# An Overview of Thin Airfoil Theory

### Key Takeaways

What is the thin airfoil theory?

Why is thin airfoil analysis used?

How is thin airfoil analysis applied?

*Aerodynamics of airfoil flow*

There are so many tools available to solve engineering problems involving fluid mechanics. There is the all-purpose Navier-Stokes equation that is used to study oil and gas through pipelines and fluid flow in thermo-, hydro- and aerodynamics. When studying airflow around airfoils, several methods can be used, depending on whether the flow is compressible, incompressible, and/or inviscid. If a simple solution is desired and height can be mostly neglected, consider using the thin airfoil theory.

## What Is the Thin Airfoil Theory?

Airfoils, also referred to as aerofoils, come in many shapes and sizes. They may be symmetrical, where the upper and lower sections are the same size and shape. However, cambered airfoils are used most often, as they generate greater lift due to the upper section being more convex than the lower. Analyzing fluid flow over airfoils can be complex and computationally expensive. However, if it can be assumed that airfoil thickness is infinitesimal and the wingspan is very long – infinitely so – then incompressible, inviscid flow can be analyzed using thin airfoil theory, which is defined below.

Obviously, no wingspans are infinitely long and no airfoil thicknesses are zero, yet there are indeed cases where these assumptions are helpful; especially when studying the lift force, which is critical for flight.

## Why Is Thin Airfoil Analysis Used?

The purpose of studying aerodynamics is to understand how solid objects move through air or how the flow of air around the object affects its movement. An analysis is undertaken with the aim of maximizing the object’s – airplane, helicopter, etc. – ability to move through the air efficiently and safely. This objective is only achievable by understanding the behavior of airflow over and around the object’s surfaces, including airfoils, and applying those results to design decisions such as what materials to use, what the airfoil shape should be, and the control technique to implement.

Answering these questions is not a simple proposition, as there are many influential parameters and methods of analysis. Among the parameters, the lift force is the most important, as it determines whether the aircraft can maintain altitude and it is impacted greatly by the angle of attack or direction of the aircraft's chord line, w.r.t., the reference direction of the incident air. The simplest way to connect these two flight characteristics is by applying the thin airfoil theory. However, certain assumptions that are listed below must be satisfied.

### Assumptions for Thin Airfoil Theory Applicability

- Airflow is incompressible
- Airflow is inviscid
- Airfoil has infinite length
- Airfoil has zero thickness

If the above can be applied, then the following equation applies:

**C _{L}= 2𝝅𝞪**

CLis the coefficient of lift and 𝞪 is the angle of attack. This simple proportionality equation, which defines a direct relationship between angle of attack and lift, is the reason for employing the thin airfoil theory. The assumptions for thin airfoil theory application eliminate the possibility of drag, which is an important consideration that opposes the forward movement of the aircraft.

## How Is Thin Airfoil Analysis Applied?

Typically, listings of coefficients of lift are available for different airfoil shapes and materials. These listings can be used to select an airfoil for your design. The accuracy of this lift data is reliant upon you incorporating real world considerations such as the effects of lift-induced drag, which increases with increasing angle of attack until a critical angle – between 15° and 20° for most airfoils – is reached. Above this angle, the aircraft will stall.

It is also important to use the correct formula for the lift coefficient. The equation above is applicable for symmetrical airfoils. For cambered airfoils, the equation below should be used.

*C**L**= 2𝝅((𝞪* -*𝞪**0*)(*180*/*𝝅* ))

In the equation above, 𝞪_{0} is the angle of zero lift.

Thin airfoil theory provides a simple way to select airfoils for your design. However, to optimize the utilization of this technique, you should make sure that your method of determining the lift coefficient is accurate, which means utilizing other fluid mechanics analysis methods to calculate the parameters of airflow at airfoil boundaries. This is best done by deploying advanced analysis tools that are available within Cadence’s CFD solver toolbox.

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