The connection between Formula 1 and Dark Energy

Perhaps to the surprise of many aerodynamicists, one of the concepts deeply familiar to them, may actually explain the existence of dark energy.

This ominous form of energy corresponds to an extra source term in the cosmological version of the Einstein field equations, and is commonly held to be responsible for the accelerating expansion of the universe.

The connection with aerodynamics lies with a concept used to represent turbulent flow, called Reynolds Averaging. Despite the supercomputer power available in Formula 1, it remains impractical to solve the exact Navier-Stokes equations for a turbulent flow. Instead, the velocity and pressure fields are split into the sum of a mean field and a fluctuating component, and the Reynolds-Averaged Navier-Stokes equations are solved to calculate the mean fields.

However, the process of taking the average of the Navier-Stokes equations generates an extra term, which is interpreted as an extra source of stress. One thinks of the mean field as having to do work against the extra stresses created by turbulent eddies, as well as the viscous stresses already inherent in the fluid.

Thus, whilst the Navier-Stokes equations for a steady flow are as follows:







The Reynolds-Averaged equations pick up an extra term on the right-hand side:







Now, as cosmologist George Ellis and his colleagues explain, whilst the exact Einstein equations hold at the local scale:



Once one averages the matter-energy and geometry over galactic scales, the Einstein equations pick up an extra term:



Sound familiar? As Ellis et al comment, this "is the effective matter source term representing the effect of averaging out smaller scale structures."

Whether this type of effect can explain the quantitative cosmological data remains to be seen, but perhaps aerodynamicists have something to offer the cosmological community here.

Wastegate-blown diffusers

Whilst the FIA have made extensive efforts to prohibit the use of exhaust-blown diffusers in Formula 1 from 2012 onwards, there appears to be no such proscription on the use of compressed air from the inlet manifold of an engine. Formula 1's engine formula changes to a 1.6 litre turbo-charged V6 in 2014, and the turbine in such an engine is constantly generating compressed air. The inlet manifold of a turbo engine has a blow-off valve, specifically designed to release pressure when the driver lifts off the throttle or the throttle is closed. Thus, the blow-off valve could be vented down to the sides of the diffuser, providing vital extra downforce when a driver comes off the throttle turning into a corner.

In terms of the legality of such a system, there is already a clear precedent. As pointed out in Giorgio Piola's Formula 1 Technical Analysis 2010/2011, the very first exhaust-blown diffuser, the Renault RE40 of 1983, had several outlets blowing each lateral channel of the diffuser; in Piola's diagram (p15), three came from the exhaust, but one came from the turbo wastegate, (in fact, in pictures featured on Craig Scarborough's site, there are only two outlets from the exhaust, and one from the wastegate).

Piola points out that the legality of the system was protested by Brabham at the 1983 Detroit Grand Prix, but the protest was rejected both in situ, and at a subsequent tribunal on 26th July. Hence, whilst the FIA might be able to regulate the position of the exhaust outlets, and the off-throttle pumping effect of the engine, the turbo wastegate could conceivably be used as an independent blowing device in 2014.

McLaren's floor tiles

The BBC recently broadcast a documentary on McLaren's new supercar, the MP4-12C. In the opening minutes of the programme, we follow Ron Dennis around the immaculate McLaren Technology Centre. As Ron strides across the lakefront atrium, he points out a broken floor tile, and expresses his annoyance: "The reality is, when it's changed, it'll be imperfection, because the colour won't match. Tiles come in batches. You can see this one here's been changed, [pointing to a darker tile.] Doesn't that bug you? It bugs me. Big time."

In fact, rather than tiles from different batches being of a different hue, in this case the reason a new tile stands out is probably that the old ones have been subjected to the daylight for a period of time, and due to the slow photodissociation of the pigments inside, will gradually be growing lighter in colour. Hence, a new tile looks darker simply because it's been exposed to daylight for a shorter period of time.

There is, then, a possible means by which McLaren can mitigate this chromo-tessellatory problem: Purchase a sufficient number of spare tiles at the outset, and then allocate a backroom at the MTC for the purpose of exposing these backup tiles to the correct diurnally-averaged spectrum and intensity of artificial sunlight. When a frontline ('customer-facing') tile suffers a fracture, the replacement will have endured the same amount of photodissociation, and will be indistinguishable in colour from its two-dimensional siblings. Problem solved.