Optimizing the breakaway position in cycle races using mathematical modelling

Gaul, Lothar; Thomson, Stuart; Griffiths, Ian M.

doi:10.1007/s12283-018-0270-5

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…The friction force F f is due to the bicycle tyres in contact with the road surface. We model Coulomb friction [24], neglecting corrections for speed and heat generated on tyres, though a simpler constant friction force is also widely used [14]. As T 2…”

Section: Forces On a Ridermentioning

confidence: 99%

“…We neglect a number of other effects in our model such as wheel bearing friction, slope resistance (ascending) and assistance (descending), frictional loss in the drive chain, and the inertial force [1,10,18], as well as environmental and physiological factors [14,29]. For simplicity, we neglect changes in aerodynamic effects when cornering [6].…”

Section: Forces On a Ridermentioning

confidence: 99%

“…A Brachistochrone problem in Cartesian coordinates solves the optimal dynamics in a velodrome [13]. For road cycling, weakly undulating courses in one dimension allow for analysis of riding dynamics, incorporating physiology for energy expenditure [14]. A further model considers the time evolution of the energy balance between kinetic and potential energy for external forces of mechanical power, drag, and rolling resistance [15].…”

Section: Introductionmentioning

confidence: 99%

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Modelling road cycling as motion on a curve

Nee

Herterich

2022

Sports Eng

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We present a mathematical model of road cycling on arbitrary routes using the Frenet–Serret frame. The route is embedded in the coupled governing equations. We describe the mathematical model and numerical implementation. The dynamics are governed by a balance of forces of gravity, drag, and friction, along with pedalling or braking. We analyse steady-state speed and power against gradient and curvature. The centripetal acceleration is used as a control to determine transitions between pedalling and braking. In our model, the rider looks ahead at the curvature of the road by a distance dependent on the current speed. We determine such a distance (1–3 s at current speed) for safe riding and compare with the mean power. The results are based on a number of routes including flat and downhill, with variations in maximum curvature, and differing number of bends. We find the braking required to minimise centripetal acceleration occurs before the point of maximum curvature, thereby allowing acceleration by pedalling out of a bend.

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Section: Forces On a Ridermentioning

confidence: 99%

Section: Forces On a Ridermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling road cycling as motion on a curve

Nee

Herterich

2022

Sports Eng

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“…Riding in a tightly formed group of riders (i.e., peloton/bunch) increases the drafting effect as the larger number of riders provides shelter from frontal air resistance (i.e., wind) [41]. Indeed minimising the wind resistance can lower the aerodynamic drag down to 50–70%, compared to riding isolated [42,43]. Moreover, sheltering in the mid-rear of a peloton can see drag reduced down to 5–10% [41], resulting in a substantially reduced energy expenditure [41,44].…”

Section: Minimising the Effects Of Cycling On Running Performance mentioning

confidence: 99%

The Rise of Elite Short-Course Triathlon Re-Emphasises the Necessity to Transition Efficiently from Cycling to Running

Walsh

2019

Sports

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Transitioning efficiently between cycling and running is considered an indication of overall performance, and as a result the cycle–run (C–R) transition is one of the most researched areas of triathlon. Previous studies have thoroughly investigated the impact of prior cycling on running performance. However, with the increasing number of short-course events and the inclusion of the mixed relay at the 2020 Tokyo Olympics, efficiently transitioning from cycle–run has been re-emphasised and with it, any potential limitations to running performance among elite triathletes. This short communication provides coaches and sports scientists a review of the literature detailing the negative effects of prior variable-cycling on running performance experienced among elite, short-course and Olympic distance triathletes; as well as discussing practical methods to minimise any negative impact of cycling on running performance. The current literature suggests that variable-cycling negatively effects running ability in at least some elite triathletes and that improving swimming performance, drafting during cycling and C–R training at race intensity could improve an athlete’s triathlon running performance. It is recommended that future research clearly define the performance level, competitive format of the experimental population and use protocols that are specific to the experimental population in order to improve the training and practical application of the research findings.

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“…As a natural consequence of reduced energy requirements in a peloton, cyclists fatigue more slowly in a group than they would when isolated (Gaul et al, 2018). This may be presumed a ubiquitous effect among organisms.…”

Section: Energy-saving Mechanismmentioning

confidence: 99%

Cell pelotons: A model of early evolutionary cell sorting, with application to slime mold Dictyostelium discoideum

Trenchard¹

2019

Journal of Theoretical Biology

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A theoretical model is presented for early evolutionary cell sorting within cellular aggregates. The model involves an energy-saving mechanism and principles of collective self-organization analogous to those observed in bicycle pelotons (groups of cyclists). The theoretical framework is applied to slime-mold slugs (Dictyostelium discoideum) and incorporated into a computer simulation which demonstrates principally the sorting of cells between the anterior and posterior slug regions. The simulation relies on an existing simulation of bicycle peloton dynamics which is modified to incorporate a limited range of cell metabolic capacities among heterogeneous cells, along with a tunable energy-expenditure parameter, referred to as an "output-level" or "starvation-level" to reflect diminishing energetic supply, proto-cellular dynamics are modelled for three output phases: "active", "suffering", and "dying or dead." Adjusting the starvation parameter causes cell differentiation and sorting into sub-groups within the cellular aggregate. Tuning of the starvation parameter demonstrates how weak or expired cells shuffle backward within the cellular aggregate.Keywords: early evolutionary stage; energy-saving mechanism; heterogeneous metabolic outputs; output phase; peloton; slime mold; Dictyostelium discoideum MSC 92-08 Highlights• A non-chemotactic model of cell-migration and sorting is presented • Model includes three main parameters:1. Cell motile speed or equivalent metabolic capacity, or diminishing energetic supply 2. Range of individual cell maximum sustainable outputs 3. An energy-saving mechanism • Model demonstrates three main phases of collective behavior • Model suggests an early-evolutionary stage for cellular slime-molds

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Optimizing the breakaway position in cycle races using mathematical modelling

Cited by 5 publications

References 16 publications

Modelling road cycling as motion on a curve

Modelling road cycling as motion on a curve

The Rise of Elite Short-Course Triathlon Re-Emphasises the Necessity to Transition Efficiently from Cycling to Running

Cell pelotons: A model of early evolutionary cell sorting, with application to slime mold Dictyostelium discoideum

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