Red Bull's double-DRS

Is there a connection between Red Bull's new double-DRS system, and their unique 'underpass' duct?

To recall, the underpass is a means of separating the 'coke-bottle' flow along the flank of the sidepod, from the exhaust-flow, sweeping down from the top of the sidepod. The coke-bottle flow feeds the starter-motor slot and the top surface of the diffuser's trailing edge, while the exhaust jet partially seals the side of the diffuser and increases the flow over the rear brake-duct assembly.

The underpass is fed by the flow along the flanks of the sidepods, which in turn is fed by the front-wing wake. By connecting the flow along the flanks of the sidepods to the low pressure area under the beam wing, the underpass not only assists with rear downforce, but also pulls the air faster over the front-wing.

Red Bull's double-DRS system purportedly stalls the central section of the beam wing, (although Craig Scarborough suggests that it is the tips of the beam-wing which are being stalled, in order to reduce the wing-tip vortex drag). 

The central part of the beam wing is the section which is pulling the air out of the underpass. Thus, if the beam wing stalls, then the underpass stalls, the flow along the flanks of the sidepods weakens, and front-wing downforce and drag are reduced.

The image above here illustrates how the front-wing streamlines on a generic open-wheeled race-car are the same streamlines which pass along the flanks of the sidepods, and thence between the rear wheels, (although there is no sidepod undercut or beam wing in this illustrative case, courtesy of the 2012 University of Southampton Racecar Aerodynamics MSc Group Design Project).

Red Bull introduced a smaller underpass inlet for the Korean Grand Prix, and if the double-DRS really does stall the centre of the beam wing, it would certainly make sense to change the underpass as well. Autosport's Mark Hughes comments in his Korean Grand Prix report that the changes to the sidepod area gave "more downforce and more diffuser stall." 

One can speculate then, that Red Bull's double-DRS is a system which reduces front-wing drag as well as helping to stall the beam wing and diffuser.

Lasers, plasmas and diffusers

The first laser, invented in 1960 by Theodore Maiman, an engineer-turned-physicist, was a product of the aerospace industry. Maiman was working for Hughes Research Laboratories, and was given nine months and $50,000 to make a laser work by Mr Hughes, (And then there was light, Pauline Rigby, Physics World, May 2010).

Perhaps it's time, then, for the introduction of the laser into Formula One, not merely as a ride-height sensor, but as a flow control device.

Racing cars have, traditionally, used the short-range repulsive forces of solid surfaces to control the flow of air. This, however, is merely one particular, very convenient solution to the engineering problem. Lasers can also control the flow of air, either by directly delivering radiation pressure to a specific region of the airflow, or by creating a plasma whose pressure can instead be used to the same effect.

The question here is merely one of practicality. Do modern lasers combine sufficient power in a lightweight, compact package? Well, probably not quite yet, but there are already some tantalising glimpses of the possibilities.

The Curiosity Rover currently exploring Mars is equipped with a Laser-Induced Breakdown Spectroscopy (LIBS) system. The laser vaporises rocks some distance away, and a separate camera system analyses the light to make inferences about the chemical composition of the rock. Most intriguingly, the weight of this powerful laser system was reduced to 500g.

A LIBS system focuses a laser on an object and ablates the surface layer of the object to create a plasma plume. This high-temperature plume has a momentum flux, and it has long been suggested that this could be used to propel lightweight objects.

In terms of an immediate Formula One application, however, one might install a laser unit low down in the aft region of the sidepods, and train the laser light upon an aluminium foil surface attached to the floor in the region where one currently finds vortex generators, just inside the rear wheel. The resulting plasma plume could be used as a surrogate exhaust jet to seal the diffuser, with perhaps the odd magnet to focus the plasma. Depending upon how the regulations evolve, KERS energy could be used to power the laser.

There are some potential hazards, such as the possibility of vaporising the rear end of the car if the laser is incorrectly focused, but these are small matters in comparison to the potential advantages of a laser-sealed diffuser system.

Race strategy equations



William Mulholland, erstwhile Vehicle Dynamics Engineer for McLaren Inter-Planetary, wrote an interesting introduction to the mathematics of Formula 1 race strategy a few years ago.

Mulholland's account considers only the effect of fuel weight rather than tyre performance, and dates back to the refuelling era, but it's still a decent account of the basic concepts. 

With t₀ denoting the notional lap-time without any fuel weight, W denoting the lap-time deficit per lap of fuel onboard, and l denoting the distance travelled in laps, then the first expression here defines the time which elapses between pitstops for fuel on laps L₁ and L₂.

The solution to this integral is then provided by the expression on the left.

Taking an intrepid approach, we can generalise these equations to include the effect of tyre performance deterioration, and deal with the absence of refuelling.

With t₀ now denoting the lap-time on pristine tyres and empty fuel tanks, L_end denoting the number of laps in the race, and T denoting the lap-time deficit per lap travelled on a set of tyres, we obtain the expression below for the stint-time between laps L₁ and L₂:

The solution to this integral is provided by the following expression:





In the absence of interference from other cars, the optimal number of stops, and the optimal timing of those stops, can be calculated once the time lost during each pit-stop is added to the time which elapses during each stint of the race.

Obviously, these equations are still highly idealised. The actual lap-time deficit T per lap travelled on a set of tyres will be fuel-load and track-condition dependent, hence in reality this will be a function T(l) rather than a constant.

Moreover, the presence of interference from other cars changes the optimal strategy, and introduces uncertainties. Dropping into slower traffic after a pitstop, and being unable to overtake that traffic, prevents a driver exploiting the full performance potential of the car at that point in time. Hence, the optimal number of pitstops in the presence of other cars tends to be less than the optimal number in the absence of other cars.

The unpredictable behaviour of other cars, and the possible occurrence of chance events such as rain and safety cars, entails the introduction of probability distributions over the optimal number and timing of pitstops. Calculating these optima in the presence of other cars becomes an exercise in game theory, where the effect of a decision is influenced by the decisions of other agents, and where the decision of an agent is influenced by that agent's beliefs about the anticipated decisions of the other agents.

Bayesian networks are precisely designed to capture the conditional probabilistic relationships between numerous chance events and unpredictable decisions. Hence Bayesian networks might be very useful for updating the most likely optimal strategy as a race progresses in real-time.