Kato Unitrack · N & HO · closing a loop
How many R282 curves close a loop?
Eight. Eight R282-45 curves are 360° of turn, and that is the whole rule: a loop of Kato Unitrack closes when its curves add up to a full circle and its straights match side for side.
Curves that add up to 360°
Every Kato N-scale curve turns the track by a fixed angle — 15°, 30° or 45°; those are the only single-track arcs sold. A full circle is any set of curves whose angles sum to 360°: 8 × 45°, 12 × 30° or 24 × 15°. At the same radius the ends meet exactly.
So eight R282-45 (20-110) is a circle. Add one S248 to each side and it is still closed: the two straights are equal, so the two half-circles are simply pushed apart by the same amount. Add two per side and you have RailMind's Starter Oval — 8 curves, 4 straights, 12 pieces.
Why an odd number of 45° curves never closes
Because 45 does not divide evenly into 360 an odd number of times. Seven 45° curves turn 315°; nine turn 405°. Neither is a multiple of 360°, so the run does not come back parallel to itself, let alone onto its own start. The same holds for any arc: the count has to make the total a whole number of circles. With 45° pieces that is 8 (or 16, for two turns of a helix you are not building). RailMind's closure solver reasons the same way — it works out the turn a gap needs and checks it against the angles the enabled curves can make. If the turn is not on that lattice, it tells you so instead of showing a millimeter gap. That is the subject of why it won't close.
The straights have to match
An oval closes if and only if its two straights are the same length; the curve bundles at each end must be the same hand and arc. That sounds obvious with S248s, but it is the rule that breaks when a turnout goes in: a #4 turnout is 126 mm through its main route, so a straight that runs through two of them is 126 + 248 + 248 + 248 + 126 = 996 mm, and the far side has to reach 996 with plain pieces — 3 × S248 + S124 + 2 × S64. The Oval + Passing Siding is built exactly that way.
A figure-8 is the same sum with a crossing
Kato's 90° crossing (20-320) is two 124 mm straights crossing at their centers, so each arm ends 62 mm from the middle. A lobe that leaves one arm and comes back onto the perpendicular one turns 270° — six 45° curves — and its two tails have to make up the offset: at R348, 348 − 62 = 286 = S248 + S38. Two such lobes of opposite hand are the Figure-8: 270° + 90° at the crossing is again a full circle per lobe.
HO: sixteen, not eight
Kato's everyday HO curves (R370 to R790) are 22.5°, so a circle is 16 curves, and an HO oval is sixteen curves plus two equal straights. The 10° R867 fitting curve (36 per circle) and the 11.25° R1546/R1606 curves (32 per circle) follow the same rule with their own counts. See HO Unitrack basics.
How RailMind uses this
The app's Close loop button is this arithmetic run backwards: it offers a fix when one straight or curve, or a run of straights, lands the open end on the other within 2 mm — the play a real Unijoiner absorbs — and anti-parallel to it, then shows the pieces as a ghost before adding them. Longer gaps get an Auto‑route this gap button, which searches straights and curves. Every example layout was proved the same way before it shipped.
See it in a plan
Eight R282-45 curves and four S248 straights, twelve pieces, closed. Starter Oval →
iPad only · iPadOS 18 or later · free to build a starter layout, one US$29.99 purchase to unlock every piece.