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Turning an articulated truck on a spreadsheet

Author - Jim McGovern


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The challenge that is addressed by this paper came about in a very straightforward way. A technical colleague from the Irish Department of Transport asked the author how much clearance to the front and to the side would be required for an articulated truck to leave a testing lane and do a U-turn. This kind of information would typically be required where a new articulated-truck-testing lane was to be set up. A more general example of the same type of problem would involve checking whether a given articulated truck could negotiate a particular turn or roundabout. Articulated trucks come in a wide range of sizes and configurations, and it soon became apparent that even the identification of the worst-case scenario would require detailed consideration of a range of different cases. On the face of it, at least some aspects of the problem seemed suitable for solving by the use of a standard and ubiquitous spreadsheet application. The functionality of the spreadsheet that was developed is illustrated by a short video clip.

A Microsoft Excel spreadsheet workbook was developed that contained two worksheets: ‘Dimensions’ and ‘Paths’. The former allowed the dimensions of the articulated truck to be specified and displayed to scale in plan view. The latter allowed steering information to be inputted, and the loci of principal points on the tractor and trailer to be plotted to scale on a diagram. A simple animation of the movement of the articulated truck was also included on the Paths sheet.

Dimensional inputs

The defining dimensions for an articulated truck are shown in Table 1. For the most part these are self-explanatory, although the term ‘axle group’ needs a little explanation.Tractors commonly have either one or two rear axles. Multiple axles can carry a greater load. If the number of rear axles is more than one, there will be some tyre dragging whenever a tractor turns. Because of this, some tractor units have the facility to raise one of the rear axles when the tractor is lightly loaded. In terms of turning behaviour, a group of rear axles can be represented by an equivalent single axle halfway between the first and the last of the active axles in a rear axle group. The turning characteristics of a tractor depend on the distance between the front steering axle and the centre of the rear axle group; for example, raising the frontmost of two tractor rear axles will lengthen the effective wheelbase for turning purposes. Semi-trailers can have a single rear axle or a rear axle group consisting of two, three or occasionally four rear axles. One or more of these could possibly be raised at light load to reduce tyre wear. As in the case of the tractor unit, for turning analysis purposes the rear axle group of a semi-trailer can be represented by an equivalent single rear axle that would be in the middle of the group of rear axles that are in use.

The ‘maximum steering angle’ is the maximum angle between the inside steering axle wheel and the centre-line of the tractor. The steering axle wheel on the inside of a turn always makes a greater angle with the centre line of the tractor than the steering axle wheel on the outside of the turn, as can be seen in Figure 1. The greater the maximum steering angle, the shorter will be the centre line turning radius of the tractor. Another significant dimensional parameter is the ‘Steering axle width between contact centres’. This is the distance between the points where the king pin pivot axes of the steering axle intersect the road. It is approximately equal to the distance between the centres of the front tyre contact patches on the road. Table 2 lists truck dimensions that can be calculated from those listed in Table 1. These data were calculated automatically within the Dimensions sheet of the workbook by the use of the appropriate formulae.

The rear axle group of the tractor rotates about a turning centre as illustrated in Figure 1. The ‘minimum centre-line turning radius’ of the tractor is calculated from the tractor dimensions, including the maximum steering angle: it is the distance from the centre of the rear axle group to the current turning centre. The ‘minimum cab front corner turning radius’ is the distance from the outside front corner of the cab to the current turning centre.

The ‘trailer angle’ describes the angular relationship between the tractor and the semi-trailer: it is zero when the trailer is straight in line with the tractor. Figure 2 and Figure 3 illustrate different angular positions of the trailer. These diagrams were in fact XY scatter plots of data generated from the input dimensions and the trailer angle. The diagrams updated automatically when any of the input data changed. If any changes were made to the X- or Y-scales it would have been necessary to use the drag handles of this graph to ensure that the grid boxes remained square. The main reference locations of the articulated truck were also identified in these figures. The origin of the articulated truck was taken to be the centre of the rear axle group of the tractor.