Datum is an imaginary plane that we use as a starting point for our measurements, we need to be able to measure distances from this plane in terms of inches. (where the engine sits)
Station is a location where we place things, it exist at fixed distances from a datum plane (where the pilot and copilot sits & luggage compartment)
Arm is a distance, a number of inches from datum to the CG of an object that we are measuring
Moment is a turning force if we have an object at a station the weight of that object pushes down down on an imaginary lever that is the length specified by the arm.
Weight X Arm = Moment
Center of gravity for a loaded airplane:
CG = total Moments / total Weight
CG Limits: the extreme forward and aft CG locations within which the airplane may be operated at a given weight.
Elevator and trim compensate for shifted CG because it is still within the CG limits.
Elevator is insufficient to compensate and because we are outside of the CG limits if we stall the airplane it will not be possible to recover since we can’t raise the tail even with full pressure on the yoke so we are headed straight toward the ground tail first.
Effects of increased weights:
- Higher takeoff speed
- Longer takeoff run
- Reduced climb ability
- Reduced cruising speed
- Shorter range
- Reduced maneuverability
- Higher stall speed
- Higher landing speed
- Longer landing roll
Effects of adverse balance:
- Forward of the CG limit: control difficulty especially during takeoff and landing (higher takeoff and landing speed)
- Aft of the CG limit: reduce the airplane ability to recover from stall and spins
Weights:
- Gasoline: 6 pounds/gallon
- Oil 7.5 pounds/gallon
1st calc: 380.0 X 64.0 = 24,320.0 (weight X arm = moment)
2nd calc: 30 gallons X 6 pounds/gallons = 180.0
3rd calc: 180.0 X 96.0 = 17,280.0
4th calc” 193.193 / 2055 = 94.01 (CG = total moments X total weight)
94.01 inches from the datum plane
Maximum weight we can have is 2300 LB and since we can only have 105 LB of baggage with the chart we are able to determine its moment which is 10.0.
So we have a total weight of 2300 LB and moment of 108.2 and looking at the center of gravity moment envelope chart we see that we are at the very top right limit but that’s ok to fly in this conditions.