Horizontal Curve Middle Ordinate
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The middle ordinate is the sagitta — the "arrow" of the arc — and it is the quantity that decides whether a driver can see around the inside of a curve. Set M equal to the horizontal clearance from the centreline to a sight obstruction (a cut slope, a noise wall, a row of trees) and the same relation tells you the length of curve over which the sightline is blocked. Highway design manuals print it as a nomograph of R against M for exactly this purpose.
A worked example: a 500 ft curve deflecting 60° has M = 500(1 − cos 30°) = 66.99 ft — so the arc bulges 67 ft off its own long chord. Field crews use the same idea in reverse to measure a curve that was never staked: stretch a chord across a rail or a curb, measure the offset at midspan, and R follows from R ≈ C²/(8M), the small-angle version of this formula. That approximation, incidentally, is how track inspectors measure curvature with a string and a ruler.
- = Middle ordinate
- = Curve radius
- = Deflection angle
- Middle ordinate — Asphalt Tonnage from Area and Thickness, Horizontal Curve Tangent Length
- Curve radius — Horizontal Curve Tangent Length, Horizontal Curve External Distance
- Deflection angle — Horizontal Curve Tangent Length, Horizontal Curve External Distance