category: literaturenote citekey: helseffectroundaboutdesignfeatures2007 title: The effect of roundabout design features on cyclist accident rate authors: "Hels, Tove; Orozova-Bekkevold, Ivanka" year: 2007 date: 2007-00-00 2007 doi: 10.1016/j.aap.2006.07.008 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2006.07.008" zotero_key: 2RFJFRDB zotero_storage: N4984AUP collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Hels, Tove"

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Accident Analysis and Prevention 39 (2007) 300–307

The effect of roundabout design features on cyclist accident rate

Tove Hels ∗, Ivanka Orozova-Bekkevold

Danish Transport Research Institute, Knuth-Wintherfeldts All´e, Building 116 West, DK-2800 Lyngby, Denmark Received 27 January 2006; received in revised form 27 July 2006; accepted 30 July 2006

Abstract

Roundabouts are known to result in fewer traffic accidents than traditional intersections. However, this is to a lesser degree true for bicycles than for vehicles. In this paper, we aimed at establishing statistical relationships through Poisson regression and logistic regression analyses between yearly rate of cyclist accidents on one hand and roundabout geometry, age and traffic volume (vehicles and cyclists) on the other. We related all roundabout cyclist accidents recorded by the hospital emergency department of the town of Odense, Denmark, through the years 1999–2003 (N= 171) to various geometric features, age and traffic volume of all roundabouts on the Danish island of Funen (N= 88). Cyclist and vehicle volumes turned out to be significant predictors in most of our models—the higher the volumes, the more accidents. Moreover, potential vehicle speed was a significant predictor, and so was age of the roundabout—older roundabouts related to more accidents and higher accident probability. Excluding 48 single cyclist accidents strengthened the relationship between accidents on one hand and vehicle and cyclist volume and potential vehicle speed on the other. This stresses the significance of speed and traffic volume for traffic accidents with more than one partner involved. The 48 single cyclist accidents were significantly related to the traffic volume of cyclists only. Due to our limited number of observations, the models should be regarded as indicative.

Keywords: Roundabout; Cyclist accident; Geometry; Speed

1. Introduction

Roundabouts are popular. During the latest 20 years, more and more intersections have been converted to roundabouts, both in Europe (e.g. Britain: Brown, 1995, Denmark: Jørgensen and Jørgensen, 1994, Finland: Ras¨ anen and Summala, 2000 ¨ , Sweden: Brude and Larsson, 2000 ¨ , Switzerland: Huber, 1995, The Netherlands: Schoon and van Minnen, 1994, France: Guichet pers. com.) and in the US, although the development in the US has come later than in Europe (Perseaud et al., 2001; Flannery, 2001). The advantages of roundabouts as compared to intersections concern two aspects: safety and mobility. Safety: roundabouts produce slowed and smooth traffic flows with few stops and no left turns in front of left coming traffic in countries where traffic drives on the right. Mobility: roundabouts have a larger capacity than give way intersections and signalised junctions due to the fact that left turns are omitted (Elvik and Vaa, 2004). Elvik and Vaa (2004) have reviewed 34 studies from Northern Europe, Australia and the US evaluating the effect on accidents

The aim of this study was to identify reasons for the relatively higher prevalence of cyclist accidents in Danish roundabouts compared to intersections (Herslund and Jørgensen, 2003). Our primary aim was to find relations between the number of cyclist accidents in roundabouts and the geometric features of a roundabout, its age and traffic volume (vehicles as well as cyclists).

of converting an intersection into a roundabout. They find a mean reduction in injury accidents of 10 to 40%. Generally, the reduction in serious injury accidents is larger than that in less serious injury accidents, while property damage only accidents typically increase in number, although this effect is highly uncertain. Roundabouts, however, do not have the same positive effect on the number of cyclist accidents (Schoon and van Minnen, 1994; Jørgensen and Jørgensen, 1994). There may be more than one explanation to this. Firstly, a roundabout represents a more challenging orientation task for all road users than an ordinary junction because of the circular design. This may increase the probability of orientation failure and the risk of accidents. Secondly, passing through a roundabout is physically more demanding due to the circular deflection of the road. This may increase the number and proportion of one-cyclist accidents.

^∗ Corresponding author. Tel.: +45 45 25 65 00; fax: +45 45 93 65 33. E-mail addresses: ths@dtf.dk (T. Hels), iob@dtf.dk (I. Orozova-Bekkevold).

Variables recorded for the 88 roundabouts the number of bicycle accidents is the dependent variable, the rest are the independent variables
Variable (NAME)	Type of variable	Range	Mean/median	N
Number of legs (LEGS)	Numeric, discrete	2–6	Median: 4
Diameter of central island (ISLAND)	Numeric, continuous	5–53 m	Mean: 19.0 m	85
Circulatory roadway width (CIRC)	Numeric, continuous	4–15 m	Mean: 6.4 m	86
Apron width (APRON)	Numeric, continuous	0–6 m	Mean: 1.6 m	84
Drive curve (DRIVCURV)	Numeric, continuous	9–40 m	Mean: 21 m	62
Cyclist facility (CYCFAC)	Binary	0 (no), 1 (yes)	–	81
Traffic volume of cyclists (CYCLISTS)	Semi-quantitative	1 (≤1000/day), 2 (>1000/day)	–	60
Traffic volume of vehicles (VEHIC)	Numeric, continuous	1100–24,500/day	Mean: 7200	69
Year of construction (CONSTRYEAR)	Numeric, discrete	1981–2004	Median: 1996	80

Location (urban or rural zone) (ZONE) Qualitative Urban, rural, urban/rural – 88 Number of bicycle accidents in each roundabout Numeric, discrete 0–29 Median: 1 152

Table 1 Variables recorded for the 88 roundabouts the number of bicycle accidents is the dependent variable, the rest are the independent variables

Secondly, we wanted to clarify the types and prevalence of various cyclist accidents. Thirdly, our aim was to quantify the degree of underreporting of cyclist accidents (cyclist accidents recorded by the police compared to the cyclist accidents recorded by the hospital emergency department).

1.1. Hypotheses

The main hypotheses of this study were:

The number of accidents with cyclists in a roundabout increases with increasing of the traffic volume of cyclists and vehicles.
Roundabout geometry, which allows higher speed of the vehicles leads to higher number of cyclist accidents.
Existence of a cyclist facility makes the roundabout safer for cyclists if the traffic volume of vehicles is high.

2. Data

The data set consisted of data on cyclist accidents and data on geometric features, age and position of the roundabouts, besides the daily number of vehicles and cyclists entering the roundabouts (measured per 24 h).

The cyclist roundabout accidents were recorded in two different ways: by the police and by the emergency department of the hospital in Odense, Funen, in Denmark. Accidents involving cyclists between the years 1999 and 2003 on the Danish island of Funen were used.

For all roundabouts at the island of Funen (N= 88) the following features were recorded (abbreviated variable name in parentheses, cf. Table 1):

The number of legs was recorded from digital maps and from construction maps of the roundabouts. The diameter of the central island, the circulatory roadway width and the apron width were all measured from construction maps of the roundabouts. If there was a cyclist facility, this was not considered part of the circulatory roadway. The drive curve was measured from construction maps according to CROW, 1998 (cf. Fig. 1):

$$D = \frac{(0.25 \times L)^2 + (0.50 \times (U+2))^2}{U+2},$$ (1)

where D (in m) is the drive curve (R on Fig. 1), and L and U can be seen from Fig. 1. Drive curve was measured for symmetrical roundabouts only (N= 62). In these roundabouts, drive curves were the same for all directions. The drive curve variable is a proxy for potential vehicle speed through roundabout in that it is a measure of how much deflection is needed over a given distance to pass through the roundabout. The drive curve was considered a continuous variable.

Information on the existence of a cyclist facility was provided by the road authorities, i.e. the municipalities (N= 46), the county of Funen (N= 38) or in the four cases of large roundabouts, the Danish Road Directorate. Any kind of cyclist facility was considered to have equal potential impact on cyclist accidents. Traffic volume of cyclists was assessed by the road authorities as the total number of cyclists riding into the roundabout per 24 h. The number was placed into an ordinal scale: 1: 0–250, 2: 250–500, 3: 500–1000, 4: 1000–2000 and 5: above 2000. The traffic volume of vehicles was counted by the road authorities as the total number of ingoing vehicles per 24 h in the roundabout. The traffic volume was counted in different years; in order to compare the numbers directly, they were all standardised to year 2001-numbers. This standardisation was done by calculating the development in the total number of kilometres driven by motor vehicles in Denmark. In 2002 the

Fig. 1. A sketch of a roundabout showing the measures necessary for the calculation of the drive curve. After CROW (1998).

number of kilometres driven equalled 1.22 times the number of kilometres driven in 1992 (source: Danish Road Directorate: http://www.vd.dk), corresponding to a yearly increase by 1.02. This factor was then used—either to multiply or to divide traffic volume numbers from years other than 2001 to standardise them to 2001-numbers. The construction years of the roundabouts were provided by the road authorities and was considered a discrete variable with values ranging from 1981 to 2004 (cf. Table 1). The location of the roundabouts (urban surroundings, country surroundings or a combination) was found on digital GIS-maps and was considered a class variable.

3. Data analysis

The goal of the analysis was to explain as much variation as possible in the number of cyclist accidents in the roundabouts by the independent variables mentioned above. We have used a

Table 2 Number of roundabouts and cyclist accidents in the various categories

| Variable | Category |------------------------|------ | LEGS (no.) | 2–3 | | 4 | | 5–6 | Total | | | | ISLAND (m) | 0–10 | | 10–20 | | 20–30 | | 30–40 | | 40–50 | | 50–60 | Total | | CIRC (m) | 4–8 | | 8–12 | | 12–16 | Total | | APRON (m) | 0–2 | | 2–4 | | 4–6 | Total | | | | DRIVCURV (m) | 9–20 | | 20–30 | Total | 30–40 | | | CYCFAC | 0 (no) | | 1 (yes) | Total | | CYCLISTS (no. per day) | <1000 | | ≥1000 | Total | | VEHIC (no. per day) | 0–5000 | | 5000–10,000 | | 10,000–15,000 | | 15,000–20,000 | | 20,000–25,000 | Total | | | | CONSTRYEAR | Total | | | | ZONE | Urban | | Rural | | Urban/rural | Total | | Number of
roundabouts | Number of emergency
department recorded accidents | | ------------------|--------------------------|------------------------------------------------------|--| | 24 | 18 | | | 59 | 108 | | | 5 | 26 | | | 88 | 152 | | | | | | | 10 | 5 | | | 34 | 96 | | | 26 | 21 | | | 12 | 21 | | | 2 | 9 | | | 1 | 0 | | | 85 | 152 | | | 76 | 116 | | | 7 | 35 | | | 3 | 0 | | | 86 | 151a | | | 46 | 111 | | | 36 | 40 | | | 2 | 0 | | | 84 | 151a | | | | | | | 28 | 30 | | | 28 | 53 | | | 6
62 | 49
132a | | | | | | | 19 | 18 | | | 62 | 129 | | | 81 | 147a | | | 46 | 28 | | | 14 | 87 | | | 60 | 115a | | | 23 | 19 | | | 34 | 45 | | | 7 | 19 | | | 4 | 50 | | | 1 | 0 | | | 69 | 133a | | | | | | | 1981–1995
1996–2004 | 38
42 | 108
37 | | | 80 | 145a | | | | | | | 60 | 132 | | | 10 | 2 | | | 18 | 18 | | | 88 | 152 | |

Categorisation of the continuous variables is arbitrary and only serves the purpose of giving an overview of data.

^a There are 152 cyclist accidents registered by the emergency department for which the location is known. Some of the totals are less than 152; this is because the rest of the accidents took place in roundabouts where the variable in question was not recorded.

Poisson model with the formal expression:

$$\log(y) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_n x_n + \varepsilon, \tag{2}$$

where y is the dependent variable (number of accidents per year after the construction of the roundabout), *x*1, ..., xn denote the independent variables mentioned above, and β0, ..., βⁿ are coefficients scaling the variables. Binary variables (e.g. existence of a cyclist facility) are given the value of one when a cyclist facility is present and 0 otherwise. Ordinally scaled variables are given a separate coefficient for each level of the variable. One level is set to be the reference level with a coefficient equal to 0. ε is the variation in the dependent variable not accounted for by the model.

However, because of the limited number of roundabouts, building a complete model and subsequently eliminate insignificant variables was not possible. Therefore, we adopted a different strategy: We checked each independent variable separately for significance and eventually put the significant variables together into a model. Proc GENMOD (SAS 9.1) was used to quantify the coefficients and the significance of the independent variables (F-tests). In order to save degrees of freedom, the categorization of the variables LEGS, CYCLISTS and CONSTRYEAR was slightly changed (cf. Table 2):

LEGS. Three categories were used: category 1: two to three legs, category 2: four legs and category 3: five to six legs.

CYCLISTS. Instead of five categories, two were used: above and below 1000 cyclists per 24 h.

CONSTRYEAR. Two categories were established: 1: 1981– 1995 and 2: 1996–2004.

Secondly, we built a logistic regression model where the dependent variable instead of being the number of cyclist accidents as above, was the probability of a cyclist accident taking place given certain values of independent variables. The same categories for variables LEGS, CYCLISTS and CONSTRYEAR as mentioned above, were used in the logistic regression analyses.

A logistic relation is described by the general formula:

$$P(y) = \frac{\exp(y)}{1 + \exp(y)},\tag{3}$$

where P(y) denotes the probability of an event, and log(y) is a linear expression of x, given in Eq. (2) (Hosmer and Lemeshow, 1989). The model building strategy was the same as for the Poisson model given above. Proc LOGISTIC (SAS 9.1) was used to quantify the coefficients and the significance of the independent variables (goodness of fit-tests).

Table 3 Details of Poisson models including one variable at a time

Variable	Poisson regression univariate analyses					Logistic regression univariate analyses
	N	d.f.	F	P	Parameter estimate	χ2	P	Parameter estimate	Odds ratio estimate
LEGS	75	2	2.89	0.06	Int.: 0.26 Cat. 1: −2.01 Cat. 2: −1.07 Cat. 3: ref.	0.36	0.83	Int: 4.5 × 10−16 3: −0.20 4: 0.12 5: ref.	Legs 3 vs. 5: 0.82 Legs 4 vs. 5: 1.13
DIAMETER	74	1	0.21	0.65	Int.: −1.08 0.71 0.40 Diameter: 0.01		Int: 0.46 Diameter: −0.02	Island: 0.98
CIRC	75	1	2.41	0.13	Int.: −2.04 0.28 0.60 Circ: 0.18		Int: 0.49 Circ: −0.07	Circ: 0.93
APRON	73	1	6.52	0.01	Int: −0.28 2.75 Apron: −0.42		0.10	Int: 0.59 Apron: −0.30	Apron: 0.74
DRIVCURV	55	1	32.95	0.0001	Int: −3.78 Drivcurv: 0.13	3.97	0.05	Int: −1.95 Drivcurv: 0.10	Drivcurv: 1.11
CYCFAC	70	2	1.81	0.18	Int: −0.69 0: −0.96 1: ref.	2.00	0.16	Int: 0.29 0: −0.88 1: ref.	Cycfac 0 vs. 1: 0.42
CYCLISTS	53	2	33.89	0.0001	Int: 1.81 ≤1000: ref. >1000: 2.17	6.02	0.01	Int: −0.45 <1000: ref. >1000: 2.06	Cyclists > 1000 vs. ≤ 1000: 7.81
VEHIC	63	1	19.71	0.0001	Int: −2.04 Vehic: 0.0001	2.21	0.14	Int: −0.60 Vehic: 9.4 × 10−5	Vehic: 1.00
CON-STRYEAR	75	1	2.70	0.10	Int: −1.33 1: 0.76 2: ref.	4.70	0.03	Int: −0.50 1: 1.04 2: Ref.	Constryear 1 vs. 2: 2.82
ZONE	75	2	2.67	0.08	Int: −3.81 Urban: 3.17 Urban/rural: 2.63 Rural: ref.	4.64	0.10	Int: −2.08 Urban: 2.37 Urban/rural: 2.20 Rural: ref.	Urban vs. rural: 10.67 Urban/rural vs. rural: 9.00

Table 4 Details of the multiple Poisson model including all significant variables from the single-variable models

Variable	d.f.	F	P	Coefficient estimate	P
INTERCEPT	1	–	–	−3.23	0.0001
CYCLISTS	2	3.86	0.028	≤1000: ref.	ref.
				>1000: 1.28	0.0045
VEHIC	1	3.68	0.062	0.00006	0.057
DRIVCURV	1	6.50	0.014	0.06	0.010

N= 50. Poisson regression analyses at left, logistic regressions at right.

Since we have data only on accidents in the period 1999–2003, roundabouts constructed in 2003 and 2004 (N= 5) were excluded from the regression analyses.

Both Poisson and logistic regression models were built with and without single cyclist accidents. Finally, logistic regression models were built with single cyclist accidents alone.

4. Results

All roundabouts at the island of Funen were included in the analysis. Details on the variables describing them are summarised in Tables 1 and 2.

A total of 171 accidents involving cyclists were recorded by the emergency department of the hospital of Odense through the period 1999–2003, 152 of which were unambiguously assigned to a given roundabout. Only 42 of these 171 cyclist accidents were recorded by the police. Of the 171 accidents recorded by the emergency department, 69 (40%) were one-cyclist accidents; of these, 48 were unambiguously assigned to a given roundabout. Almost half of the accidents (i.e. 81, equal to 47%) were vehiclefailed-to-give-way-accidents; in 57 accidents the vehicle hit a circulating cyclist on its way into the roundabout; in 24 accidents the vehicle was about to leave the roundabout when it hit the cyclist. The rest of the emergency department cyclist accidents (21 equal to 13%) were of various kinds – e.g. cyclists hitting each other – or insufficiently described.

The pattern of the 42 accidents recorded by the police in the same roundabouts in the years 1999–2003 was similar to the one above except that the one-cyclist accidents were fewer, namely no more than two accidents (equal to 5% of the recorded). Vehicle-failed-to-give-way-accidents had a higher proportion: 34 were recorded, equal to 81%. Of these, in 22 accidents the vehicle hit a circulating cyclist on its way into the roundabout; in 12 accidents the vehicle hit the cyclist on its way out of the roundabout. Six of the accidents (14%) contained too little information to be categorized.

In the univariate Poisson model drive curve, apron width and traffic volume of cyclists and of vehicles significantly explained the variation in the number of cyclist accidents per year in the roundabouts (Table 3). More cyclist accidents per year were connected to roundabouts with a narrow apron, a large drive curve and with high volumes of cyclists and vehicles. The existence of a cyclist facility did not significantly explain the variation in the number of cyclist accidents, and neither did the number of legs. There was a trend for roundabouts with more legs to have more cyclist accidents. Just about the same variables were significant in the univariate logistic regression analysis. The probability of an accident was significantly positively related to the number of cyclists and to the age of the roundabout: the older the roundabout, the higher the probability of a cyclist accident. Like in the Poisson models, there was a higher accident probability connected to roundabouts with a small apron (non-significant) and a large drive curve (significant).

In the multiple models the explanatory variables from the univariate analyses were put together into the same model to correct for each other. In Tables 4 and 5 are reported the coefficients and odds ratios only for the significant variables. In doing this, it turned out that apron width was not a significant predictor of the number of accidents in the linear model, whereas cyclist and vehicle volume and drive curve still were. In the multiple logistic model, the drive curve was significant, the number of cyclists was only an insignificant trend whereas construction year was close to being significant, the older roundabouts related to the higher accident probability.

Excluding 48 single cyclist accidents from the analyses did not qualitatively change the outcome of the univariate or the multiple Poisson models. However, it did somewhat change the results of the logistic regression analysis. The significant variables (i.e. the number of cyclists and the age of roundabout) became more significant (P = 0.001 and P = 0.004, respectively). Moreover, apron, drive curve and traffic volume of vehicles changed from insignificant to significant (P-values 0.03, 0.03 and 0.03, respectively). In the multiple logistic model, traffic

Table 5 Details of the multiple logistic model including all variables that were significant in the single-variable models

Variable	d.f.	χ2	P	Coefficient estimate	Odds ratio estimate	95% confidence limits
INTERCEPT	1	5.91	0.02	−4.80	–	–
CONSTRYEAR	1	3.94	0.05	1.60	1 vs. 2: 4.95	1.02–23.99
DRIVCURV	1	5.24	0.02	0.22	1.24	1.03–1.50

Table 6 Details of the multiple logistic model excluding single cyclist accidents

Variable	d.f.	χ2	P	Coefficient estimate	Odds ratio estimate	95% confidence limits
INTERCEPT	1	10.23	0.001	−2.25	–	–
CONSTRYEAR	1	8.36	0.004	1.68	1 vs. 2: 5.38	1.72–16.84
VEHIC	1	4.33	0.04	0.00015	1.00	1.00–1.00

N= 63. For simplicity, variables which showed insignificant effect were omitted from the table.

volume of vehicles stayed in the model instead of drive curve (Table 6).

Analysing the 48 single cyclist accidents in the 88 roundabouts separately revealed very few significant relations to the recorded independent variables. Thus, only drive curve and traffic volume of cyclists turned out to be significantly related to the probability of single cyclist accidents in a roundabout, for both variables in a positive way (N= 55, P = 0.03 and N= 53, P = 0.004, respectively). The significance of the drive curve disappeared in a multiple logistic model containing these two variables.

5. Discussion

The 88 roundabouts included in this analysis differ considerably, both in terms of geometry and traffic volumes. All of them are built in the speed-reducing way with legs more or less perpendicularly radiating from the circulatory roadway as opposed to the dynamic design that gives the roundabout a higher capacity but is not recommended where there are many cyclists (Jørgensen and Jørgensen, 2002).

Single-cyclist accidents were the type of accident most seriously underreported by the police, i.e. only 3% of this type of accident gets reported by the police. This was expected due to the nature of these accidents, since in single-cyclist accidents there are no conflicting interests for the involved partner regarding insurance matters, and the cyclist – if seriously injured – probably goes straight to the emergency department without contacting the police. It is highly likely that the number of single-cyclist accidents is vastly underreported by the emergency department as well, since most cyclists – if not seriously injured – probably go home after such an accident and then, if needed, later consults his or her general practitioner.

About 75% of the cyclist accidents recorted by the hospital were not found in the police reports. In a comparable Danish study (Bach, 2004) the author found that cyclist accidents were by far the most underreported group of accidents since the percentage of reported cyclist accidents is only 5% of the actual number.

A large part of the accidents were vehicle-failed-to-give-wayaccidents. This is in accordance with other findings (Alphand et al., 1991; Jørgensen and Jørgensen, 2002). Some or all of these may be what is also described as looked-but-failed-to-seeaccidents (Hills, 1980). In this type of accident the cyclist usually reports the driver to have looked at him but then moves on as if the cyclist was not there. Herslund and Jørgensen (2003) have examined this type of accident closely and concluded tentatively that the drivers' visual search strategy and/or mental processing somehow fails, so the driver sees but does not perceive the cyclist.

As a rule of thumb when building causal regression models, the number of observations must be about ten times the number of independent variables, including the number of levels of the semi quantitative variables. This is to ensure a fair number of observations in all categories. With a limited amount of data (i.e. 171 accidents distributed over 88 roundabouts) building models with a method like backwards elimination would clearly violate this rule. Therefore, we started out constructing univariate models to get an indication of the significance of the various variables. Later the explanatory variables were put together into multiple models to quantify the effects of the variables when correcting for other significant variables. The models developed here must be seen only as indicative due to the limited number of observations.

When working with discrete data such as counts, the most used distributions are the Poisson and the binomial distributions. The negative binomial distribution also provides a good model for discrete data, and it can be derived from the Poisson distribution by providing a prior distribution to the mean. We decided to use a Poisson instead of a negative binomial distribution since Poisson provides a good model for our data and does not require a prior distribution (which means additional assumptions) for the mean.

Many of the same explanatory variables turned out to be significantly related to the number of accidents and to the predicted accident probability (Poisson and logistic regression, respectively). It seems intuitively obvious that traffic volume is an important predictor of the number of accidents. We found significantly positive relationships between the number of cyclists and the number of accidents per year after construction of the roundabout as well as accident probability—a relation that was strengthened by excluding single cyclist accidents. By relating the original five class ordinal scale for cyclist traffic volume to the number of cyclist accidents and cyclist accident probability, it became evident that there was a significant increase in both the number of accidents and the accident probability at 1000 cyclists/day. Other authors have found positive relationships between the number of cyclists and the number of accidents as well (Schoon and van Minnen, 1994; Brude and Larsson, 1997, 2000 ¨ ). In most other investigations of cyclist safety in roundabouts, traffic volume of cyclists is not included. In cases where it is included, the relation turns out to be like the one we found: the more cyclists, the more cyclist accidents. Ekman (1996) suggested that even if the number of accidents increases with increasing number of cyclists, accident risk per cyclist is higher for low cyclist volumes. Unfortunately, our data does not allow calculating accident risk per cyclist because the number of cyclists is recorded on a semi quantitative scale.

According to the literature the relation between vehicle volume and number of cyclist accidents is clearly positive (Layfield and Maycock, 1986; Schoon and van Minnen, 1994; Brude and ¨ Larsson, 2000; Perseaud et al., 2001; Elvik, 2003; Alphand et al., 1991). This was confirmed by our models. In the logistic regression models the relation between accident probability and vehicle volume was strengthened considerably, not surprisingly, by excluding single cyclist accidents. In doing so, focus was put on accidents involving cyclists and vehicles, which is probably why vehicle volume turned out to be more significant. Refined models usually fit a levelling off of number of accidents per circulating vehicle for large vehicle volumes. We, however, regard our models indicative due to the limited amount of data.

Speed of the circulating vehicles has an intuitively obvious impact on accident risk; the speed also has a very high impact on the severity of the potential injury. We used a measure of deflection related to the length of the road deflected as a proxy for potential vehicle speed through the roundabout (i.e. drive curve). This measure turned out to be positively related to the number of cyclist accidents. A positive relation between vehicle speed and the number of cyclist accidents is also found by Brude ¨ and Larsson (2000) who measured speed of entering, circulating and exiting vehicles directly.

Excluding single cyclist accidents also strengthened the positive relation between the traffic volume of cyclists and the probability of cyclist accidents. Overall, the probability of cyclist accidents turned out to be high in older roundabouts with high vehicle volumes. These are roundabouts often situated in the town centres where the cyclist volume is high, too. The location of the roundabouts is probably more important than its age, but since the location was not recorded accurately enough, age became a significant predictor of accident probability.

Of the geometric features recorded, surprisingly few had any relation whatsoever to the number of cyclist accidents or cyclist accident probability. The effect of a cyclist facility on cyclist accidents was investigated by Schoon and van Minnen (1994). In their much cited paper they found no effect on the number of accidents of a cyclist facility in roundabouts with vehicle volumes below 8000 vehicles/day. Above 8000 vehicles/day, however, they recommended construction of cycle paths completely separated from the circulatory roadway. Jørgensen and Jørgensen (2002) did not find a difference in number of cyclist accidents with different types of cyclist facilities (no facility, cycle lane, white markings on the asphalt) or cycle path (not separated from the circulatory roadway). We did not find a relation between the existence of a cyclist facility (0/1-variable) and the number of cyclist accidents or cyclist accident probability, but it might be due to the limited amount of observations, and it does not necessarily mean that there is no relation. In Denmark roundabouts without cyclist facilities tend to be rare, and in our data set we have only 19 of them. Moreover, in our data set we have different kinds of cyclist accidents lumped together due to the relatively small number of observations. It may be that the number of, e.g. vehicle-failed-to-give-way-accidents is related to the existence of a cyclist facility whereas other types of accidents are not.

Excluding the single cyclist accidents strengthened the significance of the relation between drive curve, apron width and cyclist accident probability considerably. This stresses the connection between potential speed of vehicles and accident probability in accidents with more than one partner involved.

According to our results, the probability of single cyclist accidents is apparently related to the number of cyclists entering the roundabout, only. As it turns out, the geometric features recorded in these particular roundabouts do not pose a challenge to bicycle riders. A look at the verbal descriptions of the single cyclist accidents reveals that single cyclist accidents often happen in situations where cyclists collide with the kerb or permanent installations like lamp posts, where cyclists are driving under influence and fall over, where the road is slippery due to winter weather conditions and/or where the cyclist fails at manoeuvring the bicycle properly, e.g. by braking too hard.

One of the limitations of our study is clearly the relatively small number of observations, all of which were collected on the island of Funen. Another limitation, which is a general problem all over, is the high percentage of underreporting of cyclist accidents. Clearly, a larger database is needed, both concerning roundabouts and number of accidents, in order to construct a reliable statistical model. Until then, our results may serve as preliminary ones.

Acknowledgements

We thank Lars Binderup-Larsen, consultant orthopaedic surgeon, for a great help in extracting relevant data from the databases of the Accident Analysis Group of the Odense University Hospital. Moreover, we thank all employees of the road authorities who provided us with invaluable information: The Danish Road Directorate, The County and the Communities of Funen. This work was supported by a grant from the Danish Ministry of Transport and Energy.

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