**Question:**

Could you elucidate the method for determining the Mean Aerodynamic Chord on a tapered wing?

**Answer:**

The MAC is not merely the physical average of the chord lengths but is a value that ensures the wing’s lift characteristics are represented by a single chord length. It is the chord of an imaginary airfoil that has the same aerodynamic characteristics as the actual wing.

## Calculating the MAC on a Tapered Wing

For a tapered wing, which has a varying chord length from root to tip, the MAC can be found using the following method:

1.

## Measure the Root and Tip Chord

: Start by measuring the chord length at the root (widest part) and tip (narrowest part) of the wing.

2.

## Determine the Taper Ratio

: The taper ratio is the ratio of the tip chord to the root chord.

3.

## Apply the MAC Formula

: The MAC can be calculated using the formula:

$$ MAC = \text{Root Chord} \times \frac{2}{3} \times \left(\frac{1 + \text{Taper Ratio} + \text{Taper Ratio}^2}{1 + \text{Taper Ratio}}\right) $$ This formula accounts for the change in chord length across the span of the wing and provides the length of the MAC.

4.

## Locate the MAC Spanwise

: To find the spanwise location of the MAC, you can draw lines on a plan view of the wing as follows:

- At the root, draw a line parallel to the centerline of the fuselage extending forward from the leading edge and rearward from the trailing edge, both lines being the length of the tip chord.
- Repeat this process at the tip, but use the length of the root chord for the lines.
- Connect the ends of these lines to form an ‘X’ over the wing plan. The intersection point gives the spanwise location of the MAC.

5.

## Determine the CG Location

: If the center of gravity (CG) needs to be a certain percentage of the MAC, measure back from the leading edge along the MAC to place the CG correctly.

## Conclusion

The MAC is a fundamental concept in aerodynamics that affects the aircraft’s performance and stability. By accurately determining the MAC on a tapered wing, designers and engineers can ensure that the aircraft will fly safely and efficiently. The process involves both geometric measurements and the application of aerodynamic principles to find a value that represents the wing’s lift characteristics.

For more detailed information and visual aids, resources like “Aerodynamics for Students” provided by the University of Cambridge can be extremely helpful.

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