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Flight MechanicsAircraft Stability

ByMr. ANU JACOB PAUL, M.Tech (AERO)

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Stability - Overview• Definitions of.

– Static & dynamic stability, airplane axes, trim

• Longitudinal static stability– Centre of pressure, aerodynamic centre, neutral point

• Directional & lateral static stability• Speed stability • Longitudinal dynamic stability

– Short period pitching oscillation, phugoid

• Lateral dynamic stability– Roll damping, spiral mode, dutch roll, spin

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Stability & Control

Stability

• Consequences of small disturbances from equilibrium (trimmed conditions) which arise at random from an external medium (e.g. gusts).

Control

• Response of aircraft to deliberate applied forces/moments which causes aircraft to deviate from initial equilibrium condition.

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Axes of Motion

Longitudinal stability

pitching

Lateral stability

rolling

Directional stability

yawing

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Trim• Relates to a state of equilibrium, so that there are no net

moments or forces acting on the aircraft.

• Longitudinal (pitch) trim is provided by tailplane/elevators/trim tabs/canards/etc (depends on aircraft configuration).

No net forces:

T = D

LW = W + LT

No net moments:

MCG = 0

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Static Stability• Relates to initial tendency of body to return to

equilibrium starting position or not.

• Dynamic stability relates to subsequent time history of motions (see later).

Cone on baseStatically stable

Cone on sideNeutral static stability

Cone on pointStatically unstable

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Static Stability

Positive static stability Negative static stability

Neutral static stability

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Longitudinal Static Stability

(a) Negative static stability (b) Positive static stability

(c) Neutral static stability

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Centre of Pressure (CP)

• Position on the body through which the aerodynamic force (lift) is considered to act, also known as centre of lift.

• There can be no pitching moment (M) about a centre of pressure reference point.

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Reference Point Position• If any position other

than the centre of pressure is used as the reference point then a pitching moment must also be included in the analysis.

• Sign & magnitude of pitching moment depends on reference point position chosen.

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Pitching Moment v CL (For Wing Alone)

• Plot depends on reference point taken.

• One position for reference point at which pitching moment is constant for a change in CL.

• This point is the aerodynamic centre of the wing section.

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Zero-Lift Pitching Moment

• All plots of CM v CL will intersect the CM axis at a given point.

• This represents the zero-lift pitching moment coefficient (CMo

).

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Aerodynamic Centre

• From its definition, there can be no change in pitching moment when either CL or is varied.

• This must mean that all lift increments must also act through the aerodynamic centre for a change in .

• For conventionally cambered wings, pitching moment about aerodynamic centre is nose-down (i.e. negative).

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Movement of Centre of Pressure

• For a conventionally cambered wing the centre of pressure moves forward as the angle of attack and lift increases, due to the forward shift of the peak of the suction pressure on the upper surface.

• Post-stall, the Cp position then moves rearwards.

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Centre of Pressure Movement with

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Aerodynamic Centre Position

• This is fixed in position for a given Mach number - at around the 1/4 chord position for subsonic flight or just forward of the mid-chord position for supersonic flight.

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Symmetrical Wing Sections

• Here, both the CP and aerodynamic centre are fixed in position for a change in .

• This is at the 1/4 chord point, though boundary layer effects may move it slightly forwards by 1 or 2%.

• The zero-lift pitching moment (and its coefficient) must also then be zero for symmetrical sections (as often used on tailplanes).

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Neutral Point

• This is the mean position of the aerodynamic centre of the complete aircraft.

• The main contributions will come from the wing and horizontal stability/control surfaces (though the fuselage/nacelles/etc. will also contribute slightly).

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Longitudinal Static Stability

• If N ahead of CG - negative stability

• If N behind CG - positive stability

• If N coincident with CG - neutral stability.

• Depends on the relationship between an aircraft’s neutral point and CG.

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Longitudinal Static Stability

• Often expressed in terms of a CM v CL plot, with CM taken about the CG.

• Trim point taken for when CMCG = 0.

• Condition for stability is that pitching moment should reduce (i.e. become more nose-down) for a change in or CL.

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Directional (Yawing) Stability• Mainly provided by the

fin(s).• Acts by moving overall

yawing aerodynamic centre to behind the CG to provide a weathercock effect.

• Degree of directional stability depends on fin size and moment arm aft of CG.

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Wing Sweepback

May also be used to enhance directional stability.

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Dorsal Fin Extensions

• Often used on aircraft.• Main purpose is to prevent fin stalling by increasing

sideslip stall angle.• Also increases fin effectiveness at high .

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Lateral/Rolling Static Stability• Three standard wing design methods used to impart

lateral static stability characteristics on an aircraft:– (a) Wing dihedral

– (b) High wing position

– (c) Wing sweepback

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Lateral/Rolling Static Stability

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Speed Stability

• An aircraft flying slower than its minimum drag speed is operating in an unstable regime.– A drop in speed will increase the drag which will reduce the

speed further and so on.

• It is better to operate at speeds higher than the minimum drag speed.

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Dynamic Stability

• Refers to subsequent time history of motions following the initial response to a disturbance.

• For dynamic stability, motions have to be convergent or damped out.

• If divergent then dynamic instability exists.

• Cases (a) & (b) here are longitudinally dynamically stable, case (c) is longitudinally dynamically unstable (all are statically stable).

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Longitudinal Dynamic Stability

Short Period Pitching Oscillation• Most aircraft designed to be heavily damped in pitch

with only one or two oscillations.

• Damping due to increased opposing moment from tailplane for increasing .

• Effect reduces with increasing altitude & transonic speeds.

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Longitudinal Dynamic Stability

Phugoid• Simple case involving interchange of airspeed and

altitude from kinetic and potential energy considerations.

• Drag variation opposes speed variation and weakly damps out oscillations.

• Low frequency oscillations, typically 1 minute per cycle, and only a small problem to pilot and control system designer, though peak-peak variations of > 300m possible.

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Lateral Dynamic Stability

Roll Damping

• The wing will damp any rolling moment due to down going wing having effective increased .

• The roll damping moment depends on the roll rate not the roll angle.

• Results in heavily damped non-oscillatory motion.• Damping effect reduced for low aspect ratio aircraft.

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Lateral Dynamic Stability

Spiral Mode• Involves complicated mixture of side forces and moments

in rolling and yawing senses.• Initial sideslip produces yawing and rolling due to forces

on fin and sweepback.• Resultant rolling motion

may be dynamically unstable, producing slowly divergent non-oscillatory spiral path.

• Usually fairly weak and easily controlled by pilot.

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Lateral Dynamic Stability

Dutch Roll• Oscillatory motion combining roll & yaw with aircraft

waddling from side to side.

• Unpleasant for crew/passengers so not tolerated.

• Damping mainly affected by fin size - often primary sizing criterion.

• Problems worsen with wing dihedral (trade off with lateral static stability & spiral divergence) and high sweep.

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Lateral Dynamic Stability

Spin• Results from one wing stalling before the other, giving

large rolling moment and increased yawing moment due to increased drag.

• Complicated spiral flight match with mixture of roll & yaw.

• Spin can be flat or steep with flat spin especially difficult to recover from - involves reattachment of separated flow using rudders/elevators.