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 bioenergetic 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 bioenergetic 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.
De KoningJJBobbertMFFosterC. Determination of optimal pacing strategy in track cycling with an energy flow model. J Sci Med Sport1999; 2: 266–277.
2.
AbbissCRLaursenPB. Describing and understanding pacing strategies during athletic competition. Sports Med2008; 38: 239–252.
3.
TurnesTSalvadorAFLisboaFDet al. A fast-start pacing strategy speeds pulmonary oxygen uptake kinetics and improves supramaximal running performance. PLoS ONE2014; 9: e111621.
4.
HettingaFJDe KoningJJBroersenFTet al. Pacing strategy and the occurrence of fatigue in 4000-m cycling time trials. Med Sci Sport Exer2006; 38: 1484–1491.
5.
HettingaFJDe KoningJJMeijerEet al. Effect of pacing strategy on energy expenditure during a 1500-m cycling time trial. Med Sci Sport Exer2007; 39: 2212–2218.
6.
JonesAMWilkersonDPVanhataloAet al. Influence of pacing strategy on O2 uptake and exercise tolerance. Scand J Med Sci Sports2008; 18: 615–626.
7.
CangleyPPassfieldLCarterHet al. The effect of variable gradients on pacing in cycling time-trials. Int J Sports Med2011; 32: 132–136.
8.
ThomasKStoneMRThompsonKGet al. Reproducibility of pacing strategy during simulated 20-km cycling time trials in well-trained cyclists. Eur J Appl Physiol2012; 112: 223–229.
9.
De JongJVan der MeijdenLHambySet al. Pacing strategy in short cycling time trials. Int J Sports Physiol Perform2015; 10: 1015–1022.
10.
SwainDP. A model for optimizing cycling performance by varying power on hills and in wind. Med Sci Sport Exer1997; 29: 1104–1108.
11.
AtkinsonGBrunskillA. Pacing strategies during a cycling time trial with simulated headwinds and tailwinds. Ergonomics2000; 43: 1449–1460.
12.
GordonS. Optimising distribution of power during a cycling time trial. Sports Eng2005; 8: 81–90.
13.
DahmenT. Optimization of pacing strategies for cycling time trials using a smooth 6-parameter endurance model. In: Proceedings of the pre-Olympic congress on sports science and computer science in sport (IACSS2012), Liverpool, 24–25 July 2012. Edgbaston: IACSS Press.
14.
DahmenT. Computing a field of optimal pacing strategies for cycling time trials. In: Proceedings of the symposium der dvs-Sektion Sportinformatik, Universitt Konstanz, Konstanz. https://www.uni-konstanz.de/mmsp/pubsys/publishedFiles/Da13a.pdf. 12–14 September 2012.
15.
BoswellGP. Power variation strategies for cycling time trials. a differential equation model. J Sport Sci2012; 30: 651–659.
16.
SundströmDCarlssonPTinnstenM. The influence of course bends on pacing strategy in road cycling. Proced Eng2014; 72: 835–840.
17.
SundströmDCarlssonPTinnstenM. Comparing bioenergetic models for the optimisation of pacing strategy in road cycling. Sports Eng2014; 17: 207–215.
18.
UnderwoodLJermyM. Determining optimal pacing strategy for the track cycling individual pursuit event with a fixed energy mathematical model. Sports Eng2014; 17: 183–196.
19.
KennellyAE. An approximate law of fatigue in the speeds of racing animals. P Am Acad Arts Sci1906; 42: 275–331.
20.
AtkinsonGDavisonRJeukendrupAet al. Science and cycling: current knowledge and future directions for research. J Sport Sci2003; 21: 767–787.
21.
RobinsonSRobinsonDLMountjoyRJet al. Influence of fatigue on the efficiency of men during exhausting runs. J Appl Physiol1958; 12: 197–201.
22.
FosterCSnyderACThompsonNNet al. Effect of pacing strategy on cycle time trial performance. Med Sci Sport Exer1993; 25: 383–388.
23.
AtkinsonGPeacockOPassfieldL. Variable versus constant power strategies during cycling time-trials: prediction of time savings using an up-to-date mathematical model. J Sport Sci2007; 25: 1001–1009.
24.
SundströmDCarlssonPStåhlFet al. Numerical optimization of pacing strategy in cross-country skiing. Struct Multidiscip O2013; 47: 943–950.
25.
MartinJCMillikenDLCobbJEet al. Validation of a mathematical model for road cycling power. J Appl Biomech1998; 14: 276–291.
26.
SundströmDCarlssonPTinnstenM. On optimization of pacing strategy in road cycling. Proced Eng2013; 60: 118–123.
27.
MortonRH. Modelling human power and endurance. J Math Biol1990; 28: 49–64.
28.
FintelmanDMSterlingMHemidaHet al. The effect of crosswinds on cyclists: an experimental study. Proced Eng2014; 72: 720–725.
SundströmD. On a bioenergetic four-compartment model for human exercise. Sports Eng2016; 19: 251–263.
31.
MargariaR. Biomechanics and energetics of muscular exercise. Oxford: Clarendon Press, 1976.
32.
MortonRH. On a model of human bioenergetics. Eur J Appl Physiol O1985; 54: 285–290.
33.
MortonRH. On a model of human bioenergetics. II. Maximal power and endurance. Eur J Appl Physiol O1986; 55: 413–418.
34.
MortonRH. A three component model of human bioenergetics. J Math Biol1986; 24: 451–466.
35.
BehnckeH. A mathematical model for the force and energetics in competitive running. J Math Biol1993; 31: 853–878.
36.
McGilveryRWMurrayTW. Calculated equilibria of phosphocreatine and adenosine phosphates during utilization of high energy phosphate by muscle. J Biol Chem1974; 249: 5845–5850.
37.
ChenevièreXMalatestaDPetersEMet al. A mathematical model to describe fat oxidation kinetics during graded exercise. Med Sci Sport Exer2009; 41: 1615–1625.
38.
WattMJHeigenhauserGJDyckDJet al. Intramuscular triacylglycerol, glycogen and acetyl group metabolism during 4 h of moderate exercise in man. J Physiol2002; 541: 969–978.
39.
SundströmD. On a bioenergetic four-compartment model for human exercise. Sports Eng2016; 1–13.
40.
FittsRH. The role of acidosis in fatigue: pro perspective. Med Sci Sport Exer2016; 48: 2335–2338.
41.
WesterbladH. Acidosis is not a significant cause of skeletal muscle fatigue. Med Sci Sport Exer2016; 48: 2339–2342.
42.
WesterbladHAllenDGLannergrenJ. Muscle fatigue: lactic acid or inorganic phosphate the major cause?News Physiol Sci2002; 17: 17–21.
43.
HillAV. The heat of shortening and the dynamic constants of muscle. Roy Soc1938; 126: 136–195.
44.
SvanbergK. The method of moving asymptotes: a new method for structural optimization. Int J Numer Meth Eng1987; 24: 359–373.
45.
SvanbergK. The method of moving asymptotes (MMA) with some extensions. Optim Larg Struct Syst1993; 231: 555–566.
46.
GastinPBCostillDLLawsonDLet al. Accumulated oxygen deficit during supramaximal all-out and constant intensity exercise. Med Sci Sport Exer1995; 27: 255–263.
47.
KyleCRBertoF. The mechanical efficiency of bicycle derailleur and hub-gear transmissions. Hum Pow2001; 52: 3–11.
48.
GrappeFCandauRBarbierBet al. Influence of tyre pressure and vertical load on coefficient of rolling resistance and simulated cycling performance. Ergonomics1999; 42: 1361–1371.
49.
SahlinK. Metabolic changes limiting muscle performance. In: SaltinB (ed.) Biochemistry of exercise VI. Champaign, IL: Human Kinetics, 1986, pp.323–343.
50.
KaratzaferiCDe HaanAFergusonRet al. Phosphocreatine and ATP content in human single muscle fibres before and after maximum dynamic exercise. Eur J Physiol2001; 442: 467–474.
51.
ChenevièreXMalatestaDGojanovicBet al. Differences in whole-body fat oxidation kinetics between cycling and running. Eur J Appl Physiol2010; 109: 1037–1045.
52.
MortonRH. A new modelling approach demonstrating the inability to make up for lost time in endurance running events. IMA J Manage Math2009; 20: 109–120.
53.
HettingaFJDe KoningJJHullemanMet al. Relative importance of pacing strategy and mean power output in 1500-m self-paced cycling. Br J Sports Med2010; 46: 30–35.
54.
HillDWFergusonCS. A physiological description of critical velocity. Eur J Appl Physiol O1999; 79: 290–293.
55.
CoyleEFSidossisLSHorowitzJFet al. Cycling efficiency is related to the percentage of type I muscle fibers. Med Sci Sport Exer1992; 24: 782–788.
56.
GreenHJPatlaAE. Maximal aerobic power: neuromuscular and metabolic considerations. Med Sci Sport Exer1992; 24: 38–46.
57.
FosterCDeKoningJJHettingaFet al. Effect of competitive distance on energy expenditure during simulated competition. Int J Sports Med2004; 25: 198–204.
58.
SaltinBKarlssonJ. Muscle glycogen utilisation during work of different intensities. In: PernowBSaltinB (eds) Muscle metabolism during exercise. Stockholm: Plenum Press, 1970, pp.289–300.
