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The influence of course bends on pacing strategy in road cycling
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Sportteknologi)ORCID iD: 0000-0003-1324-9828
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Sportteknologi)
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Sportteknologi)
2014 (English)In: Conference Proceedings of The Engineering of Sport 10 / [ed] David James, Simon Choppin, Tom Allen, Jon Wheat, Paul Fleming, Elsevier, 2014, 835-840 p.Conference paper, Published paper (Refereed)
Abstract [en]

Road cycling races in general, but particularly criteriums (short circuit race), have a considerable number of bends along the race course. Sharp bends force the rider to decelerate in order to retain the grip between the tires and the road. This study focused on how these course bends influence the optimal pacing strategy in road cycling. For this purpose, we used a numerical model that simulates cycling by solving the equation of motion. The optimisation was carried out with the Method of Moving Asymptotes, constrained with the Margaria-Morton model for human energetics and a separate course bend constraint. The results showed that sharp course bends greatly affect the pacing strategy and finishing time. The average power output and the average speed decreased with a decrease in the curve radius. Moreover, the kinetic energy lost due to braking in sharp course bends is likely to be the crucial mechanism affecting the finishing time. Therefore, we believe that the outcome of races that contain sharp bends may be strongly dependent on the athlete’s pacing strategy.

Place, publisher, year, edition, pages
Elsevier, 2014. 835-840 p.
Series
Procedia Engineering, ISSN 1877-7058 ; 72
Keyword [en]
Pacing strategy; power distribution; cycling; bend; performance; optimisation
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:miun:diva-22843DOI: 10.1016/j.proeng.2014.06.141ISI: 000346367700140Scopus ID: 2-s2.0-84903794163OAI: oai:DiVA.org:miun-22843DiVA: diva2:745134
Conference
The 2014 Conference of the International Sports Engineering Association
Available from: 2014-09-09 Created: 2014-09-09 Last updated: 2016-01-26Bibliographically approved
In thesis
1. Numerical optimization of pacing strategies in locomotive endurance sports
Open this publication in new window or tab >>Numerical optimization of pacing strategies in locomotive endurance sports
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is devoted to the optimization of pacing strategies in two locomotive endurance sports; cross-country skiing and road cycling. It has been established that constant pace and variable power distributions are optimal if purely mechanical aspects of locomotion are considered in these sports. However, there is a lack of research that theoretically investigates optimal pacing for real world athletes who are constrained in their ability to generate power output through the bioenergetics of the human body.

The aims of this thesis are to develop numerical pacing strategy optimization models and bioenergetic models for locomotive endurance sports and use these to assess objectives relevant in optimal pacing. These objectives include: Investigate the impact of hills, sharp course bends, ambient wind, and bioenergetic models on optimal pacing and assess the effect of optimal pacing strategies on performance.

This thesis presents mathematical models for optimization of pacing strategies. These models are divided into mechanical locomotion, bioenergetic, and optimization models that are connected and programmed numerically. The locomotion and bioenergetic models in this thesis consist of differential equations and the optimization model is described by an iterative gradient-based routine. The mechanical model describes the relation between the power output generated by an athlete and his/her locomotion along a course profile, giving the finishing time. The bioenergetic model strives to mimic the human ability to generate power output. Therefore, the bioenergetic model is set to constrain the power output that is used in the mechanical locomotion model. The optimization routine strives to minimize the finishing time in the mechanical locomotion model by varying the distribution of power output along the course, still satisfying the constraints in the bioenergetic model.

The studies contained within this thesis resulted in several important findings regarding the general application of pacing strategies in cross-country skiing and road cycling. It was shown that the constant pace strategy is not optimal if ambient conditions change over the course distance. However, variable power distributions were shown beneficial if they vary in parallel with course inclination and ambient winds to decrease variations in speed. Despite these power variations, speed variations were not eliminated for most variable ambient conditions. This relates to the athlete’s physiological restrictions and the effect of these are hard to predict without thorough modeling of bioenergetics and muscle fatigue. Furthermore, it vi

was shown that substantial differences in optimal power distributions were attained for various bioenergetic models.

It was also shown that optimal braking and power output distributions for cycling on courses that involve sharp bends consisted of three or four phases, depending on the length of the course and the position of the bends. The four phases distinguished for reasonably long courses were a steady-state power phase, a rolling phase, a braking phase, and an all-out acceleration phase. It was also shown that positive pacing strategies are optimal on relatively long courses in road cycling where the supply of carbohydrates are limited. Finally, results indicated that optimal pacing may overlook the effect of some ambient conditions in favor of other more influential, mechanical or physiological, aspects of locomotion.

In summary, the results showed that athletes benefit from adapting their power output with respect not only to changing course gradients and ambient winds, but also to their own physiological and biomechanical abilities, course length, and obstacles such as course bends. The results of this thesis also showed that the computed optimal pacing strategies were more beneficial for performance than a constant power distribution. In conclusion, this thesis demonstrates the feasibility of using numerical simulation and optimization to optimize pacing strategies in cross-country skiing and road cycling.

Abstract [sv]

Avhandlingen handlar om optimering av farthållningsstrategier inom längdskidåkning och landsvägscykling. Det finns ett utbrett stöd för att konstant fart och varierande effektfördelningar är optimala om endast mekaniska aspekter beaktas i dessa sporter. Ändå saknas teoretiska studier som undersöker optimal farthållning för verkliga idrottsutövare som är begränsade i sin förmåga att generera effekt genom kroppens bioenergetiska system.

Målen med den här avhandlingen är att utveckla metoder för bioenergetik och optimering av farthållningsstrategier i uthållighetsidrott. Dessutom är målet att undersöka påverkan av backar, svängar, omgivande vind och bioenergetisk modellering på den optimala farthållningsstrategin samt att utreda potentialen till prestationsförbättring med optimala farthållningsstrategier.

Avhandling presenterar matematiska modeller för optimering av farthållningsstrategier. Dessa modeller delas in i en mekanisk modell för förflyttning, en bioenergetisk modell och en optimeringsmodell. De mekaniska och bioenergetiska modellerna som presenteras i avhandlingen består av differentialekvation och optimeringsmodellen utgörs av en gradient-baserad algoritm. Den mekaniska modellen beskriver förhållandet mellan utövarens effekt och den resulterande rörelsen längs banan som ger tiden mellan start och mål. Den bioenergetiska modellen beskriver människokroppens olika energisystem och dess begränsningar att generera effekt. Den bioenergetiska modellen interagerar med optimeringsmodellen genom att utgöra dess begränsningar för vad den mänskliga kroppen klarar av. Sammanfattningsvis försöker optimeringsmodellen minimera tiden mellan start och mål i den mekaniska modellen genom att variera effekten längs banan. Samtidigt ser optimeringsmetoden till att denna effektfördelning inte kränker den bioenergetiska modellen.

Studierna som ingår i avhandlingen resulterade i flera viktiga upptäckter om generella tillämpningar av farthållningsstrategier inom längdskidåkning och landsvägscykling. Det visade sig att konstant fart inte är optimalt om omgivande betingelser varierade längs banans sträckning. Däremot var varierande effektfördelning fördelaktig om den varierar parallellt med banlutning och omgivande vindpåverkan för att minska fartens variationer. Trots denna variation, visade resultaten att fartvariationerna inte eliminerades helt. Detta har att göra med utövarens fysiologiska begränsningar, vars påverkan är svår att förutspå utan genomgående modellering av bioenergetik relaterat till muskeltrötthet. Dessutom viii

visade resultaten att olika bioenergetiska metoder gav upphov till betydande skillnader i de optimala farthållningsstrategierna.

Resultaten i avhandlingen visade också att optimal effektfördelning vid kurvtagning i landsvägscykling innehåller tre eller fyra faser. The fyra faser som var utmärkande på relativt långa banor var en tröskelfas, en rullfas, en bromsfas och en maximal accelerationsfas. Resultaten visar också att positiv farthållning är optimal på relativt långa banor i landsvägscykling där tillgången på kolhydrater är begränsad. Samtidigt visade resultaten på optimala farthållningsstrategier ibland att inverkan av omgivande betingelser förbisågs till fördel för med inflytelserika betingelser som påverkar framdrivningen.

Sammantaget visar resultaten i denna avhandling att utövare gagnas av att anpassa effekten med hänsyn till varierande terräng, omgivande vind, atletens egen fysiologiska och biomekaniska förmåga, banans längd och hinder såsom kurvor. Resultaten visar också att de optimala farthållningsstrategier med varierande effektfördelning som beräknats i denna avhandling förbättrar prestationen jämfört med konstanta effektfördelningar. Sammanfattningsvis visar denna avhandling på möjligheterna att använda numerisk simulering och optimering för att optimera farthållningsstrategier i längdskidåkning och landsvägscykling.

Place, publisher, year, edition, pages
Östersund: Mid Sweden University, 2016. 122 p.
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 237
Keyword
Pacing strategy, optimization, numerical simulation, equations of motion, method of moving asymptotes, cross-country skiing, cycling, Farthållningsstrategi, optimering, numerisk simulering, rörelseekvationer, method of moving asymptotes, längdskidåkning, cykling
National Category
Applied Mechanics
Identifiers
urn:nbn:se:miun:diva-26925 (URN)978-91-88025-51-7 (ISBN)
Public defence
2016-02-25, Q 221, Akademigatan 1, Östersund, 13:00 (English)
Opponent
Supervisors
Note

Vid tidpunkten för disputationen var följande delarbeten opublicerade: delarbete 5 accepterat, delarbete 6 manuskript.

At the time of the doctoral defence the following papers were unpublished: paper 5 accepted, paper 6 manuscript.

Available from: 2016-01-26 Created: 2016-01-25 Last updated: 2016-10-31Bibliographically approved

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