From Airfoil to Finite Wing

Leaving the Infinite Span Behind

Aerospace EngineeringFinite WingsDragFree preview
⏱️ About 10 min
From Airfoil to Finite Wing — illustration
Decorative illustration.

A 2D airfoil produces lift without end, but real wings end abruptly at the tip, creating a swirling, drag-inducing wake.

💡
The big idea: Finite wings have a defined span and area, leading to 3D effects like wingtip vortices that reduce the lift slope and generate induced drag.
🎯 By the end, you'll be able to
  • Define aspect ratio (AR) for arbitrary and rectangular wings.
  • Explain how wingtip vortices form and alter the flow field.
  • Contrast 2D airfoil coefficients (c_l, c_d) with 3D wing coefficients (C_L, C_D).
📎 Helpful to know first
  • Aerospace Engineering Module 2: Aerodynamics I

The Infinite vs. The Finite

In Module 2, we treated the airfoil as a 2D section with an infinite span. This simplifies analysis because there is no airflow around the tips. However, a real finite wing has a span b and ends at the wingtips. Because high pressure exists below the wing and low pressure above it, air naturally leaks around the tips, creating powerful trailing vortices.

Wing Geometry

Two fundamental metrics define a finite wing: the span b (tip-to-tip distance) and the reference planform area S. For a rectangular wing, the chord c is constant, so S = b * c. The ratio of span squared to area is the aspect ratio (AR), a critical parameter in aerodynamic efficiency.

\[ AR = \frac{b^2}{S} \]
\[ AR = \frac{b}{c} \quad(\text{rectangular wing}) \]
🔑 3D Consequences

Wingtip vortices induce a downwash that effectively tilts the lift vector backward, creating induced drag. Furthermore, this downwash reduces the effective angle of attack, meaning a finite wing has a shallower lift-curve slope than its 2D airfoil counterpart.

📝 Worked example: A rectangular wing has a span b = 10 m and a constant chord c = 1.5 m. Calculate its area and aspect ratio.
  1. 1. Calculate wing area: S = b * c = 10 * 1.5 = 15 m^2
  2. 2. Calculate AR using span and area: AR = b^2 / S = 10^2 / 15 = 100 / 15 = 6.67
  3. 3. Verify using rectangular shortcut: AR = b / c = 10 / 1.5 = 6.67
✓ AR = 6.67
✏️ Practice: A wing has an area S = 20 m^2 and a span b = 12 m. Find its aspect ratio.
Solution
  1. Hint: AR = b^2/S.
  2. Answer: AR = 7.2

Check your understanding

1. What is the formula for Aspect Ratio (AR) of any wing planform?
Aspect ratio is defined as the square of the wingspan divided by the reference area.
2. What phenomenon primarily distinguishes a finite wing from a 2D airfoil?
Finite wings end at the tips, allowing pressure differentials to form wingtip vortices that induce drag.
🔎 Related lessons
Downwash & Induced Drag · soon
✅ Key takeaways
  • Finite wings have a finite span, leading to pressure leakage and wingtip vortices.
  • Aspect Ratio (AR) = b^2 / S, dictating how 'slender' a wing is.
  • These 3D vortices induce downwash, which creates induced drag and lowers the lift slope.
➡️ Now that we know finite wings create vortices, let's examine how that downwash directly generates induced drag.
Want to test yourself on this? Try the Aerospace Engineering Aptitude test →
🎓 Go deeper: external courses & trusted references

External sites are listed for reference only. This course is independent and has no affiliation with, or endorsement from, the institutions named.