Weight and Balance
2
Lesson Objectives
At the conclusion of this lesson you will…
 Understand why weight and balance is critical
to safety of flight
 Be familiar with the terms associated with
weight and balance
 Be familiar with the methods of calculating
weight and balance
 Understand the effect weight and balance has
on aircraft performance
3
4
Importance of Weight and
Balance
 Aircraft are designed to be operated
within specific Center of Gravity limits.
 Wings can only produce so much lift.
Weight in excess of what the wing is
designed to carry is hazardous.
 Increases in weight also effect the
general performance.
5
Weight Terms
 Empty Aircraft
– Standard Empty Weight – weight of a standard
airplane including unusable fuel, full operating
fluids and full oil
– Basic Empty Weight – Standard Empty Weight
plus optional equipment
 Starting Point of Weight and Balance
6
7
Weight Terms
 Fuel
– Usable Fuel – fuel which can be used for flight
planning
– Unusable Fuel – fuel which cannot be use in
flight due to fuel tank design
– 6 lbs per gallon
8
Weight Terms
 Useful Load – total usable fuel,
passengers, and cargo
– Maximum Ramp Weight – Basic Empty Weight = Useful Load
 Payload – passengers and cargo
– What essentially could be revenue generating
9
Weight Terms
 Loaded Aircraft
– Maximum Ramp Weight
 Maximum allowable mass for ground operations
 Assures ground maneuverability
 Includes fuel for taxi, run-up and start
– Maximum Takeoff Weight
 Maximum allowable mass for initiation of takeoff roll
 Failure to meet weight…
– Maximum Landing Weight
 Maximum allowable mass at touchdown
 Generally limitation of landing gear
– Baggage Compartment Limits
 Could cause structural failure in floor
10
11
Balance Terms
 Weight
– Force that acts straight down to the center of
the Earth
– Not always constant
 Decreases with fuel burn
12
Balance Terms
 Reference Datum
– Reference base for location of components
– Imaginary vertical plane
– Location specified from manufacturer
– Lies on longitudinal axis
– Ex. 78.4 inches from wing leading edge
13
Balance Terms
 Arm
– Distance from the datum measured along the
longitudinal axis
 If located in front of datum, negative
 If located in back of datum, positive
14
Balance Terms
 Moment
– Weight multiplied by its arm
– Tendency of a mass to cause a rotation about
the Center of Gravity
– Force acting at that point
15
Balance Terms
 Center of Gravity (CG)
– Point of a mass through which gravity acts
– Point where aircraft would balance if suspended
– Point where all three axis intercept
– Divide total moment of aircraft by weight of
aircraft
16
Basic W&B Relationships
For the next few examples…
• The seesaw is synonymous with the aircraft.
• The people are synonymous with the weight of fuel,
equipment, passengers, etc…
• The fulcrum can be thought of as lift, supporting the
entire mass.
• The datum can be considered the nose of the aircraft.
17
Basic W&B Math
 Moment = Weight X ArmSum of All Moments
 Center of Gravity =
Gross Weight








Basic Empty Weight
+ Payload
+ Usable Fuel
=Ramp Weight
- Fuel used for start, taxi and run-up
= Takeoff Weight
- Fuel used for flight
= Landing Weight
18
Basic W&B Relationships
 Balanced Condition
19
Basic W&B Relationships
 Unbalanced Condition
20
Basic W&B Relationships
 Forces Acting on an Aircraft in Flight
 Center of Gravity
forward of Center of
Pressure
 Downward force
produced at tail to
stabilize interaction
of lift and weight
 www.aero.und.edu/multimedia
21
Basic W&B Relationships
 Center of Gravity Limits
22
Results of Aircraft Overloading







Stall Speed  Increases
Takeoff and Landing Distance  Increases
Climb Rate  Reduced
Cruise Speed  Reduced
Fuel Consumption  Greater
Range and Endurance  Reduced
Stability  Increased
23
Results of a Forward CG
 Longitudinal Stability becomes excessive
– Rotation and Flare are more difficult
 Takeoff Roll  Increased
 Cruise Speed  Decreased
– A greater tail down force must be produced. This is done
aerodynamically, increasing drag.
 Climb Rate  Reduced
 Range and Endurance  Reduced
 Stall Speed  Increased
24
Effects of an Aft CG
Takeoff Roll  Reduced
– Tendency to Over-Rotate
 Cruise Speeds  Increased
– Less tail down force, is less drag




Climb Rates  Increased
Fuel Consumption  Decreased
Range and Endurance  Increased
Stall Speeds  Reduced
– Recovery hindered due to nose up tendency
25
Weight and Balance
Documentation
POH Section 6
 Section 6 contains…
– Weight and Balance Calculation procedure for
the aircraft
– Basic Empty Weight and Moment of the aircraft
– Changes to the Weight and Balance
27
CENTER FOR AEROSPACE SCIENCES
UNIVERSITY OF NORTH DAKOTA
WEIGHT AND BALANCE, AND EQUIPMENT LIST REVISION
AIRCRAFT MODEL
N
142 ND
SERIAL NO.
DATE 5-1-94
AMOUNT
DESCRIPTION
1
Fire Extinguisher
PREVIOUS EMPTY AIRPLANE
TOTAL ADDED OR SUBTRACTED
REVISED EMPTY AIRPLANE
USEFUL LOAD
PA 28-161
2841229
WEIGHT
(LB)
ARM
(IN)
+2.7
57.9
+156
E.W.
C.G.
MOMENT
1464.4
85.0
124469.5
+2.7
1467.1
804.9
MOMENT
Weight &
Balance Equipment List
Revision
+156.0
85.0
124625.5
Jim Gilstad
NAME
CERTIFICATE NO.
OGSR092N
28
Weight & Balance Equipment List Revision
PREVIOUS EMPTY AIRPLANE
E.W.
C.G.
MOMENT
1464.4
85.0
124469.5
TOTAL ADDED OR SUBTRACTED
+2.7
REVISED EMPTY AIRPLANE
1467.1
USEFUL LOAD
804.9
+156.0
85.0
124625.5
Jim Gilstad
NAME
CERTIFICATE NO.
OGSR092N
29
CENTER FOR AEROSPACE SCIENCES
UNIVERSITY OF NORTH DAKOTA
WEIGHT AND BALANCE, AND EQUIPMENT LIST REVISION
AIRCRAFT MODEL
N
142 ND
SERIAL NO.
DATE 5-1-94
AMOUNT
DESCRIPTION
1
Fire Extinguisher
PA 28-161
2841229
WEIGHT
(LB)
ARM
(IN)
-2.7
MOMENT
57.9
-156
E.W.
C.G.
MOMENT
1467.1
84.9
1
124625.5
SUPERCEDED
5-1-94
PREVIOUS EMPTY AIRPLANE
TOTAL ADDED OR SUBTRACTED
REVISED EMPTY AIRPLANE
USEFUL LOAD
-2.7
-156.0
1464.4
867.6
Weight &
Balance Equipment List
Revision
124469.5
Jim Gilstad
NAME
CERTIFICATE NO.
OGSR092N
30
Weight and Balance
Calculation
Weight & Balance
Computations




Weight and balance information
Weight and balance formulas
Weight shift formulas
Weight and balance problem set up
32
Weight & Balance
Computations
Weight Shift Formulas
33
Miscellaneous W&B Solutions
 Weight Shift
Weight to be Moved
Gross Weight
= Distance CG Moves
Distance Weight Moves
 Weight Addition / Deletion
Weight to be Added/Removed
New Aircraft Gross Weight
Distance CG Moves
= Distance Weight Moves
34
Weight & Balance Problem
Set Up




Computation - - Piper Warrior
Computation - - Cessna P210
Graph - - Piper Arrow
Table - - Beech B33 Debonair
35
Computation Method
 This method uses the basic weight and
balance formula to determine center of
gravity.
 This method can be used for most aircraft.
 Extremely accurate, less arithmetic errors.
36
Computation Method
 Procedure
1.
2.
3.
4.
Determine the Basic Empty Weight of the aircraft.
Find the moment of each weight to be carried.
Add all moments and all weights.
Divide the total moment by the total weight. This
number is your Center of Gravity
5. Compare this number to the CG limits for the aircraft.
37
Weight & Balance Piper Warrior
For our first
problem, we
use a weight
and balance
form for a
Piper
Warrior.
38
Weight & Balance Piper Warrior
Step 1
– find the zero fuel condition
39
Piper Warrior
Basic Empty Weight
Weight Arm Moment
(lbs.) (in.) (lbs.-in.)
1,500
128,850
40
Piper Warrior
Basic Empty Weight
Pilot, Front Passengers
Rear Passengers
Weight
(lbs.)
1,500
340
340
Arm Moment
(in.) (lbs.-in.)
128,850
80.5
27,370
118.1
40,154
41
Piper Warrior
Basic Empty Weight
Pilot, Front Passengers
Rear Passengers
Baggage (200 lb. Max)
Zero Fuel Condition
Weight
(lbs.)
1,500
340
340
2,180
Arm Moment
(in.) (lbs.-in.)
128,850
80.5
27,370
118.1
40,154
196,374
42
Weight & Balance Piper Warrior
Step 2
– find the ramp condition and takeoff
condition
– determine that it is within limits
43
Piper Warrior
Zero Fuel Condition
Fuel (48 gallons max)
Ramp Condition
Taxi, start, runup fuel
Takeoff condition
Weight
(lbs.)
2,180
267
2,447
-7
2,440
Arm
(in.)
95
95
90.6
Moment
(lbs.-in.)
196,374
25,365
221,739
- 665
221,074
44
45
Weight & Balance Piper Warrior
Step 3
– find the landing condition
46
Piper Warrior
Takeoff condition
Cruise fuel (30 gallons)
Landing condition
Weight Arm
(lbs.)
(in.)
2,440 90.6
-180
95.0
2,260 90.25
Moment
(lbs.-in.)
221,074
-17,100
203,974
47
Weight & Balance Piper Warrior
Step 4
– confirm that landing weight & C.G. fall
within limits
48
49
Weight & Balance - Cessna
P210
Computation
Method
50
Cessna P210






BEW: 2,632 lbs. (Moment 109,000)
Front Seat (170 lbs.)
Center Seat (160 and 150 lbs)
Aft Seat (200 and 170 lbs)
Baggage Area A (150 lbs)
Baggage Area B (0)
51
102
52
Zero Fuel Condition
Item
BEW
Front Seat
Center Seat
Aft Seat
Baggage A
Zero-Fuel
Weight
2632
170
310
370
150
3632
Arm
37
71
102
138
53.89
Moment
109000
6290
22010
37740
20700
195740
53
Ramp Condition
 Add 64 gallons of fuel
Item
Zero-Fuel
Fuel
Ramp Weight
Weight
3632
384
4016
Arm
53.89
43
52.85
Moment
195740
16512
212252
54
Takeoff Condition
 Run-up minus 16 lbs of fuel
Item
Ramp Weight
Run-up
Takeoff
Weight
4016
-16
4000
Arm
52.85
43
52.89
Moment
212252
-688
211564
55
56
57
Shift a Passenger
 Move the 200 pound passenger from the aft
seat to the front seat.
 Equation
– Weight Moved
– Total Weight
Distance CG Moves
Distance between CG Location
58
– Weight Moved
– Total Weight
 200 lbs
 4000 lbs
Distance CG Moves
Distance between CG Location
???????????????????
(102-37) 65’
 (65 x 200)/4000
 13000/4000 = 3.25
 52.89 – 3.25 = 49.64
59
60
Fuel Burn
 2.5 hour flight at 20 gallons per hour
Item
Takeoff
Fuel Burn
Landing
Weight
4000
(2.5 x 20 x 6)
-300
3700
Arm
49.64
43
Moment
198560
-12900
50.18
185660
61
62
Example






BEW
Front Seat
Center Seat
Aft Seat
Baggage A
Baggage B
2632
150 + 210
190
150 + 190
10
25
109000
63
Chart Method
 This method depends on charts provided by the
manufacturer to determine the moments.
 Accuracy of the chart method tends to decrease
as the size of the aircraft increases.
 Accuracy in general is generally within a few
hundred pound – inches.
 The procedure may vary from aircraft to aircraft.
64
Chart Method
 Procedure (General)
1. Find the charts provided by the manufacturer
in Section 6 of the POH. (These may or may
not be provided)
2. Correlate the weights to the appropriate chart
to determine the moment.
3. Add the moments determined from the charts
and correlate them to the CG Limit chart.
65
Weight & Balance Piper Arrow
 Graph Method
66
PA28-R-201 ARROW




BEW - 1774.2 lbs. (moment 147,695.8)
Pilot and Front Passenger - 370 lbs.
Rear passenger - 210 lbs.
Baggage - 100 lbs.
67
68
 Moment
–
–
–
–
BEW - 147,695.8
Front Seat - 30,000
Back Seat - 25,000
Baggage - 14,200
Item
BEW
Front Pas.
Weight
1774.2
370
Rear Pas.
Baggage
Zero Fuel
210
100
2454.2
Arm
88.38
Moment
147695.8
30000
25000
14200
216895.8
69
 Fuel (72 gallon maximum)
– 50 gallons
 300 lbs.
 Moment
– 29000
70
Item
Zero Fuel
Fuel
Ramp Weight
Run-up
Takeoff
Weight
2454.2
300
2754.2
-8
2746.2
Arm
88.38
89.17
Moment
216895.8
29000
245895.8
-1000
244895.8
71
72
 Fuel used in flight
– 3 hours at 11.6 gallons per hour
 34.8 gallons
– 208.8 lbs.
– Moment - 20,000
73
Item
Takeoff
Fuel
Landing
Weight
2746.2
-208.8
2537.4
Arm
89.17
88.63
Moment
244895.8
-20000
224895.8
74
75
Problem!




BEW
Front Pax
Rear Pax
Fuel
1774
400
150
200
147695
76
Weight and Balance
Computation
Table Method
Beech Debonair
Table Method
 This method depends on tables provided by the
manufacturer.
 Moment data is provided for specific weights only.
 Interpolation will be necessary to determine
weights not specifically listed.
 Accuracy is generally within a few hundred pound
– inches.
 This procedure may vary from aircraft to aircraft.
78
Table Method
 Procedure
1. Find the tabular data provided in Section 6 of
the POH. (These may or may not be provided)
2. Correlate the weight to the appropriate tables
to determine the moment.
3. Add the moments determined from the tables
and correlate them to the CG Limit chart.
79
Beech B33 Debonair




BEW - 1980 lbs. (Moment 1584)
Front Seat (Forward 170 lbs. and 200 lbs.)
Rear Seat (120 lbs. And 130 lbs)
Baggage (50 lbs.)
80
81
82
83
Calculations
Item
BEW
Front Pax
Rear Pax
Baggage
Zero Fuel
Weight
1980
370
250
50
2650
Arm
Moment
1584
314
295
70
2263
84
85
Adding Fuel
 Fuel (64 gallons maximum)
– 60 gallons
 360 lbs.
86
Ramp Condition
Item
Zero Fuel
Fuel
Ramp Weight
Run-up
Takeoff Weight
Weight
2650
360
3010
-10
3000
Arm
Moment
2263
270
2533
-8
2525
87
88
Fuel Burn
 3 hour flight (14.7 gallons per hour)
 44.1 gallons
– 264 lbs.
89
Landing Condition
Item
Takeoff Weight
Fuel flight
Landing
Weight
Weight
3000
264
2736
Arm
Moment
2525
198
2327
90
91
Problem!!




BEW 1980 lbs. (Moment 1584)
Front Pax (Aft)
190 And 160
Rear Pax
150
Baggage
200
 30 gallons of fuel
92