Human Robot Interaction

TRANSIT NEW ZEALAND HEAVY VEHICLE LIMITS PROJECT

Report 5

GEOMETRIC EVALUATION Excluding Appendices A-O

July 2001

Transit New Zealand Heavy Vehicle Limits Project

Page 2 of 38

An Important Note for the Reader The investigations which are detailed in this report were commissioned by Transit New Zealand. While this report is believed to be correct at the time of publication, Transit New Zealand, and its employees and agents involved in the preparation and publication, cannot accept any contractual, tortious or other liability for its content or for any consequences arising from its use and make no warranties or representations of any kind whatsoever in relation to any of its contents. The report is only made available on the basis that all users of it, whether direct of indirect, must take appropriate legal or other expert advice in relation to their own circumstances and must rely solely on their own judgement and seek their own legal or other expert legal advice in relation to the use of this report. The material contained in this report is the output of research and should not be construed in any way as policy adopted by Transit New Zealand but may form the basis of future policy. ISBN 0-478-04710-X © 2001. Transit New Zealand PO Box 5084, Lambton Quay, Wellington, New Zealand Telephone 64–4–499 6600; Facsimile 64–4–496 6666 Transit New Zealand Heavy Vehicle Limits Project. Report 5. Geometric Evaluation.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 3 of 38

Foreword This report is one of a series of seven that cover the latest investigation of the feasibility of changing the mass and dimensions of heavy vehicles on New Zealand’s roading system. Transit New Zealand (Transit) has long recognised the importance of the roading network to New Zealand’s economy, and the desire amongst the transport and export industry sectors for increased productivity. To this end Transit has supported investigations since 1992 of the potential benefits of raising weight limits. Previous studies lead Transit to the conclusion that is was not feasible to upgrade the whole road network to accommodate substantially longer heavier vehicles. Accordingly in 1998 Transit commenced the current study with the purpose of considering two new scenarios. We are grateful to Transfund New Zealand for the provision of funding for the investigations. These project reports represent the culmination of two years’ work by a group of consultants both here and in Australia. These are listed below: Transport Engineering Research NZ Ltd, Auckland Infratech Systems and Services Pty Ltd, Brisbane Roaduser International Pty Ltd, Melbourne Saturn Corporate Resources Pty Ltd, Melbourne Montgomery Watson NZ Ltd, Christchurch ARRB Transport Research Limited, Melbourne Commed Associates, Melbourne Opus International Consultants Limited, Wellington Pearsons Transport Resource Centre Pty Ltd, Melbourne Transit is grateful to the members of the project steering group who have provided expert guidance and comment on behalf of the following organisations: Land Transport Safety Authority of New Zealand Transfund New Zealand Ministry of Transport Road Transport Forum New Zealand Bus and Coach Association New Zealand Local Government New Zealand.

Robin Dunlop Chief Executive

Transit New Zealand Heavy Vehicle Limits Project

Page 4 of 38

Preface What is the Transit New Zealand Heavy Vehicle Limits Project? This report is one of seven issuing from Transit New Zealand’s Heavy Vehicle Limits Project (HVLP) undertaken in 1999–2000. The full list of reports are: 1. Bridge Evaluation 2. Safety Evaluation 3. Pavement Evaluation 4. Industry Economics

5. Geometric Evaluation 6. Environmental Evaluation(and) 7. Overview

The Heavy Vehicles Limits Project arose out of Transit’s Heavy Transport Routes (HTR) research project undertaken in 1992-96. As a result of the HTR project, Transit believed that it was not feasible to upgrade the whole road network to accommodate substantially longer vehicles. Transit therefore undertook preliminary studies on two scenarios, termed Scenario A and Scenario B. Scenario A examined the proposal that the existing vehicle fleet would be allowed to operate at different weight limits than those presently permitted on the road network but there would be no increase in vehicle dimensions. Scenario B examined the proposal that increases in both vehicle weight and dimension limits would be allowed on selected routes only. These issues were considered in a preliminary study for Scenario A undertaken by Pearsons Transport Resource Centre P/L. The work was divided into heavy vehicle weight investigations and road user charges investigations. The findings were provided in a report entitled Scoping Study for Scenario A. Preliminary work on Scenario B for three specific routes by Opus International and Allan Kennaird indicated that significant benefits would flow from network improvements giving rise to higher weights and dimensions on these routes. The Ministry of Transport undertook a separate investigation of road user charges. As a result of the preliminary studies, the goal of the Heavy Vehicle Limits Project was to evaluate the safety and economic effects of altering heavy vehicle weights on the entire road network (Scenario A) and of increasing both heavy vehicle weights and dimensions for selected routes only (Scenario B). The general approach of the Project was to consider the effects of increasing allowable weights on bridges, safety, pavements and industry economics. These issues were common to both scenarios. In addition, an investigation was required of geometric issues for Scenario B only. Separate contracts were let for evaluating the different areas. Also required were an overview of the project with recommendations, and a separate summary with recommendations. In some cases, detailed data not published in the reports is available on diskette or CD ROM upon request from Transit New Zealand. Details of the Scenario B network of routes are included in Report 5, Geometric Evaluation. Readers not wishing to pursue the detail of the project may be satisfied with Report 7, Overview alone.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 5 of 38

Project Team The following is the team that worked on the project. Project Managers

Lynn Sleath and Bob Pearson.

Team Leader

Peter Baas.

Deputy Team Leader

Dr John dePont.

Analysts / Researchers

Paul Milliken, Tim Mueller, Ken Way, Doug Latto, Phillip Brown, Glen Koorey, Dr David Hutchison, John Vessey, Rex Humpherson and David Wanty.

Field personnel

Surveyors from Opus Regional offices.

Acknowledgements We would like to thank the following companies and individuals for their support and assistance in carrying out the Geometrics Evaluation for the Heavy Vehicle Limits Project.

Carr and Haslam Limited,

Chris Carr

Halls Refrigerated Transport Limited,

Craig Madill

Sheehan’s Transport Assistance Limited, Greg Sheehan L W Bonney and Sons Limited,

Kelvin Bonney

Rodney District Council,

Bill Horn

North Harbour Stadium,

Murray Dick

North Shore City Council, Transit New Zealand,

Lynn Sleath

Opus International Consultants,

John Vessey

Trailer Rental Limited,

Neil Bretherton

Serco Group New Zealand Limited, Traffic Design Group,

Dave Wanty

Traffic Planning Consultants Limited,

Phillip Brown

Transit New Zealand Heavy Vehicle Limits Project

Page 6 of 38

Contents Project Team

5

Acknowledgements

5

List of Figures

7

List of Tables

8

Executive Summary

9

1.

Introduction

11

2. 2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 2.4.1 2.4.2

Method 12 Outline of the Tasks...................................................................................................... 12 Developing the assumptions......................................................................................... 12 Road width, road edge, and curve widening 12 Preliminaries for the curve investigation 14 Alternative assumptions for the curve investigation 15 The effect of increased trailing infidelity 15 Preliminaries for the roundabout investigation 16 Method of analysis for the curve investigation .......................................................... 18 Models used to determine offtracking 19 Model validation 20 Costs of road widening in various terrain 22 Calculating the cost of modifying a curve 24 Method of analysis for the roundabout investigation................................................ 28 Details of the method for determining the cost of modifying a roundabout 28 Costs for the three representative roundabouts 29

3. 3.1 3.2 3.3

Results and Discussion 34 The network of routes................................................................................................... 34 Results for the curve investigation .............................................................................. 35 Results for the roundabout investigation.................................................................... 36

4.

References

38

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 7 of 38

List of Figures Figure 1. Cross-section guideline for rural two-lane state highway. ...................................... 13 Figure 2. Curve Widening. ...................................................................................................... 14 Figure 3. The geometric elements of a roundabout................................................................. 16 Figure 4. Rear view of a vehicle cornering on a superelevated road. ..................................... 19 Figure 5. B-Train trial vehicle................................................................................................. 21 Figure 6. Algorithm to calculate the amount of road widening required, q, for a curve of effective minimum radius of curvature R and road width w. ........................................... 25 Figure 7. Maximum curvature (R-1) versus maximum road width occupied for B1233-62b and B1233-62f......................................................................................................................... 26 Figure 8. The road width occupied by the benchmark vehicles A123-39p and B1232-44p when negotiating curves................................................................................................... 26 Figure 9. Difference between the maximum road width occupied by each of the trial vehicles and the maximum of the two benchmark vehicles........................................................... 27 Figure 10. Modification of an existing roundabout................................................................. 29 Figure 11. Estimated cost of modifying a roundabout of arbitrary central island diameter to accommodate either of the trial vehicles.......................................................................... 31 Figure 12. Central island diameter versus required increase in inscribed circle diameter for B1233-62f and B1233-62b............................................................................................... 32 Figure 13. Central island diameter versus required decrease in non-mountable central island diameter for B1233-62f and B1233-62b. ......................................................................... 33

Transit New Zealand Heavy Vehicle Limits Project

Page 8 of 38

List of Tables Table 1. Estimated cost (in millions of dollars) for modifying curves and roundabouts on the network of routes.............................................................................................................. 10 Table 2. Maximum offtracking observed for vehicles travelling in a straight line. ................ 16 Table 3: Major vehicle dimensions. ........................................................................................ 21 Table 4. Cost of widening road by 0.5 metres. ....................................................................... 23 Table 5. Cost of widening road by 1 metre. ............................................................................ 23 Table 6. Cost of widening road by 1.5 metres. ....................................................................... 24 Table 7. Cost of modifying the representative roundabout with 34 metre diameter central island. ............................................................................................................................... 30 Table 8. Cost of modifying the representative roundabout with 21 metre diameter central island. ............................................................................................................................... 30 Table 9. Cost of modifying the representative roundabout with 7.8 metre diameter central island ................................................................................................................................ 30 Table 10. Roads selected for inclusion in the network of routes for the Scenario B vehicles.34 Table 11. Cost of modifying curves on the network of routes for B1233-62b and B1233-62f for the original set of assumptions. .................................................................................. 35 Table 12. Cost of modifying curves on the network of routes for B1233-62b and B1233-62f for Alternative assumption set 1....................................................................................... 35 Table 13. Cost of modifying curves on the network of routes for B1233-62b and B1233-62f for Alternative assumption set 2....................................................................................... 35 Table 14. Costs for modifying roundabouts on the network of routes to accommodate B123362b.................................................................................................................................... 36 Table 15. Costs for modifying roundabouts on the network of routes to accommodate B123362f..................................................................................................................................... 36 Table 16. Costs of modifying the network of routes by Route Sector. ................................... 37

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 9 of 38

EXECUTIVE SUMMARY This study investigates the amount of road width effectively occupied by vehicles longer than 20 metres and the cost of modifying a specific network of roads and roundabouts in New Zealand to accommodate these vehicles should they be introduced. There are two reasons why the longer vehicles may take up more road space than the current fleet; firstly, longer vehicles are likely to have greater offtracking when cornering. Secondly, the trailing unit of a combination vehicle travelling in a straight line may not exactly follow the path of the leading unit due to minor steering adjustments, cross winds and cross slope of the road. This is known as trailing infidelity. Unlike offtracking, trailing infidelity affects the amount of road width a vehicle occupies on straights as well as in curves. The increase in trailing infidelity on straights was predicted to be less than 50 millimetres so the effect of increased trailing infidelity of longer vehicles was ignored in this study. Specifically, the purpose of this investigation was to determine the cost of modifying roads and roundabouts to accommodate each of two trial vehicles, which are longer and heavier than vehicles currently permitted on New Zealand roads as a matter of course without a special permit. The trial vehicles are both B-trains and are referred to as B1233-62f and B1233-62b. B1233-62f has 18.8 metre overall axle spacing and B1233-62b has 22.0 metre overall axle spacing. These two trial vehicles are 2.5 metres wide, the same width as vehicles from the current fleet, and B1233-62b was also considered as part of the Heavy Vehicle Limits Project Safety Evaluation. The report is in two parts. First, the costs for modifying sections of road, excluding roundabouts and intersections, are investigated. This is known as the geometric curve investigation. Secondly, the costs for modifying roundabouts to accommodate the trial vehicles are investigated. This is referred to as the roundabout investigation. In accordance with the project brief, intersections along the specific routes not controlled by a roundabout were not considered. To determine the costs for modifying the network of routes, the following assumptions were made: •

The current network of routes is satisfactory for existing vehicles. If a trial vehicle was found to offtrack x metres more than a vehicle typical of the current fleet on a particular curve then, to maintain the same clearances, that curve should be widened by 2x. However, if 2x<0.25 metres, then it was assumed that widening would not be required.

•

Also, if 2x ≥ 0.25 metres, then widening would still not be necessary as long as two trial vehicles travelling in opposing directions could pass with 1 metre clearance between their swept paths and 0.5 metres clearance to the edge of the road.

To test the sensitivity of the cost to these assumptions, four alternative sets of assumptions, Alternatives 1 to 4 were considered. Alternative 1 was that •

The current network of routes is satisfactory for existing vehicles. If a trial vehicle was found to offtrack x metres more than a vehicle typical of the current fleet on a particular curve then, to maintain the same clearances, that curve should be widened by 2x. However, if 2x<0.15 metres, then it was assumed that widening would not be required.

•

Also, if 2x ≥ 0.15 metres, then widening would still not be necessary as long as two trial vehicles could pass with 2 metres clearance between their swept paths and 1 metre clearance to the edge of the road.

Transit New Zealand Heavy Vehicle Limits Project

Page 10 of 38

Alternative 2 was that •

The current network of routes is satisfactory for existing vehicles. If a trial vehicle was found to offtrack x metres more than a vehicle typical of the current fleet on a particular curve then, to maintain the same clearances, that curve should be widened by 2x. However, if 2x<0.15 metres, then it was assumed that widening would not be required.

Alternative 3 was that •

The current network of routes is satisfactory for existing vehicles. If a trial vehicle was found to offtrack x metres more than a vehicle typical of the current fleet on a particular curve then, to maintain the same clearances, that curve should be widened by 2x. However, if 2x<0.05 metres, then it was assumed that widening would not be required.

•

Also, if 2x≥0.05 metres, then widening would still not be necessary as long as two trial vehicles, travelling in opposing directions, could pass with 2 metres clearance between their swept paths and 1 metre of clearance to the edge of the road.

Alternative 4 was that •

The current network of routes is satisfactory for existing vehicles. If a trial vehicle was found to offtrack x metres more than a vehicle typical of the current fleet on a particular curve then, to maintain the same clearances, that curve should be widened by 2x. However, if 2x<0.05 metres, then it was assumed that widening would not be required.

The costs for modifying the network of routes under the original assumptions and under Alternative 1-4 are shown in Table 1. For the roundabout investigation, a tool for estimating the cost of modifying a roundabout based on the central island diameter of the roundabout was developed. The suggested modifications to roundabouts are such that traffic flows and traffic deflection at roundabouts were not compromised. Estimates of the costs of modifying roundabouts on the network of routes to accommodate B1233-62b or B1233-62f are also shown in Table 1. Table 1. Estimated cost for modifying curves and roundabouts on the network of routes. Assumption set Original Assumptions Alternative 1 Alternative 2 Alternative 3 Alternative 4 Cost for roundabouts

Cost for B1233-62b $43,600,000 $132,000,000 $214,000,000 $161,900,000 $292,100,000 $1,284,000

Cost for B1233-62f $18,800,000 $44,700,000 $62,600,000 $113,500,000 $191,100,000 $1,173,000 .

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

1.

Page 11 of 38

INTRODUCTION

This investigation considered the modification of curves and roundabouts required for the network of routes proposed by Transit New Zealand in the project brief to accommodate vehicles that are longer and heavier than those currently permitted on New Zealand roads. Two trial vehicles, longer and heavier than those allowed under current laws, were investigated; a B-train with 22.0 metre overall axle spacing and a B-train with 18.8 metre overall axle spacing. Two vehicles, typical of the current fleet, were used to provide a benchmark against which the trial vehicles could be compared. The two benchmark vehicles were a tractor semi-trailer with 13.1 metre overall axle spacing and a B-train with 16.0 metre overall axle spacing. Details of these four vehicles are provided in Appendix A.

Transit New Zealand Heavy Vehicle Limits Project

2.

METHOD

2.1

Outline of the Tasks

Page 12 of 38

Seven tasks were specified in the project brief. These tasks culminated in finding the cost of geometric modification of the network of routes. Briefly, the seven Tasks were Task 1. To develop an analysis tool, describing the relationships between curve geometry and offtracking for the two trial vehicles and two benchmark vehicles, typical of the current fleet. Also, it was required to develop a tool to estimate the cost of widening sections of road to accommodate the increase in offtracking. Task 2. To finalise the network of routes. Task 3. To compile an inventory of geometric information for each route. (Task 7). To conduct a survey to confirm the assumptions regarding the cross sections of road and adjacent country (including terrain slopes and soil types). Task 4. To validate the method of modelling the vehicles by experiment using a B-train. Task 5. To determine the cost of geometric modification of the network of routes. Task 6. To write this report. 2.2

Developing the assumptions

When an articulated vehicle travels around a curve, the rear wheels generally follow a different path to the front wheels. The additional road width that the vehicle occupies when cornering, over and above the road width the vehicle occupies when travelling in a straight line, is the offtracking. Offtracking may be inboard, when the rear wheels follow paths inside the paths of the front wheels, or outboard, when the rear wheels follow paths outside the path of the front wheels. At slow speeds an articulated vehicle will track inboard when turning. However, as the speed increases the inboard offtracking is reduced and if the speed is high enough the vehicle may begin to experience outboard offtracking. To investigate the modifications to curves required to accommodate vehicles longer than those currently permitted in New Zealand, four articulated vehicles were modelled. Two benchmark vehicles, typical of the current fleet, were considered; a 39 tonne tractor semitrailer with 13.1 metre overall axle spacing (denoted 'A123-39p') and a 44 tonne B-train with 16.0 metre overall axle spacing (denoted 'B1232-44p'). These two benchmark vehicles were compared with two longer trial vehicles; a 62 tonne B-train with 18.8 metre overall axle spacing (denoted 'B1233-62f') and a 62 tonne B-train with 22.0 metre overall axle spacing (denoted 'B1233-62b'). Details of these vehicles are given in Appendices A and B. 2.2.1

Road width, road edge, and curve widening

In this report road width is defined as the total sealed width of a road comprising the total traffic lane width plus the width of the sealed shoulders. The edge line is the delineated boundary of the traffic lane. The edge of the road refers to the edge of the sealed/paved part of the road. The width of the sealed shoulder is related to traffic volume in vehicles per day (VPD) and should be uniform within any link along the state highway regardless of curves and straights (Figure 1). The relationships are explained in more detail in Transit’s State Highway Control Manual, Appendix 3a: Cross Section Guidelines for Two-lane Rural State Highways.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 13 of 38

Figure 1. Cross-section guideline for rural two-lane state highway.

On straight sections of state highways the traffic lane width is normally a standard 3.5 m; on curves, the lane width is increased to include curve widening (Figure 2). The relationships are explained in the Transit policy document Rural Road Design—Guide to the Geometric Design of Rural Roads, Austroads 1989, and more clearly in Transit’s draft State Highway Geometric Design Manual.

Transit New Zealand Heavy Vehicle Limits Project

Page 14 of 38

Figure 2. Curve Widening.

2.2.2

Preliminaries for the curve investigation

Each curve was characterised by three parameters; the minimum radius of curvature of the curve R, the length of the curve l and the existing road width w. The objective of this study was to determine the cost of modifying the network of routes on which it was proposed that these longer vehicles would be permitted to operate. A number of assumptions were made, as follows. Assumption 1

While the current network of roads is generally satisfactory only for existing vehicles, in practice it is unlikely that curve widening would be undertaken where the calculated required widening is less than 0.25 metres (equivalent to 0.125 metres on each side of the road). From Assumption 1, if a curve was found to require widening by an amount less than 0.25 metres then it was assumed that widening would not be carried out. However, if the offtracking of a trial vehicle was found to be significantly greater than the offtracking of the worst of the benchmark vehicles then Assumption 2 provided the foundation for the specification of the required road width for such a curve. Assumption 2

If a curve is such that the trial vehicle takes up significantly more road width than the benchmark vehicles representing the existing fleet (Assumption 1 specifies 0.25 metres as significant) then the amount of road width is unsatisfactory unless two trial vehicles, travelling in opposite directions, can pass with 1 metre clearance between their swept paths while each vehicle remains at least 0.5 metres from the edge of the road. The 0.5 metres provided at the edge of the road was chosen to allow for two effects; firstly driver variation, and secondly avoidance of excessive edgebreak problems for unkerbed roads. The 1 metre clearance allowed between the swept paths of opposing vehicles was provided to allow for driver variation. Note that if there were to be provision for cyclists, at least 1.5 metres clearance between the path of a truck and the edge of the road would be required.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 15 of 38

Since a negligible proportion of the routes will have provision for cyclists, the cost of this widening has been ignored. 2.2.3

Alternative assumptions for the curve investigation

Assumption 1 and Assumption 2 were such that the distances between vehicles and to the edge of the road to allow for driver variability and trailing infidelity were minimal, so two alternative sets of assumptions were also considered: Alternative Set 1 - Assumption 1

While the current network of roads is generally satisfactory only for existing vehicles, in practice it is unlikely that curve widening would be undertaken where the calculated required widening is less than 0.15 metres (equivalent to 0.075 metres on each side of the road). Alternative Set 1 - Assumption 2

If a curve is such that the trial vehicle takes up significantly more road width than the existing fleet (see Alternative 1 - Assumption 1) then the amount of road width is unsatisfactory unless two trial vehicles, travelling in opposite directions, can pass with 2 metres clearance between the swept paths while each vehicle remains at least 1 metre from the edge of the road. The justification for Alternative 1 - Assumption 2 was that 250 millimetres was allowed for wing mirrors on one side of one of the vehicles and 400 millimetres was allowed on one side of each vehicle to allow for the trailer not following the predicted path due to cross winds, minor steering adjustments etc. In addition to this, 500 millimetres was allowed on each side of each vehicle to account for driver error and an additional 350 millimetres distance was allowed to the edge of the road to prevent edge break. The second alternative is as follows. Alternative Set 2 - Assumption 1

While the current network of roads is generally satisfactory only for existing vehicles, in practice it is unlikely that curve widening would be undertaken where the calculated widening is less than 0.15 metres (equivalent to 0.075 metres on each side of the road). Alternative Set 2 - Assumption 2

The current network of roads is only just wide enough to accommodate the current fleet. Therefore, any increase in vehicle offtracking would require an increase in road width. The costs for road widening corresponding to these two alternative sets of assumptions are shown in Section 3. 2.2.4

The effect of increased trailing infidelity

Trailing infidelity is when the trailing unit of a combination vehicle does not exactly follow the path of the leading unit on a straight road due to cross winds, cross slope of the road, minor steering adjustments and other asymmetries. Generally, longer vehicles may be expected to have greater trailing infidelity than shorter vehicles. In this study, the effect of increased trailing infidelity of the trial vehicles was ignored because an Australian study [Prem et al, 1999] suggested that the change in trailing infidelity would only be around 50 millimetres for a 5 metre increase in vehicle length. Prem et al [1999] estimated the effect of trailing infidelity for a number of vehicles when travelling on a straight road. Trailing infidelity values for a few vehicles are summarised in Table 2.

Transit New Zealand Heavy Vehicle Limits Project

Page 16 of 38

Table 2. Maximum offtracking observed for vehicles travelling in a straight line. Straight road offtracking 300mm over 400mm just less than 400mm 350mm just less than 400mm

Vehicle tractor semi (18.5m) truck trailer (16.8m) R12T12 truck trailer (20m) R12T22 B train (19m) B train (25m)

If there was to be road widening to allow for increased trailing infidelity, straight roads as well as curves may require modification as it is more difficult to maintain a smooth steering input on a curve than on a straight road. 2.2.5

Preliminaries for the roundabout investigation

The features of a roundabout and some terminology used in this report are illustrated in Figure 3 [Austroads, 1993].

Figure 3. The geometric elements of a roundabout.

Three roundabouts with dual circulating lanes were used as representative roundabouts because these roundabouts were considered typical of those found on the network of routes which is comprised mostly of main roads. However, a few of the roundabouts on the network of routes were single lane roundabouts. It was also assumed that a roundabout could be characterised by the size of its central island.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 17 of 38

The preferred modification is to use mountable kerbs to accommodate heavy vehicles while not interfering with the deflection of the roundabouts for other vehicles. Definition 1 relates to Figure 3 and pertains to the specification of mountable curve kerbs on a roundabout. See Figure 10 for details of how mountable kerbs might be used. Definition 1

The inscribed circle diameter of the mountable kerb is the inscribed circle diameter measured between mountable curve kerbs on opposite sides of a roundabout. Similarly, the inscribed circle diameter of the non-mountable kerb is the inscribed circle diameter measured between non-mountable curve kerbs on opposite sides of a roundabout. Also, note that not all roundabouts have mountable kerbs. Three existing roundabouts with central island diameters of 7.8 metres, 21 metres and 34 metres were used to represent a typical sample of all roundabouts on the network of routes. To calculate how these roundabouts should be modified to accommodate each of the trial vehicles Assumption 3 was made. Assumption 3

The roundabouts that currently exist in the proposed network of routes are large enough to accommodate the existing fleet but no larger. Therefore, any increase in the width of road occupied by vehicles longer than those of the current fleet will require a corresponding increase in the size of the roundabouts. For a particular roundabout, to determine the amount of additional road width needed to accommodate the trial vehicles, one of two assumptions was made. Either it was assumed that the roundabout should allow the trial vehicle to navigate the roundabout without interference from other traffic or it was assumed that one of the trial vehicles and a nonarticulated vehicle should be able to approach the roundabout side by side. The size of the roundabout was used in Assumption 4 to determine which of these scenarios was considered. Assumption 4

If the non-mountable central island diameter of the existing roundabout, D (in metres), was such that D<24 then it was assumed that the roundabout was designed to accommodate an articulated vehicle only. If the non-mountable central island diameter of the existing roundabout, D (in metres), was such that D≥24 then it was assumed that the roundabout was designed to accommodate an articulated vehicle and a non-articulated vehicle travelling side by side. The following assumption was also made. Assumption 5

For a right turn at a roundabout, the driver would approach the roundabout in the right-hand lane. For a left turn the driver would approach the roundabout in the left lane and to travel straight ahead the driver could use either lane.

Transit New Zealand Heavy Vehicle Limits Project

2.3

Page 18 of 38

Method of analysis for the curve investigation

An algorithm for determining the amount of road widening required for a given curve was determined in accordance with Assumption 1 and Assumption 2. The algorithm used the results of a number of vehicle simulations that provided an equation for offtracking in terms of the minimum radius of curvature and the vehicle's speed. The simulations were performed on hypothetical roads designed in accordance with Austroads [1997]. Details of the curves on which the simulations were performed may be found in Appendix D. Now, we consider a vehicle negotiating a curve as shown in Figure 4.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

e2

Page 19 of 38

Fn

e1

Ft

M3

h2

mv2R-1 h1

mg

θ Figure 4. Rear view of a vehicle cornering on a superelevated road.

Consider a vehicle cornering at constant speed on a road with superelevation angle θ, as shown in Figure 4. It was assumed that an articulated vehicle would take such a curve at a speed such that the acceleration in the h1 direction was between -0.05g and -0.2g. Note that advisory speed signs for curves are such that the acceleration in the h1 direction is -0.2g. Recognising that, for a curve with a greater superelevation angle, a greater speed is required to reach an acceleration of -0.2g in the h1 direction, it is not surprising that the offtracking is approximately independent of superelevation for this formulation of the problem. This result is shown in Appendix E and was useful because it allowed superelevation to be ignored for the simulations used to determine offtracking. 2.3.1

Models used to determine offtracking

Two computer programs were used to build vehicle models for simulating offtracking. They were VPATH and Mechanical Simulation Corporation’s multibody code generating software, AutoSim. VPATH VPATH is a simulation program suitable for the determination of low speed offtracking or swept path measures. The position of a vehicle is calculated using a kinematic model of the vehicle and is valid only for predicting low speed (less than 8 km/h) offtracking of vehicle combinations. TERNZ - AutoSim Models AutoSim is an equation generator for models of mechanical systems. It generates non-linear symbolic equations in the form of computer source code for solution in languages such as Fortran, C, and Matlab. AutoSim was developed for building large, complicated vehicle dynamics simulation programs at the University of Michigan’s Transport Research Institute, (UMTRI) and is sold commercially by Mechanical Simulation Corporation. With AutoSim, a mechanical system is described as a series of rigid bodies, joints, springs, applied forces and moments. The description of the system is used by AutoSim to generate the equations of motion in the chosen computer language. How well the model simulates the actual mechanical system depends on the assumptions made in describing the system. The

Transit New Zealand Heavy Vehicle Limits Project

Page 20 of 38

ability of AutoSim to then generate accurate equations of motion has been well documented by Sayers and Riley [1996] and Sayers [1989]. The B-train model, used to simulate B1233-44p, B1233-62f and B1233-62b, is a constant velocity, 29 degree of freedom (DOF) model suitable for predicting the yaw and roll response of a nine axle B-Train. The tractor sprung mass has 5 DOF, 2 translational and 3 rotational. The first and second semi-trailers have 3 rotational DOF but no translational DOF. Two rigid bodies each with 1 DOF are used to model each axle, one to account for vertical translation and one for a rotation of the axle in the yaw plane due to the sprung mass rolling relative to axle, (roll steer). The hitches are modelled as ball joints, the pitch and yaw stiffnesses are set to zero and the roll stiffness is set high enough to provide adequate roll coupling between the units (110 kNm – 340 kNm) [Sayers and Riley, 1996]. The vertical stiffness of the truck suspension is modelled with two springs per axle, the force deflection characteristics of the springs are intended to capture the observed hysteretic frictional behaviour of heavy truck suspensions. The describing equations for the spring are those originally published by Fancher [1980]. Hydraulic dampers are modelled as linear viscous dampers acting between the axles and sprung mass. The total roll stiffness of the suspension derives from the vertical stiffness of the springs and any additional stiffness due to linkages and from an anti-sway bar if fitted. The additional or auxiliary stiffness is modelled as a torsion spring whose restoring moment is proportional to the roll of the sprung mass relative to the axle. The cornering force and aligning moment properties of the tyres are modelled using a table lookup for a given slip angle and vertical load, longitudinal tyre dynamics are not included in this model. Tyre damping rate is included as a linear viscous damper acting between the ground and unsprung mass. An implementation of the driver model of MacAdam [MacAdam, 1981] is used so that the simulation can be run in closed loop mode, that is, the model can be steered to follow a specified x-y path with minimal tracking error. A complete listing of the model input data is given by Latto in Appendix C [Latto, 1999]. 2.3.2

Model validation

AutoSim models were used to calculate offtracking for vehicles when cornering both at highway speed and during low speed manoeuvres VPATH was used to estimate offtracking for vehicles during slow speed cornering at intersections and roundabouts. To verify the validity of these models, a 62 tonne, 26.5 metre long B-train was used to measure offtracking under a range of test conditions. These measurements were then compared to the offtracking of the vehicle simulated in AutoSim and in VPATH. A thorough account of the model validation is given in Latto (1999] but a brief description is given here: The vehicle combination was a nine axle B-train which consisted of a three axle tractor unit pulling two three axle semi-trailer units. The payload consisted of 40.4 tonnes of steel plate. The tractor unit was a cab-over engine Kenworth with a 525 horsepower Cummins engine, an 18 speed Eaton gearbox and Rockwell drive axles fitted with Kenworth’s eight bag air suspension. The semi-trailers were flat deck configurations. The first semi-trailer was fitted with a three leaf steel spring load-sharing suspension. The second semi-trailer had a mono leaf steel spring load-sharing suspension. Figure 5 is a photograph of the trial vehicle, loaded and on the road.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 21 of 38

The trial vehicle had a GCM of 62.09 tonnes.

Figure 5. B-Train trial vehicle.

Physical Dimensions Table 3 lists the vehicle dimensions, Overall Axle Spacing (OAS) and Overall Length (OAL). A complete list of the vehicle dimensions and masses used in the simulations is given by Latto [1999]. Table 3: Major vehicle dimensions. Unit Tractor YA9227

1st Semi H8269

2nd Semi 6713C

Whole unit

Description Front overhang Wheelbase Drive axle spacing Fifth Wheel Offset Front overhang Forward Length Axle Spacing Fifth Wheel Offset Fifth Wheel Height Front overhang Forward Length Axle Spacing Rear overhang Overall Axle Spacing Overall Length

Distance (m) 0.92 4.42 1.33 0.4 1.5 7.6 1.33 1.38 1.255 0.75 9.26 1.26 3.27 23.52 26.45

Test Procedure Data from ten tests were recorded, four low speed tests and six high speed tests. The tests are described below.

Transit New Zealand Heavy Vehicle Limits Project

Page 22 of 38

Low Speed Tests Two sites in Albany, 15 minutes north of Auckland, were used for these tests, one involving a 22 m diameter roundabout and the other a 90 degree T-intersection. For all low speed tests the driver conducted at least one practice run on the course, with the roads being closed for the duration of the tests. High Speed Offtracking Tests Paul Matthews Road in Albany The curve used for these tests is located on Paul Matthews Road between Omega Street and Saturn Place, curve has an approximate deflection of 65° and cross slope of 1.5°. On Highway Curves Offtracking data for three curves between Warkworth and Puhoi was recorded on the southbound leg of the On Highway test. The curves in order from north to south were advisory speed sign posted at 75 km/h, 55 km/h and 40 km/h, respectively. The instruments used to collect data for the model validation are described in Appendix I. Conclusions for the Low Speed Offtracking validation Both VPATH and the TERNZ AutoSim model gave offtracking predictions that were in good agreement with offtracking measurements made during the road trial. VPATH over-predicted the maximum offtracking on all tests but the one conducted at the lowest forward speed. These results are consistent with the creep speed assumption used in VPATH and show the model’s validity for offtracking predictions when the forward speed is less than eight kilometres per hour. The ease of use and minimum data set requirements makes VPATH an ideal simulation model for predicting low speed offtracking behaviour. The TERNZ AutoSim model gave very good results because it accounted for the dynamic effects at higher speeds. Conclusions for the High Speed Offtracking validation The TERNZ AutoSim model gave results within the uncertainty of measurement for all the high speed tests where the axle paths tracked by the steer axle and rear axis of the vehicle were surveyed. On the open road curves where only a spot measurement of the maximum offtracking was made, two of the three curves showed a difference higher than 6 %. This was due to the fact that the actual cross slope on the curve was ignored in the simulation. Overall both VPATH and the TERNZ AutoSim models provided offtracking predictions that were in good agreement with measured offtracking. For details of the results of the road trials used for model validation see Latto [1999]. 2.3.3

Costs of road widening in various terrain

The costs for widening sections of road, in various environments, by certain amounts were determined. A detailed account of how this was performed is given in Appendix B. Field surveys were also conducted to refine the costs and verify the assumptions for road widening. These field surveys involved the selection of 13 curves in different terrain which might require widening. The cost of widening each of these curves was determined and used to refine the costs for road widening in Tables 4, 5, and 6. Details of the field survey are given in Appendix M.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 23 of 38

The costs shown in Tables 4, 5, and 6 were used to determine the cost of modifying curves on the network of routes. Estimated costs for widening a section of road by 0.5 metres, 1 metre and 1.5 metres for various terrain types and zoning environments are given in Tables 4, 5, and 6. Table 4. Cost of widening road by 0.5 metres. Terrain

Conditions Widening Curve

0.5m Widening Widening Taper ($/m) ($) 426 4,260 1,168 11,680

Difficult

Cut Fill

Land ($/m) 0.75 0.75

Average

Cut Fill

2 1.5

401 754

4,010 7,540

Hilly

Average

Cut Fill

2 8

282 423

2,820 4,230

Flat

Average

Cut Fill

3 3

161 250

1,610 2,500

2.75

307

3,070

20

534

5,340

Mountainous

Poor Urban

Average

Table 5. Cost of widening road by 1 metre. Terrain

Conditions Widening Curve

1.0m Widening Widening Taper ($/m) ($) 570 11,400 1,607 32,140

Difficult

Cut Fill

Land ($/m) 1 1

Average

Cut Fill

3 2

499 982

9,980 19,640

Hilly

Average

Cut Fill

4 10

337 512

6,740 10,240

Flat

Average

Cut Fill

6 6

188 292

3,760 5,840

Poor

5.5

418

8,360

Average

40

608

12,160

Mountainous

Urban

Transit New Zealand Heavy Vehicle Limits Project

Page 24 of 38

Table 6. Cost of widening road by 1.5 metres. Terrain

Conditions Widening Curve

1.5m Widening Widening Taper ($/m) ($) 741 22,230 2,056 61,680

Difficult

Cut Fill

Land ($/m) 1.25 1.25

Average

Cut Fill

3 2.5

599 1,229

17,970 36,870

Hilly

Average

Cut Fill

6 12

399 610

11,970 18,300

Flat

Average

Cut Fill

9 9

220 333

6,600 9,990

8.25

542

16,260

60

715

21,450

Mountainous

Poor Urban

Average

Note that the figures in Tables 4-6 are only estimates and are not known precisely, although the actual best guesses are listed in these Tables. Appendix C and Appendix M explain how the costs presented in Tables 4-6 were calculated. Note that the taper cost is a lump sum and allows for a 1 in 20 taper at the end of each curve. That is, 10 metres of taper on each end for 0.5 metre widening, 20 metres on each end for 1 metre widening and 30 metres on each end for 1.5 metres widening. 2.3.4

Calculating the cost of modifying a curve

To calculate the cost of modifying a section of road, information from Tables 4-6 may be used in conjunction with the modifications that are required for each curve, as follows. To modify an arbitrary curve, the algorithm shown in Figure 6 is used to calculate the amount of road widening that is required for a curve of radius of curvature R, road width w and length l to accommodate B1233-62b. This algorithm is an implementation of Assumption 1 and Assumption 2 using the results of vehicle simulations. The simulations were performed to determine the amount of offtracking experienced by each of the trial vehicles and the benchmark vehicles on various curves.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 25 of 38

R f1

x2

R f2 f4

x3 w

x4 if x4<0.25 then x7=0 else x7=x4

f3

x5 x7 if x5<0 then x6=0 else x6=x5 q x6

min(x6, x7)

Figure 6. Algorithm to calculate the amount of road widening required, q, for a curve of effective minimum radius of curvature R and road width w.

where f1 : x2 = 62.8 R-1 + 2.47

(1)

f2 : x3 = 2 + 2x2

(2)

f3 : x5 = x3 - w

(3)

f4 : x4 = 43.2 R-1

(4)

Note, it follows from Assumption 1 that curves with radii of curvature greater than 250 metres could be ignored because the difference in offtracking between B1233-62b and the worst of the benchmark vehicles was less than 0.125 metres. The cost of widening a curve of minimum radius of curvature R, length l and road width w, to accommodate B1233-62b, may be determined from this algorithm which uses equations (1), (2), (3) and (4) and Tables 4-6. The algorithm shown in Figure 6 remains the same for the other trial vehicle, B1233-62f, but instead of using Equations (1) and (4), we used (5) and (6) f1 : x2 = 52.2 R-1 + 2.45

(5)

f4 : x4 = 22.0 R-1 - 0.03

(6)

Transit New Zealand Heavy Vehicle Limits Project

Page 26 of 38

Inspection of the algorithm shown in Figure 6 simply reveals the underlying assumptions Assumption 1 and Assumption 2. We will now show how Equations (1), (4), (5) and (6) were developed from the vehicle simulation results. Figure 7 shows the maximum road width occupied by B1233-62b and B1233-62f when negotiating a curve of curvature R-1. The maximum was taken over simulations performed at the advisory speed and half the advisory speed. Straight lines fitted to these data give equations (1) and (6). 4.6 B1233-62b B1233-62f

4.4

road width occupied (m)

4.2 4 3.8 3.6 3.4 3.2 3 2.8 2.6

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-1

curvature (m )

Figure 7. Maximum curvature (R-1) versus maximum road width occupied for B1233-62b and B1233-62f.

The road width occupied by the benchmark vehicles followed a similar trend 4

road width occupied (m)

A123-39p B1232-44p

3.5

3

2.5

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-1

curvature (m )

Figure 8. The road width occupied by the benchmark vehicles A123-39p and B1232-44p when negotiating curves.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 27 of 38

Note that we have defined curvature as R-1, where R is the radius of curvature of a curve. So, a curve with R=100 metres has a curvature of 0.01 metres-1. The difference between the maximum road width occupied by each of the trial vehicles and the maximum of the two benchmark vehicles is shown in Figure 9. 0.7 B1233-62b B1233-62f

difference in offtracking (m)

0.6

0.5

0.4

0.3

0.2

0.1

0

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-1

curvature (m )

Figure 9. Difference between the maximum road width occupied by each of the trial vehicles and the maximum of the two benchmark vehicles.

Straight lines were fitted to the data in Figure 9 (and doubled to account for two lanes) giving equations (4) and (6) for B1233-62b and B1233-62f, respectively. Typical curves and wheel paths used to determine the offtracking are given in Appendix D. Remarks •

The kinks in Figure 7, Figure 8 and Figure 9 that occur at a curvature of 0.01 metres are due to the imperfect nature of the driver model and have no physical significance.

•

The lines that are fitted to the data in Figure 7 and Figure 8 are for 30
•

Simulations were performed with fully loaded vehicles. The vehicle offtracking is a combination of low speed effects (tracking inboard) and high-speed effects, which result in less inboard offtracking or greater outboard offtracking. Since the high-speed effects become more prevalent as the mass of the vehicle increases, the vehicles may offtrack differently when unloaded.

•

It was assumed, for the simulations, that a curve would be taken at a speed such that the maximum lateral acceleration during the cornering manoeuvre was between 0.05g and 0.2g.

Transit New Zealand Heavy Vehicle Limits Project

2.4

Page 28 of 38

Method of analysis for the roundabout investigation

The simulation program VPATH™1, developed by Phillip Brown, was used for the assessment of low speed offtracking. The benchmark tractor semi-trailer (A123-39p) was simulated negotiating the roundabout with a path typical of one that a driver might take. This vehicle was simulated for three manoeuvres; a left turn, a right turn and a path straight through the roundabout. The other benchmark vehicle and the two trial vehicles were also simulated taking a path where the front axle of each of the vehicles followed the path taken by the front axle of the benchmark tractor semi-trailer. Since the front axle of all four vehicles followed the same path for each of the three roundabouts, the differences in the offtracking were due only to differences in the vehicles. The following example illustrates how the modifications to the roundabouts were calculated. Consider the calculation of the required modifications for one of the three representative roundabouts for one of the trial vehicles. Suppose the trial vehicle takes up an additional width a when performing a left turn at the roundabout. Consistent with Assumption 3 and Assumption 4, the required increase in the inscribed circle diameter of the non-mountable kerb is 2a. Now, suppose that, for a right hand turn, the trial vehicle takes up an additional width b which is greater than a. Using Assumption 5, the non-mountable central island diameter should be reduced by 2(b-a) for roundabouts of any central island diameter. The modifications that would be required, for a roundabout of arbitrary size, to accommodate each of the two trial vehicles were estimated by interpolating between the modifications required for the three representative roundabouts. Similarly, the corresponding cost of modifying a roundabout of arbitrary size was estimated by interpolating between the costs for modifying the three representative roundabouts. An example of a plot of the swept path of a vehicle travelling around the roundabout is given in Appendix H. 2.4.1

Details of the method for determining the cost of modifying a roundabout

Consider the modification of a roundabout of arbitrary size. Consider the generalised roundabout of Figure 10. The existing roundabout is shown with a solid line and the modifications are shown with dashed lines. The proposed modifications are a reduction in the size of the non-mountable part of the central island and an increase in the inscribed circle diameter of the non-mountable kerb. Increasing the inscribed circle diameter of the nonmountable kerb involves the removal of the part of each splitter island facing the roundabout, moving the non-mountable curve kerb back and making the corresponding changes to the entry curves and exit curves.

1

VPATH is a registered Trademark owned by P. R. Brown.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 29 of 38

Figure 10. Modification of an existing roundabout.

A relationship between the central island diameter of an arbitrary roundabout and the cost of modifying such a roundabout to accommodate each of the trial vehicles was determined as described later in this section. 2.4.2

Costs for the three representative roundabouts

Widening costs were calculated for three representative roundabouts. It has been assumed that widening would be achieved by reducing the diameter of the non-mountable central island and replacing the existing outside kerb and channel with a mountable kerb and channel and a non-mountable kerb at the extent of the widening. The area between the two kerbs would be finished as a concrete trafficable surface. This would allow heavy vehicles to track over the mountable central ring and the outer widening, if required, while directing the remainder of traffic around lanes similar to those currently marked. It has been assumed that there would be footpaths adjacent to the outside kerbs for the urban and industrial situation only. Because of the addition of a second kerb on the outside of the roundabout it will be necessary to reconstruct the footpaths at a slightly higher level over the full length of the widening. In the rural situation grass would extend from the back of the kerb to the road reserve boundary. Land costs have not been included as, generally, with larger roundabouts there would be sufficient space to accommodate the 1.2 m required, within the current road reserve.

Transit New Zealand Heavy Vehicle Limits Project

Page 30 of 38

The costs of widening included the following as appropriate •

Site clearance.

•

Traffic control.

•

Excavation.

•

Kerb (remove/new).

•

Concrete apron (centre).

•

Road construction ( subbase, basecourse, roading (asphaltic concrete), road marking).

•

Footpath (asphaltic concrete)

•

Topsoil/grassing

•

Traffic sign relocation

•

Light pole relocation

•

Fixed percentage for establishment, contingency & design fees.

A summary of costs is shown in Tables 7, 8, and 9. Table 7. Cost of modifying the representative roundabout with 34 metre diameter central island. Reduce Inner Radius Vehicle Change Urban Industrial Rural

B1233-62f 0.2m $12,345 $12,345 $12,345

B1233-62b 0.6m $16,815 $16,815 $16,815

Move Outer Kerb B1233-62f 0.6m $91,605 $91,605 $79,000

B1233-62b 0.95m $98,315 $98,315 $85,540

Total B1233-62f

B1233-62b

$103,950 $103,950 $91,345

$114,950 $114,950 $102,355

Table 8. Cost of modifying the representative roundabout with 21 metre diameter central island. Reduce Inner Radius Vehicle Change Urban Industrial Rural

B1233-62f 0.8m $12,375 $12,375 $12,375

B1233-62b 1.0m $16,500 $16,500 $16,500

Move Outer Kerb B1233-62f 0.6m $48,111 $48,111 $45,105

B1233-62b 1.05m $52,584 $52,584 $48,661

Total B1233-62f

B1233-62b

$60,486 $60,486 $57,480

$69,084 $69,084 $65,161

Table 9. Cost of modifying the representative roundabout with 7.8 metre diameter central island Reduce Inner Radius Vehicle Urban Industrial Rural

B1233-62f 1.4m $6,170 $6,170 $6,170

B1233-62b 1.4m $6,170 $6,170 $6,170

Move Outer Kerb B1233-62f 0.6m $48,150 $48,150 $41,875

B1233-62b 1.2m $53,270 $53,270 $48,045

Total B1233-62f

B1233-62b

$54,320 $54,320 $48,045

$59,440 $59,440 $52,940

Figure 11 shows a plot of central island diameter versus the cost of modifying a roundabout to accommodate either B1233-62f or B1233-62b in a rural, industrial or urban zone. Drawings of the three representative roundabouts used to generate Figure 11 are given in Appendix G.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 31 of 38

120

cost (times $1,000)

100

80 18.8m Btrain, urban/industrial zone 18.8m Btrain rural 22m Btrain, urban/industrial zone 22m Btrain rural

60

40

20

0

10

15

20 25 central island diameter (m)

30

35

Figure 11. Estimated cost of modifying a roundabout of arbitrary central island diameter to accommodate either of the trial vehicles.

Curves were fitted to the data shown in Figure 11 to give equations for the estimated cost C of modifying a roundabout as a function of the central island diameter. The cost of modifying a roundabout of diameter D to accommodate B1233-62b is given by (7) for the case where the roundabout is in a rural zone and (8) for the case when the roundabout is in an industrial or urban zone C = -0.0695D2 + 4.79D + 19.8 2

C = -0.0795D + 5.44D + 21.8

(7) (8)

The cost of modifying a roundabout of diameter D to accommodate B1233-62f is given by (9) for the case where the roundabout is in a rural zone and (10) for the case when the roundabout is in an industrial or urban zone. C = -0.0669D2 + 4.45D + 17.4 2

C = -0.0777D + 5.14D + 19.0

(9) (10)

respectively. Recall that D is central island diameter in metres and C is the cost in thousands of dollars. The modifications required for roundabouts of arbitrary central island diameter were found by interpolating between the modifications that were required for the three representative roundabouts. The modifications that were required for the three representative roundabouts are given below and an example of a plot of the swept path of a vehicle negotiating a roundabout is shown in Appendix H.

Transit New Zealand Heavy Vehicle Limits Project

Page 32 of 38

The modifications required, for a roundabout of arbitrary central island diameter, to accommodate each of the trial vehicles follow: To accommodate B1233-62f, a roundabout with non-mountable central island diameter D should be modified as follows: For the curve kerbs, a mountable kerb should be constructed in place of the existing kerb and a new non-mountable kerb should be built such that the inscribed circle diameter of the non-mountable kerb is 1.2 metres greater than before. For the central island, a mountable kerb should be constructed in place of the existing non-mountable kerb. Also, a new non-mountable kerb should be built such that the non-mountable central island diameter is reduced by e, where e = -0.0914D+3.54

(11)

To accommodate B1233-62b, a roundabout with a non-mountable central island of diameter D should be modified as follows: For the curve kerbs, a mountable kerb should be constructed in place of the existing kerb and a new non-mountable kerb should be built such that the inscribed circle diameter of the non-mountable kerb is f metres greater than before, where f = -0.0157D+2.4663

(12)

For the central island, a mountable kerb should be constructed in place of the existing non-mountable kerb. Also, a new non-mountable kerb should be built such that the non-mountable central island diameter is reduced by h, where h = -0.0611D+3.2669

(13)

The changes required to the non-mountable part of the central island and the inscribed circle of a roundabout of arbitrary size to accommodate B1233-62f and B1233-62b vehicles are shown in Figure 12 and Figure 13, respectively.

increase in inscribed circle dia.

B1233-62f B1233-62b

2

1.5

1

5

10

15

20 D

25

30

35

Figure 12. Central island diameter versus required increase in inscribed circle diameter for B1233-62f and B1233-62b.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 33 of 38

3 B1233-62f B1233-62b 2.5

reduction in D

2

1.5

1

0.5

0

5

10

15

20 D

25

30

35

Figure 13. Central island diameter versus required decrease in non-mountable central island diameter for B1233-62f and B1233-62b.

Remarks •

A result of Assumption 3 is that all roundabouts apart from those where the trial vehicles are only permitted to travel straight ahead are assumed to require modification to accommodate the trial vehicles.

•

Intersections along the specific routes not controlled by a roundabout were not considered in accordance with the project brief.

Transit New Zealand Heavy Vehicle Limits Project

3.

RESULTS AND DISCUSSION

3.1

The network of routes

Page 34 of 38

Note that in this report RS is used as an abbreviation for route sector. A network of routes was chosen to be considered for use by longer and heavier vehicles than are currently permitted on roads in New Zealand. The network of routes in Table 10 was provided by Transit New Zealand [Sleath, 1999]. The network consists of six major routes each of which consists of sectors which are mainly sections of State Highway but also include some links to industrial and port precincts. Route N1 includes route sectors RS1 to RS6 and route sectors RS12 to RS16. Route N2 consists of route sectors RS7 to RS10 and RS21 to RS24. Route N3 is route sector RS11 and Route N4 consists of sectors RS17 to RS20. Route S1 consists of route sector RS25 and RS30 to RS35. Route S2 consists of sectors RS26 to RS29. Table 10. Roads selected for inclusion in the network of routes for the Scenario B vehicles.

Released by Transit New Zealand NORTH ISLAND Route Number

N1 N1a N1b N1c N1 N1 N2 N2 N2 N2a N3 N1 N1 N1 N1 N1 N4 N4a N4 N4 N2 N2 N2 N2b

Route Sector Number RS1 RS2 RS3 RS4 RS5 RS6 RS7 RS8 RS9 RS10 RS11 RS12 RS13 RS14 RS15 RS16 RS 17 RS 18 RS19 RS 20 RS21 RS22 RS23 RS24

Location of Port/Centre Whangarei Port-Auckland City Auckland Port Links Avondale/Rosebank Link Southdown/Penrose Link Auckland City-Manukau City Manukau City-Pokeno Pokeno-Tauranga Tauranga-Rotorua Rotorua-Taupo Tauranga-Kawerau Piarere-Mt Maunganui Pokeno-Hamilton Hamilton-Piarere Piarare-Taupo Taupo-Bulls Bulls-Wellington Hamilton-New Plymouth Port Taranaki Links New Plymouth-Bulls Bulls-Woodville Taupo-Napier Napier-Woodville Woodville-Wellington Gracefield Link

Route Position Node #1 SH15 @ RS 4 SH1 @ RP 326/7.00 SH1/SH 16 @ RS 335 SH1 @ RS 345 SH1/SH 16 @ RS 335 SH1/SH20 @ RS 355 SH1/SH2 @ RS 385 SH2/SH29 @ RS 157 SH5/SH30 @ RS 54 SH2/SH29 @ RS 157 SH1/SH29 @ RS 505 SH1/SH2 @ RS 385 SH1/SH3 @ RS 462 SH1/SH29 @ RS 505 SH1/SH5 @ RS 617 SH1/SH3 @ RS 844 SH1/SH3 @ RS 462 SH3/3A @ RS 229 SH3/SH3A @ RS 258 SH1/SH3 @ RS 844 SH1/SH5 @ RS 617 SH50 @ RS 0 SH2/SH3 @ RS 802 SH1 @ RP 987/5.00

Route Position Node #2 SH1/SH 16 @ RS 335 SH1/SH 16 @ RS 335 Rosebank Precinct SH1/SH20 @ RS 355 SH1/SH20 @ RS 355 SH1/SH2 @ RS 385 SH2/SH29 @ RS 157 SH5/SH30 @ RS 54 SH1/SH5 @ RS 617 SH34 @ RS 21 Mt Maunganui Precinct SH1/SH3 @ RS 462 SH1/SH29 @ RS 505 SH1/SH5 @ RS 617 SH1/SH3 @ RS 844 SH1 @ RP 987/5.00 SH3/SH3A @ RS 258 SH3/SH3A @ RS 258 SH1/SH3 @ RS 844 SH2/SH3 @ RS 802 SH50 @ RS 0 SH2/SH3 @ RS 802 SH1 @ RP 987/5.00 Gracefield Precinct

SOUTH ISLAND Route Number

S1 S2 S2 S2 S2a S1 S1a S1 S1 S1 S1b

Route Sector Number RS25 RS26 RS27 RS28 RS29 RS30 RS31 RS32 RS33 RS34 RS35

Location of Port/Centre

Route Position Node #1

Picton-Blenheim Blenheim-Nelson Nelson-Westport Westport-Greymouth Cape Foulwind Link Blenheim-Christchurch Lyttleton Port Link Christchurch-Timaru Timaru-Dunedin Dunedin-Bluff Port Chalmers Link

SH1 @ RS 0 SH1/SH6 @ RS 28 SH6 @ RS 116 SH 6/SH67 @ RS 336 SH 6/SH67 @ RS 336 SH1/SH6 @ RS 28 SH1/SH74 @ RS 332 SH1/SH74 @ RS 332 SH1/SH8 @ RS 501 SH1/SH88 @ RS 706 SH1/SH88 @ RS 706

Route Position Node #2 SH1/SH6 @ RS 28 SH6 @ RS 116 SH 6/SH67 @ RS 336 SH6/SH7 @ RS 430 SH67A @ RS 9 SH1/SH74 @ RS 332 SH1/SH73 @ RS 347 SH1/SH8 @ RS 501 SH1/SH88 @ RS 706 SH1 @ RS 953 SH88 @ RS 13

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Page 35 of 38

Note that Table 10 specifies the network of routes only roughly. Details of the exact roads included in the network of routes may be found in Appendix L. 3.2

Results for the curve investigation

The estimated costs for widening each part of the network of routes for the two trial vehicles, B1233-62b and B1233-62f for the original set of assumptions are shown in Table 11. The estimated costs for widening for Alternative assumption set 1 and Alternative assumption set 2 are shown in Table 12 and Table 13. Table 11. Cost of modifying curves on the network of routes for B1233-62b and B1233-62f for the original set of assumptions. Cost for N1= Cost for N2= Cost for N3= Cost for N4= Cost for S1= Cost for S2= total=

Cost for B1233-62b Cost for B1233-62f $3,500,000 $1,300,000 $6,300,000 $4,000,000 $300,000 $100,000 $3,400,000 $1,600,000 $8,100,000 $3,900,000 $22,000,000 $7,900,000 $43,600,000 $18,800,000

Table 12. Cost of modifying curves on the network of routes for B1233-62b and B1233-62f for Alternative assumption set 1. Cost for N1= Cost for N2= Cost for N3= Cost for N4= Cost for S1= Cost for S2= total=

Cost for B1233-62b Cost for B1233-62f $14,000,000 $3,900,000 $23,100,000 $8,500,000 $700,000 $300,000 $18,200,000 $5,000,000 $32,500,000 $8,900,000 $43,500,000 $18,100,000 $132,000,000 $44,700,000

Table 13. Cost of modifying curves on the network of routes for B1233-62b and B1233-62f for Alternative assumption set 2. Cost for N1= Cost for N2= Cost for N3= Cost for N4= Cost for S1= Cost for S2= total=

Cost for B1233-62b Cost for B1233-62f $38,800,000 $8,100,000 $44,000,000 $12,400,000 $5,100,000 $2,100,000 $30,400,000 $7,000,000 $46,400,000 $13,300,000 $49,300,000 $19,700,000 $214,000,000 $62,600,000

The routes N1, N2, N3, N4, S1 and S2 are described in Table 10. Also note that RGDAS data and RAMM data, which give detailed information about road width, curvature, terrain etc. for roads in New Zealand were used for Tables 11, 12, and 13. Remarks •

The costs for modifying curves on the network of routes presented in Table 11 are based on Assumption 1 and Assumption 2.

•

The removal of route S2 (State Highway 6) from the network of routes would significantly reduce the costs.

Transit New Zealand Heavy Vehicle Limits Project

•

•

Clearly, there are safety implications associated with the design of the assumptions for the modification of curves on the network of routes. A recent Australian study suggested that “a 1 metre increase in seal width (either as additional lane width or shoulder seal) produced a 20 percent reduction in accident rates.” [McLean, 1996]. However, this was an Australian study and dealt with widening of an entire section of road, not just the curves. Milliken has made some attempt to estimate the safety implications of road widening in [Milliken, 1999]. The estimated costs of modifying curves on the network of routes were presented in Tables 11, 12, and 13. The costs are sensitive to the assumptions that were used to estimate widening because changing the widening assumptions alters the number of curves that require modification. The number of curves that were estimated to require modification were: Assumption Set Original Original Alternative 1 Alternative 1 Alternative 2 Alternative 2

3.3

Page 36 of 38

Vehicle B1233-62b B1233-62f B1233-62b B1233-62f B1233-62b B1233-62f

Number of curves to be modified 817 376 2531 927 3784 1247 .

Results for the roundabout investigation

The costs for modifying the roundabouts on the network of routes are shown in Table 14 and Table 15 for B1233-62b and B1233-62f, respectively. Table 14. Costs for modifying roundabouts on the network of routes to accommodate B1233-62b. cost for N1= cost for N2= cost for N3= cost for N4= cost for S1= cost for S2= total cost=

$175,000.00 $259,000.00 $205,000.00 $113,000.00 $364,000.00 $168,000.00 $1,284,000.00

Table 15. Costs for modifying roundabouts on the network of routes to accommodate B1233-62f. cost for N1= cost for N2= cost for N3= cost for N4= cost for S1= cost for S2= total cost=

$158,000.00 $236,000.00 $188,000.00 $103,000.00 $333,000.00 $154,000.00 $1,173,000.00

Details of the costs for each of the roundabouts on the network of routes that required modification are given in Appendix J. Also note that it was not necessary to modify roundabouts where only a ‘straight through’ manoeuvre was permitted. For the safety evaluation project, 119 other alternative vehicles were simulated. Estimates of the costs of modifying the network of routes to accommodate each of these alternative vehicles were made. These results and the corresponding method are presented in Appendix K. The costs for modifying curves and roundabouts on the network of routes are separated by route sector in Table 16.

Report 5: Geometric Evaluation. Paul Milliken, TERNZ.

Table 16. Costs of modifying the network of routes by Route Sector.

Page 37 of 38

Transit New Zealand Heavy Vehicle Limits Project

4.

Page 38 of 38

REFERENCES

[Austroads, 1993] Austroads, Guide to Traffic Engineering Practice Part 6 - Roundabouts, Austroads, Sydney, 1993. [Austroads, 1997] Austroads, Rural Road Design - Guide to the Geometric Design of Rural Roads, Austroads, Sydney, 1997. [Fancher, 1980] P. S. Fancher et al, Measurement and representation of the mechanical properties of truck leaf springs., SAE: Warrendale. p. 14, 1980. [Gillespie, 1992] T. D. Gillespie, Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, Warrendale, 1992. [Latto, 1999] D. Latto, Road trial for Model Validation, TERNZ report for Transit New Zealand, 1999. [MacAdam, 1981] C. C. MacAdam, Application of an Optimal Preview Control for Simulation of Closed-Loop Automobile Driving, IEEE Trans. on Systems, Man and Cybernetics, SMC - 11(6), 1981. [McLean, 1996] McLean, Review of accidents and Rural cross section elements including roadsides, ARR 297, November 1996. [Milliken, 1999] P. C. Milliken, Task 4 Summary Safety Report, TERNZ report for Transit New Zealand, 1999. [Prem et al., 1999] Prem, H., Ramsay, E., Fletcher, C., George, R., Gleeson, B., Estimation of Lane Width Requirements for Heavy Vehicles on Straight Paths, preliminary report produced at AARB, 1999. [Sayers, 1989] M. W. Sayers, Automated Formulation of Efficient Vehicle Simulation Codes by Symbolic Computation (AUTOSIM) in The Dynamics of Vehicles on Roads and Tracks, Kingston, Ontario: Swets Zeitlinger, 1989. [Sayers and Riley, 1996] M. W. Sayers and S. M. Riley, Modelling Assumptions for realistic Multibody Simulations on the Yaw and Roll behaviour of Heavy Vehicles, SAE 960173, 1996. [Sleath, 1999] L. Sleath, Email communication with Peter Baas, 30 June 1999.