Civil jet aircraft performance

Chalmers University of Technology

Civil jet aircraft performance

Chalmers University of Technology

Four forces of flight

L ift

W eight = m g

D rag

Thrust

V

x

y

Resulting force perpendicular

to the flight path

Net thrust from the engines

resulting force parallell to the flight path

α angle of attack

V velocity

sincos gmDFdt

dVm

Newton’s second law

Chalmers University of Technology

Aerodynamic equations

• L=Lift = q·S·CL [N]

• D=Drag = q·S·CD [N]

• q = dynamic pressure [N/m²]

• S = reference wing area [m²]

• CL = coefficient of lift CL = f(α,Re,M)

• CD = coefficient of drag CD = f(α,Re,M)

Chalmers University of Technology

Reference wing areaThe area is considered to extend without interruption

through the fuselage and is usually denoted S.

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Lift versus angle of attack

Chalmers University of Technology

numberMachoffunctionasCD

DC

1M Mach

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The ISA AtmosphereFrom lecture 5

Chalmers University of Technology

Equations

222

2222

2

1

2

12

1

2

1

2

1

2

SLSL

a

SL

Sl

SLSLSL

aMT

TTRM

TRMaMVq

TRp

a

V

a

VM

TRap

p

T

T

SL

2

2

1Mp

Chalmers University of Technology

Lift equation

LL

LLSL

LSLSLLSL

LL

CSMCSMconstL

CSMconstCSMp

CSMaCSaM

CSaMCSVL

242

22

constant

2222

222

100928,7

2

12

1

2

12

1

2

1

Chalmers University of Technology

Drag equation

DD

DDSL

DSLSLDSL

DD

CSMCSMconstD

CSMconstCSMp

CSMaCSaM

CSaMCSVD

242

22

2222

222

100928,7

2

12

1

2

12

1

2

1

Chalmers University of Technology

Drag polarL

D

R

R

C L

C D

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High speed drag polar

LC

0.02 0.04 0.06 0.08 0.1 0.12 0.140.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mach 0,63Mach 0,73Mach 0,80Mach 0,82Mach 0,83Mach 0,85

DC

LC

Chalmers University of Technology

A flight consists of:

• Taxi

• Take off

• Climb

• Cruise

• Descent

• Approach and landing

• Diversion to alternate airport?

Sector Distance

Flight Time & Fuel

Block Time & Fuel

En route Climb

Descent

Approach &Landing

1500 ft

Initial Cruise

Step Cruise

Takeoff &Initial ClimbStart-up

&Taxi-out

Taxi-in

Chalmers University of Technology

CruiseFor an airplane to be in level, unaccelerated flight, thrust and drag

must be equal and opposite, and the lift and weight must be equal andopposite according to the laws of motion, i.e.

Lift = Weight = mgThrust = Drag

Chalmers University of Technology

Range

m

s

sN

kgnconsumptiofuelspecific

F

mSFC

s

kgflowfuelm

s

mvelocityV

mrangeR

f

f

a

Chalmers University of Technology

Range

START

END

END

START

END

START

END

START

W

W

SLa

W

W

SL

W

W

W

W

a

a

af

a

ff

a

W

dW

D

LM

SFCg

aR

W

dW

D

LM

SFCg

a

W

dW

D

LM

SFCg

a

W

dW

D

LV

SFCgR

W

dW

D

LV

SFCgDFWL

WFSFCg

dWWVdR

FSFCg

dWV

FSFC

dmVdR

FSFC

dm

m

dm

V

dRdt

F

mSFC

dt

dmmV

dt

dR

1

1&

Chalmers University of Technology

Breguet range equation

END

STARTSL

W

W

SLa W

W

D

LM

SFCg

a

W

dW

D

LM

SFCg

aR

START

END

ln

For a preliminary performance analysis is the range equation usually simplified. If we assume flight at constant altitude, M, SFC and L/D the range equation becomes

which is frequently called the Breguet range equation

END

STARTa W

W

D

LV

SFCgR ln

1

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Breguet range equationThe Breuget range equation is written directly in terms of SFC. Clearly maximum range for a jetaircraft is not

dictated by maximum L/D, but rather the maximum value of the product M(L/D) or V(L/D).

ENDSTARTD

La

W

WD

L

D

La

D

La

D

L

D

L

L

LL

WWC

C

SSFCgR

W

dW

C

C

SSFCgW

dW

C

C

SSFCgdR

W

dW

C

C

S

W

SFCgW

dW

D

LV

SFCgdR

C

C

S

W

C

C

CS

W

D

LV

CS

WVCSVWL

END

START

22

2121

211

22

2

2

1 2

Chalmers University of Technology

Breuget range equationFrom the simplified range equation, maximum range is obtained from

• Flight at maximum

• Low SFC

• High altitude, low ρ

• Carrying a lot of fuel

D

L

C

C

Chalmers University of Technology

Range

LC

D

LM

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.82

4

6

8

10

12

14

16

Mach 0,63Mach 0,73Mach 0,80Mach 0,82Mach 0,83Mach 0,85

Chalmers University of Technology

Endurance

END

START

W

W

W

W

W

W

f

ff

W

W

D

L

SFCgt

simplifiedusuallyaboveequationtheisionapproximatfirstafor

W

dW

D

L

SFCgW

dW

D

L

SFCgW

dW

D

L

SFCgt

W

dW

D

L

SFCgDFWL

FSFCg

dW

FSFC

dm

m

dmdt

F

mSFC

dt

dmm

START

END

END

START

END

START

ln1

:

111

1&

Endurance is the amout of time that an aircraft can stay in the air on one given load of fuel

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Endurance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.94

6

8

10

12

14

16

18

20

Mach 0,63Mach 0,73Mach 0,80Mach 0,82Mach 0,83Mach 0,85

D

L

LC