CH10: Weight and Balance

Weight and Balance Notes

Weight and Balance Fundamentals

• Compliance with weight and balance limits is critical to flight safety. Operating above maximum weight compromises structural integrity and performance; CG outside approved limits causes control difficulties.

• Weight: a gravitational force acting on the aircraft; defined as the product of mass and acceleration due to gravity. Weight is the force that must be counteracted by lift.

• Lift vs. weight: Lift must counteract weight to sustain flight. Lift is limited by airfoil design, angle of attack (AOA), airspeed, and air density.

• Overloading an aircraft can prevent takeoff or result in poor flight characteristics once airborne.

Effects of Weight

• Excess weight degrades performance in many ways:

  • Higher takeoff speed and longer takeoff run

  • Reduced rate and angle of climb

  • Lower maximum altitude

  • Shorter range and cruising speed

  • Reduced maneuverability

  • Higher stall, approach, and landing speeds

  • Longer landing roll

  • Potential excess load on nose or tail wheels

• Weight can affect safety margins, especially when combined with other performance-reducing factors.

• Preflight planning should consult performance charts to determine weight effects on hazardous operations.

• Engine failure on takeoff or ice formation at low altitude may not allow weight reduction in time to stay airborne.

Lateral vs. Longitudinal Unbalance

• Lateral unbalance causes wing heaviness (e.g., empty vs. full, excess baggage).

• Longitudinal unbalance causes nose- or tail-heaviness; excessive trim can reduce aerodynamic efficiency and control travel.

• In some cases, lateral CG shifts are not calculated in all aircraft; however, awareness of lateral balance is important due to adverse effects on efficiency and fatigue.

• The AFM (Airplane Flight Manual) often addresses lateral balance as needed; longitudinal balance is typically more critical.

Balance, Stability, and Center of Gravity (CG)

• Balance refers to the location of the CG along the longitudinal axis and its effect on stability and safety.

• CG is the point about which an aircraft would balance if suspended; it is the effective mass center of the aircraft.

• The distance between the forward and aft limits of CG is the CG range, certified by the manufacturer.

• CG position shifts with weight distribution changes; it is not a fixed point.

• As weight items shift or are expended, CG location shifts accordingly.

• The CG location is referenced along the longitudinal axis using a datum; forward vs. aft relative to the datum is measured in inches.

• Lateral CG is the balance about the lateral axis; a proper balance minimizes adverse effects on stability.

• For lateral balance, if one side carries more weight, compensatory trim adjustments may be required; improper lateral balance increases drag and decreases efficiency.

Important Concepts

• Datum: an imaginary vertical plane/line from which all arms are measured; defined by the manufacturer.

• Arm: horizontal distance in inches from the datum to the CG of an item; positive if aft of the datum, negative if forward.

• Station: a location on the aircraft identified by inches from the datum (arm).

• Moment: the product of weight and arm:
  $ext{Moment} = W imes ext{Arm} ext{ (in-lb)}$

• CG location is determined by:
  $ext{CG} = rac{ ext{Total Moment}}{ ext{Total Weight}} = rac{\big( ext{sum of }W<em>i imes ext{Arm}</em>i\big)}{\big( ext{sum of }W_i\big)}$

• MAC (Mean Aerodynamic Chord): the average distance from leading edge to trailing edge of the wing; used for CG percentage references.

• CG range: allowable forward and aft CG limits for flight; ensured by manufacturer and published in TCDS, AFM/POH.

Adverse Balance and Stability Effects

• Nose-heavy: difficult to raise the nose or flare; may impact landing characteristics.

• Tail-heavy: reduces longitudinal stability, makes stalls/spins harder to recover from, and can produce very light control forces which may lead to overstress.

• Forward CG limit is often tied to landing characteristics to avoid nose-over, high nose loads, and increased stall speed.

• Aft CG limit is the most rearward position for the most critical maneuver; too far aft causes instability and reduced righting ability.

CG Limits and Operations

• CG limits are published for each aircraft in the TCDS, aircraft specification, AFM, or POH.

• If CG is out of limits after loading, relocate weight (rethink baggage, seats, or fuel) before flight.

• Forward CG limits are chosen to accommodate nose-down tendencies during high AoA/low-speed flight and to maintain elevator effectiveness at minimum airspeed.

• Restrictive forward CG positions can ensure sufficient elevator deflection at minimum airspeed for safe landing.

Weight Changes and Fuel Burn

• Weight can be changed by fuel load; gasoline weighs $6 ext{ lb/gal}$.

• Fuel burn during flight reduces aircraft weight, generally improving performance, but range is reduced when fuel is burned.

• Fixed equipment changes (additional radios, instruments) alter weight and CG and must be updated in the weight-and-balance records.

• Records must be kept current after repairs or modifications; unnecessary entries can lead to unsafe calculations.

• Some general weights (negligible weight changes) are acceptable without a weight-and-balance check according to AC 43.13-1:

  • One pound or less for empty weight < 5,000 lb

  • Two pounds or less for empty weight 5,000–50,000 lb

  • Five pounds or less for empty weight > 50,000 lb

• Negligible CG change is any change < 0.05% MAC for fixed-wing or < 0.2% MAC for rotary-wing aircraft.

Management of Weight and Balance (Regulatory Context)

• 14 CFR Part 23.23 requires establishing weight and CG ranges safe for operation.

• Manufacturer provides this information in AFM, TCDS, or aircraft specifications.

• Under 14 CFR Part 91, pilots must comply with AFM limits; no mandatory preflight weight-and-balance calculation, but limits must be followed.

• Charts/graphs in AFM help with computations.

• The aircraft owner/operator should maintain up-to-date information and record entries after repairs/modifications; weight changes must be accounted for.

• For certain operations (Part 125, Part 135), there are specific weighing and weight-and-balance requirements; see AC 120-27 for guidance on weight-and-balance control programs.

• AC 43.13-1 requires mechanics to ensure weight and balance data are current after inspections.

Terms and Definitions (GAMA Standards)

• Arm (moment arm): horizontal distance from the reference datum to an item's CG; sign convention: plus (+) aft of datum, minus (−) forward of datum.

• Basic empty weight (GAMA): standard empty weight plus the weight of optional/special equipment installed.

• Center of gravity (CG): point around which the aircraft would balance; distance from datum or in percent MAC; three-dimensional point (longitudinal, lateral, vertical).

• CG limits: specified forward and aft CG positions during flight.

• CG range: distance between forward and aft CG limits.

• Datum (reference datum): imaginary plane/line from which arms are measured; set by manufacturer.

• Delta (r): change in a value; e.g.,
  $riangle CG = r_{CG}$

• Floor load limit: maximum weight the floor can sustain per square inch/foot.

• Fuel load: expendable load; only usable fuel, not fuel in lines or sump.

• Licensed empty weight: empty weight including airframe, engines, unusable fuel, and specified standard/optional equipment; used by some manufacturers before standardization.

• Maximum landing weight: greatest weight normally allowed on landing.

• Maximum ramp weight (taxi weight): weight with full fuel including taxi/takeoff fuel burn; greater than takeoff weight due to fuel burn en route.

• Maximum takeoff weight: maximum allowed weight for takeoff.

• Maximum weight: maximum authorized weight of aircraft and equipment per TCDS.

• Maximum zero fuel weight (GAMA): maximum weight excluding usable fuel.

• Mean Aerodynamic Chord (MAC): average wing chord length from leading to trailing edge.

• Moment: weight × arm; measured in in-lb; total moment = aircraft weight × CG distance from datum.

• Moment index: moment divided by a constant (e.g., 100, 1,000, or 10,000) to simplify calculations.

• Payload (GAMA): weight of occupants, cargo, and baggage.

• Standard empty weight (GAMA): airframe, engines, fixed equipment in fixed locations, including fixed ballast and oil.

• Standard weights: predefined weights for various items used in calculations (e.g., Gasoline 6 lb/US gal, Jet A 6.8 lb/gal, Oil 7.5 lb/gal, Water 8.35 lb/gal).

• Station: a location in the aircraft identified by a distance from the datum; station 0 is the datum.

• Useful load: weight of occupants, cargo, baggage, usable fuel, and drainable oil; equals maximum allowable gross weight minus standard empty weight; applies to GA aircraft only.

Principles of Weight and Balance Computations

• Core idea: determine empty aircraft weight and then add loaded items to determine total weight; the challenge is to balance the total mass about the CG within specified limits.

• The CG is the imaginary balance point; it depends on weight distribution and can shift as loads are moved.

• A safe balance places the CG slightly forward of the center of lift to provide a nose-down tendency at high AoA and slow speeds, aiding stability.

Methods of Weight and Balance Computations

Three primary methods exist and are commonly provided by manufacturers:

1) Computational Method

• Steps (illustrative):
  1) List weights: empty aircraft, occupants, fuel, baggage, etc.
  2) Compute each item’s moment:
  $ext{Moment}<em>i = W</em>i imes ext{Arm}_i$
  3) Sum total weight and total moment.
  4) Compute CG:
  $CG = rac{ ext{Total Moment}}{ ext{Total Weight}}$

• Example data (from Figure 10-5):

  • Aircraft Empty Weight: 2{,}100 lb; Arm: 78.3 in

  • Front seat occupants: 340 lb; Arm: 85.0 in

  • Rear seat occupants: 350 lb; Arm: 121.0 in

  • Fuel: 450 lb; Arm: 75.0 in

  • Baggage Area 1: 80 lb; Arm: 150.0 in

  • Total weight: 3{,}320 lb; Total moment: 281{,}430 in-lb

  • CG:
    $CG = rac{281{,}430}{3{,}320} = 84.8 ext{ in}$

• The example shows the aircraft is within a CG range if the range is 78–86 inches.

• Notes: The weight must not exceed maximum gross takeoff weight; other factors like altitude and humidity affect takeoff performance.

2) Graph Method

• Uses manufacturer-provided loading or CG envelopes (CG envelope). The moment can be scaled (e.g., divided by 100, 1,000, or 10,000) to fit graph charts.

• Procedure:

  • Determine weights for each item (front, rear, fuel, baggage).

  • Plot weight on the horizontal axis and corresponding moment on the vertical axis (or vice versa) using the loading graph.

  • Draw lines across weights to intersect a moment line; if the intersection lies within the CG envelope, the aircraft is loaded within limits.

• Figures 10-7 and 10-8 illustrate loading graphs and the CG moment envelope.

3) Table Method

• Weight and balance data are presented in tabular form by the manufacturer.

• The same steps as computational method are applied, but using table values for moments; a table can include negative arms, zero-fuel weight scenarios, etc.

• Example (Figure 10-9): shows a loading schedule placard depiction for a loading problem.

Samples and Scenarios

Sample Loading Problem (Computational Method)

• Given data (example):

  • Basic empty weight: 2{,}015 lb; Major components: oil, fuel, pilots, passengers, baggage as shown in figure

  • The example demonstrates computing a CG using a proportional and linear method, and comparing total CG against the expected limits.

• A second example shows a negative arm scenario where some components have negative arms and must be treated as negative moments in calculations.

Computations with Negative Arm

• If the arm is negative, multiply weight by a negative arm yields a negative moment; this reduces the total moment accordingly.

• Important: the sum of moments must account for positive and negative contributions correctly to determine the final CG.

Computations with Zero Fuel Weight

• Zero Fuel Weight (ZFW) scenario: ensure total weight without usable fuel does not exceed ZFW max. If it does, adjust by moving cargo or passengers to meet the ZFW limit.

Shifting, Adding, and Removing Weight

• Shifting weight does not change total weight but changes CG by moving moments.

• If weight is moved forward, the total moments decrease (CG moves forward); if moved aft, total moments increase (CG moves aft).

• To compute new CG after a shift:

  • Compute the moments gained/lost:
    $ext{Moment change} = W<em>{ ext{shift}} imes ( ext{Station}</em>{ ext{new}} - ext{Station}_{ ext{old}})$

  • New total moments:
    $M<em>{ ext{new}} = M</em>{ ext{old}} + ext{Moment change}$

  • New CG:
    $CG<em>{ ext{new}} = rac{M</em>{ ext{new}}}{W_{ ext{total}}}$

• Example (from Figure 10-10): shifting 100 lb from station 30 to station 150 changes moment by $100 imes (150-30) = 12{,}000 ext{ in-lb}$, leading to a new CG of 78.5 in for a given total weight.

• The CG can be shifted to meet a target CG using proportional calculations:

  • If initial CG is 81.5 in and you want 80.5 in, determine the required weight shift using the proportional relationship between weight, shift distance, and CG change.

Example: Shifting to the Aft Limit

• Given an initial weight W, CG at station s, and target aft limit, solve for how much cargo must be shifted to move the CG to the aft limit using the relation:

  • 
    Weight to shift
    =
    (Target CG − Initial CG) × Total Weight / (Target shift distance)

• Example calculations illustrate moving 140 lb to move the CG from 80.0 in to 81.4 in, or moving cargo to achieve exactly the aft limit.

Weight Addition or Removal During Flight

• Fuel consumption during flight reduces weight, but CG may shift because fuel is located near the CG in many small aircraft. Shifts are usually small but must be checked.

• The addition or removal of cargo or baggage requires recalculation of CG and re-check against CG limits before flight.

• In practice, the CG will shift by amounts proportional to the weight added/removed and its distance from the datum.

Practical Takeaways

• Always compute or verify that loaded weight is within the maximum takeoff weight and that CG is within the approved CG range.

• Use manufacturer-provided methods (computational, graph, or table) to determine loaded CG and verify it.

• Understand how shifting weight within the aircraft affects CG and adjust loading to satisfy CG limits.

• Be mindful of factors that can influence CG: fuel burn, baggage/cargo distribution, passenger seating, and modifications.

• Be prepared to adjust fuel load, seating, or baggage positioning to maintain safe CG throughout all flight phases.

Chapter Summary

• Operating within weight and balance limits is essential for flight safety.

• Correctly determine and maintain CG within the approved range at all times.

• Weight and balance considerations affect stability, controllability, and performance across all phases of flight.

• Regulatory references (14 CFR parts 23, 91, 125, 135) and FAA ACs provide guidance on weight and balance computations, record-keeping, and approved procedures.

• Proficiency in weight and balance computations, including shifting weight to correct CG, is a critical skill for pilots.

References for further study: FAA weight and balance guidance in AFM/TCDS/POH, AC 43.13-1, AC 120-27.