Factors affecting drivers' choice of speed on roadway curves

Journal of Safety Research, Vol. 26, No. I. pp.49-56, 1995 Copyright Q 1995 National Safety Council and Elsevier Science Ltd F’rintedin the USA. All rights reserved 0022-4375/95 $9.50 + .I0

Pergamon

0022-4375(94)00024-7

Factors Affecting Drivers’ Choice of Speed on Roadway Curves George

Kanellaidis

Vehicle speeds depend on factors relating to drivers, vehicles, and the roadway environment. Operational studies show that curvature is the roadway element that is most successful in predicting vehicle speeds. If, however, a causative explanation of drivers’ behavior is sought, then attitude surveys are more appropriate than traffic observations. This paper features a survey of 207 Greek drivers who were asked to rate 14 elements of the road environment as to how importantly these influence their choice of speed on interurban road curves. A comparison of responses between drivers who claimed to obey speed limits (nonviolators) and those who claimed not to (violators) shows that the latter gave significantly lower ratings to all types of signing and were generally less restricted by roadway elements in choosing their speed. Factor analysis of the data indicates that speed choice on curves can be described by four road-environment factors: separation of opposing traffic; cross-section characteristics; alignment; and signing. Separate analyses show that nonviolators are primarily influenced by the signing factor in choosing their speed on curves, while violators’ speed is chiefly determined by the road-layout factor. These findings suggest that speed reduction, where necessary, could be brought about by provision of reliable signing as well as safe and consistent low-speed alignment. The four factors identified by the analysis correspond to the findings of driver-behavior studies, indicating that attitude surveys can be used as a reliable aid in forming and evaluating relevant policies, whether at a local or a strategic level.

INTRODUCTION Car travel is associated with the freedom it offers to travelers in choosing when, by which route, and how fast they will travel. The “car culture” of today’s world (Marsh & Collett, 1986) can be attributed, to a large extent, to

George Kanellaidis is an Assistant Professor in the Department of Transportation Planning and Engineering at the National Technical University of Athens (NTUA). He received his PhD in Transport&ion from the NTUA in 1984. His research interests include highway geometric design, human factors in transportation, and traffic safety.

Spring 1995Nolume 26hVumber I

this freedom, which is not found in other means of transport. For business or commuting trips in particular, minimizing travel time seems to have priority over other objectives; hence the incentive to drive faster. Speed also appears to have an “intrinsic value” (Hale, 1990) for many people, who simply want to drive fast for the excitement it offers, regardless of trip purpose. Still, there are various limits to attainable speeds. Technical limits are determined by a vehicle engine’s horsepower. Speeds on curves should not exceed certain values above which the risk of running off road is greatly 49

increased. Speed may be further constrained by the drivers themselves, in choosing to drive at a speed they consider safe and comfortable. Models for estimating “limiting speeds” as a function of the above parameters have been developed (Elkins & Semrau, 1988). In addition to these factors, authorities often consider it desirable to impose limits on vehicle speeds in order to reduce such adverse effects as: (a) probability and severity of crashes; (b) noise; (c) pollution; and (d) fuel consumption (Transportation Research Board [TRB], 1984; Hale, 1990). If speed is to be controlled, the main two options (Hale, 1990) are: (a) to take the choice of speed away from the driver (e.g., through use of automatic speed-governing devices or built-in limits in engine design); or (b) to indirectly influence speed and driving behavior in general via the drivers themselves. Obviously the former approach will have to overcome considerable hurdles, since it will involve restrictions on driver (and motor-industry) freedom. The latter option will require thorough research into the factors affecting choice of speed. Car travel involves an interaction between driver, vehicle, and road environment; in a similar fashion, a driver’s free speed (defined as the speed chosen in the absence of other traffic) depends on characteristics of these three factors. As conventional driver-behavior research usually involves observation of moving vehicles, it is not easy to take note of driver and vehicle characteristics. Indeed, it is not possible to know the personal or socioeconomic characteristics of drivers; nor can the engine’s horsepower and condition be determined by a simple observation. Only vehicle type can be accounted for (e.g., in producing separate speed-prediction relationships for cars and trucks). Typically, research has aimed to identify correlations between operating speeds and road-design characteristics, treating the effect of the other two factors as random variation. Curvature is the design element most consistently found to be correlated to operating speeds. Although it has been argued (McLean, 1979, 1981; Yagar & van Aerde, 1983) that operating speeds are affected by the characteristics of a preceding section of road, recent 50

research (e.g., Lamm, Guenther, & Choueiri, 1992) focuses on producing speed-prediction formulae for individual curves. These relationships have the advantage of being both simple and of sufficient predictive power (R2 ranging generally from .75 to .95). They have the general form of Vss = a - j3(l/R), where Vss is the 85th-percentile speed, R is the curve radius, and cx and /3 are parameters (Taragin, 1954; Lamm & Choueiri, 1987). Some linear equations include powers of (l/R) as additional regressors: for example, ( 1/R)2 (McLean, 1981) or (lIR)“.5 (Kanellaidis, Golias, & Efstathiadis, 1990). Recent studies (Lamm et al., 1992) have also produced exponential relationships of the type Vss = a + P.e-YDC, where DC is degree of curve (proportional to l/R). Lane width is also generally found to influence speeds; however, there is only a narrow range of possible lane widths, and thus it is often more convenient to produce different relationships for various lane or carriageway widths (Lamm & Choueiri, 1987; RAS-L-1, 1984) or for different types of road, such as 2lane, 4-lane single, or dual carriageway (Gambard & Louah, 1986; Mintsis, 1988). Certain other elements are usually found to be correlated to curvature. These include signing (Lamm & Choueiri, 1987), superelevation rate (Lamm, Choueiri, Hayward, & Paluri, 1988), and sight distance (Taragin, 1954). The effect of the above elements on speeds cannot be easily quantified. In addition, there is no universal agreement on the exact effect of gradient on speeds. Gambard and Louah (1986) found that Vg5 is unvaried on downgrade sections, while average speeds decrease; Yagar and van Aerde (1983) showed, on the other hand, that average speeds are significantly increased on downgrades. In both studies, speeds were found to decrease on upgrades. Other studies (e.g., Reinfurt, Zegeer, Shelton, & Neuman, 1992) show no significant effect whatsoever of gradient on speed. Typically, research has focused on observations of driver behavior; however, if one is interested in the reasons behind speed choice, conventional measurements are not sufficient. Correlations between speed and predictor variables do not necessarily offer causative explanations of speed choice. Use of attitude surveys can help provide some answers to Journal of Safety Research

why car drivers choose certain speeds in certain situations, as well as to how effectively their speed choice could be influenced. Carefully designed interviews that focus on minimizing biases can ensure that expressed attitudes will give a fairly accurate picture of true attitudes (Myers, 1983). It should not be forgotten, however, that the aim is to affect drivers’ behavior. Influencing attitudes may or may not bring about the desired change, since the link between attitudes and behavior is far from straightforward. The objective of this paper is to investigate the factors determining choice of speed on interurban road curves, as seen from the drivers’ viewpoint, as well as to assess their relative importance. In addition, an attempt is made to examine whether drivers’ attitudes toward speed limits are associated with differences in the above factors and to suggest effective means to influence choice of speed.

DATA COLLECTION

AND ANALYSIS

Data were collected through the completion of a specially-prepared questionnaire. Copies of the questionnaire were distributed to a sample of randomly-selected drivers to be completed in the absence of any interviewer and to be collected by a specific date. Two hundred and seven fully completed questionnaires were collected in this way. The issues addressed were the following: (a) drivers’ attitudes toward speed-limit violations; (b)

“self vs. other” analysis of reasons for speeding; and (c) road-environment factors that affect choice of speed, in the drivers’ view. The results regarding Parts a and b of the survey are dealt with in a separate paper (Kanellaidis, Golias, & Zarifopoulos, 1995). This paper focuses on speed-choice factors on interurban-road curves. In addition to the analysis carried out for the full sample, separate analyses were made for those who stated that they obey speed limits “always” or “most of the time” (a subgroup labelled “nonviolatars” for ease of reference) and those who stated that they “seldom” or “never” obey limits (“violators” for short). Fourteen elements of the road environment, for which there was evidence in literature of being related to vehicle speeds, were selected for the questionnaire and coded El to El4 (Table 1). Respondents were asked to rate each element on a 0 to 10 scale, showing its importance, in their view, in influencing speed choice on curves. Zero stood for “no important influence on speed choice” and 10 for “very important influence on speed choice.” Table 1 also shows the mean ratings for the 14 elements. They all exceed 5.0. On top of the list are sight distance, pavement condition, sharp curvature, and additional warning signing, all rated above 8.0 on average. Least decisive are existence of free roadside space and speed-limit signing. Of the four top-rated elements, curvature, sight distance, and additional warning signing have also emerged in driving-behavior studies

TABLE 1 DESCRIPTION. MEAN RATINGS AND RANKS OF DESIGN ELEMENTS AFFECTING SPEED CHOICE ON ROADWAY CURVES

Element

(code)

Description

El

Pavement

E2

Number

E3

_.........,.,.

of traffic

lanes

Lane width

.._._....

E4

Mean

of element condWon

Existence

of free roadside

E5

Existence

of median

E6

Existence

of safety

E7

.::

::::::

Sharp

space

barrwrs

curvature

2

7.11

10

6.72

12

5.62

14

7.60

6

7 44

7

8.31 7.78

3 5

8.09 5.78

4 13 8

Standard

E9

Additional

El0

Speed-limit

El1

SuperelevatIon

7.33

El2

Sight distance

8.64

1

Length

7.23

9

7.06

11

El4

::

::: ...,..,

Spring 1995Nohne

warnmg slgnmg

of curve

Gradient

26/Nutnber I

signmg

Rank

E6

El3

curve-warning

RatlnQ 8.34

signing

51

implies that drivers who don’t obey speed limits probably feel less constrained by the road environment in selecting their speed on curves. Spearman’s rank correlation test (Daniel, 1990) showed that the rankings resulting from the group averages of variables are significantly correlated; Spearman’s rank-correlation coefficient (rho) is .84, which is statistically significant at a = 0.01. Therefore, the evaluation of speed determinants is not radically different between violators and nonviolators. As it was aimed to determine the “dimensions of thought’* regarding drivers’ speed choice, factor analysis (Norusis, 1988) was the preferred procedure because it gives the possibility of reducing a large number of variables to a smaller number of principal factors. Each variable can then be expressed as a linear function of these factors. The coefficients of the factors in the (standardized) regression equation are known as the factor loadings. As the number of factors is lower than that of the original variables, it is typical for a factor to have high loadings on a number of variables; it can then be said that the factor is associated to these variables. The suitability of the data for factor analysis was first established by two standard tests: the Kaiser-Meyer-Olkin (KM@ measure of sampling adequacy, and Bartlett’s test of sphericity (a chi-squared test). If KM0 > 0.5and p(=2) c 0.01, the sample is suitable for factor analysis. Both tests (see Table 3) gave satisfactory results and thus the analysis proceeded.

(Taragin, 1954; Lamm & Choueiri, 1987) as significant determinants of speed. As the latter two are collinear to curvature, the attitude survey seems to confii the role of curvature as a primary determinant of operating speeds. Pavement condition does not usually show up in speed behavior studies, probably because it is assumed to be standard throughout the road network. It should be noted that pavement condition is a broad term that implies skid resistance as well as surface discontinuities, roughness, and “quality of ride.” Elkins and Semrau (1988) did identify pavement roughness as a speed limiting factor, by using a present serviceability rating in the formula for determining the “maximum allowable ride severity speed.” For violators and nonviolators alike (Table 2), sight distance was the highest-rated variable, with identical mean ratings for both groups (8.64). However, for nonviolators four other elements are rated above 8.0 on average; these are: curvature, additional warning signing, standard bend-warning signing, and pavement condition. For the average violator, only curvature and pavement condition were rated higher than 8.0. Table 2 also shows the results of normal tests for comparing the two groups’ ratings. Significant differences are observed in all three signing-related variables, and also in gradient, where all four are rated higher by nonviolators. On the whole, nonviolators tend to give higher ratings to most elements than do violators (overall rating average for nonviolators is 7.55; for violators it is 7.02); this

COMPARISON

TABLE 2 OF DESIGN ELEMENT RATINGS FOR NONVIOLATORS

Average Element

Non-violators

VS. VIOLATORS

Rating Violators

Difference

Z-statistic

El ...............

8.21

8.58

-0.37

-1.42

E2

..............

7.16

7.01

0.15

0.41

E3 E4

.............. ..............

6.83 5.85

6.52 5.21

0.31 0.64

0.86 1.54

E5

..............

7.51

7.77

-0.26

E6

..............

7.55

7.25

0.30

-0.64 0.72

E7 E8

.............. .............

8.40 8.30

8.16

0.25 1.48

0.85

6.82

4.27

l

E9

..............

8.35

7.62

0.73

2.21

f l

El0

.............

6.72

4.06

2.66

6.83

El1

.............

7.16

0.27

8.64

0.76 -0.01

El2

.............

7.43 8.64

El3

.............

7.42

6.88

El4

.............

7.34

6.55

(‘):

52

significant

-0.002 0.54 0.79

1.62 2.35

l

at a =0.05

Journal of Safety Research

TABLE 3 TESTS OF SUITABILITY

Kaser-Meyer-Olkin Sample

analyzed

Full sample

(N =207)

Nonviolators Violators

sampling

(N = 134)

IN =73)

The standard method of principal-components analysis was followed. For the full sample of 207 drivers (making no distinction between violators and nonviolators) four factors were identified, explaining 62% of the total variance (Table 4). Moderate or high factor loadings have been underlined in the table to show which variables are associated with each factor. Factor 1 features “road layout” elements, in particular sight distance and curvature. Factor 2 can be labelled “cross-section characteristics.” Factor 3 is associated to “signing.” And Factor 4 to “separation of opposing traffic.” Presented in bold type are the loadings of the four highest-rated elements (El-pavement condition, ET-sharp curvature, E9-additional warning signing, and E12-sight distance on curve). These were considered for a qualitative comparison of the factors’ importance; the factors associated with most or all of these elements (bold and underlined loa$ngs) may be seen as being of prime importance in determining choice of speed. It can be seen that sight distance and curvature have high load-

FACTOR

Factor Elements El

(“Road

.

E2

.._

E3 E4

,..._.

E5 E6

.,.._.

LOADINGS

FOR FACTOR

(KM01

measure

ANALYSIS

of

Bartlett’s

adequacy

test of sphericity [PIX’H

0.741

0.000

0.679

0.000

0.738

0.000

ings on the road layout factor; pavement condition and hazard signing have fairly high loadings on that factor, and loadings of the same order (approximately 0.5) on Factors 2 and 3 respectively. One can therefore assume that road layout is the factor of prime importance in determining drivers’ choice of speed. Since four factors emerged as significant for the full sample, it was attempted to produce the same number of dimensions in separate analyses for violators and nonviolators. The factors extracted for the two subgroups are similar to those identified in the analysis for the full sample: (a) road layout, (b) crosssection characteristics, (c) signing, and (d) separation of opposing traffic. In both samples, the four factors explained over 60% of the total variance (60.5% for nonviolators, 64.8% for violators). A comparison of factors for the two groups was attempted, again in a qualitative fashion, by considering each group’s four highest-rated variables. Since for nonviolators (Table 5) variables E7, E8, E9 and El2 were the highestrated ones, it can be said that the signing factor

TABLE 4 FOR THE FULL SAMPLE (207 DRIVERS)

1

Factor

layout”)

3

(“Signing”)

A5

.M

-.38

.12

z5

-.05

.02

.Bz

.ll

-.08

.§z

.22

.04

.36

-.08

Factor 4 (“Separation

of opposing -.ll .27 .09 .36

.a4

.lO

.12

.02

86

.62

.05

.lS

.Ol

ES

.37

-.07

.24

.04

ES El0

49 .04

-.14 .21

-62 .24

.18 -.09

E7

.._.

El1 El2 El3

.._._ _..._

El4

Bold type: l!nd&&&

highest-rated variables

traffic”)

&cl

.Ol

.14

.21

.Bl M

-.03 .30

-.Ol .35

.06 -.15

.52

.21

.38

.08

variable

characterizing

each factor

Spring 1995Nolume 26Bhmber

I

53

FACTOR

Factor (“Road

Elements

TABLE 5 FOR THE SAMPLE OF NONVIOLATORS

LOADINGS

Factor

1

layout”)

(“Cross-section

.09

El E2

.

. .

E3

2

&I

3

(“Signmg”)

(“Separation

Factor 4 of opposing

.19

-.05

.al

-.Ol

.25

.07

.Iu

-.lO

.12

E4

.21

A8

-.30

AZ

-.02

.24

-.07

a6

E6

-.03

03

.06

.a5

E7

.03

.23

xi

.I7

-.02

.25

.30

-.lO

_Bl

.06

.12

.34

.29

-.16

El1

_55

-.06

.32

.30

El2

A5

-.Ol

A6

.ll

E8

,.....

E9

.

.

El3 El4

. .._..

.15

.Ol

-.12

81

.15

.18

-.09

each factor

(on which El, E8 and E9 have high loadings and El2 a fairly high loading) is the most important one. On the other hand, violators (Table 6) were primarily influenced by El, E5, ET, and E12; for this group, the road-layout factor seems to be relatively more important than others, as it features high loadings for El and E12, and a fairly high coefficient for E7. From the above analysis, differences between violators and nonviolators can be summed up as follows:

FACTOR

Factor (“Road

LOADINGS

1

layout”)

l

l

Nonviolators seem to be primarily affected by signing in setting their speed on curves, while for violators road layout appears relatively more significant. Violators rate signing (whether warning signs or posted speed-limits) and gradient significantly lower than do nonviolators.

DISCUSSION Factor analysis of the survey data indicates that there are four general factors of the road environment that influence drivers’

Violators are less restricted by road-environment elements on curves in determining their speed.

Elements

.02 -.13

&I

Bold type: highest-rated variable U.&&n& variables characterizing

TABLE 6 FOR THE SAMPLE OF VIOLATORS

Factor (“Cross-section

2

characteristics”)

Factor

(73 DRIVERS)

3

(“Signing”1

Factor (“Separation

.,._..

_I3

.04

.ll

.09

E2

_.

.31

.38

.04

Ji2

E3

.18

M

E4

-.03

E5 E6 E7

.12 -.08 Al

E8 E9

.06 .14

-.02 -.05

-.28 .52

_. .._

El0 El1

.._..

El2 El3 El4

.

Bold type: Undarlinad:

54

highest-rated variables

4

of opposing

El

..t..

traffic”)

.03

E5

El0

l

Factor

characteristics”)

(134 DRIVERS)

-.02

.28

-23 .23

.14 .02

.27 911

.09 .17

.21 _Bl

_a8 -.lO

26 81

.12 .22

.32

.E6

-.12

19

.36

.04

.B4

.02

93

.19 .25

53 .20

M Lie?

traffic”)

.09 -.02 .17

variable

characterlang

each factor

Journal of Safety Research

choice of speed on interurban road curves. These are: (a) separation of opposing traffic, (b) cross-section characteristics, (c) alignment, and (d) signing. It is worth noticing that these dimensions, identified by analysis of drivers’ expressed attitudes, correspond, in a qualitative way, to factors identified through observations of actual driver behavior. Indeed, most relationships used for predicting operating speeds take account of the first three factors, as they constitute relationships of speed versus curvature (Lamm & Choueiri, 1987) for various road types; the term “road type” generally involves factors (a) and (b) (Gambard & Louah, 1986), and curvature is a dominant element of the “alignment” factor. Besides, there is a considerable amount of empirical evidence (e.g., Rutley, 1972; TRB, 1984,) to support the view that signing does have an effect on vehicle speeds. The correspondence between the speedchoice factors identified in this survey and those emerging in operational studies suggests that attitude surveys can be used as a reliable tool in relevant research. They can provide insight into the reasons behind the choice of speed, whereas conventional speed measurements usually produce mere correlations, not causal relationships (Myers, 1983). For example, the lack of agreement on the impact of speed limits (TRB, 1984; Yagar & van Aerde, 1983; Noguchi, 1990), as well as the otherwise unexplained conflicting findings regarding the effect of gradient on speeds (Yagar & van Aerde, 1983; Gambard & Louah, 1986; Reinfurt et al., 1992), may be due to differences in attitudes and behavior between those who obey speed limits and those who do not. Drivers’ ratings and factor analysis results showed that road layout variables (sight distance in particular) were the most significant determinants of speed choice on curves. If lower speeds are aimed for, modifying the alignment may be more effective than provision of signing in reducing speed. Safe lowspeed alignments (e.g., flowing alignments with sight distances only slightly above minimum values) should be sought in those cases. It must be emphasized that situations requiring abrupt speed reductions can be avoided by Spring I99SNolume 26/Number

I

ensuring consistency of alignment (Federal Highway Administration, 1981; Lamm et al., 1992), whether in designing new roads or improving existing ones. Signing is a factor of special interest, for a number of reasons. First, it is usually strongly correlated to alignment (Lamm & Choueiri, 1987). For example, curve-warning signs are usually found on tight bends, and thus it cannot be clear what part of the reduction is attributable to signing and what to sharp curvature. Second, characteristics such as the type, placement, and condition of a sign can vary considerably, making it difficult to precisely assess the effect of signing as a single factor. And finally, the present survey shows that drivers obeying speed limits and those violating them are affected by signing in different ways regarding speed choice on curves. The role of signing becomes most important in cases where the risk viewed subjectively is less than that viewed objectively (Wright & Boyle, 1987; Dieleman, 1990; Kanellaidis & Dimitropoulos, 1994). If increased acceptance of signing among violators is to be sought, improvements in the reliability of signing could be supplemented by campaigns emphasizing its importance for road users’ safety. It was shown (Kanellaidis et al., 1995) that young, male, University-educated drivers frequently using interurban roads should be the target group of relevant safety campaigns. Due to the evidence of a “self-serving bias” in drivers (McKenna, Stanier, & Lewis, 1991, Kanellaidis et al., 1995), it is important to convince individuals that the campaign message refers to themselves and not to “other drivers only.” Use of attitude surveys can offer flexibility in exploring possible driver reactions to planned schemes at a local level, by helping identify which options would be potentially successful. In addition, at a strategic level, it is often desirable to achieve “optimum” operating speeds, which may well be different from drivers’ desired speeds (Hale, 1990). To bridge that gap, knowledge of factors affecting choice of speed, and also of attitudes and behavior regarding advisory and mandatory speed signs, will be of great importance. 55

ACKNOWLEDGEMENT

The author wishes to acknowledge the contribution of Ioannis Dimitropoulos to the completion of this paper.

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Journal of Safety Research