McCabism

McLaren's floor tiles

2012-01-06T10:28:00.007Z

The BBC recently broadcast a documentary on McLaren's new supercar, the MP4-12C. In the opening minutes of the programme, we follow Ron Dennis around the immaculate McLaren Technology Centre. As Ron strides across the lakefront atrium, he points out a broken floor tile, and expresses his annoyance: "The reality is, when it's changed, it'll be imperfection, because the colour won't match. Tiles come in batches. You can see this one here's been changed, [pointing to a darker tile.] Doesn't that bug you? It bugs me. Big time."

In fact, rather than tiles from different batches being of a different hue, in this case the reason a new tile stands out is probably that the old ones have been subjected to the daylight for a period of time, and due to the slow photodissociation of the pigments inside, will gradually be growing lighter in colour. Hence, a new tile looks darker simply because it's been exposed to daylight for a shorter period of time.

There is, then, a possible means by which McLaren can mitigate this chromo-tessellatory problem: Purchase a sufficient number of spare tiles at the outset, and then allocate a backroom at the MTC for the purpose of exposing these backup tiles to the correct diurnally-averaged spectrum and intensity of artificial sunlight. When a frontline ('customer-facing') tile suffers a fracture, the replacement will have endured the same amount of photodissociation, and will be indistinguishable in colour from its two-dimensional siblings. Problem solved.

Autocourse 2011-2012

2011-12-30T18:08:00.012Z

This year's Autocourse is printed on golf-leaf infused paper, using inks derived from the pituitary gland of the Himalayan gazelle.

At least, that's the only justification one can imagine for a price-tag of £50.

There was a time when one could look forward to the stunning photography in Autocourse each year, but those days are long gone. This year's edition contains only one memorable image, a two-page spread of Lewis Hamilton and Sebastien Vettel, wheel-to-wheel into Turn 3 at the Hungaroring, Hamilton's outside wheels skirting the grass-verge. Unfortunately, most people will have already seen this image, and the photography elsewhere never rises above the mediocre.

In fact, the quality of the photographic reproduction in Autocourse has become remarkably dark, virtually every image dominated by the sheer quantity of black ink. As an indication of this, it's almost impossible to find an image of a car, taken from the front, in which the undernose splitter can actually be discerned. By way of contrast (excuse the pun), if you happen to have the £4.40 Autosport Formula 1 review at hand, compare the picture on p32-33, taken from Ste Devote at Monaco, with the picture on p153 of Autocourse, taken from exactly the same vantage point. The difference is almost literally night and day.

It's difficult to know whether this is determined by the combination of inks and glossy paper used by Autocourse, or whether there's some artistic motivation behind it. There's almost a photophobic, crepuscular mood running through the annual: an article on Pirelli opens with a two-page spread of Hamilton and Webber in the gloaming at Korea; the team-by-team review begins with a two-page spread of the F1 paddock in semi-darkness; the race reports are prefaced with a two-page spread of a Williams passing through a silhouetted Eau Rouge; there's a two-page spread of Lewis Hamilton beneath leaden skies at the Nurburgring; there's a two-page spread of Singapore, in the darkness; and there's a two-page spread of Jenson celebrating his Japanese victory...in the darkness. It's like a book directed by David Fincher.

Formula 1 should be bright and colourful. Autocourse makes it look like an activity which takes place at 7pm on a damp October day in Macclesfield.

So do you get anything for your £50? Well, yes, you get Mark Hughes's team-by-team analysis, which is reliably superb. Mark, of course, also does something similar in Autosport's Formula 1 review, but the Autocourse version is more detailed in places, and contains extended explanation from each team's technical director. Paddy Lowe and Pat Fry, in particular, are fascinating this year as they explain where things went awry.

So there's something good here, but not £50-worth.

Red Bull and Immersed Boundary Methods

2011-12-22T22:15:00.010Z

Autosport's recent 2011 Formula 1 review pointed out that whilst Red Bull were the first team to appear with exhausts blowing the outer extremities of the diffuser, "others, notably Renault and Ferrari, had tried the layout in their tunnels before the Red Bull appeared and couldn't make it work, and Newey later confirmed that it actually took months of simulation work to maximise."

So what is it that Red Bull were able to do that other teams weren't? Was it mere persistence in the wind-tunnel with a flow regime that transpired to be extremely sensitive to the exact position and geometry of the exhaust outlet? Or were Red Bull able to apply some form of computer simulation not currently utilised by other teams?

Perhaps the former is the most likely answer, but let's pursue the alternative explanation, and see if we can join up the dots. And let's start with the fact that Red Bull use Ansys Fluent as their CFD package. In this promotional video from late 2010, it's acknowledged that Red Bull use Fluent to model their exhaust flow, (although this obviously doesn't entail that it's their only simulation tool for doing so).

Speaking recently about the High Performance Computing solutions provided by Ansys, Nathan Sykes, CFD Team Leader at Red Bull Racing, pointed out that "To retain freedom to innovate and adapt the car quickly, we rely on a robust modeling process. This puts new designs on the track quickly. To accomplish our goal, we continually need to leverage technologies that help us introduce and evaluate new ideas. With a significant reduction in process times over the last three years, ANSYS HPC solutions have continued to be the tool of choice for us."

Now, the normal aerodynamic optimisation cycle involves shaping a part in CAD, importing it into CFD, meshing it in CFD, running the CFD solver, and then post-processing the results. Meshing, in particular, can be very time-consuming. There is, however, a means of short-circuiting the cycle, called the Immersed Boundary Method, and in an environment such as Formula 1, where aerodynamic turnover is paramount, any team able to successfully implement this method could gain a significant advantage.

Immersed Boundary Methods provide a means for dealing with geometries which may be complex, or in a state of motion. They enable one to mimic the effect that an appendage has on the fluid flow in terms of something called a 'body force'. For example, if a fixed solid object is introduced into a region previously occupied by fluid flow, then the no-slip boundary condition must be imposed on the new surface, (i.e., the velocity there must be zero). In effect, this requires the application of a force which reduces the pre-existing velocity to zero. To calculate the necessary body force, one could in principle insert the necessary acceleration into the (Reynolds-Averaged) Navier-Stokes equations, as below, with u_desired=0 in this case:

Coincidentally, Ansys Fluent 12.0, released in 2009, has an Immersed Boundary module, developed with Cascade Technologies Inc. This is what Ansys said at the time:

A conventional fluid dynamics simulation starts with the transfer of CAD data to a grid-generation package, in which a surface mesh and then a volume mesh are generated before the simulation can be set up and the solution run. The effort and time required for such pre-processing tasks can be significant. For example, in cases with complex or dirty geometry that require CAD cleanup, this part of the process may take 50 percent to 90 percent of the total time required for the simulation. The Immersed Boundary module addresses such issues by providing a rapid, automated, preliminary design approach.

Fluid flow simulations using the Immersed Boundary module for ANSYS FLUENT 12.0 software start with the surface data of the simulation geometry in the STL file format, which is commonly used in rapid prototyping and computer-aided manufacturing. This CAD geometry does not need to be clean, does not require smooth surfaces or geometry connectivity, and may contain overlapping surfaces, small holes and even missing parts. The simulation geometry is meshed automatically. Mesh refinement also is carried out automatically after specifying the desired resolution on the boundaries, ensuring the accuracy required for preliminary design evaluation. Using the immersed boundary meshing technique greatly reduces the amount of time spent preparing the geometry for meshing and creating the mesh.

At first sight, Immersed Boundary Methods do not appear to be available in Star-CCM+, one of Fluent's main competitors. Star-CCM+ does, however, provide a Surface Wrapper, a type of shrink-wrapper, which fixes gaps and overlaps in complex CAD geometries. Nevertheless, in Star-CCM+ it appears to be necessary to create a body-fitted mesh: a surface mesh must be created on the surface imported from CAD, and then a volume mesh is grown outwards from the surface mesh.

Immersed Boundary Methods have become increasingly popular over the past decade, and knowledge of such techniques will have been carried into the world of Formula 1 by many recent PhDs. Nevertheless, it's interesting to speculate whether Red Bull have stolen another march on the opposition here...

Unleashing radiation in a wind-tunnel

2011-12-13T00:42:00.020Z

There are currently two primary methods of wind-tunnel flow visualisation: Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA). Both techniques seed the airflow with tracer particles, and use lasers and optical detectors and cameras to provoke and record a pattern of scattered light. This poses a problem, in that the wheels, wings, and diffusers of interest to the aerodynamicist, are normally opaque to the passage of optical radiation. Hence, PIV and LDA experiments typically require the construction of transparent wings and aerodynamic appendages.

There is, however, a possible solution to this problem: Why not use radioactive isotopes to obtain quantitative flow data from wind-tunnel testing? One could inject a harmless radioactive tracer into the flow, such as one of those used in the medical imaging industry; technetium-99m-labelled DTPA (diethylene triamine pentaacetic acid) would be an obvious candidate here. One could then use gamma (ray) cameras to image the flow in a similar way that optical cameras are currently used in PIV and LDA.

There would, of course, be the need for some additional precautions. However, an isotope such as technetium-99 is considered sufficiently harmless to be injected into medical patients, and has a half-life of only 6 hours, so a wind-tunnel would not need to be decontaminated by the Nuclear Decommissioning Authority!

In fact, taking a closer look reveals that there are already significant areas of shared technology between wind-tunnel flow visualisation and lung scintigraphy, the use of gamma cameras to record 2-dimensional images formed by the emission of gamma rays from inhaled radioisotopes:

“99mTc labelled aerosols, 0.5-3 [microns] in size, are used routinely in lung ventilation studies. Radiolabelled aerosols are produced by nebulizing 99mTc-DTPA (or other appropriate 99mTc-products) in commerically available nebulizers,” (p276, Fundamentals of Nuclear Pharmacy, 2010, Saha).

When such aerosols are inhaled for lung scintigraphy, droplet sizes must be small enough to permit diffusion deep into the lungs; specifically, diameters smaller than 2 microns are preferred. In the case of wind-tunnel flow visualisation, the tracer particles must follow the flow. Given that the ratio of the tracer particle density to the flow density is typically of the order 10³ in gas flows, it is necessary to use tracer particles of diameter between 0.5 and 5 [microns], (p288, Springer Handbook of Experimental Fluid Mechanics, Tropea, Yarin and Foss, 2007). The method by which such tracer particles are injected into the airflow suggest close reciprocities with lung scintigraphy:

"By far the most common method of seeding gas flows is through liquid atomization. Of the many atomizer types available the common nebulizer used in inhalation devices is the most suitable...The droplet size depends primarily on the atomizing airflow rate and on the liquid used. Typical mean particle sizes range from 0.2 [microns] using DEHS...to 4-5 [microns] with water...For many applications, the common inhalation or medication nebulizer offers an economical solution and can be obtained through medical suppliers," (ibid., p293).

Thus, the medical and wind-tunnel industries already use the same nebulizing technology, and comparable droplet diameters. In particular, technetium-labelled DTPA has a comparable density, in solution, to the DEHS (di-ethyl-hexyl-sebacat) widely used for seeding airflows in PIV experiments.

One potential limiting factor, however, may be the current resolution of gamma-ray cameras. A gamma camera consists of a scintillation crystal, which converts gamma rays into optical-wavelength light, detected by photomultiplier tubes behind the crystal. There is no equivalent of an optical lens for focusing, however. Instead, a collimator, consisting of an array of tiny pin-holes, is used. The collimator absorbs some of the radiation, limiting the sensitivity of a gamma camera, and also places a limit on the spatial resolution. Typical current resolution is 7-12mm at a distance of 10cm, (p96, Nuclear Medicine Instrumentation, Prekeges, 2009).

Despite such problems, the possibilities for development abound.

How Red Bull create streamwise vorticity

2011-12-03T15:01:00.021Z

Red Bull arrived in Singapore this year with interesting little mini-arches in their front-wing, where the inner end of each main plane meets the 50cm-wide neutral central section. Craig Scarborough suggested at the time that "this shape is to create a vortex along the Y250 axis." As Craig explains elsewhere, "flow structures along this axis [250mm from the centreline] drive airflow under the floor towards the diffuser and around the sidepod undercuts."

So how does such a shape create streamwise vorticity? Well, the answer lies in a subfield of fluid mechanics called 'secondary flows', (with thanks to Professor Gary Coleman of Southampton University, for pointing me in the direction of this field). Such flows typically involve a primary flow - with the streamlines oriented in a particular direction, and a vorticity field perpendicular to the primary flow - in which there is also some type of differential convection to the primary flow. ('Convection' here simply means the transport of fluid by bulk motion, sometimes referred to as advection if there is any confusion with thermal convection). This differential convection tilts and stretches the vorticity lines, increasing the magnitude of the vorticity, and re-directing it in a streamwise orientation. The streamlines corresponding to this vorticity constitute the secondary motion, superimposed upon the primary streamlines.

This type of secondary flow is exactly what Red Bull are using to create separated streamwise vortices from the boundary layer on their front-wing. But before proceeding further, let's establish some notation. In what follows, we shall denote the streamwise direction as x, the direction normal to the wing as y, and the spanwise direction as z. We also have three components for the velocity vector field, which will be denoted as U, V and W, respectively. There is also a vorticity vector field, whose components will be denoted as ω_x, ω_y, and ω_z.

On the underside of the front-wing is a boundary layer, and like all boundary layers, there is a velocity gradient ∂U/∂y is a direction normal to the wing, given that the velocity is zero at the solid surface. This entails that the boundary layer possesses vorticity in a spanwise direction ω_z. The vortex lines in this boundary layer are perpendicular to the streamwise direction of flow. The trick is then to convert some of this spanwise vorticity into streamwise vorticity ω_x. It transpires that the way to do this is to create a lateral pressure gradient ∂p/∂z.

Now, the front-wing operates in ground effect, so the pressure in an elevated mini-arch will be less than it is underneath the adjacent portion of the main plane, creating just such a pressure gradient. The crucial point is that this lateral pressure gradient corresponds to the creation of a spanwise-gradient in the streamwise velocity ∂U/∂z > 0. To see why this is crucial, however, we need to look at the Vorticity Transport Equation (VTE) for ω_x, the streamwise component of vorticity. The effect in question can be seen by studying incompressible, inviscid, laminar flow, so we can simplify the VTE by omitting the turbulent and viscous terms to obtain:

Dω_x/Dt = ω_x(∂U/∂x) + ω_y(∂U/∂y) + ω_z(∂U/∂z)

The left-hand side here, Dω_x/Dt, is the material derivative of the x-component of vorticity; it denotes the change of ω_x in material fluid elements convected downstream by the flow. Now, we started with ω_z > 0 in the boundary layer, and by virtue of creating a lateral pressure gradient, we also have ∂U/∂z > 0. This means that the third term on the right-hand side in the equation above is positive, which (assuming the other pair of terms are non-negative) entails that Dω_x/Dt > 0.

Thus, the creation of the spanwise-gradient in the streamwise velocity ∂U/∂z, skews the initially spanwise vortex lines ω_z until they possess a significant component ω_x in a streamwise direction. The lateral pressure gradient has created streamwise vorticity.

As Peter Bradshaw writes, "if the lateral deflection that produces longitudinal vorticity extends for only a small spanwise direction, then the longitudinal vorticity becomes concentrated into a vortex," (Turbulent secondary flows, Ann. Rev. Fluid Mechanics 1987, p64). Which is exactly what Red Bull, and for that matter, many other Formula 1 teams, do when they incorporate mini-arches into their front-wings.

As a final aside, note that there is an interesting duality at the heart of fluid mechanics, namely that between a description which uses the velocity and pressure fields, and a description which uses the vorticity field instead. The vorticity has been described as "the sinews and muscles of fluid mechanics," (Kuchemann 1965, Report on the IUTAM Symposium on concentrated vortex motions in fluids, Fluid Mech. 21). P.A. Davidson points out that in the case of incompressible flow, because pressure waves can travel infinitely fast, the velocity vector field is a non-local field; the vorticity field, in contrast, is local. "While linear momentum can be instantaneously redistributed throughout space by the pressure field, vorticity can only spread through a fluid in an incremental fashion, either by diffusion or else by material transport (advection). Without doubt, it is the vorticity field, and not [the velocity field], which is the more fundamental," (Turbulence, 2004, p39).

An aerodynamicist with an especially strong visual imagination, perhaps someone who had been stimulated to develop such mental capabilities to compensate for dyslexia, might be able to develop a better understanding of the fluid flow around a Formula 1 car by thinking in terms of vorticity, or by developing the ability to mentally switch back and forth between the vorticity and velocity representations. Such an individual might even reject tools such as CAD and CFD, preferring instead to work on a drawing board...

Linking Red Bull's fuel loads to McLaren's rear-wing

2011-11-12T11:30:00.010Z

One of the oddities of the 2011 Formula 1 season has been the contrast between the alacrity with which McLaren responded to the failure of their experimental 'bagpipe' exhaust system in pre-season testing, and their belated, late-season introduction of a Red-Bull style rear-wing, featuring a more powerful DRS effect.

Whilst a new and highly effective exhaust-blown diffuser was available on the McLaren from the first race, the new rear-wing combination, with smaller flap and larger main plane, only began to make sporadic appearances in practice from the middle of the season, and the system was only definitively installed for the Japanese Grand Prix at Suzuka.

Now, it's well-understood that a major aerodynamic component cannot be changed independently of the other primary aerodynamic components on a car, so McLaren presumably needed to make changes to the airflow feeding the rear-wing, or deal with the consequent change to the centre-of-pressure, before they could introduce the smaller flap design. Nevertheless, given the clear benefits of a powerful DRS system, as demonstrated by Red Bull from day one, McLaren do seem to have been a little tardy in this respect.

There is, however, a possible exculpatory explanation. Mark Hughes has recently drawn attention to the fact that during Friday practice this year, Red Bull have apparently used a second stint fuel load in the long run phase of these sessions, whilst McLaren have used a first stint fuel load. Conversely, Red Bull have tended to fuel more heavily on the short-run practice laps. This fuel-load combination has disguised Red Bull's real qualifying pace, relative to McLaren, but exaggerated their prospective race pace.

Perhaps, then, in the early stages of the season, McLaren came away from the races believing that their potential qualifying performance was stronger than their potential race performance, relative to Red Bull, and they therefore needed to continue optimising their car for race performance. This, in turn, meant retaining a larger rear-wing flap with a less powerful DRS stall.

Airbox spillage and fluidics

2011-10-31T20:28:00.008Z

A couple of weeks ago, the FIA issued a Technical Directive to the Formula One teams, announcing that off-throttle blowing of the exhausts will be severely curtailed in 2012 by engine mapping restrictions.

In combination with stringent requirements on the position and angle of the exhaust exits, this is intended to minimise the exploitation of exhaust flow for aerodynamic purposes. It will, however, have a secondary consequence. As Gary Anderson recently explained, off-throttle exhaust flow also serves to reduce spillage from the airbox:

"In the past when the driver closed the throttle to slow for a corner, the airbox spillage became a lot worse. If the airflow attachment on the sides of the engine cover was not good, the performance of the rear wing would be compromised – not something the driver wants under braking or on corner entry.

"Step forward the blown diffuser. Hot or cold blowing allows the engine to work like an air pump, moving this airflow through and out of the exhausts. This reduces the potential turbulent airflow creating negative performance on the rear wing.

If off-throttle blowing of the exhausts is genuinely to be prohibited next year by means of engine mapping restrictions, this will presumably re-create the problem of airflow spilling out of the airbox when the driver lifts off the throttle on turn-in to a corner.

So here's an idea: Why not introduce a fluidic switch which, under certain circumstances, re-routes the airbox airflow through the chassis to the lower leading edge of the sidepods? This could have the joint benefit of boosting the velocity of the underbody flow, and improving airflow to the rear wing, just at the time when the driver most needs it, when the car is in pitch under braking and turn-in.

Exhaust-blown diffusers in 2012?

2011-10-28T13:47:00.006+01:00

The 2012 Formula One regulations are intended to prohibit the use of exhaust-blown diffusers: stringent requirements have been placed on the location of the exhaust exit, and a recent announcement from the FIA suggests that engine mapping restrictions will be imposed to eliminate off-throttle pumping of the exhaust jet.

Craig Scarborough has produced a fantastic analysis of the exact restrictions to be placed on the location and orientation of the exhaust exit. In short, these move the exhaust exit to at least 500mm in front of the rear axle line, and 250mm above the reference plane underneath the car. The exhaust exit must also be angled upwards by at least 10 degrees. Hence, it will no longer be possible to blow the exhaust directly between the outer edge of the diffuser and inner face of the rotating rear wheel. Moreover, it will be illegal to place any sprung bodywork in a cone-shaped region, aligned with the exhaust exit, diverging at 3 degrees, and terminating at the rear axle line.

So will this be sufficient to eliminate exhaust-blown diffusers? Well, the first thing to note is that whilst it will be impossible to point the exhaust exit down at the diffuser, this won't necessarily prevent the exhaust jet itself from playing in that direction. When an exhaust jet exits into a cross-stream, the jet almost behaves like a deformable solid, as emphasised by F.L.Parra and K.Kontis in their 2006 paper, Aerodynamic effectiveness of the flow of exhaust gases in a generic formula one car configuration, from which the illustration here is taken.

If the exhaust exit is placed flush in the rearward face of sidepods sweeping downwards at a fairly steep angle, then the freestream airflow could deflect the exhaust jet towards the diffuser. The degree to which the jet is deflected is determined by the ratio between the velocity of the jet and the velocity of the cross-stream flow. The smaller the ratio, the more the jet is deflected.

Hence, there is something of a trade-off necessary here. To allow the exhaust jet to be deflected down towards the diffuser requires a lower exhaust jet velocity, yet for the exhaust jet to be effective in that region, requires higher jet velocities. There may be a compromise solution available here, an optimum exhaust velocity, which permits the jet to be directed towards the outer edge of the diffuser with sufficient velocity to have an effect, but that's something which only CFD and wind-tunnel experimentation will be able to determine...

Turbulence in Singapore

2011-09-21T16:35:00.007+01:00

The fourth Grand Prix of Singapore will take place this weekend, and whilst the city-state forms an impressive backdrop for a race, overtaking has been notoriously difficult in previous years here. As difficult, in fact, as it is at Valencia, another street-circuit situated at sea level.

Which is intriguing, because the atmospheric density is greater at sea level, and this has certain aerodynamic ramifications. Assuming the pressure at Singapore is 101 kPa (the standard sea level pressure), a temperature of 20 degrees Celsius corresponds to an air density of 1.196 kg/m³.

Singapore, however, is also notoriously humid, and because water vapour is lighter than dry air, humid air is less dense than dry air. Assuming a relative humidity of 80%, and a temperature of 20 degrees, the air density at Singapore is about 1.190 kg/m³. (The tables here are taken from Soil mechanics for unsaturated soils, Fredlund and Rahardjo, p23-24).

In contrast, at a circuit such as Spa Francorchamps, which lies at an altitude of about 400m, the standard atmospheric pressure is about 95 kPa, and at a temperature of 20 degrees the air density is only 1.124 kg/m³.

Now, greater air density increases downforce and drag, but it also changes the Reynolds number:

Re = (airspeed x length x air density)/viscosity of air

The viscosity of air increases as a function of temperature, (as tabulated on the left here), but is largely independent of pressure. Hence, the increased air density entails that the Reynolds number of the airflow at Singapore (and Valencia) will be slightly greater than it is at venues such as Spa.

How much greater? Well, by a factor of 1.190/1.124 = 1.058. In other words, the Reynolds number at Singapore is about 5% greater than it is at Spa.

Now, the Reynolds number specifies the ratio of the inertial forces to the viscous forces, and this is important for quantifying the effect of turbulence. The greater the Reynolds number, the more turbulent the flow. In particular, as a rule-of-thumb, viscous dissipation of turbulent energy only kicks-in when the Reynolds number of the turbulent eddies approaches unity. Thus, if the air density at Singapore is 5% greater than that at Spa, the viscous dissipation of turbulence doesn't kick-in until the turbulent eddies reach a size about 5% smaller than at Spa.

If the premises here are correct, and the reasoning is valid, then the cars will have a slightly longer turbulent wake at Singapore (and Valencia), than they have at venues such as Spa. That would help to explain why it's so difficult to overtake at Singapore (and Valencia).

Nevertheless, circuit design is still by far the most important factor. Zandvoort, after all, was situated amongst the sand dunes bordering the North Sea, yet the racing there was amongst the best you could care to see.

The Miles-Phillips Mechanism

2011-09-18T15:15:00.014+01:00

Two distinct mechanisms have been proposed to explain the means by which the wind is capable of generating waves and perturbations on the surface of lakes and oceans: Kelvin-Helmholtz instability (KHI), and the Miles-Phillips Mechanism.

Now, KHI reputedly requires a minimum wind speed of 6 m s^-1 to make waves grow against the competing effects of gravity and surface tension. Thus, whilst KHI is relevant to the generation of large wavelength perturbations, it is the Miles-Phillips Mechanism which is relevant to low wind speeds, and short-wavelength perturbations. In particular, the Miles-Phillips Mechanism involves a resonant interaction between the surface of the water and turbulent fluctuations in the air.

So, in the interests of science, I wandered down acorn-strewn paths to my local lake, to see if I could identify the Miles-Phillips Mechanism in action. What I observed over the course of several days, were a complex sequence of meta-stable and transient patterns. All the photos here were taken at the same time of day, around 2pm.

The first couple of pictures are from Friday 16th September. There was a light breeze blowing from left-to-right here, and this appeared to maintain a band of short wavelength perturbations in the middle of the lake. There is a clearly-defined transition, however, towards the margins of the lake, where the ripples were of a visibly longer wavelength. The shorter modes completely disrupt the reflective properties of the lake, but you can still see distorted images of the surrounding trees in the areas with the longer wavelength disturbances.

This is in sharp contrast with the pattern exhibited on two days previously, when a stable pattern of short-wavelength perturbations covered most of the lake. Note the absence of any reflective images at all.

On Sunday 18th September, the breeze was light, but rapidly fluctuating, and bands of short-wavelength perturbations would arise, and then dissipate, over a timescale of just a few minutes. In the first photo here, virtually the entire surface is smooth and reflective...

But within little more than five minutes, a band of short-wavelength ripples had covered the middle of the lake.

Such patterns would rise and fall, and drift back and forth across the lake as the local wind shifted and fluctuated. The wind variation was imperceptible from the viewpoint of the observer, and the patterns became as inexplicable and mesmerising as a mere screen-saver.

The cost of motorsport books

2011-09-17T15:43:00.007+01:00

Here's a rather stark illustration of US/UK pricing differentials.

The Autocourse 60 Years of Grand Prix Motor Racing is available on Amazon.co.uk for a whopping £44.96. Exactly the same book is also available on Amazon.com for the rather more affordable sum of $41.97, which equals £26.58 at current exchange rates.

There is, it seems, a somewhat different pricing strategy in different markets...

Formula 1 aerodynamics in the 1970s

2011-09-05T12:00:00.008+01:00

For most of the 1970s, there seems to have been a fundamental schism in the front-end aerodynamic concept of Formula 1 cars. Some of the cars, such as the McLarens, Lotuses and Ferraris, continued to run with front wings, but another group appeared to abandon that concept for most of the decade, running instead a front spoiler/airdam/splitter. This latter group included luminaries such as March, Brabham and Tyrrell, with Jackie Stewart winning the 1971 and 1973 World Championships in Tyrrell designs sporting just such a front-end.

So what was the idea? Well, part of the motivation was presumably to reduce the lift, drag and turbulence created by the front wheels. The front spoilers were much wider than front wings, and partially shrouded the front wheels, diverting airflow down the sides of the car.

So that was part of the idea. The other possible motive is perhaps more interesting, because it involves ground-effect. A spoiler/airdam provides a vertical barrier which (i) maximises the high pressure stagnation point at the front of the car, and (ii) accelerates the airflow through the restricted gap between the spoiler/airdam and the ground surface. A horizontal splitter projecting from the bottom of the spoiler/airdam then takes advantage of the high pressure of the stagnation point to generate some extra downforce.

A front airdam/spoiler is partially, then, a ground-effect device, which perhaps explains why cars such as the Brabhams and Tyrrells were still able to win Grands Prix against those utilising conventional front-wing arrangements. The photo here shows a Tyrrell running quite a degree of rake, which would serve to accentuate the ground-effect of the front spoiler.

So, perhaps surprisingly, ground-effect in Formula 1 actually predates the underbody venturi tunnels and skirts used on the Lotus 78/79. And in fact, Gordon Murray began experimenting with ground-effect on the Brabham BT44 back in 1974, arriving at "an inch-deep underbody vee, something like a front airdam, but halfway down the car." (Vacuum Clean-Up, Adam Cooper, Motorsport, May 1998, pp64-69).

The introduction of underbody venturi and skirts presumably spelt the death-knell for front spoilers, as the emphasis then shifted to feeding the underbody with as much airflow as possible. Still, it would be interesting to hear from those involved, what the initial impetus was for adopting those spoilers, and how effective they really were.

Suspension camber in Grand Prix racing

2011-09-03T17:43:00.011+01:00

Formula One's latest cause celebre revolves around Red Bull's decision to race at Spa with a greater degree of negative front-wheel camber than recommended by Pirelli.

Negative camber simply means that both wheels are inclined inwards at the top. The benefit of this is that the outer wheel generates greater lateral force on the entry to a corner (so-called camber thrust, similar to the way a motorbike rider generates lateral force by keeling the bike over), but the disadvantage is that the inner shoulders of both front tyres will suffer greater stress when the car runs in a straightline, and at Spa this caused both Red Bull drivers to suffer tyre blisters.

It's interesting to recall, however, that in the pre-war era of Grand Prix racing, the cars were actually set-up with visible levels of positive front-end camber. In other words, the front-wheels were inclined outwards at the top.

So why was this? Well, there seem to be at least two distinct reasons. The first was relevant prior to the mid-1930s, when cars employed what now look like rather primitive beam axle front suspension systems. Under the extra load generated by braking, the front axle would sag, and pull the front wheels inward at the top, as illustrated in this diagram taken from Matt Joseph's excellent 'Collector Car Restoration Bible: Practical Techniques for Professional Results'. Thus, a degree of positive static camber was necessary to offset this effect.

The eventual transition to independent, double-wishbone, ball-joint suspension, meant that wheel camber was no longer affected by the loads generated under straightline braking (or acceleration). However, even after the adoption of more modern suspension in the mid-1930s, the Mercedes and Auto Union Grand Prix cars continued to run with appreciable levels of positive camber. The primary reason for this appears to involve a concept called the scrub radius.

Now, when the front wheels of a car are steered, the wheels pivot around some axis. Originally, this steering axis was implemented with a physical rod called a king-pin, which was attached to each end of the beam axle. With independent, double-wishbone suspension, this king-pin is replaced by the line drawn between the upper and lower ball-joints at the outer end of the wishbones. This axis is also the line along which the weight of the car is projected down to the ground. The distance between the point where this line intersects the ground and the contact patch of the tyre, is called the scrub radius.

As Joseph explains (p261), a non-zero scrub radius causes several problems: it puts large forces into the king-pins; it acts like a lever, thereby putting large shocks into the steering; and it makes it harder to steer a car. Positive camber was the common solution devised for minimising the scrub radius. If the wheels are inclined outwards at the top, then the contact patches will be placed directly under, or at least closer to, the point where the steering axis intersects the road surface.

There's just one more complication to consider. Under the chassis roll generated by cornering, a double-wishbone suspension system will experience a positive camber increment on the more heavily loaded outer wheel, and a negative camber change on the lightly-loaded inner wheel. By setting a car up with a degree of positive static camber, this will result in the outer wheel acquiring an even greater degree of positive camber during cornering, while the inner wheel reaches a more vertical inclination, as nicely demonstrated in the photo of the Mercedes above.

Spot the difference

2011-09-01T17:23:00.006+01:00

This is Vittorio Brambilla, otherwise know as the Monza Gorilla, and best remembered for crashing immediately after winning the 1975 Austrian Grand Prix.

Not to be confused with...

Michela Vittoria Brambilla, Italian beauty queen, philosophy-graduate, businesswoman, and erstwhile Minister of Tourism in Silvio Berlusconi's government.

Alonso vs Webber and Hamilton at Eau Rouge

2011-08-31T13:16:00.011+01:00

It's difficult to find a precedent for Mark Webber's frightening pass on Fernando Alonso last Sunday, but there is an interesting contrast.

On the first lap of the 2007 Belgian Grand Prix, McLaren team-mates Alonso and Hamilton raced wheel-to-wheel down to Eau Rouge, with Hamilton on the inside for the left-hand entry.

On that occasion, however, Fernando was able to take more speed into the corner, and claim the position into the right-handed uphill element. Here's Lewis's account of it at the time:

"At Eau Rouge it was just common sense to ease off a fraction. Fernando had the momentum and was going quicker into it. It would have been stupid of me to keep it flat, but I was tempted. That worked in a Formula 3 car in the wet, but I'm not sure it would in a Formula 1 car..."

The two situations are not completely similar, because Webber was able to use the slipstream on Sunday, and gain extra momentum over Alonso. Nevertheless, the fact that Hamilton failed to make the move stick from the inside against the same adversary, provides a vivid demonstration of just how much commitment Webber needed.

Wittgenstein's aircraft engine

2011-08-22T22:29:00.003+01:00

Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921) consists of numbered paragraphs, the first of which reads, 'The world is everything that is the case', and the last of which states, 'Whereof one cannot speak, thereof one must be silent.'

As Anthony Quinton explained in discussion with Bryan Magee, Wittgenstein "detested...the idea of philosophy as a trade, a 9-to-5 occupation, which you do with a part of yourself, and then go off and lead the rest of your life in a detached and unrelated way. He was a man of the utmost moral intensity. He took himself and his work with very great seriousness. When his work wasn't going well he got into a desperate and agonized condition. The result of this displays itself in his manner of writing. You feel that his whole idea of himself is behind everything that he says...[He] doesn't want to make the thing too easy - he doesn't want to express himself in a way that people can pick up by simply running their eyes over the pages. His philosophy is an instrument for changing the whole intellectual aspect of its readers' lives, and therefore the way to it is made difficult," (Talking Philosophy, p83).

Wittgenstein, however, came to philosophy by starting off as an aeronautical engineer at Manchester University between 1908 and 1910. Here, he devised and patented a new design of aircraft engine, but became interested in the mathematics used to describe his engine. The questions Wittgenstein began asking himself about the nature of mathematics, then brought him to Bertrand Russell's Principles of Mathematics. Discussing this with Frege in Germany, Wittgenstein abandoned his aeronautical career, and went to Cambridge to study logic under Russell.

Wittgenstein's engine design is rather interesting, and a couple of recent papers have explained his concept in detail. Ian Lemco outlined Wittgenstein's aeronautical research in a 2007 paper, and co-wrote an exposition of his combustion chamber design with John Cater in 2009.

Ludwig, it seems, was inspired by an idea proposed in the 1st century BC, by Hero of Alexandria, to drive a propeller by emitting jets of gas from nozzles placed in the tips of the rotor-blades. In particular, Wittgenstein proposed that the tips of the rotors contain combustion chambers, and the centrifugal force of the rotating propeller alone should be responsible for compressing the mixture of air and fuel; no need for pistons, in other words.

In modern terms, Wittgenstein proposed a tip-jet engine design. Such engines subdivide into cold-tip jets and hot-tip jets: the former are driven by, say, compressed air, created by a remote compressor, while the latter are driven by the direct exhaust jet flow of combustion. The Sud-Ouest Djinn helicopter, for example, employs cold-tip jets, while the Hiller YH-32 Hornet uses hot-tip jets.

All of which sounds not totally dissimilar to the distinction between hot-blown and cold-blown diffusers in modern-day Formula One...

Weak polygyny and Formula One

2011-08-21T13:22:00.013+01:00

Weak asymmetries are responsible for just about everything we experience.

Most of the universe we observe, all the galaxies and the stars and the planets, is composed of matter rather than anti-matter, yet the universe should have started with equal amounts of the two. If all the processes in particle physics were exactly symmetric, then most of the matter and anti-matter should have mutually annihilated, yielding a universe containing almost nothing but photon radiation.

What we actually observe is approximately two billion photons for every proton or neutron of matter, and in effect, this figure expresses the exact asymmetry between matter and anti-matter. It's thought that as a result of a small asymmetry in certain high-energy processes, the early universe developed slightly more quarks than anti-quarks. To be more precise, there were a billion-and-one quarks for every billion anti-quarks. Two photons were produced for each annihilation event between a quark and an anti-quark, and the remaining quarks were bound into protons and neutrons, hence the current universe possesses approximately two billion photons for every proton or neutron of matter.

So the weak asymmetry between quarks and anti-quarks is necessary to explain the existence of all the stars and planets. But what about human culture and civilization, all its cities and technologies and literature? How do these emerge from evolutionary biology?

One suggestion is that the weak polygyny of human society is a necessary condition. Polygyny is a sexual asymmetry in which some of the males in a species possess stable reproductive relationships with multiple females in so-called harems, leaving the remaining males as bachelors. This leads to varying forms of intense competition between the males, which often manifests itself in sexual dimorphism, the existence of different male/female sizes or capacities.

Human polygyny is less than that of gorillas, where there is correspondingly a large difference between the size of the males and females, but greater than that of gibbons, who are monogamous, and where the males and females are duly of comparable size.

The evidence for human polygyny is rather strong. G.P.Murdock's Ethnographic Atlas, for example, lists 849 human societies, and finds that 83% are polygynous. And as Richard Dawkins points out in The Ancestor's Tale, research conducted by Laura Betzig indicates that "overtly monogamous societies like ancient Rome and medieval Europe were really polygynous under the surface. A rich nobleman, or Lord of the Manor, may have had only one legal wife but he had a de facto harem of female slaves, or housemaids and tenants' wives and daughters."

This weak polygyny is reflected in human sexual dimorphism, but because humans are an intelligent species, it has a physical and a cultural component. Men are, on average, larger and stronger than women, but men also seek to gain access to harems, not by direct competition, but by seeking power, wealth and status. As a by-product of this, virtually all of human culture, the philosophy, the politics, the science, the technology, the art, the business, and the sport, has been produced by men.

And where else in the world can you find an activity which combines sport, business, politics and technology, in such a tightly integrated package, than Formula One? In essence, then, Formula One is a by-product of the human male desire to gain access to female harems. Small asymmetries matter.

Front-wing ground effect

2011-08-18T19:11:00.009+01:00

Red Bull, McLaren and Ferrari currently appear to be converging on the same aerodynamic solution: a high-rake, nose-down stance to maximise the ground effect component of front-wing downforce, (with the use of exhaust-blown diffusers to retain rear downforce). Front-wing ground effect has always had a role to play, but the current emphasis is perhaps a consequence of the new technical regulations introduced for the 2009 season, which permitted the front-wing to be much closer to the ground.

To understand front-wing ground effect, it's worth revisiting some research performed by Zhang, Zerihan, Ruhrmann and Deviese in the early noughties, Tip Vortices Generated By A Wing In Ground Effect. This examined a single-element wing in isolation from rotating wheels and other downstream appendages, but the results are still very relevant.
The principal point is that front-wing ground-effect depends upon two mechanisms: firstly, as the wing gets closer to the ground, a type of venturi effect occurs, accelerating the air between the ground and the wing to generate greater downforce. But in addition, a vortex forms underneath the end of the wing, close to the junction between the wing and the endplate, and this both produces downforce and keeps the boundary layer of the wing attached at a higher angle-of-attack.

The diagrams above show how this underwing vortex intensifies as the wing gets closer to the ground. In this regime, the downforce increases exponentially as the height of the wing is reduced. Beneath a certain critical height, however, the strength of the vortex reduces. Beneath this height, the downforce will continue to increase due to the venturi effect, but the rate of increase will be more linear. Eventually, at a very low height above the ground, the vortex bursts, the boundary layer separates from the suction surface, and the downforce actually reduces.
So, for a wing in isolation, the ground effect is fairly well understood. One imagines, however, that the presence of a rotating wheel immediately behind the wing makes things a little more difficult!

The diagram here, from the seminal work in the 1970s by Fackrell and Harvey, demonstrates that the rotating wheel creates a high pressure region in front of it, (zero degrees is the horizontal forward-pointing direction, and 90 degrees corresponds to the contact patch beneath the tyre). Placing a high-pressure area immediately behind a wing will presumably steepen the adverse pressure gradient on the suction surface of the wing, causing premature detachment of the boundary layer. Hence, when the wings were widened in the new regulations, most designers immediately directed the endplates of the wings outwards, seeking to direct the flow away from those high-pressure areas.

Lego Grand Prix

2011-08-18T17:36:00.000+01:00

Peridynamics

2011-08-17T19:51:00.006+01:00

Q:So what exactly is peridynamics?
A: Well, it's a new formulation of solid mechanics, which in turn, is part of continuum mechanics. Continuum mechanics represents those parts of the macroscopic world which can be idealised as continuous, extended entities. If you've got a gas or a liquid, you can represent it using fluid mechanics. Fluids, however, don't have strength, whereas solids do. To represent a solid, you need to use solid mechanics.

Q: So why the need for a new formulation?
A: Well, it's basically all about fracture. The trouble with fracture is that, by definition, it constitutes a discontinuity in a solid, and given that solid mechanics is predicated upon the continuity of things, the conventional formulation struggles to deal with fracture.

Q: And what does peridynamics postulate to resolve the problem?
A: Cauchy's momentum equation, the governing equation of continuum mechanics, defines the force at a point by the divergence of the stress tensor. The divergence is, of course, a differential operator, and if your equations are based upon derivatives, then your equations will fail in the presence of a discontinuity. Peridynamics attempts to get around this by replacing the spatial derivatives of the stress tensor at each point with the integral of a force density function centred at that point. This, then, is a radical approach, which attempts to generalise from Cauchy's conception of the internal stresses in a solid. The field equations in this formulation, it is claimed, can be applied to discontinuities such as cracks.

Q: Are there any philosophical implications?
A: Definitely, yes. On smaller length scales, where fluids and solids are discrete, people use something called Molecular Dynamics to represent substances. And the equations of Molecular Dynamics are intrinsically non-local; the net force on each particle is determined by the joint effect of all the inter-atomic forces due to other particles, not just those immediately adjacent to the particle in question. Finding the force on a particle by adding all the contributions from particles in a neighbourhood of that particle, is a discrete version of an integral. Conventional solid mechanics, however, is distinctly local. This means that the inter-theoretic relationship between Molecular Dynamics and conventional solid mechanics is very unsatisfactory. However, by using the non-local reformulation provided by peridynamics, the inter-theoretic relationship is far more satisfactory.

It's an interesting case, which demonstrates that macroscopic theories sometimes need to be reformulated using concepts and structures taken from the microscopic theory.

Multi-element wings and DRS

2011-08-12T23:15:00.015+01:00

So why are the wings on aircraft and racing cars broken up into multiple elements, with slots in-between? Well, it was found reasonably early in the history of aerodynamics that this technique enabled the total wing to continue generating lift at an angle of attack at which it would have stalled, were it to have been fashioned as a single element. The lift/downforce generated by a wing increases as the angle of attack increases, hence multiple element wings are a means of increasing peak lift/downforce. (In the case of aircraft, they are also a means of maintaining lift at the lower airspeeds associated with landing and taking-off).

But how does the introduction of slots achieve this effect? Well, A.M.O. Smith identified five distinct mechanisms in his 1974 paper, High-Lift Aerodynamics: slat effect, circulation effect, dumping effect, off-surface pressure recovery, and fresh-boundary layer effect.

So let's have a go at attempting to understand what these effects are. To start off, however, we need to recall some of the fundamental facts about how a wing works.

A wing generates lift/downforce because it generates a circulatory component to the airflow. The circulation only exists because of a thin layer of airflow adjacent to the wing called the boundary layer. Viscous effects operate in the boundary layer, but outside the boundary layer the airflow can be idealised as being inviscid.

When people speak of the velocity and pressure of the airflow above and below a wing, they are implicitly speaking of the velocity and pressure on the dividing line which separates the boundary layer from the inviscid airflow. Here, Bernoulli's law applies: if the airflow is accelerated, the pressure decreases, whilst if the airflow decelerates, the pressure increases.

The low pressure surface of a wing initially accelerates the airflow, and then decelerates it towards the trailing edge. Hence, there is higher pressure at the trailing edge than at the point of maximum velocity, and this corresponds to an adverse pressure gradient along the latter part of the boundary layer.

The circulation around a wing is crucially dependent upon the boundary layer remaining attached to the surface of the wing. If the adverse pressure gradient is too steep, reverse flow ensues, the boundary layer detaches, and the wing stalls. This will happen as one attempts to increase the amount of lift/downforce by increasing the angle of attack.

Ok, so that's some of the fundamentals of wing aerodynamics. Now, if the boundary later detaches when the adverse pressure gradient becomes too steep, it follows that reducing the severity of the adverse pressure gradient at a fixed angle of attack will keep the boundary layer attached. And this is exactly what a multi-element wing does.

Imagine for a moment a three-element racecar wing. The small leading element is called a slat, and the element behind the main plane is called the flap. Imagine the airflow coming from left to right. There will be an anti-clockwise circulatory component to the airflow around each element. One effect of this will be to reduce the acceleration of the airflow at the leading edge of the main element, and to thereby reduce the low pressure peak at that point. In simplistic terms, the circulatory component to the flow at the trailing edge of the slat is in an opposite direction to that at the leading edge of the main plane, hence the slot gap reduces the velocity of the airflow here. By reducing the low pressure peak at the leading edge of the main plane, the adverse pressure gradient along the main plane will be reduced, thereby helping the main plane to hang onto its boundary layer. This is the slat effect.

Meanwhile, the flap will have its own circulation, and as a consequence, at the point where the trailing edge of the main plane discharges its boundary layer, the airflow velocity will be greater than it would in the absence of a flap. Thus, the high pressure at the trailing edge of the main plane is reduced, once again reducing the adverse pressure gradient along the main plane, helping to keep the boundary layer attached. This is the dumping effect.

Now, according to Smith, the circulation of the flap enhances the circulation of the main plane, and in the presence of a slat, the circulation of the main plane enhances the circulation of the slat. As yet I can't intuitively see why this is the case. Smith claims, however, that this circulation effect is closely related to the dumping effect, and asserts that the downstream element induces cross-flow on the trailing edge of the upstream element, which enhances its circulation.

The off-surface pressure recovery effect, meanwhile, is a consequence of the dumping effect. A downstream element reduces the deceleration towards the trailing edge of an upstream element, keeping the boundary layer attached, and releasing the boundary layer from the trailing edge of the surface, where it completes its deceleration in a manner which doesn't cause reverse flow. The boundary layer of the main plane, for example, will discharge into the region outside the boundary layer of the flap, and continue to decelerate until it reaches the trailing edge of the entire wing system, (see the diagram here from Zhang and Zerihan, Aerodynamics of a double-element wing in ground effect, 2003).

The final effect, the fresh boundary layer effect, means that each element acquires its very own boundary layer, fed by the freestream velocity. This keeps the boundary layer of each element thinner than the boundary layer on a single wing of the same length, and thinner boundary layers are able to withstand greater adverse pressure gradients.

So it's all about increasing circulation and mitigating the causes and effects of adverse pressure gradients.

Note, of course, that the function of a DRS rear-wing in modern Formula 1 is dependent upon these aerodynamic effects. The rear wing is designed so that the main plane is at an angle of attack which would cause the boundary layer to detach in the absence of the flap. With the flap in place, the severity of the adverse pressure gradient is reduced by the acceleration of the airflow around the leading edge of the flap. Open the flap, and the main plane is suddenly dumping its boundary layer into freestream airflow, as a result of which the adverse pressure gradient steepens, and the boundary layer detaches, causing the main plane to stall.

Renormalization in quantum field theory

2011-08-07T11:11:00.012+01:00

So what exactly is renormalization in quantum field theory? Well, quantum field theory makes experimentally verified predictions about collisions between particles. In particular, it makes predictions about the probability of going from a particular incoming state to a particular outgoing state, and these are called transition probabilities:

An incoming particle is represented by a quantum state Ψ_i, the interaction process is represented by a scattering operator S, and the potential outgoing state is represented by the quantum state Ψ_f.

In many physically relevant situations, the incoming state has a specific energy E_i and momentum k_i, and each possible outgoing state also has a specific energy E_f and momentum k_f. An outgoing state with a specific momentum k_f, also has a specific direction Ω associated with it.

These transition probabilities can be used to construct cross-section data. The cross-section for a reaction is effectively an expression of its probability. In practice, cross-sections provide an economical way of bundling the transition probabilities between entire classes of quantum states. For example, the differential cross-section σ(E,Ω) is proportional to the probability of a transition from any incoming state Ψ_i of energy E to any outgoing state Ψ_f in which the momentum vector k_f points in the direction of Ω. Integrating a differential cross-section over all possible directions then gives a total scattering cross-section σ(E).

So, what about the scattering operator S? Well, this contains the information that specifies the nature of the interaction. The nature of the interaction is specified using objects from classical physics, either the interaction Hamiltonian or the interaction Lagrangian. The interaction Lagrangian will contain values for the masses and charges (aka coupling constants) of the interacting fields. The scattering operator can be expressed in terms of the interaction Hamiltonian density operator H_I(x), which in turn, can be obtained from the interaction Lagrangian density. To be specific, the scattering operator can be expressed as the following Dyson perturbation series:

T[H_I(x₁),...,H_I(x_n)] simply denotes a time-ordered permutation of the interaction Hamiltonian density operators.

Inserting the expression for the scattering operator into the expression for a transition probability, yields an infinite series, and the trouble is that every term in this series transpires to be a divergent integral. Renormalization involves taking only the first few terms in such a series, and then manipulating the integrals in those terms to obtain finite results.

The most sophisticated account of renormalization goes as follows. The troublesome integrals tend to be integrals over an infinite energy range, and the integrals go to infinity as the energy goes to positive infinity. So begin by introducing a cut-off Λ₀ at a large, but finite energy. Correlate this cut-off with a particular conventional interaction Lagrangian, with conventional values for the masses and coupling constants. Now stipulate that the masses and coupling constants are functions of the cut-off energy Λ. Thus, as the upper limit of the integral is now permitted to go to infinity, Λ → ∞, the masses and coupling constants becoming running masses and coupling constants, m(Λ) and g(Λ), and the Lagrangian also acquires evolving counter-terms which incorporate those running masses and coupling constants. The functional forms of m(Λ) and g(Λ) are chosen to ensure that the integrals are now finite as the limit Λ → ∞ is taken.

Thus, for example, in the case of quantum electrodynamics, the Lagrangian is modified as follows:

The charge and mass have the following running values (c₀ and its tilde-counterpart being proportional to ln (Λ/Λ₀):

This is called the Renormalization Group (RG) approach. It basically amounts to saying that there is a flow in the space of Lagrangians under energy-scale transformations. Changing the cut-off in divergent integrals is then seen to be equivalent to adding/subtracting extra terms in the Lagrangian, which in turn is equivalent to changing the values of the masses and coupling constants. There are, of course, numerous qualifications, exceptions and counter-examples, but that is the basic idea.

At a classical level in mathematical physics, the equations of a theory can be economically specified by a Lagrangian, hence it is typical in physics to identify a theory with its Lagrangian. Thus, a flow in the space of Lagrangians is also a flow in the space of theories; the RG approach is saying that different theories are appropriate at different energy scales.

I'm indebted here to the material in the following couple of papers, which also constitute excellent further reading for the enquiring mind:

Hartmann, S. (2001). Effective field theories, reductionism and scientific explanation, Studies in the History and Philosophy of Modern Physics, 32, pp267-304.

Huggett, N. and Weingard, R. (1995). The Renormalisation Group and Effective Field Theories, Synthese, Vol. 102, No. 1, pp. 171-194.

The Hamilton duels

2011-08-06T11:46:00.009+01:00

There were two great wheel-to-wheel battles in the Hungarian Grand Prix, both, predictably, featuring Lewis Hamilton. First off was the Hamilton-Vettel duel between laps 1 and 5, and then there was the equally thrilling Hamilton-Button contest between laps 47 and 52.

The first lap saw Hamilton and Button side-by-side, scrabbling for grip coming out of the first corner on their intermediate tyres, Hamilton taking second place down the outside into turn 2 as Button backed out of it. Lewis then set off after Vettel, the McLaren spectacularly sideways accelerating out of turn 2 on the second lap.

Once again, the McLarens were the only leading cars generating strong wing-tip vortices down the main straight, and Lewis clearly had a grip advantage over Vettel in these early laps on a damp track. Vettel, however, provided a robust defense.

On lap 3, Lewis decided to try the outside of Vettel into turn 2, briefly putting his outside wheels onto the grass as he did so. It was remarkably similar to the moment in Canada this year when Lewis was attempting to overtake Schumacher into the hairpin, although on that occasion Lewis was badly squeezed by the Mercedes driver making a second move under braking. This time round, Lewis was able to take a run around the outside of turn 2, but Vettel anticipated the move and simply ran Lewis out to the edge of the track, forcing him to back off and drop in behind the Red Bull.

On lap 4, Lewis again got a run on the Red Bull into turn 2, but this time decided to try the inside. Yet again, however, Vettel had an answer, and simply carried enough speed around the outside to retain his place into turn 3. Vettel was demonstrating all the racecraft which some have accused him of lacking, but on lap 5 he finally over-egged it into turn 2, running wide and letting Lewis into the lead.

The later Hamilton-Button duel was triggered, of course, when Lewis spun at the chicane on lap 47, Jenson taking the lead. Being on softer tyres, Lewis was potentially at an advantage in the battle which ensued, but Lewis's tyres were also wearing badly, to the extent that he was forced to pit at the end of lap 52. It's possible, therefore, that the two drivers actually had comparable levels of grip.

By lap 49, Button was extending the gap to Lewis, demonstrating he had superior grip on a mostly dry track surface. On lap 50, however, the rain began to fall again, and by the exit of the chicane, Lewis was back in the wheel-tracks of the other McLaren. Into turn 2 on lap 51, Jenson's famed ability to magically sense the levels of grip available, momentarily deserted him, and he ran ride, letting Lewis back into the lead.

Lewis immediately gained a 2 second gap over Button, but struggled badly with grip over the remainder of the lap, and coming onto the main straight to start lap 52, Button was right behind him. With the advantage of DRS, Jenson overtook his compatriot into turn 1, a quartet of wing-tip vortices briefly streaming in their joint wake.

Down they went into turn 2, and Jenson turned into the corner a little defensively on a tighter line than normal, and missed the apex, Lewis cutting underneath to re-take the lead. Great stuff!

Battle was then suspended over the remainder of the lap as both drivers attempted to absorb the information and instructions the McLaren team were communicating vis-a-vis the potential requirement to fit intermediate tyres. Lewis was able to receive messages from the team, but unable to make himself heard in response, whilst Jenson was at one stage invited to queue behind Lewis as both cars were fitted with intermediates.

Ultimately, of course, Lewis's race-winning prospects were already done-for, and the vital decision, the race-winning decision, was Jenson's choice not to pit.

A way to subvert the blown diffuser ban?

2011-08-04T18:12:00.005+01:00

Exhaust-blown diffusers will effectively be banned in Formula 1 from next year, but there may be other ways of blowing the diffuser, and generating the side-edge vortices which appear to be crucial to maximising diffuser downforce.

For example, from 2014, Formula 1's engine formula will change from a normally aspirated 2.4 litre V8 to a 1.6 litre turbo-charged V6. The turbine in such an engine is constantly generating compressed air. Moreover, the inlet manifold of a turbo engine has a blow-off valve, specifically designed to release pressure when the driver lifts off the throttle or the throttle is closed. The blow-off valve could be vented down to the sides of the diffuser, providing vital extra downforce when a driver comes off the throttle turning into a corner.

From 2012, the regulations will prohibit exhaust-blown diffusers by stipulating that the exhausts are moved to a location in which they cannot influence the diffuser. These new regulations, however, will say nothing (as far as I'm aware) about blowing the diffuser with compressed air from the inlet manifold of a 2014 turbo engine!

Unfortunately, there is at least one potential snag: the Wikipedia entry on blow-off valves claims that "Motor sports governed by the FIA have made it illegal to vent unmuffled blowoff valves to the atmosphere." There is no citation, however, so it's difficult to ascertain if this is true, or even if it will apply to the 2014 F1 engine regulations. In fact, this is presumably something yet to be determined. Worth keeping an eye, then, on how those regulations are finally worded...

In the meantime, the teams could use compressed air cylinders to blow the diffusers, perhaps just for a qualifying lap. The primary declared purpose of these cylinders would be to supply the pneumatic valve system in the engine, of course, but as a safety measure, it might be necessary to vent excessive pressure. For safety. And cooling.

Diffusers and rake

2011-08-02T13:22:00.017+01:00

A recent column by Mark Hughes (Autosport, July 21, p21), and a subsequent explanation Mark elicited from McLaren technical director Paddy Lowe (Autosport, July 28, p41), provide some extra illumination on the overall aerodynamic concept pursued in Formula 1 by Red Bull since 2010, and followed to some extent by other teams this year.

Both articles explain that the basic idea has been to run a car with a significant degree of rake, so that the front ride-height is lower than the rear. The effect of this is twofold: the front-wing generates greater downforce due to ground effect, and the rear diffuser also acquires the potential to generate greater downforce.

Maximising the downforce of the diffuser is, however, a subtle issue. The downforce generated by a diffuser is a function of two variables: (i) the angle of the diffuser, and (ii) the height above the ground. Generally speaking, the peak downforce of the diffuser increases with the angle of the diffuser. Then, for a fixed diffuser angle, the downforce generated will increase according to an exponential curve as the height reduces, until a first critical point is reached (see diagram above, taken from Ground Effect Aerodynamics of Race Cars, Zhang, Toet and Zerihan, Applied Mechanics Reviews, January 2006, Vol 59, pp33-49). As the height is reduced further, the downforce will increase again, but according to a linear slope, until a second critical point is reached, after which the downforce falls off a cliff.

Without running any rake, the diffuser is limited by regulation to a shallower angle than seen in years gone by. By increasing the rake, the effective angle of the diffuser is increased, thereby increasing the potential peak downforce. However, increasing the rake also has the effect of increasing the height of the diffuser.

So, how does one combat the detrimental effect of increasing the height of the diffuser? Well, the key, I think, is to understand exactly how a reduction in height increases the downforce generated by a diffuser. The crucial point is that the edges of the diffuser generate a pair of counter-rotating vortices, and the magnitude of the downforce generated is determined by the strength of these vortices. The downforce increases exponentially as the height is reduced, because the strength of these vortices is increasing. The first critical point corresponds to the height at which the vortex strength begins to decrease, and the second critical point corresponds to the height at which the vortices breakdown.

So, to pose the question again, how do we mitigate the downforce-reducing effect of an increase in diffuser height? Simple, one merely uses the exhaust gases to boost the strength of the side-edge vortices to levels otherwise seen at lower heights.

In fact, this is to simplify the issue, because the exhaust gases playing on the sides of the diffuser have two effects: (i) to strengthen the side-edge vortices inside the diffuser, and (ii) to act as air curtains, preventing the ingress of turbulent air created by the rotating rear wheels.

So, with exhaust-blown diffusers to be banned from next year, the trick will be to find other ways of boosting the strength of those side-edge vortices. Do so, and you'll still be able to run your car with a significant degree of rake.

Lewis Hamilton's Garden of Forking Paths

2011-07-31T17:24:00.014+01:00

It's often said that there are more ways to lose a Grand Prix than to win one, and the diagram here makes that explicit.

Lewis Hamilton lost the Hungarian Grand Prix on Sunday primarily as a result of the tyre-choice made at the third pit-stop. Leading the race from Jenson Button and Sebastien Vettel, Lewis took his third set of options, while Jenson and Sebastien took a set of the harder, prime tyres. With thirty laps to the end of the race, Hamilton would require another pitstop, whereas Button and Vettel wouldn't. That decision alone restricted Hamilton to third place, at best.

The subsequent drive-through penalty and stop for intermediate tyres merely reduced Lewis's highest possible finishing position to 4th, which he duly achieved after passing Webber.

The diagram here demonstrates twelve possible paths through the last thirty laps of the race. Branches to the left constitute errors. The branch furthermost to the left is the one actually followed, while the branch furthermost to the right is the one for which victory would have been most likely. All the other branches, with one exception, lead to an eventual 3rd or 4th place.

The one exceptional case corresponds to the scenario in which Lewis took primes at the third pit-stop, but still spun, and lost the lead to Jenson on the damp track-surface. If Lewis had avoided a drive-through penalty, he would then have finished either 2nd behind Jenson, or perhaps even have retaken the lead. Whether Lewis could have made a set of primes last thirty laps, however, is unknown.

The BBC/Sky deal

2011-07-30T18:20:00.005+01:00

To borrow a phrase used by Jonathan Miller, television is a device for transporting the mind. Each year, the BBC voraciously consumes a revenue of £3.5 billion, derived from the licence fee in the UK, and transforms this into patterns of electromagnetic radiation. These patterns possess an information content which enables the viewer to see places and events without actually being there.

Sadly, £3.5 billion per annum is not, it seems, sufficient to embrace the £40 million required to maintain exclusive rights to the broadcast of Formula 1 in the UK. The BBC, of course, has other priorities, such as maintaining the eclectic, high-brow, intellectual content of their youth-oriented channel, BBC3.

The Formula 1 teams seem to have received the news in a remarkably phlegmatic fashion. They'll receieve an additional £1 million per annum, and they are perhaps anticipating that when Sky touches Formula 1, it will boost the sport in the manner that football was financially boosted with the inception of The Premiership.

Formula 1 fans in the UK already pay a £145 BBC licence fee, and will now be required to pay at least £500 per annum for a Sky Sports subscription. So it's bad news for the fans in a financial sense, but potentially good news for those who work in Formula 1, or wish to work in Formula 1.

I wonder, however, if the teams will run the gauntlet of another FOTA fans' forum in the UK...

Maxicons

2011-07-26T20:48:00.003+01:00

A Maxicon is an elementary semantical unit, in which a linguistic phrase conveys both an explicit meaning, and a second implicit sense, which contradicts the explicit content.

An excellent example can be found in the recent Max Mosley interview, conducted by Maurice Hamilton for the August edition of F1 Racing. Discussing FIA President Jean Todt's handling of the Bahrain Grand Prix fiasco, Max comments:

"I don't want to criticise poor Jean."

The explicit meaning expresses a disinclination towards censure, whereas the implicit content is:

"Poor Jean really isn't up to the job."

Lewis Hamilton and overtaking around the outside

2011-07-26T00:26:00.004+01:00

Discussing his efforts to fend off Mark Webber in Sunday's German Grand Prix, Lewis Hamilton remarked on the BBC's post-race Forum that, "I've been overtaken on the outside once before, and I don't wanna do it again."

Lewis here is presumably referring to the first corner of the 2008 Hungarian Grand Prix, when Felipe Massa swept out of his slipstream, briefly locked-up his wheels under braking, and drove clean around the outside of the McLaren. Without the engine failure Massa subsequently suffered in that race, it would have been a championship-winning manoeuvre.

It's interesting that Lewis should be keeping count of this type of thing, and interesting to learn how much it's still in his mind, how much it still smarts.

Massa, of course, actually overtook Hamilton around the outside into the final corner of the British Grand Prix this year, only to be immediately retaken before the finish line. Perhaps that one doesn't count then.

McLaren's rear-wing vortices

2011-07-24T16:40:00.006+01:00

So did you spot them? The McLaren wing-tip vortices?

If you watch the train of cars streaming down the pit-straight at the end of both the first lap, and particularly at the end of the second lap, you'll see that the McLaren of Lewis Hamilton was generating visible rear-wing vortices. Neither the following Red Bulls, nor the Ferraris, nor the Mercedes, were doing so.

What's the reason for this? Is the McLaren rear-wing simply more powerful? Well, McLaren have been running a rear-wing this year with a larger flap than Red Bull, and although this gives Red Bull a DRS-advantage in qualifying, the flip-side is that McLaren have been equipped with a more powerful rear wing in the races. Ferrari, similarly, adopted the Red Bull solution at Silverstone. McLaren experimented with a small-flap design at Silverstone, without success, and seemed to be having similar difficulties at the Nurburgring during Friday practice.

If McLaren do still have a more powerful rear wing, it would provide a simple explanation for how they were able to switch the tyres on in the cold conditions of the Nurburgring, and provide Lewis Hamilton with a car in which he could do his stuff again. McLaren, however, might now struggle with overheating rear tyres in the mid-Summer heat of Hungary, much as they did at Valencia.

And wasn't that the fourth successive race in which Ron Dennis has been in attendance...?

Phone-hacking and spontaneous self-organisation

2011-07-20T17:18:00.007+01:00

There's something of a hullabaloo in the UK at the moment over the phone-hacking conducted by Rupert Murdoch's News International publications, and the degree of collusion which has subsequently been revealed between politicians, journalists, and the police.

Rebekah Brooks and Andy Coulson, successive editors of The News of the World during the time in which the hacking took place, have both denied all knowledge of the illegal techniques used to obtain numerous stories. One can only presume that they thought their journalists were obtaining personal and private information by means of telepathy.

The collusion between politicians, journalists and police, however, is actually quite an interesting socio-political case study. Free market thinkers, such as Matt Ridley, have long trumpeted the power of bottom-up, spontaneous self-organisation in society, over top-down regulation, and what we have here is, in fact, a perfect demonstration of just such a phenomenon.

There's been no conspiracy here, no centralised command, planning and coordinating the collusion between the various agencies. Instead, the politicians, journalists and police have spontaneously evolved a means of cooperating for mutual benefit. Each individual involved has sought merely to preserve and promote their own careers, making short-term, self-interested decisions based upon incomplete information. The collective result of all these minor, self-interested decisions, has been a high degree of collusion between those who make the law, those who enforce it, and those who report it.

It's a perfect example of the bottom-up, spontaneous formation of cooperative organisation. Unfortunately, when it's necessary for institutions to remain impartial and independent, the existence of such cooperation is equivalent to collusion and minor corruption. Which is one reason why an effective democracy requires top-down regulation to constrain the spontaneous formation of cooperative organisation.

Motegi and the Fukushima radiation

2011-07-16T22:59:00.005+01:00

Leading MotoGP riders have declared their intention not to race in the Japanese Grand Prix at Motegi this October. Their grounds for doing so are fears over the radiation released from the Fukushima nuclear power plant, over 100 miles from Motegi.

Perhaps the MotoGP riders fear that they would be conscripted into helping out at the reactor site, manning the pumps in the on-going effort to circulate cooling water to the reactor cores and spent fuel rods.

It's easy to understand their position: when you spend your working life skimming the tarmac at 140mph on two wheels, running the risk of breaking your neck at any moment and spending the rest of your life in a wheelchair, it's easy to see how a small amount of radiation might scare the bejesus out of you.

One trusts, as well, that none of the MotoGP riders smoke, for tobacco contains polonium-210, the same radioactive substance used to assassinate Alexander Litvinenko in 2006. A person who smokes one and a half packs of cigarettes a day, has been estimated to build-up a radiation dose equivalent to 300 chest x-rays a year. One also hopes that the MotoGP riders travel by boat to remote Grand Prix venues, given that passengers on long-haul air-flights are subject to a dose of radiation from cosmic ray neutrons.

Silverstone and hydrodynamical singularities

2011-07-16T11:24:00.007+01:00

There was plenty of opportunity to watch Formula 1 cars in the wet at Silverstone last week, and it's worth noting that when a car transforms a sheet of water into a spray of droplets, each droplet has been created by a topology-changing process corresponding to a hydrodynamical singularity.

Droplet formation is a liquid version of the fracture of a solid; the continuous medium is broken into disconnected fragments. Up until the point of the singularity, droplet formation is described by a solution of the Navier-Stokes equations for free surface flows. Thus, rather than solving the equations with fixed boundary conditions, such as those provided by a pipe or a wing-surface, one must also specify how the surface of the fluid evolves in time.

Droplet formation leads to a singularity in finite-time, but how the droplet forms, whether it falls from a tap (that's a 'faucet' in the USA), or is flung from the tread of a rotating tyre, is actually irrelevant to the shape of the droplet as the water is broken. As philosopher Robert Batterman points out, the shape of a breaking droplet is largely determined by the ratio of the viscosity of the breaking fluid to the viscosity of the ambient medium.

Water, in fact, is a good deal more complex than many people imagine. Weisberg et al emphasise that "water's microstructure cannot simply be described as a collection of individual molecules...There is a continual dissociation H2O molecules into hydrogen and hydroxide ions, and a continual recombination of those ions back to H2O molecules. At the same time, the H2O molecules associate into larger polymeric species."

Philosophically speaking, this has implications for understanding the relationship between microscopic and macroscopic structure. As James Ladyman argues, "Metaphysicians expect the bridges between the ontologies of the different sciences to be synchronic but they are usually diachronic. So, for example, it is the dynamics of how hydrogen bonds form, disband, and reform that gives rise to the wateriness of water and not the mere aggregation of hydrogen and oxygen in a ratio of two to one," (Many Worlds? OUP 2010, p158).

Conclusions from Silverstone

2011-07-12T17:32:00.021+01:00

As a stage on which to perform, Silverstone is very much Broadway to the Red Bull School of Performing Arts. Here, the aerodynamic superiority of Adrian Newey's design can be exploited to greatest effect.

Thus, having qualified 0.8s faster than third-placed Fernando Alonso in 2010, a gap of merely 0.1s on Saturday evening this year was clearly a matter of concern to the team from Milton Keynes. And, once the initial damp conditions had passed in the race, the Ferrari appeared to be both faster, and capable of making its tyres last longer.

It now seems, however, that what took place at the British Grand Prix last weekend was a controlled experiment; a singular chance to assess the relative performance contribution of Off-Throttle-Exhaust-Blown-Diffusers (OFTEBDs) to the different cars on this year's Formula 1 grid. And arguably, there are two principal conclusions which can be drawn:

(i) Red Bull gain a moderate relative performance benefit from OFTEBDs.

(ii) McLaren gain a large relative performance benefit from OFTEBDs.

Now, Silverstone is not the ideal place for such an experiment. In both topography and meteorology, it is something of an outlier, boasting fast, sweeping corners, and afflicted by strong winds. In addition, there were other confounding factors last weekend: the intermittently damp conditions in practice entailed that not all teams would have achieved their optimal dry-weather set-ups, and Ferrari had a number of rear-end modifications which they claim would have provided a significant performance boost even without the OFTEBD ban.

Mark Hughes puts forward the case for accepting Ferrari's argument, but whilst the Italian team might well have closed the gap to Red Bull on most types of circuit, it would be remarkable if a few modifications around the rear could have brought Ferrari to Red Bull parity on a circuit such as Silverstone.

Elsewhere, the benthic activities of the News of the World dominated the non-motorsport headlines, and the redoubtable Tony Dodgins bravely re-examines the issue of Max Mosley's NotW exposé. Tony suggests that the NotW's phone-hacking habits may offer a better explanation for how they happened upon the story than any far-fetched MI5 link, although NotW editor Andy Coulson resigned in January 2007, and such activities had supposedly ceased by the time of Mosley's 2008 misfortune.

Incidentally, author Will Self suggested on BBC's Newsnight last week that the phone-hacking scandal is merely an epiphenomenon of the transition from print to electronic media. Self is presumably implying here that the NotW only developed their phone-hacking strategy as a response to falling sales, a supposition which is difficult to test.

Irrespective of the root cause, there may be consequences of this scandal for Formula 1. If Rupert Murdoch is now impelled to switch attention from the already dwindling print media component of his business to other broadcast interests, then this may increase the probability of Formula 1 being owned by News Corporation in the near future. All parties concerned were at pains earlier this year to emphasise that they only have the best interests of the sport and its fans at heart.

After being owned for some years now by CVC private equity, it seems that Formula 1 just can't help attracting modern-day Victorian philanthropists.

McLaren's Silverstone woes

2011-07-09T16:53:00.008+01:00

"Really?" said Jenson Button yesterday, quizzical eyebrow raised, when someone said Martin Whitmarsh had predicted that the new conventional-exhaust/revised-underbody combination fitted for Melbourne would find the McLaren 1s per lap.

"I didn't know he'd said that. I'm impressed with his optimistic spirit and I would love that to be true. Let's see." He sounded unconvinced. (Mark Hughes's Friday Form Guide, March 25th 2011)

"The gap is massive. One and a half seconds is just massive. That's all I have to say, really." (Jenson Button, July 9th 2011)

For one race at least, off-throttle blowing of the diffuser has been virtually eliminated from Formula 1, and the big loser is clearly McLaren, with Jenson Button and Lewis Hamilton 1.5s and 2.0s, respectively, off the pace of the Red Bulls in qualifying. This compares to a qualifying deficit of only 0.4s at the previous race in Valencia.

It's interesting that McLaren should be particularly disadvantaged, and the explanation for this can probably be traced to the failure of their radical, 'octopus' exhaust system in winter testing.

Barely a week before the first race in Melbourne, McLaren decided to abandon this system, and simply blow the exhaust between the rear wheels and the upper-outer surface of the diffuser. It isn't an exact copy of the Red Bull design, given that Red Bull blow their exhausts underneath the extremities of the diffuser, but it is nevertheless a close cousin of the Red Bull design. And perhaps by a fluke of fortune, this stop-gap solution seemed to integrate nicely with McLaren's overall airflow concept, elevating them to Red Bull's closest competitor over the first half of the season.

Back in Melbourne, Martin Whitmarsh estimated that McLaren had gained a second from their improvised exhaust system. Bereft of their exhaust-blown diffuser at Silverstone, McLaren now find that they've lost a second. Red Bull will also have lost a chunk of lap-time, of course, but in the chilly conditions of Silverstone, it's possible the McLarens were so deprived of rear downforce that they were unable to get the rear tyres 'switched on'. For McLaren, it's possible that the exhaust-blown diffuser was an aerodynamic tourniquet, without which they are simply bleeding downforce.

Blake's Seven and the symmetry of spaceships

2011-07-08T17:32:00.012+01:00

What do most spaceships have in common with most animals and racing cars? That's right, they possess approximate mirror symmetry.

If you think of classic spaceships, like the X-Wing Fighter from Star Wars, the Enterprise in Star Trek, the Eagle in Space 1999, or even NASA's Space Shuttle, they all exhibit bilateral mirror symmetry: slice the ship in half down a longitudinal plane, and the portion on the left side will be a mirror image of the portion on the right side.

There are several exceptions from modern science-fiction, but the classic era of spaceship design features one prominent anomaly: the Liberator from Blake's Seven.

This craft is noteworthy for two principal reasons. Firstly, it features an (approximate) discrete threefold symmetry around its longitudinal axis. It therefore has no dorsal or ventral side, unlike most spaceships, animals and racing cars. Hence, there is no sense in which the Liberator is ever prostrate or supine. But secondly, its central design theme is essentially a dome and minaret structure.

Thus, aesthetically speaking, the Liberator is the first ever mosque in space.

Abu Dhabi's big mistake

2011-07-04T17:57:00.006+01:00

If last week's European Grand Prix at Valencia demonstrated one principal, salutary lesson, it is that this year's regulations will not generate exciting races at venues already fundamentally inimical to overtaking.

It is enormously disappointing, therefore, to learn that the Abu Dhabi organisers will not be making alterations to their track for this year's race. Chief Executive Richard Cregan argued:

"With all the changes implemented by the FIA, the racing so far this year has been full of overtaking and excitement. So we decided, rather than spend a whole lot of money making these changes, we'll wait and see how [this year] goes first."

Of all the countries hosting Grands Prix on the 2011 Formula 1 calendar, the one capable of building a circuit around a phosphorescent hotel, which looks like it has only just emerged from the Mariana Trench, surely has the wherewithal to make changes to the actual track layout. When you run the risk of yet another dreary race, and you have such deep pockets, why not take the opportunity to improve the circuit anyway?

Three-Mile Island, Chernobyl and Fukushima

2011-07-03T06:57:00.007+01:00

"The world's first commercial nuclear power station opened in the UK in 1956 at the Sellafield site on the Cumbrian coast, and it ran for almost half a century before closing in 2003. The four Calder Hall reactors were of the Magnox type, which means they used a magnesium 'no-oxidation' alloy to encase the uranium fuel rods.

"France initially followed the UK's lead by building reactors similar to the Magnox design during the 1960s. Meanwhile, the US realized that the most economical reactors are those that are collectively referred to as light-water reactors (LWRs).

"LWRs use ordinary water as a moderator and as a coolant, running on uranium-oxide fuel enriched with up to 5% uranium-235 and contained in a zirconium alloy cladding." (Physics World, July 2007).

"The core temperature rose to the point at which the zirconium alloy cladding began to react with steam to produce hydrogen, some of which escaped into the reactor building. Early in the afternoon of the first day, sufficient hydrogen had accumulated in the reactor building to result in a low-level explosion." (Environmental Radioactivity, Eisenbud, p370-371).

Three Mile Island, March 1979.

"Two explosions occurred at 01:24. The steam released by the failure of one or more pressurized tubes had reacted exothermally with the zirconium, producing hydrogen that exploded. Parts of the core were scattered about the building as well as on the roofs of the reactor, turbine, and auxiliary buildings." (ibid, p378).

Chernobyl, April 1986.

"The cladding, which is just the outside of the tube, at a high enough temperature interacts with the water. It's essentially a high-speed rusting, where the zirconium becomes zirconium oxide and the hydrogen is set free. And hydrogen at the right concentration in an atmosphere is either flammable or explosive.

"Hydrogen combustion would not occur necessarily in the containment building, which is inert—it doesn't have any oxygen—but they have had to vent the containment, because this pressure is building up from all this steam. And so the hydrogen is being vented with the steam and it's entering some area, some building, where there is oxygen, and that's where the explosion took place."

Fukushima, March 2011.

Air Curtains

2011-06-25T09:47:00.008+01:00

The July edition of RaceTech Magazine has an excellent, and timely article by Pat Symonds on the subject of exhaust-blown diffusers (EBDs).

Pat points out that, whilst the purpose of EBDs in 2010 was to increase the volumetric flow-rate of the diffuser, the primary purpose of 2011 EBDs, restricted by regulation to the outer extremities, is to create a curtain of air that inhibits the ingress of turbulence from the vicinity of the rear-wheels.

Symonds explains that the effectiveness of an air curtain is determined by its momentum flow-rate, which in the case of an exhaust flow jetting into the ambient flow of the car, is proportional to the exhaust velocity divided by the car velocity.

(Incidentally, in terms of naturally-occurring air curtains, a good example might be the Antarctic circumpolar vortex, which concentrates ozone-depleted air over the South polar region, and drives ocean currents which prevent warm water from mid-latitudes mixing with the cold polar waters).

On the subject of hot-blown diffusers, Pat argues that hot-blowing on the over-run is difficult to achieve by retarding the ignition spark, hence hot-blowing may actually be most effective when the temperature of the exhaust alone is used to ignite a lean air-fuel mixture.

Intriguingly, Red Bull remain the only team to blow their exhausts under the outer section of the diffuser. If one were to hazard a guess at why they do this, the explanation may revolve around the pair of counter-rotating vortices generated by the outboard edges of the diffuser. These are reputedly responsible for keeping the airflow attached to the suction surface of the diffuser under conditions at which the airflow would otherwise separate. By blowing beneath the foot plate of the diffuser, could Red Bull perhaps be using their exhaust flow to enhance this effect?

Water-blown diffusers

2011-06-24T11:13:00.012+01:00

Exhaust-blown diffusers are to be eradicated from Formula 1, with off-throttle blowing banned from the British Grand Prix in a couple of weeks' time, and a reversion to periscope-style exhaust outlets required in 2012.

Is there, however, another means of achieving some vestige of the same effect? Well, those who prefer vertical bathing might be aware of something dubbed the 'shower curtain effect'. This is the tendency of a flexible curtain to be tugged inward by the downward spray of water ejected from a shower-head. One theory holds that the falling water drags the surrounding air down with it, and this airflow creates low pressure within the shower cubicle, pulling the curtain inwards; another theory argues that the spray creates a vortex, and it is the low pressure within the centre of the vortex which explains the inward force acting on the curtain.

So, can this effect be used to any advantage in Formula 1? Well, how about using the cooling circuit pump for the sidepod water radiators to spray water into the outer part of the diffuser, the same area into which the exhaust flow is currently directed? One could reasonably argue that the primary purpose of the pump is to cool the water circulating around the engine, and any aerodynamic effect is merely a by-product.

One would quickly run out of water, of course, and it would be difficult to justify the weight of an extra water tank capable of blowing the diffuser over a race distance, so perhaps this is an idea for qualifying use only. However, consider Grands Prix such as Malaysia and Singapore, where Formula 1 races in humid environmental conditions. How about incorporating a condenser into the sidepods, which takes the ambient water vapour, condenses it, and then sprays it into a duct at the outer edge of the sidepods?

When you do the sums, of course, the benefit of spraying water into the diffuser airflow might well be negligible, and one might also query how long such a concept might survive before being banned. It's just a thought, though...

Photosynthesis and plutonium

2011-06-22T17:31:00.011+01:00

Nuclear reactors are naturally-occurring phenomena. Not only that, but ancient bacteria can be held responsible for the production of at least two tonnes of plutonium.

How so? Well, two billion years ago, a pair of separate evolutionary processes combined, for a geologically short period of time, to produce a remarkable phenomenon.

For several aeons, the Earth's atmosphere was unable to sustain the presence of free oxygen. This only changed two billion years ago, when photosynthesizing bacteria evolved. Such bacteria synthesize organic molecules from carbon dioxide, water, and photons of sunlight. And, as a by-product, they generate oxygen. Hence, when these lifeforms evolved, for the first time in the history of the Earth free oxygen accumulated in the atmosphere.

That's one half of this story, to which we'll return later. The other half concerns the evolving balance between the naturally occurring isotopes of uranium. Most natural uranium is U-238, a non-fissile isotope. A small fraction, however, consists of the fissile isotope U-235. Uranium-235 has a shorter half-life than uranium-238, hence the fraction of U-235 has been decreasing since the formation of the Earth. Two billion years ago, the natural abundance of uranium-235 reached 3%. Today, the natural abundance of U-235 has dropped to only 0.7%.

Now, nuclear reactors require a moderator to sustain a fissile chain reaction. In a uranium-fuelled reactor, this is because a U-235 nuclei is most likely to fission when it absorbs a low-energy neutron. Such neutrons are termed thermal neutrons, and possess energy levels of less than 1 electron-volt (eV). When a U-235 nucleus fissions, it releases other neutrons, but these neutrons have a mean energy of around 1 MeV (Mega electron-volt). Such neutrons are more likely to be absorbed by U-238 nuclei than they are to cause other U-235 nuclei to fission. Hence the necessity for moderators.

Moderators are materials made from light nuclei, which are likely to deprive fission neutrons of their energy in so-called elastic scattering reactions. Such reactions reduce fission neutrons to the thermal energies which will trigger further fission in U-235 nuclei.

Anthropogenic nuclear reactors employ a variety of moderators, but the most popular choice is water. Such reactors require U-235 levels of between 3-5%. On the surface of a planet which is 4.5 billion years old, this requires uranium-235 to be enriched from its naturally occurring preponderance. Two billion years ago, however, the natural abundance of U-235 was just right. Thus, to trigger a self-sustaining nuclear reactor on the surface of the Earth, all it needed was some geological means of concentrating uranium minerals in porous groundrock.

Which is where our photosynthesizing bacteria come in. Groundwater flow is capable of dissolving, transporting, and then depositing materials in concentrated zones. Uranium, however, is insoluble in anoxic water, and was therefore initially immune to this method of re-distribution. Until, that is, the evolution of photosynthetic bacteria generated free atmospheric oxygen, which in turn, produced oxygenated water, in which uranium is soluble.

Two billion years ago, in what is now the Gabon, Africa, groundwater flows containing dissolved uranium from nearby igneous deposits, met a zone of petroleum. The petroleum de-oxygenated the water, and the uranium precipitated out of solution. At least 16 separate naturally occurring reactors went critical for a period of around 100,000 years, producing heat, highly radioactive fission products, and approximately two tonnes of plutonium. These are the Oklo nuclear reactors.

The plutonium has subsequently decayed away, but the distinctive isotopic fingerprint of those fission products is still detectable. Moreover, this high-level nuclear waste appears to have been successfully sequestered underground for billions of years...

Hairpin vortices and other turbulent phenomena

2011-06-18T18:40:00.007+01:00

Living and dying within the turbulent boundary layers and wakes of every Formula 1 car, is a taxonomical cornucopia of transient hydrodynamical beasties. The ecology of these lifeforms is determined by the exact geometry and Reynolds number of the flow regime in question, but it is still possible to identify some general phenomena.

First recall that turbulence can be defined as the existence of chaotic vorticity over a range of different length and time scales, the vorticity on larger length scales cascading down to smaller length scales, where it is dissipated as heat. Now, vorticity can be packaged in the form of sheets and tubes, and these structures are subject to the following two general processes, (see Turbulence, P.A.Davidson, CUP 2004, pp206-210):

(i) Vortex tubes tend to stretch, and upon stretching, they 'burst' into vortex sheets.

(ii) Vortex sheets rolls up under Kelvin-Helmholtz instability into sequences of vortex tubes, (as seen in the diagram just above here).

As a result of these processes, the vorticity in a fluid is extruded into increasingly thinner sheets and tubes, until eventually it reaches the length scales at which viscous effects dominate, and the turbulent energy is dissipated into heat.

In a turbulent boundary layer, however, are special types of coherent structures dubbed hairpin vortices.

P.A.Davidson's explanation for the generation of these hydrodynamical parasites, (ibid., p141-142), begins by assuming the existence of spanwise vortex lines in the boundary layer. A turbulent streamwise fluctuation in the velocity field distorts such vortex lines, creating perturbed segments which resemble sections of a vortex ring. Vorticity generates its own velocity field, and the curvature in the perturbed vortex tube causes the tip of the tube to rise upwards. The higher the tip of the vortex rises in the boundary layer, the higher the mean streamwise velocity, with the consequence that the vortex tube gets stretched even further in a streamwise direction. This is a positive feedback process, causing the tip of the vortex to rise yet higher.

Elsewhere, in those parts of the turbulent wakes which can be idealised as regions of isotropic turbulence, the smallest vortices (so-called 'worms') can be idealised as Burgers vortices. A Burgers vortex is an exact solution of the Navier-Stokes equations, in which the vorticity has a constant Gaussian distribution around a particular axis. The constancy arises because the outward diffusion of vorticity perpendicular to the axis, is exactly balanced by the stretching of the fluid flow parallel to the axis.

Over the coming decades, complete solutions of the Navier-Stokes equations, so-called Direct Numerical Simulations (DNS), will steadily unveil these complex ecologies. To gain a feel for this hidden complexity, take a look at the DNS study conducted by Sandham et al (2001) of a trailing edge flow at a Reynolds number of ~ 1000.

Now, at this Reynolds number, the wake turbulence contained a Karman vortex street; i.e, staggered rows of counter-rotating spanwise vortices. What Sandham et al found was that the spanwise Karman vortex street interacts in a complex manner with the streamwise vortex tubes generated in the turbulent boundary layer upstream of the trailing edge. In fact, the streamwise vortex tubes strain, intensify, and eventually destroy the Karman vortices.

The flow regime of a Formula One car has a Reynolds number of ~ 10⁶, which is just about the upper limit for any sort of vortex street pattern to be distinguishable from random turbulence, so it's unlikely that this research is directly relevant to Formula 1. It is, however, an interesting taste of the hydrodynamical complexity yet to be revealed.

Lewis Hamilton's Canadian Grand Prix

2011-06-14T17:34:00.014+01:00

"Hamilton is almost certainly the fastest driver in F1...But then why is that not being translated into results? The answer, like reality, is complex and multi-dimensional. But it's as if Lewis feels he has not got time for that. And every time that frustration butts up against reality, it's tending to find something solid.

"The world at the moment isn't as Lewis would want it. He would like the showbiz rapper and celebrity athlete friends that came to be with him in Montreal to have seen him demonstrate his dazzling skills to leave the rest of the field dazed and confused. He had a show to put on and those other lesser drivers just got in the way." (Mark Hughes).

Some racing drivers tend towards a Heraclitean approach to the nature of time, accepting the flow of time, and the consequent importance of planning; others favour a more Parmenidean outlook, rejecting the existence of the future, living for the moment. Lewis Hamilton is clearly a Parmenidean racing driver. Unfortunately, just for the moment, he is also beginning to make Juan-Pablo Montoya look like a paragon of calm discretion.

When the Canadian Grand Prix was green-flagged at the beginning of lap 5, Lewis made a move inside Mark Webber at the first corner. Mark tried to give him room, and Lewis took a slice of the inner kerb in avoidance, but the right-front of the McLaren made contact with the left-rear of the Red Bull, tipping the unfortunate Australian into a spin, like a felon being pursued by the LAPD.

Hamilton rejoined, having lost places to Rosberg, Button and Schumacher. Almost immediately, however, Jenson went too deep into turn 6, Schumacher passing him around the outside of turn 7, Hamilton taking him down the inside onto the following straight. Into the hairpin of turn 10, Hamilton was already challenging Schumacher, the Mercedes defending the inside line as Lewis tried an unsuccessful run around the outside.

Onto lap 6, it was Rosberg in fourth, several car lengths ahead of Schumacher in fifth, Hamilton sixth, and Button now taking a familiar watching brief in seventh. On this particular lap, Jenson took a line down the pit-straight which bisected the middle of the track, far more than a car's width available to his left-hand side...

Going into the turn 10 hairpin on lap 6, Schumacher once again went to defend the inside line, and Hamilton duly tried another run down the outside. On this occasion, however, Schumacher veered across towards the McLaren under braking, and Lewis had to take avoiding action, running very wide, letting Button ahead of him once more.

At the end of lap 7, Button outbraked himself into the final corner, and Hamilton was perfectly placed to overtake accelerating onto the pit-straight. At the point that Lewis was in Jenson's wheeltracks, about to pull out from the slipstream, Button could be seen glancing in his mirror. Jenson then moved across towards the pit-wall, as per the racing line in dry conditions, at exactly the same moment that Lewis was drawing alongside his rear wheels. Button kept moving over, but Lewis kept coming, and in an instant the front-right of Lewis's car snagged the left-rear of Jenson's, sending Hamilton into the pitwall at a shallow angle, and inflicting terminal damage to the left rear.

So, does this constitute some sort of crisis in Lewis's career? To some degree, Hamilton's current malaise is merely a consequence of the particular circumstances in which he's found himself in Monaco and Canada this year, endowed with arguably the fastest car in race-trim, but relegated to a poor starting position by team errors. There is, however, also a longer-term trend in his driving tactics which can be traced back to the middle of 2010. Over this period of time, Lewis has developed a habit of sticking the nose of his car down the inside of other drivers, without getting fully alongside and winning the corner.

Lewis actually did this to Alonso last year at the turn 10 hairpin in Canada, when Fernando was momentarily boxed in behind Sebastien Buemi. Alonso saw him, gave him room, and Lewis made the move stick down the following straight. A couple of weeks later, Lewis stuck his nose inside Vettel at the first corner in Valencia, both drivers being fortunate to avoid damage as Lewis's left-front wheel snagged Sebastien's right-rear. Then, at the first corner of the British Grand Prix, Lewis did exactly the same thing, this time puncturing Vettel's tyre, but avoiding damage himself. It was only at Monza that this speculative overtaking tactic finally backfired, Lewis retiring after sticking his front-wheels inside Massa at the second chicane.

Which brings us to Monaco and Canada 2011. The collisions with Massa, Maldonado and Webber at these events all shared a common trait: Lewis took at stab down the inside, failed to get fully alongside, the other driver turned in, Lewis clambered over the inside kerb to avoid contact, and a collision occurred.

There's nothing wrong with being a warrior, and living for the moment, but this type of speculative overtaking attempt seems increasingly to be borne of frustration. If Lewis is to avoid a career in NASCAR, he either needs to take a step back, or to take a step from Woking to Milton Keynes.

Fangio, Pirelli and the Nurburgring

2011-06-10T21:15:00.010+01:00

August 4th, 1957. The Nurburgring. Lap 21 of the 22-lap German Grand Prix. At the age of 46, Juan Manuel Fangio is driving the race of his life, overcoming a 51-second deficit to catch the leading Ferraris of Mike Hawthorn and Peter Collins.

The sun close to the zenith, the heat soaking into the tarmac, Hawthorn leads, but Fangio's Maserati 250F is into second, with Collins third, fighting a hint of understeer. The cars skim past stunted silhouettes of photographers in the tall grass; tourists on safari in motorsport's Serengeti, mesmerised by the hunting patterns of the wild beasts, deluded into thinking they could never become the prey.

Look closely: are those tyre marbles off the racing line in the foreground? Everyone knows that Fangio was fighting back from a botched pitstop, but it's rarely explained why he had to make a pit-stop in the first place. The Ferraris, after all, didn't feel the need to pit.

And here, in the divergent strategies of Ferrari and Maserati at the Nurburgring in 1957, we find a remarkable past echo of 2011's tyre-wear dominated strategy-scape. Fangio explains it perfectly himself:

"We had Pirelli tires; they were a bit soft and fitted our suspension very well but, if their grip was good, they also wore faster, particularly the rear tires. That meant we were going to have a pit stop at mid-race to change tires. The Ferraris were on Engleberts, which were harder than our Pirellis and gave the drivers a rougher ride, but we were sure they would go through the race without changing. We could bet they'd start out with the fuel tanks full and try to go through nonstop.

"All this gave us a lot to think about, and finally we worked out a plan that was rather simple but seemed effective. We were going to have to change tires anyway, so we decided to start with the fuel tank half full, grab the lead and try to build up as much lead as possible before pitting. Then another half tank for the second part of the race, so we'd be driving a light, nimble car, the tires would wear less and we wouldn't have to worry about a second pit stop, which surely would be disastrous."

The inspiration behind Ferrari's riblets?

2011-06-06T19:31:00.005+01:00

Ferrari reportedly used riblets on the undersurface of their front-wing at the Turkish Grand Prix last month. At the time, Autosport's Gary Anderson claimed that the intention was to "reduce the airflow-separation problems and make the wing work more consistently."

Coincidentally, in late 2009 a group of researchers from the University of Southampton published a paper in the Journal of Fluids Engineering, entitled Flow Separation Control on a Race Car Wing With Vortex Generators in Ground Effect. This paper contained the results of an empirical investigation into "flow separation control using vortex generators on an inverted wing in ground effect." In particular, the authors claim that:

"The counter-rotating sub-boundary layer vortex generators and counter-rotating large-scale vortex generators on the wing deliver 23% and 10% improvements in the maximum downforce, respectively, compared with the clean wing, at an incidence of one degree, and delay the onset of the downforce reduction phenomenon. The counter-rotating sub-boundary layer vortex generators exhibit up to 26% improvement in downforce and 10% improvement in aerodynamic efficiency at low ride heights. Chordwise pressure measurement confirms that both counter-rotating vortex generator configurations suppress flow separation...This work shows that a use of vortex generators, notably of the counter-rotating sub-boundary layer vortex generator type, can be effective at controlling flow separation, with a resultant improvement in downforce for relatively low drag penalty."

Note that Ferrari only appeared to employ their riblets on the undersurface of the front-wing, rather than the undersurface of the rear wing. This is consistent with the Southampton University study, which specifically involved the control of airflow separation under ground effect conditions.

Quantum mechanics and consciousness

2011-06-03T18:20:00.009+01:00

The Stanford Online Encyclopedia of Philosophy has a substantially revised version of its entry on Quantum Approaches to Consciousness, and it's a pretty decent introduction to the subject.

The author, Harald Atmanspacher, begins by pointing out that because correlation doesn't entail causation, the correlation between particular mental experiences and particular areas of brain activity (as revealed in magnetic resonance imagery, for example), doesn't entail that brain activity causes those mental experiences.

This observation provides the point-of-entry for so-called dual aspect theories of the mind-brain relationship, which suggest that the mind and the brain are two different aspects of some underlying, unified reality, in contrast to the notion that the mind can be reduced to the brain. One analogy often used in this context is the relationship between electricity and magnetism: these two phenomena are merely different aspects of a unified entity, the electromagnetic field, and although there are very strong correlations between electricity and magnetism, the existence of those correlations does not entail that electricity can be reduced to magnetism or vice versa.

David Bohm's account of the mind-matter relationship, for example, falls into the category of dual aspect theories, claiming as it does the existence of an 'implicate order which unfolds into the different explicate domains of the mental and the material'.

The basic idea of these dual aspect theories is a good one, but those who espouse such approaches need to appreciate that the relationship between the mind and the brain is not one characterised merely by correlations. Rather, there is a much stronger coarse-graining relationship, in which mental states correspond to entire classes of brain states. If a brain-state is altered on a nanoscopic level, it doesn't change the corresponding mental state; each mental state corresponds to an entire class of nanoscopically distinct brain-states. It is this coarse-graining relationship which entails that the mind supervenes upon the brain, and not vice-versa. Arguably, it is precisely this asymmetry which suggests that the mind reduces to, or emerges from the brain, rather than the mind and the brain being related by a duality transformation.

Nevertheless, let's try to imagine how a dual-aspect theory of the mind-brain relationship might work. For a start, we'd need to characterise both the mind and the brain in formal terms, just as we do with electicity and magnetism. We might, for example, characterise the brain as a neural network, an abstraction from the network of nerve cells and synapses in a biological brain. A formal theory of the mind doesn't exist as yet, but the best nascent candidate is perhaps the Representational Theory of the Mind (RTM). So let's just briefly describe these two theories.

A neural network consists of a set of nodes, and a set of connections between the nodes. The nodes in a neural network possess activation levels, the connections between nodes possess weights, and the nodes have numerical rules for calculating their next activation level from (i) the previous activation level, and (ii) the weighted inputs from other nodes.

The RTM, meanwhile, attempts to provide an account of intentional mental states. These are states, such as beliefs and desires, in which the attention of the mind is directed towards something, called the 'content' of the intentional state. Many advocates of the RTM claim that the mental representations which provide the content of intentional states, possess an internal structure. They hold that this internal system of representation has a set of symbols, a syntax, and a semantics, collectively termed the language of thought. There are rules for composing the symbols into expressions, propositions, and mental images, hence the content of an intentional state can be said to possess a symbol structure. The RTM considers mental processes such as thinking, reasoning and imagining to be sequences of intentional mental states.

A dual aspect theory of the mind-brain relationship would need to find an underlying structure which incorporates both the structure of neural networks and the structure described by the RTM, and relates the two by a duality transformation.

Neural networks, of course, are part of classical physics, so whether quantum theory is actually relevant to the mind-brain relationship is another matter entirely...

Overtaking at Loews

2011-06-01T17:40:00.007+01:00

A difficult qualifying session had consigned him to a lowly grid position; surely, at Monaco, it would be difficult to make much progress from there?

Throwing caution to the wind, then, he took a stab down the inside of the Ferrari driver into the Loews hairpin. The move was never really on, and as the Ferrari turned-in, the two cars momentarily locked wheels. As luck would have it, however, it was the Ferrari which would came out worst, and he was through!

That, of course, was Olivier Panis, overtaking Eddie Irvine en route to victory in the 1996 Monaco Grand Prix. But the stewards were rather more laissez-faire in those days, before the scales of justice were to be hung in judgement over every (televised) collision.

Coulthard takes a dip

2011-05-30T16:56:00.006+01:00

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

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

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

Lewis Hamilton's Monaco Grand Prix

2011-05-30T10:58:00.020+01:00

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Anti-climax at Monaco

2011-05-29T17:00:00.016+01:00

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

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

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

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

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

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

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

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

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

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

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

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

Exhaust-blown diffusers and the Brabham fan-car

2011-05-27T17:42:00.006+01:00

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

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

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

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

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

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

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

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

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

Such patterns give Formula One its characteristic temporal texture.

Lotus-Renault opt for a flexi-wing

2011-05-26T16:32:00.004+01:00

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

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

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

The aerodynamics of buildings

2011-05-25T19:52:00.014+01:00

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

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

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

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

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

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

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

The legality of exhaust-blown diffusers

2011-05-23T17:57:00.014+01:00

Water and fire have conspired in recent weeks to vividly reveal the airflow regime created by Renault's front-exit exhaust system.

In the waterlogged conditions of Friday practice at Istanbul, staccato spasms of spray could be seen shooting diagonally under the outer front corner of the sidepods, as the Renault drivers came off the throttle and swept into turn 12. And on Saturday morning in Spain, the unfortunate Nick Heidfeld alighted from a Renault which was not only ablaze around its hind quarters, but had also quickly sprouted a yellow-orange jet of flame under the outer front corner of the 'pod.

Having invested so much in this technology, Renault were considerably peeved to receive a letter from the FIA's Charlie Whiting on Thursday May 12th, which informed them that use of exhaust-blown diffusers (EBDs) on the over-run, would henceforth be severely restricted.

This mid-season re-interpretation of the regulations has now been postponed, pending discussion at the next meeting of the Technical Working Group on June 16th, yet it remains a matter open to protest in the interim. So what's going on?

Let's start with Article 3.15 of Formula One's Technical Regulations, which dictates that any part of the car which influences its aerodynamic performance, must remain immobile in relation to the sprung part of the car. Exhaust-blown diffusers use the flow of burnt gases from the engine to influence the aerodynamic performance of the car. In effect, the flow of gas created by the exhaust stroke of the reciprocating pistons, influences the downforce at the rear of the car. The pistons, in turn, are attached to a rotating crankshaft. Neither the pistons nor the crankshaft are immobile in relation to the sprung part of the car. Hence, by connecting the exhaust stroke of a reciprocating engine to the aerodynamic performance of the car, exhaust-blown diffusers render pistons and crankshafts as illegal devices.

This is true whether the exhaust flow is under the control of the driver's throttle, or whether it is created by retarding the ignition on the over-run when the driver is off the throttle.

All this was true when exhaust-blown diffusers were introduced into Formula One in 1983. It was true throughout last season, when Red Bull re-introduced EBDs to such fine effect. And it was true this year, up until Cosworth-powered Williams Grand Prix Engineering submitted a request-for-clarification to the FIA, and Charlie Whiting wrote to the teams to inform them that the use of EBDs on the over-run was illegal.

So why now, and why just on the over-run? Whiting tried to justify his judgement over the Spanish Grand Prix weekend with the following argument:

"An exhaust system is there for the purpose of exhausting gases from the engine, so when you are off throttle it is not doing that. Therefore driver movement is being used to influence the aerodynamic characteristics of the car."

Following the invention of the F-duct in 2010, driver-influenced or activated aerodynamics are now explicitly banned (DRS excepted). But if Charlie feels that EBDs constitute driver-activated aerodynamics, then why is he seeking to limit the off-throttle function of the EBDs? That’s the one part of the EBD function which is not driver-activated. Simply banning or limiting the function of the EBDs on the over-run is not a coherent course of action.

On the question of timing, Whiting argued that things have simply reached a tipping point, with ever more extreme solutions already in the pipeline. But if, as Charlie claims, "Red Bull really took it to another plane with their low exhaust at the beginning of last year," why was no action taken over the Winter?

Some have speculated that this is a move designed to reduce Red Bull's advantage, when they're in danger of running away with the championship. Well, perhaps. But it wasn't one of Red Bull rivals that complained; they've all developed their own EBDs. No, it was Cosworth-powered Williams that requested a clarification of the regulations.

So why don't Cosworth just develop their own version of the technology? As Renault team principal Eric Boullier pointed out, "it doesn't cost a lot of money to do it, it is just mapping of the engine."

Perhaps the answer lies in the fact that FIA president Jean Todt met with representatives of Formula One's engine manufacturers on Saturday to discuss progress towards the turbocharged 1.6-litre engine, planned for 2013. Cosworth, it seems, are opposed to this new formula on financial grounds. "Costs remain an issue and regulations as currently drafted do leave a number of options to spend a great deal of money," stated Cosworth's F1 general manager Mark Gallagher.

Addendum. The redoubtable Tony Dodgins adds a crucial extra piece of the jigsaw: Renault are the only manufacturer supporting the proposed 2013 engine regulations. Thus, we have the following facts:

(i) Renault have pioneered and refined the use of EBDs on the over-run.

(ii) The only manufacturer with any enthusiasm for the 2013 engine regulations is Renault.

(iii) A manufacturer with no enthusiasm for the 2013 engine regulations (Cosworth), and with no current capability to use EBDs on the over-run, has challenged the legality of the latter.

Look, but don't stare

2011-05-22T16:31:00.010+01:00

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

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

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

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

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

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

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

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

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

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

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

S = P + 1

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

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

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

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

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

Kermode "gripped" by Senna film

2011-05-20T14:51:00.008+01:00

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

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

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

No Angel - The Ecclestone biography

2011-05-17T17:58:00.010+01:00

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

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

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

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

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

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

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

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

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

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

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

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

Or how about:

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

Ribbed, for your pleasure

2011-05-14T13:44:00.009+01:00

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

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

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

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

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

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

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

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

Formula 1 and complexity

2011-05-11T17:38:00.013+01:00

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

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

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

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

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

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

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

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

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

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

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

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

Schumacher's absence of big joy

2011-05-09T19:19:00.005+01:00

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

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

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

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

Magic paddle latched

2011-05-08T16:12:00.009+01:00

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

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

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

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

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

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

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

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

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

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

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

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

Turkish Grand Prix prospects

2011-05-07T18:58:00.013+01:00

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

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

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

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

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

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

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

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

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

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

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

The Senna film

2011-05-03T22:37:00.004+01:00

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

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

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

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

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

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

The global nature of aerodynamics

2011-05-01T15:08:00.014+01:00

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

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

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

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

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

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

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

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

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

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

A History of Modern Witchcraft: Part 3

2011-04-27T18:25:00.027+01:00

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

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

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

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

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

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

It was then that I knew I had a problem.

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

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

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

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

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

Tiger Woods and quantum theory

2011-04-22T19:01:00.007+01:00

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

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

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

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

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

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

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

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

The Red Bull Owners' Workshop Manual

2011-04-19T22:24:00.011+01:00

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

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

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

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

Hamilton's bolt from the blue

2011-04-17T11:23:00.035+01:00

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Proper racing.

Why did Vettel stay in his car?

2011-04-16T14:58:00.005+01:00

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

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

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

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

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

Sergio Perez and space junk

2011-04-15T19:13:00.010+01:00

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

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

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

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

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

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

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

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

Entering Phase Two

2011-04-10T14:55:00.007+01:00

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

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

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

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

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

To lobby or to imitate?

2011-04-07T23:26:00.020+01:00

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

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

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

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

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

How Red Bull simulate front-wing aeroelasticity

2011-04-02T12:43:00.024+01:00

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

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

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

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

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

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

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

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

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

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

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

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

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

KERS, DRS and Button's short-cut

2011-03-27T15:46:00.022+01:00

At the beginning of 2010, Bernie Ecclestone mischievously suggested that Formula One tracks should incorporate short-cuts. "It would stop people getting stuck behind others and be good for TV," explained Bernie. At the time, Jenson Button didn't seem too keen on the idea, remarking "I suppose if you are the only person who knows about [the shortcut] then it is a great idea...Bernie has a lot of very, very good ideas, and that is not one of the best."

By lap 11 of today's Australian Grand Prix, however, it seemed that Bernie's proposal must somehow have lodged deeply in Jenson's subconscious. After persistent and hitherto unsuccessful attempts to overtake Felipe Massa's obstructive Ferrari, Jenson had got alongside the Brazilian going into the fast switchback of turns 11/12. Taking the outside line into the left-hander, Jenson had the inside for turn 12, but with both cars momentarily heading for the eye-of-the-needle at high speed, Jenson bailed-out via a short-cut, and rejoined ahead of Massa.

At this point, one expected Jenson to immediately cede the place back, for the overtaking move had clearly not been completed on the racetrack. The McLaren driver, however, appeared to be in no mood to slow down and let Felipe re-pass. Perhaps sensing a means of aggravating Jenson's predicament, Massa immediately lifted off en-route to turn 13, defending briefly from Alonso, before ceding the place to his team-mate into turn 14.

The punishment meted out to Alonso for a similar pass on Kubica at Silverstone last year established a clear and recent precedent here, yet McLaren seemed intent on asking race control for an opinion rather than taking the initiative themselves. The short window of opportunity before Massa pitted a couple of laps later was squandered, and Button's race was ruined by the drive-though penalty served upon him.

McLaren team principal Martin Whitmarsh later claimed that he hadn't seen the incident at the time, a statement which reminded one of Mr Alex Ferguson's habitual claim not to have seen a foul committed within the penalty box by one of his own players.

Jenson did, of course, later pass Felipe on the track, and herein lies an interesting detail concerning the joint use of KERS and the newly instigated Drag Reduction System (DRS).

First, we need to go back to the early stages of the race. The DRS system cannot be used in the first couple of laps, but on lap 3 Button and Massa were going at it hammer and tongs, and coming out of the final corner Button duly deployed his DRS. Jenson, however, had already fully discharged his KERS during the course of the lap, and the Ferrari merely triggered its own KERS to cancel-out any potential gain by the McLaren.

At some stage over the next lap or so, Button was heard to enquire over the radio how the Ferrari could be so fast on the straight. It would be interesting to know what information the team fed back to Jenson, for by lap 7 he was saving half of his KERS charge for the exit of the final corner. Jenson was now able to deploy both the DRS and the remaining KERS charge simultaneously, yet still this wasn't sufficient to facilitate an overtaking opportunity.

When Jenson finally overtook Massa starting lap 48, the Ferrari was on worn tyres, about to pit, and this enabled him to stay closer to Felipe through the final corner. In addition, on this occasion Jenson had almost an entire lap's worth of KERS available. The McLaren duly deployed the DRS, and expended the entire KERS charge between the exit of the final corner and the timing beam, at which point a new lap's worth of KERS became available, which Jenson tapped into to complete the manoeuvre.

So, assuming that Massa used his KERS in response, and with the caveat that the DRS zone in Melbourne was perhaps not located in the ideal place, the limited conclusion we can deduce is the following:

KERS + DRS + healthy tyres > KERS + worn tyres

A History of Modern Witchcraft: Part 2

2011-03-26T12:51:00.015Z

I swallowed another clutch of paracetamol, and washed them down with a mouthful of sweet tea. This was the fifth consecutive day I'd developed a piercing head-ache by noon, and now my jaw ached like I'd been involved in a brawl with Jeff Bridges. Idly, I wondered if a brain-tumour the size of a golf-ball might be developing in some lobe or other, flagrantly disregarding my ongoing pension contributions.

Marina was strolling with cat-like insolence around the lab, picking up various pieces of kit, peering intently at their mute exteriors, and replacing them without comment. I watched her out of the corner of my eye, and tried to gauge the size of her bust. Deconvolving the volumetric displacement of a woman's breasts from the bra-dependent contour and uplift was increasingly a black art, and despite the amount of cleavage available as observational evidence, I was forced to conclude that theory was under-determined by data on this occasion.

"Do you not miss the daylight down here, Dr Bones?" asked Marina, staring down the muzzle of an ancient golf-leaf electroscope. She was still using my formal appellation; keeping an emotional distance, then.

"We have interior lighting, Marina. Admittedly, we miss out on some of that bracing UV radiation the Outer-Worlders receive, but this is more than compensated for by the gamma rays."

The lab-door opened, and Dr Burgher strode confidently across the threshold to greet our eminent VIP. "Ah, Miss Petrovium, pleased to meet you," announced Dr Burgher, his sense of brisk self-importance sadly undermined, literally at every step, by his leather shoes squeaking their way across the PVC floor. "I'm the Chief Project Scientist here, as Brod' has no doubt explained to you."

Marina's cobalt-blue eyes sparkled as she met Dr Burgher's outstretched hand. Most women at the base appeared to find Dr Burgher more attractive than a bar magnet in a box of iron filings, and as 'Miss Petrovium' flicked her eyes up and down with studied coyness, I concluded that the IAEA's Head of Paranuclear Phenomena also lacked diplomatic immunity to such attractions.

The analgesics were by now surfing down my capillaries, and things were beginning to feel delightfully fuzzy. As Burgher briefed Marina in the background, I disengaged, and felt that familiar sensation of being in mental free-fall. Inchoate ideas floated past, just out of grasp; I knew there was something I needed to be thinking about, a problem which needed resolving, a question which required an answer, but as soon as I directed my attention to any of the passing notions, they dissolved in a noxious cloud of confusion and receded from conscious awareness.

"...which we're currently unable to explain with any known physics," concluded Dr Burgher with the melodramatic flourish he'd been carefully honing over the past fortnight, ever since we'd discovered the shaft descending from the fifth chamber.

The Book of Universes

2011-03-23T19:02:00.004Z

"Universes are big at the moment." John D.Barrow.

This is a beautifully written, highly accessible account of the theoretical universes defined by modern cosmology. As Barrow comments, cosmology "is not just an exercise in describing our universe as completely and accurately as possible. It seeks to place that description in a wider context of possibilities than the actual."

Barrow takes a chronological approach, explaining the circumstances in which the various universes were proposed, and the nature of the people who devised them. The biographical information is fascinating, and Barrow's explanation of each universe is absolutely crystal-clear. This is popular science of the highest quality.

A History of Modern Witchcraft: Part 1

2011-03-21T17:54:00.020Z

It was in the long, torpid Summer of '06 that I first met Marina, and stumbled upon the discovery which would change everything forever. She stepped off a Venetian gondola in a cherry-pattern dress, clasping her IAEA accreditation in one hand, and holding her hat down with the other, as a cool Adriatic breeze blew her golden tresses across one cheek.

I greeted her with a curt nod and a perfunctory handshake, and escorted her to the waiting limousine, which was purring with satisfaction at its own mechanical harmony.

We sat in silence as the stone facades of green-shuttered apartments scrolled past, the townscape blending into scattered farmhouses and walled orchards, then dwindling into olive trees and scrub as the limo followed a dishevelled road climbing reluctantly into the hills.

Torn between the need to commence conversation with small-talk, but wary of sounding superficial, we sat, bound together in an introspective impasse.

Turning off the mountain road onto a gravel track, she glanced in my direction. "Shouldn't you be blindfolding me at this stage, Dr Bones?"

"Please," I retorted, "call me Broderick. And a blindfold won't be necessary. For the moment at least..."

A couple of miles along the track, we passed through a dense cypress grove, their boughs interlocking to form an arboreal arch, through which we emerged into a steep-sided gorge. A shallow, sparkling river swept along the rocky base of the ravine, the track winding along a narrow ledge beside it.

"You will, however, be needing this," I said, handing her a thermoluminescent dosemeter. "Keep it on you at all times. This facility doesn't officially exist, but we're still compelled by Euratom recommendations to keep a record of the radiation dose to all visitors."

Rounding a tight bend, the gully opened up slightly to reveal a large, perfectly oval pool of limpid water, from which the river channel descended. "What is this, Broderick," enquired my fellow passenger, from whom I was already detecting a distinctly acerbic air, "a geography field trip?"

"Not exactly, Marina. Watch carefully."

Our chauffeur circumnavigated the limb of the pool, and brought the limo to a stop at the end of the track, facing a blank expanse of sheer rock. He flipped a switch on the dashboard, and with a jolt, and a brief flurry of dust, the rock-face began descending with a hydraulic hum into the floor of the canyon.

"It's a good job we're not in the Pacific, Dr Bones, or I'd swear that we've just arrived on Tracy Island. Or perhaps you'll be escorting me into the caldera of an extinct volcano instead?"

"Extinct volcanoes are passé, Marina. Besides, they tend to attract various nosey scientists from the US Geological Survey, which we actively discourage."

The rock-face had by now fully retracted, disclosing a dark tunnel hewn into the naked granite. Our chauffeur switched his lights on full beam, revealing two lines of reflective studs, converging to a point in the subterranean distance. With only the briefest of pauses, we plunged at full pelt into the darkness.

To be continued...

Motorsport Magazine subscription

2011-03-19T18:37:00.027Z

There are many things the internet can do. It provides, for example, an unprecedented array of specialised, up-to-the-minute information and opinion for the curious mind. In terms of immediate access to timely information, the motorsport enthusiast has never been better served.

There are, however, things which the internet has yet to do. It rarely, for example, provides a coherent explanation and interpretation of events stretching over a period of time; it rarely tells a good story, or puts events into context. In contrast, all these things have traditionally been done by printed periodicals. So, motorsport magazines should have nothing to fear from the internet, right? As long as such magazines concentrate on the things they do best, there shouldn't be a problem.

And yet, over the past decade, many motorsport periodicals seem to have done the very opposite, and wilfully made themselves look more like the internet. Word counts have plummeted, and news stories have descended into fragments, snippets, and sidebars. There is now no magazine which provides the motorsport enthusiast with the quality of information provided by Motoring News in the 1980s and early 1990s, and F1 Racing Magazine, in particular, appears to be targeted at those with a single-digit mental age.

This seems almost like a form of business suicide, for why would anyone pay for a magazine which simply provides a less up-to-date, and sometimes inferior version of the information one can get for free on the internet?

One also gets the feeling that many modern journalists consider it unnecessary to describe, in words, events which the reader will already have seen replayed, ad nauseam, on television. This is an enormous mistake, for part of the art and craft of a great writer or journalist is to re-cast known events in an original light, evoking humour or poignancy, drawing attention to subtle details and hidden patterns.

There are, however, some surviving outposts of quality: Autosport's Mark Hughes continues to be beacon from the world of Motoring News journalistic values, and the monthly publication Motorsport Magazine, provides the type of story-telling capability which has evaporated from other periodicals. Thus it was that I recently took out a subscription to Motorsport Magazine.

Indycar designer Ben Bowlby comments that the February issue of the magazine was "stunning. There was so much good content I read it for about seven hours straight." In fact, I almost had the same experience when I received the April issue last weekend.

I am, of course, desperately simplifying the issues here, for ultimately even magazines will have to seek an electronic means of distribution, and this will not be without difficulty, given the expectation that information content on the internet should be free of charge. Nevertheless, there remains some hope that a business model based upon quality of information, story-telling capability, explanation, interpretation, and the ability to paint a picture in words, will survive the transformation.

The implications of Fukushima

2011-03-14T17:09:00.015Z

The ongoing nuclear emergency in Japan highlights a design flaw in Boiling Water Reactors (BWRs). Most Light Water Reactors (LWRs), such as the BWRs, use zirconium alloy cladding to encase the nuclear fuel, and prevent fission products mixing with the cooling water. There are basically three requirements for the cladding in an LWR: (i) it must have a low thermal neutron absorption cross-section; (ii) it must be resistant to corrosion in water; and (iii) it must have a melt/ignition temperature greater than the operating temperature of the reactor. The temperature is designed to be as high as possible to maximise the thermal efficiency of the heat engine which generates electricity from a nuclear reactor.

Now, what Fukushima has revealed is that when a complete power failure stops the flow of cooling water in a BWR, the water turns to steam, and oxidises the zirconium fuel cladding, releasing the hydrogen component of the H₂O coolant. The hydrogen is then able to escape from the reactor, whence it almost inevitably causes a detonation or deflagration in the presence of atmospheric oxygen. These are the explosions suffered by Fukushima 1 on Saturday and Fukushima 3 on Monday.

Whilst these hydrogen explosions have not damaged the reactor pressure vessels themselves, it is unwise to suggest, as Malcolm Grimston, from the Energy Policy and Management Group at Imperial College, did after Saturday's detonation, that "The explosion... wasn't a terribly important event." On the contrary, such explosions are clearly highly disruptive and destructive to the efforts being made to feed cooling water into the reactor vessels and prevent a meltdown. Reports today suggest that the explosion in Fukushima 3 has damaged four of the five available pumps, and all three reactors now seem to have suffered at least a partial meltdown.

Are there alternatives to using zirconium cladding? Well, in the Magnox reactors used in the UK for some decades, the nuclear fuel was clad in magnesium oxide, which has a low neutron absorption cross-section, and which by virtue of already being an oxide, is incapable of undergoing an oxidation reaction with the carbon dioxide cooling gas used in these reactor designs. Unfortunately, magnesium oxide corrodes in water, so cannot be used in light water reactors.

There is, however, another alternative: stainless steel cladding was used in the UK's Advanced Gas-Cooled Reactors (AGRs), because the latter operate at higher temperatures for greater thermal efficiency, and magnesium oxide would become soft and potentially flammable in such circumstances. Stainless steel cladding would be resistant to oxidation in the presence of steam, but possesses a larger neutron absorption cross-section. To compensate for this the nuclear fuel would need to be subjected to further enrichment, which costs money, power and time, possibly making the whole thing uneconomical.

The nuclear industry might well suggest that the Japanese crisis has been triggered by unique tectonic circumstances irrelevant in Europe, that only a sizeable earthquake and tsunami could cause the simultaneous joint failure of the national grid and back-up diesel generators. Disturbingly, however, one can also imagine a terrorist attack which achieves exactly the same result.

Tom Paulin on the 2011 F1 grid

2011-03-07T18:06:00.019Z

I leiked the McLaren. It spoke to me of an audacious and extravagant spirit. The sidepods made me think of Joyce at his finest, a willingness to find stark beauty in bleak alphabetic form. It has a wonderful anarchy to it. It's operatic, lyrical, and poetic; I mean it's complete nonsense, but none the worse for it.

The Ferrari, however, I saw as insipid and cliched in comparison, as if the team had asked themselves a series of questions so dull that they'd fallen into a narcoleptic coma before completing the design.

The Lotus-Renault is simply delightful and extraordinary, like it's been hewn from a block of polished obsidian. At times, I felt like it was some sort of blind, dark, repressed Freudian urge, which had been hauled out of the deep unconscious by a psychoanalytical trawler, and thrust naked into physical form.

The Red Bull is a very confident design. It's subtle, marvellous, brilliant and powerful. Its curves have a restless rhythm to them. It feels no need to be showy or flashy, or self-consciously radical, yet it exudes a quiet sense of sublime perfection.

The Hispania is provincial and amateurish. It's pure sawdust and glue. In fact I don't think I've ever seen anything so rotten, degenerate, and downright awful in my entire leif.

Systems Engineering and Technology Insertion

2011-03-06T13:26:00.013Z

Manufacturing constitutes about 12% of the UK economy compared to 25% of the German economy. There's no need to lose any sleep over this, however, because with the assistance of the East Midlands Development Agency, the UK now has a Systems Engineering Innovation Centre:

The Systems Engineering Innovation Centre at Loughborough focuses on systems engineering aspects which provide a framework for the integration of people, processes, tools and technology in order to improve the management of risk, product configuration and technology insertion for the development of innovative products.

Systems Engineering is an attempt to uplift engineering from a concrete, practical activity, into the information economy. It is predicated on the notion that because complex engineering projects are really 'systems of systems', it is necessary to create a separate discipline, with its own group of practitioners, which specialises in the abstract, top-down analysis of engineering projects in terms of requirements, capabilities and stakeholders, abstracted from concrete engineering issues.

One thing Systems Engineering has been very successful at is codifying the blindingly obvious, and transforming it into self-important acronyms and obscure management-theory language.

Consider technology insertion, one of the phrases used above to define the remit of the UK's Systems Engineering Innovation Centre. What could this possibly mean, given that engineering is all about technology anyway? What else could an engineering project consist of? Literary criticism perhaps? Fortunately, the University of Bath School of Management are at hand to provide a definition:

Technology insertion is achieved through managing supply networks whose business plans and supply interfaces are aligned to a system-level capability to insert technological upgrades into existing complex platforms.

So it's about buying new components to upgrade an existing system? Thank goodness we've been able to codify that. David Kirkpatrick of the Royal United Services Institute is able to offer further insight into this difficult concept:

Both military and industrial opinion has increasingly supported a policy of 'technology insertion' (TI) by which ageing weapon systems can be rejuvenated by successive injections of advanced technology to enhance system effectiveness and/or to reduce operating and support costs. The term 'technology insertion' can be used to describe minor improvements, in which one subsystem is replaced by a more modern version with essentially the same functionality, and also to describe major upgrades (such as the mid-life upgrades of some warship and combat aircraft) which transform the weapon system and its military capabilities. In either case the TI must be carefully designed to achieve satisfactory spatial, mechanical, electrical and electronic interfaces with the original weapon system.

Note that we've now got an acronym, TI, so this must be an important and profound idea. We've also got a proposed list of the requirements for successful TI: "it must achieve satisfactory spatial, mechanical, electrical and electronic interfaces with the original...system."

Golly. This means that a new component must actually function when it's fitted to the existing system. In particular, it must achieve a satisfactory spatial interface. I think that means it has to fit. If it's bigger than the space available for it, then it's no good brother.

But why does this list of requirements only speak of mechanical, electrical and electronic interfaces? Surely if we're going to explicitly codify the obvious, then we need to be exhaustive? Hence, there's the thermodynamic interface to think about; if the new component generates more heat than the old one, then you could be in trouble brother. And let's not forget the vibratory and shock interface; the new component might not be able to withstand the thumps and bangs the old one was capable of withstanding. And what about the radiation interface? Can the new component tolerate the electromagnetic interference from the rest of the system, and will it generate some interference of its own?

It's a good job that Systems Engineers are available to explain this type of thing, and the East Midlands Development Agency certainly aren't wasting tax-payers' money in this respect.

Ricci flow and the entropy of space

2011-03-01T22:38:00.014Z

The entropy of the universe appears to be increasing, in accordance with the Second Law of thermodynamics, and this is commonly taken to imply that the early universe resided in a state of extremely low entropy. However, given that the geometry of space in the early universe was highly uniform, and given that matter at this time resided in thermal equilibrium, there is a problem. If the universe began in what appeared to be a state of equilibrium (i.e., a maximum entropy), then why did it not remain in such a state?

The common answer proffered is to propose that there is some form of gravitational entropy, and this type of entropy is maximised by clustering, not by homogeneity. There are two primary observations which seem to support this argument: (i) a homogeneous distribution of matter is clearly unstable under gravitational attraction, and over time matter clusters into stars and galaxies; (ii) the entropy of a black hole, the most concentrated form of gravitational collapse conceivable, is huge.

Philosopher of physics David Wallace has already dispelled the complacent notion that the matter in the early universe was in a state of equilibrium. As David explains, the rate of expansion of the universe displaced the matter in the early universe from equilibrium, leaving most of it stranded in the form of hydrogen and helium. The formation of stars increases entropy because it permits such lighter elements to undergo nuclear fusion. Black holes, argues Wallace, are a special case. In addition, let us not forget that all gravitationally bound systems eventually evaporate, which is hardly consistent with clustering itself being the driving force behind the Second Law.

But what about the other half of that complacent assumption concerning the early universe? Does a homogeneous geometry of constant curvature really possess low gravitational entropy? Well, here's a possible reason for thinking that it doesn't: the Ricci flow:

The expression on the left here is the rate-of-change of the metric tensor, whilst the expression on the right is a negative multiple of the Ricci tensor. The Ricci flow is an equation used by mathematicians for, (amongst other things), evolving the geometry on a 3-dimensional manifold. There are two crucial facts about this equation: (i) it evolves a geometry of varying curvature into one of constant curvature; and (ii) it's a kind of diffusion equation.

Now, the point about diffusion equations is that they increase entropy. In the field of radiation transport, for example, whilst the radiative transfer equation is the relevant equation from non-equilibrium statistical mechanics, it is fiendishly difficult to solve, and a diffusion equation is used as a macroscopic approximation instead.

So, if the evolution of an initially random 3-dimensional geometry towards constant curvature, is represented by a diffusion equation, and if diffusion equations represent physical processes which increase entropy, doesn't this suggest that a geometry of constant curvature possesses greater geometrical entropy than one of varying curvature? Could the Ricci flow ultimately be cast as a macroscopic approximation to a random walk in the space of underlying quantum geometries?

Which is all very well, but how do we reconcile this with the fact that black holes possess a huge entropy? Well, recall Roger Penrose's long-held proposal that gravitational entropy will be associated in some way with Weyl curvature. Black holes possess zero Ricci curvature and non-zero Weyl curvature, whilst the big bang possesses the opposite combination of zero Weyl curvature and non-zero Ricci curvature. If we restrict attention to 3-dimensional geometries of zero Weyl curvature, we may be able to argue that it is actually those with the highest degree of symmetry, those of constant curvature, which possess the highest entropy. Nevertheless, it may be that gravitational entropy is increased by clustering, not because it reduces geometrical homogeneity or symmetry, but purely because it increases the Weyl curvature.

Justice and motor racing siblings

2011-02-23T14:26:00.008Z

BBC4 are currently screening Michael Sandel's superb series of lectures on political philosophy. This week's episode considered John Rawls's theory of justice, and vividly highlighted the near impossibility of providing equality of opportunity in society. A fairly self-confident chap in the audience, called Mike, argues for a meritocratic society, in which people are rewarded proportionately to how hard they work. In response, Sandel points out that even the possession of a work ethic is strongly related to the accidental economic and familial circumstances into which one is born. To demonstrate his point, Sandel asks the audience of Harvard students to raise their hands if they are the first-born in their families. You can see the result for yourself 22mins into the video.

This is all very well for educational achievement, but does the same thing apply to motor racing drivers? For example, amongst the cohort of successful drivers (those who have made a living from being a racing driver, let's say), how many are the first-born in their families? And in the case of brothers who become racing drivers, do the first-born tend to be the most successful, or does the risk-taking, rebellious streak of a younger sibling actually provide a better basis for a racing career?

These are questions which could only be answered by a serious statistical study, yet a small sample of prominent cases in Formula 1 appears to suggest that this is an arena in which younger siblings might not be particularly disadvantaged:

Ricardo Rodriguez was younger than Pedro.
Emerson Fittipaldi was younger than Wilson.
Jody Scheckter was younger than Ian.
Gilles Villenueve was older than Jacques (Snr).
Michael Schumacher was older than Ralf.

McLaren's mysterious exhausts

2011-02-22T17:32:00.005Z

Craig Scarborough points out that McLaren have been experimenting in Barcelona with an exhaust system that has no discernible exit. Now, this is slightly mysterious because the exhausts cannot exit through orifices in the underbody of the car, as stipulated by the 2011 technical regulations, designed to ban double-diffusers and exhaust-blown diffusers:

3.12.9 In an area lying 450mm or less from the car centre line, and from 450mm forward of the rear face of the cockpit entry template to 350mm rearward of the rear wheel centre line, any intersection of any bodywork visible from beneath the car with a lateral or longitudinal vertical plane should form one continuous line which is visible from beneath the car.

3.12.10 In an area lying 650mm or less from the car centre line, and from 450mm forward of the rear face of the cockpit entry template to 350mm forward of the rear wheel centre line, any intersection of any bodywork visible from beneath the car with a lateral or longitudinal vertical plane should form one continuous line which is visible from beneath the car.

The notion of a continuous line is interesting here, because solid substances are really discrete, rather than continuous, collections of atoms and molecules. The intersection of an imaginary vertical plane through a section of bodywork can only form a continuous line at a macroscopic level of idealisation. Nevertheless, it's difficult to see how modern materials science could exploit this ambiguity. In principle, one might be able to construct part of the underbody from a permeable, but stiff and macroscopically continuous material, such as a rigid polyurethane foam, through which the exhaust gases could then be diffused. However, the rate of diffusion would surely be far too low to influence the airflow aerodynamically, even though diffusion occurs faster at higher temperatures. One wishes to blow the exhaust gases under the car, not diffuse them!

McLaren could conceivably exit the exhausts through holes above the front splitter, or below the sidepod inlets as Renault have chosen to do. In neither case, however, does there appear to be any photographic evidence yet to support this. The latest suggestion, rather, is that McLaren are trying an inward blowing exhaust slit on the top surface of the floor, just in front of the rear wheels. Intriguing.

Out of body experiences and deja vu

2011-02-19T23:34:00.005Z

This week, The Daily Telegraph excitedly reported at 7:00AM GMT 18 Feb 2011 that "Out-of-body experiences are just the product of a confused mind." This was news hot off the press, for the same publication also reported at 12:01AM BST 24 Aug 2007 that "Out-of-body experiences may be nothing more than the brain becoming confused."

One of the experiments reported back in 2007 used virtual reality goggles: "A team led by Bigna Lenggenhager and Pro[f] Olaf Blanke asked people to stand in front of a camera while wearing the goggles. In one experiment, subjects saw the camera’s view of their own back, computer-enhanced to create a three-dimensional 'virtual own body.' When the subjects’ backs were stroked with a highlighter pen, at the same time that they saw their virtual back being stroked they reported that the sensation seemed to be caused by the highlighter on their virtual back, making them feel as if the virtual body was in fact their own."

Reassuringly, in 2011 we discover that "Professor Olaf Blanke [asked volunteers] to wear virtual reality goggles and then stand in front of a camera. The subjects saw the cameras view of their back on screens in the goggles, computer enhanced to create a 3D virtual version or avatar. When their back was stroked with a pen so was the virtual avatar in front of them, making them think that the virtual body was in fact their own."

Back in 2007, it was claimed that this work "could also have commercial applications...The experience of playing video games could reach a whole new level, but it could go much beyond that. For example, a surgeon could perform remote surgery...other uses could be in treating eating disorders linked with a flawed body image, such as anorexia."

In 2011 we now learn that "the work could have more commercial applications...The technique could be used to make computer games even more exciting or projecting people into robot soldiers or surgeons...They could even be used to treat eating disorders linked with a flawed body image, such as anorexia."

It's truly difficult to keep up with the pace of such research.

Ducks, geese, and Karman vortex streets

2011-02-14T17:53:00.018Z

An expert on neutrino dynamics has drawn my attention to a remarkable paper, 'Kinematics of Ducklings Swimming in Formation', written by a certain Frank E.Fish, (who I believe also had a cameo role in Finding Nemo).

Fish explains that the ducks to the rear of a formation utilise the reduced drag afforded by a Karman vortex street, created by the ducks to the front. The ducks at the rear maintain the same velocity as the ducks at the front, but do so with a reduced energy expenditure.

Now, Karman vortex streets are staggered rows of counter-rotating vortices, created by any bluff cylindrical body in relative motion with a Reynolds number greater than 90. (The upper limit at which these vortices are generated is dependent upon the exact shape of the object in question, but in the case of a cylinder, figures such as 10⁷ are quoted). The axis of rotation of these vortices will be in a plane orthogonal to the direction of motion, as seen in the topmost diagram here (taken from Joe Katz's book, Introductory Fluid Mechanics). In the region between the two vortex rows, there is a forward component to the fluid velocity, and in the case of our trailing ducks, it is this which reduces the energy expenditure required to maintain the same speed as the leading ducks. In particular, it seems that the ducks at the rear save energy by reducing the amplitude, rather than the frequency, of their power-strokes.

In contrast, the trailing vortices shed by a wing will have axes of rotation parallel to the direction of motion. Geese, for example, appear to fly in V-formations, not because of Karman vortices, but because they use the trailing wing-tip vortices to gain lift. The outer side of each trailing vortex of the bird in front has an upward component, hence less energy is expended by the bird behind
to maintain the same level of lift.

For a Formula One car, the Reynolds number is of the order of 10⁶, which is just about the upper limit for any sort of vortex street pattern to be distinguishable from random turbulence.

If Karman vortices are generated in the wake of a Formula One car, one presumes that they also interact in a complex manner with the trailing vortices generated by the wings et al...

The Fokker D8 and F1 front wings

2011-02-13T11:19:00.010Z

JE Gordon's masterly popular exposition, Structures - Or Why Things Don't Fall Down, contains a fascinating account of the early wing failures experienced by the Fokker D8 monoplane. The first world war pilots who initially flew the D8 found to their cost that placing the aircraft in a steep dive would literally twist the wings from the fuselage.

Professor Gordon's explanation of the cause for this revolves around two concepts: the centre of flexure of the wings, and the centre of aerodynamic pressure. The wings on the Fokker D8 were constructed from two spars running across the span of the wing, and a series of ribs running across the chord at regular intervals. Both spars initially had the same stiffness.

The upward force on an aircraft wing will make it bend upwards. If an upward force were applied halfway between the two spars, then both spars would bend upwards by an equal amount. Unfortunately, the centre of pressure on an aircraft wing lies approximately one quarter-chord from the leading edge. As a consequence, the forward spar on the Fokker D8 would bend upwards by a greater degree than the rear spar, twisting the wing. This also increased the angle of attack at the ends of the wing, leading to a positive feedback process in which the wings were twisted to ever greater degrees.

The point at which a load must be applied in a beam-like structure to cause no twisting effect is called the centre of flexure. The centre of flexure and the torsional stiffness of the Fokker D8 wings were dependent upon the relative stiffness of the two spars. When the two spars were equally stiff, the centre of flexure lay behind the centre of pressure, causing the wing to twist at the ends as it was bent upwards. Thus, to prevent this, is was ultimately necessary to make the forward spar stiffer than the rear spar. By stiffing the forward spar, the centre of flexure was moved forward to coincide with the centre of pressure, and the wings were prevented from twisting.

Now, one might suggest that the inverse of the twisting effect suffered by the Fokker D8s could actually be very beneficial for the front-wing aerodynamics of a Formula 1 car. If the centre of flexure of a front-wing is designed so that it lies behind the centre of pressure, then when the ends of the wing are bent downwards by the aerodynamic loads, the ends of the wing will also be twisted forwards, increasing the angle of attack of the outermost parts of the wing, and enhancing the ground effect, in a positive feedback process.

Thank goodness the FIA's front-wing deflection tests prevent this type of thing from happening.

Musical timbre and quantum theory

2011-02-12T20:30:00.008Z

In what sense does the same note, played by different musical instruments, make a different sound? Why, for example, does C played on a piano, differ from C played on a saxophone?

Well, a musical sound is uniquely characterised by three things: pitch, loudness, and timbre. The pitch is the fundamental frequency of the oscillatory vibration, the loudness is the average amplitude of the vibration, and the timbre is what characterises the difference between different instruments.

To understand timbre it's necessary to understand that a musical note played on a particular instrument does not consist of a single frequency of vibration. Rather, it consists of a superposition of different frequencies. The pitch of a note uniquely specifies the fundamental frequency, but the sound produced will be a superposition of the fundamental frequency and numerous multiples of it ('overtones'). The superposition which defines the sound is specified by the amplitude of each constituent frequency, and this is the timbre of the sound. Mathematically, if one expresses the superposition as a Fourier series, then the amplitudes are simply the Fourier coefficients.

Now, the metaphysically interesting point is that the note made by a particular musical instrument is a quite definite sound, yet it can be decomposed into numerous parts, each of which would correspond to an equally definite sound, were it to be produced in isolation. It's exactly the same sense in which a prism can decompose white light into it's component parts, the colours of the spectrum. As philosopher of physics Richard Healey has pointed out, the prism simply performs a physical Fourier decomposition.

Which brings us back to certain versions of the Many-Worlds Interpretation of quantum theory, which propose a radical compositional metaphysics in which the universe consists of numerous mutually interfering branches. It's well established that quantum superpositions cannot be treated exactly like the superpositions of sound or light waves in classical physics, yet the basic mereological scheme (i.e., the relations between parts and wholes) may still be similar, with the universe consisting of mutually interfering branches just as the note produced by a musical instrument consists of numerous mutually interfering frequencies.

Adrian Newey and Antonio Canova

2011-02-10T18:43:00.025Z

At the recent unveiling of the Red Bull RB7, Adrian Newey was moved to protest that, "I've got a reasonable ability to visualise things but I can't see the invisible airflow!" (Autosport February 3, p17).

But what exactly could have provoked Adrian to make such a 'Clark Kent denies he is Superman' comment? Well, in his MPH column in Autosport on September 3 last year, Mark Hughes reported that "They say he can visualise what the air wants to do, the way Keith Duckworth used to be able to sense the gas flow in a combustion chamber." Riffing on this theme, McCabism asserted on November 6 that "Adrian Newey, they say, can see the air." And barely ten days later, Richard Williams, writing in The Guardian, claimed that "What they say about him is that while he contemplates the shape of his next car, he can visualise the air flowing around it. In his mind he sees the invisible waves and currents, the areas of low and high pressure. Then he can start thinking about how to shape it." As Adrian now helpfully points out, he can't literally see the air, he can only visualise it!

Anyhow, Richard Williams then proceeded to draw the following sculptural comparison:

"That makes me think of someone like Antonio Canova, sitting in his Rome studio, studying a block of marble just arrived from the quarries at Carrara, then walking around the room to examine it from every angle and, as he does so, seeing within its rough form the outline of Psyche Revived by Love's Kiss, which you can see, two centuries later, in the Louvre. Some people have that kind of special vision, and Newey seems to be one of them."

It's an interesting analogy, and there are certainly parallels here. Newey does indeed share with artists such as Canova a power of vision, in the sense of an ability to vividly conceptualise a future article which transcends contemporary articles of comparable type. However, it's important not to characterise genius as some sort of inexplicable, ex nihilo expression of creative power, for this is psychologically unrealistic, and a mysticalisation of such talent. Sculptors do not carve great works of art from blocks of marble, and Formula 1 designers do not create beautiful and innovative cars, without a great deal of prior learning, experimentation, analysis and correction.

In fact, John Smythe Memes furnishes an account of Canova's creative process which testifies to this, and suggests further analogies with the design of racing cars:

"Canova naturally possessed an imagination of great energy...But over the rich treasures this poured forth, the judgement presided in severe scrutiny: in correcting he was therefore slow and fastidious. First ideas were hastily thrown upon paper in slight outlines which were often changed and retouched, so that finally little of the original design remained; yet each successive alteration evidently appears an improvement...Having at length satisfied himself with the design of any projected work, as it would appear in painting, his next care was to examine and recompose it, according to the principles of sculpture. The modelling tool was now substituted for the port-crayon, and the sketch transferred to wax or clay. In this first or smaller model, the composition was carefully studied in the arrangement of the individual parts, and in the general effect, every thing being determined with just precision. In this condition, with the masters anterior to Canova, it had served as the only guide in forming the statue. With the latter, these were merely preliminary steps conducting to the full perfection of the real model, which was composed of exactly the same dimensions as the future marble...

The Sculptor having thus effected the completion of a model,...the manual labour of the marble was safely and profitably confided to inferior powers. But, when its last superficies was to be formed-when all that finally meets the eye was to be created, the inspiring touches were trusted to the master hand alone." (Memoirs of Antonio Canova, p555-557).

Thus, Canova began by testing out his ideas in sketches, constantly refining and correcting them, before making a small-scale model of the intended sculpture, (rather like a wind-tunnel model of a Formula 1 car). Unlike his predecessors, Canova then made a full-scale model, and presumably subjected that to further scrutiny and alteration, before finally ordering a bunch of artisans to hack away at a block of marble, to which he could make the finishing touches.

There is, then, a methodology at work here, and rather more to it than simply plucking an idea from some sort of ambient inspiration field, and immediately carving its realisation out of a solid block of marble! This, of course, is not to diminish Canova's genius, but, to be fully appreciated, creative talent such as his or Newey's should be understood as the by-product of a lifelong process of dedication, learning, analysis and self-correction.

Waves are not made of water

2011-02-04T22:28:00.012Z

The Secret Life of Waves, broadcast on BBC4 this week, featured an interesting combination of the scientific, the philosophical, and the poetical.

Narrator and writer David Malone points out that water is simply the medium for ocean waves, that waves are actually patterns of energy transport. This prompts Malone to ask a more fundamental question, whether the ontology of the world consists of processes rather than objects. What we think of as the more enduring objects in the world can, when viewed over longer timescales, be re-cast as patterns of mass and energy flow.

One could add that even elementary particles are, according to modern physics, merely excitations of underlying quantum fields, their identity conditions more akin to those of waves or vibrations in a continuous medium, than the classical notion of immutable, permanent, miniature billiard balls.

Malone concludes with some reflections on human mortality, proposing that we are, not just metaphorically, but quite literally, mass-energy waves of finite duration. A seismologist might have taken the ironic opportunity here to introduce love waves into the exposition, although sadly these disturbances are poetic misnomers, being destructive waves of Earthquake-driven surface shear, rather than the ripples of dopamine sweeping across the cerebral cortices of youthful inamoratas.

Malone's programme is imbued with an undercurrent of reflective melancholy which will resonate with all quadragenarians, catching sight for the first time of the final shoreline, jutting ominously over the horizon.

Exhaust-blown undercuts

2011-02-01T22:19:00.006Z

A new constellation of Formula 1 cars is burning bright at Valencia this week, and most intriguing amongst them are the contra-flavescent Lotus-Renaults, sporting exhaust exits in front of the sidepods.

Craig Scarborough suggests that the purpose of these is to accelerate the airflow under the leading edge of the floor, and he might well be right. My immediate instinct, however, is to postulate that the function here is to increase the velocity of the airflow down the flanks of the car, beneath the undercut sidepods, and ultimately over the top of the diffuser.

The new Toro Rosso, meanwhile, exhibits severely undercut sidepods, reminding some observers of Ferrari's double-floor F92A of 1992. Rumours suggest that the McLaren MP4-26 will feature exhaust-blown undercuts of a similar depth.

Such anterior-lateral thinking is a characteristically sparkling example of Formula One's technical creativity, but one hopes that the Kelvin-Helmholtz turbulent instability arising the confluence of two distinct airflows at the rear of the car will not further hamper the quality of the racing.

Monegasque Plasma Confinement

2011-01-31T22:44:00.019Z

Joint European Torus (JET), magnetic confinement fusion Tokamak. Culham, UK.

Tunnel at Monte Carlo.

Is the universe discrete or continuous?

2011-01-29T12:13:00.012Z

The Foundational Questions Institute is currently inviting submissions for an essay contest entitled Is reality digital or analog?. Now, this is essentially the same thing as asking whether the physical universe is discrete or continuous. Whilst general relativistic cosmology represents the universe to be continuous, some aspects of quantum theory are discrete, and many people working in quantum gravity clearly expect the universe to be discrete at a fundamental level.

Let's take a step back, however, and consider the question in more general terms. In particular, given that the physical universe has many levels of structure, and given that the theories which describe different levels of structure can possess radically different properties, is it even possible to know whether the universe is discrete or continuous at a fundamental level?

Before going a little further, it's necessary to introduce a philosophical concept called supervenience. This is a useful concept relating different levels of structure because, unlike allied concepts such as reduction and emergence, its definition is generally agreed upon and fairly uncontroversial. Supervenience, then, holds that any change in the states or processes at a higher level of structure, must correspond to a change in the lower level states or processes. Supervenience asserts that a lower-level state or process uniquely determines the higher-level state or process, and that there is a many-one mapping between the lower-level states/processes and the higher-level states/processes.

Now, suppose on the one hand that there is a fundamental level of structure, and the fundamental level of structure is continuous. Discrete structures can clearly supervene upon such a continuous substratum. As an intuitive example, just think of the manner in which a chess board is defined upon a continuous plane. Given a continuous substratum, one can divide it up into discrete, contiguous 'chunks', assign a discrete set of possible states to those chunks, and then define a finite set of rules by which those states change from one discrete time-step to the next. A more formal notion of such a discrete system is a cellular automaton. Even if we found that space-time is a cellular automaton at some level, it is possible that such a discrete level of structure is merely supervening upon a more fundamental continuous substratum.

This seems to be reasonably intuitive, but does the converse also hold? If we suppose that the fundamental level of structure is discrete, is it possible that continuous structures can supervene upon it? Well, in one sense, this is already well-known to be true: for example, solids and liquids are known to consist of discrete collections of atoms and molecules, yet because such systems consist of large numbers of discrete entities, they can be conveniently and approximately represented as continuous systems, described by continuous fields such as those representing pressure, stress, density, internal energy, velocity etc.

Yet this is merely a form of approximate supervenience; we know that solids, for example, are really crystalline atomic lattices, or polymer chains, and that continuum solid mechanics is merely a handy tool with a limited domain of applicability. Is it possible, however, that a continuous level of structure could exactly supervene upon a discrete substructure?

Let's think about this in more abstract, mathematical terms. The set of real numbers is said to possess the cardinality of the continuum. There is an infinite number of them, and they cannot be placed in one-to-one correspondence with the set of 'whole' numbers (1,2,3, etc), hence the continuum is said to be uncountably infinite. Within the real numbers, however, there are discrete subsets, such as the set of integers (...-2,-1,0,1,2,...), and the set of rational numbers. The set of rational numbers essentially contains those real numbers which can be given a finite decimal expansion, such as 23.45786, or a recurring infinite expansion. Numbers such as pi, which cannot be given a finite or recurring decimal expansion, are real numbers, but not rational numbers.

Now, given the set of rational numbers, the set of real numbers can be obtained from them by simply taking the limit points of all sequences of rational numbers. In other words, those real numbers such as pi, which require an infinite non-recurring decimal expansion, can be seen as the limit of an infinite sequence of rational numbers, each member of which has a finite or recurring decimal expansion. One says that the set of rational numbers is (topologically) dense in the set of reals.

Defined in this sense, the set of real numbers, a set with the cardinality of the continuum, clearly supervenes upon the set of rational numbers, a discrete set. Any change from one real number to another entails a change in the sequence of rational numbers with which it is associated. If we suppose that the fundamental level of structure in the physical world is discrete like the set of rational numbers, then it is clearly possible for continuous structures to supervene upon discrete substructures, and for the supervenience to be exact.

This example opens up a more general question for the ontology of mathematical physics: If the physical world objectively possesses a mathematical structure, then it presumably follows that it also possesses any substructure of that structure; however, does it also follow that the physical world possesses any superstructure within which that structure can be embedded? The answer to the latter question is surely 'no', for by taking a disjoint union of structures, one can embed the structure of the physical universe within a superstructure to which it is totally unrelated. The crucial additional condition which needs to be added is that of supervenience, and I propose the following:

Any structure which can be constructed from the apparent structure of the physical world, and which supervenes upon that structure, must also be said to physically exist.

The example considered above, in which one structure is densely embedded inside another, can be seen as one of the tightest supervenience relationships it is possible to define!

So, in conclusion, it seems that discrete structures can supervene on continuous structures, and conversely, continuous structures can supervene on discrete structures. Given this fact, it seems impossible to establish what the fundamental cardinality of the universe is, unless one can also ascertain that the fundamental level of structure (if there is one) has been reached. And how could we know that?

Being the helmet

2011-01-25T22:14:00.005Z

McLaren, it seems, have a Human High Performance Programme. This double alliteration is slightly troubling, not least because the apparent need to qualify the programme as 'human', might be thought to imply that the 1998 World Champion Constructor is also in the process of preparing an army of androids or extra-terrestrials to fulfil some indispensable, high-performance function within the McLaren Technology Centre. It certainly places McLaren a step ahead of the opposition, who will have to rely upon mere fitness coaches, physiotherapists, and the odd sporting psychologist.

Of course, it may be that McLaren have taken on-board the lessons expounded in Clyde Brolin's 2010 book Overdrive, and recognise the performance benefits to be had when a driver enters a trance-like rhythm called 'the zone'.

In the spirit of Overdrive then, here's a particularly vivid account of what it feels like for a racing driver to be in such a state. What's most interesting in this recollection is that, whilst the driver doesn't lose his sense of having a spatial location fixed behind the eyes, he does describe an apparent loss of spatial extension. In effect, the driver seems to be describing a partial decoupling of the conscious mind from the body; there is temporal structure but no spatial structure to the driver's point of perception.

Those who fancy a challenge might wish to identify the driver.

"When I'm in that groove, I can go on forever. I wish I knew how I got into that state. I don't. I simply find myself in it...

"Then I drive out of that window in my helmet. I look through that window and what I see out of it is the sole and only thing that exists in the whole wide world; everything is happening out there in front of me. My legs and arms and every other part of me are just parts of a whole and doing what they're supposed to be doing automatically, so that I don't have to think consciously about gearing or braking or accelerating; that's all going on without any orders from me. I concentrate, intensely, on everything that's in front of me: be it a car or a corner, there's an invisible line extending from that window in my head to whatever's next. My body is in unison. It doesn't really exist; it's compacted, the whole of me is bunched up tight inside that little area of plexiglass. I'm entirely in my helmet and I think of myself as being the helmet, looking out. Everything, body or car, obeys that module.

"The sensation is not physical...I'm seeing more than I ever have before. My vision is enlarged and the sensation is purely mental."

Sorry, no clues.

The case for working with your hands

2011-01-18T21:54:00.007Z

"The ex-boyfriend of an older housemate, Chas was a machinist by training. Currently he worked the parts counter at Donsco, the oldest VW speed shop in the Bay Area, in Belmont. He also built race motors for them and pitted for their off-road racing campaigns. Once a classical guitar-playing Buddhist vegetarian, he was now a gun freak and brilliant misanthropist. He still had long hair, but it was rarely released from the bun under his tweed cap."

"I once attended a conference entitled 'After the Beautiful'. The premise was a variation on 'the death of God', the supposed disenchantment of the world, and so forth. Speaking up for my own sense of enchantment, I pointed out, from the audience, the existence of beautiful human bodies. Youthful ones, in particular. This must have touched a nerve, as it was greeted with incredulous howls of outrage from some of the more senior harpies."

Matthew Crawford lived in a commune between the ages of nine and fifteen, worked as a trainee electrician and mechanic, obtained a degree in physics from UC Santa Barbara, worked in several fruitless and depressing office jobs, obtained a PhD in the history of political thought from the University of Chicago, and was briefly occupied as director of a Washington think tank, before finally returning to his true vocation, as a motorcycle mechanic. He's been around, in other words. And applying his personal experience and philosophical skills to an analysis of modern work, he's come to some very salutary conclusions.

The principal thesis of the book is that working in a manual trade is vastly preferable to working in the office. A trade, argues Crawford, has objective standards of competence, makes you responsible for your own work, is motivated not purely by the extrinsic desire for money but by the intrinsic good of fixing and building things, requires people to get outside their own heads, entails a constant acquaintance with failure that engenders honesty and humility, encourages self-reliance, and satisfies the fundamental human cognitive requirement to wield tools.

Crawford argues against the wisdom of sending so many people to university, preparing them for careers in a purported post-industrial, information economy, when most of those office jobs actually consist of mind-numbing, morally debasing, routine tasks. This is largely correct, although one might point to software engineering as an office job which also possesses many of the characteristics that Crawford finds so admirable in the trades.

The philosophy, however, is also entwined with delightful personal recollections of Crawford's life as a mechanic, hence this book could be seen as a harmonic overtone to Pirsig's Zen and the Art of Motorcycle Maintenance. The highlight of these reminiscences describe Crawford's disenchantment with academia, and his initial attempt to earn a living as a mechanic in a rented Chicago warehouse:

"There were...various litters of kittens and a rotating series of questionable individuals, usually 'in between situations', living upstairs in the unheatable, uncoolable warehouse, including one very sexy young S and M model and a pizza delivery guy who shot a man in self-defense and then skipped town, leaving behind only a Koran and a pile of porn. I'd gone from the Committee on Social Thought to this."

Quality in Analytical Laboratories

2011-01-17T18:19:00.010Z

If there's two facts about the quality of an analytical laboratory that you'll never read in a Quality Manual, it's the following:

(1) Quality is primarily a function of the calibre of the people you employ, their skills and their levels of dedication.

(2) If you devise job definitions which make people's work excessively routine and repetitive, if there is insufficient opportunity to learn new skills, or to exercise discretionary judgement, and if you generally require your employees to follow the steps of a process which is prescribed for them, then those employees will lack pride in their work, will have low levels of dedication, and, unless you rigorously enforce performance metrics and have the power to sack underperforming employees, the work of those employees will generally be of a low quality.

Despite the evidential truth of these statements, the corporate management of an analytical laboratory will eagerly buy into the notion that quality is a function of management systems and processes. Such a notion not only appeals to the self-aggrandising instincts of the management, it also absolves them of responsibility for the thing they really hate doing: namely, thinking critically and imaginatively about the job definitions and career development of their own employees.

To be clear, good management processes and systems are still a necessary condition for quality. High calibre employees working within a bureaucratic, inefficient management system, will find their efforts stymied on a regular basis. The point, however, is that quality systems are not alone sufficient to ensure analytical quality.

Many managers of analytical laboratories are smart enough to realise this. They know that systems and processes won't solve the underlying problem of poor calibre staff, wafer-thin levels of talent, and levels of dedication which can only be measured with a micrometer. They despair, however, of solving this fundamental problem, and decide instead that their only goal should be to cover themselves. And in this context, the perfect way of covering your managerial backside is to introduce quality systems and processes revolving around documentation, audits and accreditation.

After doing all this, the analytical laboratory will still be as piss-poor as it was to begin with, perhaps even more so, but this is of no concern to the corporate manager, who will happily move onto his or her next role, proudly claiming to have transformed the quality of the laboratory. And they'll have the accreditation certificates to prove it.

The Quantum Theory of Formula 1

2011-01-12T22:48:00.013Z

The Chapman Uncertainty Principle: The greater the performance level of a car, the lower the reliability level, and vice versa. Performance and reliability cannot be simultaneously optimised.

Quantization of income: The possible income levels of a team, prior to sponsorship revenue, occupy a discrete set of values, specified by the Concorde Agreement. If a team drops an income level, it will emit talented drivers and technical staff in response; conversely, if a team absorbs talented new drivers and technical staff, it will jump to a higher income level.

Bose-Ecclestone statistics: No pair of teams can simultaneously possess the same level of pre-sponsorship income, as specified by the Concorde Agreement.

Intrinsic spin: Each car-driver combination possesses a purely quantum property called intrinsic spin, which specifies the propensity of that car, under the control of that driver, to complete an unintended rotation about its centre of mass.

Quantum holism: The creativity of a design team cannot be uniquely determined by the reduced creativity of its constituent members.

Non-locality: Two drivers in the same team, with similar levels of performance, can become entangled even when separated by a considerable on-track distance. Thus, when one driver sets a faster lap, the other will also set a faster lap, despite the absence of direct communication between the two, and despite the frantic entreaties from the pit-wall for both drivers to 'preserve the tyres and fuel'.

The Measurement Problem: A team can enjoy a significantly higher level of performance than the other teams for only a brief period of time, before measurement-like interactions with the governing body induce a discontinuous and non-deterministic collapse of the performance envelope.