Mean Aerodynamic Chord - MAC
Mean Aerodynamic Chord – MAC : On small airplanes and on helicopters, the center of gravity location is identified as being a specific number of inches from the datum. The center of gravity range is identified the same way. On larger airplanes, from private business jets to large jumbo jets, the center of gravity and its range are typically identified in relation to the width of the wing.
The width of the wing on an airplane is known as the chord. If the leading edge and trailing edge of a wing are parallel to each other, the chord of the wing is the same along the wing’s length. Business jets and commercial transport airplanes have wings that are tapered and that are swept back, so the width of their wings is different along their entire length. The width is greatest where the wing meets the fuselage and progressively decreases toward the tip. In relation to the aerodynamics of the wing, the average length of the chord on these tapered swept-back wings is known as the mean aerodynamic chord (MAC).
On these larger airplanes, the CG is identified as being at a location that is a specific percent of the mean aerodynamic chord (% MAC). For example, imagine that the MAC on a particular airplane is 100″, and the CG falls 20″ behind the leading edge of the MAC. That means it falls one-fifth of the way back, or at 20% of the MAC.
The illustration shows a large twin-engine commercial transport airplane. The datum is forward of the nose of the airplane, and all the arms shown in the figure are being measured from that point. The center of gravity for the airplane is shown as an arm measured in inches. In the lower left corner of the figure, a cross section of the wing is shown, with the same center of gravity information being presented. Physically, MAC is the chord of a rectangular wing, which has the same area, aerodynamic force and position of the center of pressure at a given angle of attack as the given wing has. Simply stated, MAC is the width of an equivalent rectangular wing in given conditions and the center of gravity CG is expressed as a percentage of the Mean aerodynamic chord – MAC
To convert the center of gravity location from inches to a percent of MAC, for the airplane shown in the Figure, the steps are as follows:
1. Identify the center of gravity location, in inches from the datum.
2. Identify the leading edge of the MAC (LEMAC), in inches from the datum.
3. Subtract LEMAC from the CG location. 4. Divide the difference by the length of the MAC.
5. Convert the result in decimals to a percentage by multiplying by 100. As a formula, the solution to solve for the percent of MAC would be:
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