Determine Elevation of High Point

Need some help on this one guys, I'm drawing a blank:

A 520 ft long equal tangent crest vertical curve connects tangents that intersect at station 340+00 and elevation 1325 ft. G1 is +4.0% and G2 is -2.5%

Determine the elevation and station of High Point, PVC, and PVT

So I have:

PVI = 340+00; Elev 1325

PVC = 337+40; Elev 1314.60

PVT = 342+60; Elev 1318.50

HP Station I am getting (PVC + 320 ft) = Station 340+60

For HP Elevation I am getting 1327.34 which does not agree with the solution.

I'm using:

y=ax^2 + bx + c

I think I got it:

Elevation = 1321 ft

for the 'x' value the number should have been in stations (3.2) I was using the value of 320

Yup, ElHP = 1321.0 is correct

StaHP = 340+60

ElBVC = 1314.6

StaBVC = 337+40

ElEVC = 1318.5

StaEVC = 342+60

ptatohed said:

Yup, ElHP = 1321.0 is correct

StaHP = 340+60

ElBVC = 1314.6

StaBVC = 337+40

ElEVC = 1318.5

StaEVC = 342+60

Click to expand...

Hello,

Would you have the time to show how you worked the problem? can't seem to get the high point sta. Thanks,

Bill Hall

billyluv said:

ptatohed said:

Yup, ElHP = 1321.0 is correct

StaHP = 340+60

ElBVC = 1314.6

StaBVC = 337+40

ElEVC = 1318.5

StaEVC = 342+60

Click to expand...

Hello,

Would you have the time to show how you worked the problem? can't seem to get the high point sta. Thanks,

Bill Hall

Click to expand...

I got everything except for the STA @ HP

3.2 + ? = 340.6

Thanks again.

billyluv said:

billyluv said:

ptatohed said:

Yup, ElHP = 1321.0 is correct

StaHP = 340+60

ElBVC = 1314.6

StaBVC = 337+40

ElEVC = 1318.5

StaEVC = 342+60

Click to expand...

Hello,

Would you have the time to show how you worked the problem? can't seem to get the high point sta. Thanks,

Bill Hall

Click to expand...

I got everything except for the STA @ HP

3.2 + ? = 340.6

Thanks again.

Click to expand...

AHH! I got it!` 3.2 from the PVC............

billyluv said:

billyluv said:

billyluv said:

ptatohed said:

Yup, ElHP = 1321.0 is correct

StaHP = 340+60

ElBVC = 1314.6

StaBVC = 337+40

ElEVC = 1318.5

StaEVC = 342+60

Click to expand...

Hello,Would you have the time to show how you worked the problem? can't seem to get the high point sta. Thanks,

Bill Hall

Click to expand...

I got everything except for the STA @ HP3.2 + ? = 340.6

Thanks again.

Click to expand...

AHH! I got it!` 3.2 from the PVC............

Click to expand...

Correct.

StaHP = 337.40 (StaBVC) + 3.2 (x) = 340.60 stations = Sta 340+60

For the benefit of future readers:

To determine the station of the HP:

y= 2ax + b

Where:

a = (G2 - G1)/(2L)

a=(-2.5)-(-4)/2(5.2)

a=-0.625

b=G1

So:

y=2(-0.625)x = (4.0)

y= 3.2 Stations (320 feet)

So the HP is 3.2 stations from the PVC

ElBVC = 1325 - (.04)(520/2) = 1314.6

StaBVC = 34000 - 520/2 = 337+40

ElEVC = 1325 - (.025)(520/2) = 1318.5

r = (g2 - g1)/L = (-2.5 - 4)/5.2 = -1.25%

x = -g1/r = -4/-1.25 = 3.2 sta

StaHP = 337.40 + 3.2 = 340+60

ElHP = (r/2)(x2) + (g1)(x) + ElBVC = (-1.25/2)(3.22)+(4)(3.2)+1314.6 = 1321.0