The Hidden Golden Ratio in Bicycle Geometry
The Hidden Golden Ratio in Bicycle Geometry A Surprising Discovery in Frame Proportions While designing a minimalist aluminum bicycle frame, I stumbled upon something remarkable that appears to have gone unnoticed in cycling literature: the relationship between front-center and chainstay length across most mountain bike frames approximates the golden ratio (φ ≈ 1.618). The front-center is the horizontal distance from the front wheel axle to the bottom bracket, while the chainstay length runs from the bottom bracket to the rear wheel axle. When you divide the front-center by the chainstay length across various bicycle types, a consistent pattern emerges. Road bikes typically show front-centers of 680-720mm with chainstays of 410-420mm, yielding ratios between 1.62 and 1.71. Mountain bikes display front-centers of 700-750mm and chainstays of 430-450mm, giving ratios from 1.59 to 1.67. Gravel bikes fall into similar territory with front-centers of 690-730mm and chainstays of 420-435...