W&B 2-5

Figure 2-14. Center of gravity expressed as percent mean aerodynamic chord. MAC MAC 30% MAC 15% MAC Datum Quarter chord Half semi-span Solution by Formula The problem in Figure 2-11 can be solved by using variations of this basic equation. First, rearrange the formula to determine the distance weight B must be shifted: Distance weight B is shifted = Total weight × Δ CG Weight shifted = 500 × –22 200 = –55 inches The CG of the lever in Figure 2-11 was 72 inches from the datum. This CG can be shifted to the center of the lever as in Figure 2-13 by moving weight B. If the 200-pound weight B is moved 55 inches to the left, the CG shifts from +72 inches to +50 inches, a distance of 22 inches. When the distance the weight is to be shifted is known, the amount of weight to be shifted to move the CG to any location can be determined by another arrangement of the basic equation. Use the following arrangement of the formula to determine the amount of weight that has to be shifted from station 8 to station +25, to move the CG from station +72 to station +50. Weight shifted = Total weight × Δ CG Distance weight is shifted = 500 × 22 55 = 200 inches If the 200-pound weight B is shifted from station +80 to station +25, the CG moves from station +72 to station +50. A third arrangement of this basic equation is used to determine the amount the CG is shifted when a given amount of weight is moved for a specified distance (as it was done in Figure 2-11). The following formula is used to determine the amount the CG is shifted when 200-pound weight B is moved from +80 to +25. Δ CG = Weight shifted × Distance it is shifted Total weight = 200 × 55 500 = 22 inches Moving weight B from +80 to +25 moves the CG 22 inches from its original location at +72 to its new location at +50 as seen in Figure 2-13. To complete the calculations, return to the original formula and enter the appropriate numbers. Weight to be shifted = Δ CG Total weight Distance weight is shifted 200 = 22 500 55 .4 = .4 The equation is balanced. Mean Aerodynamic Chord The CG point affects the stability of the aircraft. To ensure the aircraft is safe to fly, the CG must fall within specified limits established by the manufacturer. On some aircraft, the CG is expressed as a percentage of the length of the mean aerodynamic chord (MAC) or “percent MAC.” [Figure 2-14] In order to make such a calculation, the position of the leading edge of the MAC must be known ahead of time. CG limits are specified forward and aft and/or lateral (left and right) limits within which the aircraft’s CG must be located during flight. The area between the limits is called the CG range of the aircraft.