Vertical Easement: Smooth the Grade Break

Where two grades meet — the top of a climb or the bottom of a dip — a rigid car can’t follow a sharp corner. At a crest the couplers pull apart; in a sag they jam and override. Enter the grades and your longest car to size the gentle easement curve that lets it ride through smoothly.

Grade-break angle = |atan(gₐₕₜ/100) − atan(g₀ₖₜ/100)|. On a constant-rate vertical curve of length L the direction changes at (angle / L) per unit run, so a car of truck-center span T sees angle × T/L per coupler; minimum length = angle × T / tolerance. Coupler tolerances are practical model targets, not a published spec. A crest tends to pull couplers apart and unload wheels; a sag tends to jam/override couplers. Vertical exaggeration in the drawing is for legibility — confirm a critical transition by rolling your longest car through. Working out the grades themselves is the Grade Pull tool’s job; this one smooths the breaks between them.