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Flightlab Ground School9. Rolling Dynamics

Copyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab, 2009. All rights reserved.For Training Purposes Only

The Aircraft in Roll

The dynamics of an aircraft in roll aresurprisingly complex, given the apparentsimplicity of the maneuver. Of course, oneperson’s complexity is just another persongetting started. At the U.S. Navy Test PilotSchool, for instance, “The classic roll mode is aheavily damped, first order, non-oscillatorymode of motion manifested in a build-up of rollrate to a steady state value for a given lateralcontrol input.”1 Well, ok, that sounds right.

Our Maneuvers and Flight Notes training guidedescribes piloting technique during aerobatic orunusual attitude rolling maneuvers. Here theemphasis is on the general characteristics ofaircraft response.

A roll starts with the creation of an asymmetriclift distribution along the wingspan. In the caseof aileron roll control, deflecting an aileron downincreases wing camber and coefficient of lift;raising the opposite aileron reduces camber andcoefficient of lift. The resulting spanwiseasymmetry produces a rolling moment.

As the aircraft begins to roll in response to themoment produced by the ailerons, the liftdistribution again begins to change. The rollingmotion induces an angle of attack increase on thedown-going wing, and an angle of attackdecrease on the up-going wing (Figure 1). Thiscreates an opposing aerodynamic moment, calledroll damping (or rolling moment due to roll rate,Clp). Roll damping increases with roll rate (andvaries with other factors we’ll get to). When thedamping moment produced by the roll rate risesto equal the opposing moment produced by theailerons, the roll rate becomes constant.

1 U.S. Naval Test Pilot School Flight TestManual: Fixed Wing Stability and Control,USNTPS-FTM-No. 103, 1997. p. 5.55.

In Figure 1 you can see that as the airplane rolls,the lift vector tilts to accommodate itself to thenew direction of the relative wind, creating newvectors of thrust and drag. As a result, the rollingmotion produces adverse yaw all by itself, ayawing moment that goes away when the rollstops. This yaw due to roll rate, Cnp, is inaddition to the adverse yaw created by thedisplaced ailerons, and increases with coefficientof lift. Depending on wing planform, at aspectratios above 6 or so, adverse yaw due to roll rateactually becomes more significant than that dueto aileron deflection.

Roll Helix Angle

Resultant lift

Resultant lift

Path of down-going tip: α increases.

Path of up-going tip: α decreases.

Figure 1 Roll Damping, Clp Yaw due to Roll Rate, Cnp

Flight velocity

Roll Direction

Change in α caused by rolling motion produces an opposite damping force, Clp.

Resultant drag yaws wing backward.

Resultant thrust yaws wing forward.

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Adverse Yaw, Cnδa

Aerodynamic coupling effects keep rolling frombeing a one-degree-of-freedom proposition.Rolling moments come with yawing momentsattached, and those yawing moments affect rollbehavior.

Induced drag increases when an aileron goesdown, decreases when an aileron goes up. Theresult is usually an adverse yawing moment,opposite the direction of roll. In the absence of asufficient counteracting yaw moment—suppliedin part by the aircraft’s inherent directionalstability, in part by aileron design, and in theremainder by coordinated rudder—the aircraftwill begin to sideslip. The velocity vector willshift from the plane of symmetry toward the rolldirection if too little coordinating rudder isapplied, and shift opposite the roll direction ifthe rudder gets too emphatic an in-turn boot. In aperfectly coordinated, ball-centered roll and turn,with adverse yaw properly countered by rudderdeflection, the “instantaneous” velocity vectorremains on the plane of symmetry, as Figure 2describes.

The rudder deflection necessary to handleadverse yaw depends on the ratio of yawmoment to roll moment the ailerons produce.While the ratio is basically a function of theaileron system design, it increases withcoefficient of lift, CL. This means that asairspeed goes down, the need for ruddercoordination becomes greater. The nature ofinduced drag rise at high angles of attack is themajor reason, since induced drag increases as thesquare of the coefficient of lift. As the drag curvebecomes steeper, a given aileron deflectionproduces a greater difference in induced dragacross the span, and the yaw/roll ratio increases.Differential or Frise ailerons, initially designedto reduce aileron forces, also reduce adverse yawby increasing the drag of the up-going aileron.

Another factor is the reduction in directionalstability caused by the disrupted fuselage wake atangles of attack approaching stall. Becauseenergy is removed from the free stream, morerudder deflection is needed as weathercockstability goes down in the tired-out air.

Configuration is also important. Partial-spanflaps cause an aircraft to fly at a more nose-downangle for a given overall coefficient of lift. As a

result, the aileron portion of the wingexperiences a relative washout (leading edgedown) and generates a lower local coefficient oflift than when the flaps are up. That lower localcoefficient translates into less adverse yaw. Flapsalso reduce dihedral effect, so the sideslip thatdoes occur has less effect on roll.

Spoilers

Spoilers are generally thought to produceproverse, roll-direction yaw, but they can causeadverse yaw. Spoilers increase profile drag. Theyalso decrease induced drag, since they kill lift.When the increase in profile drag predominates,as it does at high speed, spoilers can generateproverse yaw. At low speeds, when induced dragis more important, they can generate adverseyaw, since the induced drag on the wing goingdown, the one with the deflected spoiler killinglift, is less than on the wing going up, where thespoiler remains tucked away.

Spoilers are useful in situations when aeroelasticaileron reversal could have been a problem (B-52, and just about all of the swept-wing, highaspect ratio transports that followed), or whenit’s necessary to extend the wing area availablefor flaps. They have an advantage over aileronsof producing powerful rolling moments at highangles of attack, but the disadvantage of lessermoments at low angles. The classic problem withspoilers is a possible nonlinear response as theirlocation moves forward on the wing. Smalldeflections may generate no roll, or even atemporary reversed roll response. (As the spoilerfirst rises, the tripped airflow can reattach to thewing. This results in an effective increase incamber and therefore in lift. Spoiler movementhas to be nonlinear with control wheel or stickmovement—so that the spoilers can quickly popup high enough to defeat any tendency for theairflow to reattach.) Many designs use spoilersand ailerons in combination, with the aileronsproviding both rolling moment and control feel,and a possible way of overcoming nonlinearspoiler response.

If you’re stuck in coach, the most entertainingwindow seat on a Boeing is just back of thetrailing edge, where you can watch the slot-lipspoilers being used for bank control when theflaps are extended. When the spoilers rise, theslots above the flaps open up. The change inpressure pattern reduces the lift gained from flap

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deployment and causes the aircraft to roll.Deployed symmetrically, the spoilers provideaerodynamic braking.

A pilot who looks up to find himself flyinginverted in a spoiler-equipped aircraft has aquandary, since spoilers become more effectiveat higher coefficients of lift (higher α). Does thatmean the pilot should pull while inverted, toincrease roll response, at the risk of altitude lossand airspeed gain from the resulting nose-lowattitude? It’s hard to find someone with asatisfactory answer. Aggressive use of the ruddermight be warranted to help roll the aircraft usingdihedral effect and roll due to yaw rate.

Turn Coordination

Usually, we roll in order to turn. Steep turnsdeserve to be regarded as unusual attitudes, notjust because of the high bank angles but also thehigh-gain response those angles require whenyou’re trying to be perfect. The concentrationlevel goes up when you fly a steep (45-degreeplus), coordinated turn, while holding altitude.

We’ve defined coordination during roll in termsof keeping the velocity vector on the plane ofsymmetry. While the ailerons are deflected, thatmeans using rudder to correct for adverse yawand yaw due to roll rate—companion phenomenawhose relative magnitudes can be difficult tofigure out, but then you don’t have to figure: justpush the rudder to center the ball.

Once the bank is established, the ailerons moveto the position necessary to maintain the bankangle. Rudder into the turn is often needed tocounteract yaw damping, Cnr, caused by thefuselage and tail resisting the yaw rate and by theoutside wing moving faster than the inside wingand producing more drag. That might be thepredicament shown in the center aircraft at thebottom of Figure 3. An over-banking tendencyrequires aileron deflection against theturn—possibly causing proverse yaw (since theinside aileron is down), which of course modifiesthe rudder requirement.

The gyroscopic precession of the propellercreates a force parallel to the vertical turn axis.Therefore, precession causes the nose to moveperpendicularly to the horizon, regardless ofbank angle. For a clockwise propeller as seenfrom the rear, that means nose down turning

right, nose up turning left. At high bank angles,when the aircraft’s y-axis approaches alignmentwith the turn axis, more rudder deflection may beneeded to counter precession. Step on the ball.

Banked turns are combinations of yaw and pitch(Figure 2). Coordination (keeping the velocityvector on the plane of symmetry) meansestablishing both the yaw rate and the pitch rateappropriate for the bank angle.

As bank angle increases, pitch rate becomesincreasingly sensitive. Pitch rate controls loadfactor, and for a constant-altitude turn, therequired load factor goes up exponentially withbank angle. Getting the pitch rate/load factorright at high bank angles is difficult because theload requirements change so rapidly with evensmall changes in bank angle. Because the loadfactor goes up exponentially, so do the stickforces, at least in aircraft with reversible elevatorcontrols.

As bank increases, pitch rateincreases, yaw ratedecreases.

Turn ratearound turnaxis

Pitch rate

Yaw rate

Figure 2Relative Yaw andPitch Rates.Constant-Altitude Turn

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Figure 3Coordinated Yaw Rate

Ball stays centered when the acceleration toward the outsideof the turn due to yaw rate and velocity equals the accelerationto the inside due to bank angle and gravity.

32.2 (sine φ) = Vr

“Stepping on the ball” controls yaw rate.

Bank angle φ (inradians)

Yaw rate, r

Acceleration due to gravity, g,(32.2 ft/sec2) times the sine ofthe bank angle (radians)

g(sine φ)

Velocity (ft/sec) times yawrate (radians)

Vr

g

Left. Coordinatedturn, velocity vectoron the plane ofsymmetry

x-axis

+β-β

In a turn thevelocity vector(arrow) is tangentto the flight path atany instant.

Flight path

Right. Too much rudder: Too muchyaw rate. Aircraft slips to the right ofthe plane of symmetry. Turn radiusdecreases because resulting sideforce caused by the relative windcoming from the right of the fuselagepushes aircraft toward the center ofthe turn.

Center. Too little rudder: Too little yaw rate. Aircraft slips to the leftof the plane of symmetry. Turn radius increases because resultingside force caused by the relative wind coming from the left of thefuselage pushes aircraft away from the center of the turn.

Note that for a given bank angle,coordination requires that as velocitydecreases yaw rate must increase.

x-axis

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Roll Helix Angle

As an airplane rolls, its wingtips follow a helicalpath through the sky, like the shape of astretched spring. You see the helix at airshowswhen the pilot fires up the tip smoke. The anglebetween the resultant flight path of the wingtipand flight path of the aircraft is called the rollhelix angle (Figure 4). The roll helix angleincreases with increasing aileron displacement.Maximum attainable helix angle depends onaircraft design and mission. But on a givenaircraft a given aileron deflection always buildsto a given roll helix angle.

For any aileron deflection (roll helix angle),coordinated roll rate, p, varies directly with trueairspeed. “Coordinated” means there’s nosideslip affecting the rate. For the statement to betrue, there must also be no aero-elastic effects(wing bending caused by aileron deflection athigh speeds).

As the aircraft’s forward velocity increases, itwill maintain the helix angle—by virtue ofrolling faster. As a result, for a given helix anglean aircraft will complete a roll in the sameforward distance traveled, regardless of airspeed.Slippage aside, the helix angle is like the pitch of

a screw of given length. Regardless of rpm, ittakes the same number of turns to fasten it down.

When you know the helix angle, wingspan, andaircraft velocity, you can solve the formula inFigure 4 for roll rate. The helix angle provides away of establishing minimum acceptable rollrates for different aircraft (about 0.09 minimumfor fighters; 0.07 for transports). But it doesn’taccount for roll inertia, so it’s only a partialdescription of rolling character and is no longerused as a certification or acceptance measure.

Timed bank changes are used instead. TheFAA’s requirements are listed in FAR Parts23.157 and 25.147 (e).

Figure 4Roll Helix Angle

At a given helix angle,the distance to completea roll remains constantregardless of forwardspeed.

Roll HelixAngle ( )( )

( ) Vpb2sec. per. ft.in velocity 2

ft.in wingspan secondper radiansin rate rollanglehelix Roll ==

The helix angle is the ratio of tip velocity in roll,pb/2, to the aircraft’s forward velocity, V.

2pb

b

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Roll Acceleration, Time Constant

Roll acceleration (and thus how quickly theaircraft reaches the final roll rate for a givenaileron deflection) depends on how much rollingmoment the ailerons produce versus the momentof inertia about the roll axis the ailerons have toovercome. We’re assuming the necessary ruddercoordination, and thus no inadvertent momentsdue to sideslip:

Rolling momentdue to ailerondeflection = Rolling accelerationMoment of inertiaabout the roll axis

The moment of inertia about the roll axis, Ixx,depends on how mass is distributed in theaircraft. If there’s lots of fuel in the wings, someengines hanging out there, and maybe full tiptanks, roll inertia will be higher than if most ofthe mass were confined to the aircraft’s fuselage.

Figure 5 shows the effect of inertia on rollacceleration and deceleration. Span, wingplanform, and the rolling moment due to theaileron “step” deflection are the same for bothcurves. Only the moment of inertia, Ixx, isdifferent. Notice the difference in initial slopebetween the two curves, and how maximum rollacceleration (not rate) happens at the initialcontrol input, before damping forces have achance to build. Notice the difference in the timerequired for reaching the steady rate in the two

inertia cases, and for the roll to stop when theailerons are neutralized.The roll mode time constant, τR, is the time ittakes to achieve 63.2 percent of the final rollrate, in seconds, following step input. If youcould maintain the initial acceleration (i.e. nodamping to slow things down) the airplanewould reach the target roll rate in only 63.2percent of the time actually required. In theory,the rolling aircraft “remembers” this constant.Because of damping, it takes the same amount oftime to achieve the next 63.2 percent of the finalroll rate, then the next 63.2 percent after that, andso on. At least theoretically, the asymptotic curvekeeps trying but never flattens out. After fivetime constants the roll rate will be at 99.5% ofthe final value. Close enough.

The greater the moment of inertia versus theaileron authority, the longer the time constantwill be. Two aircraft may have the samemaximum roll rate, but the one with the greatertime constant will take longer getting to it andlonger to stop rolling when the ailerons arereturned to neutral. Therefore inertiacharacteristics, and not just maximum roll rates,need to be taken into account when comparingthe rolling performance of different aircraft. In agiven aircraft, roll rate can magically increasewith increasing change of angle. Roll ratemeasured from a 45-degree bank to an opposite45-degree bank may be lower than if measuredfrom, say, 60 degrees to 60 degrees. That’sbecause the time spent accelerating is a smallerfraction of the total.

Low inertia

High inertia

“Steady” rollrate

63.2%

+

0

-

Slope indicates initialroll acceleration.

High inertia

Low inertia

Time

Roll Mode Time Constants, τR

Ailerons deflected:step input

Figure 5Time to ReachRoll Rate

Ailerons returnedto neutral

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It’s difficult for a pilot to measure the timeconstant without special equipment, becausethere’s no easy visual reference on roll initiation,and it’s usually less than a second (andimperceptible for a fast roller). Since the timeconstant is the same to stop a roll as it is to startone, and the visual references are clearer, youcan try to measure the time to stop instead. (Ithelps if there’s minimal freeplay in the controlsystem.) Begin with a 45-degree bank angle andmake a coordinated roll to upright using animmediate, step aileron deflection (the amount ofdeflection doesn’t matter, since the time constantis the same, see Figure 6). Hold that aileron inputuntil the wings become level with the horizon,then instantly neutralize the controls and watchfor any additional roll. 63.2 percent of the timeit takes for any remaining roll to subside is thetime constant due to roll inertia. You might thinkthat the more aileron you use and the faster youroll to upright the greater your overshoot pastlevel. But it doesn’t work that way, because thefaster you roll the greater the aerodynamicdamping available to stop things when youneutralize the controls.

The idea that an aircraft that accelerates quicklyinto a roll can stop just as quickly takes aerobaticstudents by surprise. In performing 360-degreerolls, most will start out leading the recovery bytoo much and stopping short of wings-level.(That’s normal, but students who over-roll andstop past wings level are obviously behind theaircraft.)

At a given altitude, roll mode time constantvaries inversely with true airspeed (TAS). That’strue to experience—the faster you go, thequicker you can accelerate into a roll. But at aconstant TAS, the time constant increases withaltitude. The air is less dense, and for a givenTAS there’s less dynamic pressure available toovercome inertia. There’s also less damping asaltitude increases, so it takes longer for the rollrate to settle.

Airplanes with noticeable time constants (ascaused by high roll inertia and/or low rolldamping, and limited aileron control power)require that pilots learn to “shape” their controlinputs, first using large initial deflections formaximum acceleration and then reducing thedeflection once the desired rate is achieved. Thenthey have to check the airplane’s roll motionwith opposite, anticipatory aileron inputs whencapturing a bank angle or returning to level

flight. The wheel or stick becomes anacceleration controller. Pilots can adapt, but theworkload increases. Because of its huge x-axisroll inertia, the B-52 has this kind of response.

On the other hand, aircraft with short timeconstants tend to feel quick and responsive.Because they accelerate quickly, the stickbecomes essentially a rate controller. Withinbounds, that’s what pilots prefer.

The FARs don’t specify time constantrequirements, but, for the military, MIL-STD-1797A 4.5.1.1 sets the maximum τR between 1and 1.4 seconds, depending on aircraft missionand phase of flight.

In an aerobatic aircraft, because of the rapid rollacceleration, you can sometimes get theimpression that the aircraft’s steady roll rate isfaster than it really is. We feel acceleration muchmore profoundly than rate, especially as passiverecipients. Studies have shown that pilots tend toestimate ultimate roll rate based on initialacceleration. One of the malicious joys ofinstructing from the backseat in a true high-performance tandem aerobatic trainer iswatching your student’s head snap sidewayswhen you demonstrate maximum accelerationpoint rolls. A given roll rate can seem muchfaster (and not such great fun) when you’re thepilot-not-flying, because you’re not performingthe initiating control inputs that prepare the restof your body for the ride.

Identical time to reach steady roll rate following step input

Time constant at a given airspeed

Time

Rol

l Rat

e

Full aileron deflection

2/3 deflection

1/3 deflection

Figure 6 Time to Reach Roll Rate

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Roll Rate

Figure 6 shows a time history, from the initialacceleration to the point where acceleration stopsand a constant rate is achieved, for rolls usingthree different aileron instantaneous stepdeflections at the same airspeed. One thing itreveals is that at a given airspeed it doesn’t takean airplane any longer to reach its highest, full-deflection roll rate than it does to reach lesserrates using lower deflections.

Figure 7 shows the effects of sideslip on roll rate.Roll moments caused by sideslip are a functionof effective dihedral and of both sideslip angleand angle of attack. (See Flightlab GroundSchool, Lateral/Directional Stability) The twodashed lines in Figure 7 show an uncoordinated,aileron-only bank, with adverse yaw allowed todo its worst. In a laterally stable aircraft, sideslipproduced by adverse yaw reduces roll ratebecause of the opposing rolling moment fromdihedral effect. Rolling in one direction whileyawing in another can also set off Dutch rolloscillation, seen in the figure as an oscillation inroll rate over time. Note that the worse case,when rolling without coordinating rudder, comeswhen dihedral effect is high and directionalstability is low.

For geometrically similar airplanes, roll ratevaries inversely with span (cutting the span inhalf gives twice the rate). The reason is that rolldamping varies directly with span. At any givenroll rate, the longer the span the faster the

wingtip moves, and therefore the greater thedamping caused by the larger roll-inducedchange in angle of attack. This explains the shortwingspans of aircraft designed to roll fast.

Roll damping is also an inverse function of trueairspeed. Because TAS increases with altitude,roll damping decreases as you climb—as doesdirectional and longitudinal damping. (SeeDamping versus Altitude in “LongitudinalManeuvering Stability.”)

At high angles of attack approaching CLmax, rolldamping begins to decrease as the wing’s CLcurve begins to level out (Figure 8). Turbulenceor yaw rate causing a wing to drop can then forcethe angle of attack of the tip section past thepoint of stall. Now the coefficient of lift, insteadof rising as it normally does as the wingdescends, starts falling down the post-stall sideof the lift curve, and damping disappears. Thetransformation of damping into autorotation isthe essence of spin departure. Quickly reducingthe angle of attack usually restores roll damping,and lateral control, before a real spin can getunderway.

Muscle Versus Roll Rate

Aileron systems are designed primarily in termsof the lateral control required at speeds nearstall—a function of aileron size. At high speeds,roll rate is a function of the available ailerondeflection.

(Directional Stability > Dihedral Effect)

(Dihedral Effect > Directional Stability)

Coordinated rudder resulting in roll only

Insufficient rudder resulting in decreased roll moment caused by sidesliptoward roll direction: Roll rate oscillates due to Dutch roll response.

Excess rudder resulting in increased roll moment caused by sideslip opposite roll direction

Time

Figure 7Dihedral Effect,Rudder use,Roll rate

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As mentioned earlier, for a given ailerondeflection (thus roll helix angle), coordinatedroll rate, p, varies directly with true airspeed.Roll rate also depends on how big a gorilla isdriving. In an aircraft without boosted orpowered flight controls, the control force felt bythe pilot increases as the square of the trueairspeed. As a result, aileron forces go up fasterthan roll rates, and ultimately the force requiredfor maximum deflection can exceed the pilot’smuscle power.

For example, a Spitfire had a maximum roll rateof around 105 degrees per second at about 175knots EAS. A clipped-wing Spitfire made it toabout 150 degrees per second at the same speed.A P-51B Mustang’s roll rate peaked at onlyabout 90 degrees per second at around 260 knotsEAS. When these airplanes went slower,maximum-performance roll rates decreased dueto the slower TAS. When they went faster, rollrates decreased because the pilot couldn’t fullydeflect the controls, as Figure 9 illustrates. Theroll rate of the Japanese Zero went down

drastically at high speed because of aileronreversal caused by wing twisting (see below).

By way of comparison, if a contemporary, high-performance aircraft designed for top aerobaticcompetition rolls less than 360 degrees persecond, at maximum sustained level flight speed,it’s considered a slug.

Angle of Attack

In the roll-dampingregion, when thewing rolls downand α increases, liftand dampingincrease.

On the backside of thecurve, in the autorotationregion, when the wing rollsdown and α increases, liftdecreases and dampingdisappears.

Figure 8Loss of RollDamping past Stall

Damping begins to decreaseas slope changes aroundCLmax.

Max force pilot can sustainwith reversible controls

Fa ∼ EAS2

Pilot maintains max force butdeflection starts going down asairspeed increases.

Symbol ∼ meansproportional.

p ∼ TAS

P∼ 1/TAS

Roll rate decreases withreversible controls becausepilot can’t hold deflection.

Airspeed

Airspeed

Airspeed

Airspeed for max roll ratewith reversible controls

Figure 9Roll Rates versusAirspeed, Muscle-Powered ReversibleControls

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In testing for certification under FAR Part23.157, aircraft are required to roll from a thirty-degree banked turn to a thirty-degree bank in theopposite direction within time limits specifiedfor aircraft weight and configuration. Under FARPart 25.147 (e), “Lateral control must be enoughat any speed up to VFC/MFC to provide a peakroll rate necessary for safety, without excessivecontrol forces or travel.”

Aeroelastic Aileron Reversal

At high speeds, aeroelastic deformation also putsa cap on roll rates. The down aileron produces atwisting moment on the wing, which forces theleading edge to deflect downward, reducing theangle of attack (Figure 10). This reduces lift andconsequently rolling moment. Roll rate thenstarts going down and at a certain speed, VR,when the decrease in lift due to twisting equalsthe increase in lift due to aileron deflection, theailerons will no longer create a normal rollingmoment. Beyond this speed “aileron reversal”occurs. A down-going aileron then produces adown-going wing.

One of the cures for aileron reversal, notsurprisingly, is to increase the torsional stiffnessof the wing (at the expense of added weight). Onswept wings it’s necessary to increase thebending stiffness because the geometry of aswept wing causes it to twist as it bends. Movingthe ailerons inboard or extending their spaninboard also helps raise VR on a swept wing.Spoilers are another option, as mentioned.

Comparing Roll Performance

You first need to specify flight regime in order tomake useful roll performance comparisonsbetween our aerobatic training aircraft and largertransports—for example the roll rates atapproach speed and configuration versus cruise.Because of yaw/roll coupling, you also need toconsider sideslip and yaw rate contributionsbased on aircraft dynamics and pilot technique.The question is complicated by all of thederivatives that have to be plugged in.

The people who create simulation algorithmshave the derivatives plugged in. Comparisons ofroll rates (and control forces) made between youraircraft and our trainers based on theperformance of your aircraft’s simulator should

be useful—especially if the simulation occurswithin the boundaries of the angle of attack, α,and sideslip, β, envelopes supported by youraircraft manufacturer’s flight-test data. Rollsthrough 360 degrees can be modeled reliably, aslong as they happen within α/β boundaries, evenif the subject aircraft has never been tested in fullrolls itself. Combined high angles of attack andhigh sideslip angles may not be well supported,however, because they’re usually not flight-tested for aircraft not receiving spin certification,and their nonlinear effects make reliablemodeling difficult. During the unusual-attitudeportion of your simulator training (if indeedthere is such), ask to observe roll rates atdifferent airspeeds, configurations, andaltitudes—and especially with differentcontributions from the rudder. Then, assumingyou passed the check and won’t be called atroublemaker, go ahead and ask where the testdata stops and the extrapolation begins.

Figure 10Aileron Reversal

Aileron deflection causeswing to twist. Roll momentreverses.