COMPARISON OF OPTIMIZATION FORMULATIONS TO DESIGN AN HYBRID RAILWAY POWER SUBSTATION

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Application of a force-velocity-endurance model to cycling, rowing and running locomotion.

International audienceIntroduction. The production of force during brief maximal effort is limited by a force-velocity relation-ship, which is characterized by a negative linear function and determined by the theoretical maximum force (F0)and velocity (V0) [1]. For longer efforts, the intensity-duration relationship has been described mathematicallyby an asymptotic decay function, with the critical intensity being the asymptote [3]. The force and velocityproduced during an exercise can be modified by changing the cadence during cycling, for example, which altersthe intensity-duration relationship [4]. As the effort is prolonged, changes in force and velocity capacities mayoccur differently. To account for the influence of the force-velocity and intensity relationships on each other, wedeveloped a three-dimensional model that describes the force production capacity as a function of velocity andtime, F (v, t). In addition, we designed a test to determine the F (v, t) relationship for an individual based on a3-min all-out interspersed with a stop-start sprint (IFLET test) [2]. The aim of this study was to evaluate theparameters of the F (v, t) relationship for various types of human locomotion (cycling, rowing and running) andto compare the parameters obtained for different populations based on their training status.Methods. The IFLET test was administered to 49 participants across cycling, rowing, and running. Dur-ing cycling, 21 moderately active individuals who were not cyclists (NC), 19 subelite trained cyclists (SC), andnine elite cyclists (EC) participated. Twelve elite rowers participated for the rowing task and 16 U21 eliterugby players participated for running locomotion. The test involved a 3- minute all-out effort, with conditionschanging every 30s to assess the force-velocity relationship at a specific point in time. During cycling, this wasachieved by suddenly blocking the flywheel, while in rowing, a motor replaced the flywheel and was controlledto produce varying force-velocity conditions. During running, the test was conducted in shuttle mode, whichrequired participants to start sprinting at zero speed. The force-velocity-time data recorded or computed duringthe various locomotions was fitted to the F (v, t) model’s parameters to obtain the initial force (F0i ), velocity(V0i ), critical force (F0c ), and velocity (V0c ) capacities, as well as the time constant (τ ).Results and discussion. The goodness of fit of the model from experimental data was excellent for alllocomotion (all r2 > 0.93). Considering the group effect for cycling task locomotion, no difference was observedfor V0c (NC : 58.9 ± 12.3 %; SC : 59.3 ± 9.7 %; EC: 55.7 ± 6.3 %). However, all groups were statisticallydifferent in terms of F0c (NC : 51.4 ± 11.2 %; SC : 64.2 ± 7.3 %; EC: 71.6 ± 10.4 %).Conclusions and perspectives. This is the first time a model has been developed that simultaneouslyconsiders both velocity and time to describe the force capacity. This model accurately fits the experimental dataobtained from the IFLET test, which is a 3-minute all-out sprint exercise interspersed with different locomotiontypes, such as running, cycling, or rowing. The applications of this approach are numerous and can be used inthe evaluation of physical capacities as well as for performance enhancement through training or optimizationof human-material interactions

Application of a force-velocity-endurance model to cycling, rowing and running locomotion.

International audienceIntroduction. The production of force during brief maximal effort is limited by a force-velocity relation-ship, which is characterized by a negative linear function and determined by the theoretical maximum force (F0)and velocity (V0) [1]. For longer efforts, the intensity-duration relationship has been described mathematicallyby an asymptotic decay function, with the critical intensity being the asymptote [3]. The force and velocityproduced during an exercise can be modified by changing the cadence during cycling, for example, which altersthe intensity-duration relationship [4]. As the effort is prolonged, changes in force and velocity capacities mayoccur differently. To account for the influence of the force-velocity and intensity relationships on each other, wedeveloped a three-dimensional model that describes the force production capacity as a function of velocity andtime, F (v, t). In addition, we designed a test to determine the F (v, t) relationship for an individual based on a3-min all-out interspersed with a stop-start sprint (IFLET test) [2]. The aim of this study was to evaluate theparameters of the F (v, t) relationship for various types of human locomotion (cycling, rowing and running) andto compare the parameters obtained for different populations based on their training status.Methods. The IFLET test was administered to 49 participants across cycling, rowing, and running. Dur-ing cycling, 21 moderately active individuals who were not cyclists (NC), 19 subelite trained cyclists (SC), andnine elite cyclists (EC) participated. Twelve elite rowers participated for the rowing task and 16 U21 eliterugby players participated for running locomotion. The test involved a 3- minute all-out effort, with conditionschanging every 30s to assess the force-velocity relationship at a specific point in time. During cycling, this wasachieved by suddenly blocking the flywheel, while in rowing, a motor replaced the flywheel and was controlledto produce varying force-velocity conditions. During running, the test was conducted in shuttle mode, whichrequired participants to start sprinting at zero speed. The force-velocity-time data recorded or computed duringthe various locomotions was fitted to the F (v, t) model’s parameters to obtain the initial force (F0i ), velocity(V0i ), critical force (F0c ), and velocity (V0c ) capacities, as well as the time constant (τ ).Results and discussion. The goodness of fit of the model from experimental data was excellent for alllocomotion (all r2 > 0.93). Considering the group effect for cycling task locomotion, no difference was observedfor V0c (NC : 58.9 ± 12.3 %; SC : 59.3 ± 9.7 %; EC: 55.7 ± 6.3 %). However, all groups were statisticallydifferent in terms of F0c (NC : 51.4 ± 11.2 %; SC : 64.2 ± 7.3 %; EC: 71.6 ± 10.4 %).Conclusions and perspectives. This is the first time a model has been developed that simultaneouslyconsiders both velocity and time to describe the force capacity. This model accurately fits the experimental dataobtained from the IFLET test, which is a 3-minute all-out sprint exercise interspersed with different locomotiontypes, such as running, cycling, or rowing. The applications of this approach are numerous and can be used inthe evaluation of physical capacities as well as for performance enhancement through training or optimizationof human-material interactions