How do I simulate a roller-coaster loop?

Open this page and use the live Optics Bench 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 Optics Bench

Optics Bench for a roller-coaster loop

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

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Ray Optics

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Ray Optics / Lens StudioLive

thin-lens equation · ray tracing

Controls

Presets

Trace principal rays through a thin lens to locate the image. Move the object inside the focal point to flip from a real to a virtual image.

Focal length

Object distance

Object height

▶ Run in Python

Data Inspector

Lensconverging

Focal length120px

Magnification-1.00×

Equation1/v − 1/u = 1/f

Governing equation

\frac{1}{v} - \frac{1}{u} = \frac{1}{f} = \frac{1}{120}

Reading this result: The object sits near 2f, so the image is real, inverted and roughly the same size (1:1).

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

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Diffraction Grating

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Diffraction GratingLive

N-slit interference

Controls

More slits make the bright maxima sharper and brighter — the principle behind spectrometers that split light into precise spectral lines.

Presets

Number of slits

Slit spacing

Wavelength

▶ Run in Python

Data Inspector

Slits5

Resolution∝ N

Maxima atd·sinθ = mλ

Governing equation

d sin θ = mλ : 30 sin θ = m \cdot 20, θ_{1} = 41. 8^{\circ}

Reading this result: The bright maxima stay locked where d·sinθ = mλ — fixed by spacing and wavelength, not slit count — but with 5 slits each principal peak is about 5× narrower and far more intense, which is how a grating resolves fine spectral lines.

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

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Wave Interference

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Wave Interference StudioLive

two-source interference · ripple tank

Controls

Speed1×

Two point sources emit circular waves — where they meet, you see constructive and destructive interference fringes. Drag either source on the canvas to reposition it and watch the pattern update live.

Presets

Frequency

Source separation

▶ Run in Python

Data Inspector

Sources2

Grid220×220

Wavelength15.7 px

Separation100 px

Patterninterference fringes

Governing equation

y = A_{1} sin (k r_{1} - ω t) + A_{2} sin (k r_{2} - ω t), Δ r = mλ, λ \approx 15.7 px, Δ s = 100 px

Reading this result: Wavelength is about 15.7 px and the two sources sit 100 px apart. Bright fringes appear where the path difference to the two sources equals a whole number of wavelengths (constructive interference); dark fringes fall halfway between, where the difference is a half-wavelength (destructive interference). Shrinking the wavelength or widening the separation would pack more fringes into the same space.

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

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Prism

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Prism DispersionLive

refraction varies with wavelength

Controls

A prism bends violet light more than red because the refractive index depends on wavelength — splitting white light into a rainbow, exactly as Newton showed.

Presets

Dispersion strength

Exit angle

▶ Run in Python

Data Inspector

Colors7 (ROYGBIV)

Causen(λ) dispersion

Most bentviolet

Snell's law of refraction

n_{1} sin θ_{1} = n_{2} sin θ_{2} : 1.00 sin 3 5^{\circ} = 1.55 sin θ_{2} \Rightarrow θ_{2} = 21. 7^{\circ}

Reading this result: At 1× dispersion and a 35° exit angle, each wavelength refracts by a slightly different amount, splitting white light into an ordered ROYGBIV band.

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

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About this simulation

The full Optics Bench 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.

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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 Optics Bench 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.