How an Aircraft Flies

During forward flight, an aircraft is kept aloft by a combination of a region of low air pressure over the upper surface of the wing with a region of high air pressure over the lower surface. The wing of the aircraft is literally sucked upwards. If you sliced off the wing tip and looked along the wing, towards the fuselage, the shape of the cut you made is known as an airfoil.

Figure 1 shows the flow (from left to right) around an airfoil visualised by introducing thin streams of white smoke into the air stream. The nose of the airfoil is called the leading edge whilst the tail is called the trailing edge. The slight nose up attitude of the airfoil indicates that it is set at a low angle of attack of 5o to the horizontal. As indicated by the white smoke filaments, the air follows a curved path over the upper surface of the airfoil. The action of the airfoil forcing the air over the upper surface causes the local air speed to increase (roughly 2.5 times greater than the flight speed of the aircraft at the leading edge) and, as explained later, this induces the pressure of the air to decrease below the normal atmospheric value (the air pressure you feel everyday).

Fig. 1 Airfoil at Low Angle of Attack.

Increasing the airfoil angle of attack forces the air to move faster over the upper surface, reducing it's pressure, and increasing the lift. However, if the angle of attack is increased to say 15o, Figure 2 shows that the air flow starts to break away from the airfoil's upper surface. Since the air flow now no longer follows the airfoil's upper surface contour, the region of low pressure becomes weaker. This causes a rapid decrease in lift which is known as airfoil stall. If this happens over the entire wing of an aircraft, the pilot will see the earth's surface rapidly approaching!

Fig. 2 Airfoil at High Angle of Attack.

As a student studying Aeronautical Engineering at the University of Limerick, you will carry out tests similar to those shown in Figures 1 and 2 in the Department of Mechanical and Aeronautical Engineering's low speed wind tunnel shown in Figure 3. This type of wind tunnel has a fan at the rear end which draws in air via a large intake (here about 1.8m diameter) which then contracts to smaller diameter of about 0.9m before exiting through the fan. Just downstream of the contraction the diameter remains at 0.9m for about 1.5m. This area is known as the working section and is where scale model aircraft are tested. The decrease in area between the intake and the working section causes the air speed to increase since the same mass of air passes through each area per second (less area, higher speed). The maximum working section airspeed of this tunnel is 40 m/s (90 mph).

Fig. 3 The Department's Wind Tunnel.

To explain why an airfoil produces lift and why the flow starts to break away from the surface as the angle of attack is increased we first have to look at how the individual air molecules interact with the airfoil surface. When air is stationary (e.g., in a room without any draughts) the molecules all move in random directions with different speeds (some as high as 500 m/s or 1120 mph). When a large mass of air moves in a particular direction (e.g., within a wind tunnel at about 40 m/s), we say it is travelling with a bulk air velocity. Each air molecule is still moving randomly about, but all the molecules are drifting in one particular direction with the bulk velocity. Confused? Well don't be! Think of a large soccer crowd made up of large groups of people where each group supports a different team and walks at different velocity. Each person is free to walk about at random whilst all the groups drift towards the stadium entrance. If a person from one group wanders into another group he will bring with him the velocity of the group he has just left. If he enters a group of people walking faster he will probably slow them down a bit. Whilst if he enters a group moving slower he will try to speed them up a bit. No doubt annoying everyone in the process! Here, the molecular velocity becomes the velocity of each person whilst the bulk air velocity is the velocity at which each group drifts towards the entrance. When one person from one group moves into another group we say he brings his momentum with him (his mass multiplied by his velocity). In a similar fashion, the random movement of air molecules can transport bulk air momentum from one place to another within a moving mass of air.

The air pressure a stationary airfoil feels is due to the intense bombardment it's surface sustains by the randomly moving air molecules. When air is forced to move past an airfoil surface, the molecules have less chance to randomly bounce off the surface and so the surface feels a lower pressure. This behaviour is known as the Bernoulli effect after Daniel Bernoulli who first discovered it in 1738. The Bernoulli effect can be easily demonstrated by holding a longish strip of paper up to your mouth which will initially droop downwards under it's own weight. If you blow hard enough over the curved top surface of the paper strip it should flutter up into a horizontal position. In a similar way, an airfoil forces the air to accelerate around the upper surface which increases the velocity and decreases the pressure of the air. When this happens to a lesser extent over the airfoil's lower surface, the wing of the aircraft is literally sucked upwards.

The Boundary Layer

No matter how smooth the surface of an airfoil seems by touch, it does not appear as a smooth plane to the air molecules passing over it. The surface of an airfoil is made up of molecules which leave spaces between each other of sufficient size to allow the air molecules to penetrate into them.

Fig. 4 Air Molecules at Airfoil Surface.

As shown in Figure 4, we can imagine the air molecules to be reflected from the surface without regard to their initial direction of impact. This behaviour can cause the bulk air velocity component of an individual molecule to change direction. When the average air velocity is taken over all the molecules, lying just above the surface, we find it's value to be zero relative to the surface (i.e., after impacting the airfoil surface as many molecules drift upstream as drift downstream). This behaviour is known as the no-slip condition since the air appears to be stuck to the airfoil surface. What effect does the no-slip condition have on the rest of the air moving around a solid object?

Fig. 5 The Free Stream Velocity.

Figure 5 indicates that at some distance d (Greek letter 'delta') away from the surface the air is free to move with the bulk velocity U, unaware that there is a surface below. This bulk air velocity is known as the free stream velocity. So, what happens within the region between the airfoil surface and the free stream? Referring again to Figure 5, imagine a line AA has been drawn through the air just above the surface. In terms of our soccer crowd, the line AA separates two groups of supporters walking at different velocities. Any person moving between the two groups will bring a certain amount of momentum with him from his previous group. In a similar fashion to the soccer crowd, any air molecules moving upward through AA from the surface will have an average bulk velocity of zero due to the no-slip condition. Therefore, the air moving above AA will suffer a loss of bulk air momentum due to the arrival of air from below AA. This reduces it's average bulk air velocity. Now consider the air molecules moving downward through AA which will have a non-zero bulk velocity. The airfoil surface below AA will gain bulk air momentum and thus, by Newton's second law (force equals rate of change of momentum), will experience a force which will try and drag the airfoil along with the air flow. This surface force is known as skin friction drag. The exchange of bulk air momentum through random molecular movements is known as the action of viscosity. The influence the airfoil surface has on the moving stream of air decreases as the plane AA moves further away from the surface.

Fig. 6 The Boundary Layer.

Thus, as illustrated in Figure 6, there is a variation in velocity from zero at the surface to the free stream value at some distance d. This velocity variation is known as a velocity profile and the region in which it occurs is known as the boundary layer. The distance d is called the boundary layer thickness. The concept of the boundary layer was first introduced by Ludwig Prandtl in 1904 and it is considered to be the region in which the effects of air viscosity are concentrated. Since then, numerous experimental studies of boundary layers over airfoils have revealed two distinct types of flow behaviour.

Fig. 7 Laminar & Turbulent Boundary Layers.

Figure 7 shows that over the airfoil's leading edge the air particles move downstream in smooth and regular trajectories without appreciable mixing between different layers of air. This type of flow is known as a laminar boundary layer. As the flow moves downstream, towards the trailing edge, the different layers of air begin to mix together and a turbulent boundary layer forms. Figure 7 shows that the flow within a turbulent boundary layer becomes highly irregular. Because of this agitated motion, clumps of the high momentum air, further away from the airfoil surface, are swirled towards the surface. This behaviour causes the velocity of the air close to the airfoil surface to be larger than in the laminar boundary layer and, although this characteristic increases the skin friction drag over the airfoil, we shall see that it makes a turbulent boundary layer less likely to break away from the airfoil surface. It should be noted that both laminar and turbulent boundary layers are very thin compared to the dimensions of the airfoil. For example, take the airfoil section half way along one wing of a medium sized passenger aircraft, where the distance between the leading and trailing edges is roughly 2 metres. At a typical cruise speed of 200 metres per second, the turbulent boundary at the trailing edge will be roughly 28 millimetres thick.

Aircraft Drag

To get the profile drag on the airfoil we have to add the skin friction drag to the form drag which comes from the fact that when the air smashes into the leading edge of the airfoil its pressure becomes higher than that at the trailing edge, and this tries to push the airfoil along with the air flow. You have probably experienced profile drag when trying to cycle home on a windy day! To get the total drag on an aircraft we have to add a third form of drag, known as the induced drag, to the profile drag of the entire aircraft.

Fig. 8 Wing Tip Trailing Vortices.

Figure 8 shows that as high pressure air leaks around the wing tip from below the wing towards the low pressure region above the wing the air rolls up into a spinning structure known as a trailing vortex. In this photograph the low air pressure regions over the aircraft's wing upper surface, and within the pair of trailing vortices, cause water molecules, normally trapped within the air, to condense out into a white mist. The two trailing vortices cause the wing lift force to tilt slightly backwards giving rise to a force which, not only keeps the aircraft aloft, but also tries to retard it's forward motion. During steady level flight, the forward thrust generated by the aircraft engines overcomes the total drag which keeps the aircraft moving such that the wing can produce enough lift and keep the aircraft in the air.

Boundary Layer Separation

To find out what causes the air flow to break away from the airfoil surface we have to first consider how the air pressure varies over the airfoil's upper surface. As shown in Figure 1, the greatest curvature of the smoke filaments is over the upper surface of the leading edge. It is within this region that the air velocity is at its maximum and, due to the Bernoulli effect, the air pressure at its minimum. As the air at the edge of the boundary layer flows over the airfoil upper surface, towards the trailing edge, its velocity decreases and its pressure increases. This rise in pressure is also felt by the slower moving air within the boundary layer. Now since air will normally flow from a region of high pressure to a region of low pressure, the slow moving air, close to the airfoil surface, has difficulty reaching the trailing edge. At low angles of attack it manages to get there, but as the angle of attack is increased, the pressure rise between the leading edge and the trailing edge increases until, the air close to the airfoil surface stops completely.

Fig. 9 Boundary Layer Separation.

As shown in Figure 9, this region of stationary air then pushes the flow away from the airfoil contour (note, for clarity, the boundary layer thickness has been highly exaggerated). We call this boundary layer separation and this is what has happened in Figure 2. Since the velocity of the air close to the airfoil surface is larger within a turbulent boundary layer than a laminar boundary layer, turbulent flow can reach higher angles of attack before separating from the airfoil surface. In most wing designs, the extra lift gained by encouraging a turbulent boundary layer to form, and thus delaying separation to higher angles of attack, outweighs the penalty of the accompanying rise in skin friction drag. On large civil aircraft, a commonly used method of encouraging a energetic turbulent boundary layer to form is to place a line of short vanes which protrude from the wing surface. These vanes are known as vortex generators and stir up the flow within the boundary layer. The next journey you make by air try and spot them out of the window.

A wise pilot will always remember that whether the boundary layer is laminar or turbulent, separation will eventually occur as the angle of attack is increased and when it does the wing will be unable to produce enough lift to keep his aircraft aloft and that's why aircraft don't always fly!

---