Fundamentals of Aerodynamics
The law of conservation of energy states that energy may neither be created nor destroyed. Motion is the act or process of changing place or position. An object may be in motion with respect to one object and motionless with respect to another. For example, a person sitting quietly in an aircraft flying at 200 knots is at rest or motionless with respect to the aircraft; however, the person and the aircraft are in motion with respect to the air and to the earth.
Air has no force or power except pressure, unless it is in motion. When it is moving, however, its force becomes apparent. A moving object in motionless air has a force exerted on it as a result of its own motion. It makes no difference in the effect then, whether an object is moving with respect to the air or the air is moving with respect to the object.
The term “aerodynamics” is generally used for problems arising from flight and other topics involving the flow of air. [Ludwig Prandtl, 1949]
The dynamics of gases, especially atmospheric interactions with moving objects. [The American Heritage - Dictionary of the English Language, 1969]
"Aerodynamics" is the study of the interaction between the air and solid bodies moving in it. "Newton’s third law of motion states that for every action there is an equal and opposite reaction". Aircraft, helicopters, gliders and autogyros produce their lift by pushing down on a mass of air. They are supported in the air when they force down an amount of air equal to their own weight. This is determined basically by the density of the air through which they are flying and the speed with which they pass through the air.
Airflow around a body
Atmosphere exerts pressure, which exerts a force on all bodies, is called static pressure and acts equally in all directions. When air is in motion, however, it possesses an additional energy (kinetic energy) due to the fact that it is moving, and the faster it moves the more kinetic energy it has. If moving air is now brought to rest against some object, the kinetic energy is turned into pressure energy. This pressure on the surface of the body which causes the moving air to stop is called dynamic pressure. The value of dynamic pressure depends on the density of the air and its speed.
Static Pressure
The weight of the air in the atmosphere creates a pressure. This is called the static pressure caused by still air. Any object in still air will experience equal pressures in all directions. Therefore the forces caused by the static pressure and which act on any object are balanced. There is no resultant force at all acting on the object.
The ICAO standard atmosphere defines the static pressure at sea level.
Dynamic Pressure
Air in motion possesses additional energy due to its speed. If this moving air is brought to rest on a surface, the energy released causes an increase in pressure in addition to the atmospheric pressure. The additional pressure registered on this surface is known as dynamic pressure or an object in moving air will experience an additional pressure in the direction of the motion of air.
At low speeds the dynamic pressure is small compared with the static pressure. However, at high speeds the dynamic pressure increases considerably.
Total Pressure
The total pressure is the sum of the static pressure and dynamic pressure.Kinetic Energy
Kinetic energy is that energy which is associated with motion. Speeding up the movement of air or any object increases its kinetic energy.
Potential Energy
Potential energy is the energy possessed by a body because of its position or its configuration. The potential energy of air relates to its pressure, and increasing its pressure increases its potential energy.
Total Energy
The total energy of the air is the sum of the kinetic and the potential energy.
Bernoulli’s Principle of Differential Pressure
A half-century after Newton formulated his laws, Daniel Bernoulli, a Swiss mathematician, explained how the pressure of a moving fluid (liquid or gas) varies with its speed of motion. Bernoulli’s Principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases. This principle explains what happens to air passing over the curved top of the airplane wing.
A practical application of Bernoulli’s Principle is the venturi tube. The venturi tube has an air inlet that narrows to a throat (constricted point) and an outlet section that increases in diameter toward the rear. The diameter of the outlet is the same as that of the inlet. The mass of air entering the tube must exactly equal the mass exiting the tube. At the constriction, the speed must increase to allow the same amount of air to pass in the same amount of time as in all other parts of the tube. When the air speeds up, the pressure also decreases. Past the constriction, the airflow slows and the pressure increases.
Since air is recognized as a body, and it is understood that air will follow the above laws, one can begin to see how and why an airplane wing develops lift. As the wing moves through the air, the flow of air across the curved top surface increases in velocity creating a low-pressure area.
Here,
- 𝜌 = Density of gas
- 𝑝1 or 𝑝2 = Pressure of gas
- 𝑐1 or 𝑐2 = Velocity of gas
Although Newton, Bernoulli, and hundreds of other early scientists who studied the physical laws of the universe did not have the sophisticated laboratories available today, they provided great insight to the contemporary viewpoint of how lift is created.
Aerodynamics of the Airfoil
An airfoil, whether being a wing of an aircraft, a rotor of a helicopter or the blade of a propeller, is a specially shaped body designed to react on the flow of air that passes over it. This reaction (or, actually: a combination of reactions) is known as aerodynamic lift and drag. It is determined to a great extent by the shape of the surface.
This figure shows that the narrow part of the Venturi tube has a shape which is similar to that of a typical subsonic airfoil. Subsonic aerodynamics consider the airflow to be non compressible, and the airfoils actually used for aircraft are similar to this figure.
They all have a round leading edge and a maximum thickness at approx. one third of the distance between the leading and the trailing edge. From that point they taper smoothly to the trailing edge. Subsonic airfoils may be asymmetrical or symmetrical in shape. A symmetrical airfoil has the same curve on each side of the chord line, but the shapes of the top and the bottom of an asymmetrical airfoil are different to each other, with the upper side being larger than the lower.
Aerodynamic Phenomena
Free Stream Airflow
The free stream airflow around a shape is the clean flow, distant enough to be unaffected by the body passing through it, and does not change direction. Lines which show the direction of the flow are called ‘streamlines’. A body shaped to produce the least possible resistance is called a ‘streamline shape’. The amount of free stream air is directly relative to the resistance applied to the airflow (DRAG). Resistance creates turbulence (Figure 2). The greater the resistance, the greater the turbulence; therefore the further the locality of the free stream air. The amount of drag depends on when the airflow separates. The airflow around the ball has remained attached for longer.
Friction
Skin friction is caused by the resistance which is set up when relative motion exists between the surface of a body and the air; contact between the two gives rise to a layer of retarded air in immediate contact with the surface over which it is passing. This layer is known as the boundary layer and the amount of drag arising from it is determined by the nature and thickness of the flow in the layer.
Boundary layer
Transition Point
That point on the wing at which the boundary layer changes from laminar to turbulent flow is called the transition point. Because the increase in drag resulting from a turbulent boundary layer is considerable, care is taken to preserve laminar flow over as much of the wing as possible, for example in a true laminar flow wing shown in Figure 5. Skin friction is a major source of drag at high speeds and it is one of the most difficult to reduce. It can never be eliminated completely.
As the speed increases the transition point tends to come further forward, so more of the boundary layer becomes turbulent and the skin friction becomes greater. If this much is understood it will be obvious that the main purpose of research work has been to discover why the transition point moves forward, and how its movement can be controlled so as to maintain laminar flow over as much of the surface as possible. On examining the flow in the boundary layer closely, it will be seen that it differs from the free air stream in that the particles of air are rotating as they move rearwards, those on the upper surface in a clockwise direction, and those below anti-clockwise, in exactly the same way as ball bearings when rolled along a surface.
Stagnation point
The stagnation point, as shown below in Figure 6 is that point at which the air is brought to rest by the leading edge and the point from which the boundary layer originates. The stagnation point is also the first point of contact of relative airflow, or, the point on the leading edge of an aerofoil where the airflow divides. Some airflow goes over the wing and some goes under the wing.
Separation Points
The separation points are the points on the wing at which the boundary layers break away from the surface.
Wake
The wake consists of the unsteady rotational flow, resulting from separation of the boundary layers from the wing, and which tends to be dragged behind the trailing edge. For a chord of seven feet the wake is about four to five inches in depth during flight at small angles of attack.
Laminar flow
Laminar flow, sometimes referred to as viscous flow, is flow in which the particles of the fluid move in an orderly manner and retain the same relative positions in successive cross sections. In other words, a flow that maintains the shape of the body over which it is flowing. This type of flow is illustrated in Figure 8.2.3, where it can be seen that the successive cross sections are represented by lines that run parallel to one another hugging the shape of the body around which the fluid is flowing. It may be described as the smooth parallel layers of air flowing over the surface of a body in motion, i.e. streamline flow.
Turbulent flow,
Turbulent flow is flow in which the particles of fluid move in a disorderly manner occupying different relative positions in successive cross sections (Figure 8.2.4). This motion results in the airflow thickening considerably and breaking-up.
Relative airflow,
Whatever direction the airplane is flying, the relative wind is in the opposite direction. If the airplane is flying due north, and someone in the airplane is not shielded from the elements, that person will feel like the wind is coming directly from the south.
We consider the effect of air resistance by studying the behavior of airflow over a flat plate. If a flat plate is placed edge on to the relative airflow, then there is little or no alteration to the smooth passage of air over it. On the other hand, if the plate is offered into the airflow at some angle of inclination to it angle of attack (AOA), it will experience a reaction that tends to both lift it and drag it back. This is the same effect that you can feel on your hand when placed into the airflow as you are travelling, e.g. in the open topped car mentioned earlier. The amount of reaction depends upon the speed and AOA between the flat plate and relative airflow.
The total reaction on the plate caused by it disturbing the relative airflow has two vector components as shown in figure 8.2.6. One at right angles to the relative airflow known as lift and the other parallel to the relative airflow, opposing the motion, known as drag.
The effect may be summarized as follows: if a flat plate is inclined in a moving stream of air, the air flowing over the upper surface decreases in pressure. This creates a depression over the upper surface which produces a sucking effect on the plate. At the same time, the higher pressure on the underside of the plate produces an upward force.
Coanda Effect
Viscosity is defined as a fluid’s resistance to flow. One of the consequences of this is the tendency of a viscous fluid to follow a reasonable curvature of, for example, the back of a spoon, or the top surface of a wing.
Upwash and downwash
We consider the effect of air resistance by studying the behavior of airflow over a flat plate. If a flat plate is placed edge on to the relative airflow, then there is little or no alteration to the smooth passage of air over it.
On the other hand, if the plate is offered into the airflow at some angle of inclination to it (angle of attack), it will experience a reaction that tends both to lift it and drag it back. This is the same effect that you can feel on your hand when placed into the airflow as you are travelling. The amount of reaction depends upon the speed and angle of attack between the flat plate and relative airflow.
Upwash
Upwash is created in the same way, when the flat plate is inclined at some AOA to the relative airflow, the streamlines are disturbed. An up wash is created at the front edge of the plate causing the air to flow through a more constricted area, in a similar manner to flow through the throat of a Venturimeter. The net result is that as the airflows through this restricted area, it speeds up. This in turn causes a drop in static pressure above the plate (as explained in the Bernoulli‟s principle)
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Downwash
In the simplest form, lift is generated by the wing diverting air down, creating the downwash. When compared with the static pressure beneath it
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In the picture, the jet has flown above the fog, not through it. The hole caused by the descending air is clearly visible. As we will see, it is the adjustment of the magnitude of the downwash that allows the wing to adjust for varying loads and speeds. From Newton’s second law, one can state the relationship between the lift on a wing and its downwash: The lift of a wing is proportional to the amount of air diverted per time times the vertical velocity of that air.
Downwash and Newton’s Third Law of Motion
Formation of Vortices
The action of the airfoil that gives an aircraft lift also causes induced drag. When an airfoil is flown at a positive AOA, a pressure differential exists between the upper and lower surfaces of the airfoil. The pressure above the wing is less than atmospheric pressure and the pressure below the wing is equal to or greater than atmospheric pressure. Since air always moves from high pressure toward low pressure, and the path of least resistance is toward the airfoil’s tips, there is a spanwise movement of air from the bottom of the airfoil outward from the fuselage around the tips. This flow of air results in “spillage” over the tips, thereby setting up a whirlpool of air called a vortex.
At the same time, the air on the upper surface has a tendency to flow in toward the fuselage and off the trailing edge. This air current forms a similar vortex at the inboard portion of the trailing edge of the airfoil, but because the fuselage limits the inward flow, the vortex is insignificant. Consequently, the deviation in flow direction is greatest at the outer tips where the unrestricted lateral flow is the strongest.
As the air curls upward around the tip, it combines with the downwash to form a fast-spinning trailing vortex. These vortices increase drag because of energy spent in producing the turbulence. Whenever an airfoil is producing lift, induced drag occurs and wingtip vortices are created.
Just as lift increases with an increase in AOA, induced drag also increases. This occurs because as the AOA is increased, there is a greater pressure difference between the top and bottom of the airfoil, and a greater lateral flow of air; consequently, this causes more violent vortices to be set up, resulting in more turbulence and more induced drag.
The intensity or strength of the vortices is directly proportional to the weight of the aircraft and inversely proportional to the wingspan and speed of the aircraft. The heavier and slower the aircraft, the greater the AOA and the stronger the wingtip vortices. Thus, an aircraft will create wingtip vortices with maximum strength occurring during the takeoff, climb, and landing phases of flight. These vortices lead to a particularly dangerous hazard to flight, wake turbulence.
Avoiding Wake Turbulence
Wingtip vortices are greatest when the generating aircraft is “heavy, clean, and slow.” This condition is most commonly encountered during approaches or departures because an aircraft’s AOA is at the highest to produce the lift necessary to land or take off. To minimize the chances of flying through an aircraft’s wake turbulence:
- Avoid flying through another aircraft’s flight path.
- Rotate prior to the point at which the preceding aircraft rotated when taking off behind another aircraft.
- Avoid following another aircraft on a similar flight path at an altitude within 1,000 feet.
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| Avoid following another aircraft at an altitude within 1,000 feet |
- Approach the runway above a preceding aircraft’s path when landing behind another aircraft and touch down after the point at which the other aircraft wheels contacted the runway.
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| Avoid turbulence from another aircraft |
A hovering helicopter generates a down wash from its main rotor(s) similar to the vortices of an airplane. Pilots of small aircraft should avoid a hovering helicopter by at least three rotor disc diameters to avoid the effects of this down wash. In forward flight, this energy is transformed into a pair of strong, high-speed trailing vortices similar to wing-tip vortices of larger fixed-wing aircraft. Helicopter vortices should be avoided because helicopter forward flight airspeeds are often very slow and can generate exceptionally strong wake turbulence.
Wind is an important factor in avoiding wake turbulence because wingtip vortices drift with the wind at the speed of the wind. For example, a wind speed of 10 knots causes the vortices to drift at about 1,000 feet in a minute in the wind direction. When following another aircraft, a pilot should consider wind speed and direction when selecting an intended takeoff or landing point. If a pilot is unsure of the other aircraft’s takeoff or landing point, approximately 3 minutes provides a margin of safety that allows wake turbulence dissipation.
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When the vortices of larger aircraft sink close to the ground (within 100 to 200 feet), they tend to move laterally over the ground at a speed of 2 or 3 knots (top). A crosswind will decrease the lateral movement of the upwind vortex and increase the movement of the downwind vortex. Thus a light wind with a cross runway component of 1 to 5 knots could result in the upwind vortex remaining in the touchdown zone for a period of time and hasten the drift of the downwind vortex toward another runway (bottom) |
Stagnation;
Stagnation point is a point in the flow field in which velocity of the fluid becomes zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure.
Airfoils and airfoil terminology
Aerofoil terminology
Leading Edge: The most forward edge of the aerofoil.
Trailing Edge: The most backward edge of the aerofoil.
Camber: Camber is the term used for the upper and lower curved surfaces of the aerofoil section, where the mean camber line is a line drawn halfway between the upper and lower cambers.
Cord Line: Chord line is the line joining the centres of curvatures of the leading and trailing edges or An imaginary line extending from the tip of the leading edge of the aerofoil to the trailing edge.. [Note that this line may fall outside the aerofoil section dependent on the amount of camber of the aerofoil being considered]
Angle of Attack: The acute angle between the cord line and direction of the relative airflow. It is affected by both the engine RPM and aircraft forward speed.
Angle of incidence (AOI): Angle of incidence (AOI) is the angle between the relative airflow and the longitudinal axis of the aircraft. It is a built-in feature of the aircraft and is a fixed “rigging angle.” On conventional aircraft the AOI is designed to minimize drag during cruise, thereby maximizing fuel efficiency.
Thickness/chord ratio (t/c): Thickness/chord ratio (t/c) is simply the ratio of the maximum thickness of the aerofoil section to its chord length, normally expressed as a percentage. It is sometimes referred to as the fineness ratio and is a measure of the aerodynamic thickness of the aerofoil.
Drag: Air resistance is known as drag.
Drag
Drag is the force that resists movement of an aircraft through the air. There are two basic types: parasite drag and induced drag. The first is called parasite because it in no way functions to aid flight, while the second, induced drag, is a result of an airfoil developing lift.
Parasite Drag
Parasite drag is comprised of all the forces that work to slow an aircraft’s movement. As the term parasite implies, it is the drag that is not associated with the production of lift. This includes the displacement of the air by the aircraft, turbulence generated in the airstream, or a hindrance of air moving over the surface of the aircraft and airfoil. There are three types of parasite drag: form drag, interference drag, and skin friction.
Form Drag
Form drag is the portion of parasite drag generated by the aircraft due to its shape and airflow around it. Examples include the engine cowlings, antennas, and the aerodynamic shape of other components. When the air has to separate to move around a moving aircraft and its components, it eventually rejoins after passing the body. How quickly and smoothly it rejoins is representative of the resistance that it creates, which requires additional force to overcome.
Notice how the flat plate causes the air to swirl around the edges until it eventually rejoins downstream. Form drag is the easiest to reduce when designing an aircraft. The solution is to streamline as many of the parts as possible.
Interference Drag
Interference drag comes from the intersection of airstreams that creates eddy currents, turbulence, or restricts smooth airflow. For example, the intersection of the wing and the fuselage at the wing root has significant interference drag. Air flowing around the fuselage collides with air flowing over the wing, merging into a current of air different from the two original currents. The most interference drag is observed when two surfaces meet at perpendicular angles. Fairings are used to reduce this tendency. If a jet fighter carries two identical wing tanks, the overall drag is greater than the sum of the individual tanks because both of these create and generate interference drag. Fairings and distance between lifting surfaces and external components (such as radar antennas hung from wings) reduce interference drag.
Skin Friction Drag
Skin friction drag is the aerodynamic resistance due to the contact of moving air with the surface of an aircraft. Every surface, no matter how apparently smooth, has a rough, ragged surface when viewed under a microscope. The air molecules, which come in direct contact with the surface of the wing, are virtually motionless. Each layer of molecules above the surface moves slightly faster until the molecules are moving at the velocity of the air moving around the aircraft. This speed is called the free-stream velocity. The area between the wing and the free-stream velocity level is about as wide as a playing card and is called the boundary layer. At the top of the boundary layer, the molecules increase velocity and move at the same speed as the molecules outside the boundary layer. The actual speed at which the molecules move depends upon the shape of the wing, the viscosity (stickiness) of the air through which the wing or airfoil is moving, and its compressibility (how much it can be compacted).
The airflow outside of the boundary layer reacts to the shape of the edge of the boundary layer just as it would to the physical surface of an object. The boundary layer gives any object an “effective” shape that is usually slightly different from the physical shape. The boundary layer may also separate from the body, thus creating an effective shape much different from the physical shape of the object. This change in the physical shape of the boundary layer causes a dramatic decrease in lift and an increase in drag. When this happens, the airfoil has stalled.
In order to reduce the effect of skin friction drag, aircraft designers utilize flush mount rivets and remove any irregularities that may protrude above the wing surface. In addition, a smooth and glossy finish aids in transition of air across the surface of the wing. Since dirt on an aircraft disrupts the free flow of air and increases drag, keep the surfaces of an aircraft clean and waxed.
Induced Drag
The second basic type of drag is induced drag. It is an established physical fact that no system that does work in the mechanical sense can be 100 percent efficient. This means that whatever the nature of the system, the required work is obtained at the expense of certain additional work that is dissipated or lost in the system. The more efficient the system, the smaller this loss.
In level flight, the aerodynamic properties of a wing or rotor produce a required lift, but this can be obtained only at the expense of a certain penalty. The name given to this penalty is induced drag. Induced drag is inherent whenever an airfoil is producing lift and, in fact, this type of drag is inseparable from the production of lift. Consequently, it is always present if lift is produced.
An airfoil (wing or rotor blade) produces the lift force by making use of the energy of the free airstream. Whenever an airfoil is producing lift, the pressure on the lower surface of it is greater than that on the upper surface (Bernoulli’s Principle). As a result, the air tends to flow from the high pressure area below the tip upward to the low pressure area on the upper surface. In the vicinity of the tips, there is a tendency for these pressures to equalize, resulting in a lateral flow outward from the underside to the upper surface. This lateral flow imparts a rotational velocity to the air at the tips, creating vortices that trail behind the airfoil.
The difference in downwash at altitude versus near the ground. Bearing in mind the direction of rotation of these vortices, it can be seen that they induce an upward flow of air beyond the tip and a downwash flow behind the wing’s trailing edge.
This induced downwash has nothing in common with the downwash that is necessary to produce lift. It is, in fact, the source of induced drag. Downwash points the relative wind downward, so the more downwash you have, the more your relative wind points downward. That's important for one very good reason: lift is always perpendicular to the relative wind. You can see that when you have less downwash, your lift vector is more vertical, opposing gravity. And when you have more downwash, your lift vector points back more, causing induced drag. On top of that, it takes energy for your wings to create downwash and vortices, and that energy creates drag.
The greater the size and strength of the vortices and consequent downwash component on the net airflow over the airfoil, the greater the induced drag effect becomes. This downwash over the top of the airfoil at the tip has the same effect as bending the lift vector rearward; therefore, the lift is slightly aft of perpendicular to the relative wind, creating a rearward lift component. This is induced drag.
In order to create a greater negative pressure on the top of an airfoil, the airfoil can be inclined to a higher AOA. If the AOA of a symmetrical airfoil were zero, there would be no pressure differential, and consequently, no downwash component and no induced drag. In any case, as AOA increases, induced drag increases proportionally. To state this another way—the lower the airspeed, the greater the AOA required to produce lift equal to the aircraft’s weight and, therefore, the greater induced drag. The amount of induced drag varies inversely with the square of the airspeed.
Conversely, parasite drag increases as the square of the airspeed. Thus, in steady state, as airspeed decreases to near the stalling speed, the total drag becomes greater, due mainly to the sharp rise in induced drag. Similarly, as the aircraft reaches its never-exceed speed (VNE), the total drag increases rapidly due to the sharp increase of parasite drag. As seen in the figure:
At some given airspeed, total drag is at its minimum amount. In figuring the maximum range of aircraft, the thrust required to overcome drag is at a minimum if drag is at a minimum. The minimum power and maximum endurance occur at a different point.
