1. Transportation Engineering Vertical curve design March 23, 2011
CE 3500
Transportation Engineering
Vertical curve design
March 23, 2011

2. ANNOUNCEMENTS

3. Group assignment due today.
Homework 4 posted later today.
No class Wednesday.

4. REVIEW

5. The shape of a vertical curve is usually parabolic. Why?
PVI
A = –8
G2= -5
G1= +3 L
PVT
PVC

6. For convenience, let x = 0 at PVC
Elevation y
For convenience, let x = 0 at PVC
PVC
PVT

7. PVC
PVT
Case I: SSD is less than the curve length.

8. PVC
PVT
Case II: SSD is greater than the curve length.

9. Case I: SSD is less than the curve length.

10. Case II: SSD is greater than the curve length.

11. The first part of vertical alignment is identifying the constant slope sections.

12. From this, we identify where vertical curves are needed and calculate their PVI.

13. So, usually we are given the PVI and have to design everything else based off of that.

14. EXAMPLE

15. Design a vertical curve that can be safely traversed at 70 mi/hr, assuming 2.5 s reaction time and coefficient of braking friction 0.348
G1= -2
G2= +4
PVI:
Elevation 7250 ft

16. Step 1: Find SSD
G1= -2
G2= +4
PVI:
Elevation 7250 ft

17. Step 2: Find curve length
SSD < L:
SSD > L:
G1= -2
G2= +4
PVI:
Elevation 7250 ft

18. Step 2: Find curve length
SSD < L:
SSD > L:
G1= -2
G2= +4
PVI:
Elevation 7250 ft
SSD is 759 ft, so we
need 1130 ft of curve

19. How do we report our answer
How do we report our answer? Give station and elevation for PVC, PVT, and every whole station in between.
PVI is at ; so PVC comes (1130/2) = 565 ft earlier:
PVT comes 565 ft after PVI:
What is the elevation of PVC and PVT?
What is the elevation in between?

20. Station
x (ft)
Elevation (ft)
(PVC)
7261.3
340+00 55
7260.3
341+00
155
7258.8
...
350+00
1055
7269.7
(PVT)
1130
7272.6

21. EXAMPLE

22. Coefficient of friction is 0
Coefficient of friction is 0.348; only one direction of travel from left to right. What is maximum safe speed?
G2= -3
G1= +5
500 ft

23. Step 1: Find SSD from curve length:
SSD < L:
SSD > L:
G2= -3
G1= +5
500 ft

24. Step 2: Find speed from SSD:

25. IN-CLASS
EVALUATIONS

26. Pace: Slow, OK, Fast
Most unclear topic right now.
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