AVUT Physics

Interactive physics visualisations and articles on rope rescue, online at physics.avut.nz. Each visualisation works out where a rescue system settles and the forces through it, and lets you change the setup with sliders to see what moves.

What's on the site

Visualisations

• Ladder Hinge Lower (/ladder-hinge-lower): a ladder hinged at the base of a wall, with a stretcher hanging from it on a rope from an anchor behind the wall and an attachment to the ladder. Either the system settles where it balances, or a ground team holds the ladder.
• Two-Point Lower (/two-point-lower): a stretcher lowered over a wall on a rope from an anchor, with a ground team pulling a line from its other end to keep it off the wall.
• Four-Point Lower (/four-point-lower): a stretcher taken from the floor beside a slot, out over it and down, on four ropes from its corners to belays beside the slot. Each belayer's rope has its own slider, linkable in pairs or all four; the stretcher goes where the ropes put it.
• Body-Belayed Two-Point Lower (/body-belay): the same lower with no anchor, held by two belayers standing on the wall top with the rope round their waists. Shows whether their feet grip.
• Multi-Point Anchor (/multi-point-anchor): two or three anchors joined to a master point, pre-equalised or sliding. Swing the load to one side and see how each rig shares it between the anchors and how far the master point moves.
• Loading a Ute (/ute-load): a dual-cab ute, side on, loaded with crew, fit-out, cargo and a trailer. Shows how the weight shares between the axles, how a tow ball lifts weight off the front wheels, and how close each total comes to the ute's ratings.
• Block on an Incline (/block-on-an-incline): a free-body diagram with static and kinetic friction. Not listed on the home page.

Articles

• A Visual Introduction to Rescue Physics (/visual): the physics of rope rescue for phones, one idea per screen (/visual/<idea>): a headline, a sentence or two, and a figure to play with, starting from velocity and force for readers with no physics. Swipe or use the arrow keys to move between them; some pages have details (such as the maths) to swipe up, and tapping the series' name brings down the contents. The first page shows how it all works.
• A Gentle Introduction to Rescue Physics (parked draft): two parts, kept for now but not listed on the home page or linked from the Visual Introduction, which has taken over their ideas. The Visual Introduction still uses some of their drawing pieces and maths (src/articles/gentle-introduction*).
  • Part 1 (/gentle-introduction/part-1): weight and kilonewtons, forces as arrows, and how angles change the load on anchor legs and redirects. Written for rescuers with no physics, with small slider figures and the maths kept in "Why is this?" boxes.
  • Part 2 (/gentle-introduction/part-2): pulleys and mechanical advantage, from a single pulley to a 2:1 on a Z-rig, working systems out with the T method, and how friction in the pulleys eats into the advantage.
• Standing Body Belays (/standing-body-belays): how much grip a belayer's boots need to hold a stretcher still, and why even the best case leaves too little margin.

Each visualisation page ends with a "How this is calculated" section setting out the model and its assumptions.

Running it

Needs Node.js 20.9 or later.

npm install
npm run dev              # http://localhost:3200 (worktrees use their own port, see AGENTS.md)

Command	What it does
npm test	Runs the tests (Vitest)
npm run test:sweep	Runs the ladder hinge sweep: 2000 random setups against a recorded snapshot
npm run figures	Works out the articles' figures again where they're out of date
npm run lint	ESLint
npx tsc --noEmit	Type check
npm run format	Formats everything with Prettier (also run on staged files by the pre-commit hook)
npm run build	Production build

How it's built

A Next.js app with React, Tailwind CSS, and maths typeset on the server by MathJax. The diagrams are plain SVG.

src/
  app/(site)/           One folder per page; each page is a thin wrapper, in the site's chrome
  app/(editor)/         The knot editor (live, but not linked or indexed), with no site chrome
  visualisations/       Each visualisation's component, solver, notes and tests
  articles/             The articles' figures
  visual/               A Visual Introduction to Rescue Physics: one folder per page, and its shared parts
  components/diagram/   SVG primitives (arrows, labels, angle arcs) and slider controls
  components/ui/        shadcn/ui pieces (sheet, drawer and the like)
  lib/                  Shared maths: Vector2/Vector3, segment geometry, numerical methods

The physics lives in the solvers (src/visualisations/*-solver.ts): plain functions that take a setup and return where everything settles and the forces involved. They don't depend on React, so the tests can run them over thousands of random setups. The tests check each result against the physics directly: everything balances, ropes only pull, surfaces only push, and nothing passes through anything else. They don't reuse the solvers' own working.

The solvers find the resting position by minimising potential energy (with Nelder–Mead), then solve the balance of forces exactly at that position. The numerical methods are in src/lib/numeric/.

The articles quote figures from the same solvers, too many to work out as the site builds. Each article's src/articles/<name>.compute.ts works them out, and npm run figures saves them in <name>.figures.json, which the article reads. The file records a hash of the compute module and every local file it imports, so changing an article's inputs or a solver it uses marks its figures out of date, and the build and the pre-commit hook refuse to go on until they're worked out again.

Licence

MIT