Solutions: E. Spirals
Problem 1
450.00 ft long entrance and exit spirals will be used with a 3000.00 radius circular curve. The PI station is 52+00 with a ∆ angle of 47⁰00' Left.
Part a. What is the total deflection angle of the entrance spiral at the TS?
Part b.What is length of the circular curve?
Part c. What is the deflection angle at the TS to the spiral midpoint?
Distance to the midpoint is 450.00/2 = 225.00 ft
Problem 2
A 300.00 ft long spiral will be used with a 3°00' circular curve. The PI station is 40+00 and the ∆ angle is 60⁰00' Right. Using the Approximate Method, compute the five-chord deflection angle notes for the spirals.
|
Chord # |
lp, ft |
ap |
|
1 |
60.00 |
0°03’36” |
|
2 |
120.00 |
0°14’24” |
|
3 |
180.00 |
0°32’24” |
|
4 |
240.00 |
0°57’36” |
|
5 |
300.00 |
1°30’00” |
Problem 3
A 275.00 ft long spiral will be used with a 2500.00 ft radius circular curve. The PI station is 63+00 and the ∆ angle is 38⁰00' Left. Determine the curve system endpoint stations.
Central Angle
Curve Length
Spiralled Tangent
Stationing
