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Flightlab Ground School 7. Longitudinal Dynamic Stability

Bill Crawford: Ground School7. Longitudinal Dynamic StabilityCopyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab , 2009. All rights Training Purposes OnlyIntroduction to StabilityStability is the general term for the tendency ofan object to return to equilibrium if Stability is an object s initial tendencyupon displacement. An object with an initialtendency to return to equilibrium is said to havepositive static Stability . For those blessed with aconventional pilot s education, the concept ofstability normally evokes the textbook image ofa marble rolling around in something like ateacup, as shown in Figure airplane can t be trimmed unless it haslongitudinal (around the y axis) staticstability in other words, unless pitching forcestending to equilibrium are pr

Longitudinal Dynamic Stability Bill Crawford: WWW.FLIGHTLAB.NET 7.3 the stick. Figure 4 shows the variation in angle of attack, α, over time. The aircraft quickly

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Transcription of Flightlab Ground School 7. Longitudinal Dynamic Stability

1 Bill Crawford: Ground School7. Longitudinal Dynamic StabilityCopyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab , 2009. All rights Training Purposes OnlyIntroduction to StabilityStability is the general term for the tendency ofan object to return to equilibrium if Stability is an object s initial tendencyupon displacement. An object with an initialtendency to return to equilibrium is said to havepositive static Stability . For those blessed with aconventional pilot s education, the concept ofstability normally evokes the textbook image ofa marble rolling around in something like ateacup, as shown in Figure airplane can t be trimmed unless it haslongitudinal (around the y axis) staticstability in other words, unless pitching forcestending to equilibrium are present.

2 But thegreater an aircraft s static Stability (thus thegreater the forces tending to equilibrium) themore resistant the aircraft is to the displacementrequired in maneuvering. For a given aircraft, themost important factor in determininglongitudinal static Stability is the aft reduces static Stability , our real subject here, refers tothe time history that transpires followingdisplacement from equilibrium, as shown inFigures 1and can either have inherent aerodynamicstability (the typical case), or de-facto Stability ,in which Stability requirements are met with theaid of a control system augmented with sensorsand feedback.

3 For example, in order to achievemaximum maneuverability, the F-18 lacksinherent Stability , and can t be flown withoutsome operational brainpower on board inaddition to the pilot. The Boeing 777 has relaxedinherent Longitudinal static Stability , whichproduces efficiencies in cruise from a morerearward and a physically lighter tailstructure than otherwise possible. Boeingtransport aircraft have conventional downward-lifting tails that, like all such tails, in effect addweight to the aircraft by virtue of the down-lift they generate (and also drag, the by-product ofthat lift).

4 The main wing has to produceadditional lift in compensation, and consequentlyproduces more drag itself, which costs money atthe gas truck. Moving the aft reduces thenecessary down-force. The 777 s digital flightcomputers make up for the resulting longitudinalstability deficit but the aircraft still has to havesufficient inherent Stability to be flown safelyand landed should the digital augmentation gobust. The monster Airbus A380 employs an aftcenter of gravity for the same reason. It canpump fuel aft to shift the : Quick to return, hard to displace Neutral: Stays put Negative: Quick to displace, hard to return Figure 1 Static Stability Positive: Slower to return, easier to displace Negative: Slower to displace, easier to return Time Displacement Time Displacement Time Displacement Time Displacement Longitudinal Dynamic StabilityBill Crawford: Stability : Short Period andPhugoidFigure 3 illustrates positive Longitudinal dynamicstability.

5 A series of damped oscillations ofconstant period, or frequency, and diminishingamplitude, that bring the aircraft back to thetrimmed condition after a is time per cycle. Frequency, which isinversely proportional to period, is cycles perunit of time. Amplitude is the difference betweenthe crest or the trough and the originalequilibrium is the force that decreases theamplitude of the oscillation with each cycle. Thedamping ratio, , is the time for one cycledivided by the total time it takes for theoscillation to subside. The higher the dampingratio, the more quickly the motion defines much about the character of anaircraft.

6 If damping is too high, an aircraft mayseem sluggish in response to control inputs. Ifdamping is too low, turbulence or control inputscan excite the aircraft too readily; its behaviorappears are two modes of pitch oscillation: theheavily damped short period mode (dampingratio about or greater), followed by thelightly damped, and more familiar, long period,phugoid mode. When you maneuver an airplanein pitch by moving the stick forward or back,you initially excite and essentially just ridethrough the short period mode. If you werethen to let go or to return the stick back to thetrim position, the aircraft would enter thephugoid mode.

7 Instead, you normally hold thepressures necessary to prevent a phugoid PeriodThe short period mode is excited by a change inangle of attack. The change could be caused by asudden gust or by a Longitudinal displacement ofDisplacement from Trim Positive Static Stability and Positive Dynamic Stability Figure 2 Dynamic Stability Positive Static Stability and Neutral Dynamic Stability Positive Static Stability and Negative Dynamic Stability Time Figure 3 Positive Dynamic Stability Displacement Time Period Amplitude Period/Time to subside = damping ratio, Time to subside Equilibrium Longitudinal Dynamic StabilityBill Crawford: stick.

8 Figure 4 shows the variation in angle ofattack, , over time. The aircraft quicklyovershoots and recovers its original angle ofattack, or its new angle of attack in the case of anintentional pilot input and a new stick motion of the tail causes most of thedamping, although other parts of the aircraft cancontribute to damping (or to oscillation). There snegligible change in altitude or airspeed by thetime the mode subsides. During the short periodoscillation the aircraft pitches around its damping of the short period is importantbecause catastrophic flight loads could quicklybuild from a divergent oscillation suddenly theairplane has oscillated into parts.

9 The shortperiod mode is also an area in which pilot-induced-oscillations, PIO, can occur, because thetypical lag time in pilot response is about thesame as the mode s period (approximately 1-2seconds). As a result, by the time a pilotresponds to an oscillation his control input is outof phase, and he ends up reinforcing rather thancounteracting the motion he s trying to some point during our flights, we can performa frequency sweep with the stick to try to isolatethe aircraft s short period natural frequency, n.(As a child you pumped a swing in rhythm withits natural frequency to make it go higher andterrify your mother.)

10 We ll do this by moving thestick back and forth over a constant deflectionrange of perhaps three or four inches, but fasterand faster until we find the input frequency thatplaces us 90 degrees out of phase meaning thatthe stick is either forward or back when the noseis on the horizon (although it can be hard to tell).We re then at the undamped short period naturalfrequency undamped because we re driving itwith the stick. Then we ll abruptly return thestick to neutral when the aircraft is at its trimattitude, and observe the damping of the shortperiod oscillation.


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