Coulthard takes a dip

Rarely have I seen anything quite as funny, in the slapstick sense, as Eddie Jordan and David Coulthard taking brief, unwilling, freefall trajectories into Red Bull's swimming pool after the Monaco Grand Prix.

DC's attempts at resistance were particularly fine, the lactescently-trousered driver-turned-commentator clinging to the railing like a limpet superglued to the hull of the Lusitania, clasping his BBC microphone like a magic amulet which would protect him from the ritualistic dowsing that surely awaited.

We may currently be in a transient window for Formula One, during which time the racing is brilliant, the cast of drivers superb, and the television coverage in the UK is, well, BAFTA-winning. No adverts, none of the crass studio conversations beloved of Sky Sports, just four hours of continuous coverage and analysis, saturating your cerebral cortex every other Sunday. Enjoy it while it's here.

Lewis Hamilton's Monaco Grand Prix

"For those regarded as warriors, when engaged in combat, the vanquishing of thine enemy can be the warrior's only concern." (Hattori Hanzo).

There is an abiding tension in Lewis Hamilton's racing psyche. On the one hand, he's a true warrior, and in motorsport terms, being a true warrior means that overtaking the driver ahead of you is your all-consuming concern; nothing matters as much as making that move, putting your opponent to the sword, leaving his entrails strewn upon the track.

On the other hand, Lewis has a desire to win multiple championships; an abstract task, which requires a strategic mindset, and the use of discretion in battle.

These two competing instincts remain unresolved, and Sunday's Monaco Grand Prix was perhaps a case in point.

The source of Hamilton's frustration, of course, was final qualifying, in which McLaren decided that Lewis should make just one run. The idea was presumably to save a set of fresh super-softs for the race, but given that Hamilton had the pace for pole position, and given that no-one else saw fit to make a single run in Q3, this seemed like an odd form of prioritisation. Heavy accidents are hardly unknown in final qualifying at Monaco, and Sergio Perez duly obliged, consigning Hamilton to seventh on the grid.

Hamilton's one and only qualifying lap was then deleted for jumping the chicane at the exit of the swimming pool, and although this dropped him to ninth on the grid, it also gave him the opportunity of choosing which tyres to start the race on. Whilst those ahead were constrained to start with the super-softs they'd qualified on, Lewis chose the harder primes, getting the slower tyres out of the way when he'd be trapped behind other cars anyway.

Hamilton got away to decent start, swerving left to get around Michael Schumacher as the Mercedes driver staggered away from the grid. Going into Ste. Devote, Lewis was eighth behind Pastor Maldonado, but appeared to brake earlier for the corner than those around him, presumably as a consequence of being on harder tyres. This had two effects: Schumacher ran into the back of him, lightly damaging the rear wing of the McLaren, and Vitaly Petrov overtook Lewis around the outside.

So Lewis was ninth. Sensing that the McLaren was lacking grip on the harder tyres, Schumacher then demoted him to tenth with a beautiful move down the inside into the Loews hairpin. Not a great first lap then.

Both Mercedes, however, had poor race pace, and as Schumacher's super-softs went off, Lewis soon began looking for a way past, swerving left and right on the climb up to Massenet each lap. As they completed lap 9, coming into the DRS zone of the start-finish straight, Schumacher had already exhausted his KERS allocation. In contrast, Lewis was able to deploy fully half of his, and combine it with both the slipstream and the DRS. Crossing the line to start lap 10, Lewis briefly dipped into his next lap's allocation of KERS, and dove down the inside of Schumacher under braking for Ste. Devote. It was a beautifully judged move, and although Schumacher briefly looked like he was going to turn-in and cause a collision, Lewis had re-gained the position. Ninth!

So that was the good in Lewis's race. The rest, however, wasn't as impressive. He made a clumsy move on Massa at the Loews hairpin, which Felipe has every reason to complain about. It was, however, just a racing incident. Unfortunately for Hamilton, the stewards had already penalised Paul Di Resta for a similar move.

Now, there's a tendency in Formula One to penalise rookies and younger drivers for mistakes, as if they somehow need to be taught a lesson by their elders, and the penalty meted out to Di Resta falls neatly into this category. Having issued that sentence, the stewards were then, on pain of inconsistency, compelled to issue the same penalty to Hamilton.

Some time later, when the race was re-started after Petrov's late accident, Lewis had a good opportunity to pass Maldonado into Ste. Devote, but rather bungled it. He was perfectly placed into the braking zone, but never got his front wheels further ahead than the sidepod of the Williams. If anything, Lewis just needed to come off the brakes a little and go deeper into the corner, for when Maldonado turned in, Lewis was able to bounce over the bollard and kerbs on the inside without losing the rear end.

And thus, after another penalty from the stewards, we come to Lewis's post-race BBC interview. By now, the successive punishments had probably triggered his persecution complex. In fact, this has likely been simmering gently since he was penalised for his shimmy down the straight in front of Alonso in Malaysia.

Lewis has this interesting habit of being able to swear without technically swearing, using 'frick' in the manner that 'smeg' was used in Red Dwarf, or 'feck' in Father Ted. But how much of Lewis's interview was pure anger, and how much of it was calculation? There'll obviously be quite a bit of squawking from the media, and perhaps even from the FIA, about the fact that Lewis 'played the race card'.

Beyond this, however, such comments must slightly intimidate the stewards of future events, if only on a subconscious level. Footballers instinctively understand this, which is why every decision there is strenuously challenged. In particular, football referees know that if they award a contentious penalty against Man Utd or Chelsea, then they'll be instantly surrounded by an aggressive scrum of irate, physically strong, 6-foot millionaires. If it's a borderline decision, why not give the benefit of the doubt to the team or the individual who'll subject you to the greatest amount of post-event criticism?

Anti-climax at Monaco

This was the thriller without a denouement, the tension building in expectation of a final ecstatic release, only to be deflated by events unrelated to the main plot.

Going into the final ten laps of the Monaco Grand Prix, Fernando Alonso looked set for victory, the Ferrari on a two-stop strategy, and crucially, the only one of the leading runners to have taken the opportunity of a free pit-stop when the safety car had been deployed at half-distance. Ahead of him was Sebastien Vettel, the Red Bull driver trying desperately to make his second set of tyres last sixty laps after being forced onto a one-stop strategy. Behind Alonso was Jenson Button, on the final stint of a three-stop strategy, but looking content to watch the battle ahead of him. These three bifurcating strategies had converged in the closing laps, when the leaders came upon a snarling juggernaut of backmarkers led by Adrian Sutil.

But how, exactly, had Sebastien Vettel ended up on a one-stop strategy, when, as leader, he should really have been shadowing the moves made by those behind him? The Red Bull had appeared comfortable in the lead during the first stint, but at the end of lap 16, the team had erroneously fitted a set of primes at his first stop. Worse, Button had pitted a lap earlier, fitted another set of super-soft options, and passed Vettel on the undercut. During Button's second stint, he then used the advantage of being on softer tyres to pull out a decent lead of over ten seconds. Jenson then made his second pit-stop at the end of lap 33, fitting his third and final set of super-softs, postponing the use of the primes, and thereby committing himself to a three-stop strategy.

So, should McLaren have switched Jenson to a two-stop strategy at this stage? They were ahead of Vettel, the primes would have lasted to the end of the race, and even if Red Bull had fitted super-softs to Vettel's car at their second pit-stop, Vettel would have needed to pass Button on-track to win the race.

Either way, the next strategic branching point came swiftly, when the safety car was triggered on lap 34 for Massa's accident in the tunnel. Red Bull had the option to bring Vettel in for his second pit-stop at this stage. If they'd done so, Seb would have resumed behind Button, but the deficit would have been minimised by the safety car, and Jenson, of course, still had another stop to make. Thus, if Red Bull had pitted at this point, they would surely have closed out the race. Yet, for whatever reason, it was only Alonso who chose to take his second pit-stop at this juncture.

The race resumed with Vettel first, Button second, and Alonso third. Jenson's super-softs still afforded an advantage over the primes on Vettel's car, and he closed onto the tail of the Red Bull, but never threatened to pass. Button, of course, then had to make his third and final pit-stop onto primes at the end of lap 48, dropping him back to third. Vettel, however, couldn't respond to McLaren's pit-stop by making his own, because that would have dropped him behind Alonso. Because Fernando had taken his second stop under the safety car, a two-stop strategy would lose Vettel the race.

So Sebastien stayed out, and tried to make his primes last to the end, and we looked set for a thrilling conclusion. Alonso had a look down the inside into Ste Devote on lap 67, but aborted the move, tucking back into the Red Bull's slipstream ascending Beau Rivage, the vanishing point spewing out armco like a naked singularity, the white lane markings flailing between the front wheels of his Ferrari. Elsewhere, however, events were unravelling in a manner which would ultimately gift victory to Vettel.

A gap of more than 50 seconds had opened between the leaders and Sutil in fourth, but things behind the Force India were considerably closer. With twelve laps to go, Kobayashi and Petrov were tracking the German in fifth and sixth, whilst a short distance down the road was Webber in seventh, Maldonado eighth, and Hamilton in ninth.

Kobayashi then made an optimistic lunge to take fourth place from Sutil going into Mirabeau. The Sauber's left-front made contact with Sutil's right-rear, and the Sauber nipped through. By the time the leaders reached this train of cars on their 69th lap, Webber and Maldonado had passed Petrov. Maldonado now forced his way down the inside of Sutil into Tabac at exactly the same moment that Hamilton was diving down the inside of Petrov. Sutil ran wide, and thumped the guardrail with his right-rear.

This was the final straw for Sutil's tyre, which deflated as he tried to gather things together and press-on. Just behind, Petrov had been forced out wide by Hamilton, and was passed by the lapped Alguesauri on the exit of Tabac. Up ahead, however, Hamilton was rolling off the throttle as he attempted to second-guess Sutil's movements going into the left-right entry to the swimming pool. The Force India stayed right, but Hamilton hung back, and Alguesauri's Toro Rosso rode up over the McLaren's right-rear wheel, from whence it slid on into the barrier. The closely following Petrov contrived to follow Alguesauri into the armco.

Despite the apparently innocuous nature of the shunt, Vitaly professed to being in a substantial amount of pain, and was clean out of paracetamol. Hence, a red flag was triggered, and the Russian driver carefully extracted from his car. "Once at hospital, it was confirmed that there was no swelling or broken bone," read a subsequent statement from the Lotus-Renault team.

Strangely, it now seems that the temporary cessation of a Grand Prix is an opportunity, without penalty, for the teams to fit new tyres, and even change rear wings. Thus was the battle for victory instantly snuffed out. It was what Lewis Hamilton might call 'fricking ridiculous'.

Exhaust-blown diffusers and the Brabham fan-car

In Thursday's Press Conference at Monaco, Adrian Newey apparently tried to defend the legality of exhaust-blown diffusers on the over-run, by claiming that the primary function of an open throttle on the over-run is to cool the exhaust valves:

"In the case of Renault, then they open the throttle to full open on the over-run for exhaust valve cooling, and that's part of the reliability of the engine...Obviously if other people are going further and perhaps firing the engine on the over-run then clearly exhaust valve cooling is not part of that and that would be something that presumably they would need to explain to keep Charlie happy."

Remarkably, this echoes the grounds on which Gordon Murray and the Brabham team tried to defend the legality of their infamous fan-car in 1978. Murray devised a gearbox-driven fan, which created downforce by sucking air out from underneath the car, but argued that it wasn't a movable aerodynamic device on the basis that it was actually designed to cool an oil/water radiator placed atop the engine:

"I used to read the rules all the time...The breakthrough was the phrase 'primary function' - if something was movable and had an aerodynamic effect on the car, its primary function had to be something else. That was the basis of the whole car being legal. We looked in the dictionary and asked the legal people, who said the primary function of a mechanical mechanism means more than 50 percent." ('Vacuum Clean-Up', Adam Cooper, Motorsport, May 1998, pp64-69).

As Peter Wright explains, there were detailed arguments at the time over how this 50% could be defined:

"[Murray] argued that if the primary purpose of the fans is to draw air through the radiators, then any secondary effect is incidental. The argument pivoted on whether the function of a fan is to move air or to generate a pressure difference. If it is to move air, the consequence of which is to create pressure differences, then the radiator flow exceeded the leakage flow under the skirts, and thus it could be argued that it is legal. If the function is to create a pressure difference, the consequence of which is the movement of air, then the area of the car on which that pressure difference acted is far greater than the area of the radiators, and thus it is illegal." (Formula 1 Technology, p216).

In the case of an exhaust-blown diffuser in 2011, the exhaust flow is clearly moving air with the purpose of creating a pressure difference. Thus, if one can demonstrate that at least 50% of the off-throttle exhaust-gas flow is necessary for cooling the exhaust valves, it follows by 1978-logic that the primary function of the exhaust-gas flow is for cooling purposes.

On the Thursday after the 1978 Swedish Grand Prix, a FOCA meeting resulted in all protests being withdrawn, and it was agreed that the fan-car would be able to race in the next three Grands Prix, but withdrawn from competition after August 1st, (Cooper p69). It was only the next day, at a meeting in Paris with the governing body, that the fan-car was banned with immediate effect.

Coincidentally, when the Technical Working Group meets on June 16th 2011 to discuss the issue of exhaust-blown diffusers on the over-run, three Grands Prix will have passed since the FIA initially attempted to ban the technology.

Such patterns give Formula One its characteristic temporal texture.

Lotus-Renault opt for a flexi-wing

Thursday's Autosport magazine contains the following job advert for an 'Aero FEA Engineer' with Lotus-Renault GP:

"The Aero FEA engineer will be involved in the initial conceptual design of components within CFD and be expected to consider both the structural and aerodynamic implications of new concepts...Experience of structural analysis with both shape and laminate optimisation using FEA is a requirement."

Fairly unambiguous that. How much benefit Lotus-Renault can expect to gain at this stage of the game is another matter. One might expect the rules on front-wing flexibility to be further tightened before the start of the 2012 season, and with Lotus-Renault going from a standing-start, they might not be able to reap any benefits this year. Unless, that is, they recruit someone straight from Red Bull.

The aerodynamics of buildings

Civil engineering is perhaps not the most exciting application of aerodynamics, but to look at some buildings, one has to wonder if questions of airflow ever entered the minds of their architects.

The diagrams here demonstrate just how complex the aerodynamics can be around even the simplest of buildings. Anyone with a passing interest in the subject should be able to predict that a low pressure area will form at the rear of a building (relative to the prevailing wind direction), and the detachment of the boundary layers atop and to the sides of the building, will create a turbulent wake.

Less expected, perhaps, will be the vortex tubes created at the front of a building, which are then stretched down the flanks of even a simple cubular or parallelepiped construction. And look at that pair of slender vertical vortices at the rear of the building in the first diagram; you wouldn't want to put a drain or a dustbin at the bottom of one of those!

The first two diagrams here deliberately ignore the turbulent wake behind a building. Instead, they represent what's called the mean flow. The idea here is that a turbulent velocity vector field can be decomposed as the sum of a time-independent mean flow, and a fluctuating component which contains all the turbulence:

If you want to simulate a turbulent airflow, then one of the short-cuts you can use is to conduct a Large-Eddy Simulation (named after a 16-stone fella called Eddy), which calculates just the mean flow, and the largest turbulent eddies. A Large-Eddy Simulation uses a parameterized model to dispose of turbulent kinetic energy which, in reality, is only dissipated after the largest eddies have broken up into a succession of much smaller eddies.

It would be interesting to know what the airflow pattern is around a cluster of buildings; do they perhaps generate a network of vortex tubes, like wormholes, capable of escorting aerosols emitted in one place, to anywhere else in the cluster?

(Second and third diagrams here courtesy of P.A.Davidson's superb tome 'Turbulence', CUP, 2004).

Look, but don't stare

On the restart of the Spanish Grand Prix, Fernando Alonso used his KERS boost to swoop inside Mark Webber's Red Bull. Webber, however, wasn't ready to concede the position, and immediately ducked out of Alonso's slipstream, aiming his Red Bull inside the tightest of gaps to re-take the position under braking into turn 1.

That, of course, was 2009. In 2011, the roles were reversed.

Alonso got excellent traction away from fourth position on the grid, quickly alongside Hamilton to his left. Ahead of them, Vettel was swooping about, looking to take the inside of Webber, then flicking back to the outside as the Australian covered him. Alonso had already latched onto Vettel's slipstream, and as Sebastien went left, Fernando was able to pick-up Webber's drag-reducing wake. Like a honey-bee flitting from one nectar-laden bloom to another, Alonso took advantage of his good traction and successive slipstreams, to thrust his Ferrari down the inside of Webber.

Shaving the white line bordering the grass on his right-hand side, and the turbulent outwash of the Red Bull on his left, Fernando took the lead under braking into the first corner. A single twitch from the Red Bull could have put the Ferrari onto the grass at 180mph, their wheel rims sufficiently close to generate a Casimir effect.

Webber, for his part, may have been slightly distracted by watching Vettel on his left, but once Alonso shot down the inside, Mark appeared slightly cautious on the brakes, allowing his team-mate to take second place.

Michael Schumacher, meanwhile, had also got away to a decent start, getting alongside Massa on his right, but momentarily finding his passage blocked by Button and Rosberg. Button, however, drifted left, and Rosberg moved right to cover a move by Massa, leaving Michael to drive straight between them.

Under braking into turn 1, Petrov challenged Hamilton on the outside, but ran slightly wide. On a tighter line, Rosberg was immediately inside the Renault, which placed him on the outside for turn 2. Behind them were Schumacher and Massa, also side-by-side, and Button in ninth.

Petrov got a little squirrelly through turn 2, which gave Schumacher the opportunity to try the outside line into turn 3, and for a moment Petrov had a Mercedes either side of him. This pinned Rosberg on an excessively tight line, and by the exit of the corner, Petrov emerged in fifth position, with the two Mercedes wheel-to-wheel behind. Rosberg, however, was rather boxed-in behind the Renault, and Schumacher took sixth place into turn 4.

Behind that battle, Buemi's Toro Rosso drove clean inside Button in the first part of turn 3, and Massa in the second part of the corner! Button got alongside Felipe in the second part of turn 4, but was boxed-in behind Buemi on the exit, and Massa was then able to out-brake the Toro Rosso down the outside into turn 5, reclaiming eighth position.

From that point on, things became rather strategic. In fact, the logic of the entire race was determined by the performance of the new harder tyre. The underlying problem, of course, was that the harder tyres were between 1.5secs and 2secs slower than the soft tyres, but the soft tyres were only lasting 10-12 laps. Moreover, even the hard tyres could still only survive somewhere in the region of 20 laps. Thus, in a 66 lap-race, that meant four stops were the only viable strategy. Unless, that is, you could nurse your soft tyres to survive 15-lap stints...

And here, I feel, it is necessary to provide a simple piece of arithmetic for the assistance of some commentators, who may still be struggling to follow the strategy this year. Let P denote the number of pit-stops, and let S denote the number of stints. Then the following rule applies:

S = P + 1

Thus, if you're doing a 3-stop race, then you'll be running 4 stints; if you're doing a 4-stop race, then you'll be running 5 stints.

Now, the number of stints equals the number of sets of tyres you need, and there's only three sets of soft tyres, and three sets of hard tyres. Hence, if like Fernando Alonso and Mark Webber in Sunday's race, you're running a 4-stop race, then you'll be needing 5 sets of tyres. And if, like Alonso and Webber, your soft tyres are only lasting for nine or ten laps, then you'll stop around lap 10, lap 20, and lap 30. At that point, you've done 3 stops and you've used all your soft tyres. There's no more. They're finished. Kaput. You'll have to spend the rest of the race on hard tyres.

And this is where Button's 3-stop strategy obviously reaped significant dividends, placing him on soft tyres between lap 30 and lap 48, during which time Alonso and Webber were struggling with the hards.

Ferrari, in particular, have generally struggled this year to get the hard tyres to their optimum operating temperature, and from the beginning of qualifying should have been planning to minimise the number of laps spent on them in the race. Doing so would have required a 3-stop strategy, but that would have required saving at least one set of soft tyres in qualifying. Unfortunately, Ferrari needlessly blew a set of Alonso's soft tyres in Q1, and from that moment on, Fernando's race was never going to work.

But perhaps Fernando already knew this, as the scarlet Ferrari squeezed through that frighteningly small gap, just seconds after the start.

Kermode "gripped" by Senna film

Asif Kapadia and Manish Pandey's film about the life of Ayrton Senna has passed a crucial litmus test, receiving the thumbs-up from cult film-critic Mark Kermode.

This was an important rite-of-cinematic-passage, not merely because of Kermode's popularity, but because he has no latent interest or understanding of Formula One. On BBC Radio 5's Mayo and Kermode Film Review, he confessed to being "gripped" by the movie, and also "terrified" by the on-board footage. On Kermode Uncut, he argues that the most exciting aspect of the film is that "it looks at people who have to some extent looked into the abyss."

When the film goes on general release in a couple of weeks time, it'll be interesting to see if it makes it into the multiplexes outside the major conurbations.

No Angel - The Ecclestone biography

Tom Bower has written a biography of Bernie Ecclestone which aspires to the omniscience of a Victorian novel, but descends to the dialogue of a Guy Ritchie screenplay:

"Where are they?" asked Dennis as he sought to collect his expensive trophies...Pointing his shotgun at Scheckter's own Mercedes, he threatened, "I'll blast a hole if you don't give them back." (p305).

"Bastard," Slavica unexpectedly shouted at her husband...Ecclestone urged his wife to calm down. Without provocation, she replied, "Motherfucker." (p285).

'Oh fuck, that's ruined the summer,' thought Mosley [on learning that confidential information had been passed from a Ferrari employee to a McLaren employee]. (p310).

"Fuck, fuck, fuck," said Ecclestone, [on learning of Max Mosley's tabloid expose]. (p322).

To some degree, one can understand why Bower has invented this semi-fictional dialogue, for the details of Formula One's repetitive financial disagreements do not otherwise make for a sparkling read. The result, arguably, is an entertaining, if occasionally ludicrous book.

However, perhaps more seriously, the expository material in Bower's work is also riven with numerous egregious inaccuracies. As Tony Dodgins points out, whilst one would not expect Bower to be an expert on Formula One, one would expect him to get someone who is, to scrutinise the manuscript and correct any errors prior to publication. Once again, authors and publishers need to understand that a book containing typographical or factual errors, is a defective product, just like a DVD with a scratch across the surface, or a mobile phone with bug-ridden software.

Bower reputedly earnt his spurs as an investigative journalist with the BBC's flagship current affairs programme, Panorama. There are lines in this book, however, which suggest that his natural metier would rather have been the editorial team of John Craven's Newsround:

"Do you know that I'm Jewish?" Todt asked Mosley. "Of course," replied Mosley, removing any suspicion of being anti-Semitic. (p352).

In Dennis's opinion, the argument showed how Ecclestone was 'crossing to the dark side', a reference to the film 'Star Wars'. (p221).

The latter, informative and perspicacious explanation of Ron Dennis's otherwise impossibly cryptic comment, surely leaves the reader gasping for the entire 'Tom Bower Guide to Popular Colloquialisms of Cinematic Provenance'. One imagines the following might be included:

"Play it again Sam," she said, a reference to the film 'Casablanca'.

Or how about:

"Frankly my dear, I don't give a damn," he said, a reference to the film 'Gone with the Wind'.

Ribbed, for your pleasure

Ferrari reportedly used riblets on the undersurface of its front-wing at the Turkish Grand Prix last week. These are finely-spaced, V-shaped grooves, typically separated by something of the order of 10-100 microns, which are used on aircraft and yachts to reduce skin friction drag. They have also naturally evolved on sharks, where they are referred to as denticles. Riblets work by reducing the amount of friction created by a turbulent boundary layer.

Now, recall that the boundary layer is a very thin layer, adjacent to a solid surface, in which the airflow is subjected to shear stresses, and Bernoulli's theorem no longer applies. In a laminar boundary layer, the velocity decreases from the freestream velocity, down to zero at the surface of the solid object, yet the pressure remains fairly constant. (In a direction normal to the surface of the solid object, the pressure inside a laminar boundary layer is basically equal to the pressure at that point on the outside of the boundary layer).

The presence of a boundary layer is necessary for a wing to induce lift or downforce. However, the pressure increases towards the trailing edge of a wing, and at some point this causes the airflow velocity at the surface of the wing to become negative, pointing in a direction opposite to the freestream velocity outside the boundary layer. This is the point at which the boundary layer separates, creating wake vortices as it does so.

To generate the maximum amount of lift (or downforce), it is necessary to push the point of separation as far back on the wing as possible. Slightly perversely, one of the mechanisms which facilitates this is the creation of a turbulent boundary layer. This arises when the freestream velocity rises above a certain critical speed, with the consequence that the boundary layer divides into three sublayers: a laminar layer at the bottom, a turbulent zone at the top, and a buffer zone in-between. The turbulent boundary layer is subject to a fluctuating flow, in which coherent structures are constantly created and then dissipated. At the point where the boundary layer transitions from laminar to turbulent flow, pairs of counter-rotating longitudinal vortices are constantly created. These vortices survive for a brief period of time before bursting, whence they release their kinetic energy. A lot of this vortex burst energy sweeps down to the surface of the solid object, causing a peak in the shear stress, and thereby contributing to the average skin friction drag.

The effect of the turbulent boundary layer can be represented as an extra type of viscosity. Particles from a turbulent boundary layer will be more likely than those from a laminar boundary layer, to wander upwards into the faster freestream flow, where they will get deflected, and returned to the boundary layer with extra velocity. A turbulent boundary layer will therefore get dragged further along before it separates. Turbulent viscosity therefore increases lift or downforce.

Famously, golf-balls are manufactured with dimples, with the purpose of inducing a turbulent boundary layer at a freestream velocity where one would not otherwise occur. However, in the case of golf-balls, the primary advantage of delaying the separation of the boundary layer is that the wake turbulence, and hence the drag, is reduced.

Riblets are slightly different, in the sense that they reduce the skin friction drag by influencing the vortex burst process within the turbulent boundary layer. The precise mechanism by which this occurs is not completely understood, but there seem to be two hypotheses: either (i) the riblets raise the height of the vortex bursts within the boundary layer, thereby reducing the downwash onto the solid surface; or (ii) the riblets reduce the duration and/or intensity of the vortex bursts.

However, if Ferrari were using riblets purely for the purpose of reducing skin friction drag, it is difficult to understand why they would only use them on the undersurface of the front-wings. Gary Anderson remarks in Autosport that "this coating works by creating small vortices on the surface that will reduce the airflow-separation problems and make the wing work more consistently." This makes them sound a lot more like the dimples on a golf ball, delaying the separation of the boundary layer rather than merely reducing skin friction drag...

Formula 1 and complexity

"It was a truly fascinating race, but you needed a slide rule and a degree in astrophysics to follow it in detail." Adam Cooper, Malaysian Grand Prix analysis.

A popular slogan employed in complex systems theory is that 'complexity lies between order and randomness'. Coincidentally, this phrase might have been coined with the express purpose of describing Formula 1, 2011-style.

Consider the lapchart of a Grand Prix to be one expression of its complexity. With 24 cars on the grid, a lapchart consists of 24 inter-dependent histories. A Formula 1 lapchart is not so random that it can be described by a collection of random walks, but neither is it completely ordered, in the sense of being a simple function of the starting line-up. It is, rather, a complex data set, which lies between order and randomness.

But let's have a closer look at what the key terms here actually mean. In complex systems theory, order and randomness are generally defined in terms of Kolmogorov complexity. This defines the complexity of a data set to equal the length of the smallest computer program capable of generating that data as output.

Any data which contains some sort of regularity or pattern, can be generated by an algorithm, and the greater the regularity, the more concise the algorithm is capable of being. Ordered data sets, (such as 'Vettel-Webber-Alonso' repeated sixty times), can be generated by very simple algorithms, and therefore have the smallest Kolmogorov complexity.

It might seem strange to define complexity in terms of the size of a computer program, but the basic idea is that ordered things can be succinctly described, whereas complex things require a more lengthy description; defining this lengthiness in terms of the size of a computer program is simply a way of defining an absolute standard.

A data set which cannot be generated by a computer program smaller than the size of the data set itself, is deemed to be random. Such a data set contains no patterns or regularities. The program which generates it has to contain the data set in its explicit form, hence the size of the program cannot be smaller than the size of the data set.

Now, Ladyman, Lambert and Wiesner have argued that Kolmogorov complexity actually provides a poor definition of complexity because it assigns high complexity to random data sets. This, they argue, fails to respect the intuition that complexity should lie between order and randomness.

However, whilst Ladyman et al proceed to consider other alternative definitions of complexity, it may be that for our purposes here, a simple qualification to the definition of Kolmogorov complexity will suffice.

Let us assert that data sets come in two basic types: those which are algorithmically compressible, and those which are not. Let us define those which are incompressible to be random. For those data sets which are compressible, let us define their complexity to be measured by the length of the shortest computer program capable of generating them.

Thus, complexity as defined here is a property of compressible data sets. (Complex systems are another matter, outside the scope of this article). Ordered data sets have low complexity, random data sets have no complexity at all, and complex data sets lie between them.

In this sense we can say that a Formula 1 lapchart from 2011 is a complex data set, which lies between order and randomness, and a 2011 lapchart has greater complexity than a 2010 lapchart. In this context, the greater complexity could be measured by the greater word-count required to provide a complete description of the course of a race, and the greater length of time required to write such an account.

Schumacher's absence of big joy

For not the first time in the past year or so, Michael Schumacher spent Sunday afternoon being mugged by a succession of Saubers, Force Indias, and Toro Rossos. And not for the first time, Michael found the concept of hard, but clean combat, an elusive one. In fact, at the end of lap 2, when Vitaly Petrov came steaming up the inside of Schumacher into Turn 12, Michael appeared to momentarily lose his bearings in space-time, nostalgically turning into the side of another car as if he believed himself to be back at Jerez in 1997, battling Jacques Villeneuve for the championship. It was, no doubt, an instinctive move once again, rather than a premeditated one.

Schumacher's driving tactics are not without more far-reaching consequences either. In particular, to stretch a point, when Michael tried to pin Rubens Barrichello against the pit-wall in Hungary last year, he ultimately cost Fernando Alonso the championship.

How so? Well, it's fair to say that, post-Hungary, Rubens's attitude to Michael hardened somewhat. And on the first lap of the championship decider in Abu Dhabi, when Michael attempted to take Barrichello into the first chicane, Rubens shut the door very firmly. This allowed Nico Rosberg the opportunity to barrel down the outside of his team-mate, and gain the inside line for the right-hand component of the corner. Michael tried to hang-on, but was off the racing line, and spun through 180 degrees on the dusty surface. Liuzzi then piled into the stationary Mercedes like a powerboat trying to climb a shingle beach.

It was, of course, the safety car triggered by this incident, which Petrov and Rosberg pitted under, enabling them to jump ahead of Alonso. Hence, Sebastien Vettel has Michael Schumacher (and a multitude of other unconnected variables!), to thank for his 2010 world championship.

Magic paddle latched

After finishing fourth in Sunday's Turkish Grand Prix, Lewis Hamilton opined that his first lap mistake had cost him an opportunity of battling for second place in the race. In fact, a close examination of the data suggests that the McLaren didn't have sufficient race pace to even challenge the Ferrari of Alonso for third. Lewis's mistake was costly at the time, but in retrospect he would probably have been confined to fourth place anyway.

But let's go back to the beginning of the race. Mark Webber got away to a poor start, immediately relinquishing second place to Rosberg, and allowing Hamilton to get alongside into turn 1. Lewis thought better at that point, but tried the outside again into turn 3. This was a somewhat optimistic move, and Lewis overcommitted, running wide, letting Alonso past into turn 4, and Button into turn 5. Jenson and Lewis duly completed the first lap in fifth and sixth positions.

Thus, Lewis had it all to do, and with the adrenalin clearly flowing, he tried the inside of Button into turn 8 on lap 2. The successful execution of such a move would have required a degree of charity from Jenson, normally only associated with Catholic missionaries, and Button duly shut the door.

After 5 laps, Button and Hamilton were running a couple of seconds behind Alonso in fourth, with Lewis still looking for a way past his team-mate. At the end of lap 6, Lewis used his DRS to out-brake Jenson into turn 12, but then missed the apex of turn 13, had a bobble at turn 14, and Jenson immediately re-took the place on traction. Crossing the start-finish line, Hamilton snuck back into his team-mate's slipstream, and then sent one up the inside again into turn 1.

Hamilton commented after the race that he was suffering from oversteer during the opening stints, with detrimental consequences to his tyre wear. Substantiating this, Lewis seemed to lose grip almost the moment he'd got past Jenson, and Button re-took fifth place into turn 1 on lap 8. On lap 9, Massa used his DRS to take Hamilton down the back straight, at which point Felipe and Lewis both made their first stops.

The gap to Alonso had grown to over 5 seconds by the time Hamilton pitted. Webber, Alonso and Rosberg made their first stops just one lap later, but Hamilton found himself behind the Mercedes when it emerged from the pits, and by lap 11 the deficit to Alonso was 7 seconds.

On lap 14, Hamilton used his DRS to overtake Rosberg down the back straight, the McLaren raising the dust on the inside of the circuit as he did so. At this juncture, the gap to the lead Ferrari was still just 7 seconds, and Hamilton now had a clear track to Alonso.

However, far from closing on the Ferrari, the gap now began to inch upwards. After 17 laps, the interval was 9.5 seconds, and thereafter Lewis began to lose huge chunks of time: after 18 laps, it was 10.5 seconds; after 19 laps it was 12 seconds; and when Lewis made his second pit-stop at the end of lap 20, the gap had grown to 14 seconds.

Alonso's second stop didn't come until lap 23, so Lewis could have been expected to make hay with the advantage of a three-lap undercut here. On the contrary, on lap 24 the gap between the Ferrari and McLaren was just over 14 seconds, exactly as before. The interval then extended to 19 seconds by lap 32. A couple of laps later, Hamilton made his third pit-stop, losing a lot of time when the right-front wheel refused to tighten properly. But by this stage, the damage had been done.

Just 7 seconds behind Alonso after 14 laps, Lewis was 19 seconds behind when he pitted twenty laps later. Hamilton finished fourth, and the superior tyre wear of the third-placed Ferrari was such that Lewis would have finished fourth even without the pit-stop problem, or his first-lap mistake.

McLaren's failure to bring any significant upgrades to the Turkish Grand Prix, combined with the minor upgrades introduced by Mercedes and Ferrari, have brought all three teams onto a similar performance level. McLaren's inability to preserve a fresh set of tyres in qualifying, and Lewis's need to go racing after his first-lap mistake, then exacerbated the tyre wear situation, presenting Ferrari with a comfortable podium position.

McLaren lost out in the latter stages of the 2010 development race, and there is already a faint echo of that in only the fourth round of the 2011 championship.

Turkish Grand Prix prospects

Saturday's final qualifying session for the Turkish Grand Prix appeared to suggest that Sebastien Vettel is unassailable this weekend. A single lap from the German in Q3 was sufficient to establish a 0.4s buffer to team-mate Mark Webber, and a gap of over half a second to Nico Rosberg and Lewis Hamilton in 3rd and 4th. Contrast that to last year, when Lewis Hamilton was merely 0.15s slower than Webber's pole-sitting Red Bull.

So, is there any chance of someone challenging Red Bull in the race? Well, there are four possible reasons why Red Bull might be vulnerable: (i) tyre wear; (ii) fuel consumption; (iii) KERS; (iv) DRS. Let's take each of these in turn.

(i) Red Bull appear to have had their tyre wear under control since Australia, and this weekend Vettel and Webber both chose to save a set of fresh options for the race. As James Allen explains, the benefits of this are multiplicative:

In comparison to a set which has been used in qualifying, a new set will give an first lap performance boost, then it will last two to three laps longer than a used set, which have done that much already. On top of that the degradation on a used set means that every lap in the stint will be about 1/10th to 2/10ths of a second slower than the new set through the stint. And finally there is another benefit, which is that you delay taking the hard tyre an extra couple of laps and that tyre is around a second a lap slower.

Assuming the Red Bulls get away first and second, they will have the freedom to monitor tyre wear, and decide whether to opt for a two-stop or three-stop strategy. The fresh set of soft tyres could be used on the second stint, and if the track rubbers-in, they might last long enough to facilitate just one further stop. However, given that Mercedes and McLaren are likely to make at least three stops, Red Bull will probably decide to minimise their risk, and simply copy this strategy.

(ii) Red Bull suffered fuel consumption problems at Turkey in 2010. This, however, was apparently due to under-estimating the McLaren challenge on that occasion, and the problem has not recurred since.

(iii) The unreliability of Red Bull's KERS system constitutes a genuine vulnerability. Whilst the system may work at the beginning of the race, its function cannot be guaranteed throughout.

(iv) Prior to this weekend, Red Bull's DRS has been extremely effective, inflating the gap between the Milton Keynes cars and the rest of the field in qualifying, when the use of DRS is unrestricted. The RB7, however, has a new rear wing this weekend, which may reduce the discrepancy between race pace and qualifying pace.

All things considered, though, it's difficult to look beyond a Vettel victory.

Second place, however, is another matter. With a qualifying deficit of only a tenth to Mark Webber, both Nico Rosberg and Lewis Hamilton have possibilities. If neither can overtake Webber on-track, the best opportunity may come at the first stops, when Vettel will have first call over when to pit, and may well delay doing so as long as possible. Thus, whilst Webber will be unable to pit at the optimal time, Rosberg and Hamilton will be free to do so whenever they want, and may therefore have the opportunity to jump ahead of the Australian.

Of course, if Hamilton has fallen behind Alonso at the start, then it may be that Rosberg will be the only man capable of challenging the Red Bulls...

The Senna film

Late on Tuesday afternoon, beneath a perfect azure sky, I took the train to Waterloo, between verdant hedgerows, liberally seasoned with Hawthorn blossom; beneath flyovers graffitied in big bulbous lettering; and past the blue-ribbed gasometer behind Battersea Power Station.

I was en route to see the UK premiere of Senna, at the Curzon cinema in Mayfair, a month before the film goes on general release. Organised by James Allen, the screening was introduced by a sprightly-looking Jackie Stewart, and included a Q&A session afterwards with director Asif Kapadia and writer Manish Pandey.

Martin Brundle delivered an eloquent analysis of the film, testifying to its rendition of Senna, and there was then a pleasant surprise when it transpired that Professor Sid Watkins had also been watching from the back of the cinema. Clearly moved, Sid was able to pay tribute to the documentary, and share with the audience a touching anecdote attesting to Ayrton's fundamental humanity.

And the film is certainly very good; I don't think any motor racing fan will be disappointed. However, in terms of the wider critical reception and commercial success of the film, there are perhaps two crucial questions: (i) What makes this a cinematic entity rather than a TV documentary? (ii) Is the material here of interest to those not already fans of the sport?

The story of Senna's fight to reach the top of his profession, his struggle against perceived injustice, and the tragedy of his ultimate demise, certainly evoke universal themes. However, a large proportion of the film also consists of what might be termed 'motor racing opera'. It's great stuff, but I'm not sure that it will necessarily interest those not already engaged by the sport. In terms of the cinematic appeal of the documentary, however, the large screen works very well. In the early shots from the 1984 Monaco Grand Prix, you can really feel the presence of the cars, their speed and latent violence.

My personal highlight? An exchange between Senna and then FISA President, the bellicose Jean-Marie Balestre, at a pre-race drivers briefing in 1991. "My decision is the best decision," asserts Balestre with finality. After a pause, Ayrton responds, "I am getting a feeling for that."

The global nature of aerodynamics

It's been a commonplace observation in motorsport over the years, that simply copying the front or rear-end of a successful car, won't necessarily assist the performance of your own car.

It's a message that Gary Anderson reiterates in his assessment of the Red Bull front-wing: "I guarantee that if you put a Red Bull front wing on any other F1 car in a wind tunnel, it would be worse than that team's current configuration. That's because it's not just the wing that makes the Red Bull the best car aerodynamically, it's the whole aero philosophy of the car, with everything working in sync with each other."

Now, it's certainly easy to understand that the shape of the front-wing will influence the pattern of airflow over the rest of the car. The airflow of a racing car possesses a well-defined directionality which enables one to distinguish between that which is upstream and that which is downstream. And, at first sight, this seems to be an asymmetrical relationship, in the sense that the upstream airflow clearly influences and determines the nature of the airflow downstream. However, aerodynamics, (and fluid mechanics in general), has a slightly spooky aspect to it, in the sense that the downstream airflow also influences and determines the upstream airflow.

To take a simple example, if one creates a blockage downstream of the front-wing, then this will reduce the velocity of the airflow over the front-wing, reducing the downforce it generates. Conversely, if one accelerates the airflow downstream of the front-wing, then this will also accelerate the airflow over the front-wing, increasing the downforce it generates.

There are also more subtle examples of this type of aerodynamic spookiness. Back in 2006, the change to 2.4 litre V8 engines in Formula 1 triggered the proliferation of so-called flow conditioners atop the nose of the chassis. These appendages re-aligned the upper-body airflow in a manner which reduced the rate of airflow over the front-wing, but increased it over the rear-wing. Recall that the downforce generated by a wing is proportional to both the speed of the airflow over it, and the angle-of-attack of the wing. Thus, Formula 1 teams wishing to compensate for the loss of engine power, could reduce the drag generated by the rear wing for a given level of downforce, by reducing the angle-of-attack, but increasing the airflow over it. (See 2006 Formula 1 Review, Mark Hughes, Autosport December 14th/21st).

The fact that information downstream influences and determines the information upstream, and vice versa, is grounded in the mathematics used to represent steady-state, subsonic (i.e., relatively incompressible) airflow. Crucially, the Navier-Stokes equations for such an airflow regime are elliptic. (Diagrams here courtesy of Computational Fluid Dynamics, J.Blazek, Elsevier 2001).

Elliptic equations are typical, mathematically speaking, of equilibrium situations, and in these circumstances, the information at any point is capable of influencing the information at any other point. In the case of steady-state aerodynamics, this means that the airflow information at any point is capable of influencing the airflow information at any other point, upstream or downstream. Hence, the aerodynamicist must seek optimal global solutions, rather than simply working from the front of the car rearwards.

Now, ellipticity is only one of the possible personalities which differential equations can possess. Other equations, for example, are hyperbolic or parabolic. In the case of hyperbolic equations, the information at a point will only influence the part of the domain enclosed within a cone-shaped region emanating from that point. Meanwhile, in the case of a parabolic equation, the information at a point will influence a block-shaped region downstream of that point.

Whilst the airflow over a racing car travelling in a straight line at a constant speed corresponds to a solution of the steady-state, incompressible Navier-Stokes equations, when a car is subject to yaw under cornering conditions, the airflow corresponds to a solution of the unsteady, incompressible Navier-Stokes equations. In this case, the equations are parabolic, and what happens at the front-wing is extra-crucial, for the information at any point upstream influences the entire solution downstream.

As ever, the key is to be a leader rather than a follower.