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by Boris Deshev, Ph.D.
Perhaps a question that many have wondered about- is the night time actually affecting the drivers at Le Mans? The centenary edition of the great race just finished, the new data, kindly provided by Al Kamel Systems, are out and we can use them to try and answer this question. The extra large entry list for Le Mans gives us opportunity to analyse separately individual car classes and drivers of different rating. The 62 strong car entry list contained 21 cars in the LMGTE-Am category, 24 LMP2 prototypes, 16 Hypercars and a Nascar car, for the pleasure of the masses. With each car having three drivers, the 186 drivers are split according to their FIA driver rating into 72 Platinum drivers, 45 Gold drivers, 39 Silver drivers and 30 Bronze drivers.
Figure 1. Distribution of racing lap times done during daytime (orange) and nighttime (blue) for the entire Le Mans field. Laps are split according to their car category (rows) and driver rating (columns). The numbers in the top right corner of each panel show the number of laps. All panels have the same x-axis span.
Figure 1 shows the distribution of lap times for the entire Le Mans entry list. Shown are only laps done under green flag and in dry weather, in order to remove the effects that rain and yellow flags would have on the recorded lap time. The available data does not offer detailed information about the rain nor about the yellow flags covering only part of the circuit (as opposed to Full Course Yellow). Because of that, the removal of laps affected by those events is done using iterative sigma clipping. The x-axis of all the panels have the same length so the offset between the different car classes is visible.
Few things are immediately obvious from this figure:
There were no Silver and Bronze drivers in the Hypercar category. Perhaps unsurprising. Top cars require top rating drivers. There were only four Gold drivers in this category.
All drivers in the Innovative Garage 56 Nascar entry were Platinum rated. This should be expected in such a high-end publicity stunt.
There are many more daytime laps than nighttime ones. The race is held in June in the northern hemisphere plus there was a lengthy rain affected period at night.
Two more points which we will analyse in greater detail below:
Many of the panels show a clear offset between nighttime and daytime lap times, with the daytime laps being faster.
The Bronze drivers appear to show the smallest offset between daytime and nighttime laps.
The aerodynamic tweaks applied to the Nascar car did a good job at matching it with LMGTE-Am field
DAYTIME VS. NIGHTTIME LAPS
Figure 2. Distributions of daytime racing lap times (orange) and nighttime ones (blue) are shown by the solid line histograms. The dashed vertical lines show the medians of the corresponding distributions. The number of laps in each set is printed in the top right corner in the corresponding color. The offset in percentage lap time between the median daytime and nighttime laps is printed in black. The p-value from a two sample Kolmogorov-Smirnov test is printed in purple.
For a more detailed analysis of the daytime and nighttime race pace we combine the laps from all classes together. This is done by normalizing each racing lap to the fastest lap that the given car has done during the entire event. For most cars this is their qualifying lap but there were 19 cars which actually went faster during the race than during the qualification. In addition there were 3 cars which did not set a qualifying time.
The distributions of the fastest 10% of those lap times are shown on Figure 2. The vertical dashed lines show the medians of the distributions and the delta between the two medians in each panel is printed in black. The deltas shown by Platinum, Gold and Silver drivers are all around 1% of their fastest lap, which for the winning #51 Ferrari is 2.03 seconds. The Bronze drivers show a very similar day and nighttime distributions with an offset of 0.23% corresponding to 0.53 seconds for the LMGTE-Am class winning #33 Corvette.
Noticeable is also the different shape of the day and nighttime distributions for Platinum, Gold and Silver drivers. The left-hand slope of the daytime lap times rises steeply indicating that the majority of the laps are clustered towards the fastest lap. Perhaps showing drivers confidently driving at or near the limit. The nighttime lap times rise more gradually towards the peak, perhaps showing drivers reaching to the limit. Both distributions for Bronze drivers are very similar to each other and to the night distributions of the professional drivers. In order to quantify how different the day and nighttime distributions for each rank of drivers is we use a two sample Kolmogorov-Smirnov test. This is a statistical test which is often used to test the hypothesis that the two samples can be drawn from the same parent distribution. High p-value indicates that the distributions are significantly different. The results from the test are printed in purple on Figure 2. The p-value for the Bronze drivers, while not very high, is significantly higher than those of the other rank drivers, once again indicating a smaller difference in daytime and nighttime race pace.
WHAT IS THE REASON FOR THE DIFFERENT LAP TIMES
Racing lap times tend to be grip limited and the grip is governed by the tires. This will be most obvious to F1 fans in the current Pirelli era. The tire compound, tire temperature, state of tire ware and track temperature all affect the amount of grip that a given tire can deliver. All other things equal, the cooler night time track temperature should result in a lower grip. Most teams used softer tire compounds during the night to compensate for the lost grip. Perhaps the overall grip was still significantly lower during nighttime than that available during the warmer daytime periods even with softer tires. Could this be the reason for the slower lap times?
We can assess that by looking at the difference in sector times for the three separate sectors of the circuit de la Sarthe. Sectors 1 and 3 have lots of corners and thus the pace through them will depend strongly on the available grip. Sector 2 on the other hand consists mostly of the Hunaudieres straight and the pace there is power limited. The grip level does affect Sector 2 pace during the acceleration out of the Tertre rouge corner and the two chicanes but this is still fewer traction zones than in sectors 1 and 2. This is confirmed when looking at the right-most panel of Figure 3, which shows the distribution of top speed, normalised to the highest top speed achieved by the given car. The speed trap is just before the braking zone for the first chicane in sector 2. If the traction was indeed an issue at night we would expect to see difference in top speed and we don't.
Figure 3. Distribution of sector and lap times for the hypercar field driven by platinum drivers, expressed as a percentage of the fastest sector/lap time of their car. Only laps within 10% of the fastest are shown. The right-most panel shows the distribution of top speed also expressed as a percentage of the best. Daytime laps are shown in orange, nighttime ones in blue.
Figure 3 shows the distribution of sector times, lap times and top speed for all Platinum drivers in Hypercars, all expressed as a percentage of the best achieved by the given car. The ks test of all samples gives a p-value of well under 1e-6 meaning that in all panels the two distributions differ significantly. The p-value for the normalised top speed is low but somewhat higher than the rest, showing that the two distributions are different but not as far apart as the sector/lap times. The similarity in offsets in day and nighttime pace in sectors 1, 2 and 3, and the similarity in top speed distributions shows that the overall grip available from the tires is unlikely to be the reason behind the different lap times recorded at daytime and nighttime.
It is interesting that the distributions shown on Figure 3 show multiple well defined peaks in all sectors. This is particularly noticeable in sector 2 but to some extent all sectors show it and both day and nighttime laps show it too, with the corresponding offset between them. Figure 3 shows only laps from platinum drivers in Hypercars. Thus the likely reason is waved yellow flags in some marshal sectors but not the entire lap sector. As expected, Planitum drivers show very consistent performance throughout the race.
CONCLUSIONS
The pace maintained by the drivers at Le Mans is slower at night than it is at daytime. The reason for that is likely extra caution exerted by the drivers. High rank drivers do have a better feeling of how close to the limit they are. Consequently they show a more pronounced drop in lap times during the night. Lower rank drivers, like Bronze ones, generally show broader distribution in lap times as they are reaching up to the limit, rather than confidently driving at it. This is true for both day and nighttime driving and thus they show a less pronounced decrease in pace during the night.
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