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.