Simulation
Tour de Romandie Prologue Optimization
Minimum lap time simulation of the 2024 Tour de Romandie prologue in Saint-Imier, comparing the optimal trajectory against a center-line baseline and demonstrating how a cyclist's energy reservoir couples all states across the lap.
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Cycling as a Dynamic Sport
For most road cycling disciplines, steady-state simulation is sufficient: the terrain is long relative to the speeds and accelerations involved, and optimal pacing can be computed segment by segment. Prologue time trialing is the exception. These short, technical events in city centres are often won by strong sprinters who can accelerate hard out of tight corners, and the trajectory geometry matters as much as the power output.
The Simulation
The minimum lap time optimizer was applied to the Tour de Romandie prologue in Saint-Imier, Switzerland. The circuit runs through a city centre with multiple corners that reward wide lines and well-timed accelerations.
To quantify the value of line choice, the optimal trajectory is compared against a constrained variant where the rider is required to follow the circuit centerline throughout. The time deficit of the centerline approach amounts to almost 15% of total prologue time — a number large enough to decide a race.
The Energy Constraint
The feature that makes cycling categorically different from motor sport lap time simulation is the rider's energy reservoir. A cyclist cannot sustain maximum power indefinitely; after a full effort, subsequent outputs are severely compromised until recovery sets in. This is included in the model by adding the rider's energy state as a variable, with coupling between the current energy level and the achievable power output at every subsequent point in the lap.
This coupling is what makes the problem dynamically rich despite the relatively simple vehicle model: the entire trajectory is connected through the energy state, and the optimizer must commit to a pacing strategy that accounts for what remains in the tank at every corner exit.
Computational Performance
Despite the added coupling, computing the optimal trajectory and pacing plan with a realistic rider power model takes minutes, not hours. That performance is what makes the digital twin framing meaningful: a simulation that could run in real time with current hardware, given properly calibrated rider and bicycle models.