Vertical Curve Problem

[pmp008]

Hey guys i was wondering if you could help me understand this problem.. I don't really know where to start.

Any help would be greatly appreciated!

 

[sac_engineer]

This is a geometrically intense solution, but doable. The first step is to lower the 2% by 1.3 m to visualize where the new PVI will be located. From there, you can use trig to determine the vertical and horizontal shift of the PVI. My calcs show a vertical shift of 1.33 m and horizontal of 21.72 m. This would result in a vertical curve length of 907 m, a reduction of 43 m from the original).

I haven't done any vertical checks but the lowered departing tangent should provide the required vertical clearance at the underpass.

Also, the term "proposed" is very misleading in the diagram. I chose to interpret "proposed" as "pre-modified".

 

[sac_engineer]

Actually, the question is asking for the maximum airport clearance. The solution above is used if the tangent road was only lowered 1.3 m.

Based on the data and developing the vertical curve equations for each scenario, I calc'd the adjusted length to be 897 m (using 7 m vertical clearance + 1.4 m structure depth at RR underpass) which yields a lowering of 1.59 m along the tangent roadway.

 

[pmp008]

When i calculated i got the same numbers as you. However, after looking into it more, it seems as if the tangent will be raised 1.59m not lowered? I found that that the original distance from the tangent to the curve is 28.5m and the distance using a 897m curve is 26.91m which means the curve has moved up. I found that the max clearance is using 4% and -2% was using a curve length of 993.33m. Which lowers the tangent by 1.3m and the clearance over the tracks is 7.255.

Shortening the curve more will result in the tangent to move up and the clearance to move closer to 7. But i need to have 1.3m of clearance, so i found that the closest i can get to 7m and still have at least 1.3m of clearance is using a 993.33m curve.

Are these assumptions correct?

Thanks!

 

[sac_engineer]

When i calculated i got the same numbers as you. However, after looking into it more, it seems as if the tangent will be raised 1.59m not lowered? I found that that the original distance from the tangent to the curve is 28.5m and the distance using a 897m curve is 26.91m which means the curve has moved up. I found that the max clearance is using 4% and -2% was using a curve length of 993.33m. Which lowers the tangent by 1.3m and the clearance over the tracks is 7.255.
Shortening the curve more will result in the tangent to move up and the clearance to move closer to 7. But i need to have 1.3m of clearance, so i found that the closest i can get to 7m and still have at least 1.3m of clearance is using a 993.33m curve.

Are these assumptions correct?

Thanks!

In this case, you are only translating or sliding the departing tangent line (-2%) to the left, while the PVC and starting tangent line (4%) remain fixed in place. As the departing line is moving toward the left, the PVI where the two lines intersect is moving to the left but also down relative to the original PVI location, thus lowering the parabolic curve.

The way I solved it was as follows:

1. The new curve had to be 7 + 1.4 m above the railroad which is 281 m from the PVC station. Using the parabolic equation of a vertical curve (y = y@pvc + (g1)(x) + (0.5)®(x^2), where R = (g2-g1)/L), you can solve for L since y = 278.7 and x = 281. I calc'd L to be 897 m, 53m shorter than the original curve.

2. The equation for the existing curve can easily be solved since the length, g1, and g2 are provided. Also, y@pvc is the same for both conditions. This is an extra step and doesn't have to be done.

3. I calc'd the elevation at station 950 for both equations to compare how much the road will need to be lowered. Since the new equation is for a length of curve less than 950, I had to subtract the elevation from the end of the new curve (279.07 @ station 897) with the vertical drop for 53m along the tangent (2%) which is 1.06m. This elevation @ 950 for the new curve is 279.07 - 1.06 = 278.01.

Since the elevation of the existing tangent is 279.6 at station 950, the road can be lowered 1.59 m throughout the length of the departing/downhill slope, which would clear the RR overpass and allow planes to land since it's lower than the 1.3 m that the landing zone required. This is the maximum vertical distance that the road can be lowered. The minimum is 1.3m.

 

[pmp008]

Alright ya that makes sense now.

What i did was find the distance from the PVT to the approaching tangent using: Y=((g2-g1)/2L)*(x)^2= -28.5m. Than i subtracted another 1.3m, so -28.5-1.3=-29.8

Than solving -29.8=((g2-g1)/2L)*(L)^2 for L I got 993.33m. Than found the elevation 281m from the PVC, which came out to be 278.955m

278.955-1.4-270.3=7.255m which provides enough clearance.

But i see now where i went wrong.

Thanks a lot for your help!

 

[sac_engineer]

Alright ya that makes sense now.
What i did was find the distance from the PVT to the approaching tangent using: Y=((g2-g1)/2L)*(x)^2= -28.5m. Than i subtracted another 1.3m, so -28.5-1.3=-29.8

Than solving -29.8=((g2-g1)/2L)*(L)^2 for L I got 993.33m. Than found the elevation 281m from the PVC, which came out to be 278.955m

278.955-1.4-270.3=7.255m which provides enough clearance.

But i see now where i went wrong.

Thanks a lot for your help!

You actually increased the vertical clearance to 7.255 m because of the longer vertical curve length rather than decrease the clearance to 7 m to solve for the maximum reduction in curve length.