Induced Moment Effects of Formation Flight Using Two F/A-18 … · 2013. 6. 27. · vortex—the trailing airplane left wingtip is receiving most of the vortex-induced upwash. This

NASA/TM-2002-210732

Induced Moment Effects of Formation Flight Using Two F/A-18 Aircraft

Jennifer L. Hansen and Brent R. CobleighNASA Dryden Flight Research CenterEdwards, California

August 2002

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NASA/TM-2002-210732


Jennifer L. Hansen and Brent R. CobleighNASA Dryden Flight Research CenterEdwards, California

August 2002

National Aeronautics andSpace Administration

Dryden Flight Research CenterEdwards, California 93523-0273

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NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)7121 Standard Drive 5285 Port Royal RoadHanover, MD 21076-1320 Springfield, VA 22161-2171(301) 621-0390 (703) 487-4650

INDUCED MOMENT EFFECTS OF FORMATION FLIGHTUSING TWO F/A-18 AIRCRAFT

Jennifer L. Hansen* and Brent R. Cobleigh†

NASA Dryden Flight Research CenterEdwards, California

Abstract

Previous investigations into formation flight haveshown the possibility for significant fuel savings throughdrag reduction. Using two F/A-18 aircraft, NASADryden Flight Research Center has investigated flyingaircraft in autonomous formation. Positioning thetrailing airplane for best drag reduction requiresinvestigation of the wingtip vortex effects induced bythe leading airplane. A full accounting of the vortexeffect on the trailing airplane is desired to validatevortex-effect prediction methods and provide a databasefor the design of a formation flight autopilot. A recentflight phase has mapped the complete wingtip vortexeffects at two flight conditions with the trailing airplaneat varying distances behind the leading one. Force andmoment data at Mach 0.56 and an altitude of 25,000 ftand Mach 0.86 and an altitude of 36,000 ft have beenobtained with 20, 55, 110, and 190 ft of longitudinaldistance between the aircraft. The moments induced bythe vortex on the trailing airplane were well within thepilot’s ability to control. This report discusses the dataanalysis methods and vortex-induced effects onmoments and side force. An assessment of the impact ofthe nonlinear vortex effects on the design of a formationautopilot is offered.

Nomenclature

AFF Autonomous Formation Flight

ay lateral acceleration, g

1American Institute of Aero

*Aerospace Engineer; Member.†Aerospace Engineer; Senior Member.

Copyright 2002 by the American Institute of Aeronautics andAstronautics, Inc. No copyright is asserted in the United States underTitle 17, U.S. Code. The U.S. Government has a royalty-free licenseto exercise all rights under the copyright claimed herein forGovernmental purposes. All other rights are reserved by the copyrightowner.

Notice: the use of trade names or names of manufacturers in thisdocument does not constitute an official endorsement of suchproducts or manufacturers, either expressed or implied, by theNational Aeronautics and Space Administration.

b F/A-18 wingspan (37.5 ft)

chord, ft

coefficient of force or moment

Cl coefficient of rolling moment

Cm coefficient of pitching moment

Cn coefficient of yawing moment

CY coefficient of side force

g unit of gravity

GPS global positioning system

h pressure altitude, ft

i integer

IX, IY, IZ moments of inertia about the X, Y, and Z vehicle reference axes, respectively; slug-ft2

IXY, IXZ, IYZ products of inertia, slug-ft2

M Mach number

m mass, slug

MX, MY, MZ moments about the X, Y, and Z vehicle reference axes, respectively; ft-lbf

p, q, r components of angular velocity about the X, Y, and Z vehicle reference axes, respectively; rad/sec

components of angular acceleration about X, Y, and Z vehicle reference axes, respectively; rad/sec2

dynamic pressure, lbf/ft2

S wing area, ft2

SG smoke generator

TAS true airspeed

X longitudinal position, b

Y lateral position, b

c

C

p q r, ,

q∞

nautics and Astronautics

Z vertical position, b

angle of attack, deg

angle of sideslip, deg

flightpath angle, deg

pitch angle, deg

heading angle, deg

Subscripts

lead leading airplane

trail trailing airplane

Introduction

For thousands of years, birds have taken advantage ofthe aerodynamic benefits obtained by flying information. The traditional “V” formation—flown bymany species of birds, including gulls, pelicans, andgeese—allows each of the following birds to fly in thewingtip vortex-induced upwash flow field that exists justto the side of the bird immediately ahead in theformation. The result for the individual birds is a lowerinduced drag, allowing for a reduction in the energyrequired to maintain a given speed. A recent study1

reported energy savings between 11 and 14 percent forpelicans flying in formation, based on a reduction inheart rate. This power reduction applies to each of thebirds aft of the leader. For migratory birds, formationflight extends the range of the formation birds beyondthe range of solo birds.

The Autonomous Formation Flight (AFF) project wasformed in an attempt to extend this beneficialrelationship to aircraft. Led by the NASA Dryden FlightResearch Center (Edwards, California), the project hasused F/A-18 aircraft (McDonnell Douglas Corporation,now The Boeing Company, St. Louis, Missouri; andNorthrop Corporation, now Northrop Grumman,Newbury Park, California) to demonstrate thetechnologies necessary to perform extended closeformation flight to reduce fuel usage or extend the rangeof a system of aircraft. The AFF team has includedBoeing, the University of California at Los Angeles, andthe NASA Ames Research Center (Moffett Field,California).

Although fighter aircraft have been used for thetechnology demonstration, formation flight dragreduction could be of most interest to improve cruiseperformance of larger military or commercial aircraft.System studies have shown that a 10-percent dragreduction for a commercial airliner conducting a daily

Los Angeles–to–New York roundtrip results in reducedfuel usage in excess of $500,000 for each airplane eachyear, as well as emission reductions of carbon dioxideand oxides of nitrogen of 10 percent and 15 percent,respectively.

One byproduct of flying in the vicinity of the highlynonlinear wingtip vortex is the torque imparted on thetrailing airplane. As figure 1 shows, when positioned in“V” formation on the right side—where the trailingairplane wingtip is near the leading airplane wingtipvortex—the trailing airplane left wingtip is receivingmost of the vortex-induced upwash. This upwashproduces greater lift on the left wing, which tends to rollthe trailing airplane away from the leading one. Thisrolling moment must be counteracted by the pilot orstation-keeping autopilot to maintain the formation.

As the trailing airplane moves further left, thedownwash side of the vortex from the leading airplanebegins to affect the left wing while the upwash sideinfluences the fuselage and right wing. The influence ofthe downwash starts to reduce the magnitude of therolling moment to the right. Eventually, the resultingrolling moment on the trailing airplane has the oppositesign of and a larger magnitude than the rolling momentof only one wingtip aligned with the leading airplanewingtip vortex.

In fact, the vortex flow field induces changes to all ofthe forces and moments on the trailing airplane, asshown in subsequent plots. Pitching moment changescan be positive or negative, depending on airplane

α

β

γ

θ

ψ

Figure 1. Formation axes system.

2American Institute of Aeronautics and Astronautics

position within the vortex flow field. Because the peakrolling moment occurs at the position of optimum dragreduction (13-percent wing overlap2), the trim dragmust be taken into account. In addition to the benefitsfor the trailing airplane, the leading airplane experiencesno negative effects as a result of formation flight.

The highly nonlinear vortex flow field significantlyincreases the pilot workload and reduces the ability ofthe pilot to precisely maintain the optimum position formaximum drag reduction. Therefore, any realisticlong-duration use of precise formation flight requiresthe use of a station-keeping autopilot. The autopilotmust be able to track a commanded relative position ortrajectory in the presence of gust disturbances andunsteady vortex effects. The design of a formation flightautopilot must be sensitive to the highly nonlinear,position-dependent vortex flow field; and requires anaccurate mathematical model of the inducedaerodynamic effects as a function of relative positionand flight condition.

In support of the AFF autopilot design, a flight testprogram has been conducted to map the formation flighteffects on two F/A-18 aircraft at four nose-to-tailseparation distances and two flight conditions. Forcesand moments have been calculated duringpilot-in-the-loop, constant relative-position test pointsand compared with data measured outside the vortexinfluence. A database model of the rolling, pitching, andyawing moments and the side force increments causedby the vortex has been assembled. This database will beused—along with similar models for the lift anddrag—to validate vortex-effect prediction codes, refinethe formation flight autopilot design, and conductaccurate formation flight simulation studies.

Experiment Description

To acquire a complete map of the vortex effects on thetrailing airplane, stable flight test points were definedover a “grid” in the lateral-vertical (Y–Z) plane(figs. 1–2). The trailing airplane pilot flew the grid ofpoints at four longitudinal distances behind the leadingairplane. A description of and the rationale for the gridpoints, four longitudinal distances, and two flightconditions are presented herein.

In a compromise between mapping resolution andflight test time, the test points were spaced one-eighth ofan F/A-18 wingspan (b) apart, or approximately 4.7 ft.The grid extended from 0.50 b high to 0.50 b low in thevertical axis, and from 0.25 b of wingtip separation to

0.50 b of wingtip overlap in the lateral direction.Figure 2 shows a graphical depiction of the test matrix.

The longitudinal positions were also referenced to b,and were selected to match previously publishedexperimental studies.3 When the location for optimumdrag reduction was identified, a finer resolution ofmapping was used in that area. Because the pilots hadno indication in the cockpit of longitudinal position, thenose-to-tail distance was monitored in the control roomand maintained by the pilot through radio calls. Thismonitoring was done to maintain both safety of flightand data quality.

The longitudinal positions were set at 2.0 b, 3.0 b,4.0 b, and 6.5 b (measured nose to nose); orapproximately 20-, 55-, 110-, and 190-ft nose to tail,respectively. Because of the origin of the formation axessystem (at the nose of the leading airplane), the Y and Zpositions were positive out the right wing and down,respectively. A Y position of 0.25 b wingtip separationcorresponds to approximately 10 ft between wings,whereas a Y position of –0.25 b wingtip separationcorresponds to approximately 10 ft of wingtip overlap.The Z position was also nondimensionalized by b, andalthough the formation axes system dictates that Z ispositive down, the vertical positions within the testmatrix are referred to as positive when the trailingairplane is above the leading airplane.

As previously described, the vortex effects from thisseries of flight tests were also to be used to validatepreexisting data from vortex-effect prediction codes.4

To allow direct comparisons with existing analytic dataacquired at a flight condition of Mach 0.56 and analtitude of 25,000 ft, extensive flight data were acquiredat the same subsonic condition. Because one possiblefuture application of AFF is for transport aircraft, flightdata were also acquired at a transonic condition ofMach 0.86 and an altitude of 36,000 ft, which isrepresentative for that class of vehicle. Note that eachflight condition has a different flap setting that alteredthe lift distribution of the wing, and therefore theproperties of the vortex.

The AFF research has been accomplished using twoNASA Dryden F/A-18 research aircraft. The aircraftflew in clean configurations without stores for mosttesting. When in-flight flow visualization was desired,smoke generators were attached to a single wingtip oneach airplane. The lead airplane is a two-seat,preproduction F/A-18 airplane; a single-seat F/A-18airplane was used as the trailing airplane. Both aircrafthave been instrumented with real-time angular rates and


4

American Institute of Aeronautics and Astronautics

Figure 2. Vortex mapping grid.

b. Test point matrix.

a. Relative lateral position.

linear accelerations; and the aircraft bus data includesuch data as control surface positions, fuel levelreadings, stick positions, and engine data. Becauseaccurate relative-position data are crucial to theexperiment, both aircraft have been equipped with arelative-position global positioning system (GPS).5 Thissystem drove the guidance needles display used by thepilot in the trailing airplane to get into and maintainrelative position with the leading airplane.

When at the flight condition, the pilot of the leadingairplane engaged the standard F/A-18 autopilots to holdaltitude, heading, and velocity. The pilot of the trailingairplane flew into the desired position behind theleading airplane by following the GPS-driven targetdisplay5 in the cockpit. This target position was selectedby the pilot of the trailing airplane using a cockpitswitch. The display consists of two needles usually usedfor an instrument landing system on a carrier-borneaircraft. The pair of needles guided the pilot to the targetposition, which was generally behind and to the right ofthe leading airplane. Using this target display system,the pilot maintained position for 30 sec. The GPSaccuracy was on the order of 2.5 ft, plus or minus astandard deviation of 2. Postflight analysis of the datataken during this time was used to calculate thevortex-induced effects on the trailing airplane.

Methodology

The incremental coefficients caused by vortexinfluence were calculated as the difference between thefree-flight coefficients (assuming no vortex interaction)and the actual flight-measured vortex coefficients(measured while the airplane was positioned within thevortex influence) at a particular flight condition.Figure 3 shows the data analysis process. A number ofbaselines, or vortex-free stabilized points, wereperiodically completed throughout each flight. Thebaselines assessed the effects of the asymmetries of thesmoke generators. These asymmetries were accountedfor in the force and moment calculations.

Free-Flight Model Calculations

The free-flight model was calculated using the F/A-18aerodynamic database, which is a function of controlsurface deflections; angle of attack ( ); angularvelocities corrected to the reference point; and flightconditions to determine the coefficients of rolling,pitching, and yawing, moments and side force (Cl , Cm,Cn, and CY , respectively). These flight data were usedas input to perform table lookups of the free-flightaerodynamic coefficients. Because of the vortexinfluence on the angle-of-attack vanes of the trailing

α


Figure 3. Data analysis methodology

airplane, approximating and angle of sideslip was necessary. The of the trailing airplane wascalculated using flightpath angle ( ) and pitch angle

and assuming the following:

and (1)

so subsequently,

. (2)

Because a reliable sideslip parameter was notavailable on the trailing airplane, the was estimated asthe difference in heading angle, , between the twoaircraft. The estimated was calculated as follows:

(3)

The necessary parameters were input into the F/A-18aerodynamic database to get the resulting Cl, Cm, Cn,and CY for the free-flight model.

Vortex Calculations

The flight-measured vortex model was calculatedusing the following closed-form equations:6, 7

(4)

Assuming the airplane is symmetric about thelongitudinal-vertical (X–Z) plane,

(5)

and the total moment equations simplify to

(6)

Flight-measured data were used for p, q, r, , anday; and the angular accelerations were calculated bydifferentiating the measured angular rates with respectto time. The vortex effect on the trailing airplane thenwas calculated as the mean difference between the

vortex and free-flight models over the steady-state testpoint:

(7)

where n is the number of data points.

Figure 4 shows an example plot of the data takenduring a 30-sec test point. These time-averaged momentand force influences were plotted against true lateralposition at each vertical position in the test point grid.

Results and Discussion

Although the vortex grid was mapped at fournose-to-tail distances and two flight conditions, only thedata corresponding with conditions and nose-to-taildistances of optimum drag reduction are discussedherein. Extrapolation of the data assumed that thevortex-induced effects on the trailing airplaneasymptotically approached zero as wingtip separationincreased. Each plot has an incremental moment orforce plotted against lateral position. Each line on theplot represents a different vertical position.

One source of possible error is GPS accuracy (on theorder of 2.5 ft, plus or minus a standard deviation of 2.)In addition, different flying styles of the five pilotsmight have influenced the data, and certain positions inthe formation were more difficult to fly because of thelack of a good visual reference (for example, very highvertical positions (0.50 b), or positions with nose-to-taildistances greater than 110 ft, or a combination thereof).

55-ft Nose-to-Tail Separation at the Subsonic Condition

The aircraft were flown with a nose-to-tail separationof 55 ft at a subsonic flight condition of Mach 0.56 andan altitude of 25,000 ft. The following sections discussincremental rolling, yawing, and pitching moment andside force.

Incremental Rolling Moment

As the trailing airplane lateral position changedfrom separation to overlap, the vortex effectsproduced an increasing right rolling momentincrement (fig. 5). The maximum rolling momentincrement occurred at the –0.13 b lateral test point.At –0.25 b, the rolling moment increment changedsign and became increasingly negative with furtherwing overlap. The rolling moment increments were

α β( )α

γθ( )

γ lead γ trail,=

γ θ α;–=

αtrail αlead θtrail θlead–+=

βψ

β

βtrail ψtrail ψlead–≈

Cl

MX

q∞Sb------------∑ ;=

Cm

MY

q∞Sc------------;∑=

Cn =MZ

q∞Sb------------;∑

CY aymgq∞S---------.=

I XY IYZ 0;= =

MX∑ pI X rI XZ q rIZ pI XZ–( )+ rqIY ;––=

MY∑ qIY r pI X rI XZ+( ) p rIZ pI XZ–( );–+=

MZ∑ r IZ pI XZ pqIY+ q pI X rI XZ–( ).––=

q∞

Vortex effect ∆C

Vortex Ci Free-flight Ci–( )i l=

n

∑n

----------------------------------------------------------------------------------,=



Figure 4. Example difference between vortex and free-flight models.

Figure 5. Incremental Cl with lateral position at 55-ft nose-to-tail separation at Mach 0.56 and an altitude of 25,000 ft.

greater for a formation airplane flying below theleading airplane, with the maximum value occurringat a vertical position of approximately –0.13 b. Notethat this point also corresponds with the point oftrimmed minimum drag.2 The vortex effect on therolling increment at the –0.13 b vertical position wassimilar to that at the level position. The vortex effectwas significantly weaker for all other verticalpositions. The pilots generally were able tocompensate for the vortex-induced rolling momentsincrements using less than 15 percent of their controlstick authority.

Incremental Yawing Moment

Starting at the same altitude and moving to the leftfrom behind and right of the leader, the trailing airplaneyawing moment increment increased in a nose-rightdirection to a maximum value when the wingtips werealigned (fig. 6). The vortex-induced yawing momentincrement at –0.25 b became nose-left at ashared-altitude vertical position. Pilots referred to theflying qualities at –0.25 b as “squirrelly” because boththe rolling and yawing moment increments reverseddirection with a small change in lateral position. At0.38 b wing overlap, the nose-left yawing momentincrement was eight times the value of the largest

nose-right yawing moment increment, but at a positiononly 15 ft further to the left.

Maintaining position was especially difficult inregions that had a large rate of change of the yawingmoment increment with lateral position (that is, greaterthan 0.25 b overlap). Additionally, the pilots noted thatthe variation in sign of yawing moment increment withvertical position (for example, Y = 0 in fig. 6) furthercomplicated the task. As noted in the rolling momentdata, the greatest effect was observed at the –0.13 bvertical position.

Incremental Pitching Moment

The trailing airplane experienced an increasingnosedown pitching moment increment as wingtipoverlap increased to 0.10 b at the level verticalposition (fig. 7). With more overlap, the pitchingmoment increment eventually became noseup. Thelargest nosedown effects were observed at the levelvertical position. Although the effect at a verticalposition of –0.13 b was similar to the effect at a levelposition, the pitching moment increment was morenoseup with wing overlap. These trends held true foralmost all vertical positions, and the vortex effectbecame more benign as the vertical distanceincreased. The pitching moment increment reversal


Figure 6. Incremental Cn with lateral position at 55-ft nose-to-tail separation at Mach 0.56 and an altitude of25,000 ft.

Figure 7. Incremental Cm with lateral position at 55-ft nose-to-tail separation at Mach 0.56 and an altitude of25,000 ft.

occurred at approximately 0.30 b wing overlap for thelevel and 0.13 b vertical positions. The pilotscommented that they did not have difficulty adaptingto the varying pitch effects.

Incremental Side Force

Starting at the same altitude and moving to the leftfrom behind and to the right of the leading airplane, thetrailing airplane encountered a side force increment tothe right (fig. 8). With increasing wing overlap, the sideforce increment steadily became more to the right,increasing rapidly as the wing overlap approached0.40 b. Like the moments, the greatest transients in sideforce increment were encountered when level or nearlylevel (±0.13 b) with the leading airplane. At positionswith significant wing overlap, the incremental side forcebecame very sensitive to position, most likely as a resultof the vortex interaction with the fuselage and verticaltails of the trailing airplane.

110-ft Nose-to-Tail Separation at the Subsonic Condition

The aircraft were flown again at the same flightcondition, but this time with a nose-to-tail separation of110 ft. Flight test results again are given for incrementalrolling, yawing, and pitching moments and side force.


The incremental rolling moments at 110-ftnose-to-tail separation had the same shape as those at55-ft, but the peak values tended to be less (fig. 9). As inthe previous condition, the vertical positions at altitudeswith or closely below the leading airplane received thegreatest effect. Of note is the variation in incrementalrolling moment for the –0.25 b vertical position. Afterpeaking at the 0.13 b lateral position, the right rollingmoment increment rapidly degraded to a much strongerleft rolling moment increment within 10 ft of lateralposition.


A few differences exist in yawing moment incrementbetween 55-ft and 110-ft nose-to-tail separation. Thepeak nose-right values for the 0.13 b and all low verticalpositions are significantly larger (positive) at 110-ft(fig. 10) than at 55-ft nose-to-tail separation. Thecorresponding peak values also occurred further inboardthan they did at 55-ft. The yawing moment increment atthe level vertical position did not change much from55-ft to 110-ft nose-to-tail separation. Also of note is theshape of the yawing moment increments with largewingtip overlap, as the values remained as variable asthose at 55-ft nose-to-tail separation.



Figure 8. Incremental CY with lateral position at 55-ft nose-to-tail separation at Mach 0.56 and an altitude of25,000 ft.

Figure 9. Incremental Cl with lateral position at 110-ft nose-to-tail separation at Mach 0.56 and an altitude of25,000 ft.



With more longitudinal distance between the aircraft,the vortex effects on the incremental pitching momentwere approximately the same (fig. 11). The vortex effecton the incremental pitching moment for the level and–0.13 b vertical positions is slightly less near the lateralposition for minimum drag, or Y = –0.13 b.


The vortex had a greater effect on the side forceincrement at 110-ft (fig. 12) than at 55-ft nose-to-tailseparation. For the lower vertical positions, the sideforce increment was consistently to the left over therange of lateral positions. Conversely, the side forceincrement for the higher vertical positions wasconsistently to the right over the same lateral range. Theexceptions were side force increments at the level and±0.13 b vertical positions. The side force increments atthese positions peaked in a leftward direction at the0.13 b lateral position, then increased steadily in arightward direction as wing overlap increased.

55-ft Nose-to-Tail Separation at the Transonic Condition

The aircraft were again flown with a nose-to-tailseparation of 55 ft, but this time at a transonic flight

condition of Mach 0.86 and an altitude of 36,000 ft. Thefollowing sections discuss flight test results forincremental rolling, yawing, and pitching moments andside force.


The rolling moment increment trends at the transoniccondition have the same shape as those at the subsoniccondition for 55-ft nose-to-tail separation, but the peakvalues for the level and –0.13 b vertical positions areslightly smaller (fig. 13). With significant wing overlap,the rolling moment increments at the transonicconditions were less transient than at the subsoniccondition. Overall, the vortex effects on the incrementalrolling moment were weaker at the transonic condition.


The trends of the incremental yawing moment at thetransonic condition and 55-ft nose-to-tail separation aresignificantly more uniform than those at the subsoniccondition (fig. 14). Of note are the –0.13 b and 0.50 bvertical positions. Their corresponding peak values mostclosely follow the trends at the subsonic condition. Thevortex effects on the incremental yawing moment wereweaker at the transonic condition.




Figure 12. Incremental CY with lateral position at 110-ft nose-to-tail separation at Mach 0.56 and an altitude of25,000 ft.


Figure 13. Incremental Cl with lateral position at 55-ft nose-to-tail separation at Mach 0.86 and an altitude of36,000 ft.



As with the subsonic condition, the vortex at thetransonic condition had the most effect on theincremental pitching moment at the level and ±0.13 bvertical positions (fig. 15), with slightly increased peaknosedown values for the latter. Although the effects onthe incremental pitching moment induced a nosedownattitude for almost all the test points at this condition,the effects of the vortex diminish with increased verticalseparation from the leading airplane.


The side force increment was much more benign atthis flight condition and nose-to-tail distance, andremained nearly zero for virtually all extreme high andlow vertical positions (fig. 16). The level, ±0.13 b, and0.25 b vertical positions yielded a rightward directionwith wing overlap, similar to the trends at the subsonicflight condition but not as severe.

110-ft Nose-to-Tail Separation at the Transonic Condition

The aircraft were flown again at the transoniccondition, but this time with a nose-to-tail separation of110 ft. Results again are discussed for incrementalrolling, yawing, and pitching moment and side force.


At 110-ft nose-to-tail separation, the vortex effecton the incremental rolling moment of the trailingairplane at the transonic condition (fig. 17) was verysimilar to that at the subsonic condition. For all highvertical positions, the peak right rolling momentincrements occurred further outboard than at thesubsonic condition. At the 0.25 b lateral position, thevortex had a greater effect on the 0.13 b and 0.25 bvertical positions at the transonic conditions than atthe subsonic condition. The greatest effects were atthe level and –0.13 b vertical positions.



15


Figure 16. Incremental

C

Y

with lateral position at 55-ft nose-to-tail separation at Mach 0.86 and an altitude of36,000 ft.


C

l



For the yawing moment increment, a few differencesexisted between the vortex effects at the subsonic andtransonic condition (110-ft nose-to-tail separation). Aswing overlap increased, the peak values at the level and±0.13 b vertical positions varied greatly and werecharacterized by steep nose-left gradients with morethan 20-percent wing overlap (fig. 18). Atapproximately 25-percent overlap, the yawing momentincrements at the 0.13 b and level vertical positionsreversed direction; this reversal is not evident from dataat any other flight condition or test point. The vortexeffects were weaker with significant wing overlap foralmost all vertical positions. Overall, the vortex had agreater effect on the yawing moment increment at thetransonic condition and 110-ft nose-to-tail separation.


Little difference exists between the two flightconditions for the pitching moment increment. Thetrends were the same at the transonic condition, but the

pitching moment increment for all vertical positions wasnosedown with less than 20 percent of wing overlap,and noseup as wing overlap increased (fig. 19). Of noteare the peak noseup values for the level and ±0.13 bvertical positions, as they are much closer in value thanat the subsonic condition.


Like the yawing moment increment, the side forceincrement caused by the vortex effect at the transoniccondition was much less uniform at the middle verticalpositions when compared with the results from thesubsonic condition (fig. 20). The vortex had the mosteffect on the level and 0.13 b vertical positions. Whenlevel with or 0.13 b above the leading airplane, the sideforce increment changed direction from left to right at25-percent wing overlap (fig. 20). This change might becaused by the vortex impingement on the fuselage andvertical tails. The influence on the other verticalpositions was slightly reduced.



17




C

Y


Concluding Remarks

In-flight measurements of the side force and momenton a trailing F/A-18 airplane induced by the wingtipvortex of a leading F/A-18 airplane were obtained.These flight tests demonstrated that nearly allvortex-induced effects are easily compensable by thepilot. The vortex mapping completed in this series offlight tests showed that the incremental side force andmoments have multiple peaks, and the sensitivity toposition in the formation changes with flight conditionand nose-to-tail distance.

The vortex-induced incremental side force andmoments first peaked at a lateral position of 13-percentwing overlap and vertical positions of level and13-percent below the leading airplane. These peakvortex effects were coincident with the position formaximum drag reduction, and the incremental force andmoments were more sensitive to formation positionfurther inboard of these peaks.

The flight data suggest the vortex effects withincreased longitudinal distance were weaker in pitchand roll, but stronger in yaw and side force. At 55-ftnose-to-tail separation, vortex effects at transonicconditions were weaker than those encountered atsubsonic conditions. At transonic conditions and 110-ftnose-to-tail separation, vortex effects were weaker inpitch and roll but stronger in yaw and side forcecompared with the effects at subsonic conditions.Although the vortex effects on the trailing airplane werefound to peak in the area of maximum drag reduction,these effects were well within the capability of the pilot;and therefore, the aerodynamic effects did not appear tojeopardize the success of a formation flight controllerdesign for this type of aircraft.

The fact that moment peaks corresponded with theareas of maximum drag reduction poses obvious issuesfor an autonomous flight control system. The controlsystem must be robust enough to handle the sensitivemoment changes that occur in the area of 13-percentwingtip overlap and 13-percent below the leadingairplane. The system must also be precise enough tomaintain position to the degree that all fuel savings arenot lost to position maintenance, trim drag, and constantthrottle changes.

Although the largest moments occurred withsignificant wing overlap, the control system mustremain stable in this very transient environment toachieve maximum fuel savings. A control system for apossible commercial application must also be able to

handle an inadvertent position change without injuringpassengers. This database can be used for further studyof autonomous formation flight control system designand flying quality analysis, and for determining ifaerodynamic prediction codes can reliably estimatethese effects for future applications.

References

1Weimerskirch, Henri, Julien Martin, YannickClerquin, Peggy Alexandre, and Sarka Jiraskova,“Energy Saving in Flight Formation,” Nature, vol. 413,Oct. 18, 2001, pp. 697–698.

2Vachon, M. Jake, Ronald J. Ray, Kimberly Ennix,and Kevin Walsh, “Measured Performance BenefitsDuring the Autonomous Formation Flight Program,” Tobe presented at the AIAA Atmospheric FlightMechanics Conference, AIAA-2002-4491, Aug. 2002.

3Hummel, D., “The Use of Aircraft Wakes to AchievePower Reductions in Formation Flight” AGARDCP-584, May 1996, pp. 36-1–36-13.

4Dunn, Ken, Calculated Aerodynamic Force andMoment Increments Induced on the Trailing Aircraft ina Two-Aircraft F-18 Formation, Boeing NorthAmerican, Inc., Long Beach, California, 1999.(Distribution restricted to AFF program participants.)

5Bever, Glenn, Peter Urschel and Curtis E. Hanson,Comparison of Relative Navigation Solutions AppliedBetween Two Aircraft, NASA/TM-2002-210728, July2002. Also presented at the AIAA First TechnicalConference and Workshop on Unmanned AerospaceVehicles, Systems, Technologies and Operations,Portsmouth, Virginia, 20-23 May 2002.

6Gainer, Thomas G. and Sherwood Hoffman,Summary of Transformation Equations and Equationsof Motion Used in Free-Flight and Wind-Tunnel DataReduction and Analysis, NASA SP-3070, 1972.

7Maine, Richard E. and Kenneth W. Iliff, Applicationof Parameter Estimation to Aircraft Stability andControl – The Output-Error Approach, NASA RP-1168,1986.


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706 55 00 E8 28 00 AFF

Jennifer L. Hansen and Brent R. Cobleigh

NASA Dryden Flight Research CenterP.O. Box 273Edwards, California 93523-0273

H-2502

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA/TM-2002-210732

Previous investigations into formation flight have shown the possibility for significant fuel savings throughdrag reduction. Using two F/A-18 aircraft, NASA Dryden Flight Research Center has investigated flyingaircraft in autonomous formation. Positioning the trailing airplane for best drag reduction requiresinvestigation of the wingtip vortex effects induced by the leading airplane. A full accounting of the vortexeffect on the trailing airplane is desired to validate vortex-effect prediction methods and provide a database forthe design of a formation flight autopilot. A recent flight phase has mapped the complete wingtip vortex effectsat two flight conditions with the trailing airplane at varying distances behind the leading one. Force andmoment data at Mach 0.56 and an altitude of 25,000 ft and Mach 0.86 and an altitude of 36,000 ft have beenobtained with 20, 55, 110, and 190 ft of longitudinal distance between the aircraft. The moments induced bythe vortex on the trailing airplane were well within the pilot’s ability to control. This report discusses the dataanalysis methods and vortex-induced effects on moments and side force. An assessment of the impact of thenonlinear vortex effects on the design of a formation autopilot is offered.

Formation, vortex, F-18, rolling, yawing 22

Unclassified Unclassified Unclassified Unlimited

August 2002 Technical Memorandum

Also presented at the AIAA Atmospheric Flight Mechanics Conference and Exhibit, Monterey, CA,August 5-8, 2002.

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This report is available at http://www.dfrc.nasa.gov/DTRS/

Documents

Induced Moment Effects of Formation Flight Using Two F/A-18 … · 2013. 6. 27. · vortex—the trailing airplane left wingtip is receiving most of the vortex-induced upwash. This