BASIC WEIGHT AND BALANCE EQUATION AND MAC (THE MEAN AERODYNAMIC CHORD)
Basic Weight and Balance Equation
This equation can be rearranged to find the distance a weight must. be shifted to give a desired change in the CG location:
This equation can also be rearranged to find the amount of weight to shift to move the CG to a desired location:
It can also be rearranged to find the amount the CG is moved when a given amount of weight is shifted:
Shifting the airplance CG
The same procedures for shifting the CG by moving weights can be used to change the CG of an airplane by rearranging passengers or baggage.
Consider this airplane:
Airplane empty weight and EWCG : 1340Lbs 37.0
Maximum gross weight : 2300 Lbs
CG limit : +35.6 to 43.2
Front seats (2) : +35
Rear seats (2) : +72
Fuel : 40 gal +48
Baggage (maximum) : 60Lbs +92
For this flight, the 140-pound pilot and a 115-pound passenger are to occupy the front seats, and a 212-pound and a 97-pound passenger are in the rear seats.
This completed loading chart shows the weight is within limits, but the CG is too far aft.
On possible solution would be to trade places between the 212-pound rear-seat passenger and the 115-pound front seat passenger.
ΔCG = Weight shifted x Distance it is shifted
Total weight
This loading chart, made after the seat changes, shows both the weight and balance are within allowable limits.
MAC (The Mean Aerodynamic Chord):
As specified by the manufacturer, safe range for each type of aircraft is different and expressed as a% of the mean aerodynamic chord [MAC].
For a rectangular wing of constant Aeroflot section dimensions MAC is just the chord
As shown in the picture above, the sate range is 3 meters length. The safe range is within station 31 and station 34 (31 and 34 meters far from the head of the aircraft). MAC is the 10 meters cord from station 30 to station 40, divided into 0% to 100%. The safe range is within 10% to 40% MAC.
The relative positions of the CG and the aerodynamic center of lift of the wing have critical effects on the flight characteristics of the aircraft.
In order to relate the percent MAC to the datum, all weight and balance information includes two items: the length of MAC in inches and the location of the leading edge of MAC (LEMAC) in inches from the datum.
The weight and balance data of the airplane above states that the MAC is from stations 144 to 206 and the CG is located at station 161.
MAC = 206" - 144" = 62 inches
LEMAC = Station 144
CG is 17 inches behind LEMAC
(161- 144= 17 inches)
How to find the CG in %MAC:
Weight to be shifted = ΔCG
Total weight Distance weight is shifted
This equation can be rearranged to find the distance a weight must. be shifted to give a desired change in the CG location:
Distance weight is shifted = Total weight x ΔCG
Weight shifted
This equation can also be rearranged to find the amount of weight to shift to move the CG to a desired location:
Weight shifted = Total weight x ΔCG
Distance weight is shifted
It can also be rearranged to find the amount the CG is moved when a given amount of weight is shifted:
ΔCG = Weight shifted x Distance weight is shifted = 200 x 55 = 22 inches
Total weight 500
Shifting the airplance CG
The same procedures for shifting the CG by moving weights can be used to change the CG of an airplane by rearranging passengers or baggage.
Consider this airplane:
Airplane empty weight and EWCG : 1340Lbs 37.0
Maximum gross weight : 2300 Lbs
CG limit : +35.6 to 43.2
Front seats (2) : +35
Rear seats (2) : +72
Fuel : 40 gal +48
Baggage (maximum) : 60Lbs +92
For this flight, the 140-pound pilot and a 115-pound passenger are to occupy the front seats, and a 212-pound and a 97-pound passenger are in the rear seats.
This completed loading chart shows the weight is within limits, but the CG is too far aft.
On possible solution would be to trade places between the 212-pound rear-seat passenger and the 115-pound front seat passenger.
ΔCG = Weight shifted x Distance it is shifted
Total weight
= (212 – 115) x (72 – 35) = 97 x 37 = 1.6 inches
2,194 2,194
This loading chart, made after the seat changes, shows both the weight and balance are within allowable limits.
MAC (The Mean Aerodynamic Chord):
As specified by the manufacturer, safe range for each type of aircraft is different and expressed as a% of the mean aerodynamic chord [MAC].
For a rectangular wing of constant Aeroflot section dimensions MAC is just the chord
As shown in the picture above, the sate range is 3 meters length. The safe range is within station 31 and station 34 (31 and 34 meters far from the head of the aircraft). MAC is the 10 meters cord from station 30 to station 40, divided into 0% to 100%. The safe range is within 10% to 40% MAC.
The relative positions of the CG and the aerodynamic center of lift of the wing have critical effects on the flight characteristics of the aircraft.
In order to relate the percent MAC to the datum, all weight and balance information includes two items: the length of MAC in inches and the location of the leading edge of MAC (LEMAC) in inches from the datum.
The weight and balance data of the airplane above states that the MAC is from stations 144 to 206 and the CG is located at station 161.
MAC = 206" - 144" = 62 inches
LEMAC = Station 144
CG is 17 inches behind LEMAC
(161- 144= 17 inches)
How to find the CG in %MAC:
CG in %MAC = Distance aft of LEMAC x 100 = 17 x 100 = 27.4
MAC 62
BASIC WEIGHT AND BALANCE EQUATION AND MAC (THE MEAN AERODYNAMIC CHORD)
Reviewed by Aviation Lesson
on
9:41 AM
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Reviewed by Aviation Lesson
on
9:41 AM
Rating:
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