Interactive Animation: Forces on Airfoil – Educational-Animation.org

The animation shows the forces on an aircraft airfoil (Clark Y profile). The slider in the upper left allows you to continuously adjust the angle of attack between −10° and +20°. The force vectors update in real time, and the aircraft climbs or descends depending on the balance of forces. This is visible through the movement of the clouds in the background.

What Is Aerodynamic Lift?

Lift is the aerodynamic force that acts perpendicular to the direction of airflow around a body. It is the force that keeps aircraft in the air and enables birds to fly. Despite its seemingly miraculous nature, lift is not magic — it follows directly from the fundamental laws of physics.

The magnitude of the lift force depends on several factors: the shape of the wing (its profile), the angle of attack (how the wing is tilted relative to the airflow), the airspeed, and the density of the surrounding air. A well-designed wing profile produces a large amount of lift while keeping aerodynamic drag as low as possible.

From a physics perspective, lift can be understood through Newton’s third law: the wing deflects the airflow downward, and in return, the air pushes the wing upward. At the same time, the principles of fluid dynamics (Bernoulli’s equation) explain how pressure differences arise around the wing. Both perspectives complement each other and together provide a complete picture of how lift is generated.

Lift in Everyday Life

Aerodynamic lift is not limited to aircraft. It appears in many everyday situations:

Frisbee: The curved top surface of a Frisbee creates a pressure difference when it flies through the air. This generates lift that keeps the disc aloft much longer than a flat plate would fly.
Paper airplane: Even a simple paper airplane uses lift. The angled wings deflect air downward, creating an upward force. The better the fold, the more stable the flight.
Car spoiler: A spoiler on a race car is essentially an inverted wing. Instead of producing lift, it generates downforce — pushing the car onto the road at high speeds to improve traction.
Sailing: A sail works like a vertical wing. The airflow around the curved sail creates a lateral force that propels the boat forward — even against the wind direction (tacking).
Birds: Birds are masters of aerodynamics. They constantly adjust the shape and angle of their wings to optimize lift during different phases of flight — gliding, flapping, and landing.

Description of the Animation

The lift force (blue arrow pointing upward) and the drag force (red arrow opposing the flight direction) are shown as force vectors at the airfoil. In addition, the animation displays the weight force (black arrow pointing downward) and the resultant force (green arrow), which is derived from the force parallelogram drawn in the animation. The corresponding coefficients C_L and C_D are plotted as curves over the angle of attack in the diagram on the right side – the current operating point is marked on the curves.

The control points on the curves can be dragged with the mouse to modify the aerodynamic properties of the profile. Using the “Polar diagram” checkbox, you can alternatively display the polar curve (green), which plots C_L against C_D.

The angle of attack \( \alpha \) is the angle between the chord line (imaginary connecting line between the leading and trailing edge of the profile) and the direction of the oncoming flow. In the animation, the chord line is drawn as a horizontal reference line at the airfoil, and the angle α is indicated by an arc marking. When the angle of attack is increased, the lift initially increases until a stall occurs at the critical angle of attack (usually between 15° and 20°) and the lift suddenly collapses.

The magnitude of the lift force can be calculated using the following formula:

\[ F_L = C_L \cdot \frac{\rho}{2} \cdot v^2 \cdot A \]

C_L: Lift coefficient. The lift coefficient depends on the shape of the wing. The value is determined through measurements in a wind tunnel or through simulations.
\( \rho \) (Rho): Density of the air through which the wing moves. It is given in kilograms per cubic meter (kg/m³) and can vary depending on altitude, temperature, and humidity.
v: Velocity of the object through the air in meters per second (m/s)
A: Reference area in square meters (m²). This is the projected wing area viewed from above (planform area).

The formula for calculating the drag force is (C_D: drag coefficient):

\[ F_D = C_D \cdot \frac{\rho}{2} \cdot v^2 \cdot A \]

The ratio of lift to drag is called the glide ratio E:

\[ E = \frac{C_L}{C_D} = \frac{F_L}{F_D} \]

The higher the glide ratio, the more efficient the profile. The Clark Y airfoil typically achieves its best glide ratio at an angle of attack of about 4° to 6°. Set this angle range in the animation and observe how the blue lift arrow is particularly long relative to the red drag arrow – the aircraft flies most efficiently at this point.

The term \( \rho/2 \cdot v^2 \) is also referred to as dynamic pressure q and has the unit Pascal (Pa) or N/m².

Typical values for the Clark Y airfoil:

Maximum lift coefficient C_L,max: approximately 1.3 to 1.5
Minimum drag coefficient C_D,min: approximately 0.008 to 0.01
Best glide ratio: approximately 60 to 80
Critical angle of attack: approximately 15° to 17°

How Is Lift Generated?

The generation of aerodynamic lift can be explained through two complementary physical principles that work together:

Flow Deflection (Newton’s Third Law)

The wing deflects the incoming airflow downward. According to Newton’s third law (“for every action there is an equal and opposite reaction”), if the wing pushes the air downward, the air pushes the wing upward with an equal force. The greater the angle of attack, the stronger the deflection — and thus the greater the lift. This explains why increasing the angle of attack increases the lift (up to the point of stall).

Pressure Difference (Bernoulli’s Principle)

The curved upper surface of the wing forces the air to travel a longer path and accelerate. According to Bernoulli’s principle, faster-moving air has lower pressure. This creates a pressure difference: low pressure on top of the wing and higher pressure on the bottom. The net result is an upward force — lift.

Important: Both effects contribute to lift simultaneously. It is a common misconception that only Bernoulli’s principle is responsible. In reality, flow deflection and pressure differences are two sides of the same physical phenomenon. The total pressure distribution around the entire profile — top and bottom, leading edge and trailing edge — determines the resulting aerodynamic force.

Understanding Stall

Stall is one of the most important phenomena in aerodynamics and a critical concept for flight safety.

At small and moderate angles of attack, the airflow follows the contour of the wing smoothly. As the angle of attack increases, however, the air on the upper surface has to travel an increasingly steep path. At a certain critical angle — typically between 15° and 20° for most profiles — the airflow can no longer follow the curved upper surface.

At this point, the boundary layer (the thin layer of air directly on the wing surface) separates from the surface. Behind the separation point, a turbulent wake forms with chaotic, swirling airflow. The consequences are dramatic:

The lift drops suddenly and significantly.
The drag increases dramatically.
The aircraft may lose altitude rapidly.

This is extremely dangerous in aviation, especially during takeoff and landing when the aircraft is close to the ground. Modern aircraft are equipped with stall warning systems that alert pilots when the angle of attack approaches the critical value. In the animation, this effect can be observed directly: set the slider to values above approximately 15°. The blue lift arrow becomes noticeably shorter while the red drag arrow grows. In the diagram on the right, the steep drop of the C_L curve and the rise of the C_D curve are clearly visible. The aircraft begins to descend, which is recognizable by the upward movement of the clouds in the background.

Understanding the Polar Diagram

The polar diagram is a powerful tool for visualizing the aerodynamic performance of a wing profile. It plots the lift coefficient C_L (vertical axis) against the drag coefficient C_D (horizontal axis). Each point on the resulting curve corresponds to a specific angle of attack.

Key features of the polar diagram:

Best glide ratio: A straight line drawn from the origin and tangent to the polar curve indicates the angle of attack at which the glide ratio \( E = C_L / C_D \) is maximized. This is the most efficient operating point of the wing.
C_L,max: The topmost point of the curve shows the maximum achievable lift coefficient. Beyond this point, stall occurs and the lift drops.
Minimum drag: The leftmost point of the curve corresponds to the minimum drag coefficient C_D,min.

In the animation, you can switch to the polar view using the “Polar diagram” checkbox. Instead of the separate C_L and C_D curves, the green polar curve is then displayed in the diagram. As you change the angle of attack with the slider, the current operating point moves along this curve.

The Clark Y Airfoil

The Clark Y is one of the most well-known airfoil profiles in aviation history. It was developed by Colonel Virginius E. Clark in the 1920s. The letter “Y” is simply the designation of this particular profile in Clark’s series of designs.

Key characteristics of the Clark Y profile:

Flat lower surface: The bottom of the profile is nearly flat, which makes it easy to manufacture and simplifies construction — especially in model aircraft building. This characteristic is clearly visible on the airfoil of the aircraft silhouette in the animation.
Thickness: The profile has a maximum thickness of approximately 11.7% of the chord length, providing a good balance between structural strength and aerodynamic performance.
Lift characteristics: The Clark Y produces good lift at moderate angles of attack and has a relatively high maximum lift coefficient.
Forgiving stall behavior: Unlike some high-performance profiles, the Clark Y stalls gradually and predictably, making it safer and easier to handle.

The Clark Y has been used in many general aviation aircraft, model aircraft, and educational contexts. Its predictable behavior and ease of manufacture make it an ideal profile for learning about aerodynamics.

Summary: Key Formulas

Quantity	Formula	Description
Lift force	\( F_L = C_L \cdot \frac{\rho}{2} \cdot v^2 \cdot A \)	Force perpendicular to the airflow
Drag force	\( F_D = C_D \cdot \frac{\rho}{2} \cdot v^2 \cdot A \)	Force parallel to the airflow
Glide ratio	\( E = \frac{C_L}{C_D} = \frac{F_L}{F_D} \)	Ratio of lift to drag
Dynamic pressure	\( q = \frac{\rho}{2} \cdot v^2 \)	Unit: Pascal (Pa)