Calculating Diverging Curves

[Tom B]

Calculating Diverging Curves

This is something which is often needed during route construction but not that many people seem to know about. That included me until I happened to think of a quite simple solution to the problem, after I happened across a mathematical question on an AS paper which is almost identical to the BVE problem.

Full guidance which hopefully should be clear to anyone with a basic understanding of maths...

http://www.brj.railuk.org/Calculating Diverging Curves.pdf

 

[The Snap]

Very useful, but you can also use Dennis' special Excel file. http://www.freewebs.com/dennislance/equataion of a circle.zip I think. This is very simple but effective!

 

[Dennis]

That is the formula I have used in the spreadsheet, the diverging distances being calculated every 25m for a constant radius curve.

Things get a bit more complicated though if both the running and diverging lines are curved and the radii are changing (look at the mess I made of the last junction on the Clarendon route!!).

 

[Tom B]

I didn't know about the spreadsheet - sorry.

As for two different radii... work out the value for the displacement of the main line from the x axis and also the displacement of the branch from the x axis and subtract them should work?

 

[Dennis]

I didn't know about the spreadsheet - sorry.

As for two different radii... work out the value for the displacement of the main line from the x axis and also the displacement of the branch from the x axis and subtract them should work?

For constant radii it does work as you have described but when the radii of either is varying then things get a little more tricky....

 

[Tom B]

Ooouok.

That's even trickier... I suppose it would be a case of making a new model for every 25m with the new values of the radius and then adding the previous values on, if you know what I mean?

Or two circles, one

x ^ 2 + (y - r1) ^ 2 = r1

then you use that to find d1 and then use

(x - 25) ^ 2 + (y - r1 - d1) ^ 2 = r2

to find d2.

 

[Dennis]

Ooouok.

That's even trickier... I suppose it would be a case of making a new model for every 25m with the new values of the radius and then adding the previous values on, if you know what I mean?

Or two circles, one

x ^ 2 + (y - r1) ^ 2 = r1

then you use that to find d1 and then use

(x - 25) ^ 2 + (y - r1 - d1) ^ 2 = r2

to find d2.

or just give up and stick to constant radius curves until the diverging one(s) are out of sight (or hidden by conviniently placed objects)!

 

[Tom B]

That would be the simple solution .

 

[micky515]

Does anybody know where I can get the smooth curves objects now, as the site doesn't appear to be available now. Thanks in advance. Am new to building routes and am trying to learn all I can at moment.

Mick.

 

[Tom B]

The site does seem to be down. Check your email shortly.