Lewis Hamilton locking up the brakes at the Azerbaijan Grand Prix in 2013 [1]
Are you braking fast enough?
By Trav Mays
Continuing our discussion on braking, I thought it would be interesting to have a look at 2 drivers tackling the same corner in the same car using the maths channel braking speed and then separating it further into aggression, and smoothness.
Braking speed is a maths channel that allows us to analyse the braking application. Initially there is a need for a quick build up to maximum pressure, the driver then needs to release the brake in a smooth and controlled manner to not upset the chassis. The speed of the pressure release will depend on whether the car has aero or not, but in either case, the driver will also need to vary the pressure for changes in grip level, ensuring the car is always at the limit of breaking.
Before we get too into it, let's first have a look at the two drivers taking the corner. We can see that the orange driver got on the brakes a lot later, 25m. This allowed them to continue accelerating to 208km/hr 2km/hr faster than blue, but if we look at the delta in the bottom row, we can see that blue lost very little time here. Orange appears to be a left foot breaker, allowing them to get off the brakes on onto the throttle in half the time. Despite their tricky footwork and the later braking point, the real time loss for Blue started when the brakes were applied. This highlights that the strategy of coasting in endurance racing doesn’t have as much of an effect on lap times as I would had instinctively thought.
Once the brakes were applied, Blue braked far more gradually than the Orange, we can see how fast they petal was pressed by the steepness of the total brake trace. Along with the slower application of the brakes, Blue didn’t press them as hard, reaching a peak brake pressure far lower than the Orange. Along with the softer and slower braking, Blue got off the brakes through the braking zone twice. Orange also had to correct their braking twice, but a lot less severely. Blue's large corrections would have caused the tire loads to oscillate between the front and rear axles, causing the car to seesaw on the way into the corner. And with it, the grip rocked between the axles, clearly this is not an ideal way to approach a corner. Ideally the driver applies the brakes hard and fast, reaching a peak pressure quickly, they then reduce the pressure as they approach the corner smoothly. This causes the chassis to pitch forward, shifting load onto the front tyres and temporarily increasing the rake of the car. As they reduce the brake pressure, depending on the car, the driver will choose to release the pedal in a way to flatten out the chassis, or they may choose to keep the chassis slightly pitched, helping produce drag, increase aero, and making it easier to get the car around the corner. Another technique used by some drivers is a quick dab of the petal just before they are completely off the brakes, this shifts the load to the front giving the driver more front axle grip and more positive rake just when they need it, Orange might have been doing this at the end of the braking zone.
The next stage of the corner is the application of the accelerator, whilst the blue driver gets off the brakes completely, the orange driver doesn’t, they are simultaneously applying brake and throttle. This is an odd choice, this car isn’t turbo and is rear wheel drive, so I’m not sure why they were applying both. Applying them one at a time is ideal as it helps to keep the chassis from rocking between the two, but there are times when both is the best option. We can also see that whilst the blue driver is able to keep the throttle constant, the orange driver needs to take their foot off the accelerator a fair bit and increase the brake pressure slightly. The drop in speed for the orange driver allowed them to get to full throttle before the blue driver, but whilst the orange driver was rocking the chassis on the way out of the corner, blue’s smoother exit allowed them to crawl back some time. Their speed from the corner’s minimum until the end of this section was higher. But orange’s total approach was the clear winner, gaining them 0.075 seconds through this section of track, had they been able to exit a bit smoother they might have kept the gap in the tens of a second.
Another way to analyse the two drivers is by using the brake speed trace, and then gating it to show just the brake aggression and smoothness, see below. Due to Blue's gradual pressing of the brake pedal and their lower peak brake pressure, they reach a peak brake aggression of just 1684 psi/sec, whilst Orane was able to reach 2270 psi/sec. Blue’s jumping on and off the brakes is clearly visible, they reached a brake speed 2/3rds that of their peak at one point.
The next stage of the corner is the application of the accelerator, whilst the blue driver gets off the brakes completely, the orange driver doesn’t, they are simultaneously applying brake and throttle. This is an odd choice, this car isn’t turbo and is rear wheel drive, so I’m not sure why they were applying both. Applying them one at a time is ideal as it helps to keep the chassis from rocking between the two, but there are times when both is the best option. We can also see that whilst the blue driver is able to keep the throttle constant, the orange driver needs to take their foot off the accelerator a fair bit and increase the brake pressure slightly. The drop in speed for the orange driver allowed them to get to full throttle before the blue driver, but whilst the orange driver was rocking the chassis on the way out of the corner, blue’s smoother exit allowed them to crawl back some time. Their speed from the corner’s minimum until the end of this section was higher. But orange’s total approach was the clear winner, gaining them 0.075 seconds through this section of track, had they been able to exit a bit smoother they might have kept the gap in the tens of a second.
Another way to analyse the two drivers is by using the brake speed trace, and then gating it to show just the brake aggression and smoothness, see below. Due to Blue's gradual pressing of the brake pedal and their lower peak brake pressure, they reach a peak brake aggression of just 1684 psi/sec, whilst Orane was able to reach 2270 psi/sec. Blue’s jumping on and off the brakes is clearly visible, they reached a brake speed 2/3rds that of their peak at one point.
Click here to see the Aim and Motec i2 Pro equations
Braking speed
Aim - deriv(Total Brake Line Pressure) (bar/sec)
Motec - derivative(Total Brake Line Pressure, X*) (bar/sec)
*X = time to differentiate over
Braking speed aggression
These need to be gated to something that just includes the initial braking. I have used greater than 20 bar/second in the below two example equations
Aim - IF(GT(brake speed, 20),brake speed, 0),
MoTeC - choose(‘brake speed’[bar/s]>20, ‘brake speed’,1/0) (bar/sec)
Braking speed smoothness
These need to be gated to something that just includes the initial braking. I have used less than 5 bar/second in the below two example equations
Aim - IF(LT(brake speed, -5),brake speed, 0)
MoTeC - choose(‘brake speed’[bar/s]<-5, ‘brake speed’,1/0) (bar/sec)
Aim - deriv(Total Brake Line Pressure) (bar/sec)
Motec - derivative(Total Brake Line Pressure, X*) (bar/sec)
*X = time to differentiate over
Braking speed aggression
These need to be gated to something that just includes the initial braking. I have used greater than 20 bar/second in the below two example equations
Aim - IF(GT(brake speed, 20),brake speed, 0),
MoTeC - choose(‘brake speed’[bar/s]>20, ‘brake speed’,1/0) (bar/sec)
Braking speed smoothness
These need to be gated to something that just includes the initial braking. I have used less than 5 bar/second in the below two example equations
Aim - IF(LT(brake speed, -5),brake speed, 0)
MoTeC - choose(‘brake speed’[bar/s]<-5, ‘brake speed’,1/0) (bar/sec)
If we then look at the brake release smoothness, this trace helps to highlight any points where the driver released the brakes a little too much, we can see that the blue driver did this twice, whilst the orange driver did it once. It’s common to see a spike at the end of the brake release, as the driver removes their foot completely, the pressure released per second can be quite high. Even for expert drivers there can be a spike, albeit it is quite a lot less as they are able to moderate their foot pressure more perfectly. But in this case the blue driver has let their foot off the brakes quite a lot twice early in the braking zone. Here we have Blue doing this to the car twice, the orange driver has been able to more smoothly release the brake, giving them a more predictable level of grip. Orange does let go off the brakes slightly too early, causing them to reapply the brakes again, but other than this correction, they have managed to more smoothly release the brake pressure.
The other thing to look at in the brake speed trace is the variance in brake release, that is everything after the initial peak. As we can see, Orange has a slightly smaller variance than Blue, they have managed to release the brake pressure more smoothly.
The other thing to look at in the brake speed trace is the variance in brake release, that is everything after the initial peak. As we can see, Orange has a slightly smaller variance than Blue, they have managed to release the brake pressure more smoothly.
What if you only have G sensors?
If you don’t have the brake line pressure sensors, you can still look at your braking speed, we can do this indirectly using a gated inverted long G channel. If we have a look below, we can see the inverted long G channel overlaid with the total brake line pressure channel. Whilst the inverted long G isn’t as detailed, it misses a couple of the corrections and starts a little earlier than the brake channel, we can still get a good approximation of the brake line pressure.
As we have a good approximation of the brake line pressure, we can use this to create a maths channel that looks at the braking speed, we simply take the derivative of the inverted Long G channel. This channel, while helpful is somewhat limited by the fact that it is
- Missing a lot of the detail,
- We are taking a derivative so we need a high recorded frequency,
- It is strongly affected by
- Conditions,
- Tyres,
- Elevation,
- Vehicle set up, and
- Location on the track
Due to all of the above, this is a good channel to use to compare braking speed at a corner, on the same day, or under similar conditions. Unlike the brake speed calculated with line pressure, this value by itself is meaningless, you can’t pick a value and think you can get that everywhere, you could use it loosely, for example I’m aiming for X ± Y, but you’d need to be careful doing that.
Having said all that, let’s have a look at the same analysis as above but this time we can compare the total brake to the inverted long G channel as well as the brake speed using the brake pressure to the inverted long g brake speed channel. If we have a look below, we can see that inverted Long G, whilst not able to pick up some of the detail, shows that we get the same general trends. It does suffer in its clarity, Orange's final correction isn’t visible and neither is their continued application of the brake whilst being on the accelerator. Also if we looked just at the inverted long G brake speed, we would wrongly assume that Blue reached their peak in a similar time, they were as aggressive on the brakes, which isn’t the case. We can see it in the inverted long G channel, so it’s not too bad, it’s just something we would need to be aware of. But other than those three, the inverted Long G gives us some really good data. I haven’t split the brake speed further down into brake aggression and smoothness, but there’s no reason why we couldn’t.
- Missing a lot of the detail,
- We are taking a derivative so we need a high recorded frequency,
- It is strongly affected by
- Conditions,
- Tyres,
- Elevation,
- Vehicle set up, and
- Location on the track
Due to all of the above, this is a good channel to use to compare braking speed at a corner, on the same day, or under similar conditions. Unlike the brake speed calculated with line pressure, this value by itself is meaningless, you can’t pick a value and think you can get that everywhere, you could use it loosely, for example I’m aiming for X ± Y, but you’d need to be careful doing that.
Having said all that, let’s have a look at the same analysis as above but this time we can compare the total brake to the inverted long G channel as well as the brake speed using the brake pressure to the inverted long g brake speed channel. If we have a look below, we can see that inverted Long G, whilst not able to pick up some of the detail, shows that we get the same general trends. It does suffer in its clarity, Orange's final correction isn’t visible and neither is their continued application of the brake whilst being on the accelerator. Also if we looked just at the inverted long G brake speed, we would wrongly assume that Blue reached their peak in a similar time, they were as aggressive on the brakes, which isn’t the case. We can see it in the inverted long G channel, so it’s not too bad, it’s just something we would need to be aware of. But other than those three, the inverted Long G gives us some really good data. I haven’t split the brake speed further down into brake aggression and smoothness, but there’s no reason why we couldn’t.
Comparing Sessions or Drivers
Once we have created the brake speed, aggression, and smoothness channels, either with the Long G or with Brake Line Pressure, we can average the non zero values and use this as a way to compare driving styles and to help with tyre management. Below I have graphed the brake aggression, using Long G, of two drivers in the same race. Clearly Driver A is a lot more aggressive on the brakes than Driver B, this doesn’t necessarily mean they are faster or that they are breaking better, driver B could be better at using their ABS system for example, we would need to do more analysis to have a concrete answer.
One thing we need to be careful with when doing this with Long G, is that as Long G is being measured at the tyres, as the tyres wear the friction potential reduces, so our braking potential reduces, our brake aggression may reduce and our smoothness may become more erratic as the driver tries to maximise braking without locking up, this wouldn’t be a problem if we were using brake line pressure instead.
One thing we need to be careful with when doing this with Long G, is that as Long G is being measured at the tyres, as the tyres wear the friction potential reduces, so our braking potential reduces, our brake aggression may reduce and our smoothness may become more erratic as the driver tries to maximise braking without locking up, this wouldn’t be a problem if we were using brake line pressure instead.
This brings us to the end of this post, but isn’t the end of our braking series, we will be back shortly asking the question "Are you braking hard enough?". If you can't wait, check out our other articles on this site below and above. And don’t forget to sign up so you don’t miss out on any of our upcoming posts. If you have any comments, suggestions, or noticed I made a mistake, write it down in the comments or get in contact via email or using the contact page, I’d love to hear it. Thanks for reading and I hope you have a great day.
By Trav Mays
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