Updated November 2016
Ongoing caravan roll-overs show that basic caravan dynamics is overlooked or ignored in caravan design, loading and use. The main cause of caravan instability is that the caravan pivots on a hitch well over a metre behind the tow vehicle’s rear axle. If the caravan yaws (sways) it causes the rear of the tow vehicle to yaw in the opposite direction. And vice versa. This is an inherently unstable system that is only stable within limits. That this is so is shown by 135 reported caravan roll overs in 2013 from one Australian insurer alone http://caravanbuyersguide.com.au/caravan-accidents/.
The tow vehicle/trailer interaction is that of a pendulum (the trailer) hung from the bob of a shorter pendulum (the tow vehicle). That second bob is the tow ball. When swaying, each pendulum adversely interacts with the other. At low levels it is annoying but usually harmless. Beyond a certain level of disturbance however the interaction is not realistically predictable. If it occurs above a critical speed (that is specific to each rig) it becomes literally ‘chaotic’. Its next action cannot realistically be predicted – and hence not driver correctable. It is likely to result in jack-knifing and consequent roll over. (A cyclone is another example of ‘chaotic’ behaviour). http://www.darkside.com.au/pendulum/index.html
This article updated by Collyn Rivers explains the issues. It provides caravan dynamics design guidelines and tips that assist owners to avoid major buying and usage errors. It may possibly assist manufacturers to build more stable product.
A sad ending (pic courtesy of the Caravan Buyers Guide)
When a strong wind gust or sudden change in direction causes the moving caravan to move out of line. The tow vehicle’s attempt to pull the caravan straight is opposed by the caravan’s yaw inertia (resistance to change in movement). Once the yawing caravan reacts to straightening, it then opposes ceasing that movement: it ‘overshoots’ such that it yaws in the opposite direction. This yaw cycle continues until the forces are dampened by friction between tow ball and socket. The tow vehicle’s and caravan’s tyres assist damping. So too (to a point) do friction sway mechanisms.
If/when yaw happens at low speed, and the damping forces extinguish it within two or three cycles it is annoying but harmless. If however a side force (such as wind gust, or an emergency swerve) causes the caravan to yaw whilst travelling above that critical speed, yaw forces can suddenly escalate. Within a few more yaw cycles they may overwhelm the rig’s ability to react them . A jack knife may then be inevitable. That ‘critical’ speed is specific to each towing combination and its loading. The factors involved are described later in this article.
The major and inherent problem in conventional caravan dynamics is the effect of that overhung hitch. The longer its overhang (distance behind the tow vehicle’s rear axle) the worse the effect.
As the caravan yaws as the result of a side wind gust, or an unintended swerve, the tow vehicle is caused (by that overhung hitch) to yaw in the opposite direction. Pic: copyright 2014 http://caravanandmotorhomebooks.com
The transport industry originally used overhung hitch attached trailers. These too had roll over problems. The action of double pendulums was however recognised (if not totally understood). Led initially by Freuhauf (in 1914) the industry (en masse) moved to positioning the hitch directly over the tow vehicle’s rear axle/s. This enabled the (now) semi-trailers to behave as a single pendulum, i.e. with predictable action. Fifth-wheeler caravans too stem from this era (1912-1920).
By eliminating the hitch overhang, the yawing trailer simply pivots around its hitch. No adverse forces are imposed on the tow vehicle. Nose weight optimum is 20-25% of trailer weight but can be as low as 10% if desired. Pic: copyright http://caravanandmotorhomebooks.com.
Stability was further enhanced by using the fifth wheel concept used by bullock carts etc for centuries. The fifth wheel clamped the steered wheel assembly to the cart chassis. It allowed only for turning and pitching. This enabled the heavy tow vehicle to assist trailer overturning stability. Its downside was (and still is) that the trailer chassis must be able to flex to cope with surface irregularities. (Fifth-wheel caravans usually requires a tow hitch that allows side-to-side rocking. Unless used, the stresses can severely damage both hitch and caravan).
Early (circa 1917) fifth-wheeler Adams Motor Bungalow. Pic: Glenn H Curtiss Museum (USA).
That conventional caravans are not inherently stable is evidenced by major industries seeking to remedy this. But rather than attempting to minimise the underlying causes, many local and US caravan makers rely on add-on sway (yaw) control mechanisms and weight distributing hitches. There are also electronic systems intended to detect and assist in emergency situations.
European caravan makers now accept the inherent yaw reversal characteristic. Following known caravan dynamics, it reduces caravan mass and yaw inertia responsible for such forces. It is also increasing the advised ratio of tow vehicle to caravan mass. It is further aided by a general towing speed limit of 80 km/h.
The (now mainly) Australian and US approach is to use the few remaining heavy tow vehicles, plus add-on WDHs, yaw control and electronic stability aids. Roll overs, primarily of long caravans, suggest this is not working.
Caravan dynamics – mass, weight and inertia
Like thrown billiard cues, caravan dynamics requires caravans to be front-heavy. This was no problem when most were 3.5-5.0 metres, about 1000 kg, and had centre kitchens. Their 70-100 kg tow ball weight was more than enough. Their tow vehicles had short overhangs. They usually weighed more than the caravan. Rigs rarely exceeded 80 km/h.
But as owners sought longer caravans, caravan makers appear to have overlooked that weight is different from mass. Understanding that caravan dynamics difference is vital.
Mass is a measure of the amount of material in something. It remains the same no matter where it is (including in space).
Weight is the effect that gravity has on mass. As on Earth, it pulls mass downward. In gravity-free space however a mass that weighs 10 kg on Earth has no weight. If freed from your hand it stays where it is. If thrown however, it will hurt just as on Earth. That thrown mass is still equivalent to a weight of 10 kg and exerts the same force.
For many purposes (such as weighing the tow vehicle) mass and weight can regarded as identical. For things that move (and caravan dynamics particularly) mass is the relevant concept. Once caused to move, mass continues 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.
Caravan dynamics – moments along a pivoted beam
Caravan makers typically recommend tow ball weight as a percentage of the caravan’s weight. But caravan dynamics are such that it cannot be. Doing so overlooks/ignores that the effect of weight (mass) increases with its distance from the axle/s. A 100 kg weight, one metre in front/rear of the axle has a mass equivalent to a weight of 100 kg. At two metres its mass is equivalent to a weight of 200 kg. At 3.5 metres it is 350 kg.
This can readily be checked on a see-saw. A 30 kg child three metres from the pivot can be counterbalanced by a 90 kg adult only one metre the other side of that pivot. Despite this, tow ball loadings are usually recommended as a percentage of trailer weight. This is done regardless of its location and distance from the axle. For this to be valid necessitates a rethink of Newton’s Laws of Motion.
For straight line stability a caravan must have some tow ball weight. But a short light central-heavy caravan requires far (percentage) less tow ball weight than a long end-heavy caravan. This is shown by the typical under four metre camper trailers. These have ‘recommended’ tow ball weights from 3%-22.5% – and all seem equally stable.
Legal reasons restrict comment to ‘follow what the caravan maker recommends’. (Caravan & Motorhome Books does not, however, necessarily endorse such recommendations). In future, the recommended amount is likely to be determined (for each caravan) by actually measuring its yaw inertia.
As with a see-saw, the effect of weight depends on where it is relative to its axle/s. Here A, B and C (plus and minus) are all 1.0 metre apart. (+D is 0.5 metres from +C). A weight of 100 kg at +C and -C has an ‘effective weight’ that is twice that at +/-B. At +D it is 2.5 times that at +/-B. The above is a very short (4.0 metre) caravan. Extrapolate that to 7.5 metres and the effective weight at the tow ball is a probably 300 kg for every 100 kg located there. Despite that many (non-UK/EU) caravans have twin gas cylinders and batteries located there. PIc: http://caravanandmotorhomebooks.com
The above becomes yet more complex when a trailer pitches or yaws. The resultant forces are then increased not only by the effect of weight location along the chassis, but are proportional to the square of the velocity at which it pitches and/or yaws.
This simple experiment dramatically shows the caravan dynamic effects of the location of weight along a pivoted beam such as a see-saw or caravan chassis. With the weight centralised the bar can be swung and stopped with ease, but if that same weight is moved outward it becomes increasingly hard to swing and to stop it swinging. The same thing happens if you simulate pitching. The faster you try to move the bar, the harder it becomes. Caravans too behave just like this. Pic: http://caravanandmotorhomebooks.com
Caravan dynamics – weight distributing hitches
The effect of tow ball weight on the overhung hitch is like pushing down on the handles of a wheel barrow. It causes the front (of the tow vehicle) to lift. This reduces the weight on its front tyres. To counteract this, a WDH (weight distribution hitch) acts like a semi-flexible springy beam. In effect it levers up the rear of the tow vehicle, using its rear axle and wheels as a fulcrum (pivot point). This fully or partly levers the front wheels back down. It assists to restore the tow vehicle’s weight balance in steady going. A WDH however introduces rapidly changing front/rear tyre footprint imbalance when a caravan pitches. It may trigger a rapid understeer/oversteer cycle (alternate tightening and increasing turning radius). This effect can reach dangerous and sometimes non-recoverable levels. A WDH also has major adverse effects with a tow vehicle that is overladen.
The purpose of a WDH is to reduce the effect of hitch overhang. A hitch that substantially extends the hitch overhang (as here), reduces the viability of that WDH. Pic: Original source unknown.
A WDH’s action is of a truss used to support a hernia. A sounder approach is to remove that hernia – and need for that truss. Doing so by reducing end-weight (that causes yawing and pitching) has long been the the major European approach. Their caravans are typically 1200-1600 kg, (about 60% of most local product). They are end light and have a tow ball weight of only 60-100 kg. They have no need for a WDH. Few even have provision for one. There are longer European caravans, but these too are far lighter per metre than any current local product. They are typically towed by cars (less so by 4WDs) with short hitch overhang.
Right now, a WDH is necessary with end-heavy caravans over (say) 5.5 metres (18 ft), and a laden weight of 1800 kg. A saner approach is to design, scale and load caravans so that no WDH is required.
Caravan dynamics – yawing
A long end-heavy (particularly front heavy) caravan’s resistance to yawing assists it to continue moving in a straight line. It is likely to feel ultra-stable whilst it continues to move in that straight line. That resistance to change assists stability against side forces (wind gusts, adverse road camber, big trucks passing). It also has a major downside. In the event of a needed emergency swerve the yaw inertia, that previously caused that rig to be so stable, becomes its undoing. The caravan’s inertia that assisted straight line stability can overwhelm the tow vehicle’s ability to turn. A long caravan with excess yaw inertia is like a big container ship. It’s normally ultra stable but a rogue wave can (and sometimes does) roll one over.
Caravans of similar length and weight, but different mass distribution, have very different yaw inertia. An end-heavy caravan has far more yaw inertia than a similar length caravan with centralised mass. But the tow ball mass needed for stability (except for short, centre-kitchen caravans) it cannot be a direct percentage of overall caravan weight. As noted above, camper trailers weight up to 1500 kg. They but rarely exceed 4.0 metres and have little rear overhang. Their makers ‘recommend’ tow ball weight from 2.5% to 22.5%: probably because that’s what the first one turned out be. But if loaded as intended all are stable at speed. (I reduced that of my own 780 kg Tvan – from 140 plus kg to little over 50 kg – with no perceivable on-road effects.)
The general consensus of those working in this field of research, backed up by real life field testing) is that optimum tow ball mass is likely to be 8-12% (a few suggest 8-14%) for locally built product. It is 6%-8% for typical EU product. In practice, many caravan makers ignore this. Many are now recommending less. In Australia several recommend much less (one of plus 2.5 tonne tare mass is under 4.3%).
Arguably the best designed and built caravans ever built in Australia, this 5.3 metre Phoenix (of the 1990s) has the axles set well back. The side’s front slopes back to ensure the side walls area is the required only marginally greater than at the rear. Note the truss-braced chassis. The only suggested change is to relocate the gas cylinder to a ventilated side locker. Pic: courtesy company founder Barry Davidson.
The major factor affecting yaw inertia is the so-called ‘radius of gyration’. This is the distance from the point about which it is rotating (the tow ball) and the point to or from which a transfer of energy has the maximum effect. Good caravan dynamics necessitates mass centralised over the caravan’s axle/s. It also requires the axle/s as far back as possible. This is aided by keeping end weight ultra-light. This necessitates a clear draw-bar. It necessitates light composite materials for the caravan body.
Excess yaw inertia is a bigger problem than excess caravan weight per se. Low yaw inertia will become essential anyway as cars and 4WDs become increasingly lighter. They less able to support high tow ball loading.
Caravan dynamics – sway (yaw) limiters
Particularly with low tow ball loading, a caravan is likely to yaw slightly at low speed. As long as the ‘van settles down of its own accord within two or three cycles this is annoying but harmless. Sway (yaw) are fine in applications like this. They are generally included on new EU caravans for that purpose. If however a sway limiter is fitted to a caravan that, without it does not cease yawing within three cycles, that sway limiter may dangerously mask serious inherent instability.
Basic sway limiters absorb low level yawing forces by friction mechanisms that assist to convert yaw energy into heat. Others are cam or similar mechanisms that lock caravan and tow vehicle in a straight line. Normal cornering is enabled by tyre footprint distortion. The mechanisms release only when turning sharply. These too mask possible underlying instability. Further, when a cam’s limitations are exceeded (in say an emergency swerve), it suddenly releases unwanted energy into an already overloaded situation. (It seems akin to having a King Brown as a guard).
An adjunct to the WDH, a Reese dual-cam mechanical sway control system partially ‘locks’ the caravan to the tow vehicle. It releases on sharp turns and when overloaded by high level yaw.
Some 4WDs have so-called inbuilt ‘sway correction’ that automatically and assymetrically brakes the tow vehicle (left/right) to partially counteract the trailer’s sway. The X3 BMW is able to interlink this to a towed vehicle.
AL-KO’s ESC (Electronic Sway Control) detects and attempts to correct caravan yawing by caravan braking. It is a ”detected emergency’ system’. It automatically operates only if the caravan exceeds a lateral acceleration of 0.4 g or four repeated successions exceeding 0.2 g.
How the AL-KO ESC works. Pic: AL-KO Europe
When the electrics are initially connected the unit tensions a strong spring. When a sensor detect that triggering level (or sequence of lower levels) of yaw the spring is instantly released. This actuates the brakes for 2-3 seconds at about 75% of their maximum effort. The spring is thn automatically wound back and braking is repeated if needed. This dampens the yaw and, by slowing the rig, reduces the kinetic energy that fuels yawing. The effect is akin to a cyclone suddenly encountering cooler water – thus losing its source of energy. The ESC does not correct yawing at less than dangerous levels. Ongoing reports that ‘my caravan was more stable at low speed once the AL-KO unit was fitted’ cannot thus be taken seriously.
The AL-KO unit can be retrofitted to trailers that have AL-KO brakes. It has proven effective in Europe. As AL-KO has, to date, released no relevant data it is unclear if caravan tyre braking can adequately reduce the forces of a long end-heavy caravan yawing strongly at high speed.
It is generally similar to the IDC system ( http://www.bpw-fahrzeugtechnik.de/en/products/caravan/idc/alr ) from Germany.
The Dexter DSC system (USA) differs from the AL-KO system in that it applies braking asymmetrically (i.e. out-of phase with the yaw). It detects yaw in a different manner and acts at lower levels of yaw (about 0.2 g).
Any ‘sway correcting’ system may mask underlying instability. Ultimately the ability to do so is limited by the tow vehicle’s inertia and the tow vehicle and the trailer’s tyre grip. All makers advice they must not be used to correct any existing instabilty – nor overcome the laws of physics.
Wind forces (including those generated by passing trucks) can introduce yaw. The side wall area in front of the ‘van’s axle needs to marginally exceed that behind it – by locating axle/s closer to the rear. This also reduces the yaw inertia of mass at the rear: that distance thus becomes shorter. The Phoenix caravan (pictured above) is a good example of this approach.
Caravan dynamics – critical speed
All mass has inertia. Moving mass continues to move in a straight line unless prevented from moving, or deflected by an equal and opposite force. This is readily seen by playing marbles or billiards. The energy associated with that moving mass quadruples with each doubling of speed. It is four times greater at 110 km/h than at 55 km/h.
Every caravan/tow vehicle combination has a critical speed. This is the speed at which, subject to sufficient disturbing side force, the rig is liable to build up yaw forces that may not be correctable. Ongoing trials of show a clear relationship between weight and its location relative to the trailer axle that determines that ‘critical speed’. No caravan yaw inertia data exists for local product. Extrapolating known test data suggests the critical speed for long end-heavy ‘vans may be too close to Australian speed limits for comfort. The towing speed limit in the UK and Europe is typically 80 km/h.
Caravan dynamics – roll centre and roll axis
Were a push to applied at any point along the length of a moving trailer, there will a height at which (when pushed) the caravan will move or turn away from you without rolling. That point is called its roll centre. If the push is applied above the roll centre, its upper part will roll away from you. If pushed below that roll centre its upper part will roll toward you.
(In engineering terms, the axis location at any point along the trailer’s length, can be defined as that point where, in the median plane of the caravan, a transverse horizontal lateral force applied to the rolling mass of the caravan will cause that caravan to move or turn sideways without causing it to roll.)
This is best seen as a concept. There is nothing absolute about roll centre height. It will vary as suspension deflects etc. The concept however has major significance in stability.
Top, regardless of its springing (leaf, coil or airbag) a typically laden beam axle trailer rolls around and axis at roughly the high part of such springs. The moment arm here (leverage) due to the distance between the trailer’s centre of gravity and the roll centre is far less than that of the typical independently spring trailer (below).
Most independent suspension systems sway (rather than roll) around a point close to (or at) ground level (above centre). This introduces a considerable moment arm (lever action) that increases overturning forces. Further, because the front is constrained against sideways movement (i.e. it can only roll around its hitch) any roll results in a diagonal force that causes the trailer’s rear to yaw sideways (see also below).
The upper drawing shows how the roll axis of a long, (typical trailing arm independently sprung) caravan, becomes increasingly lower along its length. As can be seen it is well below ground level. The moment arm (overturning effect) at the extreme rear may exceed three metres. This illustrates how vital it is to have the axle/s well back, and to minimise rear end weight. In particular it illustrates the effect of locating spare wheels high up. The roll axis of a beam axled van (lower drawing) shows that the roll axis drops to a far lesser extent: there will thus be less roll. But it is still not a good idea to locate that spare wheel as shown. All pix are copyright: caravanandmotorhomebooks.com
A trailer is located by a tow ball typically well above ground level. Its front end can roll only around that raised tow ball. This is no problem for a beam axle trailer. That trailer’s suspension causes it to roll at much the same height – not that far below its centre of gravity. In normal going, caravans accommodate road irregularities by rolling around the tow ball enforced axis. The suspension barely deflects. This is why relatively firm short travel is effective.
There is little or no need for independent suspension on trailers (it is far from common on 4WDs rear axles). It enables the 100 mm or so otherwise needed vertical travel space of a beam axle to be used for water storage etc. It has no other real benefit. That it is wrongly seen as somehow ‘better’ is due almost entirely to a lack of high quality leaf spring suspension system. (If building one’s own, use the rear springs and shock absorbers of a post 2006 Hilux.
If independent suspension has to be used, it can be achieved by twin beam axles (used by Track Trailer), or via swing axles. These provide independent suspension whilst retaining the high roll centre of a single beam axle.
Softly sprung long travel suspension (with a typically low roll centre) on a lengthy caravan introduces a long Moment Arm particularly toward its rear. This substantially increases the risk of overturning if anything heavy is located on the caravan’s end wall – such as a tool box and/or spare wheel/s.
Car suspension is designed around human physiological constraints. These constraints do not apply to caravans. As AL-KO proves worldwide there is no need for long travel suspension for caravans.
Caravan dynamics – tyre behaviour
Pneumatic tyres do not behave as do solid tyres. Their behaviour is so complex that the main paper in this area is over 680 pages. Their nature can be seen by holding an inflated balloon firmly by its sides and pressed onto a hard surface. Rotating its sides slightly causes the balloon to distort and apply, via its side walls, a torque across the its elastic surface footprint. Were the balloon a steered wheel, the revolving distorted footprint would cause the vehicle to turn in a radius that is less than that of the distorted footprint. This difference is generally known (but misleadingly) as the slip angle.
The slip angle concept.
A pneumatic tyre does not exhibit Coulomb friction (where grip is a direct function of load). Increasing vertical loading increases cornering power but less (about 0.8) of that were it linear. This causes major issues when a vehicle is subject to pitching and yawing. This causes slip angles to vary accordingly. Pitching and yawing primarily affects the tow vehicle’s rear tyres. It introduces high speed steering irregularities. As slip angles increase, so does cornering force (but not linearly). Beyond a certain point all grip is lost and the tyre/s slide out of control.
Caravan dynamics – tow vehicle
The greater the weight of the tow vehicle, relative to the caravan, the better. This is becoming a major issue as tow vehicles become increasingly lighter. The laden tow vehicle should be at least as heavy as the laden caravan, ideally 30% or more greater.
Also important is minimal distance from centre line of tow vehicle rear axle to tow ball. The average (in Australia) is 1.25 metre from tow ball to centre line of the tow vehicle’s rear axle.
The tow hitch itself should have minimum length: some extend by an unnecessary and undesirable 100 mm or more. The further the tow ball is behind the vehicles axle, the greater the extent and severity of snaking. This overhang also reduces the critical speed where chaotic behaviour may (not necessary will) be triggered. It is no coincidence that many caravan accidents involved semi-laden dual cab tow vehicles with extensive rear overhang.
Caravan dynamics – speed
This is a vital factor. The higher a caravan’s 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. Ideally keep speed below 100 km/h (80 km/h is strongly recommended for long end-heavy caravans).
This problem mostly affects end-heavy caravans, particularly long ones. It can also affect shorter caravans towed at speed on motorways. Light caravans (sanely laden) up to a probable five metres are at less risk, particularly if centre kitchened.
Caravan dynamics – owner actions
Load caravans such that anything heavy (e.g. batteries, water tank/s, stored goods, and personal effects) is above or as close to the axle/s as possible. Do not even think about having washing machines, heavy toolboxes, spare wheels etc at the extreme rear.
Minor yawing at low speed should die of its own accord. If however it begins to yaw at or above the critical speed, it enters a situation of chaotic behaviour. It may not be recoverable by driver action. This is because doing so requires the driver to counteract (by steering) the existing and ongoing action. Such ongoing action cannot (by definition) be foreseeable. It is not literally random, but from a practicable perspective, is not dissimilar.
Requirements for caravan stability
As this is of greater general interest it is presented at a less technical level: see article Making Caravans Stable.
Caravan dynamics – conclusions
Vehicle stability has been reasonably well understood since the late 1930s, and refined thereon. Considerable research into the interactions between vehicles and trailers has been done by the US military (some during WW2). Most work on caravan dynamics began in the late 1970s. There are many published peer-reviewed papers (backed up by practical real-life testing) but most are hard to follow without a background in this area. The main leader in this is the UK University of Bath – and financed by Bailey Caravans.
The article is primarily a summary of current thinking in caravan dynamics. A great deal is predicated on the basic laws of motion set out originally in Newton’s Principia Mathematica and accepted as valid ever since in areas such as this. Apart from my views on a possible link between some soft long travel forms of independent suspension and overturning, the content of this article is thus not ‘just another opinion’.
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).
Dynamics of Towed Vehicles (Bath University) http://webby.natcoa.net/Caravan.pdf
Caravan & Tow Vehicle Dynamics: Collyn Rivers. http/caravanandmotorhomebooks/caravan-and-tow-vehicle-dynamics/ This is an ongoing work in progress – it is updated and expanded frequently.
Understanding the Dynamics of Towing: Simon P Barlow. www.caravanchronicles.com/guides/understanding-the-dynamics-of-towing/ This is a very readable approach primarily relating to UK/EU type caravans.
Development of Maximum Allowable Hitch Load Boundaries for Trailer Towing: Richard Klein and Henry Szostak, Society of Automotive Engineers, Inc (SAE 800157).
Quantitative Measure of Transient Oversteer of Road Vehicles: David Renfroe, Paul T Semones and Alex Roberts. Engineering Institute, LLC, USA. (Paper number 07-0217.)
Understanding Parameters Influencing Tire Modeling: Nicholas Smith, Colorado State University, 2004.
Tyre and Vehicle Dynamics: Hans Pacejka (2006). SAE International ISBN: 978 -0 7680 -1702-1.
Stability and Control Considerations of Vehicle-Trailer Combination: Aleksander Hac, Daniel Fulk and Hsien Chen, Delphi Corporation. SAE paper 2008-01-1228.
For graphics of pendulums and how they interact:
To see an actual caravan rollover:
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