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 :).

Aging

OK, I know it was a while ago, but who watched Felix Baumgartner’s jump? If you haven’t seen it, then you seriously missed out; the sheer spectacle of the occasion was truly amazing, so unlike anything you’ve ever seen before. We’re fairly used to seeing skydives from aeroplanes, but usually we only see either a long distance shot, jumper’s-eye-view, or a view from the plane showing them being whisked away half a second after jumping. Baumgartner’s feat was… something else, the two images available for the actual jump being direct, static views of a totally vertical fall. Plus, they were so angled to give a sense of the awesome scope of the occasion; one showed directly down to earth below, showing the swirling clouds and the shape of the land, whilst the other shot gave a beautiful demonstration of the earth’s curvature. The height he was at made the whole thing particularly striking; shots from the International Space Station and the moon have showed the earth from further away, but Baumgartner’s unique height made everything seem big enough to be real, yet small enough to be terrifying. And then there was the drop itself; a gentle lean forward from the Austrian, followed by what can only be described as a plummet. You could visibly see the lack of air resistance, so fast was he accelerating compared to our other images of skydivers. The whole business was awe-inspiring. Felix Baumgartner, you sir have some serious balls.

However, I bring this story up not because of the event itself, nor the insane amount of media coverage it received, nor even the internet’s typically entertaining reaction to the whole business (this was probably my favourite). No, the thing that really caught my eye was a little something about Baumgartner himself; namely, that the man who holds the world records for highest freefall, highest manned balloon flight, fastest unassisted speed and second longest freefall ever will be forty-four years old in April.

At his age, he would be ineligible for entry into the British Armed Forces, is closer to collecting his pension than university, and has already experienced more than half his total expected time on this earth. Most men his age are in the process of settling down, finding their place in some management company and getting slightly less annoyed at being passed over for promotion by some youngster with a degree and four boatloads of hopelessly naive enthusiasm. They’re in the line for learning how to relax, taking up golf, being put onto diet plans by their wives and going to improving exhibitions of obscure artists. They are generally not throwing themselves out of balloons 39 kilometres above the surface of the earth, even if they were fit and mobile enough to get inside the capsule with half a gigatonne of sensors and pressure suit (I may be exaggerating slightly).

Baumgartner’s feats for a man of his age (he was also the first man to skydive across the English channel, and holds a hotly disputed record for lowest BASE jump ever) are not rare ones without reason. Human beings are, by their very nature, lazy (more on that another time) and tend to favour the simple, homely life rather one that demands such a high-octane, highly stressful thrill ride of a life experience. This tendency towards laziness also makes us grow naturally more and more unfit as time goes by, our bodies slowly using the ability our boundlessly enthusiastic childish bodies had for scampering up trees and chasing one another, making such seriously impressive physical achievements rare.

And then there’s the activity itself; skydiving, and even more so BASE jumping, is also a dangerous, injury-prone sport, and as such it is rare to find regular practitioners of Baumgartner’s age and experience who have not suffered some kind of reality-checking accident leaving them either injured, scared or, in some cases, dead. Finally, we must consider the fact that there are very few people rich enough and brave enough to give such an expensive, exhilarating hobby as skydiving a serious go, and even less with both the clout, nous, ambition and ability to get a project such as Red Bull Stratos off the ground. And we must also remember that one has to overcome the claustrophobic, restrictive experience of doing the jump in a heavy pressure suit; even Baumgartner had to get help from a sports psychologist to get over his claustrophobia caused by being in the suit.

But then again, maybe we shouldn’t be too surprised. Red Bull Stratos was a culmination of years of effort in a single minded pursuit of a goal, and that required a level of experience in both skydiving and life in general that simply couldn’t be achieved by anyone younger than middle age- the majority of younger, perhaps even more ambitious, skydivers simply could not have got the whole thing done. And we might think that the majority of middle-aged people don’t achieve great things, but then again in the grand scheme of things the majority of everyone don’t end up getting most of the developed world watching them of an evening. Admittedly, the majority of those who do end up doing the most extraordinary physical things are under 35, but there’s always room for an exceptional human to change that archetype. And anyway; look at the list of Nobel Prize winners and certified geniuses on our earth, our leaders and heroes. Many of them have turned their middle age into something truly amazing, and if their field happens to be quantum entanglement rather than BASE jumping then so be it; they can still be extraordinary people.

I don’t really know what the point of this post was, or exactly what conclusion I was trying to draw from it; it basically started off because I thought Felix Baumgartner was a pretty awesome guy, and I happened to notice he was older than I thought he would be. So I suppose it would be best to leave you with a fact and a quote from his jump. Fact: When he jumped, his heart rate was measured as being lower than the average resting (ie lying down doing nothing and not wetting yourself in pants-shitting terror) heart rate of a normal human, so clearly the guy is cool and relaxed to a degree beyond human imagining. Quote: “Sometimes you have to be really high to see how small you really are”.