Justice and motor racing siblings

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

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

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

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

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

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

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

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

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.