Versine artefacts?

Motto:

If you can’t explain it simply you don’t understand it well enough.
(Easy for you to say…) Einstein

Well, hello again, dear reader!

Before moving on from the TGSD Calculator allow me to explain what it measures, without any reference to waves and filters, without frustration or passive-aggressiveness (is that an actual word?) , without any hints to the best novel opening line (that thing here sounds odd even to me now) or memes that hint to one of my favourite movies

The engineering world is governed by numbers

Since David Marriott and I published the design SD articles in the PWI Journal I have been asked to explain what the problem is with these design SDs and almost every time I found difficult to explain what they are – partly because of my ignorance on the subject (I’m not saying that with false humility – it is so much I still don’t understand because …) and partly because the subject is so complex and so very different from what an infrastructure engineer is used with.

One example of my ignorance in this field of measuring track quality is that for a very long time I firmly believed that the 35m and 70m wavelengths were in fact chords to which the track irregularities were measured. Very late I understood they are not at all that.

We are used with numbers that mean something real, tangible, measurable in some physical way.

300m, 55mm/s, 15t, 250MPa, 125mph, 300 km/h – all the numbers we usually work with have a clear physical meaning. They are a measure of real stuff. Yes, I said no reference to books and movies but I’m tempted here to write something about “mene, mene, tekel, upharsin”. Never mind!

We don’t use imaginary numbers, transcendental functions, waves and other concepts like that. All the numbers we usually work with are a representation of something that can be measured or weighted.

Because of this mindset it is so difficult to explain what the track geometry design standard deviations really are.

So let’s not talk about them for now. Let’s talk about things we can measure really simply, using a chord and a ruler.

Versine artefacts?

When I started to write my story about the TGSD Calculator I mentioned versines on purpose but my frustration and whale dreams dragged me away from what I wanted to say then. So here it is the versine story …

If you read these lines, you know very well what Hallade measurements are, what a versine is.

Please note – the discussion bellow is for a track geometry without any irregularities – an ideal track.

For an ideal curve of 500m radius, the versine measured to a 20m chord (AC) is 100mm (Figure 1). At any point on that ideal curve we will always get 100mm (See Figure 1). You will get the same figure from the versine formula.

Figure 1. Versine measurement

… and if we measure the versine of an ideal straight we will always get a null value (Figure 2).

Figure 2. Versine measured on straight track

However … if we measure the versine around the tangent point T, between the ideal straight and the ideal circular curve, we get a value that is neither the one on the curve nor the null value on the straight (Figure 3).

Figure 3. Actual versine measurement at the tangent point T

As this versine is measured on an ideal track, it is called “ideal versine”. At the points where the geometry changes, the ideal versines are different from the values we calculate using the versine formula – values called “theoretical versines”.

In our example, to get an ideal versine value equal to the theoretical value we would need to extend the circular curve to allow both ends of the curve to be placed on the same element – in this case the circular arc (Figure 4). But as long as we have the chord ends on alignment segments of different curvature variation, we will always get ideal versines (measured) different from the theoretical versines (calculated).

Figure 4. Simulated versine measurement on circular arc at the tangent point T

If we show these values in a versine diagram (Figure 5) we will get for the theoretical versines a sudden change from zero to the circular curve versine at the tangent point and for the ideal versines a smoothening at the tangent point T. The length of this smoothening is matching the chord length.

Figure 5. Versine diagram for a simple curve. Versine “artefact”

If from this diagram we extract the difference between ideal and theoretical versine we can produce a diagram of the versine “artefact” – the distortion from the theoretical value due to the way the ideal versine is measured (See the second diagram in Figure 5).

This distortion, this versine “artefact”, is clearly dependent, as range and values, of the chord length. Shorter the length, smaller the distortion.

Obviously, this difference between theoretical versines (calculated) and ideal versines (measured on ideal track) will be present at every point where a geometry element changes to another.

Figure 6 presents this case for a transitioned curve. Here, due to the nature of the transition, the versine artefacts are smaller.

Figure 6. Versine diagram for a transitioned curve. Versine “artefact”

Again artefacts?

In the same way we get these versine artefacts at any point where the geometry element changes to another, the track measurement car filtering system generates filtering artefacts, at the same points.

Although the measurement system is different, their nature is the same – they are errors, distortions due to the nature of the measurement and not real geometry distortions present on site.

The straight at the tangent point to a 500m radius it is not skewed by 50mm.

In a similar way, the (high) design SD for the same alignment (assumed installed as designed, without irregularities) is not due to a design quality issue.

We don’t need to change the design in figure 3 – if it complies with all the track geometry rules and standard parameters – just because the versine at the tangent point is not zero as we would expect if we use the versine formula.

In the same way, we should never change a compliantly designed alignment just because a design SD has a certain value. For this example, the AL35 design SD is 3.798mm – if the tangent point T is 50m away from the beginning of the measured eighth 0/0.

Figure 7. AL35 design SD of 3.798mm on a perfect alignment with no irregularity.

Notice in Figure 7 that this AL35 figure is the same no matter the value of the cant (0 or adverse 150mm) and it is also independent of speed.

In the same way, the 50mm versine measured as shown in figure 3 is independent of the cant of that alignment or of the speed for which it was designed.

I hope I explained this well enough – I find this comparison with the versine “artefacts” the best to define what the design SDs are. They are as real as these versine differences, versine artefacts. They are the measure of the artefact induced in the track measurement traces by the Butterworth Filter used by the track measurement cars measurement system. They are out of our railway engineering world …

What do you think?

Does this make better sense now?

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