---
category: literaturenote
citekey: calvimodelingspeeddifferentialparameters2014
title: Modeling Speed Differential Parameters in Day and Night Environments Using Driving Simulator
authors: "Calvi, Alessandro; Bella, Francesco"
year: 2014
date: 2014-01-01 2014-01-01
doi: 10.1016/j.proeng.2014.10.482
publication: Procedia Engineering
url: "https://www.sciencedirect.com/science/article/pii/S1877705814018037"
zotero_key: U336I7C3
zotero_storage: 7F7RBKCL
collections: imporditud
folder: 001_artiklid
firstAuthor: "Calvi, Alessandro"
status: converted
---
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# Available online at www.sciencedirect.com

# **ScienceDirect**

Procedia Engineering 84 ( 2014 ) 648 – 661

"2014ISSST", 2014 International Symposium on Safety Science and Technology

# Modeling speed differential parameters in day and night environments using driving simulator

Alessandro CALVI\*, Francesco BELLA

*Department of Engineering, Roma Tre University, Via Vito Volterra, 62, 00146 Rome, Italy*

#### **Abstract**

The study presented in this paper is aimed at analyzing the drivers' speed profiles for the evaluation of speed differentials parameters (85MSR, 'V85 and '85V) during day and night driving. Speed differential parameters are commonly used for design consistency evaluation, according to an advanced approach of road engineering, based on the study of the roadway's conformance to driver expectancy that can improve road safety performance. The research was carried out using a driving simulator where a section of 10 km of an existing two-lane rural road composed by 39 tangent-curve configurations was implemented. The speed profiles of 40 drivers were recorded both in simulated daylight and nightlight driving conditions. The study proposes new relationships between speed differential parameters for different visibility condition and geometries of tangent-curve configurations and increases the actual knowledge of driver's speed choices and driving behaviour under nighttime conditions. Specifically, results demonstrate different relations between speed differential parameters among four different classes of tangent-curve geometries and under day and night driving conditions. Relations are also compared with the main literature models that correlated speed differential parameters.

© 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of scientific committee of Beijing Institute of Technology. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

*Keywords:*driving simulator; speed differential measures; design consistency; road safety Peer-review under responsibility of scientific committee of Beijing Institute of Technology

#### **1. Introduction**

In the last decades the road engineering has turned from an approach based on the design of a single geometric element (tangent, slope, vertical and horizontal curve) to an approach that evaluates systematically the coherence

<sup>\*</sup> Corresponding author. Tel.: +390657333451; fax: +390657333441. *E-mail address:*alessandro.calvi@uniroma3.it

among the geometric elements of a road alignment: this approach is called design consistency, commonly defined as the roadway's conformance to driver expectancy. The evaluation of design consistency is one of the most effective tools that a highway designer should consider to improve roadway safety performance. According to Fitzpatrick [1], a design inconsistency in a roadway indicates a geometric feature or features that violate driver expectancy, as an abrupt change in roadway geometry. It may surprise the drivers by violating their expectancies and increase the possibility of speed errors, delayed response times and unsafe driving maneuvers with the final consequence of an increased level of crash risk.

In literature there are many criteria that evaluate design consistency, but the most effective seem to be those based on the evaluation of operating speeds and speed differentials between successive elements of the alignment, assumed to be effective parameters for identifying anomalous interaction between road and driver. Several studies [2–5] proposed different speed differential parameters but only 'V85 was successfully correlated with actual road crash rates using linear regression models [2]. At the same time, 85MSR (Maximum Speed Reduction) is commonly acknowledged as the most effective measure for design consistency and road safety [5–10] as it best mirrors the driver's need for changing speed driving along a road segment composed by a tangent and a curve.

Some researchers compared speed differential parameters and proposed several relations that could be considered valid only for the case studies investigated that are different among studies and cover a small sample of road geometries and conditions. Therefore they can not be generalized and used for safety purposes.

Moreover it should be added that traditionally all the studies on design consistency evaluation and comparisons among speed differential measures are based on speed recorded under daytime conditions and there are no literature studies on speed evaluations during night driving, when visibility conditions are different from the driver's road vision during day driving. As a consequence using such evaluation procedures by day or by night provide different results, as demonstrated by previous studies [8,9]. An improvement of the knowledge of driving performance and specifically driver's speed under nightlight condition is more than needed as confirmed by accident statistics (e.g. [11,12]) and several studies (e.g. [13–15]) that demonstrated that road crash consequences and rates increased during night time.

This study is aimed at analyzing the driver speed behavior during simulated day and night driving along different tangent-curve configurations to find and propose new relations between speed differential parameters over a wide sample of geometries under different visibility conditions. The research is carried out using a driving simulator. There are several acknowledged advantages using driving simulators for the evaluation of driving performance: simulators provide objective measurements of driving performance in a safe environment also evaluating driving performance under hazardous driving tasks which would be impossible on an open road experiment; several confounding variables can be controlled in virtual environment contrarily to what could be done in naturalistic driving; driving conditions and situations can be identically repeated for each participant.

The overall objective of the present work, that starts from the results of two recent studies of Bella and Calvi [8] and Bella et al. [9], is to compare the drivers speed differential measures in simulated day and night driving for different geometries of tangent-curve configurations and propose new relations between them that could be used for design consistency and road safety evaluations.

For this purpose a real two-lane rural road, characterized by high accident rate during night time, was implemented in the Inter-University Research Centre of Road Safety (CRISS) driving simulator and the driver behavior of a large sample of participants was recorder in daytime and nighttime conditions.

#### **2. Literature Background**

#### *2.1. Design consistency evaluation*

In literature several approaches and models for evaluating and computing the design consistency are suggested (e.g. [16]). The most shared and consolidated parameters for design consistency assessment are based on operating speeds and speed differentials, vehicle stability, alignment indices and driver workload.

The operating speed is defined as the speed selected by drivers under free-flow conditions and it is commonly taken as the 85th percentile speed (V85). The operating speeds and speed differentials between successive elements of the alignment are assumed to be the most effective parameters for identifying anomalous interaction between road and driver and therefore for evaluating design consistency. It will be discussed later in a dedicated section.

Vehicle stability is related to the comparison between side friction available and side friction demanded on a curve. In these terms a design inconsistency involves a violation of driver's expectancy that may determine the inability of drivers to navigate a curve without loss of vehicle control. Lamm et al. [17] developed a design consistency measure for the evaluation of vehicle stability.

Alignment indices are quantitative measures of the geometrical features of a roadway segment. A geometric inconsistency may occur when the general alignment of a roadway changes abruptly and suddenly in adjacent segments. Alignment indices quantify the design characteristics of the roadway geometry that mostly could affect driver perception and behaviour, providing a simple method to measure design consistency.

According to Young and Stanton [18] the mental workload of a task represents the level of attentional resources required to meet both objective and subjective performance criteria, which may be mediated by task demands, external support, and past experience. It means that during a drive everyone allocates mental capacity to the guiding task based on the own estimates of the mental workload conditions ahead. The greater the mental workload estimate, the greater the attention or capacity allocated to the task. Therefore, a consistent roadway design allows the drivers to correctly perceive the road alignment allocating little mental capacity, and thus allows more capacity to be dedicated to obstacle avoidance and navigation. The evaluation of design consistency using mental workload is surely the most appealing method as it provides directly a measure of the impact of roadway on driver's perception and psychophysical condition. However it is rather difficult to quantify the driver workload correctly without obtaining biased results.

Although several studies proposed various criteria to evaluate design consistency, relatively little research has considered the relationship between consistency measures and actual crash rates. The most common of such relationships are the safety criteria recommended by Lamm et al. [2] based on an analysis of speed and collision data using linear regression models (in particular, criterion II based on 'V85). Design consistency is evaluated in relation to the magnitude of reduction in speed between successive design elements using 'V85. Criterion II considers a design "good" if the magnitude of the difference in 85th percentile operating speeds from an approach tangent to a curve ('V85) is less than 10 km/h; a design is "fair" if 'V85 is between 10 and 20 km/h; and a design is "poor" if 'V85 is greater than 20 km/h. Krammes et al. [19] also used linear regression to establish a relationship between mean operating speed reduction ('V85) and the mean collision rate.

# *2.2. Speed differential parameters for road design and safety evaluation*

Notwithstanding 'V85 is acknowledged as the most effective, if not the only, design consistency measure for road safety assessment, some researchers have raised the concern that 'V85 may underestimate individual speed reductions experienced by drivers since it is based on independent speed distributions at each location [20].

Consequently other speed differential measures based on the speed reductions on two successive elements are proposed. McFadden and Elefteriadou[3] suggested a new measure, 85MSR, based on the analysis of the speed profile of individual vehicles from the approach tangent through the horizontal curve. 85MSR is determined as the 85th percentile of the distribution of maximum speed reduction experienced by each driver computed between the maximum speed in the last 200 meters of the approach tangent and the minimum speed in the curve. Misaghi and Hassan [4] proposed '85V, defined as the differential speed under free-flow condition not exceeded by 85% of the drivers. This speed differential parameter is computed on the basis of the speeds adopted by each driver in two fixed locations: at the point on the approach tangent approximately 100 m before the beginning of the curved section and at the midpoint of the curve.

Subsequently Bella [6] showed that the calculation of the speed differential on the basis of the speeds recorded at two fixed locations ('V85 and '85V) leads to an underestimation of the speed differential. Consequently the estimation of the speed differential is significantly affected by data availability in drawing up the speed profile of each driver. Nowadays many researchers agree that 85MSR is one of the most effective indicator for design consistency and road safety [5–9] as it best mirrors the driver's need for changing speed driving along road segment composed by the tangent and curve. The main reason behind this assumption is that, differently from 'V85 and '85V that compute the speed differential value between two fixed locations, 85MSR ensures that the speed differential so computed is the maximum one adopted by drivers between the tangent and the curve.

# *2.3. Relationships between speed differential parameters*

As previously discussed, to provide an evaluation of the safety level of tangent-curve configurations, currently, it is possible to use only the Lamm criteria [2], in particular criterion II, based on 'V85. There are no thresholds or safety ranges in terms of 85MSR or '85V although, above all the first one, they are fully recognized as the most effective parameters of speed differentials and consequently the best parameters for evaluating the consistency and safety of a design.

In literature there are few studies that propose a relationship among different speed differential parameters in order to correlate 85MSR and '85V with 'V85, whose values are used as thresholds for Lamm criteria.

McFadden and Elefteriadou[3] collected vehicle speeds at 21 sites in two different US geographic regions. The sites were selected on the basis of several criteria with the aim of isolating the horizontal curve so that this geometric parameter was the major impact on speed change. The selection criteria included: rural area with level to rolling terrain; design and post speed lower than 120 km/h; lane width between 3.05m and 3.66m; shoulder width from 0 to 2.44m; curve length from 90m to 250m; degree of curvature ranged between 1 to 15 degree; curve radius ranged between 150m and 1800m; tangent length longer than 200m; grade ranged between -5% and 5%; traffic volume from 500 to 4000 vehicles per day. The authors compared 85MSR and 'V85 among the sample of tangent-curve configurations. The results demonstrated a significant difference between the two speed differential measures. Specifically they found that, on average, 85MSR was two times greater than 'V85. Therefore, if one used the existing operating speed models that evaluate consistency based on the difference in 85th percentile speeds to determine the amount of speed reduction experienced by 85 percent of the drivers for a site, one should multiply the expected 85th percentile speed reduction by two according to Equation (1):

$$85MSR = 1.97 \cdot \Delta V_{85} \tag{1}$$

Park and Saccomanno [5] found the empirical relationship between 85MSR and 'V85 reported in Equation (2):

$$85MSR = 1.595 \cdot \Delta V_{85} \tag{2}$$

The authors recorded field data of individual vehicles speeds from 18 tangent-curve configurations of two lane rural highway segments. The site selection criteria included a number of factors: level terrain with vertical grade less than 4%; daytime; good weather conditions (dry surface, unlimited visibility); only passenger vehicle speeds at headways greater than 10 s. On average, the estimated results of 85MSR were found to be approximately 1.6 times greater than the estimated results for 'V85 for the same dataset. Even though this value is slightly lower than that obtained by McFadden and Elefteriadou[3], the results are consistent in showing that 85MSR yields higher values than 'V85 for tangent-curve transitions.

Misaghi and Hassan [4] compared '85V and 'V85 on 20 tangent-curve configurations characterized by various geometric features (horizontal curve radius, length, vertical grades, etc.). The sites were selected on four different two-lane rural highways. Although no selection conditions were related to the maximum grade, several constraints were imposed for the selection of curve sites, according to previous studies: rural area; relatively low traffic volume (average annual daily traffic, AADT, lower than 10000 vehicles per day); marked and paved roadways with constant lane width; no stop-controlled or signalized intersections within 0.8 km of curve; no features that may create abnormal hazard (e.g., narrow bridge); curve radius greater than 1200 m and total curve length longer than 100 m.

The authors found the following empirical relation between '85V and 'V85(Equation (3)):

$$\Delta_{85}V = 0.97 \cdot \Delta V_{85} + 7.55 \tag{3}$$

Bella [6] reproduced a two-lane rural road in a driving simulator (the same tool used in the study presented in this paper) for evaluating speed differential parameters over a flat alignment of 30 km, characterised by the following geometries: 10.50 m wide cross section; lane widths of 3.75 m and shoulder widths of 1.50 m; 16 tangent-curve configurations with tangent length ranged between 150 m and 600 m and curve radius ranged between 340 m and 800 m; the curve length varied between 164 m and 680 m. The experiment was performed on dry pavement with the free-flowing vehicle in its own driving lane and in daylight condition. The authors compared 85MSR with 'V85 and '85V and found the following relations reported in Equation (4) and (5) respectively:

$$85MSR = 2.4 \cdot \Delta V_{85} \tag{4}$$

$$85MSR = 1.08 \cdot \Delta_{85}V + 6.35 \tag{5}$$

The fact that 85MSR was 2.4 times higher than 'V85 confirmed previous relations among the two speed differential parameters but with higher difference. In fact, the average value of 85MSR computed among the 16 configurations was 26 km/h (ranged between 7.5 km/h and 44.8 km/h), 11 km/h higher than the average value of 85MSR obtained by McFadden and Elefteriadou[3] (15 km/h, with a minimum of 6.4 km/h and a maximum of 30.6 km/h). The author did not attribute this difference to an inadequate reflection of the speeds in the simulator, but to the great difference of configurations analysed by McFadden and Elefteriadou[3] and those in the study of Bella [6].

#### *2.4. Night driving features*

However all the literature studies on design consistency evaluation, speed differentials computation and correlation, are developed during daytime driving. Only recently few studies provide information about design consistency during night driving. Hu and Donnell [21] modelled driver' deceleration and acceleration rates on a complex two-lane rural highway when drivers were approaching or departing horizontal curves under nighttime driving conditions. Particularly the authors found that the deceleration and acceleration rates approaching and departing horizontal curves during nighttime have a larger range than those in past research studies on the same road typology during daytime.

Bella and Calvi [8] measured the speed differential during simulated nighttime driving for the identification of critical road situations not detected by design consistency evaluation during simulated daytime driving. The authors used CRISS driving simulator to perform the task of the study. The analysis of the speed differential, based on 85MSR, at daytime was not able to identify few critical road situations that the same analysis revealed at nighttime. Such results demonstrated that limiting the speed analysis only to daytime driving conditions can not exclude the possibility that during night driving some road configurations could become unsafe. Later Bella et al. [9] also proposed new predictive speed models, differentiated for daytime and nighttime driving, highlighting the effects of different geometric predictors under different visibility conditions.

As accident statistics (e.g. [11,12]) and several studies (e.g. [13–15]). demonstrate that road crash consequences and rates increased during night time, the study of driving performance under night driving condition should be taken more into account in every step of the design and management of a road, and the knowledge of driver's behavior under such poor conditions of lightness should be improved.

For a wide review of the literature studies on night driving features and safety it is possible to refer to Bella and Calvi [8] and Bella et al. [9].

#### **3. Method**

The experiments are carried out using the advanced driving simulator of the Inter-University Research Centre of Road Safety (CRISS) at Roma Tre University, with the overall aim of evaluating speed differential parameters along different tangent-curve transitions of a two lane rural road, under both day and night environmental driving conditions and proposing different relationships between 85MSR and 'V85 as well as between '85V and 'V85 for all the combinations of geometries and lightness conditions investigated.

#### *3.1. Participants*

Forty drivers are recruited (twenty five men and fifteen women; mean age of 28 years old, range 23-41 years) from students and staff of the Department of Engineering at Roma Tre University. Participants' annual mileage ranged between 3000 km and 20000 km, on average being approximately 9000 km. Participants have obtained their driving license, on average, 9.4 years previously and reported they drove, on average, two times a month on rural roads by night.

#### *3.2. Driving simulator*

The CRISS driving simulator includes a complete vehicle dynamics model, specifically designed for research on road safety. It consists of a real car with a force-feedback steering wheel, brake pedal and accelerator. It is positioned in front of three angled projection surfaces that produced a 135° (horizontal) x 60° (vertical) forward view of the simulated scenario from the driver's position inside the car. Loudspeakers inside the car and a subwoofer in front of the car provide realistic engine and road noise, while speakers around the car create Doppler effects for simulating the noise of on-coming vehicles and thus further enhancing the realism of the driving experience.

The system was widely validated in previous studies [7, 22] and used for evaluating driving performance in terms of speed, acceleration and trajectory under different driving conditions and road environments (e.g. [23–28]).

The data recording system acquires all the parameters of driving performances as position, speed, acceleration and braking at rates up to 20 Hz. All the features of the simulator are designed to enhance the verisimilitude of participants' virtual driving experience in the study in order to ensure the effectiveness and reliability of results.

In this experiment some adjustments to the hardware/software system were needed to reproduce the lightness of the night scenario environment. Consequently the amount of ambient and diffuse lighting affecting the overall scene was set and opportunely calibrated and some filters were applied in front of the projectors to lower the brightness of the surrounding environment, providing more reliable simulated night driving conditions.

It should be noted that CRISS simulator is not yet validated for night driving conditions. It is surely a limitation of the present pilot study and it will be a priority for further studies, although it was already validated on rural roads, especially in terms of speeds, in daytime conditions.

Fig. 1 shows the view of the simulated scene in nightlight condition from the inside of the CRISS driving simulator.

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Fig. 1. A view of the nightlight scenario from the inside of CRISS driving simulator.

#### *3.3. Case study*

The roadway geometry implemented in the simulator was a virtual reconstruction of a two-lane rural road (SP 217 ViadeiLaghi) near Rome, Italy. It was 7 m wide (two lanes 3.50 m wide and no shoulders) with a speed limit of 60 km/h. There was no built-up area in the proximity. Low luminance conditions were observed during nighttime.

Based on the real topographic layout and environment reconstructed by photos, videos and on site investigations, the 3D road scenario included a 10 km section composed of 39 tangent-curve configurations. All the road features (lane width, road markings and signs, sight distances) were implemented in the simulation as well as the landscape layout. The driving conditions were daylight/nightlight, full friction, free vehicle in the right lane and light oncoming traffic on the opposite driving direction to induce the driver to not invade the left lane. According to previous study it was chosen not to simulate heavy traffic or lead vehicles to avoid influencing driver's speed and lateral position and obtain speed profile related only to road geometries. The length of the tangents ranged from 26 to 1312 m, with an average value of 209 m; the radius of curves ranged from 21 to 250 m, with an average value of 68 m; the length of the curves ranged from 11 to 125 m (average length equal to 45 m) and the deflection angle of curve varied from 7 to 83 degrees (average deflection angle of 36 degrees). The longitudinal grade ranged from −4.3% to +5.3%. In Table 1 some information of the geometries of such configurations are provided. Specifically configurations are grouped into 4 different classes according to tangent length (L) and curve radius (R). Fig. 2 shows some views of the real scene and the corresponding simulated environment under daylight and nightlight conditions.

#### *3.4. Procedure*

Upon arrival at the laboratory, each participant was briefed on the experimental procedure and the use of the steering wheel, pedals, and automatic gear. Then participants completed a practice drive (training) to familiarize with the handling of controls in the simulator.

Table 1. Main characteristics of tangent-curve configurations.

| Classes Characteristics      | L≥200m, R≥50m | L≥200m, R<50m | L<200m, R≥50m | L<200m, R<50m |
|------------------------------|---------------|---------------|---------------|---------------|
| # Configurations             | 9             | 5             | 11            | 14            |
| Av. Tangent Length [m]       | 460           | 335           | 89            | 98            |
| Av. Curve Radius [m]         | 106           | 33            | 92            | 36            |
| Av. Curve Length [m]         | 42            | 22            | 51            | 39            |
| Av Deflection Angle [degree] | 21 (7 to 33)  | 55 (44 to 83) | 23 (7 to 33)  | 50 (38 to 79) |
| Lane Width [m]               | 3.50          |               |               |               |
| Shoulder Width [m]           | 0.00          |               |               |               |
| Area Type                    | Rural         |               |               |               |

![](_page_6_Picture_9.jpeg)

Fig. 2. Frames of the real environment (on the left), the simulated road scenario by day (in the middle) and by night (on the right).

Following this, each participant drove both the tests under the two experimental conditions of lightness, with a rest of 1 hour in between to re-establish driver's psychophysical conditions similar to those at the beginning of the experiment. The sequence of the two tests was counterbalanced among participants to avoid influences due to the repetition of the same order in the experimental conditions. Drivers were instructed to drive as they normally would in the real world, maintain a comfortable, reasonable and safe speed according to the road features and stay in the right lane only.

### *3.5. Data collection*

According to Lamm et al. [2] the evaluation of 'V85 is based on the difference between the operating speed on the approach tangent and the operating speed on the following curve. Therefore for each distribution of drivers' speeds along every geometric element of the road alignment the operating speed at the midpoint of the tangent (V85TM) and at the midpoint of the circular curve (V85CM) were determined. To evaluate the other two speed differential parameters (85MSR and '85V), according to their definition ([3] and [4], respectively), other speed values were computed on the basis of the speed profiles continuously recorded by the simulator: the maximum speed on the last 200 m of the approach tangent (VTmax);the speed on the tangent at 100 m before the beginning of the curve (VT100);the minimum speed on the circular curve (VCmin); the speed at the midpoint of the circular curve (VCM).For the approach tangents whose length was shorter than 200 m, the maximum speed recorded on the tangent was considered as VTmax. Moreover for the approach tangents whose length was shorter than 100 m, the speed at the midpoint of the tangent was considered as VT100. Finally, based on the above speed values computed for each test, the design consistency measures (85MSR, '85V and 'V85) for each tangent-curve configuration and for both the daylight and nightlight driving condition were computed according to Equation (6), (7) and (8) respectively:

$$85MSR = 85^{th} percentile_{(V_{T max} - V_{C min})}$$
(6)

$$\Delta_{85}V = 85^{th} percentile_{-}(V_{T100} - V_{CM}) \tag{7}$$

$$\Delta V_{85} = V_{85TM} - V_{85CM} \tag{8}$$

#### **4. Results and Discussion**

Currently the only speed differential parameter effectively related to road crash rate is 'V85, proposed by Lamm et al. [2] that provided safety criteria correlating speed and collision data using linear regression models. The data analysis developed in this study involves a comparison of the three speed differential parameters for evaluating design consistency and proposes new relations between 85MSR and 'V85, and '85V and 'V85. Such relations are firstly presented over the sample of the 39 tangent-curve configurations, differentiated between daylight and nightlight conditions, and then specific relations are provided for each configurations' class presented in Table 1.

#### *4.1. Comparisons between speed differential parameters (over 39 tangent-curve configurations)*

# *4.1.1. 85MSR vs* '*V85*

#### (1) Daylight condition

The first comparison here presented is between 85MSR and 'V85, evaluated through the analysis of the drivers' speed profile performed in daylight conditions. According to all the relations previously found [3,5,6], it is here confirmed that 85MSR has the largest speed reductions when compared with the other parameters. It indicates that the use of 85MSR does yield a significantly different result than 'V85 speed reductions. Therefore 'V85 is confirmed to significantly underestimate individual speed reductions experienced by drivers, as it is based on independent speed distributions at two fixed location instead of considering the speed profile of drivers along tangent-curve transition. Fig. 3 (on the left) shows the comparison between 85MSRDay and 'V85Day evaluated for each one of the 39 configurations during daylight driving condition.

![](_page_8_Figure_3.jpeg)

Fig. 3. 85MSR and 'V85 comparison for daylight (on the left) and nightlight (on the right) driving condition

The relation found is reported in the following Equation (9):

$$85MSR_{Day} = 1.66 \cdot \Delta V_{85Day} \qquad R^2 = 0.76 \tag{9}$$

Results are really similar to that proposed by Park and Saccomanno [5].

#### (2) Nightlight condition

The speed differential parameters computed on the outcome of tests carried out in nightlight conditions allow to propose a new relation between 85MSRNight and 'V85Night that puts in light the relevance of the conditionings of night environment on drivers speed choices, already highlighted in previous studies [8,9]. In fact, it is possible to note the difference between the previous Equation (9) and the following Equation (10) that is valid for nighttime driving:

$$85MSR_{Night} = 1.95 \cdot \Delta V_{85Night}$$
 R<sup>2</sup>=0.69 (10)

Figure 3 (on the right) reproduces the comparison between 85MSRNight and 'V85Night evaluated for each one of the 39 configurations during nightlight driving condition. During nighttime the maximum speed reduction (85MSRNight) returns values proportionally even higher than 'V85Night evaluated under the same condition of visibility. As it will be presented later in the paper, it is confirmed more or less for all the four classes of geometries investigated. The underestimation of 'V85 is therefore even more pronounced under low visibility conditions. Taking into account the speed profile of drivers instead of spot and fixed speed values could provide useful information about the actual driver's difficulties to perceive the road alignment not only in daylight but also in nightlight driving conditions. It is really an important issue as, according to Bella and Calvi [8], limiting the speed analysis only to day driving condition can not exclude the possibility that during night driving some road configurations could become unsafe.

# *4.1.2.* '*85V vs* '*V85*

#### (1) Daylight condition

Similarly '85V and 'V85 are compared in both daylight and nightlight driving conditions. According to Misaghi and Hassan [4], based on the findings of this study and similar to the study by McFadden and Elefteriadou[3], it is possible to conclude that a simple subtraction of operating speeds at the approach tangent and the middle of the curve underestimates the real values of speed differential.

![](_page_9_Figure_3.jpeg)

Fig. 4. '85V and 'V85 comparison for daylight (on the left) and nightlight (on the right) driving condition.

The comparison between '85VDay and 'V85Day evaluated for each one of the 39 configurations during daylight driving condition is shown in Figure 4 (on the left). The relation found in daylight driving is reported in Equation (11):

$$\Delta_{85}V_{Day} = 1.14 \cdot \Delta V_{85Day} \qquad \qquad R^2 = 0.77 \tag{11}$$

It demonstrates that also '85VDay provides speed differential values higher than 'V85Day. It is also visible if we do not fix the origin of the linear regression at the origin of the 'V85Day'85VDaysystem. In this case the relation is reported in Equation (12):

$$\Delta_{85}V_{Day} = 0.97 \cdot \Delta V_{85Day} + 2.51 \qquad R^2 = 0.88 \tag{12}$$

According to Misaghi and Hassan [4], the relation between '85V and 'V85 is almost a straight line parallel to the line representing '85V='V85, with '85V 2.51 km/h greater than 'V85.

#### (2) Nightlight condition

Analyzing speed data in nighttime condition for the comparison between '85VNight and 'V85Night it is confirmed that, under low visibility,'V85 underestimates even more the actual speed differential of drivers along tangent-curve transition. Figure 4 (on the right) reproduces the comparison between '85VNight and 'V85Night evaluated for each one of the 39 configurations during nightlight driving condition. The relation in this case is reported in Equation (13):

$$\Delta_{85}V_{Night} = 1.28 \cdot \Delta V_{85Night}$$
  $R^2 = 0.64$  (13)

Similarly to what done previously, it is possible to note also in this case a vertical translation of '85VNight values in relation with the corresponding values of 'V85Night. The relation is given in Equation (14):

$$\Delta_{85}V_{Night} = 1.01 \cdot \Delta V_{85Night} + 5.35 \qquad R^2 = 0.72$$
 (14)

Results demonstrated that in both cases of visibility it is possible to argue that '85V values can be obtained just adding a constant to the values of 'V85, as previously found by Misaghi and Hassan [4].

# *4.2. Comparisons between speed differential parameters (over 4 geometric classes of tangent-curve configurations)*

In this section the authors propose some relations between 85MSR (or'85V) and 'V85. These relations can be used instead of the general equations previously provided when the geometries of the road alignment correspond to one of the classes here proposed and summarized in Table 1. Although the coefficients of proportionality vary among the cases, the general results are confirmed: the underestimation of speed differential using 'V85 and the higher differences between 85MSR (or'85V) and 'V85 recorded, on average, under nightlight condition than those recorded under daylight conditions.

# *4.2.1. 85MSR vs* '*V85*

#### (1)Daylight condition

Equations (15), (16), (17) and (18) provide the relations between 85MSRDay and 'V85Day for the four geometric classes of the tangent-curve configurations during daylight condition.

L≥200m, R≥50m

$$85MSR_{Day} = 1.55 \cdot \Delta V_{85Day} \qquad R^2 = 0.66 \tag{15}$$

L≥200m, R<50m

$$85MSR_{Day} = 1.87 \cdot \Delta V_{85Day} \qquad R^2 = 0.34 \tag{16}$$

L<200m, R≥50m

$$85MSR_{Day} = 1.37 \cdot \Delta V_{85Day}$$
 R<sup>2</sup> = 0.87 (17)

L<200m, R<50m

$$85MSR_{Day} = 1.64 \cdot \Delta V_{85Day} \qquad R^2 = 0.66 \tag{18}$$

*Nightlight condition*

Equations (19), (20), (21) and (22) provide the relations between 85MSRNight and 'V85Night for the four geometric classes of the tangent-curve configurations during nightlight condition.

L≥200m, R≥50m

$$85MSR_{Night} = 1.99 \cdot \Delta V_{85Night} \qquad R^2 = 0.83 \tag{19}$$

L≥200m, R<50m

$$85MSR_{Night} = 1.88 \cdot \Delta V_{85Night} \qquad \qquad R^2 = 0.58 \tag{20}$$

L<200m, R≥50m

$$85MSR_{Night} = 1.62 \cdot \Delta V_{85Night} \qquad \qquad R^2 = 0.89 \tag{21}$$

L<200m, R<50m

$$85MSR_{Night} = 2.13 \cdot \Delta V_{85Night} \qquad \qquad R^2 = 0.70$$
 (22)

# *4.2.2.* '*85V vs* '*V85*

#### (1)Daylight condition

Equations (23), (24), (25) and (26) provide the relations between '85VDay and 'V85Day for the four geometric classes of the tangent-curve configurations during daylight condition.

L≥200m, R≥50m

$$\Delta_{85}V_{Day} = 1.12 \cdot \Delta V_{85Day} \qquad \qquad R^2 = 0.77 \tag{23}$$

L≥200m, R<50m

$$\Delta_{85}V_{Day} = 1.18 \cdot \Delta V_{85Day}$$
  $R^2 = 0.81$  (24)

L<200m, R≥50m

$$\Delta_{85}V_{Day} = 1.17 \cdot \Delta V_{85Day}$$
  $R^2 = 0.41$  (25)

L<200m, R<50m

$$\Delta_{85}V_{Day} = 1.13 \cdot \Delta V_{85Day} \qquad \qquad R^2 = 0.55 \tag{26}$$

#### (2)Nightlight condition

Equations (27), (28), (29) and (30) provide the relations between '85VNight and 'V85Night for the four geometric classes of the tangent-curve configurations during nightlight condition.

L≥200m, R≥50m

$$\Delta_{85}V_{Night} = 1.15 \cdot \Delta V_{85Night} \qquad \qquad R^2 = 0.48 \tag{27}$$

L≥200m, R<50m

$$\Delta_{85}V_{Night} = 1.17 \cdot \Delta V_{85Night} \qquad \qquad R^2 = 0.21$$
(28)

L<200m, R≥50m

$$\Delta_{8S}V_{Night} = 1.20 \cdot \Delta V_{8S\,Night} \qquad \qquad R^2 = 0.17 \tag{29}$$

L<200m, R<50m

$$\Delta_{85}V_{Night} = 1.51 \cdot \Delta V_{85Night}$$
  $R^2 = 0.75$  (30)

# **4. Conclusions and further research**

The main objective of the driving simulator study presented in this paper was to analyze and compare the driver speed behavior during day and night driving in terms of speed differential experienced by drivers along tangentcurve transition. Such speed differential measures (85MSR, 'V85 and '85V) are strongly related to road design and safety as they are commonly used for design consistency evaluation, an advanced approach that evaluates systematically the coherence among the geometric elements of a road alignment, taking into account driver expectancy and perception of the road environment.

In this study new relations between speed differential parameters are proposed that can be used by road engineers to evaluate the safety level of new road infrastructure or the effectiveness of existing roadway treatments and measures. In fact, although 'V85 is commonly used as the speed differential measure to evaluate the safety level of a road alignment [2], it is also widely acknowledged, and confirmed in this study, that it underestimate the actual speed differential experienced by drivers along road alignment that, conversely, is more effectively represented by 85MSR or '85V. Therefore, the new relations here proposed for computing 85MSR and '85V,starting from 'V85 values,can be used for identifying new road safety threshold and criteria based on speed differential parameters that more effectively represent driver's difficulty to adopt homogeneous speed along a road alignment.

Moreover this driving simulator study has highlighted the difference between daylight and nightlight driving condition resulting in different relation proposed for the two condition of visibility. Specifically it is noted that during nightlight condition the relations between speed differentials parameters are generally confirmed, but they present higher coefficient of proportionality meaning that under low visibility 'V85 underestimates even more the speed variation along tangent-curve transition. Finally several relations are proposed for different geometric featuresof tangent-curve configurations under both daylight and nightlight driving conditions.

To generalize the results and provide practitioners with effective guidelines able to provide safety evaluation of a road design based on speed differential measures, some future researches are needed.

First of all, a validation of the simulation results against data from the real world in night driving conditions is essential. For this aim a research project is ongoing that will compare drivers' speeds adopted on site (using an instrumented car equipped with GPS that allows to collect speed data continuously) and the speeds recorded along the same road in the simulated environment to verify the validity of simulation outcomes also for night driving conditions. Moreover several crash studies should be developed to verify the direct correlations between speed differential parameters and crash rates recorded. A wide sample of cases studies that cover a significant range of road geometric and operating conditions has been already identified and preliminary crash investigations are developed.

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