Article

# Influence of corners and road conditions on cycling individual time trial performance and 'optimal' pacing strategy: A simulation study

Authors:
To read the full-text of this research, you can request a copy directly from the author.

## Abstract

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.

## No full-text available

... Recently, Zignoli and Biral [8], developed a curvilinear model for cycling locomotion, which was used to fit global position system (GPS) data points [9] and to simulate racing trajectories [10]. However, whilst GPS-derived trajectories might be considered accurate enough to evaluate the downhilling performance from a global perspective, they might not be accurate enough to clearly discern different cornering strategies, hence a higher precision instrumentation is required. ...
... The procedure of computing an 'optimal' cycling trajectory is described in more detail in [16]. In brief, the key elements of the optimal control problem were (A) the equation of motion of the bike-rider system (listed in [8] or in [10]), which are used to compute the bike-rider dynamics and constitute the constraints of the optimisation problem; (B) the objective function (i.e., what the cyclist is trying to achieve, i.e., in this case minimum time and minimum power variations); ...
... Usually, after hitting the apex, cyclists should be able to reduce the steering, start pedalling again and focus on the exit. There are mainly two strategies for cornering in downhill cycling [10]: ...
Article
Performance in downhill road cycling is understudied. Tools that can be used to assess the cyclists’ cornering strategies ecologically and objectively are missing. A new methodology based on motion capture and mathematical modelling is presented here. A drone was used to capture the trajectory of the centre of mass of a cyclist, who was asked to complete 10 times a ~220-m-long downhill course. The motion capture and ‘optimal’ trajectories were compared in terms of displacement, speed, and heading. In each trial, the apex, the turn-in and the braking points were detected. Whilst the ‘optimal’ trajectory suggested an ‘early’ apex strategy was best, the cyclist in this study completed the corners with a ‘late’ apex strategy. This study presents a methodology that can be used to objectively assess cornering strategies in road cycling. Discrepancies between actual and ‘optimal’ trajectories are also discussed. This study brings to light concepts such as: ‘early’ or ‘late’ apex, braking and turning points, which are discussed within the context of road cycling downhill performance.
... Here, a state-of-the-art model for cycling dynamics [6,7] was used to compute the reference optimal manoeuvres used for an ARAS. The model was deployed on a mobile device (smart phone), and it was tested off-line for real-time performances. ...
... The reaction forces, generated from the road-tire interaction, were applied to the pendulum pivot (i.e. the point of contact). The model was taken from [6,7], where the equation governing the cyclist's energy sources was excluded. The vector of the state variables was: x = [α, φ, ̇ , v, W n , δ n , n, ̇s ], and the vector of the inputs (control variables) was: u = [vδ n , vW n ]. ...
... A system of equations of the dynamics, which provides a few algebraic constraints. They are reported with more details elsewhere [6,7] and on the 'readme' file in the repository directory (see subsection Project Details). 2. The road-tire adherence limits that limit the bike-rider longitudinal and lateral accelerations within the friction circle is given by Eq. [15]: ...
Article
To mitigate the incidence of the crashes in road cycling races, new technologies that can help the riders in evaluating risks in advance are called for. An advanced rider assistance system has been developed to warn the riders before they negotiate a corner during a fast-descending section. The advanced rider assistance system was based on the optimal manoeuvre method applied to a state-of-the-art cycling locomotion model. Global positioning system data collected at 1 Hz were used to compute initial conditions for the optimal manoeuvre calculation. The advanced rider assistance system was deployed on a mobile device, and it was tested off-line for real-time performances. Computational cost was examined versus the horizon length to arrive at an optimum for the problem. The proposed advanced rider assistance system was designed to provide audible warning to the riders so they can focus their actions and improve trajectory security. This work prompts more research to reduce the incidence of crashes in cycling training and racing by means of new methods based on optimal manoeuvre calculation.
... However, at the moment, these considerations remain anecdotal. In a recent simulation study, it has been suggested that riders who can sustain larger lateral accelerations and have a better bike control, can complete corners at higher speeds and deliver lower power output levels to restore the cruise speed after a turn (Zignoli, 2020). Therefore, to make a step forward in the assessment of real and 'curvilinear' ITT performance bringing to light the influence of bike handling, models of cycling locomotion that can take into account forces acting along both the longitudinal and the lateral direction are needed (Zignoli & Biral, 2020). ...
... A bi-dimensional cycling locomotion model was used in this study to estimate the longitudinal and lateral accelerations during the races and to interpret the g-g diagrams. The model consists in a simplified inverted-pendulum rider-bike model (Fig. 3A) already adopted to predict racing trajectories in ITT races (Zignoli, 2020;Zignoli & Biral, 2020). The main difference between this and other relevant mono-dimensional models available from the cycling literature (di Prampero et al., 1979;Ingen Schenau & Cavanagh, 1990;Martin et al., 1998), is that this model takes into account both longitudinal and lateral forces on the road plane. ...
... 2018) was used to write (R Lot & Da Lio, 2004) and manipulate the equations of motion, which were used to generate the simulated trajectories. They are reported with greater level of details elsewhere (Zignoli, 2020;Zignoli & Biral, 2020)). A custom written Maple package called XOptima (Biral et al., 2015) was used to numerically solve the dynamic optimisation problem. ...
Article
Full-text available
A methodology to study bike handling of cyclists during individual time trials (ITT) is presented. Lateral and longitudinal accelerations were estimated from GPS data of professional cyclists (n=53) racing in two ITT of different length and technical content. Acceleration points were plotted on a plot (g-g diagram) and they were enclosed in an ellipse. A correlation analysis was conducted between the area of the ellipse and the final ITT ranking. It was hypothesized that a larger area was associated to a better performance. An analytical model for the bike-cyclist system dynamics was used to conduct a parametric analysis on the influence of riding position on the shape of the g-g diagram. A moderate (n=27, r=-0.40, p=0.038) and a very large (n=26, r=-0.83, p<0.0001) association were found between the area of the enclosing ellipse and the final ranking in the two ITT. Interestingly, this association was larger in the shorter race with higher technical content. The analytical model suggested that maximal decelerations are highly influenced by the cycling position, road slope and speed. This investigation, for the first time, explores a novel methodology that can provide insights into bike handling, a large unexplored area of cycling performance.
Article
Full-text available
Mountain bikes continue to be the largest segment of U.S. bicycle sales, totaling some USD 577.5 million in 2017 alone. One of the distinguishing features of the mountain bike is relatively wide tires with thick, knobby treads. Although some work has been done on characterizing street and commuter bicycle tires, little or no data have been published on off-road bicycle tires. This work presents laboratory measurements of inflated tire profiles, tire contact patch footprints, and force and moment data, as well as static lateral and radial stiffness for various modern mountain bike tire sizes including plus size and fat bike tires. Pacejka’s Motorcycle Magic Formula tire model was applied and used to compare results. A basic model of tire lateral stiffness incorporating individual tread knobs as springs in parallel with the overall tread and the inflated carcass as springs in series was derived. Finally, the influence of inflation pressure was also examined. Results demonstrated appreciable differences in tire performance between 29 × 2.3”, 27.5 × 2.8”, 29 × 3”, and 26 × 4” knobby tires. The proposed simple model to combine tread knob and carcass stiffness offered a good approximation, whereas inflation pressure had a strong effect on mountain bike tire behavior.
Article
Full-text available
Descend technique and performance vary among elite racing cyclists and it is not clear what slower riders should do to improve their performance. An observation study was performed of the descending technique of members of a World Tour cycling team and the technique of each member was compared with the fastest descender amongst them. The obtained data gives us guidelines for rider specific feedback in order to improve his performance. The bicycles were equipped with a system that could measure: velocity, cadence, pedal power, position, steer angle, 3D orientation, rotational speeds and linear accelerations of the rear frame and brake force front and rear. From our observation study, the brake point and apex position turned out to be distinctive indicators of a fast cornering technique in a descent for a tight, hairpin corner. These two indicators can be used as feedback for a slower rider to improve his descend performance.
Article
Full-text available
In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial.
Article
Full-text available
Race car drivers can offer insights into vehicle control during extreme manoeuvres; however, little data from race teams is publicly available for analysis. The Revs Program at Stanford has built a collection of vehicle dynamics data acquired from vintage race cars during live racing events with the intent of making this database publicly available for future analysis. This paper discusses the data acquisition, post-processing, and storage methods used to generate the database. An analysis of available data quantifies the repeatability of professional race car driver performance by examining the statistical dispersion of their driven paths. Certain map features, such as sections with high path curvature, consistently corresponded to local minima in path dispersion, quantifying the qualitative concept that drivers anchor their racing lines at specific locations around the track. A case study explores how two professional drivers employ distinct driving styles to achieve similar lap times, supporting the idea that driving at the limits allows a family of solutions in terms of paths and speed that can be adapted based on specific spatial, temporal, or other constraints and objectives.
Conference Paper
Full-text available
The optimal control and lap time optimization of vehicles such as racing cars and motorcycle is a challenging problem, in particular the approach adopted in the problem formulation has a great impact on the actual possibility of solving such problem by using numerical techniques. This paper illustrates a methodology which combines some modelling technique which have been found to be numerically efficient. The methodology is based on the 3D curvilinear coordinates technique for the road modelling, the moving frame approach for the derivation of the vehicle equations of motion, the replacement of the time with the position along the track as new independent variable and the formulation and the solution of the minimum lap time problem by means of the indirect approach. The case study of a GT car is presented and simulation examples are given and discussed.
Article
Full-text available
Background: The five-kilometer time trial (TT5km) has been used to assess aerobic endurance performance without further investigation of its validity. Objectives: This study aimed to perform a preliminary validation of the TT5km to rank well-trained cyclists based on aerobic endurance fitness and assess changes of the aerobic endurance performance. Materials and Methods: After the incremental test, 20 cyclists (age = 31.3 ± 7.9 years; body mass index = 22.7 ± 1.5 kg/m2; maximal aerobic power = 360.5 ± 49.5 W) performed the TT5km twice, collecting performance (time to complete, absolute and relative power output, average speed) and physiological responses (heart rate and electromyography activity). The validation criteria were pacing strategy, absolute and relative reliability, validity and sensitivity. Sensitivity index was obtained from the ratio between the smallest worthwhile change and typical error. Results: The TT5km showed high absolute (coefficient of variation < 3%) and relative (intraclass coefficient correlation > 0.95) reliability of performance variables, whereas it presented low reliability of physiological responses. The TT5km performance variables were highly correlated with the aerobic endurance indices obtained from incremental test (r > 0.70). These variables showed adequate sensitivity index (> 1). Conclusions: TT5km is a valid test to rank the aerobic endurance fitness of well-trained cyclists and to differentiate changes on aerobic endurance performance. Coaches can detect performance changes through either absolute (± 17.7 W) or relative power output (± 0.3 W.kg-1), the time to complete the test (± 13.4 s) and the average speed (± 1.0 km.h-1). Furthermore, TT5km performance can also be used to rank the athletes according to their aerobic endurance fitness.
Article
Full-text available
This investigation sought to determine if cycling power could be accurately modeled. A mathematical model of cycling power was derived, and values for each model parameter were determined. A bicycle-mounted power measurement system was validated by comparison with a laboratory ergometer. Power was measured during road cycling, and the measured values were compared with the values predicted by the model. The measured values for power were highly correlated (R2 = .97) with, and were not different than, the modeled values. The standard error between the modeled and measured power (2.7 W) was very small. The model was also used to estimate the effects of changes in several model parameters on cycling velocity. Over the range of parameter values evaluated, velocity varied linearly (R2 > .99). The results demonstrated that cycling power can be accurately predicted by a mathematical model.
Article
Full-text available
Knowledge of the age at which elite athletes achieve peak performance could provide important information for long-term athlete development programmes, event selection and strategic decisions regarding resource allocation. The objective of this study was to systematically review published estimates of age of peak performance of elite athletes in the twenty-first century. We searched SPORTDiscus, PubMed and Google Scholar for studies providing estimates of age of peak performance. Here we report estimates as means only for top (international senior) athletes. Estimates were assigned to three event-type categories on the basis of the predominant attributes required for success in the given event (explosive power/sprint, endurance, mixed/skill) and then plotted by event duration for analysis of trends. For both sexes, linear trends reasonably approximated the relationships between event duration and estimates of age of peak performance for explosive power/sprint events and for endurance events. In explosive power/sprint events, estimates decreased with increasing event duration, ranging from ~27 years (athletics throws, ~1-5 s) to ~20 years (swimming, ~21-245 s). Conversely, estimates for endurance events increased with increasing event duration, ranging from ~20 years (swimming, ~2-15 min) to ~39 years (ultra-distance cycling, ~27-29 h). There was little difference in estimates of peak age for these event types between men and women. Estimations of the age of peak performance for athletes specialising in specific events and of event durations that may best suit talent identification of athletes can be obtained from the equations of the linear trends. There were insufficient data to investigate trends for mixed/skill events. Differences in the attributes required for success in different sporting events likely contribute to the wide range of peak-performance ages of elite athletes. Understanding the relationships between age of peak competitive performance and event duration should be useful for tracking athlete progression and talent identification.
Article
Full-text available
PURPOSE: To determine the effects of heat-acclimatization on performance and pacing during outdoor cycling time-trials (TT, 43.4km) in the heat. METHODS: Nine cyclists performed 3 TTs in hot ambient conditions (TTH, ∼37ºC) on the first (TTH-1), sixth (TTH-2) and fourteenth (TTH-3) days of training in the heat. Data were compared to the average of two TTs in cool condition (∼8ºC) performed pre and post heat acclimatization (TTC). RESULTS: TTH-1 (77±6min) was slower (p=0.001) than TTH-2 (69±5min) and both were slower (p<0.01) than TTC and TTH-3 (66±3 and 66±4 min, respectively) without differences between TTC and TTH-3 (p>0.05). The cyclists initiated the first 20% of all TTs at a similar power output, irrespective of climate and acclimatization status; however, during TTH-1 they subsequently had a marked decrease in power output, which was partly attenuated following six days of acclimatization and further reduced after fourteen days. HR was higher during the first 20% of TTH-1 than in the other TTs (p<0.05), but there were no differences between conditions from 30% onward. Final rectal temperature was similar in all TTHs (40.2±0.4ºC, p=1.000) and higher than in TTC (38.5±0.6ºC, p<0.001). CONCLUSION: Following two weeks of acclimatization, trained cyclists are capable of completing a prolonged TT in a similar time in the heat compared to cool conditions, whereas in the unacclimatized state they experienced a marked decrease in power output during the TTHs.
Article
Full-text available
Abstract 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.
Article
Full-text available
Advanced simulation of the stability and handling properties of bicycles requires detailed road–tyre contact models. In order to develop these models, in this study, four bicycle tyres are tested by means of a rotating disc machine with the aim of measuring the components of tyre forces and torques that influence the safety and handling of bicycles. The effect of inflation pressure and tyre load is analysed. The measured properties of bicycle tyres are compared with those of motorcycle tyres.
Article
Full-text available
This work presents a methodological framework, based on an indirect approach, for the automatic generation and numerical solution of Optimal Control Problems (OCP) for mechatronic systems, described by a system of Differential Algebraic Equations (DAEs). The equations of the necessary condition for optimality were derived exploiting the DAEs structure, according to the Calculus of Variation Theory. A collection of symbolic procedures was developed within general-purpose Computer Algebra Software. Those procedures are general and make it possible to generate both OCP equations and their jacobians, once any DAE mathematical model, objective function, boundary conditions and constraints are given. Particular attention has been given to the correct definition of the boundary conditions especially for models described with set of dependent coordinates. The non-linear symbolic equations, their jacobians with the sparsity patterns, generated by the procedures above mentioned, are translated into a C++ source code. A numerical code, based on a Newton Affine Invariant scheme, was also developed to solve the Boundary Value Problems (BVPs) generated by such procedures. The software and methodological framework here presented were successfully applied to the solution of the minimum-lap time problem of a racing motorcycle.
Article
Full-text available
Small changes in performance, as low as 1%, are regarded as meaningful in well-trained cyclists. Being able to detect these changes is necessary to fine tune training and optimise performance. The typical error of measurement (TEM) in common performance cycle tests is about 2-3%. It is not known whether this TEM is lower in well-trained cyclists and therefore whether small changes in performance parameters are detectable. In this research, after familiarisation, 17 well-trained cyclists each completed three Peak Power Output (PPO) tests (including VO2max) and three 40km time trials (40km TT). All tests were performed after a standardised warm-up at the same relative intensity and under a strict testing-protocol. TEM within the PPO-test was 2.2% for VO2max and 0.9% for PPO, while TEM for the 40km TT was 0.9%. In conclusion, measurement of PPO and 40km TT time, after a standardised warm-up, has sufficient precision in well-trained cyclists to detect small meaningful changes.
Article
Full-text available
The aims of the present study were firstly to examine the reproducibility of outdoor flat and uphill cycling time trials (TT), and secondly to assess the relationship between peak power output (Wpeak) obtained in the laboratory and outdoor cycling performance in moderately trained cyclists. Eight competitive male cyclists first performed a progressive cycle ergometer test in the laboratory to determine Wpeak (W). Thereafter, they performed three 36 km TT (TT36) on a flat course on separate days and at the same time of the day. On a different day, they also performed three 1.4 km uphill TT (TT1.4) in a single day. The coefficient of variation (CV) values across three TT36 and TT1.4 ranged from 1.1 - 1.4% and 2.6 - 2.9%, for performance time (min) and mean power (W), respectively. The correlation between absolute Wpeak (W) obtained in the laboratory and mean power during TT36 and TT1.4 was 0.90 (p < 0.01) and 0.98 (p < 0.01), respectively. Absolute Wpeak (W) correlated significantly with performance time in TT36 (r = -0.72, p < 0.05) but not in TT1.4 (r = -0.52, p > 0.05). The correlation between relative Wpeak (W·kg-1) and performance time in TT36 and TT1.4 was r = -0.65 (p > 0.05) and r = -0.91 (p < 0.01), respectively. In conclusion, under stable environmental conditions, performance time and mean power are highly reproducible in moderately trained cyclists during outdoor cycling TT. Laboratory determined absolute Wpeak (W) may predict cycling performance on a flat course but relative Wpeak (W·kg-1) is a better predictor of performance during uphill cycling
Article
Full-text available
A study of a sample provides only an estimate of the true (population) value of an outcome statistic. A report of the study therefore usually includes an inference about the true value. Traditionally, a researcher makes an inference by declaring the value of the statistic statistically significant or nonsignificant on the basis of a P value derived from a null-hypothesis test. This approach is confusing and can be misleading, depending on the magnitude of the statistic, error of measurement, and sample size. The authors use a more intuitive and practical approach based directly on uncertainty in the true value of the statistic. First they express the uncertainty as confidence limits, which define the likely range of the true value. They then deal with the real-world relevance of this uncertainty by taking into account values of the statistic that are substantial in some positive and negative sense, such as beneficial or harmful. If the likely range overlaps substantially positive and negative values, they infer that the outcome is unclear; otherwise, they infer that the true value has the magnitude of the observed value: substantially positive, trivial, or substantially negative. They refine this crude inference by stating qualitatively the likelihood that the true value will have the observed magnitude (eg, very likely beneficial). Quantitative or qualitative probabilities that the true value has the other 2 magnitudes or more finely graded magnitudes (such as trivial, small, moderate, and large) can also be estimated to guide a decision about the utility of the outcome.
Article
Full-text available
Article
Full-text available
The purpose of the present study was to examine the reproducibility of laboratory-based 40-km cycle time-trial performance on a stationary wind-trainer. Each week, for three consecutive weeks, and on different days, forty-three highly trained male cyclists (x +/- SD; age = 25 +/- 6 y; mass = 75 +/- 7 kg; peak oxygen uptake [VO (2)peak] = 64.8 +/- 5.2 ml x kg (-1) x min (-1)) performed: 1) a VO (2)peak test, and 2) a 40-km time-trial on their own racing bicycle mounted to a stationary wind-trainer (Cateye - Cyclosimulator). Data from all tests were compared using a one-way analysis of variance. Performance on the second and third 40-km time-trials were highly related (r = 0.96; p < 0.001), not significantly different (57 : 21 +/- 2 : 57 vs. 57 : 12 +/- 3 : 14 min:s), and displayed a low coefficient of variation (CV) = 0.9 +/- 0.7 %. Although the first 40-km time-trial (58 : 43 +/- 3 : 17 min:s) was not significantly different from the second and third tests (p = 0.06), inclusion of the first test in the assessment of reliability increased within-subject CV to 3.0 +/- 2.9 %. 40-km time-trial speed (km x h (-1)) was significantly (p < 0.001) related to peak power output (W; r = 0.75), VO (2)peak (l x min (-1); r = 0.53), and the second ventilatory turnpoint (l x min (-1); r = 0.68) measured during the progressive exercise tests. These data demonstrate that the assessment of 40-km cycle time-trial performance in well-trained endurance cyclists on a stationary wind-trainer is reproducible, provided the athletes perform a familiarization trial.
Article
Full-text available
This paper takes a performance-based approach to review the broad expanse of literature relating to whole-body models of human bioenergetics. It begins with an examination of the critical power model and its assumptions. Although remarkably robust, this model has a number of shortcomings. Attention to these has led to the development of more realistic and more detailed derivatives of the critical power model. The mathematical solutions to and associated behaviour of these models when subjected to imposed "exercise" can be applied as a means of gaining a deeper understanding of the bioenergetics of human exercise performance.
Article
Full-text available
Swain (1997) employed the mathematical model of Di Prampero et al. (1979) to predict that, for cycling time-trials, the optimal pacing strategy is to vary power in parallel with the changes experienced in gradient and wind speed. We used a more up-to-date mathematical model with validated coefficients (Martin et al., 1998) to quantify the time savings that would result from such optimization of pacing strategy. A hypothetical cyclist (mass = 70 kg) and bicycle (mass = 10 kg) were studied under varying hypothetical wind velocities (-10 to 10 m x s(-1)), gradients (-10 to 10%), and pacing strategies. Mean rider power outputs of 164, 289, and 394 W were chosen to mirror baseline performances studied previously. The three race scenarios were: (i) a 10-km time-trial with alternating 1-km sections of 10% and -10% gradient; (ii) a 40-km time-trial with alternating 5-km sections of 4.4 and -4.4 m x s(-1) wind (Swain, 1997); and (iii) the 40-km time-trial delimited by Jeukendrup and Martin (2001). Varying a mean power of 289 W by +/- 10% during Swain's (1997) hilly and windy courses resulted in time savings of 126 and 51 s, respectively. Time savings for most race scenarios were greater than those suggested by Swain (1997). For a mean power of 289 W over the "standard" 40-km time-trial, a time saving of 26 s was observed with a power variability of 10%. The largest time savings were found for the hypothetical riders with the lowest mean power output who could vary power to the greatest extent. Our findings confirm that time savings are possible in cycling time-trials if the rider varies power in parallel with hill gradient and wind direction. With a more recent mathematical model, we found slightly greater time savings than those reported by Swain (1997). These time savings compared favourably with the predicted benefits of interventions such as altitude training or ingestion of carbohydrate-electrolyte drinks. Nevertheless, the extent to which such power output variations can be tolerated by a cyclist during a time-trial is still unclear.
Article
Full-text available
It is widely recognized that an athlete's 'pacing strategy', or how an athlete distributes work and energy throughout an exercise task, can have a significant impact on performance. By applying mathematical modelling (i.e. power/velocity and force/time relationships) to athletic performances, coaches and researchers have observed a variety of pacing strategies. These include the negative, all-out, positive, even, parabolic-shaped and variable pacing strategies. Research suggests that extremely short-duration events (< or =30 seconds) may benefit from an explosive 'all-out' strategy, whereas during prolonged events (>2 minutes), performance times may be improved if athletes distribute their pace more evenly. Knowledge pertaining to optimal pacing strategies during middle-distance (1.5-2 minutes) and ultra-endurance (>4 hours) events is currently lacking. However, evidence suggests that during these events well trained athletes tend to adopt a positive pacing strategy, whereby after peak speed is reached, the athlete progressively slows. The underlying mechanisms influencing the regulation of pace during exercise are currently unclear. It has been suggested, however, that self-selected exercise intensity is regulated within the brain based on a complex algorithm involving peripheral sensory feedback and the anticipated workload remaining. Furthermore, it seems that the rate and capacity limitations of anaerobic and aerobic energy supply/utilization are particularly influential in dictating the optimal pacing strategy during exercise. This article outlines the various pacing profiles that have previously been observed and discusses possible factors influencing the self-selection of such strategies.
Article
Full-text available
Performance testing is one of the most common and important measures used in sports science and physiology. Performance tests allow for a controlled simulation of sports and exercise performance for research or applied science purposes. There are three factors that contribute to a good performance test: (i) validity; (ii) reliability; and (iii) sensitivity. A valid protocol is one that resembles the performance that is being simulated as closely as possible. When investigating race-type events, the two most common protocols are time to exhaustion and time trials. Time trials have greater validity than time to exhaustion because they provide a good physiological simulation of actual performance and correlate with actual performance. Sports such as soccer are more difficult to simulate. While shuttle-running protocols such as the Loughborough Intermittent Shuttle Test may simulate physiology of soccer using time to exhaustion or distance covered, it is not a valid measure of soccer performance. There is a need to include measures of skill in such protocols. Reliability is the variation of a protocol. Research has shown that time-to-exhaustion protocols have a coefficient of variation (CV) of >10%, whereas time trials are more reliable as they have been shown to have a CV of <5%. A sensitive protocol is one that is able to detect small, but important, changes in performance. The difference between finishing first and second in a sporting event is <1%. Therefore, it is important to be able to detect small changes with performance protocols. A quantitative value of sensitivity may be accomplished through the signal : noise ratio, where the signal is the percentage improvement in performance and the noise is the CV.
Article
Full-text available
In this paper, the dynamics of bicycles is analyzed from the perspective of control. Models of different complexity are presented, starting with simple ones and ending with more realistic models generated from multibody software. Models that capture essential behavior such as self-stabilization as well as models that demonstrate difficulties with rear wheel steering are considered. Experiences using bicycles in control education along with suggestions for fun and thought-provoking experiments with proven student attraction are presented. Finally, bicycles and clinical programs designed for children with disabilities are described.
Article
A new dynamic model for predicting road cycling individual time trials with optimal control was created. The model included both lateral and longitudinal bicycle dynamics, 3D road geometry, and anaerobic source depletion. The prediction of the individual time trial performance was formulated as an optimal control problem and solved with an indirect approach to find the pacing and cornering strategies in the respect of the physical/physiological limits of the system. The model was tested against the velocity and power output data collected by professional cyclists in two individual time trial Giro d’Italia data sets: the first data set (Rovereto, n = 15) was used to adjust the parameters of the model and the second data set (Verona, n = 13) was used to test the predictive ability of the model. The simulated velocity fell in the $$\mathrm{CI}_{95\%}$$ of the experimental data for 32 and 18% of the duration of the course for Rovereto and Verona stages, respectively. The simulated power output fell in the $$\mathrm{CI}_{95\%}$$ of the experimental data for 50 and 25% of the duration of the course for Rovereto and Verona stages respectively. This framework can be used to input rider’s physical/physiological characteristics, 3D road geometry, and conditions to generate realistic velocity and power output predictions in individual time trials. It, therefore, constitutes a tool that could be used by coaches and athletes to plan the pacing and cornering strategies before the race.
Article
In road cycling, the pacing strategy plays an important role, especially in solo events like individual time trials. Nevertheless, not much is known about pacing under varying conditions. Based on mathematical models, optimal pacing strategies were derived for courses with varying slope or wind, but rarely tested for their practical validity. In this paper, we present a framework for feedback during rides in the field based on optimal pacing strategies and methods to update the strategy if conditions are different than expected in the optimal pacing strategy. To update the strategy, two solutions based on model predictive control and proportional–integral–derivative control, respectively, are presented. Real rides are simulated inducing perturbations like unexpected wind or errors in the model parameter estimates, e.g., rolling resistance. It is shown that the performance drops below the best achievable one taking into account the perturbations when the strategy is not updated. This is mainly due to premature exhaustion or unused energy resources at the end of the ride. Both the proposed strategy updates handle those problems and ensure that a performance close to the best under the given conditions is delivered.
Article
Body position is known to alter power production and affect cycling performance. The aim of this study was to compare mechanical power output in two riding positions, and to calculate the effects on critical power (CP) and W′ estimates. Seven trained cyclists completed three peak power output efforts and three fixed-duration trial (3-, 5- and 12-min) riding with their hands on the brake lever hoods (BLH), or in a time trial position (TTP). A repeated-measures analysis of variance showed that mean power output during the 5-min trial was significantly different between BLH and TTP positions, resulting in a significantly lower estimate of CP, but not W′, for the TTP trial. In addition, TTP decreased the performance during each trial and increased the percentage difference between BLH and TTP with greater trial duration. There were no differences in pedal cadence or heart rate during the 3-min trial; however, TTP results for the 12-min trial showed a significant fall in pedal cadence and a significant rise in heart rate. The findings suggest that cycling position affects power output and influences consequent CP values. Therefore, cyclists and coaches should consider the cycling position used when calculating CP.
Purpose: To explore the extent to which factors that determine performance transfer within and between time-trial and mass-start events in the track-cycling Omnium. Methods: Official finish rank in the three time-trial events, in the three mass-start events, and in the competition overall were collated in 20 international Omnium competitions between 2010 and 2014 for 196 male and 140 female cyclists. Linear mixed modelling of the log-transformed finish time for the time-trial events and of log-transformed finish rank for all events and final rank provided estimates of within-athlete race-to-race changes in performance and average between-athlete differences across a season. These estimates were converted to various correlations representing relationships within and between the various events and final rank. Results: Intraclass correlation coefficients, representing race-to-race reproducibility of performance, were similar whether derived from finish rank or finish time for the time-trial events. Log-transformed finish ranks are therefore a suitable measure to assess and compare performance in time-trial and mass-start events. Omnium cyclists were more predictable in their performances from race-to-race in the timed events, while reduced predictability was observed in mass-start events. Inter-event correlations indicated stronger links in performance between the timed disciplines, while performance in any of the mass-start events had only a slight positive relationship with performance in the other mass-start events and little or no relationship with the timed events. Conclusions: Further investigation is warranted to determine whether factors related to performance in mass-start events can be identified to improve reproducibility or whether variability in performance results from random chance.
Conference Paper
Purpose: The purpose of this study was to assess research aimed at measuring performance enhancements that affect success of individual elite athletes in competitive events. Analysis: Simulations show that the smallest worthwhile enhancement of performance for an athlete in an international event is 0.7-0.4 of the typical within-athlete random variation in performance between events. Using change in performance in events as the outcome measure in a crossover study, researchers could delimit such enhancements with a sample of 16-65 athletes, or with 65-260 in a fully controlled study. Sample size for a study using a valid laboratory or field test is proportional to the square of the within-athlete variation in performance in the test relative to the event; estimates of these variations are therefore crucial and should be determined by repeated-measures analysis of data from reliability studies for the test and event. Enhancements in test and event may differ when factors that affect performance differ between test and event; overall effects of these factors can be determined with a validity study that combines reliability data for test and event. A test should be used only if it is valid, more reliable than the event, allows estimation of performance enhancement in the event, and if the subjects replicate their usual training and dietary practices for the study; otherwise the event itself provides the only dependable estimate of performance enhancement. Publication of enhancement as a percent change with confidence limits along with an analysis for individual differences will make the study more applicable to athletes. Outcomes can be generalized only to athletes with abilities and practices represented in the study. Conclusion: estimates of enhancement of performance in laboratory or field tests in most previous studies may not apply to elite athletes in competitive events.
Article
Recent advances in theory, algorithms, and computational power make it possible to solve complex, optimal control problems both for off-line and on-line industrial applications. This paper starts by reviewing the technical details of the solution methods pertaining to three general categories: dynamic programming, indirect methods, and direct methods. With the aid of a demonstration example, the advantages and disadvantages of each method are discussed, along with a brief review of available software. The main result that emerges is the indirect method being numerically competitive with the performance of direct ones based on non-linear programming solvers and interior point algorithms. The second part of the paper introduces an indirect method based on the Pontryagin Minimum Principle (PMP). It also presents a detailed procedure and software tools (named PINS) to formulate the problem, automatically generate the C++ code, and eventually obtain a numerical solution for several optimal control problems of practical relevance. The application of PMP relates to the analytical derivation of necessary conditions for optimality. This aspect—often regarded in the literature as a drawback—is here exploited to build a robust yet efficient numerical method that formally eliminates the controls from the resulting Boundary Value Problem, thus gaining robustness and a high convergence rate. The elimination of the control is obtained either via their explicit formulation function of state and Lagrange multipliers—when possible—or via an iterative numerical solution. The paper closes presenting a minimum time manoeuvre of a car using a fairly complex vehicle model which also includes tyre saturation.
Article
Mathematical models of performance in locomotor sports are reducible to functions of the sort y = f(x) where y is some performance variable, such as time, distance or speed, and x is a combination of predictor variables which may include expressions for power (or energy) supply and/or demand. The most valid and useful models are first-principles models that equate expressions for power supply and power demand. Power demand in cycling is the sum of the power required to overcome air resistance and rolling resistance, the power required to change the kinetic energy of the system, and the power required to ride up or down a grade. Power supply is drawn from aerobic and anaerobic sources, and modellers must consider not only the rate but also the kinetics and pattern of power supply. The relative contributions of air resistance to total demand, and of aerobic energy to total supply, increase curvilinearly with performance time, while the importance of other factors decreases. Factors such as crosswinds, aerodynamic accessories and drafting can modify the power demand in cycling, while body configuration/ orientation and altitude will affect both power demand and power supply, often in opposite directions. Mathematical models have been used to solve specific problems in cycling, such as the chance of success of a breakaway, the optimal altitude for performance, creating a ‘level playing field’ to compare performances for selection purposes, and to quantify, in the common currency of minutes and seconds, the effects on performance of changes in physiological, environmental and equipment variables. The development of crank dynamometers and portable gas-analysis systems, combined with a modelling approach, will in the future provide valuable information on the effect of changes in equipment, configuration and environment on both supply and demand-side variables.
Article
Abstract To reduce aerodynamic resistance cyclists lower their torso angle, concurrently reducing Peak Power Output (PPO). However, realistic torso angle changes in the range used by time trial cyclists have not yet been examined. Therefore the aim of this study was to investigate the effect of torso angle on physiological parameters and frontal area in different commonly used time trial positions. Nineteen well-trained male cyclists performed incremental tests on a cycle ergometer at five different torso angles: their preferred torso angle and at 0, 8, 16 and 24°. Oxygen uptake, carbon dioxide expiration, minute ventilation, gross efficiency, PPO, heart rate, cadence and frontal area were recorded. The frontal area provides an estimate of the aerodynamic drag. Overall, results showed that lower torso angles attenuated performance. Maximal values of all variables, attained in the incremental test, decreased with lower torso angles (P < 0.001). The 0° torso angle position significantly affected the metabolic and physiological variables compared to all other investigated positions. At constant submaximal intensities of 60, 70 and 80% PPO, all variables significantly increased with increasing intensity (P < 0.0001) and decreasing torso angle (P < 0.005). This study shows that for trained cyclists there should be a trade-off between the aerodynamic drag and physiological functioning.
Article
Another way of improving time trial performance is by reducing the power demand of riding at a certain velocity. Riding with hands on the brake hoods would improve aerodynamics and increase performance time by ≈5 to 7 minutes and riding with hands on the handlebar drops would increase performance time by 2 to 3 minutes compared with a baseline position (elbows on time trail handle bars). Conversely, riding with a carefully optimised position could decrease performance time by 2 to 2.5 minutes. An aerodynamic frame saved the modelled riders 1:17 to 1:44 min:sec. Furthermore, compared with a conventional wheel set, an aerodynamic wheel set may improve time trial performance time by 60 to 82 seconds. From the analysis in this article it becomes clear that novice cyclists can benefit more from the suggested alterations in position, equipment, nutrition and training compared with elite cyclists. Training seems to be the most important factor, but sometimes large improvements can be made by relatively small changes in body position. More expensive options of performance improvement include altitude training and modifications of equipment (light and aerodynamic bicycle and wheels). Depending on the availability of time and financial resources cyclists have to make decisions about how to achieve their performance improvements. The data presented here may provide a guideline to help make such decisions.
Article
We develop and test a "slip-based" method to estimate the maximum available tire-road friction during braking. The method is based on the hypothesis that the low-slip, low-mu, parts of the slip curve used during normal driving can indicate the maximum tire-road friction coefficient, We find support for this hypothesis in the literature and through experiments. The friction estimation algorithm uses data from short braking maneuvers with peak accelerations of 3.9 m/s(2) to classify the road surface as either dry (mu(max) approximate to 1) or lubricated (mu(max)approximate to0.6) . Significant measurement noise makes it difficult to detect the subtle affect being measured, leading to a misclassification rate of 20%.
Article
Abstract Mechanical models of cycling time-trial performance have indicated adverse effects of variations in external power output on overall performance times. Nevertheless, the precise influences of the magnitude and number of these variations over different distances of time trial are unclear. A hypothetical cyclist (body mass 70 kg, bicycle mass 10 kg) was studied using a mathematical model of cycling, which included the effects of acceleration. Performance times were modelled over distances of 4-40 km, mean power outputs of 200-600 W, power variation amplitudes of 5-15% and variation frequencies of 2-32 per time-trial. Effects of a "fast-start" strategy were compared with those of a constant-power strategy. Varying power improved 4-km performance at all power outputs, with the greatest improvement being 0.90 s for ± 15% power variation. For distances of 16.1, 20 and 40 km, varying power by ± 15% increased times by 3.29, 4.46 and 10.43 s respectively, suggesting that in long-duration cycling in constant environmental conditions, cyclists should strive to reduce power variation to maximise performance. The novel finding of the present study is that these effects are augmented with increasing event distance, amplitude and period of variation. These two latter factors reflect a poor adherence to a constant speed.
Article
A simple mathematical model is used to find the optimal distribution of a cyclist’s effort during a time trial. It is shown that maintaining a constant velocity is optimal if the goal is to minimise the time taken to complete the course while fixing amount of work done. However, this is usually impractical on a non-flat course because the cyclist would be unable to maintain the power output required on the climbs. A model for exertion is introduced and used to identify the distribution of power that minimises time while restricting the cyclist’s exertion. It is shown that, for a course with a climb followed by a descent, limits on exertion prevent the cyclist from improving performance by shifting effort towards the climb and away from the descent. It is also shown, however, that significant improvement is possible on a course with several climbs and descents. An analogous problem with climbs and descents replaced by headwinds and tailwinds is considered and it is shown that there is no significant advantage to be gained by varying power output. Lagrange multipliers are used solve the minimisation problems.
Article
The purpose of this study was to examine the effect of environmental temperature on variability in power output, self-selected pacing strategies, and performance during a prolonged cycling time trial. Nine trained male cyclists randomly completed four 40 km cycling time trials in an environmental chamber at 17°C, 22°C, 27°C, and 32°C (40% RH). During the time trials, heart rate, core body temperature, and power output were recorded. The variability in power output was assessed with the use of exposure variation analysis. Mean 40 km power output was significantly lower during 32°C (309 ± 35 W) compared with 17°C (329 ± 31 W), 22°C (324 ± 34 W), and 27°C (322 ± 32 W). In addition, greater variability in power production was observed at 32°C compared with 17°C, as evidenced by a lower (P = .03) standard deviation of the exposure variation matrix (2.9 ± 0.5 vs 3.5 ± 0.4 units, respectively). Core temperature was greater (P < .05) at 32°C compared with 17°C and 22°C from 30 to 40 km, and the rate of rise in core temperature throughout the 40 km time trial was greater (P < .05) at 32°C (0.06 ± 0.04°C·km-1) compared with 17°C (0.05 ± 0.05°C·km-1). This study showed that time-trial performance is reduced under hot environmental conditions, and is associated with a shift in the composition of power output. These finding provide insight into the control of pacing strategies during exercise in the heat.
Article
Article
Tractional resistance (RT, N) was determined by towing two cyclists on a racing bike in "fully dropped" posture in calm air on a flat track at constant speed (5--16.5 m/s). RT increased with the air velocity (v, m/s): RT = 3.2 + 0.19 V2. The constant 3.2 N is interpreted as the rolling resistance and the term increasing with v2 as the air resistance. For a given posture this is a function of the body surface (SA, m2), the air temperature (T, degree K), and barometric pressure (PB, Torr). The mechanical power output (W, W) can then be described as a function of the air (v) and ground (s) speed: W = 4.5.10(-2) Ps + 4.1.10(-2) SA (PB/T)v2 s, where P is the overall weight in kg. With a mechanical efficiency of 0.25, the energy expenditure rate (VO2, ml/s) is given by: VO2 = 8.6.10(-3) Ps + 7.8.10(-3) SA (PB/T)v2 s (1 ml O2 = 20.9 J). As the decrease of VO2max with altitude is known from the literature, this last equation allows the calculation of the optimal altitude for top aerobic performance. The prediction derived from this equation is consistent with the present 1-h world record.
Article
This paper focuses on the solution of two problems related to cycling. One is to determine the velocity as a function of distance which minimizes the cyclist's energy expenditure in covering a given distance in a set time. The other is to determine the velocity as a function of the distance which minimizes time for fixed energy expenditure. To solve these problems, an equation of motion for the cyclist riding over arbitrary terrain is written using Newton's second law. This equation is used to evaluate either energy expenditure or time, and the minimization problems are solved using an optimal control formulation in conjunction with the method of Miele [Optimization Techniques with Applications to Aerospace Systems, pp. 69-98 (1962) Academic Press, New York]. Solutions to both optimal control problems are the same. The solutions are illustrated through two examples. In one example where the relative wind velocity is zero, the optimal cruising velocity is constant regardless of terrain. In the second, where the relative wind velocity fluctuates, the optimal cruising velocity varies.
Article
Despite interest in competitive strategy by coaches and athletes, there are no systematically collected data regarding the effect of differences in pacing strategy on the outcome of middle distance (2-4 min duration) events. In this study different pacing strategies were evaluated using a 2-km time trial on a bicycle attached to a wind load simulator. Well-trained subjects (N = 9) performed five separate time trials with the pace during the first 50% of the trial experimentally constrained within the usual real world range from very slow (approximately 55% of best time) to very fast (approximately 48% of best time). Serial VO2 was measured to estimate the oxidative contributions to the trial and accumulated O2 deficit and postexercise blood lactate measured to estimate the anaerobic contribution to the trial. The evenly paced trial (first 1 km = 50.9% final time) produced the fastest total time. The starting pace to final time relationship was described by a U shaped second order polynomial curve with the nadir for final time at a starting pace of 51% of best total time. There were no systematic differences in serial VO2, accumulated O2 deficit, or postexercise lactate that could account for the pacing related variations in performance. The data support the concept of relatively even pacing in middle distance events with negative consequences for even small variations in this strategy.
Article
This study determined whether a 4-wk high-intensity interval training program (HIT) would improve the 40-km time trial performances (TT40) of 8 competitive cyclists (peak O2 uptake 5.2 +/- 0.4 I.min-1) with a background of moderate-intensity endurance training (BASE). Before intervention, all cyclists were tested on at least three separate occasions to ensure that their baseline performances were stable. In these tests, peak sustained power output (PPO) was measured during a progressive exercise test, muscular resistance to fatigue was determined during a timed ride to exhaustion at 150% of PPO (TF150), and a TT40 was performed on a cycle-simulator. The coefficient of variation for all baseline tests was < 1.7 +/- 1.3% (mean +/- SD). Cyclists then replaced 15 +/- 2% of their approximately 300 km.wk-1 BASE training with HIT, which took place on 6 d and consisted of six to eight 5-min repetitions at 80% of PPO, with 60-s recovery between work bouts. HIT significantly improved TT40 (56.4 +/- 3.6 vs 54.4 +/- 3.2 min; P < 0.0001), PPO (416 +/- 32 vs 434 +/- 34 W; P < 0.01) and TF150 (60.5 +/- 9.3 vs 72.5 +/- 7.6 s; P < 0.01). The faster TT40 was due to a significant increase in both the cyclists' absolute (301 +/- 42 vs 326 +/- 43 W; P < 0.0001) and relative (72.1 +/- 5.6 vs 75.0 +/- 6.8% of PPO; P < 0.05) power output after HIT. These results indicate that a 4-wk program of HIT increased the PPO and fatigue resistance of competitive cyclists and improved their 40-km time trial performances.
Article
The effect of varying power, while holding mean power constant, would have on cycling performance in hilly or windy conditions was analyzed. Performance for a 70-kg cyclist on a 10-km time trial with alternating 1-km segments of uphill and downhill was modeled, with mean VO2 (3, 4, 5 L.min-1), variation in VO2 (5, 10, 15%), and grade (0, 5, 10, 15%) used as independent variables. For the conditions of 4 L.min-1, 10% variation, and 10% grade, results were as follows: finishing time of 22:47.2 with varied power, versus 24:20.3 at constant power, for a time savings of 1 min 33.1 s. Separately, a 40-km time trial with alternating 5-km segments of headwind and tailwind (0, 8, 16, 24 km.h-1) was modeled, with the following results for the conditions of 4 L.min-1, 10% variation, and wind speed of 16 km.h-1: finishing time of 60:21.2 with power variation vs 60:50.2 at constant power, for a time savings of 29 s. Time saved was directly proportional to variation in VO2, grade, and wind speed and was indirectly proportional to mean VO2. In conclusion, the model predicts that significantly time savings could be realized on hilly and windy courses by slightly increasing power on uphill or headwind segments while compensating with reduced power on downhill or tailwind segments.
Article
The purpose of this study was to assess research aimed at measuring performance enhancements that affect success of individual elite athletes in competitive events. Simulations show that the smallest worthwhile enhancement of performance for an athlete in an international event is 0.7-0.4 of the typical within-athlete random variation in performance between events. Using change in performance in events as the outcome measure in a crossover study, researchers could delimit such enhancements with a sample of 16-65 athletes, or with 65-260 in a fully controlled study. Sample size for a study using a valid laboratory or field test is proportional to the square of the within-athlete variation in performance in the test relative to the event; estimates of these variations are therefore crucial and should be determined by repeated-measures analysis of data from reliability studies for the test and event. Enhancements in test and event may differ when factors that affect performance differ between test and event; overall effects of these factors can be determined with a validity study that combines reliability data for test and event. A test should be used only if it is valid, more reliable than the event, allows estimation of performance enhancement in the event, and if the subjects replicate their usual training and dietary practices for the study; otherwise the event itself provides the only dependable estimate of performance enhancement. Publication of enhancement as a percent change with confidence limits along with an analysis for individual differences will make the study more applicable to athletes. Outcomes can be generalized only to athletes with abilities and practices represented in the study. estimates of enhancement of performance in laboratory or field tests in most previous studies may not apply to elite athletes in competitive events.
Article
Male professional road cycling competitions last between 1 hour (e.g. the time trial in the World Championships) and 100 hours (e.g. the Tour de France). Although the final overall standings of a race are individual, it is undoubtedly a team sport. Professional road cyclists present with variable anthropometric values, but display impressive aerobic capacities [maximal power output 370 to 570 W, maximal oxygen uptake 4.4 to 6.4 L/min and power output at the onset of blood lactate accumulation (OBLA) 300 to 500 W]. Because of the variable anthropometric characteristics, 'specialists' have evolved within teams whose job is to perform in different terrain and racing conditions. In this respect, power outputs relative to mass exponents of 0.32 and 1 seem to be the best predictors of level ground and uphill cycling ability, respectively. However, time trial specialists have been shown to meet requirements to be top competitors in all terrain (level and uphill) and cycling conditions (individually and in a group). Based on competition heart rate measurements, time trials are raced under steady-state conditions, the shorter time trials being raced at average intensities close to OBLA (approximately 400 to 420 W), with the longer ones close to the individual lactate threshold (LT, approximately 370 to 390 W). Mass-start stages, on the other hand, are raced at low mean intensities (approximately 210 W for the flat stages, approximately 270 W for the high mountain stages), but are characterised by their intermittent nature, with cyclists spending on average 30 to 100 minutes at, and above LT, and 5 to 20 minutes at, and above OBLA.
Variability of competitive performance of elite athletes: a systematic review
• R M Malcata
• W G Hopkins
Malcata RM and Hopkins WG. Variability of competitive performance of elite athletes: a systematic review. Sports Med 2014; 44: 1763-1774.
Effect of heat and heat acclimatization on cycling time trial performance and pacing
• S Racinais
• Périard
• Jd
• A Karlsen