Wednesday, April 27, 2011

A History of Modern Witchcraft: Part 3

Marina Petrovium had enjoyed a childhood both opulent and bohemian, as the daughter of the Russian ambassador in Istanbul. The ambassador's residence was a triple-tiered mansion of vaulted arcades, marble-pillared foyers, music rooms, and dusty libraries. Behind the mansion, a terraced garden maintained by a battalion of gardeners and horticulturalists, cascaded down to the sparkling blue Bosphorus, a gently scrolling technicolour banner of yachts, barges, trawlers, schooners, ferries and container vessels.

Cedar, cork and cypress shaded the immaculately-striped lawn of the upper terrace, which thence graded into a maze of fruit trees, flowering bushes, trimmed hedgerows, and serpentine paths between sparkling fountains and efflorescent borders.

Down in the densest, deepest dells of the garden, secreted from sight beneath a rhododendron bush, was a mossy outcrop of rock, whose dark striations fascinated the mind of eight year old Marina. An ever-resourceful, inquisitive, and largely unsupervised child, she eventually prised free a sample with hammer and chisel, and subjected it to a battery of tests within her father's workshop. Whilst the spirit-level and the voltmeter responded in mute fashion to Marina's empirical enquiries, her uncle's long-neglected Geiger counter yielded rather more garrulous results.

To Marina's disappointment, however, her pitchblende discovery provoked not parental approbation, but a sizeable degree of consternation, and she was rewarded for her initiative with a series of unpleasant visits to Dr Chezhkov's clinic in Kiev. Her curiosity, however, had been irreversibly piqued...

Two weeks ago, I'd never heard of Marina Petrovium, or the IAEA's Division of Paranuclear Phenomena. The first we knew something was wrong was when one of the Health Physics surveyors, (a fellow with a somewhat Hitchcockian profile, called Ted Straw), returned from a stint in the fifth chamber, complaining of mild nausea and a severe headache. Two hours after reporting to the medical centre, he was yelling about ghostly apparitions, and had to be restrained by a nurse and two orderlies.

We assumed at the time that the poor fellow had merely contracted some sort of virus, and developed a nasty fever. Eight days later, however, three of the trainee health physicists seconded to the chamber went mad, screaming about demonic voices exhorting them to commit acts of self-mutilation. One was found losing copious amounts of blood after severing his arm in a lift-shaft, while the other two blinded themselves with ballpoint pens. Remote CCTV revealed that a cavity had opened up in the floor of the fifth chamber, and was pulsing with a blue glow.

It was then that I knew I had a problem.

Now, myself, Marina, Dr Burgher, and two RPAs, had taken the cargo lift down to the excavations, where we had donned reflective overalls, hard-hats, and waterproof boots, and proceeded to the first chamber.

The still, damp air was saturated with a thick, viscid darkness, broken only by the static pools of wall-mounted Halogen light, and the roaming pencil-beams of our helmet-lamps, picking out glistening details on the rocky chamber floor. A tangle of braided power cables crawled blindly down the tunnel-wall leading from the chamber. A distant dink of dripping water, and the ambient hum of electric generators, provided a sonic background to the claustrolithic environment.

The tunnel leading from the chamber branched after fifty metres or so, each branch itself splitting after a further fifty metres, then branching once again. Down here, I sometimes imagined myself to be exploring the suffocatingly still lungs of a sleeping granite giant, which would imminently wake, and fling off the overlying layers of rock, sediment and soil, like a geological duvet, to bestride the Earth once more.

"I do so love spelunking, don't you?" whispered Marina in my ear, as Dr Burgher demonstrated how to operate our helmet-lamps.

"The chambers are distributed over three levels," explained Burgher as he continued his briefing. "To reach the fifth, we must proceed by vehicle down the network of tunnels here on the first level until we reach the second chamber. There is a natural vertical channel in that chamber, through which we have bored a lift-shaft. That will take us to the second level, along which the tunnels are too narrow for vehicular travel. We must then proceed on foot, and then by ladder, down to the third level."

Friday, April 22, 2011

Tiger Woods and quantum theory

"In your life! Have you ever seen anything like that?" (Verne Lundquist, CBS commentary, 2005 Masters).

If the many-worlds interpretation of quantum theory is correct, the universe branched when Tiger Woods tried to hole his chip on the 16th green of the 2005 Masters. In our branch of the universe, the ball rolled up to the side of the hole, paused on the precipice, then toppled in. In other branches, the quantum fluctuations in the centre of mass of the ball were such that it remained poised on the edge of the cup, and Tiger failed to win the tournament.

In most branches of the universe, 2010 was not one of Tiger's better years.

The point, however, about Tiger's chip is that it demonstrates the ubiquity of instability in the physical world, and the manner in which that instability opens the door for quantum effects to be amplified onto macroscopic length scales. The macroscopic world cannot be sealed off from the quantum world.

Despite this fact, in a recent paper on the interpretation of quantum mechanics, Lev Vaidman invites the reader to consider the 'Tale of a single-world Universe':

"Let us assume that we are the only civilization and that we live under a very strong dictatorship which has laws against quantum measurements. It is forbidden to perform quantum experiments in which there is a nonzero probability for more than one outcome. Manufacture of Geiger counters is banned, quantum random number generators are forbidden, and a special police prevents world splitting devices of the kind that can be found in Tel-Aviv university. There are even laws that under the threat of death enforce disposal of neon light bulbs after six months of operation, to avoid operating an old bulb, which, when flicking, splits our world. In this tale Nature does not arrange quantum experiments accidentally: no macroscopically different superpositions of a macroscopic object ever develop."

The existence of instability throughout the natural world makes it impossible to satisfy Vaidman's hypothesis. Consider, for example, the widespread presence of chaotic systems. In such systems, no matter how closely one chooses a pair of possible initial states, the distance between them will diverge exponentially with time. Thus, initial states separated by a quantum perturbation will diverge exponentially with time, amplifying the quantum perturbation onto macroscopic scales. As philosopher of physics David Wallace points out, " everywhere, and where there is chaos there is branching, (the weather, for instance, is chaotic, so there will be different weather in different branches."

Quantum effects can also kill you. On average, every cell in your body is traversed by a track of ionising radiation every year. If quantum theory provides a maximal description of the physical world, then the interactions between such radiation tracks and the particles in your body are objectively probabilistic. If you're unlucky, one such radiation track might undergo elastic Compton scattering with an electron in the outer shell of an atom close to the DNA within the nucleus of a cell. The liberated electron might then proceed to wreak havoc in its vicinity, causing numerous further ionisations on its trail of destruction. These ionisations might create free radicals, which proceed to cause double-strand breaks in the nearby DNA. Such damage might be mis-repaired, creating a mutation in the DNA. The mutation might lie within that part of the DNA which controls the cell cycle mechanism, and the mutant cell might then reproduce uncontrollably, creating a cancerous growth within the host organism. Thus, a single, objectively probabilistic quantum event has the capability to kill you.

Tuesday, April 19, 2011

The Red Bull Owners' Workshop Manual

The word from the Malaysian Grand Prix paddock ten days ago, was that many of the other Formula 1 teams will now be attempting to mimic Red Bull's flexible front-wing. As Mercedes team principal Ross Brawn pointed out, "teams have got to decide if that's the reason - or one of the reasons - for [Red Bull's] level of performance. If it is, then you need to consider going that route yourself."

McLaren, in particular, will presumably be seeking to use the recently extended capability of their CFD simulation software, STAR-CCM+, to represent "fully coupled, two-way, fluid-structure interaction (FSI)" with Abaqus, a popular FEA software tool. As CD-adapco proudly announce on their own website,

"Put simply, the close-coupling between STAR-CCM+ and Abaqus brings the solution of a wide range of FSI problems within the easy reach of a typical engineer. In terms of both practicality and accuracy, co-simulation (in which both codes exchange data as they simultaneously run) is the only way to tackle problems such as aerodynamic flutter, fluid induced bending, vortex induced vibration and galloping."

Those teams intending to imitate Red Bull, may seek to accelerate their learning curve by purchasing a copy of the Red Bull Formula 1 Owners' Workshop Manual, due to be published by Haynes in July. Chapter titles will, no doubt, include: 'Using a pull-rod suspension system', 'Passing front-wing load-deflection tests', and 'Introducing an exhaust-blown diffuser without melting the floor of your car'. A chapter on 'How to successfully install your KERS system' may now be delayed until a second edition.

Sunday, April 17, 2011

Hamilton's bolt from the blue

"A Jack-in-a-box, a Fabergé gem, a clockwork toy, a chess problem,...a cat-and-mouse game, a do-it-yourself kit." (Mary McCarthy, An Introductory Essay to Pale Fire).

This was it then: the perfect mix of the cerebral and the visceral, a Molotov cocktail of divergent strategies and wheel-to-wheel combat, four different strategic threads interacting in game theory space, five F1 World Champions in four different teams, feinting, locking wheels, overtaking inside and outside, saving the tyres, timing the pitstops, attacking with DRS and defending with KERS.

And emerging victorious from all this complexity, with a tear in his eye, was the man whose car almost didn't make the start of the race, the man who'd lost track-position after his team-mate determined the timing of the first pit-stop, the man reputedly harder on his tyres; the purest racer of them all.

So how much of Lewis Hamilton's victory in Sunday's Chinese Grand Prix was down to Lewis, and how much of it was down to the strategy of the McLaren team? Was this another case of Lewis saving the team's blushes, as in Germany 2008, or was it more like Canada 2010, when McLaren's strategic inspiration outwitted Red Bull? The three-pitstop strategy eventually selected by McLaren, clearly trumped the two-stop strategy chosen by Red Bull and Ferrari, but did McLaren luck into this option after badly fluffing their first pitstops?

Perhaps the most important parameter here was the race-day temperature, which was significantly warmer than the smoggy, then chilly conditions of Friday and Saturday. The ultimate pace of the Red Bulls in Shanghai was clearly faster than the McLarens once again, to the tune of 0.7secs in qualifying. In contrast to Malaysia, Red Bull appeared to be confident of their tyre wear this week, presumably setting-up the RB7 to maximise its ultimate speed. However, the higher race-day temperatures may have increased the tyre wear, entailing that the time loss from worn tyres on a two-stop strategy, exceeded the combined time loss from an extra pit-stop and consequent loss of track-position incurred executing a three-stop strategy.

Vettel had got away slowly from pole position, immediately losing the lead to Button. As Vettel drifted to the middle of the track to protect second place, Hamilton feinted to the outside, before slinging his McLaren down the inside, dust streaming in his wake as Vettel squeezed him off-line. Lewis wasn't to be intimidated, however, and as he slotted into second, Vettel ran a little wide in turn1, allowing Rosberg alongside into turn 2. The Red Bull, however, had the inside for turn 3, and the order at the completion of the first lap was Button, Hamilton, Vettel, Rosberg, Massa, Alonso.

Approaching the first stops, McLaren faced the same conundrum that Red Bull tripped over at Melbourne in 2010: If you're running one-two, and you grant your leading driver first-call over the timing of the first pitstop, then it's likely that your second driver will be forced to pit after the optimal point, and will find himself demoted behind people who had the freedom to pit earlier. Thus, just as Mark Webber was dropped into the pack at Melbourne in 2010, so Lewis Hamilton suffered at China in 2011. In fact, on this occasion, Jenson Button made a late decision not to pit on the lap he was initially intending to, and Hamilton was left out so long on worn tyres, that he was overtaken on his in-lap by Massa's Ferrari.

To top it all, when Button and Vettel pitted together at the end of lap 14, Jenson delayed himself by mistaking the Red Bull mechanics for his own, and was jumped by Vettel. The leading Red Bull driver therefore found himself ahead of both McLarens, and seemingly set for victory.

Mercedes, meanwhile, had committed to a three-stop strategy from the beginning, pitting Rosberg at the end of lap 12, enabling him to jump both McLarens and the Red Bull. However, with Vettel planning one pit-stop less than the Mercedes, this was not necessarily a pressing concern for Red Bull.

As the second stint evolved, Rosberg was able to maintain a gap of 4secs or so to Vettel, who was a couple of seconds clear of Button in third, with Massa a second back in fourth, and Hamilton apparently stymied, just behind the Ferrari in fifth.

Hamilton, of course, had compromised his qualifying to save an extra set of options for Sunday's race. After allowing himself to become a sitting duck in the final stages of the Malaysian Grand Prix, one could almost see Lewis Hamilton saying to himself this weekend, 'There's no frigging way I'm going to allow that to happen again!' And tellingly, in the post-qualifying TV interview, Lewis revealed that, "I've got the set of options I've just qualified on, a new set of options and a new set of primes,...and a very decent set of options again." This seems to suggest that McLaren were always considering the possibility of switching to a three-stop race strategy. Entering the first pit-stops in first and second, and emerging in third and fifth, McLaren now committed to the three-stop option, pitting again barely ten laps later, Button getting another set of options at the end of lap 24, and Hamilton doing likewise a lap later.

One of the problems of this strategy was that Rosberg was already running ahead of the McLarens, and was also three-stopping. Having lost the effective lead of the race to Vettel, by switching to a three-stop strategy McLaren were potentially surrendering another place to Rosberg. In fact, Mercedes responded to Button's stop by pitting Rosberg at the end of lap 25. The Mercedes therefore had exactly the same number of laps to complete as the McLarens on one further set of options and the final set of primes. McLaren's strategy would force Button and Hamilton to overtake both Rosberg, and the two-stopping Massa, if they were to get a shot at Vettel later in the race.

It was an audacious strategy, and one which looked unlikely to succeed at the time. For a start, Rosberg, Button and Hamilton were initially running 4th, 5th and 6th in their third stint, and needed to circumnavigate Alonso, running a two-stop strategy like his team-mate, but struggling now on his worn second set of options. Rosberg surprised Fernando down the inside into the final corner on lap 28; Button sold him a dummy into the hairpin on lap 29, accelerating past the Ferrari exiting the corner; and Hamilton also took Alonso on traction coming out of turn 6 on lap 30. Nevertheless, the McLarens were ten seconds behind Vettel at this stage, and like Vettel, they had one further pit-stop to make.

Revealing the extent to which a two-stopper was compromising the speed of the Red Bull, Massa was now drawing onto Vettel's tail, and Sebastien made his second and final pit-stop at the end of lap 31. This put him onto primes, when Rosberg and the McLarens were still on options, and it left Vettel with a 25-lap stint to reach the end of the race. Simultaneously, Hamilton was setting consecutive fastest laps, leaping onto the tail of Button.

Massa made his second and final stop at the end of lap 33, emerging a couple of seconds behind Vettel. Button, meanwhile, was holding up Hamilton, but Lewis pressured Jenson into running wide at the hairpin on lap 35. Cutting back on a tighter line, Lewis forced his team-mate to take a defensive line into the final corner. Onto the start-finish straight, Lewis deployed the last of that lap's KERS, drew into Button's slipstream, dipped into the next allocation of KERS, and ducked down the inside going into the first corner. Lewis didn't really have the corner, but remained committed. Button made as if to turn-in, but conceded the corner with a violent twitch at the last possible moment.

This was a move which wouldn't have succeeded on any other driver, Lewis simply trusting, as he did at Istanbul last year, that Jenson would avoid the catastrophe of an intra-team McLaren collision. Eventually, there may come a time when Jenson refuses to concede in such circumstances...

The order was now Rosberg, Hamilton, Button, Vettel and Massa. The first three were yet to make their final stops, but with Rosberg now 16 seconds ahead of Vettel, the three-stoppers would emerge just behind the two-stoppers. Button pitted at the end of lap 37, Hamilton at the end of lap 38, and Rosberg at the end of lap 39. Nico emerged in third, but with Hamilton immediately on his tail, looking for a way past.

Into turn 6 on lap 40, the McLaren tried down the outside, only for Rosberg to ease him out at the apex. Lewis tracked Nico with predatory zeal through the following swerves, deployed the remaining half of his KERS allocation onto the back straight, triggered the DRS, but was just out of range into the hairpin. Onto lap 41, and Lewis had a look down the inside into turn 6, but Rosberg parried, and Hamilton veered across to the outside, the McLaren's left-front locking up in desperation. The McLaren's tyre was flat-spotted, but Rosberg and Hamilton were closing on Massa even as they fought tooth-and-nail. Onto lap 42, Maldonado's Williams exited the pits right in front of Rosberg, and Hamilton was inches off the rear of the Mercedes into turn 2. This time, when Lewis swung down the inside into turn 6, Rosberg took the wide line and conceded the place under braking.

Only Massa now lay between Hamilton and his quarry. Lap 44, Felipe defended the inside into the hairpin, and Hamilton was able to undercut him on the exit, drawing alongside, almost brushing wheels. Felipe took the defensive line into the final corner, ran wide, and Lewis dragged past down the start-finish straight. The chase was on!

Vettel was 4.6secs down the road, but Hamilton swiftly began slicing into his lead. By lap 50, he'd caught the Red Bull. Onto the back straight, Lewis deployed the remaining half of his KERS, then triggered the DRS. Bereft of KERS himself, Vettel had to defend into the hairpin, Hamilton cut back on the exit, and almost drew alongside into the final corner. Vettel, however, squeezed the McLaren, its right-hand wheels mounting the kerb, and Lewis had to concede the corner. Onto lap 51, and Lewis repeated the routine, wheel-to-wheel this time into the hairpin, but Vettel sat his car on the apex, and prevented Lewis getting alongside under acceleration. Into lap 52, and Lewis was menacing the Red Bull into turn 1, almost touching its diffuser. He pressured Vettel into turn 6, and then used his KERS into turn 7 to surprise Seb, taking the lead, and then the victory four laps later.

Proper racing.

Saturday, April 16, 2011

Why did Vettel stay in his car?

Shortly after Saturday's final qualifying session for the Chinese Grand Prix, Red Bull Team Principal Christian Horner was asked why Sebastien Vettel had remained sitting in his car for some minutes after pulling to a stop in parc ferme. "He was just waiting for the FIA to say it's ok to get out," suggested Christian in response.

Now, whilst it's surely just a matter of time before the drivers do need to seek permission to alight from their vehicles, such parental guidance is not a current requirement. Moreover, Sebastien remained sitting in his car as the rest of the top ten pulled up, clambered from their cockpits, and departed elsewhere. So what exactly was he up to?

Red Bull, of course, have encountered serious problems with their KERS system in each race so far this season. Both drivers were without the system in Australia, whilst in Malaysia, Mark Webber noticed a problem with his KERS system as he drove round to parc ferme after final qualifying. Despite replacing the battery pack, Webber was subsequently bereft of KERS in the next day's race, and even Vettel's system began to fail during the final stages. Webber was then deprived of KERS in Saturday's qualifying session for the Chinese Grand Prix, after a problem with the wiring loom.

The KERS system used by Red Bull has been analysed by the superb Craig Scarborough, who points out that both the control system in the right-hand side-pod, and the battery pack in the left-hand sidepod, run at high temperature, and require their own cooling systems. The location of the battery pack in the sidepod, rather than beneath the fuel tank, is unique to Red Bull, and it seems likely that the Red Bull system is overheating. A resolution to the problem will presumably require a re-design of the installation, unavailable until Istanbul at the earliest.

Moreover, it may be that the heat soak after the car completes a series of laps, and comes to a stop in the pit-lane, is a particular problem. Could it be, therefore, that Vettel was sitting in his car, keeping the cooling pumps running until the temperature of the control unit and/or battery pack had reached an acceptable level?

Friday, April 15, 2011

Sergio Perez and space junk

Precocious Sauber driver Sergio Perez retired from last Sunday's Malaysian Grand Prix when an unidentified object penetrated the chassis of his car. The destructive path taken by the debris has been explained in vivid terms by Sauber technical director James Key:

"Sergio hit what he believed was a piece of wing or something, because it must have been big enough for him to see. It appeared to come off the car in front, which was a Toro Rosso, but subsequently we found out that they also found some damage on their car, so it looks like this piece was lying on the ground beforehand. What happened was pretty frightening. It damaged the front wing quite badly and it damaged the front of the floor. Then, it went through the side of the lower part of the chassis, in the boat area [on the underside of the nose], and pierced that. It went straight through the Zylon panel, straight through the chassis, and then into the ECU. It killed the ECU, which stopped the car, and then rolled along. It then went into the sidepod and then out the car – damaging the impact structures in the sidepod itself. So whatever it was it was either travelling very quickly, or it was very heavy and had a lot of momentum."

The Toro Rosso in front was that of Jaime Alguersuari, with whom Perez was battling for 13th place. The possibility that some ballast became detached from the Toro Rosso, has now been ruled out after the Italian team claimed that Alguesuari's car was perfectly intact at the end of the race. So what did cause Perez's retirement?

The first thing to note is that something fell off the rear of Vitaly Petrov's Lotus-Renault, going into turn 1 on lap 21. The object came to rest on the outside of the turn, and appeared to disappear shortly thereafter. It might have been retrieved by a wing-footed marshal, but it might also have been picked up by another car, and shed a few laps later in front of Alguesuari and Perez. However, as David Coulthard noted on the BBC commentary at the time, the object appeared to be a mere carbonfibre appendage, and thus unlikely to penetrate the chassis of another car.

Of more relevance, perhaps, is the fact that after his ECU was killed, Perez coasted to a halt on the inside of the circuit just after turn 14, on what was his 24th lap. This implies that the damage was incurred somewhere between the uphill hairpin of turn 9 and the downhill switchback of turns 12 and 13. And intriguingly, in the couple of laps before Perez retired, the right-hander of turn 11 appeared to become quite treacherous.

Nick Heidfeld, for one, left the road at turn 11 on lap 22, crossing the gravel before rejoining. It's possible that this excursion dragged something onto the margins of the track, or pulled some ballast off the Lotus-Renault. If so, however, there is no visual evidence of it during the couple of laps between Heidfeld's detour and Perez's retirement.

On lap 24, the other Sauber of Kamui Kobayashi lost 10th place to Mark Webber when the Japanese pilot slid wide at turn 11. Once again, there is no visual evidence of anything being pulled onto the racing line from the margins of the track. The only other car to pass through turn 11 before the arrival of Alguesuari and Perez on this lap was Rosberg, unseen by the television cameras. 'Britney' could conceivably have run wide over the kerb, flipping something onto the racing line. But if so, then Nico lost no time in the process, being 54secs behind the leader both before and after.

So, in the absence of further televisual evidence, or a confession of missing ballast from one of the teams, this seems likely to remain a mystery...

Sunday, April 10, 2011

Entering Phase Two

As Lewis Hamilton struggled vainly to make his fourth set of tyres last to the end of Sunday's Malaysian Grand Prix, one recalled his pre-season complaint, "It's not racing, it's just driving around." However, to understand why Lewis finished eighth in the race, one has to go back to Q2 on Saturday afternoon.

Recall that from the beginning of qualifying to the end of a dry race, the teams have only six sets of tyres to play with: three sets of hard tyres (the 'primes'), and three sets of soft tyres (the 'options'). Now, all of the contenders for pole position - Vettel, Webber, Hamilton and Button - used a set of hard tyres in Q1. At the beginning of Q2, however, Hamilton alone tried to set a time on hard tyres, presumably in the hope that this would be sufficient to get him into Q3, thereby saving a set of fresh soft tyres for the race.

Unfortunately, Hamilton's time on the hard tyres, a 1m37.339, wasn't quite fast enough, and as Q2 progressed, he dropped out of the top ten, and had to make a late run on soft tyres. This might perhaps have injected an element of anxiety into his driving, for whilst he got into Q3 with a 1m35.852, he locked the right-front into turn 1, badly flat-spotting the tyre. Each of the Red Bull and McLaren drivers now had two sets of fresh soft tyres available for Q3, and all four decided to make one run at the beginning of the session, and one at the end.

The ideal strategy for the race consisted of four stints, punctuated by three-stops, with the first three stints on the three sets of slightly-used softs, and the final stint on one of the fresh sets of hard tyres. Unfortunately for Hamilton, it seems that his flat-spotted set of softs was not a viable option for the race, hence he was forced to do the first two stints on his remaining sets of soft tyres, and the final two stints on the hards. Given the second-a-lap deficit of the hard tyres, this was a significant disadvantage, compounded by the fact that Lewis had also used two sets of hards, leaving only one fresh set for the race.

Lewis's race therefore consisted of two strong stints on his soft tyres, a less competitive stint on the fresh hards, and a terrible stint on one of his sets of used hards. Even worse, Hamilton had lost second place to Heidfeld going into the first corner, and was unable to overtake during the first stint. As a consequence, McLaren brought Hamilton in for an early first-stop, on lap 13, to jump Heidfeld. Whilst this released Hamilton into clear air, the timing of the stop was too early for a three-stop strategy, and Lewis became a sitting duck later in the race. Hence, Hamilton's spat with Alonso, which earned him a penalty from the stewards, was ultimately a consequence of trying to save a set of soft tyres in Q2.

Thursday, April 07, 2011

To lobby or to imitate?

In the official Thursday press conference for this weekend's Malaysian Grand Prix, Julien Febreau of L'Equipe asked the five drivers present for their opinion on Red Bull's flexible front wings: "I have nothing interesting to say, unfortunately," replied Nico Rosberg; "Not much to say," remarked Sebastien Buemi; "No, nothing to say," answered Jarno Trulli; "No," said Felipe Massa flatly.

Jenson Button, however, was a little more loquacious: "I know a few people that I have spoken to say it flexes more than what they expect is correct." Elsewhere, Button's McLaren team-mate Lewis Hamilton was quoted as saying, "When I asked what the rules are about how much the wing is allowed to flex they said 20mm. If I you show you a picture that is probably not what is happening."

In an exasperated response, Christian Horner protested that the Red Bull is simply running with greater rake than the McLaren. Which would constitute a rather disappointing return on all that investment in Fluid-Structure Interaction (FSI), one would have thought.

No, Red Bull have clearly stolen a march on the opposition here. This first became apparent at the Hungarian Grand Prix last August, yet McLaren have so far displayed no inclination to imitate the technology. Rather, their strategy has been to lobby the governing body, often via the media, in an attempt to limit the extent to which Red Bull can utilise their advantage. This strategy appeared to be successful last year, with the introduction of more stringent front-wing load-tests at Spa, and a change in the permissible articulation of the under-body plank at Monza. Despite this, Red Bull still appear to be deriving a significant performance benefit from their investment in FSI, so McLaren and the other teams have a choice: lobby or imitate.

One presumes that if McLaren were intending to introduce similar technology in the near future, then their drivers would not be making statements challenging the very legality of such developments. But why would McLaren not be seeking to imitate Red Bull? It may be that a flexible front-wing would simply not work well with the other elements of their package; alternatively, given McLaren's relatively recent troubled relationship with the governing body, they might still be reluctant to develop a technology of dubious legality. Or, more ominously, perhaps McLaren have taken a close look at this, and concluded that they're at least two years behind Red Bull in terms of developing the relevant simulation or carbon-fibre capability. If such is the case, it would certainly explain why McLaren have decided that the best strategy is to continue with the lobbying...

Saturday, April 02, 2011

How Red Bull simulate front-wing aeroelasticity

When it first became apparent in 2010 that Red Bull were using aeroelasticity to generate extra front-wing downforce, a number of eagle-eyed observers pointed out that the Milton Keynes based team had established a relationship with MSC Software in 2009, precisely to develop simulation software capable of representing this type of Fluid-Structure Interaction:

Using MSC's latest MD (multi-discipline) software versions of Nastran and Adams, we already combine mechanism and deformable finite element simulations. We also increasingly use aerodynamic output directly from CFD analysis to generate more accurate loads for the structural simulations. There are rule restrictions to limit this, but multi-physics coupling of these effects allows us to legally enhance the performance of deformable components, for example to optimise down-force and drag characteristics for flexible wing components.

It's clear that Red Bull's front wings are still flexing under load this year, so let's dig a little bit deeper to try and understand what has been achieved here, and what the other teams need to do to respond. Careful scrutiny of MSC's website reveals a detailed explanation of exactly how their software works in this respect:

The objective of modeling fluids in a structural analysis is to account for the influence of fluid pressures on the structure and for improved accuracy in structural response prediction. Structures are generally modeled using Lagrangian scheme where material is tied to a finite element mesh. On the other hand, fluids are solved with Eulerian scheme with material being independent of the mesh, but instead flowing through the mesh. Dual schemes are required because of the way structures and fluids behave.

When fluids and structures need to be modeled in a single analysis, the challenge is running these different schemes in a single run. This is accomplished through an automatic coupling algorithm, where two meshes – one for structure and another for fluid, exist. A coupling surface is created between these two domains which acts as a boundary to the flow of material in Eulerian mesh, while enabling transfer of the stresses to the Lagrangian structural mesh causing it to deform.

So we can hypothesise that Red Bull are representing the solid interior of their front-wing with a Lagrangian simulation, and coupling it to a Eulerian hydrocode to represent the airflow around it. Some further explanation of these terms is perhaps in order.

Both Lagrangian and Eulerian computer simulations divide a continuous domain, occupied by a solid or fluid, into a discrete mesh of cells. The corners of the cells are called the nodes of the mesh. In a Lagrangian simulation, the mesh moves with the motion of the solid or fluid, whereas in a Eulerian simulation, the mesh is fixed in space, and the solid or fluid moves through the mesh. A computer simulation also divides the continuous flow of time into a sequence of discrete time-steps, using the final data from one time-step as the initial data for the next.

If Red Bull are using a Lagrangian simulation to represent the solid front-wing, then they are using a mesh which moves with the wing as it deforms. At the beginning of each time-step in such a simulation, one has the coordinates of each node, the velocity of each node, and the stress and strain associated with each cell. The strain represents the relative displacement, or stretch, which the points inside the solid body are subjected to under the influence of external loads. A solid body responds to strain by generating internal restoring forces, called stresses. The stress and the strain each have isotropic components, and when the isotropic components are subtracted, what remains are essentially the shear stresses and shear strains. These are dubbed the deviatoric stress and deviatoric strain.

The task of a Lagrangian simulation is to go from the nodal positions and velocities, and the stresses and strains inside each cell, at the beginning of each time-step, to the positions, velocities, stresses and strains at the end of the time-step. In the case of Red Bull's front-wing, the aerodynamic pressures at the beginning of each time-step will simply be part of the boundary data.

The basic method for solving this problem is as follows: Use the stresses to calculate the forces on the nodes, thence the acceleration of the nodes, and from this update the velocities of the nodes; use the velocities of the nodes to update the positions of the nodes; calculate the rate-of-strain from the velocities, infer the rate-of-stress from the rate-of-strain, and update the stress and the strain. (In reality there's a lot of shuttling back-and-forth with half time-steps and the like to minimise numerical errors, but these are the basic ideas).

The method of updating the stress is quite involved. Given the nodal velocities, one can simply take the gradient of the velocity field, (and symmetrise it), to obtain the rate-of-strain. (In the case of a racing-car front-wing, all the strain will be elastic, so there is no need to worry about plastic strain). The rate-of-strain can be divided into the deviatoric rate-of-strain and the isotropic rate-of-strain. The rate of deviatoric stress can then be calculated using the shear modulus of the material, and the rate of isotropic stress can be calculated using the bulk modulus. (In the case of Red Bull's front-wing, one can expect the bulk modulus and shear modulus to vary with position across the wing). The deviatoric and isotropic stresses can then be updated.

With the Lagrangian time-step for the solid front-wing deformation completed, the boundary of the deformed configuration can be fed as initial data to the next time-step in the Eulerian hydrocode representing the airflow over the front-wing. (Although, once again, one presumes there is a more sophisticated shuttling back-and-forth between the Lagrangian and Eulerian codes to minimise errors). The Eulerian code will calculate new pressure forces on the boundary of the front-wing, and the cycle will begin all over again.

Of course, realising the desired front-wing performance not only requires the development of this type of simulation technology, but also an understanding of how to implement the requisite elasticity via the orientation of the carbon-fibre plies. Nevertheless, it remains a surprise that so many F1 teams rely on off-the-shelf simulation software rather than developing their own.