AE 430 - Stability and Control of Aerospace...

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Longitudinal Control

AE 430 - Stability and Control of Aerospace Vehicles

Primary Aerodynamic Controls

(+) (+)

δp

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Primary Aerodynamic Controls

A simple basic control system as operated by a pilot

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through pilot’s change of thrust (propulsion), and/orthrough change of configurations using aerodynamic control surfacesMain aerodynamic surfaces for longitudinal control:

– on Tail:elevator

– on Wing:slats (leading-edge)flaps (trailing-edge)spoilers

Control through Pilot

To rotate any of the aerodynamic control surface, it is necessary to apply a force to it to overcome the aerodynamic pressures that resist the motion. This force may be supplied by a human pilot through different ways:

– Mechanical Linkage Control– Power Assisted Control: pilot’s control is connected to the

control surface and the control lever– Power Operated Control: pilot’s control is connected to the

control lever ONLY– Fly-by-wire: wire carries electrical signals from the pilot’s

control to replace mechanical linkage– Fly-by-optical

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Is a measure of how effective the control deflection is in producing the desired control momentFunction of the size of the elevator and tail volume ratio

1) Control Effectiveness

Factors affecting the design of a control surface are:1) Control Effectiveness 2) Hinge moments3) Aerodynamic and mass balancing


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The aerodynamic moment that must be overcome to rotate the control surface

To have the control stick force within an acceptable range

3) Aerodynamic and Mass balancing

2) Hinge Moment


Elevator Effectiveness

How to Change Airplane Trim Angle of Attack

eL L eC Cδ

δ∆ =e

LL

e

dCCdδ δ

=

eL L L eC C Cα δα δ= +

Deflecting the elevator:Change in Lift

Change in Pitching Moment em m eC Cδ

δ∆ =e

mm

e

dCC

dδ δ=

Elevator power control

0 em m m m eC C C Cα δα δ= + +

In the case of linear lift and moment, we further have:

Elevator Effect. Deriv.

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Cm-α ; δetrim-α

Cm – α

and

CL - α

(+)

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How to find e

LL

e

dCCdδ δ

=e

mm

e

dCC

dδ δ=

t

t

t

Lt tL L e

e

L LdCS SC C

S S dη η δ

δ

∆ = ∆

∆ = ∆ =

Elevator effectiveness

t t

t

L L tL

e t e

dC dC dC

d d d α

ατ

δ α δ= =

t

te

Lt tL L

e

dCS SC C

S d Sδ αη η τ

δ= =

t

t

Lm H L H e

e

dCC V C V

dη η δ

δ∆ = − ∆ = −

t

te

Lm H H L

e

dCC V V C

dδ αη η τ

δ= − = −

Elevator Effectiveness

Tail Lift Coefficient vsTail Angle of Attack

Tail Lift Coefficient vsElevator Deflection

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Calculating Elevator Effectiveness

The elevator effectiveness– This is the slope of the graph

From this we get

Elevator control power

Flap effectiveness parameter

tL

e

dCdδ

t

e

LtL

e

dCSC

S dδη

δ=

t

te

Lm H H L

e

dCC V V C

dδ αη η τ

δ= − = −

e

t

m

H L

CV C

δ

α

τη

= −trim trimem m eC C

δδ∆ =

Elevator Angle to Trim

0

0 trimtrim

0e

e

m m m m e

m m

m

C C C C

C CC

α δ

α

δ

α δ

αδ

= + + =

+= −

trim

trim

trim trim

trimtrim

e

e

L L L

L L

L

C C C

C C

C

α δ

δ

α

α δ

δα

= +

−=

0 trimtrim

e e

m L m L

m L m L

C C C CC C C C

α α

δ α α δ

δ+

= −−

(+) (+) (+)(-)

(-) (+) (-) (+)

usually(-)

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Some conclusions

with elevator angle to trim, the slope of lift coefficient is slower, less sensitive to change of α, because configuration change due to δe

with elevator angle to trim, a zero angle of attack α = 0 still generates a lift, due to δe

( ) 0

trim

( ) ( )

trim trim trim

( )

e e

ee e

m L m LL L L L

m m

C C C CC C C C

C Cα δ δ

α δ αδ δ

α δ α

− +

−

= + = − −

(+) (+)

(-)

L LC Cα α′ <

VH set from the static longitudinal stability requirements

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Variation of δeTRIM with CLTRIM

for a zero lift, there must have a positive deflection of δe for a given CG (forward) position, increasing lift requires less δe deflectionfor a given trimmed lift, the more CG forward (larger static margin), the less elevator angle deflection δerequires

( ) ( ) ( ) ( ) ( )det

e em L m LC C C Cδ α α δ− + −− +

= −

(+) (+)

(-)

XCG=XNP

XCG<XNP

Variation of δeTRIM with the speed

for a given CG (forward) position, increase trim speed requires more elevator angle deflectionfor a given trim speed, the more CG forward (larger static margin), the less elevator angle deflection requires

XCG=XNP

Trim speed

No compressibility effects, no propulsive effects 21

02trimL

E

WCV Sρ

=0

EV V ρρ=

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Flight Measurement of XNP

trim

trim

e e

m

L m L m L

CddC C C C C

α

δ α α δ

δ= −

−trim

trim0 0cg NP mL

dx x C

dCα

δ= ⇒ = ⇒ =

trimLC

trimLdCcgxc

NPxc

0detm LC C

α−

Elevator deflection to trim

Landing & take-off Higher speed

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Elevator Hinge Moment

Only the shaded portion of the lift distribution in these figures acts on the control surface and contributes to the hinge moment.


The aerodynamic forces on any control surface produce a moment about the hinge. The coefficient of elevator hinge moment:

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Elevator, Tab and Their Hinge

eH

0

ec

ex Ldx H∆ =∫


In practice, it is often satisfactory to assume Che is a linear function of surface (wing or tail) angle of attack αt, angle of elevator δe, and angle of tab δt :

0e t e th h h t h e h tC C C C Cα δ δ

α δ δ= + + +

t

hh

t

dCC

dα α=

e

hh

e

dCC

dδ δ=

t

hh

t

dCC

dδ δ=

0hC Residual moment

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Elevator Free (Control stick released)

0

0

assuming, 0e t eh h t h e

h t

C C C

Cα δ

α δ

δ

= + =

= =free

t

e

he t

h

C

Cα

δ

δ α= −

Usually 0; 0t eh hC C

α δ< <

The elevator will float upward as the angle of attach is increased

free

t

t t te ee

hL L t L e L t L t

h

CC C C C C

Cα

α δ α δδ

α δ α α= + = −

Stick-fixed condition is an ideal approximation. The opposite extremeis also of interest: stick-free condition:

Coeff. of elevator “free” moment

Lift coefficientfor the tail “elevator free”


free1

1

t e

t t t tee t

t e

t t te t

LhL L t L e L t L t

h L

LhL L L

h L

CCC C C C C

C C

CCC C C f

C C

δα

α δ α αδ α

δα

α α αδ α

α δ α α⎛ ⎞⎜ ⎟ ′= + = − =⎜ ⎟⎝ ⎠

⎛ ⎞′ ⎜ ⎟= − =

⎜ ⎟⎝ ⎠

( )0 0 0 0w f tm m m H L w tC C C V C i i

αη ε′ ′= + + + −

1t

cg acm L m H Lw f

x x dC C C V Cc c dα α α α

εηα

⎡ ⎤ ⎛ ⎞′ ′= − + − −⎢ ⎥ ⎜ ⎟⎝ ⎠⎣ ⎦

Coeff. hinge ratio

(depend on f )

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1t

cg acm L m H Lw f

x x dC C C V Cc c dα α α α

εηα

⎡ ⎤ ⎛ ⎞′ ′= − + − −⎢ ⎥ ⎜ ⎟⎝ ⎠⎣ ⎦

For the static longitudinal stability

1tm LfNP ac

HL Lw w

C Cx x dVc c C C d

α α

α α

εηα

′′ ⎛ ⎞= − + −⎜ ⎟⎝ ⎠

0mCα

′ =

( )1 1tLNP NPH

L w

Cx x df Vc c C d

α

α

εηα

′ ⎛ ⎞− = − −⎜ ⎟⎝ ⎠

Static Margin: distance between the neutral point and the actual center of gravity position

Stick fixed static margin

Stick free static margin

cgNP xxc c

−

cgNP xxc c′

−

Desirable to have the stick fixed static margin within5% of the mean-chord

Stick fixed or stick free static neutral points represent an aft limiton the center of gravity travel for the airplane

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Stick force

( ) 2e

1fn H2eh e eF GC V S cρ= =

sl sδF

eH

e

s sG

lδ

δ=

Gearing ratio: measure of the mechanical advantage provided by the control

The work of displacing the control stick is equal to the work inmoving the control surface to the desired deflection angle

(+)

(+)

(-)

0s s e eFl Hδ δ− =

ee e

s sF H H G

lδδ

= =

Trim Tab

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Stick Force Gradients

Typical variation in control force as function of vehicle velocity for stable configuration.

0dFdV

<For airplane speed stability:

Stick force

A B

Stick force

xcg

push

pull

Negative stick force gradient

Stick Force Gradients

For a given static margin (or c.g. position) the control force gradient decreases with increasing flight velocity; andAt a given trim velocity, the gradient decreases as the c.g. is moved toward the control-free neutral point.

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Aerodynamic and mass balance

AE 430 - Stability and Control of Aerospace...

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