Related papers: On minimizing cyclists' ascent times
VAM ({\it velocit\`a ascensionale media}) is a measurement that quantifies a cyclist's climbing ability. We show that to minimize the time to attain a given height gain\, -- \,which is tantamount to maximizing VAM\, -- \,a cyclist should…
The velocit\`a ascensionale media (VAM) is measurement that quantifies a cyclist's climbing ability. It depends on both the ground speed of a bicycle-cyclist system and the slope of an incline. To maximize the ascent speed, the solution to…
We formulate an optimization of a bicycle ascent time under the constraints of the average, maximum, and minimum powers. In contrast to the first part of this study, we do not restrict the departure to flying starts with an initial speed…
This paper formulates optimal pacing of a cyclist on hilly terrain time-trials as a minimum-time optimal control problem. Maximal power of a cyclist serves as a time-varying constraint and depends on fatigue and recovery which are captured…
We formulate a phenomenological model to study the power applied by a cyclist on a velodrome\, -- \,for individual timetrials\, -- \,taking into account the straights, circular arcs, connecting transition curves and banking. The dissipative…
We combine power-meter measurements with GPS measurements to study the model that accounts for the use of power by a cyclist. The model takes into account the change in elevation and speed along with adverse effects of air, rolling and…
Improving a cyclist performance during a time-trial effort has been a challenge for sport scientists for several decades. There has been a lot of work on understanding the physiological concepts behind it. The concepts of Critical Power…
With the advent of power-meters allowing cyclists to precisely track their power outputs throughout the duration of a race, devising optimal power output strategies for races has become increasingly important in competitive cycling. To do…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…
Bicycle Power Meters have become ubiquitous in professional and amateur cycling. These devices claim high levels of accuracy, and this accuracy is indeed essential if they are to serve their purpose as reliable training aids and indicators…
This paper presents for the first time an approach to minimize direct operational costs (DOC) for all-electric aircraft during the climb phase, introducing a time-varying cost index (CI). The CI is modeled as a dynamic parameter commanded…
Many time-trial and triathlon bicycle races take place on relatively flat, closed-circuit courses. In the absence of hills, riding-speed is limited almost solely by aerodynamic drag; consequently, winds can have a big effect on elapsed…
When computing the average speed of a car over different time periods from given GPS data, it is conventional wisdom that the maximal average speed over all time intervals of fixed length decreases if the interval length increases. However,…
Optimization of energy cost determines average values of spatio-temporal gait parameters such as step duration, step length or step speed. However, during walking, humans need to adapt these parameters at every step to respond to exogenous…
The aim of this paper is to bring a mathematical justification to the optimal way of organizing one's effort when running. It is well known from physiologists that all running exercises of duration less than 3mn are run with a strong…
Theory of stochastic processes provides theoretical tools which can be efficiently used to explore properties of noise induced escape kinetics. Since noise facilitated escape over the potential barrier resembles free climbing, one can use…
Traffic-related pollution is becoming a major societal problem globally. Cyclists are particularly exposed to this form of pollution due to their proximity to vehicles' tailpipes. In a number of recent studies, it is been shown that…
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the…
The analysis of trail-running performance appears to be complex and cardio-respiratory and muscular factors could have a variable importance depending on the inclination. Our study aims to determine the role of these parameters in…
Estimating the altimeters a cyclist has climbed from noisy GPS data is a challenging problem. In this article a method is proposed that assumes that a person locally takes the shortest path. This results in an algorithm that does not need…