Aircraft Stability
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Transcript of Aircraft Stability
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Aircraft Stability and ControlAE 2350Lecture Notes #11
May 17, 1999
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We will study
What do we mean by aircraft stability and control?Static and Dynamic StabilityLongitudinal, lateral and roll stability Necessary Conditions for Longitudinal stabilityStability MarginRelaxed Stability Margin
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A system is said to be stable if it can recover from small disturbances that affect its operation.
A cone restingon its base isstable.
Unstable
Neutrally stable.Assumes new positioncaused by the disturbance.
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An aircraft is subjected to some disturbance, say a gust, a cross wind or turbulence
Unexpected Gust
Will it recover automatically, without pilots intervention, and resume its original direction of flight?If so, the aircraft is longitudinally stable.
Freestream
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Longitudinal Static Stability
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Aircraft is insteady level flight
Gust pitches the nose up
The initial tendency of the vehicleis to bring the nose down. If so,The aircraft is statically stable.
Alpha
Time
The initial tendency of the vehicle is to bringthe nose up. If so,The aircraft is statically unstable.
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Aircraft may be statically unstable, but dynamically stable
Initial tendency may be to pitch the nose upStatically unstable.
Over a long period,vehicle recovers.Dynamicallystable.
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Time, in seconds
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Longitudinal Stability
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Longitudinal Stability
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Condition for Static Stability
L
Aircraft c.g. (center of Gravity)
+ dL
The 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.
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Nondimensionalization
Lift 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.
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How can a Designer Ensure Longitudinal Static stability?
Aircraft c.g.
Lift
Rule #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.
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How can a Designer Ensure Longitudinal Static stability?
Aircraft c.g.
Tail Lift
Rule #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!
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The price paid for a large static stability margin
The 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!
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Horizontal Tail in Steady Level Flight needs to produce a download to balance all moments.
Aircraft c.g.
Tail Lift
The 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
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Relaxed Static Stability
For 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.
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Directional Stability
A 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.
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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.
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Lateral Stability
It 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.
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Anhedral
If the wing dips down from rootto tip, it has an anhedral.
Anhedral is bad forlateral stability.
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During sideslip, a relative wind flows from right to left
This 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.