01 / MECHANICS & OPTIMISATION

THE FASTEST WAY DOWN.

Three tracks. Identical endpoints. One surprising winner. Explore Bernoulli’s brachistochrone problem in a live 3D gravity laboratory.

THE TIME-OPTIMAL CURVE

x = a(θ − sin θ)

y = a(1 − cos θ)

Ideal sliding, zero energy loss

INTERACTIVE TEST BENCH / VIEW 01WEBGL2 / REALTIME

3D EXPERIMENT10.00 m span / 3.80 m drop

CYCLOID STRAIGHT CIRCULAR ARC

DRAG TO ORBIT · SCROLL TO ZOOM

ELAPSED 00.000 s

02 / LIVE TELEMETRY

Race results

READY TO LAUNCH

CYCLOID 01

— s

0.0% COMPLETE0.0 m/s

STRAIGHT 02

— s

0.0% COMPLETE0.0 m/s

CIRCULAR ARC 03

— s

0.0% COMPLETE0.0 m/s

03 / DISPLACEMENT ANALYSIS

Progress over time

0% DISTANCESIMULATION TIME (s) →100% DISTANCE

EXPERIMENT CONTROLS

Configure the run

Adjust parameters, then launch all three racers simultaneously.

ENVIRONMENT 01

Gravitational acceleration 9.81 m/s²

1 m/s²20 m/s²

Vertical drop 3.80 m

1.0 m5.0 m

OBJECT DYNAMICS 02

Body model Rolling / sliding resistance 0.000

No lossHigh loss

Quadratic air drag 0.000 m⁻¹

00.06 m⁻¹

TRACK GEOMETRY 03

Circular arc sagitta 1.55 m

0.3 m3.0 m

Simulation speed 1.00×

0.25×4×

LOAD PRESET

WHY THE CYCLOID?

A steep initial fall produces speed early, while the optimal curve balances that speed against path length. In ideal sliding, it minimises travel time between two fixed points.

BRACHISTOCHRONE · BERNOULLI, 1696

Made with 🤖 ChatGPT · Three.js