Question 4: Horizontal Alignment (25 Points)

a. (15 points) A horizontal curve has been designed with the following properties:

• Operating speed of 80km/hr
• TC Station: 5+478.400
• PI Station: 5+723.900
• Superelevation of 5% and a normal cross-fall of 3%. 

1. (4 points) Calculate the minimum radius required for the curve. Is a transition curve required for this radius? Give reason.
2. (6 points) Assume that the designer decides to do away with the transition curve. What should be the minimum radius in this case? What is the station value of CT for this radius?
3. (5 points) Sketch the elements of the horizontal curve clearly indicating stations at TC, PI and CT points. Also mark the radius value chosen in step (ii), the central angle (Δ) and the length of the circular curve.

b. (10 points) A spiral curve (transition curve) has been designed for a one-lane two-way highway (each lane is 3.6m wide) with a design speed of 90km/hr. The spiral curve transitions the geometry from a normal crown with a 3% slope to a superelevated slope of 5%. The spiral curve, containing the superelevation runoff, is 110 metres long.

1. Draw cross-sections of only

   the carriageway of the highway at the following locations. Ensure you clearly present the slopes of the cross-section (for both lanes of the highway) and the elevation of the outside edge and inside edge of the carriageway relative to the centreline.

   • TS

   • 40m into the spiral curve from TS

   • 80m into the spiral curve from TS

   • SC

2. Calculate the station for the point 80m into the spiral curve from TS. Assume the radius of circular curve as 360m and the station for TS as 3+500.0

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