How Hills Affect Racecar Braking

If you are racing at a hilly track then not only is the driving tricky but it can also make your data analysis difficult too. You want to be able to use data analysis to pinpoint areas where the driver and car can improve. Depending on whether you are driving uphill or downhill, hills affect racecar braking and also the quality of your measured data.

This article explains what is going on and presents a suggestion for how you could make your data analysis easier by accounting for the hills.

Effects of Gravity

Gravity makes a “contribution” when you are braking on a hill.

You most likely intuitively know that you can brake later into an uphill corner. Similarly, when you are going downhill you might know you need to brake earlier.

But how do you know by how much? Are you maximising all of your racecar’s braking potential? And, how could you work out how well you have performed in order to go faster?

Braking Data Analysis

It is reasonable to assume that you will perform better in some braking zones than others.

What would be great is to know how well you actually performed in each braking zone.

With that information, you know what you need to do and can prioritise where you can improve.

Longitudinal acceleration is the fore-aft “g-force” you feel when you hit the brakes (or throttle.)

These days, even the most basic datalogging systems can record your racing cars acceleration. It can look like this:

How hills affect racecar braking - long acc trace
What a recorded “Long Acc” data trace looks like ☝️

With a few pointers, you can use this recording of your racing cars longitudinal acceleration for things like:

  • assessing braking points
  • looking at your braking consistency
  • understanding how hard you are braking

As a result, longitudinal acceleration can be a really useful data channel.

But there is more you can do with it.

“Better” Braking Everywhere

“Better” braking means finding places where the racing driver can brake later and harder.

When you brake later, you end up spending more of the lap at a higher speed than if you had braked earlier than you need too.

More time at a higher speed is faster. Faster = lower lap time = a happier you!

Furthermore, there is a general theory that says:

You should be able to achieve the same amount of braking deceleration at every corner on the track.

If you have reached 1.2g deceleration on one corner, you should be able to reach that on every corner. 

This forms a general method for assessing braking performance where you compare the peaks in longitudinal acceleration of your racing car under braking.

Peak Acceleration Braking Analysis Example

Have another look at the example longitudinal data below. This time I have annotated it with how this braking theory works:

How hills affect racecar braking - long acc trace explained

Negative longitudinal acceleration typically represents braking. I have therefore drawn a dotted line at the peak maximum longitudinal acceleration in braking.

The theory says that whenever the racing driver is braking they could (and should) be hitting that maximum peak. Otherwise, they are slower than they could be.

You can hopefully see that the racing driver hits the peak at two points in the chart – ticked at 3 and 4. Nice! 😎

You can also hopefully see that the rule is also telling us that there are potentially chances for the driver to improve. In-particular at points 1, 2, 5, 6 and 7.

This method therefore gives you specific, objective information that shows you precisely how (and where) you can improve your braking.

Great news! 😎

But, being only a theory, there are lots of cases when this will not be the case.

Some of these (including how hills affect racecar braking) are noted below:

Some Caveats To The Brake Analysis Theory

  • If you run a racing car with a lot of downforce, then your braking deceleration will be affected by how fast you are going. The faster you go the more braking potential you have because of the downforce (and drag) created by your racecar
  • Not all of the track will have the same track surface everywhere. Therefore there could be different levels of grip at different corners. Without the same grip levels, this means your racing car cannot be expected to slow down at the same rate everywhere. Knowing the track surface and condition around the lap is, therefore, useful to note if you do a track walk…
  • This theory works best in areas of high “threshold” braking, like braking for a hairpin after a long straight. For other areas, such as more flowing sections of track, you would use other approaches – perhaps that look at a combination of longitudinal and lateral forces
  • Hills. When you go up a hill, gravity will be helping you to slow down. When you go downhill it will be working against you. This is why you can brake later going uphill than you would be able to on a flat track. Equally, why you need to brake earlier going downhill compared to taking the same corner on a flat track

These caveats can be significant enough that you cannot reliably use the theory and that is a real shame as it is such an easy one to look at.

What can you do?

The effect of the hills on braking performance is one that comes up quite regularly in discussion.

I, therefore, had a look at what you might be able to do with your data to compensate. The outcome of my investigation is below.

Compensating For How Hills Affect Racecar Braking Analysis

The goal was to modify the longitudinal acceleration figures so that, no matter how hilly the race track, you could still use the peak longitudinal acceleration theory for your braking assessment.

As with anything engineering (it seems!), once you look into it a bit, it rapidly becomes more complex than you initially anticipated. Adding to the above caveats are the (potential) effects of weight transfer, condition of the brakes (i.e. temperatures), tyre temperatures/pressures and even the rate of brake pedal application.

I decided to keep it simple and just see what came out.

My thought was to try something knowing and acknowledging there are limitations but with the aim of seeing if I could still help you do something useful with the data so many of you have.

Firstly What Is Actually Going On?

The big thing is that gravity sneaks into your racecar’s acceleration measurements on hills.

Gravity is about 9.81m/s, acts vertically on your racecar and, more commonly, it is referred to in “g’s.”

When driving your racing car on a flat race track this means that gravity does not really get involved in your driving. Gravity simply acts vertically to keep you on the tarmac.

The thing is, to keep us all on the ground we experience “1g” all the time.

1g is quite strong. It is the equivalent to the maximum longitudinal acceleration under braking for nearly any road car and many many racing cars.

What that means is that gravity is more than strong enough to affect racecar braking on hills.

The effect of gravity, on your racing cars longitudinal acceleration, increases with the angle of the hill you are driving on.

The steeper the hill the more gravity’s effect. The flatter the hill the less its effect.

As a result, the acceleration measurements of your racing car datalogger will be affected by gravity when you are on a hill.

On hilly tracks, this then makes using the general theory (about looking for peaks of opportunity in the longitudinal acceleration braking trace) less robust.

But If You Know The Slope Angle …

However, if you know the slope of the hill, then what could you do?

It kind of becomes a maths challenge to simply work out the acceleration your race car is “un-usefully” measuring due to gravity and correct for it.

So that is what I set out to do.

Maths Bit

Below is a sine curve:

Sine curve

My approach to the maths challenge above is to take the Sine of the slope angle (i.e. your race track’s hills) and multiply that by Gravity.

That should give you the “un-useful” contribution gravity is making to your measurements and enable you to correct for it … hopefully!

I have used the sine wave (SIN) to determine the proportion of gravity that acts on your racing car based on the angle of your race tracks’ hill:

Proportion of Gravity Caused by Hills = Gravity x SIN (Slope Angle)

The diagram below aims to show this a bit more clearly (aims too 🙂 ):

How hills affect racecar braking - g correction explained

The proportion of “un-useful-to-our-measurements” gravity is on the vertical axis. The hill angle is on the x-axis. There are some example calculations at 90 and 20 degrees slope angle.

Clearly 90 degree hills are a bit extreme, but you can see that in a range of plus or minus 20 degrees you get well over half a “g” effect.

Many, many tracks have slope angles of 10 or more degrees. These slopes are also often into the braking zones. Hopefully you can see how this could now become significant in your braking assessments.

To work out the-equivalent-to-driving-on-a-flat-race-track-longitudinal-acceleration, or, “Longitudinal Acceleration Corrected” then you need to add the measured longitudinal acceleration to the proportion of Gravity caused by hills number, like this:

Long Acc Corrected  = Long Acc + G Correction

And see if it was worth it…

Worked Example (in AIM Race Studio Analysis)

How hills affect braking raw long acc

Above is the longitudinal acceleration data you saw from earlier in the article. You may recognise that this data is shown in the AIM Race Studio 2 Analysis software. This is popular with many of you and it also has some nice benefits for doing this kind of study. Specifically, it has standard data channels of GPS_Slope (the hill angle) as well as GPS_LonAcc (your longitudinal acceleration):

How hills affect braking standard channels in AIM Solo datalogger

AIM Race Studio also enables you to write custom “Maths Channels.”

If you are not familiar with these then they are a bit like how you can write an equation in Excel. In this case, it will allow you to take your Longitudinal Acceleration data and your Slope data, and create a new corrected Longitudinal Acceleration channel.

How hills affect braking AIM Solo Maths Channel

The AIM documentation is a bit … lite … however they have produced this pdf on how to create a Maths Channel if you are not familiar with what this all about.

This is the equation you need to use. I called it: LonAcc_Corr

How hills affect braking Formula in AIM Race Studio

Pulling this together. Was It Worth It?

To test this I was fortunately to have an example data set of a fairly hilly track (thanks Matt):

Hilly race track
Hilly Race Track! … Pro Tip: Double Right click to turn GPS track map into 3D slope chart in AIM Race Studio

I created the new Maths channel and then compared the two.

You can see the result of the two data channels next to each other here. Note I have zoomed in on just the braking peaks for clarity:

How hills affect braking hill corrected longitudional acceleration

The top chart is “Hill Compensated”. The bottom is the original longitudinal acceleration.

Not a massive difference on first inspection but have a closer look. Below I have annotated the two charts to help you:

How hills affect braking hill corrected longitudional acceleration compared

There is quite a lot going on here. But in simple terms it looks like the hill compensated longitudinal acceleration is DEFINITELY worth you looking at.

I will explain…

Worked Example – What is going on?

In the original data on the bottom chart (“No Hill Compensation“) the peaks are quite inconsistent. Except for the two I identified before (at points 3 and 4), there looks like there is a lot of opportunities to brake later into a number of other corners.

The “Hill Compensated” data tells a slight different story. Now that you can see the data without the gravity effect messing with the measurement, it looks like the racing driver is much more consistent around the lap.

The maximum peak seems lower* and therefore the racing driver hits the peak at points 3, 4, 5 and 7. This is much better! It leaves only points 1, 2, and 6 as major opportunities for improvement. Particularly points 2 and 6 look a bit worse in the Hill Compensated longitudinal data than the original data, suggesting they need the most attention.

Where this is really useful is in a situation where you were looking at points 5 and 7. In the raw data, these look like there is an opportunity for improvement. However, the Hill corrected data suggests otherwise, so much so that you’d be wasting your time and effort to get improvements in this area.

Useful, hey!

* I have taken a bit of “analytics licence” at point 4, because I think there was something else going on here outside the scope of the article but alluded too here if you are curious

Wrapping Up – Hills Affect Racecar Braking

This article results in a short, simple one-line equation. As you can see there is a lot going on behind the scenes – even with the simple version!

This is typical of data analysis, including lots of ways this could be “wrong”, but hopefully, you can also see how it could still be useful.

I thought if you run an AIM datalogger and you are struggling with your braking analysis, especially at a hilly track, you might want to give this a go.

The aim always with analysis is to help steer your understanding so you can prioritise the biggest areas for most improvement first. This suggestion aims to do just that for your braking.

For something so simple to implement it might help your race drivers braking performance a lot.

As ever, I am keen to hear form readers who give this a go!

Just sign-up to the newsletter on the form below as it would be great to hear from you. Oh, and as a subscriber you also get instant access to a growing Vault of invaluable motorsports resources, such as spreadsheets, course, handouts and (much) more … so if motorsports is your thing its worth it anyway 😎

Best wishes as ever!

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