Fundamentals of Transportation/Vertical Curves/Additional Problems

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Additional Questions[edit]

Sag Vertical Curves[edit]

  1. What are the considerations when designing sag vertical curves? Which is most important?
  2. What does the comfort criteria in a sag vertical curve describe? Is there a time when comfort criterion is the determining factor? Is there a time when the appearance criteria is determining?
  3. What values are used for H and b in determining L for sag vertical curve?
  4. When calculating SSD, which grade should be used?
  5. Is it true that whether a curve is a crest or sag vertical curve is determined by the initial and final grade?
  6. Are properties of headlights different for cars and trucks? → design for worst case (shorter car). Headlights are positioned by vehicle. Some vehicles have driver adjustments. Design is for normal headlights, not highbeams.
  7. Why are there different equations for L depending on S>L, S<L
  8. Is there any trick to knowing whether S<L or S>L before starting?
  9. How does rain/fog affect sight distance? → reduces it, so drivers should reduce speed and be more alert. Design is for normal conditions.
  10. What is the drainage criterion? How is water dealt with on sag curves?
  11. Why are headlights angled?

Crest Vertical Curves[edit]

  1. Is there a limit on hill crests??
  2. What is the difference between crest and sag curves
  3. How can you determine if S > L or S < L when doing SSD calculations? --> If don’t know, trial and check. If use S > L equation and S is greater than L, great, otherwise, must solve again. Why are equations different? Think about the relationships. Solve them at S = L.
  4. If SSD or PSD is different in opposite directions over a crest vertical curve, is it common to have different speed limits/ warning signs. Usually speed is same in both directions, not always.
  5. Is darkness considered in speed/stopping calculations (since can’t see as far)? For Sag curves, there is a headlight criterion.
  6. What height is used in equations for L?
  7. Can the highest point on the curve be higher than the PVI? →:(No, but can be higher than the point on the curve under the PVI). How is it possible for the PVI elevation to be above the actual elevation
  8. When is SSD different from AASHTO guidelines? Do engineers assume different stopping sight distances under certain conditions?
  9. Why compute SSD for downgrade only?
  10. Why is it not always possible to allow passing on vertical curve two lane roads. Is passing sight regularly used ? → (on 2 lane rural roads with good sight lines, yes).
  11. Explain idea of stopping sign as it pertains to hills with (horizontal) curves → a bit complex for intro to transportation, covered in 4xxx level curve. Think about which governs, the horizontal SSD or the vertical SSD (i.e. whichever is lower, which depends on local conditions). Is passing sight distance based on big trucks or average sized cars? → cars (see h1 and compare it with where you are sitting in the vehicle). (Do trucks and small cars have enough sight to pass). → It is not the size of the car you are in so much as the size of the car you see (h2). You are more likely to see a big truck, so the equation is conservative for larger vehicles. When do you plan for each? (Always plan for SSD, consider PSD when there is possibility of dashed yellow line).
  12. What are 3 parameters that affect the design of vertical curves
  13. Explain crest vertical curve graphically
  14. Determine the minimum length of the curve.
  15. What type of curve is used in the design of crest vertical curves? (Ans: Parabola)
  16. Why is it necessary to curve roads that have different slopes on either side of the curve?
  17. Is L Arc length or horizontal displacement?
  18. Why is stopping distance important?
  19. Label PVC, PVI and PVT on a graph. What is the difference between PVC and PVT?
  20. What is an equal tangent cuve
  21. What does an aesthetically unappealing curve look like?
  22. What does SSD depend on?
  23. How does variable “a” used in elevation, differ from variable “A” used in length of curve.
  24. In what two ways can the SSD and L be related
  25. What is the first step in developing the profile of a curve -> Find the center of the curve.

Additional Problem[edit]

  1. Compute length of crest vertical curve with +2.5% and –2.% grade, speed = 90 km/hr &S < L, f=0.25, PRT = 2.5 sec
    1. Find the elevation along the curve?
    2. Find the highest point on a crest vertical curve