Auckland’s 2017 Bike Challenge winds up today; February may be the shortest month, but it is prime cycling season in Auckland, with decent weather and long evenings. I don’t usually log my saddle-time, but I tracked my activity while taking part in the challenge. In the course of the month I made 36 trips covering 345km on my bike. If I’d traveled the same distance by car, I would have emitted 69 kg of carbon dioxide.
I can add a few more stats to that: the same amount of travel by car would have cost me a couple of hundred dollars (that’s just for petrol, plus parking in central Auckland), or a bit over a hundred by bus.
On the other side of the ledger, while the running costs of a bike are close to zero, it occasionally needs a little love from a mechanic – and I find that the rider appreciates a bonus mango lassi with his lunch.
Over the last year, I’ve moved from a fair-weather cyclist to something close to a year-round rider. My trousers fit a little more loosely than they did 12 months ago, as I am around 5kg lighter. Not a huge change, but a result that goes against the run of play for a (let’s be honest) middle aged guy who spends a lot of time at a desk. I don’t puff so much going up the hills any more, and a long walk seems a lot shorter than it used to. An e-bike may lie over the horizon, but for now I’m fully pedal-powered.
It’s not easy to acquire a new habit that’s stuck as well as this one has, so what made it possible? The first answer is infrastructure; my commute is mainly along Auckland’s Northwestern Cycleway, which runs along the side of the highway to town – and it is just much (much!) nicer to be riding down a tree-lined car-free path than it is to be sitting in traffic on the adjacent motorway.
My commute – Auckland’s Northwestern Cycleway
Clearly, I am not the only person to think so, as traffic on the Northwestern cycle path has been growing at around 15% a year over the last five years, to the point where speeding road warriors need to learn to move more slowly around pedestrians and upright cyclists. It’s still not perfect, and I face a few hundred hairy metres along Symonds Street where I can dodge buses and connect with my inner cycle courier, but it’s clearly good enough.
The second ingredient you need for a year-round cycle commute is the “end of ride” facilities – not just a place to lock my bike (with a decent lock, since theft is an issue in town), but a shower at work, for reasons that surely need no explanation. In fact, with an increasing number of my colleagues starting to show up on bikes there is occasionally a queue for the shower in my building, which can make the workplace feel a little like an old-school student flat in a house with a lot more bedrooms than bathrooms.
And that is the third part of the recipe – I am not doing this on my own. Which is, of course, exactly the idea behind the Bike Challenge, since nudges from our friends and colleagues are potent tools for changing our habits.
Bikes, at the Aspen Center for Physics. Image: Richard Easther
Last month, I visited the Aspen Centre for Physics, on the outskirts of Aspen, Colorado. It is a wonderful place: they give you a desk, a wifi connection, time to think, and a bike to get around town.
Poster of Einstein, Image Richard Easther
It’s no coincidence that, in the lobby of ones its buildings, the Center has a poster of Einstein on a bike. Einstein is often quoted as saying he got his best ideas on a bicycle. (Although if Einstein actually said all the things he is supposed to have said he must have been more talkative than most human beings.)
Officially, I was in Aspen to think about the Big Bang, but while I was there I also found myself mulling over the physics of cycling. Not the physics of why bikes stay up (although that is complex and certainly interesting), but how physics lets bikes be so good at what they do.
Pedestrians: Hadazbe tribespeople, returning from a hunt. Image: Wikimedia
Physicists often look at the world in terms of energy. To a physicist, power is the rate at which a system uses energy, and we measure power in Watts. A typical pedestrian in motion has an “output” of about 70 Watts, similar to the energy emitted by an old-school incandescent light-bulb. (The 70 Watts is the extra mechanical power delivered by your body when you get up and start walking.)
Image: Jolisa Gracewood
Typical urban cyclists use energy at roughly the same rate as pedestrians, but travel about three times faster. Or put another way, you can cover three times as much ground on a bike as you do on foot, for the same amount of effort. Speeds vary, but 15 kilometres an hour is reasonable for an “upright” cyclist, whereas typical walking speeds are around 5 kilometres an hour.
Tour de France riders. Image: Wikimedia
By contrast, Tour de France riders manage a sustained output of close to 300 Watts, just over four times more effort than you need to move at a comfortable walking pace. Regular human beings can only maintain this level of activity for a minute or two before tiring.
Windsock Image: Wikimedia
So when you’re on a bike, where does the energy go? A cyclist traveling at a constant speed on flat ground must replace energy lost to friction and air resistance. The frictional forces acting on a bike (i.e. at the point of contact between the wheels and the ground, and in the chain and gears) increase in proportion to the cyclist’s speed. But air resistance is worse: “drag” really is a drag. The faster you move, the more air you move through. And when you are moving quickly, you are stirring the air more vigorously. The combination of these two effects makes air resistance a double whammy for cyclists: doubling your speed, even on a still day, increases the air resistance by a factor of four. And winds just make things worse — even a gentle headwind can double the air resistance, boosting the energy cost of cycling. So you really feel a headwind on a bike.
One Tree Hill, Auckland Image: Wikimedia
And let’s not mention the hills… Except that in Auckland we really do have to talk about the hills. Ancient Rome may have been built on seven hills, but my city of Auckland is built around something like 40 (inactive!) volcanic cones. Auckland is not as vertiginous as parts of San Francisco, but it is decidedly lumpy when you get on a bike.
Tower crane Image: Wikimedia
The problem with hills is that they turn your bike into a crane; you are not just moving horizontally, but you have to lift yourself and your bike to the top of the hill. And that costs energy.
Image: Richard Easther
It doesn’t need to be a big hill. Even a gentle slope doubles the energy output of a cyclist; the “hill” in the picture above has a slope of 2%, but if you wish to keep moving at a steady 15 kilometres an hour, you would need to double your energy output to climb it on a bike. You can climb it more slowly (that’s what gears are for) but if you want to keep moving more quickly than a pedestrian you have to work harder to climb the hills. Anyone who has ever got off their bike and pushed it up a hill knows that there is a point at which you might as well walk.
US Marines Image: Wikimedia
Given the hills and headwinds, riding to work may only be workable if you don’t mind a workout on the way to work. So for many people hills and headwinds are what keep our bikes in the garage, rather than out on the road.
Electric bike (and Auckland harbour) Image: Antoine Peters
But if physics explains why cycling can be hard work, it also generates the solution: the electric bike. In New Zealand, the energy output of an electric bike is legally limited to 300 Watts: any more and it is a motorbike, not a bike with a motor. But even this little motor is like having a Tour de France rider hidden in your hub, helping you up the hills.
The Flinstones Image: Hanna-Barbera
This explains why no-one adds pedals to a car: while a little motor is a big help to a cyclist, even a small automobile engine can deliver up to 100,000 Watts and no human being could contribute enough extra energy to make a difference to a car. (No-one told Fred Flintstone this.) But on an electric bike your legs can always make a useful contribution.
Image: Universal Pictures
The upshot is that an electric bike works the way bikes work in our dreams. On an e-bike, hills and headwinds don’t slow us down, and the motor is small enough to make sure it still feels like you are riding a bike.
A cyclist’s little helper? Image: Wikimedia
And while e-bikes can let anyone cycle like a crack athlete, you can still look our kids in the eye when you get home at the end of the day.
There is a fair bit of excitement about electric cars, but when it comes down to it, they are still cars. They might reduce your carbon footprint, but they won’t change your life – if you swapped all the regular cars on a traffic-clogged road with electric cars, it would still be clogged with cars. Whereas electric bikes let us live in ways that regular bikes (or cars) do not.
Copenhagen street scene. Image: Wikimedia
We hear a lot about how cities like Auckland should be more like Amsterdam or Copenhagen. There are all sorts of barriers between us and that aspiration, but hills don’t need to be one of them.
Over the next few years, Auckland is going to get some stunning cycling infrastructure and my hunch is that electric bikes will help Aucklanders make the most of it. Bikes gave us a better way of getting around than walking, and electric bikes give us a better way of biking.
You don’t have to be Einstein to understand this. Just get on an e-bike and take it for a ride.
CODA: This blog is based on a Pecha Kucha presentation I gave in Auckland; you can watch it on video here.
I recently blogged on the physics behind modelling traffic flow. This is not just an academic question for me, as the billion dollar Waterview Connection is a couple of kilometres from my house. The project involves the biggest road tunnels in Australasia, completes a key arterial connection in Auckland and is (surprisingly enough) coming in on time and on budget.
Simultaneously, Auckland Transport is revamping a section of the Great North Road running parallel to the Northwestern Motorway, one of the roads being connected by the Waterview Connection. As part of this work, Auckland Transport wants to widen the road to make way for a short, additional turning lane at one intersection. There are a bunch of options for accomplishing this, but the one they chose requires felling six mature pohutukawa trees.
A broad coalition of people and organisations has sprung up in the trees’ defence, including the local Board, a piece of city council itself as well as the city’s own Parks Department. The trees are now festooned with signs, banners and a “yarn bomb”, while thousands have joined the Save the Western Springs Pohutukawa group on Facebook and the trees themselves are tweeting. [The Lorax asked who would speak for the trees, but now it seems they can tweet for themselves.]
The pohotuKawa Six
Since Auckland Transport’s argument for felling the trees hinges on traffic models, I was keen to take a look at the modelling they used to settle on their “preferred option”. Either my google-fu is weak or the detailed models are not in the public domain. That said, digging into the paperwork, I found “Appendix H“, reviewing the analyses performed by Auckland Transport and its contractors, written by Leo Hills, an independent traffic engineer.
The first thing that struck me is that Appendix H is a tepid document. Its tone reminded me of an examiner’s report for a thesis whose author has done the bare minimum to get by: the student may pass, but no-one involved will be proud. (Except possibly the student, of course.) It damns Auckland Transport’s analyses with faint praise, queries the reasoning behind their choices, and points out that almost identical results could be obtained without removing the trees.
In other words, an independent analysis of Auckland Transport’s own modelling comes well short of giving it a ringing endorsement.
Meanwhile, the New Zealand Ministry of Transport’s Strategic Policy Programme has produced some fascinating reading (seriously – I know we are talking about traffic here, but it is great to see government departments sponsoring evidence-based research-driven thinking). One of the reports explores the forces shaping the future of transport in New Zealand. The study on projections of future demand is particularly illuminating:
TRansport projections for Light vehicle use against actual data for New Zealand; Ministry of Transport
Between around 1980 and 2004 vehicle-use grew by around 3% per year. In 2004, for whatever reason, this growth levelled off. What’s more, per capita usage actually declines when you account for the population increase since then.
Despite this, assumptions about future usage patterns have repeatedly assumed that the steady rise was about to kick off again – look at the colourful sequence of rainbow lines attempting to find their way to the top-right corner. But so far, the real world and its real people in their real cars have refused to cooperate. This isn’t a New Zealand-only quirk; similar trends have been observed world-wide, although the detailed causes vary from country to country. Simultaneously, public transport use in Auckland has increased and there is a growing focus on cycling, again in step with worldwide trends.
Putting all this together and looking at the trees, I have three big questions:
The traffic modelling behind Auckland Transport’s analysis evaluates the design options for the intersection in terms of expected delays for westbound drivers (i.e. the people who benefit from the extra lane) in 2026; most of them during the evening commute. There is no mention of the uncertainty in the traffic projections that go into the models, either nationally or within the corridor defined by the Great North Road and adjacent motorway. However, going by recent history and the graphs above, if the numbers are wrong, they are likely to be too high, rather than too low. So what are the assumptions that go into the models, and do they depend on the sort of projections that have been wrong for a decade or more?
Leo Hills’ report explicitly says that the modelling only considers the intersection itself, and not the overall network — despite the large changes that can be expected once the Waterview Connection is complete. Nor is it clear what the model assumes about future public transport usage and cycling levels. So is the model simply too limited to capture the full behaviour of road users in 2026?
The “figure of merit” used to choose between design options is the delay-time for commuters on the Great North Road. However, if traffic jams form when the number of cars using a road passes a given tipping point, small changes in the number of cars on the road can cause disproportionately large changes in travel time. This magnifies the impact of assumptions about vehicle numbers going into the model. Do the models account for this? And, if so, how?
Putting all this together, it seems to me that while the traffic engineers have undoubtedly done their jobs when it came to constructing the models, the uncertainties related to the specification of the models are potentially huge. Consequently, I would love to see an open discussion of the modelling used by Auckland Transport to make this decision, and to know how they accounted for uncertainties in vehicle numbers and transport patterns.
I travel past the trees (sometimes by bike, sometimes by bus, sometimes by car) twice in each working day – I would hate to see them cut down over a piece of fuzzy math.
POSTSCRIPT: Full disclosure; my partner is a spokesperson for the Pohutukawa Savers, and I am (as usual) not speaking on behalf of my employer on this blog.
New Zealand’s North Island was treated to a spectacular fireworks display around 10pm last night, and reports are consistent with a large meteor or “space rock” hitting the earth’s atmosphere. I missed it, but two people in my family saw a bright flash in the sky (“What on earth was that?” “Uh, dunno, what on earth was what?” said the resident scientist. Turns out it was something that was not on earth at all.)
Fireballs like last night’s event are sometimes called bolides and the brightness, reported sonic booms and an explosion at altitude are all consistent with this class of events. Even so, this was a far smaller rock than the one that exploded above Russia (which I blogged about here). A study by Brown et al., published in Nature (420, 294-296, November 2002), found that hundreds of objects roughly half a metre in diameter and packing an energy equivalent to 100 tons of TNT hit the earth every year; last night’s event would have been in this size range or a tad smaller. Really big events with an energy similar to the largest nuclear weapons ever tested occur much less often; maybe once every ten thousand years. (The rate of these really big, really rare events can be figured out from the number of rocks we see making a close pass to the earth, not by counting them as they happen.)
From The flux of small near-Earth objects colliding with the Earth, P. Brown, R. E. Spalding, D. O. ReVelle, E. Tagliaferri and S. P. Worden Nature 420, 294-296(21 November 2002)
The plot below shows the distribution of big fireballs collated by a NASA study; if you look carefully just one of them sits squarely on top of New Zealand.
NASA study showing detected “fireball” events.
Bolides are like lotteries – the chances of you winning the big prize are small, but the chances that someone, somewhere will win are pretty good. So if you missed last night’s fireball, you will wait a long time before seeing another one.
Reports that came in from a large part of the North Island suggest that the object was moving roughly north-south. Given that, there is a chance it was a piece of “space junk” rather than an actual meteor; many spacecraft move in orbits taking them from pole to pole. Objects in low earth orbit are routinely tracked from the ground, and if this was a piece of orbiting debris coming back to earth it was easily big enough that its absence will be obvious.
On the other hand, if this was a space rock it is likely to have been orbiting the sun since the birth of the solar system itself. For 4.6 billion years it led a largely uneventful existence, but the last few seconds of its lifetime were spectacular.
Driving home one night last week, Auckland’s Spaghetti Junction was more than normally congested and my thoughts turned to physics. Sluggish traffic provided my initial topic – the differences between sand and water. – as well as letting me follow my train of thought (an actual train would be a welcome option, but that’s another story) without endangering my fellow road-users. Admittedly, many of the differences between sand and water are obvious to anyone who visits a beach, but I was thinking about how sand sometimes flows like a liquid.
Anyone who has seen an old-fashioned egg timer knows sand can flow, but flowing sand is not the same as flowing water. If a hose is leaking from a pinprick, increasing the pressure makes the water flow faster. On the other hand, pressing down on sand flowing through a narrow funnel can cause the grains to lock together, stopping the flow entirely. The technical term for this is “jamming”, which is how I got to be thinking about sand while sitting in traffic.
Simulation showing spontaneous jamming in a granular material.
Physicists often explain the properties of “granular materials” like sand by looking at interactions between adjacent grains. The same reasoning can be used with other systems – the complex movements of flocking birds are reproduced by boids, “birdoid-objects” that obey a few simple rules; avoid collisions but stay close to the flock…
Just as scientists can explain the flocking of birds, we can also model the “flocking” of cars, exploring how patterns in traffic arise and dissipate. For instance, the videos below show an experimental traffic jam in Nagoya and a simulation from a group at MIT, each capturing the same phenomenon:
A person stuck in traffic might wonder why scientists would want an artificial traffic jam, but figuring out how they form is a step towards preventing them. As a physicist, I was pleased (but not surprised) to see that both studies were published in physics journals – the Nagoya group published in the online New Journal of Physics while the MIT paper appeared in the Physical Review. And, just in case you are wondering, I looked these papers up after I had arrived home.
The MIT group treated traffic as if it was a fluid, but real vehicles are more like a flock of birds than water in a pipe. (OK, only to a physicist: car don’t look much like birds OR liquids, but bear with me.) However, there are “agent models” or microsimulations that simulate the behavior of individual road users and the surprisingly lifelike scene below which includes vehicles sharing lanes (more common in places with lots of motorbikes or “tuk-tuks”) was generated by an agent-based simulation:
A visualization of a PTV Vissim simulation featuring non-lane-based traffic. Different vehicles with a variety of widths interact with each other and find their way wherever there is enough space to fit.
The moral of this story, if it needs one, is that some science lies just beneath the irritation of city traffic and, for this physicist at least, contemplating it made a slow drive home pass more quickly.
Coda: The Sand Reckoner is the title of a short piece by Archimedes, where he works out the number of grains of sand the universe could hold. Physicists have been thinking about sand and the universe for a very long time.
Last month, I visited the Yukawa Institute for Theoretical Physics at Kyoto University. Yukawa — Japan’s first Nobelist in physics — looks to have been an amiable man, so far as one can tell from a statue. He stands watch outside the institute, and when I was there someone had thoughtfully left a food offering (shinsen) on this otherwise secular shrine.
A few bus-stops beyond the university was Ginkakuji — the Temple of the Silver Pavilion — a far less secular site, and one of my favourite places on the planet.
Ginkakuji — Image:Wikipedia
The wooden Kannon-den (the building in the photo) still looks much as it did when it was completed in the 1490s under the aegis of shogun Ashikaga Yoshimasa. (That said, the tranquil complex acquires a darker edge when you learn that Yoshimasa made a Nero-esque retirement there while a war raged outside, during which Kyoto burned and its broad river was jammed with the bodies of the dead.)
The building has a severe charm, but for me, the most memorable aspect of Ginkakuji is the grounds. Specifically, the contrast between the hillside above the temple, which contains a lovingly tended assemblage of mosses and trees, and the haunting geometry of the Zen sand-garden that surrounds the pavilion.
When I visited, I found myself wondering about the practical aspects of Zen gardening. Within the Zen garden, the iconic, Fuji-esque “Moon-Viewing Platform” or Kogetsudai, is a conical mound of sand that stands as high as an adult. Ginkakuji is a World Heritage Site, so the Kogetsudai is almost certainly the world’s only UNESCO-listed sandcastle. Unlike a pyramid or a stone temple a sandcastle is an inherently evanescent structure, which must present a challenge to its curators.
A key parameter for any granular material is the wonderfully named angle of repose, the maximum slope a granular material can sustain before it starts to flow. (You can see the angle of repose in the kitchen — take a bowl of sugar, and tilt it a little. Initially the surface of the sugar stays fixed relative to the bowl, but if you increase the tilt past a critical angle the sugar begins to flow in a series of little avalanches — and when you return the bowl slowly to the vertical, the surface of the sugar remains at a lean. That’s the angle of repose: the highest angle at which the sugar can safely maintain itself.)
For dry sand, the angle of repose is around 30 degrees, a far gentler slope than the walls of the Kogetsudai. So this sandcastle requires artificial assistance. I was curious as to how it holds itself up, and how often it needs maintenance — surely more than once a day?
Luckily, my visit coincided with a temple worker tending to the Kogetsudai with a pair of wooden trowels and — aha! — a no-nonsense watering can, which he refilled several times from the adjacent pond. As anyone who plays in a sandpit knows, a little water does wonders for stability. In small quantities, water creates bonds between adjacent grains, so damp sand holds together more tightly than it does when dry. Now I know how Kogetsudai stays up, although I have yet to see what happens when it rains.
Simple systems with subtle behaviour are playgrounds for scientists. Composed of solid grains, granular materials can flow like liquids in the right circumstances; they are hard to model mathematically, and crop up in fields ranging from geophysics to industrial processing. A few years ago, a paper titled How to Construct The Perfect Sandcastle appeared in Scientific Reports, an offshoot of Nature. The title might be tongue in cheek, but the topic is serious; playing with sand provides work for physicists as well as for gardening monks.
Postscript: I looked, but could find very little information on the web regarding the maintenance of the Ginkakuji gardens, beyond this Youtube video. And my thanks to Jennifer Geard for reminding me of the “angle of repose”.
Just in case you haven’t seen the news, the Earth had two close encounters withspace-rocks on February 15. A small asteroid 2012-DA14 whizzed past the earth, 30,000 km above the clouds, and an even smaller rock exploded above Lake Chebarkul — the largest meteoroid to hit the earth in 100 years.
A day with a space rock is rare enough; a day with two space rocks is super-rare. Meg Urry (a former colleague of mine at Yale) did the numbers in a CNN Op-Ed — meteorites like the one that hit Russia are once in a century events, but asteroids like 2012-DA14 show up about once a decade. There are 36,500 days in a century (ignoring leap years) so the chances of getting these two events on the same day is around 1 in 100,000,000 (36,500 x 3,650, after rounding).
But if you think about it, you see a huge number of rare events in a single day — it is just that not all rare events are interesting events. And certainly not as interesting as this one:
Examples of rare-but-boring events are easy to find. Instead of looking at a dash-cam movie of an exploding space rock, you could have looked at the number plates of approaching cars, or a row of cars parked outside your office — like these:
The last digits of these plates form the sequence 7-8-0-3-0-9-9-6-9-3-8-2-0. There are 10 trillion possible combinations of 13 integers — so the odds of seeing that particular sequence of numbers are far lower than two asteroids having a close encounter with the earth on February 15th. But I didn’t walk down the street thinking “7-8-0-3-0-9-9-6-9-3-8-2-0, wow what are the odds of that?”
In saying this, I am assuming any sequence of final digits is as likely as any other — not a bad guess for cars parked on a busy street. On the other hand, these plates mostly start with letters from A to E, which would look odd if you didn’t know that New Zealand issues number plates sequentially — the distribution of first letters may be random, but it is not uniform. Or, what we learn is that these cars are mostly a few years old, but not ancient. (Cars bought in 2012 got plates starting with G)
So, how do we think about the 1 in a 100 million coincidence from February 15? Did the earth move through an asteroid field, like this one from Star Wars:
The Millennium Falcon enters the Hoth Asteroid field (image from http://starwars.wikia.com)
Unfortunately for this hypothesis, this week’s rocks came from different directions in space and could not have been formation-flying around the sun. Asteroids can have moons, but if the Earth had a close encounter with a pair of asteroids they should be very close together — the two events would be separated by seconds, not hours. (Sadly, asteroids only move round in big groups in the movies — even if a group of asteroids like this formed in our solar system, it is unlikely to be a stable configuration.)
But some interesting events appear ordinary at first glance. Many geologists and stratigraphers looked at a thin band in columns of rock which marks the boundary between the Cetaceous and Paleogene eras.
[United States Geological Survey]
There are many bands, but the band in this photo turned out to be the signature of an asteroid – much bigger than either of this week’s space rocks — that collided with the Earth 66 million years ago, triggering a mass extinction.
So the challenge for science is to explain the things that need explaining, and to explain why we ignore the things that don’t. And to have the wisdom to tell the difference.
![Waterview Connection [Russell Brown, publicaddress.net]](https://excursionset.com/wp-content/uploads/2024/04/0e1b3-splay-0-940-0-0.jpg)
![Waterview tunnel boring machine [Wikimedia]](https://excursionset.com/wp-content/uploads/2024/04/55592-alice_the_tunnel_boring_machine_1950_281028116825629.jpg)
![[United States Geological Survey]](https://excursionset.com/wp-content/uploads/2024/04/8d43d-k-t_boundary_at_starkville_south.jpg)