Aircraft Stability and ControlAE 1350Lecture Notes #11

We will studyWhat do we mean by aircraft stability and control?Static and Dynamic StabilityLongitudinal, lateral and roll stability Necessary Conditions for Longitudinal stabilityStability MarginRelaxed Stability Margin

A system is said to be stable if it can recover from small disturbances that affect its operation.A cone restingon its base isstable.UnstableNeutrally stable.Assumes new positioncaused by the disturbance.

An aircraft is subjected to some disturbance, say a gust, a cross wind or turbulenceUnexpected GustWill it recover automatically, without pilots intervention, and resume its original direction of flight?If so, the aircraft is longitudinally stable.Freestream

Longitudinal Static StabilityTimeAlphaAircraft is insteady level flightGust pitches the nose upThe initial tendency of the vehicleis to bring the nose down. If so,The aircraft is statically stable.AlphaTimeThe initial tendency of the vehicle is to bringthe nose up. If so,The aircraft is statically unstable.

Aircraft may be statically unstable, but dynamically stableInitial tendency may be to pitch the nose upStatically unstable.Over a long period,vehicle recovers.Dynamicallystable.

Chart1

5

5

5.4817450807

5.6119655025

4.9197246057

4.4577567479

4.787370779

5.3348009245

5.3459515564

4.9034776854

4.667210412

4.9081928052

5.2253371026

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4.9134742216

4.7993373415

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5.1021945112

4.9314708625

4.8811517157

4.9950977715

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4.9494323198

4.930917703

5.0059388629

5.0596084351

5.025736845

4.9644083983

Alpha

Time, in seconds

Alpha, in degrees

Longitudinal Stability

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TimeAlpha

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25

35.4817450807

45.6119655025

54.9197246057

64.4577567479

74.787370779

85.3348009245

95.3459515564

104.9034776854

114.667210412

124.9081928052

135.2253371026

145.1908390925

154.9134742216

164.7993373415

174.9678338852

185.1477766546

195.1021945112

204.9314708625

214.8811517157

224.9950977715

235.0947882534

245.0526718583

254.9494323198

264.930917703

275.0059388629

285.0596084351

295.025736845

304.9644083983

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Aircraft may be statically anddynamically stableInitial tendency and long-term tendency both are to recover from a gust or disturbanceGust pitchesnose up

Chart2

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5.2

4.3880344975

5.0802753943

5.5422432521

5.212629221

4.6651990755

4.6540484436

5.0965223146

5.332789588

5.0918071948

4.7746628974

4.8091609075

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5.2006626585

5.0321661148

4.8522233454

4.8978054888

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4.9473281417

5.0505676802

5.069082297

4.9940611371

4.9403915649

4.974263155

5.0355916017

Time

Alpha

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TimeAlphaAlpha

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255

35.48174508075.2

45.61196550254.3880344975

54.91972460575.0802753943

64.45775674795.5422432521

74.7873707795.212629221

85.33480092454.6651990755

95.34595155644.6540484436

104.90347768545.0965223146

114.6672104125.332789588

124.90819280525.0918071948

135.22533710264.7746628974

145.19083909254.8091609075

154.91347422165.0865257784

164.79933734155.2006626585

174.96783388525.0321661148

185.14777665464.8522233454

195.10219451124.8978054888

204.93147086255.0685291375

214.88115171575.1188482843

224.99509777155.0049022285

235.09478825344.9052117466

245.05267185834.9473281417

254.94943231985.0505676802

264.9309177035.069082297

275.00593886294.9940611371

285.05960843514.9403915649

295.0257368454.974263155

304.96440839835.0355916017

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Aircraft may be dynamically unstable

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3.6380457274

5.2182111456

6.8003109976

5.86225401

3.341720165

2.9071150438

5.7132087971

8.0034305241

6.0120069014

1.9661202817

1.8617185338

6.7379167171

9.9227627291

5.9638286806

-0.4083646491

0.4317842988

8.7415641287

12.9255560315

5.399290767

-4.4299445208

-1.4001794921

12.5049091736

17.5227028581

3.6850976579

-11.1196949505

-3.5008685709

19.3586769228

Time, seconds

Alpha,Degrees

Longitudinal Stability

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TimeAlphaAlpha

155

255

35.48174508075.2

45.61196550253.6380457274

54.91972460575.2182111456

64.45775674796.8003109976

74.7873707795.86225401

85.33480092453.341720165

95.34595155642.9071150438

104.90347768545.7132087971

114.6672104128.0034305241

124.90819280526.0120069014

135.22533710261.9661202817

145.19083909251.8617185338

154.91347422166.7379167171

164.79933734159.9227627291

174.96783388525.9638286806

185.1477766546-0.4083646491

195.10219451120.4317842988

204.93147086258.7415641287

214.881151715712.9255560315

224.99509777155.399290767

235.0947882534-4.4299445208

245.0526718583-1.4001794921

254.949432319812.5049091736

264.93091770317.5227028581

275.00593886293.6850976579

285.0596084351-11.1196949505

295.025736845-3.5008685709

304.964408398319.3586769228

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Condition for Static StabilityLAircraft c.g. (center of Gravity)+ dLThe gust generates a small clockwise Moment about c.g. dM, and asmall positive additional lift dL.For static stability, if dL is positive (upward gust), dM must be negative, causing the nose to drop. Otherwise the wing will pitch up further increasing lift. dM/dL must be negative for static stability.

NondimensionalizationLift and pitching moment M are usually non-dimensionalized.

L is divided by [1/2 r V2 S] to yield CL

M is divided by [1/2 r V 2 S c] to yield CM

Here c is a reference length, e.g. average chord.

From the previous slide, dM/dL must be negative for static stability.

In nondimensional form, dCM/dCL must be negative for static stability.

The quantity -dCM/dCL is called the static stability margin.Notice the negative sign.The more positive it is, the more longitudinally stable the aircraft.

How can a Designer Ensure Longitudinal Static stability?

Aircraft c.g.LiftRule #1 : Place the c.g. as far forward as possible. This willcause the nose to drop, if lift increases due to a gust, reducinga, and lift. The opposite will occur if there is downward gust.

How can a Designer Ensure Longitudinal Static stability?

Aircraft c.g.Tail LiftRule #2 : Place the horizontal tail as far aft as possible. This willcause the nose to drop, if there is a vertical gust, reducinga, and lift. The opposite will occur if there is downward gust.

A canard is a tail upstream of the c.g., statically unstable!

The price paid for a large static stability marginThe aircraft may become sluggish, hard to maneuver. The tail will resist the pilots attempt to change the aircraft angle of attack.A large tail adds to aircraft weight, and cost.A smaller tail will require a long fuselage( a long enough crowbar!) to generate enough of a pitching moment to bring the nose up or down.Tail generates drag, including wave drag!

Horizontal Tail in Steady Level Flight needs to produce a download to balance all moments.Aircraft c.g.Tail LiftThe wing produces a counterclockwise moment about the c.g.

The tail will have to produce a clockwise moment about the c.g.

These two moments (I.e. force times distance) must roughly balance.

The wing has to generate enough lift to overcome the weight + Tail lift

Relaxed Static StabilityFor improved maneuverability, some fighter aircraft sacrifice the static stability margin.Some fighter aircraft are statically unstable.Their nose will continue to pitch up, the lift will continue to go up when a upward gust is encountered. Result: A/C will stall, flip over. These aircraft must be actively controlled by the pilot, or an onboard computer.Redundant computer systems are present in case a computer based flight control fails.

Directional StabilityA cross wind may cause the nose to rotate about the vertical axis,changing the flight direction.

The vertical tail behaves like a wing at an angle of attack, producing a side force, rotates the aircraft to its original direction.

All of this occurs without pilot action or intervention.Freestream comes from pilotsright side, due to cross wind.It causes nose to rotate to leftviewed from the top.The force on the tailcauses the aircraft to rotate back to original direction.

Why twin tail?Some fighter aircraft have twin tails.Each of the tails may be small, reducing radar cross section.Alternatively, twice the surface means twice the amount of side force that can be generated, giving good directional control.Disadvantage: Cost of manufacturing, weight go up.

Lateral StabilityIt is the ability of the aircraft to recover from a roll without pilots intervention.If the wing is tilted upwardsfrom root to tip, it has adihedral.Dihedral is good forlateral stability.

AnhedralIf the wing dips down from rootto tip, it has an anhedral.Anhedral is bad forlateral stability.

What happens when the aircraft undergo a roll?LiftLiftA portion of the liftis pointed sideways. The vehicle moves laterally. This is called sideslip.

During sideslip, a relative wind flows from right to leftThis wind has a component normal to the wing onthe right, viewingfrom the front.This is an upwash.The upwash increaseslift on the right wing.A downwash occurs on the left wing,reducing lift.As a result, the aircraft rights itself,and recovers from the roll.