Drag Lesson

Air offers resistance to the forward passage of a body through it. Air that is absolutely still will create resistance to objects trying to pass through it, and stationary objects will retard similarly moving air. This resistance is called drag. Drag is the force acting rearwards in the direction parallel with the relative airflow. Drag increases at a rate approximately proportional to the square of the airspeed. For example, if an aircraft in steady level flight travelling at 100 knots is accelerated to 200 knots (airspeed doubled), the total drag of the aircraft becomes four times as great. This can be easily demonstrated by passing your hand through water in a swimming pool.

The drag tree is a great visual representation of how drag affects an aircraft, because it breaks drag down into its different components.

You will need to remember this image. Practice drawing it up.

There are two main types of drag:

Induced drag: Induced drag is lift-dependent drag. Whenever the wings are producing lift, induced drag is present.
Parasite drag: Parasite drag is that part of total drag that is not inherent to the production of lift. Parasite drag is the total sum of form drag, skin friction, interference, and cooling drag. Any object that is therefore held in a fixed position to the relative airflow—e.g., wheels, undercarriage, aerials, and struts—will create parasite drag. Efficient streamlining is one way of reducing parasite drag.

Parasite drag: Is comprised of cooling drag, interference drag, and profile drag.

Cooling drag: This type of drag arises from the cooling of the engine.

Interference drag: The airflow over one surface can upset the flow over the other, which causes a mixing of airflows, creating eddies and turbulence.

Profile drag: Any object that presents a profile relative to the airflow creates drag. Profile drag is made up from a combination of:

Skin friction drag, which is drag created due to the shear stress between successive layers of air flowing next to the surface.
Form drag, which is drag that exists due to the pressure difference between the side facing into wind and the side facing away from the wind.

We will look at each type of drag in detail now.

Remember, parasite drag is a combination of interference, cooling, and profile drag, with profile drag being comprised of skin friction and form drag. We will have a look at these now.

Interference Drag

The airflow over two or more different surfaces (e.g., a wing and the fuselage) may be upset when placed in close proximity with one another. The airflow over one object can upset the flow over the other, which causes a mixing of the airflows, creating eddies and turbulence, known as interference drag. Unless the two airflows meet smoothly, the turbulence created will increase drag. Interference drag can only be reduced by design and ‘fairing’ one object to the other to produce the best streamline result, preventing the intermixing and creating a turbulent flow.

Another form of drag sometimes discussed is cooling drag. When air flows over a surface, this is heated through friction, and energy is lost to the airflow. This is one of the principles of skin friction drag. Essentially, kinetic energy is ‘traded off’ for heat energy. This loss of kinetic energy, taken from the motion of the aircraft, can be classified as drag. The energy of airflow is altered when flowing in and around hot engine baffles. It is then exposed to the freestream airflow (maybe through cowl flaps) and, as a result, creates a similar effect to skin friction or form drag.

Skin Friction Drag: Is due to the resistance caused by the relative motion between the surface of an object and the air. The layers of air near an object’s surface will retard the layers further away due to the friction between them. In simple terms, this is because of a ‘shearing’ effect between each successive layer of air travelling at different speeds due to the viscosity of air. There is a gradual increase in velocity as the distance from the object’s surface increases. This layer of retarded air is called the boundary layer. The thickness of the boundary layer depends on the surface area of the aerofoil, the speed of the airflow, the surface condition (i.e., smoothness), and the viscosity of the air. The outer edge of the boundary layer is generally (but not necessarily) taken as being where the retarded air reaches 90% of its freestream value.

Laminar Boundary Layer

The laminar boundary layer is a smooth and orderly flow over the initial portion of the aerofoil. Laminar boundary layers are relatively thin, from a fraction of 1 mm to 2 mm thick. These layers will typically exist up to a point of maximum camber, i.e., where there is a favourable pressure gradient:

Gradual velocity change
Low skin friction drag
Low velocity next to surface

Turbulent Boundary Layer

Where the airflow transitions from laminar to turbulent flow, we have the turbulent boundary layer. This layer can be up to 6 mm in thickness and is characterised by small eddies of air, varying in size and strength, in which there is no orderly flow. The thicker the turbulent boundary layer, the greater the drag:

Sharp velocity change
Higher skin friction drag
Higher velocity next to surface

Transition Point

From the leading edge of the aerofoil to the point of maximum camber, a laminar flow over the aerofoil is maintained—the velocity of airflow is increasing and, therefore, the pressure is decreasing. Beyond the point of maximum camber, the velocity of the airflow decreases; therefore, the pressure increases and the air will have a tendency to flow back to the low-pressure area, developing eddies and creating a turbulent flow. The point on the aerofoil where the laminar boundary layer becomes turbulent is known as the transition point. As the airspeed decreases, the transition point moves rearwards. As the airspeed increases, the transition point moves forwards (assuming angle of attack remains constant).

Form drag is drag that exists due to the pressure difference between the side facing into wind and the side facing away from the wind. When a viscous fluid flows past a solid object, vortices or eddies are formed downstream, so we no longer get a streamlined flow.

Experiments show that when a flat plate is held at right angles to the airflow, the pressure in front of the plate becomes greater than atmospheric pressure, while the pressure behind the plate becomes less than the atmospheric pressure. This causes a ‘suction’ effect on the plate. Streamlined shapes offer less resistance to the relative airflow and, therefore, create less of a suction effect and smaller vortices. Form drag can be reduced by altering the shape of the plate or through streamlining.

A good example of this is the undercarriage of the C172R, where a fairing has been placed over the main wheels to reduce form drag.

Induced drag is produced every time a wing produces lift (i.e., induced drag is lift-dependent drag). When a wing is producing lift (an aircraft in flight), a pressure difference will exist between the upper and lower surfaces. The pressure on the under surface of the aerofoil is higher than atmospheric pressure, whereas the pressure over the top of the aerofoil is lower than atmospheric pressure. This pressure difference causes the air to flow from the region of high pressure to the region of low pressure. Thus, the air underneath the wing flows out towards the wing tip, spilling over the top and flowing towards the wing root. This is known as a spanwise flow. When the two airflows meet at the trailing edge, they do so at an angle to each other and create trailing-edge vortices. The trailing edge vortices tend to join up and form one large vortex at the wing tip, known as a wing tip vortex. The direction of rotation of the vortices is inwards towards the fuselage.

The wing tip vortex, combined with the trailing edge vortices, induces a downward flow of air behind the trailing edge of the wing. The lift component of the total reaction (TR) acts at right angles to the relative airflow. Because the net direction of the relative airflow has a downward component induced by the wing tip vortex, the lift vector still acting at right angles (to the effective relative airflow) is tilted backwards, and thus has a rearward component. The size of the rearward component is proportional to the angular amount of downwash and, therefore, to the amount of induced drag. As the wing tip vortices increase in size and strength, they increase downwash over the wing, which results in a greater tilt (rearwards) of the lift vector. This horizontal component is known as induced drag.

This formula for C_ID is for an elliptical wing only. The value of C_ID for wings that are not elliptical in planform has different distribution of downwash and will be slightly higher. However, for our purposes, this slight discrepancy is ignored.

Induced drag is a problem that plagues all aircraft; hence, there are factors available to reduce it:

Airspeed
Angle of attack
Aspect ratio
Wing tip design
Ground effect

Angle of Attack

Induced drag is proportional to the angle of attack (AoA). As the angle of attack is increased, induced drag increases. At –2° AoA, no lift is produced; therefore, there is no induced drag. At the stalling angle of attack, maximum lift is being produced and, therefore, a large wing tip vortex and more induced drag.

Airspeed

Induced drag is inversely proportional to the square of the airspeed. Induced drag is greatest at low airspeeds and least at high airspeeds. This is because at higher speeds, the lift coefficient is smaller (due to correspondingly lower AoA). At low airspeeds (high AoA), the lift coefficient is large and, therefore, a larger wing tip vortex develops. Also, at a high airspeeds, the wing ‘out-flies’ the wing tip vortex, leaving little time for spanwise flow to develop.

Aspect Ratio

Aspect ratio is the dimensional ratio of the span of a wing to the chord.

Wing tip vortices only influence that portion of the aerofoil close to the wing tip. The higher the aspect ratio, the smaller the area of the wing tip affected. Aspect ratio is strictly expressed as a number and has no unit of measure. On high-aspect ratio aerofoils, the spanwise flow of air has little time to develop. As a result, the area affected by the downward flow of air is decreased. There is a reduction in the size and strength of the trailing edge and wing tip vortices and, therefore, induced drag is considerably reduced. If the aspect ratio is doubled, the induced drag is halved.

As seen using the C_DI formula above, induced drag is inversely proportional to the aspect ratio. As the aspect ratio is increased, induced drag reduces. If the aspect ratio is increased (a Glider’s wing, for example) the wing tip vortex induces very little downwash compared with the total span of the wing.

Aspect Ratio and Stalling Angle: The wing tip vortex induces downwash behind the wing, thus changing the net direction of the airflow. The stall will occur when the angle of attack, measured relative to the local airflow (effective relative airflow) reaches the critical angle of attack. Thus, as the aspect ratio decreases (larger wing tip vortex, therefore steeper inclination of the local airflow), the wing will reach its critical angle of attack later (the geometric stalling angle is increased). This is shown on the graph below. Also, another point to note is that the maximum coefficient of lift is greater on high aspect ratio wings than on low aspect ratio wings, as shown below.

Wing Tip Design

To decrease spillage, considerable attempts have been made to design wing tips in such a way that wing-tip vortices are reduced. The goal was to block or restrict the wing-tip vortex from developing, to reduce induced drag.

Other ways to modify the wing to reduce induced drag are:

Tapered wings reduce wing-tip vortices and induced drag.

Ground Effect

When an aircraft is in close proximity to the ground (i.e., during take-off or landing), downwash is restricted, meaning the lift force is not tilted backwards as much, reducing induced drag. An aircraft will fly more efficiently when it is just above the surface. There is a cushioning effect caused by the air between the wing and the ground, which is known as ground effect.

Within about one wingspan of the surface, wing tip vortices are unable to form freely due to surface interference. With reduction in the vertical velocities of air close to the wing, the reaction force is tilted further forward, reducing the induced drag otherwise experienced at altitude. This effect is more noticeable the closer the aircraft gets to the ground, hence the ‘floating’ sensation one experiences when entering the flare to land and, likewise, the ‘sag’ one experiences when climbing out of ground effect.

As you can see, the formula for drag is much the same as the formula for lift. It is comprised of the same factors, meaning that an increase in lift will equate to an increase in drag.

Variation of Drag Coefficient with Angle of Attack

If the drag coefficient of a wing is plotted against angle of attack, the result would be a ‘typical’ drag curve. There are three important points to note:

Minimum coefficient of drag occurs at ~0° to 0.5° angle of attack.
On either side of this minimum drag, there is a gradual increase of drag up to ~8° angle of attack.
The increase of drag is accelerated at angles of attack beyond 8°, especially after the stalling angle has been exceeded when the airflow becomes turbulent.

Parasite drag is directly proportional to the square of the indicated speed, and induced drag is inversely proportional to the square of the indicated airspeed. Therefore, the total drag of an aircraft at any one speed consists partly of parasite drag and partly of induced drag.

There are several important points to note about a ‘typical’ total drag curve:

As the indicated airspeed increases, parasite drag increases.
As the indicated airspeed decreases, induced drag increases.
The total drag is determined by adding up the values of the two drags at any indicated airspeed.
The indicated airspeed for minimum total drag occurs at the point where profile and induced drag are equal. Minimum drag speed is important for economical operations, as it gives us best range. This also equates to the best lift-to-drag ratio.

If we combine the coefficient of lift and coefficient of drag graphs, we get the graph as shown below.

If we plot this combined graph onto a single graph, we are left with the below. This is known as the lift-to-drag ratio graph.

The lift-to-drag ratio (L/D ratio) is the ratio of the coefficient of lift to the coefficient of drag of an aerofoil at various angles of attack. The most efficient wing is one that will produce the greatest lift for the least amount of drag. The lift-to-drag ratio will determine the efficiency and performance of an aerofoil. For example:

At 3° angle of attack, L/D ratio = 24:1.
At 15° angle of attack, L/D ratio = 11:1.

Important points about the lift-to-drag ratio curve:

The L/D ratio increases rapidly up to 3° or 4° angle of attack, at which point, lift may be 12 to 20 times greater than the drag.
After 4° angle of attack, the L/D ratio decreases steadily, because lift is still increasing but drag is increasing at a faster rate.
After 15° angle of attack (stalling angle), drag is ~4 to 5 times greater than lift; thus, the L/D ratio rapidly decreases.
The angle that gives the best L/D ratio in level flight is the angle at which the aerofoil is most efficient and gives the best all-round performance, i.e., best glide and best range. For most aerofoils, this angle of attack is ~3° or 4°.

Discuss the following questions in class now.

State the Drag Formula
Draw the Drag Tree
Draw the Coefficient of Drag Curve (label the important points)
Draw the Total Drag Curve (label the important points)
How can we reduce Profile Drag?
What is the Transition Point?
What is the Separation Point?
What is the Stagnation Point?
What is the purpose of a Laminar Flow Aerofoil?
What are the disadvantages of Laminar Flow Aerofoils?
How can we reduce Interference Drag?
Define Aspect Ratio
State the Induced Drag formula

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