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LIBRARY

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This is to certify that the

dissertation entitled

Analysis of Crash Rates on Horizontal Curves

presented by

Cyrus Safdari

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Civil Engineering

 

 

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Date 2 February, 1999

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use mamas-p.14

ANALYSIS OF CRASH RATES ON HORIZONTAL CURVES

By

Cyrus Safdari

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

1 999

ABSTRACT
ANALYSIS OF CRASH RATES ON HORIZONTAL CURVES
BY

Cyrus Safdari

In Michigan over 25% of fatal traffic crashes take place on non-freeway trunkline
highways. Research has consistently demonstrated that crash rates on
horizontal curves are significantly higher than that of the tangent sections on the
same road, and most studies have found the degree of curvature to be the most
significant single factor related to curve crashes. However, other roadway
features, such as superelevation and skid resistance of the pavement surface,
traffic control elements, driving environments and human factors, individually or

in combination are major contributors as well.

The purpose of this study was to analyze horizontal curve crashes on two-lane
trunkline roads in the State of Michigan and to devise procedures to identify road
segment attributes that correspond to the crash rate on curves. A second goal
was to identify curves that exhibited crash frequencies significantly higher than
the mean for their group. Simple and multiple regression models were found to
be poor predictors of crashes, explaining only a small percentage of the variation

in the crash rate on curves.

Discriminant Analysis was used to determine variables that distinguish between
high and low crash rate curves. The curve length, the presence of a turn or curve
warning sign, the radius of the curve and the tangent crash rate are the
discriminating variables identified. Using these variables 79.1% of the curves

were correctly classified.

These variables were then used to identify those curves with a high crash rate
that should (based on their characteristics) have a low crash rate. These curves

are candidates for countermeasures implementation.

Cluster analysis was used to identify the variables with a strong association with
the crash rate. The clustering of high, medium and low crash rate curves with
other variables was clear, with cluster one having a crash rate of 3.08, cluster

two a crash rate of 7.78 and cluster three a crash rate of 18.05.

The same variables identified in the discriminant analysis were important in the
cluster analysis. The ADT, curve radius and length, and the presence of traffic

control devices (arrow and chevron) are all important in defining the clusters.

ACKNOWLEDGMENTS

First and foremost I want to thank my academic advisor Dr. William Taylor, for his
advice and guidance throughout this research and my Ph.D. work. My appreciation and
gratitude are also extended to the members of my guidance committee, Dr. Nancy
Scannell, Dr. James Stapleton, Dr. Richard Lyles and Dr. Thomas Maleck. I also would
like to thank Dr. Bruce Piggozi for what I learned from him.

During my years as a student in MSU, I was fortunate to know many people which I am
thankful to, Dr. John Hazard, Dr. Gail Blomquist, Dr. Charles Barr and Dr. Charles Cutts
to name a few.

I also want to thank the Michigan Department of Transportation for the cooperation of the
staff and for funding the project through the Michigan State University’s Transportation
Center of Excellence.

Special thanks are due to the support staff of the Department of Civil and Environmental
Engineering, Linda Phillipich, Laura Taylor, Cheryl Mollitor, Linda Steinman and Mary
Wiseman.

Finally, I wish to express my sincere gratitude to my family and friends, who shall remain

unnamed, for their encouragement, support and making my efforts worthwhile.

iv

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................... vii
LIST OF FIGURES ........................................................................ » ................ x
INTRODUCTION AND OBJECTIVES ........................................................ 1
LITTERATURE REVEW .............................................................................. 2
Modeling of Crashes on Horizontal Curves ....................................... 2
Modeling Efforts ................................................................................. 4
STUDY DESIGN .......................................................................................... 10
The Data ............................................................................................ 13
Variable Modification ....................................................................... 20
Crash Types ...................................................................................... 20
Crash Location Mile Points .............................................................. 21
Special Data Considerations ............................................................. 22
ANALYSIS .................................................................................................. 23
Data Presentation ............................................................................. 23
Data Analysis ................................................................................... 23
Test of Existing Models ................................................................... 52
Discriminant Analysis ...................................................................... 59
Analysis and Results ............................................................. 6O
Cluster Analysis ................................................................................ 65
Analysis and Results ............................................................. 65

Factor Analysis ................................................................................. 71

Analysis and Results ............................................................ 78

Analysis Including Field Data ............................................ . ............. 81
Results .............................................................................................. 93
CONCLUSION AND GUIDELINES ......................................................... 100
REFERENCES ........................................................................................... 1 18

vi

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Table 10

Table 11

LIST OF TABLES

DESCRIPTION

Curve selection criteria

Examples of disqualified roadway
segments

Number of crashes in the database

Geometric data variables coded for
the study and their names

Crash data used in the study

Variables obtained from the photo
log and field observations

Correlations of the linear regression
models

R2 of non linear (Ln) models

R2 of linear and several non linear
models

Results of the multiple linear
regression analysis for curve
crash rate (Cper380)

Results of the discriminant analysis
for curve crash rate
(Cper380)

vii

PAGE

16

17

18

21

22

24

35

54

55

67

7O

Table 12

Table 13

Table 14

Table 15

Table 16

Table 17

Table 18

Table 19

Results of the discriminant analysis
for modified curve crash rate
(Modeer)

Results of the discriminant analysis
for modified curve minus tangent
crash rate (ModC-T)

The numerical values of all variables
in defining the clusters grouped by
the modified curve crash rate

(Modeer)

The numerical values of the important
variables in defining the clusters
grouped by the modified curve crash
rate (Modeer)

The numerical values of the important
variables in defining the clusters
grouped by the curve crash rate
(Cper380)

The numerical values of the important
variables in defining the clusters
grouped by the curve minus tangent
crash rate (CmnsT)

The numerical values of the important
variables in defining the clusters
grouped by the modified curve minus
tangent crash rate (ModC-T)

Factor score coefficient matrix
for all the variables

viii

72

73

76

77

79

8O

81

89

Table 20

Table 21

Table 22

Table 23

Factor score coefficient matrix
of relatively high values

Curves with a high curve crash
rate (Cper380)

Curves with a high curve minus
tangent crash rate (CmnsT)

Curves with a curve crash rate
larger than twice the mean for
their cluster

ix

90

105

108

111

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

LIST OF FIGURES

DESCRIPTION

Actual versus predicted total accidents,
Glennon model, calculated Ars

Actual versus predicted total accidents,
Glennon model, 0.902 Ars

Actual versus predicted total accidents,
Zegeer model

Accident rate versus degree of curvature

Curve crash rate (Cper380), arranged in
ascending order

Tangent crash rate (Tper380), arranged
in ascending order

Tangent crash rate (Tper380), arranged
in ascending order of curve crash rate
(Cper380)

Curve crash rate (Cper380), and tangent

crash rate (Tper380), arranged in ascending
order of Cper380

Curve crash rate minus tangent crash rate
(CmnsT), arranged in ascending order

PAGE

10

14

29

30

31

32

33

Figure 10

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

11

12

13

14

15

16

17

18

19

Curve crash rate minus tangent crash rate
(CmnsT), arranged in ascending order of
curve crash rate (Cper380)

Curve crash rate minus tangent crash rate
(CmnsT), for various values of average
daily traffic (ADT)

Curve crash rate minus tangent crash rate
(CmnsT), for various values of tangent
crash rate (Tper380)

Curve crash. rate minus tangent crash rate
(CmnsT), for various values of curve
length in feet (HCLFT)

Curve crash rate minus tangent crash rate
(CmnsT), for various values of curve
radius in feet (HCRFT)

Curve crash rate minus tangent crash rate
(CmnsT), for various values of roadside
clearance (CLRN CW)

Curve crash rate minus tangent crash rate

(CmnsT), for various values of sight distance

to the beginning of curve (OBSDSTW)

(have crash rate (Cper380), for various
values of average daily traffic (ADT)

Curve crash rate (Cper380), for various
values of tangent crash rate (Tper380)

Curve crash rate (Cper380), for various
values of curve length in feet (HCLFT)

xi

34

36

37

38

39

40

41

42

43

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Curve crash rate (Cper380), for various
values of curve radius in feet (HCRFT)

Curve crash rate (Cper380), for various
values of roadside clearance (CLRNCW)

Curve crash rate (Cper380), for various
values of sight distance to the beginning
of curve (OBSDSTW)

Distribution of selected independent variables 48
(based on correlation with curve crash rate)

Curve crash rate minus tangent crash rate
(CmnsT), for various values of curve

length in feet (HCLFT)

Curve crash rate (Cper380), for various
values of curve length in feet (HCLFT)

Curve crash rate (Cper380), for various
values of speed difference (DIFFSPDL)

Curve crash rate (Cper380), for various
values of design speed difference
(DSGNSPDL)

Comparison of the predicted number of
curve crashes using Glennon’s model
(Glannon), and the actual number of
curve crashes (Cacc)

Comparison of the predicted number of
curve crashes using Zegeer’s model with
spiral (ZegeerS), and the actual number
of curve crashes (Cacc)

xii

45

46

47

52

53

58

59

61

62

Figure 30

Figure 31

Figure 32

Figure 33

Figure 34

Figure 35

Figure 36

Figure 37

Figure 38

Figure 39

Comparison of the predicted number of
curve crashes using Zegeer’s model
without spiral (ZegeerM), compared with
the actual number of curve crashes (Cacc)

Comparison of the predicted number of
curve crashes using Zegeer’s model
without spiral (ZegeerM), and that of the
model with spiral (ZegeerS)

Predicted curve crashes using the Glennon’s
model (Glennon), arranged in ascending
order of predicted curve crashes by
Zegeer’s model without spiral (ZegeerM)

Curve crash rate (Cper380), for various
Values of curve radius in feet, cluster 1

Curve crash rate (Cper380), for various
Values of curve radius in feet, cluster 2

Curve crash rate (Cper380), for various
values of curve radius in feet, cluster 3

Curve crash rate (Cper380), for various
values of curve length in feet, cluster 1

Curve crash rate (Cper380), for various
values of curve length in feet, cluster 2

Curve crash rate, (Cper380), for various
values of curve Length in Feet, cluster 3

Drag factor (DRGFCTR), arranged in
ascending order of curve crash rate
(Cper380)

xiii

63

64

65

82

83

84

85

86

87

93

Figure 40

Figure 41

Figure 42

Figure 43

Figure 44

Figure 45

Figure 46

Figure 47

Figure 48

Superelevation high values (SPRELVN),
arranged in ascending order of curve
crash rate (Cper380)

Superelevation low values, (SELElo),
arranged in ascending order of curve
crash rate (Cper380)

Curve crash rate (Cper380), arranged
in ascending order

Curve Crash Rate minus Tangent Crash
Rate (C-T), arranged in ascending order
of curve crash rate (Cper380)

Curve crash rate (Cper380), for various
values of drag factor (DRGFCTR)

Curve crash rate (Cper380), for various
values of superelevation high values
(SPRELEV)

Curve crash rate (Cper380), for various
values of superelevation low values
(SELELO)

Curve crash rate minus tangent crash
rate (CmnsT), for various values of
drag factor (DRGFCTR)

Curve crash rate minus rangent crash
rate (CmnsT), for various values of
superelevation high values (SPRELEV)

xiv

94

95

96

97

98

99

100

101

102

Figure 49

Figure 50

Figure 51

Figure 52

Curve crash rate minus tangent crash
rate (CmnsT), for various values of
superelevation low values (SELELO)

Curve crash rate (Cper380) for the
three clusters, arranged in ascending
order of Cper380 within each cluster

Curve radius in feet (HCRFT) for
the three clusters, arranged in
ascending order of Cper380 within
each cluster

Curve length in feet (HCLFT) for
the three clusters, arranged in
ascending order of Cper380 within
each cluster

XV

103

110

114

115

INTRODUCTION AND OBJECTIVES
In Michigan over 25 percent of fatal traffic crashes take place on non-freeway
trunkline highways. These highways typically have all the elements associated with
a high number of serious crashes. Lack of a separation buffer from the opposing
traffic, combined with rather high speeds contributes to such crashes.
Research has consistently demonstrated that crash rates on horizontal curves are
many times higher than the rate on the tangent sections on the same road, and most
studies have found the degree of curvature to be the most significant single factor
related to curve crashes. However, other roadway features, such as superelevation
and skid resistance of the pavement surface, traffic control elements, driving
environment and human factors, individually or in combination are major
contributors as well.
Several models, most notably the Glennon Model and the Zegeer Model, have been
developed to explain curve crashes. However, when applied to Michigan data, the
results are not sufficiently reliable for establishing corrective or preventative
programs.
The purpose of this study was to analyze horizontal curve crashes experienced on
two-lane rural trunkline roads in the State of Michigan, and to devise procedures to
identify curved road segment grouping attributes that are associated with the crash
rate on these curves. A second goal was to identify curves that exhibited crash
frequencies significantly higher than the mean for their group, or which potentially
may exhibit such crash frequencies.

The specific objectives were to:

1) Identify the factors influential in horizontal curve crashes based on
Michigan’s crash data.
2) Prepare guidelines as to where and to what extent improvement of

horizontal curves is warranted.

LITERATURE REVIEW
Modeling of Crashes on Horizontal Curves

Prior to 1985, modeling of crash frequencies or rates on horizontal curves was
normally based on a single variable. For example, Jorgenson (l) in 1978 reported a
linear relationship between crashes and the degree of curvature.

In 1985, Glennon et a1. (2) published a report titled "Safety and Operational
Consideration for Design of Rural Highway Curves.” The research was performed
to study the safety and operational characteristics of two-lane, rural highway curves.
A series of independent research methodologies were employed, including; (a)
multivariate crash analyses; (b) simulation of vehicle/driver operations using the
Highway Vehicle Operation Simulation Model (HVOSM); (c) field studies of
vehicle behavior of highway curves; and (d) analytical studies of specific problems
involving highway curve operations.

The results of each of these approaches confirmed that, in general, as curve radius
decreases, crash rate increases. However, radius of curve is not the only geometric
element affecting safety. The crash and field studies showed that the design of
highway curves must consider a series of trade-offs among the basic elements of a

curve: radius, superelevation, and length.

The study also found that either very sharp or very long highway curves tend to
produce more crashes. Larger angles (i.e. , greater than 45 degree) require either
sharp curvature, or a long curve length and should be avoided when possible.

Studies of crashes on highway curves showed single-vehicle run-off-road crashes to
be of paramount concern. Roadside treatment countermeasures were found to offer
the greatest potential for mitigating the frequency and severity of crashes on rural
highway curves. Studies involving a single factor have generally reached the

following conclusions:

a) As shoulder width increases, the probability that a highway curve will be a high

crash location decreases.

b) Roadside character ( roadside slope, clear zone width, and coverage of fixed-
objects) is the most dominant contributor to the probability that a highway curve is a

high-crash location.

c) As pavement skid resistance decreases, the probability that a highway curve will

be a high-crash location increases.

d) Limited sight distance increases the probability that a curve will be a high crash
location. Two special considerations of stopping sight distance are important:

(a) the increased friction demand of a vehicle that is both cornering and braking; and
(b) the loss of the eye height advantage for truck drivers on highway curves when

the horizontal sight restriction is either a row of trees, a wall, or a vertical rock cut.

MODELING EFFORTS
Based on these analyses, Glennon developed and presented the following crash
model in the Transportation Research Board's Special Report 214:
A= ARs (L)(V) + 0.0336 (D)(V) for L> =Lc '
where,

A=Total number of crashes on the roadway segment.

ARs =Crash rate on comparable straight roadway segments in crashes per
million vehicle miles.

L= Length of roadway segment in miles

V=Traffic volume in millions of vehicles

D=Curvature in degrees

Lc = Length of curved component in miles

As noted in Special Report 214, the accuracy of this horizontal curve model "may
be diminished for curves sharper than about 15 degrees, the approximate limit
recorded in the data base from which the model was calibrated.” This model does
not include the following factors and curve design parameters: curve length,
superelevation and superelevation run-off, spiral transitions, cross-slope break,
roadside, geometric design consistency.

In 1986, Zegeer et al. (3) reported the results of their study "Safety Effects of
Cross-section Design for Two-lane Roads, Volume I.” In this study, they quantified
the effects of lane width, shoulder width, and shoulder type on highway crash
experience on extended sections of roadways based on an analysis of data for nearly
5,000 miles of two-lane highway from seven states. The following crash prediction
model resulted from that study:

AO/M/Y = 0.0019 (ADT) 03324 (0.8786) W (0.9192) PA (0.9316) UP

(1.2356) H (0.8822) TERI (1.3221) TERZ
where:
AO/M/Y = related crashes (i.e. , single-vehicle plus head-on plus opposite
direction sideswipe plus same direction sideswipe crashes) per mile per year.
ADT= average daily traffic
W= lane width in feet.
PA = average paved shoulder width in feet.
UP= average unpaved shoulder width in feet.
H= roadside hazard rating, a subjective measure with values of 1 to 7
(least to most hazardous), based on a visual assessment.

TER1= 1 if terrain is flat, otherwise 0.

TER2= 1 if terrain is mountainous, otherwise 0.
This model is applicable only to:

- two-lane, two-way paved rural highways of state primary and secondary

systems.

- lane widths of 8 to 12 feet.

- shoulder widths of 0 to 10 feet.

- ADT's less than 10,000 vpd.

- homogenous roadway sections.
The model does not include intersection related crashes or those crash types that are
not expressly stated on the previous page. The model did not explain the variance in
crash experience on horizontal curves. This model does not include the effects of
horizontal or vertical alignment or the frequency of horizontal curves, or the

frequency of sight-restricted crest vertical curves.

In 1991 Zegeer et a1. (5) formulated the following model for predicting crashes on
horizontal curves:
A=[l.552(L)(V) +0.014(D)(V)- 0.012 (S)(V)](0.978)(W'3°)
where:

A=number of total crashes on the curve in a 5-year period.

L=length of curve in miles (or fraction of a mile)

V=volume of vehicles in million vehicles in a 5-year period passing through
the curve (both directions)

D=degree of curve

S=presence of spiral, S=O if no transition spiral exists and S=l if there is a

transition spiral. '

W=width of the roadway on the curve in feet.
The purpose of this study was to determine the horizontal curve features which
affect safety and operations and to quantify the effects on crashes of various curve—
related improvements. The primary data base developed and analyzed consisted of
10,900 horizontal curves in Washington State. Three existing federal data bases on
curves were also analyzed. These data bases included the cross-section data base of
nearly 5,000 miles of roadway from seven states, a surrogate data base of vehicle
operations on 78 curves in New York, and 3,277 curve roadway segments from four

other states.

Based on statistical analyses and model development, variables found to have a
significant effect on crashes include degree of curve, roadway width, curve length,

ADT, presence of a spiral, superelevation, and roadside condition.

In a comprehensive review of design features related to highway safety, McGee et
al. (6) concluded that the Zegeer and Glennon models were the best models
available for predicting crashes on horizontal curves. The authors of this report

concluded that:

"The Zegeer model relating crashes to horizontal alignment appears to
represent the best available relationship to estimate the number of crashes on
individual horizontal curves on two-lane rural roads, although it does have
limitations. While the model explicitly considers curve length, degree of
curvature, roadway width, and presence of a spiral transition, it does not
explicitly consider roadside parameters or the effect of upstream or
downstream alignment. The fact that it does not consider roadside or even
some surrogate rating for roadside is a major limitation, especially since
crash research has shown that roadside design is a determinant of horizontal
curve safety.

The model does not consider the effect of vertical alignment or the
consistency with respect to the design of all curves within the highway
section (e. g., geometric design consistency). The model also does not
consider the frequency of horizontal curves greater than three degrees within
the section, the frequency of sight-restricted vertical crest curves, or the
percent grade. The average operating speeds or design speeds are also not
considered explicitly. The model does not consider the influence of access
points, driveways or intersections that may be in close proximity to the
subject curve. "

In 1992, Kach and Benac (7) tested both the Zegeer and Glennon models with
Michigan Trunkline data, and found a poor fit between the predicted and actual
crash frequency, as shown in Figures 1 through 3.

After reviewing the models developed by Glennon and Zegeer, the authors

identified the following weaknesses of these models:

1. The model predicts total crashes instead of "curve related" crash types:
fixed object, overturn, head-on and side swipe opposite direction crashes.

2. The models do not recognize an "influence zone" for curves.

3. The models do not adequately address the variability in crash experience
for all the curves with a given length and degree of curvature.

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In 1995, Fink and Krammes (8) reported on a study of the effect of the length of the
tangent preceding a horizontal curve and the approach sight distance on crashes at
horizontal curves. To add insight on the effects of these variables on safety and
operations at horizontal curves, a base relationship between crash rates at horizontal
curves and degree of curvature was established, and the effects of approach tangent
length and approach sight distance on this relationship were examined.

The results confirm that degree of curvature is a good predictor of crash rates on
horizontal curves. Although the effects of approach tangent length and sight
distance were not as clear, the results suggest that the adverse-safety effects of long
approach tangent length and short approach sight distance become more pronounced
on sharp curves.

Four other studies considered tangent length among a set of candidate predictors of
crash rates at horizontal curves (IO-13). Their findings with respect to tangent
length were mixed. Datta et a1. (10) found tangent length to be a significant
predictor of outside-lane crash rates for one subset of 25 curve sites in Michigan.
Terhune and Parker (1 1) evaluated tangent length (among other variables) using data
bases of 78 curves in New York, 40 curves in Ohio, and 41 curves in Alabama, and
concluded that tangent length was not significant. Matthews and Barnes (12) studied
4,666 curves on the rural two-lane

portion of State highways in New Zealand. They found a significant relationship that
involved tangent length in combination with other variables and concluded that crash
risk was particularly high on short radius curves at the end of long tangents, on
steep down grades, and on relatively straight sections of roads.

Zegeer et al. (13) evaluated the significance of the minimum and maximum distance

to the adjacent curve; although neither variable was significant, they observed,

11

"there appears to be evidence that tangents above a certain length may result in some
increase in crashes on the curve ahead.”

Glennon et al. (14) concluded that approach sight distance was not a significant
variable in a discriminate analysis of curve sites with high and low crash rates.
Fambro et al. (15) concluded that available stopping sight distance is not a good
indicator of crashes, with the exception that " when there are intersections within
limited sight distance portions of crest vertical curves, there is a marked increase in
crashes. "

The report by Pink and Krammes (8) presented two models:

1) A regression model for predicting mean crashes per million vehicle kilometers

versus mean degree of curvature:
mean crash rate = 0.05 + 0.23 mean degree of curvature

The model has an r2 value of 0.94. The r2 is much higher than typically observed
in crash analyses, because the unit of observation is a grouping of curve sites into
nine degree-of—curvature categories which eliminates much of the variability among

individual sites.

2) A regression model for predicting the crash rate based on the approach tangent
length. Three categories of curves were defined representing those with the shortest
25 percent (< =107 m [350 ft]), middle 50 percent (107 m[350 ft] to 427 m [(1400
ft]), and longest 25 percent (>427 m [1400 ft]) of tangent lengths in the database.
The regression models were as follows:

mean crash rate = 0.35 + 0.16 mean degree of curvature for the shortest 25%

mean crash rate = —O.30 +0.32 mean degree of curvature for the middle 50%

12

mean crash rate = 0.52 + 0.20 mean degree of curvature for the longest 25 %

The results indicate that the slope and intercept for the middle 50 percent of tangent
lengths are significantly different from the slope and intercept for the shortest and
the longest 25 percent. (See Figure 4)

These models, like those of Zegeer and Glennon, fail to explain the variation in
crash rate experienced at different curves with the same degree of curvature or the
same approach tangent length. ‘

While the models found in the literature may have some value when the design
engineer is developing the alignment for a new road, none are suitable for
identifying hazardous curves on an existing road system.

They also provide no assistance in determining countermeasures once a location is

identified as being hazardous.

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STUDY DESIGN
Data Preparation
To accomplish the objectives of this. study, a multi-step approach was utilized. Step
one was. to acquire geometric data for all the rural, twd-way, two-lane trunkline
highways in Michigan from the Michigan Department of Transportation (MDOT).
Based on the selection criteria listed in Table 1, the candidate curves were selected
and the control section (reference system used by MDOT for trunklines) and the

mile points of the beginning and ending of the curves were noted.

15

Table 1 Curve Selection Criteria

 

Rural two-lane, two-way trunkline highways

No taper, no extra lanes

No curb, no parking

No median, and preferably no intersections

At least 306 meters (0.19 mile, about 1000 feet) of tangent at each end of
each curve

Preferably at least 611 meters (0.38 mile) of tangent between the two curves

Degree of curvature greater than one

 

 

 

The geometric selection criteria yielded a total of 285 roadway segments, each
consisting of a curve and two tangents. Based on the photo log observations, 50 of
the segments did not fit the specified criteria and were eliminated from the study.
Fifteen more were eliminated based on the field observation. Examples of such cases

are listed in Table 2. The final data set consisted of 220 valid roadway segments.

16

Table 2 Examples of the Disqualified Roadway Segments

(based on the photo log or field observations)

 

Control Listed Listed Length Actual Comments
Section BMP* EMP* km Length
km

 

23111 3670 3710 0.06 0.21 Intersection Corner

 

32092 60 190 0.21 - Intersection widening (M52/M36)

 

38073 9810 9920 0.18 0.26 Curve not found

 

38073 14350 14500 0.24 - Curve not found

 

46011 5770 5900 0.21 0.10 Three Lanes (intersection with

 

 

left turn lane)

46012 i 110 300 0.31 - Three Lanes (intersection with
left turn lane)

46051 380 490 0.18 0.27 Not found. Two curves near

listed location

 

46074 20 130 0.14 0.18 Intersection (with median and

 

 

 

 

 

 

 

right turn lanes)

 

* (coded in 0.001 mile with implied decimal point)

The next step consisted of obtaining additional data from the photo log. In addition
to data acquisition, data verification was also performed and locations which, based
on this review, did not meet the selection criteria were removed from the database.

While this step was in progress, field data collection was performed to obtain the
curve superelevation and pavement friction. Field data collection resulted in the

elimination of some additional curves where it was determined that the lane width or

17

shoulder width were modified on the curve or there was an intersection within the
study limits. After this step 220 curves were left for the final analysis. For each of
the 220 curves, all the crashes corresponding to the mile points from 306 meters
(0.19 mile) before the start of the curve to 306 meters (019 mile) after the end of
the curve were extracted from the MDOT crash files. This procedure was performed
for each year of the six year period of 1989 to 1994, yielding 3107 total crashes
(Table 3).

Table 3 Number of crashes in the database

 

 

 

 

 

 

 

 

 

 

 

 

Total Related

Crashes Crashes
1994 519 207
1993 491 166
1992 503 176
1991 532 164
1990 503 145
1989 559 136
Total 3,107 994

 

Of the 3107 total crashes, 991 were in curves and 2116 in the tangents. The total
number of “related” crashes was 994 of which 463 were in the curves and 531 in

the tangents.

l8

Thirteen of the 220 roadway segments did not have any crashes in the curve or the
two tangent sections. For the “Related” crashes 178 roadway segments had crashes
in either the curve or the tangent sections.

The crash report forms for all these crashes were obtained and processed to locate
the individual crash as being on the curve or on the tangent. After this step, various
analyses were performed, including comparison of the actual curve crashes and

those predicted by the models.

The Data

Data for the project consists of the four following sets:

1) Geometric data provided by the MDOT

2) Six years of crash data for the years 1989 through 1994
3) Data obtained from the photo log for all 220 segments

4) Field data for 81 segments.

The geometric data consisted of 44 variables such as control section, beginning
mile point, ending mile point, average lane width, total shoulder width (right and
left), etc. The variables selected from this file for use in this study are shown in

Table 4.

The crash data are from the Michigan State Police “State of Michigan Master Crash
File.” This file contains information on up to three vehicles involved in a crash, but
the data for the second and third vehicles were not used in the study. The original
source of the data is the “State of Michigan Traffic Crash Report” (Form UD-lO).
The data consisted of 120 variables such as district, control section, mile point of

crash, highway area type, highway area code, etc. The data were for the crashes for

19

both traffic directions combined. The variables selected from this file for use in this

study are shown in Table 5.

The photo log data were used for variables such as the presence of traffic signs
(arrow, chevron, etc.) and other variables such as approach distance at which the
curve was first observed, etc. The data also included a subjective measure of the
roadside clearance or hazard, on a scale of one to seven. One being “Clear” (least
hazardous) and seven being “Not Clear” (most hazardous). The data acquisition for

this variable was performed twice, once for each direction of the traffic flow.

20

Table 4 Geometric Data Variables Coded for the Study

 

 

VARIABLE DESCRIPTION VARIABLE NAME
District DNO
Control Section CS
Beginning Mile Point of Study Segment BMP
Ending Mile Point of Study Segment EMP
Average Lane Width ALW
Total Shoulder Width (Right) TSWR
Paved Shoulder Width (Right) PSWR
Total Shoulder Width (Left) TSWL
Paved Shoulder Width (Left) PSWL
No Passing Zone Code NPZC
Posted Speed Limit PSL
Degree of Curvature, Number of Degrees and Minutes HCD, HCM
Degree of Curvature, Number of Minutes HCM
Roadway segment File Record Number SFRN
Intersection File Record Number IFRN
Average Daily Traffic (Divided by 10) ADT

Using BMP, EMP, HCD and HCM, four more

variables were calculated as follows:

Degree of Curvature in decimal degrees HCDD
Oirve Length in feet HCLFT
Curve Radius in feet HCRFT
Central Angle in decimal degrees CANG

 

21

 

 

 

Table 5 Crash data used in the Study
District Driver 1 Violation
Control Section Contrib. Circumst. , Vehicle 1
Crash Mile Point Visual Obstruction, Vehicle 1
Highway Area Type Direction of Travel, Vehicle 1
Highway Area Code Alcohol/Drug use, Vehicle 1

Hour of Occurrence
Route Class

Weather Condition
Lighting

Road Surface Condition
“A” Injuries

“B” Injuries

“C” Injuries

Road Alignment

Traffic Control

Crash Type

Distance From Crossroads
Direction From Crossroads

Intersecting Street name

 

Object Hit, Vehicle 1
Situation, Vehicle 1
Vehicle Size, Vehicle 1
Impact Code, Vehicle 1
Vehicle Condition, Vehicle 1
Trailer, Vehicle 1

Road Type, Vehicle 1
Number of Lanes

Average Daily Traffic
Number of Persons Killed
Number of Persons Injured
Number of Occupants
Crash Location

Crash Route Number

 

 

Table 5 (Continued)

 

Driver 1 Intent Original Prime Street Name
Number of persons injured Operator Number, Vehicle 1
Vehicle 1 Type Year of Crash

Vehicle 1 Make Film Reel Number

Age of Driver 1 Film Frame Number
Residence of Driver 1 PR Number

Sex of Driver 1 PR Mile Point

Degree of injury to Driver 1

 

 

 

 

The field data collection was performed to obtain only two variables, a measure of
the superelevation of the road, and a measure of the skid resistance of the pavement
surface. The superelevation was obtained by use of an ordinary 48 inch level. The
difficulty with superelevation is the fact that unlike some other variables, an average
value will not substitute for the lowest value and the highest value. If there is an
optimal value, any deviation from it, positive or negative, could result in decreased
safety. However, since there was no procedure available to record continuous values
of superelevation, representative locations on the curve were selected and the
average value for each lane was coded. Occasionally the superelevations were in the
opposite direction, i.e., banking towards the outside of the curve. In these cases the
superelevation is coded with a negative sign.

The friction factor was obtained and calculated by dragging a piece of tire filled
with concrete to weigh 22.7 kilograms (50 lbs) (16). The horizontal force required
to pull it over the pavement (divided by its weight), would have been the friction

factor, had the tire been smooth. However, the reading corresponded to a value

23

higher than the actual friction factor because the treads of the tire and the gravel
particles on the road would “engage” and to some extent act like teeth gears.
Occasionally the required horizontal force exceeded 22.7 kilograms, yielding
friction factors higher than one. Since this variable was for comparison across the
curves and not for the absolute values, the resulting values were used for the study.
However, to avoid confusion it was referred to as the drag factor rather than the
friction factor. The variables obtained from the photo log and field observations are

listed in table 6.

Table 6 Variables obtained from the photo log

and field observations

 

 

VARIABLE DESCRIPTION VARIABLE NAME
Curve Sign CURVES
T urn Sign TURNS
Advisory Speed Sign MPHS
Guard Rail GRAIL
Chevron CHEVRON
Arrow Sign ARROW
Delineator DLNTR
Edge Line EDGLN
Mile point when Curve Observed OBSDSTW
. Roadside Clearance/hazard CLRNCW
Superelevation SPRELVN
Drag Factor DRGFCTR

 

24

 

Variable Modification

Since the crash data were for both directions, variables with two values, one for
each traffic direction, were reduced to a single value. This included all the photo log
data, some geometric data and the two field data variables. '

For the following variables, if for either direction of traffic the variable had a value
of YES, the variable was coded as 1. If neither direction had a value of YES, it was
coded as 0 (zero). Variables in this category were: Curve Sign, Turn Sign, Guard
Rail, Chevron, Arrow Sign and Delineator.

The variable “Mile Point Where Curve Observed” , was converted to the approach
sight distance to the curve. A value was obtained for each direction of travel, and
the lower of the two was used. Similarly for the variable “Roadside Clearance” ,
there were two values corresponding to the two traffic directions and the higher of
the two values was used.

Since the designation of right and left are associated with the direction of increasing
mile point, and not the direction of the vehicle involved in the crash, the variables
Total Shoulder Width Right and Left were combined into one value equal to the sum
of the two. Similarly the Paved Shoulder Width Right and Left was replaced by the
sum of the two values. The Shoulder or Olrb Type Right and Shoulder or Curb
Type Left, each with a value of 1 or 2 were collapsed into one value. If both values
were the same that value was used. If one value was 1 and the other 2, a value of 2
was used.

The drag factor and superelevation also had two values, one for each side of the
road. For the drag factor the lower of the two was used. For the superelevation, the
lower of the two was used for one analysis, and then the analysis was repeated using

the higher value.

25

Crash Types

For the analyses used in this project, several types of crashes were eliminated from
the crash data. Only the “Curve Related” crashes consisting of the following types
of crashes were used: Miscellaneous 1 Vehicle, Overturn, Fixed Object, Other

Object, Head-on and Side-Swipe Opposite.

Selection of the “Related” crashes yielded 994 crashes corresponding to the 178
roadway segments which had “Related” crashes. Not all selected roadway segments
had crashes in both the tangent and curve portion of the roadway segment. Table 3
listed both the number of total crashes and related crashes for each of the years

included in the study.

Crash Location Mile Points

The location of each crash along its control section is indicated by a mile point.
Based on the mile point of the crash location compared with the mile points of the
two ends of a curve, one could presumably determine if the crash was on the curve
or tangent. However, the location of a crash as recorded by the investigating police
officer is not accurate. A plot of crashes showed that the crashes tend to accumulate
at tenths or quarters of a mile from the nearest intersection. This level of accuracy
was not adequate for this study.

To remedy this problem the UD-lOs for all crashes were manually checked. If the
police sketch showed the crash occured on a curve, it was assigned to the curve,
even if based on the mile point it would fall on the tangent. The UD-10 forms also
provide a check box for the road alignment and if the box for curve was checked,
the crash was assigned to the curve. The reason being that it was unlikely that an

investigator would draw a tangent section of a road showing curve, however they

26

may draw the curve section as a tangent but check the curve box and use the code
for curve. If the sketch depicted a tangent section and the curve check box was not

marked, the crash was assigned to the tangent section of the study segment.

Special Data Considerations

Even though typically each roadway segment consists of two tangents of 306 meters
each, and the curve itself, there were exceptions. In 14 cases the control section
number changed within the 306 meters of tangent section of the roadway segment.
In these cases the 306 meters of tangents existed for both ends of the curve,
however, the mileage of tangents within the same control section was less than 306
meters. Pro-rated values were used to determine the tangent crashes for 612 meters
for these cases. There were no cases of different control section numbers within a

curve .

In another 8 cases even though there were 306 meters of tangents at (each end of the
curves, the distance between the end of one curve and start of another was less than
612 meters. In other words there was an overlap between the two tangents. In two
cases there were crashes in the overlap section of the two tangents, and one of these
cases contained “Related” crashes. The crashes corresponding to this overlapping
section of tangents, (3 crashes), were included in the data for each of the two study

segments involved.

27

ANALYSIS
Data Presentation
The crash data described in the preceding pages is presented in graphical form in
Figures 5 through 10.
Figure 5 shows the number of crashes per 380 feet of curve, (Cper380) for the 178
roadway segments which had “related” crashes in their tangent sections or their
curved section. The Cper380 values are sorted in ascending order including the
roadway segments which did not have any crashes in their curved section.
Figure 6 shows the number of crashes per 380 feet of tangent, (Tper380) for the
same 178 roadway segments, some with no crashes in their tangent sections.
Similarly, the Tper380 values are sorted in ascending order.
Figure 7 shows the Tper380 values when sorted by ascending values of Cper380.
Figure 8 is the superimposed graph of Figure 5 and Figure 7.
Figure 9 shows the values of Cper3 80-Tper3 80, referred to as (CmnsT), when
sorted in ascending order. Figure 10 shows the same values sorted by ascending
values of Cper380.
From Figures 7, 8 and 10 it is clear that the crash rate on the tangent section
approaching the curve is not sufficient to predict the curve crash rate. This is
evidenced by the fact that the values of Tper380 and CmnsT do not display a

consistent pattern when compared with the sorted values of Cper380.

Data Analysis

As a first step in the analysis, two sets of simple regressions, one for the curve crash
rates (Cper380), and the other for the difference between the curve crash rates and
tangent crash rates CmnsT, versus each of the independent variables. The results of

these analyses for ADT, Tper380, HCLFT, HCRFT, CLRNCW and OBSDSTW are

28

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shown in Figures 11 through 22. The scatter plots, the regression lines, and the
coefficients of regression all indicate that simple regression models are poor
predictors of either the crash rate on curves or the difference in the crash rate

between tangent sections and curved sections on the same Segment of the road.

 

 

Table 7 Correlations of the linear regression models
Cper380 vs. Corr. Cper380 vs. Corr. CnmsT vs. Corr. CmnsT vs. Corr.
EDT . .216 HCLFT -.377 ADT .062 HCLFT -.366
ALW -.077 HCRFT -.408 ALW -.074 HCRFT -.427
ARROW .063 MPHS .326 ARROW .087 MPHS .302
CHEVRON .280 NPZC . 187 CHEVRON .268 NPZC . 195
CLRNCW .049 OBSDSTW -. 130 CLRNCW .018 OBSDSTW -. 100
CTSIGN . 175 PSL -.073 CTSIGN . 163 PSL -.030
DLNTR .025 PSW -.091 DLNTR .060 PSW -. 108
EDGLN .057 SCT .060 EDGLN .047 SCT .012
GRAIL .068 TSW .05 1 GRAIL .040 TSW .019

 

 

 

 

 

 

 

 

 

(Table 23 shows the distribution of several of variables used in the study).

 

For the variable HCLFI' (curve length), it appeared that there might be a nonlinear
relationship. However the quadratic and cubic regression lines showed little

improvement over the linear model, as shown in Figures 24 and 25.

The scatter plots indicate that there is no linear relationship between the curve crash
rate and these variables that can be used to establish reliable crash reduction
policies. Several nonlinear regression models were then constructed with the

resulting R2 shown in Tables 8 and 9.

35

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(based on correlation with curve crash rate)

48

20

 

 

 

100’ 500’ 900’ 1300’ 1700’ 2100' 2500’ 2900'

HCLFT Std. Dev. = 545 Mean = 769

40 A. _ . .— - .- W- - M A 7. 7 ,7...7. 7.. -..- .,i._ - . 7

 

 

200' 600' 1000’ 1400’ 1800' 2200’ 2600’ 3000’

HCRFT Std. Dev. = 824 Mean = 1804

Figure 23 (continued)

49

 

 

 

 

 

 

 

 

CLRNCW Std. Dev. = 2.0 Mean = 3.9

 

0' 20’ 40’ 60’ 80' 100’ 120’ 140’

OBSDSTW Std. Dev. = 29 Mean = 41

Figure 23 (continued)

50

 

10' ll' 12’

ALW Std. Dev.=.75 Mean: 11

Figure 23 (continued)

51

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53

Table 8 R2 of non linear (Ln) models

143 cases with non-zerc values for Cper380 (4 varia ales)
Depend. Var. Independ. Var. qu. ‘
LnCper380 1 LnHCRl—‘l’.
LnHCLFT
& ADT

 

  
  
     

0.614

 

143 cases with non-zerc values for Cper380 (20 vari ables)
Depend. Var. Independ. Var. qu.
LnCper380 1 HCLFT 0.385
2 ADT 0.495
3 HCRFT 0.546
4 Tper380 0.566

  

 

92 cases with non-zero values for Cper380 and other 9 variables
Depend. Var. Independ. Var. qu.
LnCper380 1 HCLFT 0.381
2 HCRFT 0.463
3 ADT 0.542
4 Tper380 0.566

92 cases with non-zero values for Cper380 and other 9 variables
Depend. Var. Independ. Var. qu.
LnCper380 1 HCLFT 0.381
2 HCRFT 0.463
3 ADT 0.542
4 LnTper380 0.564
Depend. Var. Independ. Var. qu.
LnCper380 1 LnHCLFT 0.486
2 LnTper380 0.549
3 LnHCRFl' 0.597
4 LnADT 0.618

92 cases with non-zero values for Cper380 and other 9 variables
Depend. Var. Independ. Var. qu.

 

 

Cper380 1 LnHCLFT 0.390
2 Tper380 0.452
3 LnHCRFT 0.493
92 cases with non-zero values for Cper380 and other 9 variables
Depend. Var. Independ. Var. qu.
Cper380 1 LnHCLFl' 0.390
2 LnTper380 0.455
3 LnHCFlFT 0.497

 

 
 
  

    

   
   
     

 

 

54

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 9 R2 of linear and several non linear models
Independent Variable: Cper380
Dep. Var. Mth qu. Dep. Var. Mth Mth qu.
ADT LIN 0.100 ALW LIN LIN 0.381
ADT LOG 0.095 ALW LOG LOG 0.377
ADT INV 0.060 ALW INV INV 0.259
ADT OUA 0.102 ALW OUA OUA 0.387
ADT CUB 0.105 ALW CUB CUB 0.387
ADT COM 0.097 ALW COM COM 0.486
ADT POW 0.092 ALW POW POW 0.420
ADT S 0.058 ALW S S 0.243
ADT GRO 0.097 ALW GRO GRO 0.486
ADT EXP 0.097 ALW EXP EXP 0.486
ADT LGS 0.097 ALW LGS LGS 0.486
HCRFT LIN 0.293 OBSDSTW LIN LIN 0.010
HCRFT LOG 0.252 OBSDSTW LOG LOG 0.012
HCRFT INV 0.139 OBSDSTW INV INV 0.011
HCRFT OUA 0.294 OBSDSTW OUA QUA 0.010
HCRFT CUB 0.295 OBSDSTW CUB CUB 0.022
HCRFT COM 0.297 OBSDSTW COM COM 0.009
HCRFT POW 0.241 OBSDSTW POW POW 0.011
HCRFT 8 0.122 OBSDSTW S 8 0.010
HCFIH’ GRO 0.297 OBSDSTW GRO GRO 0.009
HCRFT EXP 0.297 OBSDSTW EXP EXP 0.009
HCRFT LGS 0.297 OBSDSTW LGS LGS 0.009
PSW LIN 0.001 Tper380 LIN LIN 0.001
PSW LOG 0.000 Tper380 LOG LOG 0.000
PSW INV 0.003 Tper380 INV INV 0.002
PSW OUA 0.017 Tper380 OUA OUA 0.008
PSW CUB 0.022 Tper380 CUB CUB 0.014
PSW COM 0.001 Tper380 COM COM 0.000
PSW POW 0.000 Tper380 POW POW 0.000
PSW 8 0.003 Tper380 S 8 0.003
PSW GRO 0.001 Tper380 GRO GRO 0.000
PSW EXP 0.001 Tper380 EXP EXP 0.000
PSW LGS 0.001 Tper380 LGS LGS 0.000

 

 

 

 

 

 

 

 

 

 

 

55

 

For the categorical variables such as the No Passing Zone Code (NPZC) with
values of 0 (zero), 1, 2 or 3, or CLRNCW, with values equal to integers 1 to 7, a
separate set of regression analyses were performed. These analyses consisted of
replacing, for example, the variable CLRNCW with 7 dichotomous variables, each
corresponding to the value of one category of the CLRN CW variable.

For instance the dichotomous variable related to the CLRNCW equal to 5 , were
given a value of 1 when the value of CLRNCW was 5, and a value of 0 (zero),
when CLRNCW was 1, 2, 3, 4, 6 or 7.

None of the categorical variables displayed significant correlation with Cper380 or

CmnsT.

In addition to analyzing all related crashes, crashes occurring under different road
surface conditions, weather conditions and lighting conditions were also analyzed.

A sub-set of curves consisting of only those with the field data, (superelevation and
drag factor), was analyzed separately. None of these stratification resulted in a

significant improvement in the prediction capability of the regression models.

Based on the field measurements of superelevation a new variable was defined and

computed . This variable called the design speed, was defined as the speed at which
the lateral friction force between the tire and the road surface would equal a value of
0.19 times the normal force of the tire on the road surface. The speed was calculated

2 / 15(e+f) where R is the curve radius in feet, V is the

from the equation: R=V
design speed in MPH, e is the superelevation and f is assigned a value of 0.19. For

each curve two design speeds were computed, the design speed based on the lower

56

value of the superelevation of the two sides of the road was named “DsgnSde” and
the one for the higher value was named “DsgnSde. ”

The difference between this design speed and the posted advisory speed was
calculated and named “DiffSde” and “Difi‘Sde” corresponding to the lower and
higher values of the superelevation as described above. Where an advisory speed
was not posted, 55 MPH was used as the posted speed limit.

Figures 26 and 27 show regression plots for Cper380 versus DsgnSde and
DiffSde.

57

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59

Test of Existing Models

The next step in the analysis was a comparison of the curve crash rate observed in
the field versus the values predicted by the Glennon and Zegeer models identified in
the literature review. In the Glennon model, the T per380 was used as a surrogate for
Ars, the crash rate on comparable straight roadway segments.

For the Zegeer model the predicted values were obtained for both the with spiral,

ZegeerS, and without spiral, ZegeerM, assumptions.

The plots of the predicted values of curve crashes versus actual values of curve
crashes, (Cacc), are shown in Figures 28-32. This analysis considered only
“related” curve crashes with the model adjusted for the length of the individual
curves, not for the 612 meters. While both the Zegeer model and the Glennon model
appear to show the correct trend, neither model explains the variation in “related”
crash rates observed in the Michigan data. Thus it does not appear that these models
are beneficial in identifying curves that should be reviewed for possible safety

improvements.

60

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65

MULTIVARIATE ANALYSIS

Having determined that the variation in crash frequency found on Michigan curves
can not be satisfactorily explained by models based on ”simple linear or non-linear
regression, various multivariate analysis techniques were performed.

Multivariate analysis almost always requires finding minimum or maximum value
of a compound of some variables (usually a linear compound).

Factor analysis, for example, maximizes the variance of a linear compound of
observed scores of sets of variables, while multiple regression deals with finding a
linear compound of some variables such that this compound has the maximum
correlation with a particular variable.

In some cases the maximum or minimum value needs to be found using additional
constraints. An example would be finding a linear compound from one set of
variables and another linear compound from another set of variables, such that the

correlation between the two linear compounds is maximized.

Multiple Regression Analysis and Results

Many different multiple regression models were analyzed but with unsatisfactory
results. Table 10 shows the results of one such model obtained by using stepwise
regression analysis where each of the variables identified in the preceding discussion
was available to be entered in the equation. In this model, the combination of
variables HCRFT, Tper380, HCLFT and MPHS best explain the “related” curve

crashes. These linear multiple regression models obtained by stepwise regression

66

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67

(forward and backward) produced low coefficients of regression, which is consistent

with previous research results.

Discriminant Analysis

Discriminant analysis is a multivariate technique used to distinguish between two or
more groups of cases and for studying the overlap between groups, or divergence of
one group from the others. Statistically, the objective is to define discriminating
functions by weighting and linearly combining the variables such that the groups
become associated with variables as distinctly as possible.

The variables with a high contribution toward explaining membership in each
group, generally not all the original variables, are considered the predictor variables
or the discriminating variables. It is then possible to predict group membership by
their association with these discriminating variables.

The discriminant functions can be thought of as the axis of a geometric space in
which each group centroid is a point. The weighting coefficients then can be
interpreted as the contribution of a variable along the respective dimension of such

space.

The only difference between discriminant analysis and multiple correlationanalysis is
that in multiple correlation analysis a continuous criterion variable isgiven, whereas
in discriminant analysis the criterion is diehotomic if we have two subgroups. In
fact, we might distinguish between the two subgroups by introducing a dummy
variable that has, say, a value of one for the first subgroup, and of zero for the
second. Discriminant analysis can then be reduced to multiple correlation analysis
by using this dummy variable as the criterion variable, and by calculating
correlations between the observed variables and the dummy (l7).

Discriminant analysis was used to determine the variables which distinguish between

high and low crash rate curves. The analysis was conducted with the definition of

68

high and low crash rates based on Cper380 and then again with some of the curves

removed from the sample as explained in the next section.

Analysis and Results

All of the variables included in the database were used to conduct the first
discriminant analysis. For this study, the analysis was used to define membership in
one of two groups, either a high crash group or a low crash group.

A value of Cper380 equals 5 resulted in approximately half of the curves belonging
to the high crash group and the other half belonging to the low crash group. Thus,
this value of Cper380 was selected as the defming value between high and low crash
rates.

The results of this analysis are shown in Table 11. The curve length and the curve
radius were the two most important discriminating variables followed by ADT.
Using only these three variables 71.9% of all cases were correctly classified. There
were 26 curves that had a Cper380 value of greater than 5, that were classified in
the low category and 24 curves that were misclassified in the other direction.

Similar results were obtained when multiple correlation analysis and a dummy
variable was used, as described above. The dummy variable was given a value of

one where Cper380 was 5 or greater and zero where it was less than 5.

Since our primary interest is determining whether it is possible to distinguish
between high crash locations and low crash locations (rather than some intermediate
group), the data set was reduced to eliminate the curves with a value of Cper380

approximately equal to five. A new variable called Modified Cper380 (Modeer)

69

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was defined. This variable is the same as Cper380 but 15 curves with a Cper380
value near the average for all curves were excluded frOm the analysis.

Table 12 shows the results of the analysis using the modified Cper380 as the
grouping variable. Group 2 was defined as curves with Modeer > 7 and group 1
was defined as curves with Modeer < 5.

The independent variables curve sign and turn sign were replaced by a single
variable called CTsign since these signs perform the same function and are mutually
exclusive. If either sign were present, CTsign was assigned the value of 1 otherwise
0 (zero).

The curve length, the presence of a turn or curve warning sign, the radius of the
curve and Tper380 are the discriminating variables identified in this analysis. Using
these variables 79.1% of the curves were correctly classified. As expected,
removing the cases near the average improved the predictive capability of the model.
With this modification, only 16 curves were misplaced as low and 18 curves were
misplaced as high.

For the next analysis the difference between the curve crash rate ‘(Cper380) and the
tangent crash rate (T per380) is used as a grouping measure. This variable, (CmnsT),
was also modified to more clearly distinguish the curves with high crash rates
relative to their tangent crash rates. The cases with a curve crash rate nearly equal
to the tangent crashes were eliminated. A total of 43 curves with CmnsT=-1.36 to
CmnsT= 1.90 were eliminated from the analysis.

As shown in Table 13, the variables curve radius, curve length and the presence of a
warning sign are the three most important discriminating variables. For this
analysis, 75.6% of the curves were correctly classified using these three variables.

Using this model, 90.7% of the high crash rate curves were correctly identified,

with only 10 curves being misclassified in this direction. The problem with this

71

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73

model is that too many low crash rate curves, (23) were placed in the high crash
category.

Despite this problem, Discriminant analysis produced satisfactory results and
provided the information useful in meeting the objectives of this study. Specifically
the results can be used to identify those characteristics of low crash rate curves
which distinguish them from high crash rate curves. However, having reached the
above results and conclusions does not mean other mathematical models need not to

be tried.

We see that the researcher has to make decision in two stages, so to speak. The first
decision stage is to choose a model, i.e., to specify the mathematical assumptions
that he takes to be valid. The second stage is to determine whether the data are
consistent with a solution of the model.

But if a solution can be accepted, it does not follow that other models would not
lead to equally good solutions. .................. researchers sometimes tend to reject
one model because another is found to work (17).

The choice of mathematical model for the remaining part of this study, arbitrarily
and due to practical considerations was set to be limited to the standard statistical
procedures among which Factor analysis and Cluster analysis were considered for

experimentation.

Cluster Analysis

Cluster Analysis is a systematic technique to look for regularities in a data set. Once
the regularities are depicted, this procedure groups the data based on these
regularities and their interpretations. Unlike discriminate analysis, which requires
prior knowledge of the group membership for the data cases, cluster analysis does

not require such knowledge.

74

Cluster analysis uses the concept of “distance” and “similarity” in generating new
clusters or collapsing them into a lesser number of clusters. There are many
methods of calculating “distance” and the analyst must use interpretative judgment
and inspection in addition to the quantitative analysis.

Cluster analysis was used to identify the variables with a strong association with the
crash rate. While any number of clusters can be created, three clusters were used in
this study. While it was not predetermined that the crash rate would be included in
each cluster, one cluster included curves that have a low crash rate, a second cluster
was formed around curves with an intermediate crash rate, and the third around high

crash rate curves. This was a useful outcome when interpreting the results.

Analysis and Results

Cluster analysis results proved to be useful for the objectives of this study. Table 14
shows the output for a three cluster case in which Modified Cper380, as discussed
previously, was used to identify the curves to be included in the analysis.

The clustering of high, medium and low crash. rate curves with other variables is
clear, with cluster one having a crash rate of 3.08, cluster two a crash rate of 7.78
while the third cluster has a crash rate of 18.05. Variables such as lane width
(ALW), that show little variance between the three clusters indicate that either this
variable is unimportant in predicting the curve crashes, or that there is little variance
in the variable across all curves. For this variable the latter is true. Other variables,
such as curve length and curve radius, show large variations between at least two of
the three clusters. This is an indication of an important variable in the prediction
model. The important variables are shown in Table 15.

The same variables identified in the discriminant analysis were important in the

cluster analysis. The ADT, curve radius, curve length, and the presence of traffic

75

Table 14
The numerical values of all variables in defining the clusters grouped by the
modified curve crash rate (Modeer)

 

 

 

 

 

 

 

 

 

Final Cluster Centers
Cluster
1 2
ADT 472.72 536.05 549.14
ALW 11.31 11.19 11.06
ARROW .21 .09 .29
CHEVRON .03 .03 .13
CLRNCW 3.69 3.66 4.09
CTSIGN .34 .44 .56
DLNTR .31 .19 .27
EDGLN 1.00 .98 1.00
GRAIL .21 .13 .23
HCLFT 1704 590 520
HCRFT 2471 2383 963
MODCPER 3.08 7.78 18.05
MPHS .10 .09 .30
NPZC .90 1.06 1.96
OBSDSTW 45.24 44.27 38.37
PSL 54.66 54.53 53.29
PSW 10.79 6.56 7.03
SCT 1.66 1.53 1.60
TPER380 2.52 3.44 2.98
TSW 19.45 18.72 18.56
Number of Cases in each Cluster
Cluster 1 29.000
2 64.000
3 70.000
Valid 163.000
Missing 15.000

 

 

 

 

76

 

Final Cluster Centers

Table 15
The numerical values of the important variables in defining the clusters
grouped by the modified curve crash rate (Modeer)

 

Cluster

 

2

 

ADT

ALW
ARROW
CHEVRON
CLRN CW
CTSIGN
DLNTR
EDGLN
GRAIL
HCLFT
HCRFT
MODCPER
MPHS
NPZC
OBSDSTW
PSL

PSW

SCT
TPER380
TSW

 

 

472.72

.21
.03

1704
2471
3.08

 

536.05

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2383
7.78

 

549.14

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.13

520
963
18.05

 

Number of Cases in each Cluster

 

Cluster

Valid
Missing

 

l

N

 

29.000
64.000
70.000
163.000
15.000

 

 

77

 

control devices (arrow and chevron)are all important in defining the clusters.
Interestingly, the high crash rate curves are associated with the highest probability
of having chevrons and target arrows deployed. However, this is explained by the
fact that this cluster contains the short radius curves, where these devices tend to be
deployed.

An analysis using Cper380 instead of Modeer shows similar results (Table 16).
Most notably, the clustering of high crash rates with short curves and low radii
while the low crash rate curves are clustered with long curves with large radii.
This finding is consistent with prior research. Using this measure of the crash rate,
ADT was replaced by the presence of an advisory speed plate and the paved
shoulder width as explanitory variables. Perhaps the most interesting cluster is the
third one, which clusters moderately high crash rate curves with curves of large
radius but short length. These tend to not have traffic control devices deployed
because of their large radius and subsequently their high design speed.

Tables 17 and 18 show two more cluster analysis results. These results are also
consistent with the previous findings. In Table 17 the difference between the curve
crash rate and the tangent crash rate, (CmnsT), is used as the crash rate variable,
while in Table 18 the variable, ModensT, as described before, is used.

It was hypothesized that the variation in crash rates within each cluster could be
explained better by regression analysis than was possible for all curves combined
To test this hypothesis, simple and multiple regression analyses were conducted on
each of the three clusters obtained from the cluster analysis. However, the
correlation coefficients within each cluster were still very low. (As examples
Figures 33 through 38 show the regression plots of Cper380 with HCRFT and
HCLFT for each of the referenced three clusters).

78

Final Cluster Centers

Table 16

The numerical values of the important variables in defining the clusters
grouped by the curve crash rate (Cper380)

 

Cluster

 

 

 

ADT
ALW
ARROW
CHEVRON
CLRN CW
CPER380
CURVES
DLNTR
EDGLN
GRAIL
HCLFT
HCRFT
MPHS
OBSDST
PSL

PSW

SCT
TPER380
TSW

 

TURNS

.19
.03

3.33

1707
2490
.09

1 1.09

 

17.10

522
974
.32

7.26

 

.10
.03

7.62

2392
.10

6.53

 

Number of Cases in each Cluster

 

Valid

 

Cluster

Missing

1

MN

 

32.000
76.000
70.000
178.000
.000

 

 

79

 

Table 17
The numerical values of the important variables in defining the clusters
grouped by the curve minus tangent crash rate (C-T)

Final Cluster Centers

 

Cluster

 

 

ADT
ALW
ARROW .10 .30 .19
CHEVRON .03 .14 .03
CLRN CW
CMNST 4.32 14.05 .88
CT SIGN
DLNTR
EDGLN
GRAIL
HCLFT 608 522 1707
HCRFT 2392 974 2490
’ MPHS .10 .32 .09
OBSDSTW
PSL

PSW 6.53 7.26 11.09
SCT
TSW

 

 

 

 

 

 

80

Table 18
The numerical values of the important variables in defining the clusters
grouped by the modified curve minus tangent crash rate (ModC-T)

 

 

 

 

Final Cluster Centers
Cluster
1
ADT
ALW
ARROW .11 .33 .25
CHEVRON .04 .18
CLRN CW
CTSIGN
DLNTR
EDGLN
GRAIL .07 .25 .20
HCLFT 607 471 1757
HCRFT 2351 902 2481
MODCMNST 5.59 17.67 1.40
MPHS .09 .37 .15
PSL
PSW 6.78 7.15 12.90
SCT
TSW
OBSDSTW

 

 

 

 

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87

Factor Analysis and Results

Factor analysis is a technique used to reduce many variables into a smaller set of
factors. Each factor describes a “concept.” Ideally the concept will be readily
understood by individuals and there may even be an eXisting name for the concept.
If not, the analyst can often understand the concept aml give it an appropriate name.

Factor analysis starts with a set of variables, or better stated, the scores related to a
set of variables. Next, a set of new variables is constructed based on the
interrelations exhibited in the data. The first factor is defined as the best linear
combination of variables explaining the variance in the data as a whole. The other
factors are similarly defined as the best linear combination of variables which
explains the variance remaining in the data as a whole. The first factor is thus more
important than the second one and so on. The first few factors usually explain most
of the variance in the data.

Factor analysis was conducted for many cases of differing variables, factoring
criteria, rotation method and number of extracted factors. However, the use of this
technique did not identify any relationships among the variables and crash rates that

was not also identified by using discriminant analysis.

Table 19 shows the results of one factor analysis with the first three factors
extracted. The variables that contribute the most to the factor score coefficients for
these three factors are shown in Table 20. Only one of the three factors includes the
crash rate (Cper380).

Factor 1 includes Cper380 and the presence of certain traffic control devices

(chevron and advisory speed panels), curve length, radius, and roadside clearance

88

Table 19

Factor score coefficient matrix for all the variables

Factor Score Coefficient Matrix

 

 

 

 

 

 

 

 

 

 

 

Factor
1 2 3
ADT .014 .507 .277
ALW -.032 .066 -.089
ARROW .033 -.109 .053
CHEVRON .128 .032 .009
CLRNCW -.176 -.289 .611
CPER380 .321 .018 -.019
CURVE .018 -.004 .049
DLNTR .012 -.022 .006
EDGLN .013 .018 .012
GRAIL -.012 -.013 .101
HCLFT -.124 .041 .024
HCRFT -.347 .105 -.038
MPHS .218 .039 .071
OBSDST -.004 .006 .006
PSL .002 -.033 -.018
PSW -.029 .097 -.031
SCT .013 .181 -.024
TPER380 .035 .142 .117
TSW -.004 .124 -.044
TURNS .103 -.062 -.063
Factor Score Covariance Matrix

Factor 1 2 3

1 .736 1.850E-03 4.219E-02
2 1.850E-03 .766 4.699E-02
3 4.219E-02 4.699E-02 .768

 

 

 

 

89

 

 

Table 20
Factor score coefficient matrix of relatively high values

Factor Score Coefficient Matrix

 

Factor

 

1 2 3

 

 

ADT .507 .277
ALW
ARROW
CHEVRON .128
CLRNCW -.176 -.289 .611
CPER380 .321
CURVE
DLNTR
EDGLN
GRAIL
HCLFT -.124
HCRFT -.347
MPHS .218
OBSDST
PSL
PSW
SCT
TPER380
TSW
TURNS

 

 

 

 

9O

 

(inversely). All of these variables, with the exception of the roadside clearance

variable were also included in the discriminant analysis and cluster analysis results.

Factor 2 describes curves with high ADT and a safe roadside, while Factor 3
describes curves with more hazardous roadside conditions and a lower ADT. This
can be interpreted to indicate that the high volume State Trunkline roads have a
safer roadside than do those trunkline highways with lower volumes. However,
nothing is revealed about the difference in crash rates between these two
combinations of variables, nor does this information help to identify specific curves

that contribute disproportionally to the crash rate.

91

Analyses Including Field Data

Since the superelevation of a curve and the coefficient of friction are both factors
considered in selecting an advisory speed for curves, a separate set of analysis was
performed using only the subset of curves for which these data were collected. A
total of 81 roadway segments containing 531 crashes, (279 in tangents and 252 in
curves), were included in these analyses. Seventy one of the 81 roadway segments
had crashes on their curved section. The values of superelevation and drag factor for
the 81 roadway segments are shown in Figures 39-41.

Analyses similar to those performed previously for all the roadway segments, were
conducted for only the roadway segments with the field data. The analyses were
conducted with the addition of the two field data variables, superelevation and drag
factor, for each direction of traffic individually and combined. The analysis was
done twice, once for the higher value of the superelevation for the two directions,
SPRELVN and again for their lower value, SELELO.

Figures 42 and 43 show graphs sorted by ascending value of Cper380 for those
curves with the field data. Figures 44-49 show the simple linear regression results of
Cper380 and CmnsT with these variables.

Neither the drag factor nor the superelevation, individually or in combination, were
significant in explaining the curve crash rate or improving the results of the
discriminant analysis or cluster analysis. In fact, neither of these two variables

entered the results of these tests as predicter variables.

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103

RESULTS

Discriminant analysis and cluster analysis provide information useful in meeting the
objectives of this study. Specifically, they can be used to depict characteristics of
low crash rate curves which distinguish them from high crash rate curves. Therefor

curves with a high crash rate that should (based on their characteristics) have a low
crash rate can be identified. These curves then could be studied for improvement by

application of appropriate countermeasures.

Using the discriminant analysis results from the Cper380 analysis, sixteen curves
fell in this category. The crash rate on these curves ranged from 7.13 to 21.71
when, based on their characteristics, they should have fallen in the group with a
crash rate below 5.0. These curves are shown in Table 21, along with the value of
some of the variables used in the analysis.

The significant characteristics of these curves include:

0 Most do not have curve signs, target arrows and delineators

0 There are no chevrons

0 The distance at which the curve is first visible to the driver is usually short

0 The radius is relatively large

0 The tangent crash rate is low

An almost identical set of curves was identified when CmnsT was used as the
grouping variable. This is consistent with the results shown in Table 21. Since most
of these curves had a high value for Cper380 and low value for Tper380, they

would fall in the high range of CmnsT values.

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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105

The results of the cluster analysis provide additional guidance that may be useful in
establishing programs to reduce traffic crashes. Low crash rate curves are clustered
with large radius and long length. The average radius for curves in this group
(based on modified Cper380) is 398 meters (1305 ft). The average length for the
same curves, is 274 meters (900 ft). These curves tend to have target arrows but no

chevrons.

High crash rates are clustered with short, sharp curves as expected. These curves
tend to have both chevrons and target arrows in place, but still tend to experience
crashes because of their limiting geometry. The countermeasures for these curves

are likely to involve a change in alignment rather than traffic control measures.

The third cluster is the group of curves where traffic engimering countermeasures
may be most effective. These curves have a crash. rate over twice as high as the low
crash rate curves, even though they have approximately the same radius. The
primary geometric difference is that they are very short curves, averaging 95 meters
(312 ft). These curves generally do not have chevrons or target arrows or advisory
speed plates in place because the large radius results in a high design speed as
determined from the AASHTO procedure.

Chevrons and target arrows are not intended for these types of curves according to
the Michigan Manual of Uniform of Traffic Control Devices (MMUTCD), since
they do not constitute a sharp change in alignment. However, based on this study, it
would be appropriate to consider the use of these signs to increase the visibility of

the curves.

106

These same curves were placed in this cluster whether the crash rate variable was
Cper380, Modified Cper380, CmnsT, or modified CmnsT. There were
approximately 70 curves that belong to this cluster. To provide additional guidance
to the process of selecting curves where traffic engineering countermeasures have a
high probability of reducind crashes, the curves in the cluster with the highest rates
should be addressed first. Table 22 lists the curves for which both the Cper380 and

CmnsT were significantly higher than the average for this cluster.

To provide additional guidance in selecting curves to be studied, the curves
categorized in each of the three clusters were plotted in ascending order of the value
of Cper380. Figure 50 shows these results. It is clear that within each cluster there
is a significant range of values for the crash rate. The curves with the highest crash
rate should be studied for possible countermeasure implementation. Table 23 lists
these curves which have a crash rate equal to or greater than twice the average value

of their cluster.

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 22 Curves with a high curve minus tangent crash rate (CmnsT)
CRVno CS BMP CTsign CHEVRON ARROW DLNTR
39 12021 490 0 0 - 0 0
200 73131 0 0 0 0 0
68 23051 2220 1 0 0 0
177 61012 4910~ O 0 0 0
14 5051 7280 0 0 0 0
4 2021 23640 0 0 0 1
3 2021 15020 0 0 0 0
82 28052 5530 0 l 1 0
81 28052 4790 l 0 0 0
94 31013 5810 0 0 0 1
33 10011 5620 1 1 1 0
12 5031 3900 1 0 0 0
214 81031 750 l 0 0 > 0
100 31051 9143 l 0 0 0
172 58032 4150 O 0 0 0
88 30062 2900 1 0 0 1
19 801 l 8990 0 0 0 1
101 3201 l 3050 l 0 0 0
62 22021 499 0 0 0 O
140 45013 11700 1 0 1 0
215 81031 1370 1 1 0 0
71 231 1 1 3670 1 0 0 0

 

108

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 22 (Continued)
BSDST HCLFT HCRFT Tper380 Cper380 CmnsT
70 739 2292 3.00 8.14 5.14
0 264 2865 2.00 7.60 5.60
20 845 2083 6.00 1 1.88 5.88
48 327 2292 12.00 18.39 6.39
40 264 2865 1.00 7.60 6.60
70 581 2865 0.00 6.91 6.91
40 739 1910 1.00 8.14 7.14
40 475 1910 1.00 8.44 7.44
50 634 2865 2.00 9.50 7.50
30 370 1910 3.00 10.86 7.86
33 475 2865 0.00 8.44 8.44
60 370 2292 2.00 10.86 8.86
10 317 2292 10.00 V 19.00 , 9.00
13 338 1910 1.00 11.88 10.88
80 370 2644 4.00 21.71 17.71
30 581 1719 3.00 20.73 17.73
80 21 1 1763 1.00 19.00 18.00
30 370 2292 4.00 27.14 23.14
49 306 1879 16.0 45.86 29.86
60 634 1910 2.00 34.83 32.83
70 370 2989 6.00 43.43 37.43
30 211 1910 3.00 47.50 44.50

 

 

 

 

 

 

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CONCLUSIONS AND GUIDELINES

Based on the results of this study, the following conclusions were reached.

1)

2)

3)

4)

5)

The variation in the crash frequency or rate between horizontal curves with
similar geometry is large, thus, regression analysis is not effective in identifying
specific curves where countermeasures would be most effective in reducing
curve crashes. The only studies that report high correlation coefficients are those
that aggregate curves into groups with similar characteristics and then conduct
the regression analysis on the group means.

This information is used in the design of new highways, (i.e., setting the
minimum curve radius as a function of the design speed, specifying the lane and
shoulder width, etc.), but it is not useful in meeting the objectives of this study.
The predicted crash rate using existing models (Zegeer and Glennon) does not
match the actual crash rates on Michigan two-way, two-lane rural trunklines, as
shown in Figures 28-32. These models can not be used to identify curve
locations where countermeasures could successfully be deployed to reduce
crashes.

The addition of data on the distance on the approach at which the curve first
becomes visible to the motorist is not highly correlated with the crash rates as a
single variable, but it was found to be a contributor to some of the models that
use multiple variables.

The superelevation and the drag factor showed a low simple correlation with the
crash rate and the addition of these two variables contributed little to multiple
variable analyses.

Discriminant analysis techniques, using the variables collected for this study, can

successfully distinguish the characteristics of high crash rate curves from low

112

crash rate curves. This technique can also be used to identify outliers in each of
the two categories (high and low) for both the absolute crash rate on curves
(Cper380) or the difference in the crash rate between the curve and the tangent
roadway segments (CmnsT).

6) Cluster analysis identified three distinct groups of curves. The group with a high
crash rate (Cper380) is characterized by short radii and short curve lengths.
These curves generally are marked with curve sign, advisory speed panels and
chevrons or delineators. The group with a low crash rate is characterized by
large radii and long curve lengths.

The third group, with an intermediate crash rate, is characterized by large radii

 

but short curve lengths. These results are shown in Figures 51 and 52.

The high crash rate on the first group of curves is probably related to constraint
the geometry imposes on drivers’ ability to negotiate the curve at their approach
speed.

The intermediate crash rate curves may be related to the driver perception (or
lack of perception) of the presence of a curve that does not require extraordinary
driver input to negotiate safely. These are the curves that are likely to benefit the
most from traffic engineering countermeasures.

7) The factor analysis results are more difficult to interpret, because the crash rate
does not appear in each cluster. The results are consistent with the discriminant
analysis and the cluster analysis results. In general, the variables significant in
defining the factor groups are the same as those used to distinguish the group

membership in these analyses.

The results of the study provide guidance on a cost effective approach to selecting

curves to be studied:

113

 

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l) The curves identified in Table 21 from the discriminant analysis results should be
targeted for analysis and potential countermeasures implementation. These
sixteen curves have the characteristics of low crash rate curves, but are
experiencing a high rate of crashes.

2) The curves identified in Table 22 from the cluster analysis results should be
targeted for analysis and potential countermeasure implementation. These
segments have been identified as experiencing a high crash rate on its curve
compared to the crash rate on the straight sections at the two ends of each
curve, (CmnsT).

3) The curves identified in Table 23 from the cluster analysis results should be
targeted for analysis and potential countermeasure implementation. These
curves have been identified as experiencing a crash rate at least twice that of the
average crash rate for curves in their cluster.

4) Curves characterized by a large radius and short curve length should be analyzed
to determine if there are inexpensive countermeasures that could be applied at
these curves to reduce the crash rate. These curves have been identified from
the cluster analysis as having an intermediate crash rate which is not explained
by the curve geometry.

5) Discriminant analysis and cluster analysis techniques should be used to analyze
other sets of curves on state trunkline highways. These techniques have been
useful in identifying specific curves that are candidates for countermeasures. It
should be determined whether these techniques are equally valid for curves that
are not screened for approach tangents and intersections and curves on four-lane

cross sections.

116

 

6)

7)

8)

Curves that are both in Table 21 and also Table 22 should, in particular, be
considered for upgrade. These are curves: 3, 14, 19, 33, 39, 81, 82, 94, 172
and 200.

Similarly, curves that are both in Table 23 and also Table 21 or Table 22,
should, in particular, be considered for upgrade. These are curves: 62, 71, 87,
88, 101, 117, 140, 177, 214, and 215.

Had there been any curves common to all the three Tables (21, 22 and 23), such

curves would have had the highest priority for countermeasure implementation.

117

LIST OF REFERENCES

 

10.

11.

. Zegeer, C.V., Hummer, J ., Reinfurt, D., Herf, L. and Hunter, W., "Safety effects E‘

. Neuman, T.R., Zegeer, C., and Slack, K.L. "Design Risk Analysis Volume II -

References

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Design Elements”, NCHRP Report 197, 1978.

Glennon, J.C., Neuman, T.r., Leisch, J .E. “Safety and Operational Considerations
For Design of Rural Highway Curve”, Jack E. Leisch & Associates, Evanston, IL,
FHWA-RD-86/035, 1985.

of cross-section Design for two-lane Roads, Volume I," Report No. FHWA/RD-
87/008, FHWA, Washington DC, December 1986.

Zegeer, C.V., and Deacon, J .A., "Effects of Lane Width, Shoulder Width, and
Shoulder Type on Highway Safety.”

 

1.“ I . n

User's Guide", FHWA Contract N o. DTFH 71-88-C-00011, US. Department of
Transportation, April 1991.

McGee, H.W., Hughes, W.E., Daily, K., Bellomo-McGee, Inc., "Effect of
Highway Standards on Safety", Final Report, prepared for National Cooperative
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Kach, Brett, Benac, Jack D., “Horizontal Curve Crash Model Assessment”, Traffic
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Fink, K.F., Krammes, R.A., “Tangent Length and Sight Distance Effects of Crash
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Zegeer, C.V., Twomey, J .M., Heckman, ML. and Heyward, J .C., “Safety
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Datta T.K. et al. , “Crash Surrogates for Use in Analyzing Highway Safety
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Terhune, K. W. and Parker, M.R. , “An Evaluation of Crash Surrogates for Safety

Analysis of Rural Highways.” Volume 2. Technical Report. Report No.
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Matthews, L.r. and Barnes, J .W. , “Relation Between Road Environment and
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Zegeer, C., Stewart, R., Reinfurt, D. et al., “Cost—Effective Geometric
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Glennon, J .C., Neuman TR. and Leisch, J .P. “Safety and Operational
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86/035. FHWA, US. Department of Transportation, 1985.

Fambro, D.B., Urbanik, T. 11, Hinshaw, W.M., Hanks Jr., J.W., Ross, M.S.,
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Baker, Stannard J. , Northwestern University Traffic Institute, The Traffic-Accident
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Berry, William D., Feldmam, Stanley, University of Kentucky. Multiple
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Bhatti, M. Ishaq, School of International Business Relations, Testing Regression
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Hand, D.J., Biometrics Unit, London University Institute of Psychiatry,
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NATO Advanced Study Institute, Edited by T. Cacoullos, University of Athens,
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Jambu, M., Centre National d’Etudes des Te’le’communications, Issy-les-
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120

23. Van de Geer, P. John, University of Leiden, the Netherlands, Introduction to
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Francisco, 1971.

 

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