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AIR DOCUMENTS DIVISION
HEADQUARTERS AIR MATERIEL COMMAND
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Copy No.
RM No. L7E09
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RESEARCH
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All No. PRELIMINARY INVESTIGATION AT LOW SPEEDS OF
SWEPT WINGS IN ROLLING FLOW
David Feigenbaum and A lex Goodman
Langley Memorial Aeronautical Laboratory Langley Field, Va.
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
WASHINGTON May 22,1847
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HACA SH No. L7B09 HESTfiUHED
XAXIDmL ADVISOHT COMCTTEE TOB AERONAUTICS
RESEARCH IfflMDBANDDM
PKEUKTNARY INVESTIGATION AT LOT SPEEDS 07
SWEPT WEÄ3S IN ROLIIHG FLOW
By David Feigenbaum and Alex Goodman
SUMMARY
An investigation was conducted to determine the characteristic« of a aeries of untapered wines having angles of sweepback of -45°, 0°, 4$°, and 00° under conditions simulating rolling flight. The rolling-flow equipment of the Langley stability tunnel was used to measure all six force and moment components. Vhe characteristics of the vlngs In straight flow were e.l3c- determined during the course of the investigation to afford a comparison vlth previous results - Teste were also conducted to determine the characteristics of ailerons on the lf5° swcptb&ck wing in both straight and rolling flow.
In general, the results of tests of the wings in straight flew were consistent with results obtained in previous low-scale Investigations.
The tests in rolling flow showed that, for the swept wings, the lateral-force coefficient varied with ving-tip helix engle. Because of this variation, the yawing-moment coefficient at a given rate of roll will be dependent upon the value of the lateral-force coefficient at that rate of roll.
Although the value of the derivative of yawing-moment coefficient with respect to wing-tip lielix angle was negative for all positive lift coefficients up to the stall for the unawept ving, the value of this derivative for each of the swept wines changed from negative to positive at some moderate lift coefficient.
In general, the damping In roll became more negative with Increasing values of the lift coefficient for all the swept wings tested. Tests on the 45° eweptbaok wing shoved an appreciable reduction In the rate of change of wing-tip helix angle with aileron angle because of the Increased damping in roll at the higher lift coefficients.
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A knowledge of the rotary stability derivatives Is required before calculations can be made to determine the dynamic stability of an airplane or the motions of an airplane after a control displacement. Theoretical values of the derivatives of the forces and moments due to rolling, pitching, or yawing have teen used in -the past because of the difficulty of obtaining experimental results with conventional test equipment. The calculated values of these derivatives have served fairly veil for the determination of the dynamic behavior of unawept or moderately 3vept wings. Good theoretical values for the stability derivatives of highly swept wings, however, have not yet been obtained, end calculations have failed to predict accurately the dynamic behavior of airplanes with highly swept wings. Several of the rotary derivatives have been determined experimentally for both unsveyt and Ewopt wings using tho forced rotation and oscillation methods described In references 1 and 2. These methods give reliable results for certain derivatives but cannot be conveniently used to determine the derivatives of all six forces and moments with respect to rotation about each of the axes. All of the force and moment derivatives with respect to rolling can be determined rather simply, however, by means of the rolling flow method described in reference 3- The results of reference 3 and unpublished data on swept wings indicate that the value of the rolling moment due to rolling obtained by the rolling flow method are In good agreement with values obtained by the forced rotation method.
/ • The results of a preliminary investigation of a series of
untapered swept vings in boUi straight and rolling flow are presented in this paper.
SYMBOLS
The data are presented in the form of standard NACA coefficients of forces and momenta which are referred in all cases to the stability exes, with the origin at the quarter chord point of the mean geometric chord of the models tested. The positive directions of the forces, moments, and angular displacements are shown in figure 1. The coefficients and symbols used herein are defined as follows:
lift coefficient (k. ©
•-»Vi
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ggy-v:*;.I-, -^;'- -:r
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SAGA SM Ho. LT»9
X
L
Z
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B
4
P
V
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1)
longitudinal-force coefficient f-i-J
lateral-force coefficient (—| Vis/
rolling-moment coefficient (-^-)
pitching-moment coefficient (-^-)
yawing-moment coefficient (-0
(^
lift, pounds
longitudinal force, pounds
lateral force, pounda
rolling moment about X-axis, foot-pounds
pitching moment about Y-axls, foot-pounds
yawing moment about Z-axls, foot-pounda
dynamlo pressure, pounds per square foot
mass density of air, slugs per cubic foot
free-stream velocity, feet per second
wing area, square feet
span of wing, measured perpendicular to axle of synmetry, feet
chord of wing, measured parallel to axis of symmetry, feat
seen geometric chord, feet (fM distance of quarter-chord point of any chordvlee section
from the leading edge of the root section, feet
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distance from leading edge of root chord to the «uarter
chord of the mean geometric chord, feet
aspect ratio © (*r-)
a angle of attack measured In plane of ayametry, degrees
A angle of sveep positive for oveepbeclc, degrees
• angle of ;'aw, degrees
Ü. wing-tip helix angle, radians 27
aileron deflection measured In plane perpendicular to aileron hinge axis, degrees
h. *x
ac, 0,
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AFPARATC6 AMI) TESTS
The tests of the present Investigation were conducted In the 6-foot circular test section of the Langley stability tunnel which le equipped with a motor-driven rotor and vanes for rotating the air stream about the tunnel axis (see reference 3). The models were rigidly mounted at the quarter-chord of the mean geometric chord on a single strut support (fig. 2) which was attached to a conventional six-component balance. By means of this equipment, rolling flight is simulated by rolling the air stream with respect to the rigidly mounted model.
The models tested consisted of four untapered wings of approximately the same area, all of which had equal chords (10 in.) and MACA 0012 sections in planes normal to the leading edge (see fig. 3)- The wings had sveepback angles of -1*5°, 0°, k3°, and 60° and the corresponding aspect ratios were 2.6l, 5.16, 2.61, and 1-31*, respectively. The U50 sweptback wing was equipped with 20-percent wing chord and 50-percent wing semispan plain ailerons. The aileron nose gaps were sealed with plasticine.
All tests were run at a dynamic pressure of 39.7 pounds per square foot, which corresponds to a Mach number of 0.17. The test Reynolds numbers, based on the mean geometric chords of the models, are
Sweepback (dee)
Reynolds number
0
60
1, too,000
990,000
l,l«30,000
1,960,000
The characteristics of these wings were determined la both straight and rolling flow. In the straight flow tests, six-component measurements were obtained for each wing through an angle-of-attack range from approximately zero lift up to end beyond maximum lift at angles of yaw of 0° and *5°. TeBts were also made at angles of attack of approximately 0°, G°, and 12°
•^ to 30°- from k30° through a yaw-angle range of
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Bw rolling flow tests were made at positiv» and negative rotor speeds corresponding to a constant value of wing-tip helix eagle Jp. of p.OUW through the sane eagle-of-attack range used.
for the straight flow tests. Tests were also made at angles of' \ ';'--' attack of approximately 0°, 6°, and 12° through a range of positive' • and negative rotor speeds•
Both straight-flow and rolling-flow characteristics of the ^5° eweptback wing with ailerons I0.20c, 0.50^1 were obtained for angles :
of attack of approximately 0°, 6°, and 12° and for aileron deflections of tlO0, t!5°, and ±30°.
CORRECTIONS
Although there has been no sycteuatio investigation of tunnel corrections for swept wings, calculations for a few specific models have indicated that corrections for tunnel wall effect are determined primarily by the spans and. areas of models and are not creatly affected by sweep. Corrections previously developed for unsvopt wings therefore were applied to the present wings regardless uf the angle of sweep. The corrections were made to lcngitudinel-force coefficients, rolling-moment coefficients, and angles of attaok by the following equations:
** ^®* ACj - KCj
Aa -57 •3\(cK where
& w
C
C,
boundary correction factor obtained from reference' If
tunnel cross-section area, square feet
unconnected rolling-moment coefficient
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X a correction factor from reference 5 modified for application to these tests
She data hare not been corrected for the effects of blocking or for the support strut tares. Several tare measurements were made and they indicated that, in general, the corrections would he very email.
SESUL33 AMD DISCUSSION
Presentation of Data
Hie data obtained In the straight flow tests are presented •• In figures k to 6. The results of the tests node through the angle-of-attack range for ±5° yaw ere not presented because they were used only for determining the lateral stability derivatives which are presented in figures 9 and 10.
The data obtained In the rolling-flow tests are presented In figures 11 to Ih- The results of the tests made through the angle-of-attack range at values of J&L of iO.OkhS are not presented
27 because they were used only to determine the rotary stability derivatives which are presented In figures 15 and 15.
The characteristics obtained from the ailerons tested on the k*i° sweptback wing In both straight and rolling flow are presented In figure 17-.
s
Characteristics in Straight Flow
She characteristics of the present series of swept wings obtained In straight flow are approximately the same as would be expected on the basis of previous low-scale tests. (See reference 6.) The aspect ratios of the swept wings used in the present investigation differed from these reported in reference 6. The wings of the present series all had approximately the same area and the aspect ratio reduced with sweep angle approximately as the cos A. Because of the variation between aspect ratio and sweep angle.
ac, the relations for C,
and "ty
acT as given In reference 6 reduce to
°L. (%) C08A
m,
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WK».
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A comparison of the calculated and. experimental values far thee« derivatives is shown in figure 10 • The arreement is reasonably good although the calculated values underestimate the effects of sweep.
It should be noted that the values for the ^5° sweptforward vlng deviate from the calculated values slightly more than do the values for the Vj° eweptback wing* Also noticeable about the 42° sweptforward wins (see fig. k) is that its aerodynamic center is located farther back on the mean Geometric chord (0.32 mean geometric chord) than the aerodynamic centers of the unswopt or sveptback wings (0.19 to 0.22 mean geometric chord) and that its maximum lift coefficient (about 0.8) Is lower than that of the unswept or h^° sveptback wings (about 1.0) end much lower than that of the 66° oweptback wing (about 1.2 at a = 36°). The value of C, for the kj0 sweptforward wing Is practically zero up to a
lift coefficient of about 0.6 (see fig. 9), and the maximum positive value of C|. for the 1*5° sweptforward wing is about two-thirds the
lMTlimim positive value attained by the V?° sveptback wing.
All the wings tested become increasingly stable longitudinally as they approached and exceeded maximum lift coefficient, which Is In agreement with the correlation presented in reference 7.
Characteristics in Boiling Flow
übe data presented in figures 11 to Ik Indicate» that for angles of attack up to a least 12°, the values CL, Cj, and CB
vb aro practically unaffected by the variations in — within the
2V b
range Investigated, and that CY, C,, and C very linearly with —.
o n
Unpublished data on tests of the h$ sveptback wing show that this •pb
linear variation of Cj and C with — holds even beyond the stall.
at least for a range of 2v
27 of *0.1. Because of this linearity the I»
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method of obtaining the derivatives C- , C, , and C_ from toe JP P HP
differences in the coefficients for Jnat two values of wing-tip helix an^le was considered applicable through the complote an^le- of-attack range used for the present tests. The derivatives obtained
from tests at values of —— of ±0.OhhS are presented In firure 15- 2T
Dynamic stability calculations in the past have neclectecl tiie effects of variation of lateral force with rate of roll nines ouch a variation vas not found to exist for unsveyt wings belov the stall. For swept wings, however, such a variation doer; e::iet as Indicated In figure 15. Figure 15 bhovs that for a limited ran^ the values of Oy- are neerly proportional to the lift coefficient,which would be expected frou calculations basod on the simplified theory discussed in reference 6. At moderate lift coefficients, hovever, the values of Cw for the svept wirißs markedly decreased in meyiitu^e, In seme
P caoes even reversing sirji.
For the uncwept wing, the negative value of C varied linearly
with lift coefficient up to the maximum lift coefficient. The values of C_ for the swept wir^s, however, wore proportional to the lift
P coefficient for only a limited range and. at moderate lift coefficients, reversed sign and assumed lerge positive values. Tor low lift
coefficients the values of the slope (?) cL=c (see fig* 16) became
more negative as the angle of BweepbacK was increased.
The values of CL shown in ficv<re 15 are for moments taken
about ttio quarter-chord point of the mean Geometric chord shown in figure 3- Because of the existence of the derivative Cy for
swept vrineSjthe value of C will vary with the longitudinal
location of the point about which the moments are calculated. That these two derivatives are Interdependent is indicated in fi£,ure 15 by the fact that both undergo abrupt varietionr. In slopo at the same lift coefficients.
For the unsweut wins, the value of the damping in roll C, was *P
nearly independent of lift coefficient up to the maximum lift
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coefficient, beyond which the sign of Cj changed from negative
to positive. The values of C, for the swept wings generally 'p
•become more negative with an increasing value of lift coefficient over the greater part of the lift-coefficient ron-e. Eo positive values of C, were obtained for the swept -fingt for the ru«<je of
P angle of attack tested, even beyond the maximum lift coefficient.
Application of the eiinplif led theory to tho present series of vlngs leads to the following expression:
C»_ « (C\ \ cos A /A=0
A comparison of the calculated values with those measured at low lift coefficients is presented in figure IS and indicates that the decrease In C. with angle of sweep is slightly more rapid than
*P predicted by the calculations.
Aileron Characteristics
The recults of the tarts made to determine the characteristics of the aileron? on the V?° sweptback win.3 are presented in figure 17. Teste were rade in both etraljjit fmd rolling flow with both ailerons deflected through the same angle, but in opposite directions. The rolling flow data are for the condition of zero rolling moment. The data indicate that the variation of rolling ncnent with alloron deflection falls off slightly with increasing angle of attack, which, coupled with the increase of damping in roll with angle of attack.
pb causes the variation in •=•— with alleren deflection to fall off
2V somevbat rapidly with an^le of attack.
For the range of angle cf attuck considered, the yawing moment due to roll (fig. 15) is of the same sign an the yavlnt; moment due to aileron deflection, (flg.l7(a))and therefore, the yawing moment of the rolling wing will be jjreater than that due to the ailerons alone. The lateral force due to roll is of the opposite sign and of a greater magnitude than the lateral force due to aileron deflection« which will result in a reversal of lateral force during the transition
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from straight to rolling flieht, and positive valves of lateral foroa for the wing In steady roll-
CONCLtEIOHB
The results of low-scale tests made In streikt and rolling flow on a series of untapered swept wings having equal chords in planes normal to the leading edge and approximately equal areas Indicate the following conclusions:
1. In General, the characteristics of the vines in straight flow are consistent vith results obtained in previous investigations-
2. A variation of lateral-force coefficient with wing-tip helix angle was found to exist for the swept wings. Because of this variation, the yawing-moment coefficient at a given rate of roll will ee dependent upon the value of the lateral) -force coefficient at that rate of roll.
3- Although the value of the derivative of yawing-moment coefficient with respect to wing-tip helix an^le wa3 negative for all positive lift coefficients up tc the stall for tho unwept wing, the value of this derivative for the swept wings changed from negative to positive at some moderate lift coefficients.
It. The damping In roll generally 'becomes more negative with Increasing vrxlues of the lift coefficient for all of the swept wings tested.
5. Tests on the U50 Bveptback wing showed an epprecia'ble reduction in the rate of change of helix angle with aileron angle with Increasing angle of attack 'because of the increased dumping In roll at higher lift coefficients.
Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics
Langley Field, Va.
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HACAHMNo. L7B09
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1. Bennett, Charles V., end Johnsen, Joseph I.: Experimental Determination of the Damping In Boll and Aileron Boiling Effectiveness of Three Wings Having 2°, 42°, and 62° Sveephack. KACA IN Ho. 1278, 1947.
£. Cotter, VI111am E., Jr.: Summary and Analysis of Data on Damping In Yaw end Fitch for a Number of Airplane Models. HACA TN No. lOfib, 1946.
3. MaeLachlan, Robert, and Letkc, Villlam: Correlation of Two Experimental Methods of Determining the Boiling Characteristics of Itasvept Wings. NACA OH No. I3C9, 1947-
k. Sllverstein, Ate, and White, Jame^ A.: Wind-Tunnel Interference with Particular Beference to Off-Center Positions of the Wing and to the Dowro/ash at the Tall. KACA Bep. No. 547, 1935.
5. Svanson, Bobert S.: Jet-Bo-'ndP-ry Corrections tc ti Yawed Model In a Closed Rectangular Wind Tunnel. tt'.CA ABB, Feb. 1943.
6*. Letko, William, and Goodman, Alex: Preliminary Wilnd-Turmel Investigation at Low Speed of Stability end Control Characteristics of Swept-Sack Winc&. NACA TN Ho. 1046, 1945.
7. Shortal, Joseph A., and Maggln, Bernard: Effect of Sweepback and Aspect Ratio on Longitudinal Stability Characteristics of Wings at Low Speeds. KACA TN No. 1093, 1946.
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AUTHO»(S)
V DIVISION, kwvtrnuu.es (2) SECTION: Wing«, Airfoils (6) CROSS REFERENCES: Flo», Air - kunraut (38950J;
Kings - Asrodjnajdcs (99150); Wing«, 3»ept-back - Boiling mo—nt (99306.7?)
ATI- 4802 C*IG. AGENCY NUMal
8>f-L7BD9
«(VISION
iKJtG-N. TITLE:
*•*•• "•*nSBmSar investigation at low spaed« of swept wing« In rolling flow
ORIGINATING AGENCY: Rational Advisory Cocmlttaa for aeronautics, Washington, 0. C. TRANSLATION:
S COUNT»*
D.S. LANGUAGE
_Sfc_ FOUG'NCLASS U. S.CLAS5. DATE
w«y't7 CAGES
21 photo», FEATURES
table», dlacra. gran ABSTBACT
Investigation is «ado to determine characteristics of untapered wings with various anglss of aweepeack under conditions sluulating straight and rolling flow. Characteris- tic« of aileron on 45° »wept-baek wing are given. Besaite of test in straight flow; correspond with previously obtained results. Lateral-force coefficient varies with wing tip helix angle in rolling flow. Dejeping in roll becoasa «»re negative with increasing lift coefficient.
ROTE: Requests for copies of this report eust be addressed tot I.A.Ca., Washington, D. C. ^^
USAAF» T-2. HQ.. AM MATEMEl COMMAND TUT WRIGHT FIELD, OHIO. USAAF WKO-XI MA« CALM
Classification cancelled I ||\|P| AQCICirn or changed t» UllU-flOOlnllU
AUTH: ^ TO / II By&**LL^J.T*~a•. O^R (*¥/^
Srenature and Grad«
Oatl /0tyJ^/9S3
oarcaoMEjfa«
Gcwhaa, Alas
AUTHQg(S)
II DIVISION Aorcdynaalco (2) ISECTIONI tdngo, Alrfoilo (6) | CROSS REFERENCES! Pics, Mr - cjaearc=>nt (38950);
tango - Aon>47oaal.es (99150) J Bingo, Soapt-back - Boiling sacant (99306.75)
|AMEU.mUi ProUninary Investigation at lea opocds of ocopt tlngo In rolling flea
IfOWN. TtTUi
03IGIHATO4G AGETCY national Advisory Ctaittco for Acronastioo, nashlngton, 0. C. TQANSIATIONi
l/OOG-NOASa U. S.CLASS. I DATE I I E~a. I Say'V?
COUWrey I LANGUAGE
0.3. I Esq. PAGES
21
U1US,
28 FEATURES
photoo. tables, dlaars. nraciw ßQSTOACT
Investigation ID cado to dotamrtrm eboraeterioties of untapCTod olngo nlth voriouo anglos of oocopSock nmlor emdltiono oinnlating straight end rolling flon. Charaetorlo- tieo of olloron on 45° oropt-baels ulng are given. Posulto of tost in otroight flea ccrrospond oith proviouojy obtained rooulto. Latoral-foreo eoofflelont vorloo oith oinj- tlp tolln 6D3I0 in rollliQ flon. Damping in roll boew 0 coro negative olth incroaolng lift eoofflelont.
COTE: Boqnooto for eopioo of this report cast bo addroosod to: Q.A.C.A., Ehshlngton, D. C. ; '
1-2. KO, Aß MATERIE! COMMAND TSnVi ECHKJCAI mom WRIGHT FIEIO. OHIO. USAAF &^ OT-O-JI OAQ a 22JZ3
