Kings and Queens of the Mountains

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I guess that most male cyclists don’t pay much attention to the women’s leaderboards on Strava. And if they do it might just be to make some puerile remark about boys being better than girls. From a scientific perspective the comparison of male and female times leads to some interesting analysis.

Assuming both men and women have read my previous blogs on choosing the best time, weather conditions and wind directions for the segment that suits their particular strengths, we come back to basic physics.

KOM or QOM time = Work done / Power = (Work against gravity + Drag x Distance + Rolling resistance x Distance) / (Mass x Watt/kg)

Of the three components of work done, rolling resistance tends to be relatively insignificant. On a very steep hill, most of the work is done against gravity, whereas on a flat course, aerodynamic drag dominates.

The two key factors that vary between men and women are mass and power to weight ratio (watts per kilo).  A survey published by the ONS in 2010, rather shockingly reported that the average British man weighed 83.6kg, with women coming in at 70.2kg. This gives a male/female ratio of 1.19. KOM/QOM cyclists would tend to be lighter than this, but if we take 72kg and 60kg, the ratio is still 1.20.

Males generate more watts per kilogram due to having a higher proportion of lean muscle mass. Although power depends on many factors, including lungs, heart and efficiency of circulation, we can estimate the relative power to weight ratio by comparing the typical body composition of males and females. Feeding the ONS statistics into the Boer formula gives a lean body mass of 74% for men and 65% for women, resulting in a ratio of 1.13. This can be compared against the the useful table on Training Peaks showing maximal power output in Watts/kg, for men and women, over different time periods and a range of athletic abilities. The table is based on the rows showing world record performances and average untrained efforts.  For world champion five minute efforts and functional threshold powers, the ratios are consistent with the lean mass ratio. It makes sense that the ratio should be higher for shorter efforts, where the male champions are likely to be highly muscular. Apparently the relative performance is precisely 1.21 for all durations in untrained people.

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On a steep climb, where the work done against gravity dominates, the benefit of additional male muscle mass is cancelled by the fact that this mass must be lifted, so the difference in time between the KOM and the QOM is primarily due to relative power to weight ratio. However, being smaller, women suffer from the disadvantage that the inert mass of bike represents a larger proportion of the total mass that must be raised against gravity. This effect increases with gradient. Accounting for a time difference of up to 16% on the steepest of hills.

In contrast, on a flat segment, it comes down to raw power output, so men benefit from advantages in both mass and power to weight ratio. But power relates to the cube of the velocity, so the elapsed time scales inversely with the cube root of power. Furthermore, with smaller frames, women present a lower frontal area, providing a small additional advantage. So men can be expected to have a smaller time advantage of around 9%. In theory the advantage should continue to narrow as the gradient shifts downhill.

Theory versus practice

Strava publishes the KOM and QOM leaderboards for all segments, so it was relatively straightforward to check the basic model against a random selection of 1,000 segments across the UK. All  leaderboards included at least 1,666 riders, with an overall average of 637 women and 5,030 men. One of the problems with the leaderboards is that they can be contaminated by spurious data, including unrealistic speeds or times set by groups riding together. To combat this, the average was taken of the top five times set on different dates, rather than simply to top KOM or QOM time.

The average segment length was just under 2km, up a gradient of 3%. The following chart plots the ratio of the QOM time to the KOM time versus gradient compared with the model described above. The red line is based on the lean body mass/world record holders estimate of 1.13, whereas the average QOM/KOM ratio was 1.32. Although there is a perceivable upward slope in the data for positive gradients, clearly this does not fit the data.

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Firstly, the points on the left hand side indicate that men go downhill much more fearlessly than women, suggesting a psychological explanation for the observations deviating from the model. To make the model fit better for positive gradients, there is no obvious reason to expect the weight ratio of male to female Strava riders to deviate from the general population, so this leaves only the relative power to weight ratio. According to the model the QOM/KOM ratio should level off to the power to weight ratio for steep gradients. This seems to occur for a value of around 1.40, which is much higher than the previous estimates of 1.13 or the 1.21 for untrained people. How can we explain this?

A notable feature of the data set was that sample of 1,000 Strava segments was completed by nearly eight times as many men as women. This, in turn reflects the facts that there are more male than female cyclists in the UK and that men are more likely to upload, analyse, publicise and gloat over their performances than women.

Having more men than women, inevitably means that the sample includes more high level male cyclists than equivalent female cyclists. So we are not comparing like with like. Referring back to the Training Peaks table of expected power to weight ratios, a figure of 1.40 suggests we are comparing women of a certain level against men of a higher category, for example, “very good” women against “excellent” men.

A further consequence of having far more men than women is that is much more likely that the fastest times were recorded in the ideal conditions described in my previous blogs listed earlier.

Conclusions

There is room for more women to enjoy cycling and this will push up the standard of performance of the average amateur rider. This would enhance the sport in the same way that the industry has benefited as more women have joined the workforce.

Chain reactions

At this year’s Royal Society Summer Exhibition, scientists and engineers from Bristol University presented some interesting work on improvements to the drive chains used by Team GB in the Rio Olympics. They reached clear conclusions about the design of the chain and sprockets, taken up by Renold. Current research is exploring the the problem of chain resonance.

Bicycle chains and sprockets and sprockets tend to receive less attention than aerodynamics, for several reasons. As noted in previous blogs, the power required to overcome aerodynamic drag scales with the cube of velocity, whereas frictional effects scale simply in proportion to velocity. Furthermore, a good well-lubricated drive chain typically has an efficiency of around 95% or more, so it is hard to make further improvements. Note that a dirty chain has significantly lower efficiency, so you should certainly keep your bike clean.

The loss of power comes from the friction between links as they bend around the chainring and the rear sprocket. Using a high precision rig, the researchers demonstrated that larger sprockets are more efficient than smaller ones. For example, with a gear ratio of 4:1, it is more efficient to use a 64/16 than a more conventional 52/13.

In fact, one of the experts told me that the efficiency of the drive chain falls off sharply as the sprocket size is reduced from 13 to 12 to 11. This is because the chain has to bend around a much sharper angle for a smaller sprocket. If you think about it, the straight chain has to bend to a certain angle that depends on the number of teeth on the sprocket. Recalling some school maths about the interior angles of polygons, for 16 teeth, the angle is 157.5º, whereas for 11 teeth, the angle is 147.3º. For the larger sprocket, each pair of links overcomes less friction bending through 22.5º and back, compared with a more dramatic 32.7º and back for the smaller one.

Note that this analysis of the rear sprocket applies to single speed track bikes. On a road bike the chain has to pass the two derailleur cogs, which typically have 13 teeth, whatever gear you choose. However, the argument still applies to the chainring  at the front, where the gains of going larger were shown to exceed the additional aerodynamic drag.

The Bristol team also explored the effect of a number of other factors on performance. Using different length links obviously requires customised sprockets and chainrings. This would be a major upheaval for the industry, but it is possible for purpose-built track bikes. Certain molybdenum-based lubricating powders used in the space industry may be better than traditional oils. Other materials could replace traditional steel.

A different kind of power loss can occur when the chain resonates vertically. A specially designed test rig showed that this can occur at frequencies, which could be triggered at certain pedalling cadences. Current research is investigating how the tension of the chain and its design can help mitigate this problem (which is also an issue for motor cycles).

In conclusion, when we see Tony Martin pushing a 58+ chainring, it may not be simply an act of machismo – he is actually be benefitting from efficiency gains.

 

Update on cycling aerodynamics

A recently published paper provides a useful review of competition cycling aerodynamics. It looks at the results of a wide range of academic studies, highlighting the significant advances made in the last 5 to 10 years.

The power required to overcome aerodynamic drag rises with the cube of velocity, so riding at 50km/h takes almost twice as much power as riding at 40km/h. At racing speed, around 80% of a cyclist’s power goes into overcoming aerodynamic drag. This is largely because a bike and rider are not very streamlined, resulting in a turbulent wake.

The authors quote drag coefficients, Cd, of 0.8 for upright and 0.6 for TT positions. These compare with 0.07 for a recumbent bike with fairing, indicating that there is huge room for improvement.

Wind tunnels, originally used in the aerospace and automotive industries, are now being designed specifically for cycling, though no specific standards have been adopted. These provide a simplification of environmental conditions, but they can be used to study air flow for different body positions and equipment. Mannequins are often used in research, as one of the difficulties for riders is the ability to repeat and maintain exactly the same position. Some tunnels employ cameras to track movements. Usually a drag area measurement, CdA, is reported, rather than Cd, thereby avoiding uncertainty due to measurement of frontal area, though this can be estimated by counting pixels in a image.

One thing that makes cycling particularly complex is the action of pedalling. This creates asymmetric high drag forces as one leg goes up and the other goes down, resulting in variations of up to 20% relative to a horizontal crank position.

Cycling has been studied using computational fluid dynamics, helping to save on wind tunnel costs. These use fine mesh models to calculate details of flow separation and pressure variations across the cyclist’s body. The better models are in good agreement with wind tunnel experiments.

Practical advice

Cycling speed is a maximum optimisation problem between aerodynamic and biomechanical efficiency

Ultimately, scientists need to do field tests. The extensive use of power meters allows cyclists to experiment for themselves. The authors provide two practical ways to separate the coefficient of rolling resistance, Crr,  from CdA. One based on rolling to a halt and the other using a series of short rides at constant speed.

Minimising aerodynamic resistance through rider position is one of the most effective ways to improve performance among well-trained athletes

Compared with riding upright on the hoods, moving to the drops saves 15% to 20% while adopting a TT position saves 30% to 35%. Studies show quite a lot of variance in these figures, as the results depend on whether the rider is pedalling, as well as body size. The following quote suggests that when freewheeling downhill in an aero tuck, your crank should be horizontal (unless you are cornering).

Current research suggests that the drag coefficient of a pedalling cyclist is ≈6% higher than that of a static cyclist holding a horizontal crank position

The authors quote the figures for CdA of 0.30-0.50 for an upright position, 0.25 to 0.30 on the drops and 0.20-0.25 for a TT position. Variation is largely, but not only, due to changes in frontal area, A. Unfortunately, relatively minor changes in position can have large effects on drag, but the following effects were noted.

Broker and Kyle note that rider positions that result in a flat back, a low tucked head and forearms positioned parallel to the bicycle frame generally have low aerodynamic drag. Wind tunnel investigations into a wide range of modifications to standard road cycling positions by Barry et al. showed that that lowering the head and torso and bringing the arms inside the silhouette of the hips reduced the aerodynamic drag.

Bike frames, wheels, helmets and skin suits are all designed with aerodynamics in mind, while remaining compliant with UCI rules. Skin suits are important, due to their large surface areas. By delaying airflow separation, textured fabrics reduce wake turbulence, resulting in as much as a 4% reduction in drag.

In race situations, drafting skills are beneficial, particularly behind a larger rider. While following riders gain a significant benefit, it has been shown that the lead rider also accrues a small advantage of around 3%. It is best to overtake very closely in order to take maximal advantage of lateral drafting effects.

For a trailing cyclist positioned immediately behind the leader, drag reduction has been reported in the range of 15–50 % and reduces to 10–30 % as the gap extends to approximately a bike length… The drafting effect is greater for the third rider than the second rider in a pace-line, but often remains nearly constant for subsequent riders

For those interested in greater detail, it is well worth looking at the full text of the paper, which is freely available.

Reference

Riding against the wind: a review of competition cycling aerodynamics, Timothy N. CrouchEmail authorDavid BurtonZach A. LaBryKim B. Blair, Sports Engineering, June 2017, Volume 20, Issue 2, pp 81–110