Überhöhung, Überhöhungsrampe, Übergangsbogen

[marcinbardzociekawy]

Hi all!

I'm big fan of II Epoche (~1920-1945) and I use german legislative acts (e.g. Oberbauvorschriften from 1939 or Eisenbahn-Bau- und Betriebsordnung from 1928) to make my projects extra realistic. I used to german terminology and sometimes I will be using german instead of english (but I hope it won't be problematic).

I really care about realism. I created my own track system with radiuses wchich are being used (I think sharp curves are main problem in model-making). I like this program because it's relatively simple and gives many opportunities for those who want create on their own. As I started to gather some knowledge about track engineering, I found many issues and minutiaes wchich have some significant impact on realism, as transition curve (Übergangsbogen), transistion to superelevation (Überhöhungsrampe) and superelevation (Überhöhung). This is really wide subject. Constructing such things in ModellbahnStudio is possible, but time- and labor-consuming, as I show you later. My point is to know if there is any chance of creating something (special track, plug-in) that could make building those things faster and more precisely. 

All the most important parameters are here and should be used as round numbers of calculations given below.

1.  Überhöhung

Überhöhung is used on curves usually in main and mainline tracks to neutralise the effect of lateral forces and improve passenger comfort. We can feel it while travelling by train - it tilts on right or left side a little bit (in some older polish electric multiple units some doors open or shut then, wchich I find ridiculous). The inner rail is placed a bit lower than outer rail. 

Überhöhung is simple to calculate. Oberbauvorschriften from 1939 (http://web.hs-merseburg.de/~nosske/EpocheII/dv/e2d_3308.html) points 2 basic formulas:

a) for tracks with trains moving with various velocities:

ü = 8 V² / H

ü = Überhöhung in mm
V = größte planmäßige Fahrgeschwindigkeit in km/h (the highest velocity planned)
H = Bogenhalbmesser in m (radius)

b) for tracks with trains moving with similiar velocities:

ü = 11,8 V² / H

I couldn't find any german drawing I wanted, so here you have polish one; h = ü:

In ModellbahnStudio we must use angle, so we must calculate α:

arcsin = ü / 1435

I built Kreisbogen mit Überhöhung with many short tracks. Below I introduce you one with ü = 50 mm, H = 1000 m and α ~= 2 degrees, with max speed 80 km/h (for various velocities):

And in 3d:

Additionaly, it would be nice to have an option of placing Neigungswechsel (change in gradient) in such track. I made it in other one (it's barely visible):

Radius should be calculated with this formula:

Ha = V²

V = max velocity

And Tangenten:

2. Überhöhungsrampe

This is soft change of level difference between two rails. Überhöhungsrampe should and usually overlaps Übergangsbogen. At beginnig of Übergangsbogen ü = 0 and at end ü = Überhöhung we calculated. It looks like this (again barely visible):

3. Übergangsbogen

Similar topic appeared here, but simplified. 

What I did is exhausting. I made it using many Kreisbogens, every single part with different radius and angle. It looks loke this:

In 3d you can see it on previous image. And in Excel:

I did many, many calculations and every value must be tapped in ModellbahnStudio. It woud be great if there was a way to transfer all this data at once and recieve Überhöhungsrampe with Übergangsbogen. This is one option, but very imperfect. Übergangsbogen made with Kreisbogens has some errors in lenght and angle. That's why I wish to use formula for Übergangsbogen directly. It could be this one:

y = x³ / 6 * H * l

and

l = V * ü / 100

Thanks to it we can find every point in Übergangsbogen. It's important to take right ü - for diffrent or similiar trains velocities.

And drawing:

I know that such things are not necessary for those who use "standard" tracks from Roco or other manufacturer. But I think that more "advanced" hobbyists would be grateful for any easment in creating those things.