Transport related Technical & Engineering Advice …...steeper rate of decline as flows further...

Task Ref: Task 263(4/45/12)

Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page |1

Transport related Technical & Engineering Advice and Research – Lot 2 Roads

Task 263: Re-validation of Speed Flow Curves

Project Sponsor: Peter Grant

Package Order Ref: 263(4/45/12)ATK



Highways Agency/DfT Framework for Transport Related Technical and Engineering Advice and

Research Lot 2

Task Ref: 263 (4/45/12)ATKS

Task Title: Re-Validation of Speed Flow Curves

Project Sponsor: Peter Grant

Final Report

Submitted by:

AECOM Limited

Notice

This document has been produced by ATKINS for the Highways Agency solely for the purpose of the task.

It may not be used by any person for any other purpose other than that specified without the express written

permission of ATKINS. Any liability arising out of use by a third party of this document for purposes not

wholly connected with the above shall be the responsibility of that party who shall indemnify ATKINS against

all claims costs damages and losses arising

Document History

Revision Purpose Description Originated Checked Reviewed Authorised Date

1 Final Report Draft Brian Vaughan

Nick Woollett George Lunt Nick Woollett 18

th Sep

2014

2 Final Report including client comments

Brian Vaughan

Nick Woollett George Lunt George Lunt

24th

October 2014

Contents



Section Page

Glossary of Terms 4

1. Introduction 5

1.1 Objectives and Aims 5

2. Background and Literature Review 7

2.1 Introduction 7

2.2 Current COBA Curves and Relationship to Modelling 7

2.3 TRL Dual Carriageways and Motorways (1990s) 10

2.4 TRL Rural Single Carriageways (1990s) 13

2.5 Comparison of Speed Flow Relationships 16

2.6 Issues to be Addressed in the Study 17

3. Methodology 19

3.1 Overview of Approach 19

3.2 Site Selection 19

3.3 Data Sources 20

3.4 Analysis Methodology 21

4. Site Selection and Data Processing 23

4.1 Introduction 23

4.2 Sites Included 23

4.3 Data Availability 25

4.4 Database Conversion Process 25

4.5 Sample of Final Data 28

5. Preliminary Analysis 32

5.1 Introduction 32

5.2 Identification of Sites with Suitable Data 32

5.3 Site-by-Site Linear Regression 33

5.4 Summary of Findings 34

6. Regression Analysis by Road Type 45

6.1 Introduction 45

6.2 Identification of Break Points 45

6.3 Dual Carriageways and Motorways – Multiple Stepwise Regression 47

6.4 Rural Single Carriageways – Multiple Stepwise Regression 72

7. Recommended Speed Flow Curves and Parameters 80

7.1 Overview 80

7.2 Single Rural Carriageways 83

7.3 Dual Carriageways and Motorways 86

7.4 Speed Flow Curve Comparisons 90

7.5 Power Curves 92

8. Areas for Future Research 95

9. Summary and Conclusions 96



Glossary of Terms

Terms used in Speed / Flow Curve Formulations

VL0 / VH0 The free flow speed of light and heavy vehicles respectively (kph)

VL / VH The speed of light and heavy vehicles respectively (kph)

Q Traffic flow. Within this report, units include: vehicles per hour, vehicles per hour per

lane, pcus per hour and pcus per hour per lane.

QB Breakpoint: the value of Q at which the speed / flow slope of light vehicles changes in

existing COBA curves.

For the new speed / flow relationships defined within this report, QB represents the point

where lane density is such that drivers begin to be constrained by slower moving vehicles

and speeds start to drop more rapidly

QC Capacity flag: defined as the maximum realistic value of Q

QF For the new speed / flow relationships defined within this report: the point at which free

flow speeds are no longer maintainable.

Slope The gradient of the line indicating the change in speed as over a given flow range for any

specified speed / flow curve.

Road and Traffic Definitions

pcus Passenger car unit, measure assigning car equivalence values to all vehicle types (e.g. a

value of 2.5 is applied to heavy vehicles in this report).

Heavy vehicles For the purposes of this report a heavy vehicle is considered to be any vehicle over 6.6m

in length (as classified by the automatic counters used on the Highways Agency’s

network)

Road type The following Highways Agency link types are included in the report:

Class 1 – S2 – rural single carriageways;

Class 2 – D2AP – rural 2-lane all-purpose dual-carriageway;

Class 3 – D3AP – rural 3-lane all-purpose dual-carriageway;

Class 4 – D2M – rural 2-lane motorway;

Class 5 – D3M – rural 3-lane motorway;

Class 6 – D4M – rural 4-lane motorway.



1. Introduction AECOM is pleased to submit this Final Report following work with the Highways Agency to

review the current speed / flow relationships on Highways Agency roads and update the current

COBA speed / flow curves that are used to forecast average hourly vehicle speeds based on a

link’s traffic flow and geometric parameters, primarily used in traffic models. For this

commission AECOM is taking the technical lead on this project on behalf of Atkins. The

existing curves are specified in the Design Manual for Roads and Bridges, Volume 13

Economic Assessment of Road Schemes, Section 1 the COBA Manual, Part 5 Speeds on Links

(Highways Agency, May 2002).

The inception and technical workshop meeting on the 11/02/2014 included a wide ranging

discussion around the project specification, the project data requirements and the required

outputs of the task. These requirements were summarised in the Scoping Report submitted to

the Agency on 27th February 2014.

A second technical workshop took place on the 24th July and focussed on the initial outcomes of

the analysis and the proposed approach to concluding the research and updating the speed /

flow relationships.

This report summarises the basis of the work undertaken, describes the process undertaken to

select sites, collate data and analyse speed / flow relationships by road type for the selected

links.

The remainder of this report is structured as follows:

Section 2: Background and Literature Review;

Section 3: Methodology;

Section 4: Site Selection and Data Processing;

Section 5: Preliminary Analysis;

Section 6: Regression Analysis by Road Type;

Section 7: Recommended Speed / Flow Curves and Parameters;

Section 8: Areas for Future Research;

Section 9: Summary and Conclusions.

1.1 Objectives and Aims

The project objectives as set out in the Highways Agency’s task specification are as follows:

1. To update the speed-flow curves for each road type on the HA network to be based on

average link speeds (not spot speeds) and link traffic flows;

2. To identify whether it is statistically significant to include link length within the speed

flow relationship; and

3. To provide guidance on the statistical accuracy of the speed flow relationship for each

set of discrete flow ranges.

The road types on the HA network are specified in Table 1.1 below.



Table 1.1 The HA’s Road Classes in COBA

COBA Road Class Road Type Description

1 S2 Rural single carriageway 2 D2AP Rural all-purpose dual 2-lane carriageway 3 D3AP Rural all-purpose dual 3 or more lane carriageway 4 D2M Motorway, dual 2-lanes 5 D3M Motorway, dual 3-lanes 6 D4M Motorway, dual 4 or more lanes

In addition to the six road types listed above, data were obtained for a small number of Smart

Motorway links (representing sections of the motorway network with one or both of the following

features: controlled motorway and hard-shoulder running.

The motivation for the review and update to the existing COBA relationships is a desire from the

Highways Agency to improve highway models. In particular, to reduce the costs of modelling by

improving the speed / flow relationships applied within models so that the calibration and

validation of models to observations is a less time intensive task. By identifying the individual

factors that dictate how speeds vary as flow changes across a wide range of link types the hope

is that less ‘local calibration’ of the models is required as the relationships defined are more

accurate across a wide range of parameters.



2. Background and Literature Review

2.1 Introduction

This section summarises the background to the research undertaken in this project. The

section is structured as follows:

Current COBA Curves and Relationship to Modelling – a discussion of the existing

COBA relationships and how they are applied in UK modelling and economic appraisal;

TRL Dual Carriageways and Motorways (1990s) – a short literature review of the

TRL research on road classes 2-6;

TRL Rural Single Carriageways (1990s) - a short literature review of the TRL

research on road class 1;

Comparison of Speed Flow Relationships – a comparison of the existing COBA

relationships with other commonly used relationships;

Issues to be Addressed in the Study – a summary of the issues identified in the

preceding sub-sections which need to be considered in this study.

2.2 Current COBA Curves and Relationship to Modelling

The current COBA speed flow curves for Classes 1 – 6 were derived in studies published by

TRL in 1992 and 19931. Since then these curves have been used extensively in transport

modelling and economic appraisal.

The existing curves are piecewise linear formulations with a minimum speed cap which applies

to flows at a point beyond the calculated capacity of the highway. Two-types of parameter

influence the relationship between speed / flow for each road class:

The proportion of heavy vehicles in the total traffic flow; and

Various geometric parameters (e.g. hilliness and bendiness).

Figure 2.1 shows typical curves for single carriageway roads for three design standards

(assuming 15% heavy vehicles). There is a reduction in speed as flow increases towards a

breakpoint (varying between approximately 900 and 1,200 vehicles per lane) and then a

steeper rate of decline as flows further increase.

1 Class 1: Transport Research Laboratory, Department of Transport Contractor Report 319, Speed/Flow/Geometry

Relationships for Rural Single Carriageway Roads, 1993 Classes 2-6: Transport and Road Research Laboratory, Department of Transport Contractor Report 279, Speed/Flow/Geometry Relationships for Rural Dual-Carriageways and Motorways, 1992



Figure 2.1 Existing COBA Speed / Flow Relationships for Class 1

Note: Curves use bendiness of 75 degrees per km, hilliness of 15 m per km and 15% heavy vehicles.

Figure 2.2 shows typical curves for dual two carriageways and motorways. There is a gentle

reduction in speed as flow increases towards the breakpoint (of approximately 1,200 vehicles

per lane) and then a steeper rate of decline as flows further increase.

40

50

60

70

80

90

100

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

Kp

h

Vehicles / hour / lane

TD9 10m TD9 7.3m Non TD9 7.3m



Figure 2.2 Existing COBA Speed / Flow Relationships for Classes 2-6

Note: Curves use bendiness of between 20 and 30 degrees per km, hilliness of 15 m per km and 15%

heavy vehicles.

Historically the curves have been applied in UK scheme economic appraisal using the COBA

software. In these cases a COBA model is constructed using traffic flow outputs from a traffic

model or other source and the speed / flow relationships are defined within the COBA software

by measuring the geometric characteristics of each modelled link to ensure that the curves are

calibrated to the COBA standard. This approach is now rare, as COBA economic appraisal is

limited to fixed-trip matrices and the majority of current appraisal requires a more sophisticated

approach where demand varies according to a number of mechanisms including time period

choice, mode choice and destination choice. UK appraisal usually now requires TUBA which

uses matrix-based outputs from transport models to calculate travel time savings and other user

benefits.

Many highway assignment models make use of the COBA curves as a reference for the speed /

flow curves specified within the modelling software; however, a number of observations should

be made:

The formulations used within highway assignment software packages differ from the

COBA specification requiring a fitting of the functional form within the software to the

COBA specification (for example, SATURN2, the most frequently used highway

assignment package in the UK, has a power formulation for speed / flow relationships).

To achieve a good degree of convergence in the highway assignment ideally requires a

continuous functional form and this is an important driver in adopting power

2 SATURN (Simulation and Assignment of Traffic to Urban Road Networks) is a suite of flexible network analysis

programs developed at the Institute for Transport Studies, University of Leeds and distributed by Atkins since 1981.

40

50

60

70

80

90

100

110

120

0 500 1,000 1,500 2,000 2,500

Kp

h


D2AP D3AP D2M D3M or D4M



formulations in SATURN. Similar functional forms have been developed such as the

Bureau of Public Roads (BPR)3 and Akcelik

4 curves;

The complexity and detail of traffic models means that speed / flow curves are not

usually calibrated by measurement of the detailed geometric characteristics of links as

defined in COBA, but by some other classification system, usually based upon a

broader definition of link type using the road standard and an indicator of design

standard/condition;

Although the existing COBA formulations define light and heavy vehicles separately at

the input stage, the resulting COBA curve is an all vehicle average relationship.

Consequently, traffic models tend to apply a curve for all vehicles with a simplistic

reduced maximum speed applied to heavy vehicles. Separately specified speed / flow

relationships for light and heavy vehicles would be an enhanced approach in terms of

the realism of traffic models.

2.3 TRL Dual Carriageways and Motorways (1990s)

The 1990 study into speed flow relationships on rural single carriageways was designed to up-

date the COBA relationships that had been developed back in 1977/78. The 1990 work was

approached as a periodic update rather than a fundamental review and as such it drew heavily

on existing knowledge.

Thirteen separate links were identified for inclusion in the study comprised of:

One D4M site;

Five D3M sites;

Two D2M sites; and

Five D2AP sites.

The travel times on the links were obtained by moving observer techniques and covered 16

hours of observations at each site. The links were selected to avoid any junction effects, and

the travel time data was filtered to eliminate any incidents and blocking back effects.

Aggregating the data into 10 minute bands resulted in around 30 speed/flow observations per

link and a relatively small sample of 755 observations in total across all the links. Due to the

small sample size and limited number of links by road type a number of issues were identified

with the data including:

An absence of observations at low flow: the majority of speed data was collected for

flow levels of 500 – 2,000 vehicles per lane. This was a particular problem for the

motorway sites, as shown in Figure 2.2, in that there were almost no observations in the

expected free flow part of the curve;

Significant scatter in the data due to the small sample sizes; and

Potential for correlations due to the small number of sites in relation to the number of

variables to be estimated. This meant that the data was pooled across the sites as

within-road type analyses could not really be supported by the data.

3 The BPR equation was originally fitted to the 1965 Highway Capacity Manual freeway speed data;

4 The Akcelik equation was derived by Akcelik from the steady state delay equation for a single channel queuing system.



At the outset the study determined that there was no evidence to support a move away from the

existing two part COBA relationships, and as such adopted the existing COBA QB (QB is the flow

at which the gradient of the existing COBA speed / flow curves increase) values of 1,080

vehicles per hour per lane and 1,200 vehicles per hour per lane for D2AP and motorway sites

respectively. All subsequent analyses were undertaken based on this assumption. The absence

of low flow data observations would have meant it would have been very difficult to examine

whether more complex relationships actually existed.

The absence of low flow data also caused problems in defining the intercept points and this

resulted in the existing COBA slope values to QB of -0.006 for light vehicles and zero for heavy

vehicles being imposed on the analysis.

The main findings from the study were:

That light and heavy vehicle speeds had increased significantly since the 1977/78

study;

A significant change had taken place in the effect of hilliness on light vehicle speeds:

this now had a much reduced impact;

That the extent of scatter led to wide variance in the estimation of the slope from QB to

QC by site of 0.015 to 0.055 which made definitive conclusions difficult; and

Bendiness and rises were shown to be the most significant contributors to explaining

variation in light vehicle speeds.

The recommended light vehicle speed flow relationship was:

VL = C – 0.12 * Bendiness - 0.28 * Rises – 0.006 * QL – 0.027 * QL

with C defined as follows:

D4M = 124kph

D3M = 118kph

D2M = 111kph

D2AP = 108kph

where VL = light vehicle speed; and

QL = total vehicle flow per lane.

The recommended heavy vehicle speed flow relationship was:

VH = 93 – 0.06 * Bendiness - 0.50 * Rises – 0.0012 * QL – 7 * D2AP

where VH = heavy vehicle speed; and

QL = total vehicle flow per lane

The study outputs were such that it was concluded that there was minimal empirical evidence to

make significant changes to the COBA curves. The following scatter plots of the data

observations available in the study show the limitations with which the study was presented.



Figure 2.2 Scatter Plots of TRL 1990 Data for D2M/D3M/D2AP



2.4 TRL Rural Single Carriageways (1990s)

Work was undertaken in 1991/2 to review and update, as necessary, the COBA curves on rural

single carriageways that had been derived from a study in 1979. The study used registration

number plate matching to obtain a large sample of vehicle speeds, as opposed to all earlier

work that used moving observer methods which restricted sample sizes. This resulted in almost

146,000 speed measurements across the 42 sites chosen for use in defining the speed flow

relationships.



The vehicle speeds were aggregated to ten minute intervals, as in previous studies, and this led

to the development of a database of speed/flow observations of 3,649 light vehicles and 3,624

heavy vehicles. With the higher sample size, more robust estimates of speeds in each ten

minute slot (due to an average of 40 observations in each period) and wider coverage of sites,

the study was able to explore a wide range of variables including:

BENDS – Bendiness;

HS - Continuous metre hardstrip;

CONSTRIP - Continuous 0.3 metre hardstrip;

CONEDGE - Continuous edge lining;

SWIDTH - Hardstrip width;

SFLOWL - Same direction light veh. Flow;

JCNS – Intersections;

NEW - Modern, designed road;

SFLOWH - Same direction heavy veh. Flow;

CWIDTH - Carriageway width;

REGION - Regional variable;

NETGRAD - Net gradient;

FIELDS - Field entrances;

OFLOWA - Opposite direction total flow;

PEAK - AM or PM peak period;

VISI – Visibility;

VERGE - Verge width;

RAIN – Rainfall;

RISES - Upgrade metres;

FALLS - Downgrade metre;

LAYBYS - Lay-bys;

TOTHILL - Total upgrade and downgrade metres;

v1 - Light vehicle speed;

Vh - Heavy vehicle speed;

P - Proportion of heavy vehicles; and

F - Total vehicle flow.

Not all the variables in the above list were considered appropriate for application in the

appraisal of road schemes (e.g. rainfall, region, day of week, time of day etc.) and these were

excluded from the final recommended relationships.

This led to the following recommendations for the variables and the coefficients that were most

appropriate for application. After the recommended set of coefficients had been determined the

constant term was recalculated so as to provide the closest replication of the speeds observed

for each class of vehicle.

The final recommended formula for light vehicle speeds was:

VL = + 72.1 - ((0.090 - (0.075 x NEW)) x BENDS) - (0.0007 x ((RISES+FALLS) x BENDS) ) - (0.11 x NETGRAD) [one-way links only] - ((0.015 + (0.027 x P)) x F) + (2.0 x CWIDTH) + (1.6 x CONEDGE) + (1.1 x SWIDTH) + (0.3 x VERGE) - (1.9 x JCNS) + (0.005 x VISI)



The recommended formula for heavy vehicles was:

VH = + 78.2 - ((0.10 - (0.10 x NEW)) x BENDS) - (0.07 x (RISES+FALLS)) - (0.13 x NETGRAD) [one-way links only] - (0.0052 x F) + (0.3 x VERGE) - (1.1 x JCNS) + (0.007 x VISI)

These formulae revealed that light vehicles are more influenced by flow and geometric effects

than heavy vehicles which are more constrained by vehicle performance. Bendiness is the most

important determinant of speed for both light and heavy vehicles although its impact is

substantially reduced on modern, designed links (no bendiness effect was discerned for heavy

vehicles on such links).

Hilliness and net gradient are important speed determinants for heavy vehicles. Carriageway

width has an impact on light, but not on heavy, vehicles. The provision of continuous edge

lining, if in both directions, adds 1.6 km/h to light vehicles speeds. Continuous hardstrips, an

element not currently incorporated within formulae, appear to increase light vehicle speeds by

some 1.1 km/h for each metre of width (averaged over both directions).

Verge width and intersections both influence speed although other forms of accesses do not

have a significant effect. Visibility also affects speed.

The above formulae form the basis for the current COBA curves for rural single carriageways

with minor modifications having been made, resulting in the following formulations.

The current COBA formula for light vehicle speeds is:

VL = + 72.1 - 0.090 x BENDS - 0.0007 x (RISES+FALLS) x BENDS - 0.11 x NETGRAD [one-way links only] - ((0.015 + (0.027 x P)) x F) + 2.0 x CWIDTH + 0.3 x VERGE -(1.9 x JCNS + 0.005 x VISI

The current COBA formula for heavy vehicle speeds is:

VH = + 78.2 - 0.10 x BENDS - 0.07 x (RISES+FALLS) - 0.13 x NETGRAD [one-way links only] - 0.0052 x F + 0.3 x VERGE - 1.1 x JCNS + 0.007 x VISI



2.5 Comparison of Speed Flow Relationships

Prior to commencing the study it is informative to compare the current COBA curves with other

commonly used speed flow relationships to identify any significant differences that exist. Three

alternative speed flow curves have been used for this comparison:

The relationships used in FORGE5;

Highway Capacity Manual (HCM)6 relationships for freeways; and

The Akcelik curves which are used extensively in Australia and other countries and

which are referred to in WebTAG as being a suitable form for determining speeds

beyond QC.

Figure 2.3 shows the form of these curves for a typical D3M in comparison to the current COBA

curve. In the diagram all of the curves have used a common intercept point for free flow speed

so that the profiles can be compared from a common base.

The diagram indicates that the COBA curve is steeper up to QB and that the implied QB in the

other curves is at a higher flow than COBA, around 1,400 veh/hour/lane compared to the COBA

value of 1,200 veh/hour/lane. After the QB point the other curves have a steeper slope and a

wider variance on what the speed at QC is, although the HCM curve is close to the COBA curve

speeds at QC.

The diagram also indicates that the non-COBA curves represent a period where the free flow

speed is almost level, up to about 600 vehs/hour/lane, and that the speed flow curves for

motorways may have three sections as follows:

A very shallow section where free flow speeds are essentially achievable and which

terminates around 600 vehs/hour/lane;

A section with gradually decreasing speeds as flow increases up to a breakdown point

QB, and that this QB may be occurring at a higher flow level than COBA predicts, around

1,400 veh/hour/lane; and

A steep decline in speeds beyond QB to QC which may be steeper than implied by the

COBA slope beyond QB simply as a result of the later point at which QB occurs in non-

COBA curves.

The FORGE, HCM and Akcelik7 curves have all been updated more recently than the COBA

curves and may better reflect the current situation on motorways due to the continuing

improvements in the vehicle fleet and its performance.

5 FORGE stands for Fitting On of Regional Growth and Elasticities, it is the highway supply module of the National

Transport Model. 6 The HCM is a publication of the Transportation Research Board of the National Academies of Science in the United

States. It contains concepts, guidelines, and computational procedures for computing the capacity and quality of service of various highway facilities. 7 The Akcelik equation was derived by Akcelik from the steady state delay equation for a single channel queuing system.



Figure 2.3 Comparison of Light Vehicle Speed Flow Formulations (D3M Example)

2.6 Issues to be Addressed in the Study

The preceding sections have identified a number of issues that the current study should be

aware of and address directly in order to undertake a thorough review of speed/flow

relationships for use in transport models. These are:

The need to have a database of speed/flow observations that covers the full flow

ranges encountered on each type of road. The TRL studies of the 1990s were unable to

collect data at low flows and this presented significant limitations, particularly for dual

carriageways and motorways;

The need to have an extensive coverage of sites by each road category in order to

enable variables to be examined both within road type and across road types to

establish whether there are significant differences. Again the TRL work on dual

carriageways and motorways had a limited number of sites and had to pool data across

road types to undertake any meaningful analyses;

That the TRL work in 1991/2 on rural single carriageways was a more robust study due

to the significantly higher speed/flow sample base and coverage of sites, 42 in total.

The main limitation in this work would again be the absence of low flow data and what

the implications of that are for the derivation of the slope to QB; and

Evidence from other speed/flow relationships, that have been updated more recently

than COBA, is that there is a different functional form in that there may be three distinct

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115

120

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

Sp

ee

d (

kp

h)


HCM FORGE COBA Akcelik



parts to the curve to QC, and that speeds are maintained at a higher level for longer

before experiencing a more rapid decline as traffic conditions deteriorate. This also

tallies with the work carried out by the HA, which prompted this study, using HATRIS

data on D3M links that indicated differences to COBA in the low and high flow ranges.

With the availability of extensive real time speed/flow data it is an opportune time to undertake a

fundamental review of the speed/flow relationships for use in traffic models. The work should

not take current COBA curves as the benchmark but derive appropriate functional forms that

are supported by the data. It is also important to bear in mind that the emphasis is on

speed/flow curves for use in transport modelling and as such the variables contained in the

relationships should be practical ones for the user to collate the necessary information. The

research should not produce overly complicated formulations that would place an undue burden

on the modelling process as this would be counter to the primary aim of the study.



3. Methodology 3.1 Overview of Approach

This section sets out the methodology adopted to develop a database and undertake the

analysis of speed and flow data for a broad selection of sites across the Highways Agency’s

network as follows:

Site Selection – the approach adopted to generate a list of Highways Agency links

which are representative of the road types and characteristics required for the study;

Data Sources – a summary of the key sources of data for establishing the database for

the purpose of analysis; and

Analysis Methodology – the framework adopted to review the data, apply filtering to

remove outliers, preliminary regression analysis on each individual site and finally

stepwise regression analysis of each road type to produce updated speed / flow

relationships.

3.2 Site Selection

The purpose of the site selection phase was to identify a set of highway links providing

reasonable coverage of all the road types and characteristics which form part of the analysis for

this project. The approach adopted is illustrated in Figure 3.1.

Figure 3.1 Site Selection Process

Table 3.1 sets out the parameters which were agreed to be included in the analysis during the

project scoping stage.

•Manually select around 300 sites on the Highways Agency networks aiming to:

•Get an even spread across English Regions; and

•An even spread across road types.

•Selection undertaken with an awareness of other analysis parameters such as length and link geometry in order to increase likelihood of good coverage across these parameters.

Bottom-up Analysis

•Tabulation of selected sites according to analysis parameters in order to demonstrate sufficient coverage.

Top-down Review

•Review sites against available data and produce updated list of sites.

Revised List of Sites



Table 3.1 Categories for Site Selection

Category Category Description

English Region Which of the nine English Regions the site lies in

Land-Use Although all of the roads selected are officially rural trunk roads, a

categorisation of urban is reported for a number of these indicating that they serve a large conurbation.

Road Type COBA classes 1-6 and additionally sections of ‘Smart Motorway’. Link Length Length of the studied link. Hilliness and Bendiness

Hilliness in terms of rises and falls per km and bendiness in terms of degrees per km for all of the selected links.

Other Class 1 Parameters

For single carriageways a further assessment of the characteristic of the nature of the road, i.e. categorisation of carriageway width, hard

strip and verge.

Heavy vehicle Percentages

The heavy vehicle percentage of each link at every observation point (could also be described in terms of absolute numbers of heavy

vehicles).

3.3 Data Sources

The project Scoping Report set out four types of data required to construct a database for the

analysis of speed / flow relationships. These are summarised in Table 3.1

Table 3.1 Required Data Types

Data Type Purpose / Definition

1 - Traffic Flow

To provide information on the flow in the middle of a link. These data need to represent average values across an hour, with the ability to

disaggregate by vehicle type and by time of year, day of week and time of day. In selecting links there is a need to ensure that the flow is essentially homogenous along the link within specified tolerances.

2 - Journey Time

To provide an average journey time along the length of a link. These data need to represent average values across an hour, with the ability to disaggregate by vehicle type and by time of year, day of week and

time of day. It is also desirable that the data has sufficient spatial detail to exclude the sections of a link around a merge / diverge, or on the

approach to a junction where the link loses priority.

3 - Category

Data sources which enable the selection of sites which provide a representative sample of all of the categories to be included in the

study. The categories are discussed in detail below, but for example, this will include link length, geometric parameters, road type and land-

use.

4 - Exclusion These data will highlight specific conditions which would require data

records to be excluded from the analysis; for example, records of incidents.



An investigation into the best available sources of each data type was undertaken at the

beginning of the project. Table 3.2 indicates the data sources chosen to cover the four

categories listed in Table 3.1.

Table 3.2 Data Sources for Analysis

Data Source Data Type

Function for Analysis Access

TRADS (HATRIS) 1

Source of all traffic flow data for the task. Records are at least hourly, generally categorised into light and

heavy vehicles and also often include mid-link spot speeds which are useful

for checking / calibration against average speeds.

Direct access through HATRIS

database.

TrafficMaster GPS data by ITN link from DfT

2

Source of light / heavy vehicle flows along links mapped to ITN GIS layer.

The ITN network is spatially more detailed than the HATRIS network

providing a means of removing merge / diverge effects for a majority of links.

Access from DfT Congestion team.

HAPMS Data 3 Geometric highway data from the

HAPMS team. Estimates of radius and change in height approximately every 10m directly mapped to HATRIS links.

Access through Highways Agency

HAPMS team

OpenOS 3 GIS data source used to look at land-use around selected links.

Online.

GoogleMaps 3 & 4 Satellite mapping and StreetView for

confirmation of number of lanes, confirming consistency of characteristics

along selected links.

Online.

HATO records 4 Database of incidents affecting live

carriageways and hard shoulders which can be provided by HATRIS link.

Access through the Highways Agency Traffic Management Directorate.

3.4 Analysis Methodology

The project specification requires an analysis of available data in order to update the following

COBA speed / flow parameters for road classes 1-6:

VL0, VH0 – the initial speed of light and heavy vehicles (kph);

QB – the vehicle flow per hour per lane at which the speed / flow slope changes; and

VB – the speed of vehicles at flow QB.

These parameters (and additionally the capacity (QC) and speed at capacity (VC)) are illustrated

in Figure 3. (the dashed portion of the line represents the current COBA for flows beyond QC.



Figure 3.2 Key Parameters of Existing COBA Speed / Flow Relationships

The approach to analysis has been divided into three distinct sections:

Identification & Filtering – reviewing the data for each selected site in order to

establish the availability and suitability of the data for analysis. Application of filtering to

remove elements of the data not suitable for analysis;

Preliminary Analysis – applying linear regression to the data on a site-by-site basis

and producing tabulations of the emerging free flow speeds, flow breakpoints etc by

road type; and

Regression Analysis by Road Type – undertaking stepwise linear regression on all

the filtered data for each road type using the outputs from the preliminary analysis to

assist with the establishment of models. The stepwise regression is applied to establish

which independent variables are significant and thereby produce the final statistical

models to evaluate speed / flow relationships.

40

50

60

70

80

90

100

110

120

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Ve

hic

le S

pe

ed

(k

ph

)

Vehicles / hour / lane / direction

Light Vehicles Heavy Vehicles All Vehicles

VL0

VH0

QB

VC

QC



4. Site Selection and Data Processing 4.1 Introduction

In this section we have set out the approach used to select a representative set of highway links

for analysis and how these data were processed and compiled to form the study database

under the following headings:

Sites Included – summarises the sites included in the database which have been directly used

in the analysis;

Data Availability – summarises the results of compiling data sources in terms of the number of

sites where sufficient data were available to undertake analysis;

Database Conversion Process – describes the processes used to collate and process the

data sources to form the project database; and

Sample of Final Data – summarises the categorisation of the sites used in analysis in order to

demonstrate the suitability of the dataset for calculating speed / flow relationships.

4.2 Sites Included

The application of the methodology described in Section 3 resulted in a final set of 127 links for

analysis (initially 292 sites were selected. Of these 189 had overlapping average speed and

flow data, and once a full review of all sites had been undertaken 127 suitable sites remained).

Figure 4.1 illustrates the location and road type of the final 127 links (Appendix A contains a

larger version of this map).



Figure 4.1 Map of HATRIS Sites used in Study Analysis

Figure 4.1 illustrates that good geographical and road type coverage has been achieved.



4.3 Data Availability

The initial list of 292 sites only included sites where the TRADS counter providing flow

information was active. Theoretically, the DfT journey time data were available on all HATRIS

links for the 2011/12 and 2012/13 school (September – August) years (and so in principal each

of these sites should contain the basic data necessary to produce a local plot of average

speeds against vehicle flows.

However, in reality there were a number of sites where this was not possible, because:

The available date ranges where speed and flow data were available did not overlap; or

The TRADS data did not provide classified count information (disaggregation between

light and heavy vehicles).

The sites mapped in Figure 4.1 include filtering to remove sites where there was no successful

match of speed and flow data. The most common reason for this is a lack of overlapping time

periods when both speed and flow data were available.

4.4 Database Conversion Process

The project methodology requires that a database is developed to hold all of the project data in

such a way that queries can be run to extract data for an individual site or a sample of sites

according to certain criteria in terms of the road type, geometric parameters etc. The following

steps were applied to the raw data in order to develop this database:

Processing of raw data into the required format;

Linking of all data to a common field, the HATRIS link reference;

Establishing a summary data table containing each site and all of its characteristics;

Developing a query tool to extract data for sites based upon a filtering of the summary

table.

Table 4.1 outlines how each of the four principal datasets were processed and indexed with a

HATRIS link reference to allow the data to be linked within the database.



Table 4.1 Data Processing and Indexing

Data Source Data Processing Undertaken Indexing Data to HATRIS

TRADS Converting all data to hourly intervals,

compiling single data file for each site

from the individual day reports

downloaded

TRADS site locations mapped

against HATRIS links in GIS and

matching undertaken. Manual check

of matching using site descriptions.

DfT Journey

Time Data

Aggregating vehicle categories into

light and heavy vehicles.

Filtering of data by HATRIS link to

remove sections of the link where the

road characteristic or flow level

changed compared to the location of

the applicable TRADS site.

Further segmentation of remaining link

to identify sections close to merges /

diverges and junctions.

Matching of ITN link data to HATRIS

network using a Dijkstra8 algorithm

based upon the closest start and end

node and manually checked against

link descriptions, direction and overall

length.

HAPMS Filtering of link sections to match the

sections resulting from the processing

of the DfT journey time data.

Calculation of bendiness and rises &

falls from the raw data to derive values

for each site.

HAPMS data provided by HATRIS

link.

HATO No processing required. HATO data provided by HATRIS link.

The summary data table produced for the front-end of the database outlines all of the key

characteristics of each selected site, both in terms of the parameters for analysis, and in terms

of describing the link and referencing the various components of data which are required to

produce the analysis. Figure 4.2 contains a small portion of the summary table as an indication

of the structure.

8 Dijkstra’s algorithm is a graph search algorithm which solves the single-source shortest path problem for a

graph producing a shortest path tree. It is therefore a useful tool in establishing the shortest path through transport networks.



Figure 4.2 Illustrative Sample of the Summary Data Table

Finally, a query tool has been developed which allows the extraction of data dependent upon

the categorisation of any of the data analysis parameters or for an individual site. This tool

provides the flexibility to extract data for any required combination of sites. A screenshot from

this tool is shown in Figure 4.3 overleaf.

Road

NameLocation Direction

HA

Region

Road

Type

Road Type

DescriptionLanes

Total

Length

(km)

Selected

Length

(km)

Length of

Merges

(km)

Length of

Diverges

(km)

Speed

Limit (kph)

Carriageway

Width

Category

Day Time

HGV%

Category

Night Time

HGV%

Category

Average

Weekday

Hourly

Flow

(PCUs) per

lane

Bendiness

(degrees

per km)

A1(M) Junction 17 - 16 Southbound 8 D3M Motorway, dual 3-lanes3 4.296 4.296 0.885 0.634 112.65 7.3 - 9m Low (0-10%)Low (0-10%) 945 9.9

A1(M) Junction 16 - 17 Northbound 8 D3M Motorway, dual 3-lanes3 4.426 4.426 0.942 1.862 112.65 7.3 - 9m Low (0-10%)Low (0-10%) 1,009 9.8

M11 Junction 7-8 Northbound 8 D3M Motorway, dual 3-lanes3 15.515 15.515 1.717 2.273 112.65 7.3 - 9m High (> 20%)High (> 20%) 1,157 17.7

M11 Junction 7-8 Southbound 8 D3M Motorway, dual 3-lanes3 15.524 15.524 3.227 0.578 112.65 7.3 - 9m High (> 20%)High (> 20%) 1,219 17.6

M180 Junction 2-3 Westbound 12 D3M Motorway, dual 3-lanes3 7.651 7.651 0.568 1.506 112.65 7.3 - 9m High (> 20%)High (> 20%) 578 9.4

M18 Junction 2-1 Eastbound 12 D3M Motorway, dual 3-lanes3 9.617 8.309 0.62 0.491 112.65 7.3 - 9m Average (10-20%)High (> 20%) 1,148 9.0

M18 Junction 1-2 Westbound 12 D3M Motorway, dual 3-lanes3 9.522 8.36 0.684 0.498 112.65 7.3 - 9m Average (10-20%)High (> 20%) 1,104 9.0

M1 Junction 14-15 Northbound 8 D3M Motorway, dual 3-lanes3 19.691 19.691 0.822 0.613 112.65 7.3 - 9m Average (10-20%)High (> 20%) 1,493 3.8

M20 Junction 11-10 Westbound 4 D3M Motorway, dual 3-lanes3 11.099 11.099 0.53 0.607 112.65 7.3 - 9m Average (10-20%)Average (10-20%)693 4.7

M20 Junction 10-11 Eastbound 4 D3M Motorway, dual 3-lanes3 11.015 11.015 0.737 0.53 112.65 7.3 - 9m Average (10-20%)Average (10-20%)692 4.7

M23 Junction 8-9 Southbound 4 D3M Motorway, dual 3-lanes3 9.016 9.016 0.544 0.535 112.65 7.3 - 9m Low (0-10%)Low (0-10%) 1,377 16.0

M25 Junction 25-24 Anticlockwise 5 D3M Motorway, dual 3-lanes3 8.898 8.898 3.773 0.62 112.65 7.3 - 9m Average (10-20%)High (> 20%) 1,659 37.2

M25 Junction 24-25 Clockwise 5 D3M Motorway, dual 3-lanes3 8.811 8.811 0.615 3.736 112.65 7.3 - 9m Average (10-20%)High (> 20%) 1,680 37.2

M3 Junction 4a-5 Southbound 3 D3M Motorway, dual 3-lanes3 2.792 2.792 3.227 2.409 112.65 7.3 - 9m Low (0-10%)High (> 20%) 1,168 11.5

M3 Junction 5-4a Northbound 3 D3M Motorway, dual 3-lanes3 3.031 3.031 0.625 3.212 112.65 7.3 - 9m Low (0-10%)High (> 20%) 1,160 11.6

M40 J11-J12 Southbound 8 D3M Motorway, dual 3-lanes3 16.516 16.516 0.876 1.361 112.65 7.3 - 9m Low (0-10%)Low (0-10%) 1,056 5.9

M40 J11-J12 Northbound 8 D3M Motorway, dual 3-lanes3 16.67 16.67 0.621 0.579 112.65 7.3 - 9m Low (0-10%)Low (0-10%) 1,122 5.8

M40 J6-J7 Southbound 8 D3M Motorway, dual 3-lanes3 8.497 8.497 1.186 0.81 112.65 7.3 - 9m Low (0-10%)Low (0-10%) 1,181 3.3



Figure 4.3 Database Query Tool

4.5 Sample of Final Data

This section presents a summary of the coverage of the analysis variables across all of the final

127 sites selected for analysis. The summary indicates that good coverage has been obtained

across each category; commentary is provided for each table.

Table 4.2 summarises the distribution of sites by road type and English Region.



Table 4.2 Number of Sites by Road Type and English Region

Road Class

NE NW Yor & Hum

EM WM E of Eng

Lon SE SW Total

S2 2 0 0 4 3 7 0 0 4 20

D2AP 8 2 2 5 2 10 0 2 6 37

D3AP 0 0 0 2 0 0 0 2 0 4

D2M 2 6 0 0 2 2 3 4 4 23

D3M 0 11 3 0 2 8 0 7 3 34

D4M 0 4 0 0 0 2 1 2 0 9

Total 12 23 5 11 9 29 4 17 17 127

Table 4.2 indicates that in general good coverage has been achieved by road type with the

following observations:

The number of D3AP and D4M sites is lower than the target, particularly for the D3AP

category:

o This reflects the fact that the D3AP category is relatively rare and also that

although a larger number of D3AP sites were included in the initial list of sites,

initial analysis indicated that a number were not suitable for analysis (for

example, one site had a 50 mph speed limit applied);

o The small number of sample D4M sites also reflects the small number of

possible sites available. Additionally, many of these have been or are in the

process of being converted into some form of smart motorway. Furthermore, a

number of D4M sites were ruled out as they operate in congested conditions for

large periods of a typical weekday and would therefore yield a limited amount of

suitable data for our analysis.

A number of smart motorway sites were included in the initial list of sites; however, of

these only two sites presented useable data (one was controlled motorway and the

other hard-shoulder running) and this was not considered sufficient to undertake any

meaningful regression analysis. It is worth noting that a review of these two sites

indicated that the speed / flow relationships reflected those of a D4M category road.

Table 4.3 summarises the distribution of sites by road type, urban / rural classification and the

length of the analysis section.

Table 4.3 Number of Sites by Road Type and English Region

Road Class

Urban Rural

Length (km)

0 – 2 2 – 5 5 – 10 10 + Total

S2 4 16 0 12 4 4 20

D2AP 17 20 1 23 11 2 37

D3AP 4 0 0 4 0 0 4

D2M 14 9 0 14 8 1 23

D3M 16 18 0 8 10 16 34

D4M 7 2 0 7 2 0 9

Total 62 65 1 68 35 23 127

Table 4.3 indicates that in general good coverage has been achieved by urban / rural

classification and across a range of link lengths:

The urban / rural classification was designed to identify sites as urban when they were

located in proximity to a large urban area (with population > 250,000) and provided

direct access to this urban area (note this definition of urban / rural is bespoke to the

study and is a different definition than the urban / rural roads definition outlined in



COBA. All of the sites included in the study are considered rural roads under the COBA

definitions);

In general links with length less than 2km were avoided in the initial site selection, in

line with the methodology TRL applied in the 1990s studies. One D2AP link has a

length of less than 2km.

Table 4.4 summarises the distribution of sites by road type and bendiness and hilliness.

Table 4.4 Number of Sites by Road Type and Bendiness and Hilliness

Road

Class

Bendiness Hilliness

Straight

(0-30

deg/km)

Moderate

(30-60

deg/km)

Bendy

(>60

deg/km)

Flat (0-

22.5

m/km)

Rolling

(22.5-45

m/km)

Hilly (>45

m/km)

S2 17 3 0 8 10 2

D2AP 35 2 0 22 9 6

D3AP 4 0 0 4 0 0

D2M 21 2 0 19 2 2

D3M 34 0 0 25 9 0

D4M 9 0 0 2 7 0

Total 120 7 0 80 37 10

Table 4.4 indicates that in general good coverage has been achieved across the categories of

bendiness and hilliness, except for a lack of sites categorised as bendy:

The category bandings reflect the range of expected values reported for Classes 2-6

(dual-carriageways and motorways) in the COBA manual, with the Bendy and Hilly

categories representing values above the maximum expected value for these road

types.

On the basis of the above it is therefore not unexpected that there are no bendy sites in

the Class 2-6 roads. A number of sites categorised as ‘Bendy’ were selected initially

amongst the S2 and D2AP categories, but none proved appropriate to be included in

the analysis.

In general there are a limited number of hilly trunk road sites in England to study. A

number of additional sites with higher gradients were included in the initial site list;

however, a lack of data in some of these locations has further limited the pool of

available sites.

Table 4.5 summarises the distribution of sites by road type and daytime (weekday 0700-1900)

HGV percentages.

Table 4.5 Number of Sites by Road Type and Daytime HGV Percentage

Road

Class 0-10% 10-15% 15-20% > 20% Total

S2 8 10 2 0 20

D2AP 20 9 8 0 37

D3AP 2 2 0 0 4

D2M 17 5 1 0 23

D3M 12 10 11 1 34

D4M 4 3 2 0 9

Total 63 39 24 1 127



Table 4.6 summarises the distribution of sites by road type and night-time (weekday 1900 -

0700) HGV percentages.

Table 4.6 Number of Sites by Road Type and Night-time HGV Percentage

Road

Class 0-10% 10-20% 20-30% 30-50% > 50% Total

S2 0 4 12 4 0 20

D2AP 2 13 14 8 0 37

D3AP 1 1 2 0 0 4

D2M 1 16 4 2 0 23

D3M 1 8 9 15 1 34

D4M 0 3 2 4 0 9

Total 5 45 43 33 1 127

Tables 4.5 and 4.6 indicate a good coverage across a range of HGV percentages for both

daytime and night-time. The range of percentages encountered can be considered typical for

the majority of UK highway links.

In summary, the review of site selection in terms of coverage across the various analysis

parameters indicates that a good range of sites has been achieved in order to undertake

stepwise linear regression with these data, having a sufficient number of observations and

range of variance in the analysis parameters.

However, there is a need to consider the particular nature of each road type; for example, it

does not make sense to consider the significance of large ranges of bendiness and hilliness on

D4M roads given the limited values included within the study dataset for this road type.



5. Preliminary Analysis 5.1 Introduction

This section describes the preliminary analysis undertaken using the project database under the

following headings:

Identification of Sites with Suitable Data – describes the review of each site’s data in order to

ensure its suitability for inclusion in the analysis;

Site-by-Site Linear Regression – outlines the approach to preliminary analysis which consisted

of applying linear regression to the data for each individual site selected for analysis; and

Summary of Findings – presents the results of the individual site regression analysis in terms of

the emerging key parameters (free flow speed, gradient to QB, QB, gradient to QC, and a review of

QC).

5.2 Identification of Sites with Suitable Data

The analysis has been structured in order to ensure that the speed / flow data at each individual

site has been reviewed by an analyst and a regression applied prior to these data being compiled

with other sites for the stepwise regression.

This approach ensures:

Any anomalies in the individual site data can be identified; and

A comparison of individual site regressions across each road category can be made for

the purposes of estimating initial free flow speeds and flow break points.

An analysis tool was developed specifically for this purpose. The tool allowed plotting of any sites

data and included various tools to identify where any data were not suitable for analysis:

Where available the spot speeds from the TRADS data were plotted against the average

speed data to highlight any periods where substantial differences occur;

An average weekly speed plot is produced to highlight any periods where changes to

long-term average speeds occur representing events such as road works, flooding or

other major incidents;

Separate scatter plots of light and heavy are available to highlight observations which

have occurred beyond the capacity of the link, and also as a check that the link in

question operates at the national speed limit for the road type.

Once an analysis of a site’s data has been undertaken using these tools filters are provided to

remove, where possible, observations which are not appropriate for the required outputs of this

study, that is:

Observations occurring beyond the capacity of the link in question;

Observations from a period when an incident occurred (using the HATO reference data);

Observations where roadworks or another event resulted in the road operating at a

reduced speed limit;

In some cases the review of a site’s data resulted in a decision to remove the site from the

analysis because the permanent speed limit of the site was not the national speed limit, the flow

data are only available categorised as all vehicles (it is not possible to identify light and heavy

vehicles separately).



The completion of the filtering exercise across all sites reduced the number available for analysis

from 189 to 127.

Figure 5.1 Screenshot of Part of the Site Analysis Tool

5.3 Site-by-Site Linear Regression

The site analysis tool provides a facility to undertake linear regression on each site’s data, splitting

the flow into 50 pcu9 flow bands per lane and producing separate linear relationships for light and

heavy vehicles. In each case the linear regression assumes a piecewise relationship with two

parts as defined in the existing COBA relationships.

The point QB at which the fit transitions between the first and second parts of the speed / flow

relationship is iterated separately for light and heavy vehicles across a wide range of flows in

order to identify the best fit location.

The regression tool is flexible and allows application of least absolute error or least squares to

either the median or mean speed value in each flow band. A cut-off for the minimum number of

observations in any flow band is used to ensure that the results are not skewed by a small number

of outliers.

For the purposes of this study least absolute error was applied to the median values (which are

considered to be less skewed by outliers in the data than the mean).

Figure 5.2 Example Linear Regression of Data for a D2M Site

Note: horizontal axis: flow in pcus per hour per lane, vertical axis: speed in kph.

The results of each site’s regression have been compiled by road type in order to provide an

indication of the range of values of the free flow speed, flow breakpoint and the gradient of both

parts of the fitted speed / flow relationship.

This summary has been used for two purposes:

To gain an appreciation for the range of values within each road type; and

To develop an initial set of parameters for use in the stepwise linear regression to identify

the final speed / flow relationships.

9 For the purposes of this study heavy vehicles have been assigned a pcu factor of 2.5. This value is in line with the

guidance for the application of speed / flow curves in models as set out in WebTAG Unit M3.1 and D.7.



The results of the regression are described in the next section.

5.4 Summary of Findings

This section provides the results of the individual site regressions by road type in order to highlight

the range of values encountered.

Table 5.1 Summary Regression Values for S2 Roads

HATRIS

Ref

Light Vehicles Heavy Vehicles Max

Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

AL3190 93.9 - 0.022 524 - 0.003 80.3 - 0.006 623 - 0.068 970

AL3084 92.8 - 0.019 522 - 0.024 90.6 - 0.028 522 - 0.013 1,527

AL3085 93.8 - 0.016 1,420 - 0.202 95.5 - 0.018 874 - 0.032 1,567

AL1344 91.9 - 0.029 374 - 81.5 - 0.017 278 - 1,064

AL1345 105.1 - 0.106 122 - 0.011 89.1 - 0.028 279 - 1,231

AL3378 98.2 - 0.027 674 - 82.8 - 0.012 773 - 1,235

AL3455 98.9 - 0.073 176 - 0.013 76.6 - 176 - 1,281

AL3295 92.9 - 0.093 127 - 0.016 93.7 - 0.043 627 - 0.000 1,303

AL3296 91.4 - 0.015 - - 0.014 81.0 - 0.372 - - 0.005 1,465

AL3508 92.8 - 0.041 326 - 0.004 79.5 - 0.022 279 - 0.018 1,091

AL3509 109.0 - 0.160 172 - 0.008 83.4 - 0.029 373 - 1,106

AL3214A 89.3 - 0.015 824 - 0.010 86.6 - 0.046 323 - 1,172

AL3215A 90.3 - 0.014 374 - 0.020 81.5 - 0.018 575 - 0.003 1,270

AL3517 92.0 - 0.101 126 - 0.020 71.4 - 328 - 0.000 649

AL2781 94.9 - 0.026 378 - 0.001 79.9 - 1,067 - 0.000 1,233

AL3231 97.6 - 0.031 380 - 0.005 122.6 - 0.106 426 - 1,447

AL3311A 89.2 - 0.018 725 - 80.3 - 76 - 0.009 1,225

AL3312A 95.8 - 0.027 623 - 0.001 87.0 - 0.029 324 - 0.002 1,285

AL3569A 94.8 - 0.032 278 - 0.007 81.2 - 0.000 172 - 0.012 858

AL3570A 98.5 - 0.038 325 - 78.6 - 28 - 789



Table 5.2 Summary Regression Values for D2AP Roads

HATRIS

Ref


Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

AL1488 115.7 -0.004 826 -0.015 89.1 -0.000 1,574 -0.013 1,881

AL758 114.0 -0.007 576 -0.043 87.2 -0.001 1,174 -0.208 2,325

AL1418B 120.8 -0.006 975 -0.036 89.1 -0.001 1,426 -0.007 2,251

AL1946B 111.5 -0.002 924 -0.016 89.6 -0.001 924 -0.002 2,319

AL3202A 116.4 -0.006 1,126 -0.012 89.5 -0.000 974 -0.027 1,289

AL3203A 113.5 -0.003 475 -0.010 110.7 -0.040 475 -0.013 1,259

AL2318 117.5 -0.008 927 -0.019 88.4 -0.000 1,374 -0.006 2,063

AL2321 114.0 -0.007 1,174 -0.024 88.7 -0.001 1,323 -0.006 2,095

AL434 114.8 -0.005 625 -0.011 88.0 -0.000 1,122 -0.016 1,310

AL435 115.0 - 624 -0.014 89.0 - 875 -0.003 1,529

AL1530A 119.7 -0.070 76 -0.006 91.2 -0.004 325 -0.005 1,020

AL1530B 112.8 -0.001 770 -0.010 89.0 - 576 -0.001 1,185

AL585 113.7 -0.002 531 -0.014 88.4 -0.004 1,026 -0.012 2,325

AL1795 112.0 -0.000 473 -0.005 90.1 -0.000 576 -0.013 1,297

AL1797 114.0 -0.001 577 -0.014 103.1 -0.000 175 - 1,310

AL3053 116.1 -0.000 223 -0.002 89.0 - 328 - 785

AL3054 106.8 - 37 - 108.3 -0.105 174 -0.006 797

AL1159 119.9 -0.008 624 -0.013 88.5 - 1,425 -0.011 1,662

AL2990 102.4 - 128 - 79.9 -0.004 626 - 1,436

AL2991 101.3 -0.006 775 -0.024 79.8 - 1,023 -0.196 2,325

AL2516 110.3 - 275 -0.006 88.5 - 26 - 1,126

AL2519 112.5 -0.006 525 -0.000 88.5 - 29 - 2,325

AL3456A 111.4 -0.003 74 -0.003 89.0 -0.000 34 -0.000 2,325

AL3457A 114.0 -0.032 126 -0.002 88.5 - 33 - 2,325

AL2652 106.6 -0.000 37 - 100.4 -0.066 228 - 2,325

AL2653 106.1 - 121 - 84.9 - 34 - 2,325

AL1301 110.5 - 325 -0.001 89.0 -0.000 523 - 2,325

AL1302 107.7 - 36 - 89.2 -0.006 275 -0.002 2,325

AL3209 109.6 - 34 - 87.3 -0.002 175 -0.002 2,325

AL3211 108.9 -0.001 326 -0.000 87.2 -0.000 33 - 2,325

AL1085A 108.0 -0.004 624 -0.006 88.2 -0.001 871 -0.008 2,325

AL2151A 107.8 -0.000 475 -0.004 88.7 -0.000 628 -0.005 2,325

AL3002 110.6 -0.006 526 -0.009 87.0 - 970 -0.015 1,108

AL3004 110.2 - 375 -0.009 85.7 - 827 -0.005 1,209

AL611A 107.8 -0.006 523 -0.011 88.5 - 35 - 2,325

AL1233 111.9 -0.000 570 -0.065 88.5 - 25 - 2,325

AL517 118.0 325 -0.000 88.5 - 28 - 2,325



Table 5.3 Summary Regression Values for D3AP Roads

HATRIS

Ref


Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

AL643 116.1 - 0.001 727 - 0.008 88.2 - 0.001 373 - 0.000 2,204

AL1285 114.9 - 428 - 0.005 90.3 - 0.002 626 - 0.000 1,317

AL641 117.0 - 0.001 924 - 0.006 88.6 - 0.000 43 - 2,029

AL1281 116.4 - 0.000 324 - 0.006 116.6 - 0.156 173 - 0.001 1,222

Table 5.4 Summary Regression Values for D2M Roads

HATRIS

Ref


Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

LM71 110.3 - 0.004 1,075 - 89.0 - 0.000 876 - 0.008 1,324

LM75 122.3 - 0.104 74 - 0.005 94.6 - 0.004 1,274 - 0.021 1,594

LM413 114.5 - 0.006 625 - 0.009 88.3 - 0.000 924 - 0.001 1,729

LM525 117.1 - 671 - 0.031 89.6 - 0.004 126 - 1,134

LM608 114.8 - 0.000 675 - 0.012 89.5 - 0.001 1,074 - 0.004 1,762

LM668 114.8 - 36 - 89.0 - 821 - 0.022 910

LM584 109.1 - 0.005 1,475 - 0.012 88.4 - 1,574 - 0.000 2,072

LM72 105.2 - 0.003 576 - 85.0 - 28 - 0.001 1,204

LM76 115.9 - 0.000 677 - 90.4 - 1,123 - 1,590

LM368 122.7 - 0.007 675 - 0.006 88.8 - 0.000 975 - 0.001 1,712

LM414 113.4 - 0.008 676 - 0.017 89.1 - 0.001 1,423 - 0.000 1,700

LM418 111.4 - 0.006 1,829 - 0.017 91.5 - 0.002 1,625 - 0.057 2,219

LM524 111.9 - 38 - 0.038 88.0 - 38 - 0.015 1,372

LM526 120.5 - 0.001 226 - 89.0 - 619 - 0.000 1,096

LM609 116.0 - 0.000 726 - 0.011 89.2 - 678 - 0.001 1,537

LM669 113.0 - 0.000 276 - 0.009 89.0 - 33 - 0.001 789

LM585 120.6 - 0.060 275 - 0.003 87.7 - 40 - 1,993

LM886 117.9 - 0.008 626 - 0.014 90.1 - 0.000 1,323 - 0.001 2,107

LM887 111.7 - 0.000 574 - 0.003 89.4 - 0.000 1,320 - 1,951

LM10 116.2 - 0.002 777 - 0.010 88.6 - 724 - 2,106

LM11 113.9 - 0.004 824 - 0.009 89.2 - 0.001 1,375 - 0.002 2,065

LM54 119.2 - 0.003 976 - 0.009 87.6 - 0.000 1,874 - 0.001 2,255

LM55 119.2 - 0.010 1,472 - 0.014 90.9 - 0.002 1,624 - 0.005 2,354




HATRIS

Ref


Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

LM8 113.2 -0.001 873 -0.013 88.5 - 30 - 2,325

LM9 113.2 - 873 -0.000 88.5 - 33 - 2,325

LM161 120.0 -0.005 1,126 -0.015 88.3 -0.000 474 -0.000 2,196

LM119 113.3 - 1,273 -0.008 99.0 - 425 -0.008 1,721

LM139 115.8 - 676 -0.011 88.7 -0.001 575 -0.001 1,659

LM140 121.8 -0.005 726 -0.010 89.3 - 874 -0.001 1,627

LM130 116.2 -0.028 74 -0.003 88.5 -0.001 576 -0.000 939

LM259 117.8 -0.002 127 - 89.0 -0.000 127 -0.000 1,201

LM260 117.5 - 576 -0.005 89.1 - 41 - 1,134

LM292 115.2 -0.004 1,024 -0.012 87.9 -0.000 1,129 - 1,893

LM441 119.6 -0.002 826 -0.010 91.3 -0.002 1,125 -0.000 1,620

LM548 121.8 - - -0.007 88.5 - - - 2,169

LM535 124.9 -0.003 976 -0.026 89.7 -0.000 927 -0.002 2,002

LM536 124.0 -0.003 1,173 -0.020 89.2 -0.000 225 - 1,844

LM544 124.1 -0.003 675 -0.007 88.8 - 826 - 1,656

LM457 125.0 -0.004 925 -0.031 88.5 - 31 - 2,325

LM458 123.3 -0.001 874 -0.012 88.5 - 33 - 2,325

LM482 124.4 -0.007 1,122 -0.042 88.5 - 35 - 2,325

LM497 116.4 - 1,027 -0.016 88.9 -0.000 1,572 -0.014 2,030

LM733 113.8 -0.001 727 -0.007 89.5 -0.000 1,372 -0.006 1,895

LM716 124.3 -0.004 1,279 -0.029 89.1 - 1,670 -0.029 1,888

LM717 123.6 -0.005 1,225 -0.030 90.2 -0.003 273 -0.002 1,694

LM592 111.4 -0.000 576 -0.000 89.0 - 1,177 -0.005 1,327

LM593 111.0 -0.001 625 - 88.6 - 1,124 -0.005 1,338

LM655 118.9 -0.000 427 -0.005 89.2 -0.000 1,273 -0.010 1,685

LM956 113.5 - - - 89.9 - - - 2,325

LM957 113.5 - 33 - 89.5 - 33 - 2,325

LM990 117.5 -0.000 277 -0.004 88.5 - 874 -0.046 2,325

LM991 117.4 - 425 -0.003 89.0 -0.000 41 - 2,325

LM818 121.2 -0.002 575 -0.005 89.4 - 43 - 1,536

LM819 120.2 -0.002 676 -0.005 89.6 - 974 -0.001 1,651

LM896 117.5 -0.001 475 -0.007 89.0 -0.000 1,224 -0.018 1,317

LM897 115.1 -0.000 974 -0.033 94.6 -0.009 625 - 1,186




HATRIS

Ref


Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

LM473 121.3 - 0.004 772 - 0.008 88.5 - 43 - 1,838

LM474 122.2 - 0.003 1,025 - 0.036 89.1 - 0.000 121 - 1,978

LM361 113.4 - 0.004 1,225 - 0.019 97.5 - 0.000 774 - 0.009 2,179

LM1 117.2 - 0.000 376 - 89.0 - 0.000 72 - 0.000 959

LM2 114.1 - 574 - 0.005 88.0 - 0.000 170 - 0.000 883

LM950 119.0 - 0.006 1,175 - 0.014 88.6 - 1,474 - 0.001 2,325

LM951 118.8 - 0.004 1,126 - 0.016 88.9 - 1,275 - 0.001 2,261

LM978 120.4 - 0.012 824 - 0.007 89.2 - 1,822 - 0.133 2,223

LM979 119.6 - 0.007 974 - 0.010 90.1 - 0.000 1,877 - 0.010 2,277

Table 5.7 Average Regression Values by Road Type

Road

Type


Obs.

pcu

per

lane

S0

Grad to

QB

QB

Grad to

QC

S0

Grad to

QB

QB

Grad to

QC

S2 95.2 -0.045 446 -0.022 85.2 -0.052 428 -0.014 1,188

D2AP 112.0 -0.007 480 -0.013 89.8 -0.010 602 -0.024 1,850

D3AP 116.1 -0.001 601 -0.006 95.9 -0.040 304 0.000 1,693

D2M 115.3 -0.012 689 -0.013 89.2 -0.001 934 -0.008 1,677

D3M 118.4 -0.004 750 -0.013 89.5 -0.001 637 -0.008 1,822

D4M 118.4 -0.005 897 -0.014 89.9 0.000 848 -0.022 1,880

The main conclusions reached from this preliminary set of individual site analyses, which were

designed to examine the expected two slopes to QB and then QC, were that:

In many cases the QB point was occurring at a much lower flow level than implied by

COBA and the slope to QB was much shallower. Indeed in many cases there was a

period where the average speeds did not vary from the free flow speed;

There was considerable variance in the slope beyond QB and that this was a function of

the fact that the above sections of stable free flow speeds resulted in the QB point being

quite variable, combined with differing values of maximum flows observed on the

individual links; and

The implications of the above may be that there is a more complex curve than implied by

the COBA two-slope approach. The presence of substantial speed/flow observations for

the low flow range enables this to be observed whereas in the past this has not been

possible.

In order to illustrate the above, the sites that had experienced some breakdown flow periods

(and as such have speed/flow observations across the full flow range) were analysed by road

type. The data for these sites was aggregated into small flow bands to remove the scatter due

to the individual points and make any underlying trends more visible. Figures 5.3 to 5.7 show

the resultant speed/flow profiles.



Each of these profiles indicates a flat section of curve, followed by a low slope section and then

increasingly steep curve as flows approach QC. The analyses described in this section clearly

show that the speed/flow relationships need to be amended to reflect the profiles shown by the

data.

The report returns to discuss the implications of the speed/flow slopes shown in figures 5.3 to

5.7 in the latter part of Section 6.1 where the implications of these for the final light vehicle

regression relationships are discussed.

Figure 5.3 D2AP Profile

40

50

60

70

80

90

100

110

120

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Sp

ee

d (

kp

h)

PCUs per hour



Figure 5.4 D3AP Profile

0

20

40

60

80

100

120

140

0 1,000 2,000 3,000 4,000 5,000 6,000

Sp

ee

d (

kp

h)

PCUs per hour



Figure 5.5 D2M Profile

40

50

60

70

80

90

100

110

120

130

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

Sp

ee

d (

kp

h)

PCUs per hour




40

50

60

70

80

90

100

110

120

130

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

Sp

ee

d (

kp

h)

PCUs per hour




The final element of the preliminary analyses of the data relates to a review of the COBA QC

values and whether there is any evidence from the current speed flow data profiles that there has

been a change in these. Data for those sites where the underlying traffic demands had clearly led

to periods of flow breakdown, and for which the maximum flow observed is then a reasonable

estimate of the value of QC, was used to determine the average values of QC by road type.

Table 5.8 summarises these values along with the current COBA estimates. The conclusion

drawn is that whilst there is some indication that there is very little difference in maximum capacity

by lane for D2AP/D3AP/D2M/D3M/D4M the limited number of sites where breakdown has

occurred is such that there is insufficient evidence to increase the D2AP/D3AP values to align

them with the D2M/D3M/D4M capacity values.

40

50

60

70

80

90

100

110

120

130

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

Sp

ee

d (

kp

h)

PCUs per hour



Table 5.8 Estimated Values of QC

Road Type QC (pcus)

HGVp COBA

D2AP 2,300 2,100

D3AP 2,200 2,100

D2M 2,300 2,330

D3M 2,200 2,330

D4M 2,270 2,330



6. Regression Analysis by Road Type 6.1 Introduction

This sections sets out the results of the regression analysis by road type.

Identification of Break Points – describes the regression analysis undertaken in order

to establish an indication of where the potential break points in flow exist by road type;

Dual Carriageways and Motorways – Multiple Stepwise Regression – describes the

stages of stepwise linear regression undertaken in order to develop updated

relationships for dual carriageways and motorways;

Rural Single Carriageways – Multiple Stepwise Regression - describes the stages of

stepwise linear regression undertaken in order to develop updated relationships for

single carriageways.

6.2 Identification of Break Points

The detailed analysis of the speed/flow data commenced with a set of regressions on the data

shown in figures 5.3 to 5.7 to provide an indication of where potential break points exist by road

type, assuming that there is a three-slope solution between free flow and QC. The analysis was

restricted to dual carriageways and motorways at this stage as there was no early evidence of

such effects in the single carriageway analysis.

Table 6.1 shows the results of a set of piecewise linear regressions to identify:

QF – the point at which free flow speeds are no longer maintainable. QF represents the

new break point that the evidence base indicates is required to properly reflect the

observed speed flow profiles. It is the point up to which all users of the road can travel at

their own desired speed without any interference from interactions with other vehicles.

That is there are unlimited overtaking opportunities to pass other vehicles without the

need to reduce speed, and the headways between vehicles is well in excess of any

required safety separation.;

QB – the point where lane density is such that drivers begin to be constrained by slower

moving vehicles and speeds start to drop more rapidly;

QC – estimated maximum capacity;

Slope to QF;

Slope between QF and QB; and

Slope beyond QB.



Table 6.1 Preliminary Analysis of Break Points

Variable Road Type

D2AP D3AP D2M D3M D4M

Free flow speed (kph)

110.8 115.1 112.6 118.7 116

QF (pcus) 565 410 625 700 750

QB (pcus) 1,320 1,270 1,375 1,167 1,480

QC (pcus) 1,700 1,800 1,900 1,900 1,900

Slope to QF -0.0002 0 -0.0008 -0.0006 -0.0012

Slope to QB -0.0148 -0.0045 -0.011 -0.018 -0.0192

Slope to QC -0.0358 -0.0141 -0.0464 -0.0348 -0.044

Figure 6.1 shows the profile of these curves. In all cases the data shows a clear almost flat

section to QF, then a lower slope to QB, and finally a steeper section to QC. The D3AP data after

filtering is fairly sparse and hence the ‘odd’ curve compared to the others.

Given the limited data for the D3AP sites greater weight has been given to the D2AP data and

hence the conclusions drawn from the above are that for further analyses of the data the

following breakpoints by road type should be used.

Table 6.2 Break Points in Vehicles per Lane

Road Type Break Points in Vehicles per Lane

QF QB

D2AP 550 1,300

D3AP 550 1,300

D2M 650 1,400

D3M 700 1,400

D4M 750 1,400



Figure 6.1 Preliminary Speed/flow Curves – Three-Slope Analysis

6.3 Dual Carriageways and Motorways – Multiple Stepwise Regression

6.3.1 Link Length The study terms of reference included the requirement to examine whether link length

contributed to the estimation of speed flow relationships on links. The first set of regression

analyses included length as a variable and Table 6.3 shows the estimated coefficient for light

and heavy vehicles by road type.

The figures show considerable variance with both positive and negative coefficients, and low

and high parameter values. The very high values for the D3AP and D4M are partly a result of a

small number of sites but also because there is limited variation in the actual link lengths

between the sites in these categories and the link length parameter is interacting with the

estimation of the free flow speed. If all the link lengths are within a small range then the

regression may see them as a contributory factor in the free flow estimation but the outturn

parameters then only apply in a very small range. For example the D3AP value of -3.83 results

in completely illogical outcomes if applied to varying link lengths i.e. at 3kms a -11.5kph effect,

at 6kms a -23kph effect, and at 9kms a -34kph.

A negative coefficient for link length, representing free flow speeds decreasing as link length

increases, is counter intuitive. The longer a link is between junctions the lower the potential

40

50

60

70

80

90

100

110

120

130

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

Sp

ee

d (

kp

h)

Vehicles per lane




impact of any residual junction effects and the flow will be more stable and if anything the

average free flow speed would be expected to slightly increase with longer links.

The extreme values, and the indication that these are interacting with the estimation of the

intercept, and the counter intuitive directionality of the speed change effect led to the conclusion

that link length should be omitted from any further regression analyses.

The fact that the sites selected for the study all exceed 2km in length, and the database has

been carefully screened to remove junction related effects, probably means that any potential

link length effects which may in fact be linked to junction spacing and shockwaves from junction

effects have been screened out of the data.

Table 6.3 Link Length Parameter Estimates

Road Type Light Vehicles Heavy Vehicles

S2 -0.117 (-6.9) -0.56 (-7.7)

D2AP -0.241 (-19.3) 0.22 (4.0)

D3AP -3.84 (-21.4) -4.91 (-5.4)

D2M 0.287 (28.1) 0.249 (4.2)

D3M -0.244 (-34.3) 0.179 (8.1)

D4M -0.948 (-25.3) -0.74 (-6.4)

Note: Figures in brackets are t-stats.

6.3.2 6.3.3 Light Vehicles

An initial set of stepwise multiple regressions were undertaken for each road type with the

variables being:

pcus – total pcus across all lanes;

HGVp – HGV proportion e.g. expressed as 0.15 for 15% HGV percentage;

Bendiness;

Sum of Rises; and

Sum of Falls.

These were undertaken for each of the three slopes, up to QF, from QF to QB, and beyond QB.

The results are shown in Tables 6.5 to 6.9. Due to the large amount of data available for each

of the regressions the t-statistics are usually very high as they are a measure of the degree of

confidence in the estimated parameter and the more data available the higher will be the t-

statistic in general. The stepwise regression removes any variables that do not reach an

acceptable level of significance and as such we have not included the t-stats in the tables.

The fact that a variable is retained through the stepwise regression does not however mean that

it should be automatically included within the final analyses and recommended speed flow

variables are produced. This may be either because they have such a small impact, although

statistically significant, or they are counter intuitive in terms of the direction of the impact, for



example a positive coefficient for HGVp would imply speeds increase with a higher proportion of

HGVs in the traffic stream which is clearly anomalous.

Prior to presenting the results of the analyses it is important to understand the average values

of the input variables so that the individual parameter estimates can be put into context. Table

6.4 shows the average values of the variables for each road type.

Table 6.4 Average Value of Variables

Road Type Variable

HGVp Bendiness Sum of Rises Sum of Falls

S2 0.10 42.1 7.5 8.3

D2AP 0.09 23.1 7.3 7.6

D3AP 0.09 23.0 6.2 5.9

D2M 0.10 17.2 5.9 6.2

D3M 0.10 10.2 5.8 5.7

D4M 0.13 13.3 6.8 7.6

There is obviously a wide range around these values but in interpreting the following results the

average values are a useful means of interpreting the importance of the variables.

Table 6.5 shows the regression results for D2AP roads. The main points to note are:

The ratio of the slopes is 1 : 3.9 : 6.9 showing the rapid increase in slope after the

point QF as the breakdown area is entered;

HGVp has relatively low parameter values, less than 1kph impact, and for the high

slope regions it is counter-intuitive. It is concluded that HGVp should be excluded;

Bendiness is consistently important and stable in its parameter estimation across the

full range of flows. As the implied speed reduction up to QF due to bendiness is 2.9 kph

then it clearly should be retained as a variable;

Sum of Rises has low parameter values, less than 0.8 kph impact, and for high flow

regions the value is potentially counter-intuitive e.g. higher speeds on inclines. It is

likely that Sum of Rises should be excluded. This is not unexpected for light vehicles

as today’s cars perform far better on inclines and only on the severest and long

sections of climb is there a noted deterioration in performance;

Sum of Falls is consistently of the right sign, i.e. increases in speed on descents, but of

low value, less than 0.7 kph impact; and

The implied average free flow speed is 110.3 kph and this and the intercept value at

113.9 kph are both higher than the COBA intercept of 108 kph;

The preliminary conclusions are that HGVp and Sum of Rises should be dropped from further

analyses for D2AP roads.



Table 6.5 D2AP Stepwise Regressions (Three-Slope Analysis)

Slope Intercept pcu per

lane HGVp Bendiness SumofR SumofF

PCUf 113.9

(1481.8)

-0.00268

(-17.2)

-10.554

(-37.3)

-0.1269

(-52.9)

-0.0534

(-11.4)

0.0851

(17.9)

PCUb -0.01056

(103.0)

-5.633

(-19.3)

-0.1117

(-51.1)

-0.1125

(-26.6)

0.0704

(16.9)

PCUc -0.01839

(-31.3)

20.131

(11.3)

0.4739

(7.3)

0.2400

(3.7)

Note: Figures in brackets are t-ratios

The regression analyses for the D3AP sites with all variables produced anomalous results as

there was evidence of high levels of correlations between some of the variables.

Table 6.6 shows the regression results for D2M roads. The main points to note are:


point QB as the breakdown area is entered;

HGVp has a low value in the low flow region but a significant value, equal to an

average reduction of 1.0 kph for speeds in the middle flow region, and a very high and

potentially counter intuitive value in the high flow region of 3.8kph;

Bendiness is important at low and medium flows but of a lower value than for D2AP

and is counter intuitive at high flows. As the implied speed reduction up to QB due to

bendiness is 1.4 kph then it should be retained as a variable;

Sum of Rises is consistently of the right sign and has an impact of 2.8kph up to QF and

as such should be considered for retention for D2M roads;

Sum of Falls is variable in its importance and is of the wrong sign in the medium flow

region. As there is a significant effect at low flows then it may that it is considered for

inclusion in determining free flow speeds only; and

The implied average free flow speed is 114.5 kph and this is higher than the COBA

intercept of 111 kph.

The preliminary conclusions are that HGVp and Sum of Rises are considered further but that

Sum of Falls should be dropped from further analyses for D2M roads.

Table 6.6 D2M Stepwise Regressions (Three Slope Analysis)



PCUf 120.0

(873.9)

-0.0043

(-24.5)

-2.994

(-6.2)

-0.0447

(-19.5)

-0.472

(-80.6)

-0.269

(-46.8)

PCUb -0.0112

(-106.5)

-10.589

(-24.1)

-0.0842

(-55.0)

-0.130

(-21.9)

0.133

(23.3)

PCUc -0.0278

(-32.4)

-39.32

(-7.9)

0.0606

(7.5)

-0.901

(-17.9)

-0.255

(-5.2)





The ratio of the slopes is 1 : 1.3 : 2.6 showing a gradual increase in slope after the

point QF;

HGVp has a low value in the low and medium flow region equal to an average

reduction of 0.5 kph for speeds, and a very high and counter intuitive value in the high

flow region;

Bendiness is important at across all flow bands. As the implied speed reduction up to

QF due to bendiness is 1.1 kph then it should be retained as a variable;

Sum of Rises is of the wrong sign for the low flow region and also for the high flow

region. The implications are that it should be removed from further analyses;

Sum of Falls is variable in its importance and is of the wrong sign in the medium flow

region. As the only significant effect was shown at low flows then it may that it is

considered for inclusion in determining free flow speeds only; and

The implied average free flow speed is 116.9 kph and this compares favourably with

the COBA intercept of 118 kph.

The preliminary conclusions are that HGVp and Sum of Falls are considered further but that

Sum of Rises should be dropped from further analyses for D3M roads.

Table 6.7 D3M Stepwise Regressions (Three-Slope Analysis)



PCUf 114.9

(1268.2)

-0.0010

(-9.5)

-4.090

(-18.3)

-0.111

(-38.8)

0.306

(42.7)

0.302

(41.9)

PCUb -0.0013

(-100.9)

-5.045

(-13.2)

-0.043

(-12.3)

-0.100

(-14.3)

-0.073

(-9.9)

PCUc -0.0258

(-20.7)

36.19

(9.7)

-0.158

(-6.7)

0.429

(9.6)




point QF;

HGVp has a low value in the low flow region but a higher value, equal to an average

reduction of 1.0 kph for speeds in the middle flow region, but a very high and counter

intuitive effect in the high flow region;

Bendiness is consistently important but appears to decrease in importance as flows

increase. This is logical in that at low flows the full effect of any bends on reducing

speeds would be observed but as flows increase and the average speeds decrease

then the net effect of the bendiness on speed reduction would be expected to

decrease. As the implied speed reduction up to QF due to bendiness is 9.4 kph then it

should be retained as a variable but the scale of the parameter requires further

investigation to ensure it is not correlated with the intercept value;

Sum of Rises is of the wrong sign for all flow regions. The implications are that it

should be removed from further analyses;



Sum of Falls is consistently of the right sign but variable in its importance. It should be

retained for further investigation; and

The implied average free flow speed is 117.8 kph and this compares favourably with

the COBA intercept of 118 kph;

The preliminary conclusions are that HGVp and Sum of Falls are considered further but that

Sum of Rises should be dropped from further analyses for D4M roads.




PCUf 123.8

(346.2)

-0.00169

(-5.8)

-4.673

(-7.2)

-0.705

(-40.4)

0.210

(12.5)

0.330

(22.3)

PCUb -0.01220

(-78.6)

-7.590

(-12.7)

-0.449

(-46.7)

0.145

(15.0)

0.207

(25.6)

PCUc -0.01560

(-16.9)

51.17

(10.8)

-0.627

(-13.5)

0.666

(15.3)

0.432

(10.7)


Table 6.9 presents a summary of the implied importance in terms of effect on speeds of each

variable. The table includes the speed change for the period up to QF based on the average

values of the variable in the database. This enables an indication of the relative importance of

the respective variables to be observed.

Table 6.9 Summary of Analysis Variables

Road Type Variable


D2AP -0.95

Low

-2.93

Medium/Include

-0.38

Low

0.65

Low

D2M

-0.29

Very Low /

Exclude

-0.77

Low

-2.78

Medium

-1.66

Wrong Sign /

Exclude

D3M

-0.39

Very Low /

Exclude

-1.11

Medium/Include

1.75

Wrong Sign /

Exclude

1.72

Medium / Include

D4M -0.61

Low

-9.37

High/Include

1.43

Wrong Sign /

Exclude

2.51

Medium / Include



The interpretation of the above is that HGVp should be excluded on the grounds that the values

are generally very low, bendiness is retained, Sum of Rises is dropped for D3M/D4M but

retained for D2AP/D2M, and Sum of Falls retained.

The exclusion of variables has been undertaken in an incremental manner to enable the effect

on other variables to be assessed. The first exclusion was of HGVp and Table 6.10 shows the

results for this exclusion.



Table 6.10 Light Vehicle Regressions Excluding HGV Proportions

Road Type

Slope

Variable

Intercept pcu per

lane Bendiness SumofR SumofF

D2AP

PCUf 112.8

(1572.4)

-0.00219

(-14.1)

-0.128

(-53.2)

-0.053

(-11.3)

0.082

(17.1)

PCUb -0.01090

(-108.2)

-0.112

(-51.1)

-0.108

(-25.6)

0.067

(16.1)

PCUc -0.01950

(-33.4)

0.116

(4.3)

0.945

(20.0)

0.738

(16.3)

D2M

PCUf 119.5

(1078.4)

-0.00405

(-23.7)

-0.044

(-19.1)

-0.464

(-81.1)

-0.262

(-46.6)

PCUb -0.0108

(-103.6)

-0.082

(-53.4)

-0.109

(-18.5)

0.145

(25.4)

PCUc -0.0275

(-31.9)

0.072

(9.0)

-0.842

(-16.9)

-0.170

(-3.5)

D3M

PCUf 114.7

-0.00992 -0.121 0.288 0.291

PCUb -0.01330

-0.047 -0.108 -0.091

PCUc -0.0276

-0.209 0.210 -0.014

D4M

PCUf 122.4

(415.3)

-0.00102

(-3.7)

-0.712

(-40.9)

0.241

(14.8)

0.228

(25.3)

PCUb -0.0125

(-80.9)

-0.449

(-46.6)

0.173

(18.3)

0.201

(28.7)

PCUc -0.0182

(-20.3)

-0.499

(-11.0)

0.375

(10.8)

0.321

(5.8)




Table 6.10 shows that the exclusion of the HGVp variable had a negligible effect on the other

parameter estimates which is as expected given the low values associated with the HGVp

variable.

The analyses in the above tables indicate that the effect of bendiness on average speeds varies

depending on the flow on the road. As the flow increases the absolute effect of bendiness on

the average speed reduces which is consistent with what would be expected. This presents

some difficulties in comparing the parameter estimates in the above tables with those in COBA

as the COBA values are essentially an average estimate across all flow bands.

A separate set of regressions were therefore run with a single equation across all flows with the

pcu values up to QF, between QF and QB, and then beyond QB included as separate variables.

This enabled the estimation of a single parameter coefficient for Bendiness, Sum of Rises and

Sum of Falls that applies across all flows, i.e. the average value which would equate to the

COBA values. Table 6.11 compares the respective parameter estimates with those in COBA.

These show that:

The bendiness parameter for D2AP/D2M /D3M is close to that in COBA, but that for the

D4M the bendiness parameter is much higher;

The COBA use of sum of rises is not supported by the current analysis for D3M/D4M

indicating that improvements in vehicle performance have significantly reduced this

impact, but that on D2AP/D2M there still appears to be an impact. This may relate to

more restricted opportunities to pass slower moving HGVs on inclines when there are

only two lanes available, and also that HGVs can use the outer lane on these road

categories which sometimes leads to HGVs occupying both lanes; and

In general the intercepts are higher implying higher free flow speeds.

Table 6.11 Comparison of Light Vehicle Parameters with COBA

Road Type

Variable COBA

Intercept Bendiness Sum of Rises

Sum of Falls Intercept

D2AP -0.123 -0.059 0.080 113.7 108

D3AP * * * * 115

D2M -0.058 -0.390 -0.159 119.7 111

D3M -0.115 0.167 0.166 116.9 118

D4M -0.586 0.249 0.321 122.6 118

COBA -0.100 -0.280 -

Note: * unable to derive D3AP models due to data correlations.

Table 6.12 shows the results of excluding the Sum of Rises from the estimations on D3M/D4M

road categories. This has an effect on the parameter estimates for the other variables with the

impact of Sum of falls being reduced for both D3M and D4M, and also a reduction in the

parameter values for bendiness. This indicates that there was some degree of correlation

between the sum of rises and the sum of falls for these road categories.



Table 6.12 Light Vehicle Regressions Excluding HGV Proportions and Sum of Rises

(D3M/D4M)

Road Type

Slope

Variable

Intercept pcu per


D2AP

PCUf 112.8

(1572.4)

-0.00219

(-14.1)

-0.128

(-53.2)

-0.053

(-11.3)

0.082

(17.1)

PCUb -0.01090

(-108.2)

-0.112

(-51.1)

-0.108

(-25.6)

0.067

(16.1)

PCUc -0.01950

(-33.4)

0.116

(4.3)

0.945

(20.0)

0.738

(16.3)

D2M

PCUf 119.5

(1078.4)

-0.00405

(-23.7)

-0.044

(-19.1)

-0.464

(-81.1)

-0.262

(-46.6)

PCUb -0.0108

(-103.6)

-0.082

(-53.4)

-0.109

(-18.5)

0.145

(25.4)

PCUc -0.0275

(-31.9)

0.072

(9.0)

-0.842

(-16.9)

-0.170

(-3.5)

D3M

PCUf 117.2

(1736.2)

-0.00083

(-8.0)

-0.098

(-35.3)

0.101

(18.3)

PCUb -0.01324

(-104.4)

-0.057

(-16.6)

-0.023

(-4.0)

PCUc -0.0284

(-22.6)

-0.155

(-8.5)

-0.327

(-6.3)

D4M

PCUf 123.1

(422.5)

-0.0013

(-4.6)

-0.544

(-41.0)

0.197

(21.7)

PCUb -0.0131

(-85.7)

-0.325

(-47.3)

0.116

(22.9)

PCUc -0.0169

(-19.0)

-0.126

(-4.6)




Table 6.13 compares the implied free flow speeds by road type with those in COBA. The free

flow speeds have been calculated using the average values of the variables in Table 6.3. The

results of this comparison indicate that light vehicle speeds have increased further since the last

update of the COBA values and that this applies across all road types.

Table 6.13 Comparison of Light Vehicle Free Flow Speeds

Road Type Current Estimates COBA Values

D2AP 110.1 101.6

D3AP * 109.3

D2M 114.4 105.9

D3M 116.8 113.7

D4M 117.4 112.8

Note: * unable to derive D3AP models due to data correlations.

Table 6.14 compares the slopes obtained from the models in Table 6.12 with those from an

analysis based on pcu per lane as the only variable. The aim of this is to examine the stability of

the slope parameter when the constant variables are excluded from the analyses. This is

important in the context of defining recommended speed/flow relationships. The results show a

good degree of consistency between the two sets of results, albeit in all cases there are slight

changes in the slopes in each road category.

The main variation between the two sets of data occur at low and high flows, with the slopes in

these flow bands being around 15% higher when the geometric parameters are excluded, but

very similar in the medium flow band with only a 1% difference in the slope estimates.

The outcome of this is that in the final speed/flow curves the geometric values should be

retained up to QB, but with different parameter estimates, where justified by the data, for the

sections to QF and then from QF to QB. Beyond QB the primary driver is the level of flow and as

such only the pcu per lane slope should be retained.



Table 6.14 Comparison of Light Vehicle Slope Parameters

Road Type Slope

Variables

pcu per lane

Bendiness

Sum of Falls

Variables

pcu per lane

D2AP

QF -0.00219

(-14.1)

-0.00200

(-12.7)

QB -0.01090

(-108.2)

-0.00914

(-86.6)

QC -0.01950

(-33.4)

-0.01933

(-31.7)

D3AP

QF * -0.00269

(-7.6)

QB * -0.00418

(-29.6)

QC * -0.02409

(-13.7)

D2M

QF -0.00405

(-23.7)

-0.00524

(-30.2)

QB -0.0108

(-103.6)

-0.01137

(-105.8)

QC -0.0275

(-31.9)

-0.03810

(-47.6)

D3M

QF -0.00083

(-8.0)

-0.00064

(-6.1)

QB -0.01324

(-104.4)

-0.01373

(-110.8)

QC -0.0284

(-22.6)

-0.03082

(-25.3)

D4M

QF -0.0013

(-4.6)

-0.00184

(-6.3)

QB -0.0131

(-85.7)

-0.01436

(-91.1)

QC -0.0169

(-19.0)

-0.01666

(-18.7)


The final set of light vehicle model regressions combine D2AP/D3AP and D3M/D4M into single

categories, due to the low number of sites for D3AP and D4M categories, but with dummy

variables for D3AP and D4M respectively. In this analysis the Sum of Falls has also been

excluded from the D2M road category as it has the wrong sign for the low and high vehicle

categories. The results of these final regressions are shown in Table 6.15.



Table 6.15 Final Light Vehicle Regressions – D2AP/D3AP and D3M/D4M combined

categories

Road

Type

Slope Variable

Intercept pcu per

lane

Bendiness Sum of

Rises

Sum of

Falls

D3AP /

D4M

D2AP/

D3AP

PCUf 112.9

(1660.6)

-0.00224

(-15.7)

-0.1235

(-52.4)

-0.0626

(-13.9)

0.0769

(16.6)

5.22

(78.2)

PCUb -0.00925

(-110.1)

-0.1221

(-58.8)

-0.0833

(-21.3)

0.0828

(21.3)

6.43

(134.6)

PCUc -0.02005

(-33.4)

-0.1329 0.926 0.745 17.79

D2M PCUf 117.1

(1186.3)

-0.00501

(-29.2)

-0.0246

(-10.8)

-0.317

(-65.8)

-

PCUb

-0.0108

(-103.6)

-0.0820

(-53.4)

-0.109

(-18.5)

0.145

(25.4)

-

PCUc

-0.0285

(-35.0)

0.0887

(13.6)

-0.710

(-21.4)

-

D3M/

D4M

PCUf 117.2

(1835.8)

-0.00094

(-9.5)

-0.1131

(-42.2)

0.1293

(26.7)

-0.90

(-11.8)

PCUb -0.01331

(-132.4)

-0.0961

(-32.0)

0.0511

(12.6)

-1.23

(-23.5)

PCUc -0.02120

(-29.2)

-0.1472

(-10.6)

-0.0774

(-3.3)

0.83

(4.0)


These show that:

The combining of D2AP/D3AP has a marginal effect on the bendiness and sum of falls

parameters compared to the D2AP models;

The pcu per lane slopes all marginally increase when D2AP/D3AP sites are combined;

The intercept value remains constant for D2AP at 112.9, and that there is a constant

adjustment factor for D3AP speeds ranging from 5.22 to 6.43 (the value beyond QB is

ignored in this respect as only the slope will be used in this region);



The combining of D3M/D4M has the benefit of removing the high, and unrealistic,

bendiness coefficient that existed in the D4M models. The outturn bendiness

parameter in the D3M/D4M combined model is close to the D3M values and consistent

with previous COBA values;

The D3M/D4M model has modified sum of falls parameters which are a combination of

the effects that were noted in the separate D3M and D4M models;

The pcu per lane slope values remain similar to those in the separate models; and most

importantly;

there is only a very small constant adjustment to the intercept for a D4M as opposed to

a D3M motorway. This implies that free flow speeds are in reality the same on each

road type which is intuitively correct.

These models are used as the basis for the recommended speed/flow relationships for light

vehicles as summarised later in Section 7. However, there is one issue which is evident when

comparing the above models with the COBA curves which requires further discussion. This

relates to the pcu per lane slope beyond QB. In many cases the slope derived from the current

analyses is shallower than that used in the COBA curves, which implies that the achievable

speed at QC is higher than currently represented by the COBA curves.

Earlier in Section 5 we presented figures 5.3 to 5.7 showing the speed/flow data aggregated in

increments of ten pcus, these are repeated in Figure 6.2. These show some potentially

interesting results as flows approach QC with a wider scatter of points and some indications

that speeds were stabilising close to QC, for example on D2AP and D4M curves. As discussed

in the preceding sections there are a limited number of sites in the D3AP and D4M categories

and this leads at the end of the analysis to the combining of the D2AP and D3AP sites but with

dummy variables for D3AP, and similarly for the D3M and D4M sites.

The D3AP data profile indicates that there are specific factors relating to some of the sites that

result in a steep decline in speeds at flows which are well below the assumed capacity of a

D3AP road (6,300 pcus). Detailed examination of these sites indicates that many of them are

really lane gain/drop between adjacent junctions and as such do not operate as a full D3AP due

to lack of utilisation of the inside lane at higher flows as drivers position themselves for the

diverge at the downstream.



Figure 6.2 Dual Carriageway and Motorway Speed/Flow Observations

40

50

60

70

80

90

100

110

120

0 500 1,000 1,500 2,000

Sp

ee

d (

kp

h)

PCUs per hour

D2AP

40

50

60

70

80

90

100

110

120

0 500 1,000 1,500 2,000

Sp

ee

d (

kp

h)

PCUs per hour

D3AP

40

50

60

70

80

90

100

110

120

130

0 500 1,000 1,500 2,000

Sp

ee

d (

kp

h)

PCUs per hour

D2M

40

50

60

70

80

90

100

110

120

130

0 500 1,000 1,500 2,000

Sp

ee

d (

kp

h)

PCUs per hour

D3M

40

50

60

70

80

90

100

110

120

130

0 500 1,000 1,500 2,000

Sp

ee

d (

kp

h)

PCUs per hour

D4M



The regression analyses undertaken to-date includes all the data points for the selected sites,

but with filtering to remove data for periods where breakdown had occurred and over-capacity

demand existed leading to excessively low speeds. Given the evidence in the plots shown in

Figure 6.2, there could be the potential for variability in the estimation of the slope beyond QB

given the scatter and speed profile at very high flows. The number of individual observations in

the higher flow bands is obviously much lower than for other flows and as such greater

variability would be expected in the aggregated plots.

A series of tests on the estimation of the slope beyond QB have been undertaken to examine

how sensitive the slope is to the exclusion of the very high flow data. This has used four

separate datasets beyond QB:

QB to 0.85QC;

QB to 0.90QC;

QB to 0.95QC; and

QB to QC (as in regression analyses reported above in Table 6.14).

Table 6.16 shows the results of these tests by road type, excluding D3AP due to the issues

discussed earlier.

Table 6.16 Comparison of Light Vehicle Slope beyond QB

Road Type Data Range from QB

To 0.85QC To 0.9QC To 0.95QC To QC

D2AP -0.0249

(-13.4)

-0.0227

(-21.8)

-0.0209

(-28.2)

-0.0193

(-31.7)

D2M -0.0281

(-17.2)

-0.0396

(-34.7)

-0.0399

(-46.7)

-0.0381

(-47.6)

D3M -0.0365

(-13.5)

-0.0356

(-20.3)

-0.0332

(-25.1)

-0.0308

(-25.3)

D4M -0.0267

(-15.3)

-0.0200

(-18.0)

-0.0170

(-18.8)

-0.0166

(-18.7)

Average -0.0291 -0.0295 -0.0278 -0.0262


The above shows that:

The D2AP slope estimation increases as more of the higher flow data is removed;

The D2M slope is also relatively stable over the higher flow bands, >0.90Qc, but is

much lower up to 0.85Qc indicating a rapid steepening of the slope;

The D3M slope estimation is relatively stable but increases as more of the higher flow

data is removed; and

The D4M data slope estimation increases as more of the higher flow data is removed.

These variances in the slope estimation are consistent with the speed/flow profiles in Figure

6.2.

The COBA recommended slope beyond QB is -0.033 for dual carriageways and motorways

whereas the outputs from the current study indicate average slopes in the range of -0.017 to -



0.038 by road type for slopes derived from all data between QB and QC. Taking a simple

average across all road types and by the different data ranges, as shown in Table 6.16,

indicates that the slope beyond QC for dual carriageways and motorways is likely to be in the

range of -0.026 to -0.0291. This is slightly lower than the COBA slope beyond QB and this would

not be unexpected given changes in driver behaviour and vehicle standards.

The analyses undertaken, and described in this section, lead to the following important

conclusions with respect to the derivation of the final recommended light vehicle speed flow

curves. Namely, that:

There are three clear sections to the curve covering:

o a free flow section to a point QF which is at flows of 670 pcus for D2AP/D3AP

roads, and between 800 and 920 pcus for D2M to D4M roads;

o a section with increasing decline of speeds from QF to QB, similar to the COBA

QB but at a higher flow of 1,590 pcus for D2AP/D3AP roads, and 1,715 pcus for

D2M to D4M roads; and

o a further decline in speeds from QB to QC with the QC values being 2,100 pcus

for D2AP/D3AP roads, and 2,330 pcus for D2M to D4M roads. These are the

same values as in the COBA curves as the study found no evidence to suggest

that has been any change in this parameter.

There is a need, supported by the evidence discussed above, to retain some measure

of bendiness and hilliness as predictors of free flow speeds on links and this would be

consistent with the aims of producing speed flow curves for use in transport models as

some degree of categorisation of roads into say three bands for bendiness and hilliness

such a low/medium/high could be developed using the unit rates derived from the

regression analyses; and

There are significant differences between D2AP/D3AP, D2M, and D3M/D4M that justify

separate speed flow curves for these road categories.

The final recommended speed flow curves are described in Section 7 and draw on the final

regression model results presented in Tables 6.15 and 6.16, but with some adjustments as

described in Section 7.

6.3.4 Heavy Goods Vehicles An initial set of stepwise multiple regressions were undertaken for each road type with the

variables being:



Bendiness;

Sum of Rises; and

Sum of Falls.

These were undertaken for each of the three slopes, up to QF, from QF to QB, and beyond QB.

The results are shown in Tables 6.17 to 6.21. Due to the large amount of data available for

each of the regressions the t-statistics are usually very high as they are a measure of the

degree of confidence in the estimated parameter and the more data available the higher will be



the t-statistic in general. The stepwise regression removes any variables that do not reach an

acceptable level of significance and as such we have not included the t-stats in the tables.

The fact that a variable is retained through the stepwise regression does not however mean that

it should be automatically included within the final analyses and recommended speed flow

variables are produced. This may be either because they have such a small impact, although

statistically significant, or they are counter intuitive in terms of the direction of the impact, for

example a positive coefficient for HGVp would imply speeds increase with a higher proportion of

HGV’s in the traffic stream which is clearly anomalous.

Table 6.17 shows the regression results for D2AP roads. The main points to note are:

There is essentially no slope up to the QB point and then a relatively shallow slope after

QB;

HGVp has no effect at low flow and the parameter values are counter-intuitive for flows

above QF. It is concluded that HGVp should be excluded;

Bendiness is consistently important but appears to decrease in importance as flows

increase. This is logical in that at low flows the full effect of any bends on reducing

speeds would be observed but as flows increase and the average speeds decrease

then the net effect of the bendiness on speed reduction would be expected to

decrease. As the implied speed reduction up to QF due to bendiness is 4.8 kph then it

clearly should be retained as a variable;

Sum of Rises has low parameter values and again for low and high flow regions the

value is potentially counter-intuitive e.g. higher speeds on inclines. It is likely that Sum

of Rises should be excluded. This is not unexpected even for heavy vehicles as

today’s trucks perform far better on inclines and only on the severest and long sections

of climb is there a noted deterioration in performance. They are, in the main, able to

achieve close to their free flow speed on most gradients;

Sum of Falls only had an effect up to QF, after QF the parameter has the wrong signs;

and

The implied average free flow speed is 85.2 kph and this and the intercept value at

87.5 kph compare favourably with the COBA intercept of 86 kph;

The preliminary conclusions are that HGVp and Sum of Rises should be dropped from further

analyses for D2AP roads.

Table 6.17 D2AP Stepwise Regressions (Three-Slope Analysis)

Slope Intercept pcu HGVp Bendiness SumofR SumofF

PCUf 87.51

(600.3)

-0.2081

(-30.9)

0.0902

(6.4)

0.2098

(15.6)

PCUb 0.000376

(3.0)

4.084

(6.6)

-0.10087

(-33.3)

-0.06993

(-9.4)

PCUc -0.00335

(-18.7)

4.3355

(3.8)

-0.0850

(-4.1)

0.0327

(1.9)





There is essentially no slope up to the QB point and then a relatively shallow slope after

QB;

HGVp was significant for the low and high flow region but of the wrong sign in the

middle flow regions;

Bendiness is of the right sign and appears to decrease in importance as flows

increase; indeed it has no effect at high flows. This is logical in that at low flows the full

effect of any bends on reducing speeds would be observed but as flows increase and

the average speeds decrease then the net effect of the bendiness on speed reduction

would be expected to decrease. As the implied speed reduction up to QF due to

bendiness is 1.5 kph then it clearly should be considered as a variable;

Sum of Rises is consistently of the right sign but decreasing rapidly in impact as flows

increase and average speeds decrease such that at high flows it has no impact on

average speeds. The implications are that it should be retained for further analysis but

that it may only have relevance in determining the free flow speed;

Sum of Falls is variable in its importance and is of the wrong sign in the low flow

region. As the only significant effect was shown at high flows then it may that it is

considered for removal from future analyses; and

The implied average free flow speed is 87.4 kph and this is somewhat lower than the

COBA intercept of 93 kph;


Sum of Falls should be dropped from further analyses for D2M roads.



PCUf 90.84

(219.2)

0.00051

(1.5)

-5.6746

(-5.2)

-0.0877

(-13.4)

-0.11821

(-7.2)

-0.10506

(-6.6)

PCUb 0.00041

(3.2)

2.3365

(2.4)

-0.04553

(-15.9)

-0.0517

(-4.8)

0.04335

(4.3)

PCUc -0.00414

(-13.7)

-20.97

(-4.5)

0.28366

(9.6)



There is very little evidence of any slope as far as QC;

HGVp has a low value in the low and middle flow region, equal to an average reduction

of 0.4 kph for speeds in the middle flow region, but has no effect in the high flow

region;

Bendiness is consistently of the wrong sign and as such should be omitted;

Sum of Rises is consistently significant and of the right sign and should be retained for

further analyses;

Sum of Falls is of the wrong sign and should be excluded from future analyses; and

The implied average free flow speed is 90 kph and this compares favourably with the

COBA intercept of 93 kph.




Sum of Falls and bendiness should be dropped from further analyses for D3M roads.



PCUf 90.81

(436.3)

-0.00042

(-4.2)

-4.06307

(-9.5)

0.0476

(11.1)

-0.166

(-16.0)

PCUb -3.8802

(-6.7)

0.0843

(18.0)

-0.1439

(-15.0)

-0.0252

(-2.4)

PCUc 0.123

(12.2)

-0.2434

(-10.2)

-0.2111

(-7.4)



There is minimal slope as far as QB but then a relatively low slope beyond QB;

HGVp has a low value in the low flow region but a significant value, equal to an

average reduction of 1.1 kph for speeds in the middle flow region, and a similar effect

in the high flow region;

Bendiness is of the wrong sign and should be excluded from further analysis;

Sum of Rises is of the correct sign and significant in scale for the low flow region but of

a much reduced effect beyond QF. It should however be retained due to its impact on

free flow speed;

Sum of Falls is of the wrong sign and should be excluded; and

The implied average free flow speed is 88.4 kph and this compares favourably with the

COBA intercept of 93 kph.


Sum of Falls and Bendiness should be dropped from further analyses for D4M roads.

Table 6.20 D4M Stepwise Regressions (Three Slope Analysis)


PCUf 83.57

(124.4)

-3.0354

(-2.7)

0.57162

(17.1)

-0.2292

(-6.2)

-0.10784

(-3.4)

PCUb -0.00063

(-6.3)

-8.539

(-7.3)

0.10786

(7.5)

0.07953

(7.3)

PCUc -0.00141

(-10.5)

-13.191

(-6.7)

-0.0703

(-2.7)

-0.07302

(-3.7)


Table 6.21 presents a summary of the implied importance in terms of effect on speeds of each

variable. The table includes the speed change for the period up to QF based on the average

values of the variable in the database. This enables an indication of the relative importance of

the respective variables to be observed.



Table 6.21 Summary of Variable Importance – Heavy Goods Vehicles

Road Type Variable


D2AP 0.00

Exclude

-4.80

High/Include

0.66

Wrong Sign /

Exclude

-1.59

Wrong Sign /

Exclude

D2M

0.55

Very Low /

Exclude

-1.51

Low/Include

-0.70

Low / Include

-0.65

Wrong Sign /

Exclude

D3M

-0.39

Very Low /

Exclude

0.49

Wrong Sign /

Exclude

-0.96

Low / Include

0.00

Exclude

D4M

-0.39

Very Low /

Exclude

7.60

Wrong Sign /

Exclude

-1.56

Medium / Include

-0.82

Wrong Sign /

Exclude

The interpretation of the above is that HGVp should be excluded on the grounds that the values

are generally very low, bendiness is excluded for D3M/D4M but included for D2AP/D2M, Sum

of Rises is included, and Sum of Falls excluded.

The exclusion of variables has been undertaken in an incremental manner to enable the effect

on other variables to be assessed. The first exclusion was of HGVp and Table 6.22 shows the

results for this exclusion but with the pcu variable changed to reflect pcu per lane so that the

slopes can be directly compared to COBA values. This has no effect on the parameter

estimates of the variables as it is simply a scaling factor.



Table 6.22 Heavy Vehicle Regressions Excluding HGV Proportions

Road Type

Slope

Variable

Intercept pcu per


D2AP

PCUf 87.51

(600.3)

-0.2081

(-30.9)

0.0902

(6.4)

0.2098

(15.6)

PCUb 0.00078

(3.1)

-0.1087

(-23.4)

-0.0604

(-6.5)

0.01567

(1.7)

PCUc -0.00709

(-20.7)

-0.05729

(-3.0)

0.08691

(2.1)

0.061175

(1.7)

D3AP

PCUf 90.21

(187.1)

-0.00263

(-2.0)

PCUb -7.7843

(-5.4)

-16.659

(-5.4)

-16.7067

(-5.4)

PCUc -0.00359

(-3.0)

D2M

PCUf 89.31

(306.9)

0.002199

(3.5)

-0.0858

(-13.1)

-0.10893

(-6.7)

-0.09283

(-5.8)

PCUb 0.000739

(2.9)

-0.04565

(-16.0)

-0.05548

-5.2)

0.0415

(4.1)

PCUc -0.00779

(-13.1)

0.01217

(1.9)

0.2961

(9.8)

D3M

PCUf 89.66

(380.4)

-0.00077

(-2.6)

0.04083

(8.9)

-0.15878

(-10.9)

0.02571

(1.9)

PCUb -0.00032

(-1.7)

0.08744

(18.3)

-0.1531

(-16.1)

-0.03413

(-3.3)

PCUc 0.123

(12.2)

-0.2434

(-10.2)

-0.12111

(-7.4)

D4M

PCUf 82.37

(163.6)

0.5839

(17.6)

-0.20585

(-5.7)

-0.08659

(-2.9)

PCUb -0.00234

(-5.9)

0.1351

(9.7)

0.07918

(7.3)

PCUc -0.00489

(-9.2)

-0.0664

(-3.6)

0.0881

(5.0)


Table 6.22 shows that the exclusion of the HGVp variable had a negligible effect on the other

parameter estimates which is as expected given the low values associated with the HGVp

variable.

Table 6.23 shows the results of excluding the Sum of Falls for all road types and the Bendiness

for D3M/D4M from the estimation.



Table 6.23 Heavy Vehicle Regressions Excluding HGV Proportions and Sum of Falls

Road Type

Slope Variable

Intercept pcu per lane Bendiness SumofR

D2AP

PCUf 88.6

(683.9)

-0.1476

(-26.5)

PCUb -0.1028

(-34.1)

-0.0696

(-9.3)

PCUc -0.0071

(-20.9)

-0.0413

(-2.7)

D3AP

PCUf 90.2

(187.1)

-0.00263

(-2.0)

PCUb

PCUc -0.00359

(-3.0)

D2M

PCUf 88.8

(317.3)

-0.0779

(-12.1)

-0.0551

(-4.1)

PCUb -0.0477

(-16.9)

-0.0823

(-9.8)

PCUc -0.00715

(-11.8)

-0.0177

(-2.7)

-0.2240

(-7.5)

D3M

PCUf 90.6

(519.3)

-0.00123

(-4.2)

-0.1738

(-16.8)

PCUb -0.1344

(-19.1)

PCUc -0.0585

(-3.7)

D4M

PCUf 89.1

(421.9)

0.2080

(10.8)

PCUb -0.00165

(-4.2)

PCUc -0.00499

(-9.5)

-0.0563

(-3.8)


Table 6.24 compares the implied free flow speeds by road type with those in COBA. The free

flow speeds have been calculated using the average values of the variables in Table 6.4. The

results of this comparison indicate that heavy vehicle speeds have increased further since the

last update of the COBA values and that this applies across all road types.



Table 6.24 Comparison of Heavy Vehicle Free Flow Speeds

Road Type Current Estimates COBA Values

D2AP 85.2 76.3

D3AP 77.6

D2M 87.4 85.3

D3M 90.0 86.2

D4M 88.4 84.7

The final set of heavy vehicle model regressions combine D2AP/D3AP and D3M/D4M into

single categories, due to the low number of sites for D3AP and D4M categories, but with

dummy variables for D3AP and D4M respectively. The results of these final regressions are

shown in Table 6.25.



Table 6.25 Final Heavy Vehicle Regressions – D2AP/D3AP and D3M/D4M combined

categories

Road Type Slope Variable

Intercept pcu per

lane

Bendiness Sum of

Rises

D3AP /

D4M

D2AP/D3AP PCUf 88.6

(338.0)

-0.1463

(-26.9)

2.70

(14.0)

PCUb -0.1044

(-37.9)

-0.0673

(-10.4)

1.28

(14.5)

PCUc -0.00689

(-21.0)

-0.0438

(-2.9)

1.80

(9.1)

D2M PCUf 88.8

(317.3)

-0.0779

(-12.1)

-0.0551

(-4.1)

PCUb -0.0477

(-16.9)

-0.0823

(-9.8)

PCUc -0.00715

(-11.8)

-0.0177

(-2.7)

-0.2240

(-7.5)

D3M/D4M PCUf 89.7

(540.0)

-0.00085

(-3.0)

-0.0625

(-6.8)

2.20

(19.0)

PCUb -0.0841

(-14.6)

1.14

(15.5)

PCUc -0.00318

(-7.9)

-0.0566

(-5.4)

-


These show that:

The combining of D2AP/D3AP has a marginal effect on the bendiness and sum of rises

parameters compared to the D2AP models;

The pcu per lane slopes all remain zero up to QB when D2AP/D3AP sites are

combined, and the slope beyond QB is slightly reduced;

The basic intercept value remains unchanged at 88.6 kph but there is a constant

adjustment factor for D3AP speeds ranging from 1.28 to 2.70 kph;



The combining of D3M/D4M stabilises the parameter estimates for sum of rises across

the three sections;

The pcu per lane slope values remain similar to those in the separate models; and

There is a constant adjustment for the intercept speed of between 1.14 and 2.20 kph.

These models are used as the basis for the recommended speed/flow relationships for heavy

vehicles as summarised later in Section 7.

6.4 Rural Single Carriageways – Multiple Stepwise Regression

6.4.1 Light Vehicles An initial set of stepwise multiple regressions were undertaken for rural single carriageways with

the variables being:



Bendiness;

Sum of Rises;

Sum of Falls;

Hilliness;

Net Gradient; and

Road standard.

The road standards that were available in the final dataset were:

Standard width and hard strip or verge (reference road type);

Standard width (VW4);

Standard width and hard strip and verge (VW5); and

Wide road with hard strip and verge (VW8).

The references in brackets are the codes used for the links in the dataset and output by the

regression analysis as separate variables. The standard width with either a hard strip or a verge

was the predominant link type, seven sites, so was taken as the reference road type. There

were five sites in the VW5 category, three in the VW8 category, and only one in the VW4

category.

Prior to describing the results of the regression analyses it is pertinent to examine the

speed/flow profile across all sites with the speed/flow observations aggregated into 10 pcu

bands, Figure 6.3.



Figure 6.3 Rural single Carriageway Aggregated Speed/Flow Profile

Figure 6.3 includes all data points, even where there are a small number of observations in the

10 pcu aggregations (i.e. less than 10). This mainly relates to flows beyond the second break

point of around 1,140 pcus. The above curve shows an initial period of relatively steep decline

from free flow speed as flow increases up to about 440 pcus. This reflects the fact that at very

low flows on S2 roads drivers are able to travel at their desired speed and when they encounter

a slower driver it is usually relatively easy to overtake. However, as flows increase the average

speeds will stabilise out as the slower drivers, and HGV vehicles, will have a dominating effect

as at higher flows the overtaking options are drastically reduced.

This leads to a stable period from 440 to 1,140 pcus where the slope is very gentle and average

light vehicle speeds are around 76 kph. Beyond 1,140 pcus there is then a steep decline in

speeds as the ability to overtake becomes much harder and platoons form behind the slowest

vehicles until at higher flows breakdown occurs.

The current COBA curves have a two slope approach with a break point QB at which is defined

as 0.8*QC with QC being a function of carriageway width and proportion of HGVs. In the case of

a standard width S2 and 15% HGVs the COBA break point would be around 900 pcus.

The slopes implied by the profile in Figure 6.3 are -0.0254 to 440 pcus, -0.0027 from 440 –

1,140 pcus, and then -0.089 after 1,140 pcus. The COBA slopes for a 15% HGV contents are -

0.019 to 900 pcus, and then -0.05 beyond 900 pcus. Table 6.26 compares the implied decline in

speeds between COBA curves and the slopes from the data in Figure 6.3

30

40

50

60

70

80

90

0 200 400 600 800 1,000 1,200 1,400

Sp

ee

d (

kp

h)

PCUs



Table 6.26 Comparison of S2 Decline in Speeds – COBA and Preliminary Analysis

Flow Implied Decline in Speed (kph)

COBA Current Data

900 -17.1 -12.4

1,200 -32.0 -18.4

The figures above indicate that speeds on S2 roads on the strategic road network (SRN) are

maintained at a higher level than COBA curves imply. To what extent this is due to the SRN

single carriageway roads being of a higher standard than the typical range of S2 roads included

in the COBA analysis is difficult to determine. However, there are clear indications from the

above analysis that the speed/flow profiles on S2 roads that form part of the SRN are

significantly different from the COBA curves in terms of the rates of decline in speeds.

Bearing the above analyses in mind, an iterative process to the regression analyses was

undertaken. Preliminary regression runs with all the variables in indicated that combining

hilliness, net gradient, sum of rises, and sum of falls introduced significant correlations into the

data and the parameter estimates for these variables became very large, and while they

cancelled each other out it made the intercept values meaningless.

Regressions were therefore run with similar variables in as the COBA curves which removed

the correlations. The results of the light vehicle stepwise regression runs are shown in Table

6.27.



Table 6.27 S2 Light Vehicle Preliminary Regression Results

Variable To QF To QB To QC

Intercept 93.6

(194.9)

pcu -0.03

(-21.8)

-0.0118

(-50.3)

-0.0311

(-9.5)

HGVp 9.25

(9.4)

-24.33

(-38.6)

-67.12

(-5.4)

Bendiness -0.0796

(-12.3)

-0.0863

(-34.1)

0.1176

(2.1)

Hilliness -0.0257

(-1.9)

-0.0728

(-11.2)

-0.2919

(4.8)

VW4 -1.0427

(-1.5) - -

VW5 0.9789

(4.2)

-0.215

(-2.3) -

VW8 2.9320

(10.0)

1.892

(14.9)

7.522

(4.6)

Net Gradient - 0.05661

(13.1) -

Note: * denotes low levels of significance.


The primary conclusions to be drawn from the results in Table 6.27 are that:

There are three distinct sections to the curve as depicted by the significantly different

slope profiles;

Bendiness is important up to QB but of the wrong sign thereafter;

Hilliness has a minor effect up to QF which is probably due to low incidence of HGVs

and ease of overtaking which enables light vehicle speeds to be maintained. Hilliness

becomes more important as flows increase and this is logical in that at higher flows the

effect of slower moving HGVs on hillier sections will have an increasing effect;

A similar effect occurs for HGVp and for very much the same reasons;

Net gradient does not show up as a significant factor, if hilliness is retained, and as

such should be excluded; and



Road types VW4 and VW5 do not show any significant effect on flows above QF, and

are small in scale, less than 1 kph impact, and as such can be excluded.

Table 6.28 shows the effect of excluding net gradient and the VW4 and VW5 road type

variables. This showed that the removal of the identified variables had a minor effect on the

parameter values for the remaining variables which indicates that the excluded variables were

not significantly contributing to the fitted curves. Where comparisons are possible against

COBA they are relatively consistent for bendiness and the slopes.

Table 6.28 S2 Light Vehicle Preliminary Regression Results – Variables Excluded

Variable To QF To QB To QC COBA Values

Intercept 94.3

(205.5)

pcu -0.031

(-22.5)

-0.0116

(-62.0)

-0.0311

(-6.3) -0.015 / -0.05

HGVp 8.676

(8.9)

-23.85

(-38.7)

-67.12

(-3.9)

Bendiness -0.0815

(-12.9)

-0.0815

(-33.2)

0.1176

(3.6) -0.09

Hilliness -0.0213

(-1.7)

-0.0702

(-14.2)

-0.2919

(-3.9)

VW8 2.4165

(9.0)

2.3343

(20.8)

7.522

(3.3)


In order to draw more direct comparisons with the COBA curves, regressions were undertaken

assuming a single QB break point in line with COBA guidance. These were run using the same

variables as in Table 6.28, but also for a test excluding HGVp as this effect is captured in COBA

in the slope in relation to flow. Table 6.29 shows the results of these tests.



Table 6.29 Single Stepwise Regression to QB and Comparisons to COBA

Variable Model (A) Model (B)

Model C

(Remove flows <300)

COBA

Intercept 93.2

(579.6)

91.9

(636.4)

89.3

(511.9) (88.3)

pcu -0.01576

(-104.5)

-0.01573

(-103.0)

-0.0121

(-64.2)

-0.015

(-0.019 with

typical HGV

effect)

HGVp -8.6477

(-17.1) - - -

Bendiness -0.09069

(-38.7)

-0.08967

(-38.3)

-0.08064

(-32.6) -0.09

Hilliness -0.04635

(-9.7)

-0.03832

(-8.0)

-0.05124

(-10.4) -

VW8 2.0351

(19.7)

2.436

(23.8)

3.282

(29.8)

(2.0 per metre

width)

Notes:

1. COBA intercept is estimated value for a typical S2 road taking into account all constant factors in the

COBA equations.

2. Model A includes all observations up to QB and retains HGVp as a variable

3. Model B includes all observations up to QB and excludes HGVp as a variable

4. Model C includes all observations from 300 pcu up to QB and excludes HGVp as a variable. This covers

a similar flow range to the data used in generating the COBA curves which did not have the low flow

values.


Table 6.29 shows that when analysed within the same confines of the COBA curves that there

is some degree of consistency in the parameter estimates for the variables. The bendiness is

very similar, there are width based effects, the slope to QB is similar but at a shallower level in

the new models. The free flow speed, intercept value, is also higher in the current data. This is

a similar pattern to that observed in the dual carriageway and motorway analyses of speeds

being higher, declining at lower rates as flows increase, and then having a steeper decline in

the vicinity of QC.

These models are used as the basis for the recommended speed/flow relationships for light




6.4.2 Heavy Vehicles A similar analysis approach was adopted for heavy vehicle speeds but given the consistency in

speed profiles up to QB very few variables were identified as of significance, see Table 6.30.

This shows that the slope to QB is slightly shallower than in COBA and that the hilliness effect is

much reduced and this is consistent with improved vehicle performance and the modernisation

of the haulage fleet that has taken place over the past twenty years.

Table 6.30 Rural Single Carriageways – Heavy Vehicles

Variable Current Model to QB COBA

Intercept 77.6

(237.4) 77.7

pcu -0.00452

(-10.9) -0.0052

Hilliness -0.02489

(-1.9) -0.07

VW8 3.838

(15.1) -

Note: COBA also had significant variables for bendiness and net gradient of -0.1 and -0.13 respectively.


Figure 6.4 shows the aggregated speed flow profile for heavy vehicles on rural single

carriageways. After an initial reduction in speed from the free flow speed at low flows the

average speed is then stable across the main flow band to QB. This is consistent with the

outputs from the regression analyses.



Figure 6.4 S2 Heavy Vehicle Aggregated Speed Flow Profile

These models are used as the basis for the recommended speed/flow relationships for heavy


0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1,000 1,200

Sp

ee

d (

kp

h)

PCU



7. Recommended Speed Flow Curves

and Parameters

7.1 Overview

The aim of the study has been to review the current evidence on the relationship between

speeds and flow on the road types that comprise the SRN with a view to defining:

New relationships that are consistent with the evidence base with a particular emphasis

on updating the following parameters by road type:

o VL and VH which are the initial speeds for light and heavy vehicles respectively;

o VB the speed at flow QB; and

o QB the capacity breakpoint for each road type.

Providing power law curve approximations of the new curves for use in traffic models.

The detailed analyses described in the preceding section led to a number of important

conclusions as to the form of the speed flow curves with strong evidence for there being at least

three sections up to QC rather than the two defined in COBA curves. The evidence also

indicates that QB, at least on motorways, occurs at a later flow than currently adopted in COBA.

As the primary application of the new speed flow curves is to be as a basis for developing traffic

models it is important to develop a set of pragmatic relationships that can be used to determine

the allocation of speed flow relationships to individual links without imposing a considerable

overhead on the modeller by requiring very detailed geometric parameters to be obtained.

In terms of the key drivers that affect average free flow speeds within a specific road type the

main variables that the study has identified are:

Bendiness;

Hilliness, represented either by Sum of Rises or Sum of Falls; and

Carriageway width, e.g. standard or wide single carriageway, D2 or D3/4 in the case

of dual carriageways.

Keeping the variables to this level of detail enables broad categories to be defined for modelling

purposes where the unit rates for the constant terms of bendiness and hilliness can be used to

define a range of free flow speeds relating to roads that fall with broad categories defined by

level of bendiness, and hilliness, e.g. low/medium/high. By specifying average values of the

variables for each category then the equations contained later in this section can be converted

to provide alternative free flow speeds.

It is important to note that all of the analysis in the study has been based on the use of pcus

rather than vehicles and as such the impact of HGVs is captured in the parameter estimates

based on the pcu ratios commonly adopted by vehicle type.

Each of the sections in chapter six resulted in a final set of regression equations by road type

and for light and heavy vehicles. In each case these defined the value of the parameters for all

of the relevant variables in each of three sections of the curve up to QC, namely, to QF, from QF

to QB, and from QB to QC. To enable the application of a single equation for the speed/flow



relationship that can later be converted to a power law approximation the following approach

has been adopted:

Take the parameter estimates for the geometric parameters relating to bendiness,

hilliness and carriageway width from the regressions fitted to the section up to QF. This

is considered the most appropriate value to use as it is not affected by flow levels and

as such is a pure indication of the impact of the geometric variable on the speeds in

free flow conditions. The level of variability in the geometric parameters across the

three separate slope regressions is also relatively low hence supporting the adoption of

a single value; and

Remove the geometric parameters from the regressions above QF and re-calculate the

slopes from QF to QB, and from QB to QC simply as a function of flow levels.

Adopting the above leaves one remaining issue with regard to specification of the speed flow

curves and that relates to the treatment of the dummy variable for D3AP in the final regression

models. The D3AP data was aggregated with the D2AP data due to the lower sample size and

the presence of some correlations in the data, due to lack of variability in some of the variables

e.g. constant bendiness, so as to better define the free flow speeds and the influence of the

geometric variables by road type.

The question is whether it is logical to expect the constants for D3AP to remain at the same

value across all flow ranges up to QC. As flows approach QC it could be hypothesised that

average speeds on D2AP and D3AP would move closer together regardless of any geometric

differences between the two road types. The same could also be said for D2M and D3M/D4M

roads. This has been examined by plotting the average speeds by road type for 100 vehicle

bands for the different road types.

Figures 7.1 and 7.2 show the results for D2AP/D3AP and D2M/D3M/D4M respectively.



Figure 7.1 D2AP/D3AP Speed Flow Comparisons

70

75

80

85

90

95

100

105

110

115

120 A

ve

rag

e S

pe

ed

(k

ph

)

Vehicles per lane

D2AP D3AP



Figure 7.2 D2M/D3M/D4M Speed Flow Comparisons

The above figures show that there is evidence that the average speed of vehicles, within a road

category but with differing road widths, begin to converge as the flows approach QC. The effect

of the geometric differences clearly appears to diminish as the density of flow increases and the

dominant factor is the total flow.

Consequently, in the definition of the final speed/flow relationships adjustments have been

made to reflect the fact that the speeds will gradually converge. This is a significant divergence

from the COBA curves which retain the difference in free flow speed due to number of lanes

throughout the full flow range which is counter intuitive and not supported by the evidence base.

7.2 Single Rural Carriageways

The final single carriageway speed flow relationships, adopting a two slope curve so that a

power curve approximation can be fitted, are:

70

80

90

100

110

120

130 A

ve

rag

e S

pe

ed

(k

ph

)

Vehicles per lane

D2M D3M D4M



Light Vehicles T-stat 95% CI

VL = 91.9 (636.4) (91.6 to 92.2)

-0.0897 * Bendiness (-38.3) (-0.0851 to -0.0943)

-0.0383 * Hilliness (-8.0) (-0.0289 to -0.0477)

+ 2.436 * WS (23.8) (2.235 to 2.637)

-0.0157 * Q (-103.0) (-0.0154 to -0.016)

-0.0487 * (Q – QB) (for Q > QB) (-10.1) (-0.0393 to -0.0582)

Heavy Vehicles T-stat 95% CI

VH = 77.6 (237.4) (77.0 to 78.2)

– 0.0249 * Hilliness (-11.9) (-0.208 to -0.0290)

+ 3.838 * WS (15.1) (3.340 to 4.336)

-0.0045 * (Q – QB) (for Q > QB) (-10.9) (-0.0037 to -0.0053)

If VH > VL then VH = VL

where

QB = 1,140 pcus

WS = wide single 10m wide

Figure 7.3 shows the light and heavy speed flow curves.



Figure 7.3 Rural Single Carriageway Speed Flow Curves – Light and Heavy Vehicles

The original three-slope curve for light vehicles is shown below for completeness of the analysis

procedure.

40

45

50

55

60

65

70

75

80

85

90 S

pe

ed

(k

ph

)

PCU per Lane

S2_Light S2_Heavy



Light Vehicles

VL = 94.3 - 0.0815 * Bendiness – 0.0213 * Hilliness – 8.68 * HGVp + 2.4165 * WS

-0.0310 * Q

-0.0154 * (Q – QF) (for Q > QF)

-0.0644 * (Q – QB) (for Q > QB)

where

QF = 440 pcu

QB = 1,140 pcu

WS = wide single 10m wide

HGVp = percentage HGV e.g. 15% HGV is expressed as 0.15.

7.3 Dual Carriageways and Motorways

The final dual carriageway and motorway speed flow relationships including any adjustments or

convergence of speeds beyond QB are:

D2AP/D3AP


VL = 112.9 (1660.6) (112.8 to 113.0)

- 0.1235 * Bendiness (-52.4) (-0.119 to -0.128)

– 0.0626 * Sum of Rises (-13.9) (-0.054 to -0.071)

+ 0.0769 * Sum of Falls (16.6) (0.068 to 0.086)

+ 5.22 * D3AP (78.2) (5.09 to 5.35)

- 5.22 * D3AP ((Q – QB) / (QC – QB)) (for QB < Q < QC)

-0.0022 * Q (-15.7) (-0.0019 to -0.0025)

-0.0031 * (Q – QF) (for Q > QF) (-58.5) (-0.003 to -0.0032)

-0.0194 * (Q – QB) (for Q > QB) (-62.4) (-0.0188 to -0.020)

where

QF = 550 pcus

QB = 1,300 pcus

QC = 2,100 pcus

D3AP = 1 if road type is D3AP

The free flow speed uplift for D3AP roads is gradually reduced after QB until speeds at, or near

to QC, are similar on D2AP and D3AP roads.




VH = 88.6 (338.0) (88.1 to 89.1)

- 0.1463 * Bendiness (-26.9) (-0.136 to -0.157)

+ 2.7 * D3AP (14.0) (2.32 to 3.08)

-0.0097 * (Q – QB) (for Q > QB) (-13.6) (-0.0083 to -0.0111)


where

QF = 550 pcus

QB = 1,300 pcus

D3AP = 1 if road type is D3AP

D2M


VL = 117.1 (1186.3) (116.9 to 117.3)

- 0.0246 * Bendiness (-10.8) (-0.0201 to -0.0291)

– 0.317 * Sum of Rises (-65.8) (-0.308 to -0.326)

-0.0050 * Q (-29.2) (-0.0047 to -0.0053)

-0.0064 * (Q – QF) (for Q > QF) (-105.7) (-0.0063 to -0.0065)

-0.0167 * (Q – QB) (Q > QB) (-47.6) (-0.016 to -0.0174)

-0.0111 * (Q – 0.85QC) (for Q > 0.85QC)

where

QF = 860 pcus

QB = 1,700 pcus

An additional section of slope has been added to the D2M definition to better reflect the

speed/flow profile in the data plots. As flow approaches QC the slope for D2M steepens further

and this is considered to be a reflection of the effect of HGVs and the increasing occurrence of

overtaking HGVs which reduce all vehicles down to the HGV speeds. On D3M/D4M roads the

presence of lanes without any HGV means that light speeds can maintain higher average

speeds at higher flows than is possible on D2M roads.


VH = 88.8 (317.0) (88.3 to 89.3)

- 0.0779 * Bendiness (-12.1) (-0.0653 to -0.0905)

– 0.0551 * Sum of Rises (-4.1) (-0.0288 to -0.0814)

-0.0072 * (Q – QB) (for Q > QB) (-11.8) (-0.006 to -0.008)




where

QF = 860 pcus

QB = 1,700 pcus

D3M/D4M


VL = 117.2 (1835.8) (117.1 to 117.3)

- 0.1131 * Bendiness (-42.2) (-0.108 to -0.118)

+ 0.1293 * Sum of Falls (26.7) (0.120 to 0.139)

-2 * (Q – QB) / (QC – QB) (for QB < Q < QC)

-0.0009 * Q (-9.5) (-0.0007 to -0.0011)

-0.0140 * (Q – QF) (for Q > QF) (-160.7) (-0.0138 to -0.0142)

-0.0075 * (Q - QB) (for Q > QB) (-30.8) (-0.007 to -0.008)

where

QF = 860 pcus

QB = 1,700 pcus

QC = 2,330 pcus


VH = 89.7 (540.0) (89.4 to 90.0)

- 0.0625 * Sum of Rises (-6.8) (-0.0445 to -0.0805)

-0.0073 * (Q – QB) (for Q > QB) (-8.5) (-0.0056 to -0.0090)


where

QF = 860 pcus

QB = 1,700 pcus

Figures 7.4 and 7.5 show the final speed flow relationships for dual carriageway and motorway

speed flow curves for light and heavy vehicles respectively.



Figure 7.4 Dual Carriageway and Motorway Speed Flow Curves – Light Vehicles

70

75

80

85

90

95

100

105

110

115

120

0

100

200

300

400

500

600

700

800

900

1,0

00

1,1

00

1,2

00

1,3

00

1,4

00

1,5

00

1,6

00

1,7

00

1,8

00

1,9

00

2,0

00

2,1

00

2,2

00

2,3

00

Sp

ee

d (

kp

h)

PCU per Lane

D2AP D3AP D2M D3M/D4M



Figure 7.5 Dual Carriageway and Motorway Speed Flow Curves – Heavy Vehicles

7.4 Speed Flow Curve Comparisons

Figure 7.6 compares the new D3M speed flow curve with the current COBA curve and typical

curves from FORGE and HCM. The primary comparison of interest is with the COBA curve and

the main points are that:

The new curve commences from almost the same intercept point but remains level until

flows reach 860 pcus per lane, similar to the HCM curve, but above the COBA curve;

There is then a gradual decline in speed after QF and the new curve and the COBA

curve briefly coincide at a flow of around 1,400 pcus per lane; and

70

75

80

85

90

95

0

100

200

300

400

500

600

700

800

900

1,0

00

1,1

00

1,2

00

1,3

00

1,4

00

1,5

00

1,6

00

1,7

00

1,8

00

1,9

00

2,0

00

2,1

00

2,2

00

2,3

00

Sp

ee

d (

kp

h)

PCU per Lane




The COBA curve then enters a steeper decline earlier than the new curve and as such

the new curve predicts average speeds that are higher than COBA across the majority

of flows in the range to QC.

A similar picture also exists for the other road types and this is all indicative of enhanced vehicle

performance and changing driver behaviour, and confidence in their vehicles, which results in

decreased gaps when travelling at speed resulting in the maintaining of higher speeds at higher

flows than implied by the COBA curves. This is not unexpected as much of the evidence base

for the current COBA curves dates from 1990 and to some extent the 1970s work by TRL.

Figure 7.6 Comparison of D3M Speed Flow Curves

Note: For ease of comparison of the curves the Forge and HCM curves have been plotted

assuming the same free flow speed as the new and COBA curves.

40

50

60

70

80

90

100

110

120

130

0

100

200

300

400

500

600

700

800

900

1,0

00

1,1

00

1,2

00

1,3

00

1,4

00

1,5

00

1,6

00

1,7

00

1,8

00

1,9

00

2,0

00

2,1

00

2,2

00

2,3

00

Sp

ee

d (

kp

h)

PCU per Lane

New HCM FORGE COBA



7.5 Power Curves

The observed speed/flow data used in the calibration of the above relationships has also been

used to fit a power curve approximation based on the following relationship. This relationship is

the same format as used in SATURN for the definition of speed/flow relationships.

where

S0 = Free flow speed at V=0

N = fitted power value

A = calibration parameter

Figure 7.7 shows the curves that have been fitted to the data up to QC for dual carriageways

and motorways. Table 7.1 also shows the values for N and A in each fitted curve. Both Figure

7.7 and Table 7.1 show that the curves have a very similar set of parameter values by road

type.

Table 7.1 Fitted Power Curves for Dual Carriageways and Motorways

Road Type/Class N A

D2AP 3.141 0.1 x 10-12

D3AP 3.154 0.099 x 10-12

D2M 3.090 0.14 x 10-12

D3/D4M 3.110 0.1 x 10-12

The above curves all meet the criteria that the speed at QC and the average speed under the

curve up to QC match that implied by the speed/flow relationships in Section 7.4.

𝑠 =𝑠0

1 + 𝑠0𝐴𝑉𝑛



Figure 7.7 Fitted Power Curves for Dual Carriageways and Motorways

Horizontal axes units: pcus per hour per lane

Vertical axes units: kph

Dashed line indicates power curve fit to data

Given the form of the rural single carriageway curve, with the very steep decline in speeds

beyond QB, it is very difficult to fit a simple power curve to the data. A polynomial curve can be

fitted as shown in Figure 7.8. Polynomial curves were also fitted to the dual carriageway and

motorway data and these showed a similar level of fit as the simple power curves shown in

Table 7.1.

0

20

40

60

80

100

120

0

250

500

750

1,0

00

1,2

50

1,5

00

1,7

50

2,0

00

2,2

50

2,5

00

2,7

50

3,0

00

D2AP

0

20

40

60

80

100

120

140

0

250

500

750

1,0

00

1,2

50

1,5

00

1,7

50

2,0

00

2,2

50

2,5

00

2,7

50

3,0

00

D3AP

0

20

40

60

80

100

120

140

0

250

500

750

1,0

00

1,2

50

1,5

00

1,7

50

2,0

00

2,2

50

2,5

00

2,7

50

3,0

00

D2M

0

20

40

60

80

100

120

140 0

250

500

750

1,0

00

1,2

50

1,5

00

1,7

50

2,0

00

2,2

50

2,5

00

2,7

50

3,0

00

D3M/D4M



Figure 7.8 Rural single Carriageway – Polynomial Curve

y = -3E-10x6 + 6E-08x5 - 4E-06x4 + 0.0001x3 - 0.0015x2 + 0.0116x + 0.6702 R² = 0.9993

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6 T

ime

PCUs



8. Areas for Future Research The project database developed for the analysis of speed / flow relationships on Highways

Agency roads contains a great deal of data for a large number of sites and generally includes

thousands of hourly observations of average speed and traffic flow for each site used in the

analysis described in preceding sections. It is likely that this is the largest database of speed and

flow observations compiled in the UK and there are many opportunities for further analysis of

these data in order to better understand the operation of the UK road network.

In developing the database AECOM encountered a number of issues in terms of matching the

different methods of recording locations across datasets and developed tools to link datasets and

cross-check the resulting database tables. The lessons learnt from developing this process mean

that the cost of future data collation on the Agency’s network could be reduced substantially and

adding sites to the database could be completed in a shorter timeframe.

Throughout the project analysis, and during discussions at the project technical workshops,

further areas of research and analysis have been recorded and we have included a list of a

number of these below for reference:

A key future task will be the validation of the new speed / flow relationships using existing

models. This should include use of the curves in a validated base model to examine the

effects of the new curves on model validation, and use of the curves in Do Minimum and Do

Something future year models to examine the likely impacts of the curves on model benefits

and economic appraisal.

Merges / diverges have been excluded from our analysis; however the database has been

structured to allow for analysis with them included as well. This facility means that it is

possible to use the database to identify sites where the influence of merges / diverges has a

noticeable effect on average link speeds and where it is therefore worth considering merge /

diverge analysis. There are also a number of locations on the Agency’s network where

merge / diverge flows are explicitly recorded and it may therefore be possible to identify

some sites in the database where a detailed study of the impact of merging and diverging

traffic on vehicle speeds could be undertaken.

A small amount of targeted investigation (now that we understand the nature and availability)

of the DfT speed data would yield the ability to undertake a proper investigation of the

operation of Smart motorways. If additional data source covering the messages on VMS

were also collected a very detailed analysis of a small number of sites could be undertaken;

The database would allow for any number of other areas of research including the variability

of speeds by time of day. This could have various applications, for example the Highways

Agency has reduced lighting levels overnight on a number of links and analysis by time of

day could provide an indication of how this affects average speeds;

The addition of some new links in the database to join sections of highway and therefore

enable the monitoring of average speeds across longer sections of highway would provide a

facility to investigate how journey time reliability is dependent upon the length of a journey.



9. Summary and Conclusions

Table 8.1 shows the estimated variables, and their COBA equivalents, for:

Light vehicle free flow speed (VL0);

Heavy vehicle free flow speed (VH0);

Speed at capacity (VC);

Free flow break point (QF);

Flow breakdown point (QB); and

Capacity (QC).

Table 8.1 Comparison of Variables v COBA

COBA

Road

Class

Description VLO

(kph)

VHO

(kph)

VC

(kph)

QF

(pcu)

QB

(pcu)

QC

(pcu)

1 S2 7.3m 88

(90)

77

(78)

51

(60) -

1140

(1130) 1400

1 S2 10.0m 90

(95)

81

(78)

51

(58) -

1440

(1440) 1800

2 D2AP 110

(104)

85

(80)

85

(71) 670

1590

(1330) 2100

3 D3AP 115

(111)

88

(80)

86

(78) 670

1590

(1330) 2100

4 D2M 115

(107)

87

(87)

81

(77) 800

1715

(1470) 2330

5 D3M 117

(114)

89

(87)

88

(84) 860

1715

(1470) 2330

6 D4M 117

(114)

92

(87)

88

(84) 860

1715

(1470) 2330

Notes:

1. Figures in brackets are standard COBA values – QC values are the same.

2. Values are based on the average value of the variables in the observed data

sets for each road type.

The main points arising from the above table are that:

Free flow speeds and speeds at capacity on rural single carriageways are lower than

those in COBA. The lower free flow speed estimates may well be a reflection of the

presence of speed cameras on most rural roads which will have moderated speeds



compared to those encountered in the 1990s research. The much lower speed at

capacity is a function of the steeper slope derived above QB and this may be a function

of a far greater degree of observed data in the low and high flow ranges in the current

datasets compared to those in the 1990s research;

Free flow speeds and speed at capacity on dual carriageways and motorways are all

higher than in COBA, and in many cases significantly so, and this applies to light and

heavy vehicle speeds. This is not unexpected as factors such as improved levels of

vehicle performance (and consequent changes in driver behaviour) since the 1990s are

likely to have had a measurable influence; and

There are three distinct parts, and in some cases evidence of a fourth section, in the

speed flow curves up to QC for dual carriageways and motorways. The first section to

the point QF is almost flat and shows little reduction in speeds. This is followed by a

section to QB where speeds begin to reduce as flow increases but with a QB which is

generally at a higher flow than the COBA values by 15%-20%. Finally a steeper section

to QC with QC being the same flow levels as derived in COBA.

The study has compiled a very rich data source from which many aspects of the relationships

between geometric parameters, flow and speed can be explored. This data source removes the

limitations that existed with the work in the 1990s, particularly on dual carriageways and

motorways, and this has led to a number of changes in the recommended speed flow curves

from those in COBA.

The underlying trend in the data, compared to COBA, is that for the majority of cases, drivers

are travelling at higher speeds throughout the range of flows up to QC.



Appendix A – Location of Analysis Sites



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