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Modeling the Benefits of Cooperative Drafting: Is There an Optimal Strategy to Facilitate a Sub-2-Hour Marathon Performance?

DOI:10.1007/s40279-018-0991-4
Authors:
Wouter Hoogkamer at University of Massachusetts Amherst
Wouter Hoogkamer
Kristine L Snyder at Stryd
Kristine L Snyder
  • Stryd
Christopher J. Arellano
Christopher J. Arellano
Christopher J. Arellano
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Abstract and Figures

Background During a race, competing cyclists often cooperate by alternating between leading and drafting positions. This approach allows them to maximize velocity by using the energy saved while drafting, a technique to reduce the overall drag by exploiting the leader’s slipstream. We have argued that a similar cooperative drafting approach could benefit elite marathon runners in their quest for the sub-2-hour marathon. Objective Our aim was to model the effects of various cooperative drafting scenarios on marathon performance by applying the critical velocity concept for intermittent high-intensity running. Methods We used the physiological characteristics of the world’s most elite long-distance runners and mathematically simulated the depletion and recovery of their distance capacity when running above and below their critical velocity throughout a marathon. Results Our simulations showed that with four of the most elite runners in the world, a 2:00:48 (h:min:s) marathon is possible, a whopping 2 min faster than the current world record. We also explored the possibility of a sub-2-hour marathon using multiple runners with the physiological characteristics of Eliud Kipchoge, arguably the best marathon runner of our time. We found that a team of eight Kipchoge-like runners could break the sub-2-hour marathon barrier. Conclusion In the context of cooperative drafting, we show that the best team strategy for improving marathon performance time can be optimized using a mathematical model that is based on the physiological characteristics of each athlete.
Simulations of marathon running performance illustrating the benefits of drafting for two elite runners sustaining a velocity of 5.89 m/s. Sustaining this velocity throughout the second half of the race would allow a marathon time of 2:01:10 (h:min:s); however, the distance that a runner can cover is limited by the total depletion of their Dʹ (the distance that can be covered above one’s critical velocity, expressed in meters) before completing the entire race. In a traditional scenario (a), the two runners could choose to max out Dʹ, whereby the lead runner (gray line) sustains this velocity for as long as possible, reaching a point where he depletes all of his Dʹ and thus must exit the race. Prior to the lead runner exiting the race, the runner in the drafting position (pink line) regains a portion of his Dʹ. When the lead runner exits the race, the other runner can no longer benefit from drafting and, therefore, begins to steadily deplete his Dʹ until he also has depleted all of this Dʹ. In a cooperative scenario (b), the two runners choose to alternate leading and drafting positions throughout the second half, allowing both runners to intermittently deplete and recover Dʹ. This strategy allows them to sustain this pace for a longer period of time, thus covering a longer distance. In this hypothetical scenario, each interval lasts 180 s and alternating between the lead and drafting position continues until the runner who began the second half in the leading position depletes all of his Dʹ and must exit the race. In the last interval, the runner who began the second half in the drafting position can still sustain this velocity for a short period of time until the point of depleting all of his Dʹ and, therefore, must exit the race
Simulations of marathon running performance illustrating the benefits of drafting for two elite runners sustaining a velocity of 5.89 m/s. Sustaining this velocity throughout the second half of the race would allow a marathon time of 2:01:10 (h:min:s); however, the distance that a runner can cover is limited by the total depletion of their Dʹ (the distance that can be covered above one’s critical velocity, expressed in meters) before completing the entire race. In a traditional scenario (a), the two runners could choose to max out Dʹ, whereby the lead runner (gray line) sustains this velocity for as long as possible, reaching a point where he depletes all of his Dʹ and thus must exit the race. Prior to the lead runner exiting the race, the runner in the drafting position (pink line) regains a portion of his Dʹ. When the lead runner exits the race, the other runner can no longer benefit from drafting and, therefore, begins to steadily deplete his Dʹ until he also has depleted all of this Dʹ. In a cooperative scenario (b), the two runners choose to alternate leading and drafting positions throughout the second half, allowing both runners to intermittently deplete and recover Dʹ. This strategy allows them to sustain this pace for a longer period of time, thus covering a longer distance. In this hypothetical scenario, each interval lasts 180 s and alternating between the lead and drafting position continues until the runner who began the second half in the leading position depletes all of his Dʹ and must exit the race. In the last interval, the runner who began the second half in the drafting position can still sustain this velocity for a short period of time until the point of depleting all of his Dʹ and, therefore, must exit the race
… 
Simulations of marathon running performance of two, three, and four runners who alternate leading and drafting positions while sustaining an average velocity of 5.89 m/s. The model predictions show that the total distance covered can be maximized with additional runners. Note that the drafting duration is 42 s, which is optimal for two identical runners and is held constant across the three- and four-runner teams for comparison. CV critical velocity
Simulations of marathon running performance of two, three, and four runners who alternate leading and drafting positions while sustaining an average velocity of 5.89 m/s. The model predictions show that the total distance covered can be maximized with additional runners. Note that the drafting duration is 42 s, which is optimal for two identical runners and is held constant across the three- and four-runner teams for comparison. CV critical velocity
… 
Simulations of marathon running performance for four runners with physiologically identical (a) and different (b) physiological characteristics. In a, the start of the second half begins with runner A1 in third position, with each team member alternating positions after a time window of 42 s. In this scenario, each runner benefits from drafting for 126 s total while only maintaining the lead position for 42 s. Alternating of the lead and trail position is continuous until runners A3 and A4 deplete all their Dʹ (the distance that can be covered above one’s critical velocity, expressed in meters), just before completing the entire marathon. Runners A1 and A2 can sustain the velocity of 5.97 m/s for a slightly longer period of time. This strategy allows them to complete the marathon in 2:00:40 (h:min:s). In b, the start of the second half begins with runner A at the front of the group. The shift durations are substantially longer than 42 s and vary between runners (355, 355, 340, and 300 s for Athletes A, B, C, and D, respectively). Eventually, Athlete A completes the marathon in 2:00:48. Note that in this scenario, Athlete A can sustain this velocity for a longer period because he has a higher rate of Dʹ recovery. CV critical velocity
Simulations of marathon running performance for four runners with physiologically identical (a) and different (b) physiological characteristics. In a, the start of the second half begins with runner A1 in third position, with each team member alternating positions after a time window of 42 s. In this scenario, each runner benefits from drafting for 126 s total while only maintaining the lead position for 42 s. Alternating of the lead and trail position is continuous until runners A3 and A4 deplete all their Dʹ (the distance that can be covered above one’s critical velocity, expressed in meters), just before completing the entire marathon. Runners A1 and A2 can sustain the velocity of 5.97 m/s for a slightly longer period of time. This strategy allows them to complete the marathon in 2:00:40 (h:min:s). In b, the start of the second half begins with runner A at the front of the group. The shift durations are substantially longer than 42 s and vary between runners (355, 355, 340, and 300 s for Athletes A, B, C, and D, respectively). Eventually, Athlete A completes the marathon in 2:00:48. Note that in this scenario, Athlete A can sustain this velocity for a longer period because he has a higher rate of Dʹ recovery. CV critical velocity
… 
Simulations of marathon running performance for one to ten runners with identical physiological characteristics. The main take-away is that every additional runner joining the team provides a smaller improvement in performance. The findings show that a team of eight runners can break the 2-hour marathon barrier, finishing in 1:59:55 (h:min:s). Teams of nine and ten athletes can run another 5 or 10 s faster, respectively, but times faster than that are not possible as the athletes will be running so fast (> 6.036 m/s) that the perceived intensity while drafting is no longer below their sustainable velocity. Therefore, they can no longer recover their Dʹ (the distance that can be covered above one’s critical velocity, expressed in meters)
Simulations of marathon running performance for one to ten runners with identical physiological characteristics. The main take-away is that every additional runner joining the team provides a smaller improvement in performance. The findings show that a team of eight runners can break the 2-hour marathon barrier, finishing in 1:59:55 (h:min:s). Teams of nine and ten athletes can run another 5 or 10 s faster, respectively, but times faster than that are not possible as the athletes will be running so fast (> 6.036 m/s) that the perceived intensity while drafting is no longer below their sustainable velocity. Therefore, they can no longer recover their Dʹ (the distance that can be covered above one’s critical velocity, expressed in meters)
… 
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Vol.:(0123456789)
Sports Medicine (2018) 48:2859–2867
https://doi.org/10.1007/s40279-018-0991-4
ORIGINAL RESEARCH ARTICLE
Modeling theBenets ofCooperative Drafting: Is There anOptimal
Strategy toFacilitate aSub‑2‑Hour Marathon Performance?
WouterHoogkamer1 · KristineL.Snyder2· ChristopherJ.Arellano3
Published online: 8 October 2018
© Springer Nature Switzerland AG 2018
Abstract
Background During a race, competing cyclists often cooperate by alternating between leading and drafting positions. This
approach allows them to maximize velocity by using the energy saved while drafting, a technique to reduce the overall drag
by exploiting the leader’s slipstream. We have argued that a similar cooperative drafting approach could benefit elite marathon
runners in their quest for the sub-2-hour marathon.
Objective Our aim was to model the effects of various cooperative drafting scenarios on marathon performance by applying
the critical velocity concept for intermittent high-intensity running.
Methods We used the physiological characteristics of the world’s most elite long-distance runners and mathematically simu-
lated the depletion and recovery of their distance capacity when running above and below their critical velocity throughout
a marathon.
Results Our simulations showed that with four of the most elite runners in the world, a 2:00:48 (h:min:s) marathon is pos-
sible, a whopping 2min faster than the current world record. We also explored the possibility of a sub-2-hour marathon
using multiple runners with the physiological characteristics of Eliud Kipchoge, arguably the best marathon runner of our
time. We found that a team of eight Kipchoge-like runners could break the sub-2-hour marathon barrier.
Conclusion In the context of cooperative drafting, we show that the best team strategy for improving marathon performance
time can be optimized using a mathematical model that is based on the physiological characteristics of each athlete.
Key Points
We revisit the possibility of a sub-2-hour marathon by
incorporating the critical velocity concept to model the
effects of intermittent high-intensity running on mara-
thon performance.
With a cooperative drafting approach, four of the most
elite runners in the world could run a 2:00:48 (h:min:s)
marathon, 2min faster than the current world record.
We explored the possibility of a sub-2-hour marathon
using more runners and our model simulations predict
that a team of eight runners with the physiological char-
acteristics of Eliud Kipchoge could break the sub-2-hour
marathon barrier.
Electronic supplementary material The online version of this
article (https ://doi.org/10.1007/s4027 9-018-0991-4) contains
supplementary material, which is available to authorized users.
* Wouter Hoogkamer
wouter.hoogkamer@colorado.edu
1 Locomotion Lab, Department ofIntegrative Physiology,
University ofColorado, Boulder, 354 UCB, Boulder,
CO80309-0354, USA
2 Department ofMathematics andStatistics, Swenson College
ofScience andEngineering, University ofMinnesota,
Duluth, 104 Solon Campus Center, Duluth, MN55812, USA
3 Department ofHealth andHuman Performance, University
ofHouston, 3875 Holman St, Houston, TX77204-6015,
USA
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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The curvilinear relationship between power output and the time for which it can be sustained is a fundamental and well-known feature of high-intensity exercise performance. This relationship ‘levels off’ at a ‘critical power’ (CP) that separates power outputs that can be sustained with stable values of, for example, muscle phosphocreatine, blood lactate, and pulmonary oxygen uptake (\( \dot{V}{\text{O}}_{2} \)), from power outputs where these variables change continuously with time until their respective minimum and maximum values are reached and exercise intolerance occurs. The amount of work that can be done during exercise above CP (the so-called W′) is constant but may be utilized at different rates depending on the proximity of the exercise power output to CP. Traditionally, this two-parameter CP model has been employed to provide insights into physiological responses, fatigue mechanisms, and performance capacity during continuous constant power output exercise in discrete exercise intensity domains. However, many team sports (e.g., basketball, football, hockey, rugby) involve frequent changes in exercise intensity and, even in endurance sports (e.g., cycling, running), intensity may vary considerably with environmental/course conditions and pacing strategy. In recent years, the appeal of the CP concept has been broadened through its application to intermittent high-intensity exercise. With the assumptions that W′ is utilized during work intervals above CP and reconstituted during recovery intervals below CP, it can be shown that performance during intermittent exercise is related to four factors: the intensity and duration of the work intervals and the intensity and duration of the recovery intervals. However, while the utilization of W′ may be assumed to be linear, studies indicate that the reconstitution of W′ may be curvilinear with kinetics that are highly variable between individuals. This has led to the development of a new CP model for intermittent exercise in which the balance of W′ remaining (\( W_{\text{BAL}}^{\prime } \)) may be calculated with greater accuracy. Field trials of athletes performing stochastic exercise indicate that this \( W_{\text{BAL}}^{\prime } \) model can accurately predict the time at which W′ tends to zero and exhaustion is imminent. The \( W_{\text{BAL}}^{\prime } \) model potentially has important applications in the real-time monitoring of athlete fatigue progression in endurance and team sports, which may inform tactics and influence pacing strategy.
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How Biomechanical Improvements in Running Economy Could Break the 2-hour Marathon Barrier
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A sub-2-hour marathon requires an average velocity (5.86 m/s) that is 2.5% faster than the current world record of 02:02:57 (5.72 m/s) and could be accomplished with a 2.7% reduction in the metabolic cost of running. Although supporting body weight comprises the majority of the metabolic cost of running, targeting the costs of forward propulsion and leg swing are the most promising strategies for reducing the metabolic cost of running and thus improving marathon running performance. Here, we calculate how much time could be saved by taking advantage of unconventional drafting strategies, a consistent tailwind, a downhill course, and specific running shoe design features while staying within the current International Association of Athletic Federations regulations for record purposes. Specifically, running in shoes that are 100 g lighter along with second-half scenarios of four runners alternately leading and drafting, or a tailwind of 6.0 m/s, combined with a 42-m elevation drop could result in a time well below the 2-hour marathon barrier.
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Critical Power: An Important Fatigue Threshold in Exercise Physiology
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  • Mar 2016
The hyperbolic form of the power-duration relationship is rigorous and highly conserved across species, forms of exercise and individual muscles/muscle groups. For modalities such as cycling, the relationship resolves to two parameters, the asymptote for power (critical power, CP) and the so-called W' (work doable above CP), which together predict the tolerable duration of exercise above CP. Crucially, the CP concept integrates sentinel physiological profiles - respiratory, metabolic and contractile - within a coherent framework that has great scientific and practical utility. Rather than calibrating equivalent exercise intensities relative to metabolically distant parameters such as the lactate threshold or V˙O2 max, setting the exercise intensity relative to CP unifies the profile of systemic and intramuscular responses and, if greater than CP, predicts the tolerable duration of exercise until W' is expended, V˙O2 max is attained, and intolerance is manifested. CP may be regarded as a 'fatigue threshold' in the sense that it separates exercise intensity domains within which the physiological responses to exercise can (<CP) or cannot (>CP) be stabilized. The CP concept therefore enables important insights into 1) the principal loci of fatigue development (central vs. peripheral) at different intensities of exercise, and 2) mechanisms of cardiovascular and metabolic control and their modulation by factors such as O2 delivery. Practically, the CP concept has great potential application in optimizing athletic training programs and performance as well as improving the life quality for individuals enduring chronic disease.
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Critical Power: Implications for the Determination of VO2max and Exercise Tolerance.
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  • Oct 2010
For high-intensity muscular exercise, the time-to-exhaustion (t) increases as a predictable and hyperbolic function of decreasing power (P) or velocity (V). This relationship is highly conserved across diverse species and different modes of exercise and is well described by two parameters: the 'critical power' (CP or CV), which is the asymptote for power or velocity, and the curvature constant (W') of the relationship such that t = W'/(P-CP). CP represents the highest rate of energy transduction (oxidative ATP production, V? O2) that can be sustained without continuously drawing on the energy store W' (composed in part of anaerobic energy sources and expressed in kilojoules). The limit of tolerance (time t) occurs when W' is depleted. The CP concept constitutes a practical framework in which to explore mechanisms of fatigue and help resolve crucial questions regarding the plasticity of exercise performance and muscular systems physiology. This brief review presents the practical and theoretical foundations for the CP concept, explores rigorous alternative mathematical approaches, and highlights exciting new evidence regarding its mechanistic bases and its broad applicability to human athletic performance.
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Factors affecting the energy cost of level running at submaximal speed
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  • Feb 2015
Metabolic measurement is still the criterion for investigation of the efficiency of mechanical work and for analysis of endurance performance in running. Metabolic demand may be expressed either as the energy spent per unit distance (energy cost of running, C r) or as energy demand at a given running speed (running economy). Systematic studies showed a range of costs of about 20 % between runners. Factors affecting C r include body dimensions: body mass and leg architecture, mostly calcaneal tuberosity length, responsible for 60–80 % of the variability. Children show a higher C r than adults. Higher resting metabolism and lower leg length/stature ratio are the main putative factors responsible for the difference. Elastic energy storage and reuse also contribute to the variability of C r. The increase in C r with increasing running speed due to increase in mechanical work is blunted till 6–7 m s−1 by the increase in vertical stiffness and the decrease in ground contact time. Fatigue induced by prolonged or intense running is associated with up to 10 % increased C r; the contribution of metabolic and biomechanical factors remains unclear. Women show a C r similar to men of similar body mass, despite differences in gait pattern. The superiority of black African runners is presumably related to their leg architecture and better elastic energy storage and reuse.
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Optimizing the Team for Required Power During Track Cycling Team Pursuit
Article
  • Mar 2017
Purpose: Since the aim of the men's team pursuit in time trial track cycling is to accomplish a distance of 4000m as fast as possible, optimizing aerodynamic drag can contribute to achieving this goal. The aim of this study is to determine the drafting effect in second, third and fourth position during the team pursuit in track cycling as a function of the team members' individual frontal areas in order to minimize the required power. Method: Eight experienced track cyclists of the Dutch national selection performed 39 trials of 3-km in different teams of four cyclists at a constant velocity of 15.75 m/s. Frontal projected areas were determined and together with field derived drag coefficients (Cd) for all four positions, the relationships between frontal areas of team members and drag fractions were estimated using Generalized Estimating Equations. Results: The frontal area (Ap) of both the cyclist directly in front of the drafter and the drafter himself turned out to be significant determinants of the drag fraction at the drafter's position (p<0.05), for all three drafting positions. Predicted required power for individuals in drafting positions differed up to 35 W depending on team composition. For a team, a maximal difference in team efficiency (1.2%) exists by selecting cyclists in a specific sequence. Conclusion: Estimating required power for a specific team composition gives insight into differences in team efficiency for the team pursuit. Furthermore, required power for individual team members ranges substantially depending on team composition.
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Thermoregulation and Marathon Running
Article
  • Aug 2001
The extreme physical endurance demands and varied environmental settings of marathon footraces have provided a unique opportunity to study the limits of human thermoregulation for more than a century. High post-race rectal temperatures (Tre) are commonly and consistently documented in marathon runners, yet a clear divergence of thought surrounds the cause for this observation. A close examination of the literature reveals that this phenomenon is commonly attributed to either biological (dehydration, metabolic rate, gender) or environmental factors. Marathon climatic conditions vary as much as their course topography and can change considerably from year to year and even from start to finish in the same race. The fact that climate can significantly limit temperature regulation and performance is evident from the direct relationship between heat casualties and Wet Bulb Globe Temperature (WBGT), as well as the inverse relationship between record setting race performances and ambient temperatures. However, the usual range of compensable racing environments actually appears to play more of an indirect role in predicting Tre by acting to modulate heat loss and fluid balance. The importance of fluid balance in thermoregulation is well established. Dehydration-mediated perturbations in blood volume and blood flow can compromise exercise heat loss and increase thermal strain. Although progressive dehydration reduces heat dissipation and increases Tre during exercise, the loss of plasma volume contributing to this effect is not always observed for prolonged running and may therefore complicate the predictive influence of dehydration on Tre for marathon running. Metabolic heat production consequent to muscle contraction creates an internal heat load proportional to exercise intensity. The correlation between running speed and Tre, especially over the final stages of a marathon event, is often significant but fails to reliably explain more than a fraction of the variability in post-marathon Tre. Additionally, the submaximal exercise intensities observed throughout 42km races suggest the need for other synergistic factors or circumstances in explaining this occurrence There is a paucity of research on women marathon runners. Some biological determinants of exercise thermoregulation, including body mass, surface area-to mass ratio, sweat rate, and menstrual cycle phase are gender-discrete variables with the potential to alter the exercise-thermoregulatory response to different environments, fluid intake, and exercise metabolism. However, these gender differences appear to be more quantitative than qualitative for most marathon road racing environments.
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Intramuscular determinants of the ability to recover work capacity above critical power
Article
  • Nov 2014
The primary purpose of this investigation was to compare the recovery of the W' to the recovery of intramuscular substrates and metabolites using (31)P- and (1)H-magnetic resonance spectroscopy. Ten healthy recreationally trained subjects were tested to determine critical power (CP) and W' for single-leg-extensor exercise. They subsequently exercised in the bore of a 1.5-T MRI scanner at a supra-CP work rate. Following exhaustion, the subjects rested in place for 1, 2, 5 or 7 min, and then repeated the effort. The temporal course of W' recovery was estimated, which was then compared to the recovery of creatine phosphate [PCr], pH, carnosine content, and to the output of a novel derivation of the W' BAL model. W' recovery closely correlated with the predictions of the novel model (r = 0.97, p = 0.03). [PCr] recovered faster [Formula: see text] than W' [Formula: see text] The W' available for the second exercise bout was directly correlated with the difference between [PCr] at the beginning of the work bout and [PCr] at exhaustion (r = 0.99, p = 0.005). Nonlinear regression revealed an inverse curvilinear relationship between carnosine concentration and the W' t 1/2 (r (2) = 0.55). The kinetics of W' recovery in single-leg-extensor exercise is comparable to that observed in whole-body exercise, suggesting a conserved mechanism. The extent to which the recovery of the W' can be directly attributed to the recovery of [PCr] is unclear. The relationship of the W' to muscle carnosine content suggests novel future avenues of investigation.
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