In the mid 19th century, a Frenchman by the name of Jules Leótard developed the art of trapeze, whilst wearing some skin-tight clothing that would later be named after him. Given that he was constantly experimenting to see what was possible, he fell frequently and violently, and it’s a wonder that he didn’t die given that his safety provision was a swimming pool, as opposed to say, netting or giant crash mats. Quite how trapeze-diving hasn’t become an Olympic sport yet baffles me, but I went trapezing last month and even without the water it was a pretty awesome time.

Flying on a trapeze is simply a combination of timing and physics and, given that I’m constantly working on the first and enamoured of the latter, it was always going to be fun. A trapeze is, essentially, a pendulum: a surprisingly heavy metal bar suspended by two ropes from the ceilings. One climbs a ladder, leans thrillingly far out on a rather precarious platform whilst being held back by a helper, grabs the bar and on a given signal, jumps into the air and lets gravity do the rest.

The potential energy of a trapeze artist is at its maximum when the artist is about to jump, a value roughly equivalent to mgh (mass * gravity * height of the pendulum above its lowest point). The maximum speed is therefore simply (2gh)/2, which comes out to about 5.8m/s (a mere 13mph) in the space where I was practising. Note that mass is omitted in this second formula: the bigger you are, the exact same rate at which you fall. Jumping forwards to get a speed boost also does nothing, the only variable is ‘h’, the height at which one starts. Pendula are quite amazing in many other ways too: no matter how high you start their swing, they will ‘always’ (physicists beware) take the same amount of time to return to where they started (their period). If you ever need to make a measurement but only have a stopwatch and some string, a pendulum with a period of one second is one metre long. I learned most of what I know about penulda from Walter Lewin and if you haven’t yet seen his lectures…enjoy.

Simply flying on a trapeze, whilst fun, will soon take a toll on the arms and air-resistance will kill the fun before too long. So, instead, we move on to tricks. One fun trick which I’m not yet skilled enough to perform is to move between standing on top of the trapeze, to hanging underneath it by one’s feet. Other than the thrill of rapid inversion, this brings a second adrenaline rush in that it extends the length of the pendulum quite significantly, and therefore brings with it a very significant sudden acceleration (h is extended by the artist’s height, upping the maximum speed).

Most tricks, however, go the other way, and involve the artist pulling themself up onto, over and around the bar in various positions. This requires very little in the way of upper-body strength. A pull-up on a static bar requires overcoming gravity (F=gm), or simply lifting one’s body weight. On a trapeze there is an additional centripetal force of mv^2/r (where r, radians, is helping us calculate the angular acceleration) at the nadir of a downswing on a trapeze, in my case 5.8m/s as calculated above, this force is around 2/3 that of gravity. Despite this fact, most male first-timers on trapeze will always try to pull-up during their initial downswing – I don’t know why, muscle reflex maybe from pull-up bars maybe – which is the equivalent of trying to lift their own body weight plus two-thirds. They invariably fail to do so.

At the zenith of a swing, however, this centripetal force nears 0 and, furthermore, the artist has significant upwards momentum in their favour. Lifting one’s legs or body at this point requires far less effort than it would on a static bar, and there’s a feeling of approaching weightlessness if the timing is precise. Physics and timing, all you need in trapeze and all you need in life.

Here’s a video of my first time.

Not the most graceful, but it got better, and I even jumped off my trapeze onto a catcher the last couple of times.

Xx

My recent Spartan Race featured a 25-foot (7.62m) jump off a cliff which, whilst scary, was by no means the longest I’d been in free-fall for recently. Ignoring any resistance for the moment – I have a lot to say on the subjects of friction and turbulence later – basic physics tells us that this fall took around 1.247 seconds, although it felt more like 10 as I plunged into nothingness.

h = vt + at^2
t = sqrt(2h/a)

h = distance travelled (metres)
v = starting velocity (metres/second)
a = acceleration (metres/second/second)
t = time (seconds)

Over at Disney’s Blizzard Beach, where I’d been a couple of weeks earlier, they have a water slide by the name of Summit Plummet which in the space of about 5 seconds takes one from 0-60mph and right back to 0 again. This is a 120ft (36.58m) drop, but the queue of happy tourists, the smiling Disney lifeguards and the general sense of organisation and safety does a lot to reduce the fear factor.

I say ‘about 5 seconds’ because, whilst waiting in the queue, I took the opportunity to count how long it took between someone pushing off at the top and splashing down at the bottom of the slide. Whilst it was fair to assume a lack of friction for a brief free-fall, omitting it for a longer trip down a water slide is a recipe for error: our formula above claims the trip should only have taken 2.73 seconds. Sometimes it helps to get a feel for these things graphically; a quick trip to Wolfram Alpha will help there. I’ve graphed it in feet rather than metres to help with your intuition. From here on I’ll be providing links to Wolfram Alpha equations when I give values.

Inclined Planes
There are a wide range of factors leading to this 2.27 second discrepancy. The first and easiest to comprehend is that Summit Plummet is, of course, not a sheer free-fall. There is a wildly varying range of guesses on the Internet as to the incline of Summit Plummet, ranging from 66 to 88 degrees. It certainly feels like a sheer drop, but people are notoriously terrible at estimating inclines: ask someone climbing a steep hill what the incline is an they’re likely to say around 45 degrees when it’s more like 15. As such, let’s take a conservative guess that Summit Plummet has a 70 degree incline.

a = sin(θ)g

a = acceleration
theta = angle with plane
g = acceleration due to gravity

We now have an acceleration of only 9.209m/s/s down the slope. A 36.58m vertical fall at a 70 degree angle means a total distance to travel of 38.92m (thanks Pythagoras), which – according to our first formula – accounts for 0.175 extra seconds of fall-time, leaving us with well over 2 seconds left to explain.

Friction
The second-most easily calculable factor at play here is that of the friction between the rider and the slide. It is extremely difficult to calculate this exactly, and becomes near-impossible if the water flowing between the two were to be considered. We can, however, make a quick approximation.

Given my mass of 60kg, borrowing a water-slide coefficient of friction of 0.2 from this physical analysis of a loop-the-loop water slide, and assuming the frictional force is proportional to the normal force, friction merely slows our acceleration by an additional 6.84%. Together with the incline, this explains a total of 0.28 seconds of our discrepancy, leaving a full 2 seconds left over.

Air Resistance
The human body is not a particularly aerodynamic machine. When jumping in free-fall, air resistance will quickly come to equal gravitational acceleration (known as terminal velocity) after about 12 seconds giving humans a top speed of 125mph in the traditional ‘flat’ sky-diving posture. The traditional ‘bullet’ water-slide posture ups this to about 210mph, assuming no other sources of friction. Whilst people have been known to survive falls from thousands of metres, such cases are pretty rare, and a fall onto a hard surface from 50m or so is fatal more often than not.

The actual calculations needed for terminal velocity and drag are quite complex, but we can sketch a quick approximation here. I have size 7.5 feet, in the UK system, which implies a length of 2 hands and 8.5 barleycorns. These are Anglo-Saxon units of measurement; in Continental Europe shoe sizes are instead based on measurements in Paris Points. More usefully, my feet are around 26.7cm long and 11cm wide which gives a crude surface area of 0.029m^2.

D = Cd * ρ * (V^2 * A)/2

D = Drag force
Cd = Coefficient of drag
ρ = Air density
V = Velocity
A = Reference Area

Given a final speed of 60mph (26.82m/s) and assuming constant linear acceleration – which isn’t quite true, but I’ll take it – we can use 13.41m/s as our velocity. We have a reference area of 0.029m^2. The density of the air will be roughly 1.225 kg/m³ and I’m taking the drag coefficient from Wikpedia’s value for a streamlined half body of 0.09. The air resistance will average at 0.2875N. Gravity is dropping me at 60 * 9.8 = 588N, so either the impact of air resistance is negligible, or I need to revisit my calculations.

A standard BSA (body surface area) for an adult male is 1.9m^2, so I can assume my flat body might be just 1m^2. This value gives me a terminal velocity of around 103.28m/s or 231mph, which isn’t too far off the 210mph speed I identified earlier for a feet-first drop. Plugging in the actual velocity to use, this corrected formula gives an average of 35.69N of air resistance, cutting my acceleration by 6%. These figures are getting very lax right now, but keeping my eyes firmly to the ground, I’ll assume a final figure of 0.18 seconds accounted for.

Turbulence

When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.
~ Werner Heisenberg

Water is gently pumped from the top of the slide, but is generally overtaken by the rider, leading to the spray effect seen coming off big slides. One may, recalling the words of Galileo Galilei that all bodies fall at the same magnitude, wonder why this is. Water, as a liquid, is constantly in complete contact with the body of the slide, and so even with its lower coefficient of friction, has a larger frictional force overall acting on it. Much more importantly however, the water is constantly interacting with itself in vastly complex ways that can’t be modelled with any degree of certainty in even the most closed environments. As water-slide designer Marvin Hlynka says:

In terms of actually predicting where a particular drop of water or a particular body is going to be in the slide at any given time, you can’t do it, it’s just not possible.

There are 1.635 seconds as yet unaccounted for. No doubt, my calculations above are flawed and some of the remaining time may lie above. My initial prediction of 5 seconds also has some margin of error. Turbulence, however, is incalculable and mysterious. Falling is fun, but trying to work out how it happens can kill you.

Xx

The term ‘Jet Ski’ is a trademark held by Kawasaki Heavy Industries, but is popularly used to refer to any brand of personal watercraft (the correct generic term) which allows a rider to cruise over the waves on the aquatic version of a really cool sports bike. This type of popularisation, if not checked the the company owning the trademark, can lead to a trademark becoming ‘genericised’, at which point it becomes extremely difficult for that company to defend its trademark from misuse.

That said, having one’s brand name become the metonym for a type of product, as with Jet Ski for personal watercraft or, in the USA, ‘Band Aid’ for plasters, can in itself be somewhat of a lucrative opportunity for a business, with people unconsciously associating their desire for a product with that specific brand. The most famously successful corporation in this world is Coca-Cola, who have enough mind-share that people will unthinkingly ask for ‘a Coke’ rather than ‘a cola’, but have defended their trademark vigorously enough that it is still, in the UK at least, an offence to serve someone a Pepsi if they ask for a Coke, without first correcting their order.

Vaseline, Hoover, Kerosine, Zipper, Asprin and even Heroin (the latter two once owned by Bayer AG) were all once strongly-held trademarks which have since become appellatives for their respective products, and no longer enjoy any legal protection. No court has yet decided on the Jet Ski brand, but a quick trawl of news sites and other literature suggests that Kawasaki would have a hard time defending their trademark should they choose to do so.

None of this, of course, changes the fact that Jet Skis – or personal watercraft – are amazing fun. Thanks to renowned thrill-seeker Isaac Newton’s laws of motion, Jet Skis are able to easily reach 70mph or so by pumping water through their impeller out of back of the vehicle at terrific pressure. In order to achieve this pressure, they need fantastically disproportionate engines, and the Jet Ski’s I saw for rent had an engine nearly as powerful as that in my first car, which was a hell of a lot larger, and came with seatbelts, windows and doors. With all that on offer, I couldn’t pass up the opportunity to head on down to Far Rockaway a mere 8 hours after landing back in New York from my vacation in Florida to go and ride around on one.

Sailing is fun, with the wind in your hair and the rocking of a boat. Windsurfing – a favourite activity of mine back when I lived in London – is even more so, with much less protection from the elements and the ability to feel even the smallest wave beneath your feet. Jetskiing takes this raw experience, and adds to it the thrill of being able to speed up to 40mph on a whim, with precious little protection other than a cheap life-jacket and the knowledge that, if one were to fall off, the Jet Ski would be a safe 50 metres away before one even hits the sea.

Being able to accelerate and turn so quickly, Jet Skis are classed as ‘power boats’ in the informally titled Rules Of The Sea, more properly known as the International Regulations for Preventing Collisions at Sea and, as such, required to give way to sail boats, windsurfers, kayakers and the like, all of whom would have a harder time making a sudden turn.

I once had to learn the various, slightly complicated rules as to which of a pair of sail boats has right of way – a free-running boat has right over a close-hauled boat, for example, as they are much more manoeuvrable in general – but I had to quickly recap what happens when two power boats meet before I jumped on the Jet Ski. It seems there is no hard-and-fast rule for which boat has a right-of-way when two power boats meet, but on the rare occasion it came up whilst I was out there, I simply decided to turn to Starboard (one must never turn to Port to avoid a collision) and get the hell out of there, so I could resume concentrating on not falling off or flipping the Jet Ski.

The most important rule, whilst not explicitly present in the International Regulations for Preventing Collisions at Sea, is one I was taught by a windsurfing instructor, and is one I hope I never forget: if it’s big enough to destroy your vessel without noticing, it has right of way, so move.

Fair advice.

Xx

Eight weeks ago today, I agreed to join the Ab Challenge. What started as a throwaway email between a few capoeiristas in LA who were inspired by how shredded one of the girls in my class was, is now an organised, collaborative effort between some 200 capoeiristas around the globe. Although, it should be noted, the majority of participants are, in fact, based in LA or NYC, but as any resident of one of those two cities will tell you, the rest of the world doesn’t really matter too much.

My days now start with a glance at the Ab Challenge daily email, which generally comes with an inspirational quote, a story or message from one of the participants, and any updates to the suggested workout routine for the day. Once a week, the routine has been changing to encompass a different subset of muscles – the obliques, the transverses, or so on – or techniques, with specially-recorded video guides as reference. The leitmotif of the daily update is ‘Abs three times a day, breakfast, lunch and dinner’, and that’s exactly what I’ve been doing.

Breakfast
For breakfast, I’ll have a banana, yoghurt, and at least 300 reps of abs exercises in my room, where I have a multi-purpose workout bar, a medicine ball, and a yoga mat constantly set up. I’m also taking the opportunity of having such regimented workout sessions to work on a longer-term goal of being able to do 100 pushups on a whim, and so doing an increasing number of these daily. I started being able to do around 20 or so consistently, with proper technique throughout, and I’m up to 55 right now.

Snacks
After that, it’s a trip to the office, and it’s here that I’ve discovered that exercise is not just for the gym. I was initially very self conscious about doing so, but now I feel no qualms whatsoever about taking a few minutes away from work and doing a quick 100 reps or 50 pushups in the office. A few people have walked past mid-session, and a couple of them have commented, but no-one seems to really mind and, so long as I space out the exercises, I don’t end up sweaty and smelly at work. Food-wise, I’m always loaded up with fruit, nuts or trail mix, meaning I can eat smaller portions at mealtimes and never be hungry.

Lunch
For lunch, I was originally taking things a bit too far, only eating green salads or veggies & protein, but after losing about as much weight as I could healthily tolerate (I started out pretty skinny), I’ve moved away from that and instead I’m just trying to avoid overly fatty or sugary stuff. No more trips to Chipotle or Five Guys for me, but I’m not going to obsess about having some rice, bread or potatoes with my lunch.

If it’s not a workday, I’m generally out at a park or beach, which provides a perfect location for a more prolonged workout, but, even if not, I’ve discovered that New Yorkers don’t look twice no matter where I work out. I’ve managed a full two-minutes of planking on a busy sidewalk, 100 bicycle crunches on the cleanest bit of ground I could find in midtown and so-on. I should be a poster-boy for the Make New York City Your Gym campaign that’s running.

Dinner
In the evenings, the fact that I’m not drinking again definitely helps me to avoid a whole bunch of unhealthy crap – both the beers themselves and the inevitable cravings for greasy junk food – and, I’m working on it, but about 8 times out of 10 I manage to get a full workout done back in my room before I get to bed, no matter what hour I stay out until.

Naturally, all of this is in addition to Running Club – my effort to get myself and any local friends out running at 7am every morning – and Capoeira, which I’m training three-to-four times a week. I feel great. I feel healthy, and stronger than I ever have and, as there’s no-one else here to say it, thanks to this Ab Challenge I also look pretty great right about now too.

Time for a quick 100 crunches.

Xx

I like to think of myself as a fairly intelligent person. I can write combinations of letters from the Greek alphabet that look intimidating and sometimes even have some mathematical value. I can make some nice sounds on a piano and I can communicate, with varying degrees of fluency, in a number of different languages. However, the practical side of real life has always bewildered me, and since moving country this has only gotten worse. Nowhere is this more clear than in my attempted interactions with the US Postal Service.

Back in the UK, I, at some unspecified point, developed a full understanding of the postal service. It was never explicitly taught to me, I never spent hours perusing websites, I just knew how to do what I wanted to do. But, every time I interact with the postal system here, it causes me so much stress that I back out of the operation and leave with a clinging sense of shame and failure. As an example, I qualified for my Advanced Open Water Diver license back in March of 2011. The form has sat, un-posted, in the three apartments I’ve lived in since that date because the very thought of somehow obtaining a passport photo and then posting it in forces me to prolonged, intense bouts of procrastination.

The first problem is that of getting a passport photo. Pharmacies – the ubiquitous home of all convenience needs in the city – all seem to advertise this service, but on the >10 times I’ve tried to take advantage of it, I’ve either been presented with blank, empty spaces or claims that the necessary machines are temporarily out of order. Photo booths appear to be a novelty item (there’s even a FourSquare badge for finding them), found in the back of bars and seemingly installed for the sole purpose of giving newly-met lovers a place for intimate privacy without them taking up much-needed bathroom space.

Next, the actual act of mailing the form, or anything else, defeats me. The fundamentals are, as far as I can tell, pretty much the same as back home. One writes a letter, buys an envelope and a stamp, combines the three and places the resulting compound into a postbox. But still, there’s something holding me back.

Maybe it’s that the paper is the wrong size. Maybe it’s that I feel dubious about entrusting my mail to a postbox that isn’t large and red and clearly stamped with the Crown and the words Royal Mail. Maybe it’s that I’ve never successfully bought stamps here — there are confusing machines at the post office, and apparently with a secret wink and handshake they can be obtained at the bodegas, but I haven’t yet tried this. Even if I procured stamps, I have no idea how many I need to use. Are there weight limits? Size limits? Does it cost more to post things out of state? I could probably look up some of this, but already I feel my heart racing and my mouth drying up just considering these permutations.

The few times I have managed to get a postcard back home or send in my taxes, I’ve simply embraced my shame, queued up at the gigantic post office near WTC, and pretended I’m only in town for the week and let the (un)friendly counter assistants walk me through the process as they would a small child, waiting patiently whilst I fill in a return address (a concept I’ve never understood), fill out customs forms and so on.

But now, I’m in trouble. On my SCUBA certification form, I’ve already crossed out the original Manhattan address I put down and filled in my next address in Queens. There is now no room for my new Brooklyn address, so I’m going (soon, I swear) to rely on the USPS’s ‘free’ mail-forwarding service to get the license to me. This service, provided for a simple $1 credit-card transaction to prove my identity, and in return for my agreeing to receive a number of confirmation letters through the post, which feature, on average, 23 separate adverts and targeted newly-moved offers.

There’s a reason I throw away unread all my post, other than exciting looking packages and handwritten letters of love from abroad.

Xx

American pie is a much-vaunted cultural export, a sweet comfort food that Americans from any state can unite behind enjoying and the subject of much regional pride. Don McClean wrote an eight-and-a-half minute long song about this delicious dessert, and a whole series of Hollywood documentaries have been produced detailing the delight that American Pie can bring to school-aged teens. However, in the pie-speaking world, it’s a poor cousin to the other pies that Americans miss out on in their devotion to sweet and sugar snacks, especially their beloved apple pie.

Historically, the pie-polarity across the Atlantic was reversed. With few apple trees available in the Americas, the colonists would much more commonly eat meat pies, and the apples they did have would go towards making (hard) cider instead. Now, cider in America is normally non-alcoholic and served to children, meat pies are a relative rarity and apple pie has become as American as… well, you see my point.

Pie in America is generally a sweet dish, with a double-crust encasing a layer of fruit. Some variants exist, such as deep-dish apple pie, containing only a top-crust, and various bottom-crust tarts, such as the Christmas staple of pecan pie, or The Official Pie of the State of Florida, key-lime pie, whose status was determined by a 38-1 vote in the Senate and a 106-14 vote in the House of Congress. 4 of the 14 naysayers in Congress, it should be noted, later changed their votes in favour of the pie.

I. Summary:
This bill designates key lime pie as the official state pie.
This bill creates section 15.052, Florida Statutes.

II. Present Situation:
Currently, no pie is designated as the official state pie.

Meat pie is a relative rarity in the USA, but they do have one offering that comes close, pot pie (most commonly filled with chicken), which I have yet to have a good experience with. A pot pie is closer to a pasty than a true pie, and generally requires a pie dish to maintain its shape, being fully encased with puff pastry. The interior is often a light stew, not to be confused with British chicken & mushroom or chicken & leek pies.

A true meat pie, however, is an experience not to be trifled with. Instead of a flaky puff pastry, the bottom crust of this pie is a solid, stable crust made with suet (raw beef fat) or lard (raw pig fat), neither of which appear to be readily available in the USA, but can apparently be obtained from some butchers. The inside is a thick gravy, stuffed with meat and bursting at the seams as soon as it is touched. Local pubs and breweries in the UK will often offer a steak & ale pie made with their signature ale and served with mash & peas — there’s no better treat after a day out in the countryside.

Britain has yet more to offer aside from these. Cornish pasties, which the Cornish claim as their ‘national dish’ – refusing to accept English dominance in true Celtic style – are an inimitable treat and finding one at the bottom of a well-used rucksack that hasn’t been touched for weeks is a cause for immediate celebration. They are, however, best enjoyed warm and from within Cornwall, with the various supermarket brands a mere shadow of the real stuff. A Cornish pasty is generally made with minced beef, potato, swede and onions, wrapped in a thick crust, crimped at one side.

Pork pies likewise confuse the Americans. They’re one of the few meat products which can be brought through US customs without being wrapped in innumerable jumpers and accidentally missed off the customs declaration forms, but when my father brought one over for me when he came to visit, the customs officers were very much intrigued, and spent a long time questioning him over them. Then again, it possibly didn’t help when he replied to the innocent question, “What’s a pork pie?” with “It’s pork. In a pie.” For the record, it’s cooked pork and pork fat, wrapped in pork jelly, sealed in a hot-water crust pastry, generally eaten cold, and it’s lovely.

Finally, I failed to work this into the narrative, but I still want to take a moment to note that there’s such a thing as a pie bird. In the old days, at kingly feasts, a bird would be placed on top of each pie to indicate the filling, and this led to the concept of the pie bird, which is a decorative cooking aide that allows steam to escape from a cooking pie.

Now, if you’ll excuse me, I’m off to wipe the saliva from my keyboard before it drowns.

Xx