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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

TECHNICAL NOTE. "". : ~~

No. 1169 ~~~

THE EFFECT OF GEOMETRIC DIHEDRAL ON THE

AERODYNAMIC CHARACTERISTICS OF A 40°

SWEPT-BACK WING OF ASPECT RATIO 3

By Bernard Maggin and Robert E. Shanks

Langley Memorial Aeronautical Laboratory Langley Field, Va.

^0£^ Washington

December 1946

] 3 1176 01425 7597

NATIOJSAL ADVISORY COMMITTEE FOR AERONAUTICS

TECHNICAL NOTE NO. HÖ9

THE EFFECT OF GEOMETRIC DIHEDRAL ON THE

AERODYNAMIC CHARACTERISTICS OF A J*0°

SWEPT-BACK WING OF ASPECT PATIO 3

By Bernard Maggin and Robert E. Shanks

SUMMARY

Force tests at low Reynolds numbers were made to determine the effect of changes in the geometric dihedral an the aerodynamic characteristics of a wing of aspect ratio 3 having an angle of swoepback of 40° measured at the quarter-chord line. The results of the tests for the swepWback wing of aspect ratio 3 indicated that, for low and moderate lift coefficients, changes in geometric dihedral from -10° to 10° resulted in a change in the effective dihedral that was about 75 percent as great as that obtained for an unswept wing of aspect ratio 6. For dihedral angles out- side the range of -10° to 10°, changes in geometric dihedra.1 produced about half as much change in effective dihedral as for dihedral angles between -10° and 10°. At a lift coefficient above a value of 0.8, the maximum values of effective dihedral obtained with large negative geometric dihedral angles were greater than those obtained with 0° geometric dihedral. Over the linear range of the lift curve, the directional-stability param- eter generally increased with increasing negative dihedral and increasing lift coefficient, but did not change appreciably with increasing positive dihedral. Increasing positive dihedral resulted in an increase in the nosing-up pitching moments (destabilizing) at the stall, and increasing negative dihedral resulted in an increase in nosing-down moments (stabilizing) at the stall. Increasing positive or negative dihedral caused a decrease in the lift-curve slope and an increase in the variation of lateral force with sideslip.

NACA TN No. II69

IMKOEOCTION

One undesirable characteristic of highly ewopt-back wings is the large variation in affective dihedral with a variation in lift coefficient. This variation tends to give excessive values of effective dihedral at moderate and high lift coefficients, In order to limit the maximum value of- off active dihedral to a value that will permit attainment of satisfactory dynoaic luteral stability and control characteristics, it airy bo necessary in many cases to use negative geometric- dihedral. In order to obtain some indication of tho effects of changes in geometric dihedral on the aerodynamic characteristics of a swept-baclc wing/ an Investigation has been made at low Reynolds "numbers in the Langloy free-flight tunnel. This investigation consisted in force tests of a '+0 ewept-back wing of aspoct ratio 3 wiLh geomotric dihodral angles ranging from 20° to -3O0. The results of the investigation are presented herein.

3YWBCLS

The forces and moments wore measured with respcct^to the stability axes, (See fig. 1.)

CL • lift coefficient (H£$\

Cy, drag coefficient (P3^3 'D

/rItoag\

Cm pitching-moment coefficient

0, rolling-moment coefficient f _k_]

Cn yawing-moment coefficient (~^;)

Cv lateral-force coefficient /Lateral^orgjA

L rolling moment about X axis, foot-pounds

M pitching moment about J .axis, foot-pounds

NA.CA TN ITc. H69

N yawing moment cJbout Z axis, f £>ot-pounda I

S wing area (0° dihedral wing), square feet

b wing span. (0° dihedral wing), feet

c wing chord, measured in plane parallel to plane of symmetry, feet "

c wing mean aerodynamic chord measured in plane parallel to plane of symmetry, feet

y lateral location of wing mean aerodynamic chord measured from axis of symmetry, inches

z vertical location of wing mean aerodynamic chord measured from lower surface of the wing' (0 dihedral), inches

wing asnect ratio 1 _£. ] \S /

dynamic pressure, pounds per square foot \2 /

p mass density of air, slugs per cubic foot :_...„._ . ._

T airspeed, feet per Becond

0 angle of roll, degrees

ß angle of sideslip, degrees

•ty angle of yaw (-ß), degrees

p geometric dihedral angle, measured with respect to under-surface of wing, degrees

a angle of attack at the lower surface of the wing, degrees

X taper ratio, ratio of tip chord to root chord

C, effective-dihedral parameter, rate of change of rolling- , \ ß moment coefficient with angle of sideslip, per degree [ ~2LJ

GJV, direcbional-stability parameter, rate of change of yawing- moment coefficient with angle of sideslip, per degree

N

NACA TN No. II69

Cy lateral-force parameter, rate of change of lateral-force ß coefficient with angle of sideslip, per degree £^ft

lß_ rate of change of effective-dihedral parameter with d" r geometric-dihedral angle, per degree

CT lift-curve slope, per degree (..tfyXi) cc, \ da,;

APPARATUS AND TESTS

The force tests to determine the aerodynamic character- istics of the various wing configurations were made on the Langley froe-flight-tunnol six-component balance which rotates in yaw with the model so that all forces and moments are measured with respuct to the stability axes. (See fig. 1.) I: complete description of the balance system 1-& given in reference 1. All the- trfsts wore run at a dynamic pressure""öf^3^CTp^ünas per square" foot corresponding to a test EoynolAs number of 2h9,OOQ based on a mean aerodynamic chord of 0.77Ö foot.

A sketch of the tapered wing (X, = 0.5) of aspect ratio 3, with a sveepback of U0° measured at the quarter-chord line, is presented in figure 2. The wing has a Ehode St. Genese 33 airfoil section parallel to the plane of symmetry. This wing section was U3ed in accordance with the free-flight-tunnel practice of using airfoil sections that obtain maximum lift coefficients in the low-scale tests more nearly equal to those of full-scale wings. The wing was constructed of pine in three sections: a 0.10b center panel, and two O.V?b outboard panels. The outboard panels were hinged to the center panel and faired wedge blocks were used to give a range of geometric dihedral angles from 20° to -3O0

measured at the under surface of the panels perpendicular to the plane of symmetry.

A series of force tests were made for dihedral angles of 0°, ±5°, +10°, ±20°, and -30° to determine the aerodynamic characteristics of the wing over the lift-coefficient range for yaw angles of 0° and ±5°. A few force teats were made over a range of yaw angles of 3O0 to -3O0 at an angle of attack of 2° to determine whether the values of the lateral-stability parameters obtained from angle-of-attack tests at ±5° yaw were reliable over a reasonable yaw-angle range.

NACA TIT No. 1169

RESULTS AND DISCUSSION

All the tö st data are "based on the area, span, and mean aerodynamic chord of the zero-dihedral configuration and are measured with respect to the same moment-reference axes unless otherwise stated. The origin of the moment-reference axes shown in figure 2 is the quarter-chord point of the mean aerodynamic chord when the wing is set at 0° geometric dihedral. Since the mean aerodynamic choi'd moves upward with respoct to the moment- reference point as positive dihedral is increased and downward as negative dihedral is increased, it is necessary to correct the "basic data presented with respect to the moment-reference axes when moment data are desired ah out some point on the mean aerodynamic chord of the wing.

The results of the angle-of-attack tests at angles of yaw of 0° and 1-5° are presented in figure 3. The results of the yaw tests at a = 2° are presented in figure k. A comparison of the data of figure 3 with data of figuro k indicates that at least over the linear range of the lift curve, the lateral-force, parameter CYR, the directional-stability parameter Cno> sxid. the effective-

dihedral parameter C, obtained from the tests at yaw angles of

±5° give reliable values of these parameters over a range of yaw angles of approximately ±15°. "

The longitudinal-stability characteristics of the wing over the dihedrtil range have been summarized in figure 5 and the lateral-stability characteristics in figures 6 to 8. Symbols^ which have been used in some of the summary plots to aid in distinguishing the curves, should not be taken as test points,

Lift Characteristics

The data of figure 5 indicate that the lift-curve slope decreases with increasing positive or negative geometric dihedral. The investigation of reference 2 showed that the decrease in lift-curve slope with geometric dihedral can be expressed as

.2

S'^-o" <x>

This theoretical relationship is presented in figure 5 and is in good agreement with the experimental rosulta.-

HACA TN No. II69

The low-scale lift data in figure 3 indicate that the maximum lift coefficient generally decreased with increasing positive or negative geometric dihedral. This decrease in maximum lift coefficients resulted from the fact that the lift coefficients were "based on the area of the wing with zero dihedral and not the projected- wing area, which decreased with dihedral.

The data of figure 3 alao show an increase in the angle of attack of maximum lift with increasing positive and negative geometric dihedrals. As pointed out in reference 2, this increase is caused by a reduction in the angle of attack measured in the plane normal to the wirig surface'as the geometric dihedral is increased either in the positive or negative direction.

Pitching-Moiiient Characteristics

/ The data of figure 5 indicate that, when the pitching moments are referred to the momont^reference axes, an apparent increase in longitudinal stability dC^/dCL with increasing *

geometric dihedral results. When the pitching moments are referred to the mean aerodynamic chord for each dihedral angle, however, only a slight change in longitudinal stability—with geometric dihedral results.

The pitching-moment data of figure 3 indicate that goometric dihedral affected the low-scale pitching-moment characteristics at high lift coefficients. These data obtained at low Reynolds number indicated that-increasing positive goometric dihedral resulted in an increaso in nosing-up pi telling moments (destabili- zing) at the stall and increasing negative dihedral resulted in an increa3e in nosing-down momenta (sbabilizing) at the stall. The changes In pitching moment at stall are not so pronounced when these data are corrected to the mean aerodynamic chord for the corrospending dihedral configuration.

Rolling-Moment Characteristics (Effective Dihedral)

The data of figure 6 indicate that up to a lift coefficient" of O.80 the offective-dihodral parameter -Cj increases with

lift coefficient and posit!vo geometric dihedral and decreases with negative geometric dihedral. The wing with 0° geometric dihedral reaches a maximum value of -Cj„ at a lift coefficient of

1.0. With increasing positive geometric dihedral the maximum

NACA TN Wo. 1169 7

value of -Cjß occurs at increasingly lover lift coefficients

(O.90 for 20° dihedral). With negative geometric dihedral, maximum values of -C^ would "be reached at some lift coefficient "beyond

maximum lift. This phenomena can be explained "by the fact that the change in Cj with lift coefficient near maximum lift is governed

by the nature of the wing stall. With positive geometric dihedral the angle of attack resulting from sideslip is such as to increase the angle of attack on. the leading-wing panel and to decrease the angle of attack on the trailing-wing panel. With negative geometric dihedral the opposite effect takes place and the leading-wing panel has the smaller angle of attack. As maximum lift is approached in a sideslip, the wing panel with the higher angle of attack therefore begins to stall first a.nti a decrease in lift (and rolling moment) produced by that panel results.

The data of figure 7, which is a cross plot of figure 6, indicate • that, for any lif t coefficient in the linear portion of the lift curve, an approximately linear variation of effective- dihedral Tiarameter C, with geometric dihedral occurs for a

tß t

range of geometric dihedrals from -ID to 10 . The variation of

,ß ar

outside the range of -10" to 10". The curves of figure 7 are cross-plotted in figure 8, which show3 that the dihedral effectivo-

neso parameter ß for geometric dihedral angles between -10°

*r - and 10 varies over the lift range from about -0.OOOI7 to -0.00012

and is more than twice the value of zß for geometric dihedrals

in the range outside ±10°. For an unswept wing of aspect- ratio 6, which is representative of wings on many present-day conventional

airplanes, the value of l&- is 0.00021 (reference 3). The

average value of E over the low and moderate lif t-coefficient

range for dihedral angles between tlO for the wing tested was 0.00016 or about 75 percent of the value for the unswept wing of

Cj with dihedral -^_"- decreases for geometric dihedral angles

0 NACA TN No. II69

aspect ratio 6. This reduction in the value of z2l£> for the oi'

ewept-back wing a3 compared to the unswept wing is attributed in part to the lower lift-curve elope of.the sWept-back wing.

The data of figures 6 and f indicate that at any lift coefficient up to a lift coefficient of 0.8, increaaing the negative geometric dihedral causes a reduction in the value of -C. . At a lift

coefficient above 0.8, however, increasing the negative geometric dihedral increases the value of -C^ . For example, for lift

coefficients above 1.0, the values of -Cj are greater for

goomotrlc dihedral angles of -20° and -30°~ than for zero geometric dihedral.

Yawing Moment K&A. Lateral Force

The cross-plots of figures 6 and 7 indicale^thttt the directional- stability parameter C generally increases with increasing

negative dihedral and Increasing lift coefficient over the linear range of the lift curve hut is not appreciably affected by incruaaing positive dihedral. An analysis of tho forces acting on the wing indicated that at any lift coefficient in the linear range of the lift curve the directional-stability parameter C^ ahould

increase with an increase in negative dihedral and decrease with an increase In positive dihedral. The discrepancy between tho analysis and the teat data for wings with positivo dihedral h^3 not heen explained. The data of figures 6 and 7 also Indicate that, over the linear portion of the lift curve, the variation of lateral force with side3lip Cyfl increases with increasing

positive or negative dihedral but does not vary with lift coefficient.

CONCLUDING REMARKS

The effects of varying the dihedral angle of a wing of aspect ratio 3 having an angle of sweepback of kO° meacured at

HACA TN No. II69

the quarter-chord line were determined 'by force teste made at low Reynolds numbers and the results arc summarized as follows:

1. For low and moderate lift coefficients changes in geo- metric dihedral from -10° to 10° resulted in an effective dihe- dral change approximately 75 percent as great as that obtained for an unswept wing of aspect ratio 6. For dihedral angles outside the range between -10° to 10°, changes in geometric dihedral produced only about half as much change in effective dihedral as for dihedral between 10° -and -10°. At lift coef- ficients above 0.8, the maximum values of effective dihedral for wings with large negative dihedral angles were greater than the maximum value obtained for wings with 0° geometric dihedral,

2. Over the linear range of the lift curve, the directional- stability parameter generally increased with increasing negative dihedral and increasing lift coefficient but showed no appreciable change with increasing positive dihedral.

3. Increasing positive dihedral resulted in increasing nosing-up pitching moments (destabilizing) at the stall and increasing negative dihedral resulted in increasing nosing-down • moments (stabilizing) at the stall.

h. Increasing positive or negative dihedral resulted in a decrease in the lift-curve slope and an increase In the variation of lateral force with sideslip.

Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics

Langley Field, Va., September 19, 19^6

10 NACA TN No. 1169

1. Shortal, Joseph A., and Draper, John V.: Freö-Flight-Tunnel Investigation of the Effect of the Fuselage Length and the Aspect Ratio and 3ize of the Vertical Tail on Lateral Stability and Control. HACA APE'No. 3D17, 19^3.

2. Purser, Paul E., and Canrpbell, John P.: Experimental Verification of a Simplifled Vee-Tail Theory and Analysis of Available Data on Complete Models, with Vee Tails. NACA ACS No. L5AO3, 19^5.

3. Shortal, Joseph A.: Effect of Tip Shape and Dihedral on Lateral-Stability Characteristics. NACA Hep. No. 548, 1935-

*N.

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NACA TN No. 1169 Fig. 1

Wind direction

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

Figure 1.- The stability system of axes; arrows indicate positive directions of moments, forces, and control- surface deflections. This system of axes' is defined as an orthogonal system having the origin at the center of gravity and in which the Z-axis iB in the plane of symmetry and perpendicular to the relative wind, the X-axis is in the plane of symmetry and perpendicular to the Z-axis, and the Y-axis is perpendicular to the plane of symmetry.

Fig. 2' NACA TN No. 1189

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS.

27

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Fig. 5 NACA TN No. 1169

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D/hedra/ asig/e., /3 c/e.p NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

Figure 5.- 'Variation of lift-curve slope Cj.^ ai*d longitudinal stability (dCm/dCL) with dihedral angle for a 40o swept-back wing of aspect ratio 3.

Angle of aftckcff^^deg

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~P* ~P' VP aspect ratio 3 at various dihedral angles.

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ATI-71 182

Langley Aeronautical Lab., Langley Air Force Base, Va. (NACA RM L6117)

THE EFFECT OF GEOMETRIC DIHEDRAL ON THE AERODYNAMIC CHARACTERISTICS OF A 40° SWEPT- BACK WING OF ASPECT RATIO 3, (RESEARCH MEM- ORANDUM), by Bernard Maggln and Robert E. Shanks. 8 Oct 1948. 27 pp. CONFIDENTIAL

(Not abstracted)

DIVISION: Aerodynamics (2) SECTION: Wings and Airfoils (6) PUBLISHED BY: National Advisory Committee for Aeronautics, Washington, D. C. DISTRIBUTION: U. S. Military Orgaiüzations request copies from ASTIA-DSC. Others route re(y to ASTIA-DSC thru AMC, Wright-Patterson k^Jorce Base, Dayton, 0. Atta; NACA.

SECURITY INFORMATION

CONFIDENTIAL

L Maggin, Bernard H, Shanks, Robert E.

ARMED SERVICES TECHNICAL INFORMATION AGENCY

DOCUMENT SERVICE CENTER

XSfJ./ CONFIDENTIAL