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Weights & Balances www.GeoffHatcher.com Moment:

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Torque and moment are expressed in in-lbs or ft-lbs Force x leverage(moment arm) = torque Weight x Moment Arm = Moment The measure of the distribution of mass or force relative to a given axis. (datum plane) Torque www.GeoffHatcher.com

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Moment: The measure of the distribution of mass relative to a datum line. Mass x arm= moment One pound placed I foot from the datum…..If it is moved a foot further from the datum line….. It’s moment would increase to 2 foot pounds (2 ft·lbs)has a moment of one foot pound (1 ft·lb ) www.GeoffHatcher.com

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Left side 20 X -4 = -80 Right side 20 x 4 = 80 Balance Bar 10 X 0 = 0 We use the formula Mass x arm = moment Total 500÷ 50 =0 Total Moment ÷ Total weight = center of gravity Finding a 3000 pound aircrafts balance point requires mathmatics because you can’t very well pick it up and balance the thing on your fingers. Mass x arm = moment www.GeoffHatcher.com

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Left side 20 X -4 = -80 Right side 20 x 6 = 120 Balance Bar 10 X 0 = 0 Mass x arm = moment Total 5040÷ 50 =.8 Moment÷ weight= arm center www.GeoffHatcher.com

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It’s important to notice that the placement of the datum line can be anywhere you want as long it is consistent throughout the calculations. The Datum line is never the actual C.G. because it is constantly shifting. Left side 20 X 2 = 40 Right side 20 x 10 = 200 Balance Bar 10 X 6 = 60 Mass x arm = moment Total 50300 ÷ 50 = 6 Total Moment ÷ total weight = total moment arm Center of gravity www.GeoffHatcher.com

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The Datum on an Aircraft is usually placed at the fire wall, the nose, or the base of the nose cone to avoid the complex arithmetic associated with negative numbers. Negative numbers can cause spatial disorientation, in many pilots. Stations Forward seats 42 Fuel Tanks 52 middle seats 76 rear seats 101 rear baggage 128 Each Area of the plane is assigned a “station” according to how many inches away it is from the datum The aircraft is drained of fuel and oil and its empty weight and C.G is determined. 2,179 lbs at 41” moment 89,609 in·lbs www.GeoffHatcher.com

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Forward seats 400 lbs X 42 = 16,800 Middle seats 400 lbs X 76 = 30,400 Rear seats 200 lbs X 101 = 20,200 Mass X arm = moment Total 3,795lbs196,641 ÷ 3795 = 51.82” Total Moment ÷ total weight = total moment arm Center of gravity Baggage 100 lbs X 128 = 12,800 Fuel 516 lbs X 52 = 26,832 Aircraft 2,179 lbs X 41 = 89,609 www.GeoffHatcher.com

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Forward seats 400 lbs X 42 = 16,800 Middle seats 400 lbs X 76 = 30,400 Rear seats 200 lbs X 101 = 20,200 Mass X arm = moment Total 3,795lbs196,641 ÷ 3795 = 51.82” Total Moment ÷ total weight = total moment arm Center of gravity Baggage 100 lbs X 128 = 12,800 Fuel 516 lbs X 52 = 26,832 Aircraft 2,179 lbs X 41 = 89,609 Weight shift Problem www.GeoffHatcher.com

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Mass X arm = moment 196,641 Total Moment ÷ total weight = total moment arm Weight shift Problem Lets drop off one of the two middle passengers (200 lbs) and move a rear passenger (150 lbs) to the middle. 3,795 lbs -200 lbs X 75 = -15,000 -150 lbs X 101 = -15,150 150 lbs X 75 = 11,250 Passenger gets out of middle Passenger gets out of back And moves to the middle Total weight 3595 lbs177741 ÷ 3595 = 49.4 www.GeoffHatcher.com

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