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View of Castle Hill, the principal hill modelled in this article, from Jezzine Barracks.
My tricycle at the top of Castle Hill on 18 October 2026.

This article derives the equations of motion of a tricycle going downhill after brake failure. This article definitely does not advocate sabotaging one's brakes, as modelling the descent clearly shows that potentially lethal and uncontrollable speeds are achieved rather quickly. Further, on Castle Hill, where many of these models are specifically applied to, the velocities modelled would be illegal given it has a 40 km/hr speed limit. For those unfamiliar, Castle Hill is a 286-metre granite monolith in Townsville, Australia.

See this notebook showing some simulations, conducted with the help of ChatGPT, based on the equations of motion formulated in this article.

© Brenton Horne. I do not claim to be infallible, so feel free to open issues or pull requests on GitHub if you notice flaws or things that can be improved.
I favour Oxford spelling, so if you notice I generally use different spelling to Australian spelling, that is probably why.
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Last modified: October 23, 2026.