City-Link's delivery standards

Autocourse 2012-13 arrived today. Courtesy of City-Link, it was left unprotected, outside the house, on one of the wettest days of the year. The book is ruined.

I presume the package was left in such a manner by an individual who faces a daily struggle to successfully wield a knife and fork.

I'm certainly looking forward to asking the Managing Director of City-Link, Mr David Smith, how employing such individuals contributes to the company's business plan.

Red Bull's double-DRS

Is there a connection between Red Bull's new double-DRS system, and their unique 'underpass' duct?

To recall, the underpass is a means of separating the 'coke-bottle' flow along the flank of the sidepod, from the exhaust-flow, sweeping down from the top of the sidepod. The coke-bottle flow feeds the starter-motor slot and the top surface of the diffuser's trailing edge, while the exhaust jet partially seals the side of the diffuser and increases the flow over the rear brake-duct assembly.

The underpass is fed by the flow along the flanks of the sidepods, which in turn is fed by the front-wing wake. By connecting the flow along the flanks of the sidepods to the low pressure area under the beam wing, the underpass not only assists with rear downforce, but also pulls the air faster over the front-wing.

Red Bull's double-DRS system purportedly stalls the central section of the beam wing, (although Craig Scarborough suggests that it is the tips of the beam-wing which are being stalled, in order to reduce the wing-tip vortex drag). 

The central part of the beam wing is the section which is pulling the air out of the underpass. Thus, if the beam wing stalls, then the underpass stalls, the flow along the flanks of the sidepods weakens, and front-wing downforce and drag are reduced.

The image above here illustrates how the front-wing streamlines on a generic open-wheeled race-car are the same streamlines which pass along the flanks of the sidepods, and thence between the rear wheels, (although there is no sidepod undercut or beam wing in this illustrative case, courtesy of the 2012 University of Southampton Racecar Aerodynamics MSc Group Design Project).

Red Bull introduced a smaller underpass inlet for the Korean Grand Prix, and if the double-DRS really does stall the centre of the beam wing, it would certainly make sense to change the underpass as well. Autosport's Mark Hughes comments in his Korean Grand Prix report that the changes to the sidepod area gave "more downforce and more diffuser stall." 

One can speculate then, that Red Bull's double-DRS is a system which reduces front-wing drag as well as helping to stall the beam wing and diffuser.

Lasers, plasmas and diffusers

The first laser, invented in 1960 by Theodore Maiman, an engineer-turned-physicist, was a product of the aerospace industry. Maiman was working for Hughes Research Laboratories, and was given nine months and $50,000 to make a laser work by Mr Hughes, (And then there was light, Pauline Rigby, Physics World, May 2010).

Perhaps it's time, then, for the introduction of the laser into Formula One, not merely as a ride-height sensor, but as a flow control device.

Racing cars have, traditionally, used the short-range repulsive forces of solid surfaces to control the flow of air. This, however, is merely one particular, very convenient solution to the engineering problem. Lasers can also control the flow of air, either by directly delivering radiation pressure to a specific region of the airflow, or by creating a plasma whose pressure can instead be used to the same effect.

The question here is merely one of practicality. Do modern lasers combine sufficient power in a lightweight, compact package? Well, probably not quite yet, but there are already some tantalising glimpses of the possibilities.

The Curiosity Rover currently exploring Mars is equipped with a Laser-Induced Breakdown Spectroscopy (LIBS) system. The laser vaporises rocks some distance away, and a separate camera system analyses the light to make inferences about the chemical composition of the rock. Most intriguingly, the weight of this powerful laser system was reduced to 500g.

A LIBS system focuses a laser on an object and ablates the surface layer of the object to create a plasma plume. This high-temperature plume has a momentum flux, and it has long been suggested that this could be used to propel lightweight objects.

In terms of an immediate Formula One application, however, one might install a laser unit low down in the aft region of the sidepods, and train the laser light upon an aluminium foil surface attached to the floor in the region where one currently finds vortex generators, just inside the rear wheel. The resulting plasma plume could be used as a surrogate exhaust jet to seal the diffuser, with perhaps the odd magnet to focus the plasma. Depending upon how the regulations evolve, KERS energy could be used to power the laser.

There are some potential hazards, such as the possibility of vaporising the rear end of the car if the laser is incorrectly focused, but these are small matters in comparison to the potential advantages of a laser-sealed diffuser system.

Race strategy equations



William Mulholland, erstwhile Vehicle Dynamics Engineer for McLaren Inter-Planetary, wrote an interesting introduction to the mathematics of Formula 1 race strategy a few years ago.

Mulholland's account considers only the effect of fuel weight rather than tyre performance, and dates back to the refuelling era, but it's still a decent account of the basic concepts. 

With t₀ denoting the notional lap-time without any fuel weight, W denoting the lap-time deficit per lap of fuel onboard, and l denoting the distance travelled in laps, then the first expression here defines the time which elapses between pitstops for fuel on laps L₁ and L₂.

The solution to this integral is then provided by the expression on the left.

Taking an intrepid approach, we can generalise these equations to include the effect of tyre performance deterioration, and deal with the absence of refuelling.

With t₀ now denoting the lap-time on pristine tyres and empty fuel tanks, L_end denoting the number of laps in the race, and T denoting the lap-time deficit per lap travelled on a set of tyres, we obtain the expression below for the stint-time between laps L₁ and L₂:

The solution to this integral is provided by the following expression:





In the absence of interference from other cars, the optimal number of stops, and the optimal timing of those stops, can be calculated once the time lost during each pit-stop is added to the time which elapses during each stint of the race.

Obviously, these equations are still highly idealised. The actual lap-time deficit T per lap travelled on a set of tyres will be fuel-load and track-condition dependent, hence in reality this will be a function T(l) rather than a constant.

Moreover, the presence of interference from other cars changes the optimal strategy, and introduces uncertainties. Dropping into slower traffic after a pitstop, and being unable to overtake that traffic, prevents a driver exploiting the full performance potential of the car at that point in time. Hence, the optimal number of pitstops in the presence of other cars tends to be less than the optimal number in the absence of other cars.

The unpredictable behaviour of other cars, and the possible occurrence of chance events such as rain and safety cars, entails the introduction of probability distributions over the optimal number and timing of pitstops. Calculating these optima in the presence of other cars becomes an exercise in game theory, where the effect of a decision is influenced by the decisions of other agents, and where the decision of an agent is influenced by that agent's beliefs about the anticipated decisions of the other agents.

Bayesian networks are precisely designed to capture the conditional probabilistic relationships between numerous chance events and unpredictable decisions. Hence Bayesian networks might be very useful for updating the most likely optimal strategy as a race progresses in real-time.

Michael Schumacher's marmite nightmare

Richard Feynman once remarked that experimental particle physics is somewhat akin to smashing watches together, and examining the various gears, cogs and springs which fly out, in order to better understand how such an intricate device is first put together.

Inspired by his academic counterpart, one can only assume that Michael Schumacher has recently developed a deep interest in the transmission internals and rear-wing assembly of a Formula One car, and wishes to better understand how they are put together.

Hurtling down Esplanade Drive at the re-start of last week's Singapore Grand Prix, approaching the ninety-degree right of turn 14, Michael appeared either to mis-judge his braking, or under-anticipate the braking point of those on worn tyres ahead of him. Locking up all four wheels, and slewing marginally sideways, Michael plunged into the rear of Jean-Eric Vergne's Toro Rosso.

On time-scales brief to the human eye, this triggered a complex hierarchy of energy degrading processes over a range of different length-scales. The front-wing of the Mercedes broke off and partially shattered as the nose of the Mercedes was driven into the rear of the Italian car, lifting it into the air. As the Mercedes rode up and over the rear crash structure on the Toro Rosso, the detached front-wing was briefly trapped under the rear of Vergne's car. The front wheels of the Mercedes folded inwards, the rear-wing of the Toro Rosso shattered into a characteristic fragment-size distribution (large numbers of small fragments, small number of large fragments), and a titanium end-plate of the Mercedes front-wing was simultaneously dragged along the road, raising a cascade of sparks, diffraction-spiked in subsequent photos like an astrophysical star cluster. It was a frightening freeze-frame moment of beautiful complexity.

The ultimate cause of the accident, however, may lie with a comment Schumacher made in the October issue of F1 Racing magazine. Here, Michael was quizzed with readers' questions, and at one point was asked if, looking back over his career, he had any regrets. The answer was terse, but revealing:

"Jerez. In 1997."

Now, far from being a confession or admission, this actually constituted an implicit rebuttal. Michael was, in effect, saying that he doesn't regret any of the litany of other transgressions of which he is often accused: the other deliberate accidents; the dragging of wounded cars back onto the track to get races red-flagged; the deliberate blocking of the track in final qualifying, etc etc. None of that is regretted, presumably because Michael was only stripped of points for that one incident in 1997, when, as Nigel Roebuck put it, the FIA came down on him "like a tonne of feathers."

Michael's latest denial was only going to provoke further action from the Karma Police, who've had the former wunderkind in their cross-hairs for some time now. The combination of circumstances on the restart at Singapore was simply their latest move; an elegantly planned and executed slice of 'fate'.

Elsewhere in the same interview, Michael was asked if there was something which irritates him about Formula One today, and his response was somewhat enigmatic: "Black gold." Prompted to elaborate, Michael merely added "Think about it."

Could Michael possibly be expressing concern about the use of petroleum-derived energy sources in Formula One? Surely not; after all, the total greenhouse gas emissions from the sport are an infinitesimal fraction of global emissions, and McLaren Pan-Galactic, for one, announced late last year that they're actually a carbon-neutral organisation. 

Perusing the list of other possible referents for 'black gold', one's eye immediately alights upon that notoriously polarizing condiment, marmite. Joining up the dots to understand Michael's source of vexation, it should be remembered that Lewis Hamilton is Formula One's Mr Marmite: loved by some, loathed by others.

And, as we all found out on Friday this week, Michael's marmite discomfort transpired to be fully justified.

Quasi-particles

A recent BBC Horizon documentary on the smallest things in the universe, claimed to present experimental proof that the electron has been split.

With the tone of indulgent bemusement that characterises contemporary television accounts of modern physics, the viewer was told that, in principle, it is possible to split the fundamental properties of the electron. These properties, we were told, are (intrinsic) spin, (electric) charge and orbital (angular momentum), and in the experiment in question, "when the x-ray beam strikes, the electron split into new quasi-particles, called spinons, orbitons and holons, which carry the properties of the electron, and can travel off in different directions."

In point of fact, the electron hasn't been split at all. Quasi-particles are collective excitations in the state of condensed matter, typically the atomic lattice of a crystal. Some of these collective states possess properties which formally resemble properties possessed by states of the individual electron. In 1996, holons and spinons were produced for the first time in the collective state of a crystal, and now a new collective state, containing orbitons and spinons, has been created.

Quasi-particles, however, are certainly of very deep interest, not least because they reveal that particle-like entities can be created as nothing more than transient disturbances within a substrate. As philosopher of physics David Wallace points out, quasi-particles "can be created and annihilated; they can be scattered off one another; they can be detected (by, for instance, scattering them off 'real' particles like neutrons); sometimes we can even measure their time of flight...We have no more evidence than this that 'real' particles exist...and yet they consist only of a certain pattern within the constituents of the solid-state system in question," (p51, The Emergent Multiverse, OUP, 2012).

Moreover, according to quantum field theory, elementary particles such as electrons are merely excited states of underlying quantum fields. This in itself should undermine confidence in the fundamentality of so-called elementary particles, but unfortunately quantum field theory provides a rather sparse characterisation of what a quantum field actually is, merely specifying it to be a self-adjoint operator-valued field on space-time (technically an operator-valued 'distribution'). The significance of quasi-particles is that they provide a very concrete substrate upon which particle-like entities can be realised, and a discrete substrate at that.

Perhaps, then, there is no lowest level to the structure of the universe; no foundations and no basement level, just an infinite multi-storey subterranean car-park.

Ride-height matters

There was a suggestion on this blog at the beginning of the season that Mercedes's DRS-activated F-duct might be utilising more than one means to reduce straightline drag.

In this context, Adrian Newey recalls that in the early 1990s, when active suspension was permitted, "We realised in the wind-tunnel that if we lowered the rear and raised the front, you could stall the diffuser and that reduced the drag of the car significantly...I can't remember the figure but that would give them something like an extra 10 kph," (p233-234 in Williams, Maurice Hamilton, 2009). 



Stalling the front-wing not only reduces drag, but by virtue of reducing front downforce also increases front ride-height. Hence, using DRS to stall the front-wing could, in principle, also stall the diffuser.

Admittedly, diffuser dimensions were somewhat different in the early 1990s, and there hasn't been any suggestion from rival engineers this year that Mercedes are indeed exploiting this mechanism. It would, for a start, require a car very softly sprung in dive. Nevertheless, it's interesting to look at the ride-height map above, reproduced from Toet, Zhang and Zeridan's 2006 paper, Ground Effect Aerodynamics of Racecars.

The top diagram provides the front downforce contour map, while the image at the bottom offers the rear downforce contours. In each case, front ride-height is on the vertical axis, and rear ride-height is on the horizontal.

It can be seen that front downforce is maximised when the car has maximum rake, with a low front ride-height and a high rear ride-height. This is simply because the front-wing operates in ground-effect. Rear downforce, however, is slightly more subtle because the diffuser downforce is dependent upon (i) the strength of the side-edge vortices, and (ii) the prevention of turbulent ingress from the rotating rear wheels. As the rear ride-height lowers, downforce increases up to a certain point, but if the car goes any lower, the side-edge vortices dilate and weaken, and the diffuser stalls. There is therefore something of an escarpment in the rear downforce contour map.



The other feature of interest in this rear downforce map is the sheer cliff evident when the front ride-height increases to about 30mm. This may be the behaviour Adrian Newey was exploiting in the early 1990s. Sadly, no indication is given of the provenance of these diagrams; they are referred to merely as the downforce contours for a 'generic open wheeled race car'.

One might wish to compare and contrast with some actual ride-height maps for the F1-2000 Ferrari, (Ferrari Formula 1, Peter Wright, David Bull Publishing, p120), reproduced on the left here. One can see the same diagonal pattern to the front downforce contours, and a similar rear downforce plateau. Sadly, these diagrams don't extend up to a front ride-height of 30mm, so it's not possible to discern if the diffuser of an F1 car from the early 2000s could be stalled by raising the front ride-height.

As to what the current state-of-play is, these are questions which can, perhaps, only be answered by a tweet from Lewis Hamilton.

The 1982 Grand Prix season: A bibliography

Autocourse 1982 (Maurice Hamilton).

Decent race reports from Maurice Hamilton, old-style lapcharts, and an excellent technical survey from Doug Nye. Photography, however, is mainly black-and-white, and fairly average.

1982: The inside story of a sensational Grand Prix season (Christopher Hilton, Haynes 2007).

A desert-island book, this one. A superb account of the season, full of insight from the major players. Good selection of photographic images as well.

Autosport 1982 (Nigel Roebuck, available on Autosport.com).

The best race reports from 1982. Roebuck at his peak: pithy, judgemental, and on occasion, devastatingly sarcastic. Although there's a somewhat curious over-use of ellipsis...Only disappointment of the downloadable versions is the photography, which consists of some very bland images from the LAT archive.

When F1 Ran Wild (Autosport, August 16th 2012).

Interesting Mark Hughes profile of Keke Rosberg, and Frank Dernie annotated cutaway of FW08, but the latter is less informative than one would have wished (compare and contrast with Frank's guide to the FW07 in Motorsport, November 2004, pp75-77).

Formula One's Wildest Year, (Motorsport Magazine, February 2002).

Short insights into a particular facet of each race from various authors, but accompanied by Keke Rosberg's race-by-race recollection of the season. For this reason alone, indispensable.

Autosport and 1982

A 1982 extravaganza is promised this week, both in Autosport magazine, and on Autosport.com. The latter, in particular, are undertaking to publish all of Nigel Roebuck's 1982 race reports, and this will be a real treat.

Back in the 1980s, there seemed to be an understanding that the entire race weekend provided a captivating story, replete with numerous strands, which could be followed from practice on Friday all the way through to the end of the race. Each report duly began with an 'Entry and Qualifying' section, in which the context for the weekend was established, the main plot-lines drawn, and the technical innovations were explained, all tied together via anecdotes and conversations with the drivers. 

To some degree, things have changed irreversibly in the years since: the drivers are no longer directly accessible to journalists, and practice no longer features the mechanical dramas it once did. The engineers, however, continue to be reasonably open to enquiry, and there is still very much a weekend-long story to be charted. Thus, whilst the quality of the technical information these days is incomparably superior, and whilst the writers themselves are not to blame, something important has been lost from motorsport journalism.

Anyway, as some recompense, enjoy the video above of Keke demonstrating the art of overtaking at Zandvoort. Pay particular attention to how close he's able to sit behind Tambay going through Bos Uit, the fast corner onto the main straight. 

And watch out for Warwick's rear wing flying off in the corner of the picture as Rosberg overtakes Lauda!

Experimental British Nuclear Reactors

The book featured here was published by the Atomic Energy Research Establishment in 1960. It contains cutaway drawings of several British reactors. All the experimental reactors featured have now been shut-down. Replacements have not been commissioned.

Suffice to say, there are no plans for a second edition of the book.

Publications you can look forward to, however, include the following:




Indian Nuclear Reactors
Iranian Nuclear Reactors
The Occidental power crisis of 2025
The technological decline of the West
The Triumph of the Thickos

The Grid Girls' Guide to Wind-tunnel/CFD Correlation

A number of grid girls have contacted me recently, complaining that the F1 Show on SkySports fails to provide the level of informative technical discussion they seek in a programme nominally targeted at the motorsport enthusiast.

In particular, they've asked to understand a little more about the correlation issues which crop up between Computational Fluid Dynamics (CFD), wind-tunnel testing, and full-scale track testing. 

Perhaps the best way to begin such an explanation is to introduce the concept of a commutative diagram, familiar to all mathematically inclined grid girls.

The idea here is that two operations can be applied to object A. One operation is depicted as a horizontal path, the other as a vertical path. If the same result is obtained irrespective of the order in which the operations are applied, then the operations are commutative. In terms of the labelling in this particular version of the diagram, it is written that:



Now, in the motorsport arena, aerodynamic data can be acquired by four distinct means: (A) Scale-model CFD simulation; (B) Scale-model testing in the wind-tunnel; (C) Full-scale CFD simulation; and (D) Full-scale track testing. 

Whilst the data acquired from full-scale track testing can be treated as veridical, it has increasingly been considered to be an expensive means of generating such information, and has therefore become a severely limited form of data acquisition. This has placed greater emphasis on CFD and wind-tunnel testing. However, both of the latter techniques have systematic errors associated with them, and to go from one data set to another requires the application of correction factors and more general mathematical transformations. For example, scale-model testing in the wind-tunnel can only be mapped to full-scale data if correction factors are applied for the blockage imposed by the walls of the wind-tunnel. Moreover, it is impossible to replicate both the Reynolds number and the Mach number of the full-scale flow with a scale model, hence Reynolds number corrections must be introduced.

Given any pair of data-sets, if one of them can be treated as veridical, then a regression analysis can establish the corrections which must be applied to compensate for the bias of the non-veridical data-set. One might, for example, have CFD and wind-tunnel coefficient-of-lift (C_L) values for each combination of ride-height and angle-of-attack. By allowing a single parameter to vary (e.g. angle of attack), a particular set of paired C_L-values can be isolated and represented as a scatter-plot, the x-coordinate of each data-point being the wind-tunnel C_L-value, the y-coordinate being the CFD C_L-value. A regression analysis then establishes a functional relationship between the CFD coefficients and the wind-tunnel coefficients.

A vital test to ensure that one has a self-consistent scheme of correctional transformations is to test for the commutativity of these relationships. Thus, for example, if one begins with a set of half-scale wind-tunnel data, one should be able to: (i) map the half-scale wind-tunnel data to scale-model CFD data, then map the scale-model CFD data to full-scale CFD data, and then map the full-scale CFD data to full-scale track testing data;  (ii) map the half-scale wind-tunnel data directly to full-scale track testing data; and (iii) the results of these two transformations should be in agreement, within some reasonable approximation. If there is any doubt, the results should be statistically tested with something like Analysis of Variance (ANOVA) to determine if the variation is simply the result of random sampling error.

Similarly, one should be able to start with half-scale CFD data, and map the results to full-scale track testing data by the two possible routes, without getting different results. In terms of the commutative diagram we started off with, there actually needs to be a bi-directional arrow between objects A and B.

As ever, the generalities are simple, the implementation difficult and messy.

A query about the BT42/44

Gordon Murray's place in the F1 design pantheon is assured, but a question arises over the aerodynamics of the iconic BT42 and BT44.

Speaking to David Tremayne some years ago, Murray explained his rationale as follows:

"I knew a lot about aerodynamics from practical experience. With any moving form you have a stagnation point where air meets it and decides how much is going to flow over, below or around it...I decided, instead of presenting some sort of parabolic-shaped bluff body to the air, I wouldn't give the air a chance." He sketches a triangular shape. "That way the stagnation point was there," he says, pointing to the leading edge of the triangle's base, which is very low to the ground. "So all the air had to go over the top and you had the minimum coming under the car," (F1 Magazine, May 2001, p140-141).

Murray spoke about this issue more recently on the BBC4 documentary, 'How to go faster and influence people':

"The BT42 was like an upturned saucer...so very little air went underneath the car and most of it went over the top, because all the air that goes under the car produces lift, which counteracts the downforce you're getting from the wings."

This leaves me slightly confused, for a couple of reasons: (i) my understanding is that air going over the top of the car will be accelerated by the curvature, and will therefore produce lift; and (ii) the best way to generate downforce is to turn the region between the ground plane and the floor of the car into a mobile nozzle.

The greater the mass-flow beneath the car, the better; hence the presence of a diffuser, whose 'pumping effect' is maximised by increasing the ratio between the outlet area and the area of minimum cross-section at the leading edge of the floor. The raised nose on a contemporary F1 car also presumably contributes to increasing mass-flow under the car, although it's also designed to minimise the turbulent intensity of the air feeding the underbody.

But Gordon Murray is clearly no mug, so why does he think that it's important to minimise the air going under the car? My best guess is that Murray's idea was specific to cars from the 1970s, which lacked diffusers and raised noses. If there's no diffuser pumping air under the car, then perhaps excess underbody flow can be detrimental.

Gordon Murray's future F1 vision

This month's Motorsport Magazine revisits Gordon Murray's year 2000 vision for the future of Formula 1 (pictured above): a largely wingless, gas-turbine powered car, with wheel fairings, surface cooling, and a driver in a g-suit under a canopy.

One thing I would disagree with is the gas turbine; the 21st century should be about liberating nuclear energy, not chemical energy. I would therefore propose instead a mini nuclear reactor, a slightly smaller version of the US Hyperion reactor design suggested several years ago. The core of this reactor employs low-enriched uranium-hydride UH₃ to obtain a negative coefficient of reactivity.

Whilst the neutrons released in fission have a mean energy around 1 MeV, the uranium-235 fission cross-section is highest at thermal neutron energies, at or below 0.025eV. Hence, to maintain a fission chain-reaction, it is necessary to moderate the energy of the neutrons, and elastic collisions between the neutrons and hydrogen nuclei are an efficient means to achieve this. "If the uranium hydride gets too hot, the hydrogen is driven out of the uranium metal and the chain reaction stops. But as the system is sealed, the hydrogen flows back into the uranium when it has cooled, allowing the reaction to restart." This provides an intrinsically safe, negative coefficient of reactivity.

I'm also worried that Gordon's future vision might generate lift rather than downforce, so I might add a diffuser or a couple of venturi tunnels under the car in the style of Ben Bowlby's recent DeltaWing design. But that's another story...

The Great Interregnum

A large collection of dullards have recently assembled in London, and appear to be generating more than a modicum of media attention. Normally, this would just signal the opening of the annual Police Federation conference, but on this occasion it seems the fuss concerns a bunch of masochistic minority sports, many of which suffer an apparent absence of technological development.

If, however, you find this all rather tiresome, then just try to look upon it as an arms-race, by proxy, between underworld pharmaceutical purveyors and accredited analytical chemists. Seen from this perspective, it's almost as interesting as Formula One.

Oh, and watch out for the Red Bull sponsored pole vaulters, who've devised a means of manually lowering the bar, against the regulations, but are permitted to continue competing because they say they haven't actually used it. It's a non-issue, apparently.

The pain engendered by the Anabolics, however, is as nothing compared to that caused by the five-week break before the next Grand Prix. There may have been comparable in-season gaps before, but perhaps they occurred when the racing was a little less interesting than it has been this year. Going back several decades, there was a similarly interminable five-week break in 1983 between the Canadian and British Grands Prix, but on that occasion the latter race was still being held on a Saturday, so strictly speaking the break was only 34 days in length.

So, how to bridge this gap? Well, here's a thought experiment for starters: What would happen if diffusers were completely banned? Would it still be advantageous to have a raised nose, or does the latter depend upon the so-called 'pumping effect' of the diffuser? Without a diffuser, would a raised nose increase the mass-flow rate under the car?

Secondly, suppose that the underbody regulations were completely opened up, so that anything was permitted. If you designed a car with underbody venturi tunnels and sliding skirts, would it still be advantageous to have a raised nose and diffuser? Would a car with a raised nose, sliding skirts, venturi tunnels, and a diffuser, corner so fast that the drivers would need g-suits? What sort of lap-time would be achieved around Brands Hatch by such a car equipped with a 1.5 litre V6 twin-turbo engine, pumping out over 1,000bhp?

Red Bull's engine maps

Mark Hughes has a revealing explanation on the Sky F1 website of the engine map loophole exploited by Red Bull last weekend. As the regulations are written, the torque demand at full-throttle, at any engine speed, can be reduced from the maximum possible torque demand at those revs by retarding/advancing the ignition.

In fact, on the basis of the regulations quoted here, it would even be permissible for the full-throttle torque demand to decrease as the engine speed increases. There seem to be three relevant regulations in this respect, 5.5.3, 5.5.5 and 5.5.6:

5.5.3  The maximum accelerator pedal travel position must correspond to an engine torque demand equal to or greater than the maximum engine torque at the measured engine speed.

5.5.5 At any given engine speed the driver torque demand map must be monotonically increasing for an increase in accelerator pedal position.

5.5.6 At any given accelerator pedal position and above 5,000rpm, the driver torque demand map must not have a gradient of less than – (minus) 0.030Nm / rpm.

Now, 5.5.5 is a condition which applies at 'any given engine speed'. Thus, at any fixed engine speed, the torque demand must be a monotonically increasing function of accelerator pedal position. This does not entail that the maximum torque demand must be a monotonically increasing function of engine revs; 5.5.5 quite specifically applies to a function at a fixed engine speed.

Similarly, 5.5.3 requires that at each fixed engine speed, the maximum accelerator pedal position generates a torque demand greater than or equal to the maximum torque demand at that fixed engine speed. Once again, this condition applies to a function at a fixed engine speed, not to a function of engine speed. In fact, 5.5.3 is entailed by 5.5.5, and is, strictly speaking, logically redundant.

Perhaps the FIA had something else in mind...

A solution to Silverstone's parking problems?

Following the quagmire-induced congestion at Silverstone last week, the circuit has discounted the possibility of transforming the grass car parks into asphalt, Autosport reporting that "it would be hugely expensive and it's unlikely that Silverstone would get planning permission...It's also deeply questionable whether it's right to coat fields in asphalt for parking for three days a year," (p12, July 12th, 2012) .

But why not erect temporary upper storeys on all the existing asphalt car parks? One purveyor of these solutions is Another Level:

Another Level Pioneered the development of the concept of the Portable, Modular Multi-Storey Car park. The company invented, designed and developed this pioneering concept of a solid, safe and portable modular deck structure that simply sits over you existing car park allowing you to nearly double its capacity. The benefit of the demountable nature is apparent on both multi storey, and single story applications.

Another Level has both the experience and capability with nearly 30 installations and by far the largest fleet of decks available for nationwide installation.

Our experienced team coupled with world-class purpose built equipment are able to assemble a 124 space modular deck car park in 3 1/2 days.

With every installation to date the existing car park’s surface has been adequate to support the structure without the need for traditional foundations. This eliminates the risk of disturbing contaminated land, underground services and archaeological remains.

Given that Silverstone need to accommodate tens of thousands of cars, it wouldn't solve all their problems, but combined with extra park-and-ride, it might be part of the solution.

Aerodynamic wheel-wing interaction

In 2007 Martinus van den Berg published a PhD thesis on the interaction between a rotating wheel and an inverted wing. The research was sponsored by the Honda F1 team, which has, of course, evolved into the Mercedes F1 team; the same team responsible for the 2012 front-wing F-duct.

The most interesting conclusion of van den Berg's research was that the front-wheel drag is greater at high front-wing ride-heights than it is at low ride-heights.

Figure 1: High ride-height, high wheel drag

Previous research conducted by James McManus (who was snapped up by McLaren before completing his PhD) had identified that the flow field of an isolated rotating wheel contains an arch vortex in the upper region of the near wake (E and F in Figure 1), and a pair of counter-rotating vortices in the lower, ground-level region of the near wake (H and I). There is also a bow wave (D) created by the upstream side of the contact patch. 

When an inverted wing equipped with an endplate is placed in front of such a rotating wheel, van den Berg identified three further primary flow features: a vortex from the upper edge of the endplate (A); a vortex from the junction between the trailing edge of the flap and the endplate (B); and a vortex from the lower edge of the endplate (C).

With a 50% scale 580mm front wing-span (relevant to pre-2009 F1 regulations), van den Berg identified that the top edge front-wing vortex passes over the crown of the wheel at high ride-heights (Figure 1), but passes inside the wheel at low ride-heights (Figure 2). At high ride-heights this vortex over the crown keeps the flow attached for longer, increasing the lift of the wheel, and creating a zone of re-circulation (G) behind the wheel, which increases the wheel drag:

"When this vortex...passes over the wheel it starts a strong interaction with the wheel vortex originating from the top of the wheel (feature “F”), the vortex originating from the flap trailing edge (TE) junction (feature “B”) and the lower edge vortex (feature “C”), accumulating in a strong circulation," (Journal of Fluids Engineering, October 2009, Vol. 131).

Figure 2 shows the flow field at a lower front-wing ride-height, where the top-edge vortex goes inside the wheel. In addition, it can be seen that both the bow wave to the inboard side of the wheel, and the inside leg of the counter-rotating vortex pair in the wheel wake, have been replaced by the vortex generated by the bottom-edge of the front-wing, which is strengthened in ground-effect.



Figure 2: Low ride-height, low wheel drag

At first sight, this might seem to be inconsistent with the concept of the 2012 F-duct, which stalls the front-wing, and permits the front ride-height to increase, with the intention of reducing drag (and balancing front-rear downforce when the DRS is operated). One presumes, however, that the reason for this discrepancy is that the research was conducted with a narrow, pre-2009 front-wing, the endplates of which were on the inboard side of the wheel. Post-2009, with 1800mm wide front-wings, the endplates and the vortices they generate, lie upstream of the outer shoulder of the wheel. It may be that the top-edge vortex now goes outside the front-wheel at all front-wing ride-heights, and certainly the outward curvature of the front-wing endplates would achieve this.

One note of caution should be sounded here: the Figures reproduced above are obtained from steady-state simulations, whereas the actual flow in the wheel-wake tends to flap about in an unsteady manner, as close observation of the water droplets shed by the wheel in wet-weather conditions reveals. Flow features which appear to exist in a steady simulation are sometimes completely absent in the instantaneous flow fields of an unsteady simulation.

A guide to the Higgs boson for the perplexed

Mass and the Higgs field

The standard model of particle physics is an application of quantum field theory, and the latter holds that the fundamental structure of the physical world consists of quantum fields on space-time. Within quantum field theory, particles are represented as localised excitation states of the underlying quantum fields.

One of the fields postulated by the standard model is the Higgs field. The excitation states of the Higgs field are Higgs bosons. Whilst the Higgs field permeates all of space, Higgs bosons are localised excitations of that field, and at the energy levels available in a universe 14 billion years old, these are difficult to produce.

According to modern cosmology, the Higgs field dropped into its 'vacuum' state (i.e., its lowest energy state) when the universe was only 10^-11 s old. However, the potential energy function of the Higgs field is such that its lowest energy state corresponds to a non-zero value of the Higgs field. This value is referred to as the vacuum expectation value of the Higgs field.

The Higgs field is represented to interact with all the quarks and all the leptons (e.g. electrons) in the universe. When the universe was younger than 10^-11 s, the quarks and leptons were believed to be massless. Since the time at which the Higgs field dropped into its vacuum state, the non-zero vacuum expectation value of the Higgs field is considered to be responsible for the masses of the quarks and leptons.

The Higgs field is also a self-interacting field, so the Higgs field is considered to be responsible for the mass of the Higgs boson itself.

The statistics of Higgs detection

Figure 1

The Higgs boson has not been directly detected at CERN. Instead, the Higgs decays into various different particles which can be detected. For example, sometimes the Higgs decays into a pair of gamma-ray photons, and sometimes it decays into a pair of Z particles. These are referred to as detection ‘channels’.

For example, Figure 1 depicts the number of gamma-gamma detection events as a function of their energy. The red dotted line plots the ‘background’, which in this context is the number of expected gamma-gamma events, as a function of energy, if the Higgs boson hadn’t been produced.

Assuming there is no Higgs production, at each energy level there is a normal (‘Gaussian’) distribution over the number of detection events (see Figure 2). This distribution has a standard deviation (‘sigma’), and by taking integer multiples of sigma, confidence bars can be plotted either side of the red dotted line in Figure 1.

This approach enables one to estimate the probability of a false positive. Thus, if the number of detection events at a particular energy is outside the 3sigma bars, it means that the probability of that result being produced by the play of chance alone is less than 0.3%. By requiring a result to be established at the 5sigma level, this means that the probability of it being a false positive is less than 0.0001%.

Figure 2

In the case of Figure 1, the result from the CMS detector, there appears to be a particle which has decayed into pairs of gamma-ray photons with an energy of 125 GeV, at the 5sigma level of confidence.

A couple of other points should be noted from Figure 1. Firstly, particle physicists use the term ‘luminosity’ to refer to the flux, and 'integrated luminosity' to refer to the ‘fluence’. The latter is the total number of incident particles per unit area over the course of the experiment.

The standard unit of integrated luminosity in use at CERN is the inverse femtobarn (fb^-1). A barn (b) is 10^-24 cm², and a femtobarn is 10^-15 b. Thus, an integrated luminosity of 5.3 fb^-1 means that there was a fluence of 5.3 particles per femtobarn of area.

The number of detected events, (in the case of Figure 1 the bump at 125 GeV), is dubbed the ‘signal strength’. Now, in general, the number of reactions per unit fluence is called the ‘cross-section’ of a reaction, and is specified in units of area. Thus, by multiplying the fluence (integrated luminosity) with the cross-section for Higgs production, the number of Higgs particle production events can be estimated.

However, only a fraction of the Higgs particles will decay into pairs of gamma-rays, and this fraction is specified by the so-called ‘branching ratio’. Thus, the number of detection events N in a particular channel will be the product of the fluence F with the Higgs production cross-section C and the branching ratio R for that channel:

N = F x C x R

Given the experimentally ascertained signal strength, and the known fluence, the quantum field theory for the Higgs field must supply a consistent Higgs production cross-section and branching ratio.

Jim Holt and 'Why does the world exist?'

Whilst this year's 'publishing sensation' appears to be Fifty Shades of Spunk, those seeking to increase the blood-flow to their brain will derive comparable stimulation from Jim Holt's new book, Why does the world exist: An existential detective story.

This is a truly brilliant book. It's accessible and engaging, but written with a sophisticated understanding of the relevant philosophy, mathematics and physics. Holt visits luminaries such as Adolf Grunbaum. David Deutsch, Steven Weinberg and John Updike, asks all the right questions, and has the confidence and ability to construct his own lines of reasoning.

Amanda Gefter raises a mild criticism in New Scientist that the book "could have benefited from some deeper delving into physics." There might be something in that, but in this respect, Holt's book can be treated as a philosophical counterpart to Michael Heller's 2009 work, Ultimate explanations of the Universe, the first part of which provides a more detailed, if slightly terse account of the various proposals within mathematical physics.

The only criticism I'd make of Holt's book is that the travelogue he tries to weave into his philosophical investigation doesn't really work. Much of this travelogue consists of nothing more than an unimaginative enumeration of European place-names. Consider the following account of Holt's journey from Paris to Oxford as an example of such name-dropping, with my own sound effects added:

"I hauled my bags onto the metro and headed to the Gare du Nord [clang], there to catch the Eurostar train [clang] to London. Arriving at Waterloo station [clang] a few hours later, I caught the tube to Paddington [clang], where I hopped on a local train to Oxford....Next afternoon I left my hotel on the High Street, made my way down Queens Lane, passed under the Bridge of Sighs [clang] and by the Bodleian Library [clang] and Ashmolean Museum [clang]."

Jim is a contributor to The New Yorker, and the New York Times, and lives in Greenwich village, New York. Far too often one feels that this is a book written for educated New Yorkers, and it is never clear why Jim spends so much time musing at the Cafe de Flore in Paris, or the Athenaeum Club on Pall Mall.

Nevertheless, despite this failing, be in no doubt that this is a great book, and for anyone with an interest in philosophy and the philosophy of cosmology, it would be surprising to read a better book this year.

John Leslie, miracles, and free will

For readers in the UK, the name of John Leslie may conjure up images of the erstwhile Blue Peter presenter with a penchant for home video production. Elsewhere, however, John Leslie is known as the Canadian-domiciled philosopher who argues that the universe is ethically required to exist.

Leslie is interviewed in Jim Holt's fantastic new book Why Does the World Exist, (which I'll review separately), and one of his arguments particularly caught my attention. When asked why the ethical requirement for good doesn't create a bowl of rice for a starving child, Leslie responds:

"If you're going to have an orderly world that runs according to laws of nature...you can't have bowls of rice suddenly appearing miraculously. Moreover, the fact that the child doesn't have a bowl of rice may very well be the result of a misuse of human freedom, and you can't have the goodness of a world where agents are free to make decisions unless you also have the possibility that those agents will make bad decisions."

So Leslie makes two claims:

(i) Miracles can't happen because it would break the laws of nature.

(ii) A good world requires that agents have free will, i.e., that the decisions of such agents are not determined by the laws of nature.

So the laws of nature cannot be broken to alleviate suffering, but the laws of nature can, and are, over-ridden billions of times every second to permit a particular biological species to exercise free will. It's ethically required.

I can only conclude by recalling that theologian Richard Swinburne once tried to justify the holocaust on the basis that it gave the Jews a chance to be courageous and noble; a suggestion which prompted the following response from Peter Atkins:

"May you rot in hell."

Valencia retrospective

Despite its previous association with the induction of narcolepsy, this year's European Grand Prix at Valencia provided a perfect combination of visceral, wheel-to-wheel thrills; fascinating technical innovation from Red Bull; and an engrossing race-long strategic weave; all played out against a sociologically and aesthetically stimulating juxtaposition of beach-front, quay-side, container-port, harbour-scape, and residential apartment complex.

For Sky TV viewers, the post-race analysis provided an opportunity to admire Georgie Thompson's gluteal sulcus and word-perfect diction, but failed to deconstruct one of the most fascinating phases of the race: that which occurred between laps 13 and 20. This period essentially consisted of an interference pattern between two travelling waves of different phase. The first wave contained those who pitted early (Hamilton at the end of lap 13, Raikkonen, Kobayashi and Maldonado on lap 14, Alonso on lap 15, and Vettel and Grosjean on lap 16), and the second contained those intending to pit later (di Resta and Rosberg leading this bunch, followed by Schumacher, Senna and Webber).

Hamilton had rejoined behind Senna and Schumacher, and dealt with Senna a little tentatively into turn 12 on lap 15, and then DRS-ed Schumacher down the straight into the same corner on lap 16. Grosjean rejoined in front of Hamilton at the beginning of lap 17, having lost places to only di Resta and Rosberg. Alonso, in contrast, had rejoined just in front of Raikkonen, Kobayashi and Maldonado, (although it should be noted that Fernando actually passed the Williams before the pit-stops, using the DRS to overtake into turn 12 on lap 14).

After 17 laps, then, the order was as follows:

Vettel
di Resta
Rosberg
Grosjean
Hamilton
Schumacher
Senna
Webber
Alonso
Raikkonen
Kobayashi
Maldonado

Whilst the first five were reasonably spaced, the group led by Alonso had immediately closed on Schumacher, Senna and Webber. Into turn 2 on lap 18, Alonso plunged down the outside of Webber, and further round the same lap outbraked Senna into turn 12, again around the outside. Seconds later, he was trying the outside of Schumacher into turn 17. Onto lap 19, with a madly snaking train of cars behind them, Schumacher again defended the inside from Alonso, this time into turn 2, but the Ferrari cut a tighter apex through the left of turn 3, resisted a squeeze from Michael, and outbraked him into turn 4.

Fernando now set off after Grosjean and Hamilton, who were calmly DRS-ing their way past di Resta and Rosberg. Things, however, were getting frantic behind Schumacher. Senna unsuccessfully tried the outside of the Mercedes into turn 17, but at the same moment Raikkonen was going around the outside of Webber. Massa, Hulkenberg, Button and Perez, meanwhile, had joined the tail of this train, and disaster seemed inevitable.

At the end of lap 19, Schumacher and Webber pitted, and as they left the pits Raikkonen was out-accelerating his way past Senna exiting turn 4. When Kobayashi tried to follow him through, contact ensued, the Williams slewed sideways down the track, and this phase of the race reached its culmination.

The entire seven-lap period was an interesting 2012 case-study, demonstrating the high probability of destructive interference between waves of different phase in a field which doesn't disperse. Through all the perilous complexity, however, came one man, pulling successive audacious moves around the outside with barely a locked wheel. Impressive.

Coffee slosh breakthrough

Those who contend that there may be limits to human knowledge, should pay heed to recent research published in Physical Review: Walking with coffee: Why does it spill?

This ground-breaking work pointed out that "The natural frequencies of oscillations of a frictionless, vorticity-free, and incompressible liquid in an upright cylindrical container (cup) with a free liquid surface are well known from liquid sloshing engineering."

After some empirical observation, the following conclusions were made:

"We spill coffee either by accelerating too much for a given coffee level (fluid statics) or through more complicated dynamical phenomena due to the particular range of sizes of common coffee cups, which is dictated by the convenience of carrying them and the normal consumption of coffee by humans. Namely, first the maximum acceleration occurring early on in the walking sets an initial sloshing amplitude. This interface deflection is then amplified by the back-and-forth and pitching excitations. Vertical excitation does not lead to resonance as it is a subharmonic excitation (Faraday phenomenon). The noise component of motion contains higher-frequency harmonics, which make the antisymmetric mode unstable, thus generating a swirl [although the swirl does not contribute much to coffee spillage]. Time to spill generally depends on whether walking is in a focused [i.e., trying not to spill] or unfocused regime and increases with decreasing maximum acceleration (walking speed)."

Sadly, the discovery of the Higgs boson may prevent this work from getting the attention it deserves.

Rose-petal accumulation dynamics

Contrary to the hypothesis suggested in the previous post, I suspect that non-aerodynamic factors are dominant in the formation of at least two of the pictured rose-petal accumulations.

In the case at the top here, it seems likely that the spider webs (just discernible against the black background) formed sticky nucleation points, trapping an initial collection of petals, which then accreted further layers, in much the same way that a crystal precipitates from solution.

Meanwhile, with respect to the largest pool of petals, adjacent to the slatted gate, the original hypothesis suggested some influence from the chair positioned at the exit of the passageway. This hypothesis was tested by removing the chair. No change was observed in the petal distribution, hence the hypothesis was refuted.

Closer inspection indicates that this accumulation occupies a shallow depression in the paving slabs (across which a thriving population of red insects hurries to and fro on inscrutable entomological errands). Given the occurrence of rain showers in the days preceding the petal pattern formation, it seems likely that this region became damper than its surroundings, increasing the local coefficient of friction, and nucleating the pool of petals.

These petal distribution inhomogeneities, then, are a consequence of positive feedback processes operating on small existing background inhomogeneities.

Did you never wonder as a child what was responsible for the small knots in a wooden fence? Or question why the knots were of different shapes and sizes, and why there was a knot here, and (k)not somewhere else? And why, for that matter, is one cloud shaped differently from another?

All these questions are special cases of a more general and profound question:

Why is the universe not exactly homogeneous?