Horse Riding
Geometry & Trigonometry
Model the geometry of a horse's circular exercise track (or any circular training path) using real GPS data from your own riding, running or cycling session.
Introduction
A horse moving in a circle on a lunging line, or a rider circling on a track, covers different distances depending on the circle's radius, even at the same angular speed. GPS data from a phone or watch during a real riding, running or cycling session records positions over time, and from that track you can measure radius, speed and lap length directly rather than relying on textbook numbers. This exploration uses your own GPS data (or a real session's) to model circular and near-circular motion.
Guiding Questions
- A horse (or rider) on a circular exercise track covers different distances at different radii. How does lap length depend on the radius?
- For a rider circling at constant speed, how do lap time and the rate of turning (angular speed) change with radius?
- Plan a training session combining circles of different radii to hit a target total distance.
- Use GPS data from a real riding, running or cycling session to model the actual paths ridden, and compare the modelled and measured distances.