I was finishing my Formula 1 Cornering Performance Breakdown project when I came up with the idea of using the existing code infrastructure to generate cornering data for every track on the 2024 calendar. As part of that project, I tagged every corner with a tag highlighting how fast that corner is. With that information, I can determine how much time is spent on each type of corner. The remainder of the time in lap, which isn’t spent negotiating a corner, is the time the drivers spend at full throttle on a lap, tagged below as STRAIGHT.
| Corner type | LOW | MEDIUM-LOW | MEDIUM-HIGH | HIGH | STRAIGHT |
|---|---|---|---|---|---|
| Corner apex speed | <100kph | 100kph-150kph | 150kph-200kph | >200kph | Full throttle |
The data Link to heading
Now that we’ve gone over the basics, let’s take a moment to understand how to interpret the data that will be shown in this blog post. Take a look at the example below:
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH
Azerbaijan GP 51.201 24.801 24.201 0.000 0.000
Qatar GP 29.035 6.520 10.301 16.001 21.921
We can see that the Azerbaijan GP is dominated by low and medium-low-speed corners, whereas medium-high and high-speed corners dominate the Qatar GP. This makes complete sense and matches our preconceptions of these two tracks: Azerbaijan is a street track, and Qatar is a flowing MotoGP track.
Without further ado, here’s the data for all 24 GPs of the 2024 F1 calendar:
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH
Bahrain GP 37.177 23.139 16.394 4.899 8.099
Saudi Arabian GP 44.187 7.720 6.880 19.399 10.079
Australian GP 31.573 4.516 14.603 6.166 19.874
Azerbaijan GP 51.201 24.801 24.201 0.000 0.000
Miami GP 39.961 35.099 6.654 0.000 5.100
Monaco GP 24.805 29.750 10.180 6.630 0.000
Spanish GP 30.637 0.000 17.951 14.060 9.624
Austrian GP 34.312 6.522 9.658 2.220 11.679
British GP 39.236 4.900 18.582 4.320 19.682
Hungarian GP 27.946 5.800 27.523 10.561 4.779
Italian GP 44.692 9.579 6.516 13.027 6.480
Singapore GP 33.632 22.850 27.577 4.119 2.806
Japanese GP 42.847 16.477 5.660 15.734 8.159
Qatar GP 29.035 6.520 10.301 16.001 21.921
United States GP 35.539 32.403 10.903 2.963 12.915
Mexico City GP 27.789 25.319 13.496 10.562 0.000
São Paulo GP 33.454 6.120 19.887 7.080 3.480
Las Vegas GP 49.586 26.140 13.200 0.000 3.800
Abu Dhabi GP 37.663 8.720 17.381 13.180 6.501
Chinese GP 35.122 33.319 8.646 6.646 7.814
Dutch GP 26.664 7.822 22.118 5.655 8.083
Belgian GP 46.945 17.060 7.678 21.639 10.343
Canadian GP 34.337 14.883 21.020 0.000 0.000
Emilia Romagna GP 38.293 0.000 21.866 11.245 3.007
This is a good starting point, but before we start running clustering algorithms on this data, we should normalize the data in relation to the lap time of each track. Doing this prevents tracks like Spa from having more time spent in corners simply because it has a higher lap time. The Python code below does just that by normalizing the data to a 100-second (1m40s) lap time:
def normalize(dt : pd.DataFrame) -> pd.DataFrame:
res = dt.copy(True)
res["Total"] = res["STRAIGHT"] +\
res["LOW"] +\
res["MEDIUM-LOW"] +\
res["MEDIUM-HIGH"] +\
res["HIGH"]
for c in ("STRAIGHT", "LOW", "MEDIUM-LOW", "MEDIUM-HIGH", "HIGH"):
res[c] = res[c] * 100 / res["Total"]
res = res.drop(["Total"], axis=1)
return res
The normalized data:
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH
Bahrain GP 41.442235 25.793686 18.274847 5.461051 9.028180
Saudi Arabian GP 50.061746 8.746389 7.794709 21.978134 11.419022
Australian GP 41.147109 5.885419 19.031173 8.035761 25.900537
Azerbaijan GP 51.097273 24.750756 24.151971 0.000000 0.000000
Miami GP 46.030594 40.430115 7.664662 0.000000 5.874629
Monaco GP 34.757935 41.687102 14.264696 9.290268 0.000000
Spanish GP 42.391244 0.000000 24.838112 19.454284 13.316360
Austrian GP 53.286950 10.128745 14.998991 3.447687 18.137628
British GP 45.244465 5.650369 21.427583 4.981550 22.696033
Hungarian GP 36.478743 7.570912 35.926588 13.785587 6.238170
Italian GP 55.660448 11.929908 8.115177 16.224126 8.070341
Singapore GP 36.964741 25.114306 30.309725 4.527170 3.084059
Japanese GP 48.209323 18.539105 6.368352 17.703118 9.180103
Qatar GP 34.657070 7.782473 12.295591 19.099286 26.165580
United States GP 37.518871 34.208165 11.510404 3.128068 13.634492
Mexico City GP 36.011974 32.811083 17.489568 13.687375 0.000000
São Paulo GP 47.777095 8.740235 28.401480 10.111252 4.969938
Las Vegas GP 53.475832 28.190583 14.235490 0.000000 4.098095
Abu Dhabi GP 45.135119 10.449997 20.829289 15.794835 7.790760
Chinese GP 38.364993 36.395513 9.444329 7.259659 8.535506
Dutch GP 37.906230 11.119957 31.443519 8.039294 11.491001
Belgian GP 45.285294 16.456856 7.406550 20.873969 9.977331
Canadian GP 48.885251 21.188781 29.925968 0.000000 0.000000
Emilia Romagna GP 51.461477 0.000000 29.385440 15.112013 4.041069
Time to run the k-means clustering method Link to heading
Now that we have our data, we can run k-means clustering on it. I decided to go for 4 clusters, even though the elbow method only suggested 2.
def kmeans_clustering(dt : pd.DataFrame, n : int = 2) -> Dict[int, Tuple[pd.DataFrame, List[str]]]:
kmeans = KMeans(n_clusters=n, n_init='auto')
kmeans.fit(dt)
dt1 = dt.copy(True)
dt1["Cluster"] = kmeans.labels_
res = {}
for i in range(n):
gp_cluster = dt1[dt1["Cluster"] == i]
print(gp_cluster)
print(list(gp_cluster.index))
print()
res[i] = (gp_cluster, list(gp_cluster.index))
return res
Cluster 1: The street tracks with high top speeds Link to heading
Every track on this cluster is dominated by low and medium-low-speed corners. The length of the straights on these circuits (except Singapore) makes top speed a priority, which conflicts with the requirements of the low-speed corners.
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH Cluster
Azerbaijan GP 51.097273 24.750756 24.151971 0.00000 0.000000 0
Singapore GP 36.964741 25.114306 30.309725 4.52717 3.084059 0
Las Vegas GP 53.475832 28.190583 14.235490 0.00000 4.098095 0
Canadian GP 48.885251 21.188781 29.925968 0.00000 0.000000 0
['Azerbaijan GP', 'Singapore GP', 'Las Vegas GP', 'Canadian GP']
Cluster 2: The flowing high-speed racetracks Link to heading
Every track on this cluster (except Monza) could be a MotoGP track, looking purely at the track layouts. This set of tracks rewards teams that can put a ton of downforce while maintaining a respectable top speed.
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH Cluster
Saudi Arabian GP 50.061746 8.746389 7.794709 21.978134 11.419022 1
Australian GP 41.147109 5.885419 19.031173 8.035761 25.900537 1
Austrian GP 53.286950 10.128745 14.998991 3.447687 18.137628 1
British GP 45.244465 5.650369 21.427583 4.981550 22.696033 1
Italian GP 55.660448 11.929908 8.115177 16.224126 8.070341 1
Japanese GP 48.209323 18.539105 6.368352 17.703118 9.180103 1
Qatar GP 34.657070 7.782473 12.295591 19.099286 26.165580 1
Belgian GP 45.285294 16.456856 7.406550 20.873969 9.977331 1
['Saudi Arabian GP', 'Australian GP', 'Austrian GP', 'British GP',
'Italian GP', 'Japanese GP', 'Qatar GP', 'Belgian GP']
The traction-sensitive racetracks Link to heading
You will struggle at these tracks if your car has poor handling characteristics. This cluster is dominated by low-speed corners, highlighting the suspension quality and ride height.
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH Cluster
Bahrain GP 41.442235 25.793686 18.274847 5.461051 9.028180 2
Miami GP 46.030594 40.430115 7.664662 0.000000 5.874629 2
Monaco GP 34.757935 41.687102 14.264696 9.290268 0.000000 2
United States GP 37.518871 34.208165 11.510404 3.128068 13.634492 2
Mexico City GP 36.011974 32.811083 17.489568 13.687375 0.000000 2
Chinese GP 38.364993 36.395513 9.444329 7.259659 8.535506 2
['Bahrain GP', 'Miami GP', 'Monaco GP',
'United States GP', 'Mexico City GP', 'Chinese GP']
The all-rounders Link to heading
I have nothing interesting to say about these tracks besides that you need a good car at both medium-low and medium-high-speed corners.
STRAIGHT LOW MEDIUM-LOW MEDIUM-HIGH HIGH Cluster
Spanish GP 42.391244 0.000000 24.838112 19.454284 13.316360 3
Hungarian GP 36.478743 7.570912 35.926588 13.785587 6.238170 3
São Paulo GP 47.777095 8.740235 28.401480 10.111252 4.969938 3
Abu Dhabi GP 45.135119 10.449997 20.829289 15.794835 7.790760 3
Dutch GP 37.906230 11.119957 31.443519 8.039294 11.491001 3
Emilia Romagna GP 51.461477 0.000000 29.385440 15.112013 4.041069 3
['Spanish GP', 'Hungarian GP', 'São Paulo GP',
'Abu Dhabi GP', 'Dutch GP', 'Emilia Romagna GP']
Final remarks Link to heading
There are multiple ways to improve the clustering of the racetracks: the two I can think of from the top of my head are adding the average speed and the longest continuous throttle-on time (i.e., longest straight) as two new columns. Calculating the isochronal ratio would also be interesting, but generating that data would be far too time-consuming for me.
If you also have ideas to iterate on this project, you are more than welcome to do it! The code is available on GitHub.