A Novel Approach of Modelling and Predicting Track Cycling Sprint Performance

In cycling, performance models are used to investigate factors that determine performance and to optimise competition results. We present an innovative and easily applicable mathematical model describing time-resolved approaches for both the physical aspects of tractional resistance and the physiological side of propelling force generated by muscular activity and test its validity to reproduce and forecast time trials in track cycling. Six elite track cyclists completed a special preparation and two sprint time trials in an official velodrome under continuous measurement of crank force and cadence. Fatigue-free force-velocity profiles were calculated, and their fatigue-induced changes were determined by non-linear regression analysis using a monoexponential equation at a constant slope. Model parameters were calibrated based on pre-exercise performance testing and the first of the two time-trials and then used to predict the performance of the second sprint. Measured values for power output and cycling velocity were compared to the modelled data. The modelled results were highly correlated to the measured values (R2>0.99) without any difference between runs (p>0.05; d<0.1). Our mathematical model can accurately describe sprint track cycling time trial performance. It is simple enough to be used in practice yet sufficiently accurate to predict highly dynamic maximal sprint performances. It can be employed for the evaluation of completed runs, to forecast expected results with different setups, and to study various contributing factors and quantify their effect on sprint cycling performance

Modeling Optimal Cadence as a Function of Time during Maximal Sprint Exercises Can Improve Performance by Elite Track Cyclists

In track cycling sprint events, optimal cadence PRopt is a dynamic aspect of fatigue. It is currently unclear what cadence is optimal for an athlete’s performance in sprint races and how it can be calculated. We examined fatigue-induced changes in optimal cadence during a maximal sprint using a mathematical approach. Nine elite track cyclists completed a 6-s high-frequency pedaling test and a 60-s isokinetic all-out sprint on a bicycle ergometer with continuous monitoring of crank force and cadence. Fatigue-free force-velocity (F/v) and power-velocity (P/v) profiles were derived from both tests. The development of fatigue during the 60-s sprint was assessed by fixing the slope of the fatigue-free F/v profile. Fatigue-induced alterations in PRopt were determined by non-linear regression analysis using a mono-exponential equation at constant slope. The study revealed that PRopt at any instant during a 60-s maximal sprint can be estimated accurately using a mono-exponential equation. In an isokinetic mode, a mean PRopt can be identified that enables the athlete to generate the highest mean power output over the course of the effort. Adding the time domain to the fatigue-free F/v and P/v profiles allows time-dependent cycling power to be modelled independent of cadence

Experiments to enhance the effectiveness of riblet structures by introducing a lateral velocity component

Ribletstrukturen können den Reibungswiderstand in voll turbulenten Grenzschichten um bis zu 10% im Vergleich zu glatten Oberflächen senken. In der vorliegenden Arbeit wurde experimentell untersucht, ob durch zusätzliches Einbringen einer periodischen lateralen Geschwindigkeitskomponente ähnlich der über einer lateral oszillierenden Wand diese widerstandsvermindernde Eigenschaft weiter gesteigert werden kann. Die Lateralgeschwindigkeit wurde sowohl aktiv durch extern angetriebene, in Querrichtung um ihren Aufstandspunkt auf der Wand oszillierende Lamellen, als auch passiv durch Riblets mit in der Wandebene zickzack- oder sinusförmig gestalteten Rillentälern generiert. In einem ölgefüllten Strömungskanal wurden bei Reynoldszahlen zwischen 10.000 und 30.000 gleichzeitig die Widerstandskräfte an einer Ribletgeometrie und einer glatten Referenzoberfläche mit einer absoluten Messgenauigkeit von +/-0,003 tau_0 gemessen. Mit oszillierenden Lamellen und einem Verhältnis von Lamellenhöhe zu -abstand h/s=0,8 wurde bei Oszillation der Lamellen mit 0,5 Hz bis 4 Hz eine systematische Veränderung der Widerstandsverminderung beobachtet. Für einen dimensionslosen Lamellenabstand s^+=17 stimmt der Zusammenhang zwischen Oszillationsfrequenz und Änderung des Widerstandsverhaltens qualitativ mit DNS-Daten aus einem Partnerprojekt überein und die Widerstandsverminderung kann bei Oszillation mit einer Periodendauer T^+=100 von 1,4% für stillstehende Lamellen auf 2,7% verbessert werden. Die mit diesem rechteckigen Rillenquerschnitt erzielbare maximale Widerstandsverminderung wurde dabei nicht erhöht. Mit zickzackförmig ausgelenkten Trapezrillen und Querschnitten von h/s=0,3 und 0,9 wurde unter Variation der Amplitude eine im Vergleich zu geraden Rillen gleichen Querschnitts erhöhte Widerstandsverminderung gefunden, die günstigste Beeinflussung gelang dabei mit Amplituden a/s=0,9. Im Falle h/s=0,3 konnte die maximale Widerstandsverminderung der Ribletstrukturen von 6,3% für gerade Rillen auf 7,6% gesteigert werden. Die mit geraden Trapezrillen von h/s=0,5 erreichbare Senkung der Wandschubspannung um 8,1% wurde von keiner Oberfläche mit wellenförmigen Riblets übertroffen. Die gefundene günstige Konfiguration mit zickzackförmigen Rillen stellt jedoch eine mögliche Alternative dar, falls sich gerade Rillen mit h/s=0,5 im konkreten Anwendungsfall als schwierig realisierbar erweisen.Riblets are capable of reducing the skin friction in fully turbulent boundary layers by up to 10% compared to a smooth surface. In this work, experimental investigations were conducted to investigate wether those drag-reducing characteristics can be enhanced by introducing an additional periodic lateral velocity component similar to that generated by the oscillating wall technique. The lateral velocity component was induced actively by externally-driven oscillating lamellae, that tilt around their contact point to the wall in the lateral direction, as well as in a passive manner by riblets consisting of grooves arranged in a sinusoidal or zigzag pattern when viewed from above. In an oil-filled flow channel at Reynolds numbers between 10,000 and 30,000 the drag forces on a riblet test plate and a smooth reference surface were captured simultaneously with an absolute precision of +/-0.003 tau_0. With oscillating lamellae and a ratio of lamella height to spacing of h/s=0.8, a systematic modification of the drag reduction was observed for frequencies between 0.5 Hz and 4 Hz. For a non-dimensionalised lamella spacing s^+=17, the correlation of the oscillating frequency and its effect on the drag behaviour agrees qualitatively with DNS-data from a joint project and the drag reduction is enhanced from 1.4% for lamellae at rest to 2.7% when oscillating with a period T^+=100. The maximum drag reduction achievable with a rectangular riblet groove cross-section could not be improved. With trapezoidal riblet grooves laterally deflected in a zigzag pattern and cross-section shapes of h/s=0.3 and 0.9, an augmented drag reduction was found under a variation of the zigzag amplitude and the most beneficial manipulation was attained at amplitudes of a/s=0.9. In case of h/s=0.3, the maximum drag reduction of the riblet structures was improved from 6.3% for straight grooves to 7.6% for zigzag grooves. The drag reduction attainable with straight trapezoidal riblet grooves at h/s=0.5 of 8.1% was not exceeded by any test geometry with laterally deflected riblet grooves. The beneficial zigzag modification found is a possible option if in certain cases straight riblet grooves with h/s=0.5 are difficult to apply

A Novel Approach of Modelling and Predicting Track Cycling Sprint Performance

In cycling, performance models are used to investigate factors that determine performance and to optimise competition results. We present an innovative and easily applicable mathematical model describing time-resolved approaches for both the physical aspects of tractional resistance and the physiological side of propelling force generated by muscular activity and test its validity to reproduce and forecast time trials in track cycling. Six elite track cyclists completed a special preparation and two sprint time trials in an official velodrome under continuous measurement of crank force and cadence. Fatigue-free force-velocity profiles were calculated, and their fatigue-induced changes were determined by non-linear regression analysis using a monoexponential equation at a constant slope. Model parameters were calibrated based on pre-exercise performance testing and the first of the two time-trials and then used to predict the performance of the second sprint. Measured values for power output and cycling velocity were compared to the modelled data. The modelled results were highly correlated to the measured values (R2>0.99) without any difference between runs (p>0.05; d<0.1). Our mathematical model can accurately describe sprint track cycling time trial performance. It is simple enough to be used in practice yet sufficiently accurate to predict highly dynamic maximal sprint performances. It can be employed for the evaluation of completed runs, to forecast expected results with different setups, and to study various contributing factors and quantify their effect on sprint cycling performance

A Novel Approach of Modelling and Predicting Track Cycling Sprint Performance

In cycling, performance models are used to investigate factors that determine performance and to optimise competition results. We present an innovative and easily applicable mathematical model describing time-resolved approaches for both the physical aspects of tractional resistance and the physiological side of propelling force generated by muscular activity and test its validity to reproduce and forecast time trials in track cycling. Six elite track cyclists completed a special preparation and two sprint time trials in an official velodrome under continuous measurement of crank force and cadence. Fatigue-free force-velocity profiles were calculated, and their fatigue-induced changes were determined by non-linear regression analysis using a monoexponential equation at a constant slope. Model parameters were calibrated based on pre-exercise performance testing and the first of the two time-trials and then used to predict the performance of the second sprint. Measured values for power output and cycling velocity were compared to the modelled data. The modelled results were highly correlated to the measured values (R2>0.99) without any difference between runs (p>0.05; d<0.1). Our mathematical model can accurately describe sprint track cycling time trial performance. It is simple enough to be used in practice yet sufficiently accurate to predict highly dynamic maximal sprint performances. It can be employed for the evaluation of completed runs, to forecast expected results with different setups, and to study various contributing factors and quantify their effect on sprint cycling performance

A Novel Approach of Modelling and Predicting Track Cycling Sprint Performance

In cycling, performance models are used to investigate factors that determine performance and to optimise competition results. We present an innovative and easily applicable mathematical model describing time-resolved approaches for both the physical aspects of tractional resistance and the physiological side of propelling force generated by muscular activity and test its validity to reproduce and forecast time trials in track cycling. Six elite track cyclists completed a special preparation and two sprint time trials in an official velodrome under continuous measurement of crank force and cadence. Fatigue-free force-velocity profiles were calculated, and their fatigue-induced changes were determined by non-linear regression analysis using a monoexponential equation at a constant slope. Model parameters were calibrated based on pre-exercise performance testing and the first of the two time-trials and then used to predict the performance of the second sprint. Measured values for power output and cycling velocity were compared to the modelled data. The modelled results were highly correlated to the measured values (R2>0.99) without any difference between runs (p>0.05; d0.1). Our mathematical model can accurately describe sprint track cycling time trial performance. It is simple enough to be used in practice yet sufficiently accurate to predict highly dynamic maximal sprint performances. It can be employed for the evaluation of completed runs, to forecast expected results with different setups, and to study various contributing factors and quantify their effect on sprint cycling performance

Modeling Optimal Cadence as a Function of Time during Maximal Sprint Exercises Can Improve Performance by Elite Track Cyclists

In track cycling sprint events, optimal cadence PRopt is a dynamic aspect of fatigue. It is currently unclear what cadence is optimal for an athlete’s performance in sprint races and how it can be calculated. We examined fatigue-induced changes in optimal cadence during a maximal sprint using a mathematical approach. Nine elite track cyclists completed a 6-s high-frequency pedaling test and a 60-s isokinetic all-out sprint on a bicycle ergometer with continuous monitoring of crank force and cadence. Fatigue-free force-velocity (F/v) and power-velocity (P/v) profiles were derived from both tests. The development of fatigue during the 60-s sprint was assessed by fixing the slope of the fatigue-free F/v profile. Fatigue-induced alterations in PRopt were determined by non-linear regression analysis using a mono-exponential equation at constant slope. The study revealed that PRopt at any instant during a 60-s maximal sprint can be estimated accurately using a mono-exponential equation. In an isokinetic mode, a mean PRopt can be identified that enables the athlete to generate the highest mean power output over the course of the effort. Adding the time domain to the fatigue-free F/v and P/v profiles allows time-dependent cycling power to be modelled independent of cadence

Modeling Optimal Cadence as a Function of Time during Maximal Sprint Exercises Can Improve Performance by Elite Track Cyclists

In track cycling sprint events, optimal cadence PRopt is a dynamic aspect of fatigue. It is currently unclear what cadence is optimal for an athlete’s performance in sprint races and how it can be calculated. We examined fatigue-induced changes in optimal cadence during a maximal sprint using a mathematical approach. Nine elite track cyclists completed a 6-s high-frequency pedaling test and a 60-s isokinetic all-out sprint on a bicycle ergometer with continuous monitoring of crank force and cadence. Fatigue-free force-velocity (F/v) and power-velocity (P/v) profiles were derived from both tests. The development of fatigue during the 60-s sprint was assessed by fixing the slope of the fatigue-free F/v profile. Fatigue-induced alterations in PRopt were determined by non-linear regression analysis using a mono-exponential equation at constant slope. The study revealed that PRopt at any instant during a 60-s maximal sprint can be estimated accurately using a mono-exponential equation. In an isokinetic mode, a mean PRopt can be identified that enables the athlete to generate the highest mean power output over the course of the effort. Adding the time domain to the fatigue-free F/v and P/v profiles allows time-dependent cycling power to be modelled independent of cadence

Modeling Optimal Cadence as a Function of Time during Maximal Sprint Exercises Can Improve Performance by Elite Track Cyclists

In track cycling sprint events, optimal cadence PRopt is a dynamic aspect of fatigue. It is currently unclear what cadence is optimal for an athlete’s performance in sprint races and how it can be calculated. We examined fatigue-induced changes in optimal cadence during a maximal sprint using a mathematical approach. Nine elite track cyclists completed a 6-s high-frequency pedaling test and a 60-s isokinetic all-out sprint on a bicycle ergometer with continuous monitoring of crank force and cadence. Fatigue-free force-velocity (F/v) and power-velocity (P/v) profiles were derived from both tests. The development of fatigue during the 60-s sprint was assessed by fixing the slope of the fatigue-free F/v profile. Fatigue-induced alterations in PRopt were determined by non-linear regression analysis using a mono-exponential equation at constant slope. The study revealed that PRopt at any instant during a 60-s maximal sprint can be estimated accurately using a mono-exponential equation. In an isokinetic mode, a mean PRopt can be identified that enables the athlete to generate the highest mean power output over the course of the effort. Adding the time domain to the fatigue-free F/v and P/v profiles allows time-dependent cycling power to be modelled independent of cadence