W&B 2-4

Figure 2-10. Proving the new balance point is correct. Item Weight (lb) Arm (in) Moment (lb-in) −6,000 −2,000 +8,000 0 Weight A Weight B Weight C 100 100 200 −60 −20 40 Figure 2-11. Locating balance point with three weights. C = 200B = 200 A = 100 80 72 100 CG Datum Before Weight Shift Figure 2-12. Proving the new balance point is correct. Item Weight (lb) Arm (in) Moment (lb-in) −5,000 +10,000 +5,000 Weight A Weight B Weight C 100 200 −50 +50 Figure 2-13. Weight distribution to balance lever. B = 200 A = 100 C = 100 −50 50 −25 CG Datum After Weight Shift Figure 2-14. Weight shift provides correct CG. Item Weight (lb) Arm (in) Moment (lb-in) −5,000 −5,000 +10,000 0 Weight A Weight B Weight C 100 200 200 −50 −25 +50 The new arm for weight A would be –100 + 40 = –60; for weight B, –60 + 40 = –20; and point C, is +40. The lever is balanced and the balance point is correct when the sum of the moments is zero. [Figure 2-10] Shifting the Balance Point or CG One common weight and balance problem involves moving or shifting weight from one point to another in order to move the balance point or CG to a desired location. This can be demonstrated by using a lever with three weights to work out the problem. Solution by Chart As the lever is loaded in Figure 2-11, it balances at a point 72 inches from the CG of weight A. To shift weight B so the lever balances about its center, 50 inches from the CG of weight A, first determine the arm of weight B that produces a moment that causes the total moment of all three weights around this desired balance point to be zero. The combined moment of weights A and C around this new balance point is 5,000 lb-in, so the moment of weight B must be –5,000 lb-in for the lever to balance. [Figure 2-12] Determine the arm of weight B by dividing its moment, –5,000 lb-in, by its weight of 200 pounds. The arm is –25 inches. To balance the lever at its center, weight B must be placed so its CG is 25 inches to the left of the center of the lever. [Figure 2-13] Figure 2-14 indicates that the shift in weight depicted in Figure 2-13 allows the lever to balance as the sum of the moments is zero. Basic Weight and Balance Equation The following formulas can be used to determine the distance weight must be shifted to obtain a desired change in the CG location. The equation can also be rearranged to fi d the amount of weight required to be shifted to move the CG to a desired location, to find the distance the CG is moved when a specified amount of weight is shifted, or to find the total weight that would allow shifting a specified amount of weight to move the CG a given distance. Weight to be shifted = Δ CG Total weight Distance weight is shifted Total weight = Weight shifted × Distance weight is shifted Δ CG Weight shifted = Total weight shifted × Δ CG Distance weight is shifted Δ CG = Weight shifted × Distance weight is shifted Total weight Distance weight is shifted = Total weight × Δ CG Weight shifted