Flightlab Ground School 9. Rolling Dynamics

1 Bill Crawford: Ground School9. Rolling DynamicsCopyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab , 2009. All rights Training Purposes OnlyThe Aircraft in RollThe 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 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 Maneuvers and Flight Notes training guidedescribes piloting technique during aerobatic orunusual attitude Rolling maneuvers. Here theemphasis is on the general characteristics ofaircraft 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.

2 The resulting spanwiseasymmetry produces a Rolling 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 Naval Test Pilot School Flight TestManual: Fixed Wing Stability and Control,USNTPS-FTM-No. 103, 1997. p. 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.

3 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 Helix Angle Resultant lift Resultant lift Path of down-going tip: increases. Path of up-going tip: decreases. Figure 1 Roll Damping, Clp Yaw due to Roll Rate, Cnp Flight velocity Roll Direction Change in caused by Rolling motion produces an opposite damping force, Clp. Resultant drag yaws wing backward. Resultant thrust yaws wing forward. Rolling DynamicsBill Crawford: Yaw, Cn a Aerodynamic coupling effects keep Rolling frombeing a one-degree-of-freedom moments come with yawing momentsattached, and those yawing moments affect drag increases when an aileron goesdown, decreases when an aileron goes up.

4 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 rudder deflection necessary to handleadverse yaw depends on the ratio of yawmoment to roll moment the ailerons the ratio is basically a function of theaileron system design, it increases withcoefficient of lift, CL.

5 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 or Frise ailerons, initially designedto reduce aileron forces, also reduce adverse yawby increasing the drag of the up-going 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 is also important. Partial-spanflaps cause an aircraft to fly at a more nose-downangle for a given overall coefficient of lift. As aresult, the aileron portion of the wingexperiences a relative washout (leading edgedown) and generates a lower local coefficient oflift than when the flaps are up.

6 That lower localcoefficient translates into less adverse yaw. Flapsalso reduce dihedral effect, so the sideslip thatdoes occur has less effect on are generally thought to produceproverse, roll-direction yaw, but they can causeadverse yaw. Spoilers increase profile drag. Theyalso decrease induced drag, since they kill 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 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.

7 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 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.

8 The change inpressure pattern reduces the lift gained from flapRolling DynamicsBill Crawford: and causes the aircraft to symmetrically, the spoilers provideaerodynamic 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 ). 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 CoordinationUsually, 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 ve defined coordination during roll in termsof keeping the velocity vector on the plane ofsymmetry.

9 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 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 gyroscopic precession of the propellercreates a force parallel to the vertical turn , precession causes the nose to moveperpendicularly to the horizon, regardless ofbank angle.

10 For a clockwise propeller as seenfrom the rear, that means nose down turningright, 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 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 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 bank increases, pitch rateincreases, yaw ratearound turnaxisPitch rateYaw rateFigure 2 Relative Yaw andPitch TurnRolling DynamicsBill Crawford: 3 Coordinated Yaw RateBall 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 (sine ) = Vr Stepping on the ball controls yaw angle (inradians)Yaw rate, rAcceleration due to gravity, g,( ft/sec2) times the sine ofthe bank angle (radians) g(sine )Velocity (ft/sec) times yawrate (radians) VrgLeft.