Aerofoil Terminologies, Lift Coefficient

Introduction

Aerofoil terminologies and lift coefficient are important concepts to determine the design of a flying object. Have you ever wondered how aeroplanes stay up in the air? What is it about their design that allows them to soar across the sky? The answer, as it turns out, is as interesting as the question.

Let us start by discussing the forces that aid in keeping aeroplanes up in the air. These are four in number, and we call them drag, thrust, weight, and lift. Together, they make it possible for aeroplanes to fly. Of these, the concept of lift is the most remarkable. In fact, without lift, no aeroplane would be able to raise itself even a single inch off the ground. But how is lift generated? We have the answer to that as well. When an object moves through the air, its “pushes” its surrounding molecules to make way for itself and thus, experiences aerodynamic force. One can resolve this aerodynamic force into two components, viz. drag, and lift. Lift “lifts” up the object, while drag tends to slow down its motion. For the object to be able to fly, there must be a balance between lift and drag. And aerofoils are what make this balance possible. In this article, we are going to explore the concepts of aerofoils.

What is Aerofoil?

Aerofoils are the cross-sectional shapes of objects which have been designed to produce the most favourable ratio between the drag and lift forces. In the image below, you can see a few examples of aerofoils along with their usages and size.

As we recently discussed, an object requires a balance between lift and drag to be able to fly. The idea behind aerofoils is to create curved shapes that provide increased amounts of lift with decreased amounts of drag, i.e., they maximise efficiency. Interestingly, it’s not necessary for aeroplanes to utilise aerofoils for their flight. Indeed, there are a plethora of shapes that can produce lift and drag. Even flat plates can theoretically serve that purpose. However, aerofoils generate far more lift than flat plates and the amount of drag experienced is significantly lower.

Aerofoil Terminology

Given below are a few important terms necessary to understand the working of aerofoils. We suggest taking a look at the diagram attached to maximise you’re understanding.

• Leading edge − The leading edge of the aerofoil is the front-edge, which collides with the air particles before all other portions of the aerofoil.

• Trailing edge − One can think of this as the tail of the aerofoil. It is the rear-most part of the aerofoil which interacts with air molecules last.

• Chord line − The chord line is the straight line that connects the trailing and leading edges of the aerofoil. Depending on the shape of the aerofoil, it can lie outside the aerofoil. The length of this line, called the chord, is an important parameter in describing the aerofoil.

• Angle of attack − This is the angle made by the chord line and the relative direction of air as the aerofoil moves through it. Remember: the angle of attack significantly affects how much lift the aerofoil generates.

• Upper surface − The surface of the aerofoil which one can associate with low pressure and high velocity is called the suction or upper surface. It is on the upper side of the aerofoil, as evidenced by its name.

• Lower surface − The lower surface is the opposite of the upper surface and encounters high static pressure. It is also known as the pressure surface.

• Camber line − If you were to take the midpoints of the aerofoil all the way from the leading to the trailing edge and connect them with a line, you would have the camber line. The distance of this line from the chord line is known as camber.

How does Aerofoil produce lift?

In the image above, you can see an aerofoil moving through air, as well as the relative motion of air particles. Notice how air particles tend to “stick” to the aerofoil. That is, they follow the same path as the shape of the aerofoil. And since aerofoils have a curved shape, air molecules are forced to follow a curved path as well.

Due to this curved nature of air flow, as well as the angle of attack of the aerofoil, when air molecules collide with the leading edge of the aerofoil, a larger portion of them goes towards the underside or the pressure surface. In simpler terms, there is more air below the aerofoil than there is above it. Naturally, in such a scenario, there will be a pressure difference above and below the aerofoil. Due to this pressure difference, the air below the aerofoil pushes it upwards, leading to what is known as the lift. Moreover, the curved surface of the aerofoil ensures that the ratio between lift and drag is most favourable for flight. Hence, aerofoils allow planes to fly.

Lift Coefficient

To describe the relationship between the lift generated by the aerofoil and its area to the velocity and density of the medium around it, we use a quantity that is known as the lift coefficient. Mathematically, this lift coefficient is dimensionless, and is larger when the lift generated is larger.

Let us start with the lift equation

$$\mathrm{L=C_L\times \frac{1}{2} ρv^2 A}$$

Here −

• L = generated.

• C_L = lift coefficient

• ρ = density of the fluid

• v = velocity of the fluid

• A = area of the aerofoil.

Solving the above equation for the lift coefficient gives

$$\mathrm{C_L=\frac{2L}{ρv^2 A}=\frac{L}{qA}}$$

Here, q is the pressure of the fluid. Lift coefficient includes information about the dependence of lift on various factors like the shape of aerofoil, air viscosity, compressibility, etc., and is determined experimentally.

Types of Aerofoils

Depending on the geometry of the aerofoil, we can classify them into the following two categories −

Symmetrical Aerofoil

In symmetrical aerofoils, the lower and upper surfaces are congruent. The chord line coincides with the camber line, and perfectly divides the aerofoil into two equal halves. Symmetrical aerofoils are used in helicopter blades. An interesting property of these types of aerofoils is that they produce no lift if the angle of attack is zero.

Non-symmetrical Aerofoil

In non-symmetrical aerofoils, the chord and camber lines do not coincide. The latter has a larger curvature and lies above the chord line. These types of aerofoils provide a better lift to drag ratio and can even produce a lift when the angle of attack is zero. However, they are less economical than symmetrical aerofoils.

Conclusion

Lift, thrust, drag, and weight forces come into play when we fly aeroplanes. Of these, lift and drag are intricately connected and are generated due to aerodynamic force. The lift force is what pushes aircrafts into the air, while drag slows it down. Aerofoils are cross-sections of shapes that are curved to provide the most efficient ratio between lift and drag. They produce lift by pushing a larger amount of air beneath them, leading to a pressure difference. Aerofoils are classified into

symmetrical and non-symmetrical types, of which, the latter provides better lift but is less economical.

FAQs

1.Who designed and invented aerofoils?

The first conception of aerofoils was by a German mathematician named Max Munk. In the 1920s, Hermann Glauert further enhanced and improved their designs.

2.Where are aerofoils used?

All aircrafts and helicopters utilise aerofoils in their wings and rotors. Wind turbines also have an aerofoil shape. Aeronautics sector finds the most use of aerofoils.

3.What is the significance of the four forces that aid an aircraft to fly?

• The weight of the aircraft pushes it downwards.

• The thrust is the force that allows it to move forwards.

• The drag force slows it down.

• The lift force pushes it upwards.

All four forces must be factored into account while studying aircrafts.

4.At what angle of attack is the maximum lift force generated?

At the critical or stall angle of attack, lift is maximum. Its value changes depending on numerous factors. For most aerofoils, it is between 15o-20o.

5. Is the concept of aerofoils applicable in liquids too?

Yes. The physics remain almost similar while an object is travelling across a liquid. However, in such a case, we use the term hydrofoil instead of aerofoil.