The Value of Transparency

Once you start looking for it, it can be quite staggering to realise just how much of our modern world is, quite literally, built on glass. The stuff is manufactured in vast quantities, coating our windows, lights, screens, skyscrapers and countless other uses. Some argue that it is even responsible for the entire development of the world, particularly in the west, as we know it; it’s almost a wonder we take it for granted so.

Technically, out commonplace use of the word ‘glass’ rather oversimplifies the term; glasses are in fact a family of materials that all exhibit the same amorphous structure and behaviour under heating whilst not actually all being made from the same stuff. The member of this family that we are most familiar with and will commonly refer to as simply ‘glass’ is soda-lime glass, made predominantly from silica dioxide with a few other additives to make it easier to produce. But I’m getting ahead of myself; let me tell the story from the beginning.

Like all the best human inventions, glass was probably discovered by accident. Archaeological evidence suggests glassworking was probably an Egyptian invention in around the third millennia BC, Egypt (or somewhere nearby) being just about the only place on earth at the time where the three key ingredients needed for glass production occured naturally and in the same place: silica dioxide (aka sand), sodium carbonate (aka soda, frequently found as a mineral or from plant ashes) and a relatively civilised group of people capable of building a massive great fire. When Egyptian metalworkers got sand and soda in their furnaces by accident, when removed they discovered the two had fused to form a hard, semi-transparent, almost alien substance; the first time glass had been produced anywhere on earth.

This type of glass was far from perfect; for one thing, adding soda has the unfortunate side-effect of making silica glass water-soluble, and for another they couldn’t yet work out how to make the glass clear. Then there were the problems that came with trying to actually make anything from the stuff. The only glass forming technique at the time was called core forming, a moderately effective but rather labour-intensive process illustrated well in this video. Whilst good for small, decorative pieces, it became exponentially more difficult to produce an item by this method the larger it needed to be, not to mention the fact that it couldn’t produce flat sheets of glass for use as windows or whatever.

Still, onwards and upwards and all that, and developments were soon being made in the field of glass technology. Experimentation with various additives soon yielded the discovery that adding lime (calcium oxide) plus a little aluminium and magnesium oxide made soda glass insoluble, and thus modern soda-lime glass was discovered. In the first century BC, an even more significant development came along with the discovery of glass blowing as a production method. Glass blowing was infinitely more flexible than core forming, opening up an entirely new avenue for glass as a material, but crucially it allowed glass products to be produced faster and thus be cheaper than pottery equivalents . By this time, the Eastern Mediterranean coast where these discoveries took place was part of the Roman Empire, and the Romans took to glass like a dieter to chocolate; glass containers and drinking vessels spread across the Empire from the glassworks of Alexandria, and that was before they discovered manganese dioxide could produce clear glass and that it was suddenly suitable for architectural work.

Exactly why glass took off on quite such a massive scale in Europe yet remained little more than a crude afterthought in the east and China (the other great superpower of the age) is somewhat unclear. Pottery remained the material of choice throughout the far east, and they got very skilled at making it too; there’s a reason we in the west today call exceptionally fine, high-quality pottery ‘china’. I’ve only heard one explanation for why this should be so, and it centres around alcohol.

Both the Chinese and Roman empires loved wine, but did so in different ways. To the Chinese, alcohol was a deeply spiritual thing, and played an important role in their religious procedures. This attitude was not unheard of in the west (the Egyptians, for example, believed the god Osiris invented beer, and both Greeks and Romans worshipped a god of wine), but the Roman Empire thought of wine in a secular as well as religious sense; in an age where water was often unsafe to drink, wine became the drink of choice for high society in all situations. One of the key features of wine to the Roman’s was its appearance, hence why the introduction of clear vessels allowing them to admire this colour was so attractive to them. By contrast, the Chinese day-to-day drink of choice was tea. whose appearance was of far less importance than the ability of its container to dissipate heat (as fine china is very good at). The introduction of clear drinking vessels would, therefore, have met with only a limited market in the east, and hence it never really took off. I’m not entirely sure that this argument holds up under scrutiny, but it’s quite a nice idea.

Whatever the reason, the result was unequivocal; only in Europe was glassmaking technology used and advanced over the years. Stained glass was one major discovery, and crown glass (a method for producing large, flat sheets) another. However, the crucial developments would be made in the early 14th century, not long after the Republic of Venice (already a centre for glassmaking) ordered all its glassmakers to move out to the island of Murano to reduce the risk of fire (which does seem ever so slightly strange for a city founded, quite literally, on water).  On Murano, the local quartz pebbles offered glassmakers silica of hitherto unprecedented purity which, combined with exclusive access to a source of soda ash, allowed for the production of exceptionally high-quality glassware. The Murano glassmakers became masters of the art, producing glass products of astounding quality, and from here onwards the technological revolution of glass could begin. The Venetians worked out how to make lenses, in turn allowing for the discovery of the telescope (forming the basis of the work of both Copernicus and Galileo) and spectacles (extending the working lifespan of scribes and monks across the western world). The widespread introduction of windows (as opposed to fabric-covered holes in the wall) to many houses, particularly in the big cities, dramatically improved the health of their occupants by both keeping the house warmer and helping keep out disease. Perhaps most crucially, the production of high-quality glass vessels was not only to revolutionise biology, and in turn medicine, as a discipline, but to almost single-handedly create the modern science of chemistry, itself the foundation stone upon which most of modern physics is based. These discoveries would all, given enough time and quite a lot of social upheaval, pave the way for the massive technological advancements that would characterise the western world in the centuries to come, and which would finally allow the west to take over from the Chinese and Arabs and become the world’s leading technological superpowers.* Nowadays, of course, glass has been taken even further, being widely used as a building material (its strength-to-weight ratio far exceeds that of concrete, particularly when it is made to ‘building grade’ standard), in televisions, and fibre optic cables (which may yet revolutionise our communications infrastructure).

Glass is, of course, not the only thing to have catalysed the technological breakthroughs that were to come; similar arguments have been made regarding gunpowder and the great social and political changes that were to grip Europe between roughly 1500 and 1750. History is never something that one can place a single cause on (the Big Bang excepted), but glass was undoubtedly significant in the western world’s rise to prominence during the second half of the last millennia, and the Venetians probably deserve a lot more credit than they get for creating our modern world.

*It is probably worth mentioning that China is nowadays the world’s largest producer of glass.

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 :).