Flying Supersonic

Last time (OK, quite a while ago actually), I explained the basic principle (from the Newtonian end of things; we can explain it using pressure, but that’s more complicated) of how wings generate lift when travelling at subsonic speeds, arguably the most important principle of physics affecting our modern world. However, as the second World War came to an end and aircraft started to get faster and faster, problems started to appear.

The first aircraft to approach the speed of sound (Mach 1, or around 700-odd miles an hour depending on air pressure) were WWII fighter aircraft; most only had top speeds of around 400-500mph or so whilst cruising, but could approach the magic number when going into a steep dive. When they did so, they found their aircraft began suffering from severe control issues and would shake violently; there are stories of Japanese Mitsubishi Zeroes that would plough into the ground at full speed, unable to pull out of a deathly transonic dive. Subsequent aerodynamic analyses of these aircraft suggest that if any of them had  in fact broken the sound barrier, their aircraft would most likely have been shaken to pieces. For this reason, the concept of ‘the sound barrier’ developed.

The problem arises from the Doppler effect (which is also, incidentally, responsible for the stellar red-shift that tells us our universe is expanding), and the fact that as an aircraft moves it emits pressure waves, carried through the air by molecules bumping into one another. Since this exactly the same method by which sound propagates in air, these pressure waves move at the speed of sound, and travel outwards from the aircraft in all directions. If the aircraft is travelling forwards, then each time it emits a pressure wave it will be a bit further forward than the centre of the pressure wave it emitted last, causing each wave in front of the aircraft to get closer together and waves behind it to spread out. This is the Doppler Effect.

Now, when the aircraft starts travelling very quickly, this effect becomes especially pronounced, wave fronts becoming compressed very close to one another. When the aircraft is at the speed of sound, the same speed at which the waves propagate, it catches up with the wave fronts themselves and all wave fronts are in the same place just in front of the aircraft. This causes them to build up on top of one another into a band of high-pressure air, which is experienced as a shockwave; the pressure drop behind this shockwave can cause water to condense out of the air and is responsible for pictures such as these.

But the shockwave does not just occur at Mach 1; we must remember that the shape of an aerofoil is such to cause air to travel faster over the top of the wing than it does normally. This means parts of the wing reach supersonic speeds, effectively, before the rest of the aircraft, causing shockwaves to form over the wings at a lower speed. The speed at which this first occurs is known as the critical Mach number. Since these shockwaves are at a high-pressure, then Bernoulli’s principle tells us they cause air to slow down dramatically; this contributes heavily to aerodynamic drag, and is part of the reason why such shockwaves can cause major control issues. Importantly, we must note that shockwaves always cause air to slow down to subsonic speeds, since the shockwave is generated at the point of buildup of all the pressure waves so acts as a barrier between the super- and sub-sonic portions of the airflow. However, there is another problem with this slowing of the airflow; it causes the air to have a higher pressure than the supersonic air in front of the shockwave. Since there is always a force from high pressure to low pressure, this can cause (at speeds sufficiently higher above the critical Mach number) parts of the airflow close to the wing (the boundary layer, which also experience surface friction from the wing) to change direction and start travelling forwards. This causes the boundary layer to recirculate, forming a turbulent portion of air that generates very little lift and quite a lot of drag, and for the rest of the airflow to separate from the wing surface; an effect known as boundary layer separation, (or Mach stall, since it causes similar problems to a regular stall) responsible for even more problems.

The practical upshot of all of this is that flying at transonic speeds (close to and around the speed of sound) is problematic and inefficient; but once we push past Mach 1 and start flying at supersonic speeds, things change somewhat. The shockwave over the wing moves to its trailing edge, as all of the air flowing over it is now travelling at supersonic speeds, and ceases to pose problems, but now we face the issues posed by a bow wave. At subsonic speeds, the pressure waves being emitted by the aircraft help to push air out of the way and mean it is generally deflected around the wing rather than just hitting it and slowing down dramatically; but at subsonic speeds, we leave those pressure waves behind us and we don’t have this advantage. This means supersonic air hits the front of the air and is slowed down or even stopped, creating a portion of subsonic air in front of the wing and (you guessed it) another shockwave between this and the supersonic air in front. This is known as a bow wave, and once again generates a ton of drag.

We can combat the formation of the wing by using a supersonic aerofoil; these are diamond-shaped, rather than the cambered subsonic aerofoils we are more used to, and generate lift in a different way (the ‘skipping stone’ theory is actually rather a good approximation here, except we use the force generated by the shockwaves above and below an angled wing to generate lift). The sharp leading edge of these wings prevents bow waves from forming and such aerofoils are commonly used on missiles, but they are inefficient at subsonic speeds and make takeoff and landing nigh-on impossible.

The other way to get round the problem is somewhat neater; as this graphic shows, when we go past the speed of sound the shockwave created by the aeroplane is not flat any more, but forms an angled cone shape- the faster we go, the steeper the cone angle (the ‘Mach angle’ is given by the formula sin(a)=v/c, for those who are interested). Now, if we remember that shockwaves cause the air behind them to slow down to subsonic speeds, it follows that if our wings lie just behind the shockwave, the air passing over them at right angles to the shockwave will be travelling at subsonic speeds, and the wing can generate lift perfectly normally. This is why the wings on military and other high-speed aircraft (such as Concorde) are ‘swept back’ at an angle; it allows them to generate lift much more easily when travelling at high speeds. Some modern aircraft even have variable-sweep wings (or ‘swing wings’), which can be pointed out flat when flying subsonically (which is more efficient) before being tucked back into a swept position for supersonic flight.

Aerodynamics is complicated.

The Development of Air Power

By the end of the Second World War, the air was the key battleground of modern warfare; with control of the air, one could move small detachments of troops to deep behind enemy lines, gather valuable reconnaissance and, of course, bomb one’s enemies into submission/total annihilation. But the air was also the newest theatre of war, meaning that there was enormous potential for improvement in this field. With the destructive capabilities of air power, it quickly became obvious that whoever was able to best enhance their flight strength would have the upper hand in the wars of the latter half of the twentieth century, and as the Cold War began hotting up (no pun intended) engineers across the world began turning their hands to problems of air warfare.

Take, for example, the question of speed; fighter pilots had long known that the faster plane in a dogfight had a significant advantage over his opponent, since he was able to manoeuvre quickly, chase his opponents if they ran for home and escape combat more easily. It also helped him cover more ground when chasing after slower, more sluggish bombers. However, the technology of the time favoured internal combustion engines powering propeller-driven aircraft, which limited both the range and speed of aircraft at the time. Weirdly, however, the solution to this particular problem had been invented 15 years earlier, after a young RAF pilot called Frank Whittle patented his design for a jet engine. However, when he submitted this idea to the RAF they referred him to engineer A. A. Griffith, whose study of turbines and compressors had lead to Whittle’s design. The reason Griffith hadn’t invented the jet engine himself was thanks to his fixed belief that jet engines would be too inefficient to act as practical engines on their own, and thought they would be better suited to powering propellers. He turned down Whittle’s engine design, which used the forward thrust of the engine itself, rather than a propeller, for power, as impractical, and so the Air Ministry didn’t fund research into the concept. Some now think that, had the jet engine been taken seriously by the British, the Second World War might have been over by 1940, but as it was Whittle spent the next ten years trying to finance his research and development privately, whilst fitting it around his RAF commitments. It wasn’t until 1945, by which time the desperation of war had lead to governments latching to every idea there was, that the first jet-powered aircraft got off the ground; and it was made by a team of Germans, Whittle’s patent having been allowed to expire a decade earlier.

Still, the German jet fighter was not exactly a practical beast (its engine needed to be disassembled after every use), and by then the war was almost lost anyway. Once the Allies got really into their jet aircraft development after the war, they looked set to start reaching the kind of fantastic speeds that would surely herald the new age of air power. But there was a problem; the sound barrier. During the war, a number of planes had tried to break the magical speed limit of 768 mph, aka the speed of sound (or Mach 1, as it is known today), but none had succeeded; partly this was due to the sheer engine power required (propellers get very inefficient when one approaching the speed of sound, and propeller tips can actually exceed the speed of sound as they spin), but the main reason for failure lay in the plane breaking up. In particular, there was a recurring problems of the wings tearing themselves off as they approached the required speed. It was subsequently realised that as one approached the sound barrier, you began to catch up with the wave of sound travelling in front of you; when you got too close to this, the air being pushed in front of the aircraft began to interact with this sound wave, causing shockwaves and extreme turbulence. This shockwave is what generates the sound of a sonic boom, and also the sound of a cracking whip. Some propeller driver WW2 fighters were able to achieve ‘transonic’ (very-close-to-Mach-1) speeds in dives, but these shockwaves generally rendered the plane uncontrollable and they invariably crashed; this effect was known as ‘transonic buffeting’. A few pilots during the war claimed to have successfully broken the sound barrier in dives and lived to tell the tale, but these claims are highly disputed. During the late 40s and early 50s, a careful analysis of transonic buffeting and similar effects yielded valuable information about the aerodynamics of attempting to break the sound barrier, and yielded several pieces of valuable data. One of the most significant, and most oft-quoted, developments concerned the shape of the wings; whilst  it was discovered that the frontal shape and thickness of the wings could be seriously prohibitive to supersonic flight, it was also realised that when in supersonic flight the shockwave generated was cone shaped. Not only that, but behind the shockwave air flowed at subsonic speeds and a wing behaved as normal; the solution, therefore, was to ‘sweep back’ the shape of the wings to form a triangle shape, so that they always lay ‘inside’ the cone-shaped shockwave. If they didn’t, the wing travelling through supersonic air would be constantly being battered by shockwaves, which would massively increase drag and potentially take the wings off the plane. In reality, it’s quite impractical to have the entire wing lying in the subsonic region (not least because a very swept-back wing tends to behave badly and not generate much lift when in subsonic flight), but the sweep of a wing is still a crucial factor in designing an aircraft depending on what speeds you want it to travel at. In the Lockheed SR-71A Blackbird, the fastest manned aircraft ever made (it could hit Mach 3.3), the problem was partially solved by having wings located right at the back of the aircraft to avoid the shockwave cone. Most modern jet fighters can hit Mach 2.

At first, aircraft designed to break the sound barrier were rocket powered; the USA’s resident speed merchant Chuck Yeager was the first man to officially and veritably top 768mph in the record-breaking rocket plane Bell X-1, although Yeager’s co-tester is thought to have beaten him to the achievement by 30 minutes piloting an XP-86 Sabre. But, before long, supersonic technology was beginning to make itself felt in the more conventional spheres of warfare; second generation jet fighters were, with the help of high-powered jet engines, the first to engage in supersonic combat during the 50s, and as both aircraft and weapons technology advanced the traditional roles of fighter and bomber started to come into question. And the result of that little upheaval will be explored next time…

The Pursuit of Speed

Recent human history has, as Jeremy Clarkson constantly loves to point out, been dominated by the pursuit of speed. Everywhere we look, we see people hurrying hither and thither, sprinting down escalators, transmitting data at next to lightspeed via their phones and computers, and screaming down the motorway at over a hundred kilometres an hour (or nearly 100mph if you’re the kind of person who habitually uses the fast lane of British motorways). Never is this more apparent than when you consider our pursuit of a new maximum, top speed, something that has, over the centuries, got ever higher and faster. Even in today’s world, where we prize speed of information over speed of movement, this quest goes on, as evidenced by the team behind the ‘Bloodhound’ SSC, tipped to break the world land speed record. So, I thought I might take this opportunity to consider the history of our quest for speed, and see how it has developed over time.

(I will ignore all unmanned human exploits for now, just so I don’t get tangled up in arguments concerning why a satellite may be considered versus something out of the Large Hadron Collider)

Way back when we humans first evolved into the upright, bipedal creatures we are now, we were a fairly primitive race and our top speed was limited by how fast we could run.  Usain Bolt can, with the aid of modern shoes, running tracks and a hundred thousand people screaming his name, max out at around 13 metres per second. We will therefore presume that a fast human in prehistoric times, running on bare feet, hard ground, and the motivation of being chased by a lion, might hit 11m/s, or 43.2 kilometres per hour. Thus our top speed remained for many thousands of years, until, around 6000 years ago, humankind discovered how to domesticate animals, and more specifically horses, in the Eurasian Steppe. This sent our maximum speed soaring to 70km/h or more, a speed that was for the first time sustainable over long distances, especially on the steppe where horses where rarely asked to tow or carry much. Thus things remained for another goodly length of time- in fact, many leading doctors were of the opinion that travelling any faster would be impossible to do without asphyxiating. However, come the industrial revolution, things started to change, and records began tumbling again. The train was invented in the 1800s and quickly transformed from a slow, lumbering beast into a fast, sleek machine capable of hitherto unimaginable speed. In 1848, the Iron Horse took the land speed record away from its flesh and blood cousin, when a train in Boston finally broke the magical 60mph (ie a mile a minute) barrier to send the record shooting up to 96.6 km/h. Records continued to tumble for the next half-century, breaking the 100 mph barrier by 1904, but by then there was a new challenger on the paddock- the car. Whilst early wheel-driven speed records had barely dipped over 35mph, after the turn of the century they really started to pick up the pace. By 1906, they too had broken the 100mph mark, hitting 205km/h in a steam-powered vehicle that laid the locomotives’ claims to speed dominance firmly to bed. However, this was destined to be the car’s only ever outright speed record, and the last one to be set on the ground- by 1924 they had got up to 234km/h, a record that stands to this day as the fastest ever recorded on a public road, but the First World War had by this time been and gone, bringing with it a huge advancement in aircraft technology. In 1920, the record was officially broken in the first post-war attempt, a French pilot clocking 275km/h, and after that there was no stopping it. Records were being broken left, right and centre throughout both the Roaring Twenties and the Great Depression, right up until the breakout of another war in 1939. As during WWI, all records ceased to be officiated for the war’s duration, but, just as the First World War allowed the plane to take over from the car as the top dog in terms of pure speed, so the Second marked the passing of the propellor-driven plane and the coming of the jet & rocket engine. Jet aircraft broke man’s top speed record just 5 times after the war, holding the crown for a total of less than two years, before they gave it up for good and let rockets lead the way.

The passage of records for rocket-propelled craft is hard to track, but Chuck Yeager in 1947 became the first man ever to break the sound barrier in controlled, level flight (plunging screaming to one’s death in a deathly fireball apparently doesn’t count for record purposes), thanks not only to his Bell X-1’s rocket engine but also the realisation that breaking the sound barrier would not tear the wings of so long as they were slanted back at an angle (hence why all jet fighters adopt this design today). By 1953, Yeager was at it again, reaching Mach 2.44 (2608km/h) in the X-1’s cousing, the X-1A. The process, however, nearly killed him when he tilted the craft to try and lose height and prepare to land, at which point a hitherto undiscovered phenomenon known as ‘inertia coupling’ sent the craft spinning wildly out of control and putting Yeager through 8G’s of force before he was able to regain control. The X-1’s successor, the X-2, was even more dangerous- despite pushing the record up to first 3050km/h  one craft exploded and killed its pilot in 1953, before a world record-breaking flight reaching Mach 3.2 (3370 km/h), ended in tragedy when a banking turn at over Mach 3 sent it into another inertia coupling spin that resulted, after an emergency ejection that either crippled or killed him, in the death of pilot Milburn G. Apt. All high-speed research aircraft programs were suspended for another three years, until experiments began with the Bell X-15, the latest and most experimental of these craft. It broke the record 5 times between 1961 and 67, routinely flying above 6000km/h, before another fatal crash, this time concerning pilot Major Michael J Adams in a hypersonic spin, put paid to the program again, and the X-15’s all-time record of 7273km/h remains the fastest for a manned aircraft. But it still doesn’t take the overall title, because during the late 60s the US had another thing on its mind- space.

Astonishingly, manned spacecraft have broken humanity’s top speed record only once, when the Apollo 10 crew achieved the fastest speed to date ever achieved by human beings relative to Earth. It is true that their May 1969 flight did totally smash it, reaching 39 896km/h on their return to earth, but all subsequent space flights, mainly due to having larger modules with greater air resistance, have yet to top this speed. Whether we ever will or not, especially given today’s focus on unmanned probes and the like, is unknown. But people, some brutal abuse of physics is your friend today. Plot all of these records on a graph and add a trendline (OK you might have to get rid of the horse/running ones and fiddle with some numbers), and you have a simple equation for the speed record against time. This can tell us a number of things, but one is of particular interest- that, statistically, we will have a man travelling at the speed of light in 2177. Star Trek fans, get started on that warp drive…