Basic Aerodynamic Theory Lesson
An aerofoil is simply a cross-section of a wing. Below is an image of an aerofoil and its different sections. Since you will need to know this image well, practice drawing it up.
Leading edge: The term used to describe the front of a wing.
Trailing edge: The term used to describe the rear of a wing.
Chord: The chord, or chord line, of an aerofoil is an imaginary straight line joining the leading edge to the trailing edge.
Relative airflow: The airflow relative to the path of motion of the aerofoil.
Angle of attack (AoA): The angle between the chord line of the aerofoil and the relative airflow. Usually, it is about 4° for normal flight conditions.
Thickness: The vertical thickness of the aerofoil.
Camber: Camber has a couple of definitions. It can be described as the curvature of the aerofoil. Technically, it is the difference between the chord line and the mean camber line.
Daniel Bernoulli, a Swiss mathematician and physicist who lived in the 1700s, discovered certain properties relating to fluids in movement. These are expressed in the following mathematical statement:
In a streamlined flow of an ideal fluid or gas (i.e., one that is not viscous), the sum of the energy of position, the energy of motion, and the pressure energy will remain constant.
In other words, an increase in velocity equates to a decrease in pressure, and vice versa. Next, we will look to adapt this theory to how an aircraft flies.
Before we jump into understanding how lift is produced, we will have a closer look at Bernoulli’s theorem, how it relates to the venturi effect, and how the venturi effect relates to our aircraft.
A venturi can be described as a tube or a passage where part of that tube narrows and then expands. In the image below, you can see that the passage narrows once the air flows in and expands as the air exits. As the air flows into the throat of the venturi, the air gets squeezed together. In order for all of the air to pass through the venturi, the air accelerates. According to Bernoulli, with an increased velocity, the pressure must reduce. After passing through the venturi, the air expands and decelerates and, according to Bernoulli, the air must therefore increase in pressure. As a result, we get the following:
Below is an animation of exactly what happens in a venturi. As air enters the venturi, it is squeezed together and speeds up; as air exits the venturi, it expands and slows down.
Now that we understand how air flows through a venturi, let’s look at an aerofoil.
Looking at the image below, we have removed the top section of the venturi, and it looks a lot like an aerofoil, doesn’t it? We can see the airflow around an aerofoil, as illustrated by the image below. The airflow over the top of the aerofoil has to deviate up over the aerofoil, whereas the airflow underneath the aerofoil has an approximately straight flow. As a result of this airflow having to deviate up over the wing, the air accelerates. Relating this back to Bernoulli, the pressure above the aerofoil therefore decreases. The airflow underneath the aerofoil relative to the airflow above is higher.
Air will always flow from areas of high pressure to areas of low pressure, as it is always trying to create areas of equal pressure. A great example of this is a car or bicycle tyre. The air inside the tyre has a relatively high pressure compared to that of the outside air. If you were to get a puncture on your tyre, the air would come rushing out, meaning the high pressure inside the tyre moves to the lower pressure outside the tyre. We can now apply this to the aerofoil. With high pressure below the aerofoil and low pressure above it, the air tries to move upwards, and this creates the lifting force.
Upwash and Downwash
Airflow at the leading edge warns the air ahead of the wing that the aerofoil is approaching. Air will always seek the easiest path (i.e., the one with the lowest pressure) and will therefore curve upwards towards the top surface. This is termed upwash. Upwash is an inherent feature of any surface that is producing lift. The greater the low pressure region, the greater the amount of upwash, e.g., an aerofoil with large camber or at a high angle of attack. Due to the curved section of the wing, or camber of the aerofoil, the streamlines of the air are deflected downwards as they approach the trailing edge. This is termed downwash.
The greater the camber of the aerofoil or angle of attack, the greater the downwards deflection of the streamlines, thus the greater the downwash.
Total reaction is the result of lift and drag. Let’s look at some diagrams.
If we look at the distribution of lift around an aerofoil with differing angles of attack, we get pressure envelopes like those below. And we can summarise these pressure envelopes to what is known as the centre of pressure. It is just a simple way to illustrate the average of lift on a diagram by summarising lift to act through one point. As the angle of attack increases, the pressure envelope changes and, therefore, the centre of pressure will also change; it actually moves forward.
Looking at the drag aspect, as the angle of attack increases, drag also increases (which we will discuss later on, but for now accept that drag increases). When we combine lift and drag vectors, we get the total reaction (TR). If lift and drag change with differing angles of attack, then the total reaction must also differ, as we see in the image below.
Thickness to chord ratio (t/c) is the maximum thickness of an aerofoil compared to the chord. This is expressed as a percentage (or ‘length to depth’).
Increasing or decreasing the thickness to chord ratio by as little as 1% will alter the characteristics. In particular, changes in the shape of the leading edge will have a large effect on the maximum lift and drag obtained at the stall; a sharp leading edge will stall more readily than a well-rounded leading edge.
The performance of an aerofoil is sensitive to small changes in the contour; any dents or scratches on the wing surface will bring about deterioration in the general performance.
Medium Aerofoils = 10% t/c Ratio
This is known as a general-purpose aerofoil, i.e., good all-round characteristics. The t/c ratio is 10% (i.e., the chord is 10 times longer than its thickness), which results in less drag and a lower lift coefficient than a high-lift aerofoil. These aerofoil sections have less camber and a sharper leading edge than those of a high lift type, but the point of maximum camber is still about 25 to 30% of the chord aft of the leading edge. A general-purpose aerofoil will give a good range of speeds.
Thick Aerofoils = 15% to 20% t/c Ratio
This is known as a high-lift aerofoil, i.e., high lift, low airspeeds, and high weight-carrying capabilities. The t/c ratio is about 15% to 20% (high). These aerofoil sections have a pronounced camber, and a well-rounded leading edge; the point of maximum camber is about 25% to 30% of the chord aft of the leading edge. Due to the large curvature of the mean camber line, the range of movement of the centre of pressure will be large on a high-lift aerofoil. Reflecting the trailing edge of the wing upwards can decrease this movement of the centre of pressure. A high-lift aerofoil is used on aircraft where a high coefficient of lift is important and speed is a secondary consideration.
Thin Aerofoils = 5% to 7% t/c ratio
This is known as a high-speed aerofoil, i.e., low lift, high airspeeds, and low weight-carrying capabilities. The t/c ratio is about 5% to 7% (low). These aerofoil sections have very little camber (if any), and a sharp leading edge. Their point of maximum camber is about 50% of the chord. Often referred to as a laminar flow aerofoil, it is very sensitive to any accumulation of ice or other surface impurities. The thinner section produces a low maximum lift coefficient but also low drag. This aerofoil section suits flight in the transonic/supersonic flight regime as well.
Reflex Curve:
A reflex curve is an aerofoil shape where the camber line curves back up near the trailing edge of the chord line. This helps to limit the movement of the centre of pressure, and can reduce the moment about the aerodynamic centre to 0. This can reduce the unstable nose down pitching moments which are common on conventional aerofoils. These are sometimes called ‘negative camber’ wings.
Airspeed indication in an aircraft is taken from a pitot tube. The reading from the pitot tube is known as indicated airspeed. Indicated airspeed is derived from what is known as freestream static pressure and dynamic pressure.
Freestream static pressure is the pressure value of the air at rest. This is the pressure that air exerts to an object from all directions.
Dynamic pressure is the pressure value of the air when given motion. This can be expressed as ½ ρV².
The combination of freestream static pressure and dynamic pressure is known as total pressure, or pitot pressure.
The following table refers to the relationship between different types of airspeed. You should have a good working knowledge of the following.
Instrument error: Diaphragm expansion/contraction, transmission shafts/chains, pulleys, and other mechanical items within the ASI all cause errors. This type of error is often the result of wear and tear, i.e., age.
Position error: Also known as pressure error, position error is caused by incorrect pick-up of either static pressure or dynamic pressure at the intakes. The error is aggravated by interference with the flow within the tubes through bends, restrictions, or mere drag. Flight conditions that tend to contribute to this error are:
- Flight at high angles of attack, where the pitot tube is not straight into the airflow
- Unbalanced flight, where some kinetic energy can enter the static vents
- Flight at higher airspeeds
- Influence on the ambient air and its pressure when undercarriage, flaps, etc., are lowered or raised.
As a rule, the effects of instrument error and pressure error are combined and applied to the IAS so that one can obtain the calibrated airspeed (CAS), also known as the rectified airspeed.
Compressibility error: The deflection of the diaphragm should truly represent the actual kinetic energy / dynamic pressure under exact ambient static pressure (SE). As altitude is gained and air becomes less dense, it also becomes easier to compress. The result, therefore, is an increasing error as altitude and speed increase. Since the error is always positive, i.e., the IAS is higher than it should be, the correction for it must always be negative. This error is most pronounced over 20,000 ft or 250 kt, i.e., at high airspeed and/or high altitude.
Density error: During construction of the ASI, standard conditions are used for calibration. It follows that if the atmospheric pressure and temperature are different from ISA, some error will present itself. In general, this error is not very large at sea level, but as altitude is gained, the error does magnify.