Horizontal curve layout
degree of curvecircular curveroad curve stakingtangent length
Setting out a circular road curve: radius from degree of curve, then tangent, curve length, external distance, middle ordinate and long chord.
Radius from Degree of Curve (Arc Definition)
Converts degree of curve to radius using the arc definition, where D is the central angle subtending one 100 ft station of arc.
Horizontal Curve Tangent Length
Distance from the point of intersection back to the point of curvature, from the curve radius and its total deflection angle.
Horizontal Curve Length from Degree of Curve
Length of a circular curve in 100 ft stations, from the total deflection angle and the degree of curve, on the arc definition.
Horizontal Curve External Distance
Clearance from the point of intersection to the midpoint of the curve, the distance a curve cuts back from the corner.
Horizontal Curve Middle Ordinate
Offset from the middle of the long chord to the middle of the arc, the number that governs sight distance around obstructions.
Horizontal Curve Long Chord
Straight-line distance from the point of curvature to the point of tangency, the chord that spans the entire circular curve.
How they fit together
Every one of these is fixed by two numbers: the radius R and the deflection angle between the tangents. Choose those and the whole curve follows — where it starts, how long it runs, how far its midpoint sits from the intersection, and the straight chord across it. North American practice usually specifies a curve by its degree rather than its radius, which is why that conversion sits first.
The trap is mixing the arc and chord definitions of degree of curve. The arc definition, standard for highways, sets the degree as the central angle subtending 100 ft of arc; the chord definition, traditional on railroads, uses 100 ft of chord. They diverge as curves sharpen, and staking a railway curve from a highway table puts the pegs in the wrong place.