This document describes an agent-based model called MOPED that simulates peloton dynamics in competitive cycling. The model incorporates both dynamical parameters inspired by flocking models to simulate movement and energetic parameters using established physiological equations to calculate energy expenditure. Simulation results demonstrate emergent behaviors like rotation and convection that resemble real-life pelotons. However, the model has limitations and its prediction that active cyclists expend less energy requires improvement. The author presents this work as an initial step toward modeling both the dynamics and energetics of cycling pelotons.

1. Introduction
Model
Results
Discussion
MOPED
An agent-based model for peloton dynamics in competitive
cycling
Erick Martins Ratamero
21/10/2011
Erick Martins Ratamero MOPED

2. Introduction
Model
Results
Discussion
Table of contents
1 Introduction
2 Model
Dynamical Parameters
Energetic Parameters
Overview
3 Results
General Behaviour
Dynamical Parameters
Energetic Parameters
4 Discussion
Erick Martins Ratamero MOPED

3. Introduction
Model
Results
Discussion
Introduction
Drafting as the basis for complex behaviours
Mathematical, Physiological and Dynamical concepts
First effort into an agent-based model of pelotons
Main objective: consistency with real-life behaviour
Erick Martins Ratamero MOPED

4. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
Dynamical Parameters
Inspiration from flocking models
Only cohesion and separation forces apply to our model
Lateral movement instead of steering
Improvement - Swarm Chemistry model
Erick Martins Ratamero MOPED

5. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
From Swarm Chemistry to MOPED
What to change?
No isotropic vision - humans can’t look back!
Different scales of distance for different forces
Bias to the center of the road
Small random acceleration
Active agents: small bias to the front
Erick Martins Ratamero MOPED

6. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
Energetic Parameters
Well-know set of equations
Abundant Physiological data
Calculate energy expenditures
Address both energy and dynamics
Erick Martins Ratamero MOPED

7. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
Draft Coefficient
2
CFdraft = 0.62 − 0.0104dw + 0.0452dw
”Comet’s tail” effect
Different weights for different angles
Drafting is negligible for distances bigger than 3m
Erick Martins Ratamero MOPED

8. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
Power Equations
Pair = kCFdraft v 3
Proll+PE = (Cr + Gr )g (M + Mb)v
Constants k and Cr are from empirical data and have typical
values
Valid for relatively small values of Gr (smaller than 10%,
typically)
Erick Martins Ratamero MOPED

9. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
Time to Exhaustion
How to model the time it takes for a cyclist to run out of
energy?
Ptot
ln(Tlim ) = −6.351 ln( Max10 ) + 2.478
Typical Max10 for professional cyclists: 450W
Lactate Threshold as a measure of recovery
Cyclists spending more than their LT power are using their
”reserves”
Erick Martins Ratamero MOPED

10. Introduction
Dynamical Parameters
Model
Energetic Parameters
Results
Overview
Discussion
Energetic Parameters
Dynamical and Energetic model influence each other
Drafting coefficient and exhaustion as coupling factors
Erick Martins Ratamero MOPED

11. Introduction
General Behaviour
Model
Dynamical Parameters
Results
Energetic Parameters
Discussion
General Behaviour
Rotation when frontrunner feels under the peloton average
Narrow front, wider back conform to real life
Convection dynamics - see demo!
Dissipative dynamics - Rayleigh-Bernard cells, penguin huddle
rotations
Relevant result in terms of energy without considering energy
for dynamics!
Active cyclists take over the head of the peloton
Exhausted riders give up on the peloton, but can eventually
come back
Erick Martins Ratamero MOPED

12. Introduction
General Behaviour
Model
Dynamical Parameters
Results
Energetic Parameters
Discussion
Dynamical Parameters
Difficult to quantify
General dynamics seem to conform to real life
Convection dynamics shown graphically
Erick Martins Ratamero MOPED

13. Introduction
General Behaviour
Model
Dynamical Parameters
Results
Energetic Parameters
Discussion
Simulated Race
Erick Martins Ratamero MOPED

14. Introduction
General Behaviour
Model
Dynamical Parameters
Results
Energetic Parameters
Discussion
Uphills and Downhills
The peloton arriving on top of a climb...
and then during the downhill.
Erick Martins Ratamero MOPED

15. Introduction
General Behaviour
Model
Dynamical Parameters
Results
Energetic Parameters
Discussion
Active Cyclists - a paradox?
Active riders are actually spending less energy - how is that
possible?
Erick Martins Ratamero MOPED

16. Introduction
General Behaviour
Model
Dynamical Parameters
Results
Energetic Parameters
Discussion
Independence of number of active riders
The same result holds for 5 active cyclists instead of 20.
Erick Martins Ratamero MOPED

17. Introduction
Model
Results
Discussion
Discussion
Interesting, even counter-intuitive results
Active cyclists problem: a bit worrying. However, model can
be improved in that sense (look for draft)
Many real-life factors are not present (e.g. wind)
Strategical aspects were not modelled (unfortunately)
First try ever to couple dynamics and energy expenditure
analysis in one single model
Not a complete work in any way, rather a first step
Erick Martins Ratamero MOPED