Properly Scaling the Speed of a Model Roller Coaster
Jared Pincus

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 495–498
Short Papers

Abstract

The scale-model roller coaster is a niche artform growing in popularity among coaster enthusiasts. These gravity-powered models present unique design challenges compared to, say, model railroads. In particular, gravity does not scale proportionately with a model’s size; this commonly produces a cognitive dissonance in which a model coaster’s train appears to travel inappropriately “fast.” The physics underlying this discrepancy is frequently misunderstood, and most commonly proposed solutions are either invalid or imprecise. This paper will properly assess these proposals, and show definitively how this dissonance is mathematically reconcilable.

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