The Slightly Chubby Brigade

As the news will tell you at every single available opportunity, we are living through an obesity crisis. Across the western world (USA being the worst and Britain coming in second) our average national BMI is increasing and the number of obese and overweight people, and children especially, looks to be soaring across the board. Only the other day I saw a statistic that said nearly a third of children are now leaving primary school (ie one third of eleven year-olds) overweight, and such solemn numbers frequently make headlines.

This is a huge issue, encompassing several different issues and topics that I will attempt to consider over my next few posts (yeah, ‘nother multi-parter coming up), but for many of us it seems hideously exaggerated. I mean yes, we’ve all seen the kind of super-flabby people, the kind the news footage always cuts to when we hear some obesity health scare, the kind who are wider than they are tall and need a mobility scooter just to get around most of the time. We look at these pictures and we tut, and we might consider our own shape- but we’re basically fine, aren’t we. Sure, there’s a bit of a belly showing, but that’s normal- a good energy store and piece of insulation, in fact, and we would like to have a life beyond the weight-obsessed calorie counters that hardcore slimmers all seem to be. We don’t need to worry, do we?

Well, according to the numbers, actually we do. The average height of a Briton… actually, if you’re stumbling across this at home and you consider yourself normal, go and weigh yourself and, if you can, measure your height as well. Write those numbers down, and now continue reading. The average height of a Briton at the moment is 1.75m, or around 5’9″ in old money, and we might consider a normal weight for that height to be around 80 kilos, or 170 pounds. That might seem normal enough; a bit of a paunch, but able to get around and walk, and certainly no one would call you fat. Except perhaps your doctor, because according to the BMI chart I’ve got pulled up a 5 foot 9, 80 kilo human is deemed clinically overweight. Not by much, but you’d still weigh more than is healthy- in fact, one stat I heard a while ago puts the average Briton at this BMI. Try it with your measurements; BMI charts are freely available over the web.

This, to me, is one of the real underlying causes of ‘the obesity epidemic’- a fundamental misunderstanding of what ‘overweight’ consists of. Whenever our hideously awful everyone-dead-from-McDonalds-overdose etc. etc. diet is brought up on the news, it is always annotated by pictures of hanging bellies and bouncing flab, the kind of bodies that make one almost physically sick to look at. But, whilst these people certainly exist, there are not enough of them for the obesity issue to be even worth mentioning in everyday society; whilst the proportion of morbidly obese people is significant, it’s not seriously worth thought for most of us.

No, the real cause for all the chilling statistics we hear on the news is all the people who don’t look to be overweight. The kind whose diet isn’t appalling (no 24/7 McDonaldses), who are quite capable of exercise when it suits them, and who might take a rough glance at the dietary information of the stuff they buy in the supermarket. But these people are nonetheless hovering on the overweight borderline, pulling up the national average, despite the fact that they don’t consider anything to be wrong; in fact, some women who are according to the evil numbers overweight, may consider it almost dutiful to not become obsessed over shedding every pound and to maintain their curves. Having a bit of excess weight is, after all, still better than being underweight and anorexic, and the body image pressures some young women are coming under are just as much of an issue as national obesity. Even for those who don’t have such opinions, many of the slightly overweight feel that they don’t have any weight issues and that there’s surely no significant health risk associated with a ‘bit of meat on your bones’ (it’s actually muscle, rather than fat, that technically forms meat, but ho hum); as such, they have absolutely no motivation to get their weight down, as they don’t think they need to.

I won’t waste much of my time on all the reasons for this statement, but unfortunately even this slight degree of overweight-ness will significantly increase your risk of major health problems somewhere down the line, particularly that of heart disease (which is going through the roof at the moment); diabetes isn’t likely to be a risk for the overweight unless they’re really overdoing things, but that’s also a potential, and very serious, health hazard. The trouble is that many of us find it hard to make this connection if we basically feel healthy. Despite what the doctor says and no matter how much we trust them, if we are capable of going for a nice walk and generally getting about without getting out of breath or feeling bad then we probably feel justified in thinking of ourselves as healthy. Our heart doesn’t seem about to give out, so why worry about it.

The thing to remember is that the heart is just a muscle, so if it isn’t stressed it will degrade just like any other. You know those triceps that haven’t done a press up in five years? Feel how small and weak they are? Yeah, that kind of thing can quite easily happen to the muscles that are responsible for keeping you alive. Your heart might be pumping all day long and be a different type of muscle, so the process will be slower, but give it twenty years and you might start to see the effects.

But anyway, I’m not here to lecture you about your health; that’s far too depressing and dull for my liking- the only point I was trying to make is that many of the accidental contributors to ‘the obesity epidemic’ are probably unaware that their health is in any way a problem, and not really through fault of their own. So whose fault is it then? Well, that one can wait until 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 :).

Why we made the bid in the first place

…and now we arrive at the slack time, that couple of weeks between the end of the Olympics and start of the Paralympics where everyone gets a chance to relax, wind down a little, and take time away from being as resolutely enthusiastic and patriotic as we have been required to for the last two weeks (or a lot longer if you factor in the Royal Wedding and Queen’s Jubilee). However, it’s also an undoubtedly good time to reflect on what have been, whatever your viewpoint, a very eventful last couple of weeks.

To my mind, and certainly to those of the Olympic organisers, these games have been a success. Whether you feel that it was all a colossal waste of money (although how anyone can think that of an event featuring the Queen parachuting out of a helicopter alongside James Bond is somewhat puzzling to me), or the single most amazing thing to grace the earth this side of its existence (in which case you could probably do with a nice lie down at the very least), its motto has been to ‘Inspire a Generation’. From a purely numerical perspective, it appears to have worked- sports clubs of all sorts up and down the land, even in niche areas such as handball, have been inundated with requests from enthusiastic youngsters after membership, and every other sentence among BBC pundits at the moment appears to include the phrase ‘the next Mo Farah/Usain Bolt/Ben Ainslie/Chris Hoy’ (delete as applicable).

However, I think that in this respect they are missing the point slightly, but to explain what I mean I’m going to have to go on a bit of a tangent. Trust me, it’ll make sense by the end.

So…, what is the point of sport? This has always been a tricky one to answer, the kind of question posed by the kind of awkward people who are likely to soon find an answer flying swiftly towards them in foot-shaped form. In fact, I have yet to hear a convincing argument as to exactly why we watch sport, apart from that it is for some unexplained reason compelling to do so. But even if we stick to the act of participation, why do we bother?

Academics and non-sportspeople have always had a whole host of reasons why not, ever since the days that they were the skinny, speccy one last to be picked in the dreaded playground football lineup (I’ve been there- not fun). Humans are naturally lazy (an evolutionary side-effect of using our brains rather than brawn to get ahead), and the idea of running around a wet, muddy field expending a lot of precious energy for no immediately obvious reason is obviously unappealing. Then we consider that the gain of sport, the extent to which it contributes to making the world a better place is, in material terms at least, apparently quite small. Humankind’s sporting endeavours use up a lot of material for equipment, burn a lot of precious calories that could be used elsewhere around the world to help the starving, and often demand truly vast expenses in terms of facilities and, in the professional world, salaries. Even this economic consideration does not take into account the loss in income presented by the using up of acres upon acres of valuable land for sports facilities and pitches. Sport also increases the danger factor of our lives, with a heavy risk of injury ranging from minor knocks to severe, debilitating disabilities (such as spinal injury), all of which only adds to the strain on health services worldwide and further increases the ‘cost’ of sport to the world.

So why do we bother with it at all? Why is it that the question governments are asking themselves is “why aren’t enough kids playing sport?” rather than ‘why are so many of them doing so’? Simple reason is that, from every analytical perspective, the benefits of sport far outweigh the costs. 10% of the NHS’ entire budget is spent on dealing with diabetes, just one of a host of health problems associated with obesity, and if just half of these cases were to disappear thanks to a healthier lifestyle it would free up around an extra £5 billion- by 2035, diabetes could be costing the country around £17 billion unless something changes. Then there are the physical benefits of sport, the stuff it enables us to do. In the modern world being able to run a kilometre and a half in four minutes might seem like a pointless skill, but when you’re being chased down the street by a potential mugger (bad example I know, but it’ll do) then you’d definitely rather be a fit, athletic runner than slow, lumbering and overweight. Sport is also one of the largest commercial industries on earth, if not on a professional level then at least in terms of manufacture and sale of equipment and such, worth billions worldwide each year and providing many thousands or even millions of jobs (although some of the manufacturing does admittedly have a dubious human rights record). The health benefits of sport go far beyond the physical & economic too, as both the endorphins released during physical activity and the benefits of a healthy lifestyle are known to increase happiness & general well-being, surely the ultimate goals of all our lives. But perhaps most valuable of all is the social side of sport. Whilst some sports (or, more specifically, some of the &%^$£*)@s involved) have a reputation for being exclusive and for demoralising hopeful youngsters, sport when done properly is a powerful force for social interaction & making friends, as well as being a great social equaliser. As old Etonian, heir his father’s baronet and Olympic 110m hurdles finalist Lawrence Clarke recently pointed out in an interview ‘On the track it doesn’t matter how rich your family is or where you’ve come from or where you went to school; all that matters is how fast you can get to the finish line’ (I’m paraphrasing, but that was the general gist). Over the years, sport has allowed mixing between people of a myriad of different genders and nationalities, allowing messages of goodwill to spread between them and changing the world’s social and political landscape immeasurably. This Olympics was, for example, the first in which Palestinian and Saudi Arabian women competed, potentially paving the way for increased gender equality in these two countries.

Clearly, when we all get behind it, sport has the power to be an immense tool for good. But notice that nowhere in that argument was any mention made of being the physical best, being on top of the world, breaking world records because, try as one might, the value of such achievement is solely that of entertainment and the odd moment of inspiration. Valuable though those two things surely are, they cannot begin to compare with the incalculable benefits of a population, a country, a world united by sport for the good of us all. So, in many respects, the success of an Olympic games should not be judged by whether it inspires a new superstar, but rather by how it encourages the guy who turns up with him at that first training session, who might never be that good a competitor… but who carries on turning up anyway. The aim of top-flight sport should not be to inspire the best. It should simply be to inspire the average.