Airbox spillage and fluidics

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?

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

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

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

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

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

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

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

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

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

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.