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.