## Motorsport Data Analysis: **Delta-t**

“I’ve got data but I’m not sure how to interpret it.”

Motorsport data acquisition systems promise to make you faster. In practise, it is easy to get overwhelmed by the data and subsequently put off.

“Easy” and “intuitive” if you have an engineering degree or you wrote the software, but a confusing mess of squiggly lines otherwise.

The promise of your high-tech kit can get agonisingly reduced down to no-more than an (extremely) expensive lap timer.

What if you could however **start with just one channel of data**.

A single channel that would show you your gains and losses in a simple, meaningful way.

Ignoring all the other data for now, one chart that would enable you to at least get going with data.

One that was able to truly help you **evaluate different race driving approaches** and provide **solid guidance** on where to look for improvements.

If you knew about what to expect from this data channel, how it was derived and how it can help, **perhaps that would give you more confidence when approaching data?**

Without data logging in motorsports, you can only judge your race driving performance on lap times.

Lap times alone are a crude metric to use when you are looking to improve.

In motorsport data analysis, **delta-t** gives you objective information on your gains and losses in much more detail.

It is not perfect, however, in **motorsports data analysis, delta-t** is where you should start.

Armed with delta-t, “paddock opinion”, feel and lap times alone, become obsolete.

### Consider delta-t the ultimate measure of a racing drivers’ performance.

Here is how it works …

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## The Racing Car: **Think Inputs & Outputs**

Start by thinking of the racing car as system that has things you can control (inputs) and things that happen as a result (outputs.)

The question for the racing driver is how do I operate these inputs to give the fastest lap time.

The way the racing driver can judge their performance is by looking at the outputs.

## Imagine this chart: **Distance verses Elapsed Time**

Along the bottom axis is **distance travelled**.

Along the vertical axis is **elapsed time**.

Distance is the length the racing car has travelled from the start-finish line on this lap.

Elapsed time is the time that has past since the racing car last crossed the start-finish line.

The diagonal line represents what the racing car did.

This is not normally a chart you will see but to understand how delta-t is derived it is important to follow this through.

Looking at what the racing car did, you can then find the lap time and how far it travelled around the lap.

## Finding the Distance and Lap time

By reading along the bottom you can find the distance travelled on the lap:

By reading back across, you can find the time taken to complete the lap.

Hopefully this is fairly simple so far.

But we want to compare laps so I’ll add another one:

## Adding Another Lap: Which was faster?

I’ve now added another lap and you can see that this lap took less time.

By comparing the second lap time to the first, you can see that Lap 2 was faster.

Still all straight forward.

But what if we compared the difference earlier in the lap?

## Finding the time difference at an earlier distance.

The difference in the elapsed time shows that the time taken for the second lap to get to 1km distance was *less* than the first lap.

Put another way:

At 1km, Lap 2 was faster than Lap 1, although the gap is less than for the full lap.

Easy but important – for the **first time you can see which was faster part way round the lap.**

Taking that on a step further then.

What if you were to find the time differences at **1000’s** of distance points?

## Finding the time difference at 1000s of distance points

By finding the **time difference at every measured distance point**, you can find out the time gap **throughout the whole lap** – not just at discrete distances like 1km or the end of the lap.

**This is delta-t.**

*Technical Note:*

*Depending on your data logging system distance is measured more or less frequently. A system that uses a wheel speed sensor might measure distance a few hundred times per second. Systems that use GPS data might measure data between 5 or 20 times per second. *

*The wheel speed systems have the advantage of higher fidelity but are often an additional sensor to fit, plus are susceptible to errors from wheel locking. GPS systems are not effected by wheel locking but can be slow and suffer issues depending on the number, position and visibility of their satellites. *

*It is also worth noting that the distance driven will be slightly different each lap – as the driver tries different lines or when they make a mistake. There are ways to work around this but it will effect the comparison to varying degrees so it is worth considering if you get strange values.*

Whatever the technology used, Delta-t calculations gives 1000’s of data points so you can put Delta-t into its own chart:

## Motorsport Data Analysis Delta-T Chart.

Note that the vertical axis is now Delta-t in seconds.

What the chart enables you to do is find the precise time difference between the two laps **at any distance** around the track.

### Just to reinforce this:

- Lap time alone enables you to compare the time difference
**once**per lap. - Delta-t enables you to compare the time difference practically
**continuously**.

Much more useful that lap times alone.

## In reality …

In reality the lines for distance verses elapsed time are never straight like in my example.

This is because the racing car is constantly changing speed.

Therefore if you plotted distance verses elapsed time for the two laps it is more likely to look like this:

In the example above, you can see that at times the lines are closer, and at other times further apart. They even cross a couple of times.

This means that sometimes Lap 1 was faster and sometimes Lap 2 was faster.

This information is exactly what we are after then – to know **precisely where** one lap gained in lap time and another lost out.

Plotting the delta-t chart you can see more clearly:

## Delta-t shows gains and losses in detail.

Walking through from the start of the lap on the left and looking just at the lower delta-t chart you can see that as the lap progresses:

- Lap 2 was initially ahead.
- Then Lap 1 gained back a lot and became faster.
- Then near the end, Lap 2 regained its advantage to finish fastest overall.

Hopefully that makes sense?

In practise it can be a bit confusing sometimes which lap is faster going up and which is faster going down. Once you understand that though you instantly gain clarity on how they compare.

It is amazing really, as from this one channel, without any other data or video, you can quickly develop an understanding of a drivers confidence, consistency and progression during a session. You also know exactly where to look and how to quantify what you find.

It can be a revelation!

## Next Steps

Armed with this new knowledge, I suggest you try doing this for yourself.

If you have your own data great, but even if do not have any data of your own yet that is not an issue. Most of the data logger manufacturers allow free downloads of their analysis software. These also typically come with demo data for you to experiment with.

I recommend trying AIM Studio as this has a good range of data samples. You can get the software here.

I’ve put together a few slides taking you through an AIM Studio example in the handout slides to accompany this article. This includes more details on how to interpret the chart. The hand out is free for newsletter subscribers (who also get instant access to several other useful resources like spreadsheets, courses and videos) so if this is something you’re interested in having a look at, just **sign up** on the form below.

## Levelling up

The next step is to try to **determine** **why** there is a difference.

In terms of interpreting this, I’d be interested to consider what happened on Lap 1 to make it faster and see whether that could be incorporated to go faster overall.

I’d start by considering what was different between the two laps (driver, setup, weather etc.)

Then I would start to look at the other data channels to try to develop an explanation. Whilst doing this, I typically keep referencing back to the delta-t channel to try to quantify the explanations, before coming to a conclusion and recommendations.

In motorsport data analysis, delta t is the one go to channel so hopefully you are now super clear on it. To recap.

## Motorsport Data Analysis: Delta-t Recap

**Delta-t …**

- … is the
**first place to start**when doing motorsports data analysis. - … compares the
**time difference between two laps**around the lap. - …
**shows gains and losses**in a meaningful metric – lap time. - … enables you to
**evaluate different race driving approaches**and see which is better. - … acts as your
**sign-post for investigating**why there are differences.

It is fascinating when you first see this data for real on your own race car. Truly!

Happy analysing!

Do not forget to grab the **free 23-page handout** to accompany this article by **signing up** below. This includes a real data worked example using the popular **AIM Studio software**. Subscribers automatically also get access to our **Vault of free resources**, including useful spreadsheets, courses and exclusive videos.

### Enjoyed this? Check out these other articles:

Levelling up, how about visualising your GPS derived delta-t data in 3D with using Google Earth? Here’s a detailed guide, including walkthrough video, on how to set this up: https://www.yourdatadriven.com/compare-racing-laps-using-google-earth-pro/

Want to take the guess work out of setting your tyre pressures? Try this article including a **free** **calculator**: https://www.yourdatadriven.com/how-to-set-your-racing-car-tyre-pressures-perfectly-every-time/