Aircraft Stability & Control

Aircraft St abilit y & Cont rol

11/8/05

Aircraft Performance: Stability and Control

Static Longitudinal Control

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 C Mcg ?

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11/8/05

Elevator Deflection to Trim The tail lift coefficient is a function of both ! and " t

e

!C L !"

t

=

rate of change of C of C L with respect t

to " t at constant # e

!C L !# e

new tail zero lift line

t

=

rate of change of C of C L with respect t

to # e at constant "

!it

C L

=

t

!C L !C L " t + !" t !# e t

t

# e

=

at " t +

!C L !# e

t

# e

So we have for the pitching moment about the center of gravity: C Mcg = C M

+

acwb

C L

wb

(

hcg $ hac

wb

& !C L $ % + a " ( ) H ' t t !# e

t

)

# e +

*

Elevator Deflection to Trim

Taking the partial derivative of C Mcg wrt to ! e gives "C Mcg "! e

=

#$ H

"C L

where $ H

t

"! e

but we see by the figure that

"C L

t

"! e

=

l t S t c S

=

tail volume ratio

is constant and since $ H depends on

the aircraft type then, the increment in C Mcg due only to a given elevator deflection ! e is %C Mcg

=

#$ H

"C L

t

"! e

! e

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11/8/05

Elevator Deflection to Trim

C Mcg = C M 0 + =

C M 0 +

!C Mcg !" !C Mcg !"

" a

+

#C Mcg !C L

" a $ % H

t

!& e

& e

Elevator Deflection to Trim What elevator deflection will give the aircraft a new equilibrium angle of attack ! n? At a new trim C Mcg = 0 at ! a

C Mcg = C M 0 + M 0

#C Mcg

So

#!

! a $ % H

" trim

=

! n where " e

#C L

t

#" e

" e

+ C M 0 M 0 =

%H

=

" trim so we can write

and 0 = C M 0 + M 0

#C Mcg #! #C L

#C Mcg #!

! n $ % H

#C L

t

#" e

" trim

! n

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 , #C Mcg / #! , and #C L / #" e are known values derived from wind-tunnel or C M 0 M 0 t

free-flight data.

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11/8/05

Stick-free Longitudinal Static Stability

Free elevator deflection generally reduces the static longitudinal stability.

Takeoff Static Stability

The CG affects our longitudinal control requirements at takeoff.

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11/8/05

Directional and Lateral Stability and Control

Directional stability and control refers to airplane behavior in yaw Movement of longitudinal axis when it’s rotated about its vertical axis. Rotation caused by yawing moments. In pure yawing case, there is no pitching or rolling. Dynamic directional stability is coupled with dynamic roll stability.

Directional and Lateral Stability and Control

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11/8/05

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 directional stability if trimmed for non-sideslip flight and reacts to perturbation by turning into the new relative wind and tends 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

The Yawing Moment Equation

Yawing moment about aircraft CG N CG

=

C N ( N ( CG )

=

C N ( q Sb N ( CG ) !

N CG q Sb !

where N CG

=

yawing moment about CG (ft-lb)

C N ( N ( CG )

=

coefficient of yawing moment about CG

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11/8/05

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.

Graphic Representation of Static Directional Stability

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

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11/8/05

Contribution of Aircraft Components to Yaw Stability

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


CP near quarter length of fuselage (subsonic), which is ahead of CG ∴ the fuselage is destabilizing. Effect of engine nacelles is comparable to 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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11/8/05


• Vertical Tail (ie vertical stabilizer). stabilizer). As name implies, strongly stabilizing. • Dorsal tail better, because it does not increase parasite drag as much.


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11/8/05

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.

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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11/8/05

Directional Control Five conditions of flight can be critical to directional 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

Lateral Stability and Control

Lateral stability refers to behavior of airplane in roll • 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 in sideslip angle impact

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11/8/05

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)

The Rolling Moment Equation

Rolling moment about aircraft CG

L'CG L 'CG

=

C '

=

C L '(CG '( CG))

L ( CG )

qSb where

rolli rolling ng momen momentt about about CG =

coeff coeffici icient ent rolli rolling ng momen momentt about about CG

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11/8/05

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

Contributions of Aircraft Components to Roll Stability Wing Dihedral: Makes angle of γ with horizontal Sideslip gives velocity of V y Roll gives velocity of V z Vn

=

V z cos ! + V y sin !

For ! small, Vn

=

V z + V y!

! "# due to dihedral $

V y % V

V&% =

V

=

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

&%

Vx

Wing line Vy

Vy Vz

γ

V Vn z

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11/8/05

Contributions of Aircraft Components to Roll Stability • 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.

CG Vβ CG

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

Contributions of Aircraft Components to Roll Stability

Vertical tail: Side forces stabilizing since tail is above CG

Complete aircraft: Total airplane must have positive lateral stability Some components may have negative nega tive stability. Okay as long as this is overcome by b y other components

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11/8/05

Lateral Control

• Accomplished by providing differential lift on wings with with ailerons or spoilers. • Delta wing aircraft aircraft often combine ailerons and elevators into single control unit called elevon or ailevator. • Both left and right surfaces surfaces act together when elevator action is is needed. Left and right surfaces act in opposition when roll motion is required. • A combination of pitch and roll response is also possible. possible. High roll rates desirable.

Dynamic Directional and Lateral Coupled Effects

• From before, static stability stability depends on aircraft’s aircraft’s reaction to imposed sideslip angle. • Both yawing and rolling 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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11/8/05

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

Roll Due to Yawing Roll Induced Spin Characteristics

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11/8/05

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

Types of Motion Resulting from Coupled Effects (a) (a) Spir Spiral al dive diverg rgen ence ce ➣

➣

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

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11/8/05

Types of Motion Resulting from Coupled Effects Roll Coupling

Notes

Questions?

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11/8/05

Notes

See you next time.

19

Aircraft Stability & Control

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