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Weight & Balance

Introduction:

  • Weight and balance is a key factor in not only design, but in the performance and stability of an aircraft under various operating conditions
  • Balance is maintained through the Center of Gravity (C.G.), whose location determines aircraft characteristics
  • Position of the center of gravity is affected not only by the total but also the distribution of weight throughout the aircraft
  • Weight parameters ensure the wings and overall structure are able to support the aircraft throughout all flight envelopes
  • Prior to every flight, pilots must determine the weight and balance to ensure the aircraft is operated in accordance with the manual
  • Weight and balance data more than an exercise in determining where an aircraft's C.G. will fall
    • It is a safety concern that has cost the lives of several pilots and their passengers
Balanced Center of Gravity
Figure 1: Balanced Center of Gravity
Aft Center of Gravity
Figure 2: Aft Center of Gravity
Forward Center of Gravity
Figure 3: Forward Center of Gravity

Center of Gravity:

  • The Center of Gravity is the specific point where the mass or weight of an aircraft may be said to center; that is, a point around which, if the aircraft could be suspended or balanced, the aircraft would remain in place at any attitude
  • It is computed during initial design and construction and is further affected by the installation of onboard equipment, aircraft loading, and other factors
  • C.G. is of major importance in an aircraft, for its position (within a designed range) has a great bearing upon longitudinal stability
  • Location of the Center of Gravity:

    • The C.G. must always be within limits, however, depending where in the allowable range the C.G. falls will effect performance [Figure 1]
      Balanced Center of Gravity
      Figure 1: Balanced Center of Gravity
      • Forward CG: [Figure 2]

        • Stable feeling
        • Nose Heavy
        • Longer takeoff distance (more airflow required to provide more force to lift heavy nose)
        • High stall speeds (more airflow deflection of the elevator required to maintain altitude at slower airspeeds resulting in high AOAs)
      • Forward Center of Gravity
        Figure 3: Forward Center of Gravity
      • Rearward CG: [Figure 3]

        • As the CG moves rearward (towards the tail), the aircraft becomes more and more dynamically unstable
        • The tail will feel heavy to compensate which requires additional nose down force
        • Should the aircraft stall or spin, it will be much more difficult to recover without the nose drop to increase airspeed
        • Higher true airspeed
        • More tail down force
      • Aft Center of Gravity
        Figure 2: Aft Center of Gravity
  • Center of Pressure:

    • It is important to understand that an aircraft’s weight is concentrated at the CG and the aerodynamic forces of lift occur at the CP
    • When the CG is forward of the CP, there is a natural tendency for the aircraft to want to pitch nose down
    • If the CP is forward of the CG, a nose up pitching moment is created
    • Therefore, designers fix the aft limit of the CG forward of the CP for the corresponding flight speed in order to retain flight equilibrium

Aircraft Weight:

  • Aircraft weight must be distributed in accordance with the design described in the aircraft's flight manual
  • Center of Gravity can also be considered the point at which all the weight of the aircraft is concentrated which can be expressed in several different ways:
    • Basic Empty Weight (BEW): weight of standard airplane, optional equipment, unusable fuel (fuel that cannot be drained), and full operating fluids, including full engine oil
    • Licensed Empty Weight: like BEW, but does not count full engine oil, only undrainable oil
    • Gross Landing Weight: takeoff weight minus the fuel burned en-route
    • Ramp Weight: airplane loaded for flight prior to engine start
    • Zero Fuel Weight: weight of the aircraft before addition of fuel
    • Gross Takeoff Weight: weight of the airplane just before brake release to begin takeoff roll
    • Useful Load: weight of crew and usable fuel
    • Maximum Ramp Weight: max weight for ground operations
    • Maximum Takeoff Weight: max weight for takeoff
    • Maximum Landing Weight: max weight for landing based on stress of impact on gear
  • Overweight Aircraft:

    • Most aircraft will never be too light to fly however overweight aircraft pose very serious safety threats
    • People like R&B singer Aaliyah have died when pilots neglect to complete a proper preflight
    • Limitations:
      • Longer takeoff run
      • Higher takeoff speed
      • Reduced angle and rate of climb
      • Reduced cruising speed
      • Shorter range
      • Higher stalling speed
      • Longer landing roll

Definitions:

  • Payload: weight of only the passengers, baggage, and cargo
  • Loading Graph: used to find the moment for loads in the airplane
  • Center of Gravity Moment Envelope: shows limits with proposed loading
Weight and Balance Data
Figure 4: Weight and Balance Data

Determining Weight and Balance:

  • FAR 21.5 sets forth the requirement for weight and balance data ("operating limitations and information") to be furnished to the pilot
    • The data is presented under the conditions which the airplane or rotorcraft was type certificated
    • The weight and balance information falls under "operating limitations" and is a required document in determining legal airworthiness,
  • Weight and balance is measured against a reference datum which is an imaginary vertical plane from which all horizontal distances are measured (firewall, leading edge, etc.)
  • From that datum an arm, or distance from the datum can be measured
  • Taking a known weight and multiplying it against the arm gives a pilot what they care about and that is the moment, or measurement of the tendency of the weight to cause rotation at the fulcrum
  • Weight and balance specifics are unique to different aircraft
    • A weight and balance example should be included with your POH
  • Most pilots however, will learn and therefore be able to relate to the Cessna 172: [Figure 4]
    • Block 1: Determine the Basic Empty Weight (BEW) of the airplane (found in POH)
    • Block 2: Determine the basic empty weight moment of the airplane (found in POH)
    • Block 3: Determine the weight of the pilot and passenger
    • Block 4: Determine the moment of the pilot and passenger (weight x arm = moment)
    • Block 5: Determine the weight of the rear passengers
    • Block 6: Determine the moment of the rear passengers (weight x arm = moment)
    • Block 7: Determine the weight of the baggage
    • Block 8: Determine the moment of the baggage (weight x arm = moment)
    • Block 9: Determine the weight of the baggage as in step 7
    • Block 10: Determine the moment of the baggage as in step 8, using the new arm
    • Block 11: Add all weights together to get the Zero Fuel Weight (Z.F.W.)
    • Block 12: Add all moments together
    • Block 13: Determine the weight of the ramp fuel
    • Block 14: Determine the moment of the ramp fuel (weight x arm = moment)
    • Block 15: Determine the ramp weight (Z.F.W. + Ramp Fuel)
    • Block 16: Determine the ramp moment (Z.F.W. moment + Ramp Fuel moment)
    • Block 17: Subtract taxi fuel used (~8 lbs)
    • Block 18: Subtract taxi fuel moment (~384)
    • Block 19: Add Z.F.W. and Ramp Weight together, then subtract Taxi Fuel to get the Gross Takeoff Weight (G.T.W.)
    • Block 20: Add Z.F.W. moment and Ramp Weight moment together, then subtract Taxi Fuel moment
    • Block 21: Estimate trip fuel weight
    • Block 22: Determine the moment of the trip fuel (weight x arm = moment)
    • Block 23: Subtract trip fuel weight from G.T.W. to get the Gross Landing Weight (G.L.W.)
    • Block 24: Subtract trip fuel moment from G.T.W. moment
    • Block 25: Divide block 12 by block 11
    • Block 26: Divide block 20 by block 19
    • Block 27: Divide block 24 by block 23
    • Block 28: Determine maneuvering speed (Va)
Weight and Balance Data
Figure 4: Weight and Balance Data
  • Weight Shift Formula

    • If you shift weight after determining the aircrafts weight and balance then verify your calculations with the weight shift formula

    Weight Moved = Distance C.G.Moves
    Aircraft Weight Distance Between Arm Locations

Case Studies:

  • National Transportation Safety Board Identification: ANC13FA091: The NTSB determines the probable cause(s) of this accident to be:
    • The pilot's improper decision to load the airplane beyond its allowable takeoff weight and center of gravity limits, which resulted in a loss of control during the initial climb. Contributing to the accident was the external load and the downwind takeoff
  • National Transportation Safety Board Identification: ERA14LA450: The NTSB determines the probable cause(s) of this accident as follows:
    • The pilot's inadequate preflight planning, which resulted in a takeoff with the airplane's center of gravity aft of its limit and led the airplane to exceed its critical angle of attack and experience an aerodynamic stall during the initial climb. Contributing to the accident was the pilot's lack of flight experience in the aircraft make and model
  • National Transportation Safety Board Identification: ERA14CA408: The NTSB determines the probable cause(s) of this accident as follows:
    • The pilot/owner/builder's improper weight and balance calculations, which rendered the airplane uncontrollable in the pitch axis
  • National Transportation Safety Board identification: ERA14FA343: The NTSB determines the probable cause(s) of this accident as follows:
    • The pilot’s failure to secure the cargo in the cargo compartment, which resulted in a weight shift that led to the center of gravity exceeding its aft limit during a go-around attempt and a subsequent aerodynamic stall. Also causal to the accident were the pilot’s inadequate preflight inspection and his loading the airplane beyond the cargo compartment weight limit
  • National Transportation Safety Board Identification: CEN13IA563: The NTSB determines the probable cause(s) of this incident as follows:
    • The pilot’s improper weight and balance calculations, which resulted in the airplane exceeding its weight and center-of-gravity limits and led to a loss of pitch control during takeoff, and the operator’s failure to obtain required weight information and to ensure that the flight was properly loaded

Conclusion:

  • Understanding weight and balance allows us to determine the relationships with how heavy an aircraft is, and how the location of that weight will impact performance and handling characteristics
  • Aside from the weight and balance data that is required to be carried on board the aircraft in determining its legality to fly, an individual weight and balance is not required to be filled out prior to every flight
    • Pilot's should not allow the lack of regulation to allow complacency
    • It is directed in part 91.103 that "Each pilot in command shall, before beginning a flight, become familiar with all available information concerning that flight"
      • It goes on to specify "information appropriate to the aircraft, relating to aircraft performance under expected values of airport elevation and runway slope, aircraft gross weight, and wind and temperature"
  • Weight and balance is directly relates to the stability of the aircraft
  • Instructions and examples can be found in the aircraft manual under section 6 for your specific aircraft

References: