Related papers: Optimal Time-Trial Bicycle Racing with Headwinds a…
In match race sailing, competitors must steer their boats upwind in the presence of unpredictably evolving weather. Combined with the tacking motion necessary to make upwind progress, this makes it natural to model their path-planning as a…
Pumping airborne wind energy (AWE) systems employ a kite to convert wind energy into electricity, through a cyclic reeling motion of the tether. The problem of computing the optimal reeling speed for the sake of maximizing the average cycle…
Our aim is to present a new model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem. We provide…
A numerical model of 100 m and 200 m world class sprinting performances is modified using standard hydrodynamic principles to include effects of air temperature, pressure, and humidity levels on aerodynamic drag. The magnitude of the…
A quick and fun investigation into the effects of correcting for wind assistance/resistance and drag on 100m sprint performances. Considered are World 100m rankings, as well as Canadian rankings
We analyse the classical problem of the stability of bicycles when moving quickly and upright. Developing a lean causes the front wheel to turn thereby setting the bicycle instantaneously into circular motion. The centripetal force…
Modeling preference time in triathlons means predicting the intermediate times of particular sports disciplines by a given overall finish time in a specific triathlon course for the athlete with the known personal best result. This is a…
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…
Both the shortest and the longest blowup time for a controlled system are considered. Existence result and maximum principle for optimal triple are established. Thanks to some monotonicity of the controlled system, some kinds of "the front…
Extensive research has been dedicated to optimizing the cyclist's position on the bike to enhance aerodynamic performance. This study aims to further investigate the aerobars position effect on cycling speed. Drawing from previous work…
Based on a mathematical simulation which reproduces accurate split and velocity profiles for the 100 and 200 metre sprints, the magnitudes of altitude and mixed wind/altitude-assisted performances as compared to their sea-level equivalents…
In drone racing, the time-minimum trajectory is affected by the drone's capabilities, the layout of the race track, and the configurations of the gates (e.g., their shapes and sizes). However, previous studies neglect the configuration of…
We prove that, given an average power, the ascent time is minimized if a cyclist maintains a constant ground speed regardless of the slope. Herein, minimizing the time is equivalent to maximizing -- for a given uphill -- the corresponding…
Airborne Wind Energy is a lightweight technology that allows power extraction from the wind using airborne devices such as kites and gliders, where the airfoil orientation can be dynamically controlled in order to maximize performance. The…
In ride-hailing systems, en-route time refers to the time that elapses from the moment a car is dispatched to pick up a rider until the rider is picked up. A fundamental phenomenon in ride-hailing systems is that there is a trade-off…
Consider the circle $C$ of length 1 and a circular arc $A$ of length $\ell\in (0,1)$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds…
We consider the problem of controlling a vehicle to arrive at a fixed destination while minimizing a combination of energy consumption and travel time. Our model includes vehicle speed and accelaration limits, aerodynamic drag, rolling…
Minimum-time navigation within constrained and dynamic environments is of special relevance in robotics. Seeking time-optimality, while guaranteeing the integrity of time-varying spatial bounds, is an appealing trade-off for agile vehicles,…
The optimal control problem for the kinematic bicycle model is considered where the trajectories are required to satisfy the safety constraints in the continuous-time sense. Based on the differential flatness property of the model,…
In this paper, we propose the reduced model for the full dynamics of a bicycle and analyze its nonlinear behavior under a proportional control law for steering. Based on the Gibbs-Appell equations for the Whipple bicycle, we obtain a…