Solving Curve Station

[galindo]

Hello Everyone!

Has anyone ever had an engineer request a specific station along a curve when the alignment's stationing is based upon the tangents of said curve?

My supervisor followed the station along the tangents then drew a line from the rad point and used the intersection at the curve.

Hope to get some clarification.

Thanks in advanced!

[Dave Lindell]

That's a new one on me!
I can't wait to see what some other kind of "solutions" turn up.

Is it a large radius with a small delta? (That would make the tangent lengths near the arc length.)
Was it a critical point? Or a search radius point?

[galindo]

Not really, the delta was probably around 40 degrees. The point was critical for a sewer line and if you were to hold the stationing along the curve it was closer to the EC. He knew it was suppose to be near the MC which is why he did what he did.

We talked about mathematically solving it with a ratio, but no one has confirmed or denied a solution.

[steffan]

Create separate curve only alignments. Provide station equations at curve ends where they intersect the tangents. At the curve begin the station should be equal to the tangent alignment station.

[galindo]

Do you have any references for station equations for curves and tangents?

[dedkad]

Steffan recommended a good solution. Equations are used all the time for highway realignments. I'm not sure if I understand your reason for asking for references, but if it is because you are trying to understand what Steffan is saying, I'll try to explain it. Call the tangent alignment "T" and the curve alignment "C", or whatever you want. Your first equation would be at the BC where the curve and tangent intersect. So let's assume that is 1+00 "T" = 1+00 "C". From that point, the tangent alignment and the curve alignment will be stationed independently from each other based on the length of each. When they come back together again at the EC, you'll end up with something like 2+50 "T" = 2+25 "C". The continuation of the alignment after that would need to be labeled either "T" or "C" depending on which stationing you choose to carry through to the end of your route.

[pls5528]

I may be missing something here, but perhaps he is referring to the Tangent Offset Method?
Tangent Offsets:
In the tangent offset method, distance measured from the PC and PT toward the PI (called TO's or tangent offsets)
are used to set stations on the curve. Since deflection angles are the basis for this method, it is recommended that
points on the curve be set at 100-ft, 50-ft, or 25-ft intervals.
Procedure:
1. Determine the stationing to be used (i.e. 100 feet, 50 feet, or 25 feet)
2. Calculate the tangent distance and tangent offset for each station:
β = 100
Stationing
For each station to be established:
γ = D
β * station number on curve
TD = R sin γ
TO = R ( 1 - cos γ )