The Mean Aerodynamic Chord (MAC) is the mathematically averaged chord length of a tapered wing, representing its aerodynamic characteristics as a simple rectangular wing. Engineers use MAC to locate the center of gravity (CG) and ensure aircraft stability. The Mathematical Formula
For a standard trapezoidal (tapered) wing, MAC is calculated using this formula:
MAC=Croot⋅23⋅(1+λ+λ21+λ)cap M cap A cap C equals cap C sub r o o t end-sub center dot two-thirds center dot open paren the fraction with numerator 1 plus lambda plus lambda squared and denominator 1 plus lambda end-fraction close paren Crootcap C sub r o o t end-sub
: Root chord length (wing width at the aircraft centerline). Ctipcap C sub t i p end-sub : Tip chord length (wing width at the very tip). λ (Taper Ratio): Calculated as
CtipCrootthe fraction with numerator cap C sub t i p end-sub and denominator cap C sub r o o t end-sub end-fraction Step-by-Step Calculation Guide Step 1: Measure Wing Dimensions Gather three core measurements from your wing geometry: Root chord length ( Crootcap C sub r o o t end-sub Tip chord length ( Ctipcap C sub t i p end-sub Wing span (b) Step 2: Calculate the Taper Ratio (λ) Divide the tip chord by the root chord. Example: If Ctipcap C sub t i p end-sub is 4 feet and Crootcap C sub r o o t end-sub is 8 feet, Step 3: Solve the Formula Bracket
Plug the taper ratio into the polynomial part of the equation:
1+λ+λ21+λthe fraction with numerator 1 plus lambda plus lambda squared and denominator 1 plus lambda end-fraction Example: Step 4: Multiply by Root Chord Factor Multiply your Step 3 result by the root chord and 23two-thirds (or 0.667).
Example: 8 ⋅ 0.667 ⋅ 1.167 = 6.22 feet. Your MAC is 6.22 feet. Locating the MAC Along the Wing
Knowing the length of the MAC is only half the battle; you must also find where it sits on the wing span ( Ymaccap Y sub m a c end-sub ) to properly align your center of gravity.
Ymac=b6⋅(1+2λ1+λ)cap Y sub m a c end-sub equals b over 6 end-fraction center dot open paren the fraction with numerator 1 plus 2 lambda and denominator 1 plus lambda end-fraction close paren
Using the previous example with a total wing span (b) of 30 feet: Calculate the fraction: Calculate the bracket: Multiply them: 5 ⋅ 1.333 = 6.67 feet.
The MAC is located 6.67 feet out from the aircraft centerline on each wing panel. Why MAC Matters in Aviation
CG Limits: Aircraft weight and balance sheets express safe center of gravity limits as a percentage of MAC (e.g., 25% MAC).
Pitch Stability: The aerodynamic center of the wing sits roughly at 25% of the MAC length.
Performance: Proper CG placement relative to MAC reduces trim drag and maximizes fuel efficiency.
To help apply this to a specific aircraft design, could you provide the root chord, tip chord, and wing span dimensions? Alternatively,
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