ROAD DESIGN ELEMENTS
4.2 HORIZONTAL ALIGNMENT
4.2.6 Lane widening
When vehicles negotiate a horizontal curve, the rear wheels track inside the front wheels. In the case of semi trailers with multiple axles and pivot points, this off-tracking is particularly marked. The track width of a turning vehicle, also known as the swept path width, is the sum of the track width on tangent and the extent of off-tracking, with the off-tracking being a func-tion of the radius of the turn, the number and location of pivot points and the length of the wheelbase between axles. The track width is calculated as
U = u + R - (R2- ΣLi2)0,5 (4.15) where U = track width on curve (m)
u = track width on tangent (m)
R = radius of turn (m)
Li = wheel base of design vehicle between suc-cessive axles and pivot
Strictly speaking, the radius, R, should be the radius of the path of the midpoint of the front axle. For ease of calculation, however, the radius assumed is that of the road centreline.
The front overhang is the distance from the front axle of the vehicle to the furthest projection of the vehicle body in front of the front axle. In the case of the turning vehicle, the width of the front overhang is defined as the radial distance between the path followed by the outer front edge of the vehicle and the tyre path of the outer front wheel. The width of the front overhang is calculated as
FA = [R2+ A(2L + A)]0,5- R (4.16)
where FA = width of front overhang (m)
R = radius of curve (m)
A = front overhang (m)
L = wheel base of single unit or tractor (m)
The width of the rear overhang is the radial dis-tance between the outside edge of the inner rearmost tyre and the inside edge of the vehicle body. In the case of a passenger car this
dis-tance is typically less than 0,15 m. The width of truck bodies is usually the same as the wheel-base width so that the width of the rear over-hang is zero.
A typical turning path is illustrated in Figure 4.6.
Turning paths for numerous vehicles are provid-ed in the 2000 provid-edition of the AASHTO Policy on geometric design of highways and streets and the designer is directed towards Exhibits 2-3 to 2-23 of that document.
It is necessary to provide an allowance, C, for lateral clearance between the edge of the road-way and the nearest wheel path, and for the body clearance between passing vehicles.
Typical values of C are:
•
0,60 m for a travelled way width of 6,0 m;•
0,75m for a travelled way width of 6,6 m, and•
0,90 m for a travelled way width of 7,4 m.A further allowance, Z, is provided to accommo-date the difficulty of manoeuvring on a curve and the variation in driver operation. This addi-tional width is an empirical value that varies with the speed of traffic and the radius of the curve.
It is expressed as
Z = 0,1(V/R0,5) (4.17)
where V = design speed of the road (km/h)
By combining Eqs 4.12, 4.13 and 4.14 with the clearance allowances, C and Z, the width of the travelled way can be calculated as
WC = N (U + C) + FA(N - 1) + Z (4.18)
where N = number of lanes
and the other variables are as previously defined.
As a general rule, values of curve widening, being (WC- W) where W is the width of the trav-elled way on tangent sections, that are less than 0,6 m are disregarded. Lane widening is thus generally not applied to curves with a radius greater than 300 metres, regardless of the design speed or the lane width.
Widening should transition gradually on the approaches to the curve so that the full addi-tional width is available at the start of the curve.
Although a long transition is desirable to ensure that the whole of the travelled way is fully usable, this results in narrow pavement slivers that are difficult, and correspondingly expen-sive, to construct. In practice, curve widening is thus applied over no more than the length of the super elevation runoff preceding the curve. For ease of construction, the widening is normally applied only on one side of the road. This is usually on the inside of the curve to match the tendency for drivers to cut the inside edge of the travelled way.
In terms of usefulness and aesthetics, a tangent transition edge should be avoided. A smooth graceful curve is the preferred option and can be adequately achieved by staking a curved transition by eye. Whichever approach is used, the transition ends should avoid an angular break at the pavement edge.
Widening is provided to make driving on a curve comparable with that on a tangent. On older roads with narrow cross-sections and low design speeds and hence sharp curves, there was a considerable need for widening on curves. Because of the inconvenience attached to widening the surfacing of a lane, it follows that the required widening may not always have been provided. Where a road has to be rehabil-itated and it is not possible to increase the radius of curvature, the designer should consid-er the need for curve widening.
In the case of an alignment where curves in need of widening of the travelled way follow each other in quick succession, the inconven-ience associated with the application of curve widening can be avoided by constructing the entire section of road, including the intervening tangents, to the additional width.