Mass & Balance - Complete ATPL Subject Guide
Mass & Balance, officially designated as ATPL Subject 031, is one of the most calculation-intensive subjects in the ATPL curriculum. It covers the determination of aircraft weight and center of gravity (CG) position, both critical parameters that directly affect aircraft performance, stability, and safety.
For professional pilots, mass and balance knowledge is essential for pre-flight planning, load optimization, ensuring regulatory compliance, and understanding aircraft handling characteristics.
What is Mass & Balance?
Mass & Balance encompasses the study of:
- Weight terminology and definitions
- Center of gravity (CG) calculations
- Loading procedures and load sheets
- Weight and balance computations (index method, moment method, graph method)
- Aircraft loading systems (bulk cargo, unit load devices, baggage)
- Weight limitations (structural, performance, regulatory)
- CG limits and effects on stability and control
- Ballast requirements and use
Subject 031 Exam Details
Number of Questions: 25 questions Exam Duration: 1 hour Pass Mark: 75% (19 correct answers) Difficulty Level: Medium-Hard (calculation-heavy) Recommended Study Hours: 40-50 hours Prerequisites: Basic mathematics (algebra, ratios); understanding of Aircraft General Knowledge and Principles of Flight helpful
Mass & Balance requires comfort with calculations and careful attention to detail. Questions often involve multi-step problems requiring systematic approach.
Weight Terminology and Definitions
Understanding terminology is foundational to Mass & Balance. Different aircraft manufacturers and regulatory authorities use slightly different terms, but the concepts are the same.
Basic Weight Terms
| Term | Description |
|---|---|
| Basic Empty Mass (BEM) / Basic Empty Weight (BEW) | Aircraft as manufactured plus standard equipment, unusable fuel, unusable oil, lavatory chemicals, crew seats and galley structures. Does NOT include crew, catering, or potable water. |
| Dry Operating Mass (DOM) / Dry Operating Weight (DOW) | BEM + crew and crew baggage + catering equipment (fixed galleys, ovens) + removable equipment. Does NOT include trip fuel or payload. |
| Operating Mass (OM) / Operating Weight (OW) | DOM + operational items (variable): potable water, crew meals, removable passenger service equipment. Some operators include this in DOM. |
| Zero Fuel Mass (ZFM) / Zero Fuel Weight (ZFW) | Aircraft mass with all payload but no usable fuel. ZFM = DOM + payload (passengers, baggage, cargo). |
| Takeoff Mass (TOM) / Takeoff Weight (TOW) | Aircraft mass at brake release for takeoff. TOM = ZFM + takeoff fuel. |
| Landing Mass (LM) / Landing Weight (LW) | Aircraft mass at touchdown. LM = TOM - trip fuel + reserve fuel. |
| Ramp Mass / Taxi Weight | Aircraft mass including taxi fuel. Ramp mass = TOM + taxi fuel. Typically 100-300 kg greater than TOM. |
- Mass: Quantity of matter (kg in SI units)
- Weight: Force due to gravity = mass × gravitational acceleration (Newtons)
- In aviation, terms "mass" (EASA/ICAO) and "weight" (FAA) often used interchangeably, though technically mass is correct
Maximum Weight Limitations
Aircraft operations are limited by various maximum weights, determined by structural, performance, or regulatory considerations:
| Limitation | Description |
|---|---|
| Maximum Ramp Mass (MRM) | Maximum mass for ground maneuvering (taxiing). Slightly higher than MTOM to allow for taxi fuel burn. |
| Maximum Takeoff Mass (MTOM) | Maximum mass at brake release. Limited by structural strength, climb performance, takeoff distance. |
| Maximum Landing Mass (MLM) | Maximum mass for landing. Lower than MTOM due to structural limits on landing gear and airframe during impact. |
| Maximum Zero Fuel Mass (MZFM) | Maximum mass without fuel. Protects wing structure from excessive bending loads. |
- If aircraft weight exceeds MLM at planned landing, must:
- Reduce payload (offload passengers/cargo), or
- Reduce fuel (if safe reserves maintained), or
- Burn or jettison fuel during flight (if fuel jettison system available)
- MZFM: ~75-85% of MTOM
- MLM: ~80-90% of MTOM
- MRM: ~100.5-101% of MTOM (taxi fuel allowance)
Payload and Fuel Definitions
Payload:
- Revenue-earning load: passengers, baggage, cargo
- Standard passenger weights (EASA):
- Male passengers: 88 kg (includes 13 kg hand baggage)
- Female passengers: 70 kg (includes 13 kg hand baggage)
- Children (2-12 years): 35 kg (includes 10 kg hand baggage)
- Infants (<2 years): 0 kg (carried on adult lap, no separate seat)
- Checked baggage: Typically 15-23 kg per bag
- Cargo: Variable, weighed individually
- Fleet average: Calculated from actual surveys (more accurate)
- Seasonal variation: Summer (lighter clothing), winter (heavier clothing)
- Regional variation: Different regions may use different standard weights
- Block fuel: Total fuel on board at start of taxi (ramp fuel)
- Taxi fuel: Fuel used from ramp to takeoff (typically 100-300 kg)
- Trip fuel: Fuel used from takeoff to landing at destination
- Contingency fuel: Extra fuel for unforeseen circumstances (typically 5% of trip fuel or 5 minutes holding, whichever greater)
- Alternate fuel: Fuel to fly from destination to alternate airport
- Final reserve fuel: Fuel to hold for 30 minutes at 1,500 ft above alternate (jets) or 45 minutes at cruise speed (propeller aircraft)
- Additional fuel: Extra fuel at captain's discretion (weather, delays, etc.)
- Minimum fuel: Trip + contingency + alternate + final reserve
- Block fuel: Taxi + minimum fuel + additional fuel (if any)
Center of Gravity (CG) Concepts
The center of gravity is the point where the entire weight of the aircraft can be considered to act. CG position directly affects aircraft stability, control, and performance.
CG Definition and Reference
Center of Gravity (CG):
- Point where all weight moments balance
- If aircraft suspended from CG, it would balance perfectly
- Imaginary vertical plane from which all distances are measured
- Datum location: Chosen by manufacturer, often at nose, firewall, or wing leading edge
- Arms measured from datum:
- Positive (+): Aft of datum
- Negative (-): Forward of datum (rare, depends on datum location)
- Moment = Mass × Arm
- Turning effect about the datum
- Units: kg·m (kilogram-meters) or lb·in (pound-inches)
- CG = Total Moment / Total Mass
- CG expressed as distance from datum (in meters, inches, or % MAC)
CG Limits and Effects
Forward CG Limit:
- Determined by:
- Elevator authority (must be able to rotate for takeoff)
- Nose wheel load (must not exceed limit)
- Stability (must not be excessively stable)
- Effects of too far forward CG:
- Increased stability (nose-heavy)
- Higher stall speed (need more elevator to maintain AOA)
- Longer takeoff run (difficult to rotate)
- Reduced fuel efficiency (trim drag from nose-down elevator)
- Possible nose wheel overload during landing
- Determined by:
- Stability (must maintain acceptable static stability)
- Elevator authority (must be able to recover from stall, control at all speeds)
- Control (must not become uncontrollable)
- Effects of too far aft CG:
- Decreased stability (tail-heavy, less stable)
- Lower stall speed (less elevator required to maintain AOA)
- Shorter takeoff run (easier to rotate)
- Risk of uncontrollable pitch-up
- Possible tail strike during takeoff or landing
- Spin recovery difficult or impossible
- Slightly forward of mid-range for best compromise
- Provides adequate stability while minimizing trim drag
Mean Aerodynamic Chord (MAC)
MAC Definition:
- Average chord length of wing, accounting for taper and sweep
- Used to express CG position as percentage for convenience
- %MAC = [(CG position - LEMAC) / MAC] × 100
- LEMAC: Leading Edge of Mean Aerodynamic Chord (distance from datum)
- Forward limit: 15-20% MAC
- Aft limit: 35-40% MAC
- Varies by aircraft type
- Independent of aircraft size: %MAC allows comparison between different aircraft
- Easier to interpret: 25% MAC has same meaning regardless of wing dimensions
- Standardized: Used internationally
- CG can be expressed as:
- Distance from datum (meters or inches)
- Percent MAC (%MAC)
- Both are equivalent, just different units
Weight and Balance Calculations
There are several methods for calculating weight and balance. The exam may test any of these methods, so familiarity with all is important.
Moment Method (Basic)
Steps:
- List all masses and their arms from datum
- Calculate moment for each item (Moment = Mass × Arm)
- Sum all masses to find total mass
- Sum all moments to find total moment
- Calculate CG position (CG = Total Moment / Total Mass)
- Check CG against limits
| Item | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| BEM | 42,000 | 12.5 | 525,000 |
| Crew | 300 | 2.0 | 600 |
| Passengers | 12,000 | 14.0 | 168,000 |
| Cargo (fwd) | 2,000 | 8.0 | 16,000 |
| Cargo (aft) | 1,500 | 20.0 | 30,000 |
| Fuel | 18,000 | 13.0 | 234,000 |
| Total | 75,800 | 973,600 |
- Check: If forward limit = 12.0 m and aft limit = 14.0 m, CG is within limits ✓
Index Method
The index method simplifies calculations by using an index unit rather than moments.
Index Definition:
- Index = Moment / Constant
- Constant chosen to keep index values manageable (e.g., 100 or 1000)
- List all masses and their indices (from loading manual)
- Sum all masses to find total mass
- Sum all indices to find total index
- Calculate CG position (CG = Total Index × Constant / Total Mass, or use graph)
- Check CG against limits
- Smaller numbers, easier arithmetic
- Reduces calculation errors
- Commonly used in commercial aviation
| Item | Mass (kg) | Index |
|---|---|---|
| DOM | 40,000 | 4,200 |
| Passengers | 14,000 | 1,540 |
| Cargo | 3,000 | 330 |
| Fuel | 20,000 | 2,100 |
| Total | 77,000 | 8,170 |
Graph Method
Loading Graph / CG Envelope Chart:
- X-axis: Mass (kg or lbs)
- Y-axis: CG position (m, inches, or %MAC) or Index
- CG envelope: Bounded region representing allowable combinations of mass and CG
- Forward and aft limit lines: Boundaries of envelope
- Calculate total mass and CG (or index) using moment or index method
- Plot point on graph (mass on X-axis, CG or index on Y-axis)
- Check if point falls within envelope
- If inside envelope → Weight and balance acceptable
- If outside envelope → Weight and balance unacceptable, must adjust loading
- Graphs often have multiple limit lines for different configurations (flaps, slats, etc.)
- Some graphs show takeoff, landing, and zero fuel envelopes separately
Load and Trim Sheet (Real-World Application)
In airline operations, weight and balance calculations are performed using standardized load and trim sheets (also called loadsheets or weight and balance manifests).
Loadsheet Sections:
- Aircraft identification: Registration, flight number, date
- Weights:
- DOW (or DOM)
- Passenger load (number and weight)
- Baggage
- Cargo (compartment by compartment)
- Fuel
- ZFW, TOW, LW
- Index or CG position
- %MAC
- Check against limits
Load Planning Software:
- Modern airlines use computerized load planning systems
- Automatically calculate weight and balance, optimize loading
- Generate loadsheet and provide CG position
- Pilot reviews and accepts loadsheet before departure
- Verify loadsheet accuracy: Check passenger count, cargo, fuel match reality
- Check weight and balance limits: Ensure TOW ≤ MTOM, ZFW ≤ MZFM, CG within limits
- Ensure performance compliance: TOW acceptable for runway, temperature, altitude
- Sign loadsheet: Captain signs to accept weight and balance
Loading Procedures and Cargo Systems
Passenger Loading
Seating Zones:
- Aircraft divided into zones for weight and balance purposes
- Example (narrow-body): Forward, middle, aft zones
- Example (wide-body): Forward, center forward, center aft, aft zones
- Ideal: Even distribution fore and aft to keep CG centered
- Reality: Passengers choose seats, may not be evenly distributed
- Adjustments: If CG out of limits, may need to:
- Reseat passengers
- Adjust cargo distribution
- Add ballast (last resort)
- Standard weights: Used for flight planning (male, female, child, infant)
- Actual weighing: Required in some situations (e.g., small aircraft, known weight issues)
Baggage and Cargo Loading
Cargo Compartments:
- Forward hold (or cargo compartment 1): Below forward cabin
- Aft hold (or cargo compartment 2/3): Below aft cabin
- Bulk cargo hold: Loose items, odd-sized cargo
- Containerized cargo: Unit Load Devices (ULDs)
- Containers and pallets that fit aircraft cargo holds
- Standardized sizes: LD-3, LD-8, etc. (various dimensions)
- Advantages:
- Faster loading/unloading
- Better space utilization
- Protection for cargo
- Weight and CG pre-calculated
- Floor loading limits: Maximum weight per unit area (kg/m² or lbs/ft²)
- Compartment limits: Maximum weight per compartment
- CG control: Load heavier cargo forward or aft to adjust CG
- Dangerous goods: Special handling, segregation, documentation
- Passenger or cargo changes after loadsheet finalized
- Procedure:
- Note change (passenger deplaned, cargo removed, fuel added, etc.)
- Recalculate weight and balance
- Issue revised loadsheet or LMC report
- Captain reviews and accepts
Ballast
Ballast Definition:
- Non-revenue weight added to aircraft to bring CG within limits
- Light passenger load with aft CG (empty aft cabin)
- Cargo heavy in aft hold
- Ferry flights (no passengers, minimal cargo)
- Permanent ballast: Fixed in aircraft (e.g., in tail cone), part of BEM
- Removable ballast: Lead weights, water, sand bags, added as needed
- Forward ballast: Moves CG forward (used when CG too far aft)
- Aft ballast: Moves CG aft (used when CG too far forward, rare in commercial ops)
- Reduces payload capacity
- Increases fuel consumption
- Last resort, prefer optimal cargo/passenger distribution
CG Shift Calculations
Understanding how loading changes affect CG position is critical for load planning and troubleshooting.
Adding or Removing Mass
Formula:
- CG shift = (Mass added/removed × Distance from old CG) / New total mass
- If mass added aft of CG → CG shifts aft
- If mass added forward of CG → CG shifts forward
- If mass removed aft of CG → CG shifts forward
- If mass removed forward of CG → CG shifts aft
- Aircraft mass: 60,000 kg, CG at 12.5 m
- Add 2,000 kg cargo at 20.0 m (aft of CG)
- Distance from CG: 20.0 - 12.5 = 7.5 m aft
- New mass: 60,000 + 2,000 = 62,000 kg
- CG shift = (2,000 × 7.5) / 62,000 = 15,000 / 62,000 = 0.24 m aft
- New CG = 12.5 + 0.24 = 12.74 m
- Old moment: 60,000 × 12.5 = 750,000 kg·m
- Added moment: 2,000 × 20.0 = 40,000 kg·m
- New moment: 750,000 + 40,000 = 790,000 kg·m
- New CG: 790,000 / 62,000 = 12.74 m ✓
Moving Mass Within Aircraft
Formula:
- CG shift = (Mass moved × Distance moved) / Total mass
- If mass moved aft → CG shifts aft
- If mass moved forward → CG shifts forward
- Total mass unchanged (mass only relocated)
- Aircraft mass: 65,000 kg, CG at 13.0 m
- Move 1,000 kg cargo from position 10.0 m to position 18.0 m
- Distance moved: 18.0 - 10.0 = 8.0 m aft
- CG shift = (1,000 × 8.0) / 65,000 = 8,000 / 65,000 = 0.12 m aft
- New CG = 13.0 + 0.12 = 13.12 m
Fuel Burn Effects
Fuel CG:
- Fuel typically stored in wings, near CG
- As fuel burns, CG shifts slightly
- Depends on fuel tank CG relative to aircraft CG
- Fuel tank aft of CG: Burning fuel shifts CG forward
- Fuel tank forward of CG: Burning fuel shifts CG aft
- Most aircraft: Fuel CG close to aircraft CG, so CG shift minimal during fuel burn
- CG must remain within limits throughout flight (takeoff, cruise, landing)
- Worst case: Usually takeoff or landing, depending on fuel CG location
- Load planning ensures CG within limits at all flight phases
Special Loading Considerations
Seating and Cargo Restrictions
Critical Stations:
- Areas where small weight changes cause large CG shifts (far from CG)
- Careful control of loading at critical stations
- Hazardous materials (flammable, corrosive, explosive, radioactive, etc.)
- Regulations: ICAO Technical Instructions, IATA Dangerous Goods Regulations
- Segregation: Some dangerous goods must be separated from others (e.g., oxidizers from flammables)
- Documentation: Shipper's Declaration, NOTOC (Notification to Captain)
- Passenger notification: "Dangerous Goods as Cargo" placard on NOTOC
- Special handling, ventilation, feeding, watering
- Load position: Typically aft cargo hold (temperature controlled, ventilation)
- CG outside normal limits but within extended limits
- May be permitted with operational restrictions (reduced speed, special procedures)
- Requires special approval, typically avoided
Underfloor Cargo Compartments
Compartment Numbering:
- Fwd (Compartment 1): Forward cargo hold
- Aft (Compartment 2): Aft cargo hold
- Bulk (Compartment 3): Aft bulk cargo (loose items, odd shapes)
- Heavier items first: Load heavy items before light items
- CG control: Adjust forward/aft loading to optimize CG
- Weight distribution: Avoid exceeding compartment or floor limits
- Maximum compartment weight: Each hold has maximum weight limit
- Maximum floor load: Weight per unit area (kg/m², lbs/ft²)
- Maximum concentrated load: Maximum weight on single ULD or pallet
Weight and Balance Documentation
Aircraft Flight Manual (AFM) / Aircraft Operating Manual (AOM)
Weight and Balance Section:
- Definitions of weights (BEM, DOM, MTOM, MLM, MZFM)
- CG limits (forward and aft, vs. weight)
- Loading instructions
- CG envelope charts
- Sample weight and balance calculations
Loading Manual
Detailed Loading Information:
- Station locations and arms
- Compartment capacities and limits
- ULD types and weights
- Passenger seating zones and weights
- Index values for each station
- Loading graphs and tables
- Ballast locations and procedures
Load and Trim Sheet / Loadsheet
Completed Before Every Flight:
- Pilot responsibility to review and accept
- Kept as part of flight paperwork
EASA Learning Objectives - Subject 031
According to the EASA ATPL syllabus, candidates must demonstrate knowledge of:
Definitions and Terminology
- Mass terminology: BEM, DOM, ZFM, TOM, LM, payload, fuel
- CG terminology: CG, datum, arm, moment, MAC, %MAC, LEMAC
- Limitations: MTOM, MLM, MZFM, MRM
CG and Stability
- CG effects on stability and control: Forward vs. aft CG
- CG limits: Forward limit, aft limit, determination factors
- MAC and %MAC: Definition, calculation, interpretation
Weight and Balance Calculations
- Moment method: Calculating CG using masses, arms, and moments
- Index method: Using index units for simplified calculations
- Graph method: Plotting on CG envelope chart, checking limits
- CG shift calculations: Adding/removing mass, moving mass, fuel burn effects
Loading Procedures
- Passenger loading: Standard weights, seating zones, distribution
- Cargo loading: Compartments, ULDs, floor limits, distribution
- Ballast: Purpose, types, placement, disadvantages
- Loading documentation: Loadsheet, loading manual, AFM/AOM
Operational Considerations
- Load planning: Optimizing CG, complying with limits
- Last Minute Changes: Procedure for revising weight and balance
- Dangerous goods: Restrictions, segregation, documentation
- Special loads: Live animals, heavy cargo, oversized items
Exam Tips & Common Questions
Memory Aids
Weight Definitions (Increasing Order):
- "BEM → DOM → ZFM → TOM"
- Basic Empty Mass < Dry Operating Mass < Zero Fuel Mass < Takeoff Mass
- "Forward CG = More Stable, Higher Stall Speed, Nose Heavy"
- "Aft CG = Less Stable, Lower Stall Speed, Tail Heavy"
- "Add mass aft → CG shifts aft"
- "Remove mass aft → CG shifts forward"
- "Move mass aft → CG shifts aft"
- "%MAC = [(CG - LEMAC) / MAC] × 100"
High-Yield Topics
Based on historical exam analysis, these topics appear frequently:
- Weight definitions and limitations (15-20% of questions)
- BEM, DOM, ZFM, TOM, LM
- MTOM, MLM, MZFM
- Calculating maximum payload, fuel capacity
- CG calculations using moment method (25-30% of questions)
- Multi-step problems: Add masses, calculate moments, find CG
- Check CG against limits
- CG shift calculations (20-25% of questions)
- Adding/removing mass, moving mass, fuel burn
- Calculate new CG after loading change
- %MAC calculations (10-15% of questions)
- Convert CG position to %MAC
- Check %MAC against limits
- CG effects on stability and performance (10-15% of questions)
- Forward vs. aft CG effects
- Stall speed, stability, takeoff distance
- Loading procedures and limitations (10-15% of questions)
- Cargo compartments, ULDs, ballast
- Floor loading limits, dangerous goods
Common Mistakes to Avoid
- Unit confusion: Mixing kg and lbs, meters and inches—always check units
- Sign errors: Forgetting to use negative arms (if datum ahead of item) or positive/negative moment directions
- Arithmetic errors: Double-check calculations, especially in multi-step problems
- Misreading graphs: Ensure correct axis (X = mass, Y = CG or index), check units
- Forgetting to check all limits: Must check MTOM, MLM, MZFM, and CG limits
- Ignoring fuel burn: CG changes during flight as fuel burns—ensure CG within limits at takeoff, landing, and throughout
Tricky Question Types
Maximum Payload Calculations:
- Given MTOM, DOM, fuel: "What is maximum payload?"
- Answer: Max payload = min(MTOM - DOM - fuel, MZFM - DOM)
- Must check both MTOM and MZFM constraints
- "Passenger moves from row 10 to row 25, cargo added to aft hold, fuel increased. What is new CG?"
- Approach: Calculate each change separately, sum CG shifts, or recalculate total moment and total mass
- "Aircraft takes off at CG 25% MAC. Fuel burned during flight has CG at 23% MAC. CG at landing?"
- Approach: Fuel burn removes mass at 23% MAC. If aircraft CG at 25% MAC, fuel forward of CG, so CG shifts aft.
- Calculate CG shift = (fuel burned × distance from CG) / landing mass
- Given mass and index, "Is weight and balance acceptable?"
- Approach: Plot point on graph, check if inside envelope
- "CG is 0.5 m too far aft. How much ballast required in forward hold (8 m forward of CG) to bring CG to aft limit?"
- Approach: CG shift needed = 0.5 m forward
- Ballast mass = (CG shift × total mass) / distance from CG
- Ballast mass = (0.5 × total mass) / 8
Practical Application for Pilots
Pre-Flight Load Planning
Load Sheet Review:
- Verify passenger count matches boarding pass count
- Check cargo weights and compartment loading
- Confirm fuel load matches flight plan
- Check all weights (ZFW, TOW, LW) within limits
- Verify CG within limits at all flight phases
- Coordinate with load planner for optimal CG
- Adjust cargo distribution if CG out of limits
- Minimize ballast (reduces payload and increases fuel burn)
- Passenger no-show, extra baggage, fuel added, cargo offloaded
- Ensure revised loadsheet issued and checked
- Confirm weight and balance still acceptable
In-Flight Considerations
CG Changes During Flight:
- Fuel burn shifts CG (typically minimal)
- Passenger movement (e.g., all passengers to aft lavatory) can shift CG significantly on small aircraft
- Cargo shifting (improperly secured) can cause CG shift and handling problems
- Forward CG: Heavier elevator forces, more stable, higher stall speed
- Aft CG: Lighter elevator forces, less stable, lower stall speed
- Pilot must be aware of CG position and adjust technique accordingly
- If landing weight will exceed MLM (long flight delayed, emergency return shortly after takeoff):
- Option 1: Burn fuel by holding (time-consuming)
- Option 2: Jettison fuel (if system available, emergency only)
- Option 3: Overweight landing (structural inspection required afterward)
Weight and Balance Incidents/Accidents
Real-World Examples:
- Improper loading: Cargo loaded in wrong compartment, causing CG out of limits → Loss of control
- Incorrect passenger count: Loadsheet assumes 150 passengers, actually 180 onboard → Overweight takeoff
- Cargo shift: Unsecured cargo slides aft during takeoff → Aft CG, loss of control
- Fuel calculation error: Fuel load entered incorrectly on loadsheet → Takeoff weight calculation wrong
- Always verify loadsheet accuracy
- Ensure cargo properly secured
- Cross-check critical data (passenger count, fuel, cargo)
- Be aware of CG effects on handling
Study Strategy for Mass & Balance
Recommended Study Sequence
- Terminology and definitions (2-3 days)
- Master weight terms (BEM, DOM, ZFM, TOM, etc.)
- Understand CG, datum, arm, moment, MAC, %MAC
- Basic CG calculations (moment method) (1 week)
- Practice calculating moments
- Calculate CG from masses and arms
- Check CG against limits
- CG shift calculations (1 week)
- Add/remove mass problems
- Move mass problems
- Fuel burn problems
- Combined problems
- Index method and graph method (3-4 days)
- Understand index calculation
- Practice plotting on CG envelope charts
- MAC and %MAC (2-3 days)
- Calculate %MAC from CG position
- Convert between CG and %MAC
- Loading procedures and limitations (3-4 days)
- Cargo compartments, ULDs, ballast
- Maximum weights, floor limits
- Loadsheet interpretation
- Practice exam problems (1 week)
- Work through full-length practice exams
- Focus on time management and accuracy
Study Resources
- EASA Syllabus: Review the official learning objectives
- Textbooks: CAE Oxford, Bristol Ground School, ATPL Ground Training
- Question banks: Aviationexam, Bristol GS, ATPL Ground Training (heavy practice essential)
- Aircraft Flight Manuals: Real weight and balance sections (Boeing, Airbus)
- Online calculators: Practice with interactive weight and balance tools
Study Tips
- Master the basics first: Ensure comfort with basic moment calculations before moving to complex problems
- Practice, practice, practice: Mass & Balance is calculation-heavy, must practice many problems
- Use systematic approach: Write down all given data, organize work, show all steps
- Check units: Always verify kg vs. lbs, meters vs. inches, etc.
- Double-check arithmetic: Calculation errors cost points, slow down and verify
- Time management: Exam is 1 hour for 25 questions, ~2.4 minutes per question, don't get stuck on one problem
- Use calculator efficiently: Learn your calculator well, use memory functions
- Draw diagrams: Sketch aircraft with datum, arms, and masses to visualize problem
Common Calculation Shortcuts
CG Shift Approximation:
- For small mass changes (< 5% of total mass), CG shift ≈ (Mass change × Distance from CG) / Original mass
- Saves time, adequate accuracy for most problems
- If CG roughly in middle of allowable range, ~25-30% MAC typical
- If CG at forward limit, ~15-20% MAC
- If CG at aft limit, ~35-40% MAC
- Use for quick sanity check of answer
- If fuel CG very close to aircraft CG, CG shift minimal, may be negligible
- If problem states "fuel CG at aircraft CG," CG unchanged by fuel burn
Integration with Other Subjects
Mass & Balance connects with several other ATPL subjects:
- Performance: TOW affects takeoff distance, climb performance, landing distance; CG affects stall speed, trim drag
- Flight Planning: Fuel planning, payload optimization, weight limits affect route planning
- Aircraft General Knowledge: Fuel systems, loading systems, structural limits
- Operational Procedures: Load planning procedures, loadsheet use, dangerous goods handling
- Principles of Flight: CG effects on stability (longitudinal, lateral), control authority
Conclusion
Mass & Balance is a highly practical and calculation-intensive subject. Every commercial flight requires weight and balance calculations, and pilots must understand the principles, perform calculations accurately, and recognize when weight or balance limits are approached or exceeded.
The key to success in Mass & Balance is practice. Work through many problems, master the moment method, CG shift calculations, and %MAC conversions. Develop a systematic approach: organize data, show all steps, check units, double-check arithmetic.
Understand not just how to calculate CG, but why CG position matters. Forward and aft CG have distinct effects on stability, control, performance, and handling. A pilot with strong Mass & Balance knowledge can optimize loading for efficiency and safety, recognize problematic loading situations, and make informed decisions.
Time management is critical in the exam. With 25 questions in 1 hour, you have ~2.4 minutes per question. Practice working quickly and accurately. If stuck on a problem, mark it and move on—return if time permits.
Finally, connect Mass & Balance knowledge to real operations. Review loadsheets, loading manuals, and AFM weight and balance sections for real aircraft. Understanding real-world applications solidifies theoretical knowledge and prepares you for professional flight operations.
Related Articles:
- Aircraft Performance - ATPL Subject 032
- Aircraft General Knowledge - ATPL Subject 021
- Flight Planning - ATPL Subject 033
- Operational Procedures - ATPL Subject 070
- Principles of Flight - ATPL Subject 081
- Review EASA Learning Objectives thoroughly
- Practice basic moment calculations until comfortable
- Work through CG shift problems systematically
- Begin practicing with Mass & Balance question banks