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  • 1.
    Björklund, Glenn
    et al.
    Mid Sweden University, Faculty of Human Sciences, Department of Health Sciences.
    Danvind, Jonas
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Management and Mechanical Engineering.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Management and Mechanical Engineering.
    The effect of speed and gradient on running economy and oxygen uptake during downhill running2019Conference paper (Refereed)
    Abstract [en]

    Downhill running poses challenges were the gradient is of importance for energy cost and oxygen uptake. While demonstrated that downhill running at a slight gradient is most efficient, the energy cost increases with a steeper gradient (1). However, the additional effect of running speed has not been studied for downhill running. Therefore, the aim of the study was to analyse the combined effect of gradient and speed in downhill running on oxygen cost and running economy. METHODS:Runners (n=6) were recruited for the study and performed 1) VO2max and running economy (J·kg-1·m-1) tests and 2) an experimental running protocol at two speeds,12 km·h-1 and 80% of the speed at VO2max (V80) and three gradients (0, -5° and -10°). V80 was higher than 12 km·h-1 for all participants. All testing was performed on a large treadmill 3x5 m (Rodby, Sweden) that were controlled for speed and gradient. The experimental protocol was performed continuously with 5 min at each workload in a randomized order, 30 min in total. VO2 was measured throughout the experimental protocol using a mixing chamber (Moxus Metabolic Cart, USA). RESULTS:VO2 expressed as ml·kg-1·min-1 increased because of speed (F1,5=27.8, p=0.003) and decreased with gradient (F1,5=87.6, p<0.001). Between -5° and -10°, VO2 decreased less during V80 compared to 12 km·h-1 shown by an interaction (F2,10=7.9, p=0.009). However, speed did not influence running economy (F1,5=0.9, p=0.38) while gradient increased running economy (F1,5=90.1, p<0.001). A non-significant interaction effect suggests a shift in running economy between -5° and -10° depending on speed (F2,10=3.5, p=0.07). The running economy at V80 was higher compared to 12 km·h-1 at -5° but reversed at -10°. While a relation between running economy at V80 -10°, V80 -5° and 12 km·h-1 -10° (rs>0.88, p<0.019) was found, no relations between running economy on level terrain and steep downhill running (-10°) were recognised. CONCLUSION:While we found no effect on running economy from speed alone, we did see a shift in the running economy for different speeds at an increased downhill gradient. This indicates that a high speed (V80) is more efficient at moderate downhill gradients, while a lower speed (12 km·h-1) is more efficient in steeper downhill gradients. While previous research demonstrate that gradient is of great influence to running economy, the findings of this study suggest that speed also affects the running economy in downhill running.

  • 2.
    Bäckström, Mikael
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Danvind, Jonas
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Koptioug, Andrei
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    A New Wind Tunnel Facility Dedicated to Sports Technology Research and Development2016In: Procedia Engineering, Elsevier, 2016, Vol. 147, p. 62-67Conference paper (Refereed)
    Abstract [en]

    It is desirable to test sportswear and sports equipment at exactly the same conditions experienced during use. Although outdoor tests are in many cases the most adequate, they are at the same time quite complex, demand special measurement technology and wearable equipment. Results of such tests are often hard to interpret due to large variations because of rapidly varying ambient conditions and individual specifics of human objects, among other factors, which are hard or impossible to control. One common alternative is provided through indoor tests made in a stable, controlled environment. Controlling such parameters as temperature, wind speed and direction, air humidity with indoor facilities intended to replicate ambient conditions, and designed to house large objects, is a complex undertaking. Furthermore, replicating seasonal conditions complicates matters even more. A significant amount of research and development related to the operation of sports and other related equipment at high speeds and windy conditions has been carried out in wind tunnels with different degrees of climatic realism. However, the majority of such facilities are designed and constructed for the automotive industry, the aerospace industry and for marine research. A new wind tunnel facility, opened in March 2015 at the Sports Tech Research Centre at Mid Sweden University, is currently among the very few facilities in the world designed under the direct control of sports technology specialists and dedicated primarily to research and development within sports, outdoor clothing and footwear as well as equipment development and testing. The main goal when constructing this dedicated facility has been to successfully replicate ambient conditions for training and equipment testing in environments with controlled wind speed, temperature (+4 to +35°C) and precipitation (from fine mist to heavy downfall). The wind tunnel facility houses the largest moving belt in Sweden (5 m long and 2.7 m wide) which can be adjusted for leveled, uphill and downhill motion. The moving belt is placed in a 10 m2 test section in which the wind speed can be adjusted to match belt speed or independently up to 55 km/h (without narrowing the test section). A fog and rain system, mounted in the test section, can generate rainy conditions varying from fine mist to heavy monsoon. It is also possible to open the facility in order to allow experiments to be performed in wide range of outdoor, ambient conditions. This paper presents the basic parameters of the new wind tunnel facility. As this facility is open for wider international cooperation, we also report the general directions of current research and the future work planned to be carried out at this facility.

  • 3.
    Carlsson, Peter
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Ainegren, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Esping, Björn
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Koptioug, Andrey
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Bäckström, Mikael
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Cross-Country Ski2015In: The Engineering Approach to Winter Sports / [ed] Braghin F., Cheli F., Maldifassi S., Melzi S. and Sabbioni E., Springer, 2015, p. 107-152Chapter in book (Other academic)
    Abstract [en]

    Cross-country skiing, biathlon and ski orienteering are competitive sports with practitioners who are mostly from countries in the northern hemisphere. The competition season is during the time when the ground is covered with snow, which roughly extends from mid-November to late March. During the rest time of the year, which is a long preparatory period of training for the skiers before the competition season, the skiers use roller skis for dryland training with the aim of imitating skiing on snow. Furthermore, over the last few decades, fairly specific indoor testing methods for cross-country skiers have become possible due to the development of treadmills that allow roller skiing using classical and freestyle techniques.

  • 4.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Anpassa farten för snabbare tider2016In: Svensk Idrottsforskning: Organ för Centrum för Idrottsforskning, ISSN 1103-4629Article in journal (Other (popular science, discussion, etc.))
  • 5.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Numerical optimization of pacing strategies in locomotive endurance sports2016Doctoral 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.

  • 6.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    On a bioenergetic four compartment model for human exercise2016In: Sports Engineering, ISSN 1369-7072, E-ISSN 1460-2687, Vol. 19, no 4, p. 251-263Article in journal (Refereed)
    Abstract [en]

    Bioenergetic models for exercise performance simulations and pacing strategy optimizations currently lag behind empirical knowledge in human bioenergetics. Therefore, the objective of this study was the construction of a four compartment bioenergetic model that incorporates separate oxidative phosphorylation of lipids and carbohydrates and describes the regulation of these energy substrates’ utilization. Furthermore, the aim was also to model efficiency and the impact of muscle fatigue and the force-velocity relationship on the maximal attainable rate of energy expenditure. The model was formulated with five systems of differential equations that regulated the fluid levels in three of the compartments, while the lipid compartment energy was kept constant. Regulations had to be imposed on the system of compartments to achieve the desired carbohydrate dependent functionality and efficiency of the model. Equilibrium equations were modeled for the alactic compound composition and a constraint was modeled for the maximal energy expenditure rate, dependent on the intramuscular inorganic phosphate. A separate force-velocity relationship was modeled to constrain power output at low speeds and efficiency was modeled with a linear but off-set relationship between power output and rate of energy expenditure. The relative aerobic contribution to total energy expenditure showed good congruence with empirical results, while time to exhaustion was overestimated due to the constraint on maximal rate of energy expenditure. Therefore, further experimental studies are necessary for complete validation of the model.

  • 7.
    Sundström, David
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Optimized Pacing Strategies in Cross-Country Skiing and Time-Trial Road Cycling2013Licentiate 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.

  • 8.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Bäckström, Mikael
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Optimization of pacing strategies for variable wind conditions in road cycling2017In: Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, ISSN 1754-3371, Vol. 231, no 3, p. 184-199Article in journal (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.

  • 9.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Bäckström, Mikael
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    A four compartment model on human exercise bioenergetics2015In: Procedia Engineering / [ed] A. Subic, F.K. Fuss, F. Alam, T.Y. Pang and M. Takla, Elsevier, 2015, Vol. 112, p. 4-9Conference paper (Refereed)
    Abstract [en]

    Performance in endurance sports depends on the athlete's ability to generate power output through muscle contraction. The energy requirements of muscles are satisfied by the alactic and lactic bioenergetic pathways, working anaerobically, and the aerobic oxidative phosphorylation of fats and carbohydrates. The aim of this study was to apply further extensions to hydraulic bioenergetic modelling to better describe the regulation of oxidative fuel selection. For this reason, a four compartment bioenergetic model was introduced and regulation of fat and carbohydrate oxidation was implemented. Further regulation was applied to both oxidative fuel selection and anaerobic glycolysis to depend on the current carbohydrate store. The model was formulated mathematically as differential equations, which were solved numerically to perform simulations of human bioenergetics in exercise. Simulation results showed good consistency with experimental findings.

  • 10.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Bäckström, Mikael
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Optimal distribution of power output and braking for corners in road cycling2015Conference paper (Refereed)
  • 11.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Management and Mechanical Engineering.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Management and Mechanical Engineering.
    Andersson, Erik
    Mid Sweden University, Faculty of Human Sciences, Department of Health Sciences.
    Comparison of Power Output Estimates in Treadmill Roller-Skiing2018In: Proceedings / [ed] Hugo G. Espinosa, David R. Rowlands, Jonathan Shepherd and David V. Thiel, Basel: MDPI AG , 2018, Vol. 2, article id 312Conference paper (Refereed)
    Abstract [en]

    The purpose of this study was to evaluate and compare various power output estimates and estimate anaerobic energy supply during treadmill roller-skiing. Roller-skiing sprint time-trial performance on a treadmill was compared to numerical simulations of three different power output estimates; non-inertial power estimate (NIP), inertial power estimate (IP), and optimization power estimate (OP). The OP was in best agreement with the measured speed of the skier. However, the IP was in better agreement with the measured finishing time of the real time trial, which may suggest that the IP better approximated the mean power than the other two estimates. Moreover, the NIP and IP are more simplistic than the OP and thereby more practical from a scientific standpoint. Based on this we recommend the use of the IP estimate.

  • 12.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Ståhl, Fredrik
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Numerical optimization of pacing strategy in cross-country skiing2013In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 47, no 6, p. 943-950Article in journal (Refereed)
    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.

  • 13.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Comparing bioenergetic models for the optimisation of pacing strategy in road cycling2014In: Sports Engineering, ISSN 1369-7072, E-ISSN 1460-2687, Vol. 17, no 4, p. 207-215Article in journal (Refereed)
    Abstract [en]

    Road cycling performance is dependent on race tactics and pacing strategy. To optimise the pacing strategy for any race performed with no drafting, a numerical model was introduced, one that solves equations of motion while minimising the finishing time by varying the power output along the course. The power output was constrained by two different hydraulic models: the simpler critical power model for intermittent exercise (CPIE) and the more sophisticated Margaria–Morton model (M–M). These were compared with a constant power strategy (CPS). The simulation of the three different models was carried out on a fictional 75 kg cyclist, riding a 2,000 m course. This resulted in finishing times of 162.4, 155.8 and 159.3 s and speed variances of 0.58, 0.26 and 0.29 % for the CPS, CPIE and M–M simulations, respectively. Furthermore, the average power output was 469.7, 469.7 and 469.1 W for the CPS, CPIE and M–M simulations, respectively. The M–M model takes more physiological phenomena into consideration compared to the CPIE model and, therefore, contributes to an optimised pacing strategy that is more realistic. Therefore, the M–M model might be more suitable for future studies on optimal pacing strategy, despite the relatively slower finishing time.

  • 14.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    On Optimization of Pacing Strategy in Road Cycling2013In: 6TH ASIA-PACIFIC CONGRESS ON SPORTS TECHNOLOGY (APCST), Melbourne: Elsevier, 2013, p. 118-123Conference paper (Refereed)
    Abstract [en]

    The wide-spread use of power-meters in today’s competitive road cycling has been an incentive for optimizing the distribution of power output i.e. the pacing strategy. Therefore, the aim of this study was to examine the effects of course profile on the optimal pacing strategy in road cycling. For that reason, three course profiles, built up by cubical splines, were simulated with a numerical program for a fictional cyclist. The numerical program solves the equations of motion of the athlete and bicycle while an optimal design algorithm is connected to the simulation, aiming to minimize the time between start and finish. The optimization is constrained by a power-endurance concept named the critical power model for intermittent exercise. Three course profiles with the same total elevation but different number of hills were studied. The time gains of an optimized pacing strategy were 3.0%, 5.0%, and 2.3% and the speed variances at the optimized pacing strategy were 6.54%, 1.18%, and 0.84% for the single plateau, double hill, and quadruple hill courses respectively. Hence, the course profile has great effect on the optimal pacing strategy. In addition, the results show that the potential improvement of adopting an optimized pacing strategy is substantial at the highest level of competition.

  • 15.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Optimizing pacing strategies on a hilly track in cross-country skiing2011In: Procedia Engineering, Elsevier, 2011, Vol. 13, p. 10-16Conference 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.

  • 16.
    Sundström, David
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Tinnsten, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    Carlsson, Peter
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.
    The influence of course bends on pacing strategy in road cycling2014In: Conference Proceedings of The Engineering of Sport 10 / [ed] David James, Simon Choppin, Tom Allen, Jon Wheat, Paul Fleming, Elsevier, 2014, p. 835-840Conference 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.

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