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.

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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…