Finite-Wing Effects vs 2D Airfoil Results: Induced Drag and Lift Distribution

The section result is an input

A two-dimensional polar assumes an infinite wing. No tip vortex, no downwash, no induced drag, the same angle at every station. A real wing of aspect ratio AR and span efficiency e has all four. The strip-theory lesson is how to add the polar up. This lesson is the difference you should expect before you run that sum.

Downwash, slope and induced drag

The trailing vortex sheet induces a downward velocity at the wing. The local flow meets the section at a smaller angle than the geometric angle. Lift is perpendicular to that local flow, so part of the section force points downstream in freestream axes. That downstream part is induced drag. For an elliptic lift distribution in inviscid flow the downwash is constant across the span and

CDi = CL² / (π AR)

A real distribution is not elliptic, so e drops below 1 and CDi = CL² / (π AR e). Nothing in the section CD contains this term. Adding it twice, once inside a fitted parabola and once from this formula, is a common bookkeeping error. The section polar supplies profile drag. This formula supplies induced drag.

The wing lift slope is shallower than the section slope for the same reason. The lifting-line estimate in the theoretical-slope lesson, a = a0 / (1 + a0/(π AR)) with angles in radians, is that downwash written as a change of dCL/dα. Sweep, viscosity and a non-elliptic planform move the number. They do not put the wing slope back at 2π.

Lift distribution decides where it stalls

Quote section coefficients as section coefficients. Quote wing coefficients only after induced drag and the spanwise sum. The gap between them is the finite wing, and it is often larger than the gap between two candidate airfoils.

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Where this sits in the series

In simple words: what this page is for

A finite wing flies at a lower effective angle than the geometric angle, pays an induced drag the section never had, and stalls where some station reaches its section limit first.

This lesson exists because section decisions fail when geometry, method labels and selection reasons are scattered. Finite-Wing Effects vs 2D Airfoil Results: Induced Drag and Lift Distribution helps you keep a clean trail from shape to polar to choice.

Why the topic matters

Engineers lose time when a title sounds clear but the page only sketches the idea. This article expands Finite-Wing Effects vs 2D Airfoil Results: Induced Drag and Lift Distribution so you can answer three questions without jargon: what is the idea, when do you use it, and how do you check it in a HENDOI product.

Read the sections above for the core definitions. Use the steps below to move from reading into a real project trail you can share with a teammate.

How to apply this in HENDOI

In practice: create a HENDOI account or log in, open HENFOIL, bring a section in (create, import DAT, or digitize), pass the geometry gate, climb the analysis ladder only as far as the decision needs, then compare and archive. Every calculated number should keep its method label.

When the section choice is ready for the aircraft, continue in HENSYNTH for mission, compliance and trades. Same account. Same plans.

What this page will not claim: a teaching polar or geometry note is not a flight-Re certificate. HENFOIL labels methods so you know what you bought. Tunnel data and professional judgement still sit outside any single software run.

Checklist before you leave this page

• Can you state the idea of Finite-Wing Effects vs 2D Airfoil Results: Induced Drag and Lift Distribution in one sentence?
• Do you know which product owns the next action — HENFOIL or HENSYNTH?
• Will every number you keep carry a method label or a stored-run source?
• If you are new here, have you opened Register or Login?

Related reading on this site

• Active Flow Control on Airfoils: Suction, Blowing and Synthetic Jets
• How Adverse Pressure Gradients Affect Airfoil Boundary Layer Separation
• What Is the Aerodynamic Center of an Airfoil? Location, Meaning and Applications
• What Is Airfoil Aerodynamic Efficiency Across a Range of Flight Conditions?
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These pages teach the ideas. They are not wind-tunnel data and not a certification analysis. When a number matters, compute it at a stated Reynolds number, Mach number and transition setting, and keep the method label on the result. In HENFOIL that production polar is a VIC polar — see the analysis ladder and the polar field guide.