A mathematical model of a bike-rider’s longitudinal and lateral dynamics was used to study the influence of road conditions (tyre-road friction coefficient) on cycling individual time trial (ITT) performance and pacing strategy. A dynamic optimisation approach was used on different simulated 40-km-ITT courses, where environmental variables (i.e. slope and wind), the presence of corners and the tyre-road friction coefficient were varied. The objective of the optimisation was the performance time. Maximal velocity was constrained by road geometry and the tyre-road friction coefficient. The maximal deliverable power output was constrained accordingly to the critical power model. The simulation results suggest that when technical sections constitute 25% of the entire course, road conditions can meaningfully affect the final performance time and peak power required, but not the pacing strategy. In fact, the time lost in slow technical sections cannot be regained during fast straight sections, even if technical sections are used to restore anaerobic energy stores. However, more experimental research is needed to test the applicability of these predictions.
FosterCSnyderACThompsonNN, et al. Effect of pacing strategy on cycle time trial performance. Med Sci Sports Exerc1993; 25: 383–388.
2.
FosterCSchragerMSnyderAC, et al. Pacing strategy and athletic performance. Sports Med1994; 17: 77–85.
3.
AbbissCRLaursenPB.Describing and understanding pacing strategies during athletic competition. Sports Med2008; 38: 239–252.
4.
OldsT.Modelling human locomotion. Sports Med2001; 31: 497–509.
5.
AtkinsonGPeacockOPassfieldL.Variable versus constant power strategies during cycling time-trials: prediction of time savings using an up-to-date mathematical model. J Sports Sci2007; 25: 1001–1009.
6.
GordonS.Optimising distribution of power during a cycling time trial. Sports Eng2005; 8: 81–90.
7.
SwainDP.A model for optimizing cycling performance by varying power on hills and in wind. Med Sci Sports Exerc1997; 29: 1104–1108.
8.
WellsMAtkinsonGMarwoodS.Effects of magnitude and frequency of variations in external power output on simulated cycling time-trial performance. J Sports Sci2013; 31: 1639–1646.
9.
MarońskiR.On optimal velocity during cycling. J Biomech1994; 27: 205–213.
10.
BurkeE.High-tech cycling. Champaign, IL: Human Kinetics, 2003.
11.
Di PramperoPCortiliGMognoniP, et al. Equation of motion of a cyclist. J Appl Physiol1979; 47: 201–206.
12.
MartinJCMillikenDLCobbJE, et al. Validation of a mathematical model for road cycling power. J Appl Biomech1998; 14: 276–291.
13.
MullerSUchanskiMHedrickK.Estimation of the maximum tire-road friction coefficient. J Dyn Syst Meas Control2003; 125: 607–617.
14.
De JongJFokkinkROlsderGJ, et al. The individual time trial as an optimal control problem. Proc IMechE, Part P: J Sports Engineering and Technology2017; 231: 200–206.
15.
SundströmDCarlssonPTinnstenM.The influence of course bends on pacing strategy in road cycling. Procedia Eng2014; 72: 835–840.
BertolazziEBiralFDa LioM.Symbolic–numeric indirect method for solving optimal control problems for large multibody systems: the time-optimal racing vehicle example. Multibody Syst Dyn2005; 13: 233–252.
18.
MujikaIPadillaS.Physiological and performance characteristics of male professional road cyclists. Sports Med2001; 31: 479–487.
19.
WolfSBiralFSaupeD.Adaptive feedback system for optimal pacing strategies in road cycling. Sports Eng2019; 22: 6.
20.
MortonRH.The critical power and related whole-body bioenergetic models. Eur J Appl Physiol2006; 96: 339–354.
21.
AstromKJKleinRELennartssonA.Bicycle dynamics and control: adapted bicycles for education and research. IEEE Control Syst Mag2005; 25: 26–47.
22.
ZignoliABiralF.Prediction of pacing and cornering strategies during cycling individual time trials with optimal control. Sports Eng2020; 23: 13.
23.
LotRBiralF.A curvilinear abscissa approach for the lap time optimization of racing vehicles. IFAC Proc Vol2014; 47: 7559–7565.
24.
BiralFBertolazziEBosettiP.Notes on numerical methods for solving optimal control problems. IEEJ J Ind Appl2015; 5: 154–166.
25.
BatterhamAMHopkinsWG.Making meaningful inferences about magnitudes. Int J Sports Physiol Perform2006; 1: 50–57.
26.
CurrellKJeukendrupAE.Validity, reliability and sensitivity of measures of sporting performance. Sports Med2008; 38: 297–316.
27.
HopkinsWGHawleyJABurkeLM.Design and analysis of research on sport performance enhancement. Med Sci Sports Exerc1999; 31: 472–485.
28.
LaursenPShingCJenkinsD.Reproducibility of a laboratory-based 40-km cycle time-trial on a stationary wind-trainer in highly trained cyclists. Int J Sports Med2003; 24: 481–485.
29.
WoolrichRWLambertMISwartJ, et al. Measurement error associated with performance testing in well-trained cyclists: Application to the precision of monitoring changes in training status. Int SportMed J2009; 10: 33–44.
30.
HopkinsWMarshallSBatterhamA, et al. Progressive statistics for studies in sports medicine and exercise science. Med Sci Sports Exerc2009; 41: 3.
31.
MalcataRMHopkinsWG.Variability of competitive performance of elite athletes: a systematic review. Sports Med2014; 44: 1763–1774.
32.
PhillipsKEHopkinsWG.Performance relationships in timed and mass-start events for elite omnium cyclists. Int J Sports Physiol Perform2017; 12: 628–633.
33.
DoriaATognazzoMCusimanoG, et al. Identification of the mechanical properties of bicycle tyres for modelling of bicycle dynamics. Veh Syst Dyn2013; 51: 405–420.
34.
DresselASadauckasJ.Characterization and modelling of various sized mountain bike tires and the effects of tire tread knobs and inflation pressure. Appl Sci2020; 10: 3156.
35.
PeifferJJAbbissCR.Influence of environmental temperature on 40 km cycling time-trial performance. Int J Sports Physiol Perform2011; 6: 208–220.
36.
RacinaisSPériardJDKarlsenA, et al. Effect of heat and heat acclimatization on cycling time trial performance and pacing. Med Sci Sports Exerc2015; 47: 601–606.
37.
LindsayFHHawleyJAMyburghKH, et al. Improved athletic performance in highly trained cyclists after interval training. Med Sci Sports Exerc1996; 28: 1427–1434.
38.
DantasJLPereiraGNakamuraFY.Five-kilometers time trial: preliminary validation of a short test for cycling performance evaluation. Asian J Sports Med. Epub ahead of print 28September2015. DOI: 10.5812/asjsm.23802.
39.
TanFHYAzizAR. Reproducibility of outdoor flat and uphill cycling time trials and their performance correlates with peak power output in moderately trained cyclists. J Sports Sci Med2005; 4: 278–284.
40.
ReijneMBregmanDSchwabA.Measuring and comparing descend in elite race cycling with a perspective on real-time feedback for improving individual performance. In: ISEA 2018: 12th Conference of the International Sports Engineering Association ‘Engineering of Sport’, Brisbane, Australia, 3–28 March 2018, vol. 2, no. 6, p.262. Basel, Switzerland: MDPI.
41.
KegelmanJCHarbottLKGerdesJC.Insights into vehicle trajectories at the handling limits: analysing open data from race car drivers. Veh Syst Dyn2017; 55: 191–207.
42.
KordiMFullertonCPassfieldL, et al. Influence of upright versus time trial cycling position on determination of critical power and W’ in trained cyclists. Eur J Sport Sci2019; 19: 192–198.
43.
FintelmanDMSterlingMHemidaH, et al. The effect of time trial cycling position on physiological and aerodynamic variables. J Sport Sci2015; 33: 1730–1737.
