Lewis Hamilton's Garden of Forking Paths

It's often said that there are more ways to lose a Grand Prix than to win one, and the diagram here makes that explicit.

Lewis Hamilton lost the Hungarian Grand Prix on Sunday primarily as a result of the tyre-choice made at the third pit-stop. Leading the race from Jenson Button and Sebastien Vettel, Lewis took his third set of options, while Jenson and Sebastien took a set of the harder, prime tyres. With thirty laps to the end of the race, Hamilton would require another pitstop, whereas Button and Vettel wouldn't. That decision alone restricted Hamilton to third place, at best.

The subsequent drive-through penalty and stop for intermediate tyres merely reduced Lewis's highest possible finishing position to 4th, which he duly achieved after passing Webber.

The diagram here demonstrates twelve possible paths through the last thirty laps of the race. Branches to the left constitute errors. The branch furthermost to the left is the one actually followed, while the branch furthermost to the right is the one for which victory would have been most likely. All the other branches, with one exception, lead to an eventual 3rd or 4th place.

The one exceptional case corresponds to the scenario in which Lewis took primes at the third pit-stop, but still spun, and lost the lead to Jenson on the damp track-surface. If Lewis had avoided a drive-through penalty, he would then have finished either 2nd behind Jenson, or perhaps even have retaken the lead. Whether Lewis could have made a set of primes last thirty laps, however, is unknown.

The BBC/Sky deal

To borrow a phrase used by Jonathan Miller, television is a device for transporting the mind. Each year, the BBC voraciously consumes a revenue of £3.5 billion, derived from the licence fee in the UK, and transforms this into patterns of electromagnetic radiation. These patterns possess an information content which enables the viewer to see places and events without actually being there.

Sadly, £3.5 billion per annum is not, it seems, sufficient to embrace the £40 million required to maintain exclusive rights to the broadcast of Formula 1 in the UK. The BBC, of course, has other priorities, such as maintaining the eclectic, high-brow, intellectual content of their youth-oriented channel, BBC3.

The Formula 1 teams seem to have received the news in a remarkably phlegmatic fashion. They'll receieve an additional £1 million per annum, and they are perhaps anticipating that when Sky touches Formula 1, it will boost the sport in the manner that football was financially boosted with the inception of The Premiership.

Formula 1 fans in the UK already pay a £145 BBC licence fee, and will now be required to pay at least £500 per annum for a Sky Sports subscription. So it's bad news for the fans in a financial sense, but potentially good news for those who work in Formula 1, or wish to work in Formula 1.

I wonder, however, if the teams will run the gauntlet of another FOTA fans' forum in the UK...

Maxicons

A Maxicon is an elementary semantical unit, in which a linguistic phrase conveys both an explicit meaning, and a second implicit sense, which contradicts the explicit content.

An excellent example can be found in the recent Max Mosley interview, conducted by Maurice Hamilton for the August edition of F1 Racing. Discussing FIA President Jean Todt's handling of the Bahrain Grand Prix fiasco, Max comments:

"I don't want to criticise poor Jean."

The explicit meaning expresses a disinclination towards censure, whereas the implicit content is:

"Poor Jean really isn't up to the job."

Lewis Hamilton and overtaking around the outside

Discussing his efforts to fend off Mark Webber in Sunday's German Grand Prix, Lewis Hamilton remarked on the BBC's post-race Forum that, "I've been overtaken on the outside once before, and I don't wanna do it again."

Lewis here is presumably referring to the first corner of the 2008 Hungarian Grand Prix, when Felipe Massa swept out of his slipstream, briefly locked-up his wheels under braking, and drove clean around the outside of the McLaren. Without the engine failure Massa subsequently suffered in that race, it would have been a championship-winning manoeuvre.

It's interesting that Lewis should be keeping count of this type of thing, and interesting to learn how much it's still in his mind, how much it still smarts.

Massa, of course, actually overtook Hamilton around the outside into the final corner of the British Grand Prix this year, only to be immediately retaken before the finish line. Perhaps that one doesn't count then.

McLaren's rear-wing vortices

So did you spot them? The McLaren wing-tip vortices?

If you watch the train of cars streaming down the pit-straight at the end of both the first lap, and particularly at the end of the second lap, you'll see that the McLaren of Lewis Hamilton was generating visible rear-wing vortices. Neither the following Red Bulls, nor the Ferraris, nor the Mercedes, were doing so.

What's the reason for this? Is the McLaren rear-wing simply more powerful? Well, McLaren have been running a rear-wing this year with a larger flap than Red Bull, and although this gives Red Bull a DRS-advantage in qualifying, the flip-side is that McLaren have been equipped with a more powerful rear wing in the races. Ferrari, similarly, adopted the Red Bull solution at Silverstone. McLaren experimented with a small-flap design at Silverstone, without success, and seemed to be having similar difficulties at the Nurburgring during Friday practice.

If McLaren do still have a more powerful rear wing, it would provide a simple explanation for how they were able to switch the tyres on in the cold conditions of the Nurburgring, and provide Lewis Hamilton with a car in which he could do his stuff again. McLaren, however, might now struggle with overheating rear tyres in the mid-Summer heat of Hungary, much as they did at Valencia.

And wasn't that the fourth successive race in which Ron Dennis has been in attendance...?

Phone-hacking and spontaneous self-organisation

There's something of a hullabaloo in the UK at the moment over the phone-hacking conducted by Rupert Murdoch's News International publications, and the degree of collusion which has subsequently been revealed between politicians, journalists, and the police.

Rebekah Brooks and Andy Coulson, successive editors of The News of the World during the time in which the hacking took place, have both denied all knowledge of the illegal techniques used to obtain numerous stories. One can only presume that they thought their journalists were obtaining personal and private information by means of telepathy.

The collusion between politicians, journalists and police, however, is actually quite an interesting socio-political case study. Free market thinkers, such as Matt Ridley, have long trumpeted the power of bottom-up, spontaneous self-organisation in society, over top-down regulation, and what we have here is, in fact, a perfect demonstration of just such a phenomenon.

There's been no conspiracy here, no centralised command, planning and coordinating the collusion between the various agencies. Instead, the politicians, journalists and police have spontaneously evolved a means of cooperating for mutual benefit. Each individual involved has sought merely to preserve and promote their own careers, making short-term, self-interested decisions based upon incomplete information. The collective result of all these minor, self-interested decisions, has been a high degree of collusion between those who make the law, those who enforce it, and those who report it.

It's a perfect example of the bottom-up, spontaneous formation of cooperative organisation. Unfortunately, when it's necessary for institutions to remain impartial and independent, the existence of such cooperation is equivalent to collusion and minor corruption. Which is one reason why an effective democracy requires top-down regulation to constrain the spontaneous formation of cooperative organisation.

Motegi and the Fukushima radiation

Leading MotoGP riders have declared their intention not to race in the Japanese Grand Prix at Motegi this October. Their grounds for doing so are fears over the radiation released from the Fukushima nuclear power plant, over 100 miles from Motegi.

Perhaps the MotoGP riders fear that they would be conscripted into helping out at the reactor site, manning the pumps in the on-going effort to circulate cooling water to the reactor cores and spent fuel rods.

It's easy to understand their position: when you spend your working life skimming the tarmac at 140mph on two wheels, running the risk of breaking your neck at any moment and spending the rest of your life in a wheelchair, it's easy to see how a small amount of radiation might scare the bejesus out of you.

One trusts, as well, that none of the MotoGP riders smoke, for tobacco contains polonium-210, the same radioactive substance used to assassinate Alexander Litvinenko in 2006. A person who smokes one and a half packs of cigarettes a day, has been estimated to build-up a radiation dose equivalent to 300 chest x-rays a year. One also hopes that the MotoGP riders travel by boat to remote Grand Prix venues, given that passengers on long-haul air-flights are subject to a dose of radiation from cosmic ray neutrons.

Silverstone and hydrodynamical singularities

There was plenty of opportunity to watch Formula 1 cars in the wet at Silverstone last week, and it's worth noting that when a car transforms a sheet of water into a spray of droplets, each droplet has been created by a topology-changing process corresponding to a hydrodynamical singularity.

Droplet formation is a liquid version of the fracture of a solid; the continuous medium is broken into disconnected fragments. Up until the point of the singularity, droplet formation is described by a solution of the Navier-Stokes equations for free surface flows. Thus, rather than solving the equations with fixed boundary conditions, such as those provided by a pipe or a wing-surface, one must also specify how the surface of the fluid evolves in time.

Droplet formation leads to a singularity in finite-time, but how the droplet forms, whether it falls from a tap (that's a 'faucet' in the USA), or is flung from the tread of a rotating tyre, is actually irrelevant to the shape of the droplet as the water is broken. As philosopher Robert Batterman points out, the shape of a breaking droplet is largely determined by the ratio of the viscosity of the breaking fluid to the viscosity of the ambient medium.

Water, in fact, is a good deal more complex than many people imagine. Weisberg et al emphasise that "water's microstructure cannot simply be described as a collection of individual molecules...There is a continual dissociation H2O molecules into hydrogen and hydroxide ions, and a continual recombination of those ions back to H2O molecules. At the same time, the H2O molecules associate into larger polymeric species."

Philosophically speaking, this has implications for understanding the relationship between microscopic and macroscopic structure. As James Ladyman argues, "Metaphysicians expect the bridges between the ontologies of the different sciences to be synchronic but they are usually diachronic. So, for example, it is the dynamics of how hydrogen bonds form, disband, and reform that gives rise to the wateriness of water and not the mere aggregation of hydrogen and oxygen in a ratio of two to one," (Many Worlds? OUP 2010, p158).

Conclusions from Silverstone

As a stage on which to perform, Silverstone is very much Broadway to the Red Bull School of Performing Arts. Here, the aerodynamic superiority of Adrian Newey's design can be exploited to greatest effect.

Thus, having qualified 0.8s faster than third-placed Fernando Alonso in 2010, a gap of merely 0.1s on Saturday evening this year was clearly a matter of concern to the team from Milton Keynes. And, once the initial damp conditions had passed in the race, the Ferrari appeared to be both faster, and capable of making its tyres last longer.

It now seems, however, that what took place at the British Grand Prix last weekend was a controlled experiment; a singular chance to assess the relative performance contribution of Off-Throttle-Exhaust-Blown-Diffusers (OFTEBDs) to the different cars on this year's Formula 1 grid. And arguably, there are two principal conclusions which can be drawn:

(i) Red Bull gain a moderate relative performance benefit from OFTEBDs.

(ii) McLaren gain a large relative performance benefit from OFTEBDs.

Now, Silverstone is not the ideal place for such an experiment. In both topography and meteorology, it is something of an outlier, boasting fast, sweeping corners, and afflicted by strong winds. In addition, there were other confounding factors last weekend: the intermittently damp conditions in practice entailed that not all teams would have achieved their optimal dry-weather set-ups, and Ferrari had a number of rear-end modifications which they claim would have provided a significant performance boost even without the OFTEBD ban.

Mark Hughes puts forward the case for accepting Ferrari's argument, but whilst the Italian team might well have closed the gap to Red Bull on most types of circuit, it would be remarkable if a few modifications around the rear could have brought Ferrari to Red Bull parity on a circuit such as Silverstone.

Elsewhere, the benthic activities of the News of the World dominated the non-motorsport headlines, and the redoubtable Tony Dodgins bravely re-examines the issue of Max Mosley's NotW exposé. Tony suggests that the NotW's phone-hacking habits may offer a better explanation for how they happened upon the story than any far-fetched MI5 link, although NotW editor Andy Coulson resigned in January 2007, and such activities had supposedly ceased by the time of Mosley's 2008 misfortune.

Incidentally, author Will Self suggested on BBC's Newsnight last week that the phone-hacking scandal is merely an epiphenomenon of the transition from print to electronic media. Self is presumably implying here that the NotW only developed their phone-hacking strategy as a response to falling sales, a supposition which is difficult to test.

Irrespective of the root cause, there may be consequences of this scandal for Formula 1. If Rupert Murdoch is now impelled to switch attention from the already dwindling print media component of his business to other broadcast interests, then this may increase the probability of Formula 1 being owned by News Corporation in the near future. All parties concerned were at pains earlier this year to emphasise that they only have the best interests of the sport and its fans at heart.

After being owned for some years now by CVC private equity, it seems that Formula 1 just can't help attracting modern-day Victorian philanthropists.

McLaren's Silverstone woes

"Really?" said Jenson Button yesterday, quizzical eyebrow raised, when someone said Martin Whitmarsh had predicted that the new conventional-exhaust/revised-underbody combination fitted for Melbourne would find the McLaren 1s per lap.

"I didn't know he'd said that. I'm impressed with his optimistic spirit and I would love that to be true. Let's see." He sounded unconvinced. (Mark Hughes's Friday Form Guide, March 25th 2011)

"The gap is massive. One and a half seconds is just massive. That's all I have to say, really." (Jenson Button, July 9th 2011)

For one race at least, off-throttle blowing of the diffuser has been virtually eliminated from Formula 1, and the big loser is clearly McLaren, with Jenson Button and Lewis Hamilton 1.5s and 2.0s, respectively, off the pace of the Red Bulls in qualifying. This compares to a qualifying deficit of only 0.4s at the previous race in Valencia.

It's interesting that McLaren should be particularly disadvantaged, and the explanation for this can probably be traced to the failure of their radical, 'octopus' exhaust system in winter testing.

Barely a week before the first race in Melbourne, McLaren decided to abandon this system, and simply blow the exhaust between the rear wheels and the upper-outer surface of the diffuser. It isn't an exact copy of the Red Bull design, given that Red Bull blow their exhausts underneath the extremities of the diffuser, but it is nevertheless a close cousin of the Red Bull design. And perhaps by a fluke of fortune, this stop-gap solution seemed to integrate nicely with McLaren's overall airflow concept, elevating them to Red Bull's closest competitor over the first half of the season.

Back in Melbourne, Martin Whitmarsh estimated that McLaren had gained a second from their improvised exhaust system. Bereft of their exhaust-blown diffuser at Silverstone, McLaren now find that they've lost a second. Red Bull will also have lost a chunk of lap-time, of course, but in the chilly conditions of Silverstone, it's possible the McLarens were so deprived of rear downforce that they were unable to get the rear tyres 'switched on'. For McLaren, it's possible that the exhaust-blown diffuser was an aerodynamic tourniquet, without which they are simply bleeding downforce.

Blake's Seven and the symmetry of spaceships

What do most spaceships have in common with most animals and racing cars? That's right, they possess approximate mirror symmetry.

If you think of classic spaceships, like the X-Wing Fighter from Star Wars, the Enterprise in Star Trek, the Eagle in Space 1999, or even NASA's Space Shuttle, they all exhibit bilateral mirror symmetry: slice the ship in half down a longitudinal plane, and the portion on the left side will be a mirror image of the portion on the right side.

There are several exceptions from modern science-fiction, but the classic era of spaceship design features one prominent anomaly: the Liberator from Blake's Seven.

This craft is noteworthy for two principal reasons. Firstly, it features an (approximate) discrete threefold symmetry around its longitudinal axis. It therefore has no dorsal or ventral side, unlike most spaceships, animals and racing cars. Hence, there is no sense in which the Liberator is ever prostrate or supine. But secondly, its central design theme is essentially a dome and minaret structure.

Thus, aesthetically speaking, the Liberator is the first ever mosque in space.

Abu Dhabi's big mistake

If last week's European Grand Prix at Valencia demonstrated one principal, salutary lesson, it is that this year's regulations will not generate exciting races at venues already fundamentally inimical to overtaking.

It is enormously disappointing, therefore, to learn that the Abu Dhabi organisers will not be making alterations to their track for this year's race. Chief Executive Richard Cregan argued:

"With all the changes implemented by the FIA, the racing so far this year has been full of overtaking and excitement. So we decided, rather than spend a whole lot of money making these changes, we'll wait and see how [this year] goes first."

Of all the countries hosting Grands Prix on the 2011 Formula 1 calendar, the one capable of building a circuit around a phosphorescent hotel, which looks like it has only just emerged from the Mariana Trench, surely has the wherewithal to make changes to the actual track layout. When you run the risk of yet another dreary race, and you have such deep pockets, why not take the opportunity to improve the circuit anyway?

Three-Mile Island, Chernobyl and Fukushima

"The world's first commercial nuclear power station opened in the UK in 1956 at the Sellafield site on the Cumbrian coast, and it ran for almost half a century before closing in 2003. The four Calder Hall reactors were of the Magnox type, which means they used a magnesium 'no-oxidation' alloy to encase the uranium fuel rods.

"France initially followed the UK's lead by building reactors similar to the Magnox design during the 1960s. Meanwhile, the US realized that the most economical reactors are those that are collectively referred to as light-water reactors (LWRs).

"LWRs use ordinary water as a moderator and as a coolant, running on uranium-oxide fuel enriched with up to 5% uranium-235 and contained in a zirconium alloy cladding." (Physics World, July 2007).

"The core temperature rose to the point at which the zirconium alloy cladding began to react with steam to produce hydrogen, some of which escaped into the reactor building. Early in the afternoon of the first day, sufficient hydrogen had accumulated in the reactor building to result in a low-level explosion." (Environmental Radioactivity, Eisenbud, p370-371).

Three Mile Island, March 1979.

"Two explosions occurred at 01:24. The steam released by the failure of one or more pressurized tubes had reacted exothermally with the zirconium, producing hydrogen that exploded. Parts of the core were scattered about the building as well as on the roofs of the reactor, turbine, and auxiliary buildings." (ibid, p378).

Chernobyl, April 1986.






"The cladding, which is just the outside of the tube, at a high enough temperature interacts with the water. It's essentially a high-speed rusting, where the zirconium becomes zirconium oxide and the hydrogen is set free. And hydrogen at the right concentration in an atmosphere is either flammable or explosive.

"Hydrogen combustion would not occur necessarily in the containment building, which is inert—it doesn't have any oxygen—but they have had to vent the containment, because this pressure is building up from all this steam. And so the hydrogen is being vented with the steam and it's entering some area, some building, where there is oxygen, and that's where the explosion took place."

Fukushima, March 2011.