Rose-petal accumulation dynamics

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

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

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

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

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

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

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

Why is the universe not exactly homogeneous?

Rose petal aerodynamics

Here's an interesting puzzle for armchair aerodynamicists: why are the rose petals deposited in the pattern depicted in the photo on the left?

The perspective is North-facing, but the prevailing wind-direction is Southerly. The passage behind the photographic point-of-view zig-zags through a pair of ninety-degree bends, but nevertheless channels the wind blowing from the South, down the passageway and into the garden.

The petals are falling from above, and the flowers are fairly uniformly distributed on the rose-plant, so I don't think the petal distribution on the ground reflects the flower-distribution above.

If the wind were blowing from the North, one might explain the pattern by postulating that there are three regions of 'dead air', formed by the boundary layer detaching from the three visible bluff bodies: the chair, the right-hand gate-post, and the gate itself.

Given that the wind is Southerly, however, the best hypothesis I can suggest is that the gate and gate-post create stagnation points for the oncoming flow, and the third pool of petals is explained by some complex interaction between the wake of the gate, the adverse pressure gradient approaching the stagnation point of the chair, and the sudden overall deceleration as the air exits the passageway into the garden.

From this, one can see clearly why horticulturalists, just like architects, need to develop a proficiency in Star-CCM+.

On being the helmet: an answer

Last year, I challenged readers to identify the racing driver responsible for the following vivid account of what it feels like to be 'in the zone'.

"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."

Sadly, there were no correct suggestions, so I must now reveal that these were the reflective and introspective words of Alan Jones, 1980 F1 World Champion, elicited by Keith Botsford, and published in Driving Ambition.

The occidental decline

In 2003, Mary Poovey wrote a disturbing analysis of modern financial culture, Can Numbers Ensure Honesty?. Published in the Notices of the American Mathematical Society, it's unlikely that many politicians, journalists or bankers read it, and even if they had, it's fanciful to think that it could have changed the course of events.

Poovey pointed out that "the International Bank of Settlements estimates that in 2001 the total value of derivatives contracts traded approached one hundred trillion dollars, which is approximately the value of the total global manufacturing production for the last millennium."

A decade later, here's the national debt league, as a percentage of GDP:

Greece 153%
Italy 123%
Ireland 113%
Portugal 112%
United States 107%
Great Britain 88%
Japan 236%

The good news is that China has more than a trillion dollars in foreign reserves, and "could buy all of the outstanding sovereign debt of Spain, Ireland, Portugal and Greece, solving the euro area’s debt crisis in a trice. And it would still have almost half of its reserves left over."

So what the banks and the financiers and the politicians have done, is to hand long-term economic dominance to the most powerful hive-mind in the world.

On the quantitative financial methods underpinning this disaster, Poovey wrote: "the mathematical model has to assume that no unprecedented economic events or conditions will intervene or disrupt the pattern graphed by statistical probability. In other words, in order to work, the mathematical model must assume that a limited and stable set of factors will be at work in the market and these will generate a normal distribution about a mean...

"Very few people inside or outside the global financial community question whether the foundational assumptions implicit in financialization are true...what if markets are too complex for mathematical models? What if irrational and completely unprecedented events do occur, and when they do - as we know they do - what if they affect markets in ways that no mathematical model can predict?"

Too late now.

Andy Fraser and the lot of the bass guitarist

"You're fucking shit mate!"

It was not the first time the leather-jacketed, middle-aged man standing a few yards to my left, pint-glass in hand, had yelled such a finely-judged critical appraisal in the direction of the stage. In fact, he'd been barracking Noel Redding, one-time bass guitarist for Jimi Hendrix, almost continuously for two hours now.

The place is Mr Smith's, a small music venue on Poole Hill, Bournemouth. It's sometime in the winter of 1998/1999, and I've been dragged here by housemate and Hendrix obsessive, Sue, to see Noel play a small gig with a couple of other guys. The music is fine, but the evening is ruined by the heckling. The audience stands a matter of yards from the stage, and despite initially fielding the abuse with good humour, Redding has no choice but to spend the balance of the evening trying to ignore it.

Sue, a bustling, gregarious, flame-haired Londoner, who insists on pronouncing the venue as 'Mr Smiffs', turned up earlier in the evening to get Redding's autograph, but her joy has now turned to silent fury.

Indeed, as we return home later, she can barely bring herself to speak. Home, incidentally, is in this case a sprawling, three-storey shared house overlooking Branksome, wherein our rooms are rented from a landlord who styles himself as 'JD', and drives a Saab in dark sunglasses to the local architects' office.

JD displays a level of generosity towards his tenants which makes Rigsby look like the inspiration for the Bill and Melinda Gates' Charitable Foundation. As a consequence, the house resides in a state of permafrost, its tenants drawing their only warmth from the small black-and-white TV in a back room.

Sue would subsequently write to Redding, apologising for the abuse, and is over-the-moon some weeks later when she receives a friendly and courteous reply. The letter is stored away as a holy relic, and is, I suspect, still cherished to this day. Redding, however, sadly died in 2003.

The sometimes unfortunate lot of the bass guitarist occurred to me again today as I read the opening sections of 'All Right Now: Life, Death, and Life Again', the story of Andy Fraser. Fraser was bass guitarist in 1970s blues-rock band, Free, and his life is charted here with a combination of first-person recollection, linked together by narrative and analysis from Mark Hughes.

In fact, the style is very similar to that employed in 'Crashed and Byrned', Hughes's fabulous book on racing driver Tommy Byrne. It's a style which is more honest than the ghost-written autobiography, for it makes clear where the division lies between the contribution from the subject, and that from the professional writer. It also gives the writer an opportunity to engage in third-party analysis which would be impossible in a work purporting to be the product of self-observation alone.

It's only available in electronic form at the moment, but let's hope it gets a print-run some time soon.

Nothingness and decoherence

More than twenty years ago, philosopher of science David Albert suggested that the global state of the universe might be akin to a vacuum state in relativistic quantum field theory. Albert argued that if one endorsed the many-worlds interpretation of quantum theory, then whilst the global state might correspond to the vacuum, the different local branches of the universe would possess physical substance:

"Observers such as ourselves cannot establish, by any practical means, that our experience is not merely a constituent, merely a branch, of that vacuum...What if the Creator, the Selector of Initial Conditions, had decided not to create; to create nothing, to create the vacuum? That vacuum would already have contained us and what we see around us. The option not to create some world like ours, given the physics [of] relativistic quantum field theory,...is not a logical possibility." (Philosophy of Science Association Symposium 1988, Volume 2, p129).

Albert has since abandoned the many-worlds interpretation, and indeed, now throws scorn on those, such as Lawrence Krauss, who suggest that quantum theory can explain why there is something rather than nothing. However, I'd like to suggest that Albert's proposal can now be resurrected.

The many-worlds interpretation has become increasingly popular in recent years, not only amongst philosophers of physics, but also amongst quantum cosmologists, who are driven to this approach by the fact that the universe has no external observers or measurement devices to collapse the quantum state.

Indeed, in the last month the many-worlds interpretation has received perhaps its most sophisticated defence with the publication of The Emergent Multiverse, the culmination of research pursued by philosopher of physics David Wallace over the past decade.

Central to the modern understanding of the many-worlds interpretation is the notion of decoherence, a process which effectively eliminates interference between macroscopically distinct branches of the quantum state. As Wallace writes, "there is, in fact, every reason to think that the microscopic degrees of freedom of even an isolated system suffice to destroy coherence between macroscopic superpositions of that system's macroscopic degrees of freedom," (p81).

Wallace argues that the quasi-classical, macroscopic branches of the world are an emergent, approximate structure, instantiated in the quantum state of the universe.

In addition to this modern understanding of the many-worlds interpretation, the notion of decoherence can explain how a stationary (i.e., unchanging) global state is consistent with the passage of time in the different macroscopic branches:

The candidate fundamental equation [in canonical quantum cosmology]—the Wheeler-DeWitt equation—is an analogue of a time-independent Schrödinger equation, and does not contain time at all. The problem is thus in a sense simply: where does time come from? In the context of decoherence theory, one can construct toy models in which the analogue of the Wheeler-DeWitt wave function decomposes into non-interfering components (for a suitable sub-system) each satisfying a time-dependent Schrödinger equation, so that decoherence appears in fact as the source of time.

(n29). An analogy from standard quantum mechanics may be helpful here. Take a harmonic oscillator in equilibrium with its environment. An equilibrium state is by definition a stationary state under the dynamics, i.e. it is itself time-independent. However, one can decompose the equilibrium state of the oscillator as a mixture of localised components each carrying out one of the oscillator's possible classical motions (time-dependent!). (Guido Bacciagaluppi, The Role of Decoherence in Quantum Mechanics, Stanford Encyclopedia of Philosophy).

Thus, whilst Krauss attempts to explain the existence of the universe by supposing that the global vacuum state must have been unstable, decoherence explains how the existence of evolving, quasi-classical branches of the universe is consistent with the global state of the universe being the stationary, vacuum state.

Sausage roll review

Due to some recent changes in location, an opportunity arose to sample the comparative quality of the sausage rolls produced by three well-known UK grocers: Waitrose, Sainsburys, and the Co-op.

So let's start with the Co-op, a company proudly bearing the slogan 'Good with food'. Unfortunately, if their sausage rolls are representative, then perhaps they should concentrate instead on the sale of batteries and sanitary products.

Two large sausage rolls were purchased from a local outlet; the first was eaten, the second binned. The one consumed, and thereby unfairly inflicted on a living gastro-intestinal tract, tasted like a turd wrapped in a layer of greasy cardboard. If it was the first sausage roll you'd ever eaten, you would have vowed never to eat another one again.

Further away than the Co-op, however, lay a Waitrose store, and predictably their sausage rolls are fabulous. A sausage roll from Waitrose is a genuine gustatory treat. In fact, it's difficult after eating one not to return to the still-beckoning oven, and replenish its warm bosom with another pork-filled delight.

Sadly, post-location change, the nearest store is now a Sainsburys, 4 miles away. Their sausage rolls proved to be edible, but very ordinary; neither fair nor foul.

And, whilst Co-ops tend to be as common as chlamydia, Waitrose outlets are distributed in a selective fashion, often within snobbish districts, so the nearest one is now 13 miles away. Surely I can't justify going that distance just for some sausage rolls, can I?

Red Bull's double-floor

One of Red Bull's technical trademarks is the refusal to abandon an idea just because it doesn't work at the first attempt.

At the beginning of the season, let us recall, they devised an underpass which separated the coke-bottle flow along the flanks of the sidepods, feeding the starter-motor slot and the top surface of the diffuser's trailing edge, from the exhaust-flow, sweeping down from the top of the sidepod. That didn't quite provide the type of handling consistency required, and the underpass was duly blocked off.

In Valencia, however, the RB8s have appeared with what amounts to a double-floor. Whereas the first iteration of the idea featured merely a short tunnel, the flow along the flanks of the sidepods now enters a sizeable duct, and re-emerges into the daylight from an outlet between the rear wheels.

There seems to be some sort of separator just inside the duct inlet, so it may be that there are two exits to this duct, and some of the internal flow is directed to the starter-motor slot. A photo from the rear, however, confirms that at least some of this airflow exits under the beam wing, and connects up to the gurney flap on the trailing edge of the diffuser.

So is this a double-diffuser? Well, the point about a double-diffuser, I think, is that the inlet was in the floor, so it increased the mass-flow capacity of the entire underbody, accelerating the air quicker under the leading edge of the floor, increasing the low pressure peak there, as well as accentuating the low pressure peak(s) at the kick-up point(s) of the diffuser(s).

In contrast, because the double-floor inlet on the RB8 is fed by the flow along the flanks of the sidepods, and because that flow is fed by the front-wing wake, it should be sucking the air faster over the front-wing.

The double-floor duct will also presumably increase the flow-rate over the top of the diffuser, and in particular, the flow-rate over the diffuser's gurney-flap, both of which will have the effect of increasing the mass-flow capacity of the diffuser and underbody. Moreover, the stronger the suction through this upper-floor duct, the smaller the quantity of air which gets sucked under the floor just in front of the rear-wheels, a detrimental effect which can increase the turbulence in the outer channels of the diffuser.

So the double-floor should increase both front-wing downforce and underbody downforce. Very neat.

McLaren MP4/1B exhausts in detail

Courtesy of Ultimatecarpage.com, here's some modern photos of the 1982 McLaren MP4/1B, clearly showing how the exhausts were used to blow the trailing edge of the extended diffuser channels.

Note also the rocker-arm suspension, rendered largely obsolete by the end of that year, (for the front suspension at least), the rockers reportedly behaving as undamped springs under the large, ground-effect loadings of the era (Doug Nye, Autocourse 1982 Technical Review).

Meanwhile, the final photo here shows John Barnard's previous car, the 1979 Chaparral 2K Indycar. You can clearly see where the extended diffuser tunnels come from, but the use of the exhausts to blow those diffusers seems to have been an innovation on the McLaren.

For those puzzling over the plumbing here of the turbocharged Cosworth DFX engine, the turbine/compressor is the unit immediately behind the engine. The ambient pressure air inlet is the 'sucker' on the left, whilst the exhaust pipe itself is the large bore unit on the right. The exhausts from each bank of cylinders blend into a single pipe, then immediately bifurcate, one branch feeding the turbine unit, the other feeding the wastegate, which sits between the diffuser tunnels at the rear. When the compressed air reaches some threshold level, and the exhaust gases are not required to maintain boost, a spring opens a valve in the wastegate, and the exhaust gases bypass the turbine, exiting to the atmosphere via the smaller pipes either side of the wastegate.

The future of F1

Can you see the way the wind is blowing?

Historically, there have been seven main performance differentiators in Formula One: engines, chassis, tyres, aerodynamics, set-ups, drivers and strategy. The engines have been homogenised by regulation in the past decade; chassis construction was eliminated as a performance variable by the 1990s; we now have a control tyre formula; and whether by chance or design, the powers-that-be have realised that tyres with negative load-response coefficients can be used to negate, or at least attenuate the benefit of aerodynamic downforce.

That's a piece of knowledge which cannot be un-discovered. The financial structure of Formula One dictates the need to maintain high television viewing figures; this requires close competition, which in turn entails the need to eliminate performance differentiators between the cars. It seems likely, then, that the future of Formula One is a future in which engineering design becomes increasingly irrelevant.

As a sport, if the only performance differentiators are set-ups, drivers, and team strategy, then it could be argued that this is a welcome development.

Other people, however, may wish to start a new formula: a championship for single-seater open-wheeled cars, racing on traditional closed circuits, in which the regulations are as open as the current hillclimb regulations; a championship in which there are no television deals, no revenue streams, no marketing executives, no big corporations; a championship in which engineers can let their imaginations run free without constraint; a championship in which drivers can race on proper circuits rather than go-kart tracks in the desert.

The first-ever exhaust-blown diffuser in F1?

Conventional wisdom holds that Formula One's first exhaust-blown diffuser appeared on the Renault RE40 in 1983. “The exhaust-blown diffuser first appeared in F1 28 years ago…first conceived by Renault’s Jean-Claude Migeot…Migeot was a 29-year old Renault aerodynamicist when he conceived the exhaust-blown diffuser in 1982. The system made its debut on the Renault RE40 at the Monaco Grand Prix a year later” (Technical Focus: Blown Diffusers, Edd Straw, Autosport March 10th 2011, pp32-35).

Certainly, Renault were the first to blow their exhausts into the diffuser, and in fact, Migeot actually piped both exhaust and turbo wastegate flow directly into the diffuser. However, exhaust-blown diffusers include not only those which blow into the diffuser, but also those which blow over the top of the diffuser, and it could be argued that the first such device actually appeared on the 1982 McLaren, the MP4-B, as seen in the contemporaneous drawing below by Giorgio Piola.

Unlike most of the ground effect cars of the generation, the diffuser tunnels on the MP4-B extend all the way back to the trailing edge of the rear suspension. The engine cowling and rear deck is fitted from above and also extends to this point, but a gap remains between the two. The exhausts exit into this slot, above the diffusers, and beneath the rear deck. In fact, the exhausts are almost invisible on the fully clothed car, and do not protrude into the ambient airstream.

On most cars of this era, the exhausts were clearly treated, at best, as aerodynamically neutral elements, or at worst as disruptive devices. This is understandable because, in general aerodynamic terms, exhaust jets are particular examples of round jets, a type of paradigmatic turbulent flow. Exhaust jets are sources of heat and turbulence, neither of which appear, at first sight, to offer any beneficial contribution to downforce. The nature of a round jet is succinctly explained as follows by P.A.Davidson:

"The instantaneous interface between the turbulent jet and its surroundings is highly convoluted...since the turbulence is a manifestation of the vorticity which is extruded from the inside of the nozzle and then swept downstream...When Re is large, this vorticity is virtually frozen into the fluid and so the convoluted outer edge of the jet, which marks the outer limits of the vorticity, is an inevitable consequence of the eddying motion within the jet. As with a planar jet there is entrainment of the ambient fluid as the convoluted outer edge engulfs irrotational fluid. Thus the mass flux of the jet increases with [axial distance]," (Turbulence, Cambridge University Press, 2004, p154)

Bearing this in mind, Williams used an interesting approach on the FW07 (1979-1982) and FW08 (1982), where they extended the exhaust pipes into the centre of the rear deck, and pointed them in double-barrelled style at the central rear-wing pillar.

This is clearly not ideal for structural reasons, and indeed it ultimately caused Keke Rosberg’s rear wing failure at Monza 1982, when he was close to sealing the championship. One has to conclude, then, that this configuration was aerodynamically motivated. In particular, it seems likely that Williams wanted to remove the exhaust jets as far as possible from the diffuser exits of the sidepod venturi. The reason for this is perhaps best explained by these comments from Frank Dernie:

“The rear wing was a significant part of defining the wake pressure which drove the underbody performance, it is impossible to separate them. The rear wing was not at the legal limit because overall performance was better with the underbody and wing coupled.

“Most people’s diffusers stopped at the [leading edge of the] rear suspension. It was very difficult to keep the flow attached any further back, so all you got was more weight and less accessibility.” (X-ray spec: Williams FW07, Motorsport, November 2004, pp75-77).

Which brings us back to the McLaren MP4-B, and its extended diffuser tunnels. Directing the exhausts over the top of the diffusers might well have disrupted the link between the rear wing and underbody, but whilst exhaust flow creates turbulent kinetic energy, it also locally increases the mean-flow kinetic energy. Hence, it might have been McLaren's intention to use exhaust blowing to keep the airflow attached to their extended diffusers.

Whether this hypothesis is true, is something that perhaps only John Barnard or Alan Jenkins can answer...