Transition Curves

[Leicester North]

I have been out of action for a few weeks for various reasons, but now back with the data sheet I thought I'd attached last time. Originally intended for my own use, I've now added some explanatory notes in the event it may be of use to other modellers.

q t DataSheet.pdf

[Harlequin]

Hi Brian,

 

Are there any practical guidelines about good values for theta, t and the resulting length of the curve segment? I guess for most situations 0 < theta <= 90deg? The resulting spiral segment must have a minimum length to have a useful effect - maybe a multiple of the longest vehicle length?

 

Do you know which track planning software supports transition curves and how easy it is to transfer them accurately to the real world layout?

 

 

In your drawing:

The Euler spiral segment should have 0 curvature where it touches the straight line but it appears to be curving immediately so it does not look convincing as a transition curve, I'm afraid.

 

I think R' is potentially confusing. It's an arbitrary curve that you have drawn for illustration purposes but is nothing to do with the Euler Spiral segment.

 

I don't understand how the two q distances can always be equal, as your drawing implies. For example if theta was large but t was small wouldn't the q distances be different?

Edited March 26, 2018 by Harlequin

[Bomag]

Hi Brian,

 

Are there any practical guidelines about good values for theta, t and the resulting length of the curve segment? I guess for most situations 0 < theta <= 90deg? The resulting spiral segment must have a minimum length to have a useful effect - maybe a multiple of the longest vehicle length?

 

Do you know which track planning software supports transition curves and how easy it is to transfer them accurately to the real world layout?

 

 

In your drawing:

The Euler spiral segment should have 0 curvature where it touches the straight line but it appears to be curving immediately so it does not look convincing as a transition curve, I'm afraid.

 

I think R' is potentially confusing. It's an arbitrary curve that you have drawn for illustration purposes but is nothing to do with the Euler Spiral segment.

 

I don't understand how the two q distances can always be equal, as your drawing implies. For example if theta was large but t was small wouldn't the q distances be different?

 

Anything more than twice the longest coach has little visual improvement in keeping the gap between coaches smooth. In OO this may result in very little of the curve being a constant radius, For N gauge a 90 degree curve would work out a third/third/third for 23m coaches (Mk 3 and 4).

[Crewlisle]

As I commented before on this subject, the best way to do transition curves is by doing it by eye.  Forget trying to draw them accurately on the baseboard either by calculation or computer programs.  As they say in the ship building/repair business, "If it looks right it is right.".  I did this on my layout 'Crewlisle' 40 years ago & at subsequent exhibitions many visitors have asked me how I got my transition curves looking so natural,

 

Peter

[Harlequin]

As I commented before on this subject, the best way to do transition curves is by doing it by eye.  Forget trying to draw them accurately on the baseboard either by calculation or computer programs.  As they say in the ship building/repair business, "If it looks right it is right.".  I did this on my layout 'Crewlisle' 40 years ago & at subsequent exhibitions many visitors have asked me how I got my transition curves looking so natural,

 

Peter

Hi Peter,

 

I agree that you can judge by eye whether a transition is good or not but in my experience it takes a lot of fiddling to get a curve that looks good and so I think it would be valuable to have a tool, either software or a set of guidelines, to make it a bit easier.

 

Do you have any rules of thumb?

 

For instance, what is a good offset for a transition between a straight and a constant radius curve? (I.e. The closest distance between the curve and the straight line if you imagine the line continuing on forever.)

 

Obviously 0 is no good because that's no transition at all. And if the offset were as great as, say, the curve radius R that would obviously be too far - the transition curve would probably need an entire revolution or more to meet the constant radius.

 

So somewhere within the range 0 < offset < R there's a range of offset values that would work well. But what is that range?

[bike2steam]

I have been out of action for a few weeks for various reasons, but now back with the data sheet I thought I'd attached last time. Originally intended for my own use, I've now added some explanatory notes in the event it may be of use to other modellers.

 

Thanks, that'll save me having to use my 1896 copy of G.H.A.Krohnke's book ' Handbook for laying out curves'.   

[Leicester North]

 

From the www I've read that prototype mainline transitional curves are of the order of 80metres which scales to approx 1metre on the oo layout! Also a line speed of 50mph requires a minimum curve radius of approx 350metres which scales to 4.6 metres in oo. Although these  dimensions are unlikely to appear on a layout they produce a ratio L/R of 0.23 which may be a useful guide. I have also seen a ratio of 0.6 recommended but no reason given (see www.youtube.com/watch?v=Nu9qlIckU7Q.)

I personally have been satisfied with the 22.5 degree case using setrack.

 

As for the diagram which  I created in Word, my apologies, I should have added that it is not to scale and is only indicative of the geometry. Points A & B are intended to be tangential. The offset t is a function of theta and is an ouput of the equations not an input: as theta increases so do q and t.

 

I believe the program AnyRail has an "easement curve" option which can be printed out as a template, but I haven't used it.

 

I totally agree "if it looks right it probably is right" all I've done is attempted to get there quicker more consistently.

In the end I'm just sharing what works for me.

Cheers

Brian

[Poor Old Bruce]

As I commented before on this subject, the best way to do transition curves is by doing it by eye.  Forget trying to draw them accurately on the baseboard either by calculation or computer programs.  As they say in the ship building/repair business, "If it looks right it is right.".  I did this on my layout 'Crewlisle' 40 years ago & at subsequent exhibitions many visitors have asked me how I got my transition curves looking so natural,

 

I too have commented on the subject before by saying that I have used a length of nylon curtain rail as a guide which naturally forms the transition for you. Even though it works fine it was poo-pooed as too old fashioned by the technophiles who apparently would rather play with a computer than a model train.

 

Edited to add "as a guide"

Edited April 1, 2018 by Poor Old Bruce

[tynewydd]

Hi Peter,

 

I agree that you can judge by eye whether a transition is good or not but in my experience it takes a lot of fiddling to get a curve that looks good and so I think it would be valuable to have a tool, either software or a set of guidelines, to make it a bit easier.

 

Do you have any rules of thumb?

 

For instance, what is a good offset for a transition between a straight and a constant radius curve? (I.e. The closest distance between the curve and the straight line if you imagine the line continuing on forever.)

 

Obviously 0 is no good because that's no transition at all. And if the offset were as great as, say, the curve radius R that would obviously be too far - the transition curve would probably need an entire revolution or more to meet the constant radius.

 

So somewhere within the range 0 < offset < R there's a range of offset values that would work well. But what is that range?

 

If you do want to use a tool to start the process - XTrackCAD (a free track design tool for Mac/Windows and Linux) has an upgraded transition/easement tool in V5.1 based on what are called "Cornu" curves from mathematics - which are the basis of what are termed in physics "the elastica" -> such as wood battens, curtain rods and so on and which were used by Talbot and others for railway easement curves. You can easily draw one in the tool by placing your two tracks and then joining them - and then you can adjust the easement length (and/or move the end tracks) until you are happy and print that out at 1::1 as a guide.  Self-interest warning -> I contributed the code... 

 

The safe speed you can run over a transition depends on the length and total change in radius. A commonly used modelling rule of thumb is that to want to transition over distances related to the longest piece of rolling stock you have (some use 0.5x its length as the minimum transition but 1x or more is better to allow higher speeds).  The offset value you need is L*L/(24*R) = so if we say 24 inch transition for a 2 ft radius curve we get 1 inch offset. A 12 inch transition length to the same curve gives a 0.5 inch offset (or a roughly a track-width in OO).

 

Finally, although a tool can be handy to put you in the right ballpark, ultimately the Mk 1 human eyeball looking at the track from a low angle (possibly using a mirror) is the best judge when you actually install it.

 

Hope that helps,

Adam

[DCB]

As I commented before on this subject, the best way to do transition curves is by doing it by eye.  Forget trying to draw them accurately on the baseboard either by calculation or computer programs.  As they say in the ship building/repair business, "If it looks right it is right.".  I did this on my layout 'Crewlisle' 40 years ago & at subsequent exhibitions many visitors have asked me how I got my transition curves looking so natural,

 

Peter

 I think the quotation came from Sydney Camm of Hawker Aircraft who said "If it is right it will probably look right,"  I have an idea he also said "Simplicate and add more lightness," probably as useless a piece of advice as anyone has ever given a model railway loco builder, but back to the plot.

The problems with computer design is getting it onto the layout, few of us have any way of printing larger than A4 and trying to mosaic up larger lash ups is challenging.  If you have a solid layout board then drawing accurate track centres or sleeper edges is straight forward, if the fulcrum point of the curve is actually suspended in mid air in the operating well not quite so easy though I have tacked a batten in place before now, out in the garden its even more tricky with frequent trips to the bedroom window to check if it looks right.   I spent ten minutes re laying a bit of track last evening trying to get the best curve possible between a curved point and a re arranged angle into a tunnel mouth, I doubt any of it moved more than 4mm sideways but it looked much better afterwards, at least I hope it does, and the King no longer smashes its chimney the track bed above just inside the tunnel.

Check out Crewlisle, some of his trackwork is quite amazing, like 2ft radius Y points on a main line high speed junction yet it looks right. Quite amazing. I reckon it is his attention to detail that makes it possible.