Low point calculation in InRoads

I don't have access to the Route Location and Design manual, but I did some research and found that the calculation for the turning point (low point) of an unsymmetrical curve involves two calculations, one from the PVC and one from the PVT. If you use the formula from the PVC and find that your low point does not fall between the PVC and the PVI, then you need to use the other formula. The formulas I found are:

 From the PVC:

X_t = [(l₁)² g₁] / 2e

From the PVT:

X_t=[(l₂)²g₂] / 2e

 Where:

l1 is the distance from the PVC to the PVI

l2 is the distance from the PVI to the PVT

g1 is the entrance grade (decimal format)

g2 is the exit grade (decimal format)

e is the middle vertical offset, calculated by

e= [(l₁ l₂) / 2(l₁ + l₂)] x (g₂ - g₁)

Plugging these numbers in, you get:

From PVC, x_t=-31.3592 (negative number, which might be a clue)

From PVC, x_t=62.5997

 When you subtract the second one from the PVT station, you get Low Point= 11+57.90, which seems to be what InRoads came up with (difference probably due to rounding errors)

 The attached spreadsheet shows the calculations.

The information came from this link: http://gisceu.net/PDF/U74.PDF

I hope this helps.

Chris

Here's the equation I used to verify that the InRoads result is correct:

x_m=L+G₂L₂L/(G₁-G₂)L₁

This gave me an X_m of 37.36m added to the PVC 11+20.50 = 11+57.861 which matches InRoads within 0.018 which might be due to my not having the full precision on the grades. 

Here's the info from InRoads on the geometry in question:

Project Name: glf-prop
              Description: Alt 2 alignment
Horizontal Alignment Name: Prop SR 1006 Constr Baseline
              Description: Prop Baseline tied to Exist Survey & ROW Baseline
                    Style: Default
  Vertical Alignment Name: Prop SR 1006 Constr Baseline
              Description: Prop Baseline tied to Exist Survey & ROW Baseline
                    Style: Prop_1"=25'
             Input Factor: 1.0000
                                       STATION         ELEVATION

Element: Linear 
                      P.O.B.         10+13.000          1525.268
                      P.V.C.         11+20.500          1523.062
             Tangent Grade:             -2.052
            Tangent Length:            107.500

Element: Parabola
                      P.V.C.         11+20.500          1523.062
                      P.V.I.         11+50.500          1522.446
                        PVCC         11+50.500          1522.741
                      P.V.T.         12+20.500          1522.973
                        VLOW         11+57.843          1522.737
                    Length:             30.000            70.000
            Entrance Grade:             -2.052
                Exit Grade:              0.753
       r = ( g2 - g1 ) / L:              6.547             1.202
       K = l / ( g2 - g1 ):             15.274            83.161
           Middle Ordinate:              0.295

Element: Linear 
                      P.V.T.         12+20.500          1522.973
                      P.O.E.         14+48.600          1524.692
             Tangent Grade:              0.753
            Tangent Length:            228.100

The engineer is using the previously stated method from section 75 of Route Location and Design and arrives @ the following conclusion:

VLOW=P.V.C.+31.35'=11.51.85 as opposed to sta. 1157.843 as shown above.

Let me know whatever you uncover. Thanks!

Would it be possible for you to send the vertical curve data? Tangent grades, curve length, PVI station, etc. This sounds like it could be a problem for others, and it might be a good idea to have someone try to replicate the problem (both using InRoads and manually). If you could send the information along with the differences in the results, someone might be able to determine the source of the problem.

Chris

It can be found in Route Location and Design by Thomas F. Hickerson (ISBN 07-028680-9)

In the 5th Edition look at Section 75 Turning Point on Vertical Curve.

I would copy the page, but that would violate copyright laws and may break the duct tape that is holding my book together!