Highway Curve Design

What is a simple curve?

Circular arc of constant radius connecting two tangent sections of a roadway.

What is PC?

Point of Curvature - where tangent meets beginning of circular curve.

What is PT?

Point of Tangency - where circular curve ends and tangent begins.

What is PI?

Point of Intersection - where back tangent and forward tangent would meet if extended.

What is the tangent distance (T)?

Distance from PC or PT to PI along tangent. T = R × tan(Δ/2)

What is the external distance (E)?

Distance from PI to midpoint of curve. E = R × [sec(Δ/2) - 1]

What is the middle ordinate (M)?

Distance from midpoint of long chord to midpoint of curve. M = R × [1 - cos(Δ/2)]

What is long chord (LC)?

Straight-line distance from PC to PT. LC = 2R × sin(Δ/2)

What is the central angle (Δ)?

Angle at center of curve subtended by arc from PC to PT. Equals intersection angle of tangents.

What is arc definition of degree of curve?

Central angle subtended by 100-foot arc. R = 5729.58/D (feet)

What is chord definition of degree of curve?

Central angle subtended by 100-foot chord. Used in railroad design. R = 50/sin(D/2)

How do you calculate arc length?

L = R × Δ (radians) or L = (Δ/D) × 100 for arc definition

What is deflection angle in curve staking?

Angle between tangent and chord to curve point. For full station: d = D/2. Total deflection to PT = Δ/2.

What is a compound curve?

Two or more circular curves of different radii with common tangent at junction, curving in same direction.

What is a reverse curve?

Two circular curves turning in opposite directions with common tangent at junction.

What is a spiral curve?

Transition curve of varying radius connecting tangent to circular curve, providing gradual entry.

What is TS?

Tangent to Spiral - point where spiral begins at tangent.

What is SC?

Spiral to Circular - point where spiral meets main circular curve.

What is superelevation?

Banking of roadway on curves to counteract centrifugal force. Expressed as percentage or rate (e/100).

What determines minimum curve radius?

Design speed, maximum superelevation rate, and side friction factor. Higher speeds require larger radii.

What is PVC?

Point of Vertical Curvature - beginning of vertical curve where it meets back tangent grade.

What is PVT?

Point of Vertical Tangency - end of vertical curve where it meets forward tangent grade.

What is PVI?

Point of Vertical Intersection - where back and forward tangent grades would intersect.

What is K-value?

Horizontal distance required for 1% change in grade. K = L/(|g2 - g1|)

What is a crest curve?

Vertical curve where grade changes from ascending to descending (convex upward).

What is a sag curve?

Vertical curve where grade changes from descending to ascending (concave upward).

How do you calculate vertical curve elevation?

y = tangent elevation + offset Offset at x from PVC = (rate of change × x²)/2 Rate = (g2-g1)/L

What controls crest curve length?

Stopping sight distance - driver must see obstacle in time to stop safely.

What controls sag curve length?

1. Headlight sight distance 2. Rider comfort (vertical acceleration) 3. Drainage 4. Appearance

What is stopping sight distance?

Distance for driver to perceive hazard, react, and stop. SSD = perception-reaction distance + braking distance.

What is design speed?

Maximum safe speed a roadway can accommodate under favorable conditions. Determines all geometric elements.

Where is the high point on a crest curve?

Station where grade = 0. x from PVC = -g1 × L/(g2 - g1)

What is spiral length selection based on?

• Comfortable transition at design speed • Superelevation runoff distance • Appearance Typically 200-400 feet

What is the spiral angle?

Angle between tangent at TS and tangent at SC. θs = Ls/(2R) radians = Ls × D/200 degrees