Disclaimer: This is a work of fiction. Any resemblance to actual persons or events is purely coincidental.

A long time ago, a good friend of mine had an interesting design experience.

He was young then, young and unafraid, dreaming, still humming a Peter O’Toole’s song about impossible quests and fighting windmills (a lesson he seems to never learn).

It was just after this young chap moved to the Texas of Great Britain (or God’s own County – as some rightly believe it to be).

Whilst he was still getting used to the second most disappointing design software he has ever used, he had to design an alignment in a very constrained space, forced to use an acceptable at the time but now so ostracised curve to curve connection without transition, a “virtual transition” as so many of us improperly calls it, merging confusingly the imaginary calculation method with the actual geometrical design feature.

Due to the constraints of the site, he got a rate of change of cant deficiency of 55.5mm/s, calculated using the Virtual Transition principle.

Obviously, when displaying the alignment data, he forced that figure to integer, displaying 55 mm/s, at the margin of compliance by the rules of the day.

This trick was noticed by his too careful checker, and even though he understood the spirit of it, he asked my friend to change the design and insert a short transition between the two curves.

A 20m transition was enough to reduce the rate of change of cant deficiency from the dangerous 55.5mm/s to a safe 33.9mm/s!

Well, my friend had his gauging already done, with the slues and geometry defined based on the VTed alignment.

One of the curves was also placed on a bridge where no slues were allowed due to the tight distances to existing girders.

How could he insert a 20m transition without affecting the design too much and not re-run the gauging?!

Recalling the death of Archimedes, he decided to use the dark knowledge hidden deep inside our Sacred Book – The Track Design Handbook. This book mentions a mystical parameter called the “transition shift”.

(Later edit: Yes, the formula should be with 2688 instead of 2668 … My mistake. I trusted the standard!)

Our wise grandfathers discovered that to insert a transition between two curves (or a straight and a curve) the lower radius curve needs to be shifted inside the flatter one by a tiny little value, cleverly called “shift”.

Or vice versa, the flatter radius to be shifted out.

Or …

Using this dark knowledge, he calculated the shift required for a 20m transition discovering it to be a massive movement of 2.4mm.

2.4mm shift meant slues close to this value, so he used a trick to split the shift in two between the two curves when inserting the 20m transition.

How did he do it?

Then he traced this new alignment and re-displayed the horizontal and the vertical profile, passing the updated drawing to his checker, for review.

The horizontal alignment passed the check. RcD =33.9 mm/s! 

But now the vertical profile was questioned, because, you see, the slues were EXACTLY THE SAME to the ones he had before, when the alignment had the 55.5mm/s RcDVT. Only a few were varying by only +/-1mm.

CHEATER!

Slues for RcDVT = 55.5mm/s can’t be practically the same as the ones for RcD=33.9mm/s.

A non-compliant alignment can’t be exactly the same as a compliant one!

To prove he did not cheat, my friend created a slue report to 6 decimal places, to show the differences between the two alignments.

The difference was indeed unnoticeable when displaying the slues in mm, as the maximum difference was only 0.9mm, decreasing quickly to insignificance.

As this was for sure a devilish work, the checker asked a colleague to replicate my friend’s design, and insert, using the design software, the 20m transition into the VTed alignment.

But their slues were different, on a longer extent and some even bigger than that shift, as the transition did not want to sit where the VT was unless my friend’s design lengths were copied over. Regression analysis works perfectly when you already know the solution.

It was then when they found out that a multiple realignment calculator can’t do what my friend can.

It was then when one of them called my friend “The Grey Wizard”.

 Wizard or not, he even today wonders, which rate of change of cant deficiency is now on site, the 55.5 or the 33.9 …?!

Sometimes, a more terrifying thought comes to his mind: Is this rate of change of cant deficiency a real thing and so dangerous as we think it to be?

Because, you see, we changed its limit from 55 to 35 (25?) and now to 70 …

People who called unsafe any increase of it above 35 now accept it to be close to 70 with no safety issues whatsoever.

Or perhaps this rate of change of cant deficiency is elastic? Or affected by climate change? Or, perhaps, by inflation?

mm/s? Is that a speed?

Well, now, that’s a good question!

Isn’t he smart, this friend of mine?!

PS: Doesn’t add up, you say?