Summary: On an overhead crane runway the load argument for monitoring is weaker than it looks, and the instrument argument is different from the one usually assumed. EN 1991-3 sizes the lateral force from skewing out of three additive parts, clearance, wear and a flat tolerance of 0.001 rad, and on a five metre wheelbase with a hundred millimetre rail head the tolerance part is one fifth of the total. Because the friction response saturates, removing that whole term changes the guide force by eleven percent. Of the six track tolerances in ISO 12488-1 only two are slopes, and those two are the ones a tilt channel reads natively. The binding number is not accuracy but zero stability: the published zero deviation of a high accuracy tiltmeter is larger than the whole allowance the standard gives a twenty metre runway to move in service. So a permanent instrument on a runway is a comparator in time, not a reference, and the survey that measures the other four tolerances is not something it can replace.

 

1. The Allowance That Is Not About the Rail

A crane that travels down a runway never runs perfectly square to it. One end carriage runs slightly ahead of the other, the whole bridge rotates a little about a vertical axis, and the wheel flanges bear against the side of the rail. That rotation is called skewing, and the standard that sizes the resulting lateral force is Eurocode 1 Part 3, EN 1991-3, clause 2.7.4.

The guide force on the leading wheel flange is given as S = f x lambda x the sum of the wheel loads, where lambda is a factor taken from tables in the standard according to the wheel arrangement and the position of the centre of mass. The part that carries the geometry is f, the friction or non-positive factor, and it is a function of a single angle:

f = 0.3 (1 – exp(-250 alpha)), and f is not to be taken above 0.3

The skewing angle itself is not measured. It is assembled from three contributions, and this is the part of the calculation that matters for anyone thinking about monitoring:

alpha = alpha_F + alpha_V + alpha_0, and alpha is not to exceed 0.015 rad

alpha_F comes from the clearance between the rail and the guiding means. It is 0.75 x divided by a_ext, where x is the lateral clearance and a_ext is the spacing of the outer flanged wheels on the guiding rail, in other words the wheelbase. The standard sets a floor: 0.75 x is at least 10 mm where wheel flanges do the guiding.

alpha_V comes from wear. It is y divided by the same a_ext, where y is the wear of the rail and the guiding means, and the standard again sets a floor: y is at least 0.10 b, b being the width of the rail head. For a hundred millimetre rail head that is 10 mm of wear.

alpha_0 is a flat 0.001 rad, and the standard describes it as the tolerance on wheel and rail directions.

Put those three on a real machine. Take a wheelbase of five metres and an A100 crane rail with a hundred millimetre head, and take the floors the standard specifies. The clearance term is 10 divided by 5000, which is 0.002 rad. The wear term is the same 10 divided by 5000, also 0.002 rad. The tolerance term is 0.001 rad. The total is 0.005 rad, one third of the cap.

Wheelbase a_ext	alpha_F from clearance	alpha_V from wear	alpha_0 tolerance	Total alpha
3000 mm	0.00333 rad	0.00333 rad	0.001 rad	0.00767 rad
5000 mm	0.00200 rad	0.00200 rad	0.001 rad	0.00500 rad
8000 mm	0.00125 rad	0.00125 rad	0.001 rad	0.00350 rad

Two things follow before any instrument is discussed. The first is that the alignment of the runway is the smallest of the three contributions, at one fifth of the total on the five metre wheelbase and at thirteen percent of it on a three metre one. The second is that the wheelbase sits in the denominator of two of the three terms, so a machine with a short wheelbase carries the same clearances and the same wear as a larger angle, and a machine with a long wheelbase carries them as a smaller one. The same millimetres of clearance spend very differently on two cranes of different size.

The third thing, which matters most for the monitoring question, is that alpha_0 bundles the wheel and the rail together. The standard gives one number for the tolerance on wheel and rail directions and does not separate them. So the rail’s share of that 0.001 rad is something less than the whole of it, and any claim about what perfect rail alignment would buy has to be stated as an upper bound.

2. A Response That Saturates

The friction factor is not proportional to the angle. It rises steeply at first and then flattens, because the exponential term approaches one and f approaches its cap of 0.3. That shape is worth writing out, because it decides whether an alignment error is worth chasing.

Skewing angle alpha	Friction factor f	Multiple of f at 0.001 rad	Multiple of the angle
0.001 rad	0.0664	1.00	1.0
0.002 rad	0.1180	1.78	2.0
0.005 rad	0.2141	3.23	5.0
0.010 rad	0.2754	4.15	10.0
0.015 rad	0.2929	4.41	15.0

Fifteen times the angle gives four and a half times the force. The response is strongly sub-linear, and it is the opposite of what happens on a flat roof where water collects, where the same kind of geometric feedback produces a response with a denominator that approaches zero and no equilibrium at all. On a runway the force saturates.

Now apply that to the alignment term alone. On the five metre wheelbase the total is 0.005 rad and f is 0.2141. If the rail direction tolerance were somehow reduced to nothing, the total would fall to 0.004 rad and f would fall to 0.1896. That is a reduction of eleven percent in the guide force. If instead the alignment error doubled, the total would rise to 0.006 rad and f would rise to 0.2331, an increase of nine percent.

So the load argument for monitoring a runway is weak, and it is worth saying so plainly. Doubling the alignment error of a crane runway moves the design lateral force on the wheel flanges by under ten percent, and the standard has already budgeted for the error by including it as a term. Anyone specifying monitoring on the basis of the skewing force is specifying against a quantity that has been designed for and that barely responds.

What does respond is the other term. alpha_V sits in the same sum, and unlike alpha_0 it grows on its own, because y is wear and wear accumulates with every pass of the machine. The runway does not have to move at all for the skewing angle to increase. Take the same five metre wheelbase and let the wear allowance double from 10 mm to 20 mm, which is a fifth of the width of a hundred millimetre rail head. The wear term goes from 0.002 rad to 0.004 rad, the total goes from 0.005 rad to 0.007 rad, and f goes from 0.2141 to 0.2479. That is a rise of sixteen percent in the guide force, from wear alone.

Set that beside the other result. Doubling the alignment error of the runway is worth nine percent. Ten more millimetres of wear on the rail and the wheels is worth sixteen. The thing that can be surveyed and corrected is the smaller of the two, and the thing that cannot be corrected without taking the bay out of service is the larger, and it gets larger by itself.

The standard builds this in deliberately by requiring a minimum wear allowance in the calculation, and by measuring that allowance as a fraction of the rail head width. A narrow rail therefore wears its way through the same angular budget faster than a wide one, which is one reason rail section selection and alignment belong in the same conversation.

That is the honest framing for the whole application. The criterion on a crane runway is not a load and it is not a deflection. It is a consumable: wheel flanges and rail head, bought in millimetres and spent by misalignment. The load calculation is how the structure is sized. The wear is how the money goes.

3. Six Tolerances, Only Two of Which Are Slopes

The document that tolerances the track is ISO 12488-1, adopted identically in China as GB/T 10183.1. It is titled for crane wheels and travel ways, it carries three tolerance classes selected by the total distance the crane will travel in its service life, and Grade 2 is the default for ordinary bridge and gantry cranes.

Six quantities carry the track geometry for Grade 2. All six are published in millimetres, and that is the point: an instrument that reports an angle has to have each of them converted before anyone can say whether it can see them.

Symbol	Grade 2 value	What it is, and what it comes to as a slope	A tilt channel reads it
A	plus or minus [5 + 0.25 (S – 16)] mm, cap 15 mm	Span between the two rail centrelines. A distance, not a slope	No
B	plus or minus 10 mm	Horizontal straightness over the whole rail. A plan deviation from a line	No
b	1 mm	Horizontal straightness over any 2000 mm sample, which is 0.5 mrad or 0.029 deg	No, it is a plan direction
C	plus or minus 10 mm	Vertical straightness over the whole rail. A deviation from a line: 0.33 mrad at 30 m, 0.1 mrad at 100 m	Only by integrating from a datum
c	2 mm	Vertical straightness over any 2000 mm sample, which is 1.0 mrad or 0.057 deg	Yes
E	plus or minus S mm, cap 10 mm	Cross-level between opposite points across the span. 1.0 mrad up to a 10 m span, 0.5 mrad at 20 m	Yes

Two of the six reduce to slopes once the length they are measured over is divided out. c is a change in elevation over a fixed two metres, so it is a slope as published. E is a height difference across the span, so it is a slope across the span, and because the published value is proportional to the span up to its cap, that slope is a constant one milliradian until the cap takes over. Those two are exactly the ones a tilt instrument reports in its own units, with no conversion, no datum and no second measurement. The other four are not slopes in any axis a tilt instrument can see. They are a distance between two rails, a deviation of a rail from a line in plan, a deviation of a rail from a line in elevation, and a two metre sample of the plan direction, which is a slope in its own right but a slope in plan rather than in elevation.

There is a second pattern in the same table that is easy to miss. The horizontal two metre sample b is 1 mm and the vertical two metre sample c is 2 mm. As slopes that is 0.5 mrad against 1.0 mrad, so the standard holds the plan alignment to half the slope it allows in elevation. The tighter axis is the horizontal one, and the horizontal one is the axis that feeds the skewing angle. A tilt channel reads the looser axis of the two.

The general rule is worth carrying away from this section, because it applies well beyond cranes. An instrument resolves the tolerances that are already written in its own units. Before specifying anything, sort the published tolerances by whether they are slopes or positions: the slope subset is the instrument’s scope, and the position subset belongs to whoever is holding the survey equipment.

4. The Governing Slope Depends on How Long the Runway Is

The two vertical straightness tolerances in ISO 12488-1 are the same kind of number measured over two very different lengths. C is the deviation of the rail from its theoretical elevation line over the whole runway. c is the change in elevation over any two metre sample. The first is a position, the second is a slope, but both can be read as slopes, and which of them governs depends entirely on how long the runway is.

As slopes they are C divided by the runway length L, against c divided by 2000 mm. They are equal at a crossover length equal to the ratio of the two tolerances multiplied by the sample length:

L* = (C / c) x 2000 mm, which for Grade 2 is 10 m for the vertical pair and 20 m for the horizontal pair

Below the crossover the sample is the tighter constraint. Above it the full-length allowance is. Every real runway is above it, usually far above it.

Runway length	C as a slope	In degrees	Against 0.005 deg resolution	Against the 1.0 mrad sample
10 m	1.000 mrad	0.0573 deg	11.5 times	Same
20 m	0.500 mrad	0.0286 deg	5.7 times	2 times tighter
30 m	0.333 mrad	0.0191 deg	3.8 times	3 times tighter
50 m	0.200 mrad	0.0115 deg	2.3 times	5 times tighter
100 m	0.100 mrad	0.0057 deg	1.1 times	10 times tighter
200 m	0.050 mrad	0.0029 deg	0.6 times	20 times tighter

On a hundred metre runway the full-length vertical allowance works out at one tenth of a milliradian, which is about one resolution step of a 0.005 deg instrument, and it is a deviation from a line rather than a slope. Reaching it from slope readings means integrating those readings from a datum along the whole length, which is precisely the operation that turns a small zero error into a large position error.

So the runway’s headline straightness number is the one a tilt channel is worst at, and the local two metre sample, which it reads well, is the looser of the two by a factor that grows with the length of the bay. That inversion is not obvious from the table of millimetres, and it is the reason a tolerance comparison has to be done in the instrument’s units before any conclusion is drawn.

5. The Axis the Load Feels Is the Axis the Instrument Cannot Read

Put sections 1 and 3 together and the result is uncomfortable but clear. The quantity that drives the lateral force is the skewing angle, and its tolerance contribution alpha_0 is described in EN 1991-3 as a tolerance on wheel and rail directions, which is to say directions in plan. The tolerance that governs the plan alignment of the rail is b. At 0.5 mrad it is half the slope that the same table allows for the vertical sample over the same two metres, and half the slope it allows for cross-level on any span up to ten metres.

A tilt sensor mounted on a rail or on a runway girder measures inclination to the horizontal. It reports the cross-level between the two rails, which is tolerance E, and the gradient along the rail, which is what tolerance c samples. Both are vertical plane quantities. Neither of them is the direction of the rail in plan, and no arrangement of tilt sensors recovers a plan direction, because a rotation about a vertical axis leaves every tilt channel unchanged.

This is the structural reason a crane runway alignment check is a survey. The tolerances are written as positions and directions in plan, and the instrument that measures positions and directions in plan is a total station or a laser tracker, used on a runway that is unloaded. A permanently mounted tilt array measures a different set of quantities on the same structure, and it is not a cheaper version of the survey. It is a different measurement.

The consequence for a specification is that the two have to be written separately and neither can be described as covering the other. The survey decides whether the runway is in tolerance. The instrument, if it is there at all, answers a question the survey cannot answer, which is what happened between two surveys.

6. What the Crane Does to the Reading While It Is Working

ISO 12488-1 is explicit about its scope: it covers construction and operational tolerances for crane wheels and tracks, and it excludes elastic deformation caused by loading. That sentence settles the question of when a reading may be taken. The tolerances are defined on an unloaded track, so a reading taken while the crane is standing on the bay is not a smaller or larger version of the same measurement. It is not comparable to the tolerance at all.

The size of the effect is not marginal. A tilt channel on a runway girder sees the girder rotate as the crane passes over it. For a simply supported member under a distributed load the rotation at the support is 3.2 times the midspan deflection divided by the span, the same shape factor that turns up in roof deflection checks. At a deflection of L over 600 that works out at about 5.3 mrad.

Deflection limit	Support rotation	In degrees, against 0.005 deg resolution	Times the 0.5 mrad cross-level tolerance at 20 m
L / 600	5.33 mrad	0.306 deg, 61 times the resolution	10.7
L / 800	4.00 mrad	0.229 deg, 46 times the resolution	8.0
L / 1000	3.20 mrad	0.183 deg, 37 times the resolution	6.4

The crane passing over a bay produces a slope reading roughly ten times the whole cross-level tolerance the runway is allowed, and about sixty times the resolution of the instrument. Any trend built from ungated readings is a record of where the crane was, not of where the runway went.

The remedy is straightforward, and it is worth noting how it differs from the comparable problem on a roof. There the confounder is temperature, it is not logged by anything, and the only remedy is to take the readings in a window where the thermal state is repeatable. Here the confounder is the crane, and the crane knows where it is. Its position, or the state of its travel drives, is available from the machine’s own controller. So the confounder can be subtracted rather than merely avoided, provided the reading and the crane state are recorded together.

Take the reference epochs with the crane away from the instrument, and log the crane position with every reading thereafter. That is an instrumentation requirement, not an analysis preference, and it belongs in the specification.

7. The Number That Governs Is the Zero, Not the Accuracy

The datasheet for the ZCT2xxM-LBS-Ax-H5-460x, a two axis RS485 inclinometer with a published accuracy of 0.005 to 0.01 deg, carries four numbers that matter here and they are not the same size. Accuracy is 0.005 to 0.01 deg. Resolution is 0.001 deg. Zero deviation is plus or minus 0.05 deg. Zero temperature drift is plus or minus 0.002 deg per degree Celsius, with a maximum of 0.13 deg across the stated range.

Accuracy is not the binding constraint. 0.005 deg is 0.087 mrad, and against a cross-level tolerance of half a milliradian on a twenty metre span that leaves about six resolution steps inside the tolerance. Even at the widest published accuracy figure the instrument has resolution to spare. Specifications written around accuracy are answering a question that was never in doubt.

Zero deviation is the binding constraint. 0.05 deg is 0.873 mrad, and at a twenty metre span that is 17.5 mm of cross-level. The construction tolerance is 10 mm. So the published zero deviation of the instrument, on its own, is one and three quarter times the entire tolerance the runway is built to.

The temperature term is worse. The published maximum of 0.13 deg is 2.27 mrad, which at a twenty metre span is 45 mm, four and a half times the tolerance. Even the typical figure of 0.002 deg per degree Celsius, over a twenty degree Celsius change, is 0.04 deg, which is 0.70 mrad and 14 mm at the same span, more than the tolerance on its own.

Published figure	As a slope	As cross-level at 10 m	At 20 m	At 30 m
Accuracy 0.005 deg	0.087 mrad	0.9 mm	1.7 mm	2.6 mm
Zero deviation 0.05 deg	0.873 mrad	8.7 mm	17.5 mm	26.2 mm
Zero temp drift, typical, 20 degrees Celsius	0.698 mrad	7.0 mm	14.0 mm	20.9 mm
Zero temp drift, maximum 0.13 deg	2.269 mrad	22.7 mm	45.4 mm	68.1 mm

There is one conclusion to draw from that table and it changes the design of the whole installation. A permanently mounted tiltmeter on a crane runway cannot serve as an absolute reference for cross-level. Its own zero is larger than the thing it is being asked to measure. What it can serve as is a comparator between two epochs, provided three conditions hold: the mounting is permanent and cannot be refitted any other way, the sensor’s own temperature is logged with every reading, and the epochs being compared are taken at the same point in the thermal cycle.

The corollary for the specification is that the number to write down is the zero stability requirement, in degrees per year or degrees per degree Celsius, and not the accuracy. A procurement that asks for 0.005 deg accuracy and says nothing about zero stability will buy an instrument whose accuracy is six times finer than the tolerance requires and whose zero is one and three quarter times the tolerance itself.

8. The Life Budget the Standard Publishes

ISO 12488-1 publishes two sets of tolerances: construction tolerances, which apply to a new, modified or repaired track before operational use, and operational tolerances, which apply to a track in service. The relationship between them is the most useful thing in the document for a monitoring engineer, and it is not often quoted. For the vertical quantities the operational tolerance is exactly double the construction tolerance, in all three tolerance classes.

Grade 2 gives a cross-level of plus or minus S mm capped at 10 mm at construction, and plus or minus 20 mm in service. Horizontal straightness is plus or minus 10 mm at construction and plus or minus 20 mm in service. The same doubling appears in Class 1, at 5 mm against 10 mm, and in Class 3, at 20 mm against 40 mm.

Span	At construction	In service	Drift budget	As a slope	Resolution steps
6 m	6 mm	20 mm	14 mm	2.33 mrad	27
10 m	10 mm	20 mm	10 mm	1.00 mrad	11
16 m	10 mm	20 mm	10 mm	0.63 mrad	7
20 m	10 mm	20 mm	10 mm	0.50 mrad	6
30 m	10 mm	20 mm	10 mm	0.33 mrad	4

That doubling is a published life budget. The standard concedes that the runway will move in service, and it says by how much: on a twenty metre span, 10 mm of additional cross-level, which is half a milliradian, or 0.029 deg, or about six resolution steps of the instrument, and a little over half of its published zero deviation. It is a small budget and it is a finite one.

The causes that spend it act between surveys rather than during them. A column settles, a bracket creeps, a second crane is added to a bay that was designed for one, the building cycles thermally and the runway goes with it. None of those announce themselves, and the interval between statutory alignment surveys is measured in years.

So the alarm on a runway belongs on the rate, expressed in millimetres per year against the construction to operational difference, and not on a level against the tolerance. A level alarm against a 10 mm tolerance would either never fire or fire on the instrument’s own zero. A rate alarm against a 10 mm budget spent over an expected service of some decades is at least asking the question the budget actually poses.

And the reason the rate is worth asking about is the one from section 2. The criterion on this structure is a consumable. Wheel flanges and rail head are replaced on a cycle, and the cost of that cycle is dominated by the replacement rather than by the diagnosis. A rate record is what lets a replacement be planned instead of reacting to a flange that has already gone.

9. What to Specify

Start with the document, not the instrument. Name the standard, the edition and the tolerance class in the acceptance papers before anything else. The published values differ between ISO 12488-1, EN 15011 and the national documents that adopt them, and a specification that says the rails are to be within tolerance without naming the document has not said anything.

Decide which quantity is being monitored, and say so. Cross-level E and the two metre vertical sample c are the two published tolerances a tilt channel reports in its own units. Span, plan straightness and full-length elevation are not, and no amount of sensor count changes that.

Mount on the girder, never on the rail. The rail is a wear item. It gets shimmed, adjusted and eventually replaced, and every one of those moves the zero of anything attached to it. The girder top flange is the reference the rail is set out from.

Treat the mount as part of the measurement. Because the instrument is a comparator in time and not an absolute reference, a mounting that can be removed and refitted destroys the measurement. Fix it once, and protect it from anything the crane or the maintenance crew can touch.

Record the crane state with every reading. The tolerances exclude elastic deformation, and the girder rotates by about ten times the tolerance as the crane passes. Take the reference epochs with the crane away, and log the crane position or the drive state alongside every subsequent reading so the loaded readings can be identified rather than merely discarded.

Log the sensor temperature with every reading. The published zero temperature drift, at its maximum, is worth four and a half times the tolerance at a twenty metre span. Compare like with like in the thermal cycle, log the temperature that makes that possible, and do not trust a trend that mixes epochs taken at different temperatures.

Space the sensors to match the tolerance you are chasing. The sample tolerance is defined over two metres. One sensor per bay cannot see a kink of that length, so if local kinks are the target the spacing has to be two metres, and if only the cross-level trend is the target one sensor per column line is enough.

Set the alarm on the rate. The standard publishes a life budget, the difference between the construction and the operational tolerance. Write the alarm in millimetres per year against that difference, and let the annual survey decide whether the absolute tolerance still holds.

Keep the survey. A tilt array does not measure span, it does not measure plan straightness, and it does not measure the deviation of the rail from a line over the runway length. The survey that decides whether the runway is in tolerance is a separate activity with separate equipment, and the instrument’s value is that it tells you when to bring that survey forward.

Limits

The arithmetic in this article is reconstructed from published standards and from one published datasheet. No crane runway deployment is claimed here. The nearest published work in this family is warehouse racking, which is an indoor steel structure with a different load case and a different failure mode, and the two should not be read as the same application.

The tolerance values quoted are Grade 2 of ISO 12488-1 as reproduced by two independent secondary sources and by the identical national adoption GB/T 10183.1, and the operational values as reproduced from the same sources. Editions, national annexes and the way individual documents group these quantities differ, and every value must be confirmed against the document and edition the project actually specifies before it is used in an acceptance.

The skewing calculation is the one in EN 1991-3 clause 2.7.4, worked with the minimum values the standard sets for the clearance and wear terms and with a round wheelbase and rail head width chosen for the example. A real crane has a specific wheel arrangement, a specific lambda factor from the tables in that standard and a specific rail section, and its own values replace these.

The guide force from skewing is not the whole lateral load on a runway. Acceleration, braking, the drive force and the dynamic factors for the crane are separate terms in the same standard, and an assessment of a runway beam or a column uses all of them together.

The instrument figures are the published typical and maximum values for one model, quoted at the stated test condition of room temperature. A different model, a different mounting, a different thermal regime or a different supply gives different numbers, and the zero figures in particular are the ones to re-read from the datasheet of the unit actually being bought.

A tilt channel does not replace a rail survey, a fatigue inspection of the runway girders and their connections, a check of the rail fasteners and column bases, a check of the crane’s own wheel and end carriage geometry, or the crane manufacturer’s alignment and commissioning procedure. It records the two slopes that are written as slopes, between surveys, and the decisions about the runway still belong to the survey and to the inspection.

Frequently Asked Questions

Can a tilt sensor check crane runway gauge? No. Gauge, or span, is the distance between the two rail centrelines, and ISO 12488-1 tolerances it as a length, plus or minus [5 + 0.25 (S – 16)] mm with a cap of 15 mm for Grade 2. A tilt channel measures neither a distance nor a direction in plan, and no number of sensors recovers one. Gauge is measured by the survey, along with the plan straightness of each rail.

Is the skewing force the reason to monitor a runway? No, and this is the least intuitive part of the whole subject. EN 1991-3 already includes the rail and wheel direction tolerance as a term in the skewing angle, and because the friction response saturates, doubling that term changes the guide force by about nine percent. Removing it entirely changes the force by about eleven. The load has been designed for. What is not designed for is the rate at which the rail and the wheels wear, and that is the consumable the money goes on.

How accurate does the instrument have to be? Accuracy is not the number that binds. A 0.005 deg accuracy is 0.087 mrad, which leaves about six resolution steps inside a half milliradian cross-level tolerance on a twenty metre span. The published zero deviation of the same instrument, 0.05 deg, is 0.873 mrad and is one and three quarter times the whole tolerance, and the maximum zero temperature drift of 0.13 deg is four and a half times it. Write the specification on zero stability and on the mounting, not on accuracy.

Do the readings have to be taken with the crane stopped? The tolerances have to be, and the readings should be. ISO 12488-1 excludes elastic deformation caused by loading, so a reading taken with the crane on the bay is not comparable to the tolerance at all, and the girder’s own rotation under that load is roughly ten times the cross-level allowance. Take the reference epochs with the crane away from the instrument and log the crane position with every reading thereafter, so that loaded readings can be identified rather than thrown away.

---