What is an Airfoil?
An airfoil is a specialised 2D shape that efficiently produces the maximum lift for a fluid flowing across it.
If you’ve ever seen the cross-section of a wing, you’re likely to have seen an airfoil already. An airfoil (or a hydrofoil for water) is employed in aircraft, cars, propeller blades, turbines, sailboats… you name it.
The reason for its wide usage? Its ability to produce the most lift possible of all the known shapes. Let’s see what makes this distinctive teardrop shape so special.
How does it produce lift?
Around the world, there are a few theories that try to explain the phenomenon of lift generation by an airfoil. Interestingly, there’s still debate among scientists about which theory is the most simple & intuitive. There are also a few partially erroneous theories. Let’s start with the flawed ones first.
1) Equal times theory:
Say we have an airfoil. For simplicity, we consider the airfoil’s frame of reference, with the fluid moving past it. The incoming fluid stream first encounters the leading edge, where it splits to go over the top and bottom parts.
Both of the streams must arrive at the trailing edge at the same time. But the distance to be covered by the upper stream is larger, and so it must have a higher velocity to arrive at the same time.
According to the Bernoulli principle, a higher velocity is associated with a lower pressure. Therefore, a region of low-pressure forms above the airfoil. Similarly, the lower stream has a smaller velocity and thus a higher pressure. Hence, an area of high pressure is created below the foil. This pressure difference produces the required lift.
This theory, although quite intuitive, is partially flawed.
No rule in physics states that the upper and lower streams must arrive at the same time at the trailing edge. In reality, the upper stream arrives about 20% faster. Having a longer distance to travel does not increase the velocity of the upper stream.
If it does, the following shape must produce an exceptional amount of lift—
But it doesn’t. This theory can’t explain how planes can fly inverted.
2) Newton’s third law:
This theory uses Newton’s third law to treat air as a collection of particles. Air just bounces off the underside of the wing, the reaction force of which produces lift. Although this is true to an extent, we can’t consider air to be a bunch of small balls. Its behaviour is much more complex.
How does it really work?
There are mainly 2 schools of thought around fluid flow. One—known as the inviscid fluid flow theory— ignores the viscosity effects of air to explain lift generation. It uses potential flow, and circulation concepts with the Kutta-Joukowski theorem to explain lift.
The other theory takes into account the viscous nature of air. As the airfoil moves through a fluid stream, the point that first encounters the fluid is known as the stagnation point. Here, the velocity of fluid becomes 0, and this point splits the fluid stream to go over the upper and lower contours. The air flowing over the upper surface accelerates and has to travel faster than the air below. A faster fluid is associated with a lower pressure, and vice-versa from the Bernoulli principle. This produces a pressure difference, which causes lift.
Further, the incoming airstream is purely horizontal which is deflected downwards after encountering the airfoil. This is due to the airfoil pushing down on the air and from Newton’s third law, the air pushes back on the airfoil. A combination of these two factors produces lift as we know it.
An important point is that air tends to follow the airfoil surface until the trailing edge rather than just moving off tangentially. This is due to the Coandă effect which describes a fluid’s tendency to follow a curved surface due to pressure differences caused by streamlined curvature.
Parts of an Airfoil
To describe the shape of an airfoil accurately, it is important to understand the different terminologies associated with it.
The leading edge is the forwardmost edge of an airfoil, which makes the first contact with the fluid stream.
The trailing edge is at the rear of the airfoil. It is where the upper and lower contours meet.
A straight line from the trailing edge to the leading edge is known as the Chord Line.
The angle made by the chord line with the incoming airflow is said to be the angle of attack. A higher angle of attack generates more lift for the same velocity. The lift increases up to the stall point, beyond which it decreases sharply. If an aircraft tries to take off too aggressively, it might stall.
A line equidistant from the upper and lower contours is known as the camber line. The maximum distance of the camber line from the chord line gives the camber. It’s a measure of the asymmetricity of the airfoil. It is usually expressed as a percentage of the chord length.
Depending on the camber, airfoils are categorised into 3 types:
Positive cambered airfoils are characterised by their ability to produce lift even at a 0° angle of attack. They are the most common types of airfoils & found in aeroplanes and bird wings.
Symmetric airfoils (or 0 camber airfoils) are airfoils with their chord line coinciding with their camber line. They produce no lift at 0° angle of attack and are commonly employed in stunt planes that fly inverted.
Negative cambered airfoils have the camber line below their chord line. They produce a “negative” lift and are employed in Formula cars for downforce that offers better traction and handling.
Varying each of these parameters, hundreds of variations of airfoils are possible. Each airfoil might be suited for a particular flight regime. Modern aircraft use different airfoils along the cross-section of the wing from root to wingtip, with a gradual transition in between. They are also equipped with slats (leading edge) and flaps (trailing edge) which optimise the airfoil shape for different flight regimes. During takeoff, a high amount of lift is needed, so flaps are extended. But this increases drag, so flaps are retracted during the cruise phase to maximise fuel efficiency.
The 4 fundamental forces
In aerodynamics, there are 4 fundamental forces: Lift, Weight, Thrust and Drag. Lift balances weight, and thrust balances drag. When an object produces more lift than its weight, it can take flight. An intricate balance between these 4 forces gives us controlled flight.
The pressure around an airfoil varies continuously from leading to trailing edge. Understanding this pressure distribution is crucial for CFD analysis, as it directly relates to the forces generated and helps identify potential flow separation points. We will cover more about flow separation in upcoming posts.
NACA Airfoils
The National Advisory Committee for Aeronautics (NACA) was established in 1915 to address the United States’ deficiency in aeronautical research. They developed a system of standardised airfoil geometries which are encoded in a 4-digit system.
This 4-digit system uniquely encapsulates the airfoil geometry through 4 digits:
- First Digit: Denotes maximum camber as a percentage of chord length. E.g., In the NACA 2415 airfoil, “2” denotes a 2% camber relative to the chord length.
- Second Digit: Position of maximum camber from the leading edge, expressed in tenths of the chord. E.g., For NACA 2415, “4” denotes the maximum camber at 40% of the chord.
- Third and Fourth Digits: Maximum thickness as a percentage of the chord length. In NACA 2415, “15” signifies a 15% thickness-to-chord ratio.
Examples:
- NACA 0006: A symmetrical airfoil with 0% camber and 6% thickness, used in helicopter rotors and stabilizers for neutral lift at zero angle of attack
- NACA 2415: A cambered airfoil (2% camber at 40% chord) with 15% thickness, employed in general aviation wings for balanced lift and structural robustness
- NACA 4412: Features 4% camber at 40% chord and 12% thickness, common in low-speed aircraft due to high lift characteristics
This system allows engineers to quickly select airfoils tailored to specific performance criteria, such as maximizing lift or minimizing drag, without requiring physical prototyping. We’ll be simulating fluid flow across the 4-digit airfoils in upcoming posts.
Quantitative Performance Metrics
The performance of an airfoil is quantitatively measured through 3 dimensionless quantities:
Lift Coefficient (\(C_l\)):
In Aerodynamics, we typically deal with “Lift Coefficient” rather than “Lift”. It’s defined as:
$$C_l = \frac{L}{\frac{1}{2}\rho v^2 c}$$Where:
- \(L\) = Lift force
- \(\rho\) = Fluid density
- \(v\) = Velocity
- \(c\) = Chord length
A \(C_l\) of 1.2 at a 10° angle of attack is considered efficient lift generation.
Drag Coefficient (\(C_d\)):
Similarly, the Drag Coefficient is defined as:
$$C_d = \frac{D}{\frac{1}{2}\rho v^2 c}$$Where \(D\) is the drag force. A low \(C_d \approx 0.02\) signifies minimal air resistance.
Since we’re dividing by the velocity & chord length, these quantities are more generalised than the actual forces, allowing airfoils with different shapes and sizes to be compared.
Lift to Drag ratio (L/D):
The Lift to Drag ratio compares lift generated to drag incurred:
$$\frac{L}{D} = \frac{C_l}{C_d}$$Higher L/D values allow for extended glide ranges (\(\sim\)50:1 for gliders) while fighter jets tend to keep it low for increased manoeuvrability.
Reynolds Number
Reynolds Number measures the ratio of inertial forces to viscous forces in fluid flow. It’s calculated as:
$$Re = \frac{\rho V L}{\mu}$$Where:
- \(\rho\) = Fluid density
- \(V\) = Velocity
- \(L\) = Characteristic length (chord)
- \(\mu\) = Dynamic viscosity
Low Re flows (\(\sim\)10,000) are dominated by viscous effects, while high Re flows (\(\sim\)1,000,000+) are more inertial. This affects airfoil performance significantly—the same airfoil behaves differently on a model aeroplane versus a commercial jet.
Additional Resources
For further exploration of airfoil theory and applications:
Videos & Online Tools:
- Lift and Wings - Sixty Symbols
- How Airplane Wings REALLY Generate Lift
- How do Wings generate LIFT?
- Mastering Airfoil Selection for Drones - Part 1: Theory
- Understanding Aerodynamic Lift
- NACA Airfoil Generator - Interactive airfoil coordinate generation. We’ll be using this in our simulations in later posts.
Conclusion
Airfoils are fascinating structures that play a crucial role in the world of aerodynamics. From their unique shapes to their ability to generate lift, they are integral to every machine operating in fluids. Understanding the principles behind airfoil design and performance is essential for anyone interested in aerodynamics or aerospace engineering.
That’s it for this post! If you’ve made it this far, give yourself a pat on the back, ‘cause it’s all downhill from now! The real fun is about to begin!