⚡ electrical engineering

A Coupled Geodetic-Atmospheric-Physiological Model of Sustainable Cycling Performance at Altitude

This study presents a coupled geodetic-atmospheric-physiological model demonstrating that while sustainable cycling speed on climbs consistently decreases with altitude, level cycling exhibits an elevation-dependent optimum (around 2.0–2.5 km) driven by the complex interplay of reduced air density, gravitational variations, and physiological limitations.

Original authors: Carlos Alberto Gomez Tarazona, Carlos E. Guerra-Londoño, Daniel R. Izquierdo

Published 2026-09-16

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CC BY 4.0

Original authors: Carlos Alberto Gomez Tarazona, Carlos E. Guerra-Londoño, Daniel R. Izquierdo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Cycling at high elevations presents a unique physical puzzle where two opposing forces battle for dominance. On one side, the thin air found at altitude offers a mechanical advantage: with fewer air molecules to push against, a cyclist encounters less wind resistance, making it easier to maintain speed. On the other side, the same thin air creates a physiological disadvantage: because there is less oxygen available to breathe, the human body cannot generate as much power. For decades, athletes and scientists have debated where the balance lies. Does the benefit of thinner air outweigh the cost of lower oxygen, or does the lack of oxygen always win? The answer depends heavily on what the cyclist is actually doing, specifically whether they are riding on flat ground or climbing a steep hill, and where on the globe they are riding.

A team of researchers from Colombia and the United States has built a detailed computer model to solve this question, moving beyond simple rules of thumb to account for the complex reality of the Earth and the atmosphere. Instead of treating altitude as a single number, they created a system that links the shape of the Earth, the changing state of the atmosphere, and the biology of the rider. They accounted for how gravity changes slightly depending on how far north or south a rider is, and how air density shifts based on the time of year, the time of day, and solar activity. By combining these precise environmental factors with a modern understanding of how human lungs and muscles respond to low oxygen, they simulated sustainable cycling speeds across a range of elevations from sea level up to 4,000 meters.

The results reveal that the idea of a single "perfect" altitude for cycling is a myth. The model confirms that for a rider climbing a hill, the answer is straightforward: the lower, the better. When the road slopes upward, the effort required to fight gravity becomes the main challenge. In this scenario, the small gain from thinner air cannot compensate for the loss of power caused by low oxygen. The researchers found that on a 6 percent grade, which is a common steep climb, the fastest sustainable speed is always found at sea level. As the rider goes higher, their speed drops continuously, with no point where the thin air suddenly makes them faster. The physiological penalty of the altitude simply overwhelms the mechanical benefit.

However, the story changes completely when the road is flat. In level cycling, where wind resistance is the primary enemy, the model predicts a distinct sweet spot. Here, the reduction in air density does provide enough of an advantage to offset the loss of oxygen power, but only up to a certain point. The simulation shows that for a flat course, the ideal altitude is not at sea level, nor is it at the highest possible peak. Instead, there is an interior optimum, a specific height where the rider can go fastest. Depending on the latitude and the atmospheric conditions, this peak performance occurs between 2,000 and 2,500 meters. Below this height, the air is still too thick to fully exploit the aerodynamic gain. Above it, the lack of oxygen becomes too severe, and the rider slows down.

This optimal height is not a fixed number that applies everywhere; it shifts based on where you are and when you ride. The researchers discovered that the time of year matters significantly, but only at certain latitudes. Near the equator, the difference in performance between seasons is negligible, and the ideal altitude remains steady. But as you move toward the middle and high latitudes, the seasons begin to pull the optimal altitude and the maximum speed apart. In these regions, the atmospheric density changes enough throughout the year that a rider could see a difference of nearly 1 percent in their top sustainable speed depending on the date. This means that the best place to ride is not just a matter of elevation, but a specific combination of geography, season, and the slope of the road.

The study also clarifies why past observations about altitude records can seem contradictory. Some historical data suggests that cycling records are broken at high altitudes, while other data suggests they are not. The model explains that both are true, but for different reasons. The records that benefit from altitude are almost exclusively those set on flat ground, where the aerodynamic advantage is the deciding factor. The records that suffer at altitude are those involving sustained climbing, where the physiological cost is too high. By separating the mechanical demand of the road from the biological limits of the rider, the researchers have shown that the "best" altitude is not a universal truth, but an emergent property of the specific conditions of the ride.

Ultimately, this work demonstrates that human performance in cycling is a delicate negotiation between the environment and the body. The thin air of the mountains offers a gift of reduced resistance, but it demands a tax in the form of reduced power. Whether that gift is worth the tax depends entirely on the task at hand. If the road goes up, the tax is too high, and the rider is better off staying low. If the road is flat, the gift is valuable, and there is a specific height where the balance is perfect. The findings suggest that for anyone planning a ride, the question of "how high is too high?" cannot be answered without first asking "how steep is the road?" and "where on the map are we?" The answer lies not in a single number, but in the complex interplay of gravity, air, and human biology.

Technical Summary: A Coupled Geodetic–Atmospheric–Physiological Model of Sustainable Cycling Performance at Altitude

Problem Statement
Cycling performance at altitude is governed by a complex competition between reduced mechanical resistance (due to lower air density) and altitude-induced physiological impairment (due to hypoxia). Previous approaches have often treated these mechanisms separately or relied on simplified environmental descriptions, such as the International Standard Atmosphere (ISA), which fails to capture the explicit dependence of atmospheric density on geographic latitude, season, universal time, and solar/geomagnetic activity. Furthermore, the variation of effective gravity with latitude and altitude is often neglected, despite its influence on gravitational and rolling-resistance forces. This study addresses the need for a unified framework that simultaneously accounts for geodetic, atmospheric, and physiological factors to determine sustainable cycling speed and identify potential optimal altitudes.

Methodology
The authors developed a coupled model that distinguishes between the mechanical power required by the cyclist-bicycle system ( $P_{req}$ ) and the physiologically available mechanical power ( $P_{avail}$ ).

Geodetic Component: The model utilizes the WGS84 reference ellipsoid to calculate normal gravity, $g(h, \phi)$ , as a function of geometric altitude ( $h$ ) and geodetic latitude ( $\phi$ ). This accounts for Earth's oblateness and rotation, providing a systematic latitude-dependent correction to gravitational and rolling-resistance forces.
Atmospheric Component: Instead of the standard ISA, the study employs the NRLMSIS 2.0 empirical atmospheric model. This model provides neutral atmospheric mass density ( $\rho_{atm}$ ) and temperature based on altitude, geographic location (latitude and longitude), time of day, day of year, and solar/geomagnetic activity indices ( $F_{10.7}$ , $Ap$ ). A modified standard atmosphere (ISA-m) was also derived analytically to isolate the geodetic contribution of latitude.
Physiological Component: The reduction in maximal aerobic capacity ( $\dot{V}O_2max$ ) with altitude is modeled using a corrected meta-regression by MacInnis et al., which accounts for baseline aerobic capacity and acute hypoxic exposure. This physiological scaling factor, $F_{MI}(h, V_0)$ , is applied to the sea-level sustainable power ( $P_0$ ) to determine available power at altitude. Historical formulations (Howley-Bassett) were retained for sensitivity comparison but not used as the primary model.
Mechanical Coupling: The sustainable cycling speed ( $v_{sus}$ ) is determined by solving the power-balance equation where $P_{req} = P_{avail}$ . $P_{req}$ includes aerodynamic drag (dependent on $\rho_{atm}$ ), gravitational resistance (dependent on $g(h, \phi)$ and road gradient $\theta$ ), and rolling resistance. The model was numerically solved over an altitude range of 0–4000 m for various latitudes (0°, 45°, 71°) and road gradients (0%, 3%, 6%, 9%).

Key Contributions

Integrated Framework: The paper presents the first coupled model explicitly separating geodetic (WGS84 gravity), atmospheric (NRLMSIS 2.0 density), and physiological (MacInnis scaling) dependencies to predict sustainable cycling performance.
Gradient-Dependent Optima: The study demonstrates that the existence of an optimal cycling altitude is not a universal function of elevation alone but is an emergent property of the interaction between road gradient, aerodynamic resistance, and physiological capacity.
Atmospheric Sensitivity: By using NRLMSIS 2.0, the model reveals that atmospheric effects on performance are not solely altitude-dependent but vary significantly with latitude and day of year, particularly at mid-to-high latitudes.

Results

Mechanical vs. Physiological Trade-off: While the mechanical power required to maintain a fixed speed decreases monotonically with altitude (due to lower air density and slightly lower gravity), this does not guarantee improved sustainable speed.
Climbing Conditions: Under a reference 6% climbing gradient, physiological impairment dominates the mechanical benefits. Consequently, sustainable speed decreases monotonically from sea level to 4000 m, with no interior optimum predicted; the optimal altitude is effectively sea level.
Level Cycling: In contrast, level cycling (0% gradient) produces an interior optimum where the reduction in aerodynamic drag initially outweighs the physiological penalty. This optimum occurs at approximately 2.0–2.5 km, depending on latitude and atmospheric state.
Latitude and Seasonality: Seasonal variations in atmospheric density have minimal impact on performance at the Equator but result in progressively larger differences at mid and high latitudes. At 45° and 71° latitude, seasonal shifts can alter the maximum sustainable speed by up to ~1% and shift the optimal altitude by several hundred meters.
Sensitivity: The location of the interior optimum is highly sensitive to road gradient; as the gradient increases, the optimum shifts toward lower altitudes and eventually disappears.

Significance and Claims
The paper claims that optimal cycling altitude should be regarded as a multivariable quantity emerging from the specific balance of aerodynamic resistance, gravitational demand, and physiological impairment, rather than a universal elevation. The study reconciles seemingly contradictory findings in literature (e.g., benefits in hour records vs. penalties in climbing) by showing that the mechanical regime (level vs. climbing) dictates whether an altitude advantage exists.

The authors emphasize that their framework is a "controlled theoretical framework" rather than a route-specific predictor. They explicitly note limitations, including the use of acute hypoxia models (MacInnis) which do not account for acclimatization, the exclusion of wind and transient gradients, and the assumption that sustainable power scales directly with $\dot{V}O_2max$ . The significance of the work lies in demonstrating that standard atmospheric models are insufficient for precise performance modeling and that geographic and temporal atmospheric variations must be explicitly considered when analyzing small performance differences at altitude.

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