The math behind a time trial: A nerdy preview of the Giro d’Italia stage 7 time trial

How do you optimise for a Grand Tour time trial? The 2024 Giro d’Italia time trial course with 420 metres elevation acquire is the proper enviornment to delve into a while trial efficiency geekery. Our first problem is to optimise our time with a crafty pacing technique; then we’ll uncover if a motorcycle swap will likely be quicker for the professionals on Friday; and eventually, will the stage be a day for a powerhouse like Filippo Ganna or a climber resembling Tadej Pogačar?

The attention-grabbing facet of the 40.8km Giro time trial course is the place the elevation acquire is. The first 33km are comparatively flat. If the course was to finish at kilometre 33, your greatest wager is to easily attempt to maintain your highest sustainable energy from Foligno to Ponte San Giovanni. However, our remaining vacation spot is Perugia an extra 7km uphill, with gradients peaking at 16%.

Below are two elevation charts. The first is the normal elevation chart, with distance alongside the X-axis. The second chart reveals a simulation time alongside the X-axis, revealing the importance of that remaining 7 km on the course.

Now to our problem, optimising our energy output for this course. Imagine we’re a professional bicycle owner competing within the Giro d’Italia particular person time trial. Our goal energy for the person time trial is round 400 watts (~1300Kj). We select to assign a conservative 20Kj further ‘finances’ to optimise energy technique. I’ll clarify why a finances could be determined this fashion shortly.

We can both:

• Evenly tempo our time trial by spreading the kilojoules over the 40km
• Spend all our further kilojoules on the ultimate 7km uphill sector. 

First of all, what’s a kilojoule and why finances our power this fashion and never in watts? A kilojoule is a measurement of power. A watt is basically one joule per second. So, to find out what number of watts our 20Kj equates to, we should divide our kilojoules by the period in seconds. By distributing power slightly than watts we will be positive we give every of our pacing plans a good digital race. 

Let’s start by taking a look at how power is distributed when biking. This may give us a clue as to the place our finances could be greatest spent.

First, we should take care of drivetrain losses. Anywhere two transferring components meet, there’s a friction loss. The best drivetrains are working at 2% losses, whereas a normal well-maintained drivetrain will likely be round 3%. This means a rider biking at 200 watts with a normal drivetrain has a internet 194 watts contributing to the propulsion of the bicycle. 

Next, I discover it is sensible to separate the remaining forces appearing towards us once we cycle into two classes, resistances affected by our mass (system weight) and Air Resistance. You’ll see why that is helpful once I present you ways the 2 behave in another way as we alter the speed (velocity) enter in our formulation.

In our class ‘mass affecting resistances’, now we have Gravity and Rolling Resistance. Cycling uphill clearly requires higher effort as we improve our mass on account of gravity, however the generally missed impact of mass is on tyre rolling resistance. 

Rolling resistance has a Coefficient. This is a ratio that describes how a lot power is required to beat the vertical loading mass on the tyre. Typically a great highway bike tyre is between 0.004 – 0.005. The greater the coefficient the higher the power required for a similar velocity.

Take a have a look at how growing mass impacts each resistances.

Air Resistance is what we name an exponential power. The subsequent chart reveals how Air Resistance responds to our Speed growing. Notice the way it wouldn’t be straightforward to attract this line with a ruler.

Air Resistance will get out of hand in a short time in comparison with our linear mass affected resistances. 

The inputs for Air Resistance is Air Speed, Air Density, and our Coefficient of Drag (CdA). Notice we’re utilizing Air Speed and never Ground Speed.

So, there’s a really fast run-through of the resistances we should overcome to cycle quicker. Now again to our time trial problem. 

As we aren’t utilizing a supercomputer resembling myWindsock.com to course of each metre of our time trial together with the climate, we’ll must simplify our course into two sections, a 33km 0% gradient sector and a 7km sector with a mean gradient of 4.5%.

So far our formulation give us the required energy to beat resistance at a given velocity. Our pacing experiment requires us to find out Velocity (velocity). Now this will get difficult as you’ll discover we require Velocity in each our linear and exponential (quadratic) equations. In order to unravel our linear equations we want the reply to our exponential equation and vice-versa. To remedy this, plotting on a chart turns out to be useful.

Below are our charts to unravel our preliminary estimates of time period. We’ll begin with a baseline period for each the 33km flat sector and the ultimate 7km uphill sector. We are doing this so we’re in a position to pretty distribute our 20Kj finances in our two situations over the estimated time period.

For the next calculations now we have a CdA of 0.2, rolling resistance of 0.0044 and our system weight (mass) is 80kg.

Using the above graphs, now we have situated our velocity estimates. To get our durations for every part, we should divide velocity over distance. 

Now, we calculate our further wattage for our evenly paced time trial. Dividing our 20Kj over the overall baseline time of 52:13 provides us an extra 6 watts. 52:13 equates to 3133 seconds, and 20Kj (or 20,000 joules) divided by 3133 equals 6.38 joules per second. For simplicity, we have rounded down to six joules per second, which equates to six watts. 

Using the formulation mentioned earlier let’s generate our graphs one other time. This time with our energy set for an evenly paced time trial at 406 watts (authentic 400 plus 6 watt further ‘finances’)

 Again we calculate our whole time in the identical method.

The further wattage has gained us 18 seconds. This is unsurprising given we’re 6 watts up on baseline energy. However, did you discover the relative change of our speeds was a lot higher for our remaining uphill 7km?

Now for our 20Kj finances to be deployed solely within the remaining 7km uphill sector. We revert again to our preliminary estimated time of 13:47 and divide our 20Kj. This provides us 24 further watts, taking us as much as 424 watts for the climb. We already know the time of our first 33km at 400 watts was 38 minutes 26 seconds. But, what is going to our remaining 7km be? Let’s run the maths and have a look at the graph.

One final time, we calculate our whole time in the identical method.

For the identical power expenditure, we gained an extra 15 seconds just by distributing it in another way. In truth, it might be greater than this on account of the truth that now we have shortened our sector time, which means we may probably output much more energy and be even faster. To completely match Kilojoules, we might once more must carry out a number of iterations to get inside our acceptable margin of error.

Of course, the precise Giro course has various gradients. As the gradient will increase, the effectiveness of our further energy will improve.

Why are we faster when making use of our further energy to the uphill sector? Let’s refer again to these linear and exponential equations. As air resistance will increase our return for every watt turns into much less and fewer, as demonstrated by the exponential curve. Whereas the linear forces, gravity and rolling resistance, have a way more beneficial input-to-output return.

Looking ahead to stage 7 of the Giro, what does our time trial geekery reveal? For the next insights, we should issue all of the twists and turns, inclines and declines and the evolving climate. 

To do that, I attain for the AI-powered simulator, myWindsock.com.

Would a motorcycle swap make sense?

We’ve already explored the truth that within the remaining 7km to Perugia has a mean 4.5% gradient. But, that solely tells half the story. For the primary 1.5km the highway averages 10%, peaking at 16%. At these grades, we could possibly be within the territory of a motorcycle swap. The fundamental requirement of the mathematics right here is to work out whether or not the lowered weight of the highway bike when in comparison with the time trial bike makes sufficient distinction to the rider’s velocity to offset the aerodynamic detriment plus the time it takes to cease and swap. To work this out, we’ll do the sum for 2 riders: heavyweight Filippo Ganna and light-weight Tadej Pogačar, however we additionally need to make some assumptions. 

For our simulations, we’ll assume the highway bike obtainable is round 2kg lighter than the aero bike and each riders are using at their reported FTPs (Functional Threshold Power), and we’ll use the load reported by ProfessionalCyclingStats. We’ll additionally assume a set CdA for each bikes/riders. 

So a number of seconds misplaced between swapping bikes may go away a small benefit. The simulated benefit could also be smaller than you’d count on, however our simulation additionally takes under consideration the discount of ‘potential power’ because of the smaller mass. 

To exhibit potential power, would you slightly be hit by a practice or a feather travelling at 30kph? 

Digging deeper, if we think about aerodynamic losses we discover that the highway bike will put the rider at an general drawback, particularly after the primary 1.5km have been climbed and the highway ranges off some. We can rapidly simulate this to seek out out. 

Assuming our rider on a highway bike has a set CdA of 0.3, whereas above 20Kph (ie, after the preliminary part of the climb) our time trial bike will return to a slippery CdA of 0.2.

In this sum, the highway bike is half a minute down on the TT bike setup, so a motorcycle swap wouldn’t make sense. However, groups will know extra precisely the CdA, weight and energy outputs for every of their riders on each highway and time trial setups, in addition to how rapidly they’ll swap from one bike to a different. If the CdA detriment is smaller, or the load distinction is bigger, then it’d swing issues in favour of a motorcycle swap, assuming they’ll get it performed rapidly!

Can a heavyweight like Ganna maintain off a light-weight like Pogačar?

This takes a little bit of guesswork as to the facility outputs on the day. However, we are able to see that this course will fantastically expose the strengths and weaknesses of each kinds of rider. Assuming each are using at their reported FTPs, we are able to see how shut this might get with a time delta graph. Below reveals a simulated time comparability between Ganna and Pogačar.

The pink line reveals Ganna taking trip of Pogačar as much as time checkpoint 2. In the ultimate sector, Ganna is rapidly shedding his benefit. For Ganna to be in rivalry, he wants to steer Pogačar by greater than 50 seconds at time test 2.

As we discovered earlier, it’s going to pay for each riders to ‘adverse break up’ the race, saving some joules on the flat floor earlier than setting the matchbook alight on the climb. It would possibly simply be powerful for the lighter riders to simply accept the time deficit on the first checkpoints and imagine that the mathematics will come good ultimately.

It’s definitely going to be one to observe.