Aspect Ratio Given Span Efficiency Factor Calculator

Wing Aspect Ratio Formula:

\[ AR = \frac{C_L^2}{\pi \cdot e_{span} \cdot C_{D,i}} \]

Lift Coefficient (C_L):

(dimensionless)

Span Efficiency Factor (e_span):

(dimensionless)

Induced Drag Coefficient (C_D,i):

(dimensionless)

Wing Aspect Ratio (AR):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Wing Aspect Ratio?

Wing Aspect Ratio is defined as the ratio of the square of wingspan to the wing area or wingspan over wing chord for a rectangular planform. It is a key parameter in aerodynamics that affects the lift and drag characteristics of a wing.

2. How Does the Calculator Work?

The calculator uses the wing aspect ratio formula:

\[ AR = \frac{C_L^2}{\pi \cdot e_{span} \cdot C_{D,i}} \]

Where:

\( AR \) — Wing Aspect Ratio (dimensionless)
\( C_L \) — Lift Coefficient (dimensionless)
\( \pi \) — Archimedes' constant (≈3.14159)
\( e_{span} \) — Span Efficiency Factor (dimensionless)
\( C_{D,i} \) — Induced Drag Coefficient (dimensionless)

Explanation: The formula relates the wing's aspect ratio to its lift coefficient, span efficiency factor, and induced drag coefficient, showing how these parameters interact in aerodynamic performance.

3. Importance of Aspect Ratio Calculation

Details: Accurate aspect ratio calculation is crucial for aircraft design, performance prediction, and optimizing aerodynamic efficiency. Higher aspect ratios generally provide better lift-to-drag ratios and improved fuel efficiency.

4. Using the Calculator

Tips: Enter the lift coefficient, span efficiency factor (typically between 0.7-1.0), and induced drag coefficient. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for wing aspect ratio?
A: Aspect ratios vary widely depending on aircraft type - gliders may have AR > 20, while fighter jets may have AR < 3. Commercial airliners typically range from 7-10.

Q2: How does aspect ratio affect aircraft performance?
A: Higher aspect ratios reduce induced drag and improve fuel efficiency but may compromise structural strength and maneuverability.

Q3: What is the span efficiency factor?
A: The span efficiency factor represents how close a wing's lift distribution is to the ideal elliptical distribution, with 1.0 being perfect elliptical distribution.

Q4: Can this formula be used for any wing shape?
A: While derived for conventional wings, the formula provides reasonable estimates for various wing configurations, though actual performance may vary.

Q5: How does induced drag relate to aspect ratio?
A: Induced drag is inversely proportional to aspect ratio - higher aspect ratio wings generate less induced drag for the same lift coefficient.