Lecture 8 Longitudinal Stability

8/2/2019 Lecture 8 Longitudinal Stability

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Lecture 8 Longitudinal stability

Dr Jian Wang

08/03/2010


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Aims To understand the concepts of stability

To know the basic requirements for longitudinaland Lateral Stability

To learn procedures for Longitudinal Stabilityanalysis

To learn procedures for Lateral Stability analysis

To take the students through the exercises ofStability and Control


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What is stability:

Natural stable: The bodyalways stays in equilibrium

Statically stable: If the forces & themoments on the body cause by thedisturbance tend initially to return the bodytowards its equilibrium position

Statically unstable: If the forces& the moments are such that the body

continues to move away from itsequilibrium position after being disturbed

Is this dynamicstable?


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What is stability:--dynamic stability

Dynamic Stability: deals with the time history of the bodys motion afterit initially responds to its static stability

Dynamic Stable Behaviour Dynamic Unstable Behaviour


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What is stability:--Aircraft Motion


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Stability and Control:--What have be done before?

Historical data were used: Volume coefficients: Chapter 8.10.3

Those data come from the statistical data for different types of aircraft

There are no aerodynamics being considered

Stability and Control:--What will we do?

Forces and moments balance: equilibrium Considering of aerodynamic equations

Equilibrium

Characteristics of controlling surfaces


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h0

h

hG

lT


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Stability and Control: A classical airplane has three basic controls: ailerons, elevator,and rudder (tailplane and fin)

Longitudinal Stability

The size, shape & location of the tailplane necessary to provide aspecific degree of longitudinal stability

The range of elevator deflection necessary to control the aircraft

Lateral Stability

The size, shape & location of the fin necessary to provide a specificdegree of directional stability

The size of the ruder & the range of its deflection necessary to controlthe aircraft throughout its speed envelope

The wing dihedral angle

The size & location of the ailerons


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Longitudinal Stability and Control:

Tailplane sizing

i. Evaluate the cruise trim condition

ii. Evaluate the range of elevator angles required forthe chosen value of

iii. Calculate the minimum value of required at eachvalue of h

iv. Rotation in the takeoff

v. Estimate the damping for the short period oscillation

vi. Select that lowest value of consistent with theconditions in parts (iii), (iv) and (v)

T

S

ST

S

ST


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CMG: pitch moment for C.G.

CM0: pitch moment for aerodynamiccentre (zero lift)

CL: Lift coefficient

h: Position of C.G.

h0: Position of aerodynamic centre zT: Distance that the thrust line lies

belowthe C.G.

Equation we use:

21

11 aa

d

d

a

aCV

c

zChhCCC

TLT

T

ToLMM OG

a: wing and body lift curve slop

a1: tailplane lift curve slope d/d: change of down wash

T: the tailplane setting angle

: elevator deflect angle

: M.A.Cc

qSTCT


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During cruise, L=W, T=D. Moment aboutC.G. = 0.

Zero elevator angle

d

d

a

C

Fc

l

S

Sa

czChhCC

L

TT

TToLM

T

O

1

1

1

1

d

d

a

a

S

SFFG

factorcorrectaisFF

T11

:1

1

1


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ii.Evaluate the range of elevator angles

required for the chosen value of

Equation we use:

T

T

L

TT

TToLM

d

d

a

C

a

a

Fc

l

S

Sa

c

zChhCC

O

1

1

12

1

2

Use the same range of and CG position, h, employed in part (i)

The landing configuration (flaps down), more negative, higher

Compare the maximum elevator angle required with the maximum

movement available, 67% is the limit.

SST

OM

CL

C


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iii.Calculate the minimum value of

required at each value of h

Equation we use:

is the static margin

S

ST

d

d

a

a

Fc

l

S

Shh

d

d

a

aVhhK TToToN 1

1

11 11

NK

d

d

a

a

Fc

l

hhK

S

S

T

oNT

11

11

Minimum Static Stability: h = minimum


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iv.Rotation in the takeoff

Limited by forward C.G.

Use

the minimum value of h

the previously selected value of ,

the maximum (negative) value of elevator angle

Calculate the required tailplane area

T

21

12

1 aad

d

a

aCV

c

zChh

qS

MghhCC

cS

MkTLT

GTGOGLM

B

O


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iv. Rotation in the takeoffMIk yB the pitch radius of gyration of the aircraft

a specified pitch acceleration

the non-dimensionalised longitudinal position of the aftwheels (analogous to h)

Gz the vertical distance of the aft wheels belowthe engine thrust

line

Gh

211

2

1 aad

d

a

aC

cS

Mk

c

zChh

qS

MghhCC

V

TL

BGTGOGLM

T

O

c

laa

d

d

a

aC

cS

Mk

c

zChh

qS

MghhCC

S

S

TTL

BGTGOGLM

T

O

211

2

1


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v.Estimate the damping for the short

period oscillation

Equation used

cS

MaKa

c

lVCa

k

c

ac

lV

d

d

k

cCa

nTTD

B

TT

B

D

2

2

1

1

1

2

Calculate for the sae range of and CG position, h,

employed in part (i)

Carpet plot the results Ideally great than about 0.5

SST


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vi.Select that lowest value of

consistent with the conditions in

parts (iii), (iv) and (v)

In Figures 9.1 to 9.3, a value of 0.25satisfies all the conditions (except for thecondition on SPO damping, is lessthan 0.5)

S

ST


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-6

-5

-4

-3

-2

-1

Tailplanesettinga

ngletotrim(

degrees)

ST/S

0.10

0.40

0.28

0.16

0.300.25

0.20

0.15

h

Chosen T

Chosen ST/S

Take-off

rotation

Static stability

in cruise


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-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Elevatorangletotr

im(

degrees)

ST/S

0.10

0.40

0.28

0.16

0.300.25

0.15

h

Limit on

Chosen ST/S

Take-off

rotation

T = -3.65 degrees


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0.2

0.3

0.4

0.5

SPOda

mpingratio

ST/S

0.10

0.40

0.28

0.16

0.30

0.25

0.20

0.15

h

Chosen ST/S

= 0.3

Lecture 8 Longitudinal Stability

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