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Numerical optimization of pacing strategies for variable wind conditions in road cycling
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Sports Tech Research Centre)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.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

It has been shown theoretically that performance can be enhanced by varying power in parallel with variable ambient conditions. However, no theoretical model has considered aerobic substrate utilization dynamics, limited carbohydrate stores, force-velocity relationships, and proper efficiency modelling. Furthermore, no study has investigated optimal pacing for courses with continuously variable ambient wind directions. Therefore, the aim of this study was to develop a model for the optimization of pacing strategies in road cycling with an updated bioenergetics model. The purpose of this model was to optimize pacing strategies for courses with continuously variable wind directions on both short (2 km) and long (100 km) courses. For this purpose, a numerical model consisting of three sub-models was programmed into the MATLAB software. This model consisted of one mechanical simulation model for cycling locomotion, one bioenergetics model based on the Margaria-Morton-Sundström model, and the method of moving asymptotes for optimization of the pacing strategy. Results showed that by optimizing the pacing strategies, time gains of 4.9 and 5.7% were attained for the 2 km courses with and without an ambient wind of 5 m·s-1 respectively. The corresponding time gains for the 100 km courses were 1.4 and 2.0% with and without ambient wind respectively. The theoretical model in this study further resulted in all-out strategies for the flat 2 km courses with and without ambient wind. Moreover, the 100 km course without wind was met with a positive pacing strategy and the 100 km course with ambient wind was met with a compromise of positive pacing and variable power distribution in parallel with the variable ambient wind conditions. In conclusion, the model presented in this study performed more detailed bioenergetic simulations than previous pacing strategy optimization studies and this resulted in more detailed pacing strategies for long courses.

Keyword [en]
Pacing strategy, Differential equation, Power, Performance, Bioenergetics
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:miun:diva-26924OAI: oai:DiVA.org:miun-26924DiVA: diva2:897515
Available from: 2016-01-25 Created: 2016-01-25 Last updated: 2016-01-27Bibliographically 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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