# How an Airfoil's Angle of Attack Creates Lift and Drag

### Key Takeaways

• Airfoils produce flow rate differences across their top and bottom surfaces.

• The flow rate difference across an airfoil produces a pressure gradient, resulting in lift.

• As angle of attack increases, flow separation will eventually occur, creating excess drag and resulting in stall.

The wings on aircraft are very slightly tilted in order to produce lift during flight, and this tilt angle needs to be carefully chosen. The angle an airfoil makes with its heading and oncoming air, known as an airfoil’s angle of attack, creates lift and drag across a wing during flight. Pilots control the angle of attack to produce additional lift by orienting their heading during flight as well as by increasing or decreasing speed.

At some point, an airfoil’s angle of attack can become too large, leading to flow separation and stall. Aircraft designers who want to prevent stall and ensure a craft can achieve desired lift need to carefully design the shape and angle of attack of an airfoil. CFD simulations can help qualify a design and ensure it can access enough lift during flight while also preventing excessive drag and stall.

## Effects of Airfoil Angle of Attack on Flight

The angle of attack of an airfoil can be visualized by looking at the airfoil’s cross section and the direction of oncoming wind during flight. The image below shows a free body diagram for an airfoil as viewed looking into the cross section.

Although only lift and drag are shown above, there are four forces acting on an aircraft during flight:

• Lift: This is the primary force keeping a plane or other aircraft airborne. The amount of lift will determine how fast an aircraft can climb or descend during flight.
• Drag: Friction between oncoming airflow in the boundary layer and the surface of the airfoil will produce drag, which acts to slow down the craft. The drag force is proportional to speed to first approximation in laminar flow, although the flow can become turbulent if flow separation occurs at high attack angle.
• Gravity: This will be determined by the mass of the aircraft. The point of applying lift is to ensure that an aircraft can remain airborne during flight. In equilibrium, lift will perfectly cancel gravity and the aircraft’s altitude will remain constant.
• Thrust: The craft’s engines will produce thrust so that the aircraft can maintain its speed to achieve lift during flight. The aircraft’s speed increases and rudders can be used to orient the aircraft’s angle of attack and velocity so that lift is achieved and the aircraft can climb to higher altitude.

The direction of oncoming wind (airflow) is marked above to illustrate the definition of an airfoil’s angle of attack; as air flows over the airfoil, it should be clear that it will form streamlines across the top and bottom surfaces. The shape (radius of curvature) and velocity of these streamlines will determine the amount of lift acting on the airfoil, while the velocity and shape of the airfoil’s surface will determine drag acting on the aircraft.

## Streamlines, Lift, and Drag

Even if it is not obvious from the above discussion, it should be intuitive that the shape of an airfoil will determine both the angle of attack (due to the chord length orientation shown above) and the forces acting on the aircraft. Lift and drag exerted on the airfoil during flight can both be calculated in terms of two coefficients, namely the lift coefficient and skin friction coefficient, respectively.

Lift coefficient - The ratio of the lift force to the kinetic energy gradient is equal to the lift coefficient. This value, in turn, can be calculated in terms of the streamline radius of curvature, which will determine the pressure gradient along the span of the airfoil. The lift coefficient is calculated using integration in the streamline curvature theorem:

Pressure gradient as a function of streamline radius of curvature. The lift coefficient for an airfoil can be calculated by integration as long as the velocity and pressure vs. streamline functions are known.

The streamlines traced along the surface of the airfoil will be a function of air pressure, and it is the pressure difference between the top and bottom surfaces of the airfoil that will create lift. If you look at a typical airfoil, you will see that the streamlines change with angle of attack. Therefore, the parameters in the above integral are all functions of attack angle. Lift begins increasing with attack angle because the bottom surface of the airfoil will have a larger radius of curvature than the top surface; thus the pressure gradient will point downwards. This means the bottom surface will have higher pressure than the top surface, and the airfoil will experience lift.

Pressure gradient as a function of streamline radius of curvature. The lift coefficient for an airfoil can be calculated by integration as long as the velocity and pressure vs. streamline functions are known.

Skin friction coefficient - The skin friction coefficient is a function of Reynolds number and is also calculated with an integral over the surface of the airfoil. The drag force created by skin friction in the boundary layer is defined as follows:

Drag force equation integral.

Eventually, the velocity gets large enough that the Reynolds number for the flow corresponds to turbulent flow rather than laminar flow, and drag will begin increasing. At an excessive attack angle, flow separation occurs and the flow on the top surface of the wing becomes heavily turbulent, leading to a sudden loss of lift and resulting stall. Airfoil design requires considering the limits of attack angle for an airfoil so that the aircraft will not stall and fail during flight.

### Solve Airfoil Design Problems With a CFD Simulator

Airfoil design problems involve more than just calculating lift and drag given the airfoil’s angle of attack—they also require determining the transition to turbulent flow as the angle of attack increases. This involves the use of CFD simulation applications to predict the transition to turbulent flow from the Navier-Stokes equations or a reduced turbulence model. This transition can be determined by generating a lift coefficient vs. attack angle graph from multiple simulations, or by calculating turbulent flow above the airfoil directly at multiple attack angles.

Once the transition to turbulence is noticed, the wing could be redesigned to accommodate a larger attack angle or to reduce drag and change the aircraft’s performance while cruising. These important considerations in aircraft design and simulation will affect all other mechanical and structural aspects of an aircraft and will determine the overall efficiency and top speed of the aircraft during flight.

Advanced CFD simulation suites can be used to investigate the best airfoil angle of attack and shape to help maximize lift and minimize drag during flight. The complete set of fluid dynamics analysis and simulation tools in Omnis 3D Solver from Cadence are ideal for defining and running CFD simulations with modern numerical approaches, including aerodynamic lift explanations in complex aircraft.