The fractal nature of GPS routes

The mathematician, Benoît Mandelbrot, once asked “How long is the coast of Britain?“. Paradoxically, the answer depends on the length of your measuring stick. Using a shorter ruler results in a longer total distance, because you take account of more minor details of the shape of the coastline. Extrapolating this idea, reducing the measurement scale down to take account of every grain of sand, the total length of the coast increases without limit.

This has an unexpected connection with the data recorded on a GPS unit. Cycle computers typically record position every second. When riding at 36km/h, a record is stored every 10 metres, but at a speed of 18k/h, a recording is made every 5 metres. So riding as a lower speed equates to measuring distances with a shorter ruler. When distance is calculated by triangulating between GPS locations, your riding speed affects the result, particularly when you are going around a sharp corner.

Consider two cyclists riding round a sharp 90-degree bend with a radius of 13m. The arc has a length of 20m, so the GPS has time to make four recordings for the a rider doing 18km/h, but only two recordings for the rider doing 36km/h. The diagram below shows that the faster rider will have a record of position at each red dot, while the slower rider also has a reading for each green dot. Although the red and green distances match on the straight section, when it comes to the corner the total length of the red line segments is less than the total of the green segments. You can see this jagged effect if you zoom into a corner on the Strava map of your course. Both triangulated distances are shorter than the actual arc ridden.

It is relatively straightforward to show that the triangulation method will underestimate both distance and speed by a factor of 2r/s*sin(s/2r), where r is the radius of the corner in metres and s is speed in m/s. So the estimated length of the 20m arc for the fast rider is 19.4m ridden at a speed of 35.1km/h (2.5% underestimate), while the corresponding figures for the slower rider would be 19.8m at 17.9km/h (0.6% underestimate).

We might ask whether these underestimates are significant, given the error in locating real-time positions using GPS. Over the length of a ride, we should expect GPS errors to average out to approximately zero in all directions. However, triangulation underestimates distance on every corner, so these negative errors accumulate over the ride. Note that when the bike is stationary, any noise in the GPS position adds to the total distance calculated by triangulation. But guess what? This can only happen when you are not moving fast. The case remains that slower riders will show a longer total distance than faster riders.

The simple triangulation method described above does not take account of changes of elevation. This has a relatively small effect, except on the steepest gradients, thus a 10% climb increases in distance by only 0.5%. In fact, the only reliable way to measure distance that accounts for corners and changes in altitude is to use a correctly-calibrated wheel-based device. Garmin’s GSC-10 speed and cadence monitor tracks the passage of magnets on the wheel and cranks, transmitting to the head unit via ANT+. This gives an accurate measure of ground speed, as long as the correct wheel size is used (and, of course, that changes with the type of tyre, air pressure, rider weight etc.).

According to Strava Support, Garmin uses a hierarchy for determining distance. If you have a PowerTap hub, its distance calculation takes precedence. Next, if you have a GSC-10, its figure is used. Otherwise the GPS positions are used for triangulation. This means that, if you don’t have a PowerTap or a GSC-10 speed/cadence meter, your distance (and speed) measurements will be subject to the distortions described above.

But does this really matter? Well it depends on how “wiggly” a route you are riding. This can be estimated using Richardson’s method. The idea is that you measure the route using different sized rulers and see how much the total distance changes. The rate of change determines the fractal dimension, which we can take as the “wiggliness” of the route.

One way of approximating this method from your GPS data is, firstly, to add up all the distances between consecutive GPS positions, triangulating latitude and longitude. Then do the same using every other position. Then every fourth position, doubling the gap each time. If you happened to be riding at a constant 36km/h, this equates to measuring distance using a 10m ruler, then a 20m ruler, then a 40m ruler etc..

Fractal dimension 1.01

Fractal dimension 1.11

Fractal dimension 1.34

Using this approach, the fractal dimension of a simple loop around the Surrey countryside is about 1.01, which is not much higher than a straight line of dimension 1. So, with just a few corners, the GPS triangulation error will be low. The Sella Ronda has a fractal dimension of 1.11, reflecting the fact that alpine roads have to follow the naturally fractal-like mountain landscape. Totally contrived routes can be higher, such as this one, with a fractal dimension of 1.34, making GPS triangulation likely to be pretty inaccurate – if you zoom in, lots of corners are cut.

In conclusion, if you ride fast around a wiggly course, your Garmin will experience non-relativistic length contraction. Having GPS does not make your wheel-based speed/cadence monitor redundant.

If you are interested in the code used for this blog, you can find it here.

Strava Fitness and Freshness

The last blog explored the statistics that Strava calculates for each ride. These feed through into the Fitness & Freshness chart provided for premium users. The aim is to show the accumulated effect of training through time, based on the Training-Impulse model originally proposed by Eric Banister and others in a rather technical paper published in 1976.

Strava gives a pretty good explanation of Fitness and Freshness. A similar approach is used on Training Peaks in its Performance Management Chart. On Strava, each ride is evaluated in terms of its Training Load, if you have a power meter, or a figure derived from your Suffer Score, if you just used a heart rate monitor. A training session has a positive impact on your long-term fitness, but it also has a more immediate negative effect in terms of fatigue. The positive impact decays slowly over time, so if you don’t keep up your training, you lose fitness. But your body is able to recover from fatigue more quickly.

The best time to race is when your fitness is high, but you are also sufficiently recovered from fatigue. Fitness minus fatigue provides an estimate of your form. The 1976 paper demonstrated a correlation between form and the performance of an elite swimmers’ times over 100m.

The Fitness and Freshness chart is particularly useful if you are following a periodised training schedule. This approach is recommended by many coaches, such as Joe Friel. Training follows a series of cycles, building up fitness towards the season’s goals. A typical block of training includes a three week build-up, followed by a recovery week. This is reflected in a wave-like pattern in your Fitness and Freshness chart. Fitness rises over the three weeks of training impulses, but fatigue accumulates faster, resulting in a deterioration of form. However, fatigue drops quickly, while fitness is largely maintained during the recovery week, allowing form to peak.

In order to make the most of the Fitness and Freshness charts, it is important that you use an accurate current figure for your Functional Threshold Power. The best way to do this is to go and do a power test. It is preferable to follow a formal protocol that you can repeat, such as that suggested by British Cycling. Alternatively, Strava premium users can refer to the Strava Power Curve. You can either take your best effort over 1 hour or 95% of your best effort over 20 minutes. Or you can click on the “Show estimated FTP” button and take the lower figure. In order for this to flow through into your Fitness and Freshness chart, you need to enter your 1 hour FTP into your personal settings, under “My Performance”.

The example chart at the top of this blog shows how my season has panned out so far. After taking a two week break before Christmas, I started a solid block of training in January. My recovery week was actually spent skiing (pretty hard), though this did not register on Strava because I did not use a heart rate monitor. So the sharp drop in fatigue at the end of January is exaggerated. Nevertheless, my form was positive for my first race on 4 February. Unfortunately, I was knocked off and smashed a few ribs, forcing me to take an unplanned two week break. By the time I was able to start riding tentatively, rather than starting from an elevated level, my fitness had deteriorated to December’s trough.

After a solid, but still painful, block of low intensity training in March, I took another “recovery week” on the slopes of St Anton. I subsequently picked up a cold that delayed the start of the next block of training, but I have incorporated some crit races into my plan, for higher intensity sessions. If you edit the activity and make the “ride type” a “race”, it shows up as a red dot on the chart. Barring accident and illness, the hope is to stick more closely to a planned four-week cycle going forward.

This demonstrates how Strava’s tools reveal the real-life difficulties of putting the theoretical benefits of periodisation into practice.

Modelling Strava Fitness and Freshness

Supercompensating with Strava

See other blogs on Strava Power Curve, Strava Ride Statistics or going for a Strava KOM.

Strava Ride Statistics

If you ride with a power meter and a heart rate monitor, Strava’s premium subscription will display a number of summary statistics about your ride. These differ from the numbers provided by other software, such as Training Peaks. How do all these numbers relate to each other?

A tale of two scales

Over the years, coaches and academics have developed statistics to summarise the amount of physiological stress induced by different types of endurance exercise. Two similar approaches have gained prominence. Dr Andrew Coggan has registered the names of several measures used by Training Peaks. Dr Phil Skiba has developed as set of metrics used in the literature and by PhysFarm Training Systems. These and other calculations are available on Golden Cheetah‘s excellent free software.

Although it is possible to line up metrics that roughly correspond to each other, the calculations are different and the proponents of each scale emphasise particular nuances that distinguish them. This makes it hard to match up the figures.

Here is an example for a recent hill session. The power trace is highly variable, because the ride involved 12 short sharp climbs.

Metric	Coggan TrainingPeaks	Skiba Literature	Strava
Power equivalent physiological cost of ride	Normalised Power 282	xPower 252	Weighted Avg Power 252
Power variability of ride	Variability Index 1.57	Variability Index 1.41
Rider’s sustainable power	Functional Threshold Power 312	Critical Power 300	FTP 300
Power cost / sustainable power	Intensity Factor 0.9	Relative Intensity 0.84	Intensity 0.84
Assessment of intensity and duration of ride	Training Stress Score 117	BikeScore 101	Training Load 100
Training Impulse based on heart rate			Suffer Score 56

Weighted Average Power

According to Strava, Weighted Average Power takes account of the variability of your power reading during a ride. “It is our best guess at your average power if you rode at the exact same wattage the entire ride.” That sounds an awful lot like Normalized Power, which is described on Training Peaks as “an estimate of the power that you could have maintained for the same physiological “cost” if your power output had been perfectly constant (e.g., as on a stationary cycle ergometer), rather than variable”. But it is apparent from the table above that Strava is calculating Skiba’s xPower.

The calculations of Normalized Power and xPower both smooth the raw power data, raise these observations to the fourth power, take the average over the whole ride and obtain the fourth root to give the answer.

Normalized Power or xPower = (Average(P_smoothed⁴))^1/4

The only difference between the calculations is the way that smoothing accounts for the body’s physiological delay in reacting to rapid changes in pedalling power. Normalized Power uses a 30 second moving average, whereas xPower uses a “25 second exponential average”. According to Skiba, exponential decay is better than Coggan’s linear decay in representing the way the body reacts to changes in effort.

The following chart zooms into part of the hill reps session, showing the raw power output (in blue), moving average smoothing for Normalised Power (in green), exponential smoothing for xPower (in red), with heart rate shown in the background (in grey). Two important observations can be made. Firstly, xPower’s exponential smoothing is more highly correlated with heart rate, so it could be argued that it does indeed correspond more closely with the underlying physiological processes. Secondly, the smoothing used for xPower is less volatile, therefore xPower will always be lower than Normalized Power (because the fourth-power scaling is dominated by the highest observations).

Power

Why do both metrics take the watts and raise them to the fourth power? Coggan states that many of the body’s responses are “curvilinear”. The following chart is a good example, showing the rapid accumulation of blood lactate concentration at high levels of effort.

Screen Shot 2017-04-20 at 15.08.31

Plotting the actual data from a recent test on a log-log scale, I obtained a coefficient of between 3.5 and 4.7, for the relation between lactate level and watts. This suggests that taking the average of smoothed watts raised to the power 4 gives an indication of the average level of lactate in circulation during the ride.

The hill reps ride included multiple bouts of high power, causing repeated accumulation of lactate and other stress related factors. Both the Normalised Power of 282W and xPower of 252W were significantly higher than the straight average power of 179W. The variability index compares each adjusted power against average power, resulting in variability indices of 1.57 and 1.41 respectively. These are very high figures, due to the hilly nature of the session. For a well-paced time trial, the variability index should be close to 1.00.

Sustainable Power

It is important for a serious cyclist to have a good idea of the power that he or she can sustain for a prolonged period. Functional Threshold Power and Critical Power measure slightly different things. The emphasis of FTP is on the maximum power sustainable for one hour, whereas CP is the power theoretically sustainable indefinitely. So CP should be lower than FTP.

Strava allows you to set your Functional Threshold Power under your personal performance settings. The problem is that if Strava’s Weighted Average Power is based on Skiba’s xPower, it would be more consistent to use Critical Power, as I did in the table above. This is important because this figure is used to calculate Intensity and Training Load. If you follow Strava’s suggestion of using FTP, subsequent calculations will underestimate your Training Load, which, in turn, impacts your Fitness & Freshness curves.

Intensity

The idea of intensity is to measure severity of a ride, taking account of the rider’s individual capabilities. Intensity is defined as the ratio of the power equivalent physiological cost of the ride relative to your sustainable power. For Coggan, the Intensity Factor is NP/FTP; for Skiba the Relative Intensity is xPower/CP; and for Strava the Intensity is Weighted Average Power/FTP.

Training Load

An overall assessment of a ride needs to take account of the intensity and the duration of a ride. It is helpful to standardise this for an individual rider, by comparing it against a benchmark, such as an all-out one hour effort.

Coggan proposes the Training Stress Score that takes the ratio the work done at Normalised Power, scaled by the Intensity Factor squared, relative to one hour’s work at FTP. Skiba defines the BikeScore as the ratio the work done at xPower, scaled by the Relative Intensity squared, relative to one hour’s work at CP. And finally, Strava’s Training Load takes the ratio the work done at Weighted Average Power, scaled by Intensity squared, relative to one hour’s work at FTP.

Note that for my hill reps ride, the BikeScore of 101, was considerably lower than the TSS of 117. Although my estimated CP is 12W lower than my FTP, xPower was 30W lower than NP. Using my CP as my Strava FTP, Strava’s Training Load is the same as Skiba’s Bike Score (otherwise I’d get 93).

Suffer Score

Strava’s Suffer Score was inspired by Eric Banister’s training-impulse (TRIMP) concept. It is derived from the amount of time spent in each heart rate zone, so it can be calculated for multiple sports. You can set your Strava heart rate zones in your personal settings, or just leave then on default, based on your maximum heart rate.

A non-linear relationship is assumed between effort and heart rate zone. Each minute in Zone 1, Endurance, is worth 12 seconds; Moderate Zone 2 minutes are worth 24 seconds; Zone 3 Tempo minutes are worth 45 seconds; Zone 4 Threshold minutes are worth 100 seconds; and Anaerobic Zone 5 minutes are worth 120 seconds. The Suffer Score is the weighted sum of minutes in each zone.

The next blog will comment on the Fitness & Freshness charts available on Strava Premium.

Which Strava KOMs will fall in the Tour of Flanders?

This series looking at Strava leaderboards now turns to the action in Belgium, where the spring classics season is under way. Greg Van Avermaet, Philipe Gilbert, Michal Kwiatkowski and Peter Sagan are among the riders in top form ahead of the Tour of Flanders, not forgetting former winners Tom Boonen, Alexander Kristoff and Stijn Devolder. This year’s race includes 18 climbs, finishing with a loop that takes in six famous ascents in the last 50km. Will the pros to be setting KOMs on these Hellingens?
Making the top 10 on any leaderboard, towards the end of a 260km race, sounds like a tall order. KOMs are more likely to fall on longer faster climbs where riders can benefit from drafting in a group. In fact the riders will be climbing the Oude-Kwaremont three times and the Paterberg twice, so the top times are more at risk on those two, if someone decides to make a strong attack. The weather forecast is good: sunny, about 16°C, with a light breeze from the WNW. The wind will be against the riders on the Taaienberg, but it will provide a small benefit on the other final hills, which happen to be ridden in directions between East and South.

Koppenberg

Surface: Cobbles, Distance: 444m, Avg Grade: 14.3%, Elevation Gain: 64m, Bearing: 104°

Rank	Name	Time	Date	Race
1	Reinardt Janse van Rensburg	00:01:27	19-Feb-14	–
2	Joris Van Der Auwera	00:01:28	01-Jan-10	–
2	gijsade holstege	00:01:28	01-Jan-10	–
2	Dries Devenyns	00:01:28	27-Nov-15	–
5	Cameron Bayly	00:01:30	06-Sep-15	–
6	Dylan Kennett	00:01:32	26-Jun-15	–
7	FOCUS Rides	00:01:34	01-Jan-10	–
7	Korneel De Viaene	00:01:34	06-Aug-15	–
7	Arjen Palstra	00:01:34	02-Apr-16	–
7	Korneel De Viaene	00:01:34	06-Aug-15	–

Pro rider van Rensburg holds the KOM up the Koppenberg, set on a pre-race recce. Dries Devenyns is not far behind, but none of the top ten times appear to have been set in races. Although there will be a weak tailwind, it seems unlikely that a new record will be set in this year’s Tour of Flanders.

Steenbeekdries

Surface: Cobbles, Distance: 724m, Avg Grade: 2.8%, Elevation Gain: 24m, Bearing: 121°

Rank	Name	Time	Date	Race
1	Niki Terpstra Racing	00:01:22	01-Apr-15	–
2	Jasper Stuyven	00:01:25	06-Apr-13	Flanders U23
2	Lawson Craddock	00:01:25	06-Apr-13	Flanders U23
4	Michal Kwiatkowski	00:01:26	01-Apr-16	–
5	Jered Gruber	00:01:27	06-Apr-12	–
5	Walter Eikelenboom	00:01:27	04-Aug-15	–
7	Pierre-Henri LECUISINIER	00:01:28	06-Apr-13	Flanders U23
7	Marcus Burghardt	00:01:28	02-Apr-15	Three Days of De Panne
9	Michael Schär	00:01:29	02-Apr-15	Three Days of De Panne
10	Stijn Steels	00:01:30	29-Mar-17	–

Two riders made the top ten in the 2015 edition of the Three Days of De Panne and three others in the Flanders Under 23 race in 2013. We can also see quick times in recce rides by Terpstra in 2015, Kwiatkowski, last year, and Steels this week. There’s a chance this KOM could go on Sunday.

Taaienberg

Surface: Cobbles, Distance: 639m, Avg Grade: 7.8%, Elevation Gain: 46m, Bearing: 262°

Rank	Name	Time	Date	Race
1	Daniel Oss	00:01:12	25-Mar-16	E3 Harelbeke
2	Jasper Stuyven	00:01:13	25-Feb-17	Omloop Het Nieuwsblad
3	AlliGator Junior	00:01:14	06-Mar-13	–
3	Edward Theuns	00:01:14	25-Feb-17	Omloop Het Nieuwsblad
3	Greg Van Avermaet	00:01:14	24-Mar-17	E3 Harelbeke
6	Wesley Van Dyck 2090874575184	00:01:15	28-Mar-17	Three Days of De Panne
7	Arnaud Demare	00:01:16	22-Mar-17	Dwars door Vlaanderen
7	Johnny Cecotto	00:01:16	22-Mar-17	Dwars door Vlaanderen
9	Jarl .	00:01:17	18-Mar-14	–
9	Bryan Coquard	00:01:17	24-Mar-17	E3 Harelbeke

This is another segment that is dominated by the pros and tends to be smashed in races. The problem is that there will be a slight headwind, so this KOM will probably hold on Sunday.

Kruisberg (Oudestraat)

Surface: Asphalt, Distance: 1813m, Avg Grade: 4.9%, Elevation Gain: 89m, Bearing: 142°

Rank	Name	Time	Date	Race
1	Daniel Lloyd	00:04:03	03-Apr-11	Tour of Flanders
2	Cor ~~	00:04:05	03-Apr-11	Tour of Flanders
3	davide COM	00:04:06	03-Apr-11	Tour of Flanders
4	Jeremy Cameron Ⓥ	00:04:24	29-Jun-16	–
5	Pascal Eenkhoorn	00:05:00	13-Mar-16	–
6	Pieterjan Spyns	00:05:02	06-Jul-15	–
7	dylan de kok	00:05:03	21-Feb-14	–
8	Eloy Raas	00:05:04	21-Feb-14	–
9	Lenard Maes	00:05:06	21-Jul-15	–
10	kobe vdv	00:05:09	30-Mar-17	–

The KOM is held by GCN‘s Daniel Lloyd, set in the Tour of Flanders in 2011, in very similar weather conditions. The three leading times stand a long way ahead of the rest. It will be very interesting to see how the current pros perform on this climb. Daniel’s time could be at risk.

Oude-Kwaremont

Surface: Cobbles, Distance: 2509m, Avg Grade: 3.6%, Elevation Gain: 91m, Bearing: 163°

Rank	Name	Time	Date	Race
1	Niki Terpstra Racing	00:04:55	25-Mar-16	E3 Harelbeke
2	Daniel Oss	00:04:58	25-Mar-16	E3 Harelbeke
3	Tiesj Benoot	00:04:59	25-Mar-16	E3 Harelbeke
4	Nikolas Maes	00:05:01	23-Mar-16	Dwars door Vlaanderen
5	Michal Kwiatkowski	00:05:02	25-Mar-16	E3 Harelbeke
6	Scott Thwaites	00:05:04	23-Mar-16	Dwars door Vlaanderen
7	Greg Van Avermaet	00:05:06	28-Feb-16	Kuurne–Brussels–Kuurne
8	Oliver Naesen	00:05:07	24-Mar-17	E3 Harelbeke
9	Stijn Vandenbergh Racing	00:05:08	28-Mar-14	E3 Harelbeke
10	Antoine Duchesne	00:05:10	28-Feb-16	Kuurne–Brussels–Kuurne

The leaderboard of segment is packed with pro racing performances, led once again by Niki Terpstra. With the last ascent coming at a crucial time in this year’s Tour of Flanders, the KOM could fall again.

Paterberg

Surface: Cobbles, Distance: 358m, Avg Grade: 11.7%, Elevation Gain: 42m, Bearing: 96°

Rank	Name	Time	Date	Race
1	Eli Iserbyt	00:00:53	27-Jul-16	–
2	Dries Devenyns	00:00:54	19-Feb-14	–
2	mathias Declerck	00:00:54	01-Sep-16	–
4	Jarl .	00:00:55	23-Mar-14	–
5	Pascal Eenkhoorn	00:00:56	04-May-16	–
6	Joeri Calleeuw	00:00:57	24-Feb-14	–
6	Frederik Vandewiele	00:00:57	19-Mar-14	–
6	Antoine Loy	00:00:57	18-Jun-14	–
6	Aaron Midgley	00:00:57	20-Aug-14	–
6	Merten De Wever	00:00:57	06-May-15	–

This short, steep climb seems to be the target of specific KOM hunters. None of the top ten times were set in the big races. Although this will be the final place to attack in this year’s race, the riders will be fatigued by 247km of tough roads. The top time is likely to hold firm, especially if barriers are used to block smoother edges of the road.

Conclusion

KOMs to hold: Paterberg, Koppenberg, Taaienberg

KOMs at risk: Kruisberg, Oude-Kwaremont, Steenbeekdries

Watch out Dan!

Pro Cyclist KOMs on Strava

This series has explored what it takes to get a KOM on Strava, but what about the pros? Don’t they come home with a sackful of KOMs after every training ride? Which pro rider tops the most Strava leaderboards?

You can follow over a thousand pro athletes on Strava. These include runners, triathletes, mountain bikers and professional cyclists. Although you will not find Peter Sagan, Chris Froome, Nairo Quintana or Alberto Contador (you can ignore all the fake Strava ids with these names), there is a good selection of UCI team riders. There are also riders who do not claim Strava pro status, like some guy called Phil who recently went out for an afternoon ride.

Some pros upload just a limited number of rides, for example, Marianne Vos only has 243 rides on Strava, with nothing new since December. Other riders, such as Ian Stannard, upload their rides, but withhold their (monstrously high) power data. Nevertheless, many pro riders are more open about making their data available on Strava, including power. Take a look at the Col d’Eze segment on the final stage of Paris Nice. The little lightning bolt symbol indicates that the rider was using a power meter, but rather confusingly, some pro riders (Team Sky) are able to hide their average power for the ride, in which case the figure is a Strava estimate. But you can find the real number by highlighting the segment in the analysis view of the ride.

This review considers over 200 active professional road cyclists who are on Strava. The riders with the highest number of KOMs need to have uploaded a lot fast rides, in regions where many segments have been recorded. Here are the current top 10 pro riders from the sample.

Rank	KOMs	Name	Team
1	1907	Laurens ten Dam	Team Sunweb
2	1381	Elisa Longo Borghini	Wiggle Honda
3	1296	Annemiek van Vleuten	Orica AIS
4	1230	Niki Terpstra Racing	Quick-Step Floors
5	1162	James Gullen	JLT Condor
6	1070	Thibaut Pinot	FDJ
7	1035	Dan Evans	Cannodale-Drapac Pro Cycling Team
8	978	Romain Bardet	AG2R
9	864	Joe Dombrowski	Cannodale-Drapac Pro Cycling Team
10	852	Dani King	Cylance

A bit further down the list, Michal Kwiatkowski has 559 KOMs, including eight that he picked up in his Milan San Remo victory. After riding the first 140km at a relatively easy 35kph and an average power of just 124W, he upped the effort to traverse the Passo del Turchino. His power and heart rate rose progressively all the way to the Cipressa, from which point he earned a KOM for the segment to the finish. He claimed four KOMs as he followed Peter Sagan’s dramatic attack on the Poggio, though these would have undoubtably been Sagan’s, if he’d put his data on Strava. Viewing the ride analysis, we see that after over seven hours of riding, Michal ascended the 3.6km 4% climb at 37kph, generating 443W (about 6.5 W/kg) for 5 minutes and 47 seconds, rather than the 536W estimated on the leaderboard. He peaked at over 900W near the summit as he an Alaphilippe desperately fought to get onto Sagan’s wheel.Lauren ten Dam has the most KOMs by a long way, though he does match Maryka Sennema’s haul of QOMs. Interestingly there are three women in the top ten, in spite of the fact that most of the riders in the sample were men. It is no surprise to see Elisa Longo Borghini and Annemiek van Vleuten at the head of the women’s rankings. Niki Terpstra follows his Dutch compatriot, while James Gullen is the leading Brit, followed by Dan Evans representing Wales alongside Dani King. Thibaut Pinot and Romain Bardet are the kings of the French mountains. Nice-based American rider Joe Dombrowski also makes the top ten.

The next blog will explore some more feats of the professionals.

Going for a QOM on Strava

In exploring how to chase a KOM on Strava, this series of articles has fallen into the trap of under-representing the achievements of the Queens of the Mountains (QOMs). Although this is partly because Strava tends to attract male data geeks, there are plenty of women who use the platform to monitor their fitness and performance in a social way. This blog looks at the performance of women cyclists, once again featuring the popular Tour de Richmond Park segment.

More women are riding their bikes as the interest in women’s cycling continues to grow. Top riders like Lizzie Deignan, Marianne Vos and the Drops Cycling Team are receiving broader recognition for their amazing performances. This year’s Women’s Tour will benefit from broad media coverage, as it finishes in the heart of London. The Cycling Podcast Féminin is now into its ninth episode.

Analysis of the top 1000 (mostly male) riders on the Tour de Richmond Park leaderboard established that the majority of personal bests (PBs) were set during the summer months, either early in the morning or in the evening, with Saturday and Wednesday being popular days or the week, especially when the wind was blowing from the East. The charts below compare these statistics from the male and female leaderboards.

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Female PBs are a little more evenly spread over the year, peaking in July. Women have tended to achieve their best times later in the morning, perhaps reflecting a stronger preference for cycling around the park on the weekend, particularly on Sunday, when men seem to be off chasing KOMs elsewhere.

An Easterly wind has also been helpful, though the effect has been less marked than for the men. In fact only three out of the top 25 women benefited from a favourable wind direction. This suggests that, as the weather warms up, there’s an opportunity to post a very good time when there is a strong tailwind up Sawyers Hill, perhaps seeing the first woman under sixteen minutes for the segment. So watch the forecast and get out there girls!

The last post noted that riders can be classified according to their strengths as sprinters, climbers or time trialers. Whatever kind of rider you are, it is important to balance dietary energy intake with exertion. Given the non weight-bearing nature of the sport, this is particularly important for very lean female cyclists, who may experience disruption of hormonal function, resulting in reduced bone mineral density. See Nicky Keay’s blog for more information on Relative Energy Deficiency in Sport, which is also relevant to men and young athletes.

No discussion of Strava QOMs could fail to mention the incredible performance of Maryka Sennema. Her dedication to training and cycling at the highest level has earned her over 2,200 QOMs, making her the undisputed Goddess of the Mountains.

The next blog will continue to apply the scientific microscope to cycling data, in search of helpful insights on pro cyclists.

The best rider for a Strava KOM

So far this series of article has explored to the time of year, wind and weather conditions when riders have set their best times on the Strava leaderboard, using the popular Tour of Richmond Park segment as a case study. This blog considers how the attributes of the cyclist affect the time to complete a segment. The most important components are power, bodyweight and aerodynamic drag area or CdA. Your best chance of picking up a KOM is to target a segment that matches your strengths as a cyclist.

A power curve plots the maximal power a cyclist can sustain over a range of time periods. Ideally, the curve is plotted from the results of a series of maximal effort tests performed over times ranging from 5 seconds to an hour. Alternatively, Strava Premium or software such as Training Peaks or Golden Cheetah can generate power curves from a history of power data files. Power can be expressed in Watts or in Watts per kilogram, as in the example below.

The shape of the power curve reveals a lot about the characteristics of the cyclist. Dr Andrew Coggan explains how this information can be used to define a cyclist’s individual power profile. In the chart above, the 5 minute and functional threshold (1 hour) Watts/kg rank more highly than 5 second and 1 minute figures, indicating that this cyclist can generate fairly high power for long periods, but has a relatively weaker sprint. For a heavier rider this profile would be consistent with a time trialer, who can generate a high absolute number of Watts, whereas a light rider with this profile may be a better climber, due to a good sustainable power to weight ratio.

If you have a power meter or access to a Wattbike, it is well worth gathering this data for yourself. It can help with training, racing or selecting Strava segments where you have the best chance of moving up the leaderboard.

The power required to maintain a constant speed, V, needs to balance the forces acting on a rider. Aerodynamic drag is due to the resistance of pushing the rider and bike frame through the air, with some additional drag coming from the rotating wheels. Drag can be decreased by reducing frontal area and by adopting a streamlined shape, while wearing a skinsuit. Additional mechanical factors are due to gravity, the rolling resistance of the tyres on the road surface and drive chain loss.

Power = Drag Factors * V³ + Mechanical Factors * V

Since the power needed to overcome aerodynamic drag scales with the cube of velocity, it is the dominant factor when riding fast on flat or downhill segments. However, on a climb, where speed is lower, the power required to do work against gravity quickly becomes important, especially for heavier riders.

Consider a rider weighing 60kg, call him Nairo, and another weighing 80kg, say Fabian. Suppose they are cruising along side by side at 40kph. Under reasonable assumptions, Fabian rides at 276 Watts or 3.4 Watts/kg, while Nairo benefits from a smaller frontal area and lower rolling resistance, requiring 230 Watts, though this equates to 3.8 Watts/kg. Reaching a 5% hill, they both increase power by 50%, but now Nairo is riding at 27kph, dropping Fabian, whose extra weight slows him to 26kph. You can experiment with this interactive chart.

Climbers are able to sustain high force on the pedals, taking advantage of their ability to accelerate quickly on the steepest slopes. Time trialers generate high absolute power for long periods, on smoother terrain, while maintaining an aerodynamic tuck. Sprinters have more fast-twitch muscle fibres, producing extremely high power for short periods, while pedalling at a rapid cadence.

The following chart shows the gradient and length of 1364 popular Strava segments from around Britain. Distances range from 93m to 93km, with an average of 2.3km. Gradients are from 21% downhill to 32% uphill (Stanwix Bank Climb).

You should be able to click on the chart (no need to sign up) for an interactive version that allows you to zoom in and display the names of the segments that suit your ability: short segments for sprinters, steep ones for climbers and longer flat ones for TTers. The Tour de Richmond Park segment is 10.8km with an average gradient of zero, so it is no surprise that the KOM is held by an accomplished time trialer.

The next blog takes a look at QOMs. Are women different?

The best weather conditions for a KOM on Strava

This is the third in a series of articles investigating factors that determine the best times on Strava leaderboards, using the popular Tour de Richmond Park segment as a case study. So far we have established that the fastest times have tended to be in the summer, with a decent wind blowing from the East. This blog investigates how atmospheric conditions affect the density of air, which, in turn, determines the aerodynamic drag that a cyclist needs to overcome.

The power required to offset the mechanical forces, of gravity and rolling resistance, increases in proportion to speed, but the power needed to overcome aerodynamic drag rises with the cube of velocity. When riding fast, your effort goes principally into overcoming drag: maintaining a speed of 50kpm requires almost double the power of riding at 40kpm (50³/40³= 125/64 = 1.95). The aerodynamic drag force is proportional to the density of the air though which a cyclist is pushing both body and bike. So you have a better chance of winning a KOM (or QOM) when the air density is low.

A previous blog noted that most personal bests (PBs) on the Richmond Park leaderboard were set in the summer. The following chart superimposes, in red, the average air density in London on a histogram showing the number of PBs set in each month. The trough in the air density implies that aerodynamic drag is about 5% lower during the warmer months.

So how much difference would a 5% reduction in air density make to your time round Richmond Park? For the same power, the cube of your speed can go up by 5%, resulting in a reduction of your PB time of 1.6%. For example, a cyclist completing a lap of Richmond Park in 16 minutes and 16 seconds (averaging 40kph) in December, would finish in 16 minutes dead, at exactly the same average power, in the less dense air of July. The difference is a second per minute, which equates to a saving of a minute for a one hour TT.

The air density depends on temperature, pressure and humidity. The reason that air density is lower in the summer is that temperatures are higher: warm air expands. Monthly mean atmospheric pressure is pretty much the same all year round. Humidity tends to be higher in the winter. Contrary to what most people think, higher humidity reduces air density (because water vapour, H₂O, with a molecular mass of 18, is lighter than the main constituent of air, nitrogen, N₂, which has a molecular mass of 28). However, as the following chart shows, changes in humidity have a tiny effect on air density relative to changes in temperature.

Although temperature is the primary determinant of seasonal variations in air density, both atmospheric pressure and humidity can vary significantly from day to day, so it is important to consider these factors when aiming for a KOM. The next chart shows the variability of air density, measured on a particular day, for an extreme range of temperatures, pressures and humidities.

When Bradley Wiggins was going for the hour record, he became obsessed with the weather forecast, because even though it was possible to raise the temperature and humidity in the velodrome, he ideally needed a low pressure weather system to pass over the UK at the same time, as this would have further reduced the density of the air that he was riding through. On 2 May 2015, the air pressure in Manchester, which is close to sea level, was 1009hPa. If it had been about 3% lower, at say 980hPa (historically very low), he should have been able to go about 1% further, to exceed 55km.

Since Strava segments tend to be outdoors, your priority should be to choose a very warm day, ideally with low atmospheric pressure and not worry too much about humidity, though higher is better. Returning to the leaderboard for the Tour de Richmond Park segment, the final chart shows the temperature and pressure on the days that the top 1000 PBs were set, split into quartiles of 250 riders (fastest riders in Q1).

Observe that most records were set when the temperature was well above the annual mean of 12 °C, shown by the vertical red line. Slightly more PBs were set when the atmospheric pressure was disadvantageously higher than the average horizontal red line. There was no significant difference in air density for the top 250 riders versus the other groups of 250. Clearly the best place to be is the lower right quadrant. Finally, we have found something that would have allowed Rob Sharland to improve upon his KOM, as the prevailing conditions were 21 °C and 1022hPa – a warmer day with a lower atmospheric pressure would have helped him go faster – but then he might not have had the ideal wind conditions noted in the previous blog. The relative importance of wind versus air density is something I hope to come back to.

The next blog explores the factors relating to the rider and bike that influence the time to complete a Strava segment.

The best wind for a KOM on Strava

Two key aspects of the weather influence the time to complete a Strava segment: the wind and the air density. This blog considers the direction and speed of the wind. The following blog will examine how aerodynamic drag is affected by changes in air density.

Clearly, on an exposed, arrow-straight segment, the most favourable weather would be a hurricane tailwind. Like other KOM hunters, I have searched for segments that align with the predicted wind direction when a gale is forecast, though I’ve usually ended up going kitesurfing instead.

When the segment is a loop, such as the Tour de Richmond Park, discussed in the previous blog, the question becomes more interesting. Consider a light aircraft flying above the Richmond Park segment at an altitude of 300m. Any constant wind, regardless of direction, will result in a slower time than completing the circuit in still air. Why? Since any headwind slows down the plane, it hinders the pilot for more time than the tailwind provides assistance, resulting in a net increase in the total time.

However, cyclists do not ride in constant winds. Trees, buildings and the terrain all affect the wind’s speed and direction. Variability is so strong that it is recommended that multiple anemometers should be positioned at intervals alongside the 100m track at important athletics meetings.

All this means that it is quite likely that there are optimal wind conditions for all Strava segments. Most people suggest that a tailwind up Sawyers Hill is best for Richmond Park, as this part of the segment is an uphill drag that is exposed to the wind, whereas other sections of the route are much more sheltered. The bearing of a tailwind would be from just North of Easterly. Historically, this is not a very common wind direction for London. The following charts shows the prevailing wind direction over the year is Southwesterly.

Easterly winds are even rarer in July and August, when many PBs have been set, though in September they have been a little more frequent. (An interactive version of the chart can be found on this site.)

Now, if the wind had no effect on the Strava segment, we would expect the distribution of wind directions on which riders set their PBs to be similar to the historic distribution. So we are interested in the difference between the distribution of wind directions on the dates derived from the leaderboard relative the background average. The following chart compares the segment against the historic average annual average. The compass rose clearly shows a much higher frequency (13%) of the PBs of the top 1000 riders were set when the wind was blowing from the East and a relatively lower incidence in the opposite direction.

rosesegment

The next hand chart “unwraps” the two curves to show the relative difference, which is statistically highly significant (p<0.01). A forensic analysis of the data confirms that the best wind direction for a PB around Richmond Park is indeed an Easterly tailwind up Sawyers Hill.

barsegment

So far we have not considered the strength of the wind. The next chart shows the average windspeed on the days that PBs were set, according to the direction of the wind. This shows a bias towards stronger winds from the East, consistent with the frequency of PBs.

windspeedbydirn

Combining this with the results of the previous blog, the following conclusions may be drawn. However good a cyclist you are, your best chance of achieving a high ranking on the Tour de Richmond Park leaderboard is to choose the evening or morning of one of the rare summer days when the wind is blowing strongly from the East. And, you guessed it, on the evening of August 2015 when Rob Sharland achieved his KOM, the wind was blowing at 11mph on a bearing of 80° .

The next blog will examine how temperature, pressure and humidity, as well as altitude, change the air’s density. This is the principal environmental factor affecting your aerodynamic drag, when you are going for a KOM.

When to go for a KOM on Strava

The dates and times that people achieved their PBs on the Tour de Richmond Park

As the number of cyclists using Strava continues to grow, it is becoming increasingly difficult to achieve a high ranking on the leaderboard of any popular segment. Whilst it is possible to hunt for a top performance on some obscure route, attaining a KOM (or QOM) on a segment attempted by tens of thousands of other athletes is a real challenge.

Consider the Tour de Richmond Park, in southwest London. On 17 February 2017, the leaderboard had 35,833 entries. Note that the leaderboard does not show the 35,833 fastest times, rather it displays the personal best (PB) times of 35,833 individuals – it doesn’t matter how many times you do the segment, you only have one entry on the leaderboard. The current KOM is held by Rob Sharland, who completed the 10.8km segment in 13 minutes 57 seconds.

The top 1,000 entries on the leaderboard reveal some interesting patterns. This initial blog explores the dates and times that people achieved their PBs. The first striking observation is that hardly anyone sets a PB during the winter. The following chart shows that most records were set between June and September.

This suggests that riders tend to be in better form in the summer and that conditions are more favourable. In fact, it turns out that hours of daylight play an important role, as demonstrated by the following chart showing that most PBs are set either in the evening, around 7pm or in the early morning, between 6am and 9am. These represent times before or after work, when car traffic is lighter. Very few records are set in during the middle of the day and none at night.

A look at the days of the week, when record are set, reveals that Wednesday and Saturday are particularly popular. It turns out the most Wednesday records were achieved in the evening with some in morning, whereas almost all Saturday records were completed by 10am.

So the best time to achieve a PB around Richmond Park is on a Wednesday evening in August. And it turns out that Rob Sharland set the KOM at 8:31pm on Wednesday 12 August 2015.

But Rob deserves additional kudos, because quite a few riders have set their personal bests riding in groups, whereas it looks like Rob was riding solo. Nine other riders set their PBs on the same day, but these were all earlier than Rob’s. There were three other dates on which 10 or more riders achieved their fastest times. It is easy to spot those riding as a group, because they all start together and finish with similar times (show in red here). So chapeau to Rob for beating them all.

The next blog explores the prevailing weather conditions.

Tag: Cycling