1. Weight and Balance

3. 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

5. 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.

6. 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

8. 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

9. 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

10. 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

12. Balance Terms
Weight
Force that acts straight down to the center of the Earth
Not always constant
Decreases with fuel burn

13. Balance Terms Reference Datum
Reference base for location of components
Imaginary vertical plane
Location specified from manufacturer
Lies on longitudinal axis
Ex inches from wing leading edge

14. 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

15. 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

16. 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

17. 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.

18. Basic W&B Math Moment = Weight X Arm Center of Gravity =
Basic Empty Weight
+ Payload
+ Usable Fuel
=Ramp Weight
- Fuel used for start, taxi and run-up
= Takeoff Weight
- Fuel used for flight
= Landing Weight
Sum of All Moments
Gross Weight

19. Basic W&B Relationships
Balanced Condition

20. Basic W&B Relationships
Unbalanced Condition

21. 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

22. Basic W&B Relationships
Center of Gravity Limits

23. 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

24. 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

25. Effects of an Aft CG Takeoff Roll  Reduced Cruise Speeds  Increased
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

26. Weight and Balance Documentation

27. 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

28. Weight & Balance - Equipment List Revision

29. Weight & Balance - Equipment List Revision

30. Weight & Balance - Equipment List Revision

31. Weight and Balance Calculation

32. Weight & Balance Computations
Weight and balance information
Weight and balance formulas
Weight shift formulas
Weight and balance problem set up

33. Weight & Balance Computations
Weight Shift Formulas

34. Miscellaneous W&B Solutions
Weight Shift
Weight to be Moved Distance CG Moves =
Gross Weight Distance Weight Moves
Weight Addition / Deletion
Weight to be Added/Removed Distance CG Moves =
New Aircraft Gross Weight Distance Weight Moves

35. Weight & Balance Problem Set Up
Computation - - Piper Warrior
Computation - - Cessna P210
Graph - - Piper Arrow
Table - - Beech B33 Debonair

36. 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.

37. Computation Method Procedure
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
Compare this number to the CG limits for the aircraft.

38. Weight & Balance - Piper Warrior
For our first problem, we use a weight and balance form for a Piper Warrior.

39. Weight & Balance - Piper Warrior
Step 1
find the zero fuel condition

40. Piper Warrior Weight Arm Moment (lbs.) (in.) (lbs.-in.)
Basic Empty Weight , ,850

41. Piper Warrior Weight Arm Moment (lbs.) (in.) (lbs.-in.)
Basic Empty Weight , ,850
Pilot, Front Passengers ,370
Rear Passengers ,154

42. Piper Warrior Weight Arm Moment (lbs.) (in.) (lbs.-in.)
Basic Empty Weight , ,850
Pilot, Front Passengers ,370
Rear Passengers ,154
Baggage (200 lb. Max)
Zero Fuel Condition , ,374

43. Weight & Balance - Piper Warrior
Step 2
find the ramp condition and takeoff condition
determine that it is within limits

44. Piper Warrior Weight Arm Moment (lbs.) (in.) (lbs.-in.)
Zero Fuel Condition , ,374
Fuel (48 gallons max) ,365
Ramp Condition , ,739
Taxi, start, runup fuel
Takeoff condition , ,074

46. Weight & Balance - Piper Warrior
Step 3
find the landing condition

47. Piper Warrior Weight Arm Moment (lbs.) (in.) (lbs.-in.)
Takeoff condition , ,074
Cruise fuel (30 gallons) ,100
Landing condition , ,974

48. Weight & Balance - Piper Warrior
Step 4
confirm that landing weight & C.G. fall within limits

50. Weight & Balance - Cessna P210
Computation Method

51. 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)

52. 102

53. Zero Fuel Condition Item Weight Arm Moment BEW 2632 109000 Front Seat
170 37
6290
Center Seat
310 71
22010
Aft Seat
370
102
37740
Baggage A
150
138
20700
Zero-Fuel
3632
53.89
195740

54. Ramp Condition Add 64 gallons of fuel Item Weight Arm Moment Zero-Fuel
3632
53.89
195740
Fuel
384 43
16512
Ramp Weight
4016
52.85
212252

55. Takeoff Condition Run-up minus 16 lbs of fuel Item Weight Arm Moment
Ramp Weight
4016
52.85
212252
Run-up
-16 43
-688
Takeoff
4000
52.89
211564

58. Shift a Passenger
Move the 200 pound passenger from the aft seat to the front seat.
Equation
Weight Moved Distance CG Moves
Total Weight Distance between CG Location

59. Weight Moved Distance CG Moves
Total Weight Distance between CG Location
200 lbs ???????????????????
4000 lbs (102-37) 65’
(65 x 200)/4000
13000/4000 = 3.25
52.89 – 3.25 = 49.64

61. Fuel Burn 2.5 hour flight at 20 gallons per hour Item Weight Arm
Moment
Takeoff
4000
49.64
198560
Fuel Burn
(2.5 x 20 x 6)
-300 43
-12900
Landing
3700
50.18
185660

63. Example BEW 2632 109000 Front Seat 150 + 210 Center Seat 190
Aft Seat
Baggage A 10
Baggage B 25

64. 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.

65. Chart Method Procedure (General)
Find the charts provided by the manufacturer in Section 6 of the POH. (These may or may not be provided)
Correlate the weights to the appropriate chart to determine the moment.
Add the moments determined from the charts and correlate them to the CG Limit chart.

66. Weight & Balance - Piper Arrow
Graph Method

67. PA28-R-201 ARROW BEW - 1774.2 lbs. (moment 147,695.8)
Pilot and Front Passenger lbs.
Rear passenger lbs.
Baggage lbs.

69. Item Weight Arm Moment BEW 1774.2 147695.8 Front Pas. 370 30000
Front Seat - 30,000
Back Seat - 25,000
Baggage - 14,200
Item
Weight
Arm
Moment
BEW
1774.2
Front Pas.
370
30000
Rear Pas.
210
25000
Baggage
100
14200
Zero Fuel
2454.2
88.38

70. Fuel (72 gallon maximum)
50 gallons
300 lbs.
Moment
29000

71. Item Weight Arm Moment Zero Fuel 2454.2 88.38 216895.8 Fuel 300 29000
Ramp Weight
2754.2
Run-up -8
-1000
Takeoff
2746.2
89.17

73. Fuel used in flight 3 hours at 11.6 gallons per hour 34.8 gallons
208.8 lbs.
Moment - 20,000

74. Item
Weight
Arm
Moment
Takeoff
2746.2
89.17
Fuel
-208.8
-20000
Landing
2537.4
88.63

76. Problem!
BEW
Front Pax 400
Rear Pax 150
Fuel 200

77. Weight and Balance Computation
Table Method
Beech Debonair

78. 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.

79. Table Method Procedure
Find the tabular data provided in Section 6 of the POH. (These may or may not be provided)
Correlate the weight to the appropriate tables to determine the moment.
Add the moments determined from the tables and correlate them to the CG Limit chart.

80. 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.)

84. Calculations Item Weight Arm Moment BEW 1980 1584 Front Pax 370 314
Rear Pax
250
295
Baggage 50 70
Zero Fuel
2650
2263

86. Adding Fuel
Fuel (64 gallons maximum)
60 gallons
360 lbs.

87. Ramp Condition Item Weight Arm Moment Zero Fuel 2650 2263 Fuel 360 270
Ramp Weight
3010
2533
Run-up
-10 -8
Takeoff Weight
3000
2525

89. Fuel Burn
3 hour flight (14.7 gallons per hour)
44.1 gallons
264 lbs.

90. Landing Condition Item Weight Arm Moment 3000 2525 264 198 2736 2327
Takeoff Weight
3000
2525
Fuel flight
264
198
Landing Weight
2736
2327

92. Problem!! BEW 1980 lbs. (Moment 1584) Front Pax (Aft) 190 And 160
Rear Pax 150
Baggage 200
30 gallons of fuel