When in-race refuelling was still part of the game, calculating fuel strategies was one of the things the F1 amateur strategist could try to play along with. (For a summary of what was involved, see the Royal Academy of Engineering/McLaren worksheet on Formula One Fuel Strategy [PDF].)
Fuel loads still have a part to play now, of course: for every lap travelled, the car uses up fuel, gets lighter, and as a result travels faster (the available kinetic energy has less mass to accelerate around the circuit). Another way of thinking about it is that a fuel weight penalty apples in the form of an increase in laptime for each extra kilogram of mass carried. At the start of a race, when the car is heaviest, a large penalty applies. At the end of the race, when the car is lightest, the penalty is small. If we know how much fuel a car burns per lap, and what the approximate time saving is per unit mass, we can calculate the "fuel corrected" laptimes.
The Williams Turkey preview suggests that the Fuel Consumption round the circuit is 2.7kg / lap with a Fuel Laptime Penalty of 0.3 s / 10kg.
That is: fuelConsumption=2.7, fuelPenalty=0.03, fuelLapsWeightPenalty=mass of fuel * fuelPenalty = (fuelConsumption * laps worth of fuel) * fuelPenalty
We can see how at the start of the race there is a approximately a 4.5 second time penalty due to the weight of the fuel at the start of the race compared to at the end. If we take this time from the laptimes we get a fuel corrected laptime, shown here for VET:
(The label also shows the tyre strategy, as published by Pirellli.)
Note how the unadjusted laptime comes down naturally over the course of the race as the fuel weight penalty is burned off. When we take the fuel weight penalty into account, we get the fuel corrected laptime, which shows an increasing gradient towards the end of each stint as the tyres go off. (It's particulary noticeable in the final stint.) [UPDATE: In a comment, HenningO suggests this final slowing is probably just VET easing off, rather than tyres going off...That's probably right, isn't it?! Doh!]
Another correction we can make is to subtract the fuel corrected fastest laptime for each driver from their laptimes. (That is, take their fastest race lap, caculate the fuel penalty, and subtract that to give a fuel corrected fastest laptime.) If we take this from each laptime, we can see whether the fastest lap was actually the fastest lap (taking into account the fuel penalty).
The lowest fuel and fast lap fuel corrected laptime is actually (fuel weight penalty considered) the fastest lap.
Here are the fuel and fast lap fuel corrected laptimes for HAM, BUT and AMB, all of whom had different tyre strategies:
Note how AMB's soft tyres go off (the corrected laptimes increase towards the end of the corresponding stints), but the hard tyres last well. We also see how BUT's tyres aren't doing him any favours in the final laps of the race.
(Note that the fuel corrected laptime chart could be produced live/during a race from published laptimes, Do any F1 sites publish such a live chart during races?)
Howto make the graphs
The generic fuel penalty chart was plotted using Gnuplot:
gnuplot> set term x11
//My mac doesn't display anything with the aqua setting?
gnuplot> set datafile separator ","
//my data file is CSV, so define the separator, just in case...
gnuplot> set xrange [1:58]
gnuplot> set xlabel "Lap"
gnuplot> set ylabel "Fuel Weight Time Penalty"
gnuplot> plot 0.03*(58-x)*2.7 title "Fuel mass * fuel weight penalty"
The fuel adjusted lap time chart was generated from a CSV file (turlapTimeFuel.csv) of the form:
"Driver,Lap,Lap Time,Fuel Adjusted Laptime,Fuel and fastest lap adjusted laptime
using the following gnuplot command (howto):
plot 'turlapTimeFuel.csv' using ($1==3 ? $2:1/0):5 with lines title "HAM Su | Su(9) Su(20) Hn(34) Hn(46)",'turlapTimeFuel.csv' using ($1==4 ? $2:1/0):5 with lines title "BUT Su | Su(13) Su(26) Hn(39)",'turlapTimeFuel.csv' using ($1==25 ? $2:1/0):5 with lines title "AMB Sn Su(16) Hn(33)"