Some may call it exciting and others farcical. For a fledging series, Formula E certainly attracted the wrong kind of attention with the slipshod finish yesterday resulting in only 9 drivers being classified at the end. While it is easy to call out the FIA or Da Costa for the extra lap, the reality, as always, is more complex. This analysis thus aims to clarify the events as they unfolded.
The first big question that I came across on the web was about the big change in energy reduction percentage during the various SC periods. While there was only a 3% reduction during the 3-minute safety car (SC) at the 20-minute mark, the final 5-minute SC resulted in a 12% reduction. Well, this is quite easy to explain keeping in mind the starting available capacity of 52 kWh. Essentially, the percentage value displayed on the screen is a relative value whereas the absolute reduction is happening in terms of kWh, both to the usable energy as well as available energy.
At 20:38 remaining, we can see that the available energy is 61%.
Moments later, it drops to 58% after the reduction.
The reduction itself is 3 kWh for that SC period and a total of 9 kWh for the race.
This latter part is the most important as it indicates the total available energy after the reduction. Back of the envelope calculations for this scenario is as follows. Note that these calculations are based on the whole number figures displayed in the TV graphics while the actual numbers with the correct precision would be slightly different.
Usable energy before reduction: 46 kWh (52 – 6)
Available energy before reduction: 61% of 46 kWh = ~28 kWh
Usable energy after reduction: 43 kWh (52 – 9)
Available energy after reduction: 58% of 43 kWh = ~25 kWh (28 – 3)
Now let us take a look at the final SC. The available energy is 18% prior to reduction.
It drops to 6% after reduction.
The total energy reduction is 19 kWh in total and 5 kWh for that SC period.
The calculations now are as follows:
Usable energy before reduction: 38 kWh (52 – 14)
Available energy before reduction: 18% of 38 kWh = ~7 kWh
Usable energy after reduction: 33 kWh (52 – 19)
Available energy after reduction: 6% of 33 kWh = ~2 kWh (7 – 5)
As you can see above, the percentage value can be quite confusing for the viewer as both the numerator and the denominator change by the same amount and thus the change in the actual percentage value will be more drastic for lower energy values than the higher ones.
That explains the TV graphics but then why were the teams caught so unawares towards the end? For, let us go to the period just as the final SC came out.
At this point, Da Costa has 22% of 38 kWh usable energy i.e. 8.4 kWh. The fastest lap as can be seen in the office notice was about 1m 40s. It thus indicates that at this point, there was enough time to cover 5 laps.
However, when the SC came out at 5:38 remaining, there was still a part of the lap remaining. Luckily, Da Costa floored the car at about the same place after the SC, so we can easily make out the time needed to reach the finish line from that part of the track.
As can be seen from the images above, it takes about 25 seconds implying that Da Costa would have crossed the line with 5:13 remaining if there was no SC. Considering the fastest lap of the race, 3 laps would have taken around 5 minutes. Thus, if Da Costa was to complete 3 more laps in 1:44 to 1:45 minutes, he would have needed to complete only 4 laps to finish the race with about 8 kWh remaining which is perfectly feasible.
The problem then is that the SC pace was not enough to scrub off a lap and thus the cars still had to complete 4 laps to finish the race, around 2 laps under the SC and a little more than 2 laps at race pace. While the race pace target was 2 kWh/lap, under the SC, assuming a lap time of 2m 30s, the reduction would have been 2.5 kWh/lap. This implies that the cars lost around a kWh of energy behind the safety car due to the time elapsed and at the same time utilised closed to 1.5 kWh of energy following the SC.
Thus, while in race conditions, Da Costa was expected to have 4.4 kWh of energy at the point where he started the final run with 2 laps to go, in reality he had about 2 kWh. The only feasible option was to limit the race to one lap after the SC which he was unable to do so. At the same time, Mercedes seems to have a 5-lap target in mind before the SC and thus were keeping more energy in hand compared to Da Costa who was hoping to limit the race to 4 more laps at the time the final SC came out.
While it was a shambolic end to the race with the
FIA shifting blame to Da Costa for not controlling the pace, the FIA is not without blame. They had never made a provision for such a scenario and the fixed reduction of 1 kWh/min applied by the FIA is excessive when the usable energy is low.
One way of tackling such a scenario could have been to reduce the energy allocation for a race lap over a SC lap duration (i.e. ~2 kWh reduction over a 2:30m SC lap). This results in a reduction rate of 0.8 kWh/minute. If this seems too low a reduction, then the rule can be changed to apply this limit only for the final 10 minutes of the race.
The other option could have been to not deduct the energy consumed by the car behind the SC which seems to be about 0.3 kWh/minute (can be calculated from the fact that usable energy reduced from 22% to 18% behind the 5-minute SC with 38 kWh available energy). However, this would result in a reduction rate of 0.7 kWh/minute and thus even more benevolent that the previous approach which is in fact more practical as it takes in to account the energy consumption by the race car and SC for a specific track.
Will this situation be addressed? That is anybody’s guess as Formula E certainly seems to be quite disorganised at present. However, the solution to the problem is available as highlighted above and all it needs is the FIA to act on it. Most probably though, I think the teams will adjust the software to account for the SC loss going forward and we might see a slow but secure finish if such a scenario arises in the future.
