Transition Curves

[Leicester North]

You do come across some SOAP in our hobby; there's one in my club; usually best ignored, but ...plastic curtain rail the only way....computer aided design a waste of time... OMG.

Joking apart, like many others, I've been there, done it and moved on. Obviously there's a place for free-form curves in model railway track design, but as in the real world, I think there should also be some attempt at engineering. After all, aren't we trying to model the protoype? This may involve a bit of maths etc, not everyone's cup of tea, but still worthy of serious consideration. For those that want to take up the challenge see my earlier posts.

That's all folks,

Cheers

Brian

[Poor Old Bruce]

 

You do come across some SOAP in our hobby; there's one in my club; usually best ignored, but ...plastic curtain rail the only way....computer aided design a waste of time... OMG.

Joking apart, like many others, I've been there, done it and moved on. Obviously there's a place for free-form curves in model railway track design, but as in the real world, I think there should also be some attempt at engineering. After all, aren't we trying to model the protoype? This may involve a bit of maths etc, not everyone's cup of tea, but still worthy of serious consideration. For those that want to take up the challenge see my earlier posts.

That's all folks,

Cheers

Brian

 

 

I take it that you are modelling to P4 standards or finer, you are using fully sprung locomotives and stock (with scale weight of course) on properly canted track with a 15 MPH speed limit on check-railed curves of less than three feet radius. You seem to be having a dig at me for suggesting the curtain rail idea even though I do not claim originality. Some people apparently spend hours learning how to use computer programs for something simple. Good luck to them if that is what floats their (and your) boat. Even after your have done the computering, you still have to mark out the baseboard and lay the track. I have never been a computer fanatic and probably never will be. Don't mock the simple solutions just because they are not computerised and don't mock those who use them. If you haven't tried it, don't knock it! After all, this is a hobby to enjoy, not a chore to endure.

[Bomag]

 

You do come across some SOAP in our hobby;

Cheers

Brian

 

 

Situation On A Page; keeps it nice and easy for the Politicians - if that is not what you mean please don't use ambiguous acronyms.

 

As for the curtain rail, as long as there is enough either end to be bent to the correct radius (and assuming it has not been deformed i.e. elastic deformation only) although crude, the bit in the middle will be a OK approximation of a transition curve for OO.  However, to look good in N on a reasonably large layout really needs to be done in software if there is a need for consistency. The benefit is (well should be) that you can print it off 1:1 and paste the printout on the baseboard.

 

As for 'simple' solutions, I have no problem is highlighting any deficiencies if the response is 'it's good enough'  - however, if the response is 'it's good enough for me' then I don't mention anything.

[NittenDormer]

Yeah, but what does this have to do with transition curves? Ah! Curtain rails. Something to do with how they sag in the middle when I hang them? I have to say I'm not a fan of CAD, probably because I can't do it. I need to see things 'in the flesh' to picture how it goes together. Help, I'm a luddite!

[Harlequin]

Mr Euler, he of the transition curve spiral fame, also helped to develop the maths to describe the deformation of elastic beams (e.g. a piece of curtain rail held rigidly at one end and with a point load applied somewhere to cause it to bend).

 

It may be that one can be derived from the other (i.e. that a piece of curtain rail does form a Euler spiral segment when bent) but I'm not smart enough to work it out.

 

P.S. @Brian: If you want to add further comments please don't add a fourth "transition curves" thread, please reply to one of the existing ones.

Edited April 4, 2018 by Harlequin

[Grovenor]

P.S. @Brian: If you want to add further comments please don't add a fourth sixth "transition curves" thread, please reply to one of the existing ones.

Perhaps one of our esteemed moderators could merge these 5 threads started by Leicester North on 29/12, 6/1, 14/2, 24/3 and 2/4.

Regards

[tynewydd]

Mr Euler, he of the transition curve spiral fame, also helped to develop the maths to describe the deformation of elastic beams (e.g. a piece of curtain rail held rigidly at one end and with a point load applied somewhere to cause it to bend).

 

It may be that one can be derived from the other (i.e. that a piece of curtain rail does form a Euler spiral segment when bent) but I'm not smart enough to work it out.

 

P.S. @Brian: If you want to add further comments please don't add a fourth "transition curves" thread, please reply to one of the existing ones.

 

If you are interested in the maths (or have difficulty sleeping, I suppose  ) the whole subject of how these different things are all really one family of curves  which describes curtain rods, beams and other physical "splines", railway transition curves, boat-building splines and optimal font outlines and have been discovered and rediscovered as useful curve functions many times historically is covered in a PhD paper (online see link) by Raph Levien, now of Google. Chapters 4, 5 and 6 provide a historical survey including Galileo, Hooke, Bernoulli, Euler, Fresnel, Talbot's railway transition curves, etc. I got a lot out of this paper by reading it and simply skipping the hard maths initially - for a maths paper it is unusually/surprisingly readable.

 

To produce transitions that can join two tracks with different radii or none (rather than the simpler problem of one straight and one curve) is quite complex mathematically as he describes in the paper. Physically, however, you can constrain the ends of a spline (like the aforementioned curtain rod) to follow the radius at one end and then bend it to the radius at the other as long as you to allow the curve to be natural (the rod slides along the curve at one end to ensure it is optimal). You'll see some photos of boat-builders doing just that but with wooden splines in the paper. 

 

Fortuitously, Raph also published an open-source code library of the algorithms he used in the later chapters of his paper to build smoothed font outlines - which formed the nucleus of my little addition to XTrackCAD so that others could easily incorporate these curves into trackplans using a "virtual" curtain rod, if you like, without any need to understand the maths.    

 

Adam

Edited April 25, 2018 by tynewydd