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Zorluk: OrtaLoad Distribution and Balancing

During a routine weight and balance check, a small aircraft is parked horizontally on weighing scales. The scale under the nose wheel reads 500500 pounds, and the combined reading from the scales under the two main wheels is 1,5001,500 pounds. The nose wheel is located exactly 100100 inches forward of the main landing gear axis. How many inches forward of the main landing gear axis is the aircraft's center of gravity?

Cevap: 25 inches

Cevap

25
In static equilibrium, the sum of the moments around any point must be zero. By using the main landing gear axis as the reference point, the moment created by the total weight of the aircraft (2,0002,000 pounds) acting at the center of gravity must equal the moment created by the nose wheel's load. The nose wheel is 100100 inches away and supports 500500 pounds, creating a moment of 50,00050,000 pound-inches. Dividing this total moment by the total weight (50,000÷2,00050,000 \div 2,000) gives a center of gravity located 2525 inches forward of the main gear.

Adım Adım Çözüm

1
Determine the total weight of the aircraft.
500+1,500=2,000500 + 1,500 = 2,000 pounds
The total weight is needed to find the proportion of the load carried by each support.
2
Set up the balance equation (sum of moments) around the main landing gear axis.
(Total Weight)×(CG Distance)=(Nose Wheel Weight)×(Distance to Nose Wheel)(Total\ Weight) \times (CG\ Distance) = (Nose\ Wheel\ Weight) \times (Distance\ to\ Nose\ Wheel)
In static equilibrium, the moment generated by the total weight at the CG equals the sum of the moments of individual components.
3
Substitute the known values into the equation and solve for the CG distance.
2,000×d=500×100⇒2,000d=50,000⇒d=252,000 \times d = 500 \times 100 \Rightarrow 2,000d = 50,000 \Rightarrow d = 25 inches
Solving the algebraic equation isolates the distance from the main gear to the center of gravity.

Anahtar Kavram

Center of Gravity and Static Equilibrium

Alternatif Yöntem

Instead of using the main gear as the pivot, you can use the nose wheel as the pivot. The moment of the main gear is 1,500×100=150,0001,500 \times 100 = 150,000. Dividing by the total weight (2,0002,000) gives 7575 inches from the nose wheel. Subtracting this from the total wheelbase (100−75100 - 75) gives 2525 inches from the main gear.
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Load Distribution and Balancing

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