One difficulty with BVE is to compute curves, switches and junctions. The principal question is how compute
distance from rail(0) to the others tracks.
We begin by a little refreshing course of trigonometry:
If we got a right-angled triangle ABC, we have a right angle ABC and two others angles as:
angle AC + angle BAC + angle BCA = 180 °
As, angle ABC = 90°, angle BAC + angle BCA = 90°.
Sinus(angle BAC) = sin(angle BAC) = BC / AC .
Cosinus(angle BAC) = cos(angle BAC) = BA / AC.
That's all we need.
Now, train is running on a line, reach a switch on A, and turn on right, on AC.
We want to compute BC, deviance from strait road AB, when we arrive at AC.
We get :
A Circle : center O, radius OA = OC, some right-angled triangles, and Right angles:: OAB, ODA, ODC, ABC
Angle of deviation BAC is yellow:
We got : Angle BAC + Angle CAO = 90°
So, as Angle BAC + Angle BCA = 90° too (right-angled triangle), we arrive to:
Angle BAC + Angle CAO = Angle BAC + Angle BCA= 90° => Angle CAO = Angle BCA.
As Right-angled triangles ADO and CDO are the same (they have OD in commun, and AO=CO=Radius),
 Angle DAO = Angle DCO, and Angle AOD = Angle DOC.
 Angle AOC = 2 * Angle AOD = 2 * Angle BAC.
 Or Angle BAC = Angle AOC / 2
Remember: Angle AOC = 360° * arcAC / Circumference of circle.= 360° * arcAC / (2* Π*Radius)
Now, we get two ways for computing:
A) ArcAC is nearly equal to AC (25meters) in reality.with large radius.
 Angle BAC = 360°* AC/ (2* Π*Radius)
 AC = (2* Π*Radius) * Angle AOC / 360°.
 As 360° = 2* Π in radian, we get: AC = Radius * Angle AOC = Radius * 2 * Angle BAC.
As Sin(Angle BAC) = BC/AC,
=> BC = AC * sin( Angle BAC) = AC * sin( 180°* AC/ 2* Π*Radius) = AC * sin ( AC/2*Radius) (in radian).
B) If an Angle is small, and in radian, we can write : Sin(Angle) = Angle, because Arc is nearly equal to string
under arc.
So, we find:
BC/ArcAC = Angle BAC. ( Beleave me, I am not going to rewrite more complex maths)
= circumference of circle * 2 * Angle BAC / 360° = 2* Π*Radius * 2 * Angle BAC / 360°
= 2* Π*Radius * 2 * Angle BAC / 2* Π (in radian)
= 2 * Radius * Angle BAC.
= 2 * Radius * BC / ArcAC.
 BC = ArcAC * ArcAC / (2 * Radius) = ArcAC2 / (2 * Radius).
=> ArcAC
As AC is nearly equal to ArcAC:
 BC = AC2 / (2 * Radius).
 Radius =AC2 / (2 *BC).
So, there are two ways to compute the deviance BC of a track from others in curves.
A simple for small angles :
 BC = AC2 / (2 * Radius).
 Radius =AC2 / (2 *BC).
And a more complex if you need:
=> BC = AC * sin( 180°* AC/ 2* Π*Radius) (in degrees) = AC * sin ( AC/2*Radius) (in radian).
If you are using Excel, remember than all computes are in RADIAN.
Enjoy with them and BVE.