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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The Interesting Instrument

Music has been called the greatest thing that humans do; some are of the opinion that it, even if only in the form of songs sung around the campfire, it is the oldest example of human art. However, whilst a huge amount of music’s effect and impact can be put down to the way it is interpreted by our ears and brain (I once listened to a song comprised entirely of various elements of urban sound, each individually recorded by separate microphones and each made louder or softer in order to create a tune), to create new music and allow ourselves true creative freedom over the sounds we make requires us to make and play instruments of various kinds. And, of all the myriad of different musical instruments humankind has developed, honed and used to make prettyful noises down the years, perhaps none is as interesting to consider as the oldest and most conceptually abstract of the lot; the human voice.

To those of us not part of the musical fraternity, the idea of the voice being considered an instrument at all is a very odd one; it is used most of the time simply to communicate, and is thus perhaps unique among instruments in that its primary function is not musical. However, to consider a voice as merely an addition to a piece of music rather than being an instrumental part of it is to dismiss its importance to the sound of the piece, and as such it must be considered one by any composer or songwriter looking to produce something coherent. It is also an incredibly diverse tool at a musician’s disposal; capable of a large range of notes anyway in a competent singer, by combining the voices of different people one can produce a tonal range rivalled only by the piano, and making it the only instrument regularly used as the sole component of a musical entity (ie in a choir). Admittedly, not using it in conjunction with other instruments does rather limit what it can do without looking really stupid, but it is nonetheless a quite amazingly versatile musical tool.

The voice also has a huge advantage over every other instrument in that absolutely anyone can ‘play’ it; even people who self-confessedly ‘can’t sing’ may still find themselves mumbling their favourite tune in the shower or singing along with their iPod occasionally. Not only that, but it is the only instrument that does not require any tool in addition to the body in order to play, meaning it is carried with everyone absolutely everywhere, thus giving everybody listening to a piece of music a direct connection to it; they can sing, mumble, or even just hum along. Not only is this a wet dream from a marketer’s perspective, enabling word-of-mouth spread to increase its efficiency exponentially, but it also makes live music that other level more awesome (imagine a music festival without thousands of screaming fans belting out the lyrics) and just makes music that much more compelling and, indeed, human to listen to.

However, the main artistic reason for the fundamental musical importance of the voice has more to do with what it can convey- but to adequately explain this, I’m going to need to go off on a quite staggeringly over-optimistic detour as I try to explain, in under 500 words, the artistic point of music. Right, here we go…:

Music is, fundamentally, an art form, and thus (to a purist at least) can be said to exist for no purpose other than its own existence, and for making the world a better place for those of us lucky enough to be in it. However, art in all its forms is now an incredibly large field with literally millions of practitioners across the world, so just making something people find pretty doesn’t really cut it any more. This is why some extraordinarily gifted painters can draw something next to perfectly photo-realistic and make a couple of grand from it, whilst Damien Hirst can put a shark in some formaldehyde and sell it for a few million. What people are really interested in buying, especially when it comes to ‘modern’ art, is not the quality of brushwork or prettifulness of the final result (which are fairly common nowadays), but its meaning, its significance, what it is trying to convey; the story, theatre and uniqueness behind it all (far rarer commodities that, thanks to the simple economic law of supply and demand, are thus much more expensive).

(NB: This is not to say that I don’t think the kind of people who buy Tracy Emin pieces are rather gullible and easily led, and apparently have far more money than they do tangible grip on reality- but that’s a discussion for another time, and this is certainly how they would justify their purchases)

Thus, the real challenge to any artist worth his salt is to try and create a piece that has meaning, symbolism, and some form of emotion; and this applies to every artistic field, be it film, literature, paintings, videogames (yes, I am on that side of the argument) or, to try and wrench this post back on-topic, music. The true beauty and artistic skill of music, the key to what makes those songs that transcend mere music alone so special, lies in giving a song emotion and meaning, and in this function the voice is the perfect instrument. Other instruments can produce sweet, tortured strains capable of playing the heart strings like a violin, but virtue of being able to produce those tones in the form of language, capable of delivering an explicit message to redouble the effect of the emotional one, a song can take on another level of depth, meaning and artistry. A voice may not be the only way to make your song explicitly mean something, and quite often it’s not used in such an artistic capacity at all; but when it is used properly, it can be mighty, mighty effective.