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Optimized Pacing Strategies in Cross-Country Skiing and Time-Trial Road Cycling
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics. (Sportstech)ORCID iD: 0000-0003-1324-9828
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is devoted to the analysis and optimization of pacing strategies in cross-country skiing and time-trial road cycling. In locomotive sports, it is well known that variable pacing strategies using changes in the distribution of power output are beneficial when external forces vary along the way. However, there is a lack of research that more in detail investigates the magnitude of power output alteration necessary to optimize performance.A numerical program has been developed in the MATLAB software to simulate cross-country skiing and time-trial road cycling, as well as pacing strategy optimization in these two locomotive sports. The simulations in this thesis are performed by solving equations of motion, where all the main forces acting on the athlete are considered. The motion equations also depend on the course profile, which is expressed as a connected chain of cubical splines.The simulation process is linked to an optimization routine called the Method of Moving Asymptotes (MMA), which strives to minimize the finishing time while altering the power output along the course. To mimic the human energetic system, the optimization is restricted by behavioural and side constraints.Simple constraints like maximum average power output are used for cross-country skiing in Papers I and II. In Paper III a more sophisticated and realistic constraint is used for the power output in time-trial road cycling. It is named the concept of critical power for intermittent exercise and combines the aerobic and anaerobic contributions to power output.In conclusion, this thesis has demonstrated the feasibility of using numerical simulation and optimization in order to optimize pacing strategies in two locomotive sports. The results are clearly showing that these optimized pacing strategies are more beneficial to performance than an even distribution of power output.

Abstract [sv]

Denna avhandling är dedikerad att analysera och optimera farthållningsstrategier i längdskidåkning och tempocykling på landsväg. I idrotter som bygger på kontinuerlig framåtdrivning är det väl känt att farthållningsstrategier med variabel effekt är fördelaktiga om de yttre krafterna varierar längs banan. Ändå saknas forskning som mer i detalj utreder hur mycket effekten ska variera för att optimera prestationen.Ett numeriskt program har utvecklats i programvaran MATLAB för att simulera längdskidåkning och tempocykling samt optimera farthållningsstrategin i dessa idrotter. Simuleringarna använder sig av rörelseekvationer som består av de huvudsakliga krafter som verkar på idrottsutövaren under färd. Rörelseekvationerna påverkas också av banprofilen, som är uppbyggd av en sammankopplad kedja av tredjegradspolynom.Simuleringsprogrammet är kopplat till en optimeringsalgoritm med namnet Method of Moving Asyptotes (MMA), som strävar efter att minimera tiden mellan start och mål genom att ändra effekten längs med banan. Optimeringen begränsas av bivillkor i ett försök att efterlikna den mänskliga kroppens fysiologiska begränsningar.Enkla begränsningar såsom maximal medeleffekt används för längdskidåkningen i artikel I och II. I artikel III används mer sofistikerade och realistiska bivillkor för att begränsa uteffekten vid landsvägscykling. Här används modellen för kritisk effekt vid intervallträning, som kombinerar aerobt och anaerobt arbete.Sammanfattningsvis har denna avhandling visat på möjligheterna med att använda numerisk simulering och optimering för att optimera farthållningsstrategin i två idrotter. Resultaten visar tydligt att dessa optimerade farthållningsstrategier med varierande effekt är mer fördelaktiga för prestationen jämfört med en farthållningsstrategi med helt jämn effektfördelning.

Place, publisher, year, edition, pages
Östersund: Mid Sweden University , 2013. , 34 p.
Series
Mid Sweden University licentiate thesis, ISSN 1652-8948 ; 95
Keyword [en]
Optimization, numerical simulation, equations of motion, MMA, cross-country skiing, cycling
Keyword [sv]
Optimering, numerisk simulering, rörelseekvationer, MMA, längdskidåkning, cykling
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:miun:diva-18634ISBN: 978-91-87103-59-9 (print)OAI: oai:DiVA.org:miun-18634DiVA: diva2:612610
Presentation
2013-03-06, Q221, Akademigatan 1, Östersund, 14:33 (Swedish)
Opponent
Supervisors
Available from: 2013-03-25 Created: 2013-03-22 Last updated: 2014-02-03Bibliographically approved
List of papers
1. Optimizing pacing strategies on a hilly track in cross-country skiing
Open this publication in new window or tab >>Optimizing pacing strategies on a hilly track in cross-country skiing
2011 (English)In: Procedia Engineering, Elsevier, 2011, Vol. 13, 10-16 p.Conference paper, (Refereed)
Abstract [en]

During events involving locomotive exercise, such as cross-country skiing, it is believed that pacing strategies (i.e. power distribution) have a significant impact on performance. Therefore, a program was developed for the numerical simulation and optimization of cross-country ski racing, one that numerically computes the optimal pacing strategy for a continuous track. The track is modelled by a set of cubic splines in two dimensions and can be used to simulate a closed loop track or one with the start and finish at different locations. For an arbitrary point on the two dimensional track, equations of motion are formulated parallel and normal to the track, considering the actual slope and curvature of the track. Forces considered at the studied point are the gravitational force, the normal force between snow and skis, the drag force from the wind, the frictional force between snow and ski and the propulsive force from the skier, where the latter is expressed as the available power divided by the actual speed. The differential equations of motion are solved from start to finish using the Runge-Kutta-Fehlberg method. The optimization of the ski race is carried out with the Method of Moving Asymptotes (MMA) which minimizes the racing time by choosing the optimum distribution of available power. Constraints for minimum, maximum and average power are decided by conditions of scaling by body size. Results from a simulated ski competition with optimized power distribution on a real track are presented.

Place, publisher, year, edition, pages
Elsevier, 2011
Series
Procedia engineering, ISSN 1877-7058 ; 13
Keyword
Cross-country skiing, Numerical simulation, Optimization, Splines
National Category
Engineering and Technology
Identifiers
urn:nbn:se:miun:diva-15364 (URN)10.1016/j.proeng.2011.05.044 (DOI)000300214900002 ()2-s2.0-80051639016 (Scopus ID)
Conference
5th Asia-Pacific Congress on Sports Technology: Impact of Technology on Sport IV, APCST; Melbourne, VIC; 28 August 2011 through 31 August 2011
Available from: 2011-12-18 Created: 2011-12-18 Last updated: 2016-12-16Bibliographically approved
2. Numerical optimization of pacing strategy in cross-country skiing
Open this publication in new window or tab >>Numerical optimization of pacing strategy in cross-country skiing
2013 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 47, no 6, 943-950 p.Article in journal (Refereed) Published
Abstract [en]

When studying events involving locomotive exercise,such as cross-country skiing, one generally assumesthat pacing strategies (i.e. power distributions) have a significantimpact on performance. In order to better understandthe importance of pacing strategies, a program isdeveloped for numerical simulation and optimization of thepacing strategy in cross-country ski racing. This programcomputes the optimal pacing strategy for an arbitrary athleteskiing on a delineated course. The locomotion of theskier is described by introducing the equations of motionfor cross-country skiing. A transformation of the motionequations is carried out in order to improve the simulation. Furthermore, a nonlinear optimization routine is connectedto the simulation program. Simulation and optimization areperformed on a fictional male skier. Results show that it ispossible to attain an optimal pacing strategy by simulatingcross-country skiing while connecting nonlinear optimizationroutines to the simulation. It is also shown that an optimalpacing strategy is characterized by minor variations inspeed. In our opinion, this kind of optimization could serveas essential preparations before important competitions.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2013
Keyword
Optimization, Numerical simulation, Cross-country skiing, Pacing strategy, Power distribution
National Category
Applied Mechanics
Identifiers
urn:nbn:se:miun:diva-17529 (URN)10.1007/s00158-012-0856-7 (DOI)000318624100012 ()2-s2.0-84879103889 (Scopus ID)
Projects
Sportstech 2
Available from: 2012-12-04 Created: 2012-11-30 Last updated: 2016-01-26Bibliographically approved

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