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Home , Lift (force)

The Description of and How They Generate Lift

By Josh Moser Introduction

Engineers have been experimenting and studying airfoils, or , for a long time trying to determine what the best characteristics are for . An is the shape of a or blade of a viewed in cross-section. Since the early 1900’s, when the performed the first sustained flight, people have tried various designs for trying to replicate and improve the previous feat.

Airfoils come in many different sizes and shapes. The question of what shape performs best continues to be asked. The answer however, is that there is no single “best” shape for an airfoil. The best shape depends on the purpose of the airfoil. Airfoils have applications in today’s world for aircraft such as planes and , and also for applications with fan and blades. People in today’s society rely on airfoils and they don’t even know it. This description explains one of their main characteristics, how they generate lift.

Basic Terminology of Airfoils

Figure 1. Basic Airfoil Terminology http://adg.stanford.edu/aa241/airfoils/images/AirfoilGeom.gif

Figure 1 shows some of the basic terminology associated with airfoils and their cross-section view. Many of these terms are required to understand the remaining of this description.

 The chord is the full length from the leading edge to the trailing edge of the airfoil. The chord is an important dimension of the area of the wing when looking at the lift equation later in this description. It also is a straight line unlike that of the line.  The camber line is a line that connects the leading edge to the trailing edge, but it also shows the curve of the airfoil. Generally, it is midway from the top surface and the bottom surface at every location on the line.  Camber itself is a term to define the vertical length between the chord line and the camber line. Airfoils typically have a positive camber, meaning that they curve up instead of down. This is crucial in most applications to create a lift that pushes up rather than pushing down towards the earth at low angles of attack (even zero ).  The angle of attack is defined as the angle between the chord and the direction of the free stream velocity of the air. Any term described by free stream is a term associated with a quantity unaffected by the airfoil or the aircraft. This means that free stream velocity is the velocity of the air approaching the aircraft before it has a chance to interact with the structure.  Other terms of interest are span and aspect ratio. Span (b) is the full length of a wing on an aircraft, which can be thought of a going into or out of the page from figure 1. Aspect ratio (AR) is the ratio of span compared to area of the wing. This is shown in the 푏2 푏 equation 퐴푅 = = (푓표푟 푟푒푐푡푎푛푔푢푙푎푟 푤𝑖푛푔푠 푤ℎ푒푟푒 푆 𝑖푠 푎푟푒푎). 푆 푐

Lift and the Bernoulli Principle

As an flies through the air, it constantly has to oppose the force of from Earth. This opposition of gravity in steady level flight requires the lift force to be exactly equal to the force of gravity. How does this happen when gravity is always present, but lift is not always 1 present? Lift has been determined to be equal to 퐿 = 휌푣2푆퐶 , where 휌 is the air density, 푣 is 2 퐿 the velocity of the air, 푆 is the area of the wing, and 퐶퐿 is the coefficient of lift, which is dependent upon the angle of attack and is usually determined experimentally. This equation holds true for all applications of 3D situations where lift is important.

Airfoils follow a principle called the Bernoulli Principle. This principle states that there is a for at one scenario to another scenario. This can be modeled by the 1 1 equation 푃 + 휌푣 2 + 휌푔ℎ = 푃 + 휌푣 2 + 휌푔ℎ . From this equation P is the 1 2 1 1 2 2 2 2 1 energy, 휌푣2 is the kinetic energy per unit volume, and 휌푔ℎ is the potential energy per unit 2 volume. The subscript 1 means at one initial instance while the subscript 2 means at a final later instance in time.

Lift can be thought of as being possible because an increase in velocity above the airfoil creates a decrease in pressure. Below the airfoil, the velocity either remains unchanged from free stream velocity or only changes slightly, and therefore provides a steady pressure force below the airfoil. With a decrease in pressure above the airfoil and a steady pressure below, a net pressure force is created on the airfoil that is directed upward.

Shape of the Airfoil

The shape of the airfoil is perhaps the main characteristic that allows the Bernoulli Principle to hold true. The shape of airfoils, for the most part, curve up instead of curve down. This is important because this positive camber requires the air to increase its velocity above the airfoil because the curvature increases the distance from the leading edge to the trailing edge. This increase in velocity is associated with a decrease in pressure above the airfoil. The bottom surface of the airfoil is also curved, but does not alter the velocity of the air as much. This means that a net pressure force acts on the airfoil pushing up, which is the lift force.

Wing Area

The wing area is defined as the top view area of the wing when looking down on the aircraft from above or below. This is the area that is normal, or perpendicular to the lift force that is generated. From intuition, it can be thought of that a larger wing area will create a larger lift force because more air will be affected by the airfoil, causing more lift. Increasing the span of an airfoil can increase lift, but it can also increase certain types of .

Angle of Attack

The angle of attack is defined as the angle between the free stream air and the chord line connecting the leading edge and the trailing edge. This is shown in figure 2. For most cases, increasing the angle of attack increases the coefficient of lift. There is however a critical angle where the coefficient of lift becomes a maximum and an increase in lift is no longer possible. This creates separation of airflow behind the airfoil and can be thought of as an aerodynamic , causing no lift generation Figure 2. Airfoil at an Angle of Attack and a large drag force on the airfoil. http://www.aerospaceweb.org/question/ae rodynamics/angles/airfoil.jpg Air Density

The air density is the amount of air particles in a volume of space. The density of air varies with altitude, and changes the amount of lift generated by an airfoil. As altitude increases, the density of air decreases. This decrease of air density means that there are less air particles that “push” on the airfoil to create pressure. If there are less particles pushing on the airfoil, then there is going to be a decrease in lift for the airfoil and the aircraft.

Airspeed

The airspeed can either be thought of as the velocity of the aircraft approaching still air or it can be thought of as the velocity of the air added with the velocity of the aircraft summing to one relative velocity. This velocity is often called free stream velocity, as it is the velocity of the air in front of the aircraft before it as a chance to deflect out of the way. Lift of an aircraft actually depends on velocity squared, meaning that as velocity increases, it has a tremendous affect on lift. However, at slow speeds, a change in velocity does not have as large of an effect. This is why most aircraft have to take-off and land when moving at relatively large speeds on runways.

Summary

Airfoils are used in today’s society and are crucial for a number of applications. Many people do not possess the background information required to understand how they work and how their characteristics are utilized to perform certain functions. Lift from airfoils are used to fly aircraft, generate energy from wind , and even to allow that simple fan on your desk to cool you off on a hot summer day. Understanding this concept of lift provides a unique perspective on society and life.