# Calculating Diverging Curves

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#### Tom B

##### Established Member
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

R

#### Dennis

##### Established Member
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

##### Established Member

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

##### Established Member
Cockfosters said:

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

##### Established Member
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

##### Established Member
Cockfosters said:
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

##### Established Member
That would be the simple solution .

#### micky515

##### New Member
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

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

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