Hairpins a ball can take

At model scale a real hairpin is far too tight: a bend of 15 m at 1:45,000 is a third of a millimetre. So every hairpin is opened up into a U-turn about 1.3 ball widths across at the middle of the channel, and the leg after it moves sideways by a full turn's width. A stack of switchbacks opens up like an accordion, and if it is too long for the bed it curves round a little. Where there is still not enough room, two neighbouring hairpins are taken out together (one leg of the stack goes) and the page says how many: always in pairs, so the rest of the road still turns the same way. A smaller ball, a bigger bed or tiles keep more of them.

A slope that keeps it rolling

The track gets its own profile, separate from the ground under it: always downhill, never flatter than about 2° (a steel ball on printed plastic needs that much to beat rolling resistance with some to spare) and never steeper than 7½°. Where it runs below the terrain it sits in a cutting; where it runs above, on an embankment, so it stays printable without supports. The terrain height is set so the route falls at about 3½° on average; you can change both.

The roll, simulated

A solid ball rolling without slipping speeds up at 5⁄7 of g·sin(slope); the rest of the energy goes into spin. Against that come rolling resistance on the layer lines (worse for small balls), a little air drag, and in turns the scrub of riding up the channel side. In a turn the ball settles where gravity and the pull of the turn balance, tan ψ = v²⁄(r·g); the channel is banked into fast turns and the outer wall raised where the ball rides high. The simulation flags spots where the ball would stall, fly off a crest or ride over a wall, and flattens or steepens the track until it gets to the cup.

Printing it

• Print the track in a contrasting colour: in the 3MF the track, terrain, water, finish cup and lettering are separate parts.
• A smooth channel floor matters most. Use fine layers on the track (the page suggests a height for your ball) or ironing on top surfaces.
• No supports needed: the channel is an open U with walls that lean at most 20°.
• The terrain is mostly air inside; 8 to 10% infill is plenty. Tiles have holes for printed alignment pins.
• Slide the gate into the two slots at the top, put the ball behind it, and lift.

Which ball

Bearing balls are round to a few thousandths of a millimetre and heavy for their size, so they roll true. Chrome steel (often sold as G25 bearing balls) is cheap and very smooth but rusts if handled a lot; stainless steel (AISI 420 or 440) costs a little more and stays shiny. The 16 mm setting fits an ordinary glass marble. A small disc magnet under the finish cup stops a steel ball with a click and holds it.

What to keep in mind

The simulation is a model, with friction values for a typical PLA print; every printer, filament and ball is a bit different, which is what the test piece is for. The track follows the route's hairpins in order and on the right side, but not its exact path: it needs room the real road does not. The finish cup sits where the track ends. Tunnels are never used: a route through one is cut where the tunnel starts.