Center of Gravity Limitations

8/13/2019 Center of Gravity Limitations

1/63

C-1

Center of Gravity Limitations


2/63

C-2

Example

777-200 Center of

Gravity Limits(Ref. AFM or WBM)

Example

777-200 Center of

Gravity Limits(Ref. AFM or WBM)

How does Boeingdetermine C.G.

limits such as

these for any givenairplane model?


3/63

C-3

Development of the Weight versus

Moment C.G. Grid


4/63

C-4WT

LMoment = WT * L

Development of the Weight versusMoment C.G. Grid


m.a.c.Datum

(+)(-)

Da

tumforB.A.

lemac


5/63

C-5



WT

L

Datum

(+)(-)

Moment2 = WT * 2L

WT

2L

m.a.c.

Weight(~1000lb)

Moment (in-lb)

Datum

Moment1 = WT * L

ar

m=L

arm

=2

L

Moment3 = WT * (-2L)

WT

-2L

arm

=-

2L


6/63C-6



W

eight(~1000lb)

Moment (in-lb)

D

atum

c.g. (%mac)

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


7/63C-7



Weight(1000kg)

Moment (kg-in)

D

atum

c.g. (%mac)

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

W

eight(1000

kg)

Center of Gravity ~ %MAC

Convert from weight

versus %MAC to weight

versus moment


8/63C-8



Weight(1000

kg)

Moment (kg-in)

D

atum

c.g. (%mac)

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

Enlarge this

Area of Interest


9/63C-9



W

eight(1000

kg)

c.g. (%mac)

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

Moment (kg-in)


10/63C-10

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

Ability to Add Vectors Graphically

W

eight(1000

kg)

c.g. (%mac)

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

m

Order of application does not

affect final result

2

1

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


11/63C-11

Determining Desired Forward and Aft

C.G. Limits


12/63C-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 allowfor loading of the airplane within these selected (andeventually certified) limits.

Lets look at an example of how this process mightproceed using an airplane model we will call the 7G7-X00.


13/63C-13

Determining Desired Fwd and Aft C.G. Limits:

Accounting for OEW Variations


14/63C-14

Accounting for OEW VariationsAccounting for OEW Variations

Boeings design objective is to provide forward andaft C.G. limits which will allow for airline variations inairplane 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.)


15/63C-15

Accounting for OEW VariationsAccounting for OEW Variations

AIRPLANE OEW AND CG VARIATION

CENTER OF GRAVITY (%MAC)

GROS

SWEIGHT

(1000LB)

210

220

230

24019%

19%

24%

24%

NOMINAL OEW(based on tri-class, plus aselected set of nominal

options)

AFT OEW(based on tri-class, plus

other options whichmove the C.G. aft)

FWD OEW(based on dual-class,

plus other options whichmove the C.G. fwd)

(7G7-X00

Example)


16/63C-16


Accounting for Interior SeatingArrangement Variations


17/63C-17

Boeings design objective is to provide forward

and aft C.G. limits which will allow for airlinevariations 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 arrangementson narrow body aircraft.

Accounting for Interior SeatingArrangement VariationsAccounting for Interior SeatingArrangement Variations


18/63C-18


OEWGROSSWEI

GHT(1000LB

)


200

30010% 20% 30% 40%

2

Extreme Fwd Loading: Front-to-Rear

Load first-class seats

Load economy-class seats

1

2

1

(7G7-X00

Example)


19/63C-19


2

1

OEWGROSSWEI

GHT(1000LB

)


200

30010% 20% 30% 40%

Extreme Fwd Loading: Rear-to-Front


Load first-class seats4

3

4

3

(7G7-X00

Example)


20/63C-20


OEWGROSSWEI

GHT(1000LB

)


200

30010% 20% 30% 40%

Dual-Class Defines the Most

Forward Loading InteriorArrangement Considered

FC

ECDC

Most ForwardC.G. ConsideredBased on Dual-Class Seating

(7G7-X00

Example)


21/63C-21


OEWGROSSWEI

GHT(1000LB

)


200

30010% 20% 30% 40%

Extreme Aft Loading: Front-to-Rear

Load first-class seatsLoad business-class seats


2 1

3

2

3

1

(7G7-X00

Example)


22/63

C-22


OEWGROSSWEI

GHT(1000LB

)


200

30010% 20% 30% 40%

Extreme Aft Loading: Rear-to-Front

Load economy-class seatsLoad business-class seats

Load first-class seats

5

4

6

5

6

4

(7G7-X00

Example)

Chosen as morereasonable

passenger loadingfor most-aft C.G.

(rare to have

business and firstempty, with

economy full)


23/63

C-23


OEWGROSSWEI

GHT(1000LB

)


200

30010% 20% 30% 40%

Tri-Class Defines the Most

Aft-Loading InteriorArrangement Considered

FC

EC

TC

Most Aft C.G.Considered Based

on Tri-Class

Seating

BC(7G7-X00

Example)


24/63

C-24

Accounting for Interior SeatingArrangement Variations - SummaryAccounting for Interior SeatingArrangement Variations - Summary

(7G7-X00

Example)

GROSS

WEIGHT(1000LB)


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. ConsideredBased on Dual-Class Seating


25/63

C-25


Accounting for Cargo Loading Variations


26/63

C-26

Boeings design objective is to provide forward and aftC.G. limits which will allow for airline variations in cargoloading:

Loading any number of passengers and only theirbaggage in the cargo compartments. (Baggage maybe placed forward or aft for balance.)

Loading any number of passengers with no baggageor cargo in the cargo compartments.

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

Loading any number of passengers with fullcontainerized cargo only. (There should be norequirement to balance the airplane with bulk cargo.)

Accounting for Cargo VariationsAccounting for Cargo Variations


27/63

C-27


(7G7-X00

Example)

GROSSWE

IGHT(1000LB

)


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


28/63

C-28

(7G7-X00

Example)

Loading Cargo: Most fwd C.G.

Passenger Bags

Forward Cargo compartment

Aft Cargo compartment

Bulk Cargo compartment

1


2

3

4

GROSSWEIGHT(1000LB

)


10%

200

OEW

20% 30% 40%0%

300

400


1

2

3

4

Most ForwardC.G. Considered

Based on LoadingPassengers andFull Cargo (no

bulk)


29/63

C-29

Loading Cargo: Required MZFW





Bulk Cargo compartment

5


6

7

8

9

GROSSWEIGHT(1000LB

)


10%

200

OEW

20% 30% 40%0%

300

400


5

6

7

8

9

Possible Point toConsider for

Required MZFW

(7G7-X00

Example)


30/63

C-30

Loading Cargo: Required MZFW

Repeat steps 5 through 9,

beginning at the highest

weight for tri-class

passengers

10


(7G7-X00

Example)

Another PossiblePoint to Consider

for Required MZFW

GROSSWEIGHT(1000LB

)


10%

200

OEW

20% 30% 40%0%

300

400


10


31/63

C-31


Loading Cargo: Most aft C.G.

Passenger Bags

Aft and Forward Cargo

11

12

(7G7-X00

Example)

GROSSWEIGHT(1000LB

)


10%

OEW

20% 30% 40%0%

300

400


200

11

12

Most ForwardC.G. Considered

Based on LoadingPassengers andFull Cargo (no

bulk)

Most Aft C.G.Considered Based

on LoadingPassengers and

Baggage


32/63

C-32


Accounting for Fuel Loading and Usage

Variations

A ti f F l L di d


33/63

C-33

Accounting for Fuel Loading andUsage VariationsAccounting for Fuel Loading andUsage Variations

Boeings design objective is to provide forward and aft

C.G. limits which will allow for airline variations in fuelloading and usage:

Use of the total fuel capacity from empty to full.

Ability to load to the maximum gross weight.

A i f F l di dA ti f F l L di d


34/63

C-34


Fuel Vector Added toMost FWD C.G. Point

Being Considered

(7G7-X00

Example)

GROSSWEIGHT(1000LB)


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 BeingConsidered

A ti f F l L di dA ti f F l L di d


35/63

C-35


(7G7-X00

Example)

40%

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

Notice that adding thefuel vector to full cargo(no bulk) would haveactually produced a

slightly more fwd C.G.

GROSSWEIGHT(1000LB)


10%

OEW

20% 30%0%

300

400

200

500

34%


36/63

C-36


Accounting for Operational CurtailmentVariations

A ti f O ti lA ti f O ti l


37/63

C-37

Accounting for OperationalCurtailment VariationsAccounting for OperationalCurtailment Variations

Boeings design objective is to provide forward and aft C.G.limits which will allow for airline variations in operationalcurtailments to these C.G. limits. Operational curtailmentsare generally used to account for:

Landing gear and flap movement.

In-flight movement of passengers, crew, and servicecarts.

Difference between actual and assumed C.G. locationsfor 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.) *



38/63

C-38


(7G7-X00

Example)

GROSSWEIGHT(1000LB)


10%

OEW

20% 30% 40%0%

300

400

200

500

Including Forward and Aft Curtailments

Estimated Fwd

C.G. Curtailments

Estimated AftC.G. Curtailments



39/63

C-39


(7G7-X00

Example)

GROSSWEIGHT(1000LB)


10%

OEW

20% 30% 40%0%

300

400

200

500

Required C.G. Limits

Required Fwd Limit Required Aft Limit


40/63

C-40

Weight and Structural Limitations on

the C.G. Envelope

W i ht d St t l Li it tiW i ht d St t l Li it ti


41/63

C-41

Weight and Structural Limitationson the C.G. Envelope

Weight and Structural Limitationson the C.G. Envelope

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

Certified weight limitations MTW, MTOW, MLW, MZFW.

Structural limitations imposed by various parts of theairplanes structure.

Additional limitations imposed in order to maintain control

of the airplane during its operation.

C tifi d W i ht Li it tiCertified Weight Limitations


42/63

C-42

Certified Weight LimitationsCertified Weight Limitations

(7G7-X00

Example)

GROSSWEIGHT(1000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500

Basic Gross Weight / C.G. Limits

MTOW

MLW

MZFW


C t t Wi L dConstant Wing Load


43/63

C-43

The strength of the wings structure can impose alimitation on the forward C.G. limits.

WING LOAD

For the airplane to be in equilibrium, the sum of the moments about the

tail must = 0:M 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 LoadConstant 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 ofgravity. Eventually, the wings limits are reached.

C t t Wi L dConstant Wing Load


44/63

C-44

Constant Wing LoadConstant Wing Load

(7G7-X00

Example)

GROSSWEIGHT(1

000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500


Constant

Wing Load

MLW

MZFW


MTOW

Constant Tail LoadConstant Tail Load


45/63

C-45

TAIL LOADFor the airplane to be in equilibrium, the sum of the moments about the wing

must = 0 :M 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)


The strength of the tail and aft body structure canimpose 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 ofthe center of gravity. Eventually, the tail or aft bodys limitsare reached.

Weight

Lift Wing

Lift Tail



46/63

C-46

(7G7-X00

Example)


GROSSWEIGHT(1

000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500


ConstantTail Load

MLW

MZFW


MTOW

Constant Nose Landing Gear LoadConstant Nose Landing Gear Load


47/63

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 :M 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)


LoadMLG

Load NLG Weight

The strength of the nose gear structure canimpose 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 ofgravity. Eventually, the NLG limits are reached.



48/63

C-48

(7G7-X00

Example)


GROSSWEIGHT(1

000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500


Constant

NLG Load

MLW

MZFW


MTOW

Constant Main Landing Gear LoadConstant Main Landing Gear Load


49/63

C-49


LoadMLG

Load NLG Weight

The strength of the main landing gear structure canimpose 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 :M 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 ofgravity. Eventually, the MLG limits are reached.



50/63

C-50

(7G7-X00

Example)


GROSSWEIGHT(1000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500


ConstantMLG Load

MLW

MZFW


MTOW

Combining All Structural LimitationsCombining All Structural Limitations


51/63

C-51

(7G7-X00

Example)

Combining All Structural LimitationsCombining All Structural Limitations

GROSSWEIGHT(1000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500

Design Gross Weight / C.G. Limits

MLW

MZFW


MTOW

Additional Limitations for Control:Additional Limitations for Control:


52/63

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 apossibility of reduced nose gear steering effectiveness, oractual 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 :M 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 canbecome negative causing the airplane to tip up.

Load MLGLoad NLG Weight

Thrust

h

Brake Release Tip UpBrake Release Tip-Up


53/63

C-53

(7G7-X00Example)

Brake Release Tip-UpBrake Release Tip-Up

GROSSWEIGHT(1000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500


MLW

MZFW


MTOW

Brake

Release

Tip

-Up

Additional Limitations for Control:Additional Limitations for Control:


54/63

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 mainlanding 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 account3% 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 :M 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)

Load MLGLoad NLG Weight

Ground Handling - TippingGround Handling - Tipping


55/63

C-55

(7G7-X00Example)

Ground Handling - TippingGround Handling - Tipping

GROSSWEIGHT(1000LB)

10%

OEW

20% 30% 40%0%

300

400

200

500


MLW

MZFW


MTOW

Ground

Stabi

lity

Lim

it

A

ftTip

pin

gL

imit


56/63

C-56

Examples of C.G. Envelopes for

Actual Airplanes


57/63

C-57

(For trainingpurposes only.

Not kept up to date)

Example777-200 Center

of GravityLimits


of Gravity

Limits

Limitations on 777-200Limitations on 777-200


58/63

C-58

Limitations on 777 200Center of GravityCenter of Gravity

CENTER OF GRAVITY ~ % MAC

BodyStrength,Loadability,TailSize

Stabilit

y&

Con

trol

WingMainGear

MissionPerformance

FuelV

ector

Brak

eR

ele

as

eT

ip-Up

Loa

dability,Stability&Control

0 5 20 25 30 35 40 45 50

120000

160000

140000

180000

200000

220000

240000

260000

280000

300000

GROSSWEIG

HT~KG

Nose

Gear

15


59/63

C-59


of GravityLimits


of GravityLimits





60/63

C-60

Center of GravityCenter of Gravity

Stabilit

y&Control

WingMainGear

MissionPerformance

FuelV

ecto

r

Tail

Power

Loadability

,Stability&Control

0 5 10 15 20 25 30 35 40


35000

40000

45000

50000

55000

60000

65000

70000

75000

80000

85000

GROSSWEI

GHT~KG

BodyStrength,L

oadability,TailSize

Brak

eR

elea

se

Tip

-Up


61/63

C-61


of Gravity

Limits


of Gravity

Limits





62/63

C-62

Center of GravityCenter of Gravity

LandingLimitforGear

HorizontalStabilizer

TrimLineforTakeoff

Wing

MissionPerformance

FuelVector

Br

ak

eRele

ase

Tip

-Up

Load

ability,Stability&C

ontrol

0 5 25 20 25 30 35 40

180000

220000

200000

240000

260000

280000

300000

340000

360000

400000

GROSSWE

IGHT~KG

Nose

Gear

10

Brak

eRele

ase

Ti

p-Up

TailLoad

WithTailFuel

Landing Performance

FuelVector


320000

380000

420000

BodyStrength,

Loadability,TailSize


63/63

End of

Center of Gravity Limitations

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Center of Gravity Limitations