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…

Hitting the hay

OK, so it was history last time, so I’m feeling like a bit of science today. So, here is your random question for today; are the ‘leaps of faith’ in the Assassin’s Creed games survivable?

Between them, the characters of Altair, Ezio and Connor* jump off a wide variety of famous buildings and monuments across the five current games, but the jump that springs most readily to mind is Ezio’s leap from the Campanile di San Marco, in St Mark’s Square, Venice, at the end of Assassin’s Creed II. It’s not the highest jump made, but it is one of the most interesting and it occurs as part of the main story campaign, meaning everyone who’s played the game through will have made the jump and it has some significance attached to it. It’s also a well-known building with plenty of information on it.

[*Interesting fact; apparently, both Altair and Ezio translate as ‘Eagle’ in some form in English, as does Connor’s Mohawk name (Ratonhnhaké;ton, according to Wikipedia) and the name of his ship, the Aquila. Connor itself translates as ‘lover of wolves’ from the original Gaelic]

The Campanile as it stands today is not the same one as in Ezio’s day; in 1902 the original building collapsed and took ten years to rebuild. However, the new Campanile was made to be cosmetically (if not quite structurally) identical to the original, so current data should still be accurate. Wikipedia again tells me the brick shaft making up the bulk of the structure accounts for (apparently only) 50m of the tower’s 98.6m total height, with Ezio’s leap (made from the belfry just above) coming in at around 55m. With this information we can calculate Ezio’s total gravitational potential energy lost during his fall; GPE lost = mgΔh, and presuming a 70kg bloke this comes to GPE lost= 33730J (Δ is, by the way, the mathematical way of expressing a change in something- in this case, Δh represents a change in height). If his fall were made with no air resistance, then all this GPE would be converted to kinetic energy, where KE = mv²/2. Solving to make v (his velocity upon hitting the ground) the subject gives v = sqrt(2*KE/m), and replacing KE with our value of the GPE lost, we get v = 31.04m/s. This tells us two things; firstly that the fall should take Ezio at least three seconds, and secondly that, without air resistance, he’d be in rather a lot of trouble.

But, we must of course factor air resistance into our calculations, but to do so to begin with we must make another assumption; that Ezio reaches terminal velocity before reaching the ground. Whether this statement is valid or not we will find out later. The terminal velocity is just a rearranged form of the drag equation: Vt=sqrt(2mg/pACd), where m= Ezio’s mass (70kg, as presumed earlier), g= gravitational field strength (on Earth, 9.8m/s²), p= air density (on a warm Venetian evening at around 15 degrees Celcius, this comes out as 1.225kg/m3), A= the cross-sectional area of Ezio’s falling body (call it 0.85m², presuming he’s around the same size as me) and Cd= his body’s drag coefficient (a number evaluating how well the air flows around his body and clothing, for which I shall pick 1 at complete random). Plugging these numbers into the equation gives a terminal velocity of 36.30m/s, which is an annoying number; because it’s larger than our previous velocity value, calculated without air resistance, of 31.04m/s, this means that Ezio definitely won’t have reached terminal velocity by the time he reaches the bottom of the Campanile, so we’re going to have to look elsewhere for our numbers. Interestingly, the terminal velocity for a falling skydiver, without parachute, is apparently around 54m/s, suggesting that I’ve got numbers that are in roughly the correct ballpark but that could do with some improvement (this is probably thanks to my chosen Cd value; 1 is a very high value, selected to give Ezio the best possible chance of survival, but ho hum)

Here, I could attempt to derive an equation for how velocity varies with distance travelled, but such things are complicated, time consuming and do not translate well into being typed out. Instead, I am going to take on blind faith a statement attached to my ‘falling skydiver’ number quoted above; that it takes about 3 seconds to achieve half the skydiver’s terminal velocity. We said that Ezio’s fall from the Campanile would take him at least three seconds (just trust me on that one), and in fact it would probably be closer to four, but no matter; let’s just presume he has jumped off some unidentified building such that it takes him precisely three seconds to hit the ground, at which point his velocity will be taken as 27m/s.

Except he won’t hit the ground; assuming he hits his target anyway. The Assassin’s Creed universe is literally littered with indiscriminate piles/carts of hay and flower petals that have been conveniently left around for no obvious reason, and when performing a leap of faith our protagonist’s always aim for them (the AC wiki tells me that these were in fact programmed into the memories that the games consist of in order to aid navigation, but this doesn’t matter). Let us presume that the hay is 1m deep where Ezio lands, and that the whole hay-and-cart structure is entirely successful in its task, in that it manages to reduce Ezio’s velocity from 27m/s to nought across this 1m distance, without any energy being lost through the hard floor (highly unlikely, but let’s be generous). At 27m/s, the 70kg Ezio has a momentum of 1890kgm/s, all of which must be dissipated through the hay across this 1m distance. This means an impulse of 1890Ns, and thus a force, will act upon him; Impulse=Force x ΔTime. This force will cause him to decelerate. If this deceleration is uniform (it wouldn’t be in real life, but modelling this is tricky business and it will do as an approximation), then his average velocity during his ‘slowing’ period will come to be 13.5m/s, and that this deceleration will take 0.074s. Given that we now know the impulse acting on Ezio and the time for which it acts, we can now work out the force upon him; 1890 / 0.074 = 1890 x 13.5 = 26460N. This corresponds to 364.5m/s² deceleration, or around 37g’s to put it in G-force terms. Given that 5g’s has been known to break bones in stunt aircraft, I think it’s safe to say that quite a lot more hay, Ezio’s not getting up any time soon. So remember; next time you’re thinking of jumping off a tall building, I would recommend a parachute over a haystack.

N.B.: The resulting deceleration calculated in the last bit seems a bit massive, suggesting I may have gone wrong somewhere, so if anyone has any better ideas of numbers/equations then feel free to leave them below. I feel here is also an appropriate place to mention a story I once heard concerning an air hostess whose plane blew up. She was thrown free, landed in a tree on the way down… and survived.

EDIT: Since writing this post, this has come into existence, more accurately calculating the drag and final velocity acting on the falling Assassin. They’re more advanced than me, but their conclusion is the same; I like being proved right :).

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…

Scrum Solutions

First up- sorry I suddenly disappeared over last week. I was away, and although I’d planned to tell WordPress to publish a few for me (I have a backlog now and everything), I was unfortunately away from my computer on Saturday and could not do so. Sorry. Today I would like to follow on from last Wednesday’s post dealing with the problems faced in the modern rugby scrum, to discuss a few solutions that have been suggested for dealing with the issue, and even throw in a couple of ideas of my own. But first, I’d like to offer my thoughts to another topic that has sprung up amid the chaos of scrummaging discussions (mainly by rugby league fans): the place, value and even existence of the scrum.

As the modern game has got faster and more free-flowing, the key focus of the game of rugby union has shifted. Where once entire game plans were built around the scrum and (especially) lineout, nowadays the battle of the breakdown is the vital one, as is so ably demonstrated by the world’s current openside flanker population. Thus, the scrum is becoming less and less important as a tactical tool, and the extremists may argue that it is no more than a way to restart play. This is the exact situation that has been wholeheartedly embraced by rugby league, where lineouts are non-existent and scrums are an uncontested way of restarting play after a minor infringement. To some there is, therefore, something of a crossroads: do we as a game follow the league path of speed and fluidity at the expense of structure, or stick to our guns and keep the scrum (and set piece generally) as a core tenet of our game?

There is no denying that our modern play style, centred around fast rucks and ball-in-hand play, is certainly faster and more entertaining than its slow, sluggish predecessor, if only for the fans watching it, and has certainly helped transform rugby union into the fun, flowing spectators game we know and love today. However having said that, if we just wanted to watch players run with the ball and nothing else of any interest to happen, then we’d all just go and play rugby league, and whilst league is certainly a worthwhile sport (with, among other things, the most passionate fans of any sport on earth), there is no point trying to turn union into its clone. In any case, the extent to which league as a game has been simplified has meant that there are now hardly any infringements or stoppages to speak of and that a scrum is a very rare occurence. This is very much unlike its union cousin, and to do away with the scrum as a tool in the union code would perhaps not suit the game as well as it does in union. Thus, it is certainly worth at least trying to prevent the scrum turning into a dour affair of constant collapses and resets before everyone dies of boredom and we simply scrap the thing.

(I know I’ve probably broken my ‘no Views’ rule here, but I could go on all day about the various arguments and I’d like to get onto some solutions)

The main problem with the modern scrum according to the IRB concerns the engage procedure- arguing (as do many other people) that trying to restrain eight athletes straining to let rip their strength is a tough task for even the stoutest front rower, they have this year changed the engage procedure to omit the ‘pause’ instruction from the ‘crouch, touch, pause, engage’ sequence. Originally included to both help the early players structure their engagement (thus ensuring they didn’t have to spend too much time bent down too far) and to ensure the referee had control over the engagement, they are now arguing that it has no place in the modern game and that it is time to see what effect getting rid of it will have (they have also replaced the ‘engage’ instruction with ‘set’ to reduce confusion about which syllable to engage on).

Whether this will work or not is a matter of some debate. It’s certainly a nice idea- speaking as a forward myself, I can attest that giving the scrum time to wind itself up is perhaps not the best way to ensure they come together in a safe, controlled fashion. However, what this does do is place a lot of onus on the referee to get his timing right. If the ‘crouch, touch, set’ procedure is said too quickly, it can be guaranteed that one team will not have prepared themselves properly and the whole engagement will be a complete mess. Say it too slowly, and both sides will have got themselves all wound up and we’ll be back to square one again. I suppose we’ll all find out how well it works come the new season (although I do advise giving teams time to settle back in- I expect to see a lot of packs waiting for a split second on the ‘set’ instruction as they wait for the fourth command they are so used to)

Other solutions have also been put forward. Many advocate a new law demanding gripping areas on the shirts of front row players to ensure they have something to get hold of on modern, skintight shirts, although the implementation of such a law would undoubtedly be both expensive and rather chaotic for all concerned, which is presumably why the IRB didn’t go for it. With the increasing use and importance of the Television Match Official (TMO) in international matches, there are a few suggesting that both they and the line judge should be granted extra responsibilities at scrum time to ensure the referee’s attention is not distracted, but it is understandable that referees do not want to be patronised by and become over-reliant on a hardly universally present system where the official in question is wholly dependent on whether the TV crews think that the front row binding will make a good shot.

However, whilst these ideas may help to prevent the scrum collapsing, with regards to the scrum’s place in the modern game they are little more than papering over the cracks. On their own, they will not change the way the game is played and will certainly not magically bring the scrum back to centre stage in the professional game.

For that to happen though, things may have to change quite radically. We must remember that the scrum as an invention is over 150 years old and was made for a game that has since changed beyond all recognition, so it could well be time that it began to reflect that. It’s all well and good playing the running game of today, but if the scrum starts to become little more than a restart then it has lost all its value. However, it is also true that if it is allowed to simply become a complete lottery, then the advantage for the team putting the ball in is lost and everyone just gets frustrated with it.

An answer could be (to pick an example idea) to turn the scrum into a more slippery affair, capable of moving back and forth far more easily than it can at the moment, almost more like a maul than anything else. This would almost certainly require radical changes regarding the structure and engagement of it- perhaps we should say that any number of players (between, say, three and ten) can take part in a scrum, in the same way as happens at lineouts, thereby introducing a tactical element to the setup and meaning that some sneaky trickery and preplanned plays could turn an opposition scrum on its head. Perhaps the laws on how the players are allowed to bind up should be relaxed, forcing teams to choose between a more powerful pushing setup and a looser one allowing for faster attacking & defending responses. Perhaps a law should be trialled demanding that if two teams engaged correctly, but the scrum collapsed because one side went lower than the other then the free kick would be awarded to the ‘lower’ side, thus placing a greater onus on technique over sheer power and turning the balance of the scrum on its head. Would any of these work? Maybe not, but they’re ideas.

I, obviously, do not have all the definitive answers, and I couldn’t say I’m a definite advocate of any of the ideas I voiced above (especially the last one, now I think how ridiculously impractical it would be to manage). But it is at least worth thinking about how much the game has evolved since the scrum’s invention, and whether it’s time for it to catch up.