Aircraft Stability & Control

Aircraft Stability & Control 11/8/05

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MECH 594

Aircraft Performance: Stability and Control

MECH 594

If we wish to trim the aircraft at a

higher or lower trim speed we have to

alter the equilibrium angle of attack, !e.

The most practical manner is through

elevator deflection. But how does !e

affect CMcg

?

Static Longitudinal Control


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The tail lift coefficient is a function of

both !t and "

e

!CL

t

!"= rate of change of C

Lt

with respect

to "t at constant #

e

!CL

t

!#e

= rate of change of CL

t

with respect

to #e at constant "

CL

t

=!C

Lt

!"t

"t+!C

Lt

!#e

#e= a

t"

t+!C

Lt

!#e

#e

So we have for the pitching moment about

the center of gravity:

CMcg

= CM

acwb

+CL

wb

hcg$ h

acwb

( )$ %Ha

t"

t+!C

Lt

!#e

#e

&

'(

)

*+

new tail zerolift line

ti!

Elevator Deflection to Trim

MECH 594

Taking the partial derivative of CMcg

wrt to !e gives

"C

Mcg

"!e

= #$H

"CL

t

"!e

where $H=

lt

c

St

S= tail volume ratio

but we see by the figure that "C

Lt

"!e

is constant and since $H

depends on

the aircraft type then, the increment in CMcg

due only to a given elevator

deflection !e is

%CMcg

= #$H

"CL

t

"!e

!e



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MECH 594

CMcg

= CM 0

+

!CMcg

!""

a+ #C

Mcg

= CM 0

+

!CMcg

!""

a$ %

H

!CL

t

!&e

&e


MECH 594

What elevator deflection will give the aircraft a new equilibrium angle of attack !n?

At a new trim CMcg

= 0 at !a=!

n where "

e= "

trim so we can write

CMcg

= CM 0

+

#CMcg

#!!

a$ %

H

#CL

t

#"e

"e and 0 = C

M 0+

#CMcg

#!!

n$ %

H

#CL

t

#"e

"trim

So "trim

=

CM 0

+#C

Mcg

#!!

n

%H

#CL

t

#"e

This equation gives the elevator deflection necessary to trim the aircraft at a given

angle of attack !n. %

H is a known value from the aircraft design, and

CM 0

, #CMcg

/ #! , and #CL

t

/ #"e are known values derived from wind-tunnel or

free-flight data.



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MECH 594

Free elevator deflection generally reduces the static longitudinal stability.

Stick-free Longitudinal Static Stability

MECH 594

Takeoff Static Stability

The CG affects our longitudinal controlrequirements at takeoff.


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MECH 594

Directional and Lateral Stability and Control

Directional stability and control refersto airplane behavior in yaw

Movement of longitudinal axis whenit’s rotated about its vertical axis.Rotation caused by yawing moments.

In pure yawing case, there is nopitching or rolling.

Dynamic directional stability iscoupled with dynamic roll stability.

MECH 594

Directional and Lateral Stability and Control


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MECH 594

Static Directional Stability

Sideslip angle β is angle between relative wind and airplane’s longitudinal axis. When relative wind to right, the sideslip is positive.

Airplane has positive static directionalstability if trimmed for non-sideslipflight and reacts to perturbation byturning into the new relative wind andtends to reduce sideslip angle to zero.

Has negative static directional stability if it tends to increase sideslip angle.

Has neutral static directional stability if it doesn’t react to sideslip.

Figure (a) is negative, figure (b) is positive

MECH 594

The Yawing Moment Equation

Yawing moment about aircraft CG

NCG

= CN (CG )

q!Sb

CN (CG )

=N

CG

q!Sb

where

NCG

= yawing moment about

CG (ft-lb)

CN (CG )

= coefficient of yawing

moment about CG


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MECH 594

Graphic Representation of Static Directional Stability

Positive static directional stability has slope which is exactly opposite for static pitch stability.

• For positive slope, plane experiencing right (+) sideslip develops nose-right yaw coefficient and yaws into new relative wind

• Trim point is where there is no yawing moment. As with pitch stability, degree of slope is indication of degree of stability. Steeper slope means increased stability.

MECH 594

Graphic Representation of Static Directional Stability

As with pitch, it is not unusual for airplane to be stable at smallsideslip angles and unstable at high sideslip angles.


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MECH 594

Contribution of Aircraft Components to Yaw Stability

Wing contribution to positive static directional stability is small, but increases with amount ofsweepback.

In the figure, the right wing produces more drag, so plane turns toward RW. The right wing produces more lift,and this is a roll factor.

MECH 594


CP near quarter length of fuselage (subsonic),which is ahead of CG ∴ the fuselage is destabilizing.

Effect of engine nacelles is comparableto impact discussed for pitch stability.

• For propeller or engine inlet ahead of CG, effect is destabilizing.

• For propeller or engine inlet behind CG, effect is stabilizing.


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MECH 594


• Vertical Tail (ie vertical stabilizer). As name implies, strongly stabilizing.

• Dorsal tail better, because it does not increase parasite drag as much.

MECH 594



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MECH 594

Rudder Fixed versus Rudder Free Stability

• Fixing rudder in neutral position prevents rudder float and increases vertical tail area. This increases directional static stability.

• For aircraft with conventional, reversible controls, there is increased directional stability results if the pilot keeps both feet on pedals and holds the rudder in a neutral position.

MECH 594

Effect of High Angle of Attack

• If vertical tail engulfed in stalled air from wings at high angles of attack, it will not be effective in developing sideward forces.

• Static directional stability will deteriorate.

• Stalled air will have a strong, negative effect on ability to recover from spins and unusual attitudes


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MECH 594

Directional Control

Five conditions of flight can be critical todirectional control exerted by rudder:

1. Spin Recovery 2. Adverse yaw 3. Slipstream rotation · Rotates about fuselage as shown · If strikes left side of stabilizer, will cause nose-left yawing moment · Yawing moment must be overcome with rudder force to maintain directional control 4. Crosswind takeoff and landing 5. Asymmetrical thrust · Left engine assumed to have lost thrust, resulting in nose-left yawing moment · Opposite yawing moment must be developed by rudder / vertical stabilizer

MECH 594

Lateral Stability and Control

Lateral stability refers to behavior of airplane inroll

• Movement of lateral axis when rotated about longitudinal axis. Results when rolling moment (L´) acts on aircraft.

• Caused by either pilot activating ailerons or sideslip angle

From stability standpoint, more interested insideslip angle impact


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MECH 594

Static Lateral Stability

Picture shows airplane sideslipping to right

• Rolling moment developed Since yawing to right, left wing moves faster than right wing, left wing develops more lift, plane rolls to right

• For static lateral stability need wings leveling rolling moment

Three possible tendencies:

(a) Left-wing-down rolling moment (positive lateral static stability) (b) No rolling moment developed (neutral lateral static stability) (c) Unstable airplane (negative lateral static stability)

MECH 594

The Rolling Moment Equation

Rolling moment about aircraft CG

L'

CG= C

L' (CG )qSb where

L 'CG

= rolling moment about CG

CL '(CG )

= coefficient rolling moment about CG


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MECH 594

Graphic Representation of Static Lateral Stability

• Same slope as for static longitudinal stability

• Trim point is where there is no rolling moment. Occurs at zero sideslip angle

• Assume plane trimmed and has right (+) sideslip Negative rolling moment coefficient (-CL) developed Right wing raised Degree of slope indication of degree of stability

MECH 594

Contributions of Aircraft Components to Roll Stability

Wing Dihedral:

Makes angle of γ with horizontal Sideslip gives velocity of Vy Roll gives velocity of Vz

Vz

Vy

Vx

γ

Vn

Vy

Vz

Wing line

Vn= V

zcos! + V

ysin!

For ! small,

Vn= V

z+ V

y!

! "# due to dihedral $

Vy%

V=

V&%

V= &%

Dihedral increases α by βγ on right wing and decreases it by same amount on left, tending to bring wings level


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MECH 594


• Vertical wing position gives pendulum effect.

• High wing position places airplane CG below wing CP. Results in positive effective dihedral.

• Low mounted wing with airplane. CG above wing CP is unstable and has negative effective dihedral.

• Low-wing airplanes/larger dihedral. Wing sweepback stabilizing, because right wing has more drag but also more lift.

CG

CG

Vβ

MECH 594


Vertical tail:

Side forces stabilizing since tail is above CG

Complete aircraft:

Total airplane must have positive lateral stability

Some components may have negative stability. Okay as long as this is overcome by other components


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MECH 594

Lateral Control

• Accomplished by providing differential lift on wings with ailerons or spoilers.

• Delta wing aircraft often combine ailerons and elevators into single control unit called elevon or ailevator. • Both left and right surfaces act together when elevator action is needed. Left and right surfaces act in opposition when roll motion is required.

• A combination of pitch and roll response is also possible. High roll rates desirable.

MECH 594

Dynamic Directional and Lateral Coupled Effects

• From before, static stability depends on aircraft’s reaction to imposed sideslip angle.

• Both yawing and rolling produce sideslip. Conversely, sideslip produces yawing and rolling moments.

• Two moments interact and result in coupled effects that determine dynamic stability in yaw and roll.


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MECH 594

Roll Due to Yawing

Rolling moments usually produced by use of ailerons.However, as stated previously, yawing can produce roll.

Example: pilot applies right rudder and

• The aircraft yaws to right• The left wing moves faster than right wing• The left wing develops more lift, and aircraft rolls to the right

MECH 594

Roll Induced SpinCharacteristics

Roll Due to Yawing


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MECH 594

Adverse Yaw

• Airplane normally yaws in same direction as it is rolled.

• Possible for airplane to yaw in opposite direction to roll can lead to loss of control, and is called adverse yaw.

• Effective wind on up-going right wing is resultant of freestream and downward winds. Lift vector tilted backward.

• Lift vector on down-going wing tilted forward.

• Lift vector on up-going wing and lift vector on down-going wing both oppose yaw in direction of turn.

Try to turn to right∴ adverse yaw

MECH 594

(a) Spiral divergence

➣ Static directional stability great in comparison to static lateral stability. ➣ Wing lowered, but dihedral effect is weak, and wing will not raise to level position.

(b) Directional divergence

➣ Results from negative directional stability➣ Airplane disturbed in either roll or yaw and develops yawing moment that makes it yaw even further

(c) Dutch roll

➣ Sideslips to right, yaws to right➣ Right wing develops more lift , plane rolls to left➣ If not controlled, right wing causes sideslip to left

Types of Motion Resulting from Coupled Effects


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MECH 594

Roll Coupling

Types of Motion Resulting from Coupled Effects

MECH 594 Notes

Questions?


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MECH 594 Notes

See you next time.

Aircraft Stability & Control

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