Tuesday 20 November 2012

Statistics from the 2012 WEC season - LMP1

Now that the World Endurance Championship season is over, and Christmas only a little more than a month away, it is a good time to reflect on the past season. Inevitably, I suppose, this summary will focus on the numbers.

Let's look at the LMP1 class first, particularly the works Audi and Toyota teams. The following table shows the average speed across those races in which Audi and Toyota competed together. For the purposes of this, I have included the first five hours of the Le Mans 24 hours, then compiled the data from the six hour races at Silverstone, Interlagos, Bahrain, Fuji and Shanghai.

Car No. No.1 Audi No.2 Audi No.7 Toyota
Average Speed (excluding pit stops) 188.40 km/h 188.31 km/h 189.56 km/h
Total time spent in pits 44m 56.867s 55m 02.654s 55m 39.240s
Total number of pit stops (excluding penalties) 38 39 42
Average stint on tank of fuel 157.23 km 158.12 km 141.48 km
Average Median Pit Stop Time 1m 07.148s 1m 10.965s 1m 04.484s

A word of explanation is appropriate here, to describe some of my calculations.

Average Speed is the total distance travelled in all the races, divided by the time spent by each car on the track. I have subtracted time spent in the pit lane.

Average Stint length is slightly debatable figure, as I have attempted to include only those stints where the reason for stopping was for re-fuelling. I have excluded any stint that was affected by a safety car period, and any where the reason for the stop was for some other reason: e.g. to repair damage. However, some stints are curtailed because of tyre wear - and towards the end of a race, stints may be shortened to balance the final two stints. Hence this row is somewhat subjective.

The "Average Median Pit Stop" time is calculated by taking the average of the median pit stop times from each race. The median is the middle value of the pit stops, arranged in order of length (in the case of there being an even number of stops, it is the average of the middle two). I have done this to reduce the impact of long 'repair' pit stops and short 'splash and dash' stops. I have also excluded Stop and Go penalties from this calculation.

However, it seems that the No. 2 Audi suffers here due to longer stops in the early stages of Le Mans and at Interlagos, which materially affected its average.

Also, note that the numbers for car no. 2 are a mixture of data from the non-hybrid Audi R18 ultra that was used at Silverstone and Interlagos, and the hybrid-engined e-tron quattro that was used everywhere else.

I'm not entirely sure that there are any great surprises from this data. The Toyota is demontrably quicker, but it cannot go as far on its tank of petrol as the diesel Audis. Although the Toyota spent more time in the pits altogether, the average time for each stop is less. This is mainly due to more efficient use of tyres in the races at Interlagos and Fuji. It also made more stops.

As a purely academic exercise, I thought it might be interesting to project these figures across a theoretical seventy-two hour race. This is equivalent to the entire WEC season, including the twelve hours of Sebring, twenty-four hours of Le Mans, and the six other six-hour races. Note that the average speeds shown above include time spent behind the safety car, so in a sense, safety car periods are allowed for.

Car No. No.1 Audi No.2 Audi No.7 Toyota
No. of pit stops 84 83 94
Projected Distance Covered 13,268.4 km 13,247.0 km 13,328.2 km

To put this into some sort of perspective, this means that over the course of the WEC season, the leading cars could just about get from London to Cape Town - and the Toyota's winning margin is less than 60km!

What this 'aggregate race' fails to do though, is to take account of the length of a particular race, and the length of a lap at an individual circuit. In effect, there is an underlying assumption that the pit is available whenever the car needs it, and that each pit stop will refuel the tank to capacity. In reality, particularly on a long cicuit like Le Mans, where re-fuelling is only possible every 13.6km, compromises have to made in order to optimise the overall strategy.

Extrapolating the the actual data from the first five hours of Le Mans across the full twenty-four hours, assuming that the pace and strategy continued as it started, and that no safety car periods occurred, provides the following potential result at Le Mans, had the Toyotas kept going:

No. Car No. of pit stops Projected Distance No. of Laps
1 Audi R18 e-tron quattro 33 5,444.34 km 399
7 Toyota TS030 Hybrid 36 5,435.18 km 399
3 Audi R18 ultra 33 5,433.52 km 399
8 Toyota TS030 Hybrid 37 5,418.02 km 398
4 Audi R18 ultra 33 5,410.51 km 397
2 Audi R18 e-tron quattro 34 5,400.46 km 396

Note how the first three cars are separated by less than a lap at the end of the race. Yet another indication of how close things were this year!

Postscript: A good deal of crunching of numbers has gone on in the background here, which I have spared you, for the sake of readability. Leave me a message below if you would like further details, or if you spot any errors.

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