1) An aircraft's static stability and center of gravity (CG) position depend on the CG being ahead of the aerodynamic center. 2) The CG position affects aircraft performance characteristics like stall speed, takeoff distance, and landing distance, as well as drag and fuel consumption. 3) The CG must remain within certified forward and aft limits that depend on the aircraft's weight and are expressed as a percentage of the mean aerodynamic chord.

1. MASS & BALANCE
1

2. Aircraft stability depends directly of C.G. position
Static stability:
W
W
Aircraft must be in static stability in whole flight regimes.
Therefore, C.G. position must be always ahead of
Aerodynamic Centre i.e. Centre of Wing’s Lift (Centre of
Pressure).
2

3. Influence of C.G. position on aircraft performance
V2 TOD
VS
VREF ALD
3

4. MORE FWD C.G. => DRAG FUEL CONSUMPTION
MORE AFT C.G. => DRAG FUEL CONSUMPTION
4

5. C.G. LIMITS
Range of C.G. position (FWD & AFT limit)
C.G.
Aft
Forward Mean Aerodynamic Chord. limit
limit
The CG position is expressed as a percentage of the Mean Aerodynamic Chord
(MAC) / Referent Chord (RC).
It must remain between a forward and an aft limit depending on the aircraft weight.
5

6. C.G. Envelope
Weight
MIT LI
FWD
IMIT
AFT L
C.G. position
(H-arm)
6

7. Certified vs. Operational C.G. limits
Certified Limits
•Limits determined during aircraft testing phase (only flight crew
onboard, no PAX, no CARGO).
•Certified C.G. envelope are published in the AFM and WBM
Operational Limits
•Certified Limits accounted for possible errors during operations:
•standard PAX weight error
•pax/crew movement during flight (catering service, toilette)
•fuel density error
•movable parts error (landing gear, flaps/slats)
•cargo distribution error
•PAX distribution error
•human accuracy error (balance chart on manual loadsheet)
•Operational C.G. envelope to be used in operations (published on
the Loadsheet form).
7

8. Errors affecting C.G. position are expressed in term of narrower C.G.
envelope limits – certified limits become operational limits.
Certified limits (AFM)
Operational limits (Loadsheet)
ng
n di
La
ff
eo k
Ta
W
ZF
ing
nd
La
&
off
ke
Ta Accounted
for errors
8

9. WEIGHTS
Ramp Weight
MRW
Weight of aircraft at block-off.
MTOW Taxi fuel
Actual Takeoff Weight (ATOW)
Weight of aircraft at beginning of takeoff
(line-up position). + Traffic Load (TL) - Trip fuel
Takeoff fuel(TOF)
Weight of total payable load (PAX, (TRIPF)
BAGG, CARGO, MAIL). and other
load. MLW Actual Landing Weight (ALW)
Operating Weight (OW) Weight of aircraft at landing at destination
- Reserve
Weight of aircraft ready for operations, fuel
without payload (ready for embarkation
MZFW
+ Takeoff Fuel Actual Zero Fuel Weight (AZFW)
of passengers and baggage/cargo).
Weight of total usable fuel onboard Weight of aircraft in flight when all usable
aircraft at beginning of takeoff fuel is burned (engine shut down)
(line-up position).
Structural/performance limited weights:
Dry Operating Weight (DOW) /
Operating Empty Weight (OEW) •MRW: Max. Ramp Weight
+ Operator’s Items
Weight of aircraft ready for
operations, without fuel and payload.
•MTOW: Max. Takeoff weight
Weight of items added by the
Operator: Crew & crew’s baggage, •MLW: Max. Landing Weight
Catering, Catering removable
equipment, Potable water, Toilet •MZFW: Max. Zero Fuel Weight
Manufacturer’s Empty Weight fluids, Documentation, ...
(MEW) / Basic Empty Weight / Relations:
Basic Weight
Weight of structure, power plant, •DOW + PL=AZFW
systems and other items that are
integral part of the aircraft, •AZFW+TOF=ATOW
including fluids inclosed systems
(hydraulic oil,...) •ATOW-TRIPF=ALW
9

10. MAX. TRAFFIC LOAD CALCULATION
MAX. TL = MATOW – TOF – DOW
MTOWSTRUCT
MTOWTAKEOFF = Min. of
MTOWT/O PERF.
MATOW – Max. MLWSTRUCT
Allow. Take Off = Min. of MLW + TRIPF ; MLW = Min. of
Weight MLWLDG PERF.
MZFW + TOF
10

11. Passengers’ weight
•Usually, standard (statistic) passengers weight is used. Actual weights – weighing
of passengers is complicated.
•If unusual group of passengers exist, they must be weighed or must declare own
weight.
•Carry-on luggage included in PAX weight
OPS 1.620 prescribe min. standard passengers’ weights to be used in operations:
Passenger seats P20 P 30
Male Female All Adult
All flights except 88 kg 70 kg 84 kg
holiday charters
Holiday charters 83 kg 69 kg 76 kg
Child 35 kg 35 kg 35 kg
Infant 0 kg 0 kg 0 kg
All Adult weights applicable only for aircraft with 30 PAX seats or more
11

12. Baggage weight
Usually, baggage (checked-in) is weighed and actual weights are used. If baggage is
not weighed (check-in system out of service), standard weights may be used
OPS 1.620(f) Type of flight Bagg. weight/piece
Domestic 11 kg
Within Europe 13 kg
Intercontinental 15 kg
All other 13 kg
Similar to PAX standard weights, operator may perform weighing process with specific
survey, statistical analysis and obligatory use of results.
Cargo Weight
All cargo is weighed before loading – Actual weights are used.
Fuel Weight
Actual volumetric values are used (liters).
Fuel(kg) = Fuel(lt ) × ρ FUEL
Precision of fuel weight depends on fuel density determination.
12

13. C.G. POSITION
OPS 1.605 Aircraft weighing
An operator must establish the mass and the centre of gravity of any aeroplane by
actual weighing prior to initial entry into service (usually before delivery) and
thereafter at intervals of 4 years if individual aeroplane masses are used and 9
years if fleet masses are used.
The accumulated effects of modifications and repairs on the mass and balance
must be accounted for and properly documented.
Furthermore, aeroplanes must be reweighed if the effect of modifications on the
mass and balance is not accurately known (e.g. aircraft painting).
Whenever the cumulative changes to the dry operating mass exceed ± 0·5% of the
maximum landing mass or the cumulative change in CG position exceeds 0·5% of
the mean aerodynamic chord, the mass and the CG of each aeroplane shall be re-
established either by:
- Weighing; or
- Calculation, if influence of modification is exactly known
13

14. C.G. determination
Index method – large aircraft
By large aircraft, moments are big figures (~105). Therefore, it is inpractical to
manipulate with such a big numbers.
By introducing INDEX, moments are transformed into small figures that are
practical for use.
Moment
INDEX = +K
C
C and K are constants arbitrary chosen by operator.
Constant C reduce Moment to acceptable figure.
Constant K prevent negative values (when C.G. is ahead of balance line)
14

15. Datum Line
•Origin point arbitrary chosen by manufacturer as reference for positioning items (firewall, leading
edge, or any other point outside the aircraft).
•Position of any item is expressed as distance from Datum Line.
•Also known as H-arm or Arm or STA (Station)
Balance Line
•Point arbitrary chosen as reference for balance calculation (to avoid big figures when calculating
moments).
•Moments are calculated around balance line.
•Position of balance line is known as Referent Station (Ref. STA) and is expressed as distance from
Datum Line.
•Datum Line may be chosen as Balance Line (usual by smaller aircraft)
Balance Line
Referent Station (Ref.STA)
MAC (RC)
LEMAC
Datum Line
15

16. Balance Line
Referent Station (Ref.STA)
MAC (RC)
LEMAC
c.g.
Datum Line
H-arm c.g. (STA c.g.) Aircraft Weight (W)
Moment
INDEX = +K
C
Moment = W × ( H − arm c.g. − Re f . STA )
Belle Air values for C and K: W × ( H − arm c.g. − Re f . STA )
C=1000 INDEX = +K
K=50 C
16

17. DOW × ( Harm c.g . − 17.25)
A319: DOI = + 50
1000
DOW × ( Harm c.g . − 18.85)
A320: DOI = + 50
1000
DOW/DOI values are pre-calculated for possible crew configurations and are
given in form of DOW/DOI table.
DRY OPERATING WEIGHT / DRY OPERATING INDEX
DOW/ DOI (kgs/ index)
A320-233
Applicable for aircraft registration:
DRY
OPERATING DRY
CONFIGURATION WEIGHT* OPERATING REMARKS
INDEX*
kg
2+0 42344 48
3+0 42429 47
4+0 42514 46
2+4 42904 50 2FWD/2AFT(Ld)
2+5 42979 51 2FWD/3AFT
3+4 42989 48 2FWD/2AFT (Ld)
3+5 43064 49 2FWD/3AFT
4+4 43074 47 2FWD/2AFT (Ld)
4+5 43149 48 2FWD/3AFT
17

18. Balance Line
Index correction
Referent Station (Ref.STA)
MAC (RC)
LEMAC
Datum Line
H-arm
Loaded/Unloaded Weight (±∆W)
±∆ ×( Harm −Re f .STA )
W
∆ =
I
C
New INDEX = INDEX +∑ I ∆
Indexes are aditive
18

19. Example: A320 , Crew 2+4, DOW 42904 DOI 50, 300kg .EIC in Cargo 1 and 400kg .EIC in Cargo 4 added.
Maximum capacity
Length of
Compartment Volume arm from Index value
Gross
Description reference +/-
Number Weight (m3) station per1kg
(meters)
1 FWD 3402 13.28 -6.424 - 0.00642 300*-0.00642 ~ -2
3 AFT 2426 9.76 +4.013 + 0.00401
4 AFT 2110 8.5 +7.408 + 0.00741
400*0.00741 ~ 3
5 AFT 1497 7.22 +10.532 + 0.01053
WEIGHT INDEX
Crew 2+4 DOW/DOI 42904 50
.EIC/1/300 +300 -2
.EIC/4/400 +400 +3
NEW DOW/DOI CONFIGURATION 43604 51
19

20. Last Minute Changes (LMC)
OPS 1.625:
“An operator must specify procedures for Last Minute Changes to the load.”
LMC Policy: ??
20

21. Fill the Load & Trim Sheet for following conditions:
Flight LZ222T, BGY-TIA, A319 F-ORAG, Crew 2/4,
Version 144Y
DOW: 40406, DOI: 50
TOF=5600kg, TRIPF=3000kg
PAX: 40M/35F/0CH/0INF 144Y
BAGGAGE: 975kg @ CC4+5
CARGO:NIL
MAIL: NIL
Boarding scenario:
Section 0A:24 PAX 12M/12F
Section 0B:34 PAX 17M/17F
Section 0C:17 PAX 11M/6F
21

22. B GY
LZ 2 2 2 T F- O RAG 144Y 2 4 20.04.12
57000 61000
5600 3000
40406 62600 70000 64000
5600 46006
46006 16594
T 975 975 75
50
I 40 35 0 0 75
12
A 2
40 35 0 0 975 975 12
0
6
12 70
29.0 12
58
28.3 - 1
57
40 35 0 975 975
16594
5970
6945 6945
40406 9649
47351
57000 TOW
5600 
ZFW
52951 
70000 75
3000
SMITH
49951
22
61000

23. Fill the Load & Trim Sheet for following conditions:
Flight LBY72T, BRU-TIA, ATR72-500 F-ORAA, Crew 2/2,
Version 68Y
DOW: 13 474, DOI: 16
TOF=1970kg, TRIPF=1200kg
PAX: 20M/20F/0CH/0INF 68Y
BAGGAGE: 300kg @ CC4+5 and 300kg @ CC4+6
CARGO:NIL
MAIL: NIL
Boarding scenario:
Section 0A:14 PAX 7M/7F
Section 0B:12 PAX 6M/6F
Section 0C:14 PAX 7M/7F
23

24. B RU
LBY72T F- O RAA 68Y 2 2 20.04.12
20800 22350
1970 1200
13474 22770 22800 23550
1970 15444
15444 7326
T 6 0 0 300 300 40
16
I 20 20 0 0 40 29
A 2
34
20 20 0 0 600 300 300 16
19
23.9 45 71
45
25.1 26
26
20 20 0 6 0 0 300 300
3160 7326
3760 3760
13474 3566

TOW
17234
20800 
1970 ZFW
19204
22800 40
1200
18004 SMITH
24
23550