Peloton-Aware Breakaway Strategy Model

A physics-based and optimisation-driven model for analysing cycling breakaway strategies under realistic race conditions, including terrain variation, rider physiology, and peloton dynamics.

This project answers a key question:

When should a rider attack, and at what power, to beat the peloton?

Overview

This model simulates a cycling race over a continuous course and evaluates:

• Peloton dynamics (passive vs strategic)
• Rider endurance constraints
• Terrain-dependent resistance
• Breakaway feasibility and optimal timing

The model integrates a physical description of cycling motion with rider-specific endurance profiles and numerical optimisation techniques. It evaluates breakaway strategies by combining terrain-dependent dynamics, physiological constraints, and brute-force search over possible attack scenarios.

Project Context

This project builds on earlier group work developed for the Tour de Oxford modelling study: https://github.com/PabloSavina/MM-Tour-de-Oxford

The current implementation extends that work by moving from MATLAB-based experimentation to a modular Python framework, introducing rider-specific endurance models, flexible terrain profiles, and a systematic optimisation pipeline. In addition, the peloton is no longer treated as purely constant-power: the model now includes a strategically responsive peloton that adjusts effort based on terrain (e.g. increasing power on climbs) and race phase (e.g. late-race surges), allowing direct comparison between passive and adaptive group dynamics.

Core Idea

At every point along the track, speed is determined by solving:

$$\frac{P}{v} = \gamma v^2 + \mu_r m g + m g \sin(\theta(x))$$

which balances:

• aerodynamic drag
• rolling resistance
• gravity
• rider power

From this, total race time is computed via:

$$T = \int \frac{1}{v(x)} \, dx$$

Breakaways are evaluated by splitting the race into:

• Peloton phase (before attack)
• Solo phase (after attack)

subject to rider endurance limits.

Rider Models

Three archetypes are implemented:

Rider Type	Model	Strength
Sprinter	Exponential decay	High short-term power
Climber	Hyperbolic	Sustained climbing ability
Time-Trialist	Composite	Balanced endurance

Each rider has a power-duration relationship.

Sprinter

$$P(t) = b + (M - b)e^{-kt}$$

Climber

$$P(t) = a t^{-d}$$

Time-trialist

$$\Delta t(P) = \alpha \cdot (\text{hyperbolic}) + (1-\alpha)\cdot (\text{exponential})$$

Track Profiles

Supports multiple terrain types:

• Flat
• Hill / Steep hill / Sharp hill
• Double hill
• Mountainous (“hills and valleys”)
• Custom composite profiles

Terrain influences speed via slope:

$$\theta(x)$$

Peloton Models

Passive Peloton

• Constant power output

Strategic Peloton

• Increases effort on climbs
• Late-race surge
• Terrain-aware pacing

Breakaway Optimisation

The model evaluates:

• Breakaway location x_b ∈ [0,1]
• Breakaway power P_b

Using:

• brute-force grid search
• feasibility constraint:

$$T_{\text{solo}} \leq \text{endurance}(P_b)$$

Outputs:

• Optimal breakaway point
• Required power
• Total finishing time
• Time gained vs peloton

Visualisations

The notebook produces:

1. Finishing Time vs Breakaway Point

• Separate plots for:
  • Passive peloton
  • Strategic peloton
• Shows optimal attack timing

2. Optimal Breakaway Points on Track

• Elevation profile
• Markers showing:
  • where each rider should attack
  • required power (W/kg)

3. Comparative Strategy Analysis

• Side-by-side rider comparisons
• Time advantage vs peloton

Project Structure

src/
│
├── backward_method.py      # Core physics + breakaway evaluation
├── grid_search.py          # Strategy optimisation
├── rider_models.py         # Rider endurance models
├── strategic_peloton.py    # Peloton behaviours
├── track_profiles.py       # Terrain definitions
├── plotting.py             # Visualisation utilities
│
notebooks/
└── demo.ipynb          # Main simulation + plots

Installation

git clone https://github.com/ChamuV/peloton-aware-breakaway-model.git
cd peloton-aware-breakaway-model

pip install -r requirements.txt

Usage

Run the notebook:

jupyter notebook notebooks/analysis.ipynb

Or use the API:

from src.grid_search import run_grid_search_best
from src.rider_models import get_rider

rider = get_rider("climber")

result = run_grid_search_best(
    rider=rider,
    track_name="hill"
)

print(result)

Example Output

[CLIMBER]
Power:     5.6 W/kg
Break @    31 km
Breakaway: 134.96 min
Peloton:   135.72 min
Lead:      0.77 min

[SPRINTER]
Power:     10.3 W/kg
Break @    90 km
Lead:      1.84 min

Key Insights

• Late breakaways dominate for high-power riders (sprinters)
• Climbers benefit from earlier attacks on terrain
• Strategic pelotons significantly reduce breakaway success
• Optimal strategy is highly sensitive to:
  • terrain profile
  • endurance curve
  • peloton behaviour

Possible Extensions

• Drafting effects
• Stochastic race dynamics
• Multi-rider breakaways
• Game-theoretic peloton response
• Real-world race data calibration

License

This project is licensed under the MIT License. See the LICENSE file for details.