 000461 . 000203 . 000664 . 00172 . 0000544 . 00167
20 0 + . 00087 .00015 +.000297 . 000141 . 000438 +. 000818 . 0000513 +. 000767 25 -5 -.00020 . 00017 -. 0000845 . 000154 +. 000070 -. OOOJ81 . 0000718 -.000253 30 - 10 -.00110 . 00034 I -. 00055 . 000294 -. 00026 -. 000952 . 000170 -. 00ll22
ao=25 degrees
25+Aa
0 25 0. 00255 o. 00136 0 0. 00136 +o. 00135 0. 00255 0 -0. 00255 5 30 .00261 . 00166 .0002275 . 001654 . 00143 . 00260 . 001447 . 00274 10 35 . 00250 . 00.194 . 000434. . 00191 L . 00148 . 00246 . 0003367 . 00280 15 40 . . 00241 . 00221 . 000624 . 002135 . OOJ53 . 002328 . 000572 .00290 20 45 . 00231 . 00248 . 000790 . 0023:l . 00154 . 002170 . 000848 . 00302 25 50 .00215 . 00270 . 000908 . 002446 . 00154 . 001947 . 001140 . 00309 30 55 . 00193 . 00288 . 000965 . 002-192 . 00153 . 001671 . 001440 . 003ll 35 60 .00169 .00301 . 000912 . 002465 . 00155 . 001384 . 001725 . 00311
25-Aa
0 25 . 00255 . 00136 0 . 00136 +. 00136 . 00255 0 +. 00255 5 20 . 00265 . 00100 . 000231 . 000996 . 00123 . 00264 . 0000872 . 00255 JO I 15 . 00307 . 00053 . 000533 . 000522 . 001055 . 003024 .000092 . 00293 15 JO . 002 4 . 00033 . 000683 . 000319 . 00100 . 00255 . 0000854 . 00247
20
I
5 . 0017 .00021 . OOOC09 . 0001973 .00081 . 001673 . 0000718 . OOJ60 25 0 +.00087 . 00015 +. 000367.5 . 000 13.58 . 00050 +. 00078 . 0000634 +. 00072 30 -5 -. 00020 .00017 -. 000100 . 0001472 +. 000047 -. 0001731 . 000085 - . 000258 35 -10 -. 00110 . 00034 -. 000631 . 0002782 -. 00035 - . 00090J . 0001948 -.001096
I
ao=30 degrees
30+Aa I
0 30 o. 00261 o. 00166 0 0. 00166 + o.OOJ66 0. 00261 0 +o. 00261 5 35 . 00250 . 00194 . 000218 . 001932 . 00171 . 00249 . 0001692 . 00266 10 40 . 00241 . 00221 . 0004182 . 002176 . 00176 . 002372 . 0003834 . 00275 15 45 . 00231 . 00248 . 000598 . 002395 . 00180 . 002231 . 000642 .00287 20 50 . 002J5 . 00270 . 000735 . 002538 . 00180 . 002020 . 000923 . 00294 25 55 . 00193 . 00288 . 0008J5 . 002610 . 001795 . 001748 . OOJ2J6 . 00296 30 60 . 00169 . 00301 . 000845 . 002606 . 001795 . 001463 . OOJ505 • 00297 35 65 . 00145 . 00314 .000832 . 002570 . 00174 . 001187 . 001802 .00299
30-Aa
0 30 I . 00261 .00166 0 .00166 +.00166 . 00261 0 +. 00261 5 25 .00255 . 00136 . 000222 . 001354 . 00158 . 00254 . OOOJ186 . 00242 10 20 . 00265 . 00100 . 000460 . 0009 5 . 001445 . 00261 . 0001736 • 00244 15 15 . 00307 . 00053 . 000795 . 000512 . 00131 . 002965 . 0001372 . 00283
20 10 . 00264 . 00033 . 000902 . 0003102
I
. 00121 . 00248 . 000112 . 00237
I
25 5 . 0017 . 00021 . 000752 . 0001903 . 000942 . 001612 .0000 7 . 00152 30 0 +. 00087 . 00015 +. 0004348 . 0001298 . 000565 +. 000753 . 000075 +.00068 35 -5 -. 00020 . 00017 -. 0001147 . 0001392 +. 0000245 -. 0001637 . 0000975 -. 000261
-~ - - -
30
A1tlololation calculation for 0-2E3 model-Continued
Calculation of Kv and Ka
ao=35 degrees
C.a 35+C.a K, K, Kl. Sin Lla K, Cos Ila Kv K, Cos Ila Kx Sin L\a KR
0 35 0. 00250 o. 00194 0 o. 00194 +o. 00191 o. 00250 0 -0. 00250
.5 40 . 00241 . 00221 . 000210 . 00220 . 00199 . 00240 . 0001927 . 00259
IO 45 .00231 . 00248 . 000401 . 00244 . 00204 . 002274 . 000431 . 00270
15 50 . 00215 . 00270 . 0005533 . 002608 . 002055 . 002078 . 000699 . 00278
20 ,55 . 00193 . 00288 . 000660 . 002612 . 00195 . 001814 . 000987 . 00280
25 60 . 00169 . 00301 . 000714 . 002725 . 00201 . 001530 . 001272 . 00280
30 (;5 .00145 . 00314 . 00072.5 . 002718 . 00199 . 001256 . 001520 . 00278
3.5 70 . 00118 . 00321 . 000677 . 002627 . 00195 . 000966 . 001840 .00281
40 75 . 00088 .00314 . 000565 . 002404 . 00184 . 000674 . 002018 . 00269
45 80 . 00059 .00301 . 000417 . 002127 • .00171 . 000417 . 002127 . 00254
35-Lla
0 35 . 00250 . 00194 0 . 00194 . 00194 . 00250 0 +. 00250
5 30 . 00261 . 00166 . 0002274 . 00165 . 00188 . 00260 . 0001447 . 00246
JO 25 . 00255 .00 136 . 0004425 . 00134 . 00178 . 00251 . 000236 . 00227
15 20 . 00265 .00100 . 000686 . 000966 .00165 . 00256 . 000259 . 00230
20 1.5 . 00307 . 00053 . 001050 . 000498 . 00155 . 002886 . 0001 12 . 00270
25 10 . 00264 . 00033 . 001115 . 000299 . 00141 . 00239 . 0001395 . 00225
30 5 .0017 . 00021 .00089 . 0001818 . 00107 . 001541 . 0001050 . 00144
35 0 +.00087 . 00015 +. 000499 +. 0001228 +. 00062 +. 000712 . 0000860 + . 000626
40 -5 -. 00020 . 00017 -. 0001285 +. 0001302 +.000002 -. 0001532 . 0001093 -. 000262
45 - IO -. 00110 . 00034 -. 000777 +. 0002402 -. 000537 -. 000778 . 0002402 -. 001018
ao=45 degrees
----
45+6a
0 45 o. 00231 0. 00248 0 o. 00248 +o.00248 0. 00231 0 -0. 00231
5 50 . 00215 . 00270 . 0001961 . 00269 . 00249 .00214 . 0002352 . 00237
10 55 . 00193 . 00288 . 000335 . 00284 . 00251 . 00190 . 000500 .00240
15 60 . 00169 . 00301 . 000437 . 002908 . 00247 . 001633 . 000779 . 00241
20 65 . 00145 . 00314 . 000496 . 00295 . 00245 . 001363 . 001074 . 00244
25 70 . 00118 . 00321 . 000498 . 00291 . 00241 . 001069 . 001356 .00242
30 75 . 00088 .00314 . 000440 . 00272 . 00228 . 000762 . 001570 . 00233
35 80 . 00059 . 00301 . 000338 . 002464 . 00213 . 000483 . 001726 . 00221
40 5 . 00032 . 00287 . 0002058 . 002198 . 00199 . 000245 . 001845 . 00209
45 90 . 00010 . 00265 . 0000707 . 001873 .00180 . 0000707 . 001873 . 00194 ---
45-Lla
0 45 . 00231 . 00248 0 . 00248 +. 00248 . 00231 0 +. 00231
5 40 . 00241 . 00221 . 000211 . 00220 . 00241 . 00240 . 0001926 .00221
JO 35 . 00250 .00194 . 000434 . 00191 . 00234 .00246 . 0003366 . 00212
15 30 . 00261 . 00166 . 000676 . 0016():3 . 00228 . 00252 . 0004296 . 00209
20 25 . 00255 . 00136 .000872 . 001278 . 00215 . 002397 . 0004650 . 00193
25 20 . 00265 . 00100 . 001120 .000906 . 00203 . 00240 .0004226 . 00198
30 15 . 00307 . 00053 . 001535 .000459 . 00199 . 002658 . 0002650 . 00239
35 10 . 00264 . 00033 . 001514 . 0002702 .00178 . 002161 . 0001892 . 00197
40 5 . 00178 . 00021 . 001145 . 000161 . 001306 . 001364 . 0001350 .00123
45 0 . 00087 . 00015 . 000615 . 000106 . 000721 . 000615 . 0001060 .00051
Calculation of vertical force and rotating moments for 0 -2E3 model (center of rotation al center of span)
C.a
22. 84 0 2 0
20. 56 41. 8 1 4
15. 98 .';t. 8 l 24
11. 42 51. 8 I 0
6. 85 51. 8 0 36
2.28 42. 8 0 12
0 0 0
2. 28 42. 8 0 12
6.8.) 51. 8 0 36
I 1. 42 51.8 1 0
15. 98 51. 8 1 24
20. 56 41. 8 1 4
22. 84 0 2 0
ao= 15 degrees. 6a1 = 2 degrees
Sec'C.a Kv KvSec'ila.ls KvSec2.6.aLhl
---------- ------------- ---- --------- -------------
J. 001 +o. 00063 0. 0263 -0.541.
J.000 .00061 . 0316 .505
1.000 . 00059 . 03ll . 355
1. 000 . 00057 . 0295 . 202
l.000 . 00055 . 0235 . 0536
---------- ---------- .. -- ------------- ---- +.-0520-- 1.000 . 00053 . 0227
l.000 . 00053 . 0274 .187
1.000 . 00054 . 0280 .320
l.000 . 00054 . 0280 .447
1. 001 . 00055 . 0230 . 473
---------- ------------- +. 2711 -.178
Kn
-------------
-0. 00290
-. 00293
-. 00297
- . 00300
-. 00305
---+.-00306--
+. 00303
+. 00301 +. 00298
+. 00294
-------------
Kn!See•
LlaL\s'
------------
-2. 494
-2.427
-l. 757
- l.064
. 298
---- --------
+.299
!. 075
!. 7 1
2.468
2. 529
+.112
1·
I
31
, __
I;. !<:-;;, '• I/
r~. -
~ .. ,. , ,. ,_ 'J -
,;;,ii I o~~ J:.. 1,.,., . -
!'".Y 4 lo 1-"l · ~,~
/h . •"
r ~ - l'-..V
/"' ,_ I v ,, J .....
' / '
/
/ ,.,. ~,. - / .........
I !/', ....... ......
/ ~ ,·~ I / ' r-..
' /l V,;<-
7 ....
I I/ \
I?,,~ I J "\
I/ \
I l?h/'. 0 J ,, I \
/l~ ' I r\:
l.,i :-.... I I/ I\.
/) ' I '-.
I /?,h,., '-.
j ' /A ~n, I " "' Let >v, -
?/J -11?- I O J. ,.,. ,_. <1- • C.o ,,~. Lno 7. '>" ,~. -· ,,_. ,.,_. ,,J.
i...:. ,_, ~ - "'
J
FIG. 21
- -
-i'--- -
- -+-----
--~ -
FIG. 22
I
32
Calculation of ·vertical for ce, and rotating moments for 0-BE3 model-Continued
22. 84
20. 50
15. 98
11. 42
6.85
2. 28
0
2. 28
6. 5
11.42
15. 98
20, 56
22. 4
22. 84
20 . .56
15. 98
11.42
6. 85
2, 28
0
2. 28
6.85
11. 42
15. 98
20. 56
22. 84
22, 84
20.56
15. 98
11.42
6. 5
2. 28
0
2. 28
6. 85
11. 4.2
15. 98
20. 56
22.84
22. 84
20. 56
15. 98
11. 42
6. 85
2. 28
0
2. 28
6. 85
11. 42
15. 98
20. 56
22. 84
22.84
20. 56
15. 98
11. 42
6. 85
2. 28
0
2. 28
6. 85
11.42
15. 98
20. 56
22. 84
t.s t.a
(Center or rotation at center of span)
a o=l5 degrees. t.a=5 degrees
Sec2.1.a Kv K vSec•t.at.s K vSec2t.allsl K n. Kn I Rec'
6a!lf
--- ---- ---- - ----- -----1------1--
0 5 0
41.8 4 30
51. 8 3 30
51. 8 2 30
51. l 30
42. 0 30
0 ----------
42. 8 0 30
51. 8 I 30
51.8 2 30
51.8 3 30
41.8 4 30
0 0
0 15 0
41. 13 33
51. 8 10 37
51. 8 7 38
51.8 4 35
42. 8 l 32
0 ----------
42.8 1 32
51. 8 4 35
51. 8 7 38
51. 8 JO 37
41. 8 13 33
0 15 0
0 5 0
41. 8 4 30
51.8 3 30
51.8 2 30
51. 8 1 30
42. 8 0 30
0 ---------- 4.2. 8 0 30
51.8 1 30
51. 8 2 30
51. 8 3 30
41. 8 4 30
0 5 0
0 15 0
41. 8 13 33
51.8 10 37
51.8 7 38
51.8 4 35
42. l 32
0 --- ----- -- 42. 8 l 32
51.8 4 35
51. 8 7 38
51. 8 10 37
41. 8 13 33
0 15 0
0 25 0
41. 8 22 46
51. 18 4
51. 8 13 7
51. 8 7 58
42. 8 2 40
0 ---2- -40-- 42. 8
51. 8 7 58
51. 8 13 7
51.8 18 4
41. 8 22 46
0 25 0
------ --- - ------------- ------ ------- 1.007 + o. 00015 o. 0316
1.004 '00071 .0369
1.002 '00067 '0348
1.001 '00062 '0322
1.000 '00056 .0240
--------- - ·------------ -------- -- --- LOOO ' 00053 ' 0231
LOOI '00055 . 0285
1.002 '00055 .0285
1.004 . 00055 .0286
1.007 . 00056 . 0236
------- --- ------- -- ---- +. 2918
-- --- ---- ---- -0.650
'590
'397
'220
. 0547
--- ----------
+. 0527
.195
. 325
. 457
'485
-.397
-------------
-0. 00275
-, 002i9
-, 00285
-, 00292
-. 00301
------------
+. 00301
+. 00297
+. 00288
+.00277
+ . 00265
---- ----- ----
-~. 380
-~. 320
-l. ~9 0
-1.037
-, 294
+. 297
1. 055
I . iOi
2. 302
2. 292
- . 068
a o= 15 degrees . t.a=15 degrees
---------- ------------- ------------- ------ ------- --- ---------- ------------
l.059 + o. 00093 0. 0412 -0. 847 -0. 00290 -2. 640
I. 035 ' 00091 .04 '780 -, 00277 -2. 372
LOIS ' 00084 ' 0443 '506 -. 00272 -1.637
1.007 '00075 ' 0391 '268 -. 00275 - .9 3
LOOI . 00062 '0266 .0606 -. 00292 -.285
---------- ------------- ------------- --- ---------- ------------- ------------ 1.001 '00055 . 0236 +. 0538 +. 00298 +. 291
I. 007 '00056 '0292 . 200 +. 00264 . 943
1.018 . 00055 .0290 '331 +. 00218 1. 312
l. 035 '00052 . 0279 .446 +. 00162 l.3
1. 059 ' 00042 ' 0186 . 382 +. 00105 . 956
------ -- -- --- -- -------- +. 3283 -1.049 ------------- -3. 027
ao=20 d egrees. t.a=5 degrees
---i:oo1-- --+o:ooii3-- ------------- ----:.:0:978-· --- ---------- ----- ------- 0. 0476 -0. 00265 - 2. 292
1.004 '00111 .0577 . 922 - . 00265 - 2. 203
1.002 .00109 . 0566 .646 -. 00265 -1.571
1. 001 '00106 ' 0550 ' 377 -. 00265 -.942
1.000 '00102 . 0437 . 0996 -. 00265 -.259
---i:ooo-- ------------- ------------- ------------- ------------- --------- --- . 00097 . 0415 +. 0946 +. 00268 +. 261
1. 001 . 00092 . !H77 . 327 +.00276 .981
1.002 . 00088 . 0457 . 522 +. 00288 1. 708
1.004 ' 00084 . 0437 .699 +. 00297 2.470
1. 007 .00081 . 0341 . 701 +. 0030 l 2. 602
---------- ------------ - +. 4733 -.479 -- ----- ------ +. 755
ao=20 degrees. t.a = 15 degrees
--- i:o59-- --+o:ooi22-- ------------+------------ ____________ J _________ _I
o. 0540 -1. 110 -0. 00288 -2. 620 1. 035 +. 00199 ' 1067 1. 706 -. 00283 -2. 424
l. 018 +. 00170 . 0896 1. 023 -. 00272 -1. 637
l. 007 +. 00113 . 0590 '404 -, 00266 -.951
1. 001 +. 00106 '0553 .126 -, 00265 - . 259 ------- --- ------------- ------------· ------------- ---- ---------- -- ----- ---- 1.001 +. 00092 ' 0480 +.109 +.00276 +.270
1.007 +. 00081 .0423 . 290 +. 00301 1. 075
1.018 +. 00077 .0406 . 463 +. 00287 1. 728
l. 035 +. 00078 '0418 .668 +. 00245 2.099
1.059 +. 00072 . 0319 .656 +. 00194 1. 764
--- -------------------- +. 5692 -2. 183 ----- ---- ---- -, 955
ao= 20 degrees. t.a=25 degrees
1. 177 --+o:ooi21-- -----0:0025-- -------1-.- -28-4- --1-----0-.- 0--03-0-9- -- ---=ii24.--
1.107 . 00125 . 0717 1.146 -, 00298 -2. 730
1. 053 ' 00122 .0666 . 760 - , 00288 -1. 794
1.020 . OOJJ7 . 0618 . 423 - ' 00273 -.9
1.002 '00109 . 0468 . 107 -. 00265 -.259
---i:oo2-- --------- --- ------------- ------------- ------------ - ------------ .000 7 . 0373 +.085 +.00290 +. 283 1.020 '00077 . 0407 . 279 +. 00283 1.024
1. 053 . 00073 . 0398 . 454 +. 00202 1. 258
1.107 . 00054 . 0310 .496 +. oouo 1. 008
1. 177 . 00025 '0123 '253 +. 00020 . 202
---------- ------------- +.4705 -2.153 ------- -- ---- -5. no
I
I
33
Calculation of vertical force and rotating moments for 0 -2E3 model-Continued
---
22. 84
20. 56
15. 98
11.42
6. 85
2.28
0
2. 28
6.85
11.42
15. 98
20. 56
22. 84
22.84
20. 56
15. 98
ll. 4.2
6.85
2. 28
0
2. 28
6.85
11. 42
15. 98
20. 56
22.84
22.84
20.56
15. 98
11.42
6. 85
2. 28
0
2. 28
6. 85
11. 42
15.98
20.56
22. 84
22.84
20. 56
15. 98
11. 4.2
6. 5
2. 28
0
2. 28
6. 85
11. 42
15. 9
20.56
22. 84
22. 84
20. 56
15. 9
11. 42
6. 85
2. 28
0
2. 28
6. 5
11. 42
15. 98
20.56
22. 4.
A• C.a
(Center of rota lion at center of s pan)
a o= 25 degrees. C.a=5 degrees
Sec•Aa K v K vSec•AaC., Kv ec•AaAsl Ka Kn I Sec'
da~s
- -.-, 1
0
41. 8
51. 8
51. 8
51. 8
42. 8
0
42. 8
51.
51.8
51. 8
41. 8
0
0 I
4.1. 8
I 51. 8
51.8
51. 8
42.8
0
4.2.
51. 8
51. 8
51. 8
I
41. 8
0
0
41. 8
51. 8
51. 8
51. 8
42.
0
4.2.8
51.
51. 8
51.
41. 8
0
0
4.l.8
51. 8
51. 8
51. 8
4.2. 8
0
42.8
51.8
51. 8
51. 8
41. 8
0
0 I
4.1.
51. 8
51.8
51. 8
42.8
0
4.2.
51. 8
51.8
51.8
41. 8
0 I
5 0
4 30
3 30
2 30
1 30
0 30
0
0 30
l 30
2 30
3 30
4 30
5 0
15 0
13 33
10 37
7 38
4. 35
1 32
0
1 32
4 35
7 38
10 37
13 33
15 0
25 0
22 4.6
18 4
13 7
7 58
2 40
2 40
7 58
13 7
1 4.
22 4.6
25 0
5 0
4 30
3 30
2 30
l 30
0 30
0
0 30
l 30
2 30
3 30
4 30
15 0
l3 33
JO 37
7 38
4 35
l 32
---1:001-- --+o.-ooi4:i-- -----0.-0602- - ----:..:i:231--/--:..:o.-00213- - ---:..:2::i6i--
i. 004 . 00142 . 0739 1.182 -. 00269 -2. 237
1.002 .00140 .0727 .830 - .00267 - 1.583
1. 001 . 00138 . 0716 . 4.90 -. 00263 - . 934
1. 000 . 00137 . 0586 . 134 -. 00258 - . 252
1. 000 . 00135
1. 001 . 00133
1. 002 . 00130
J.001 . 00128
1. 007 . 00125
. 0578
.0690
. 0675
.0666
. 0526
+. 6505
+.132
. 473
. 771
1. 065
1.082
-.350
ao=25 degrees. Aa= 15 degrees
---------- ------------- -- ----------- ------ ------- 1. 059 +o. 00152 0. 0673 -1.384
!. 035 . 00149 . 0799 1. 277
1. 018 . 00147 . 0775 85
1. 007 . 00143 . 0746 . 511
1. 001 . 00138 . 0591 .135
---------- ------------- ------------- ------ -------
1. 001 . 00133 . 0570 +.130
l.007 . 00125 . 0652 . 447
1.018 . 00113 . 0596 . 681
1. 035 . 00105 . 0563
I
.900
1.059 .00102 . 0452 . 929
---------- ------------- + . 6417 -.105
ao=25 degrees. Aa=25 degrees
I
--- ------- ------------- ------------- ------- ------
1.177 + o. 00154 o. 0758 -1. 557
1.107 .00155
I
. 0889 1. 4.21
1. 053 .00152 . 0829 . 947
1.020 . 00142 . 0751 . 514
1.002 . 00140 .0601 .137
---1:002-- -------------!----------- -· --- ----- --- --
. 00130 . 0558 +.127
1.020 . 00112 . 0592 .405
1. 053 . 00102 . 0556 . 635
1.107 . 00090 . 0516 .825
!--:~~~~~-- . 00065 .0320 . 658
------------- +. 6370 -1.826
a o=30 degrees. Aa=5 degrees
+. 00253 + 00252 I +. 00252
+. 00253
---~~=~:: __ I
+.247
.895
1.494
2.103
2. 207
+.569
------------- ------------ -0. 00287 -2. 611
-. 00280 - 2. 398
-.002i7 -1.669
- . 00273 -.976
-. 00262 -. 256
----- --------------------
+. 00252 + .246
+. 00255 . 911
+. 00281 1. 693
+. 00292 2. 502
+. 00267 2.430
1-------------i -.128
-------------- ----- -- --- -
-0. 00307 -3. 104
- . 00297 -2. 722
-. 00285 -1. 775
- . 00277 -1.003
- . 00267 -. 255
--- ------ ---- ----------- -
+.00253 + .242
+.00283 1.024
+. 00273 1. 700
+. 00195 1. 7
+. 00105 1.062
-------------! -3. 043
_________ _!_ _____ _______ --------- ---- ------------- ------------- ---- --------
1. 001 I +o. 00111 o. 0120 -l.480 -o. 00255 - 2. 292
1. 004 . 00170 . 0884 1. 413 - . 00265 -2. 202
1. 002 . 00169 . 0877 1. 001 -. 00263 - 1. 559
l. 001 . 00168 . 0871 . 596 - . 00262 -. 931
1. 000 . 00167 . 0715 . 163 -. 00262 -. 256
--Tm--, -----:-~m-- -- - --Jilr -----+~~-- --1~~-- ----~~~--
1. 004 . 00160 . 0832 1. 330 +. 00246 2. 04.4
1. 007 . 00158 . 0666 1. 369 +. 00243 2. 102
----------i- ---------- -- +. 7963 -. 250 -.452
ao=30 degrees. C.a= 15 d egrees
---------- ----- -------- -------------- ----------- - --:..:0:00283-- ------------
1. 059 +o. 001so 0. 0797 -1. 638 -2. 572
1. 035 . 00178 .0955 1. 526 -. 00275 -2.3-
1. 018 . 00175 .0924 l. 055 -. 00270 -1.62
1. 007 . 00171 . 0892 . 611 -. 00265 -.947
1.001 . 00168 . 0720 .164 -. 00262 - . 256
-------- ------------ --- ---------- ____ _________ ; _____________
---+:00255-- ----+.-249-- 1 32 1. 001 . 00164 . 0703 +.160
4 35 1. 007 . 00158 . 0825 I . 565 +.00243 . 869
7 38 1. 018 . 00152 .0802 . 915 +.002.JO l.446
10 37 1. 035 . 00143 . 0763 I 1. 219 +.00249 2. 133
13 33 1.059 . 00135 .0598 1. 229 +.0027 2. 528
15 0 I- --------- ----- -------- +. 7979 I -. 904. ------------- -.536
I
34
Calclllation of vertical force and rotating moments for 0 -2ES model-Continued
(Center or rotation al center or span)
a o=30 degrees. 6a=25 degrees
Sec2.!la Kv Kn
------ ---- ____ , _____ , _____ , _____ -----1----
22. 4 0
20. 56 41. 8
15. 98 51. 8
11. 42 51. 8
6. 5 51. 8
2. 28 42. 8
0 0
2. 28 42.8
6. 85 SL.
11.42 51. 8
15. 98 5 l. 8
20. 56 41. 8
22. 84 0
22. 84 0
20. 56 41.
15. 98 51. 8
11. 42 5 1. 8
6.85 51. 8
2. 28 42.
0 0
2. 2 42. 8
6. 85 51. 8
11. 42 51. 8
15. 98 51. 8
20. 56 41.8
22. 84
22. 84 0
20. 56 41.8
15. 98 51. 8
11. 42 51.8
6. 85 51.
2. 28 42. 8
0 0
2. 2 42. 8
6. 85 51.
11. 42 5 1. 8
15. 98 51.
20. 56 41. 8
22.84 0
22. 84 0
20. 56 41.
15. 98 51. 8
II. 42 51.
6. 85 51. 8
2. 28 42.
0 0
2. 28 42.8
6. 5 51.
11. 42 51.
15. 98 51. 8
20. 56 41.8
22. 4 0
22. 84 0
20. 56 41.
15. 9 51. 8
11. 42 51.
6. 85 51.
2. 28 42. 8
0 0
2. 28 42. 8
6.85 51. 8
11. 42 51.8
15. 98 15. 8
20. 56 41.
22. 84 0
25 0
22 46
18 4
13 7
7 58
2 40
---- --- ---
2 40
7 58
13 7
18 4
22 46
25
15 0
13 33
10 37
7 3
4 35
1 32
0
1 32
4 35
7 38
10 37
13 33
15 0
25 0
22 46.
18 4
13 7
7 58
2 40
0
2 40
7 58
13 7
18 4
22 46
25 0
35 0
32 12
26 6
19 16
11 52
4 0
0
4 0
ll 52
19 16
26 6
32 12
35 0
15 0
13 33
10 37
7 38
4 35
1 32
0
I 32
4 35
7 38
10 37
13 33
15 0
-- - ---- --- ------------- -- ---- ------- ------------- ------------- --------- ---
I. 177 +o. 001so 0. 0886 -1.821 -0. 00295 -2. 986
I. 107 . 001 2 .1044 1. 668 -. 00291 -2. 666
I. 053 .00180 .09 2 1.121 -. 00281 -1.127
I. 020 . 00175 . 0925 . 634 -. 00270 -.977
1.002 . 00169 . 0725 . 165 -.00264 -. 258
---------- ------- ------ ---- --- ------ ------------- ------------- ----------- -
I. 002 . 00162 . 0695 +.158 +. 00250 +.245
1.020 . 00150 . 0792 . 543 +. 00240 .869
I. 053 . 00136 . 0742 . 847 +. 00275 1. 712
1.107 .00126 . 0723 1.156 +. 00263 2. 410
1.177 . 00108 . 0532 J.09-l +. 00190 I. 922
----- -- --- ----- - --- -- -- +. 8046 - 1. 611 ------------- -.856
a o= 35 degrees. 6a = 15 degrees
---------- ------------- ------------- ----- - ------- -------- ----- ------------
I. 059 +o. 00206 0. 0912 -1.875 -0. 00276 -2. 510
I. 035 +. 00205 .1099 I. 756 -. 00271 -2. 322
1.018 . 00202 . 1066 1. 216 -.00263 -1.585
I. 007 . 00199 . 1038 . 711 -. 00258 -.922
L -~~()()~-- . 00195 . 0836 .1906 -. 00253 -.247
------------- ------------- ------ - ------ ------------- ------------
1.001 . 00192 .0823 +.1876 +.00250 +.244
J. 007 . 00188 .0981 .672 +:1l0246 . 879
1. 018 .00184 .0971 I. 108 +. 00236 I. 423 I I. 035 . 00178 .0954 I. 524 +. 00227 l. 945
1.059 .00170 . 0752 l. 546 +. 00227 2.064
---------- __________ .. __ +. 9432 -. 711 ------------ - - .931
ao=35 degrees. Aa=25 degrees
--+o.-ooi9s-- -----0:0014-- ------------- -- :.::0:00280-- ---:.::2:332--I 1.177 -2. 002
1.107 . 00200 .1147 1. 833 -. 00280 -2. 568
]. 053 . 00206 .1124 1. 283 -. 00275 -1. 715
l. 020 . 00203 . 1072 . 734 -.00265 -.959
1. 002 . 00197 . 08-!5 .1926 -. 00255 -.249
---------- ------------- ------------- ---------- - -- --- ---------- ----- -------
1.002 . 00191 . 0 19 +. 187 +. 00249 +. 244
1. 020 .00183 .0967 .662 + . 00235 51
1. 053 . 00171 . Q<J33 1. 065 +. 00227 I. 415
1.107 . 001 57 . 0901 1. 440 +. 00258 2. 366
1.177 . 00148 . 0728 ). 496 +. 00251 2.538
---------- ------------- +. 9510 -1.195 --- -- ------ -- -.909
a o=35 degrees. Aa=35 degrees
,_ ______ J ____________ I - --
-----0:1274-- ------------- -- :.::0:00280-· -·------1 1. 397 +o. 00198 -2. 619 -2.160
I. 242 . 00202 . 1174 2. 414 -. 00278 ·2. 860
I. 122 . 00198 .1071 J. 223 -. 00280 1 858
I. 044 . 00205 . 1108 . 759 - . 00273 l. 012
1. 003 . 00198 .0850 . 194 -. 002&7 -. 252
--- - ------ ------------- ------------- ------------ - ------------- ------------
1.003 . 00190 . 0815 +.186 +. 00247 +.242
I.OH . 00175 .0946 . 648 +. 0022J .838
1. 122 .00156 .0844 .964 +.00268 1. 778 I. 242 . 00135 . 0785 1. 614 +. 00208 2.140 I
I. 397 . 00090 . .0579 1.190 +. 00106 I. 272
1---------- ------------- +. 9446 -2. 607 -------------! - 1. 872 I
ao=45 degrees. Aa= J.5 degrees
-----------------------'---------------------------------------------------
!. 059 +o. 00249 0. I l02 -2. 264 -0. 00241 -2. 192
I. 035 . 00251 . 1346 2. 7 -. 00240 -2. 057
1.018 .00250 .1319 l.506 -.00239 - 1.440
l. 007 . 00249 . 1299 . 789 -. 00236 -. 843
I. 001 . 00249 . 1067 . 243 - . Q0?..33 - . 228
1.001 . 00246 .1054 +. 240 +. 00228 +.223
1. 007 . 00242 .1263 . 865 +. 00222 . 793
1.018 . 00238 . 1256 1. 434 +. 00217 . I. 307
I. 035 . 00234 . 1254 2. 57 +. 00213 1. 825
,-- -'.~~:~--1-----~~~~-- .1018 2.092 +.00210 1. 910
+1. 1978 -.361 ----- ---- ---- -. 702
ao
Aa1
Fv
Vv
T
w
AT
MRB
Vv2 .
MRH
MRv
~2
Mnv
ao
Aa1
----
Fv
Vv
T
w
AT
MRH
VV2
MnH
MR\'
V\T
~lRv
35
Calculation of vertical force and rotating nwments for 0-BES model-Continued
(Center of rotation at renter of span)
a o=45 deg~ee s. Aa =25 degrees
Aa Kn I K vSec•AaAsl K vSec•AaAsl
----------- ----- -----1-----1------1-----1
22. 4 0 25 0 ---------- ------------- -------------1------------- ------------- ------------
20. 56 41. 22 46 1. 171 +o. 00244 o. 119 -2. 462 -0. 00242 -2. 442
15. 98 51. 8 18 4 , ,., I .,,., . ... , ~· -. 00242 -2. 21
11. 42 51. 8 13 l. 053 . 00250 . 1364 l. 55 7 -.002-11 -1.501
6. 85 51. 8 7 1.020 .00250 .13~1 .904 - . 00239 -.865
2. 28 42.8 2 40 J. 002 . 00249 . I 068 . 244 -. 00234 -.229
0 0 0 --- ------- ------------- ------------- ------------- ------------- ------------
2. 28 42. 8 2 40 I. 002 . 00244 . 1046 +. 238 +. 00227 +.222
6. 85 51.8 7 58 1.020 . 00237 .1252 . 857 +. 00216 . 782
I l.42 51. 8 13 7 I. 053 . 00232 . 1266 I. 444 +.00211 1.314
15. 9 51. l 4 1. 107 . 00222 . 1272 2. 032 +.00200 1.832
20. 56 41. 8 22 4fi I. 177 . 00208 . 1022 2.090 +. 00193 l. 949
22.84 0 25 0 1----------1-------------1 +J.2213 -. 750 ---- -------- -1.156
ao=45 degrees. Aa=35 degrees
22. 84 0 35 0 ---------- ----- -------- ------------- ------------- ------------- -- - ----- - ---
20.56 41. 8 32 12 l. 397 +o. 00222 0.1296 -2. 662 -0. 00227 -2. 724
15. 98 51.8 26 6 I. 242 . 00240 . 1541 2. 468 -. 00240 -2. 469
11.42 51. 8 19 16 1.122 . 00245 . 1424 I. 625 -. 00243 -1.614
6.85 51.8 11 52 1.044 . 00250 . 1352 . 926 -. 00240 -. 889
2. 28 42.8 4 0 1.003 . 00219 .1069 . 244 -. 00235 -. 230
0 0 0 ---------- ------------- ------------- ------------- ---- --------- ------------
2. 28 42.8 4 0 I. 003 . 00243 . 1044 +. 238 +. 0022.3 +.21
6. 85 51. 8 f l .>2 l. 044 . 00233 . 1260 . 863 +. 00212 . 785
11. 42 51. 8 19 16 1.122 .00218 . 1267 I. 446 +. 00197 l. 303
15. 98 51.8 26 6 I. 242 .0020:3 . l:l06 2. 088 +. 00206 2. I l9
20.SG 41. 8 32 12 I. 397 .00100 . l 1 lO 2. 281 +.00228 2. 736
22.84 0 35 0 ---------- ------ -----1 + J. 2672 - 1.009 ------------- -. 760
ao=45 degrees. Aa=45 degrees
22.84 0 I 45 0 ---------- ------------- --- -- -------- ------------- ------------- ------------
20. 56 41.8 41
15. 98 51.8 I 35
ll.42 51.8 26
6. 5 51. 8 16
2. 28 4.2. 5
0 0 0
2. 28 42. 8 5
6. 85 51. 8 16
11. 42 51. 8 26
15. 98 51. 8 35
20. 56 41. 8 41
22. 84 0 45
15 15
2 5
0. 2711 0. 2918
.192. 5 185. 5
21.36 8. 84
. 294 . 711
4110 1640
+.112 -.068
+l,928 -l,088
- . 17 -.397
-3, 065 -6, 350
30 30
5 15
------
0. 7963 0. 7979
112. 2 112. 2
14. 62 4. 775
. 430 I. 316
1640 536
- . 452 - .. >36
-2, 650 -3, 135
-. 250 - .904
-l,465 -5, 290
59
0
34
42
42
1.808
1.491
I. 251
J.090
1.010
+o. 00192
. 00214
. 00239
. 00245
. 00250
42 I. 010 . 002-10
42 I. 090 . 00225
o 1 491 . ool7s
59 I. 808 . OOLIO
0.1451
. 1653
. 1549
. 1384
.1081
.1037
.1271
.1309
. 1374
. 0832
- 2. 982
2. 641
I. 768
.948
. 246
+. 236
. 870
l. 494
2.196
I. 710
-0. 00202
-.00221
-. 00240
-. 00242
-. 00237
+. 00219
+. 00208
+. 00210 +. 00l96 +. 00092
-3.13
-2. 729
-L 776
-.937
-. 234
+. 216
05
I. 555
2.420
I. 42'J
341 l. 251 0020?
0 ---------- ------------­--~----~---~----~---~
+!.29H -2. 079 -2.389
, ummary of results for 0-BF' model
(Center of rotation at center of span)
15 20 20 20 25
I
25 25
15 5 15 25 5 15 25
--
0. 3283 0. 4733 0. 5692 0. 4705 o. 6505 0. 6417 0. 6370
175. 0 145. 7 132. 146. l 124. 3 125. 2 125. 6
3. 07 11. 26 4. 03 2.11 13. 19 4. 28 2. 43
2. 0-18 .558 1.558 2. 98 . 4i6 I. 467 2. 585
537 1640 536 308 1640 536 30.5
-3. 027 +. 755 -.955 -5. llO +.569 -.128 -3. 043
-43, 000 +1. 450 -7, 830 -50, 700 +4, 086 -932 -22, 300
-1.049 -.479 -2.183 -2.153 -. 350 -.105 -1.826
-14, 920 -4, 730 -17, 900 -21, 350 -2, 513 -765 -13, 380
30 35 35
I
35 45 45 45 45
25 15 25 35 15 25 35 45
0. 8046 o. 9432 0. 9510 0. 9446 I. 197 I. 2213 1. 267 l. 294
111. 103. 2 102. 8 103. 2 91. 6 90. 7 89. I . I
2. 75 5.19 2. 99 J.99 5. 85
I_
3.42 2. 30 I. 63
2. 28 I. 21 2. 10 3. 16 J. 074 l. 837 2. 73 3. 85
308 536 308 205.4 536 308 205 144
-.856 -.931 -.909 -1.872 -. 702 -1.156 -. 760 -2.3 9
-4, 967 -4, 610 -4,462 -9, 250 -2, 734 -4,415 -2,800 -8, 610
-!. 611 -. 711 -1.195 -2. 607 -.361
I
- . 750 -1.009 -2. 079
-9,350 -3, 520 -5, 70 -12,880 -1,406 -2, 865 -3, i20 -7, 500
36
llh?
Fra.23
-· -
IM I - ,
111/.l ~ l'J- PF.~
l.o~ I ~'-. p B , ll.t.I ,,,.
I'\ IX I"- -r- - 'to• ~ ""1 . • '""''" I\. I'\ I"
1?11M ' ' I'-
\ \ '9,.
l ~n. IM ' \
I\ '
di)/ 111 I\
i~·. '\
i.-111 "" \ 191.
IM
0 I> ,.
"-
etn1MI '""' ...... 1 --~ :--r--. - ~ :s•
'\ --~ :;-~. r.?•. ""3'>'
l?/11 1171) ~ ......
' "-
IW .... """ \
,, ... - ,,., ,, . ,_
I/ I - I? I=
I \
- I
I
17 ~D 'r" '"...., _'IC?,.. ---~ "' ~" ,_
FIG. 24
I
37
Lift and drag on 1/2.'; scale model oj 0- 1 airplane tested in McCook Field 5-foot wind tunnel at 40 m. 7J. h.
Angle of
attack,
degrees
-4
-2
0
2
4
6
8
10
12
14
16
20
24
28
32
t:.a 15+aa
K, I
0 +15 0. 00308
5 20 . 00269
10 25 . 00255
15 30 . 00257
20 35 . 00251
25 40 . 00244
15-.la
0 15 . 0030& I
5 JO . 00256
10 5 . 00171 I 15 0 . 000i9
20 -5 -. 00027
25 -10 - . 00080
20+t:.a
0 20 0. 00269
5 25 . 00255
10 30 . 00257
15 35 .00251
20 40 . 00244
25 45 . 00232
30 50 . 00216 ----
20-t:.a
0 20 . 00269
5 15 . 00308
10 JO . 00256
15 5 . 00171
20 0 . 00079
25 -5 -. 00027
30 -10 -. 00080
25+t:.a
0 25 0.00255
5 30 . 00257
10 35 . 00251
15 40 . 00244
20 4.5 . 00232
25 50 . 00216
30 55 . 00200
35 60 . 00179 ----
25-t:.a
0 25 . 00255
5 20 . 00269
10 15 . 00308
15 10 . 00256
20 5 . 00171
25 0 . 00079
30 -5 . 00027
35 -lO -. 00080
K, K,
Angle of
attack, K,
degrees
---
-0. 000062 +o. 000141 36 0. 002502 +. 000385 . 000128 40 . 002444
. 000794 . 000131 44 . 002359
. 001167 . 000147 48 . 002210
. 001534 . 000171 52 . 002116
. 001889 . 000208 56 . 001977
. 002227 . 000251 60 . 001795
. 002561 . 000306 64 . 001602
. 002870 . 000369 68 . 001359
. 003111 . 000436 72 . 001118
. 002985 . 000629 76 . 000876
. 002690 . 000916 80 . 000628
. 002558 . 001224 84 . 000396
. 002587 . 001472 90 . 000075
. 002560 . 001725
A utorotation calculation for 0- 1 model
K,
0. 00052
. 00092
.00129
.00160
.00190
. 0021 ,
. 00052
. 00031 : ooorn
.00013
.00015
. 0001
0. 00092
. 00129
. 00160
.00190
. 00218
. 00248
. 00276
. 00092
. 00052
. 00031
.00019
. 00013
. 00015
. 00018
0. 00129
. 0016 0
. 0019
. 0021
.0024
. 0027
.0029
. 0031
0
8
8
6
5
5
. 00129
.0009
.0005
.0003
2
2
l
. 0001
. 0001
. 0001
.0001
9
3
5
8
'-·
Calculation of K,· and Kn
ao= 15 degrees
K,Sin t>a
0
.0002 34
.0004
.0006
.000
.00
42
6-5
85
1031
22~
I K xCoslla:
I 0. 00052
. 000916
. 001270
. 001545
. 001785
. 001074
. 00052
. 000308
I
I
I 0
.000
.000
.000
2<J7
20 1
.0001 1 1
. 0001256
- . 0000\ U2'J .000141
- . 000 33S . 000163
a o= 20 degrees
0 0. 00092
. 000222 .0012 5
. 000146 . 001576
. 000649 . 001834
. 000834 . 00205
. 000980 .00224
. 001079 . 00239
0 . 00092
. 000268 . 00051
. 000444 . 000305
. 000442 . 000183
. 000270 . 000122
-. 000114 . 000136
-. 000400 I . 000156
a o= 25 degrees
0 o. 00129
. 000224 . 00159
. 000435 . 0018i
. 000631 . 002105
. 000794 . 00233
. 000912 . 00250
. 001000 . 00255
. 001026 . 00258
0 .00129
. 000234 . 000916
. 000534 . 000512
. 000662 . 000299
. 000585 . 000178
. 000334 . 000118
-. 000135 . 000130
-. 000458 . 000147
--- --
Kv
+o. 00052
. 00068
. 00083
.00088
. 00093
. 00094
+. 00052
+. 00053
+. 00048
+. 00033
+. 000049
-. 000175
+o. 00092
. 00106
. 00113
. 001185
. 00122
. 00126
. 00131
+ .00092
. 000786
. 000749
. 000625
. 000392
+. 000022
-. 000244 I
+o. 00129
. 00137
.00144
.00147
. 00154
. 00159
. 00155
. 00155
+.00129
+ . 00115
+. 00105
+. 00096 +. 00076 +. 000452
-. 000005
-. 000311
K,
o. 001952
. 002184
. 002407
. 002683
. 002825
. 002995
. 003152
. 003287
. 003369
. 003375
. 003403
. 003325
. 003128
. 002973
K,Cost>a K,Sinl'>a Ka
o. 00308 0 -0. 00308
. 00268 . 0000802 . 00276
. 00251 . 000224 . 00273
. 00248 . 000414 . 00289
. 00236 .000649 . 00301
. 00221 . 000921 . 00313
. 00308 0 +. 00308
. 00255 . 0000272 +. 00252
.00168 . 000033 +. 00165
. 000763 . 0000336 +. 000i3
- . 000254 . 0000513 - . 000305
-. 000725 . 0000760 -. 000801
0. 00269 0 I -0. 00269
. 00254 . 000ll2 . 00265
. 00253 . 000278 I . 00281
. 00242 . 000492 .00291
. 00229 . 000745 . 00303
. 00210 . 001047
I
. 00315
. 00187 . 001380 . 00325
00269 0 +. 00269
. 00306 . 0000453 1 .00301
. 00252 . 000053 . 00247
. 00165 . 0000492 .00160
. 00074.2 . 0000444 +. 000698
-. 000244 . 0000634 1 -. 000307
-. 000693 . 0000900 -. 000783
'
0.00255 0 -0. 00255
. 00256 . 000139 - . 00270
. 00247 . 00033 -. 00280
. 00235 . 000564 -. 00291
. 00218 . 000848 -. 00303
. 00196 . 001166 -. 00313
. 00173 . 001474 - . 00320
.001466 . 001805 -. 00327
. 00255 0 +. 00255
. 00268 . 000072 +. 00261
. 00303 . 0000903 +. 00294
. 00247 . 0000802 +. 00239
. 001610 . 0000649 +. 00155
. 000716 . 0000549 +. 00066
-. 000234 . 0000750 - . 000309
-. 000655 . 0001032 - . 000758
lla 21+aa K,
--
0 27 0. 00257
.5 32 . 00256
JO 37 . 00249
15 42 . 00240
20 47 . 00226
25 52 .00212
30 57 .00192
35 62 . 00169
27-~a
0 +27 . 00257
5 22 . 00259
JO 17 . 00290
15 12 . 00287
20 7 . 00206
25 +2 . 00117 30 -3 .00016 I
30+aa I 0 30 0. 00257
5 35 . 00251
IO 40 . 00244
15 15 . 00232
20 50 . 002JG
25 55 . 00200
30 60 . 00179
35 65 . 00154
---
30-..la
0 30 . 0025i
fi 25 . 00255
JO 20 . 00269
15 15 . 00308 .
20 10 . 00256
25 5 . 00171
30 0 . 00079
35 -5 . 00027
35+aa.
0 35 0. 00251
5 40 . 00244
10 45 . 00232
15 50 . 00216
20 55 . 00200
25 60 . 00179
30 65 . 00154
35 70 .00124
40 75 . 00093
45 80 . 00063
35-lla.
0 35 . 00251
5 30 . 00257
10 25 . 00255
15 20 . 00269
20 15 . 00308
25 10 . 00256
30 5 .00171
35 0 . 00079
40 -5 . 00027
45 - 10 .00080
45+lla.
0 45 0. 00232
5 50 . 00216
JO 55 .00200
15 60 . 00179
20 65 . 00154
25 70 .00124
30 75 . 00093
35 80 . 00063
40 85 . 00033
45 90 . 00007
45- .6.a
I
0 45
I
. 00232
5 40 . 00244
10 35 . 00251
15 30 . 002.57
20 25 . 002.55
25 20 . 00269
30 15 . 00308
35 10 . 00256
40 5 . 00171
45 0 . 00079
38
Autorotation calculation for 0- 1 model-Continued
Calculation of Kv and KR
ao = 2i d egrecs
K, I K , Sin lla K,Coslla I Kv K,Coslla
0. 001415 0 o. 001415 +o. 001415 0. 00257
. 00172 . 000223 . 001713 . 00149 . 00255
. 00201 . 000432 . 0019 0 . 00155 . 00245
. 00230 . 000621 . 00222 .00160
I
. 00232
. 00263 . 000772 . 00247 . OOiiO .00212
.00282 . 000895 . 00255 . 00166 .00192
. 0030.3 . 000960 . 00262 .00166 . 00166
. 00322 . 000969 . 00264 . 00167 . 001383
I
. 001415 0 . 001415 +. 001415 . 00257
.00108 . 000226 . 001076 .00130 . 00255
.00071 . 000503 . 000699 .00120 . 00285
. 00037 . 000743 . 000357 . OOllO . 00277
. 000225 . 0007().J . 0002114 . 000915 . 001935
.00015 . 000498 . 000136 . 00063 . 00106
.00013 . 000080 . 0001126 . 00019 . 0001385
a o=30 degrees
I
0. 00160 0 0. 00160 +o. oorno o. 00257
. 00190 . 0002190 .00189 . 00167 . 002,j()
.00218 . 000423 . 00215 . 00173 . 00240
. 00248 . 000600 . 00239 . 00179 . 00224
. 00276 . 000738 . 002.59 . 001 5 . 00203
.00295 . 000845 . 00267 . 00183 .00181
. 00315 . 000895 . 00273 .00184 . 00155
. 00330 . 000883 . 00270 .00182 . 00126
. 00160 0 .00160 +. 00160 . 00257
.00129 . 000222 .00128 . 00150 . 00254
. 00092 . 000467 . 000906 . 00137 . 00265
. 00052 . 000797 . 000502 . 00130 . 00297
. 00031 . 000875 . 000291 . 00117 . 00240
. 00019 . 000722 . 000172 '00089 . 00155
.00013 . 000395 . 000112 +. 000507 . 00068'1
.00015 . 000155 . 000123 -. 000032 -. 000221
ao = 35 d cgrees
o. 00190 0 0. 00190 +0.00190 o. 00251
.00218 '000213 . 00217 . 00196 . 00243
. 00".A . 000403 . 00244 .002().J . 00228
. 00276 . 000559 . 00267 . 00211 . 00209
. 00295 . 000684 . 00277 . 00209 . 001
. 00315 . 000756 . 002 5 . 00209 . 00162
. 00330 . 000770 . 00286 . 00209 . 00133
. 00338 . 000711 . 00277 . 00206 . 001016
. 00339 . 000598 . 00260 . 00200 . 000712
. 00332 . 000446 . 00235 . 00190 . 000445
. 00190 0 . 00190 +.00190 . 00251
.00160 . 000224 . 00159 . 00181 . 00256
.00129 . 000442 . 00127 . 00171 . 00251
. 00092 . 000691) . 000889 . 00158 . 00260
. 00052 . 001053 . 0004 . 00154 . 00289
. 00031 . 001081 . 000281 .00136 . 00232
.00019 . OOO&'i5 .OOOIM6 . 00102 .00148
. 00013 . 000!53 . 0001064 +. 00056 . 000639
. 00015 -. 0001735 +. 0001148 -. 000059 - . 000207
. 00018 -. 000566 +. 000127 -. 00044 - . 000565
a o=45 degrees
0. 00248 0 0. 0024 +o. 00243 0. 00232
. 00276 . 000188 . 00275 . 00255 . 00215
. 00295 . 000347 . 00290 . 00255 . 001970
. 00315 . 000463 . 003().J . 00258 . 001730
. 00330 . 000527 . 00310 . 00257 . 00145
. 00338 . 000524 . 00306 . 00254 . 00112
. 00339 . 000465 . 00294 . 00248 . 000805
. 00332 . 000361 . 00272 . 00236 . 000516
. 00310 . 000212 . 00237 . 00216 . 000253
. 00297 . 0000495 . 00210 . 00205 . 0000495
. 00248 0 . OOZJ +.002-18 . 00232
. 00218 . 000213 . 00217 . 00238 . 00243
.00190 . 000435 . 00lb70 . 00230 . 00247
.00160 . ()()()tjfi5 . 001 545 . 00221 . 00218
.00129 . 000872 . 001212 . 00208 . 00239
. 00092 .001136 . 000834 . 00197 . 00244
. 00052 . 001538 . 000450 . 00199 . 00267
. 00031 . 001466 . 000254 . 00172 . 00210
.00019 . 001098 . 000145 .00124 . 00131
. 00013 . 000559 . 0000919 . 00065 . 000558
,
K ::.:Si11aa K R
0 -0. 00~5 7
. 00015 . 002/0
. 000349 . 00280
. 000595 . 00291
. 000899 . 00302
. 001191 . 00311
. 001515 . 00317
. 001847 . 00323
0 +. 00257
. 0000942 . 00246
. 0001232 . 00273
. 0000957 . 00267
I . 00007i0 . 00186
. 000063J . 00100
. 000065 . 00007
I
0 -0. 00257
. 000166 -. 00267
. 000378 -. 00278
. 000641 -. 00288
. 000944 -. 00297
. 001246 -. 00306
. 001574 - . 00312
.001 90 - . 00315
0 +. 00257
. 0001124 . 00243
. 0001596 . 00249
. 0001346 . 00284
. 000106 . 00229
. 000080.J . 00147
. 000065 +. 000619
. 0000859 -. 000307
0 -0. 00251
. 000190 -. 00262
. 000430 -. 00271
. 000714 -. 00280
. 001008 -.00289
. 001330 -. 00295
. 001650 -. 00298
. 001937 -. 00295
. 002180 - . 00289
. 002350 -. 00279
0 +. 00251
. 000 1394 . 00242
. 000224 . 00229
. 000238 . 00236
. 00017 . 00271
. 000131 . 00219
. 000095 . 00139
. 0000745 +. 000565
+. 0000965 - . 000303
+. 0001272 -. 000692
0 -o. 00232
. 000240 . 00239
. 000512 . 00248
. 000815 . 00254
. 001128 . 00258
. 001428 . 00255
. 001694 . 00250
. 001903 . 00242
. 001993 . 00225
. 00210 . 00215
0 +. 00232 I
.00019 . 00224
. 00033 .00214
. 0004 14 . 00207
. 000441 .00195
. 000388 . 00205
. 000260 .00243
. 0001776 . 00192
. 000122 . 00119
. 0000919 . 00047
39
IO I ~ V7- 1...1. v
AA · ~ IL t,ct - A .I. ~- ~- ~~
>< Ir 1,.,, 'r,. _,. ,c .-~, rA ,.,, ·- ,/ v · i---..
IK, na
"" 17 0 -1. " ~z '1- ~ C< /e i-n. c/t!I ~V
I -- "' .. :a ~I ~H v v A~ ~A - -r<-,..___ I
j / ....... ,.......
A :,,,., I v ---. ....
I- )-' ....... r-..
1,,r ~~ / r--
! v ~ !'-..
In,- 1'7 ... v r--- ,___
I v "'>. .I
VV\ hD I / --~
./ ~
[ ,-,, lrM I "
.....
~ ,_ ~ ~
~ I ['-,
- I*
,,,r,.,
14r ,-,/ I> r If I llf, l,,..J
- . I .,.,, ro t.i; ; I? ,[5" '0 '15" -ro rJ;" 0
'°""
0 M 0 l'5" I 'O ,r.., 'l•'l
FIG. 25
•
I In 7- r. r...-
~,.,. •/.•.- "'",. !'.:,,;; / lh ,_,
· ~
,--, _,,. .... .
-, l I / " ~1£
- ~ - r- r---
,., '" r-t-- --
.3C:+ pa ~~ "" ~ ·' r,'.'..". '
-r-."- -A Ii- ~ .............
r l\-t -- r-""-
,_.. ......_ 1--..... r-..
-=:;;; - - ,._ ~ - - [T .U f'" -r----. ['.. i-- --,..__ r-. r-.. r-......_ .... ,__ ........, f'I"'" .aa -- - I>'-.. r--. ~ ...... ..... r---. .... ......_ -~
l/1 -r--.... ,.....,_ ......... r.u• ~ -- ........
- ~ ,..__
t--i ~1;! b,:; - "'"' ~ 'j'--...
~ ~.:> !<'<> -~ --
11"°'"
11• ~ ·- ,o- 115 - <:p c.p .;!f-1 .;7,p ., J .. "'
-..-
F10. 26
•
40
Calculation of vertical force and rotating moments for 0 - 1 model
(Center of rotation at cen ter of span)
a a=l5 degrees . ~a1 =2 degrees
Kv Kv Sec•
I I .<l.• .<l.a Sec•.'l.a fia~s K a --------___________ , _____ ,
19
17
13
9
5
2
0
2
5
9
13
17
19
19
17
13
9
5
2
0
2
5
9
13
17
rn
19
J7
13
9
5
· 2
0
2
5
9
13
17
19
19
17
13
9
5
2
0
2
5
9
13
17
19
19
17
13
9
5
2
0
2
5
9
13
17
19
I
I
I
I
0
33. 91
39. 96
39. 96
39. 96
24. 21
0
24. 21
39. 96
39. 96
39. 96
33. 91
0
0
33. 91
39. 96
39. 96
39. 96
24. 21
0
24. 21
39. 9G
39. 96
39. 96
33. 91
0
0
33. 91
39. 96
39. 96
39. 96
24. 21
0
24. 21
:39. 96
39. 96
39. 96
33. 91
0
0
33. 91
39. 96
39. 96
39. 96
24. 21
0
24. 21
39. 96
39.96
39. 96
33. 91
0
0
33. 91
39. 96
39. 96
39. 96
24. 21
0
24. 21
39. 96
39. 96
39. 96
33. 91
0
2
l
l
0
0
0
0
0
0
0
I
l
2
5
4
3
2
1
0
0
0
1
2
3
4
5
15
13
10
7
4
l
0
1
4
7
10
13
15
2
1
l
0
0
0
0
0
0
0
1
1
2
5
4
3
2
1
0
0
0
1
2
3
4
5
0 ---------- ------------------------ ------------- ------------
47 l.001 0. 00058 0. 01967 -0. 00292 ------------
22 1.001 . 00057 . 02280 -. 00297 -- ------ ---- ·" I. 000 . 00055 . 02197 -. 00299 --------- --- 32 1.000 . 00053 .02118 -. 00303 ------ ------ 13 1.000 . 00052 .01259 -. 00307 ---- --- -----
1.000 0 0 0 ------------ 13 J.000 . 00052 . 01259 +. 00307 ------------
32 1.000 . 00052 . 02078 +. 00303 ------------
57 J. 000 . 00052 . 02078 +. 00299 ------------
22 1. 001 . 00052 . 02079 +. 00297 ------------
47 1.001 . 00052 . 01765 +. 00292 ------------
0 ------ -- -- ------------ --------- --- --- ---------- -----------
i +. 19080
a o= l 5 degrees . .<l.ar=5 degrees
0 --------------- --- ---- ------------ ------------- --- ---------
29 J.007 0. 00067 0. 02288 -0. 00273 -1.585
26 l. 00-I . 0000.3 . 02527 - . 00282 -1.471
22 I.002 . 00060 . 02402 -. 00289 -1.041
19 !. 001 . 00057 . 02280 - . 00297 - . 59-1
32 I.000 .00053 .012&3 - . 00303 - . 1466
J.000 0 0 0 0
32 l. 000 . 00052 . 012.59 +. 00.303 +. 1466
19 J. 001 . 00052 . 02080 +. 00297 +. 594
22 1.002 . 00052 .02081 +. 00286 + 1.0~0
2R I. 00~ . 00052 . 02087 +. 00273 +I. 423
29 !---'.~~~~-- . 0005:3 .01810 +. 00260 + J.509
0 -- ------- +. 200!17 ------------- -. 135
a:o= 15 degrees. Lla1 = 15 degrC('S
0 ---------------------- ------------ ------------- -------- --
28 1. 057 0.000 0. 031.55 -0. 00287 -1. 749
23 J. 032 . 00083 . 03421 -. 00275 -l.473
16 l. 017 . 00076 . 030h8 -. 002725 -. 997
8 1.005 . 00005 . 02610 -. 002SO - . . 562
37 J. 001 . 00057 . 01381 -. 0029-l -.1425
1.000 0 0 0 0
37 J. 001 . 00052 . 01260 +. 00294 +. 1425
8 I. 005 .00053 .02127 +. 00265 . 532
16 1. 017 . 00052 . 02111 +. 00217 . 793
2'J I. 032 . 000475 . 01958 +.OOJ.58 . 847
28 1. 057 . 00039 . 01397 +. 00100 .610
0 --------- - ------------ +. 22508 ----- ---- ---- - 1.999
ao=20 degrees . .<l.a1=2 degrees
4~ ---1~ooi-- ---0:00001·- ---0~03200-- -- :.:0:00253·- -- :.:1:5is __ _
22 I. 001 . 00095 . 03800 -. 00264 -1. 370
57 I. 000 . 00095 . 03795 -. 00265 -. 953
32 !. 000 . 00093 . 03715 -. 00267 -. 534
13 l. 000 . 00092 . 02228 -. 002 -.1297
13
32
57
22
47
0
0
29
26
22
19
32
32
19
22
26
29
0
1.000 0 0 0 0
1. 000 . 00090 . 02180 + . 00272 +. 1316
i. ooo . 00089 I 03555 +. 00211 . 5518
1. 000 . 00088 . 03515 + . 00282 I. 014
~:gg~ ----~=~--1 +.~~~: ---~~~:--1 :::::
ao= 20 degrees .<l.at = 5 degrees
---------- 0 ------------ -- ------- ---- -- --- ----- --
1.007 . 00104 0. 0343 -0. 00263 -1. 526
1.004 . 00102 .0402 -.00263 -1.372
1.002 . 00100 . 0400 -. 00263 -.947
1. 001 . 00097 .0388 - . 00264 -.528
1.000 . 00093 .0225 -. 00267 -.129
1.000 0 0 0 0
1. 000 .00089 . 02155 +. 00277 +. 134
1. 001 . 00087 .0348 +. 00286 . 572
1.002 . 00085 . 0340 +. 00296 I. nr'
1.004 . 00082 . 0329 + . 00301 I. 510
1. 007 . 00079 . 0270 +. 00302 1. 753
---------- ------------ + . 32605 --------- ---- +.592
41
Calculation of vertical force and rotating moments for 0- 1 model-Continued
I
I
I --
I
l9
17
13
9
5
2
0
2
5
9
13
17
I 19
19
17
13
9
5
2
0
I 2
5
9
I
13
17
19
-
19
17
13
9
5
2
0
2
5
9
13
17
19
19
17
13
9
5
2
0
2
5
9
13
17
19
19
Ii
13
9
5
2
0
2
5
9
13
17
19
a, .:ia
--- ---
0 '
0 15 0
33. 91 I 13 28
39. 96 10 23
39. 96
I
7 16
39. 96 4 18
24. 21 1 37
0 0
24. 21 l 37
39. 96 4 8
39. 96 7 16
39. 96 10 23
33. 91 13 28
0 15 0
0 25 0
33. 91 23 46
39. 96 17 42
39. 96 12 2
39. 96 7 0
24. 21 2 49
0 0
24. 21 2 49
39. 96 7 0
39. 96 12 28
39. 96 Ji 42
33. 91 23 46
0 25 0
----
0 I 5 0
33. 91 4 29
39. 96 3 26
39. 96 2 22
39. 96 I l l9
24. 21 0 32
0 0
24. 21
I
0 32
39. 96 1 19
39. 96 2 22
39.96 3 26
33. 91 I 4 29
0 I 5 0
(Center of rotation at center of s pan)
a o=20 degrees. II.at = 15 degrees.
8ec2.1a Kv Kv Sec• KR 6..aJ.f
---
----- ----- ----------- - --- -------- - -- ----- ------ 1.057 o. 00117 0. 04192 -0. 00290
1. 032 . 00113 . Q.166 - . 00288
1. 017 . OOJlO . 0447 -.00273
1.005 . 00103 . 0413 -. 00263
1. 001 . 00097 . 0235 -. 00263
1.000 0 0 0
1. 001 .00087 .0213 +. 002SS
1. 005 . 00080 . 0321 +. 00303
1. 017 . 00075 . 0305 +. 00287
1.032 . 00075 . 0309 +. 00241
1. 057 . 00072 . 0257 +. 00190
--- ------- ----------- - +. 3458 !------------- -- ---
a o= 20 degrees. ll.at =25 degrees
I I
---- - ---- - ----------- - ------------ -------- -- -- - 1.193
I 0. 00126 0. 0510 -0. 00312
1.102 .00120 . 0528 -. 00299
1. 050 . 00116 . 0486 -. 00288
I. 015 .00109 . 0442 -. 00272
1.002 . 00101 . 0245 - .00263
l.000 0 0 0
I. 002 . 00083 . 0201 +. 00299
1. 015 . 00075 . 0304 + . 00289
I. 050 . 00073 . 0306 +. 00207
J. 102 . 00055 . 0242 + . 00113
J. 193 . 00010 . OQ.105 - . 00010
---------- ------------ + .3314 -------------
a o=25 degrees. II.at = 5 degrees
1---n~r- ------------1------------1------------- 0. 00137 o. 0468 -0. 00268
. 00135 . 0542 I . 00265
I I. 002 . 00133 . 0532 . 00263
1.001 . 00131 . 052•1 . 00259
1.000 . 00130 . 0315 . 00257
1.000 0 0 0
1.000 . 00130 . 0315 +. 00255
1.001 . 00125 . 0500 . 00255
J.002 .00122 . 04 . 00255
1. 004 . 00118 . 04 3 . 00257
1.007 . OOJ15 . o:j93 ---- ------ -------- ---- +.4552 1-----~~~~--
I
a o=25 degrees. ll.a1 = 15 degrees
-
0 15 0 ------ ---- ------- ----- -- -- -------- ---------- --- 33. 91 13 28 1. 057 0. 001475 0. 0529 -0. 00287
39. 96 10 23 1.032 . 00145 . 0598 . 00281
39. 96 . 7 16 1.017 . 00141 . 0573 . 00275
39.96 4 8 1.005 . 00136 . 0546 . 002675
24. 21 1 37 1. 001 . 00132 . 0320 . 00260
0 0 1.000 0 ------------ 0
24. 21 1 37 1. 001 . 00123 . 029 + . 00255
39. 96 4 8 1.005 . 00117 . ()470 . 00258
39. 96 7 16 1.017 . 00109 . 0443 . 00277
39. 96 10 23 1.032 . 00104 . 0429 . 00292
33. 91 13 28 1. 057 . 00099 . 0355 . 00262
0 15 0 ---- ------ ---- -------- +. 4561 ----------- --
ao=25 degrees. II.at =25 degrees
0 25 0 -- -- ---- -- -- -- ----- --- ----- ----- --I -- --------- -- 33. 91 23 46 1.193 o. 00158 0. 0639 - 0. 00312
39. 96 17 42 1.102 . 00149 . 0656 . 00297
39. 96 12 28 1. 050 . 00147 . 0617 . 00285
39. 96 7 0 1. 015 . 00140 . 0568 . 00275
24. 21 2 49 1. 002 . 00133 . 0323 . 00263
0 0 1.000 0 0 0
24. 21 2 49 1.002 .00120 . 0291 +. 00256
39. 96 7 0 1. 015 . 00110 . 0446 . 00274
39. 96 12 28 1. 050 . 00101 . 0424 . 00274
39. 96 17 42 I. 102 . 00087 . 0383 ,-----~:~--1 33. 91 23 46 1. 193 . 00055 . 0222
0 25 0 ---- -- -- -- ----------- - +.4569
K11I Sec~1 Lla..lf
-l. 767
-1. 542
-.998
-.528
-.127
0
+.139
.608
1. 049
+1. 291
I. 158
-. 717
------- --- --
-2.145
-1. 712
-1.087
-. 551
-.128
0
+.145
. 585
. 7 2
+ .647
-. 0688
-3. 533
I
---=1~556--1
1.382
. 947
. 518
. 124
0
+.123
. 510
. 919
1. :141
1. 503
-. 130 I
---- --- -----
-1. 750
1. 506
1.006
. 537
.126
0
+. 124
. 51
L 013
J. 565
1. 597
-.108
----- ---- -- -
-2. 147
1. 700
1. 076
. 557
. 1276
0
.1242
. 555
I. 034
1.110
. 619
- 2.136 -I
42
Calc1tlation of vertical force and rotating moments for 0 - 1 model-Continued
-----
19 0
17 33. 91
13 39. 96
9 39. 96
5 39. 96
2 24. 21
0 0
2 24. 21
5 39. 96
9 39. 96
13 39. 96
17 33. 91
19 0
19 0
17 33. 91
13 39. 96
9 39. 96
5 39. 96
2 24. 21
0 0
2 24 . 21
5 39. 96
9 39. 96
13 39. 96
17 33. 91
19 0
19 0
17 33. 91
13 39. 96
9 39. 96
5 39. 96
2 24. 21
0 0
2 24. 21
5 39. 96
9 39. 96
13 39. 96
17 33. 91
19 0
19 0
17 33. 91
13 39. 96
9 39. 96
5 39. 96
2 24. 21
0 0
2 24. 21
5 39. 96
9 39. 96
13 39. 96
17 33. 91
19
19 0
17 33. 91
13 39. 96
9 39. 96
5 39. 96
2 24. 21
0 0
2 24. 21
5 39. 96
9 39. 96
13 39. 96
17 33. 91
19 0
(Center or rotation at center or span)
ao=27 degrees. Lla1=5 degrees
Sec•aa Kv Kv Sec•
~a.6.S" Kn KnJ ec•
.1a ds
---
5 0 ---------- --------- --- ------ ------ -- ---- --- ---- ------- --- -- 4 29 l. 007 0. 00148 0. 0505 -0. 00269 -l. 562
3 26 l. 004 . 00147 . 0589 - . 00267 - 1. 391
2 22 1.002 . 00145 . 0581 -. 002fi3 -. 947
1 19 I. 001 . 00143 . 0572 -. 00260 -. 519
0 32 1.000 . 00142 . 0344 -.00258 -. 125
0 1.000 0 0 0 0
0 32 1.000 . 00140 . 0.339 +. 00255 +.124
1 19 I. 001 .00138 . 0552 +. 00252 . 504
2 22 1.002 . 00136 . 0544 +. 0024 . 893
3 26 1.00! . 001~3 . 0533 +. 00246 I. 282
4 29 l. 007 . 00130 . Q.!4 '1 +. 00246 1.428
0 -- - ---- --- -- -- -------- +. 5003 ------------- -.313
a o=27 degrees. Lla1=15 degrees
15 0 ---------- _______ __ ___ __ _________ _!_ _____ _______
------------ 13 2 I. 057 0. 00159 0. 0570 -0. 00288 -1. 756
10 23 I. 032 . 00155 . 0639 -. 00281 -1.506
7 16 I. 017 .00152 . 0618 -. 00275 -1.006
4 8 1. 005 . 00147 . 0590 - . 00267 -. 536
1 37 l. 001 . 00143 . 0347 - . 00261 -. 1265
0 1. 000 0 0 0 0
l 37 1. 001 .00138 . 0334 +. 00250 +. 1212
4 8 1.005 . 00131 . 052(i +. 002~6 . 494
7 16 l. 017 . 00125 . 0508 +. 002.15 . 932
JO 23 1. 032 ----~~::: __ ,
. 0195 +. 00277 J. 485
13 28 1. 057 . 04()<J +. 00282 l. 718
15 0 +. 5036 --------- ---- -.180
ao=27 degrees. Lla1=10 degrees
10 \---n~r ------------ -- --0~0535- - -- :.::0~00278 --
_________ __ _ ,
58 0. 00154 -1.643
6 ,53 .00152 . 0615 - . 00274 -1.443
4 47 1 1~ . 00148 . 0596 - . 00270 -.979
2 39 .00145 . 0580 -. 00263 ---~~'.~~---! l 4 . 00143 . 0346 -. 00260
0 1 4 l. 000 ----.-ooi3ii-- -----~0337-- ---+~00253-- . 1225
2 39 I. 002 . 00135 . 0540 . 00248 . 496
4 47 1. 008 . 00130 . 0523 . 00247 . 895
6 53 1. 013 .00125 .0506 . 00253 1. 332
8 58 ·L 025 . 00122 .Q.l24 . 00265 1.566
10 ---------- ------------1 +. 5002 -------- --- -- -.3400-1
ao=27 degrees. ""'' = 25 degrees
25 I
23 46 - --i~i9:i -- ---o.-ooi68-- --- -----:--- -------------1-------~;;--- 0. 0619 - 0. 00310 -2. Jo_
17 42 1. 102 .00167 . on.; - . 00291 - 1. 699
12 28 1. 050 . 00158 . 0663 - . 00286 -1. 080
7 0 1. 015 . 00152 . 0616 - . 00274 -. 556
2 49 1. 002 . 00145 . 0352 -. 00265 -.1286
0 ---------- ---- --- --- -- ------------ ---------- -- ------------ 2 49 1. 002 .00135 . 0328 +. 00247 +. 1199
7 0 1. 015 . 00125 .0507 +. 00254 . 515
12 28 1. 050 .00115 .~82 +. 00285 I. 076
17 42 1. 102 .00101 .OH5 +. 00227 1. 298
23 46 I. 193 . 00011 . 0287 +. 00123 . .846
25 0 ---------- --