Huge speeds and instant transformations, mysterious harmony of forms and errors in calculations - everything is mixed in this picture. A foggy cone suddenly appears around the rapidly speeding plane, but this is not a "sound barrier". There are many incorrect stamps and common myths associated with the cone. The aerodynamics of the fog cone is interesting, and it is interesting to understand how it arises and why it looks like this. No one has ever analyzed it the way we do.
Before you - carrier-based fighter-bomber and attack aircraft F / A-18F Super Hornet, flying at a speed close to the speed of sound. The rear of the plane is hidden behind a foggy cone with even outlines: it, like a wide skirt, enveloped the tail unit. What is it and where did it come from?
Flight speed and Mach number
Aircraft flights are subsonic and supersonic. The difference between them is fundamental: the physics of the air flow around an aircraft in these modes is radically different. Between these different forms of flight is the region of transonic velocities with transient phenomena. Here are the habitats of the fog cone.
Velocity in aerodynamics is considered relative to the surrounding air, not relative to the ground or, say, the deck of an aircraft carrier. In this case, the air becomes a stream for the aircraft. In any flight, it is important not only whether it is slower or faster than sound, but also how much slower or faster: this determines the flow pattern.
The speed of sound is always considered to be local, in a given flight condition, as it depends on air temperature and therefore can change with altitude, weather and season. In summer heat, the speed of sound increases, in winter frosts it decreases. At sea level under standard atmospheric conditions, the speed of sound is 340.29 meters per second. With increasing altitude, it changes only due to temperature: changes in atmospheric pressure and density do not affect the speed of sound in any way. As it rises to the stratosphere, the speed of sound decreases with an increase in the upper frost there, dropping to 295 meters per second. From the middle of the stratosphere to its top, the speed of sound increases as the air warms up, decreases again behind the stratosphere, and then increases again.
The Mach number, denoted by the letter M, is the speed of flight or air flow (generally gas) compared to the speed of sound. We can say that the Mach number is a scale that weighs speed in "sounds". In the cartoon "38 parrots" this is the length of the boa constrictor, measured in the lengths of a parrot. In the same way, flight speed can be measured at the speed of sound - and you get the Mach number, or rather, its numerical value.
Mach number has no unit of measurement, only value. One meters per second (the considered speed) is divided by the Mach number by the same meters per second (the speed of sound) - these same units of measurement cancel each other out, and just a fraction remains, only a number. These are all the similarity criteria - dimensionless numbers adopted in aerodynamics, including the Mach number. Therefore, the unit “Mach” or “Mach” is not present in principle, and it is wrong to speak of “speed of three Machs” or “five Machs” - this is just careless jargon.
It is also wrong to speak of “speed of three Mach numbers” or “with three Mach numbers”, because the Mach number is not a constant with a constant value. It is a variable that can take on any specific value. Each speed corresponds to its own value of the Mach number. If M = 1, then this is exactly the local sound speed. For M1 (for example, M = 2, 3) - supersonic.
Near the speed of sound, or the birth of a shock wave
Take M = 0.8 at low altitude. The standard speed of sound at sea level is 340 meters per second. Multiplying it by M will give 272 meters per second - this is the speed of the aircraft relative to the air. And at what speed does the air flow around the plane? It seems, of course, with the same - 272 meters per second. But, paradoxically, this is not the case.
On convex places - the surfaces of the wing and keel, cockpit, air intakes - the air flowing around is locally accelerated. As a result, the flow velocity at different points of the aircraft is different. This difference is most evident on the wing.
The upper surface of an aircraft wing is more convex than the lower one. On it, the air flow is accelerated more.
The pressure decreases with acceleration of the subsonic flow, which is described by Bernoulli's law for the subsonic flow. This is a manifestation of the great principle of the continuity of flow, or medium. The reduced pressure above the wing "sucks" it up, creating lift. The growth of the local air speed over the wing depends on the aircraft speed and the curvature of the streamlined surface and can reach + 0.2 M.
At an aircraft speed of about M = 0.8, the local acceleration of the flowing stream leads to the appearance on the upper surface of the wing of a point with a sound speed (here the flow velocity is M = 1). At a speed of about M = 0.85, this point expands into a small supersonic region above the wing, which ends at the back of a flat surface, standing perpendicularly in the stream. The air on it instantly becomes denser, and its speed drops sharply to subsonic.
This is a supersonic shock wave - the surface of shock gas-dynamic compression of air.
Compression occurs here instantly, in leaps and bounds, at a distance of only a couple of molecular runs, in one ten-billionth of a second. A shock wave exists only in a supersonic flow; therefore, it does not appear in front of the wing, where the flow is still subsonic, but in a supersonic flow in the middle part of the wing.
With a further increase in the aircraft speed, the region of supersonic flow and the shock wave grow and extend perpendicularly from the wing into the space surrounding the aircraft. At M = 0.9, a slightly convex wing bottom begins to create a supersonic region. At M = 0.95, large supersonic regions are formed at the top and bottom of the wing, and the shock waves move to the trailing edge of the wing and lengthen by ten meters up and down from it.
With the transition to supersonic flight, the shock waves deflect back and combine behind the aircraft with the shock wave that appears from the leading edge of the wing, forming a Mach cone diverging in space at a distance from the aircraft.
A supersonic shock can leave a flow behind it both supersonic and subsonic, depending on how strong it is. In any shock, the flow always slows down and due to this it becomes denser (hence the name of the shock) - it is compacted by the incident supersonic flow. He hits the jump with great energy of his movement, like a hammer; this impact produces shock gas-dynamic compression in a supersonic shock, forming it. In the resulting tamped and compressed state, the compressed air is squeezed out beyond the jump by new portions of the compressed incoming flow.
Behind the shock wave, the air can remain compressed and flow without expansion - for example, on rigid inclined surfaces that caused the shock. In a compressed flow, the density, pressure and temperature remain the same, without returning to the pre-shock values. This means that there is no wave process with its return to the initial parameters.
We are interested in another option - the far part of the supersonic jump, extending into the surrounding space. Here, the shock-compacted air is not supported by any hard surface. When compressed, it immediately expands unhindered, returning to atmospheric pressure and density. This return to the initial state demonstrates the presence of a wave process, and the supersonic shock wave, together with the air changed behind it, forms a shock wave.
Shock Wave - Fog Paint Brush
A shock wave is a strong elastic compression propagating in the air at a supersonic speed with the subsequent restoration of the air parameters to atmospheric. Compression in the face of a shock wave is the beginning of the shock wave, its front surface and the most characteristic part. Here there is a multiple increase in density, pressure and temperature. The contraction generates a great elastic force, which, having gained freedom to act, becomes a great expansion force. It rapidly levels the resulting compression to atmospheric pressure.
Gas expansion is a form of movement of material points.
The faster this movement, the greater its inertia. It does not matter in what form it will be realized: mass is inert, and inertia keeps motion. Rapidly reaching atmospheric parameters, the accelerated expansion of the air skips them without stopping and continues inertially further, "bending" the pressure in the opposite direction and creating a vacuum.
Pressure, density and temperature in it drop significantly below atmospheric. The resulting rarefaction starts the reverse process - its compression by the surrounding atmosphere. Where the pressure is finally equalized with atmospheric pressure, the shock wave ends. By their nature, these are the usual humps and troughs for a wave on air charts.
With very strong shock waves with a huge compression in the front (much larger than in the Mach cone), the inertial force of the expansion is capable of creating a deeper rarefaction. Then recovery to atmospheric pressure may also have sufficient inertia for a second slight compression, followed by a second expansion. Such an oscillatory compression-expansion cycle occurs in powerful shock waves from large high-explosive charges, nuclear explosions, when large fireballs fall from space. But the foggy cone around the plane is formed only by a single compression-expansion.
The wave portrait of a shock wave has characteristic features on the graphs of density, pressure and temperature: a peaked peak, high, and therefore short, as well as a shallow but extended trough. Although the rarefaction in the rear part of the shock wave is quite strong (more than in the region of subsonic pressure drop above the wing), the difference with the atmosphere in it is several times less than in the front compression region. This means that the force equalizing the vacuum to atmospheric pressure is also less. Therefore, the rarefaction of air is "drawn in" by the disturbed atmosphere more slowly, existing much longer than compression.
If the air around the aircraft is humid, its temperature can be close to the dew point: the temperature at which fog falls at a given humidity. When the temperature, which falls in the shock wave along with the pressure, falls below this point, the transparent water vapor instantly condenses into a mist of water droplets. The cone of fog exposes an area with temperatures below the dew point. As soon as the temperature rises above the dew point again, the fog instantly turns back into invisible vapor.
Now the physical picture of what is happening becomes clear. The plane does not "break the sound barrier", as is often incorrectly said in such a situation. This expression is figurative and does not carry any physical meaning, since in reality - physically, aerodynamically - no "sound barrier" exists. This is just a metaphor for human achievement of the technological level that allows supersonic flights.
In the form of fog, a cold region is visible - a zone of short-term air cooling at the rear of the shock wave that has arisen around the aircraft.
In fact, the plane flies here with a constant, steady-state subsonic speed of the order of M = 0, 9. Zones of supersonic flow have formed on it and around it. They generated shock waves, behind which the structure of the shock wave was formed, as it should be in the open surrounding air. The shock surface is supported behind by a thin compressed layer, followed by a much thicker and longer layer of inertial rarefaction and cooling. In the "strong" part of this rarefied zone, air moisture condensed into fog. The atmosphere "collapses" the mist enclosing rarefaction, raising the temperature above the dew point, and the mist returns to vapor.
Why a clear cone and not a shapeless cloud?
Who gave the fog this shape - like a cone in front, even behind? Near the surface of the wing, the speed increased more strongly; the supersonic jump is more powerful than in the distance, where everything weakens to the disappearance of the jump. The more powerful the compression in the jump on the wing surface is the faster the expansion and closer behind the jump the passage of the dew point by the falling temperature. With increasing distance up and down from the wing, the compaction in the weakening supersonic shock decreases, and the shock disappears at the farthest edge of the supersonic region that has arisen around the wing. Continuing a little more in space with weakening ripple effects. This is still a large local jump, ending nearby, a dozen meters from the plane.
As one approaches its edge, the expansion in a weakening shock wave proceeds more slowly, stretching in time, and the dew point is reached later and, therefore, further behind the shock. The higher from the wing, the later and for a shorter period of time the fog appears, passing in the stream a shorter line of its life. These lines of existence of the fog contract with distance from the surface of the wing, starting later and folding into a cone.
The atmosphere finally regains pressure behind the jumps on the wings at approximately the same distance, cutting the cone at the back perpendicular to the stream and parallel to the jump in front.
Therefore, the farther from the wing, the later and for a shorter period of time the fog appears, forming by its fallout the inclined surface of the cone and its thinning towards the edges. And the rear surface of the fog, corresponding to the reverse passage of the dew point, is flat.
We can say that the foggy cone is a "sweep" of the wave process taking place in time, into the space around the aircraft.
There are stories that a misty rarefaction in a cone causes air to flow into it from nearby areas. In fact, there is no air movement from the adjacent areas into the cone. Gas flow and wave oscillation are two fundamentally different forms of motion. A shock-wave process is moving forward in the stream. It is too fast: it does not blend from different places. Compression-expansion only, without the formation of an ordered flow. Filling the foggy cone with ambient air is one of his myths.
Is he supersonic or not? Can you give an answer from the photo?
Due to the supersonic shock waves around the aircraft, the aerodynamic drag is greatly increased. A supersonic jump always creates gas-dynamic losses, spending part of the flow energy on them, or, which is the same, taking away part of the kinetic energy of the aircraft, reducing its speed. In order not to slow down, the plane needs to increase its jet thrust - and also strongly.
If you look closely, you can see a streak with dull light spots behind the jet nozzles in the main photo. This is a jet supersonic afterburner with typical Mach discs - also shock waves, in the form of which the supersonic jet is decelerated in the atmosphere. At the moment when the photo was taken, the Superset's engines were running in afterburner mode. The increased afterburner thrust allows the aircraft to fly at transonic speeds, compensating for the increased drag. The afterburner is incomplete: in full afterburner mode, the F / A-18 goes at low altitude with a "full" supersonic sound (M = 1, 2).
The photo was taken during demonstration flights at the air show. If the plane was flying at supersonic speed, the shock wave of the Mach cone could deafen to the extent of damage to the eardrums and light concussion, or even knock down spectators and knock out windows in buildings. Low-altitude supersonic flights are prohibited. They were used in military exercises to simulate the shock wave of a nuclear explosion, and the wave hit hard.
Once, two air defense fighter pilots were sent to participate in combined-arms exercises at a large training ground. Their task was to pass by a pair of supersonic Su-9s at a low altitude above the troops. And make this passage in supersonic mode, simulating the shock wave of a nuclear explosion. At the same time in the "epicenter of the explosion" several barrels of gasoline were to be blown up to simulate an atomic mushroom cloud.
For a more realistic imitation of the wave from the explosion, the pilots chose the strongest, almost direct jump at a speed of 1300 kilometers per hour, calculated and agreed on the place and time of the transition to supersonic, the duration of the passage on it and the flight route, and the fuel supply for afterburner consumption. They took off, approached the troops, dropped to three hundred meters, they did not take below for peace of mind on supersonic in the conditions of a possible manifestation of the Kazakh hummock. Having passed the landmarks of the line, they fired up the afterburner, went into supersonic sound and went low over the relief at a speed of 1300 kilometers per hour - approximately from M = 1, 15, taking into account the cold weather.
The action turned out great. A shock wave swept through the military units behind the black mushroom of smoke from the exploded barrels. High-ranking observers, who stood with binoculars and watched the actions of the troops, also did not understand how they ended up in the zone of the agreed route of the pair's flight. The shockwave deafened and knocked the observers to the ground. The caps flew in a friendly flock to the Kazakh steppe. After that, there was a lot of overbearing indignation against the pilots and organizers of the "nuclear strike". But the pilots only clearly fulfilled their task. The author knew well one of them, who told how everything happened.
In photographs with a foggy cone, carrier-based aircraft are usually "posing" - most often variants of the F / A-18 Hornet "Hornet". The pilots flying them have a lot of experience in flying low over the water, accumulated during approaches to landing on the deck of an aircraft carrier and overflights near it, which pilots demonstrate at air shows. The close surface of the ocean saturates the lower layers of the air with moisture, facilitating the formation of fog.
Fog inwave and non-wave
Shock fog does not only occur around aircraft. It happens around launch vehicles while moving in transonic modes under appropriate atmospheric conditions. Due to the geometry of the nose fairing of the rocket, the shape of the fog can differ from the cone, sometimes taking a cylindrical shape. And then it seems that the front of the launch vehicle is equipped with a muff made of fog. Due to the rapid acceleration of the rocket, such a fog appears for several seconds and does not last long, disappearing with an increase in the Mach number.
Also, the fallout of fog in the shock wave is sometimes visible visually during strong explosions in humid air. For example, when powerful high-explosive aerial bombs explode, rapidly scattering whitish surfaces are noticeable, surrounding the explosion in a bubble and scattering to the sides. This visualizes the rarefaction zones in shock waves. Rapidly passing foggy surfaces are also visible on the filming of nuclear and thermonuclear explosions - the same instantaneous fog of a shock-wave nature.
It should be noted that not all rarefaction is created by a wave process. And cooling to fog is created not only by rarefaction.
Fog can occur in rarefaction of any nature - up to the "haze" from a shot of a cork from a bottle of champagne. The often visible foggy vortex cords stretching behind the ends of aircraft wings have nothing to do with shock-wave matters: rarefaction in the form of a filamentary vortex cord interior is created by the rapid rotation of air with an inertial-centrifugal pressure reduction mechanism inside the vortex. A zone of low pressure with cooling and condensation of clouds arises in cyclones - huge rotating air masses.
Finally, fog is formed without lowering the pressure, whenever the moist air is cooled below the dew point. In winter, fog flows from an open window - the humid air of the room is cooled, mixing with the frosty outside air. The launch vehicle, fueled with liquid oxygen, also “smokes” at the start - in the area of the discharge of very cold evaporating oxygen from the tank, a dense fog appears in the cooled air. Morning fogs that cover the lowlands of the meadows and flow into the ravines are due to the nighttime cooling of the land and the surface layer of the air due to heat radiation.
But it is precisely the conical shape of the fog around the aircraft and the even, without jets and eddies, the rear boundary of the cone that show the shock-wave nature of the fog in these photographs. Therefore, a fog cone is a sure sign of transonic speed.
What will happen next? With the transition to supersonic flight (for example, with M = 1, 3), the wave pattern unfolding around the rear of the aircraft will change greatly. The shock wave over the wing will move to its trailing edge and deflect back. The compression in the shock wave will increase, and the atmospheric pressure recovery behind it will become very fast and short. The rarefaction zone will also turn into a thin layer. The fog will become the "embodiment" of the inner surface of the Mach cone, stretching from the aircraft far into space in a translucent conical blanket. And if the plane gets into drier air, then it will disappear too, leaving no visual traces of flow.
The Myth of Prandtl and Glauert
There is another common mistake associated with the fog cone. It is often called the "Prandtl-Glauert effect" (for example, there is such an article on Wikipedia). This name has been widely circulated, however, you will not find a mention of such an effect in any textbook of aerodynamics or in any scientific work. It simply doesn't exist.
There is the concept of the Prandtl – Glauert singularity. The German physicist Ludwig Prandtl was looking for a mathematical description of supersonic motion at the beginning of the 20th century. Due to incorrect assumptions, he came to the wrong result: from his equations it came out that the air pressure and its resistance to flight at a speed of M = 1 tend to infinity. What is strange: at that time, supersonic rifle bullets and projectiles were already flying perfectly, which, with an infinite force of air resistance, would not only immediately fall, but also, probably, would be dispersed by this infinite force in the opposite direction.
Prandtl nevertheless incorporated his findings into the course he taught to the students. But the first to publish them was an English aerodynamicist of German origin Hermann Glauert (or Glauert, English Hermann Glauert - it is not entirely clear how this English German or German Englishman pronounced his last name, in German or in English). Therefore, the method itself, and the singularity that follows from it (infinity of pressure) began to be called by the names of both scientists.
In fact, the transformations proposed by Prandtl do not work when approaching M = 1, but it was not easy to figure it out at that time, since the very first steps were then taken in experimental studies of supersonic flows (with the active participation of Prandtl himself, who took these steps and did).
Ludwig Prandtl, despite the mistake with the singularity, was an outstanding aerodynamicist, the founder, who worked very much and fruitfully with supersonic. It was he who first proposed the theory of a supersonic shock wave, which we touched upon above. He calculated and built the world's first supersonic wind tunnel. And later he came up with a method for calculating a supersonic nozzle, according to which all rocket nozzles are calculated today. He created a powerful school of aerogasdynamics that evolved into today's Max Planck Society. He is rightfully called the father of aerodynamics, and one of the aerodynamic similarity criteria (to which the Mach number belongs) is named after him - the Prandtl number. He lived to see the flights of supersonic aviation that arose from his work, leaving this world in 1953.
The "effect" attributed to Prandtl and Glauert arose from free folk art and took a place among other similar myths that are so easily spread in our time. Neither Prandtl nor Glauert formulated it, did not describe foggy cones, did not predict them - and indeed have nothing to do with them. One can only wonder how bizarrely erroneous ideas are sometimes refracted in aerodynamics, giving rise to myths.