Round the Bend

[What About The Bee]

Austria adopted the metric system in 1875, so it is completely logical that any Roco track produced a century later would also be exclusively metric

Bee

[Rallymatt]

Interestingly many British scientists and engineers were using metric in mid 1800’s but it took a long time to make it official…. In fact we are still in the process of the switch 🤣

[What About The Bee]

26 minutes ago, Rallymatt said:

…. In fact we are still in the process of the switch 🤣

Speaking as a USA based engineer, with what was an international clientele, being ambidextrous is a benefit.  Surely it teaches the value of writing down the units!

With System 6 identified as the decoupling from imperial units, is there someone with a System 6 track geometry specification from Hornby?  Hopefully with a date!?!?

I would still very much like to resolve the conundrum raised by @Gordonvale.  Is it 438 mm or 438.15 mm? 

At this moment, I believe that as Roco produced metric track for Hornby, starting 50 or so years ago, the imperial units no longer apply and the standard is 438 mm.  I can always be convinced otherwise.....

Bee

[Going Spare]

@Gordonvale Is it correct to use the present tense?  Certainly the geometry was in imperial measure when Tri-ang & Hornby-Dublo produced track in the UK but is it correct to use the metric equivalents of the imperial measures (suggesting roundings in Hornby's descriptions) when describing current trackage?

[What About The Bee]

I can move the demarcation line.  

In the 1984, Hornby Track Plans 6th Edition, the radii of the curves are given

While it is a bit hard to see, R606 is denoted "2nd Radius 17¼, 438 mm".  Apologies, but the image is scraped from the internet.

This likely isn't the terminal date of the conflicted reference , as there were many more track plan editions after the 6th.

Bee

 

[BritInVanCA]

We were exclusively taught metric in school (born in 1966) but had to deal with an imperial world until I left in 1991 and moved to a metric country…well mostly!

[Gordonvale]

On 08/08/2024 at 06:38, Going Spare said:

@Gordonvale Is it correct to use the present tense?  Certainly the geometry was in imperial measure when Tri-ang & Hornby-Dublo produced track in the UK but is it correct to use the metric equivalents of the imperial measures (suggesting roundings in Hornby's descriptions) when describing current trackage?

Y & Y

Hornby state standard track centres as 67mm and double track centres at 133.

I'm pretty sure that 67 x 2 = 134, and 66.675 x 2 = 133.35 which becomes 133 when rounded.

 

[ColinB]

Go round the wood yard in the UK. The wood comes in 3 metre lengths but it is sold by the foot.

[What About The Bee]

Hi @ColinB

This is certainly not a debate over units.  It matters not if it is in imperial or metric.  The issue is one of standards.

You may have heard me muttering about standards before. Some chatter about the barrel size on early tenders, the capacity of chaldrons and about the word "ton" as it relates to mineral waggons.

Yet this "standard" is far from that.  How can it be a standard if 17¼" is not equal to 438 mm?  This standard is far closer to our hobby than some measurememt regarding an actual railway.

I would still very much like to know when Hornby dropped imperial units in the spec, and exactly what radius the set track curves really are.   Is it 17¼" round to 438 mm but still actually 17¼?  Or is it actually 438 mm, precisely?

Bee

[Going Spare]

@bee I would not be surprised if both imperial and metric dimensions were shown in sales material until production was moved to China in the late 1990s.  I do not have catalogues or track plan books of the period but am not aware of any appearing since then, particularly references to a 133mm spacing and continuing to use an imperial measure base for the metric conversion.

But in any event, these are only descriptions, not actual production specifications, and used because rounding to the nearest mm is perfectly fine for their intended use as layout planning guides. 

Is not your principal consideration here knowing for certain the specifications (and permitted tolerances) to which the actual track is currently manufactured?  Information that is known only to Hornby and their contracted factory.

Edit: Typed while Bee was doing likewise.

Edited August 10 by Going Spare

[What About The Bee]

Just now, Going Spare said:

Is not your principal consideration here knowing for certain the specifications (and permitted tolerances) to which the actual track is currently manufactured?  Information that is known only to Hornby and their contracted factory.

Hi Going Spare

Exactly that.  Its not so proprietary, as SCARM and Anyrail, to name a few, can put up precise geometry on screen.  SCARM complains about minute misalignment, so it must be using a precise value.  A precise value to match what is manufactured.

It is just a side interest to understand a bit of the history and public specification 

Bee

[Going Spare]

What is "minute misalignment" to the online track planners? 15 hundredths of a millimetre across c.438mm?? Or, to that extent, compromised?

[What About The Bee]

Hi GS

I had to resort to trigonometry to get two tracks to "couple" in SCARM.  As I recall, it was a very small value but memory is a bad choice for this discussion!  I will set up an experiment in SCARM to determine what it thinks the value for R2 is and report back later.   

I'm in the middle of trying to get OO Twin Sisters to go "round the bend", and it is very tight indeed. The current chassis is just a wee bit too wide, but the motor is inside of the chassis.  The motor also has manufacturing tolerances and is a wee bit bigger than claimed (12.06 mm diameter instead of 12.00 mm diameter).  A miracle is about to occur! 😄 

When in CAD, the tool requires mathematical precision.  Its not meaningful or practical, but the numerical computations must resolve themselves or the designer (me) suffers the consequences.  My self imposed requirements are to resolve to 1 micron.  This is because the volumetric pixel (vixel) was ~0.016³ mm in Shapeways 3D fine plastic prints.  That means everything is quantized. 

As a rule of thumb, design to about an order of magnitude better than the machinery used to create your object, and then place reasonable manufacturing tolerances on it

Bee

[What About The Bee]

Hello @Gordonvaleand @Going Spare

here is the promised SCARM EXPERIMENT and the inescapable result.

Controls.  

I used FreeCAD to obtain arithmetic values.  I selected R606 as the curve.  R606 has a 22½° angle.

I drew two segments of a circle with the same starting point.  Both segments were at 22½°.

Values

All to 1 nanometer.  0.000001 mm.

For a radius of 438 mm the endpoints in X,Y are
X 167.615343 mm 
Y 33.340765 mm

For a radius of 438.15 mm the endpoints in X,Y are
X 167.672746 mm
Y 33.352183 mm

The distance between the endpoints of the curves is 0.058527 mm

SCARM Curves

I set an initial start point at X=0 Y=0 and angle A=0.  I placed an R606 curve.

I then set a start point defined by the geometry for a radius of 438 mm and placed a straight section at that start point.  SCARM accepted values to 1 nm.

close up

Notice that the join between the track segments is one line, indicating a perfect join.

I then repeated this, setting the second start point at the geometry defined by a 438.15 mm radius.  I placed a straight section at that start point.

Notice that the join is TWO lines, indicating that SCARM does not think these tracks join.

Conclusion.

The delta between endpoints was 0.059 mm (rounded to 1 micron). Scarm noticed this.  The delta between 17¼" and 438 mm is 0.150 mm, a larger dimension.

The R2 radius that SCARM uses is 438.000 mm, not 438.150 mm.  If SCARM did not produce valid set track plans, it would be dispensed with, forthwith.  

Therefore, Hornby must define R2 as 438.000 mm.  There can be no other mathematical solution.

Bee
 

[LTSR_NSE]

There must be manufacturing tolerances with set track production - is it certain that the tolerances are less than 0.15mm?

If not, the fantastic levels of accuracy  computer programs demand may be slightly excessive?

[What About The Bee]

Hi LT&SR_NSE 

This is a fundamental question in manufacturing. Well played!

I do not claim to know what Hornby accepts but the tolerance permitted only permits a range around nominal in manufacturing. It does not change the nominal.

A specification would be properly written xxx.xx mm +/- y.yy mm.  Where xxx.xx is the nominal and y.yy is the tolerance band around nominal.  They need not be uniform, thus xxx.xx mm +y.yy mm -z.zz mm.  In all my decades in using dimensional specifications, I have yet to see a tolerance of +/- 0.000 mm.  It may exist, but will cost a veritable fortune to produce and require a temperature specification as well.  As in, what temperature must the object be when measured.

The numbers produced by FreeCAD and used in SCARM represent nominal, as shown, because they are the virtual representation.  The join line only becomes one when the correct nominal values are used. 

The nominal dimension is 438.00 mm.  Hopefully, this particular discussion clarifies the issue for you

Bee 

Edited August 10 by What About The Bee

[What About The Bee]

The Wiggle Waggle Model Railway is an end to end layout.

It consists of 28 sections of R607. 

14 will turn to the left, 14 will turn to the right, alternately.  Back to back curves, one after the other.

R607 is a double radius curve.  The included angle is 45° for each. 

The length of the chord, across the curve is straight forward.

Chord Length = 2 * sin(angle/2) * radius

If radius = 438 mm, then chord length is 335.230687 mm

If the radius is 17¼" (438.15 mm), then the chord length is 335.345492 mm

Fairly tiny difference.  But here at the WWR, we have 28 of sections, not just 1.  Simply multiply each by 28 and find the difference.  The difference is now 3.214541 mm (⅛").

I set up the WWR in SCARM.  I placed 28 pieces of R607, as described.  I then added a start point, as if the radius was 438.15 mm.  Here is the result

R2 curves are 438 mm, not 438.15 mm (17¼").  Inescapably resolved.

This is also a good way to illustrate Build up of Tolerance (Hornby Post) .  A tiny error accumulates.

Bee

[LTSR_NSE]

@What About The Bee Forgive my ignorance, I am not questioning your math(s) - since it is mostly to a far higher level than I understand!

(I am merely seeking clarification of your determining ‘right’ from ‘wrong’)

You appear to have used a computer program* to ‘prove’ the nominal that the actual track pieces** must use?

Whilst I wouldn’t attempt to claim that the actual track doesn’t share that nominal, if the decimal & imperial nominals are both within the manufacturing tolerance - how can either be said to be wrong?

*(with a nominal set to the decimal one that has been used for at least the last 40 yrs)

**(that potentially have been designed to the same tolerances as those from approx 60 yrs ago)

[What About The Bee]

Happy to explain LT&SR_NSE, no worries.

TL;DR: 

SCARM uses one value for R2.  It is deterministic.  The mathematics tell us where points should be, and when I use the correct value, SCARM agrees.  When I compare to SCARM using an incorrect radius, SCARM does not agree.  Thus, we know the one value it uses. 438 mm. Further, this must agree with the nominal value of the physical track, or it cannot produce layout confirmation, particularly so with lots and lots of pieces. 

The slightly longer version:

This is an advanced mechanical engineering topic.  It talks to the relationship between the theoretical aspects of CAD and practical manufacturing.  Its a fairly complicated topic, but the over view is presented thusly:

SCARM is essentially a simple CAD tool. We pick from a library of preprogrammed parts.  We pick R607, for example.  We do not specify the radius of that track, we just get that piece of track.  The dimensions, like included angle and radius are fixed. 

So the first thing we must understand is the behavior of SCARM, to see if  it is deterministic.  Does it use the same value for the angle and radius of R607, each and every time I select that from the library?  The short answer is yes, it is deterministic.  I can mathematically predict where the endpoint is, to a very high degree of precision, given the inputs from the starting point.  It is always the same values, the same endpoint.  

SCARM uses a singular value for the radius.  A singular value for the included angle.  R607 is parameterized.
 
The issue of tolerance does not apply for SCARM as it relates to manufacturing.  The theoretical track in SCARM must match the nominal, or the accumulation of error could render the program useless.  This is a subtle point, but critical to understanding. 
 
Suppose I accept a tolerance of 438 mm +/-0.15 mm.  In actual practice, there will be a gaussian curve (bell curve) of parts compared to the nominal specification.  So some parts could be as low as 437.85, some as high as 438.15. 

So what should SCARM use?  Will it be a random selection for each track piece?   Random selection will not work well for 8 sections of R607 arranged in a circle, as the endpoints of 1 and 8 will likely not meet.  It's not just the radius that has a tolerance, its also the included angle. 

SCARM does look at the endpoints of two tracks in close proximity and decides if they can join, or not.  If the tracks endpoints are within some distance, SCARM says they will join. A tolerance of join-ability.  Afterall, SCARM is to validate your track configuration. 

For a circle of R607, with 8 segments, the value used in the SCARM library should be at the one value, such that the circle joins.  Will it join if you use random angles and radii?  Maybe, maybe not.  That would be a poor tool indeed.  If all the included angles are low, they do not add up to 360°.  Will the circle join if you use any one value?  Of course it will.  SCARM checked our circular layout and all the endpoints connected! 

How does SCARM relate to the physical parts?

So I run out and purchase my 8 pieces of R607.  These have true manufacturing tolerance, with that gaussian distribution centered around 438 mm.  I connect them up.  Even with tiny errors, the tracks will go together.  The tiny dog legs will not affect running.  As long as the Hornby track is within a manufacturing tolerance, what SCARM tells you will likely go together.  Why? Because in the real world, it is extremely unlikely that the errors add up linearly, to give a max build up.  As the errors are on both sides of nominal, they tend to cancel the overall error.  You must still plan for and account for the extrema, but in all likelihood, it will not be thus. 

Think it through.  What value should SCARM pick for the radius?  It cannot be a random distribution around nominal.  It cannot be a gaussian distribution about nominal.  If I am to pick one value, I should pick the nominal.  This will permit SCARM to validate my layout to the highest order of accuracy.  It will match.  It cannot match if the radius is consistently wrong.

Now examine the Wiggle Waggle Railway.    I compare two fixed values.  They are either R2= 438mm or R2=438.15mm.  SCARM could use either one,  but which one?  Or perhaps another radius.

When I accumulate the difference in chord length over multiple segments, the difference is magnified.  The error is linearly proportional to the number of segments. It is strictly multiplication. 

So with SCARM commanded to install 28 curves, it does so.  In a deterministic sense.  I then tell SCARM I want a new starting point.  Of course, I will select a new starting point strictly by the trigonometry and maths.  If the new starting point agrees with the old endpoint the track join lines will be perfect.  Therefore, what I used for the radius was correct.  If there is a gap at the new / old, then the radius I selected is wrong.  Easy peasy.  Either its 438 or 438.15 mm.  And we can immediately see the mathematical answer that agrees with SCARM is 438.00 mm.

In the first SCARM experiment, we have perfect agreement with the 438 mm radius.  At 438.15, we do not.  We confirm this by intensifying the conflict.  In the second SCARM experiment, use 28 segments, connected back to back.   We see that if I compute an overall length, using 438.15 mm and set the start point, it is off by ⅛". 

Hold up Bee, you rascally rascal.

28 pieces? That's well below the threshold for the free version of SCARM.  What happens when I pay for SCARM and inject 280 segments of R607?  The error between the two accumulated chord lengths is 1¼".  Remember, the pay version has unlimited components.  Suppose I pick 2800  sections of R607.  It grows to 12½" or more than a foot!!  Yes, I think most anyone would notice that.  A one foot gap?  Yes, even I might pick up on that minor gap.

Intensify the conflict, again.  What if I have 28,000 segments of R607?  Okay, most would think me daft for such a layout, but the delta is now over 10 feet.  That's one heck of a keep alive.

SCARM uses one value for R2.  It is deterministic.  The mathematics tell us where points should be, and when I use the correct value, SCARM agrees.  When I compare to SCARM using an incorrect radius, SCARM does not agree.  Thus, we know the one value it uses. 438 mm. 

Further, this must agree with the nominal value of the physical track, or it cannot produce layout confirmation, particularly so with lots and lots of pieces. 

This should be enough to explain it.    If not, ask away.  I really do not mind a bit. 

Bee

Edited August 13 by What About The Bee

[LTSR_NSE]

Thanks for extra detail Bee. 👍

I still believe it’s a bit of an assumption to expect that real world track will conform to computer modelling levels of accuracy - especially considering most using set track are building small layouts & most building large layouts use flexi.

However I do accept that computers & designers using math(s) require nominals & precision for calculating.  So hopefully manufacturing tolerances for both track & rolling stock can accommodate any real world variances & inaccuracies. 👍

[What About The Bee]

3 hours ago, LTSR_NSE said:

 ...it’s a bit of an assumption to expect that real world track will conform to computer modelling levels of accuracy ...

Ah, I see the difficulty now.  Excellent question. 

Part 1: A Hornby Engineer

The Hornby Engineer will be using a genuine CAD station.  It too will have extraordinary levels of precision.  Once the design is complete, the next step is the "reduction to practice".  The object is extracted from CAD and placed on drawing sheet.  It will typically have side, end and plan views.  Tiny details and cross sections may be added for clarity.  The HE will then consider the machines and techniques that will be used to make the part.  The drawing is provided with detailed dimensions, with that consideration in mind.  The nominal will be present, but not to a nanometer.  For track, I would guess 2 places (tens of microns), but would not be surprised by 3 (one micron). The tolerance band associated with the dimension is also assigned as a function of the machine.  The drawing is presented to manufacturing for production 

The key takeaway is that the production team references the drawing, not the CAD.  They understand that the mathematical purity of CAD is not expected, they only need to conform to the drawing. 

Materials cost money.  Sloppy tolerances are wasteful, as is chasing mindless precision.  The production of track for the hobby is a commercial practice.  A good Engineer squeezes cost out of a design.

Dimensional tolerances on the drawing are selected with the machine and commercial practices in mind.

Part 2: SCARM

SCARM has no control over the production of parts.  Indeed the Hornby parts rule SCARM, not the other way round.  SCARM must conform to whatever Hornby, or other track system, says.  Hornby could add an R6 radius curve and the SCARM guy will just add it to the library, just as he did for TT:120 track.

SCARM need only match the nominal, the only tolerance it cares for is that your tracks join in theory.  It could just use two or one places for the dimensions, but the build up of tolerance in the computations will swiftly obviate the utility.    The easiest thing for the designer of SCARM is to select floating point variables for calculations.  It just so happens that these computations are fairly straightforward and subject to reverse engineering by me.  Who could see that coming !?

Part 3: Intensify the Conflict

This is an engineering phrase.  It means to exacerbate the issue.  There are some others like "eat the ugliest frog first" but we may discuss that at another time. 🙂

Intensify the conflict: of course, no one will ever use set track for 2800 pieces.  But it does exacerbate the issue.  If I put 2800 pieces into SCARM, tiny errors in computation are magnified 2800 times!  In this case, the intensity reveals the values with certainty.  We can see the radius that SCARM uses.  The nominal radius that Hornby dictates.

Helpful?

Bee

Edited August 13 by What About The Bee
Extra word removed, the phrases should be in intelligible English!

[Gordonvale]

 

The bottom SCARM diagram is lifted straight from my layout plan. It's been around for a few years, but I recall having fun trying to get things to join up. So, I've just knocked up the top SCARM diagram, and guess what, there's a "no joiner". Fiddling about, you can alter the location of the "no joiner" and if you get lucky you can get all to join. Both diagrams are contained in the one SCARM "page".

What does this tell me?

[What About The Bee]

57 minutes ago, Gordonvale said:

What does this tell me?

That you wish to change the subject. 

You have no analysis to contradict the extensive proof provided against your original assertion.  R2 is 438 mm, not 438.15 mm (17¼"), as demonstrated.   It may have been this historically, but no more.

Further, your diagram could also mean that the design you offered to SCARM is marginal.  It can be forced to join, as SCARM will accept track as joined whenever the ends are within tolerance.   But if they fall just outside that tolerance, SCARM says they don't join.  SCARM does not demand that the ends are in mathematical agreement, just that the ends are "close enough".  So depending upon exactly how those pieces are placed can cause your design to be joined or not. 

Interesting as the design may be, its a deflection with little to do with the definition of a second radius.  

Bee

[What About The Bee]

Here are the equation results that resolve the lateral compliance for OO Twin Sisters.  

In the top of the image, I check the lateral compliance Y against the flanges of the center axle.  I find that I will need 0.012 mm (12 microns) of lateral compliance.  As Q, the track gap is 0.148 total, the lateral compliance Y is much less than Q.  There is no issue with a fixed center axle. It will fit into the curve.

The first and last axles must now have full compliance on each side.  The chord formed by the first and third axles must always have the middle axle fixed, and further, the chassis does not shift.  Thus, knowing the chord length Wt, I can find Y for the first and third axles, being 0.499 mm.  Bottom half of equations.  Note, same equations as above.

With the redesign accomplished for the new parts (see OO Twin Sisters), I show here that indeed it will clearly go around a second radius curve 

Bee