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 :).

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Gaming continued…

Okay, gaming again (I have got to get a LOT better at writing only one post per topic). Last time I did my own analysis of the ‘games make people violent’ accusation so often levelled at them. My plan was to devote this post to expounding upon a number of other issues that people tend to take with gaming, but part way through writing it I realised that the only ones typically levelled at gaming by non-gamers could all be basically grouped under one heading, so you instead are getting another in-depth analysis of a single complaint about gaming

So, without further ado…

2) ‘Games are a waste of time/are antisocial/make you fat’
The one my parents always used to take serious issue with, and if I’m honest it’s a perfectly valid concern. Games tie you to a computer or TV screen for hours upon end, seemingly endlessly shooting bad guys, running through cities or conquering vast swathes of human civilisation. Not only that, but this time there is PLENTY of evidence showing how this can get out of hand- game addiction can get to be a serious problem for some people, to the extent that it starts to have a seriously debilitating effect on the rest of their life (For a good example, check out this: http://extra-credits.net/episodes/game-addiction-part-1/ and then move onto part two. I would also recommend checking out some more of Extra Credits if you get a chance- they do some really great video lectures on the subject of gaming, which can be kind of nerdy but really good to watch). I’ve never been sufficiently in to games to get properly addicted to them, and even the most game-obsessed of my friends only fit into the ‘hardcore-but-still-casual-gamers’ bracket (for most of them, gaming is just the main thing they do outside of the day-to-day, and as such the hours tend to rack up a bit. This might also explain why so many of them are single). However, everyone knows the stories of the addicts, the people who’ll complete the latest Call of Duty within a few hours of release, the people who spend 10 hours a day on World of Warcraft and refer to everyone as a noob, the people who somehow allow Starcraft II to be the national sport of South Korea and whose actions per minute rate make a concert pianist look lazy and sluggish. Then there is the stereotypical image that gets lambasted and piss-taken by the internet generally, and that has entered web culture as the very picture of the stereotypical hardcore nerd gamer- the obese mid-twenties guy, living in his parents’ basement fuelled by energy drinks and fast food and dedicating his life to Star Wars, being angry on the internet, and gaming. Lots of gaming. This image may be largely fanciful, but its very existence shows that there is a world of game addicts to point and laugh at, and the fact that they are there points to the existence of game addiction as a large-scale problem.

Clearly, addiction to games, just as with nicotine, alcohol or adrenaline, can be a very dangerous thing, and I am not even going to begin to defend the indefensible by denying that fact. But what about the rest of us? What about the casual gamers, the people who like a few hours of Skyrim of a weekend or whatever? What about the few hours we like to kill- does that qualify as ‘wasting time’?

It is quite easy to say yes to that idea- I mean, lets face it, games are not something you do to demonstrate your superlative contribution to the human race. Think of people like Ranulph Fiennes, Ellen MacArthur, Nelson Mandela or any other inspiring figure who springs to mind as an example of the pinnacle of human achievement in their field. Now, ask yourself- can you picture any of them spending 3 hours on a sofa playing Battlefield? Chances are the answer’s no.

However, there is one thing in this argument that I take issue with, and which leads me to reject the whole ‘waste of time’ idea- the very concept of a ‘waste of time’. Yes, whilst gaming you are not in any way being productive- but neither are you doing so if you are watching TV, playing in the garden, going to a film, chatting with friends, reading a book- I could go on. Even the most amazing people on earth need their down time occasionally, when they can stop being special and just be themselves- just be happy in the state of absorbed flow a good film, book or game, both digital and real-life, can inspire. People play games as a release, a way to relax and enjoy themselves. Different emotions may make you want to play different games (you would not, for instance, play a dark survival horror game to chill after a long day), but the point stands- one plays games to take your mind off the day-to-day, to compel oneself, and to enjoy oneself. Your brain needs that down time, that time left to its own devices, where the pressures of work and school aren’t constantly chipping away at it. Productive? Of course not. Waste of time? Not a chance