The Dynamics of Caravan Stability

This article attempts to discuss the technicalities of caravan towing dynamics in relatively plain English for those keen to know more on the topic but, like so many, cannot understand far more technical documents that cover this complex subject. Written by Collyn Rivers, an internationally recognised author on technical subjects in the automotive electrical, solar, and caravan/camping industry, this article provides design guidelines and tips that assist owners to avoid major buying and usage errors. This article has been written specifically for ExplorOz, with a longer, more technical version to be available from the author’s website at a later stage.

A Towing Overview

Ongoing reports of caravan (but rarely camper trailer) accidents suggest problems with caravan design and/or usage. The basic issue: how trailers and their towing vehicles interact has been understood by the transport industry since WW1, but almost all has been described in engineering papers and substantially in mathematical terms.

To put it into simple terms however, laws of physics cannot be overcome by driver “skill” once a trailer begins to swing and sway in a “chaotic” fashion. Let’s look at what happens when a trailer is swaying: the trailer, being pivoted behind a tow vehicle’s rear axle, exerts side forces on the rear of the tow vehicle that causes it to yaw in the opposite direction. The action is akin to that of a pendulum with the trailer hung from the bob of a shorter pendulum (the tow vehicle) with its tow ball acting as the bob. Each thus affects the swing of the other. Beyond a certain level of disturbance, their interaction suddenly becomes effectively random – this action is correctly termed “chaotic”. (A cyclone is another example of such so-called ‘chaotic’ behaviour).


Note: The term ‘react’, used in this article, is a common term in physics, which for the purposes of this article, can be read as ‘to counteract in equal opposition, as against some force’.

If a (side) wind gust causes a moving caravan to sway (technically known as ‘yaw’), that yawing force can only be reacted by the tow vehicle’s inertia, plus the frictional grip of its tyres on the road. That force however is applied at a distance (in effect a 1.25-1.5 metre lever) behind the rear axle of the tow vehicle. As the tow vehicle attempts to pull it straight, the ‘van overshoots: yawing in the opposite direction.

Below a certain speed such swaying may die down, but above a critical speed specific to each caravan and tow vehicle, this oscillatory action self-escalates (so-called ‘positive feedback’). Within a few seconds, yaw forces exceed the tow vehicle’s inertial ability and the tyre’s frictional ability to oppose them. Jack-knifing is then virtually inevitable.

Up to a point, a caravan’s yaw inertia (resistance to yawing) assists stability. A big rig typically feels ultra-stable, but if a side force, or often combination of forces (e.g. wind, adverse camber, sudden swerve) strong enough to cause the caravan to yaw more strongly than the tow vehicle can counteract, the yaw inertia that previously caused that caravan to seem so stable, is now its undoing. A caravan thus needs enough yaw inertia to assist stability, but not such that it can overwhelm the tow vehicle. It is much the same as a big container ship, or a ferry with an overladen upper deck. Its sheer inertia normally keeps it ultra stable - but a rogue wave may roll one over.

Caravans of similar length and weight, but different mass distribution, may have quite different yaw inertia. An end-heavy caravan has more yaw inertia than a similar length caravan with its mass centralised. But whatever that tow ball mass needed for stability, it cannot be a direct percentage of overall weight (except for short, centre-kitchen caravans). Camper trailers demonstrate this superbly. Few exceed 4.0 metres and have little rear overhang. Some have a ‘recommended tow ball weight as low as 3% - yet are totally stable at speed.

Fifth Wheelers are Safer

An effective solution was developed over 90 years ago by the transport industry– which is to eliminate tow-ball overhang by locating the hitch directly over the tow vehicle’s rear axle/s. This enables the trailer to behave as a single pendulum and with predictable action. There is now a growing trend to the fifth wheeler caravan configuration worldwide. It is fundamentally more stable, and thus a far safer approach for caravans over 1600 kg and/or 20 ft.
With conventional caravans, the current European approach is to accept the sway reversal characteristic, but to limit its consequences by reducing the mass and yaw inertia (see below) of the caravan. The previous US approach was very high tow ball mass, in some cases of 20% or more of trailer weight, and truly long and heavy tow vehicles - such as the Ford 350 or 550.

Mass, Weight and Inertia

Like an arrow, caravans must be front-heavy to travel straight. Early day caravan were typically 3.5-5.0 metres long, weighed about 1000 kg, and had centre kitchens. With these configurations, a 70-100 kg tow ball weight was enough. Tow vehicles of the era had short overhangs, often weighed more than the caravan, and rarely towed at over 80 km/h. But, as owners sought longer caravans, caravan makers apparently overlooked a fundamental matter: that weight is not the same thing as mass.

Mass is a measure of the amount of material in something. It remains the same no matter where it is (including space). Weight is the effect gravity has on mass: i.e. on Earth it pulls mass downward. In space, a mass that weighs 10 kg on Earth is weightless but, if thrown at something, will make an impact upon that object much as it would on Earth - because its mass is still equivalent to a weight of 10 kg. For some purposes, mass and weight can be regarded as identical. For things that move, mass is the relevant concept. Once caused to move, mass continues to move in a straight line unless an equal and opposite force deflects, slows, or stops it. The effect is known as inertia. In effect, inertia resists change.

Moments along a Beam

Diagram 3 below shows the effect of Moments along a pivoted beam.
Positions A, B and C (both plus and minus) are 1.0 metre apart. D+ is 0.5 metre from C+.
Here, a weight of 100 kg at each +B and -B and has an equivalent mass of 100 kg. At +C and -C that same 100 kg weight, has an equivalent mass of 200 kg at each position. The effect that weight has on caravan stability is thus substantially a function of how far that weight is from the pivot – i.e. the axle/s. The above is a 4.5 metre ‘van. Extrapolate this for a 7.5 metre van and the mass at +C is a probable 300 kg for every 100 kg placed there.

Historically, caravan makers have typically recommended tow ball weight as a percentage of caravan weight. In Europe it was typically 7%, in Australia 10% and in the USA from 10%-20%. Over the years this became virtually a mantra (that I too accepted without thinking about its implications until some years ago). But this recommendation needs to be revised because it does not take into account that the implications of the Moment Arm (virtually leverage) is such that the weight’s effect increases in proportion to its distance from the axle/s. The effect of 100 kg in weight, one metre in front/rear of the axle has a mass equivalent to a weight of 100 kg. At 2.0 metres its mass is equivalent to a weight of 200 kg, at 2.5 metres it is 250 kg. Tow ball loadings nevertheless are commonly being recommended as a percentage of trailer weight - regardless of the location of various masses, and their distance from the axle. This implies that resultant forces along a pivoted beam remain the same regardless of their distance from that pivot, e.g, a caravan axle. A heavy person sitting at one end of a see-saw cannot balance that of a light child, sitting at the same distance from the centre. To do so requires the heavier person to move much closer to the pivot. For caravans to be somehow immune to this effect would require a rethink of Newton’s Laws of Motion.
In Diagram 4 above, you can see a physical demonstration of the Moment Arm effect (and also the physical difference between weight and mass) is readily shown by holding a bar that carries two identical weights (each of about 5 kg). Swing as shown, (or rock to show pitching) and you will find it hard to start and stop. But move the weights close together and it started and stopped with relative ease.

Currently, most Australian and American caravans are designed as shown in the first diagram with chassis (bar) being long and end-heavy. This inevitably requires a high tow ball weight to reduce instability, necessitating a tow vehicle able to withstand such weight. It also ignores the dynamic effects of mass during yawing and/or pitching. The required weight can theoretically be reduced by having mass centralised over the axle/s (e.g. via a centre-kitchen, centrally-located batteries and tanks, replacing gas anything (except eventually for fuel cells) by diesel powered water, space heating and cooking. For any given distribution of mass, the shorter the caravan the better.

Legal reasons currently restrict any recommendation of tow ball weight beyond: ‘do what the caravan maker advises’, but however the recommendation is determined, it must take the overall length into account, i.e. where weight is distributed along that length, how far the axle/s are to the rear – and the distance from the tow ball to the tow vehicle’s rear axle (the shorter the better). The recommended amount is likely eventually to be determined (for each caravan) by actually measuring its yaw inertia (the resistance to yaw). As I’ve hopefully made it clear here, the laws of physics preclude it being only a function of overall ‘van weight when considering trailers much over 14 ft, and then only if that weight is centralised.

Roll Centre

This is another issue that seems little considered, let alone addressed. Because a trailer is located by a tow hitch typically well above ground level, a trailer’s front end can only roll around that point. This presents no problem for a beam axle trailer, because its suspension causes it to roll vaguely around the height of the rear spring shackle, and not that much below its vertical centre of mass.

See Roll Centre - in pictures (below).
Left: Beam axles.
As the caravan rolls the axle remains parallel to the ground, so only its body can roll – and at about spring height at wheel/s location. The Moment arm (leverage) is thus desirably short.

Centre: Swing arms.
Used on Allard sports cars, the independent half-axles raise the roll centre yet higher. A minor downside is that the wheels tilt in slightly as it rolls, thus requiring some positive camber whilst level. (Alan Mawson, who designed the Tvan’s brilliant suspension, substantially overcame that by having a full length beam axle for each wheel).

Right: this is typical of most independent suspension systems (the typical pivoted trailing arms that locate the wheels are omitted as they cannot be shown in this plane). The Moment arm (shown here at wheel location) progressively lengthens. At the far end roll centre is way below ground level thus the Moment arm at that location is substantial. This is the reason why adding weight (such as twin spare wheels) high up at the rear of caravans with independent suspension is, to put it mildly, not a good idea.

Most independent suspension systems for caravans however, have a roll centre close to, or at ground level. A trailer with independent suspension is nevertheless still forced, by the tow bar, to roll (at the hitch) at tow ball level. Most, but not all, independent suspension systems thus, by virtue of a roll centre at about ground level, introduce a much longer (vertical) moment arm at wheel level.

For the caravan to be restricted to only roll around the hitch at the front, and only around a close to ground level roll centre at its wheels, creates a roll axis. In lay terms, that term refers to any point along that axis where, if one were to push it horizontally whilst the caravan was moving, the caravan would move without inducing any roll. For example, pushing at any point along that line, would cause all of the ‘van above the line to roll away from you. If pushed at any point below that line, the ‘van above that line will roll toward you. (To clarify my point for technical thinkers, the roll axis can be defined as ‘a situation where, in the median plane of the caravan, a transverse plane in which horizontal lateral forces applied to the rolling mass of the caravan will cause that caravan to move or to turn sideways without causing it to roll.’)

As the roll centre and roll axis tends to move slightly as the caravan traverses bumps etc, roll centre needs to be seen as only a concept (that may aid your visualisation of what's going on). There is nothing absolute about roll centre position at any time whilst a vehicle is in motion. It can and will move – but not by any major amount.

As can be seen, the effective centre of mass (centre of gravity) of a caravan with independent suspension will be way above its roll centre, and extremely so at the rear. The result is a considerable lever action as the caravan’s mass will now roll around a centre close to or at ground level, and even more so at its extreme rear. This is not as serious an issue with beam or swing axles as the roll centre line drops far less. It is rarely understood that the soft ride provided by car suspension is tailored to human physiology but what is comfortable for people is less necessary in a well-made caravan (one would not want to ride in an early Phoenix, that nevertheless are known for their longevity). Independent suspension is far from required. A well sprung beam axle caravan with long leaf springs (to limit bump steer) overcomes all of the above.
Do note this article is primarily relates on-road and dirt-road going. Suspension systems for serious rock-hopping, mostly confined to specialised off-road camper trailers, have very different criteria.

The issue is not independent suspension per se, but rather the forms commonly used on caravans that introduce a low centre. It is perfectly feasible to have an independent suspension that provides a high roll centre. A swing axle system for example has a roll centre much at the level as a beam axle. The roll centre issue is brilliantly explained in Maurice Olley’s superb book Chassis Design – Principles and Analysis. It does use full-on engineering terminology and mathematics throughout and is unlikely to be understandable without such a background.

Diagrams below show the Line of roll centre between two differently designed caravans.
In the two diagrams above, the Line of roll centre (i.e. roll axis) of a beam axled caravan is still high at axle level. For a long caravan with (typical) independent suspension however will have a roll axis that is well below ground level at its rear. What this implies is that if the rear of that caravan is (as above) hanging over a cliff – and one were then, for the purpose of this test, to extend that extreme rear end downward by (say) clamping a plank or ladder that extended downward to that roll axis line (roll centre line) a push applied to that ladder above that line will cause that caravan to roll sideways away from you. If pushed above that line, it will roll sideways toward you. This is a hard concept to grasp and any suggestions on how to clarify this (without using maths) would be appreciated. Incidentally, if you try this do not forget to remove the plank or ladder before driving away!

The roll centre of the beam axle caravan can be raised considerably by locating the beam axle below the leaf springs. Whilst this raises the caravan’s Centre of Gravity by that amount, the Moment Arm is likewise shortened. The overall result is an increase of stability – this is contrary to what might otherwise be suspected – particularly so at the extreme rear of the caravan. The downside is that you may need longer entry steps.

The Moment Arm implications of placing (say) a 50 kg washing machine at the very rear, let alone some 50 kg of twin spare wheels high up are defined by basic physics. The effect is obvious from these diagrams.

A diagonal falling roll axis, if associated with a caravan constrained against horizontal movement at the tow ball, also causes the rear of the caravan’s Centre of Gravity to move sideways – thus introducing side forces at Centre of Gravity level. Unless most of the above is proven incorrect, I feel this is seriously bothering. I thus draw it to caravan builders’ and chassis builders’ attention and to associated industry and other regulatory bodies for consideration.

Wind Forces

If a caravan has more or less equal areas of side wall front/rear of the axle, a wind gust will not normally cause it to yaw. If however there is a substantially greater area at the front (as a result of rear located axle/s) a gust will cause the ‘van to turn away from the wind. If greater at the rear, it will turn into the wind. The former is safer but not in excess. If the axles/s are way back it is necessary to reduce the side area in front of the axle, to make that area slightly larger than at the rear. These changes will contribute to improved dynamic stability of the caravan. A good example is the original Phoenix caravans that Barry Davidson designed and built in Australia.

With that said however, there still exists the potential for a roll over to occur from side gusts hitting the van on its right hand side, whilst being overtaken by say, a large truck that masks only part of the caravan as it passes. In this scenario, the ‘van is momentarily subject to wind forces that may be at the front or rear! There will also be a corresponding suction on its lee side. Without getting overly technical, the forces are about 160 kg per square metre for a 40 km/h gust, and about 350 kg per square metre at a far from uncommon 60 km/h gust.
Pictured above is the early (original Phoenix Caravan. From a safety perspective, this is a superb example of caravan design with good stability dynamics. Note the braced A-frame, the sloping wall area at the front to ensure that, for stability, whilst side wind forces need to act on more area than the rear. This must not be excessive. The central kitchen layout ensures mass is centralised, thus permitting the axles to be well to the rear.

Critical Speed

The energy associated with a moving caravan and tow vehicle (by virtue of it being accelerated to speed) is four times greater each time its speed is doubled, e.g. its energy at 110 km/h is four times that at 55 km/h: it follows a square law. The energy needed to accelerate a mass to speed actually fuels the action of a swaying caravan: catastrophically so once the yaw forces exceed the ability of the tow vehicle to react them, the ongoing dynamic behaviour of that unfortunate caravan cannot be predicted, and thus not driver correctable (in physics terms it has become chaotic). Jack-knifing is then virtually inevitable.

Every combination of caravan and tow vehicle has a critical speed above which, if subject to sufficient disturbing yaws forces, cannot be corrected. Trials of a loaded test trailer in the UK showed the relationship between mass distribution and stability. Whilst the trials were of shorter and lighter trailers than are common in Australia and the USA, there was a clear relationship between weight and its location relative to the axle: this particularly affected the ‘critical speed’ at which correction becomes impossible. This effect appears to be scalable and if proven to be so, the critical speed above which this may happen (not necessarily does happen) could, for long (say 20 ft and over) end-heavy ‘vans be too close to towing speed limits for comfort.

Experience shows that some caravan owners dispute the above by quoting from their own experience, in particular that their long end-heavy rig shows no signs of instability. Firstly, long end-heavy ‘vans have so much inertia, that it takes a considerable force to unsettle them. But, if such disturbing force is experienced, the very inertial characteristic that causes them to normally be stable is suddenly its nemesis. Secondly, it does not necessarily follow that a long end-heavy ‘van will have an accident. The necessary disturbing force may never be experienced.

Nevertheless such rigs are at much greater risk, particularly if they begin to sway at speed whilst descending a hill – and then braking. What happens then is that the rear of the yawing ‘van has its yaw augmented by a gravitational component. There is also increased risk on motorways if overtaken by, or overtaking a large truck, if there is also a gusting side wind.

As a search through this and other topic-related forums will show, the most common first comment following a major caravan accident is: “it had always felt so stable until then . . .”

Weight Distributing Hitches (WDH) count

A WDH (weight distribution hitch) has no direct role in yaw control/reduction but by partially restoring the tow vehicle’s weight balance may marginally increase its ability to counteract yawing forces. A WDH can however have adverse effects with a tow vehicle that is overladen. Its action can trigger that vehicle into and out of an understeer/oversteer cycle (i.e. alternately tightening and increasing its turning radius) to possibly dangerous levels.

Its action is not unlike a truss used to support a hernia. It assists, but is not a substitute for removing that hernia, and thus the need for that truss. This is already happening (at least WDH-wise) in Europe - where ‘vans are typically 1200-1600 kg, and light at the front and rear. Right now a WDH is virtually essential with any caravan over (say) 18 ft and heavier than 1600 kg. A far sounder approach however is to design and scale caravans such that a WDH is not required.
Pictured above is a long end-heavy caravan with so much load on the tow ball that it lifts the front of the tow vehicle (note space difference front/rear wheel arch despite the rear being almost empty). There appears to be no WDH.

Sway Limiters

Basic sway limiters assist to absorb yawing forces via simple mechanisms - that convert yaw energy into heat. Others employ spring loaded cam, or ball and socket mechanisms that direct the sway energy such that the tow vehicle counteracts it via its own inertia and tyre grip.
Whilst effective at low levels, if friction sway units’ limitations are exceeded, they may suddenly release yaw energy into an already overloaded situation. There is also concern they may mask a rig’s underlying instability.

Some 4WDs have so-called inbuilt ‘sway correction’, that automatically brakes the tow vehicle (left/right) to partially counteract trailer sway.

AL-KO Europe has a system that detects caravan swaying. If swaying exceeds pre-determined levels, as the caravan’s nose sways right, it brakes the left wheel/s, and vice versa. This dampens the sway and, by slowing the rig, reduces the kinetic energy fuelling the action. The unit’s action is akin to a cyclone encountering cooler water, and losing its source of energy. The unit is offered for retrofitting to any trailer that has AL-KO brakes. It has proven effective on European caravans that are lighter, reasonably stable, and have less yaw inertia than lengthy end-heavy products. It is unclear if selective caravan braking could react (via its tyres) the forces involved with a long end-heavy caravan swaying at high speed.

There is concern that any ‘sway correcting’ system may ‘mask’ underlying instability issues. Ultimately their ability is limited by the tow vehicle’s inertia and both tow vehicle and trailer’s tyre grip. Here again, a better approach is to design for stability and to regard such systems as added insurance.

Design & Purchase Implications


The issue of roll centre height is discussed above – in essence the higher the better.

Design and construction need to be such that mass is both minimised and in particular, centralised (thus minimising yaw inertia). Minimising weight will be necessary anyway as cars and 4WDs become lighter - and hence less able to counteract yaw inertia. Stability can be optimised by keeping overall length to a minimum, reducing trailer yaw inertia, centralising mass distribution, and having the axle/s as far to the rear as feasible. To reduce the effect of side wind forces, there needs to be more side wall area in front of the ‘van’s axle than behind it. The amount required is not yet totally known however. If the axle or axle group is (desirably) way back, it may be necessary to reduce that frontal area, (as done with the early Phoenix caravan). This also reduces the yaw inertia of mass at the rear - as that distance thus becomes shorter. Tyre pressures affect stability but to a lesser extent. The further back the caravan’s axle/s the better. Tyre sidewall stiffness assists: the higher the better.

Tow Vehicle

The greater the weight of the tow vehicle, relative to the caravan, the better (a major issue as tow vehicles become increasingly lighter). It should be at least as heavy as the caravan, ideally more. Also vital is that there is ample payload to accept the recommended tow ball weight. Contrary to common belief, “payload” does indeed include the weight of the driver and passengers.

Ideally choose a vehicle with minimum distance from centre line of rear axle to tow ball. Avoid or replace hitch receivers, and/or tow ball shanks that have excess overhang. The average total overhang is about 1.25 metre from tow ball to centre line of the tow vehicle’s rear axle. The further the tow ball is behind that vehicle’s axle, the greater the resultant lever effect (on both pitching and snaking), and the lower the critical speed where chaotic behaviour can (not necessary will) be triggered. It is probably no coincidence that many caravan accidents involve semi-laden dual cab tow vehicles with extensive rear overhang.

Driving Implications


This is a vital factor: the higher the ‘van’s yaw inertia, the lower the critical speed. That critical speed may well be below the legal limit for high yaw-inertia caravans - or too close to it for comfort. Keep speed below 100 km/h (less is strongly recommended for long end-heavy caravans).This issue mostly affects end-heavy caravans, particularly long ones (but also shorter caravans towed at speed on motorways). Except in extreme cases, light caravans up to a possible/probable five metres are at less risk, particularly if they have a centre kitchen.

Driver Skill

Up to a certain level, caravan sway can be counteracted by driver correction, but this can lead to believing that a sufficiently skilled driver can correct a jack-knifing situation. This is literally impossible. The reason is that correcting any such situation requires knowing what will happen next if not corrected. A rig that enters that ‘critical speed’ situation exhibits so-called chaotic behaviour. As its next immediate action cannot realistically be known, no driver (no matter how skilled) can know the correction required.

Where ‘skill’ and ‘experience’ (the latter definable as the ability to recognise a mistake after you’ve made it for the fourth of fifth time) is handy, is in recognising a rig’s inherent limitations – and driving accordingly.


Caravan stability is an evolving area in which a fair amount has yet to established and proven. The basis of the above is however based on two major articles initially published in 8-10 page articles in Caravan World in 2010 and 2010. These attracted global attraction and not one single part of either has been questioned to date. They are both on my website and are periodically reviewed when updates are required to keep facts current with new knowledge. There too, there has not been even a single disputed comment.

I am about the only technical writer attempting to explain this subject in reasonable clear English. I am however far from the only one arriving at the generality of this article: this is because for such generality to be wrong invalidates seemingly universal Laws set out (in Newton’s Principia Mathematica) in 1687 and accepted as valid ever since. Except, of course by various internet forum posters who suggest it is ‘just another opinion’.


My definition of ‘roll axis’ is adapted from that used by W. F. and D.G Milliken in Maurice Olley’s Chassis Design Principles and Analysis, published by the Society of Automotive Engineers in 2012. (ISBN-0-7680-0826-3). That the roll axis concept is best seen as to aid ‘visualisation’ is in the Technical Notes of GM Research Engineer Maurice Olley on which the above book is based. (It was my good fortune to have attended lectures on the subject given by Mr Olley in the late 1950s – he died in the early 1970s – some 30 years before ‘his’ book was published).

I also express a very genuine thank you to’s Michelle for her invaluable recommended changes and corrections (almost all of which have been made) to make this necessarily complex article more readable.

Further Information

An experimental investigation of car-trailer high-speed stability: Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 223 (4), pp. 471-484.

Chassis Design: Principles & Analysis: Milliken and Milliken (based on technical notes of Maurice Olley - who died in 1972, some 40 years before its publication).

The Dynamics of Towed Vehicles: (

Vehicle Dynamics: Collyn Rivers. (Currently under revision.)

For graphics of pendulums and how they interact:

Copyright & Disclaimer

This article’s text and associated drawings is copyright Caravan & Motorhome Books, Church Point, NSW 2105 (Australia). The copyright of its actual presentation in ExplorOz however is held exclusively by I.T. Beyond Pty Ltd. (owner & publisher of As is covered by this site’s Terms of Use policy, this article may not be copied nor reproduced in any manner, nor changed in any way or form, without the express written permission of the copyright holder. If it desired to refer to it within another forum, website etc, please do so ONLY by providing a link to this ExplorOz version, or a link to the (forthcoming) more technical version at

The reason for this is that both versions will be updated from time to time, enabling readers to be sure that they have our most current version of this increasingly understood subject.

This is a very specialised topic not covered so far in depth in any of my existing books. Collyn Rivers books however (stocked by and described in the ‘Books’ section of this site) do cover a wide range of camper trailer, caravan, fifth wheel caravan and motor home topics. The second edition of the Camper Trailer Book discusses camper trailer suspension in depth. Everything is thoroughly researched prior to publication, and the books are updated (between print runs) at least once a year.

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