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Weight and Balance

Objective​

Understand the concept of weight and balance, the relationship of center of gravity on aircraft performance and limitations, and how to compute a weight and balance problem.

Motivation​

The effect of weight and CG location is critical to the safety of flight and an essential part of cross-country flight planning. Pilots should have a clear understand of the limits of their airplane with regards to weight and balance.

Timings​

45 minutes

Format​

Elements​

Weight and Balance Concepts​

  • Basic torque
    • Moment = weight * radius (arm)
    • Moments are additive, we can sum them to determine total pitching moment
  • Definitions
    • Datum: Fixed reference point to measure from, in the POH
    • Station: Area where item can be loaded (front seat, back seat, fuel tanks)
    • Arm: Distance from datum to the item
    • Moment: Item arm * item weight
    • Center of Gravity: Location of new C.G. = Total moments / total weights
    • Loading Envelope: Graph of acceptable weight and CG ranges
  • Types of weights
    • Basic empty weight
      • The standard empty weight plus the weight of optional and special equipment that have been installed
      • Includes all oil, fluids, and unusable fuel
    • Standard empty weight
      • All oil, fluids, and unusable fuel
      • This is the weight of the aircraft as it comes from the factory, with standard equipment installed
      • This is not normally used for weight and balance calculations
    • Licensed empty weight
      • Similar to standard empty weight for aircraft built before GAMA standardization of standard empty weight
      • Older term, does not include full engine oil
    • Max ramp weight (MRW): The maximum weight for ground operations (no flight)
    • Max takeoff weight (MTOW): Maximum weight for takeoff
      • Our 182 is 3100 lbs
    • Max landing weight (MLW): Max weight for landing
      • More common on large airplanes, our 182 has a max landing weight of 2950 lbs
  • Common fluids
    • Fuel: 6 lbs / gallon
  • Example documents
    • NW Airtech W&B Amendment: Empty weight, empty arm
    • Loading arrangements diagram (POH pg. 110)
    • Sample loading problem worksheet (POH pg. 112)
    • Loading Graph (POH pg. 114)
    • CoG Moment Envelope (POH pg. 115)
    • CoG Limits (POH pg. 116)

Weight and Balance Sample Problem​

  • N2017E Problem A
    • Setup
      • Fuel: 50 gallons of 100LL
      • Pilot: 160lbs
      • Co-pilot: 180lbs
      • Rear passenger: 120lbs
      • Expected fuel burn during the flight: 40 gallons
    • What is the takeoff and landing weight?
    • What happens if we move our 180 passenger to the rear seats?
    • What happens if we add a forth passenger to the copilot seat who weighs 200?
    • Have students do the math/read numbers while you write
    • Double checking our work in ForeFlight

Effects of CG and Weight​

  • Effect of heavy weight
    • Longer takeoff roll
      • Wings need to produce more lift
      • Either need higher AoA or more airspeed
      • To gain that airspeed we'd need longer to accelerate on the runway
      • It takes us longer to accelerate
    • Longer landing roll
      • Higher airspeed
      • More mass to decelerate
    • Slower rate of climb
      • Less excess thrust
    • Potential damage on landing
      • Landing gear takes considerable load on landing
      • More weight = more load
  • Loading fore/aft CG
    • Loading CG too far aft:
      • Elevator needs to produce less force
      • Pros: Faster cruise speed, lower fuel burn
      • Cons: Less stable, controls more sensitive
      • Too far aft: May not have enough elevator authority to recovery from a stall condition
    • CG forward:
      • Elevator needs to produce more force
      • Pros: Stable, less sensitive controls
      • Cons: Slower cruise speed, higher fuel burn
      • Too far forward: Limited after elevator authority, may prevent adequate landing flare

Questions​

  • You show up to the plane, ready to take three friends flying. The last pilot topped off the airplane with 88 gallons, which will put you over gross weight.
    • How would you deal with the situation?
  • You're planning a cross-country with a passenger who's new to flying. He brings 100lbs of baggage and want to put it in the back, which will put you aft of your CG limits. He says "there's plenty of room!"
    • How would you respond?

References​