# What's the best refuelling strategy in Formula 1?

I'm interested in how race strategy changed during the refueling eras. Say we have a 60 lap race, you could pit on lap 20 and 40, or you could pit on lap 21 and 42. I wanted to see which strategy would be best on paper, using a very simple approach. Firstly, I assumed that pit stops don't cost time (both strategies require 2 stops anyway).

Secondly, I assumed that each extra lap of fuel difference between the strategies costs 0.1 seconds. So for example, on lap 1 the first strategy is 0.1 seconds. Having used these assumptions, I found that the strategy which pits on laps 20 and 40 is 0.3 seconds faster.

I'm struggling to understand why this is? If both strategies fuel up 60 laps of fuel over the stints then surely the pace should be the same? Taking this to its extreme, if you pit on lap 58 and 59 you are -6952.4 seconds slower. Using my knowledge of F1, this makes sense, but when thinking about it mathematically it doesn't make as much sense. Why does it matter how you split up the 60 fuel load, as long as it's split into 3 portions?

Carrying extra fuel adds more weight

For simplicity, let's assume only 1 pit stop, which will occur at either lap 30 or lap 59 in a 60-lap race. If you don't refuel until lap 59, you're spending the first part of the race lugging around all the fuel that you won't even need until the second half of the race. Starting the race with 59 laps' worth of fuel, laps 1-29 will be slower than if you had brought only 30 laps' worth of fuel. The second half of the race will be mostly the same. With a fuel efficiency of roughly 0.75L/km, the fuel required to finish a 300km race is roughly one-quarter of the minimum weight of an empty F1 car.

Ideally, you'd bring as little fuel as possible and have frequent refuelings, but since each refueling takes time, it needs to be balanced with the benefit of carrying less fuel. If refueling took no time at all, the optimal strategy would be to take only 1 lap of fuel and refuel 60 times, but that's obviously impractical.

In addition to this, there's a small effect that carrying the extra fuel itself requires more fuel - the quantity of fuel that will take you 60 laps is actually more than double the amount it would take to go 30 laps, since the car with 60 laps of fuel weighs more than the car with only 30 laps of fuel. Adding more fuel to the tank actually decreases the fuel efficiency of any vehicle!

There are several reasons for that.

1. Speed. If you're faster than the one before you and just fail to overtake them you stay out longer. Let them pit first and use the extra laps to gain some seconds without them slowing you down. Then you can pit and hope to come back on the track in front of your opponent.

2. The other way round. If you're obviously slower than the car behind you and you can prevent them from overtaking you'll want to stay out as long as possible. Either they have to pit before you or they won't have many laps left before they have to (to gain the advantage from 1.).

3. Weather. If the forecast is predicting a change of weather (dry -> rain or vice versa) you'll want to stay out as long as you can to get the right tyres for the upcoming weather. Or if the weather doesn't allow full pace you could just do like Frentzen in France '99. His team had the strategy to add enough fuel to complete the race when the weather changed, while the other top cars had to pit for fuel later again.

4. Safety car. You can pit sooner than planned to make use of the safety car phase. This costs you basically nothing as the whole field is already at slow pace behind the SC. You'll just have to overtake those who had the same idea before you. The others have to pit sooner or later and are out of your way.