Echelons at UAE Tour 2022, image credit GCN+.
At PickleTech we thrill when two -apparently- separate projects end up connected in some way. And when the reason is related to Physics, writing about it becomes an imperative. Do you know what connects a Tour de France stage with the management of a constellation of satellites?
In this post we write about aerodynamic drag and its implications in two -only literally- distant contexts: cycling, and low Earth orbit satellites. Estimating drag with precision and integrating it on complex operational strategies are key to their success. Data Science is contributing to optimize such complex challenges with the use of Artificial Intelligence and Machine Learning techniques.
Aerodynamic Drag – a very short intro
Anyone that cycles has experienced -consciously or not- the impact air resistance has on it. What maybe not so many realize is that, even at a moderate speed, most of the muscle power we generate when cycling goes to overcome this force. It is the dominant force already at around 16km/h, and for speeds reaching 50km/h, around 90% of our power goes against it.
Aerodynamic drag, caused by air pressure drag and direct friction, is thus arguably the main force a cyclist has to overcome when moving forward. The equation that describes it, attributed to Lord Reyligh, involves an interesting combination of physical variables:
There, FD is the aerodynamic drag, usually in opposition to the object moving direction. ⍴ is the air density, something cyclists can not control. Its value is around 1.2 kg/m³ at sea level. This value decreases with altitude and one may think that it becomes null when we cross the frontier with space. But does it? We will see later.
The impact of the cyclist relative speed with the air flow* appears through its square power. This means aerodynamic drag does not simply double if we double our speed, but the effect of drag becomes more and more dramatic the faster we move. Hence, the air resistance dominance we were talking about. Finally, CD stands for the drag coefficient, related to the shape of the moving object, while A stands for its reference surface, that for a cyclist may be larger than the area of the cross section along the plane perpendicular to the direction of motion.
Assuming we want to go as fast as possible for a fixed effort, CD y A are actually the two quantities a rider needs to minimize to reduce air resistance as much as possible. These two depend heavily on the rider positioning, as well as on the bike, the rider apparel, specially its helmet and clothes, their materials and technology.
Describing the impact of all these factors in detail is beyond the scope of this post, but you can find good resources elsewhere. If you are an amateur cyclist, you should find your optimal balance between aiming to be aggressively aerodynamic, in exchange for comfort and… money.
For professional cycling, minimizing CDA is key to be competitive, and that actually keeps pushing innovation around cycling and bikes to unthinkable limits. We comment below on a couple of cases illustrating this quest in one of the most significant competition modalities when it comes to aerodynamic drag: time trials.
Always better as a collective!
Beyond individual time trials, professional cycling involves riding together with your team members, and against hundreds of opponents in each race. And to make it even more interesting, aerodynamic drag is heavily affected when cycling in a group, with other cyclists, and moving objects around. Understanding how drag reductions depend on group formation and positioning is thus key to finding an optimal race strategy for professional teams.
Aerodynamic drag can be assessed by field tests, by wind tunnel measurements, or by numerical simulations with computational fluid dynamics. Luckily, in recent years several papers have provided new estimates on these drag reductions, see for instance here or here. Numbers are really illustrative:
As you can see in the image, cycling right behind one or two colleagues reduces your aerodynamic drag already by 36% to 48%. This is, you can keep the same speed as the colleague at the front of the group, but by generating roughly only 70% to 50% of the power the group leader is producing**. Drag reduction becomes dramatic inside the peloton. There, the optimal positioning in the center-rear of the peloton comes with a 95% drag reduction! You can travel there almost for free.
La effects of aerodynamic drag are even more crucial in windy conditions. In particular, cross wind races provide us with some of the most spectacular race days, with the formation of the famous echelons, leaving us with spectacular images.
With such aerodynamic drag reduction numbers depending on the riding formation, and combined with the effects of gravity in mountain stages, every race becomes a positioning game extended over 3-7 hours and quite some kilometers to cover. Knowing when and how each of the riders in your team has to deliver the best of their power performance is crucial.
Who, when, how to breakaway? How much to push when someone else has made its move? How you gauge the efforts of your team members in key moments becomes quite an interesting optimization challenge. Aerodynamics plays such a huge role in cycling that strategy across a race (and a season) is a key element for any elite team. There is where Data Science, Machine Learning, and PickleTech, have a lot to say.
The same ol’ marginal gain philosophy?
As the image above with the drag reductions by drafting illustrates, not only the cyclists on the back of a peloton benefit from drag reduction, but even the peloton leader also gets a -smaller- drag reduction. It is always better to cycle in a group! This is true for the lead in a peloton, and also for any isolated rider with a moving object in its back. Recently, this has been a source of recurrent discussions, as some professional teams have tried to maximize this effect in individual time trials. Do you see something odd in the following picture?
If you do, you may have spotted the reason behind the few seconds some people argue Filippo Ganna gained to reach some of his time trial victories (so far) this season, see here or here.
Another example of innovation and aerodynamic drag is the revolutionary skinsuit Mathieu van der Poel will wear at the opening time trial at Tour de France.
This year, in addition to that individual time trial in the first stage, a section of 18km series of windy bridges in a potentially explosive second stage, are the appealing starters for the 2022 Tour de France that is about to kick off. We will certainly hear a lot about aerodynamic drag and how teams have come with innovative ways to get an extra competitive edge. Aerodynamic drag in cycling has never been any more exciting!
Highway to Space
While a priori they are quite distant from cyclists, it turns out spacecraft flying in space also face aerodynamic drag. That should be no surprise, aerodynamic drag applies to any object moving through a fluid. And even if air density decreases as we move up the atmosphere and into Space, Low Earth Orbit (LEO) satellites fly at altitudes from only a few hundred kilometers to around 2000km. There, the atmosphere air density is still sizable enough to produce relevant drag.
The aerodynamic drag there slows satellites effectively pulling them down closer to the Earth. But the closer to the Earth they are, the bigger the air density is, and thus, looking at the drag equation above, the bigger aerodynamic drag gets. As a result the satellite is pulled down even more. This implies satellites in LEO have to boost their orbits about four times per year to make up for atmospheric drag. But this is only when solar activity is small. When solar activity goes up, the extra solar energy added to the atmosphere makes the low density layers at LEO rise. In exchange, these are replaced by higher density layers that were at lower altitudes. In these conditions, satellites need to boost their orbits a few times… in a week!
Low Earth Orbit satellites have a privileged view of the planet Earth, and this is why thousands of them are continuously collecting data from our planet. This data contains very valuable information about many aspects of our planet. Some famous examples are the constellations for Earth observations, such as the Copernicus project. But to successfully manage these constellations we must understand and predict the impact of aerodynamic drag. It is fundamental for precision orbit determination: satellite positioning, to avoid collisions, and debris. Unfortunately, there is still little information to determine air density with a controlled uncertainty at that altitude. And in addition, obtaining well-known estimates for the drag equation terms CDA up there is a necessary but complex task. See here for more details.
And this is only to determine with precision the orbit of one object. Conversely, constellations have thousands of them to monitor, including debris. Operating them becomes a complex task that benefits from Data Science and Artificial Intelligence solutions as we wrote about here. Machine learning can be used to predict atmospheric drag at LEO, or other examples involve using Reinforcement Learning for Satellite Communications: From LEO to Deep Space Operations, or to Schedule Earth Observation satellites with Deep Reinforcement Learning.
Powered by Data, Driven by Science
Aerodynamic drag heavily impacts both cycling and LEO satellites. Estimating it with precision and integrating it on complex operational strategies are key to their success. In both cases, Data Science is contributing to optimize such complex challenges with the use of Artificial Intelligence and Machine Learning techniques.
At PickleTech, we work developing tailored solutions to improve competitive aspects related to Salud, Sports, and DeepTech. We believe Data Science y advances in Machine Learning coupled with domain knowledge and experimentation have the potential to provide new tools to better understand, monitor, and systematically improve the competitive performance of organizations.
Header Image: Echelons at UAE Tour 2022, image credit GCN+.
*Roughly the cyclist speed if there is no wind.
**Assuming realistic conditions where most of the resistance comes from drag, i.e. more or less flat sections at a competitive peloton speed.
[1] How Air Resistance of the Cyclist Affects Cycling Speed: https://ridefar.info/bike/cycling-speed/air-resistance-cyclist/
[2] Aerodynamic drag in cycling pelotons: New insights by CFD simulation and wind tunnel testing: https://www.sciencedirect.com/science/article/pii/S0167610518303751
[3] Aerodynamic benefits for a cyclist by drafting behind a motorcycle: https://link.springer.com/article/10.1007/s12283-020-00332-z
[4] Drag reductions by drafting in cycling: https://twitter.com/realBertBlocken/status/1338384609466339330?s=20&t=xyMk4pEu4QkO4YLmQiLz7g
[5] Individual performance… a team effort! https://pickletech.eu/blog-uci/
[6] Why was Filippo Ganna’s Tirreno-Adriatico team car stacked with spare bikes?https://www.cyclingnews.com/news/why-was-filippo-gannas-tirreno-adriatico-team-car-stacked-with-spare-bikes/
[7] How much time gained by stacking team cars with bikes like Ganna at Tirreno TT?https://www.stickybottle.com/coaching/how-much-time-gained-stacking-team-cars-with-bikes-like-ganna-at-tirreno-tt/
[8] Could an 18km bridge ruin the GC ambitions of the climbers at the Tour de France?https://www.velonews.com/news/road/could-an-18km-bridge-ruin-the-gc-ambitions-of-the-climbers-at-the-tour-de-france/
[9] Satellite Drag: https://www.swpc.noaa.gov/impacts/satellite-drag
[10] Analysis of Satellite Drag: https://archive.ll.mit.edu/publications/journal/pdf/vol01_no2/1.2.6.satellitedrag.pdf
[11] Data Science in Space: ready for launch! https://pickletech.eu/blog-space/
[12] Machine Learning for Atmospheric Drag Prediction of LEO satellites: https://issfd.org/ISSFD_2019/ISSFD_2019_AIAC18_Kato-Hiroshi.pdf
[13] Reinforcement Learning for Satellite Communications: From LEO to Deep Space Operations: https://ieeexplore.ieee.org/document/8713802
[14] Schedule Earth Observation satellites with Deep Reinforcement Learning: https://arxiv.org/abs/1911.05696
[15] Mathieu van der Poel to challenge for Tour de France yellow with $3,400 TT skinsuit: https://www.velonews.com/events/tour-de-france/mathieu-van-der-poel-to-challenge-for-tour-de-france-yellow-with-3400-tt-skinsuit/