Weight & Balance

Weight and Balance

Materials

• You will need
  • Pen/Pencil/Eraser/Sharpener (erasable pen recommended)
  • Ruler
  • Basic Calculator (or phone calculator)
• Provided
  • AIP GEN 2.6 Conversion Tables
  • W/B Calculation Grid for Cessna 172R, Cessna 172S, Cessna 152 and Eurofox 3K
  • CG Envelope for Cessna 172R and Cessna 172S
  • Loading Graph for Cessna 172 and Cessna 152
  • Link to handout
    • Cessna 172R
    • Cessna 172S
    • Cessna 152
    • Eurofox 3K

Weight and Balance

Aims and Objectives

• To explore & internalise the general principles of Weight and Balance applied to fixed-wing aircraft
• Apply the principles of Weight and Balance to both simple and complex aircraft types
• Perform a Weight and Balance calculation for typical training aircraft
• To gain knowledge of legislative requirements for Weight and Balance
• Develop a strategy to reliably and efficiently calculate Weight and Balance

Weight and Balance

• It is an offence to take-off in an aeroplane outside of weight/balance limitations
• See Civil Aviation Order (CAO) 20.7.4
• You, Pilot in Command, must calculate these limitations before every flight
• Perhaps you have not seen your instructor calculate weight and balance before your flight
• Please be assured, it has been done

Weight then Balance

• A weight limitation calculation is separate to a balance calculation
• However, a balance calculation depends on the result of a weight limitation calculation
• Therefore, we do a weight limitation calculation first
• A “balance calculation” is also sometimes called a CG calculation

Types of weight limitations

Where to find weight limitations?

According to CASR1998

• For aircraft that are not type-certificated
  • the certificate of airworthiness for the aircraft
  • or if not specified in the certificate of airworthiness, the aircraft flight manual

Maximum Take-off Weight (MTOW)

• You will find the MTOW in the flight manual
• It is an offence to take-off in an aircraft outside of weight limitations
• It is also extremely dangerous

Maximum Take-off Weight (MTOW)

Examples

Maximum Take-off Weight (MTOW)

Example Flight Manual Eurofox 3K 24-8881

Important Note: Empty weight is attached to the flight manual as a supplement for each individual aircraft (non-standard)

Maximum Take-off Weight (MTOW)

Example Flight Manual Cessna 172R

Units of Measurement

• You may have noticed that some aircraft use pounds (lb) while others use kilograms (kg) for weight
• Units of measurement are the most common source of error in calculating Weight and Balance
• We will use a specific technique to minimise this source of error

Units of Measurement

Conversion Tables

• Conversion Tables for different units of measurement can be found in AIP GEN 2.6
• This includes fuel weight conversions to and from volume and weight

Units of Measurement

AIP GEN 2.6 General Conversion Tables

Units of Measurement

AIP GEN 2.6 Fuel Volume/Weight Conversion Tables

Stations

• Each aircraft will have various “stations”
• Stations can be thought of loosely as, places we can put stuff in an empty aircraft

Stations

For example

• Flight crew station
• Fuel station
• Baggage area station
• Oil/fluids station
• Some aircraft have more than one of these and each are their own station
  • Row 1 crew
  • Row 2 crew
  • Forward fuel tank
  • Baggage areas A and B

Empty Aircraft

• Each individual aircraft will have a specified empty weight in the flight manual
• This station is called the aircraft Basic Empty Weight (BEW)

Empty Aircraft

Eurofox 3K 24-4844

Basic Empty Weight: 288.5 kg

Empty Aircraft

Eurofox 3K 24-8881

Basic Empty Weight: 303.8 kg

Empty Aircraft

Cessna 172R VH-SCN

Basic Empty Weight: 761.8 kg or 1679.4 lb

Calculating Weight Limitations

• Let’s calculate weight limitations for a given scenario
• We will use the same general technique for any given scenario
• Our scenario:
  • Eurofox 24-8881
  • Me (80kg) and Bob (80kg)
  • Full fuel (86L)
  • 10 kg Baggage

Calculating Weight Limitations

• Draw a grid
• One row per station (including aircraft BEW)
• One column per Unit of Measurement
• Leave room for more columns, since we will use these for calculating balance

Calculating Weight Limitations

Eurofox 3K Stations

Calculating Weight Limitations

Draw the Grid

• An extra row & column for heading information
• Put the Fuel station last
• Leave an extra empty row before the Fuel station
• You’ll see why soon

Calculating Weight Limitations

Draw the Grid

Calculating Weight Limitations

• Enter initial known values
• Ensure the values are under the correct unit of measurement

Calculating Weight Limitations

• The blank line is for a subtotal value
• This subtotal will be the aircraft with all stations loaded except for Fuel
• This station is called Zero Fuel Weight (ZFW)

Calculating Weight Limitations

• Using the conversion tables in AIP GEN 2.6, convert all stations to kilograms
• Litres to kilograms: multiply by 0.72

Calculating Weight Limitations

• Compute the total for Zero Fuel Weight
• Compute the total including fuel (called All Up Weight)

Calculating Weight Limitations

• Verify we are within all weight limitations
• MTOW: 560 kg
• MLW: 560 kg
• Maximum Baggage: 20 kg
• Minimum Crew Weight: 54 kg

Calculating Weight Limitations

We are within weight limitations

Balance

Balance

• All aircraft have a Centre of Gravity (CG) at any given configuration
• All aircraft have both a forward CG limit and an aft CG limit
• We wish to ensure our aircraft is within these limits at all times
• We need to calculate the balance of the aircraft

Balance

• Flying outside CG limits is both illegal and extremely dangerous
• If the aircraft is outside the forward CG limit, full-aft elevator may not raise the nose
• If the aircraft is outside the aft CG limit, full-forward elevator may not push the nose down
• This lesson is written in blood

Balance

11 May 2020, Rockhampton Airport

Balance

Some basic principles of levers

• You are already familiar with levers — it’s how your joints and muscles work
• You’ve also probably used a spanner to tighten a nut to a bolt
• The longer the spanner, the easier it is for you to tighten the nut
• In fact, if you double the length of the spanner, it is twice as easy

Balance

Some basic principles of levers

• All aircraft have a specified CG position before any load is added (empty weight CG)
• This CG position is a distance measurement from the reference datum
• The reference datum may be thought of as the “zero position” from which all other CG measurements are taken
• You don’t need to know exactly where the reference datum actually is, only that it exists

Balance

Some basic principles of levers

• When we add load to an aircraft, the CG position changes
• We need to calculate that the CG position stays within the limits given our intended load
• This includes staying within limits during fuel burn

Balance

Some basic principles of levers

• When we add 10kg some distance from CG, then the CG position will change
• Adding 5kg at double the distance from CG, will have the same effect
• Adding 20kg at half the distance from CG, will also have the same effect
• This is called a linear relationship
  • between distance and effect on CG position
  • between weight and effect on CG position
  • if you create a graph of this relationship, you will see a straight line

Balance

Some basic principles of levers

Balance

Some basic principles of levers

Balance

Some basic principles of levers

Balance

CG calculation

• Some terminology
• The parameters to a CG calculation include a weight and a distance called the arm
• The total effect caused by a given weight and arm is called moment
• In fact, given any two of these, we can easily determine the other

Balance

CG calculation

Moment = Weight x Arm

• Weight = Moment ÷ Arm
• Arm = Moment ÷ Weight

Balance

CG calculation

Moment = Weight x Arm

• If we apply weight 10kg at a distance/arm of 200mm
  • then we have created a moment
  • 10kg per 200mm
  • or 2000 kg/mm
• Similarly, if we apply weight 5kg at a distance/arm of 400mm
  • then we have created the same moment (do the maths!)

Balance

CG calculation

• Aircraft include their empty CG position arm (from the reference datum) in the flight manual
• Sometimes the empty moment is also included, since it is the empty weight multipled by the empty CG arm

Balance

Cessna 172R VH-SCN Arm and Moment

Balance

Eurofox 24-4844 Arm

Balance

Eurofox 24-8881 Arm and Moment

Balance

Calculating balance limitations

• Name the two new columns
• Enter the empty CG arm

Balance

Calculating balance limitations

• The arms for each station are provided in the flight manual
• Enter those as well

Balance

Calculating balance limitations

Balance

Calculating balance limitations

• Calculate the moment for each station
• Hmm… how do we do that again?

Balance

Calculating balance limitations

Moment = Weight x Arm

Balance

Calculating balance limitations

• Add up the moments at each station to ZFW
• Add the Fuel moment to the ZFW moment to get total moment

Balance

Calculating balance limitations

• We now need to calculate the ZFW arm and the total arm
• Do we have a way to do this?

Balance

Calculating balance limitations

Arm = Moment ÷ Weight

Balance

Calculating balance limitations

• Are we within CG limits?
• All through the fuel burn?

Balance

We are within balance limitations

Balance

Considerations

• In the Eurofox 3K, burning fuel moves CG position forward
• In our example, we are not close to CG limits
• However, if we were say, near aft limit, we would expect to use more forward elevator in level flight
• Note: Eurofox 8881 has 85L of usable fuel, 86L total, so we can’t burn that last litre anyway!

Balance

Considerations

• More complex aircraft have fuel tanks in the nose and also aft position → CG considerations during flight
• The more aft the CG position, the shorter the tail moment arm → less longitudinal stability
• The more forward the CG position, the longer the tail moment arm → more longitudinal stability
• Remember longitudinal stability from your Straight and Level lesson?

Cessna 172R

• We will do another example for the Cessna 172R
• This is a little more complex but the same general principles apply
• We have 2 rows for PAX, 2 baggage areas
• There is also a “utility category” within which certain additional operations are permitted
• The Cessna 172R also has a Maximum Ramp Weight (MRW)

Cessna 172R

Maximum Ramp Weight

Cessna 172R

Certificated Weights

Cessna 172R

Baggage Limits

Cessna 172R

Load Factor Limits

Cessna 172R

Stations

Cessna 172R

Our scenario

• VH-SCN
• Me (72kg) and Mary (65kg) front row
• Susan (67kg) rear seat
• Fuel 43 USG (max: 56 USG = 212.8 L)
• Baggage A 28kg
• Baggage B 10kg

Cessna 172R

Important Note

• Unusable fuel is included in an aircraft Basic Empty Weight
• The Cessna 172R has 3 USG of unusable fuel
• This is significant and we will consider it this time

Cessna 172R

Let’s Do Our Weight and Balance

Cessna 172R

VH-SCN

Cessna 172R

Add our known values

Cessna 172R

Units of Measurement

• We will normalise our units of measurement using the Conversion Tables to:
  • Litres
  • kilograms (kg)
  • millimetres (mm)
• However, the flight manual may provide parameters in other units of measurement
• We will convert and record these other units of measurement on our W/B sheet
• This is to both minimise and detect error

Cessna 172R

Convert our weights

Cessna 172R

Add up our weights

Cessna 172R

We are over MTOW!

Cessna 172R

We are over MTOW!

• However, we are under Maximum Ramp Weight (2457 lb / 1116.82 kg)
• Although we are legal with respect to weight, we will take this into consideration
• We can take no more weight
• “Your small extra bag will need to stay behind, sorry”

Cessna 172R

We are under baggage weight limits

• Baggage Area A ≤ 120 lb (54.4 kg)

• Baggage Area B ≤ 50 lb (22.7 kg)

• Baggage Area A + Baggage Area B ≤ 120 lb (54.4 kg)

Calculating Weight Limitations

We are within weight limitations (but only just)

A Note on Baggage

• It is a legal requirement to restrain any baggage on all flights
• That restraint must meet certain strength and other parameters
• Civil Aviation Order 20.16.2

Cessna 172R

Balance

Cessna 172R

Balance

• There are two methods to calculate moment
  • The Cessna 172R flight manual provides the station arms in inches (M = W x A)
  • The flight manual also provides a linear graph to calculate the moment for each arm
• We can calculate moment using one method, then cross-check against the other
• Today, we will use the first method

Cessna 172R

Station Arms

Cessna 172R

Station Arms

Cessna 172R

Linear Moment Graph

Cessna 172R

Balance

• Furthermore, the flight manual provides more than one arm for some stations:
  • forward/mid/aft for both baggage areas
  • forward/mid/aft for row 1 crew
• We will calculate moment using both the forward and aft points for each station

Cessna 172R

Balance

• Record each forward arm station from the flight manual
• Also record the stations that have only one arm provided (no forward/aft movement)
• Make it very clear to yourself that we are calculating a forward CG limit in this case

Cessna 172R

Balance

Convert inches to millimetres (multiply by 25.4)

Cessna 172R

Balance

Moment = Weight x Arm

Cessna 172R

Balance

• Calculate the moment for each station
• Remember to multiply the correct columns!

Cessna 172R

Balance

Add up the moments for ZFW and planned fuel

Cessna 172R

Balance

Arm = Moment ÷ Weight

Cessna 172R

Balance

Calculate the arm (mm) for ZFW and total weight

Cessna 172R

Balance

• We have calculated the arm (in millimetres) at the forward limit
  • Front row seats all the way forward
  • Baggage placed at the forward limit of each baggage area
• Now let’s do the same for front row seats and baggage at the aft limits

Cessna 172R

Balance

Add the arms for each station at their aft limits

Cessna 172R

Balance

Convert inches to millimetres

Cessna 172R

Balance

Calculate the moments for each station

Cessna 172R

Balance

Add the moments to get the ZFW and total moment

Cessna 172R

Balance

Arm = Moment ÷ Weight

Cessna 172R

Balance

Summary

Cessna 172R

Balance

• The Cessna 172R includes two different grids for plotting our result against CG limits
  • One grid plots weight against moment
  • The other plots weight against arm
• We could use either to find our limits
• We will use both

Cessna 172R

Balance

• Each grid (or envelope) will contain four of our points:
  • (ZFW forward weight, ZFW forward moment)
  • (ZFW aft weight, ZFW aft moment)
  • (Total forward weight, Total forward moment)
  • (Total aft weight, Total aft moment)

Cessna 172R

Balance

Cessna 172R

Balance

Cessna 172R

Balance

Cessna 172R

Balance

• We are within CG limits in the Normal Category
  • through the fuel burn
  • regardless of the position of row 1 seats and baggage within baggage area

Cessna 172R

Balance

Let’s cross-check on the Weight vs Arm grid

Cessna 172R

Balance

Cessna 172R

Balance

Balance

We are within balance limitations

Weight and Balance throughout your training

• What you have seen is one, reliable method of calculating weight and balance
• You may have a slight variation on this method, and that is OK …
• … as long as you consistently arrive at the correct answer

Weight and Balance throughout your training

• Some aircraft types are easier than others to exceed weight and/or CG limitations
• For example:
  • two 85kg adults in 24-8881, with full fuel (86L) and baggage (20 kg) is within all limits
  • however, VH-NKJ (Cessna 152), with two 85kg adults and maximum baggage (54kg), with NO FUEL is already over MTOW

Weight and Balance throughout your training

• RA-Aus students training in Group A aircraft (MTOW ≤ 600kg) may be aware of the upcoming Group G aircraft category
• The MTOW of Group G aircraft is 760 kg
• However, many of these aircraft types will very easily exceed weight and/or CG limitations
• Many Group A aircraft types easily exceed limits e.g. Sling 2
• It is important to understand Weight and Balance, regardless of the aircraft type that you train in

Further Reading

• Your Basic Aeronautical Knowledge (BAK) text book discusses Weight and Balance
• All CASA flight crew licence exams (RPL/PPL/CPL/ATPL) include Weight and Balance questions
  • The sample aircraft in the exams are freely available
  • Search for “CASA RPL,PPL & CPL Workbook”

Weight and Balance

Be awesome