# What is a wing theory?

I have an assignment to summarize the topic "wing theory", with the preferred reference used is the book Fundamentals of Aerodynamics by John D. Anderson. But there's no dedicated chapter called "wing theory".

The gist I got is that the closest one is chapter 5, that's discussing "incompressible flow over finite wings". But I haven't got a clue what a "wing theory" is and what structure should I use to make a summary regarding that topic.

There are no search results on that topic either, not in Google, nor a Wikipedia page for it.

So, what is it really?

• Lifting line theory maybe? Thin airfoil theory? Boundary layer theory? I'd ask your professor for a clarification Jun 21, 2023 at 19:35
• Well, I guess you'll have to "wing it". But do check with the person giving the assignment. Logically it flows from: what wings are used for --> how do they work --> details in air flow --> how lift is created. I would take a peek at Anderson's preface for insights on how and why the book was written. Jun 21, 2023 at 20:10

Wing theory refers to the different mathematical tools which can be used to model the lift-generation mechanisms at work in a wing moving through (typically) air. These include:

Bernoulli theory, where the faster-moving air on the upper surface of the wing exerts a lower pressure on it compared to the slower-moving air flowing past its underside

Circulation theory, where the airflow surrounding the wing acts as if there was a net rotation of that air about the axis defined by the main spar

Vortex-sheet theory, in which lift is generated by the shedding of vortices at the trailing edge of the wing

No single model properly accounts for all the net lift generated by a wing in practice; each is a simplification, where some of the models furnish better predictions than others.

I would add to the excellent answer of @niels-nielsen theory of conformal transforms which greatly helps with airfoils - Zhukovsky transform, Kármán–Trefftz transform etc

Wing theory is only a bigger term used to describe how lift is generated with regards to aerofoils and various shapes. Two utmost physicist and mathematician had described this generation of lift with their formulas. i.e the Bernoulli's theory and Newton's Laws 2nd and 3rd law

All in all the important thing to bare in mind is that lift can only be generated if there is a difference in pressure sorrounding the regions of a shape(or aerofoil for this matter such as the wing).

The word aerofoil is a generic term for objects that are capable of generating lift and this can be either a wing or a propeller. The wing theory can be described as:

In order for a wing to generate lift there as to be differential in pressure sorrounding the top and bottom chamber of the wing. The efficiency of the wing to produce lift is dependent on the transition point or the boundary layer(this is the point where the laminar flow of the relative wind breaks and becomes turbulent). The longer the laminar stream flows over the wing, the more efficient lift can be produced.

Another thing to consider is the wings aspect ratio. The higher the aspect ratio the more efficient the wing is to produce lift.

In addition you might want to also talk about the center of pressure on the wings. There's a lot of things involved in wing theory. However, the important thing is how you can describe each of the formulas(mentioned) and how they relate to lift and why aerofoil shapes are ideal.

• "physicians" -- are you sure that's the term you wanted?
– Ralph J
Jun 25, 2023 at 3:13
• I meant physicist. Jun 25, 2023 at 3:30
• Just a couple of corrections if you want to implement them. 1. "lift can only be generated if there is a difference in pressure surrounding the regions of a shape": a symmetrical airfoil at zero AoA has plenty of difference in pressure on its surface but generates null lift. 2. "The word aerofoil can be either a wing or a propeller": an airfoil is a pure 2D concept so it cannot be a wing nor a blade which are 3D objects made up of several airfoils. 3. "The higher the aspect ratio the more efficient the wing is to produce lift": the higher the wingspan is, the lower the induced drag is. Jun 25, 2023 at 13:58
• Thanks for the correction. I've learnt a lot from your explanation Jun 25, 2023 at 16:27
• @LudwigT: you're welcome. The matter with the aspect ratio is unfortunately a deep rooted misconception, the wingspan is important, not the aspect ratio. And just for the record I didn't downvote your answer. Jun 25, 2023 at 17:04