When I heard about “breaking the sound barrier” for the first time, this seemed to me even more supernatural than, for example, a bunch of metal weighing more than 77000 kg lifting up from the ground and transporting about 180 passenger from one place to another. Coincidentally, the same science made me understand both phenomena, but still nowadays, after having studied a bit of aerodynamics, I am impressed by videos showing fighters breaking the sound barrier.

But what does sound have to do with the speed? Why is the sound a sort of physical limit to the speed of a body displacing in the air? What happens when this barrier is broken? Are there closer examples of supersonic behaviors in our day-to-day?

What is sound?

We can define sound as “something that you can hear or that can be heard”. And since that “hear” itself means “become conscious of a sound using your ears”, we can imagine the ear as a hypersensitive membrane that whenever it vibrates, it communicates to the brain this piece of information called sound. Being said that, imagine a bell ringing. The metal structure vibration disturbs the surrounding air layer and this disturbance itself, unsettle the adjacent air layer and so on, continuously, until finally hitting our hypersensitive membrane, the ear. In physical terms, we have just described the propagation process of a sound wave. A funny way to visualize the propagation of a longitudinal wave (as it is the sound) is using one of those slinkies.

Notice that the sound propagation through the air has an associated (finite) speed, i.e, when the phenomenon causing the air disturbance happens (the bell ringing in our example), it takes a certain amount of time to reach our ears. This amount of time can be very small, but it is not instantaneous (what would mean infinite speed of propagation). A good exercise to be aware of the speed of sound it is to observe the time elapsed between the lightning (light propagating) and the thunder (sound propagating). If a lightning happens very far away from our current position, the bang of the thunder takes few seconds to reach us (the distance, by the way, can be easily calculated).

We can visualize the sound wave propagation by the air particles movement. An object displacement disturbs the air particles surrounding it and these particles, by themselves, disturb the adjacent particles until finally they reach our ears, which detect this disturbance. We could measure the speed of this wave propagation by observing the displacement of this domino effect of the particles, i.e., measuring the position of the next domino piece to fall. For future references, we will call this “place” wavefront. In other words, the speed of sound can be measured by observing the displacement of the wavefront.

Moving at the speed of sound

Now we are ready to imagine a moving object, let’s say an aircraft, which produces sound (Figure 1). The faster the object moves, the closer the wavefronts are to each other (related to the displacement direction) until the point where the object reaches the speed of sound in that environment, such that a new wavefront is produced even before the next one leaves the sound source, creating a mega-front of coincident waves (in this example, at the nose of the aircraft), the so-called shock wave. Notice that even if the aircraft of our example was not producing any sound, the pressure build-up in the surrounding air caused simply by the supersonic displacement would still be able to cause shock waves.

Figure 1. Sound wavefronts with the source (object) displacing at speed less than the speed of sound (first, on the left), equals to the speed of sound (in the middle) and greater than the speed of sound (last, on the right). If the object was an aircraft, the arrow would corresponding to the nose. (Source: Wikipedia)

If we think again the sound propagation in the air as particles micro-shocks, when the aircraft nose is moving at the speed of sound, the summation of all the collisions caused by the coincident wavefronts will be so intense (and often) that will provoke a brutal air resistance, preventing the object to speed up more. It is like there was a barrier at that very speed. For a long time, the engineers believed that this sound barrier was impassable, until the October 14th, 1947, when the captain Charles (Chuck) Yeager overcame the speed of sound, flying the experimental aircraft Bell XS-1. Many aspects of the previous aircraft were improved in order to achieve the sound barrier breaking, but we could roughly say that the most decisive factors were a powerful engine and a structure effective enough to get along the discontinuities of the supersonic flight.

Figure 2. Bell XS-1. First aircraft to fly beyond the sound “barrier”. (Source: NASA)

When we are dealing with supersonic speeds (this meaning speeds greater than the speed of sound), we usually use an dimensionless quantity called Mach number (because of Ernst Mach) which is defined by the ratio of the local speed of the flow to the speed of sound at that same temperature and pressure conditions (and yes, the temperature, mainly, is able to considerably affects the speed of sound). Notice that we said speed of the flow instead of speed of the aircraft. Under the so called assumption of “steady atmosphere” we can use these two terms indistinctly such that we can imagine the equivalent situation in which the aircraft is at rest and the “wind” is blowing at the given speed. Being said that, we can say that the u in the equation of the Figure 3 is the speed of the aircraft.

Figure 3. Mach number: u is the speed of the flow and c is the speed of sound propagation.

For instance, imagine that a fighter F/A-18 Hornet is moving in low altitude, at 1500 km/h (about 810 kt). In such conditions (where the speed of sound is around 1235 km/h or 660 kt), the aircraft would be moving at Mach around 1.2, and, therefore, supersonic, since the Mach number is greater than 1. Flights at a corresponding speed lower than Mach 1 are called subsonic (for example, the nowadays airliners flights, since the Concorde is retired). In a Mach range surrounding 1 (0.7, for example) we can also call it a transonic flight. For Mach number greater than 5, we call it a hypersonic flight.

Figure 4. The Concorde was a passenger aircraft able to fly at supersonic speeds. It was operated from 1976 to 2003. (Source: pixabay).

An important fact to highlight is that the speed of sound varies according to the air temperature, and therefore, to the altitude. For example, at sea level, the speed of sound is about 1225 km/h (661 kt), but at 10,000 m (32,800 ft), which is more or less the cruising altitude of an airliner, the temperature is lower and the speed of sound drops to 1078 km/h (582kt) (try it yourself at this calculator). Putting in simpler terms, for example, at sea level, the air is more dense, less incompressible and, then, more “resistant” to the supersonic flight at this altitude, more “demanding”, this meaning that it requires more energy to happen.

Where are the shock waves?

A shock wave, physically, is a very thin region (with thickness of around 1 mm divided by 10,000) through which the supersonic flow passes by, having your properties drastically changed: temperature and pressure increase, speed (of the flow) decreases, etc. We can realize that it may be very challenging to live with this phenomenon. In the following items we enumerate some shock waves examples from day-to-day life. We start from the most dramatic ones to the easily observable ones.

  1. The Space Shuttle (vehicle bringing the astronauts back to the Earth) re-entering the atmosphere can reach up to Mach 25 (that is it, 25 times the speed of sound) and even in the rarefied air of the highest layers of the atmosphere, this speed is approximately 28,163 km/h (15,207 kt). As describe in the Glenn Research Center website, the energy of the shock waves are so brutal that “the chemical bonds of the diatomic molecules of the air are broken. The molecules break apart producing an electrically charged plasma around the aircraft”. To bear such conditions, the spacecraft needs a powerful system of thermal protection.
  2. As we may have seen in the video in the beginning of this text, when an aircraft flies supersonically, the shock wave shows up as a double boom which is associated to the sudden flow pressure variations: a shock wave itself, attached to the aircraft nose, and another wave known as expansion wave that, roughly speaking, happens when the flow goes through the rear part of the aircraft and gets back to its prior pressure/temperature condition. The expansion wave can be seen as a kind of white cone covering and flying along the aircraft. This is because the pressure drop can cause the water vapor condensation, forming the cone.
  3. Have you ever seen a supersonic aircraft with propellers? Probably not. Theoretically it is possible, but the propellers should be strong enough to bear and get over the sound “barrier”. In real life, this presents a very bad benefit-cost ratio. The reason is relatively simple. When the flow goes through the spinning propeller, we have two components for the flow velocity afterwards: the original direction of the flow, and, now, the direction tangent to the propeller circle. In summary, the speed magnitude of the flow increases, such that even before the aircraft is flying supersonically, it is possible that shock waves rise on the propellers, followed by, at least, a dramatic increase of the drag force.
  4. The airliners in the cruising flight are able to attain (and keep) speed values in the range of the transonic Mach (still lower than Mach 1). But if, for example, we know that the flow around the aircraft has a Mach 0.83, some parts of the aircraft may experiment supersonic flow surrounding them (that is to say, local Mach number greater than 1). One of these possible parts is the upper surface of the wing. The full story is a bit longer (although very interesting) but will skip it now, just accepting the fact that there is a pressure difference between the upper and lower surfaces of the wing (what actually makes the aircraft fly), such that it is possible to have a Mach number greater than 1, locally, even if the aircraft is flying at a speed lower than the speed of sound for that condition. We would have then, very gentle shock waves rising in the upper surface of the wing and the associated discontinuity can even be seen if we observe very carefully.

We do not have supersonic airliners anymore since the Concorde, which was able to do New York to Paris in 3.5 hours, reaching Mach 2.0. The operational costs became unaffordable to compensate keeping the flights in the passenger transportation scenario by that time (2003). But as far as the company Boom Supersonic is concerned, we can start the countdown for breaking the sound “barrier” in passengers flights again. The company promises flights from New York to London in 3h and 15min, reaching Mach 2.2, costing the same price as today’s long haul, business-class travel. Anyway, we all agree that the sound “barrier” is a myth very well overcome by the aviation and by the superman.

Note: this article was originally published in Portuguese at AeroFlap by this same author.

Flight Control Laws Engineer and Software Developer https://www.linkedin.com/in/andre-ferreira-da-silva

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