IMPROVEMENTS IN RAIL WAGON AND ROAD TRAILER ARRANGEMENTS

Field of the Invention

The present invention relates to improvements in rail wagon and road trailer arrangements.

The invention has been primarily developed for use with railway wagons and cars and medium to heavy road freight vehicles and will be described hereinafter with reference to these applications.

Background of the Invention

Railway wagons and road trailers both utilise axles supported by wheels. The axles are mounted to a frame of the wagon/trailer by a device known as a bogey.

A disadvantage of the bogeys used in known railway wagons is that they do not radially align the wheel axles to the railway track when the wagon is negotiating a curve. The primary disadvantage of this non-radial alignment of the wheels is wear of both the wheels and the rail. Additionally, the increase in friction between the wagon and the tracks can often lead to grades being required to be lessened at curves (known as compensation) to enable a reasonably constant resistance to the locomotive's tractive effort to be maintained.

Bogeys used in known road vehicles suffer from similar alignment problems, in which non-radial axle alignment to the curve of the road results in a high degree of tyre scrub during the passage of curves. This leads to higher rates of wear. Another disadvantage of known arrangements is that the bogey fixed to the trailer at its rear-end must turn through a reduced radius compared to that followed by the prime mover. This results in drivers having to deliberately outwardly swing a prime mover wide during such curves to compensate for the tendency of the trailer bogey to track through a smaller radius, which can lead to the trailer bogey mounting footpaths and/or entering neighbouring traffic lanes. Additionally, during slippage or jack-knifing of a trailer, the bogey wheels have a greatly reduced ability to assist in steering the trailer back to its correct alignment.

Object of the Invention

It is the object of the present invention to substantially overcome or at least ameliorate one or more of the above disadvantages.

Summary of the Invention Accordingly, in a first aspect, the present invention provides a bogey for a rail wagon or road trailer having a longitudinal axis, said bogey comprising: a bogey frame; a first axle group connected to the bogey frame, the first axle group having at least one first axle supporting a first pair of wheels; a second axle group connected to the leading bogey frame, the second axle group having at least one second axle supporting a second pair of wheels; the first and second axle groups being hingedly connected to allow relative lateral rotation therebetween about a first pivot located substantially midway between the first axle group and the second axle group; engagement means for pivo tally connecting the bogey to the rail wagon or road trailer at a second pivot offset from the first pivot, by a predetermined distance, toward one of said first and second axle groups; and first link means operable between the bogey frame and the first pivot and adapted to bias the first pivot toward the longitudinal axis.

Preferably, the predetermined distance is dependent upon geometric parameters of the bogey and rail wagon or of the bogey and road trailer.

In a second aspect, the present invention provides a rail wagon arrangement, the arrangement comprising: a wagon frame having a leading end, a trailing end and a longitudinal axis; a leading bogey comprising: a leading bogey frame; a. leading outboard axle group connected to the leading bogey frame, the leading outboard axle group having at least one outboard axle supporting a leading outboard pair of wheels; a leading inboard axle group connected to the leading bogey frame, the leading inboard axle group having at least one inboard axle supporting a leading inboard pair of wheels;

the leading outboard and inboard axle groups being hingedly connected to allow relative lateral rotation therebetween about a first pivot located substantially midway between the leading outboard axle group and the leading inboard axle group; a trailing bogey comprising: 5 a trailing bogey frame; a trailing outboard axle group connected to the trailing bogey frame, the trailing outboard axle group having at least one outboard axle supporting a trailing outboard pair of wheels; a trailing inboard axle group connected to the trailing bogey frame, the Q trailing inboard axle group having at least one inboard axle supporting a trailing inboard pair of wheels; the trailing outboard and inboard axle groups being hingedly connected to allow relative lateral rotation therebetween about a second pivot located substantially midway between the trailing outboard axle group and the trailing inboard axle group; s the leading end of the wagon frame being pivotally connected to the leading bogey at a third pivot located inboard, with respect to the wagon frame, of the first pivot; the trailing end of the wagon frame being pivotally connected to the trailing bogey at a fourth pivot located inboard, with respect to the wagon frame, of the second pivot; Q first link means operable between the wagon frame or the leading bogey frame and the first pivot and adapted to bias the first pivot toward the longitudinal axis; and second link means operable between the wagon frame or the trailing bogey frame and the second pivot and adapted to bias the second pivot toward the longitudinal axis.

₅ Preferably, the wagon arrangement is configured to satisfy the following relationship: 0.75 x W ² /D <G <1.25 x W ² /D wherein:

D = half of the distance between the first pivot and the second pivot, measured along the longitudinal axis; 0 W = the distance between the longitudinal centre of the axles comprising the leading outboard axle group and the first pivot, measured perpendicular to the rotational axes of the axles comprising the leading outboard axle group, which is substantially equal to the distance between the longitudinal centre of the axles comprising the trailing outboard axle group and the second pivot, measured perpendicular to the rotational axes ₅ of the axles comprising the trailing outboard axle group; and

- A -

G = the distance between the first and third pivots, which is substantially equal to the distance between the second and fourth pivots.

Preferably, the distance G falls within the range 0.9 x W ² /D <G ≤l.l. x W ² ZD. More preferably, the distance G is substantially equal to W ² ZD.

Preferably, the first and second link means maintain the respective first and second pivots substantially on the longitudinal axis. More preferably, the first, second, third and fourth pivots are substantially aligned on the longitudinal axis.

Preferably, the link means of the leading bogey takes the form of a leading outboard pin fixedly connected at one end relative to the leading end of the wagon frame and hingedly connected at its other end to the sub-bogeys at the first pivot. More preferably, the link means of the trailing bogey takes the form of a trailing outboard pin fixedly connected at one end relative to the trailing end of the wagon frame and hingedly connected at its other end to the sub-bogeys at the second pivot.

Preferably, the leading bogey includes a leading steering beam hingedly connected at one end relative to the leading outboard axle and hingedly connected at its opposite end relative to the leading inboard axle. More preferably, the trailing bogey also includes a trailing steering beam hingedly connected at one end relative to the trailing outboard axle and hingedly connected at its opposite end relative to the trailing inboard axle. In a preferred form, when the wagon arrangement traverses a curve, the steering beams are adapted to rotationally bias the axles of the respective bogeys toward radial alignment with the curve.

Preferably, the leading end of the wagon frame is pivotally connected, at the first pivot, relative to the axles of the leading bogey and pivotally connected to the steering beam of the leading bogey at the third pivot. More preferably, the trailing end of the wagon frame is pivotally connected, at the second pivot, relative to the axles of the trailing bogey and pivotally connected to the steering beam of the trailing bogey at the fourth pivot.

Preferably, the outboard and inboard axles of the leading bogey are mounted to respective outboard and inboard leading sub-bogey frames. More preferably, the leading sub-bogey frames are hingedly interconnected. Even more preferably, the leading steering beam is

hingedly connected at its outboard end to the outboard sub-bogey frame and at its inboard end to the inboard sub-bogey frame. In a preferred form, a steering link extends between the ends of the steering beam and the respective sub-bogey frame. Preferably, a spherical joint is provided between the steering link and the steering beam, as well as between the steering link and the respective sub-bogey frame.

Preferably, the outboard and inboard axles of the trailing bogey are mounted to respective outboard and inboard trailing sub-bogey frames. More preferably, the trailing sub-bogey frames are hingedly interconnected. Even more preferably, the trailing steering beam is hingedly connected at its outboard end to the outboard sub-bogey frame and at its inboard end to the inboard sub-bogey frame, hi a preferred form, a steering link extends between the ends of the trailing steering beam and the inboard and outboard sub-bogey frames. Preferably, a spherical joint is provided between the steering link and the trailing steering beam, as well as between the steering link and the respective sub-bogey frame.

In some preferred embodiments, the outboard and/or inboard axle groups of the bogeys comprise two or more axles.

In a third aspect, the present invention provides a road trailer arrangement for a prime mover having at least a front axle, as well as a rear axle group comprising at least one axle, each said axle supporting a pair of wheels, the trailer arrangement comprising: a trailer frame having a leading end, a trailing end and a longitudinal axis; the trailer frame being adapted for mounting to the prime mover by a first pivot near the frame leading end; a trailing bogey comprising: a trailing bogey frame; a trailing outboard axle group connected to the trailing bogey frame, the trailing outboard axle group having at least one outboard axle supporting a trailing outboard pair of wheels; a trailing inboard axle group having at least one inboard axle supporting a trailing inboard pair of wheels; the trailing outboard and inboard axle groups being hingedly cqnnected to allow relative lateral rotation therebetween about a second pivot located midway between the trailing outboard axle group and the trailing inboard axle group;

the trailing end of the trailer frame being pivotally connected to the trailing bogey at a third pivot located inboard, with respect to the trailer frame, of the second pivot; and link means operable between the trailer frame or the trailing bogey frame and the second pivot and adapted to bias the second pivot toward the longitudinal axis.

Preferably the trailer arrangement is configured to satisfy the following relationship:

0.75 x 2W ² L/(W ² +L ² - δ ² ) <G ≤1.25 x 2W ² L/(W ² +L ² - δ ² ) wherein: δ = the distance between the first pivot and a longitudinal centre of the rear axle group of the prime mover, measured perpendicular to the rotational axes of the axles of the rear axle group;

L = the distance between the first and second pivots, measured along the longitudinal axis; W = the distance between the longitudinal centre of the axles comprising the trailing outboard axle group and the second pivot, measured perpendicular to the rotational axes of the axles comprising the trailing outboard axle group; and

G = the distance between the second and third pivots.

Preferably, the distance G falls within the range 0.9 x 2W ² L/(W ² +L ² -δ ² ) <G r≤ l.l x 2W ² L/(W ² +L ² -δ ² ). More preferably, the distance G is substantially equal to

2W ² L/(W ² +L ² -δ ² ).

Preferably, the link means maintains the second pivot substantially on the longitudinal axis. More preferably, the first, second and third pivots are substantially aligned on the longitudinal axis. In a preferred form, the link means is an actuator connected at one end relative to the trailing bogey frame and at its opposite end to the sub-bogey frames at the second pivot.

Preferably, the bogey includes a steering beam hingedly connected at one end relative to the outboard axle and hingedly connected at its opposite end relative to the inboard axle. In a preferred form, when the trailer arrangement traverses a curve, the steering beam is adapted to rotationally bias the bogey axles toward radial alignment with the curve. Preferably, the trailing end of the trailer frame is pivotally connected to the steering beam

at the third pivot. In a preferred form, the actuator is connected at one end to the steering beam and at its opposite end to the sub-bogey frames at the second pivot.

Preferably, the outboard and inboard axles of the bogey are mounted to respective outboard and inboard sub-bogey frames. More preferably, the sub-bόgey frames are hingedly interconnected. Even more preferably, the steering beam is connected at its outboard end to the outboard sub-bogey frame and at its inboard end to the inboard sub- bogey frame.

In some embodiments, the rear axle group comprises a single axle and in other embodiments the rear axle group comprises two or more axles. Also, in some embodiments, the outboard and/or inboard axle group of the trailing bogey comprises two or more axles.

Brief Description of the Drawings

Preferred embodiments of the present invention will now be described, by way of examples only, with reference to the accompanying drawings in which:

Figure IA is a schematic plan view of a preferred embodiment of a rail wagon arrangement according to a first aspect of the invention;

Figure IB is a schematic side view of the rail wagon arrangement of Figure 1;

Figure 2 is a side view of a bogey for use in the arrangement of Figure 1 ;

Figure 3 is a plan view of the bogey of Figure 2, shown on a section of straight track;

Figure 4 is a plan view of the bogey of Figure 3, shown on a 100m curve; Figures 5 A and 5B show simplified side and plan views of a preferred embodiment of a rail wagon arrangement according to the invention;

Figures 6A and 6B are schematic side and plan views of a preferred embodiment of a road trailer arrangement according to a second aspect of the invention;

Figure 7 is a schematic plan view of a preferred embodiment of a road trailer arrangement according to the invention, shown on an exaggerated road curve;

Figure 8 is an enlarged view of the circled portion of Figure 7; and

Figure 9 is a schematic illustration of a preferred embodiment of a road trailer arrangement according to the invention, shown traversing a curve.

Detailed Description of the Preferred Embodiments

Rail Wagon

Figures 1 to 5 illustrate a rail wagon arrangement 10 comprising a wagon frame 20 having a leading end 201, a trailing end 202 and a longitudinal axis 203. Leading outboard 204 and inboard 205 pins are provided at the leading end 201 of the wagon frame 20 and trailing outboard 206 and inboard 207 pins are provided at the trailing end 202 of the wagon frame 20. The leading and trailing outboard and inboard pins 204, 205, 206 and 207 are all aligned on the longitudinal axis 203 of the wagon frame 20. A leading bogey 30 supports the leading end 201 of the wagon frame 20 and a trailing bogey 40 supports the trailing end 202 of the frame 20.

The leading 30 and trailing 40 bogeys are substantially identical, such that the wagon arrangement 10 is substantially symmetrical about a vertical plane taken through its longitudinal midpoint. Accordingly, the leading and trailing bogeys are both described with reference to Figures 2 to 4.

The leading bogey 30 comprises an outboard sub-bogey 301 and an inboard sub-bogey 302. Each sub-bogey 301, 302 includes an axle group having at least one axle, respectively 303 and 304, supporting a pair of wheels 305. The outboard 301 and inboard 302 sub-bogeys are hingedly connected to allow relative lateral rotation therebetween about a first pivot 306 located substantially midway between the outboard 303 and inboard 304 axle groups. The leading bogey 30 is pivotally connected to the leading end 201 of the wagon frame 20, via the leading inboard pin 205, at a third pivot ^' 307 located inboard, with respect to the wagon frame 20, of the first pivot 306. The outboard 301 and inboard 302 sub-bogeys of the leading bogey 30 are pivotally connected to the wagon frame 20, as well as to each other, via the leading outboard pin 204, which defines the first pivot 306.

A leading steering beam 308 and associated steering links 309 are operable between the outboard 301 and inboard 302 sub-bogeys. The leading steering beam 308 is hingedly connected at one end 310, via a steering link 309, to the outboard sub-bogey 301 and at its opposite end 311, also via a steering link 309, to the inboard sub-bogey 302. Spherical joints 312 are provided between the steering links 309 and the respective ends of the

steering beam 308, as well as between the steering links 309 and the respective sub-bogey 301, 302.

The trailing bogey 40 comprises an outboard sub-bogey 401 and an inboard sub-bogey 402. Each sub-bogey 401, 402 includes an axle group having at least one axle, respectively 403 and 404, supporting a pair of wheels 405. The outboard 401 and inboard 402 sub-bogeys are hingedly connected to allow relative lateral rotation therebetween about a second pivot 406 located substantially midway between the outboard 403 and inboard 404 axle groups. The trailing bogey 40 is pivotally connected to the trailing end 202 of the wagon frame 20, via the trailing inboard pin 207, at a fourth pivot 407 located inboard, with respect to the wagon frame 20, of the second pivot 406. The outboard 401 and inboard 402 sub-bogeys of the trailing bogey 40 are pivotally connected to the wagon frame 20, as well as to each other, via the trailing outboard pin 206, which defines the second pivot 406.

A trailing steering beam 408 and associated steering links 409 are operable between the outboard 401 and inboard 402 sub-bόgeys. The trailing steering beam 408 is hingedly connected at one end 410, via a steering link 409, to the outboard sub-bogey 401 and at its opposite end 411, also via a steering link 409, to the inboard sub-bogey 402. Spherical joints 412 are provided between the steering links 409 and the respective ends of the steering beam 408, as well as between the steering links 409 and the respective, sub-bogey 401, 402.

As the wagon arrangement 10 traverses a curve, the steering beams 308, 408 rotate in a generally horizontal plane, as can be seen by comparing Figures 3 and 4. This rotation of the steering beams 308, 408 causes in turn a corresponding rotational realignment of the outboard 303, 403 and inboard 304, 404 axles onto a radius of the curve. It will be appreciated that the rotational realignment of the outboard axles 303, 403 is greater than that of the inboard axles 304, 404 as a result of the larger lever arm between the third 307 and fourth 407 pivots and the respective outboard axles 303, 403.

The improved radial alignment of the bogey axles 303, 304, 403, 404 ensures that the flanks of the flanges of the bogey wheels never meet the rail head, except in very severe cases of over-speed on curves. According, the probability of derailment is reduced, as is the rate of wheel and rail wear. A reduction in fuel consumption also results from the

abovementioned advantages, and from this, result substantial ecological benefits. The improvements may also render the use of flange lubricators unnecessary, thereby reducing rail system operating costs.

The bogeys 30, 40 utilise a conventional suspension system. The suspension system is arranged in such a way as not to hinder movement of the sub-bogeys 301, 302 and 401, 402 relative to one another.

In use, during the traversing of a curve, the axles 303, 304, 403, 404 of the leading 30 and trailing 40 bogeys present substantially radially, or at least closer to radial than is the case in prior art wagon arrangements, to the curve if the wagon arrangement 10 is configured such that the following relationship is satisfied:

0.75 x W ² /D ≤G <1.25 x W ² /D

where:

D = half of the distance between the first pivot 306 and the second 406 pivot, measured along the longitudinal axis 203;

W = the distance between the longitudinal centre of the axles 303 comprising the leading outboard axle group and the first pivot 306, measured perpendicular to the rotational axes of the axles 303 comprising the leading outboard axle group (also equal to the distance between the longitudinal centre of the axles 403 comprising the trailing outboard axle group and the second pivot 406, measured perpendicular to the rotational axes of the axles 403 comprising the trailing outboard axle group); and G = the distance between the first 306 and third 307 pivots (also equal to the distance between the second 406 and fourth 407 pivots).

The geometrical basis of the above relationship is explained below.

In the embodiment shown in the drawings, the distance W is simply the distance between the midpoints of the outboard 303, 403 and inboard 304, 404 axles of each bogey 30, 40 and the respective pivot (i.e. the first pivot 306 in the case of the leading bogey 30 and the second pivot 406 in the case of the trailing bogey 40). However, in embodiments (not shown) where the sub-bogeys 301, 302, 401, 402 have multiple axles, the distance W is the distance between the centroid of the multiple axles of each sub-bogey 301, 302, 401,

402 and the relevant pivot (i.e. the first pivot 306 in the case of the leading bogey 30 and the second pivot 406 in the case of the trailing bogey 40), measured perpendicular to the rotational axes of the axles.

5 In other embodiments, where the geometry of the rail wagon arrangement 10 differs from that shown in the drawings, appropriate adaptations must be made to the above formula, as would be understood by those skilled in the art.

The improvement in terms of radial disposition of the bogey axles 303, 304, 403, 404 io increases as G tends toward W ² /D. Accordingly, it is preferred that G be set as close as practically possible to W ² /D.

The geometrical basis for the optimised value of G is provided below, with reference to Figures 5A and 5B, where the leading bogey 30 is shown traversing a curved section of i ₅ rail 100 having a centre-line 101:

The Point K corresponds to the first pivot 306. The Point J corresponds to the third pivot 307. Points P and S are the midpoints of the respective inboard 304 and outboard 303 axles. The Point T is the midpoint of the line PS. The Point V is the longitudinal 0 midpoint of the wagon frame 20. The Point N is the centre of the rail curve. B is the distance between N and K. H is the distance between the steering beam 308, 408 and K, measured perpendicular to the axis of the steering beam 308, 408.

It will be appreciated that triangles PNK and KPT are similar right-angled triangles. ₅ Accordingly, Angles PNK and KPT are equal, as they are corresponding angles of similar right-angled triangles PNK and KPT. Also, B/W equals W/H (ratios of corresponding sides of similar triangles).

Triangles VKN and JKT are also similar. Accordingly, B/D equals G/H (ratios of 0 corresponding sides of similar triangles).

However, if B/D = G/H, then G = BH/D Expression 1

Likewise, if B/W = W/H, then B = W ² /H Expression 2 5

Accordingly, substituting W ² /H for B in Expression 1 results in: G= [W ² /H]H/D

= W ² /D

5 Road Trailer

Figures 6A and 6B illustrate a road trailer arrangement 50 comprising a trailer frame 60 having a leading end 601, a trailing end 602 and a longitudinal axis 603. A leading pin 604 is provided at the leading end 601 of the trailer frame 60 and a trailing pin 605 is provided at the trailing end 602 of the frame 60. The leading 604 and trailing 605 pins o are aligned on the longitudinal axis 603 of the trailer frame 60. The leading end 601 of the trailer frame 60 is adapted for connection, via the leading pin 604, to a prime mover 70, about a first pivot 701. The prime mover 70 has at least a front axle 702, as well as a rear axle group comprising at least one axle 703, with each axle supporting a pair of wheels 704. In the illustrated embodiment, the rear axle group includes a single drive s axle 703. The trailing end 602 of the trailer frame 60 is adapted for connection, via the trailing pin 605, to a trailing bogey 80.

The trailing bogey 80 comprises an outboard sub-bogey 801 and an inboard sub-bogey 802. Each sub-bogey 801, 802 includes an axle group having at least one axle, o respectively 803 and 804, supporting a pair of wheels 805. The outboard 801 and inboard 802 sub-bogeys are hingedly connected to allow relative lateral rotation therebetween about a second pivot 806 located substantially midway between the outboard 803 and inboard 804 axle groups.

s As shown in Figures 7 and 8, the bogey 80 also includes a steering beam 807 hingedly connected at one end 808 to the outboard sub-bogey 801 and hingedly connected at its opposite end 809 to the inboard sub-bogey 802. The trailing end 602 of the trailer frame 60 is pivotally connected to the steering beam 807 via the trailing pin 605, at a third pivot 810 located inboard, with respect to the trailer frame 60, of the second pivot 806. 0

As shown in Figure 7, an actuator 811 is operable between the steering beam 807 and the second pivot 806 to maintain the second pivot 806 substantially on the longitudinal axis 603 of the trailer frame 60. When the trailer arrangement 50 traverses a curve, the actuator 811 is adapted to rotationally bias the sub-bogeys 801, 802 relative to- one ₅ another, such that the bogey axles 803, 804 move substantially into radial alignment with

the curve. Also, in situations where the trailer arrangement 50 moves into an abnormal configuration, such as during jack-knifing, the actuator 811 restores the second pivot 806 into alignment with the longitudinal axis 603 to restore stability to the trailer arrangement 50.

The actuator 811 is controlled by a controller (not shown), based on the real-time geometry of the trailer arrangement 50. For example, in some embodiments, the controller actuates the actuator 811 based on the plan view rotational movement/orientation of the prime mover 70 relative to the trailer frame 60. The controller operates the actuator 811 only at relatively low speeds and/or during severe curvature. In high speed and low curvature scenarios, such as on highways, the bogey 80 is locked into a rigid unit.

The improved radial alignment of the bogey axles 803, 804 results in the elimination, or at least reduction, of tyre scrub when traversing curves. This in turn reduces wear and fatigue of associated equipment, such as axles, bearings and suspension mountings. • The reduction of tyre scrub also reduc'es wheel rolling resistance during cornering, with a complementary increase in fuel economy. Reducing tyre scrub also serves to reduce the quantity of airborne rubber particles surrounding highways, and therefore provides a health and ecological benefit.

The improved radial alignment of the bogey axles also causes the bogey axles to track more closely to the locus of the prime mover drive axles when traversing curves, thus reducing "inswing" of the trailer frame during cornering. This improved tracking is illustrated in Figure 9, where reference numeral 900 indicates the locus of the prime mover drive axles, 901 indicates the locus of a preferred embodiment of a trailing bogey according to the invention and 903 indicates the locus of a prior art bogey. Reference numeral 904 indicates the locus of the outer nose of the prime mover and reference numeral 905 indicates the locus of the inside edge of the trailer frame when utilising a prior art trailing bogey.

The bogey 80 utilises a conventional suspension system (not shown). The suspension is arranged in such a way as not to hinder movement of the sub-bogeys 801, 802 relative to one another.

In use, during the traversing of a curve, the axles 803, 804 of the trailing bogey 80 present substantially radially, or at least closer to radial than is the case in prior art trailer arrangements, if the trailer arrangement 50 is configured such that the following relationship is satisfied:

0.75 x 2W ² L/(W ² +L ² - δ ² ) ≤G <1.25 x 2W ² L/(W ² +L ² - δ ² )

where:

δ = the distance between the first pivot 701 and a longitudinal centre of the axles 703 of the rear axle group of the prime mover 70, measured perpendicular to the rotational axes of the axles 703 of the rear axle group;

L = the distance between the first 701 and second 806 pivots, measured along the longitudinal axis 603;

W = the distance between the longitudinal centre of the axles 803 comprising the trailing outboard axle group and the second pivot 806, measured perpendicular to the rotational axes of the axles 803 comprising the trailing outboard axle group (also equal to the distance between the longitudinal centre of the axles 804 comprising the trailing inboard axle group and the second pivot 806, measured perpendicular to the rotational axes of the axles 804 comprising the trailing inboard axle group); and G = the distance between the second 806 and third 810 pivots.

In the embodiment shown in the drawings, the distance W is simply the distance between the midpoints of the outboard 803 and inboard 804 axles of the trailing bogey 80 and the second pivot 806. However, in embodiments (not shown) where the sub-bogeys 801, 802 have multiple axles, the distance W is the distance between the centroid of the multiple axles of each sub-bogey 801, 802 and the second pivot 806, measured perpendicular to the rotational axes of the axles.

Another variable between different embodiments is the _. number of axles 703 in the rear axle group of the prime mover 70. In some embodiments, such as that shown in Figures 5 and 6, the rear axle group comprises a single axle 703. In these embodiments, the distance δ is simply the distance between the midpoint of the rear axle 703 and the first pivot 701. However, in other embodiments (not shown) the rear axle group comprises two or more axles. In these other embodiments, the distance δ is the distance between the

longitudinal centre of the group of axles and the first pivot 701,. measured perpendicular to the rotational axes of the rear axles.

In other embodiments where the geometry of the road trailer arrangement 50 differs from 5 that shown in the drawings, appropriate adaptations must be made to the above formula, as would be understood by those skilled in the art.

The improvement in terms of radial disposition of the bogey axles 803, 804 increases as G tends toward 2W ² L/(W ² +L ² - δ ² ). Accordingly, it is preferred that G be set as close as

10 practically possible to 2W ² L/(W ² +L ² - δ ² ).

The geometrical basis for the optimised value of G is provided below with reference to Figures 7 and 8, where the trailer arrangement 50 is shown traversing a curved section of road 900 having a centre-line 901:

I ₅

The Point Z corresponds to the first pivot 701. The Point K corresponds to the second pivot 806. The Point J corresponds to the third pivot 810. Points P and S are the midpoints of the respective inboard 804 and outboard 803 axles. The Point T is the

^• midpoint of the line PS. The Point V is the point on the trailer frame 60 where a line o drawn perpendicular to the trailer frame 60 passes through the centre of the road curve. The Point N is the centre of the road curve. B is the distance from N to K. R is the radius of the road curve. E is the distance from N to V. L is the distance between the first 701 and second 806 pivots. D is the distance between K (806) and V. A is the distance between Z (701) and V. C is the distance between N and Z (701). δ is the distance ₅ between the longitudinal centre of the axles 703 comprising the rear axle group of the prime mover and the first pivot 701, measured perpendicular to the rotational axes of the axles 703 comprising the rear axle group. H is the distance between the steering beam 807 and K (806), measured perpendicular to the axis of the steering beam 807.

0 It will be appreciated that triangles PNK and KPT are similar triangles. Accordingly, Angles PNK and KPT are equal, as they are corresponding angles of similar triangles PNK and KPT. Also, B/W equals W/H (ratios of corresponding sides of similar triangles).

Triangles VKN and JKT are also similar. Accordingly, B/D equals G/H (ratios of corresponding sides of similar triangles).

However, if B/D = G/H, then G = BH/D Expression 1

5

Likewise, if B/W = WZH, then B = W ² /H Expression 2

Accordingly, substituting W ² /H for B in Expression 1 results in:

G= [W ² /H]H/D o = W ² /D Expression 3

Also, C ² = A ² + E ² , and therefore E ² = C ² - A ² and B ² = D ² + E ² , and therefore E ² = B ² - D ^{2 ■ Accordingly, it follows that C 2 - A 2 = B 2 - D 2 s and therefore that D 2 = B 2 + A 2 - C 2 Expression 4}

However, L = A + D, and therefore A = L - D Expression 5

Accordingly, substituting L-D for A in Expression 4 results in: o D ² = B ² + [L ² - 2LD + D ² ] -C ²

And therefore it follows that D = (B ² + L ² - C ² )/(2L) Expression 6

But, B ² = W ² + R ² Expression 7 and C ² = R ² + δ ² Expression 8 5

Accordingly, substituting Expressions 7 and 8 into Expression 6 results in: D - {[W ² + R ² ] + L ² - [R ² + δ ² ]}/(2L) _. - (W ² + L ² - δ ² )/(2L) Expression 9

0 And, substituting Expression 9 into Expression 3 results in:

G - W ² /[(W ² + L ² - δ ² )/(2L)] = 2W ² L/(W ² + L ² - δ ² )

Although the invention has been, described with reference to the preferred embodiments, it will be appreciated by those persons skilled in the art that the invention may be embodied in many other forms.