Air Curtains

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

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

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

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

"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

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?

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

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

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.