NACA- L'20< 
 
 ARR No. Ll+IX)3 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 
 WARTIME REPORT 
 
 ORKJlNALLy ISSUED 
 
 April ISkk as 
 Advance Eestrlcted Report LI+DO3 
 
 VIKD-TUHHEL INVESTIG5ATI0N OF CONTROL-SURFACE CHARACTERISTICS 
 
 IVI - PRESSURE DISTRIBUTION OVER AN NACA OOO9 AIRFOIL WITH 
 
 0.30 -AIRFOIL-CHORD BEVELED -TRAILING-EDGE FLAPS 
 
 By H. Page Hoggard, Jr., and Marjorie E. Bulloch 
 
 Langlej Memorial Aeronautical Laboratory 
 Langley Field, Va. 
 
 nwx: "^ 
 
 WASHINGTON 
 
 NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of 
 advance research results to an authorized group requiring them for the war effort. They were pre- 
 viously held under a security status but are now unclassiiied. Some of these reports were not tech- 
 nically edited. All have been reproduced without change in order to expedite general distribution. 
 
 L - 205 
 
n'b f^^ H'i '^toqi'^'f 
 
 NATIONAL AD'/ISORY COLnvIITTEZ FOR AERONAUTICS 
 
 AD'.^'A^'^CS R'']3TRICTFD RT]?CRT NO. lIiDOJ 
 
 'A'IND-TTJIIT'jEL Br^'ESTIGATinn OT'' CONTROL- SURFACE GNARACTERISTICS 
 
 XVT - PRESSURE LISTRIBUTION 0\'ER AN NACA 0000 AIRFOIL V/ITH 
 
 O.JO-AIRFOIL-CRORr> BE^/ELED-TRA ILING-SDGE FLAPS 
 
 Ey 11. Page Hoggard, Jr., and Marjorie E. Bulloch 
 
 SUMMARY 
 
 Pres3-are-dl3tribntlon tests have heen made in the 
 NACA [(.- hy (-.-foot vertical tunnel of a plain flap with 
 interchangeable beveled trailing edges on an 
 NACA 0009 airfoil. The flap chord vms 30 percent of the 
 airfoil chord and the bevel chords were I5 and 20 percent 
 of the flap chord. The IS-percent bevel was tested with 
 the bevel corner faired with both large and snail radii. 
 The ourpose of these tests wts to supply pressure- 
 distribution data that may be used for structural and 
 aerodynamic design of horizontal and vertical tail sur- 
 faces , 
 
 The results are presented as diagrams of resultant 
 pressure coefficients and of increments of resultant 
 pressure coefficient for the airfoil with the flap h.iving 
 beveled trailing edges. The diagrams are preserited for 
 the control surface with the gap at the flap nose sealed 
 and unsealed. 
 
 A comxoarison of the beveled-flap pressure data with 
 plain-flap data indicated that the addition of a bevel 
 reduced the pressures over the entire airfoil, including 
 the peak at the airfoil nose, and caused a reversal of 
 pressiire over the beveled part of th'j flap. The 
 normal-force coofficient for the beveled-tralling-edge 
 flap was loss than the coofficient for the plain-alrfoll- 
 contour flap. The open gap produced a tendency toward 
 overbalance by docroaslng the negative pressures over 
 the upper surface of a flap when deflected downv/ard. 
 The results gen-^^r-allj^ were in fair agreement with force- 
 test data previously published. 
 
MAC A ARR No. L^DOJ 
 INTx'^ODIJCTION 
 
 The !<lational Adv5.sory CojTimi.ttee for Aeronautics has 
 Instituted an sxtenaive investigation of the aerod^/nariic 
 characteristics of various control surfaces. The force- 
 test data fi-ora this investigation have been surmnarizGd in 
 reference 1. The two-dinension&l pressure-^distributicn 
 data obtained as part of the investigation have been 
 analysed and the variation with flap chord of the various 
 aerodvnaraic charactorj sties of a flap has been presented 
 in reference 2. 
 
 Two-dimensional force tests have been previously run 
 on a similar model of an ITACA OOC9 airfoil with several 
 beveled trailing ed3es; the resixlts of these tests are 
 presented in reference 5 (-^^Iso summarized in reference 1). 
 Prom the results of these force tests of trailing-edge 
 shapus having various included tralllng-edge angles and 
 ether airfoil tests, a method based on tjie included angle 
 at the trailing edge has been found for predicting the 
 values of hinge-moment pax^'ameters to be expected from a 
 bevel. This correlation can be found in figure 150 of 
 reference 1. 
 
 The two-dimensional- flcv; tests presented herein were 
 made to investigate the pressure acting on a control sur- 
 face with a beveled trailing edge. Such data should be 
 valuable for stri^ct^jrel design of the control surfaces, 
 for explanation of the baltuicing action of the bevel, 
 snrj for study of boundary-layer conditions. The investi- 
 gation v,ra3 made at all smgles of attack and flap deflec- 
 tions considered necessary for the 3truocu.i'al design of 
 ailerons, elevators, and riidders. 
 
 SYr'.!BOLS 
 
 Cf flap chord roai'vard of flep hinge axis, percent 
 
 airfoil chord 
 
 c chord of basic airfoil v/i th flap neutral 
 
 q d^/namic pressure of free air 3trear;i 
 
 P pressure coefficient 
 
NAriA ARR To , LipOJ 
 
 Pp res-ultant pressure coefric3.ent 
 
 aPfj increment of rcsult^^nt pressure coefficient 
 
 p static pressure at a poirt on airfoil 
 
 Pq statj.c pressure in free air stream 
 
 Qq angle of attack for infinite aspect ratio 
 
 5f flap def]-ectlon 
 
 M Mach number, ratio of local velocity to speed of 
 sound 
 
 Cj^ airfoil section normal-force coefficient (n/qc) 
 
 c™, airfoil section ni tchin.-'-moment coefficient 
 
 a'bci:)t quarter-chord point of airfoil \m/r\c'^ ) 
 
 c^_p flap section nor-nal-f orce coefficient (^n^/qc-j-) 
 
 c-^^ fl'^P section hinge-moment coefficient (hf/qcf"^) 
 
 n normal force of airfoil section per unit span 
 
 m pitching moment of airfoil section about quarter- 
 chord point ver -onit span 
 
 n^ normal force of flap section per unit span 
 
 h-^ hinge moment oi flap section per unit span 
 
 Cn = i -^^ 1 
 
 "arree V^-^o;ev,^=0 
 
 «6 = 
 
 .^^f/'c 
 
 n 
 
 
[,_ FACA ARR Ho. LI|.D03 
 
 ■^5 
 
 
 "i^fs 
 
 
 Pa 
 
 
 
 o 
 
 The subscripts outside the parentheses indicate the 
 factors held constant during*; the measurement of the 
 parameter, 
 
 STi.bscripts ; 
 
 U point on upper siirface 
 
 L point on lower surface 
 
 R resultant 
 
 APPARATUS AND J,!ODELS 
 
 The tests were made in the NAGA l\.- by ^-foot vertical 
 tunnel, Tlie test section of this t'unnel has been con- 
 verted), from the original open, circular, p-^C'Ot-diame ter 
 let (reference Ij.) to a closed rectangular l\.- by 6-foot 
 test section, as shown in figure 1. The model completely 
 spanned bhe tesb section; therefore, two-dimensional flow 
 was approximated. 
 
o. L/1.DO3 
 
 The model iised for the prsssure-distrxbiition tests 
 of this investigation v/as designed to be an exact co;5y of 
 the model used for the force tests in reference 3 "but 
 v/ith only the 0.15cf and O.SOCf l)3veled-trailing-edge 
 shapes. The O.l^Cf bevel was tested v/ith the bevel 
 corner faired with both large and small radii. The 
 2-foot-chord model was made of laminated mahogany to the 
 modified NACA OOO9 Drofile (table I). The airfoil was 
 equipped with a O.JOc plain fl-ap, as shown in figure 2(a), 
 A gap of 0,005c was provided at the flap nose. The flap 
 ViTas constructed v/ith interchangeable blocks that formed a 
 beveled trailing edge and a thickened profile, as shov/n 
 in figure 5 of reference 5. 
 
 A single chordwise row of pressure orifices was 
 built jnto the upper and lower surfaces of the airfoil 
 and flap at the midspan locatione The orifice loca- 
 tions are presented in figure 2(b) in percent of airfoil 
 chord from the leading edge. 'rhe copper tubes from the 
 pressure orifices were brought out of the ;:iodel at one 
 end through the torque tube and the tunnel wall to a 
 multiple-tube, open-faced manometer. Readings v/ere 
 recorded by a camera . 
 
 TESTS 
 
 All of the tests, except those with large flap de- 
 flection and high positive angle of attack (flap deflec- 
 tion, 30° and 45°; angle of attack. ll.>3° and 19.3°) were 
 run at an average d'^/namic pressure of 15 pounds rer 
 square foot. The large flap deflections at high positive 
 angles of attack required more power than was available to 
 maintain a dynamic pressure of I5 pounds per square foot; 
 therefore, these tests were run at an average djmamic 
 pressure of 12 poionds per square foot* The airspeed in 
 the test section at d;'/naraic pressures of I5 and 12 pounds 
 per square foot is about 76 an.d 69 miles per hour, respec- 
 tively, at stanaard sea-level conditions. The corre- 
 sponding values of effective i^e /molds number are 
 2,760,000 and 2,208,000. (Effective Reynolds num- 
 ber -■ Test Re:;/nolds number x Turbulence factor; the turbu- 
 lence factor of the HAGA ]+- by 6-foot vertical tunnel is 
 1.93.) 
 
 The tests were made at angles of attack ranging from 
 -20'-' to 20° at intervals of 5^ and at angles giving maxi- 
 mum positive and negative lift. It m.ay be noted that all 
 
ITACA ARR No. L4.DO5 
 
 angles of attac'^c are o.'^rset Troin the exact values of 
 0°, 5", IC^, 15", and 20° by -0.7° ov/lng to an error 
 :n setting the zero angle of attack. This error was 
 foimd to be consistent throughout the tests and the data 
 v;ere corrected acccrdinsly. Tae inodel v/as tested with 
 the 0.50c T)l8.in flap deflected 0°/ 1'^, 2°, 5°, 10°, 
 150^ 20°, 250^ 30°, and [^50. 'fne tests were run with 
 the flap gap both open (O.JO5C gap) and sealed v/ith 
 plasticine. During the tests with 30° and [|.5° flap 
 deflection, pressure orifice I5 for the lower surface 
 (fig. 2(b)} was sealed because its position at both 
 large flap deflections was insile the gap. 
 
 Check tests were nade for each flap deflection as 
 an indication of the accuracy of the test results. 
 ■.'.h.en the 0.005c gap was used, the check tests v/ere made 
 after both angle of attacK and flap deflection had been 
 reset. The sealed-gap check tests had only the angle 
 of attack reset, because the plasticine seal would have 
 to be refaired if tne flap deflection were changed. 
 
 The speed of the tunnel was maintained at the test 
 value of q for approximately 2 minutes before readings 
 were recorded in order to allow the alcohol in the 
 manometer tubes to reach the correct height. 
 
 RESULTS 
 
 Presentation of Data 
 
 The results of the pressure-distribution tests ai'e 
 given in the form of diagrams of resultant pressures v/ith 
 flap neutral and resultant-pressure increments caused by 
 varying the flap deflection. The resultant pressui^'es and 
 increments of resultant pressure are presented for the 
 various bevel and gap combinations and for various angles 
 of attack in figures 5 to 10. The resultant normal 
 pressure at any point along the chord of the airfoil was 
 determined by taking the algebraic difference of the 
 pressures normt'l to the upper and lower surfaces of the 
 airfoil at that point. All diagrams of resultant pres- 
 sures or resultant-pressure increments of the airfoil 
 and flap combinations are plotted as pressure coeffi- 
 cient P-:^ or as aPn. The resultant press^jre coeffi- 
 cient is' defined as ' 
 
 Pp = P, - P 
 
 TT 
 
NACA ARR ^To. 1J4DO5 7 
 
 where 
 
 PlJ- 
 
 Pf - ?o 
 
 Pt 
 
 'o 
 
 P pressure coefficient 
 
 p static pressure at a point on airfoil 
 
 Pq static pressure in free air stream 
 
 q dynaiaic pressure of free air stream 
 
 and the subscripts 
 
 U upper surface 
 
 L lower surface 
 
 R resTiltant 
 
 The resultant-pressure diagram for any condition may 
 be obtained by adding the distribution at a given angle 
 of attack and the distribution at a given flap deflection, 
 A comparison of resultant-pressure distributions over the 
 bevel ji.ancture v/ith large and snail radii is presented in 
 figure 11 at several angles of attack and flap deflec- 
 tions , 
 
 Pressure distribu*:ions for the upper and lower sur- 
 faces of the flap having a 0.15Cf bevel with sealed gap 
 are presented in figure 12 for larious angles of attack 
 and flap deflections. The resultant -oressures over the 
 NACA OCOQ airfoil with CJOc plain flap and sealed gap 
 (reference 5) ^^® compa^r'od. v/lch uhe i-esultant pressures 
 over the modified airfoil with 0,15c-f--be vel flap in 
 
 figure 13. Figure ll\. presents upper- and lower-surface 
 pressures over the plain flap and bhe O.l^c^-bevel flap 
 for the same conditions for which resultant pressures 
 are given in figure IJ . 
 
 The rates of change of pressure coefficient with 
 angle of attack and with flap deflection are presented for 
 
8 ^'ACA ARR Ho. lIvDOJ 
 
 the various bevel and gap combinations in figures 15 
 to 18 for convenience in calculating distributions at 
 small values of a^ and 5|>. The flap section normal- 
 force coefficieiit as a fianction of flap deflection is 
 presented for all combinations of bevel and gap in 
 figures I9 and 20 at several angles of attack. Com- 
 plete chorduise pressure distrib\itioas for various 
 combinations of Qq and 6f that might occur on the 
 horizontal tail of a dive bomber in highly accelerated 
 maneuvers at various speeds are presented in figure 21 
 for the 0,15c-f>-bevel flap with sealed gap. 
 
 The section aerod3,"nanic coefficients of the airfoil 
 and flap are presented as functions of angle of attack 
 for all bevel and gap combinations in figures 22 to 2ii. 
 The coefficients were obtained in each case by mechanical 
 integration of the original pressure diagrams. 
 
 The parameter values for beveled flaps are pre- 
 sented in table II along v/ith values for the plain- 
 airfoil-contour flap for convenient comparison. The 
 plain-flap parameter values wore obtained from refer- 
 ences 1 and 6 . 
 
 Precision 
 
 The angles of attack are believed accurate within 
 ±0.1°. riap deflections are believed accurate within 
 
 -0,2°. Plotted values of pressure coefficient P are 
 correct within t2 percent except for peaks at the 
 leading edge and flap hinge a::is or for stalled con- 
 ditions . 
 
 have 
 
 by .. _. ^^^„ _, ., ._ .__. ^ .. 
 
 accuracy of the plot; others vary a negligible amount. 
 The accuracy of the corrected zero angle of attack is 
 indicated by the deviation from zero of lift and m.oment 
 coefficients at zero angle of attack. Prom figures 19 
 and 22, it appears that the maximum error in setting the 
 angle o^ attack at 2ero lift is 0,2°. This discrepancy 
 may be caused by flov/ misallnem.ent in the tunnel or by an 
 asymmetrical model. 
 
 Two-dimensional flow having been approximated, the 
 results ma;/ 03 considered as section characteristics. 
 
NACA ARR No. i4D03 
 
 J 
 
 Experimental tunnel corrections were applied only to the 
 airfoil section norrial-f orce coefficient Cn . Although 
 no corrections were made for the other coefficients, the 
 tunnel values are believed to be higher than the free-air 
 values and hence are on the conservative side for struc- 
 tural purposes. The magnituc'e of the airfoil resultant 
 pressure coefficients as represented in the resultant- 
 pressure diagrams (figs. 5 to 10) is known to be too large 
 by about 7 percent because these curves v;ere plotted 
 directly from manometer records without the application 
 of the experimental tunnel correction, which allows for 
 the increase in lift produced by tunnel-wall interference. 
 
 DISCUSSION 
 
 Re suit ant- Pressure Distribution 
 
 The resultant-pressure diagrams should prove useful 
 in determ.ining loading conditions for the structural 
 design of ailerons and horizontal and vertical control 
 surfaces. Tests have indicated that the increments of 
 pressure and the increments of section aerod;^7namic 
 coefficients caused by flap deflection are approximately 
 independent of the airfoil section for airfoils of 
 anproximately the same maximum thickness and thickness 
 distribution (references 7 ^^<i 8)» It is therefore 
 believed that, for structural design, the incremental 
 data presented herein may be applied to other basic 
 sections of approximately the same thickness and thick- 
 ness distribution. The increments of the section aero- 
 dynamic coefficients may be taken from figures 22 to 2l\. 
 by using the flap-neutral curve as a reference line. 
 
 From a study of the incremental-resultant-nressure 
 curves for the s balled conditions (Qq - 19 -J^ ^rid -20.7°) 
 for both bevel chords and gap conditions (figs. 1]., 6, 8, 
 and 10), it anpears that the bevel continues to reduce 
 the flap hinge moment in the stalled condition from the 
 hinge mom.ent for a plain flap under the same conditions. 
 The tests of beveled elevators on the fuselage of a 
 typical pursuit airplane also indicated that the bevel 
 was effective in the stalled attitude and reduced the 
 floating angle of the elevators ^oj about 10° (reference 9) 
 from the angle at which airfoil-contour elevators would 
 float. The resultant-pressure curves (figs. 3 to 10), 
 especially for the 0.005c gap, show a tendency toward a 
 decrease of resultant pressure over the main airfoil just 
 ahead of the flap. 
 
10 FACA ARR No. LI;D03 
 
 The results indicate that the size of the radius at 
 the bevel juncture is relatively unimportant in its 
 effect on the loads over a oe veled-trailing-edge flap 
 (fir. 11). 
 
 Pressure Distribution over Uppsr and Lov/er 
 
 Surfaces of Beveled Flap 
 
 The distributions presented at various angles of 
 attack and flap deflections in figure 12 indicate that 
 only on the siirface of the flap which is deflected 
 against the relative wind does the bevel affect the 
 pressure distribution to any great extent. The only 
 exceptions occur at low angles of attack and small flap 
 deflections, for vi/hich the upper- and lov.-er-surf ace 
 distributions shov/ nearly equal effect of bevel. The 
 pressure distribution on the side avvay from the rela- 
 tive wind, when at large angles of attack or flap deflec- 
 tion, resembles that of a flap and tab in a stalled 
 condition. 
 
 It will be noticed in figure 13 that the resultant- 
 pressure peak at the flap hinge axis is higher for the 
 beveled flap with the 0.005c gap than for the beveled 
 flap -with the sealed gap. Inasmuch as the resultant 
 pressure is the algebraic difference of the upper- and 
 iower-surface pressures at any point, the positive peak 
 on the lower surface makes the resultaxit-pressure peak 
 higher, (See fig. 1l\.,) 
 
 The pressure distribution produced over the upper 
 and lower surfaces of a flap by a beveled trailing edge 
 is compared with the pressures over a plain flap in 
 figure ll\.. The effect on the pressure distribution of 
 the bevel on the surface deflected against the relative 
 wind is more pronounced when the ^";ap is open. The main 
 effect of the open gap on the flari pressure distribution 
 a-opears to be the decrease in magnitude of the negative 
 pressures over the upper surface of the flap, which 
 results in a tendency toward lower or even overbalanced 
 hinge moments. 
 
 Curves of Pq. and Pg 
 
 For convenience in calculating the pressure distri' 
 butions over both surfaces for small values of a^ 
 
rJACA APR Wo. L'^DOJ H 
 
 and 5f;; the curves of Pg and P5 v/ere calculated and 
 are presented In figures 15 to iG. From the experi- 
 mental data, it was found impossible to predict with any 
 degree of accuracy the variation of pressure with angle 
 of attack over the nose of the airfoil because the 
 stagnation point moves considerably and the pressures 
 change rapidly and are not linear v;ith angle of attack. 
 The variation of pressure with angle of attack over the 
 rest of the airfoil appeared from these tests to remain 
 a linear variation only from 0^ to 5°; therefore, the 
 P^-curves should not be used for calculating pressures 
 beyond a value of ao of 5°* 
 
 The variation of prsssiire with flap deflection for 
 any point on the airfoil contour appeared fi'om these 
 tests to be linear to 5°, The P5-curves therefore 
 
 should not be used for flan deflections greater than S*^. 
 The final loressure distribution required is found by 
 multiplying the values of P(j and P5 by the values 
 
 of ttQ and 5f for which the distribution is desired 
 
 and adding algebraically to the basic distribution 
 (P at Qq = 6f = 0°) given in the lower part of fig- 
 ures 15 to 18. 
 
 Flap Section Normal-Force Coefficient 
 
 For all combinations of bevel and gar) tested, the 
 values of Cnf were smaller than for the plain flap v/ith 
 
 sealed gap at the same angles of attack. The values 
 of Cn„ and Cn^- for beveled and plain flap may be 
 
 conveniently compared in table II, The variation 
 of c^f, as a function of angle of attack is clearly 
 
 shown in figures I9 and 20. The effect of a is small 
 at Of = 280 with the gap open and at 5-f = 20° with 
 
 the -^ar sealed. 
 
 Pressure Distribution on Horizontal Tail For 
 Highly Accelerated Maneuvers 
 
 The flight condition diiring which high structural 
 loads and the formation of a compression shock on the 
 horizontal tail are most likely to occur is a highly 
 
12 . MAC A ARR No. LJ4.DO5 
 
 accelerated maneuver in v/hich the horizontal tail is 
 operating at a high angle of attack at high speed. The 
 pressure data presented herein are not applicable to 
 tail design for high-speed flight unless they are cor- 
 rected for the variation of pressure with Mach number, 
 
 v;hich is given aoproximately bj?- the relation l/vl - M-. 
 Theoretical variations of pressurs^ with Mach number are 
 compared with experimental pressure-distribution data at 
 various Mach numbei'S in reference IG, The pressure 
 distributions presented in figure 21 at angles of attack 
 of -0.7<^, 5.7°, and 10.?^ and with flap deflections 
 of C^, -^°, -10°, and -15° are test data that cover the 
 highly accelerated raaneuvers estimated from unpublished 
 dive-bomber test data. 
 
 Aerodynamic 3ection Characteristics 
 
 Normal -force coefficient .- The force -test lift data 
 
 of reference 5 ^'^^ given in terms of section lift 
 coefficient whereas the pressure-distribution data are 
 given in term.? of normal-force coex'f icient . Inasmuch as 
 the lift coefficient and normal-force coefficient have 
 nearly the same value, this value is referred to as "lift" 
 in the following discussion. 
 
 The slorie of the lift curve from table II 
 
 for the airfoil v/ith O.l^c^ beveled trailing edge and 
 
 sealed gap is 0.038 as compared with O.O9I from the 
 force-test data in reference 3. These results are in 
 fair agreement if account is taken of the fact that 
 different models and methods of calculation were used for 
 the force and pressure tests. 
 
 The lift-curve sloriss from the force and pressure 
 tests for the G.20c^ bevel with sealed gap have the same 
 
 value, 0.092. For the open gap the lift-curve slopes 
 from the force and pressure tests are, resoecti vely, 
 0.088 and 0.087 (table II and reference 1)". The iift- 
 curve slopes obtained from, the prossure-distribtition tests 
 appear to check very well with the force-test results. 
 Opening the gap appeared to change the angle of attack at 
 which the stall occurred by about 1°, This angle of 
 attack, approximately ±12° with flap neutral, was net 
 affected by bevel chord. 
 
NACA ARR No. I,liD05 13 
 
 The values of llTt effectiveness I r J siiven in 
 
 VoSf/c 
 °n 
 
 table II were taken at zero lift and show the expected 
 
 decrease in effectiveness as a lesulL. of the beveled 
 
 trailing edge. The small radius on the bevel jimcture 
 
 increased Cj-;^ about O.OO,^ for open and sealed gap when 
 
 compared with the lift-curve slope for the large-radius 
 bevel. Reducing the radius at "the bevel juncture 
 decreased the effectiveness froiu -0,56 to --0.52. 
 
 The -oarameter Cv^ (table II) is a measure of 
 
 ""^'free 
 control-free stabillt;/ only at aQ = 6f = 0°. The 
 
 values in table II indicate the expected tendency of the 
 beveled flap to float upward at a smaller angle than the 
 plain flap, 
 
 A ire thod for estimating the- pressure distr.i bution 
 (and normal force) over a bevel from available tab 
 pressure-distribution data is given in the appendix. 
 The results of this nethod are illusti-ated and a com- 
 parison is made in figure 25, at several angles of attack 
 and flap deflections, between actual and estimated pres- 
 sure distributioris for a O.ZOc-f bevel with sealed gap 
 
 and 5:n included ongle at the trailing edge of 25*^. 
 
 ■ Plat) hinge -moment coefficient.- The values of c]n„ 
 -^ -1 ^ 
 
 (table II) were taken over the linear part of the hinge- 
 moment curve, -which was over a snail range (i5°) ^^^ 
 the O.OOpc-gap tests and a larger range (tlO°) for the 
 sealed-gap tests (figs. 2^ and 21+). The values of c^f 
 
 (table II) v.-ere taken from 5f = 0*-^ to 5f = ^'^ because 
 
 the curve appeared linear over this range. For a com- 
 plete picture of the effect of various bevel and gap com- 
 binations, all the hinge-moment curves (figs. 22 to 2l\.) 
 must be taken into consideration and too much reliance 
 should not be placed on the slope values measured over a 
 small part of each curve, except for stick-free stability 
 calculations. 
 
 The values of chf. snd c^f. as found for the 
 
 0.15C|' and 0.20c-p bevels v/ith sealed gap are in fair 
 
 agreement v/ith the values of reference $. Values of both 
 hinge -moment parameters for the 0c20c bevel with 0.005c gap 
 
IJ4. NACA ARR No. Li^DOJ 
 
 v/ore road from the curves In figure I|.9 of reference 1 and 
 vv'ere fornd to be in fairly close agreement. The values 
 of ci^|> and chf,- for both bevel chords were found 
 
 to fall near the correlation curve of figure I50 in 
 reference 1 v-^ith less scatter than the average scatter 
 of the correlation points. 
 
 Prom the values of hinge-moment parameters in 
 table II it anpears bhat decreasing the radius at the 
 bevel Juncture tends to decrease the negative valixes 
 
 of Chf for both gap conditions. Decreasing the 
 
 -"•6 
 radius had no effect on the value of cv^^ when the gap 
 
 was open but decreased the positive value when the gap 
 was sealed. 
 
 Pitching-momcnt coeff i cient .- The slopes of the 
 
 curves of pi tching-moment coefficient as a function of 
 lift coefficient at a constant angle of attack aiid at a 
 constant flap deflection are glv^n in table II. The 
 aerodjmamic center of additional lift caused by varying 
 the angle of attack generally was located at approxi- 
 mately the 0.22c station for the sealed-gap tests and the 
 0.21c station for the O.OO^c-gap tests. The bevel chord 
 had little effect on the location of this aerodynamic 
 center. 
 
 The aerodjTiamic center at which the lift produced by 
 flap deflection may be considered to act is located at 
 approximately the O.lilc station for either gap ccnliticn. 
 All aerodynamic-center locations for the gap-sealed condi- 
 tion are in fair agreement with the values presented in 
 reference 5, 
 
 C0NCLU3I0KS 
 
 Pressure-distribution tests have been made in the 
 NACA i|- by 6-foot vertical tunnel of a plain flap with 
 interchangeable beveled trailing edges on an 
 NACa 0009 airfoil. The flap chord was 30 percent of the 
 airfoil chord and the bevel chords were 1^ and 20 percent 
 of the flap chord. The results of these, tests indicated 
 the following conclusions : 
 
NAG A ARE No. i4D03 15 
 
 1* At a given angle of attack and flap deflection, 
 the addition of a bevel reduced the resultant pressures 
 over the entire airfoil, except for the pressiire at the 
 flap hinge axis, including the peak at the airfoil nose, 
 and caused a reversal of pressu.re over the beveled part 
 of the flap. 
 
 2. The normal-force coefficient for the beveled- 
 tralling-edge flap v;as less than the coefficient for the 
 plain-airfoil-contour flap with the airfoil at the same 
 angle of attack and the flap deflected through the same 
 angle. 
 
 3. The open gap at the flap nose gave the flap a 
 tendency toward overbalance because of a decrease in the 
 negative pressures over the upper surface of a dovmv/ard 
 deflected beveled flap and because of a slight increase 
 in the negative peak on the lov/er-surface bevel juncture, 
 
 ii. The size of the radiiis used to fair the bevel 
 juncture appeared to have no appreciable effect on the 
 pressure distribution developed, 
 
 5. The results obtained from the pre s sure - 
 distribn.tion tests generally were In fair agreement with 
 force-test results of a comparable arrangement. 
 
 Langley Memorial Aeronautical Laboratory, 
 
 National Advisory Comimittee for Aeronautics, 
 Langley Field, Va. 
 
l6 NACA ARIl No. Li|D05 
 
 KTTI^OD FOR GALCinLA^-'IMO PRESSURE DISTRIBUTION OVER A BEVEL 
 FROII TAB PR3;SSUxRE-DIST:xIBUTI0N DATA 
 
 "rtTien an elevator, aileron, or I'udder is designed, 
 the general practice 13 to use the total load ovex'' the 
 surface, r.Iotlon pictures of tul^^ed fabr-ic on ailerons 
 in hlgh-speud dives indicate that the pressures along 
 the chord should be used to deteriaine how securely the 
 covering riust be fastened to the structural nerabers. In 
 the case of a beveled surface for -.'.hich a pressure peak 
 occu.rs at the be vel ji-ncture , a st^idy of the chordvvise 
 distribution might prevent a covering failure. A method 
 for predicting the chordwise pressure distribution over 
 a beveled surface without having to test it is advan- 
 tageous, particularly as such a method supplements a 
 method already established for predicting "the hinge- 
 moment characteristics. 
 
 \ nethod for predicting the chordv/i se load distribu- 
 tion on the flap is descrloed herein ^ Po attempt is 
 made to predict flap section hinge-moment coefficients; 
 the hinge-morient correlation based on tlie included angle 
 at the trailing edge (for sealed-gap condition) may be 
 found in figure ISO of reference 1. 
 
 The bevel contour was developed (fig. 3 of refer- 
 ence 3) bj'- doflecting a C.20c^ tab ±10^ and deflecting 
 the flap slightly each vaj oo'keep the tab trailing edge 
 centered on the airfoil chord line. Inasmuch as the 
 bevel profile was developed by using deflected-tab 
 contours. It was decided to use tab pressure diagrams to 
 estiiuate the pressvj^e distribution of a beveled flap. 
 Only the upper-suriace distribution for a tab deflected 
 dov^nward and the lov/er-surface distribution for a tab 
 deflected upward are considered. It is necessary to 
 correct these pressures by means of Pg to allow for the 
 
 small flap deflections necessary to keep the tab trailing 
 edge centered on the airfoil chord line. The resulting 
 diagrams (fig. 25) were integrated and found to give 
 Values of Cj^„ that v/ere in good agreement v'ith the 
 
 bevel test data for flap deflections of 10° and 20° at 
 values of a^ of -0.7° and [1.3° (figs. 25(c), 25(d), 
 25(g), and 25(h)). The value of c,^ ^ based on tab 
 
N/VCA A^R No. LJ4-DO3 17 
 
 data viras in rreneral sonewhat larger than th^-3 bevel test 
 va].ue . 
 
 At the smaller flap def l.ections , the values of 0^ 
 
 f 
 
 from tab data were generally much largpi' than from bevel 
 
 test data out, from a comparison of th.e valiies with those 
 
 for a plain flat) in fi.r^ure 20, the estimated values were 
 
 found to be closer to the bevel test values than to the 
 
 plain- flap values. 
 
 In order to use tlie present correlation method, it 
 is necessary to have pressure-distribution diagrams for 
 a flap and tab of the desired chords. The tab chord 
 should approximately eqizai the distance froin bevel 
 .juncture to trailing edge. 
 
 The included angle of the bovel must be reproduced 
 by the correct tab and flan deflections. These deflec- 
 tions must be foimd in order that the tab-deflection 
 diagram m.ay be chosen and corrected. The following 
 equation gives the amount that the flap must be deflected 
 to keep the tab trailing edge centered en the airfoil 
 chord line ; 
 
 . >^oevel " i^airfoil 
 ct sin 
 
 A5f = sin ~ 
 
 Cf - c^ 
 
 v;he re 
 
 ^bevel Included angle at trailing edge of bevel (for 
 which prediction is being m.ade ) 
 
 ^airfoil included angle at trailing edge of airfoil 
 from tests of which flap and tab pressure 
 diagram.s are to be used 
 
 c^ chord of tab, percent airfoil choi'd 
 
 Cf chord of flap, percent airfoil chord 
 
 With ASjf, i^bevel> ^^-^"^ ^airfoil known the angle 
 through which the tab is deflected ±5t to reproduce 
 the included angle of the bevel may be found by the fol- 
 lowing equation: 
 
 ,^ _ ,r ^ ^bevel - ^airfoil ,,, 
 
 ± 6 1- = A G f. + 1 ) 
 
l3 MCA ARR No. L4DO3 
 
 It may 'be noticed in flgiire 25 that the tab data used 
 v;ere for 6-^ = ±13*^ vvhsreas equation (1) gives 
 
 6t = ±3.i|-0°. By using the diagrai^is for 5t = ±10°, the 
 
 included angle was found to ne 27,6'^ instead of the 
 correct value cf 25*^; but, inasmuch as the correlation 
 for the hinge-?nonent ■oarame teis based on included angle 
 shows a change of 0.001 in the value of the hinge -moment 
 uarameters for a change of 2''^ in the included angle, there 
 could be only a sllghb change in the si^e or shape cf the 
 pressui'e diagram. 
 
NAG A ARR No. Lk'DOy 19 
 
 REF3RENGES 
 
 1. Sears, Richard I.: Wind-Tunnel Data on the Aerody- 
 
 namic Characteristics of Airplane Control Surfaces, 
 FAGA ACR No. 5L08, 19l|5. 
 
 2. Ames, Milton B., Jr., and Sears, Richard I.: Deter- 
 
 mination of Control-Surface Characteristics from 
 NAG A Plaln-Plar) and Tab Data. NAG A Rep. No. 721, 
 19U. 
 
 5. Jones, Rotert T., and Ames, Milton B., Jr.: Wlnd- 
 
 Tunnel Investigation of Control-Surface Character- 
 istics. V - The Use of a Beveled Trailing Edge 
 to Reduce the Hinge iMoment of a Control Surface, 
 NAG A AF^R, March 19^42. 
 
 [(.. Wenzinger, Carl J., and Ha-x'ris, Thomas A.: The 
 Vertical ¥/ind Tunnel of the National Advisory 
 Committee for Aeronautics , NAGA Rep. No. 387, 
 
 1931. 
 
 5. Ames, Milton B., Jr., and Sears, Richard I.: Pressure- 
 
 Distribution Investigation of an N.A.G.A. OOO9 Air- 
 foil with a 30-?ercent-Ghord Plain Flap and Three 
 Tabs. NACA TN No. 759, 19i4-0. 
 
 6. Sears, Richard I.: Wind-Tunnel Investigation of 
 
 Control-Surl'ace Characteristics. I - Effect of 
 Gap on the Aerodynamic Gharactsristics of an 
 NACA 0009 Alrfoli with a JQ-Percent-Chord Plain 
 Flap. NAG A ARR, June I9I1.I. 
 
 7. Allen, H. Julian: Calculation of the Ghordwlse Load 
 
 Distribution over Airfoil Sections v/lth Plain, 
 Split, or Serially Hin^-ed Trailing-Edge Flaps, 
 NAGA Rep. No. 6'}k, 193o. 
 
 8. Allen, H. Julian: A Simplified Method for the Calcu- 
 
 lation of Airfoil Fressiire Distribution. 
 NACA TN No. 703, 1939- 
 
 9. Glllis, Clarence L. : Characteristics of Beveled- 
 
 Tralling-Sdge Elevators on a Typical Pursuit 
 Fuselage at Attitudes Simulating Normal Flight and 
 Spin Conditions. NACA ARR, Dec. I9/4.2. 
 
20 NAG A ARR No. lI|D05 
 
 10, Stack, John, Lindse^, \V, F., and Li'.ttell, Robert E.; 
 The Coripressibility "»3>urble and the Effect of 
 Compressibility on Pressures and Forces Acting on 
 an Airfoil. NACA Rep. No. 6I4.6, 1953. 
 
ITACA ARR No. li^-DOj TA^LE I 
 
 21 
 
 ORDIFAT'^S CF I'OrT^iT^D ?TACA OOO9 AIRFOIL 
 Stations and ordinates in psrcent of airfoil chord 
 
 
 Station 
 
 Ordinate 
 
 NAG A 0009 
 airfoil 
 section. 
 
 
 
 1.25 
 
 2.5 
 5.0 
 
 7.5 
 10 
 15 
 20 
 
 25 
 
 30 
 1.0 
 50 
 
 
 
 ±1.1^2 
 ±1.96 
 ±2.67 
 
 ±3.15 
 ±3.51 
 ±k . 01 
 
 ±1|.30 
 ±^..'+6 
 ±Il.50 
 ±i|-.55 
 ±5.97 
 
 straight 
 portion 
 
 60 
 70 
 80 
 90 
 ICO 
 
 ±5.42 
 ±2.85 
 ±2.25 
 ±1.67 
 ±1.08 
 
 L.E. radius: O.89 
 
NACA ARR Vg. LI4.DO3 
 
 22 
 
 M 
 M 
 
 
 CO 
 < 
 
 M 
 
 PL, 
 
 hi 
 
 
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 o 
 
 o 
 
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 M 
 
 c.:> 
 
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 CD I^ 
 
 
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 f\j 1 ; 
 
 
 
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 1 
 
 
 
 
 
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NACA ARR No. L4D03 
 
 Fig. 1 
 
 -^ 
 
 -^ 
 
 
 -\A vv- 
 
 s 
 
 -V- 
 
 — I 
 
 -'W- 
 
 P/tch axis a/ 
 -.SSc 
 
 Rectangular 
 'test section 
 
 -AV- 
 
 -A^- 
 
 ^ 
 c 
 
 .8 
 
 
 -vv- 
 
 Model 
 sSupporf 
 
 1 
 /6 
 
 Mode/ nnounfed /n A/ACA A-bi^C-foof t^er/ical funnel 
 Tunnel ^va//3 
 
 ^ 
 
 ■^ 
 
 -^24 
 
 -\ 
 
 >> 
 
 -^ 
 
 ^ 
 
 (^ of orifices 
 
 -48' 
 
 -\- 
 
 
 Z4 
 
 72" 
 
 ii 
 
 '/6 
 
 ^ 
 
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 4 
 
 444 
 
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 ^ 
 
 -^ 
 
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 ^^- 
 
 MATIONAL ADVISORY 
 CIlUMITTEE FOR AERONAUTICS 
 
 Figure 1 .- /nsfa/lation of beveled -trailing- edge pressure - 
 d/sfribufion model in NACA4-by6-^foof verficol tunnel. 
 
NACA ARR No. L4D03 
 
 Fig. 2 
 
 Straight confour from t>ere 
 to hei^e/ed trailing edge 
 
 Airfoil with ./5cf bevel 
 
 4.50 
 
 Gap sealed 
 or .OOSc open 
 
 .20c^ bevel 
 
 /A 
 
 ff=133- 
 tSCf bevel mlh 
 small radius 
 
 (a) Two -fool- chord NACA 0009 a/rfo/l model yvilh a 
 0.30c plain flap having O.I5c^ and 0.20 c^ beveled 
 I railing edges. Dimensions are in percent of airfoil 
 chord. 
 
 NATIONAL ADVISOHY 
 COMMtTIEl FOR AERONAUTICS 
 
 ^9 ^' 12 IS/4 
 
 J5 
 
 .^ ,, 21 23 
 
 ^^17 J8 19 20 
 
 22^4^25 
 
 Ori- 
 fice 
 
 Loca 
 tion 
 
 
 
 
 
 1 
 
 i.25 
 
 2 
 
 250 
 
 3 
 
 6.00 
 
 4 
 
 7.50 
 
 5 
 
 lom 
 
 6 
 
 /5.00 
 
 7 
 
 6 
 
 20130 
 30.0C 
 
 S> 
 
 40.00 
 
 10 
 II 
 
 50.00 
 55.0C 
 
 12 
 
 6oa 
 
 65.00 
 
 6750 
 
 70.00 
 
 72S0 
 
 75D0 
 
 6000 
 
 65.00 
 
 9Q00 
 
 92J00 
 
 94.00 
 
 96.00 
 
 98.00 
 
 25 100.0C 
 
 (6) Chordkvise localions of pressure orifices on airfoil 
 and or) the flaps f)aving 0.15 c^ and 0.20 c^ beve/s. 
 
 f^igure 2. ~D/mens'or)s and cf^ordwise pressure-orifice localions 
 for MAC A 0009 beveled- lrailing-e<dge pressure-disiri button model. 
 D/mensions and orifice locations are in percent of airfoil chord. 
 
NACA ARR No. L4D03 
 
 Fig. 3a 
 
NACA ARR No. 
 
 L4D03 
 
 Fig. 3b 
 
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