# Rail Question?

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#### The Snap

##### Established Member
Hi guys,
If I wanted to create a branch in BVE, where say two tracks go off left, and you carry on straight, is there a formula or program to work out the distance of the track from track 0 to make it smooth or curved?
If so, can someone tell me what it is?

Thanks,

R

#### Nick

##### Member
Can you make that question a little clearer please

#### Tom B

##### Established Member
There's a formula, I can't remember it off the top of my head but it should be possible to derive it - it's only simple trig IIRC.

#### Dennis

##### Established Member
Seem to remember this dicussion a while ago...

http://www.railuk.org/mainbox/viewtopic.php?t=3253

After which I smoothed out all the diverging lines on the Clarendon route using the equation of a circle. It was a bit more complicated calculating diverging curves from a curved running line but by effectively adding two divergences from a straight line it is possible.

Useful hint....make sure all turnouts are of the correct radius.

#### Derek Kaye

##### Member
there is one formula:

x = z x SIN(90z / (PI.r))

where
x = the x-offset from track 0 of the track you want to know the distance of. (you will need to add onto this the offset from before the start of the curve (e.g. 3.5m))

z = the distance down the track from the start of the curve

r = the radius of the curve you want

so, if you had a track 3.5m from rail(0), and at 100m down the track you wanted to start turning it away from rail(0) with a radius of 1000m, you would enter the following

after 25m

x = 25.SIN((90.25)/(PI.1000)) (+ the initial offset of 3.5m)

after 50m

x = 50.SIN((90.50)/(PI.1000)) (+ the initial offset of 3.5m)

etc etc

hope this helps!

#### Dennis

##### Established Member
I would be interested in seeing the results from the equation just given, not sure if I've set up my spreadsheet properly as I am getting a wave of increasing amplitude!

I would have thought that the disadvantage of using any trig functions like this is that although giving lovely curves, the radius is not constant which can make curved rail sections not fit together very well - this problem does not occur if the equation of a circle is employed (although if radius changes are needed on a diverging curve, the calculations get a bit more difficult).

#### The Snap

##### Established Member
Derek Kaye said:
there is one formula:

x = z x SIN(90z / (PI.r))

where
x = the x-offset from track 0 of the track you want to know the distance of. (you will need to add onto this the offset from before the start of the curve (e.g. 3.5m))

z = the distance down the track from the start of the curve

r = the radius of the curve you want

so, if you had a track 3.5m from rail(0), and at 100m down the track you wanted to start turning it away from rail(0) with a radius of 1000m, you would enter the following

after 25m

x = 25.SIN((90.25)/(PI.1000)) (+ the initial offset of 3.5m)

after 50m

x = 50.SIN((90.50)/(PI.1000)) (+ the initial offset of 3.5m)

etc etc

hope this helps!

Thanks for that, only I don't quite get it. Is there an actual solution to the formula, to which you enter in the .rail command?

For example, if the answer was 3.56662, you would put .rail 1;3.56662;;0,

Is this right?

I did the formula (x = 25.SIN((90.25)/(PI.1000)) (+ the initial offset of 3.5m) in my scientific calculator, and got the answer: 3.59025

Is that right? :?

#### Derek Kaye

##### Member
That sounds about right - obviously the difference will increse the further down the line you go. try doing the first 100m and have a look at the results in track viewer.

in BVE of course, you only need to go down as far as mm, so you would enter 3.590

#### The Snap

##### Established Member
OK, thanks for that Derek! Will try, and see the result! #### The Snap

##### Established Member
Just downloaded that Excel document Dennis, works great! (Sorry, Derek, the document is easier to use than the formula - I am in top set Maths group, only we haven't come accross anything as complex as that yet! )

#### Tom B

##### Established Member
I bunged your calculations in and got 3.81 (3SF) but there you go. It's not that complex, just multiplying numbers then finding the sine of them... surely you've multiplied numbers and found the sine of numbers in Maths ?!

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