How do I simulate a roller-coaster loop?

Open this page and use the live Spring-Mass Systems tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a roller-coaster loop from your own measurements.

Use case · powered by Spring-Mass Systems

Spring-Mass Systems for a roller-coaster loop

Simulate a roller-coaster loop live in your browser. This runs the real Spring-Mass Systems solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Cloth

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Cloth / Spring-Mass StudioLive

Verlet integration · constraint relaxation

Controls

Speed1×

A grid of masses linked by springs, pinned at the top. Grab any node and drag it around — it's a real Verlet cloth simulation.

Presets

Gravity

Wind

▶ Run in Python

Data Inspector

Nodes28×20

IntegratorVerlet

Constraintsdistance (×3/frame)

Governing equation

x^{'} = 2 x - x_{p r e v} + a Δ t^{2}, ∣ p_{i} - p_{j} ∣ = 16

Reading this result: No wind, so the cloth hangs straight down from its pinned top row and settles into a smooth catenary once the motion damps out.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Standing Waves

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Standing Waves on a StringLive

harmonics · nodes & antinodes

Controls

Speed1×

A string fixed at both ends can only vibrate at its harmonics. Each mode n has n+1 nodes (pink) that stay still while the antinodes swing — the physics of every stringed instrument.

Presets

Harmonic n

Fundamental (Hz)

Amplitude (cm)

▶ Run in Python

Data Inspector

Harmonicn = 3

Frequency330 Hz

Nodes4

Antinodes3

Wavelength2L/3

Governing equation

y = 2 A sin (k x) cos (ω t), f_{3} = \frac{3 v}{2 L} = 330 Hz

Reading this result: 3 half-wavelengths fit the string, so there are 3 antinodes (max swing) and 4 nodes (fixed points). At harmonic n = 3 the string sings at 330 Hz — exactly 3× the 110 Hz fundamental, and the wavelength is 2L/3.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

About this simulation

The full Spring-Mass Systems tool models a roller-coaster loop with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Spring-Mass Systems

Spring-Mass Systems for a projectile from a cannon Spring-Mass Systems for a bouncing ball Spring-Mass Systems for a pendulum clock Spring-Mass Systems for a car braking Spring-Mass Systems for a satellite orbit Spring-Mass Systems for a mass on a spring Spring-Mass Systems for a skydiver's free fall Spring-Mass Systems for a two-cart collision

Other ways to simulate a roller-coaster loop

Particle / N-Body for a roller-coaster loop Heat & Wave Fields for a roller-coaster loop GPU Compute (WebGPU) for a roller-coaster loop WebGPU Fluid for a roller-coaster loop GPU N-Body for a roller-coaster loop GPU PDE Solver for a roller-coaster loop

Frequently asked questions

How do I simulate a roller-coaster loop?: Open this page and use the live Spring-Mass Systems tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a roller-coaster loop from your own measurements.