# Detailed Facts About Aircraft Shock Waves: Definition, Formation, Types.

## Aircraft Shock Waves: Definition, Formation, Types.

You may not have heard of the term “shock wave” before, but you’ve most likely heard of the sonic boom which is actually the sound produced when a shock wave from an aircraft hits the ground. They don’t just come from any aircraft, but aircraft flying at super high speeds. You can’t really see shock waves with the naked eye, but their impact can definitely be felt.

What are shock waves? In this article, you’ll find out all you need to know about shock waves including:

• The definition of shock waves and how they are formed.
• Transonic Airflow
• Supersonic Airflow
• Types of shock waves.

## Shock wave Theory: Definition and Formation

To understand shock waves, we must first look at the principles of high-speed flight and a figure known as the Mach number is key to explaining the nature of high-speed flight.

The Mach number is a ratio which is representative of the speed of an aircraft with respect to the speed of sound. In engineering, there is always the need for comparison of a parameter to a constant. In aerospace engineering, one such comparison is needed for the speed of an aircraft. There are two constant speeds in science: the speed of light and the speed of sound. The speed of sound varies from place to place as it is dependent on the density of air. The density of air is dependent on temperature, therefore the change in the speed of sound is only significant between places with large temperature differences. It is more realistic to compare the speed of an aircraft to the speed of sound, therefore a ratio called the Mach number was established.

M= V/a

Where M= Mach number

V = speed of the aircraft

a= speed of sound

The speed of an aircraft is considered subsonic when the Mach number is below 1, transonic when the Mach number is close to 1 (0.8 to 1.2) and supersonic when it is above 1.2. There are also hypersonic speeds which have very Mach numbers of 5 and above.

Sound is even more significant in flight because it moves with the same mechanism the pressure transmitted by a moving aircraft does. Sound is a result of pressure disturbances in the air being transmitted to our ears in a wavelike fashion. Sound is a longitudinal wave meaning it requires a medium to move, unlike light waves. Thus, the transmission of the pressure disturbances resulting in sound is made possible by a series of air molecules bumping into adjacent molecules until they get to the molecules close to our eardrums. Similarly, when aircraft fly through the air, pressure disturbances are transmitted through the air by normal molecular collision. These pressure disturbances are carried at the same rate as the speed of sound.

In the transonic region, some parts of the aircraft have subsonic speeds while some parts have supersonic speeds. At very high speeds, the elasticity of air, which has to do with its ability to undergo compression and expansion, has a more pronounced effect on flight. As the speeds of airflow increase, the air becomes compressed and the pressure disturbances/waves begin to accumulate in front of all the parts of the aircraft. Eventually, these buildups of pressure waves known as shock waves are formed.

Essentially, what happens is that as the aircraft starts moving faster than sound, the pressure waves do not have room to escape and travel as they normally do. The faster and faster the aircraft flies, the more and more pressure waves pile on.

The transonic speed region is where shock waves are first formed at some parts of the aircraft. In this region, there are sudden changes in the lift and drag forces, as well as the stabilising forces of the aircraft due to the erratic nature of the airflow. As the speed increases to supersonic, the shock waves become more pronounced and all around the aircraft as the air becomes more compressed. They follow aft of the aircraft in the form of a wedge or cone. Although the shock waves are of insignificant thickness, the air undergoes very significant increases in pressure, density and temperature such that sonic booms can be formed. There are mathematical equations which can be used to predict the behaviour of air and the characteristics of the shock waves in this region.

## Airflow in Transonic Regime

As the nature of the airflow changes due to changes in speed, a turbulent wake is set. This turbulence is a result of the airflow breaking away from the surface of the aircraft. Naturally, drag will increase since it is directly proportional to the square of the airspeed, however, this turbulent flow will cause even more increase in drag. As the speed of the aircraft increases, the point at which the airflow breaks away moves forward such that the turbulent wake becomes thicker and goes forward on the trailing edges of the aircraft aerofoils.

The increase in drag is accompanied by a decrease in the lift as the shock waves tend to weaken the aerodynamic efficiency of the aerofoils. There are also resultant changes in the Centre of Pressure of the aircraft, as the pressure distribution of the aircraft changes, and consequently pitching moment. All these changes can lead to an unbalancing of the aircraft. Simultaneously, the turbulent wake trailing the shock wave can strike the tailplane of the aircraft with great force. This will result in a phenomenon similar to a stall which is therefore called a ‘shock stall’. The major difference between the shock stall and the normal type of stall is that the normal stall is only prone to happening at high Angles of attack (AOAs) while the shock stall can happen at even low AOAs.

When the Mach number first reaches the transonic regime, an incipient shock wave is formed. This is a line which is normal to the surface of the aerofoil and signifies a sudden rise in the pressure and density of the air. This rise makes it more difficult for the air to flow freely, meaning the speed of the airflow decreases. Shock waves usually meet the aircraft at its region of maximum camber where the speed of the air is greatest. The turbulent wake usually starts from this point as well, because, at this point, the airspeed might be equal to or even exceed the speed of sound so there is a huge buildup of pressure waves.

The Mach number at which any point on the aerofoil first reaches the speed of sound, i.e. M=1, is called the critical Mach number. As said before, in the transonic regime, regions of the aircraft/aerofoil simultaneously have subsonic and supersonic speeds. This is because the speed of the airflow varies from point to point on the aerofoil. In the image below, we see that all the local airflow speeds are below Mach 1 when the general airflow speed is Mach 0.7. However, once the Mach number gets to 0.85, the Mach number at the region of maximum camber gets to 1. This means the critical Mach number of that aerofoil is 0.85.

Once the plane exceeds the critical Mach number, some regions of the aircraft will then have supersonic speeds. However, the plane is not said to be moving in the supersonic regime until there are no longer any local subsonic speeds.

Shock waves form at the point where the flow changes from supersonic back to subsonic. These shock waves are normal to the airflow and are thus called normal shock waves. As the speed of flow increases (still within transonic), the normal shock wave moves further back on the aerofoil, with a resultant larger area of supersonic flow. This is represented by the shaded regions in the diagram below. At this point in time, the speeds on the lower surface of the aerofoil would also have increased so that a shock wave is formed on the lower surface too. As the speed is increased further, the upper and lower surface shock waves both move to the trailing edge of the aerofoil so that almost the entire aerofoil is surrounded by supersonic airflow. The shock waves are now no longer normal to the flow but are now oblique shock waves. If the airflow speed exceeds Mach 1, a shock wave known as a bow wave is then formed ahead of the aerofoil. Behind the bow wave, there is a small region of subsonic air flowing around the leading edge of the aerofoil, but the rest of the flow is supersonic.

Shock waves can be formed on any part of the aircraft, not just the aerofoil planes. The drag associated with shock stalls, termed ‘shock drag’ comprises two parts. The first is the ‘wave drag’ which is the energy dissipated due to the resistance to the wave formation. The second is the boundary layer drag due to the skin friction caused by the associated turbulent wake. Shock stalls, just like normal stalls, make the aircraft harder to control. Different aircraft have different Mach numbers at which they experience shock stalls, i.e. they have different Critical Mach numbers (Mcr).

Airflow in Supersonic Regime

We can now consider airflow in the supersonic speed regime, where there are no more any regions with local subsonic speeds. At this point, the bow wave at the leading edge and the tail wave at the trailing edge of the aerofoil are both fully developed. You can see this in the diagram below.

The shock waves formed in supersonic flight become more acute as the speed increases. In the supersonic region, this variation in the shock pattern is quite small. The variation can be understood by studying a parameter called the Mach Angle. The incipient shock wave formed due to the accumulation of the air in front of a body, as described in the previous section, acts perpendicular to the direction of airflow. As the pressure waves move from consecutive points at the speed of sound, those points will also move faster than the speed of sound. This will result in the formation of circles such that a common tangent to these circles can be drawn. This tangent is called the Mach line.

The tangent represents the limit to which the pressure wave will have moved when the point has reached its final position. The radius of the first circle, which is the distance from its centre to its tangent, represents the speed of sound. The distance from the centre of the first circle to the final position represents the speed of the aircraft, V. As stated before, the Mach number is. The acute angle, α,  formed between the line passing through the points and the common tangent is called the Mach Angle. This is illustrated in the diagram above.

If the moving point is three-dimensional, e.g. the fuselage of the aircraft,  the Mach Cone is formed. The angle at the apex will then be 2α. If the moving point is a straight line, e.g. the leading edge of a wing, a wedge is formed instead. The Mach Line represents the angle at which small wavelets are formed. The velocity of the airflow can be determined by inspecting pictures of the wavelets and measuring their angle. The faster the airflow inside the wedge region, the sharper the wedge. The air flowing outside of the wedge region is undisturbed.

Shock waves which have larger amplitudes than pressure waves form at larger angles to the aircraft’s surface. Each bump on the aircraft’s surface will have its corresponding Mach line. If the airflow speed is constant, the Mach lines will be parallel. If there is acceleration, the Mach lines will have a divergent outlook as the Mach Angles become more acute with increasing speed. If there is deceleration, the Mach lines will have a convergent outlook as the Mach Angles become less acute with decreasing speed. Shock waves travel faster than sound. They are at a steeper angle than the Mach Lines

The boundary layer is almost insignificant in supersonic flow. This is because here, it is thin as compared to subsonic, transonic and hypersonic flows. Also, the forces of viscosity within it are small. These factors contribute greatly to supersonic flow’s ability to turn sharp corners. It also simplifies supersonic flow a bit.

## Types of Shock Waves

Here, we will look at normal and oblique shock waves in more detail.

• Normal shock waves: this is the basic type of shock wave and is so called because its wavefront is normal (perpendicular) to the incident airflow. They arise when the flow changes from supersonic to subsonic along the surface of the aerofoil. Normal shock waves are used in the inlet compression system of gas turbine engines in supersonic aircraft. This is so that they can absorb some of the kinetic energy of the incident airflow before it enters the engine; the engines operate under subsonic conditions.

• Oblique shock waves: these shock waves are inclined with respect to the (incident) airflow coming from the leading edge. They are formed when the airflow at supersonic speeds meets a concave corner such as a wedge. Hitting the corner forces the flow to slow down, turn into itself and compress, causing oblique shock waves to occur as Mach lines (M1 and M2 in the diagram below) converge. The incident air will keep flowing straight until it hits the shock wave, causing the streamlines of the airflow to be deflected. [

The oblique shock waves formed to cause a decrease in the magnitude and velocity of the airflow. This is because it is only the component of the velocity that is perpendicular to the shock waves that is reduced. The component which is parallel to the shock wave does not change as it passes through the shock wave. The resulting new direction of the velocity will be parallel to the aircraft surface. The airflow after passing the wedge will have greater pressure, density(due to compression) and temperature, and a slightly lower velocity as seen in the image below. The lines of the airflow are also closer to each other. This type of supersonic flow is termed compressive flow. It occurs when the supersonic flow goes through shock waves, at the leading edge of the wing or the nose of the fuselage

## Expansion Waves

Expansion waves are essentially the opposite of (oblique)shock waves, but they are worth considering because they are associated with the formation of shock waves in high-speed flight. They are formed when supersonic flow meets a convex corner. When the airflow meets this corner, it expands, i.e., expansive flow. This means its density, temperature and pressure decrease. The lines of flow are further apart from each other. However, the speed increases. The Mach Lines also experience change. The Mach line after expansion of the airflow is at a more acute angle to the surface than the initial Mach Line is to the initial surface. This can be seen in the diagram below. The flow changes gradually, not suddenly as is the case with supersonic flow meeting oblique shock waves. This is because the Mach Lines now diverge. Although the change is gradual, it still happens much faster than in the subsonic flow.

There is a limit to the angle at which supersonic airflow can turn at one expansion wave, however, an arrangement of successive expansion waves can allow for a larger overall angle. This will result in even more gradual changes in density, pressure, the direction of flow and temperature. This allows for supersonic flow to pass both sharp corners and curved surfaces. This is beneficial to flight as curved surfaces enable slower speeds for supersonic aircraft.

The application of the phenomena of expansive and compressive flow can now be explained with a double-wedge aerofoil. At zero AOA, there will be compressive flow at the nose. This means the shock waves there will cause increases in temperature, pressure and density, and a decrease in speed. At the point of maximum camber, there will be expansive flow and its corresponding effects will be demonstrated by the airflow at the trailing edge of the aerofoil. Finally, the compressive flow will occur again.

References

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