STAC Thinks About: Cornering

These guys are way better at cornering than the author
Credit: Wikimedia

Two years after finishing on the podium at the 2015 Tour de France, Alejandro Valverde's 2017 Tour ended on stage 1 after hitting the deck on a slippery corner and breaking a knee cap. Cornering can be tricky in the rain, but even in optimal conditions, riders miss out on free speed by not cornering as efficiently as possible.  The magnitude of the time gains available help explain why the pros like Valverde push their cornering speeds all the way to the limit and sometimes beyond.

Today we're going to dig into the physics of cornering on a bike and run some simulations to see just how much time can be gained, or lost, every time the race course changes directions.

 About the author:

Multisport Canada K-Town Long Course 2016: Where others see a well-marked, well-paved corner, I see my imminent grisly demise.

Ever since a crash on a mysteriously slippery roundabout in 2014 that resulted in a bruised ribcage, I’ve been very hesitant and cautious while cornering on my triathlon bike.  Often during a triathlon, I will be passed just before, during, or shortly after a corner because of my extremely cautious approach to each corner.  In my mind are always the thoughts: “What if there’s gravel on the exit of the corner?”  “What if I need to suddenly dodge a pothole?”, and most often: “what if this corner is as slippery as that roundabout?”.  Because of this, I’ve had competitors mention, unprompted, that my cornering ability is pretty lackluster.  So today, I want to do some research on just how much time my poor cornering is costing me.

Cornering

Cornering in a triathlon is an underappreciated but very important skill.  Every time you corner, there’s three phases: braking, cornering, and re-accelerating.  During the braking phase, you bleed off speed so that you can safely go around the corner.  During the cornering phase, you lean over and change direction, usually at a constant speed.  Once you’ve straightened out enough, you start applying power to the pedals and re-accelerate to your cruising speed.

The first two phases are affected by a rider’s bike handling skill.  The re-acceleration phase is primarily governed by the rider’s athletic/cardio capabilities and strategic considerations about power output.  This means that the first two phases represent an opportunity for true “free speed” - faster bike splits without needing greater cardio OR better equipment.

Let’s go through each phase in turn:

Phase 1: Braking

Despite the fact that braking is all about _reducing_ your speed, the braking phase in a corner is possibly the easiest place to get some speed.  If you brake a little later and a little harder, it means that no matter your ultimate speed during the cornering phase, you will have carried your speed from the previous straight for as long as possible.  Braking too early means you spend more time moving slower.  The optimal braking point is when it isn’t possible to slow down any faster before the spot where you start turning.  If you flip your bike over while braking, you braked too hard.

Phase 2: Cornering

During the corner, your speed is ultimately limited by the amount of grip your tires deliver against the road.  Imagine cornering on ice or wet pavement: since you have less grip, you need to reduce your speed in order to complete the corner upright.  Cornering is ultimately an extremely skill and confidence-based ability: you need to be able to smoothly lean your bike over and accurately complete the _widest_ corner possible so that you carry as much speed through the corner as possible.

Phase 3: Re-acceleration

Once you’ve straightened out, it’s time to mash on the pedals and get back up to speed.  This is primarily cardio-oriented, and the length of the re-acceleration phase is mainly determined by how much speed you carried through the corner and your level of fitness.  There is some strategy in determining how much effort to put into re-acceleration: if you do a sprint out of each corner you may burn too many matches and pay for it later with fatigue.  If you keep up a steady-state wattage, it may take you extremely long to return to your peak speed.

The Simulation

Code available at: https://github.com/arthare/stac_cornering_sim

In order to compare apples to apples, I’ve written a simple simulation that goes through these phases.  In the simulation, the rider attempts to complete a 4km course with a single 90-degree corner in it.  This seems to me like a decent approximation of a triathlon course, which typically has long straight stretches interrupted by terrifying 90-degree corners.

Fixed Parameters:

• The lane in the road is 3.7m wide.
• The corner is a 90-degree corner, which results in an optimal corner radius of 12.63m
• The rider outputs 250W
• The air temperature is 25C, leading to an air density of 1.184kg/m^3
• The rider weighs 80kg (=176lbs)
• The rider’s CdA is 0.27, which is a pretty-good-but-not-elite aero position
• The rider’s tire Crr is 0.0033, which is a fairly good race tire
• All these parameters result in a cruising speed in a flat, windless straight line of about 40.1km/h.

Varied Parameters

• We will independently vary the rider’s maximum braking grip and maximum cornering grip, expressed in Gs. The fastest cyclists or cars will corner at about 1g, or 9.8m/s^2.  This will let us simulate riders that are scared of braking and cornering (like me!) as well as riders that are aces on the bike.

Results

• We will look at the time taken to complete the course and average speed.

Results

As you would expect, riders with more confidence on the brakes and cornering did better, with a big bias towards riders that carried more speed through a corner.  The interesting question to me was _how much_ better.  With a bit of research, I found that a skilled rider can brake at about 0.83g before their bike starts catapulting them over the handlebars.  For cornering, I’m going to assume that the best a bicycle rider can manage is about 0.9g, as the physical limitation of rubber-on-pavement is about 1.0g.  Read below for the results.

Hesitant rider (that’s me!)

Braking: 0.5g

Cornering: 0.25g

Time on course: 6m 7s

Average speed: 39.15km/h

This rider brakes lightly and then corners hesitantly.  They decelerate from 40.1km/h down to 20km/h, then re-accelerate back to cruising speed.  Most of the time loss compared to their competitors below happens as they’re bringing themselves back up to speed - their harder-cornering competitors are doing several km/h more than they are once the corner ends, so the slower rider has to watch them fade into the distance while both riders pick speed back up.  This rider can compensate by sprinting out of the corner, but each sprint means energy spent that their competitors didn’t have to.

Hard-braking rider:

Braking: 0.8g

Cornering: 0.25g

Time on course: 6m 7s

Average speed: 39.16km/h

This rider has learned how to brake hard.  They might surprise riders behind them with their pavement-ripping stopping power, but they still are very hesitant with their cornering speed, and that’s still where they lose time.  They take a couple tenths of a second out of the hesitant rider that we saw earlier simply from braking harder and later, but further improvements are possible.

More confident rider:

Braking 0.8g

Cornering: 0.5g

Time on course: 6m 3s

Average speed: 39.57km/h

After gaining confidence on the brakes, now our rider has improved their cornering skill.  Instead of slowing all the way down to 20km/h, this rider now holds a solid 28.3km/h through the corner.  Not only does this mean they complete the corner faster, but the real savings is that they don’t have to spend as much time and energy getting back to cruising speed.

Pro rider:

Braking: 0.8g

Cornering: 0.9g

Time on course: 5m 59s

Average speed: 40.02km/h

This rider has mastered both the braking and bike-handling aspects of cornering.  In fact, they only barely have to brake for this corner- their 0.9g cornering capabilities allow them to do the corner at 38.01km/h, just below their cruising speed of 40.12km/h.

Mitigation:

There’s one obvious way for a slow cornerer to compensate: sheer power.  If the slower cornerer simply puts out more watts, then they can negate the time that the more confident rider is gaining on each corner.  But how many watts do they need to put out?  By increasing the simulated rider’s watts in my simulation, I found what each rider would need to do in order to make up for the pro rider’s cornering abilities:

Rider	Watts needed to catch “Pro Rider”
Hesitant Rider (slow at corners, slow at braking)	268W
Hard-braking rider (slow at corners, good at braking)	267W
More-confident rider (medium at corners, good at braking)	259W
Pro Rider	250W

So we see that the “pro rider”, with their excellent cornering abilities, can maintain an average wattage 7% less than the hesitant rider and go the exact same speed, as long as the course has one corner every 4km.  In cycling, this could mean having more matches to burn during the final sprint.  In triathlon, this could mean a much stronger run.  It takes a lot of quiet time on your STAC Zero to build 7% more fitness!

Simulation Thoughts

In this short simulation, we saw a 0.9km/h (0.5mph) improvement in average speed simply from braking harder and cornering faster on a single corner in a 4km segment.  All these riders put out the same wattage, but the rider that did the lone corner aggressively saved 8 seconds over the rider that took the corner the most hesitantly.  Over the course of even a very straight 20km sprint triathlon (with maybe 5-6 corners), this might represent a 40 second savings in a 33-minute ride.  Over a 90km half-distance bike leg with a corner every 4km, the rider that took each corner quickly would save energy AND finish faster, to the tune of 3 minutes: that’s a 2-3% reduction in time.  

Training Opportunities

Much like flip turns or underwater work for a competitive swimmer, cornering on a bike represents a completely free source of speed that can be practiced with every corner you take during training.  With an opportunity to steal up to 8 seconds on your less-confident opposition on every single corner, leaning over and cornering hard is an angle (zing!) that can’t be ignored.  Finding a safe spot like a parking lot to practice can be an excellent way to work up the confidence to take every corner quickly.

Reality Check:

Simulations are all well and good, but how does this finding stack up in real life? Well, I have a perfect example. At the 2015 Wasaga Triathlon, I came out of the water just ahead of local FPRO Kristen Marchant, and we both had Strava running, so we both ended up on the awesome Strava Flyby feature. For the first half of the bike we were neck-and-neck: I would pull a gap on a straight stretch, then Kristen would blast past me on a corner. You can actually see this effect on the Strava time-gap chart: The blue line indicates the time distance between Kristen and I, and each little spike upwards correlates to Kristen gaining several seconds in a corner that I tip-toed through that she attacked. You can view this comparison on Strava at this link.