Aircraft Stability and ControlAE 1350

Lecture Notes #11

We will study

• What do we mean by aircraft stability and control?

• Static and Dynamic Stability

• Longitudinal, lateral and roll stability

• Necessary Conditions for Longitudinal stability

• Stability Margin

• Relaxed 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.

Unstable Neutrally stable.Assumes new positioncaused by the disturbance.

An aircraft is subjected to some disturbance, say a gust, a cross wind or turbulence

Unexpected Gust

Will it recover automatically, without pilot’s intervention, and resume its original direction of flight?If so, the aircraft is longitudinally stable.

Freestream

Longitudinal Static Stability

Time

Alpha

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.

Aircraft may be statically unstable, but dynamically stable

Longitudinal Stability

3

3.5

4

4.5

5

5.5

6

0 5 10 15 20 25 30 35

Time, in seconds

Alp

ha

, in

de

gre

es

Initial tendency may be to pitch the nose upStatically unstable.

Over a long period,vehicle recovers.Dynamicallystable.

Aircraft may be statically anddynamically stable

33.54

4.55

5.56

0 10 20 30 40

Time

Alp

ha

Initial tendency and long-term tendency both are to recover from a gust or disturbance

Gust pitchesnose up

Aircraft may be dynamically unstable

Longitudinal Stability

-20

0

20

40

0 10 20 30 40

Time, seconds

Alp

ha

,D

eg

ree

s

Condition for Static StabilityL

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.

NondimensionalizationLift and pitching moment M are usually non-dimensionalized.

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

M is divided by [1/2 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.

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, reducing, and lift. The opposite will occur if there is downward gust.

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, reducing, 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 margin

• The aircraft may become sluggish, hard to maneuver. The tail will resist the pilot’s 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 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

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.

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 pilot’sright 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 Stability

• It is the ability of the aircraft to recover from a roll without pilot’s intervention.

If the wing is tilted upwardsfrom root to tip, it has adihedral.

Dihedral is good forlateral stability.

Anhedral

If the wing dips down from rootto tip, it has an anhedral.Anhedral is bad for

lateral stability.

What happens when the aircraft undergo a roll?Lift

Lift

A portion of the liftis pointed sideways. The vehicle moves laterally. This is called sideslip.

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.