Explore the Track
Use the animation to compare a track that moves abruptly into circular curvature with a track that transitions gradually using an Euler spiral. Watch the curvature graphs and notice how the smoother design avoids sudden jumps in bending.
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Curvature and Loop Design
The visual compares circular curvature with a smoother clothoid-style transition. The graphs below the track show how curvature changes.
Where It Started
This project began with the question of why real roller coaster loops are not perfect circles.
That question leads naturally to curvature: how sharply a track bends, and how that bending changes as the coaster moves along the track.
Going Further
The next step is to connect curvature to acceleration and g-forces.
\[
a_c=v^2\kappa=\frac{v^2}{R}.
\]
This connects the geometry of the track to the forces riders feel.