Thursday, November 10, 2011

Fuel Load is Important

I really miss refueling.  Anything that added fire to the sport was okay by me.  But I understand the safety concern.  How many crew members needlessly got dragged down the pit lane from an unsafe release in the Ferrari pits?  Too many for sure.  But now pit-stop bogie times are in the low 20s from the previous 30-40 second range.  We now get to watch in wonder as the tire change can get completed in as little as 2.9 second.  And while that is amazing, and truly sometimes the most entertaining part of some races, we lose something without refueling.

One of those missing things is the knowledge of how much fuel is actually in the car at the start of the race.  In the 2009 season each team reported on the fuel load of the car at the start of the race.  This made for some interesting guessing games in terms of strategy and pit-stop timing.  The fix for the truly dull almost no-pitstop race, though, was the quickly degradable Pirelli tire.  Still, I'm fixated on the fuel.  And it's not just because of fire.

Almost all season, we've watched Sebastian Vettel of Red Bull get pole.  Then on race day, he pulls away from the pack and in two or three laps he has a multi-second lead over the rest of the field.  How can he be doing this?  From practice and qualifying we know that the Red Bull is not the fastest in a straight line.  That honor regularly goes to someone running a Ferrari engine, like Torro Rosso.  But straight-line speed isn't everything.  F1 is not a drag-race or even Indy on banked ovals.  Obviously, how fast you get around the corners ends up being more important than pure straight-line speed.

After doing all the engineers can to maintain grip, they also need to overcome inertia.  The faster you are going entering a corner, the more effort you need to put into overcoming the inertia that wants to keep the car going straight.  Weight has a huge influence on inertia.  If you can lower your weight, then you can rotate and change direction more easily.  So, I think Vettel can pull away from the rest of the field because his car starts with a lighter fuel load than most of the rest of the field.

How can Red Bull do this for Vettel?  Probably because 1) the Renault engine is relatively more fuel efficient and 2) with Vettel on pole, if he can get a clean start, he can run in clean air and a clean race line also enhancing his fuel economy.

The backmarker teams have stated that they calculate their fuel load to be able to run one lap short of a full race.  Since they don't have the pace to compete with the front runners and they know they are going to get lapped, they lighten their fuel load as much as they think reasonable so that they can be the fastest of the back-of-the-pack.  So, how can this work if you are in the front?

Don't be afraid, but here comes the bad math...

Since engine design has been frozen, we can reasonably look at the fuel usage numbers from 2009 to get an idea about how things are working in 2011.  Let's look at the Italian GP since Monza is a historic circuit and we can make adjustments between the 2009 results and attempt to correlate them to the 2011 performance.

(Team - Engine)
Performance at Monza
Q3 TimeFastest Race LapTotal Race Time - Pit-Stops
(Red Bull - Renault)
(McLaren - Mercedes) 
(Ferrari - Ferrari)

I tried to take a representative top driver/team combination, but people and teams shifted around quite a bit between 2009 and 2011.  So I'll apologize to Kimi and Fernando as while neither are the same in terms of drivers, they were at the time the No. 1 for Ferrari that year.

The first interesting thing to notice is that in 2009, even through refueling meant much longer pit-stops, the races completed in less time and the Q3 times were much closer to each driver's fastest race lap.  Obviously, the cars are much heavier at race start in 2011, the blown diffusers make a difference, the aero is much different, tires are very different, and driver skill and performance varies from day-to-day, let alone year-to-year.  Regardless, let's press ahead.

The difference in economy per lap of Red Bull and McLaren is actually in McLaren's favor (2.49 kg/lap vs 2.41 kg/lap respectively).  Of the top teams, the real pain is for Ferrari with a 2009 season average consumption of 2.54 kg/lap.

That doesn't seem like much, but F1 is a game of tenths and those differences add up fast.  In the 53 lap, 306.720 km race at Monza, the weight difference because of fuel at race start among the top three teams might have been around 1.59kg (Red Bull) and 6.91kg (Ferrari) in McLaren's favor.  Being almost 7kg heavier sure hasn't helped Ferrari's cause this year.

Weight eats speed and every kg of added weight will penalize the car's performance.  The teams know this (obviously) and have precise calculations for how many additional tenths per lap the car will require per kg of added weight.

I've attempted to guestimate this penalty (P) by taking the Q3 lap time (T), the fastest in-race lap time (C), and estimated the fuel weight (F) for that in-race fastest lap.  This assumes that the Q3 time is the fastest that driver/car combination could go on the track with the lightest fuel load possible and that the in-race fastest lap would be equivalent to the Q3 time except that the car has more fuel onboard.  The formula comes to P = (C - T]) / F.  You get a chart like below:

Monza 2011 Speeds, Times, and Fuel and Time Penalty Estimates
(Team - Engine)
Avg. Speed
Fastest Lap Time
(lap #)
Q3 Time
Est. Initial
 Fuel Load (kg)
Weight Penalty
Lewis Hamilton
(McLaren - Mercedes)
241.97186.187 (52)82.725127.730.7182
Jenson Button
(McLaren - Mercedes)
241.91586.207 (52)82.777127.730.7116
Sebastian Vettel
(Red Bull - Renault)
240.93786.557 (49)82.275129.320.3510
Fernando Alonso
(Ferrari - Ferrari)
239.18587.191 (50)82.841133.560.4315

...or you can take that estimated weight penalty and plot the race lap times for the four drivers like below:
Monza Lap Times (Normlized w/o Pit Stops or Busted Laps)
Notice how much faster Vettel is at the beginning of the race.  What's amazing is how close Alonso is to Vettel's times considering how much extra weight his car is carrying.  I think this has to do with how Monza is fast track with very low downforce.  This is one of the few tracks in the calendar which actually favor the cars with the highest top-end speed.  And the Ferrari engined cars certainly have that.

What's surprising is that the McLaren cars are not closer to Vettel in this race.  I think this is where aerodynamics and chassis balance comes into play.  The McLaren cars were both having control issues that weekend.  So, let's look at a race where they weren't in theory suffering.

At Singapore Jenson Button had a great race moving from 4th at the start to podium second.  He finished a mere 1.7 seconds behind Vettel.  Alonso fought hard, but in the end he was nearly a minute behind at the finish and Hamilton even further behind.  In many respects, how well Alonso is driving the Ferrari in spite of the weight penalty is a testament to his driving skill.  And now I just barfed a little.  Anyway, here's a diagram...
Singapore Lap Times (Normalized w/o Pit Stops or Busted Laps)
Even with pole position, a clean start and clean air for the beginning of the race, Vettel was unable to pull off his normal dominant lead.  Singapore is a much slower track than Monza and the weight penalty ended up being lesser.

But I think it is clear that the combination of the great chassis along with running lighter gives the Red Bull drivers an advantage over the pack.  What would be interesting is if you could shove the more powerful and slight more fuel efficient Mercedes engine into the Red Bull how much faster it would go and how much further would it pull away from the pack?  Or even more ludicrous, let the drivers switch up cars.  Everyone gets 30 laps in Kinky Kylie around some course which Vettel truly whipped all their asses and see if anyone can make a better time.

My guesses are based on the awesome work presented by Making Up The Numbers and their analysis of the 2009 season.

Alcohol content: 0 (penalty 0.9999)

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