Calculating Mean Aerodynamic Chord

Mean Aerodynamic Chord Formula:

\[ MAC = \frac{2}{S} \int_{0}^{b/2} c(y) \cdot y \, dy \]

Wing Area (S):

m²

Wing Span (b):

Root Chord:

Tip Chord:

Mean Aerodynamic Chord (MAC):

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1. What is Mean Aerodynamic Chord?

The Mean Aerodynamic Chord (MAC) is the average chord length of an aircraft's wing. It represents a chord that, when multiplied by the wing area, dynamic pressure, and lift coefficient, gives the total lift force acting at the aerodynamic center.

2. How Does the Calculator Work?

The calculator uses the standard MAC formula:

\[ MAC = \frac{2}{S} \int_{0}^{b/2} c(y) \cdot y \, dy \]

Where:

\( MAC \) — Mean Aerodynamic Chord (m)
\( S \) — Wing area (m²)
\( c(y) \) — Chord length at position y along the wing span
\( b \) — Wing span (m)
\( y \) — Distance from wing root along the span

Explanation: For linearly tapered wings, this simplifies to: \( MAC = \frac{2}{3} \cdot c_{root} \cdot \frac{1 + \lambda + \lambda^2}{1 + \lambda} \) where \( \lambda \) is the taper ratio.

3. Importance of MAC Calculation

Details: MAC is crucial for determining the aerodynamic center location, calculating pitching moments, and establishing the reference point for aircraft stability and control analysis. It's essential for proper weight and balance calculations.

4. Using the Calculator

Tips: Enter wing area in square meters, wing span in meters, root chord and tip chord in meters. All values must be positive numbers. The calculator assumes a linearly tapered wing configuration.

5. Frequently Asked Questions (FAQ)

Q1: Why is MAC important in aircraft design?
A: MAC determines the aerodynamic center location, which affects aircraft stability, control characteristics, and is used as a reference for center of gravity calculations.

Q2: How does MAC differ from standard mean chord?
A: MAC is weighted by the local chord's contribution to lift, while standard mean chord is simply the average chord length without considering aerodynamic effects.

Q3: Can MAC be used for non-tapered wings?
A: Yes, for rectangular wings, MAC equals the constant chord length. The formula simplifies accordingly.

Q4: What is the typical MAC position along the wing?
A: For tapered wings, MAC is typically located closer to the root chord than the geometric center of the wing.

Q5: How accurate is this simplified calculation?
A: This provides a good approximation for preliminary design. For complex wing shapes, numerical integration of the actual chord distribution is recommended.