A normal puff of air falls apart in a few centimetres. A spinning ring of the same air can cross the whole room. In the next few minutes you'll figure out why — by playing with it — and then build one for real.
Air is a fluid, like water. Shove a blob of it forward and the still air around it drags, tears it up, and it's gone. Yet the ring above keeps its shape for metres. Something is locking it together — and that something is spin.
When you push air out through a round hole, the edge of the hole drags on the outside of the flow. The air curls back on itself and rolls into a spinning donut — a torus. Watch the two colours: the top of the ring spins one way (magenta) and the bottom spins the opposite way (cyan). That paired, opposite spin — physicists call it circulation — is the glue. It's also what quietly drives the whole ring forward.
Try it: shrink the hole, then push harder. Push the distance slider all the way up — see the messy tail that trails behind? That tail is the clue for the next slide.
You just met the formation number, written L/D — short for length over diameter. Real fluid-dynamics labs found the magic value is about 4: below it the ring is underfed and weak; above it the ring is already "full," so the extra air you push can't join and spills out behind as a wasted jet. Best ring per push is right at L/D ≈ 4.
A real result (Gharib, Rambod & Shariff, 1998) — it holds for smoke rings, dolphins blowing bubble rings, and the cannon you're about to build. One catch: L isn't the distance you push. Squeezing air through a hole narrower than the barrel stretches the slug longer than the membrane's travel — which is exactly why the sandbox formula stacks barrel² over hole³.
The same amount of air has to get through a smaller opening, so it has to move faster — that's continuity, and it's why a thumb over a hose makes the water shoot. The jet speed climbs with the square of how much you shrink the hole:
Halve the hole and the jet gets four times faster. That's a lot of punch from a small change — and exactly why the hole size matters so much when you build it.
You've been programming without typing. Each control you dragged is a variable; the physics is a few lines of arithmetic on those variables. Drag the slider and watch the numbers recompute live — the machine does the same steps you did in your head, just faster and without mistakes.
That's the exact idea behind the big Blender fluid simulation — same variables, same formula for the sweet spot, just running millions of little air parcels instead of a few glowing dots.
Here's the tension: barrel sits on top of that fraction (squared) and hole sits underneath (cubed), so they pull L/D in opposite directions. Grow the barrel and watch L/D shoot past the sweet spot — then try to walk it back to about 4 using the hole alone. That trade-off is the engineering.
Model predicts — m for the settings above. Build it, fire it, measure how far the ring actually flew, type that number in, and the model rescales so its distances match your cannon.
A round tub, big coffee can, or a cardboard box. Rigid is better — it shouldn't flex when you hit it.
Cut a clean, round hole about a third to a half of the barrel's width — that keeps you near the L/D sweet spot you found.
Cover the open back with a shower cap, cut balloon, or trash-bag sheet, taped tight. Thump the middle to fire.
Fill it with fog (a fog machine, vape, or incense) so the ring glows — just like the dye in this lab.
A membrane you whack by hand fires a different amount of air every time — so your L/D jumps around and "aim for 4" means nothing. Swap it for a piston: a disc that slides in the barrel and gets pushed a fixed distance into a hard stop. Same slug of air, every single shot. That repeatability is what turns the sweet spot from a nice idea into a target you can actually hit.
Two details earn their keep: a hole that's round, sharp-edged, and dead-centre (the ring rolls off that lip, so a ragged or off-centre one flings it sideways), and a barrel stiff enough that it doesn't flex when the piston hits the stop.
Pick your barrel and hole, and here's the exact distance to set your stop at, so the cannon fires L/D ≈ 4 — the sweet spot, straight out of the sandbox formula.
Keep the hole about a third to a half of the barrel and this lands in a buildable range. If you can, make the stop slightly adjustable — then you can fine-tune to the real sweet spot once you start measuring.
You built for L/D ≈ 4 — but you don't assume you hit it, you check. This is the part that makes it real science instead of a guess.
Phone at 120–240 fps, fog in the barrel, even light, and a ruler in the frame for scale. Now every frame is data.
The free tool Tracker steps through frame by frame. Read off the ring's diameter, its speed (distance ÷ time), and how far it survives.
Clamp the cannon to a stand and fire it the same way a dozen times. The spread in your numbers is your real-world precision.
The honest part: even built well, reality won't perfectly match the model — real air has friction, swirl, and decay the simulation skips. That gap isn't failure, it's the experiment. What should survive is the sweet spot itself: plot range against stroke and watch it stop improving right around L/D ≈ 4. Find that plateau in your own data and you've measured a real law of fluid dynamics with a cardboard tube and a phone. That's the whole game.
Fire water through the hole instead of air and you get the very same vortex ring — same roll-up, same L/D ≈ 4. Seed the water with fine air bubbles and they get sucked into the low-pressure core and light it up as a glowing silver circle. Two differences you can watch above: water rings are slow and long-lived, and the buoyant bubbles make the ring drift gently upward as it goes. The exact twin of the air cannon — just wetter.