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...