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__.— L ..t NATIONALADVISORY COMMITTEEFOR AERONAUTICS- - , No. 761 .——- PRESSURE-DISTRIBUTION INVESTIGATIONOF AN N.A.C.A. 0009 AIRFOIL WITH AN 80-PERCENT-CHORD PLAIN l’LAP AND THREE TABS .._ and Richard I. Sears By Milton B. Ames, Jr., Langley Memorial AeronauticalLaboratory .- ..— : TIWDOCUhfkkT C;/ LOAN FROM THE FILU CF ..-.
NATIONM ADWRYWMMI~E FOR MROMU~U UNGLEy4ER0WuTIWL LABORATORY . . . .
LMGLEY FIELD, tLAMPTON, ViRGINIA . ... . ---- —. — . .. _-m . . NATIONAL ADVISORY COMMITTEE FOR AEGw?!Jy)a ~724STREH, ~,iv,, ” _.. ._-= ---- wA9iWvJ,l/p5,D.c.” ‘“ Washington May 1940 . ———— NATIONALADVISORY COMMITTI!E FOR AERONAUTICS TECHNICALNOTE NO. 761 PRE!SSURPJ-DISTRIBUTION INVESTIGATION03’ AN N.A.C.A. 0009 AIRYOIL W.ITH AN 80-PERCENT-CHORD PLAIN R’LAP AND THREE TABS By Milton B. Ames, Jr., and Richard 1. Sears ,’.
SUMMARY Pre.ssure-distrib”ution tests of an 11.A.C.A. 0009 air- foil with an 80-percent-chord “plainflap and three plain tabs, having chords of 10,’20, and 30 percent of the flap chord, we’re made in the N.A.C.A. 4- by 6-foot ver5ical tunnel. Section data suitable for applicationto the de- sign of horizontaland vertical tail surfaces were o11- tained.
*.
Resultant-pressure diagrams for the airfoil with the flapand the’20-percent-chord tab are presented. Plots “ u are also given of incrementsof normal-forceand hinge- ‘momentcoefficientsfor the airfoil, the flap, and the-– A ,comparison of some characterie’tic slopes three tabs.
for the.30-, the 50-, and the 80-percent-chbrd flaps, tested in the general investigationof plain flaps for control surfaces, is included. Section aerodynamicant load data have been’ made availablefor a wide range of flap and tab chords to be used o“nan N.A.C.A. 0009 air- -. — ‘foil or on other conventionalsections. ‘ ., ,.
INTRODUCTION The Nat-ional Advisory Committeefor Aeronauticshas conducted~nvestigation.s “ofplain flaps and.trailing-edge tabs on a~rfoilsof different-profiles and with finite ‘- spans. The re-suits’”of some of these investigations@re reported +n references.1, 2, and 3. No avtiilable data ap- ‘“- placable to tail-surfacedesign give the aerodynamicsec- ~ tion charac~er.istics 9f a thin airfoil as affected >y .——-—- --- .
flaps and tabs of different sizes.
In order to provide this inz’ormation, an investigationwas started of an i N.A,C.A:0009 airfoil having ‘flapsand tabs” of various The results of -thetests of a 50-porce.nt-chord” chords.
L N.A.C.A. !I!ochnical Note No. 761 ?.
flap and throo tabs are reported in reference4 and of a 30-percent-chord flap with three ta%s, in reference5.
The present report gives the results of pressure-distri- bution tests on the N.A.C.A. 0009 airfoil with an 80- percent-chordplain flap and three“tabshaving chords 10, 20, and 30 percent of the flap chord. Trom the data obtained,normal-forceand pitching-moment coefficients were calculatedfor the airfuil section completewith tho flap and the various tabs. In addition,normal-forceand hinge-nomentcoefficientswere calculatedfor the flap with the different tabs and for the tabs alone.
APPARATUS The tests were conducted.inthe N.A.C.A.4- by 6- foot verticalwind tunnel (reference6) with modifica- tions asshown in figure 1 and described in reference5.
The 3- by 4-foot model was made of mahogany, shaped to the N.A.C.A.0009 profile. It was equippedwith a plain flap having a chord 80 percent of the airfoil chord and three seriallyhinged plain tabs having chords 10, 20, and 30 percent of. the flap chord, as shown in figure 2.
The nose radii of the ~lap and the tabs were approxi- mately one-half the airfoil thicknessat the hinge axes.
All gaps at.th”e flap and the tab hinges were sealed with plasticizeand-cellulosetape to pr~vent air leakage dur- ing the tests. A single row of pressure orificeswas located at the airfoil midspan, as shown in figure 3.
Because the aodel completelyspanned the test s@c- tion, two-dimensional flow was approximated. The airfoil was attached to the balance franc by torque tubes, which were extended through the sides of the tunnel and were rotated by a calibratedelectric drive outside the tunnel in order to set the angle of attack, Ylap and tab de- flectionswere set by varying the position of lever azms on the model. The pressure orificeswere connectedby rubber tubing to a photographically recordingmultiplo- tube manometer located outsidethe tunnel.
TllSTS The tests were mad-eat an effectiveReynolds Number of .3,410,000. (Effe.ctive. Reynolds Number = tunntil ,Reynolds N.A.C.A. TechnicalNote No. 761 3 Number x turbulencefactor. The turbulencefactor for the 4- by 6-fcot vertical tunnel is 1.93.) The a+ertige dynamic pressure was 10.8 pounds per square foot, corre- sponding to an air speed of about65 miles per hour at standard sea-levelconditions, The range of angles of.
attack from -14-l/20 to 10-1/20 was investigatedat in- At each angle of attack, the airfoil wa8 tervals of 50.
tested with the flap deflected 0°, 5°0 10°, 20°, and 30° Tests wore made throughoutthe entire angle-of- down.
attack ravge for each flap deflectionwith tab deflections of 00, +lo~, i20°, and +30° for each of the tab sizes.
RESULTS ,- Presentationof Data . .
The results of the distributionof pressures are given in the form of resultant-pressure and resultant- pressure-increment diagrams,which reprasentchanges in resultant~pressure distributioncaused by a change in angle of any one part or any combinationof the component parts of the airfoil. The resultantnormal pressure at any point along the chord lines of the airfoil was deter- mined by taking the algebraic differenceof tha pressures “nornal to the surfaces of the airfoil at that point. All diagrans of resultantpressure or resultant-pressure in- crements of the airfoil, flap, and tab combinationara plotted as pressure coefficients P or as AP, where P- Po -, P=— .
q and static pressure at a po”int on the airfoil.
P static prf3ssure in j?reeair strean.
Po ,, .- dynanic pressure of free air stream.
q .— .—. . ..
Resultant-pressure diagrams are given“In figure 4 for the basic saction (i.a., with flap and tab neutral).
Tha resultant-pressure diagram for any other.;condition may ba obtainedby adding (to the basic diagram) the resultant-pressure incrementfor the particularcondi- tion,. The resultant-press,ure-tngr.?ment diagrams are given ., in figures 5 to 9.
. .
4 N. A, C.A. ‘Technical Note No. 761 Because the large quantityof”data prohibitedthe inclusionof all the resultant-pressure-increment dia- grams for all tab sizes, only the diagrams for tab d.efl&c- tions of O-Oand +30° for the 0.20cf tab, which was consid- ered to be an average sizes are presentientValues of angle of” attack were selected to represent(1) an un- stallednegativeanglp of attack, a = -9-l/20; (2) a low angle of attack, a = 1/2°; and (3) an unstalledhigh an- These values of angle of at- gle of attack, a = 5-1/2a.
tack were also selected to make the data in this reporti comparablewith the results presented in reftirence~ 4 and 5.
Previoustests have indicatedthat the incrementsof pressuredistributionand the incrementsof section aero- dynamic coefficientsdue to flap deflectionare independ- ent o.fthe basic section; it is thereforebelieved that, for “structural-design purposes, the data heroin ~resented may be applied to other basic sectionsof conventional shape and the same thickness, The section characteristics of the airfoil, the flap, ‘“ and the tab, as fun~tions of flap and tab deflection,are also plotted as increments,which were obtained by deduct- ing the basio “section coefficientsfrom those for the sec- tion with the tab, the flap, or the combinationdefleoted.
The characteristics were obtained in each case by mechanl- oal integrationof the originalplotted pressure diagrams.
..
Computations were made to determine the s6~tion””coef- ficients,which are defined as follows: Cn=A airfoil section normal-forcecoefficient.
qc m Cmci= = — airfoil section pitohing-moment coeffi- qc2 ciont about the one-fifth-chord point (0.20c point) of the airfoil.
nf Cnf = — fiap section normal-foroeooeffic’ient.
qcf ~ flap se~tion- hi.nge-mbment coefficient.
Chf = nt Cnt = — tab section norm’al-force” coefficient.
qct . .
ht ch=— tab seo-t”io~ hinge-momentcoefficient.
t qcta .
?J, A.C.A. TechnicalNote No. 761 . . .
where the forces and moments pe”runit span are: n normal. foroe of airfoil section. “.
m pitohing moment of airfoil section” ’aboutthe one-fifth-chord point. o’fthe airfoil.
nf normal force of flap section.
hinge moment of flap section.
hf nt nornal force of,tab section.
ht hinge moment of tab section.
and c chcrd of basic airfoil with flap and tab neutral.
,.
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. .. . .
C“f fl-ap chord.
‘, Ct ,tabchord.
,.
,an”gle., of attack.
a 6 deflection of flap or tab.
The subscript f refers to the flap with the tab; and the subscript t, to the tab alone.
,- The integratedcoefficientsfor the basic airfoil The are plotted against angle of attack in figure 10.
incrementsforvarious tab and flap deflectionsaro pr~- $ented in figuresllto 19- ,, Prec-ision As rn”en.tioned in reference-5,no air-flow-alinement tests hav,e be,en made *n”this tunnel lnitall angles of &t- tack have been correctedfor a misalinement’ of l/20 that appeared to be’present in the air”flow.”‘Thea,bsolute flap and tab deflectionswere correct to within +2°, The rela- tive angles of attack, however, wero set to within*O.lO, and the relative flap and tab deflectionsto within *1.Oo.
Over most of the airfoil, plotted pressureswere accurate to.withi,n *2 percent but, at the peaks, the accuracy was less at high angles of attack; The dynamic-pressureread- ings were correct to within *1 percent.
Inasmuchas two-d”imensional flow was approximated, ,, ,, b: N.. A.C;A. !lhchnical Note No. 761 , I k, the integratedresults may he consideredas section ohar- aoteristics. Correctionsfor tunnel-wallinterference I effectswere made only to the values of airfoil normal- The ccu?rections for flap and tab force coefficient Cn* coefficientsare not definitelyknown, but the uncorrect- ed values are probably conservativefor purposes of stress analysis.
DISCUSSION Pressure Distribution The effects of ‘the0.20c+ tab and the 0.80c fla~ de- flectionson the distribution’ofresultant-pressure ~n- crements over the main airfoil are shown In figure 4 to 9. These diagrams should be useful for applicationto the structuraldesign of horizontaland vertical tail sur- faces having plain flaps and tabs with very small or As the same basic sectionwas used in these sealed gaps.
tests as was used in the tests reported in references4 and 5, the basic distribution(fig. 4) is the same as was previouslyobtained.
Because the distributioncurves In figures 4 to 9 were plotted from data uncorrectedfor tunnel effects, the distributionsrepresentedin these curves will bo high or conservativewhen used for structuralpurposes.
It likewiseshould be rememborodthat sealedgaps were used and consequentlyhigh peak pressureswere obtained at the flap and the tab hinge axes.
The incrementaldistributionsresultingfrom the de- flection of the 0.20cf tab (fig. 5) show that the highest peak pressures occur at the tab hinge axis. Similarly, when t~e flap is deflected (figs. 6 to 9), the peak values of the pressure incrementson,the flap occur at the flap . .- hinge axis.
When the tab and the flap are simultaneously deflect- ed in the same direction,the peak values of the lo&d incrementsoccur at both hinge axes, and tho resultent * pressuresact In the same direction. If,the tab and the flap are deflectedat the same tine in oppositedirections, the peak values of’the presoure incrementsoccur at both t hinge axes but the resultantpressuresact in opposite directions (figs. 6 to 9).
Comparisonwith the resultant-pressure-increment diagrams in references4 and 5 shows that”the shapes of- the curves in the.diffe~entinvestigationsare similtir although the greatest loads were, of course, obtained with the largest flap. As.shown in reference 5,“certain ‘irregularities occurred ~n”the curves over the first 3 percent of the chord frod the airfoil nose. !l?hese irreg- ular humps may ,%ecaused. by laminar separationresulting fron severe adverse pressure gradients.
Aerodynamic “Soctio~ “Characteristics .
Airfoil characteristics.- The basic airfoil section gave results (fig. 10) that“arein agreement With the data for the basic sectioris in references4 and 5. !Che” slope of the-normal-force curve a Cn/~CL iS 0.095, which agrees‘withthe slopes obtained in references4, 5, and 7. A slight diqcrepancy,isnoticeable in the data plot- ‘“tqd in fi~ure 10, in that<the Cn .axid the curves Crocis * ., for the a’irfoil d-onot pass through zero at 0° a.ngie “of attack. This shift of the curves was probablycatised~y * hodel imperfectionsand-~ab misalinement. The airf-oil section increaentcoefficientsof normal force and pitch- ing nonent are plotted in figures 11, 14,and 17. The m.aximun value of was 2.40 at a = -14-l/20 “ both the flap and %: 0.30cf tab deflected30° (fi~~t??(a)).
Acn Deflectingthe tab to -30° reeulted in a value of of:l.16, The change in Acn with the tab re~ersedwas 1.24, or about 52 percent of the increnentwith both- the flap and the tab deflected in the same direction. com- — parisonswith references and 5 of changes” in”th6-”maxf- nun values of Acn caused by reversing the tab deflec- tion showed that, fortheO.50c flap, the difference was ’42percent and, for the 0.30c flap, 39 percent.
The stall of ‘theflap, as shown by the data, gener- ally occured at a deflection of about 20° for low angles of attack and at about 50 for the high angles of attack.
~hese points are indicatedby the breaks, or change in slope, of the and the cm curves. No t~s~ were Cn c/5 nade of the 0.30cf tab deflected 30° with a = 10-1/2° because of the stalled and very unsteady flow over the nodel.
~he pitching-nomentcoefficientsof the airfoil are 8 N,A.C.A. Teclinidal Note No. 761 r given about the 0.20c pointbecause it wqs the location of the flap hinge axis.
The results for the basic air-.
foil section (fig. 10) gave a linear variation of Acmcj~ with angle of-attack. also ‘he ‘alues ‘f- ‘c~c/5 varied ltnearlywith 8 within. the”unstalledflap range.
The,effectiveness of t e tats in reducing de- i Acmc/5 ,.
creased as the tab deflection’wasincreasedpositively or negativelyfrori zero.
Flap and tab characteristics.- The fiap section in- crement coefficients, Acnf and varied nearly Achf, linearlywith flap deflectionthroughoutthe unstalled range. It was noted that the 0.80c flap was rather effec- tive, in that shall deflectionsproduced large changes In the’flap section coefficientincrements. In general, parallel to the tab deflectionsshifted Acn and bChf f themselves,and the rate of change of the incrementswith the tab deflectiondecreased as tho tab deflectionsln- b creasod positively or negativelyfrom tho neutral position.
was fneff~ctiv~ in reducing The O.10cf tab deflected .3OO ?
This characteristicis in agreementwith the re- iichf.
suits reported in references1, 2, and 5.” As stated in the discussion of the airfoil characteristics, the flap stalled at a“deflection of about 200 for low“anglesof I ., attack and between 5° and 10° for high angles of attack.
At the low angles of attack, the upward deflectionsof the tabs showed a tendency tu--dolay the flap stall at flap deflectionsof 20° or 30°.
The incrementsof tab sectionnormal-forceand hinge- moment coefficientstended to vary linearlywith tab de- flectionuntil the tab stalled. (See figs. 13, 16, and 19.)
Deflectionof the flap caused greater incrementsof Acnf and Achf when the tab was deflected in the same directionas the flap than when th? tab was d6flected in the oppositedirection. As observed in references 4 and 5, the -30° deflection of the O,lC)cf and thb t).20cf’ tabs frequent-ly gave unsteady or irregul&rincrementcooffi- Cionts.
., Comparisonof the Three Sizes of I?lain ~,lap “ ,, As a comparisonof the general characteristics and as a sumrnaryl some average,.elopo$ obtainedfrom the ex- N.A.C.A. TechnicalNote No. 761 9 perimentallydeterminedsection characteristicsof the N.A.C.A. 0009 airfoil with the 0.30c, the 0.50c, an~ the 0.80c flaps having tabs are given in the followingtable.
(All slopes are for inftnite aspect ratio.)
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I dmm 0202!3 . . .
l% o o .si H
El
El , 4 d8 O* m m
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4 OQ .
t-d s ,10’ N.A.C.A. TechnicalNote No. 761 CONCLUDINGREMARKS .
With the presentationof data on an 80-percent-chord flap, the inve~tigationof section aerodynamicand load characteristics of an N.A.C.A. 0009 airfoil with a wide The data range of sizes of flaps and tabs is conpleted.
suppliedshould be applicableto the design of any plain flap and tab combinationthat is likely to be used for horizontal or vertical tail surffices,The incremental .
data presentedare believed to be applicableto other con- ventionalairfoils of approximatelythe same shape and thickness.
In the applicationof the data, it nust be ronemberod that the results herein containedare for hinged surfaces with completelysealed gaps and that only the values of airfoil normal-forcecoefficientare correctedfor tunnel effects. Although the other coefficientsare uncorrected, they aro believed to be conservativefor application in stress analysis.
Langley Memorial AeronauticalLaboratory, NationalAdvisory Committeefor Aeronautics, Langley Pield, Vs., April 4, 1940.
# N.A.C.A. TechnicalNote No. 761 REFERENCES 1. Wenzinger,Carl J.: Pressure Distributionover an Air- foil Sectionwith a I’lap and Tab. T.R. N’0, 574, N.A.C.A. , 1936.
Reduction of Hinge Moments of Air- 2. Harris, Thomas A.: plane Control Surfacesby Tabs.
T.R. ~Oo 528, N.A,C.A.91935.
Xffects of Eleva- 3. Goott, Harry J., and Reeder, J. P.: tor Nose Shape, Gap, Balance, and Tabs on the Aero- dynamic Characteristics of a HorizontalTail Sur- face. T.R. No. 675, N.A,C.A.9 1939.
4. Street,William G., and ADOS, Milton B., Jr.: Pre”ssure- DistributionInvestigationof an N.A.C.A. 0009 Air- foil with a 50-Percent-Chord Plain Flap and Three Tabs. T.N. No. 734, N.A,C.A., 1939.
Pressure- 5. Ames, Milton B., Jr., and Sears, Richard I.: DistributionInvestigationof an N.A.C.A. 0009 Air- foil with a 30-Percent-Chord Plain Flap and Three Tabs.
T.N. No. 759, N.A.C.JI. , 1940.
6. Wenzinger, Carl J., and Harris, Thonas A.: The Verti- cal Wind Tunnel of the NationalAdvisory Committee for Aeronautics. T.R. NO. 387, N.A.C.A., 1931.
7. Goett, Harry J., and Bullivant,W. Kenneth: Tests of N.A.C.A. 0009, 0012, and 0018 Airfoils in the Eull- Scale Tunnel. T.R. No. 647, N.A.C.A. , 1938.
N. A.C.A. Teohnioal Note No.761 Fign. 1,2,3 I I Rectungu/ur J%+ ------ ------- ,.,
+1
Iil i
Figure 1.-Model mounted in4-by 6-foot vertioal tunnel.
.- m Figure 2.-TheN. A. C. A. 0009 preesure-distribution model with 0.800 plain flap endO.10cf, 0.20cf, and0.300f tabs.
K Lo- 70.0 !ioe 17 72.0 18 74.0 + 7 75.25 20 76.0 1:% 21 78.0 2.5 : 22 80.0 QJ 4 5.0 23 82.0 10.0 5 24 83.25
!s
6 15.0 25 84.0 & 7 18.0 26 86.0 20.0 8 27 88.0 22.5 28 90.0 1: 25.0 91.25 30.0 11 % 92.0 40.0 Figure 5.-Chordwise looations ofpressure orifices ontheN. A. C.A. 31 94.0 0009 airfoil inperoent chord.
E 50.0 32 96.0 14 60.0 98.0 15 65.0 E — Fige. 4,5 N.A.C.A. Technical NoteNo.761 -1 ..
+ (+ .
Pe7cenf chord — Percentchod of resultant Figure 5.-Increments Figure 4.-Diskribution of resultant pressures forvarious pressure overtheN.A.C.A.
snglea of attack andvarious 0009airfoil at various angles of deflections of a 0.200f tabon a attack. Flapandtabneutral.
0.80c plain flapdefleoted Oo.
Figs. 6,7 N.A.C.A. Teohnical NoteNo.761 .- .— — i — Aercenfchord Percent&ord Figure 6.-Increments of resultant Figure 7.-Incrementa of reeultant pressures forvarious preaaurea forvarious angles of attack andvarious angles of attack andvarious deflections of a 0.20cf tabon a deflections of a 0.20cf tabon a 0.80c plain flapdeflected 5°. 0.80c plain flapdeflected 10o.
N.A.C.A. Technical NoteNo.761 -# -2 AP .
-2 —.— (J -2 — — —. — -4 60 80 100 0 20 80 loo 0 20 40 %rcenfct+ord As%7fc%rd Figure 9.-Incremente of resultant Figure 8.-Inorements of resultant pressures forvariouu preasurea forvarioua angles ofattack andvarious angles ofattack andvarious.
deflections ofa 0.20cf tabena deflections ofa 0.20cf tabona 0.80c plain flap deflected 200. 0.80c plain flap deflected 30°.
w o .
I ,_ m ri- P.
Ca m “+ .
N.A.C.A. Teahnical Note No.’761 Fig. 11 .
c ~’ .5 ~.
$ ~ ~ L o c s -= u ?
> @ L : ~ $ b & .— Flapdeflection, df, deg (a)a= -141/2°(b)u=-9 1/20 (o)a=-41/2° (d)a=l/2° (e)a=5 1/2° (f)a=10_l/2° Figure 11,a tof.-Increments of airfoil section normal-force andpitohing-moment ooeffioientn forvarioue deflections ofan0.800 plain flap and a O.10of tab.
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o 0 10 .277 .90 o 0 10 20 30 Flap &fkc#iOn, 6/;---- ‘- Flqodeflecfk df, &g ~=.4~0 a=-uvw .Z.-9VZ+ F&un lZ, a tof.- Mmwent# of flap #oatim norml.forae ml hlugaamnt wffioimtn ‘for ?U1OUS ddlmbim of I 0.60a phin flmp d I O.10q tab, ., Ii !.
I ,, ,; 1,‘,”, ,,1 ,!
t~, i’,, _ ,1
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Flq oW7ed/CM, ~ ,&g ,%p dekfti. d/,d.g Fkw &fkctlm, 6.,deg a*B1/20 .z=lou% O.=w, Flgm 12 .mmllded.
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l \\ I I I Iu hl I I I I I . ..
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T& &flecikw,6t, deg Tabdeffdwzd,, dq a=-91/2° a= -14 W g F’&ura lS,ato f.- Ium=tnof tab ~tioa~l-fca’oo andhinge+mnt ooeffiolentd f.rm+muddflmtimc ofao 0.800 plalnflqmd. O.10q hb.
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. , , I I I I I I I I I 1 ,- I ?-i: 1 d ,P I I I I I I,, I I -. -12 -. -D (e) -3 -20 -10 0 10 20 .x7 -m -w -to o 10 20 m T& d?ikib,dt, dcg FigM-p q mlolded. ~ [ ,.
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4,’ ‘b hcremenf of airfoil secfion normol-forcw coefficient, Acn $- Increment of aidoil secfion normol-fwce coe Wcient Ac.
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l b .
l 2.8 2,6 2.4 2.2 > :2.0 -!& R+4w4—H %.
-,9 -,4 -,6 -Lo H
,;jtfgHi,fi+133
-,80 10 20 30 10 20 .30 10 20 30 -’”b Flap defkcfkm, ~t, deg Flop defledjo;, 6*; deg a = -14 1/20 CL=-9 V2Q Fi@re 15, a to f.- Inoruwdm” of flap sooth nod-form M hinge-mmuk oocffioiontm for VW1OU6 ddhotions of tO.Wlc plain flap and l 0.2oof tab. 0 tlb deflecfim. L+, ,&a I a= 51/@’” ‘ ., FI.gue E. comlnd,d.
b7C~~Wf Of fob5ecf/m7nwmo/- f-* cosfficl”=n+. A C,,.
l .
a fncremenf of tab secfkm normaf-forcecoeffi”cl”cnf. Ac.
* I & l -.
lacremeh”of tab secfionnc.m?ol-force coefficient, A%, hii-rmewi of tab sectioniwrmal-f=e coeffia”-i, At..
* .
“n — .
. * > I I I I I I h I I I I -,8 -f.
dkm d. . deu -,. .
~=rj@l” - u = 101/’20 ; FlppraM.00M1cdd.
-h .,w.
I x 1 1 , 1 , , \! Ii l\ .
.- .- I I h), Iv% ~. , ,-, L,l,,,,%:,sr-.:- I A-+emenf of oli-foil’secflon plfching-mommf coeffi cienf, Acme ~ :~ ., ., ,t ,1 I .1 .1 - ,1 .1 .1 Eli h < b.”; m * f.u L ‘2 m M 0) ‘2 :$Q ~ I I I I 1! r , I I I I I I i-l N1 I +- l . * \ > -,9 -Lo +.1 (u 10.?0300 o 1020.?0 Fhp a&~&~, &g I%P dt?l’kCtiOrI 4, &g &=-4uw Fi@m lfI, a h f.- Iamaat. of ?lLP notion noinl-fc.roo d Mwo-mmnt MO?? Icimta for VUIMIB deflmtiiw of l O.Me plain fhp mnd l 0.31LY tab. ~ I .
> -+ a, I I I I I .loo~ ‘- J 10 2u30~o 10 20 30 fbp &%t.&I, 6,, dq Fhp de&&on, 6,,&g i7qD deflecflbn 6,,deq ~=fj~o a. 1/20 a = 101/20 Um 18omnldei.
I ,,, ,, :, I :!,i .M , ,! I I :1;, ,, 1,,’ I a Tab d=fledion,c$, &g a.-9 l/Y ‘-, Tob ddkatm, J3f ,dq Tob dm7ection, &t,deg U=-4V’W d = 1/?.0 g 10 ountinmi.
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,.:, ., I r I /- \ \ >-3 ,, \ \ 1 5/ ~.7 \, s“ -, -, -, ,- 1, T& ddkf,kn, 8,, dew Tab dMxAbJI, 6$, &g . .
s .0 a=evzo a = 101/20 “ molvdeh.
rip 19 ;“