MaryJ, I''ve taken a look at this problem. If the PI STA is 20+00 and EL 106.00 (difficult to see from the scan) then I get an EL of low point of 107.14. I'm also not sure about the 106.14'. You also don't show the solution for part A. I am interested in how that was calculated. I couldn't get Green Book equation 3-52 or 3-53 to come out right. Now I'm confused, hope we can figure it out!
The first part is the simpliest. Just need to find SSD at the given speed limit, then satisfy one of the two basic equation for sag vertical curve. The meat of the problem (at least for me) is finding out how the offset distance was calculated, especially the value 106.05 in the calculation for offset. Also the low point station is indeed 106.14
The elevation of the road at Station 21+00 where the obstruction is located is 124 - 16 = 108 feet.
The elevation along the upgrade slope at station 21+00 (i.e. 100' from the PVI) is 105 + (100 * 0.0105) = 106.05 feet.
Therefore, at Station 21+00 the offset elevation between the upgrade slope (106.05) and the road (108) is 108 - 106.05 = 1.95 feet.
To calculate L:
use the formula (L + 2h)/(L - 2h) = sqrt((v - g1*h)/(v - g2*h))
where L = length of curve, h = horizontal distance in stations (100 feet = 1 h), v = total vertical offset between PVI and curve at station, g1 and g2 in percent
For this problem:
h = 1
v = 108 - 105 = 3 feet
g1 = -1.25
g2 = 1.05
solve for L = 10.398 stations
You really don't need to solve for the 1.95 feet offset, just need to know that there's 3 feet difference between the PVI and the point along the road where the obstruction is located.
Good luck!
