Peloton Shape Geometry
The Escape Collective recently published an article arguing that rider safety, and not aerodynamics dictates the shape of the peloton. This theory is not just counterintuitive, it’s counter to basic aerodynamics, physiology, and geometry. It’s disappointing to read an article based on such poorly researched science. As a peloton expert, I feel compelled to correct the misleading information in the article.
The article is based on a research paper by a group scientists who appear to lack any peloton experience. Sadly, it appears that their research is based on reviewing video of pelotons rather than spending any time riding in a peloton making scientifically repeatable measurements, or at least gaining an intuitive understanding of peloton shape dynamics. Research based on analysis instead of real world measurements and experience is termed dry lab research. Theory and mathematical analysis can be useful, but it needs to be combined with real-world experience and observation to provide substantial value.
The World Champ Tech Bike+ app was developed in the wet lab of the peloton - not the sterile environment of a laboratory. I certainly studied aerodynamics and bioenergetics extensively during my time at UC Berkeley and MIT, and had the incredible fortune to have Professor Mark Drela - one of the world’s leading low-speed aerodynamicists - join the MIT cycling club on group rides where I could pepper him with questions as we pedaled along. But, this theory was always bolstered by my decades of competition in the peloton, where I could feel the real world application of this theory. This peloton experience shaped and molded the Bike+ app.
Race Tactics
This may come as a shock to the scientists who wrote the research paper, but the goal of a bike race is to win the race. Safety is secondary. To win a race, you want to try and conserve as much energy as possible until the point of the race where you plan to put in your race winning attack. For a sprinter, this point is only 150-200 meters from the finish line. For a strong rider who plans to win solo, this might be several kilometers from the finish. Until that point, each rider attempts to minimize the amount of energy they expend while still placing themselves in a position to get the best result possible. Even riders who go in breakaways, typically choose to go in breakaways with other riders instead of riding solo since they can share the extra workload with their breakaway companions which minimizes their energy expenditure. Claudio Chiappucci’s audacious solo attack in the 1992 Tour de France stage to Sestriere is a notable exception to this rule. And, to be clear about what it means to win a race: at the finish line you must be in front of all the other riders.
The two safest places to sit in a peloton are the very front and the very back. The very front boundary row is safe since you cannot crash into anyone in front of you. The very back is also reasonably safe since you have the maximum possible time to apply your brakes to avoid a crash in front of you, and no riders behind you who may not be as attentive with their brakes, and crash into you from behind as you slow to avoid a crash in front. The problem with riding in the row of riders on the frontal boundary of the peloton is that it takes much more energy than riding behind in the draft. Your physical safety is maximized, but you will most likely lose the race since you are spending 30-40% more energy than the riders in your draft. Riding at the very back also provides safety benefits over riding closer to the front, but at the cost of increased energy expenditure late in the race when you want to win. If the peloton is strung out single file late in a race, a rider at the back can be 150 to 200 meters behind the riders at the front. To move forward to place yourself in a position to win the race - i.e. in front of all the other riders - requires you to expend substantial extra effort compared to the riders already riding near their maximum at the front. Typically a racing field is balanced enough where no rider is so much stronger than the rest where they could put in such a superhuman effort, and have enough strength left once they approached the front of the peloton to best the second strongest rider.
Riders intentionally sacrifice safety for reduced aerodynamic drag so as to conserve energy for their hoped for, race winning attack. And, once a rider has made the decision to sacrifice some safety to minimize energy use, the ideal location in the peloton is as close to the front of the peloton as possible to facilitate race winning attacks or sprints.
Rider Packing Geometry
The research scientists suggest that riders in a peloton form repeating diamond shape patterns due to constraints on human vision. This is false. Riders - due to race tactics - want to be as close to the front, boundary edge of the peloton as possible so they can make attacks or respond to attacks. As a result, riders pack in as tightly as possible to minimize the distance to the front of the peloton. Geometrically, a hexagonal tiling pattern is the densest way to pack objects in two dimensions.
Hexagonal tiling packs the greatest number of riders in the smallest possible space
The repeated diamond pattern that the researchers observe in race video of pelotons, emerges from the hexagonal tiling pattern.
Diamond patterns emerge from a hexagonal tile packing pattern
The 30° angles measured by the scientists between the packed riders are a basic characteristic of the geometry of hexagonal packed objects. A hexagon has six equal length sides with a 120° angle between sides, and the 30° angle separating each rider is an artifact of the hexagonal packing geometry.
30° angles characterize the geometry of a hexagon
The advantage of riding this close is that the distance between a rider and the front of the pack is reduced. If you ride directly behind the rider in front, the distance between you and the front is one rider in length, if you ride in a hexagonal pack pattern, the distance between you and the rider in front is reduced by 13.4% This follows from simple geometry where the linear distance separating the objects is multiplied by cosine(30°). The hypothesis that the measured 30° angle results from the nature of the human vision system is easily refuted with an understanding of race tactics, rider motivation, and simple geometry.
Hexagonal packing reduces the distance between each rider and the front of the peloton by 13.4%
If the researchers had spent time riding and racing in a peloton, they would be well aware that touch and hearing are equally critical as vision in determining the position of other riders in relation to yourself. You don’t need to only see riders with your eyes. You can feel them with your shoulders and hips once you are tightly packed into the peloton. You can hear their pedal stroke, the sound of the rear wheel freewheel as the chain pulls against the cogs, the sound of tires against the pavement, and the sound of riders breathing hard under the strain of racing.
Finally, if the researchers had spent time racing in a peloton, they would have also observed that riders don’t always pack that tightly together. It’s really only the bigger races such as the Tour de France where you see this type of close packing occur for much of the race. At smaller events riders will cluster this closely on the final laps in preparation for a sprint finish, but spend most of the race spaced more sensibly with greater separation distance.
Aerodynamics & Boundary Layers
A thin boundary layer of slow moving air forms in aerodynamics as air flows around a moving object. Riders inside the boundary layer, or wake, experience reduced aerodynamic forces compared to the lead rider. This allows riders to ride slightly beside and behind a leading rider and still enjoy a bit of aerodynamic drafting advantage. The width of this layer of slow moving air in the wake of cyclist is a function of the properties of air - its density (ρ) and viscosity (μ) - along with the speed of the rider (v). As the speed of the lead rider increases, the width of the wake, or boundary layer thickness, decreases. This reduces the aerodynamic benefit from riding slightly aside and behind the rider in front. The geometry of aerodynamic boundary layers molds the peloton to form a rounded leading edge, and gives the peloton a distinct prolate spheroid shape. A prolate spheroid is a football shape (either American or Australian footy, but not European football, or soccer).
Aerodynamic boundary layer thickness shrinks as velocity increases
Aerodynamic boundary layer geometry shapes the peloton into an prolate spheroid at moderate speeds
Human Physiology
Each riders’ lactate, or anaerobic, threshold determines how long they can spend in the boundary layer before they want to tuck directly behind the rider in front to maximize the drafting benefit. As the speed increases, each rider much increase their effort to keep pace, and the thickness of the boundary layer simultaneously decreases to further increase the effort required to maintain pace. At some point, this effort exceeds their anaerobic threshold. Once this threshold is crossed, a clock starts ticking as lactate floods into the body. Maintaining the effort becoming increasingly painful until the rider is unable to sustain the strain anymore, and has to dramatically slow down. In the language of the peloton, the rider is popped. So, as the speed increases, more riders will have to tuck in directly behind another rider to stay below their anaerobic threshold, leading eventually to a long, single-file line of riders. Rider don’t form a single-file peloton because their field of vision has narrowed under the effort. They ride single file because they can no longer ride in the boundary layer behind the rider in front without getting popped from the peloton.
As a concrete example, when I was at my peak racing in the peloton, I could ride at a power output of about 400 watts for about 20 minutes. If I was drafting other riders, the first rider in line would have to put out 30-40% more power, or about 520 to 560 watts, to force me to put out 400 watts just sitting on their wheel. Once you are above your lactate threshold, the amount of time you can spend at that effort decreases exponentially with the increase in effort. I could maintain an effort of 420 watts for about 10 minutes at my best. I held over 480 watts for about four minutes once, but that was during the finale of the World Championships when I was exceptionally motivated. I could hold 550-600 watts for only a minute. The limits of human physiology - not vision - determine when the pack lines out single file under the pace imposed by the leading riders.
Team Webcor rides single file at front of peloton to minimize aerodynamic drag while other teams bunch up behind to ride as near to the front as possible
Echelons and Cross Winds
When a peloton encounters a cross wind, the optimal draft position shifts from directly behind the rider in front to a location slightly to the leeward - the side away from the wind - of the leading rider. This results from the vector sum of the direction of travel of the peloton and the angle of the wind.
Echelons form when cross wind shift the wake behind the leading rider to the leeward side of the peloton
The leading riders have a substantial benefit in an echelon, and can place themselves on the leeward side of the road so that they get a draft but trailing riders in the gutter don’t get the benefit of riding in the wake behind the riders in front. Guttered riders - riders forced to the leeward edge of the road - face a brutal choice: cooperate with your opponents to form a second echelon, or quickly get popped as they are forced to exceed their anaerobic threshold to keep up with the pace of the leaders.
Echelons form in cross winds where the wind causes the maximum draft to shift leeward instead of directly behind the rider in front
The design of World Champ Tech’s apps - including the Bike+ app - has been guided by my experience in the peloton. Features such as the patent-applied-for fatigue detection system, or the new precision sweat loss and hydration alerts, were conceived, designed, and engineered in the peloton.
— James
Photos © 2004 Rob Karman