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HO Scale Grade Transition & Vertical Easement Calculator

Crest pull-apart · Sag override · Easement length

INPUTS

Grades stay in percent; angles in degrees.
Grades at the break (direction of travel: in → out)
+ uphill, − downhill
+ uphill, − downhill
Longest car over the break
Fills truck centers; tweak freely.
Bolster to bolster (the bridging span)
Max vertical angle a coupler pair should absorb.
Length of vertical curve you plan to build.

RESULTS

Grade-break angle
—
total direction change at the break
Break type
—
crest pulls apart · sag overrides
Min. easement length
—
to stay within coupler tolerance
Per-coupler angle
—
what your car sees on your easement
Your easement
—
—
Margin vs. minimum —
Hard corner (no easement) Eased vertical curve Rigid car on its trucks
Vertical bulge (mid-ordinate)
—
how far the curve departs the corner
Grade-change rate
—
percent of grade per unit length

Working out the grades themselves — how steep you can go and how many cars a loco will pull — is the RailGrade tool’s job. This one smooths the breaks between those grades.

Grade-break angle = |atan(g₀ₖₜ/100) − atan(gₐₕₜ/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; min length = angle × T / tolerance. Coupler tolerances here are practical model targets, not a published spec. A crest (grade decreasing) tends to pull couplers apart and unload wheels; a sag (grade increasing) tends to jam/override couplers and strike pilots. Vertical exaggeration in the drawing is for legibility. Confirm critical transitions by rolling your longest car through.