2010-10-11

1

Airplane sizing

climb w=X1m/s

descend w=-X8km/h

hold t=X9h

cruise V=X4km/h

loiter t=X6h

cruise V=X7km/h

X3 km

H1=

X2

m

H2=

X5

m

H1=

X1

0m

X8 km

takeoff landing

Mission profile

2010-10-11

2

Commercial airplane

Agricultural airplane

Motorized glider

Dogfight

Mission profile

epfcTO WWWWW

expnexppWWW

WTO – takeoff weight

Wc – crew weight

Wf – fuel weight

Wp – payload weight

We – empty weight

Wexp – expendable payload weight

Wnexp – nonexpendable payload weight

2010-10-11

3

Airplanes expending their payloads in flight

1) Assume the takeoff weight

2) Calculate weight after takeoff

3) Calculate weight after climb (ATTENTION: weight before this

phase is equal to the weight after previous phase)

4) Calculate weight after cruise (ATTENTION: as above)

5) Calculate weight after task execution (ATTENTION1: as above,

ATTENTION2: airplane can release a parto of its payload)

6) Calculate weight after return cruise (ATTENTION: as above)

7) Calculate weight after holding (ATTENTION: as above)

8) Calculate weight after landing and taxi (ATTENTION: as above)

9) Calculate an empty weight (ATTENTION: subtract weights of

crew, remaining payload, fuel reserve weight and trapped fuel

weight from weight after landing)

10) Calculate realistic empty weight from We/WTO=f(WTO) plot

11) Calculate the difference between weights calculated in points

9) i 10)

12) Modify takeoff weight

Takeoff

Takeoff = engine ignition and warmup + taxi + takeoff run +

+ climbing to prescribed altitude

975,0)W/W(97,0 fTO1

2010-10-11

4

Climb and acceleration

P

Corke

Wf/W

i

1)

2)

Ad 1 jet airplane

Ad 2 propeller airplane

L – Lift

D – Drag

- propeller acceleration

C – specific fuel consumption in lbfuel/h/lbthrust for jets

lbfuel/h/SHP for propeller

driven airplanes

Cruise - Breguet’s equations

)W/Wln(D

L

C

VR

1nn

)W/Wln(D

L

CR

1nn

(Imperial)

2010-10-11

5

)W/Wln(C

C

gC

VR

1nn

x

z

Cruise - Breguet’s equations

)W/Wln(C

C

gCR

1nn

x

z

1)

2)

Ad 1 jet airplane

Ad 2 propeller airplane

Cz – Lift coefficient (CL in English)

Cx – Drag coefficient (CD in English)

- propeller acceleration

C – specific fuel consumption in kg/h/kN for jets

kg/h/kW for propeller

driven airplanes

(SI+Polish symbols)

or

E. Cichosz „Charakterystyka i zastosowanie napędów”

Raymer

8,0

Piston

Turboprop

Turbofan

Bypass turbojet

Turbojet

Ramjet

Turbojet with afterburner

2010-10-11

6

Raymer

maxD

L

D

L

C

C94,0

C

C

Raymer

2010-10-11

7

Raymer

B-47 Avro Vulcan

Sr reference area 1430 3446

Sw wetted area 11300 9600

Wing span 116 90

Sw/Sr 7,9 2,8

AR 9,4 3,0

AR*Sr/Sw 1,2 1,1

L/D max 17,2 17,0

B-47

Vulcan

Acceleration

P

M

1

1,0

P

1,0

M

1,0

M

P

1,0

1,0

1,0

P

M

P

M

n

1n

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

W

Corke

2010-10-11

8

Combat

tTCWWmaxmax1nn

n

maxmax

n

1n

W

tTC1

W

W

T- thrust

t - time

Loiter

e.g. reconnaissance aircraft

)W/Wln(C

C

gC

1t 1nn

D

L

)W/Wln(V

1

C

C

gCt 1nn

D

L

2010-10-11

9

Return cruise

)W/Wln(C

C

gC

VR 1nn

D

L

)W/Wln(C

C

gCR 1nn

D

L

W is lower so it is advantageous to fly higher. Airplane should

be re-trimmed what increases the drag.

Holding before landing

)W/Wln(C

C

gC

1t 1nn

D

L

)W/Wln(V

1

C

C

gCt 1nn

D

L

2010-10-11

10

Landing

975,0)W/W(97,0fn1n

Airplanes expending their payloads in flight

1) Assume the takeoff weight

2) Calculate weight after takeoff

3) Calculate weight after climb (ATTENTION: weight before this

phase is equal to the weight after previous phase)

4) Calculate weight after cruise (ATTENTION: as above)

5) Calculate weight after task execution (ATTENTION1: as above,

ATTENTION2: airplane can release a part of its payload)

6) Calculate weight after return cruise (ATTENTION: as above)

7) Calculate weight after holding (ATTENTION: as above)

8) Calculate weight after landing and taxi (ATTENTION: as above)

9) Calculate an empty weight (ATTENTION: subtract weights of

crew, remaining payload, fuel reserve weight and trapped fuel

weight from weight after landing)

10) Calculate realistic empty weight from We/WTO=f(WTO) plot

11) Calculate the difference between weights calculated in points

9) i 10)

12) Modify takeoff weight

2010-10-11

11

emptyfuelpayloadcrewTO WWWWW

TO

TO

eTO

TO

fpaycrTO W

W

WW

W

WWWW

TO

e

TO

f

paycr

TO

W

W

W

W1

WWW

Airplanes not expending their payloads in flight

m

L

1

2

TO

1

m

m

2

2

1

1

TO

LfTOL

W

W...

W

W

W

W

W

W...

W

W

W

W

W

W)W/W(

W1...m – airplane weights after each phase of the flight

)/1(06,1/ TOLTOF WWWW

TOF

L W06,1

WW

1W06,1

W

W

W

TO

F

TO

L

2010-10-11

12

Wing and power loading

estimation

Takeoff

1

T

W

C

1

S

WTOP

TOmaxLTO

SLTO/

)W/T)(TOP(87)TOP(9,20sTO

ang. - CL= CZ – pol.

2010-10-11

13

Landing

maxLC

1

S

WLP

400)LP(118sL

Climb

GW

DTsin

dH

dV

g

V1

W/PsinV

dt

dH s

)DT(VPs

for dV/dH=0

Ps – excess power

G - gradient

2010-10-11

14

Climb

0S

WG

W

T

Aeq

1

S

WqC

2

0D

Climb

Aeq

2

Ae

C4G

W

TG

W

T

S

W

0D

2

Ae

C2G

W

T 0D

2010-10-11

15

Range – propeller driven airplane

)W/Wln(C

C

gCR 1nn

D

L

Maximum range will be reached for CL

reflecting maximum gliding ratio:

0DCeAqS

W

Range – jet airplane

)W/Wln(C

C

gC

VR 1nn

D

L

Maximum range will be reached when VCL/CD

achieves the maximum

3

AeCq

S

W 0D

2010-10-11

16

Turn

r

L

sinLr

mV

cosLW

2

nW

L

cos

1

Turn

V

1ng2

1g

V

qC

S

W

2

maxL

2010-10-11

17

Sustained turn

DT

Sustained turn

CD0

2010-10-11

18

Sustained turn

Aeq

n2

Ae

Cn4

W

T

W

T

S

W2

0D

22

Ae

Cn2

W

T 0D

Sustained turn

S/W

qC

W

T

S/W

Aeqn 0D

max

max

V

1S/W

qC

W

T

S/W

Aeqg 0D

max

max

2010-10-11

19

Maximum altitude

1n

2

VCqC

S

W2

maxh

maxLmaxL

1

T

W

C

1

S

WTOP

TOmaxLTO

)W/T)(TOP(87)TOP(9,20sTO

maxLC

1

S

WLP

400)LP(118s

L

Aeq

2

Ae

C4G

W

TG

W

T

S

W0D

2

Ae

C2G

W

T0D

0DAeC

n

q

S

W

0DCeAq

S

W

3

AeCq

S

W0D

1g

V

qC

S

W2

maxL

Aeq

n2

Ae

Cn4

W

T

W

T

S

W2

0D

22

Ae

Cn2

W

T0D

2

VCqC

S

W2

maxhmaxLmaxL

Takeoff

Landing

Climb

Acceleration

Range

Turn

Sustained turn

Maximum altitude

or

2010-10-11

20

T/W

W/S

Takeoff

Landing

Climb

Cruise

Example

Assumptions:

Takeoff weight 33100kg

Fuel weight 9700kg

Cruise airspeed 780km/h na 10000m

Minimum airspeed 200km/h

Aspect ratio 8

L/D 15

Takeoff & landing distance 1100m

Climb 9m/s

2010-10-11

21

Takeoff

)W/T)(TOP(87)TOP(9,20sTO

1

T

W

C

1

S

WTOP

TOmaxLTO

maxL

TO

maxL

CS

W834,3S

C

1

S

W133,0

W

T

Imperial

SI

Takeoff

2C maxL

takeoff

2010-10-11

22

Landing

400)LP(118sL

maxLC

1

S

WLP

75,0

C122S

S

W maxLL

Imperial

SI

Landing

2/2920 mN

S

W

L

17,2C maxL

75,0

C122S

S

W maxLL

2010-10-11

23

Example

Assumptions:

Takeoff weight 33100kg

Fuel weight 9700kg

Cruise airspeed 780km/h na 10000m

Minimum airspeed 200km/h

Aspect ratio 8

L/D 15

Takeoff & landing distance 1100m

Climb 9m/s

Landing

2/2920 mN

S

W

L

17,2C maxL

75,0

C122S

S

W maxLL

kgmL 23400970033100

279

2920

81,923400mS

2/4130

79

81,933100mN

S

W

TO

2010-10-11

24

Takeoff and landing

Takeoff

Landing

Climb

G

S

W

Aeq

1

S

WqC

W

T

2

0D

0S

WG

W

T

Aeq

1

S

WqC

2

0D

V

wG z

0DmaxD

L

C

eA

2

1

C

C

2010-10-11

25

Takeoff, climb and landingVclimb = 350 km/h G=0,094, CD0 = 0,0222

T/W

W/S

Takeoff

Landing

Climb

Climb

Aeq

2

Ae

C4G

W

TG

W

T

S

W

0D

2

Ae

C2G

W

T 0D

0S

WG

W

T

Aeq

1

S

WqC

2

0D

2010-10-11

26

Takeoff, climb and landing

Ae

C2G

W

T 0D

T/W

W/S

Takeoff

Landing

Climb

Cruise

2m/N3757

S

W

3

AeCq

S

W 0D

2010-10-11

27

Cruise

2m/N3757

S

W

W/S

t

Cruise

2m/N3757

S

W

W/S

t

2010-10-11

28

Cruise

2m/N3757

S

W

W/S

t

Cruise

t

2010-10-11

29

Example

Assumptions:

Takeoff weight 33100kg

Fuel weight 9700kg

Cruise airspeed 780km/h na 10000m

Minimum airspeed 200km/h

Aspect ratio 8

L/D 15

Takeoff & landing distance 1100m

Climb 9m/s

Cruise

2m/N3757

S

W

274

3757

81,9*28250mS

kgm 28250485033100

3

AeCq

S

W 0D

2/4405

74

81,933100mN

S

W

TO

2010-10-11

30

Design point

If smallest engine is desired

T/W

W/S

Takeoff

Landing

Climb

Cruise

If maximum range is desired