Lotus 72 CFD

For those interested in a bit of retrospective CFD, I've written an aerodynamic analysis of the 1970 Lotus 72, as a contribution to Mark Hughes's latest work, F1 Retro 1970.

We were extremely fortunate here in being able to utilise the CFD resources of Sharc, and in particular the patient and responsive cooperation of Richard Bardwell. Many thanks to all concerned!

You can read the full text in the published work, but there is an omission in that, to avoid deterring the non-technical reader, I decided not to list there the full details of the CFD configuration.

For the technically curious, however, I can now put that to rights: We used a k-epsilon turbulence model, and employed a mesh containing approximately 20 million cells, with a boundary layer mesh comprising 3 layers. A y⁺₁ of around 30 was chosen. The vehicle was simulated with rotating wheels on a rolling road at a freestream airspeed of 50m/s. The sidepod radiator and airbox inlets were treated as outlets (if you see what I mean).

Two ride-height combinations were used: 40mm front/60mm rear, and 60mm front/90mm rear. Runs were conducted for the Straight Ahead case, and with 4 degrees of steering angle. The frontal area used in the lift-coefficient calculations was 1.372msq. For each CFD case, the solver was run for 1000 iterations.

The legality of Brabham's 1983 World Championship

A couple of recent pieces in the motorsport press have raised separate issues over the legality of the Brabham-BMW which won the 1983 World Drivers' Championship in the hands of Nelson Piquet. Gary Watkins's Autosport article re-considered the exotic, ex-Luftwaffe fuel brew used by BMW in the latter stages of the season, while Mike Doodson's Motorsport article elicited the following admission from then-Chief Mechanic Charlie Whiting that, "All I will say is that we always, um, attempted to make the car as light as possible."

Indeed, and not just in qualifying it seems, for Gordon Murray rather gave the game away earlier this year with the following comment:

"Whenever we planned to stop - we could go without on street circuits - we tended to do 60-70 per cent of the race on the first set of tyres because that meant we could run very close to, or under, the minimum limit before adjusting the weight with the amount of fuel we put in," (Motorsport, May 2013, p86).

That's a pretty unambiguous admission that the Brabhams ran under the legal weight limit in many 1983 Grands Prix, and used fuel-weight as ballast. If you go through the races in 1983 you'll see that Piquet's Brabham was almost always the last of the leading runners to pit for fuel, and that he sometimes pitted 5-10 laps or so after the Ferraris and Renaults, his championship competitors. At Hockenheim, for example, Prost's Renault stopped on lap 20, while Piquet stopped on lap 30.

Why would Brabham want to stop after everyone else? Well, in the era of refuelling, a car on empty tanks and worn tyres was generally faster than a car which was fuelled-up on fresh tyres. Moreover, in 1983 the Ferraris were shod with bias-ply Goodyear tyres, and thereby tended to suffer greater tyre warm-up difficulties than the Michelin-tyred Brabham. Thus, it was in this 5-10 lap window that the Brabham would often make hay.

At Spa, Tambay's Ferrari was running ahead of Piquet until stopping on lap 21; Piquet stopped on lap 24, and jumped ahead of the Ferrari, forcing Tambay to re-pass some laps later. Similarly, at the Osterreichring, leader Arnoux's Ferrari stopped on lap 28, Piquet on lap 31, after which Piquet emerged ahead, forcing Arnoux to re-pass some laps later.

So why, then, wouldn't everyone schedule their pit-stops at 3/4 distance? Well, that extra fuel-weight costs lap-time, and it costs you lap-time on each and every lap that you carry the extra weight around on your back. If you started a race with about 20kg of extra fuel, that would cost you about 0.6seconds of lap-time, which over 30 laps would mount up to a very substantial 18 seconds or so.

However, if your car was 20kg beneath the legal weight limit when drained of fuel, you could start the race at the same weight as your competitors, but with the ability to run 5 laps or so further. You would suffer no disadvantage in the early stages of the race, and you would also be able to jump ahead of your competitors by running longer. Perfect.

In fact, just about the only time Piquet didn't run long was in the final race at Kyalami, when he shot off into the distance on a light fuel load, pitting on lap 28 of 77, able to resume without having lost the lead. It's possible that the Brabham started the race over the legal weight limit, but was running underweight for a significant portion of this stint. Moreover, in the late stages of the race Piquet slowed considerably, sacrificing what appeared to be an easy victory. Contrary to the explanation given on the day, that Piquet was merely trying to ensure the reliability of his car, he might also have been minimising fuel consumption to ensure the car was actually over the legal weight limit at the end of the race!

Ferrari's illegal brake ducts

When Ferrari launched their 1976 car, the 312T2, it appeared with a pair of outrageous front brake-duct appendages. These extended forwards, and curved around the inner front shoulder of the tyres, presumably with the intention of reducing front-wheel drag and turbulence.

These brake-duct extensions appeared only once during the racing season, in modified form, at the French Grand Prix (above). Pete Lyons reported in Autosport/Autocourse that "As a member of the CSI [the sport's governing body], Jabby Crombac pointed out that these appeared to contravene the regulations about 'movable aerodynamic devices' and the first session times for both cars were disallowed."

Note that these brake ducts were declared illegal, not because they intruded into a region from which bodywork was prohibited, but because they constituted movable aerodynamic devices. That is to say, being attached to the wheel uprights, they moved with respect to the sprung mass of the car, the reference frame against which movability is judged in this context.

It is a curiosity, then, that despite this precedent, and despite the fact that section 3.15 of the current Formula One Technical Regulations still requires bodywork influencing the aerodynamics to be "immobile in relation to the sprung part of the car," brake ducts are explicitly exempted. Devices such as those pictured below seem not dissimilar to those on the 312T2 at Paul Ricard in 1976. Perhaps Ferrari should ask for their Friday morning times to be reinstated...

Rush and the 1976 Austrian Grand Prix

Rush is currently No. 1 at the UK box-office, and Ron Howard's populist mix of stereotypical rivalry, heroism, sex and danger, is sure to attract a new generation of fans to the fight between 3-stop strategies and pace-managed 2-stoppers.

For those seeking the real thing from 1976, this was the video of the entire Austrian Grand Prix at the Osterreichring. It has now been stripped from Youtube by the guardians of copyright, who don't appear to be protecting any commercial interest given that there is no alternative outlet in which the entire race can be viewed. 

Which is a pity, because the original Osterreichring was a majestic, Styrian theatre of motorsport. The 1976 race started with localised showers of rain, until, as Pete Lyons reported, "The Sun now broke out on the highest slopes above, kindling the tents there into incandescent yellows and reds. Within minutes the entire landscape was brilliant, rain-washed green." 

Proper drivers, proper cars, and a proper circuit.

Chapman, side-thrust, and the America's Cup

In the summer of 1975, Colin Chapman composed a list of requirements for a Future F1 Car.  Reproduced in Karl Ludvigsen's excellent engineering biography (Colin Chapman - Inside the Innovator), many of the points continue to be relevant today. In particular, the list includes the following laudable objectives:

5...We must get maximum cornering force from the tyres. This is maximised by:
(i) The largest possible contact patches.
(ii) With the softest compound.
(iii) Kept in contact with the ground as long as possible.
(iv) With highest possible download.
(v) Spread as evenly as possible over the contact patch.
(vi) And spread as evenly over the four contact patches in proportion to the sideloads they have to carry.

In a more quirky vein, Chapman includes the following speculative thought:

9. Total cornering force can also be increased aerodynamically
Should we try to use vertical lifting surfaces to provide additional side load derived from the speed and yaw angle of the car whilst cornering?

Which is interesting, because apart from the use of fins atop the engine cover, there appears to have been little effort in Formula 1 to generate a direct aerodynamic side-thrust. In contrast, it seems to be an extremely important part of racing yacht design, of which The America's Cup might be held as the foremost example.

If a yacht is your chosen mode of travel, and the wind rather inconveniently happens to be blowing from a direction close to the direction in which you wish to travel, you can still generate a thrust in that direction by means of some aerodynamic and hydrodynamic magic.

Firstly, you use your sail as an aerofoil, and generate low pressure on one side of it, so that an aerodynamic force is produced at right angles to the effective direction in which the wind is travelling. This alone wouldn't get you to where you want to go, but here you can use the fact that there are actually two fluids in play: air and water. Whilst your sail can generate a force from the airflow, the hull of your yacht can also generate a force from the flow of water. With a yaw angle between your direction of travel and the effective wind direction, the water will accelerate around one side of the hull, creating a hydrodynamic side-force which can be used to cancel out the sideways component of the force generated by the sail. What remains of the aerodynamic force is a component pointing in the direction you wish to travel!

As Alfio Quarteroni explains (Mathematical Models in Science and Engineering, from which the diagram above is taken), the presence of two fluids with different densities and viscosities, separated by a free surface endowed with surface tension and variable curvature, adds many interesting dimensions to the fluid mechanical problem. Moreover, the sail itself needs to be treated as an aero-elastic medium, deforming in response to the pressure field upon it, and thereby changing the airflow, in a coupled manner. Seen in this light, it's no surprise that The America's Cup once exerted such a pull over the imagination of Chapman's modern counterpart, Adrian Newey.

What is a quantum field?

Philosopher of Physics Meinard Kuhlmann has a brilliant article, What is real?, in the August 2013 edition of Scientific American.

Kuhlmann provides a clear account of why the particle and field ontologies provide equally inadequte interpretations of quantum field theory. Whilst most physicists tend to resort to the lazy claim that the particle and field concepts are somehow 'complementary', Kuhlmann points out that this doesn't help "because neither of these conceptions works even in those cases where we are supposed to see one or the other aspect in purity."

Kuhlmann's account of how a quantum field is mathematically defined is particularly striking: "A classical field is like a weather map that shows the temperature in various cities. The quantum version is like a weather map that does not show you '40 degrees', but '√'.

The article concludes with a nice explanation of two alternative ontologies: structural realism, and the bundle theory of properties.

If you want an insight into the philosophical problems of modern physics, this is an excellent introduction.

Front-wing vortex breakdown

With the assistance of Mercedes GP, Jacques Heyder-Bruckner completed a PhD thesis in 2011 which analysed the front wing-wheel interaction on a racing car. Of particular interest in this work is the fact that Detached Eddy Simulation (DES) was used to represent the phenomenon of vortex breakdown, which occurs when the front-wing approaches low ride-heights under conditions of roll and pitch.

Whilst Reynolds Averaged Navier-Stokes (RANS) simulations are the CFD workhorse of modern motorsport, RANS is known to be inadequate for representing separated flows, and in particular for representing large-scale vortical phenomena, such as vortex evolution and breakdown. In contrast, Detached Eddy Simulations use RANS to represent the attached flow, but directly solve the Navier-Stokes equations in the regions of separated flow.

Q-criterion isosurfaces of the vortex breakdown phenomenon, taken from the instantaneous DES flowfield, are depicted here. Bruckner points out that “the vortex breakdown moves forward as the wing is moved closer to the ground…The large vortex expansion…is composed of a recirculation region enclosed by the spiralling tail shed from the vortex breakdown.This causes high pressure fluctuations on the endplate and flap, resulting in a more unstable wing with variations in downforce and drag three times larger than at higher ride-heights.” (p116).

 

The Lynx effect

Hidden within the dark torrent of subliminal messages communicated by commercial advertising and branding, it seems that aerodynamic information from contemporary Formula One is being transmitted on the side of Lynx anti-perspirant cans.

In the case shown here, one can see the vortices on a transverse plane just in front of the floor. The large structure on the right is clearly the Y250 vortex, created by the transition between the front-wing camber and the mandatory neutral central section astride the nose pylons. To the left, one can see two smaller vortices, probably shed by a guide vane hanging down from the underside of the nose.

Doubtless, the transient effect that such products have on axillary diaphoresis is matched only by the transient instability of these vortices.

Tyre feathering

"If a new tyre is punished too heavily, too quickly, its critical tread compound temperature may be exceeded and blisters will appear and burst...Heavy cars, unsympathetically-driven cars and badly set-up cars may burn-out their tyres (particularly at the front) in a less abrupt manner. This phenomenon, known as 'graining' or 'feathering', rolls little pieces of rubber off the tread - diminishing its grip. A watchful driver will recognise the condition as one edge of his front tyres - or of the rears seen in his mirrors - will blacken. The car's cornering power will be limited and if he presses on the condition will worsen. A sensitive driver will ease off, roll-away the loose granulation, and after a few laps will see his tyres regain their normal appearance and will find much of their adhesion restored."

(Doug Nye, Motor Racing in Colour, Blandford Press, 1978, p44).

BBC Sport and Potential Flow theory

It is a fact, sadly unacknowledged, that BBC Sport's default background animation represents a doublet from Potential Flow theory.

Potential Flow theory is a branch of aerodynamics in which flows are idealised as being inviscid and irrotational. This means, respectively, that there is no friction resistance to shear between adjacent layers of fluid, and there is no vorticity. Hence, Potential Flow theory does not recognise the existence of boundary layers adjacent to solid objects.

Now, there is, within aerodynamics, a distinction between circulation and rotation, which has the potential (if you'll excuse the term) to confuse. In a flow with circulation, you can integrate the velocity vector around a closed loop and obtain a non-zero value. In a rotational flow, the vorticity field is non-zero.

In a Potential Flow (guaranteed, by definition, to be irrotational), if the region of space occupied by the fluid is simply connected topologically-speaking, (entailing that any loop can be smoothly deformed to a point) then the flow will have zero circulation. However, if the region is not simply connected, then the irrotational flow can possess circulation. The presence of solid objects in a fluid prohibits the region of space occupied by the fluid from being simply connected, (in 2-dimensional terms, at least), hence Potential Flows around solid objects can possess circulation.

This loophole (if you'll excuse the term) within Potential Flow theory enables one to represent the circulatory flow around wing sections. Because the equations of Potential Flow theory are linear, one can superpose several solutions of the theory to obtain other solutions. To represent the flow around a cylinder, for example, one superposes a uniform flow with a so-called doublet. The latter provides the stagnation points to the flow at the leading and trailing points of the cylinder.

To represent the circulatory flow around a wing section one basically just adds a free vortex to the superposition.

Hence, despite the BBC's apparent aversion to covering all the Grands Prix in a Formula One season, aerodynamics is clearly a subject close to their heart.

Descent to bathos

Whilst the odiferous obligations of life suggest a strictly utilitarian approach to bathroom use amongst much of the population, there are those of us who continue to resist the anxious, volatile, blinding spray of the shower-head, and stubbornly insist on prolonged semi-submergence in a liquid heat source as an opportunity for rest, relaxation, and consumption of excellent prose.

This sub-class of the population, however, has to endure a flagrant design flaw which besets many a bathroom, yet receives scant public attention. This, namely, is the tendency of negligent bathwrights to erroneously align the tap-end of the tub towards the centre of the bath-space. This places the reclined reader's head at the opposite end of the bath-axis, where illumination from the central, ceiling-located light source is typically inadequate.

Until bathwrights can be prevailed upon to mend their ways, there is, fortunately, an interim measure which can be undertaken: remove a large mirror from the hallway, and balance it on the junction between the bath and the ceramically tessellated wall; obtain a lofty chair, a long electrical extension cable, and place an anglepoise lamp on the chair, facing the mirror. This cunning configuration will provide the recumbent, heat-absorbent reader with an adequate level of reflected light, from which the world of the imagination can once more be accessed, and the stresses of the modern world temporarily dissolved. There is nothing which could possibly go wrong.