Formula for Distance of Opposite Track

LAST EDITED ON May-17-03 AT 08:51 AM (EDT)

Is there a forumla for calculating the distance of the track going the other direction from the one we are driving?
E.g.
We are going straight but the besides ours goes a curve of Xm.
So, let's say both tracks, start at 0m,0m,0m (X,Y,Z). So, its like a point. We go straight but the other tracks goes Xm radius.
So after 25m, what will be the distance from my track to the other track?Let's assume X is 470m. I know my drawing is not accurate.

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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RE: Formula for Distance of Opposite Track, ferrovipathe, May-17-03, 09:21 AM, (1) RE: Formula for Distance of Opposite Track, Stooopid_person, May-17-03, 09:40 AM, (2) RE: Formula for Distance of Opposite Track, TomBoyRacer, May-17-03, 11:15 AM, (3) RE: Formula for Distance of Opposite Track, Stooopid_person, May-17-03, 11:17 AM, (4) RE: Formula for Distance of Opposite Track, ferrovipathe, May-17-03, 12:28 PM, (5) RE: Formula for Distance of Opposite Track, Stooopid_person, May-20-03, 04:45 AM, (6) RE: Formula for Distance of Opposite Track, Routemaster J, May-20-03, 06:16 AM, (7) RE: Formula for Distance of Opposite Track, Stooopid_person, May-20-03, 07:40 AM, (8) RE: Formula for Distance of Opposite Track, Routemaster J, May-20-03, 02:27 PM, (9) RE: Formula for Distance of Opposite Track, ferrovipathe, May-21-03, 02:20 AM, (10) RE: Formula for Distance of Opposite Track, Stooopid_person, May-25-03, 03:02 AM, (11) RE: Formula for Distance of Opposite Track, ferrovipathe, May-26-03, 04:25 AM, (12) RE: Formula for Distance of Opposite Track, Stooopid_person, May-26-03, 05:55 AM, (13) RE: Formula for Distance of Opposite Track, etjason, May-26-03, 11:29 AM, (14) RE: Formula for Distance of Opposite Track, ferrovipathe, May-26-03, 02:22 PM, (15) RE: Formula for Distance of Opposite Track, ferrovipathe, May-26-03, 02:31 PM, (16) RE: Formula for Distance of Opposite Track, Stooopid_person, May-27-03, 07:23 AM, (17)

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Simple:distance= lenght * sinus(lenght / (2* radius) ) in radian.If you use excel, you may use that straight ahead.
If not, 360° = 2*PI (radian).For example, radius = 328.6 mSo, distance between tracks become :
0.951 m at 25 m
3.8 m at 50 m
and so on.But, there is a little error over 100,150m.
So use formula and try result with trackviewer to correct values.You can find a good example in Loop, when train enter in right tunnel when it leave Sandymill.Good luck, that's a hard work.All the best.

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>distance= lenght * sinus(lenght / (2* radius) ) in radian.
>
>If you use excel, you may use that straight ahead.
>If not, 360° = 2*PI (radian). Huh???
>You can find a good example in Loop, when train enter in
>right tunnel when it leave Sandymill. Can't download it. No download page...

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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you need your calculator for that one mate!
PI is actually a way of entering 'pie' (1 PI=approx 3.14)
sinus, I think he actually meant 'sin' on your calculator
* is a way of saying 'x' or multiply. he's just using scientific notation
/ is a way of saying 'divide by'

Easternsim: Routes for BVE

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>you need your calculator for that one mate!
>PI is actually a way of entering 'pie' (1 PI=approx 3.14)
>sinus, I think he actually meant 'sin' on your calculator
>* is a way of saying 'x' or multiply. he's just using
>scientific notation
>/ is a way of saying 'divide by' So
distance= length * sinus(lenght / (2* radius) ) in radian.What Distance and Length?

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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Sorry, I forget some time than some don't understand Maths.So, if you want to understand, read 'How to build smooth switches' on my site, every thing is updated and avaible:http://ferrovipathe.free.fr/Curves&Switches.docIf you don't, use formula, it work quite fine.
You must use scientific calculator or something like EXCEL.In your case, I had made the compute:For a radius of 470 m, if Distance from your straight track is X (you call it <?> on your graph) , and Lenght of your straight track from the begining of curve is Y (you draw 25...), you get:Y : X (in meters)25 : 0,665
50 : 2,658
75 : 5,978
100 : 10,618
125 : 16,573
150 : 23,835
175 : 32,392
200 : 42,233
225 : 53,344
250 : 65,708
275 : 79,309
300 : 94,128
325 : 110,142
350 : 127,329
375 : 374,970Don't forget to add to X the offset of your track at the begining of curve. For example, if right track just before curve is at 3.8 m from the right straight track, add 3.8 m each time.I have made an Excel sheet to compute such a thing for Loop, and it is very easy with that formula.In Loop, everything had be computed with that, curves, switches, and map. That one is exact, with less than 15 m error (0.0375%) at Balfearn.
And Loop's map you can find in screenshots is the real map, compute as graph from route by Excel, copy and paste to Photoshop as I may add rivers, names, others routes ,...That's why I said good luck if you begin such a work, it's a long and hard way, but the result is quite fine, I think.If you need some more help, send me a mail.All the best.

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I still don't get it.
length * sin (length / (2* radius) ) = distance
I assume
25(sin)(25/diameter)=distance from opposite track

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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First of all pi is spelt "pi" and is 3.14159, it is used to calculate things to do with circles, eg area is pi×radius², Circumference is pi×Diameter (where diameter is 2×radius).The Radian is a unit that is used by mathematicians and Physicists (like me) as a simple unit similar to degrees, but seaier to work with algebraically. pi radians is 180­°.

Joshim,
currently constructing the DLR Route for BVE check out MY NEW WEBSITE http://joshimsbveroutes.gamehorizons.net/

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>First of all pi is spelt "pi" and is 3.14159, Erm...pi = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 ... I could continue if you want...

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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I had to do that once for a school project. We had to do 1500-2000 dp for FUN?! (sad teacher really!) And we didn't have the internets help! Just some lovely formulas involving trigonometric functions.....

Joshim,
currently constructing the DLR Route for BVE check out MY NEW WEBSITE http://joshimsbveroutes.gamehorizons.net/

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What you are refusing to understand, I am sorry to tell you that, really, is there is not other simple way to compute that. (And we are making a small error...)All railways in real life use trigonometric formula, and parabolic curves and....So don't complain you have no help. You have it, but you don't want a such. You want magical receipes, a button to press. But, in that case, it don't work.
I compute distance, and I post it. If it is not internet help, what is it?It is not possible to progress in anything without reading, learning, understanding, even if BVE is a game.

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>I still don't get it.
>length * sin (length / (2* radius) ) = distance
>I assume
>25(sin)(25/diameter)=distance from opposite track So using the above forumla, let's say the distance from opposite track in the end is 3m while the start is 0m.So
25(sin)(25/d)=3
0.4226(25/d)=3
10.5654/d=3
10.5654=3d
d=3.5218
???
If diameter is 3.5m, then radius will be 1.76m!
Impossible!

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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>???
>If diameter is 3.5m, then radius will be 1.76m!
>Impossible! Yes, you're right, but running 25m around a 3.5 m diameter's circle mean you turn nearly three times around it . Don't forget also:- there are two rails by track.
- and nobody had ever seen a radius's track in real life, even in small gauges, (except models'), of 1.75 m.As I said, we make a small error with that formula, because we compute radius from the middle of track.
So, until a radius of 200m, error is lower than 1%, and not visible.
With smaller radius, you must compute each rail (radius of track +/- 1/2 gauge) alone.But, for simple deviation , as you wanted to know, formula works as well as possible.All the best.

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>>???
>>If diameter is 3.5m, then radius will be 1.76m!
>>Impossible!
>
>Yes, you're right, but running 25m around a 3.5 m diameter's
>circle mean you turn nearly three times around it .
>
>Don't forget also:
>
>- there are two rails by track.
>- and nobody had ever seen a radius's track in real life,
>even in small gauges, (except models'), of 1.75 m.
>
>As I said, we make a small error with that formula, because
>we compute radius from the middle of track.
>So, until a radius of 200m, error is lower than 1%, and not
>visible.
>With smaller radius, you must compute each rail (radius of
>track +/- 1/2 gauge) alone.
>
>But, for simple deviation , as you wanted to know, formula
>works as well as possible.
>
>All the best. I don't get it? I used your formula and calculated, and I even substituted it back. But I still get 1.76m as the radius!

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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I don't get something here. I know the formula works as Jean-louis said for modeling tracks it works because it used by most to make smooth curve. based a breaking 25 meter tracks into 5 meter sections.And I see your numbers don't work correctly. But I don't understand where the 3 meters came from.I don't understand which track we are on. once you compute the curve and place it as a free object and it curves away from the running track we are in whats the point.To me the best way is to do it on paper. and then count the boxes it would be a lot faster for one or 2 curves.Jason

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>I don't get it? I used your formula and calculated, and I
>even substituted it back. But I still get 1.76m as the
>radius! Hi!I think that I found your mistake:
You make a mistake with degree, radian and sinus.Formula is:
distance (in meters) = lenght (in meters)* sinus( angle).Angle = lenght/(2*radius) in radian
angle = lenght*180 / (2 * PI * radius) in degree, as one radian = 180°/PI.and not lenght *(sin)*(lenght/(2*radius)).So:distance= lenght * sinus in radiandistance = lenght * sinus in degree.
or lenght * sinusCheers.

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Sorry, the end of my post had been erased.So:
distance = lenght * sinus( lenght / (2 * radius)) in radian
distance = lenght * sinus( lenght*180 / (2 * PI *radius ) in degree
= lenght * sinus( lenght* 90 / (PI * radius ) in degree.

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>Distance = length * sin( length* 90 / (PI * radius ) in
>degree. So based on your new formula(square brackets don't work so I use the next bracket, {})
3 = 25*sin{(25*90)/(PI*r)}
3 = 0.42261{2250/PI(r)}
3 = 950.8725/PI(r)
3PI(r) = 950.8725
9.42478r = 950.8725
r = 100.89
Substituting "r = 100.89" back, it gives distance of 3.0028m, not 3m due to rounding off of decimal places. Doing another forumla, assuming "distance = 2",
2 = 25*sin{(25*90)/(PI*r)}
2 = 0.42261{2250/PI(r)}
2 = 950.8725/PI(r)
2PI(r) = 950.8725
6.28319r= 950.8725
r = 151.33
Substituting "r = 151.33" back, it gives distance of 2.0001m, not 2m due to rounding off of decimal places. It does look rather tight but at least more realistic answer than the first forumla.

------My favourite LUL train------

HAPPY NOW? It's not moving anymore.
It's still the same train but in another livery, that's all.

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