When it comes to historical races, the Monaco Grand Prix is definitely an odd one. Older than Formula 1 itself, it is F1’s most glamorous and most prestigious race on the calendar, featuring a track layout that remains largely unchanged1 since the race’s inception in 1929. Unfortunately, when it comes to on-track action, it is an absolutely dreadful race, with cars that are impossible to race on this track. So, when Formula E announced that the full track layout would be used for the 2021 Monaco E-Prix, people were hopeful that the premier electric series would provide a good race in this historical venue.

Well, it surely didn’t disappoint: the 2021 Monaco E-prix was probably the best dry race Monaco had seen for over two decades, with a three-way battle for the lead between da Costa, Mitch Evans and Robin Frijns. António Felix da Costa eventually won the race with a daring last-lap overtake on Mitch Evans. It was a moment of vindication for both Formula E and this legendary track.

This race was such a hit that the Monaco E-Prix became a permanent fixture of the FE calendar. The media reaction was also quite positive: Inside Electric’s2 Hazel Southwell even suggested that Formula E should consider going to other legendary street circuits, such as Pau and Macau. I could definitely see a future where FE goes to Pau in every year that we don’t go to Paris3. Hosting a Formula E race in Macau’s treacherous Guia circuit would be a lot trickier, however…

The Macau Grand Prix track layout Link to heading

Guia circuit track layout
Guia circuit track layout. ©FIA

The Guia circuit is one of the most challenging race circuits on the planet. It combines an extremely twisty and technical section of road with an enormous 2 kilometer-long straight. Overtaking around this track is done pretty much exclusively on the straight with the aid of slipstream4.

This massive straight does pose a problem for Formula E’s energy-constrained races: Are the Gen2 cars capable of enduring ~47 minutes5 of this track? Probably not. How about the Gen3 cars? Well, they have a trick up their sleeves…

The Gen3 recharging pit stop: a track designer’s panacea Link to heading

The Gen3 Formula E car represents an improvement on the Gen2 car on almost all areas:

Stats Gen2 Gen3 Change
Qualifying power output 250kw (335hp) 350kw (469hp) +40%
Race power output 200kw (268hp) 300kw (402hp) +50%
Battery weight 284kg 180kg -36.6%
Battery charge 54 kwh 51kwh -5.6%
Regeneration (back/front) 250 (250/0) kW 600 (350/250) kw +140%
Total weight (inc. driver) 903kg 780kg -13.6%

The one area that wasn’t improved on was battery charge… or was it? Surprise: the Gen3 era will feature recharging pit stops! The Gen3 car will be able to come into the pits and stop for 30 seconds to recharge the battery at a rate of 600kw, putting 5kwh back into the battery. This is revolutionary because for every pit stop you add to a race, not only less time is spent racing (and consuming energy), but also more energy is added to the car. Hopefully, this means that circuit designers won’t need to add chicanes to their layouts because they can add another pit stop instead.

How many pit stops would Macau need? Link to heading

Now that we know that FE could go to Macau by using recharging pit stops. How can we determine the exact number? Lets take a look at the math (feel free to skip this chapter):

Before we get started, lets name our variables:

  • $P_g$ - Guia circuit power requirement (kw)
  • $t_g$ - Guia circuit lap time in race pace (s)
  • $E_g$ - Energy required to do a lap of the Guia circuit in race pace (kwh)
  • $P_r$ - Average race pace power (kw)
  • $t_r$ - Race time (s)
  • $N_p$ - Number of pit stops
  • $E_s$ - Battery charge at the start of the race (kwh)
  • $E_p$ - Energy gained during a pit stop (kwh)
  • $t_d$ - Time necessary to drive through the pit lane without stopping (s)
  • $t_p$ - Time spent stationary recharging in a pit stop (s)

The goal is to have more than enough power to sustain the power requirements of the Guia Circuit $$P_r \geqslant P_g$$

The power requirement of the guia circuit is straightforward to determine $$P_g = \frac {E_g}{\frac {t_g}{3600}} = 3600 \frac{E_g}{t_g}$$

The total energy available to the car in the entire race can be calculated as follows $$ E_s + N_p E_p$$

The time spent under racing conditions (measured in hours) is calculated in a similar manner $$\frac{t_r - N_p(t_d + t_p)}{3600}$$

Determining the average race pace power is a matter of dividing the total energy by the time $$ P_r = \frac{E_s + N_p E_p}{\frac {t_r - N_p(t_d + t_p)}{3600}} = 3600\frac{E_s + N_p E_p}{t_r - N_p(t_d + t_p)}$$

We now have everything necessary to isolate $N_p$, but there is no point continuing this exercise, now that we know how to define $P_g$ and $P_r$. Lets do something a lot more interesting with these formulas instead…

Seeing the bigger picture Link to heading

With the formulas that we derived, we can visualize every pit stop strategy worth considering, by putting the charging time ($t_p$) on the X axis and the average race pace power ($P_r$) on the Y axis. All the dots that are above the Guia circuit power requirement (gray line) are strategies that work. Feel free to change the values below, if you wish!

Guia circuit power requirement:

  • (kw)
  • (s)
  • (kwh)

Pit stop-related values:

  • (minutes)
  • (kwh)
  • (kw)
  • (s)

Looking at the chart, only a 4-stop strategy is possible with the current Gen3 capabilities. A 3-stop strategy with a 39s stop time could be possible in the near future, however.

The actual challenge that Formula E has to overcome Link to heading

Formula E could have already used the full Monaco layout when it raced there in season 5. It chose not to due to fear of being naively6 compared to Formula 1. Luckily for Formula E, the race was so good that whenever a comparison of F1 and FE appeared, they had this fantastic E-Prix on back of their minds and realized that speed doesn’t necessarily correlate with good racing.

Formula E will face the same conundrum if it wishes to go to Macau. The Macau Grand Prix features Formula 3 cars that would narrowly beat FE cars in the straights7 and soundly beat them in the corners, because they are lighter and have more downforce. Will this dissuade Formula E from coming to Macau? I very much hope not.

  1. There have been some track changes, including a couple made to prevent drivers from accidentally launching themselves into the sea. For more Monaco Grand Prix-related information, the wikipedia page is a good place to start. ↩︎

  2. Unfortunately, this publication was sunsetted after the end of season 7 due to pandemic-related factors. ↩︎

  3. At the time of writing, the Paris E-Prix is only hosted every other year. ↩︎

  4. Formula 3 cars have the luxury of DRS if they are within 1 second of the car ahead. ↩︎

  5. This is just an educated guess of how long a 45 minutes + 1 lap race actually is. ↩︎

  6. Lets take the front and rear wings off and put all-weather tyres in a Formula 1 car, then we can talk about comparisons. A Formula E car could easily go 4-5 seconds faster if it used slick tyres. It simply chooses not to because developing all-weather tyres for electric cars is a much better value proposition (and a lot more road-relevant) for a tyre manufacturer. ↩︎

  7. Formula E cars are biased towards acceleration, rather than top end. ↩︎