Posts Tagged ‘Formula One’
Digging around looking for stats and data relating to the first Formula One Grand Prix of the new season, I came across some interesting looking technical info on the Race Car Engineering website (Formula 1 2009: Round 1 Australia tech data), as well as details of the staring weighs of the vehicles following qualification (post-qualifying car weights).
Assuming that the weight of the fuel is the post-qualifying weight of the car minus the minimum weight of the car, it should be possible to have a guess at when the teams are planning their first pit stop. So I started doodling a spreadsheet that could be used to try and work out fuel’n'pitting strategies (albeit very simplistically).
If you’re interested, you can find it here: Race Day Strategist Spreadsheet:
I’ve made a few assumptions about how to calculate how far the fuel will take a car, so if you can tell me if/where I’ve made any mistakes/errors/bad assumptions, please post a comment.
I’ve tried to make the working clear, where possible:
I also put together a ‘quick calculator’ that could be used to play-along-a-strategist while watching the race.
All the formulae were made up on the fly (“hmm, this could be interesting?”) so when I get a chance, I do a little reading to find out how other people have addressed the issue. (I’ve already found links for a couple of things I probably ought to reqad: Practice Work – Optimization of F1 – PIT STOP TACTICS (which may contain some interesting ideas) and the rather more involved Planning Formula One race strategies using discrete-event simulation (subscription required – so OU folks should be okay through the OU library. If there are any other things you think I should add to the list, please pop a reference to them in the comments.)
This spreadsheet could obviously go much further – addressing other pit stop timing delays, tyre considerations etc. Being able to pull in live timing data – e.g. time intervals between the car of interest and other vehicles – and predict car lap times would also add a little more intrigue when trying to decide whether or not to pit.
But it’s a start, and it got me asking a few questions that might not otherwise have come to mind ;-)
All I need to do now is work in the visual angle, maybe taking a little inspiration from Visualising Lap Time Data – Australian Grand Prix, 2009…
For the first Formula One Grand Prix of the year, I put together a spreadsheet that would let you play the role of a pit stop fuel strategist (F1 Pit Stop Strategist – Fuel Stop Spreadsheet).
I missed the last couple of races, but I did get to see today’s, so whilst I was watching I also made a few tweaks to the spreadsheet.
First thing was to tweak the first pit stop estimator, by adding an offset that factors in a 3 lap fuel penalty to account for the procession lap, the formation lap, and some slack!
Secondly, I added a new sheet that allows you to play along with the race so that you can try to work out when all the other cars are likely to be pitting throughout the race.
This is very much the first pass of this spreadsheet – I’m not sure how the BBC calculate or guess at the amount of fuel added on the few occasions they do pop up an info bar, although they do show quite a few of the pit stop timings. So over the next few races (or maybe by watching replays – and with knowledge of when all the stops were actually taken) I’ll try to work on the formula that takes the pit stop time – or an estimate of how long the fuel hose was attached – and calculates the fuel loaded (and hence number of extra laps that car can complete).
The other thing I added to the strategist spreadsheet was a display of the best sector times from each driver in Q3, charted relative to the best sector times of a nominated driver:
(Obviously, a similar chart could also be used to display the best sector times for each driver during the race.)
You can find the race day strategist spreadsheet here: Race Day Strategist Spreadsheet.
As far as post-race stats go, I was intrigued as to whether lap times show any benefit to decreasing car weight as fuel is used up each lap – so here are the time differences between consecutive laps for Button:
(For the pit stops, I limited the time to 3s.)
I’m not sure whether an improvement in lap time should be shown above the line, or below the line?
It’s F1 race weekend again, so I’m back pondering what to do next on my F1 Race Day Strategist spreadsheets. Coming across an article on (BBC F1′s fuel-adjusted Monaco GP grid), I guess one thing I could do is look to try and model the fuel adjusted grid for each race. That post also identifies the speed penalty per kg (“each kilo of fuel slows it down by about 0.025 seconds”) so I need to factor that in too, somehow, into a laptime predictor spreadsheet, maybe?
Note that I didn’t really see many patterns in lap time changes when I tried to plot them previously (A Few More Tweaks to the Pit Stop Strategist Spreadsheet) so maybe the time gained by losing weight is offset by decreasing tyre performance?
One thing the spreadsheet has (badly) assumed to data was a fuel density of 1 kg/l. Checking the F1 2009 technical specification, the actual density can range between 0.72 and 0.775 kg/l (regulation 19.3), so relating fuel timings (l/s), lap distances/fuel efficiencies (km/l), and car starting weight (kg) means that the density measures need taking into account.
Unfortunately, I factored density into some of the formulae but not others, so the spreadsheets could take some picking apart trying to take density into account to keep the different calculations consistent. Hmm, maybe I should start a new spreadsheet from scratch to work out fuel adjusted grid positions, and then use the basic elements from that spreadsheet as the base elements for the other spreadsheets?
Something else that I need to start considering, particularly given that there won’t be any race day refuelling next year, is tyre performance (note to self: track temperature is important here). A quick scout around didn’t turn up any useful charts (I was using words like “model”, “tyre”, “performance”, “timing” and “envelope”) but what I think I want is a simple, first approximation model of tyres that models time “penalties” and “bonuses” about an arbitrary point, over number of laps, and as a function of track temperature.
For the spreadsheet, I’m thinking something like an “attack decay” or attack-decay-sustain-release (ADSR) envelope (something I came across originally in the context of sound synthesis many years ago…)
On the x-axis, I’m guessing I want laps, on the y-axis, a modifier to lap time (in seconds) relative to some nominal ideal lap time. The model should describe the number of laps it takes for the tyres to come on (a decreasing modifier to the point at which the tyres are working optimally), followed by an increasing penalty modifier as they go off.
Ho hum, quali over, so I’ve run out of time to actually do anything about any of this now… maybe tomorrow…?