c center of gravity limitations - smartcockpit - airline ... · pdf filecenter of gravity...

C-1

Center of Gravity Limitations

C-2

Example777-200 Center of

Gravity Limits(Ref. AFM or WBM)

Example777-200 Center of

Gravity Limits(Ref. AFM or WBM)

How does Boeing determine C.G. limits such as

these for any given airplane model?

C-3

Development of the Weight versus Moment C.G. Grid

C-4WT

L Moment = WT * L



m.a.c.

Dat

um

(+)(-)

Dat

um fo

r B.A

.

lemac

C-5



WT

L

Dat

um(+)(-)

Moment2 = WT * 2L

WT

2L

m.a.c.

Wei

ght (

~ 10

00 lb

)

Moment (in-lb)

Dat

um

Moment1 = WT * L

arm

= L

arm

= 2

L

Moment3 = WT * (-2L)

WT

-2Larm

= - 2L

C-6



Wei

ght (

~ 10

00 lb

)

Moment (in-lb)

Dat

um

c.g. (%mac)

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

C-7



Wei

ght

(100

0 kg

)

Moment (kg-in)

Dat

um

c.g. (%mac)

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Wei

ght

(100

0 kg

)

Center of Gravity ~ %MAC

Convert from weight versus %MAC to weight

versus moment

C-8



Wei

ght (

1000

kg)

Moment (kg-in)

Dat

um

c.g. (%mac)

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Enlarge this Area of Interest

C-9



Wei

ght

(100

0 kg

)

c.g. (%mac)

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Moment (kg-in)

C-10

Advantage of this Format is the Ability to Add Vectors GraphicallyAdvantage of this Format is the

Ability to Add Vectors Graphically

Wei

ght

(100

0 kg

)

c.g. (%mac)

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%D

atum

• Order of application does not affect final result

21

3

WTInit

1

2

3

Total Moment = WTInit * xInit +(∆WT1 * x1 ) + (∆WT2 * x2 ) - (∆WT3 * x3 )

Total Weight = WTInit + ∆WT1 + ∆WT2+ ∆WT3

∆WT1

x1∆WT2

x2

∆WT3

x3

xInit

• Starting point does not affect final ∆ weight and ∆ moment

C-11

Determining Desired Forward and Aft C.G. Limits

C-12

Design ObjectivesDesign Objectives

• The forward and aft C.G. limits for a given airplane model are selected by Boeing during the design of the airplane, and are meant to allow for airline-to-airline variations in:

- Operational Empty Weights- Interior Seating Arrangements- Cargo Loading – Bulk, Pallets, Containers- Fuel Loading and Usage- Operational Curtailments

• The airplane structure and layout is then designed to allow for loading of the airplane within these selected (and eventually certified) limits.

• Let’s look at an example of how this process might proceed using an airplane model we will call the 7G7-X00.

C-13

Determining Desired Fwd and Aft C.G. Limits:Accounting for OEW Variations

C-14

Accounting for OEW VariationsAccounting for OEW Variations

Boeing’s design objective is to provide forward and aft C.G. limits which will allow for airline variations in airplane configuration:

• Interior seat layout, locations of galleys, lavatories, emergency equipment, etc.

• Optional configurations and features (e.g., in-flight entertainment, pallets vs. containers, EE bay options, etc.)

C-15

Accounting for OEW VariationsAccounting for OEW Variations

AIRPLANE OEW AND CG VARIATION

CENTER OF GRAVITY (%MAC)

GRO

SS W

EIG

HT (

1000 L

B)

210

220

230

24019%

19%

24%

24%

NOMINAL OEW(based on tri-class, plus a selected set of ‘nominal’

options)

AFT OEW(based on tri-class, plus

other options which move the C.G. aft)

FWD OEW(based on dual-class,

plus other options which move the C.G. fwd)

(7G7-X00Example)

C-16

Determining Desired Fwd and Aft C.G. Limits:Accounting for Interior Seating

Arrangement Variations

C-17

Boeing’s design objective is to provide forward and aft C.G. limits which will allow for airline variations in interior seating arrangements:

• Ability to load various combinations of passengers, from empty to full.

• Ability to use various combinations of tri-class and dual-class seating arrangements on wide body aircraft.

• Ability to use various combinations of dual-class and single-class seating arrangements on narrow body aircraft.

Accounting for Interior Seating Arrangement VariationsAccounting for Interior Seating Arrangement Variations

C-18


OEWGR

OS

S W

EIG

HT (

10

00

LB

)


200

30010% 20% 30% 40%

2

Extreme Fwd Loading: Front-to-Rear

Load first-class seats

Load economy-class seats

1

2

1

(7G7-X00Example)

C-19


2

1OEWG

RO

SS

WEIG

HT (

10

00

LB

)


200

30010% 20% 30% 40%

Extreme Fwd Loading: Rear-to-Front


Load first-class seats4

3

4

3

(7G7-X00Example)

C-20


OEWGR

OS

S W

EIG

HT (

10

00

LB

)


200

30010% 20% 30% 40%

Dual-Class Defines the Most Forward Loading Interior Arrangement Considered

FC

EC

DC

Most Forward C.G. Considered Based on Dual-Class Seating

(7G7-X00Example)

C-21


OEWGR

OS

S W

EIG

HT (

10

00

LB

)


200

30010% 20% 30% 40%

Extreme Aft Loading: Front-to-Rear


Load business-class seats


2 1

32

3

1

(7G7-X00Example)

C-22


OEWGR

OS

S W

EIG

HT (

10

00

LB

)


200

30010% 20% 30% 40%

Extreme Aft Loading: Rear-to-Front


Load business-class seats


5

4

65

6

4

(7G7-X00Example)

Chosen as more “reasonable”

passenger loading for most-aft C.G.

(rare to have business and first

empty, with economy full)

C-23


OEWGR

OS

S W

EIG

HT (

10

00

LB

)


200

30010% 20% 30% 40%

Tri-Class Defines the Most Aft-Loading Interior

Arrangement Considered

FC

EC

TC

Most Aft C.G. Considered Based

on Tri-Class Seating

BC(7G7-X00Example)

C-24

Accounting for Interior Seating Arrangement Variations - SummaryAccounting for Interior Seating Arrangement Variations - Summary

(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)


30010%

200

20% 30% 40%

OEW

TCDC

FC

EC

BC

FC

EC

Most Aft C.G. Considered

Based on Tri-Class Seating

Most Forward C.G. Considered Based on Dual-Class Seating

C-25

Determining Desired Fwd and Aft C.G. Limits:Accounting for Cargo Loading Variations

C-26

Boeing’s design objective is to provide forward and aft C.G. limits which will allow for airline variations in cargo loading:

• Loading any number of passengers and only their baggage in the cargo compartments. (Baggage may be placed forward or aft for balance.)

• Loading any number of passengers with no baggage or cargo in the cargo compartments.

• Loading any number of passengers with full cargo (containerized and/or bulk).

• Loading any number of passengers with full containerized cargo only. (There should be no requirement to balance the airplane with bulk cargo.)

Accounting for Cargo VariationsAccounting for Cargo Variations

C-27


(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

200

OEW

20% 30% 40%0%

300

400

AIRPLANE WEIGHT & C.G.WITH PASSENGERS & CARGO

1

Loading Cargo: Most fwd C.G.

Passenger Bags1

C-28

(7G7-X00Example)

Loading Cargo: Most fwd C.G.

Passenger BagsForward Cargo compartmentAft Cargo compartmentBulk Cargo compartment

1


2

3

4

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

200

OEW

20% 30% 40%0%

300

400


1

2

34

Most Forward C.G. Considered

Based on Loading Passengers and Full Cargo (no

bulk)

C-29

Loading Cargo: Required MZFW

Forward Cargo compartmentAft Cargo compartmentForward Cargo compartmentAft Cargo compartmentBulk Cargo compartment

5


6

7

8

9

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

200

OEW

20% 30% 40%0%

300

400


5

6

7

8

9

Possible Point to Consider for

Required MZFW

(7G7-X00Example)

C-30

Loading Cargo: Required MZFW

Repeat steps 5 through 9,beginning at the highest weight for tri-class passengers

10


(7G7-X00Example)

Another Possible Point to Consider

for Required MZFWG

RO

SS

WE

IGH

T (

10

00

LB

)


10%

200

OEW

20% 30% 40%0%

300

400


10

C-31


Loading Cargo: Most aft C.G.

Passenger BagsAft and Forward Cargo

11

12

(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

OEW

20% 30% 40%0%

300

400


200

11

12

Most Forward C.G. Considered

Based on Loading Passengers and Full Cargo (no

bulk)

Most Aft C.G. Considered Based

on Loading Passengers and

Baggage

C-32

Determining Desired Fwd and Aft C.G. Limits:Accounting for Fuel Loading and Usage

Variations

C-33

Accounting for Fuel Loading and Usage VariationsAccounting for Fuel Loading and Usage Variations

Boeing’s design objective is to provide forward and aft C.G. limits which will allow for airline variations in fuel loading and usage:

• Use of the total fuel capacity – from empty to full.• Ability to load to the maximum gross weight.

C-34


Fuel Vector Added to Most FWD C.G. Point

Being Considered

(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

OEW

20% 30% 40%0%

300

400

200

500

AIRPLANE WEIGHT & C.G.WITH PASSENGERS, CARGO & FUEL

Fuel Vector Added to Most Aft C.G. Point Being

Considered

C-35


(7G7-X00Example)

40%

AIRPLANE WEIGHT & C.G.WITH PASSENGERS, CARGO & FUEL

Notice that adding the fuel vector to full cargo (no bulk) would have actually produced a

slightly more fwd C.G.

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

OEW

20% 30%0%

300

400

200

500

≈ 34%

C-36

Determining Desired Fwd and Aft C.G. Limits:Accounting for Operational Curtailment

Variations

C-37

Accounting for Operational Curtailment Variations Accounting for Operational Curtailment Variations

Boeing’s design objective is to provide forward and aft C.G. limits which will allow for airline variations in “operational curtailments” to these C.G. limits. Operational curtailments are generally used to account for:

• Landing gear and flap movement.• In-flight movement of passengers, crew, and service

carts.• Difference between actual and assumed C.G. locations

for cargo, passenger seating, fuel loading and usage, water movement and usage.

* (Note: Later in this course we will be discussing the concept and use of operational curtailments in detail.) *

C-38


(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

OEW

20% 30% 40%0%

300

400

200

500

Including Forward and Aft Curtailments

Estimated Fwd C.G. Curtailments

Estimated Aft C.G. Curtailments

C-39


(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)


10%

OEW

20% 30% 40%0%

300

400

200

500

Required C.G. Limits

Required Fwd Limit Required Aft Limit

C-40

Weight and Structural Limitations on the C.G. Envelope

C-41



The allowable forward and aft C.G. limits may be further constrained by:

• Certified weight limitations – MTW, MTOW, MLW, MZFW.• Structural limitations imposed by various parts of the

airplane’s structure.• Additional limitations imposed in order to maintain control

of the airplane during its operation.

C-42

Certified Weight Limitations Certified Weight Limitations

(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)10%

OEW

20% 30% 40%0%

300

400

200

500

Basic Gross Weight / C.G. Limits

MTOW

MLW

MZFW


C-43

• The strength of the wing’s structure can impose a limitation on the forward C.G. limits.

WING LOADFor the airplane to be in equilibrium, the sum of the moments about the tail must = 0:

ΣM Tail = W (B.A.Tail – B.A.C.G.) – L Wing(B.A.Tail – B.A.Wing) = 0

L Wing = W (B.A.Tail – B.A.C.G.)(B.A.Tail – B.A.Wing)

Constant Wing Load Constant Wing Load

Weight

Lift Wing

Lift Tail

• The load on the wing is increased both by increasing airplane weight, and by forward movement of the center of gravity. Eventually, the wing’s limits are reached.

C-44

Constant Wing Load Constant Wing Load

(7G7-X00Example)

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500


Constant Wing Load

MLW

MZFW


MTOW

C-45

TAIL LOADFor the airplane to be in equilibrium, the sum of the moments about the wing must = 0 :

ΣM Wing = W (B.A. Wing – B.A. C.G.) – LTail (B.A.Tail – B.A.Wing) = 0

LTail = W (B.A. Wing – B.A. C.G.)(B.A.Tail – B.A.Wing)

Constant Tail Load Constant Tail Load

• The strength of the tail and aft body structure can impose a limitation on the forward C.G. limits.

• The load on the tail and aft body is increased both by increasing airplane weight, and by forward movement of the center of gravity. Eventually, the tail or aft body’s limits are reached.

Weight

Lift Wing

Lift Tail

C-46

(7G7-X00Example)

Constant Tail Load Constant Tail Load

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500


Constant Tail Load

MLW

MZFW


MTOW

C-47

NOSE LANDING GEAR LOAD

For the airplane to be in equilibrium, the sum of the moments about the main landing gear must = 0 :

ΣM MLG = W (B.A. MLG – B.A. C.G.) – LNLG (B.A. MLG – B.A. NLG) = 0

LNLG = W (B.A. MLG – B.A. C.G.)(B.A. MLG – B.A. NLG)

Constant Nose Landing Gear Load Constant Nose Landing Gear Load

Load MLGLoad NLG Weight

• The strength of the nose gear structure can impose a limitation on the forward C.G. limits.

• The load on the NLG is increased both by increasing airplane weight, and by forward movement of the center of gravity. Eventually, the NLG limits are reached.

C-48

(7G7-X00Example)

Constant Nose Landing Gear Load Constant Nose Landing Gear Load

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500


Constant NLG Load

MLW

MZFW


MTOW

C-49

Constant Main Landing Gear Load Constant Main Landing Gear Load


• The strength of the main landing gear structure can impose a limitation on the aft C.G. limits.

MAIN LANDING GEAR LOAD

For the airplane to be in equilibrium, the sum of the moments about the nose landing gear must = 0 :

ΣM NLG = LMLG (B.A. MLG – B.A. NLG) – W (B.A. C.G. – B.A. NLG) = 0

LMLG = W (B.A. C.G. – B.A. NLG)(B.A. MLG – B.A. NLG)

• The load on the MLG is increased both by increasing airplane weight, and by aft movement of the center of gravity. Eventually, the MLG limits are reached.

C-50

(7G7-X00Example)

Constant Main Landing Gear Load Constant Main Landing Gear Load

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500


Constant MLG Load

MLW

MZFW


MTOW

C-51

(7G7-X00Example)

Combining All Structural Limitations Combining All Structural Limitations

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500

Design Gross Weight / C.G. Limits

MLW

MZFW


MTOW

C-52

Additional Limitations for Control: Brake Release Tip-Up

Additional Limitations for Control: Brake Release Tip-Up

• At brake release (full thrust, static airplane) there is a possibility of reduced nose gear steering effectiveness, or actual airplane tip up.

BRAKE RELEASE TIP-UP

For the airplane to be in equilibrium, the sum of the moments about the airplane CG must = 0 :

ΣM CG = LMLG (B.A. MLG – B.A. C.G.) – T ∆h – LNLG (B.A. C.G. – B.A. NLG) = 0

LNLG = LMLG (B.A. MLG – B.A. C.G.) – T ∆h(B.A. C.G. – B.A. NLG)

• The load on the NLG is reduced by: decreasing airplane weight, aft movement of the C.G., and increasing thrust. At light enough NLG loads, steering effectiveness is reduced, and eventually, the NLG load can become negative causing the airplane to tip up.


Thrust

∆h

C-53

(7G7-X00Example)

Brake Release Tip-Up Brake Release Tip-Up

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500


MLW

MZFW


MTOW

Brake

Rele

ase T

ip-U

p

C-54

Additional Limitations for Control: Ground Handling - Tipping

Additional Limitations for Control: Ground Handling - Tipping

• On the ground, if the C.G. moves aft of the main landing gear, the airplane will tip up.

• To account for the effects of towing and ground operations, a ‘ground stability limit’ is imposed at C.G.’s forward of the absolute aft limit. This ground stability limit takes into account 3% ramp slope, Towing forces, 40 knot headwind, etc.

NOSE LANDING GEAR LOAD

For the airplane to be in equilibrium, the sum of the moments about the main landing gear must = 0 :

ΣM MLG = W (B.A. MLG – B.A. C.G.) – LNLG (B.A. MLG – B.A. NLG) = 0

LNLG = W (B.A. MLG – B.A. C.G.)(B.A. MLG – B.A. NLG)


C-55

(7G7-X00Example)

Ground Handling - TippingGround Handling - Tipping

GR

OS

S W

EIG

HT (

10

00

LB

)

10%

OEW

20% 30% 40%0%

300

400

200

500


MLW

MZFW


MTOW

Grou

nd S

tabi

lity

Lim

itAf

t Tip

ping

Lim

it

C-56

Examples of C.G. Envelopes for Actual Airplanes

C-57

(For trainingpurposes only.

Not kept up to date)

Example777-200 Center

of Gravity Limits


of Gravity Limits

C-58

Limitations on 777-200Center of Gravity


CENTER OF GRAVITY ~ % MAC

Bod

y St

reng

th,L

oada

bilit

y, T

ail S

ize

Stab

ility

& C

ontr

ol

WingMainGear

MissionPerformance

Fuel Vector

Brak

e Re

leas

e Ti

p-Up

Loadability, Stability & C

ontrol

0 5 20 25 30 35 40 45 50120000

160000

140000

180000

200000

220000

240000

260000

280000

300000

GR

OSS

WEI

GH

T ~

KG

Nose

Gea

r

15

C-59


of Gravity Limits


of Gravity Limits



C-60



Stab

ility

& C

ontro

l

WingMainGear

MissionPerformance

Fuel Vector

Tail

Pow

er


ontrol

0 5 10 15 20 25 30 35 40


35000

40000

45000

50000

55000

60000

65000

70000

75000

80000

85000

GR

OSS

WEI

GH

T ~

KG

Bod

y St

reng

th,L

oada

bilit

y, T

ail S

ize

Brak

e Re

leas

e Ti

p-Up

C-61


of Gravity Limits


of Gravity Limits



C-62



Land

ing

Lim

it fo

r Gea

r

Hor

izon

tal S

tabi

lizer

Trim

Lin

e fo

r Tak

eoff

WingMission

Performance

Fuel Vector

Brak

e Re

leas

eTi

p-Up


ontrol

0 5 25 20 25 30 35 40180000

220000

200000

240000

260000

280000

300000

340000

360000

400000

GR

OSS

WEI

GH

T ~

KG

Nose

Gea

r

10

Brak

e Re

leas

e Ti

p-Up

Tail Load With Tail Fuel

Landing Performance

FuelVector


320000

380000

420000

Bod

y St

reng

th,

Load

abili

ty, T

ail S

ize

C-63

End ofCenter of Gravity Limitations

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