# Weight and Balance.

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Weight and Balance

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

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.

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

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

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

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

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

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

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

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

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

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.

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

Basic W&B Relationships
Balanced Condition

Basic W&B Relationships
Unbalanced Condition

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

Basic W&B Relationships
Center of Gravity Limits

Stall Speed  Increases Takeoff and Landing Distance  Increases Climb Rate  Reduced Cruise Speed  Reduced Fuel Consumption  Greater Range and Endurance  Reduced Stability  Increased

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

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

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

Weight & Balance - Equipment List Revision

Weight & Balance - Equipment List Revision

Weight & Balance - Equipment List Revision

Weight and Balance Calculation

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

Weight & Balance Computations
Weight Shift Formulas

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

Weight & Balance - Cessna P210
Computation Method

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)

102

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

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

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

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

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

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

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

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.

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.

Weight & Balance - Piper Arrow
Graph Method

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

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

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

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

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

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

Problem! BEW Front Pax 400 Rear Pax 150 Fuel 200

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.

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.

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.)

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

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

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

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

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

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