Summary: Track twist is the algebraic difference in cross level between two points a stated distance apart, and every standard that regulates it publishes the limit as a gradient over that distance. The distance is not a unit. In the European standard the limit is a hyperbola in the measuring base, 20 divided by the base plus 3 millimetres per metre, which multiplies out to an absolute allowance of 20 millimetres plus 3 millimetres per metre times the base; that allowance is capped at 7 millimetres per metre up to 200 kilometres per hour and 5 above it, and the caps bind below 5 and 10 metres, so at the 3 metre base the standard itself uses the length dependent term never appears. In the American table the same 1.5 inch allowance is printed for a 10 foot base and a 62 foot base, so one number is worth 12.5 and 2.0 millimetres per metre depending on which row you read. At the Angerstein Junction derailment the same track measured 22 millimetres over 3 metres and 18 millimetres over 1.8 metres, which is 5 percent and 43 percent over the allowance at those two bases. A sleeper mounted pair measures at about 0.6 metres, below the 2 to 5 metre window the interoperability specification permits.

 

1. The One Number on a Track That Has No Fixed Value

Every other structure in this series is regulated by a quantity that has one value at one place. A tilt, a settlement, a plumb, a cross fall: the standard names the limit, the instrument reports the quantity, and the comparison is a subtraction. A railway track breaks that pattern in a way that is easy to miss, because the quantity is called by different names in different documents and the difference is disguised as vocabulary. Cant, cross level, twist, warp and torsion are five names for one height difference divided by four different lengths, and the length is the argument.

The cleanest evidence is a single table. The American track safety standards, in the section of Title 49 of the Code of Federal Regulations that governs track surface, print a few lines apart two limits that carry the same number. The difference in cross level between any two points less than 62 feet apart may not exceed 1.5 inches for the top class of track in the table. The difference in cross level between any two points less than 10 feet apart, called short warp, may not exceed 1.5 inches for the same class, on curves operated at a cant deficiency above five inches. Thirty eight point one millimetres, twice, in the same document, for the same failure. Read as a gradient the first is 2.0 millimetres per metre and the second is 12.5, and the ratio between them is exactly the ratio of the bases, 6.2.

A reader who has spent a career in millimetres will say the second row is obviously the tighter one and move on. That is the wrong conclusion, and the reason it is wrong is the subject of this article. The two rows do not describe two severities of the same defect. They describe two mechanisms, and the base is the only thing that tells them apart.

The European standard takes the opposite editorial route and ends up in the same place. Instead of printing a table of bases it prints one equation in which the base appears, so that the limit is explicitly a function of the length the measurement is taken over. That is more honest and considerably more confusing, because it means a single number quoted from that standard, without its base, says nothing at all.

The conversion that makes all of this comparable is the ordinary small angle one, and it is worth writing down once. One millimetre per metre is one milliradian, which is 0.0573 degrees. One percent is ten millimetres per metre, which is 0.573 degrees. One in 136, a figure that appears in a British accident report, is 7.35 millimetres per metre or 0.421 degrees. Every number in the rest of this article converts through that constant, and none of the standards publishes it, because to the people who wrote them the gradient and the angle are the same object seen from two trades.

Sort the five track geometry quantities by what has to be divided by what, and the shape of the problem appears. Gauge is a length with no denominator at all. Longitudinal level and alignment are lengths measured against a chord, and the chord is a second variable on top of the base. Cross level is a length over a transverse base that the standard fixes at 1500 millimetres, which is why it converts to an angle once and stays converted. Twist is a length over a longitudinal base that the standard does not fix, and that is why it is the only one of the five whose published limit moves when the survey moves.

Track quantity	What is measured	The denominator	Can a tilt channel report it
Gauge	Distance between the inner faces of the rail heads	None, it is a length	No
Longitudinal level	Height of the rail relative to a chord	Chord length, then a second base for the gradient	Partly, as a gradient along the track
Alignment	Lateral position relative to a chord	Chord length	No, it is a plan quantity
Cross level	Height difference across the track	Fixed at 1500 millimetres, the cant base	Yes, after the design cant is removed
Twist	Difference of two cross levels	Chosen, and usually not by the instrument	Yes, as the difference of two readings

The last row is the one that pays. Twist is the only quantity in the table whose denominator is a decision rather than a definition, and the decision has already been made by somebody else, for a reason that has nothing to do with measurement.

2. Cant, Cross Level and Twist Use Two Different Denominators

The three words are used loosely in practice and precisely in the documents, and the precision matters because a tilt channel sits between them. Cant is the designed height difference between the two rails on a curve, put there so that the component of gravity helps rather than fights the turn. Cross level is the unintended part, the amount by which the track is not where the design says it should be. Twist is cross level compared with cross level, a stated distance further along.

The arithmetic that a tilt channel actually performs is published, and it is not the one most installations assume. The measured cross level equals the cant base multiplied by the sine of the angle the channel reports, minus the design superelevation. In words, the instrument reports the sum of the design and the error, and the standard regulates only the error. On a high speed curve carrying 150 millimetres of designed cant, a channel bolted across the track reads 5.73 degrees, and the top class allowance of one inch is 0.97 degrees. The quantity under regulation is seventeen percent of the number on the wire.

Designed cant on the curve	Angle the channel reads	The regulated residual at the top class	Residual as a share of the reading
50 mm	1.910 deg	0.970 deg	51 percent
100 mm	3.820 deg	0.970 deg	25 percent
150 mm	5.730 deg	0.970 deg	17 percent
180 mm	6.875 deg	0.970 deg	14 percent

The last row is the top of the range, and it is not decorative. Cant is capped at about 150 millimetres on mixed traffic lines and rises to 180 where freight is excluded, so the reading on the fastest curves is nearly seven times the number the standard cares about. Subtracting a designed value of that size from a measured value is a different operation from comparing two similar numbers, and it moves the error budget. One millimetre of cant is 0.667 millimetres per metre across the 1500 millimetre base, which is 0.038 degrees. A design cant known only to plus or minus 10 millimetres therefore injects 0.38 degrees, and the whole top class allowance is 0.97 degrees, so the reference has to be better than the instrument by a comfortable margin before the comparison means anything.

There is a second denominator hiding in the same paragraph. The height difference is divided by 1500 millimetres to become an angle, and 1500 is not the gauge. The gauge is 1435 millimetres, measured between the inner faces of the rail heads; the cant base is the centre to centre distance, and the two references differ because the measurement is taken at the running surfaces. Every conversion in this article uses 1500. A conversion done with the gauge instead gives an angle four and a half percent too large, which on a curve carrying 150 millimetres of cant is 0.26 degrees, or fifty times the accuracy figure of the instrument.

Twist then repeats the operation along the track instead of across it. Take the cross level at one point, take it again a distance away, and divide the difference by the distance. The quotient is the quantity every derailment investigation in the world ends up discussing, and it has an unusual property: it is the only track geometry parameter that is already an angle in the unit the standard prints, because millimetres per metre and milliradians are the same number.

So the same twenty millimetres is three different gradients depending on which length it is divided by, and the three values are not close to each other. Across the track it is 13.3 millimetres per metre, over ten feet it is 6.6, and over sixty two feet it is 1.1. A single height difference of twenty millimetres is worth twelve times more as a cross level error than as a long base warp, and both statements are true of the same piece of steel.

The same 20 mm divided by	Base	Gradient	In degrees	Used by
The transverse cant base	1.500 m	13.33 mm per m	0.764 deg	Cross level
A longitudinal base of ten feet	3.048 m	6.56 mm per m	0.376 deg	Short warp
A longitudinal base of sixty two feet	18.898 m	1.06 mm per m	0.061 deg	Long warp

3. The Standard Writes the Limit as a Function of Your Ruler

The European track geometry quality standard, EN 13848-5, devotes one clause to twist, and that clause does not give a number. It gives a relation in which the measurement base appears as a variable, with two curves selected by curvature and a cap selected by design speed. Written out, the limit in millimetres per metre is twenty divided by the base in metres, plus three, for the curve that applies at low cant deficiency, capped at seven millimetres per metre on lines designed for 200 kilometres per hour or less and at five above that. The second curve replaces the three with one and a half and carries a cap of six.

The relation is not an invention of the standards committee. It is the summary of a twenty year study into twist related derailments across Europe, published as the UIC report ORE B55 RP8, and the shape it produces is the interesting part. Multiply the limit by the base and a much simpler statement falls out: the permitted difference in cross level is twenty millimetres, plus three millimetres per metre times the base. A constant and a slope. An absolute step that the vehicle cannot absorb at any length, plus a gradient that it can absorb over a long enough distance.

That decomposition is the whole engineering content of the clause, and it is invisible in the form the standard prints. In the printed form a user sees a rate, and a rate suggests a single mechanism. Multiplying out shows two, and they behave in opposite ways: as the base grows the allowance grows, but the rate falls, so a long base is allowed more absolute movement and less gradient at the same time. The table below evaluates the clause at the bases that matter, and the limits in its second and third columns are in millimetres per metre while the last two columns are millimetres.

Measuring base	Limit at 200 km per h or less	Limit above 200 km per h	Permitted difference, lower speed	Permitted difference, higher speed
0.6 m, one sleeper pair	7.00, capped	5.00, capped	4.2 mm	3.0 mm
1.8 m, one wagon bogie	7.00, capped	5.00, capped	12.6 mm	9.0 mm
3 m, the standard base	7.00, capped	5.00, capped	21.0 mm	15.0 mm
5 m	7.00	5.00, capped	35.0 mm	25.0 mm
10 m	5.00	5.00	50.0 mm	50.0 mm
18.898 m, sixty two feet	4.06	4.06	76.7 mm	76.7 mm
20 m	4.00	4.00	80.0 mm	80.0 mm

Read down the fourth column and the number rises from four millimetres to eighty as the base rises from a sleeper spacing to twenty metres, a factor of nineteen. Read down the second column and the number falls from seven to four, a factor of one and three quarters. One clause, two monotonic directions, and no way to compare a reading taken at one base with a limit quoted at another without doing the multiplication.

4. The Cap Deletes the Length Term Where Everyone Measures

The cap is usually read as a safety floor and skipped. It is better read as the clause switching itself off. Take the low cant deficiency curve and ask where the hyperbola meets the cap of seven millimetres per metre: at a base of five metres. Below five metres the cap is the answer and the twenty millimetre term contributes nothing, because twenty divided by a number smaller than five already exceeds seven before the three is added. For a line designed above 200 kilometres per hour the cap is five, and the crossover moves to ten metres.

Both of those crossovers sit above the base the standards themselves instruct their users to measure over. Three metres is the conventional base in the British and European track standards, and the interoperability specification requires at least one base somewhere between two and five metres without saying which. At three metres the uncapped value is 9.67 millimetres per metre, which is above both caps, so the operating limit is a flat seven or a flat five and the length dependent term never enters the calculation. The clause that made the base a variable is, at the base in daily use, a constant.

That has a consequence worth stating plainly, because it inverts the usual reading of the speed classes. Since the cap only acts below a base of five metres at 200 kilometres per hour and below ten metres above it, the entire difference between a conventional line and a high speed line is a difference at short bases. At ten metres the two are identical, 5.00 millimetres per metre, and at sixty two feet they are still identical at 4.06. A high speed line is held twenty nine percent tighter than a conventional one when the defect is short and identically when it is long, which is what a mechanism governed by the vehicle geometry produces and not what a mechanism governed by track quality would produce.

The practical form of this for a monitoring scheme is uncomfortable. The number that gets quoted in a specification, seven millimetres per metre, is the cap, and it carries no information about how long the defect is. A track that is at seven millimetres per metre over half a metre is a different structure from one at seven over fifteen metres, and the same number describes both. Any alarm built on the gradient alone will therefore be silent about the difference that matters.

5. The Vehicle Has Two Bases and the Track Has One

The reason a short base and a long base are not the same defect is that the vehicle is not rigid, and the suspension has two scales. The accident record states the mechanism better than any textbook. In April 2014 a freight train derailed at Angerstein Junction in south east London, and the investigating report measured the track at the point of derailment over two bases. Over three metres, the base the maintenance standard uses, the dynamic twist was twenty two millimetres, a gradient of 0.73 percent, one in 136. Over 1.8 metres, the wheelbase of the wagon bogie, the twist was eighteen millimetres, a gradient of 1.00 percent, one in 100.

Four millimetres less movement, thirty six percent more gradient. The absolute difference fell by eighteen percent while the rate rose by thirty six, and the vehicle responds to the rate. The report’s own sentence is the whole argument: if twist is measured over a length of three metres it is possible for the measurement to bridge greater changes in cant that occur within that distance. The three metre base averaged a step that the 1.8 metre bogie felt in full.

Set against the clause from the previous section, the same location gives two margins. The allowance at three metres is 21.0 millimetres, and the measured 22.0 millimetres is 5 percent over it. The allowance at 1.8 metres is 12.6 millimetres, and the measured 18.0 millimetres is 43 percent over it. One track, one train, one afternoon. The base decides whether the site is marginal or grossly defective.

Measurement	Base	Difference measured, and as a gradient	Margin against the allowance at that base
The maintenance standard	3.0 m	22 mm, which is 7.33 mm per m	5 percent over the 21.0 mm allowance
The wagon bogie	1.8 m	18 mm, which is 10.00 mm per m	43 percent over the 12.6 mm allowance

Two vehicle bases are involved, not one, and the report sets them out. A cant difference over the bogie wheelbase twists the bogie frame and its primary suspension, and a cant difference over the bogie centres twists the whole vehicle through both suspensions and the body. Short base and long base twist acting in the same sense add at the wheel, one wheel load rising and the diagonally opposite one falling, and the derailment quotient is the lateral force divided by the vertical load, so an unloading wheel is the mechanism and a flange climb is the outcome. The British vehicle acceptance standard therefore tests both at once, a long base twist of one in 300 combined with a short base twist of one in 150, which is 3.33 and 6.67 millimetres per metre and a ratio of two.

The decisive confirmation that the law belongs to the vehicle and not to the track is that the vehicle standard contains the identical equation. The European vehicle testing standard, EN 14363, gives the limiting track twist for a vehicle as the lesser of seven per mille and twenty divided by the pivot distance plus three, and for the bogie alone as seven per mille up to four metres, twenty divided by the axle base plus two between four and twenty metres, three per mille between twenty and thirty, and ninety divided by the axle base beyond that. That is the track clause rewritten with the vehicle’s dimensions in place of the survey’s. The same twenty divided by a length, the same three, the same seven. Whatever the constant twenty millimetres represents, it is not a track construction tolerance.

That is the single transferable finding of this family. When a limit appears in two documents with the same shape but different denominators, the version with the object’s own dimension in it is the original and the version with the survey’s dimension is the approximation. The track standard is not regulating a length of track. It is regulating the twist that a vehicle of unknown dimensions would experience, expressed over a length chosen as a compromise between the vehicles in the fleet, and every measurement taken at another base is an extrapolation of that compromise.

6. Two Documents, One Failure, and a Crossover at Six Metres

The American and European documents disagree, and the disagreement is not a difference of degree. The American table holds the permitted difference constant and lets the base vary, which is a statement that the absolute step is what unloads the wheel at any length. The European clause holds neither constant, letting the absolute grow with the base and the gradient fall, which is a statement that a gradual warp is less damaging per millimetre than a short one. Those are different physics, and a track cannot satisfy one interpretation and be described by the other.

The disagreement has a single crossing point, and it is easy to compute because one side of the comparison is a constant. The top American class permits 38.10 millimetres between two points. The European curve at the lower speed permits twenty plus three times the base. Setting them equal gives a base of 6.03 metres. Below that the American allowance is the looser of the two and above it the European one is, and the reversal happens inside the range of bases that real surveys use.

Base	European allowance at 200 km per h or less	American allowance at the top class, and which is stricter
3.048 m, ten feet	21.34 mm	38.10 mm, so the American table is 1.79 times looser
5 m	35.00 mm	38.10 mm, so the American table is 1.09 times looser
6.033 m	38.10 mm	38.10 mm, the crossing point where the two agree
10 m	50.00 mm	38.10 mm, so the European clause is 1.31 times looser
18.898 m, sixty two feet	76.69 mm	38.10 mm, so the European clause is 2.01 times looser

For a high speed line the crossing moves, because the European cap of five millimetres per metre acts as a straight line of five times the base up to ten metres. Five times the base equals 38.10 millimetres at 7.62 metres, so above 200 kilometres per hour the American table is looser below seven and a half metres and tighter above it.

Two things follow that a specification has to absorb. The first is that a compliance statement is meaningless without the document and the base, because the same track passes one and fails the other depending on where the comparison is made, and neither document is wrong. The second is that the crossover itself is the useful engineering quantity: it says that a defect shorter than about six metres is bounded by the gradient and one longer than that by the absolute step, which is a physical statement about suspensions and not a political one about regulators. The investigating report reached the same conclusion from the other direction, noting that no criteria are provided for choosing a base within the permitted two to five metre window, and that a maintenance regime using a length comparable to the bogie spacing might have avoided the derailment.

7. The Channel, and a Third Base Fixed by Sleeper Spacing

A tilt channel reports an angle, and the first two quantities in this article are angles already, so the instrument is unusually well matched to the subject. Cross level becomes an angle by division by a constant that the standard supplies. Twist becomes an angle by division by a base, and the base is where the instrument’s mounting geometry enters the argument as a design decision that was made before anybody read the standard.

A pair of sensors on two adjacent sleepers measures the cant difference over the sleeper spacing, which is typically 0.6 to 0.65 metres, and the pair produces a gradient over a base an order of magnitude shorter than the one the standard uses. Application of the European clause at that base gives the cap and nothing else, seven millimetres per metre at the lower speed, which is 4.2 millimetres of permitted difference across one sleeper spacing and 0.401 degrees of permitted angle. The same cap over three metres permits 21 millimetres, and over sixty two feet it permits 76.7.

Base a pair can have	What fixes it	Permitted difference, 200 km per h or less	Permitted angle	Inside the interoperability window
0.60 m	One sleeper spacing	4.2 mm	0.401 deg	No, below two metres
1.20 m	Two sleeper spacings	8.4 mm	0.401 deg	No, below two metres
2.00 m	Shortest permitted base	14.0 mm	0.401 deg	Yes, at the lower edge
3.00 m	The conventional base	21.0 mm	0.401 deg	Yes
5.00 m	Longest base inside the window	35.0 mm	0.401 deg	Yes, at the upper edge

Two properties of that table matter more than the numbers. The permitted angle is constant, 0.401 degrees, for every base at or below five metres, so an instrument quoted in degrees will appear to have the same allowance whatever its mounting. The permitted difference is not constant at all, rising from 4.2 millimetres to 35 across the same range. A monitoring scheme therefore has to decide which of the two it is alarming on, and the answer is not the same at both ends of the table: at a 0.6 metre base the trigger is a 4.2 millimetre step between two adjacent sleepers, and at five metres it is 35 millimetres between two points that may be eight sleepers apart.

The difference of two readings is also not the same measurement as one reading, and this is where the arithmetic turns against the obvious design. Two units each carry a zero deviation, published for the instrument quoted in this article as plus or minus 0.05 degrees, and the two zeros are independent, so the difference carries up to 0.1 degrees and typically 0.071 on a root sum square basis. Against the 0.401 degree allowance that is 25 percent worst case and 18 percent typical, where a single unit would have consumed 12.5 percent. A single unit moved between the two stations instead cancels its own zero exactly, because it is the same zero, and pays for it with everything that changed in the interval between the two readings. There is no arrangement that cancels both, and the choice between them is a decision about which of the two errors is smaller on the site in question.

The published deployment in this family is a useful illustration of both problems at once. In 2020 the China Academy of Railway Sciences instrumented a four kilometre tunnel in Qinghai Province above 3,000 metres, two tracks in a single chamber with no cellular coverage, using dual axis wireless tiltmeters mounted on the sleepers and reporting over a local LoRaWAN gateway to a server inside the railway intranet. The published specification of those units is a plus or minus 30 degree range with plus or minus 0.005 degree accuracy, and the alarm delay is adjustable from 0.3 to 25.5 seconds, a window that exists because a passing train produces a transient rotation of the sleeper that a short delay would report as a structural event. That is the difference between one unit and two in another form: the field solved the false alarm problem in time, by waiting for the reading to persist, rather than in space.

8. The Datasheet Is Comfortable Here

The instrument quoted throughout this series is the ZCT2xxM-LBS-Ax-H5-460x, a two axis RS485 unit with a plus or minus 15 degree range, accuracy of 0.005 to 0.01 degrees, resolution of 0.001 degrees, zero deviation of plus or minus 0.05 degrees, and a zero temperature drift of plus or minus 0.002 degrees per degree Celsius typical with a published maximum of 0.13 degrees. Converted into the unit the twist clause uses, and set against the two caps, the table is short.

Datasheet term and value	In millimetres per metre	Against the 7 mm per m cap	Against the 5 mm per m cap	Against the American top class cross level
Resolution, 0.001 deg	0.017	0.2 percent	0.3 percent	0.1 percent
Accuracy, 0.005 deg	0.087	1.2 percent	1.7 percent	0.5 percent
Accuracy, worst case, 0.01 deg	0.175	2.5 percent	3.5 percent	1.0 percent
Zero deviation, 0.05 deg	0.873	12.5 percent	17.5 percent	5.2 percent
Drift, 0.002 deg per degree Celsius over 40 kelvin	1.396	19.9 percent	27.9 percent	8.2 percent
Drift, maximum, 0.13 deg	2.269	32.4 percent	45.4 percent	13.4 percent

Every term in that table sits inside the criterion, and the worst of them leaves more than half the budget. That completes a sequence of four positions worth naming, because the same datasheet has now been read against four criteria of very different size. On a crane runway the same instrument had a zero deviation at one and three quarter times the whole tolerance and a maximum zero drift at four and a half times it, which made the zero the deciding term; on a pile the criterion was twenty times looser and every term fell to a quarter or less; on a belt conveyor the ranking landed between the two. Here the criterion is a milliradian scale gradient, so the accuracy is under two percent of it and the worst datasheet line is under half.

The consequence is that precision is not the constraint on a track, and a procurement that spends its budget on accuracy is buying something the criterion cannot use. The constraint is the two things the datasheet does not contain: the base over which the difference is taken, and the reference the design cant is subtracted against. The second is the sharper of the two, because one millimetre of cant is 0.667 millimetres per metre and the whole high speed allowance is five, so a design value known only to plus or minus five millimetres has already spent two thirds of the budget before the sensor is switched on. A track monitoring scheme whose cant reference comes from a drawing rather than from an as-built survey is measuring the drawing.

There is one more asymmetry that belongs here rather than in the datasheet. Cross axis error is published as plus or minus 1 percent, which sounds negligible until it is applied to the quantity being subtracted. On a curve with 150 millimetres of cant, one percent of the reading is 1.5 millimetres of apparent cant error, or 1.0 millimetres per metre, which is 20 percent of the high speed allowance and comparable with the maximum zero drift. The term that matters on a curve is not the one the procurement table lists first, it is the one that multiplies the largest number on the wire.

9. What to Specify

Five requirements follow from the arithmetic, and unlike most specification advice these are not preferences. Each of them changes a number by more than the instrument’s own error.

Name the document and the base in the same sentence. A twist limit of seven millimetres per metre is a different structure depending on whether it is read over 0.6 metres or over 18.9, and the two documents that publish limits disagree by a factor of two at the longer base. An acceptance that quotes a gradient without a base cannot be audited, and an alarm that fires on a gradient without a base cannot be explained to the person who has to walk out and look at the track.

Convert from the mounting base before comparing, and say what the conversion assumes. A pair on adjacent sleepers measures 0.6 metres. The conversion to the standard’s three metre base is exact only if the twist is linear across the longer length, and it is not: the whole reason the shorter base found the Angerstein defect is that the step was local. The honest form is to publish both the local gradient and the absolute difference, and to treat the absolute difference as the primary record, because it is the one that does not change when the mounting changes.

Treat the permitted angle and the permitted difference as two separate limits. Below five metres the angle allowance is constant at 0.401 degrees while the difference allowance scales with the base, so a scheme that alarms only on the angle will be equally sensitive at every spacing and a scheme that alarms on a fixed difference will fire at 8.4 millimetres on a 1.2 metre spacing and stay silent until 35 millimetres on a five metre one. This is a choice about which defect the site actually has, and it should be made from the settlement pattern rather than from the sensor.

Estimate the reference before buying the instrument. The design cant is subtracted, not measured, and one millimetre of it is 0.667 millimetres per metre against an allowance of five. An as-built cant survey is worth more to this measurement than an accuracy improvement of a factor of five, and the same is true of the alignment that defines where the cant is supposed to be.

Alarm on the rate between surveys, and use the delay for the train. Twist is a quantity that maintenance changes deliberately, by tamping and lining, so a level threshold is a statement about the last tamp rather than about the structure. The published field practice of a delay window of a few seconds to half a minute exists to separate a passing train from a settled sleeper, and it is the cheapest available substitute for a reference channel.

One boundary has to be stated because it is easy to overrun. A tilt channel on a sleeper measures the attitude of the sleeper, and the standards in this article regulate the geometry of the rail. The two are related by the fastening and the ballast, and the relationship is not a constant: a sleeper can rotate in the ballast without the rail moving relative to its neighbour, and a rail can be worn or the fastening can lose toe load without the sleeper rotating at all. The channel is a proxy, and a good one, for the settlement component of the problem, which is the component that grows. It is not a substitute for a track geometry recording vehicle, and it is not a substitute for an inspection of the fastening.

Frequently Asked Questions

1. Why is the permitted twist different in the European and American standards for the same track? Because the two documents made opposite assumptions about what stays constant. The American table holds the absolute difference fixed, 38.10 millimetres at the top class over either ten feet or sixty two feet, which treats the step as the mechanism. The European clause holds neither fixed, permitting 20 millimetres plus 3 millimetres per metre of base, which treats a long gradual warp as less damaging per millimetre. The two cross at a base of about six metres, and which one is stricter above or below that crossing follows from arithmetic rather than from either document being wrong.
2. Can a tilt sensor measure track twist directly? It measures the angle at one point, and twist is a difference of two such angles divided by the distance between them, so the instrument supplies the numerator and the installation supplies the denominator. That makes the mounting geometry part of the measurement. A pair on adjacent sleepers produces a gradient over about 0.6 metres, which is below the two to five metre window the interoperability specification permits and a fifth of the conventional three metre base, so the reading is a local rate that has to be converted before it can be compared with a published limit.
3. Why did the same defect read 5 percent over at one base and 43 percent over at another? Because the allowance shrinks faster than the measurement does. At Angerstein Junction the measured dynamic twist was 22 millimetres over three metres and 18 millimetres over 1.8 metres. The European clause allows 21.0 millimetres at three metres and 12.6 at 1.8, because below five metres the limit is the flat cap of seven millimetres per metre and the allowance is therefore seven times the base. Four millimetres less movement against eight and a half millimetres less allowance, which is the whole of the difference.
4. What does the flat cap mean physically, given that it makes the length term vanish? It means that below a certain length the vehicle cannot bridge the defect at all, so only the gradient matters and the absolute difference is simply the gradient multiplied by the base. Above that length the vehicle spans the defect and the absolute step starts to govern, which is why the clause lets the allowance grow with the base while the rate falls. The crossover at five metres on a conventional line and ten on a high speed one is the length at which the mechanism changes, and the practical reading is that short defects and long defects are two different problems that happen to share a name.

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