THE DEVELOPMENT OF F1 INSIGHTS, POWERED BY AWS
Driver Performance – % of Car Limit
F1 Chief Technical Engineer Rob Smedley helps break down each of the new F1 Insights powered by AWS in a series of blogs during the 2021 FORMULA 1 season
Wouldn’t it be great if we could really understand which driver had done the best qualifying lap independent of the machinery under them? It is a question that all of us as FORMULA 1 fans constantly ask ourselves. How would Lewis Hamilton or Max Verstappen fare in a car that was at the back of the grid, or how would George Russell or Antonio Giovanazzi get on if they had a car from the front of the grid to play with?
Certainly, in my time within F1 teams I was asked this question almost on a yearly basis by the senior management. For a team, investing in an F1 driver is a huge decision. Get it right and the return on investment can be brilliant as the team starts to qualify well and collect lots of points on a Sunday afternoon. Get it wrong, however, and the team can find itself in the doldrums, not getting the results and points it needs for its final world championship standing, but also being led in the wrong direction on car development by erroneous driver comments.
Therefore, an F1 team’s senior management need to build pictures of drivers that go beyond the simple face value results, and instead give a view on the driver talents regardless of the machinery at their disposal. Enter our latest F1 Insight powered by AWS: Driver Performance.
The aim of Driver Performance is to give the fans an in-depth view of how each driver is exploiting performance from their respective machinery. In order to give a pure driver performance metric, we have to remove the car element. We have once again teamed up with our partners at AWS in order to build analytical models and algorithms that can give us the result we're looking for.
Let's look at a simple example: if driver X at the front of the grid in the best car is able to complete a lap time of 1’30s by extracting 100% of the performance of his car, then if he extracts less than the maximum performance his lap times will be slower. In this simple example we will say that driver X extracts only 91% of the maximum performance and the result in lap time will be 3 seconds slower resulting in a 1’ 33s lap. Now we take driver Y who is in the slowest car on the grid. In this case, driver Y is only able to attain a 1’ 32s laptime even when exploiting 100% of the performance of his car. On the other hand, when driver Y exploits only 91% his lap time drops to 1’ 35s.
Let's take an example of the face value qualifying result of drivers X and Y as being lap times of 1’31.1s and 1’32.3s, respectively. If we use a simple linear interpolation of the numbers given above then this would result in the following:
• Driver X is exploiting his car to 96.7% of the maximum
• Driver Y is exploiting his car to 99.1% of the maximum
We would end up with the situation where, on face value, driver Y is 1.2 seconds behind driver X on the grid. But, in reality, the slower driver has exploited his car to a much higher degree (99.1% versus 96.7%).
The example above shows us just how complex F1 racing really is and how it is invariably the case not to take results at face value. There is always a myriad of complex numbers and science behind the result that we need to dig into if we want the real picture.
In order to get to this percentage of maximum car performance then we have had to build some complex car and simulation models. The principal element was the front and rear grip available to the driver. If we were able to calculate this then this would give us the performance envelope of the car. In order to do this, we have models of the car and models of the tyres that represents the “grip” available at each moment through a lap. Using this, we then leverage the fact that the tyres are a constant throughout the season to tune the model using past events and to forecast future events. Knowing the grip available, then allows us to calculate the maximum force that each tyre is capable of exchanging with the ground, and consequently we can reconstruct the tyre forces that are exchanged between the tyres and the ground. This provides us with the data to calculate the actual grip, so in reality, how much the driver is actually using. By comparing the two numbers we end up with the percentage values as described above.
The next phase of the exercise was to split the corner up into the three principal phases - braking, lateral or cornering, and exit phase. We have then extracted the percentage performance value for each of the three phases. We should note that our assumption here is that the driver is always exploiting the car to 100% of its potential in a straight line where there is commensurably less skill involved than the cornering phase.
What we must note is that we are dealing with 20 of the best racing drivers in the world. Therefore, we are more than likely to see a mix of relative scores through the three phases. For example if we take the two McLaren drivers it may well be the case over a single time lap that Daniel Ricciardo is able to extract slightly higher relative percentages in the entry and cornering phase, but lower in the exit phase with respect to Lando Norris and this results in an overall similar lap time. The levels of skill are so high and so close between F1 drivers that it would be very rare to see one driver consistently ahead in all three phases.
In the next section we go into a little more detail about how the models and algorithms were developed.
The modelling starts from reconstructing the tyre forces from the available telemetry signals that we use in in-car camera images (accelerometers, speed sensors, etc). We then fit a parametric tyre model to the data and from this we can calculate the maximum force that each tyre is capable of generating in all the various car conditions. In the plot below we have reported the forces and the limits in the case of pure cornering. This is known as lateral tyre force.
A racing car, when fully exploited, is always limited and this overall limitation defines the minimum lap time possible. Broadly, the car will be limited by the power of the engine (e.g. car in a straight line, an excess of tyre grip for that condition, if we added more power the car would go faster) or by the grip of the tyres (car in a cornering condition, not able to use all available engine power, if there was more overall grip the car would go faster around the corner). These conditions are known as “power limited” and “grip limited,” respectively. When the car is in the power limited condition (tyre grip is not a limitation) the tyre forces are significantly lower than the maximum achievable. In the grip limited condition (braking, cornering, and acceleration) the performance is dictated by the tyre grip – it is the job of the driver to drive the car right up to this grip limit, but not beyond, in order to maximise performance.
In general, the limitation can come from the front or rear tyres. Front tyre limitation is known as understeer – the car turns with a curvature greater than the ideal corner radius. Rear tyre limitation is known as oversteer – the car turns with a smaller curvature than the ideal corner radius. Only in very particular circumstances the limitation comes from both front and rear at the same time – this is known as 4 wheel sliding. All of this leads us to the fact that in order for the driver to exploit all of the available tyre grip they need to have a car they are comfortable with. The engineers will work with the setup to find a car balance that suits their particular pilot’s driving style and it’s this, along with the driver’s innate skill, that allows the car/driver pairing to reach the tyre limit.
This model calculates how close the car/driver is compared to the tyre grip limit. This is done across the 3 principal phases of the corner: braking, cornering (lateral), and acceleration. We express this in percentage terms and then average across all the corners throughout the lap. This then gives us a mathematical analysis of how close the driver is to the limit of the car.
This new addition to our suite of F1 Insights powered by AWS should give F1 fans another data insight into how drivers are performing. It gets behind the simple face value results that we can see on a Saturday and Sunday afternoon. We should always remember that F1 is a blend between human and technical excellence and therefore we cannot discount the car’s contribution to the result. It is hugely insightful, however, to understand how close each driver can get towards the limit of their respective machinery.