continuous three-dimensional stopping sight distance control on crest vertical curves

Advances in Transportation Studies an international Journal 2012 Special Issue

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Continuous three-dimensional Stopping Sight Distance control on crest vertical curves

S. Mavromatis1 S. Palaskas2 B. Psarianos2

1Technological Educational Institute of Athens, Dept. of Surveying Engineering,

2 Agiou Spiridonos Str., GR-12210 Athens, Greece email: [email protected]

2National Technical University of Athens, School of Rural & Surveying Engineering 9 Hiroon Polytechniou Str., GR-15780 Athens, Greece email: [email protected], [email protected]

subm. 15th December 2011 approv. after rev. 16th May 2012

Abstract In current road design practice still a 2D approach is in use both with respect to the road configuration and the vehicle’s motion, despite the fact that a 3D approach regarding these aspects is the only accurate and realistic method to control the provision of critical design parameters such as the adequacy of Stopping Sight Distances (SSD). This paper describes an accurate SSD control method that relates the 3D configuration of a roadway to the dynamics of a vehicle moving along the actual roadway path, based on the difference between the provided and the demanded SSD. The SSDDEMAND is defined from the mass point model adopted by AASHTO enriched by the actual values of grade and friction variation. On the other hand the SSDPROVIDED is described as the 3D driver’s line of sight towards the object height. From this method the conditions of SSD provision could be derived for a variety of 3D alignment combinations and a wide range of design speeds and compared with the design elements’ limiting values as suggested by the AASHTO 2004 design guidelines. The relevant investigation revealed a satisfactory SSD reserve only in cases of horizontal curved alignments overlapped with vertical curves. The analysis showed that, in order to ensure SSD adequacy on road alignments designed according to the AASHTO design guidelines, a slight increase of the AASHTO minimum values for Crest Vertical Curvature Rates is necessary. The SSD control methodology presented in the paper is suitable for SSD evaluation regarding both existing and new road sections. Keywords – Stopping Sight Distance (SSD), 3D road alignment

1. Introduction

It is widely accepted that in every road environment safety is the key challenge. Road safety violation involves various issues, among which are errors due to the driver’s misjudgement of the road background and his inability to perceive unfavourable overlapping elements of design.

Current road design standards [1, 3, 18, 19] examine the vehicle motion from a rather simple and fragmentary point of view, where critical geometric design parameters are being introduced without taking into account the interaction between horizontal and vertical alignment. As a result, there are cases where the road user feels uncomfortable, since the length of roadway ahead that is visible to the driver known as Sight Distance [1] is not adequate.


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The minimum Sight Distance known as Stopping Sight Distance (SSD) is a highway geometric design control of fundamental importance. As far as safety is concerned, SSD must be provided at every point along the road surface since it directly affects the design values of critical road elements such as vertical curvatures (crest and sag) as well as the middle ordinate values, due to roadside obstacles, on left curved divided highways and right curved sections of two lane rural roads.

Current practice, as illustrated in Design Guides worldwide, addresses as well the SSD control as a separate and independent evaluation process in horizontal and vertical alignment. Consequently, existing road design guidelines suggest minimum values for design plus certain grouping of horizontal and vertical alignment from which adequate SSD is provided based on experience and empirical background. The Green Book [1] for example, underlines the desired case according to which the vertical transition curve should be entirely designed inside the horizontal curve, where the Spanish Design Guidelines [18] specify that a vertical crest curve must be completely inside the horizontal curve including spirals. In other words, horizontal and vertical arrangements of this kind are delivered as clear recommendations, since these suggestions are not an outcome of three dimensional road environment validation.

Under this scope, the objective of the present paper is, on undivided road environment, to investigate the SSD adequacy on combined horizontal and crest vertical alignments along an existing topography while applying the suggested geometric values according to AASHTO 2004 design guidelines.

2. SSD modelling

The investigation of SSD adequacy is grounded on either 2D or 3D models. The 2D SSD investigation is rather fragmentary and may underestimate or overestimate the available sight distance and consequently lead to safety violation [7]. The 2D SSD investigation is based either on horizontal or vertical profile.

From the horizontal alignment point of view, the 2D SSD adequacy is controlled by using road geometry elements referring to plan view, the vehicle speed and the horizontal offsets of both driver – obstacle from the road axis. It is clear that parameters such as road’s vertical profile as well as the heights of both the driver and the obstacle are ignored. As a result, the lateral clearance area is theoretical.

The relevant investigation based on road’s vertical profile, is conducted by utilizing the vertical road geometry. This approach is once again incomplete, since although the vehicle speed as well as the heights of both the driver and the obstacle are taken into account, the horizontal geometry is limited to tangents, while the layout visibility influenced by the cross slope transition, especially at the area where the alignment superelevation values change sign [17], is ignored as well.

In the near past, in order to assess the actual sight distance in real driving conditions, a number of 3D models are found in the literature [2, 3, 5, 6, 9, 10, 13, 17, 21-23] which base their performance through the correlation between the road surface, the ground terrain and the roadside environment. The delivered 3D models are capable to simulate accurately compound road environments where an unsuccessful arrangement of vertical and horizontal alignment may exist, and thus allow the definition of the actual vision field to the driver.

A recent research [4], aiming to investigate the SSD adequacy on 3D road environment, define the actual sight distance values, as well as take under consideration the driver’s workload, recommends the use of certain criteria in order to:


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• avoid the extremely unsafe experience of hiding the preceding horizontal curve due to road’s vertical profile

• elude partial road disappearance areas • ensure the 3D perspective of a horizontal curve as to assist the driver in recognizing the

formed curvature

The first of the above mentioned criteria is considered to be particularly critical from a safety point of view since the driver’s ability to perceive the area where the horizontal curve begins, is a major safety prerequisite throughout the cornering process. Moreover during night driving, additional unfavourable conditions rise as the tangent direction of the headlight beams may entirely hide the curve [8].

However most of the above research studies are focused in optimizing the available SSD by introducing either new algorithms or design parameters combinations, ignoring in many cases the topographic visual restraints, providing therefore an integrated, all-included SSD evaluation approach that satisfies completely designer’s expectations. The present paper investigates SSD adequacy based on minimum design values given by AASHTO on compound alignments resulting from any combination of design elements in the vertical and horizontal alignment on one hand while on the other the surrounding ground form is derived by the Digital Terrain Model. In this compound and realistic roadway environment both SSDPROVIDED and SSDDEMAND are calculated and their corresponding values substracted. If this difference is positive SSD sufficiency is granted. In other words, the applied methodology, for various speed values and alignment arrangements, is based in defining areas of interrupted vision lines between driver – obstacle being less than the demanded distance that safely routes a vehicle to stop condition, thus creating SSD shortage issues.

3. Demanded and provided SSD values determination

In highway engineering, under the similar lighting conditions, the following two SSD values are reported:

• SSDDEMAND related with the ability of the vehicle to reach stop condition depending on the road, in terms of geometry the driver, in terms of perception – reaction utilization the vehicle, in terms of provided dynamic characteristics

• SSDPROVIDED associated with the frontal sight field visible to the driver during daytime conditions and depends on the roadside environment (roadside obstacles) road geometry

3.1. Demanded SSD calculation

According to existing design policies the demanded SSD consists of two distance components: the distance travelled during driver’s perception – reaction time to the instant the brakes are applied and the distance while braking to stop the vehicle. For example, the SSD model adopted by the AASHTO 2004 Design Policy is represented by Equation (1).

)(2

2

sgag

VtVSSD oo

(1)


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where : Vo (m/sec) : vehicle initial speed (usually the design speed as defined by [1]) t (sec) : driver’s perception – reaction time [2.5sec [1]] g (m/sec2) : gravitational constant a (m/sec2) : vehicle deceleration rate [3.4m/sec2 [1]] s (%/100) : road grade [(+) upgrades, (-) downgrades]

However the above approach ignores curved areas of both horizontal and vertical alignment, since, on one hand, the portion of friction provided in the longitudinal direction, assigned to serve the braking process, is associated directly to the friction demanded laterally [11], and on the other, the grade values involved in vertical curves are variable. In order to incorporate the effect of these parameters, simple considerations based on the mass point model as well as the laws of mechanics were applied respectively.

Assuming a friction circle [11], the actual longitudinal friction provided for braking on curved sections is expressed by Equation (2):

22

2 )-(-)( egRV

gafT

(2)

where : fT : friction demand in the longitudinal direction of travel V (m/sec) : vehicle (design) speed a (m/sec2) : vehicle deceleration rate [3.4m/sec2 [1]] g (m/sec2) : gravitational constant R (m) : horizontal radius e (%/100) : road cross – slope

Aiming to quantify the grade effect during the braking process, the laws of mechanics through Equation (3) and Equation (4) were applied, assuming time fragments (steps) of 0.01sec, in order to determine both the instantaneous vehicle speed and pure braking distance.

tsfgVV Tii )(-1 (3) 2)(

21- tsfgtVBD Tii

(4)

where : Vi (m/sec) : vehicle speed at a specific station i Vi+1 (m/sec) : vehicle speed reduced by the deceleration rate for t = 0.01sec t (sec) : time fragment (t = 0.01sec) s (%/100) : road grade in i position [(+) upgrades, (-) downgrades] fT : friction demand in the longitudinal direction of travel BDi (m) : pure braking distance g (m/sec2) : gravitational constant

By applying Eq. (3) and (4) subsequently there is a sequence value i=k-1 where Vk becomes equal to zero. The corresponding value of ΣBDk-1 represents the total vehicle pure braking distance for the initial value of vehicle speed being, according to AASHTO 2004, equal to the design speed.


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Note: 2xT: Vertical Curve Length = 2x102m, Hk: Crest Vertical Curve Radius, s1, s2 : grade values

L: Length of Horizontal Spiral Curve, A: Spiral Parameter, R: Radius of Horizontal Curve Black Line: Vertical Profile Grey Line: Horizontal curvature diagram Vertical Line: Station of Braking Procedure Commencement

Fig. 1 - Examined cases of demanded SSD variation between AASHTO policy and suggested approach for critical design values given by AASHTO referring to VDesign=70km/h

Tab. 1 - Critical design values used in the SSD adequacy investigation

Vdesign (km/h) Rmin (m) Ldesirable (m) Kmin (m) srange (%) 50 60 70 80 90

79 123 184 252 336

28 33 39 44 50

7 11 17 26 39

-7 - +7 -6 - +6 -6 - +6 -5 - +5 -5 - +5

Note. Vdesign: design speed, Rmin: minimum horizontal radius, Ldesirable: desirable length of spiral curve, Kmin: rate of crest vertical curve, srange: grade range

The demanded SSD is produced by adding the final pure braking distance to the distance travelled during the driver’s perception – reaction time [first component of Equation (1)] as follows:

1-koDEMAND BDtVSSD (5)

where : Vo (m/sec) : vehicle initial speed t (sec) : driver’s perception – reaction time [2.5sec [1]] ΣBDk-1 (m) total vehicle pure braking distance for the initial value of vehicle speed

Summarizing the demanded SSD determination, the formula adopted by AASHTO, Equation (1) is applied, enriched by the utilized longitudinal friction and actual grade value portions respectively. Figure 1 illustrates three cases of the variation in demanded SSDs between the values adopted by AASHTO policy and the relevant ones based on the enriched approach as defined above, for critical design values given by AASHTO referring to 70km/h design speed (as shown in Table 1):


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• Case 1. Braking procedure begins on a tangent in the horizontal alignment and in the vertical crest curve

• Case 2. Braking procedure begins on a horizontal curve and on a constant grade in the vertical alignment

• Case 3. Braking procedure begins on a horizontal curve and a vertical crest curve In Figure 1 the combination of the horizontal curvature diagram and the vertical alignment is

shown along the section of a highway. For example, station 1300 of Case 1 falls inside a crest vertical curve and on a tangent horizontally. In all three examined cases of Figure 1 it can be seen that the AASHTO SSD demanded values are smaller compared to the relevant values as delivered by the suggested improvements, where the effect of the longitudinal profile proves to be critical for the resulting real 3-D SSD length.

3.2. Provided SSD calculation

The provided SSD is described as the uninterrupted line of sight between the driver’s eye and the obstacle. A typical height of the driver’s eye is 1.00m for passenger cars and 2.00m regarding trucks, where the obstacle height ranges between 0.50m and 1.00m. A prerequisite in order to calculate the available SSD is to create a digital terrain model (triangles) from the 3-D road environment. This digital terrain model can be readily provided by common road design softwares or alternatively by topographic mapping softwares, where each feature is rendered as a cluster of triangles. The available SSD is formed by driver’s line of sight towards the object height at a certain offset (usually half of the driving lane) from the road centerline. Equations of analytical geometry are applied in order to describe lines of sight beginning from the driver’s eye and to determine the intersection points of these lines with triangles formed by the road geometry as well as features that may restrict the driver’s vision towards the object [16]. Figure 2 shows a line of sight interruption example on a right-turn curved road section, which cannot be evaluated in a conventional 2-D road design approach. The same figure illustrates the surface of the roadway, including the road’s side formations and the applied sideslopes, as well as the ground which are represented by a sequence of elementary triangles whose nodes coordinates were derived from the digital terrain model and the roadway alignment provided by the designer. The precision of the available SSD definition depends on the selected incremental distance (calculation step) between two sequential available SSDs. In the present analysis, the calculation step was set equal to 10m, in order to reduce the calculation time for each run. This means that the determined available SSD values are rounded in bundle of tens which obviously leads in slight overdesigning.

Fig. 2 - Line of sight interruption on a right curved road section


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Fig. 3 - Flow chart of SSD adequacy investigation

3.3. SSD adequacy

SSD adequacy is granted when:

SSDDEMAND ≤ SSDPROVIDED (6)

The provided and demanded SSD values are defined through the difference of the road stations between starting and ending points, assumed at an axis offset equal to half of the lane width. The necessary information for defining the provided and demanded SSD values as well as the procedure for the investigation of the SSD adequacy referring to a single road station is illustrated in Figure 3. The flow chart in Figure 3, is recently incorporated in road design software [20], used by many engineering firms in Greece for road designing, and applied for the assessment that follows.

4. SSDPROVIDED validation The credibility of the road design software in defining the SSDPROVIDED was validated against

an existing road section which was surveyed via laser scanner [15]. The existing road section consists of an unfavourable overlapping of vertical and horizontal alignment, where the vertical crest curve precedes the horizontal curve, thus providing limited capability for the driver to perceive the right turning horizontal curve. The definition of the available SSD values was performed using appropriate market software [12].

Figure 4 illustrates in point cloud form the driver’s frontal sight field in different locations, where the reduction of the available sight distance in certain cross sections, as the vehicle approaches the horizontal curve, can be seen as well as the available sight distance between driver – object, extracted by the laser scanner software [12] at station 74.89. The correlation in defining the available SSD between the above mentioned research and the present approach revealed a complete match.


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Fig. 4 - 3D cross section views (St.54.93, St.74.89, St.94.89) of a combined horizontal and vertical alignment

from the driver’s frontal sight field, as well as available sight distance at St.74.89 in point cloud form

5. SSD adequacy investigation for AASHTO 2004 design policy In order to investigate potential safety violation while investigating SSD adequacy on

combined horizontal and crest vertical alignments right turned curves were assumed since a recent research study revealed this case as the most critical one [17].

The SSD adequacy investigation, based on AASHTO policy, was performed for a wide range of design speed values where the corresponding minimum values of crucial design parameters, as well as the approach and exit grade values are shown in Table 1. Furthermore, in the present paper the travel area width was assumed 2x3.75m (2x12ft approximately) and the unpaved shoulder equal to 1.50m. The pavement cross slopes were assumed 6% on curves and 2% on tangents, where the unpaved shoulder cross slope grade was taken 8%.

Figure 5 shows an example regarding SSD adequacy investigation on a 3D compound road surface for 70km/h design speed. The horizontal axis once again represents the road stations where the horizontal and vertical curvatures are projected linearly. The vertical axis illustrates various SSD values corresponding to the stations of the compound alignment shown horizontally. Three different types of SSDs are shown: SSDDEMAND (black line), SSDPROVIDED (2D) (dashed line) based on roadway’s longitudinal profile, and SSDPROVIDED (3D) (grey line) based on 3D perspective analysis.

Note: Dashed Line [SSDprovided (2D)]: SSD Available Based on Roadway’s Longitudinal Profile Grey Line [SSDprovided (3D)]: SSD Available Based on Suggested Approach Black Line [SSDdemand]: SSD Demand Based on Suggested Approach Vertical Lines: Boundary of Variable Demanded SSDs to Accommodate the Vertical Transition SSDprovided (2D) and SSDprovided (3D) Overlay up to Station 1320 Approximately Vertical Vertex Station: 1350

Fig. 5 - SSD adequacy investigation on compound alignment for 70km/h design speed


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In the same Figure, it can be seen that the SSDDEMAND display (black line) is formed by two parallel lines and a transition area where the variable grade range is accommodated, the boundaries of which are shown with two vertical lines. The beginning of the transition area was found before the starting point of the vertical curve at a distance equal to the vehicle SSD where the grade value is constant (s1= 6%).

The transition area is terminated in advance of the vertical curve endpoint by the distance travelled during driver’s perception – reaction time in order the driver to be able to perform the pure braking manoeuvre at the constant grade of s2= -6%. It is obvious that the presence of horizontal curves impose additional restrictions in the utilized longitudinal friction thus increasing the SSDDEMAND values.

A closer look of Figure 5 reveals an underdesign zone, located at the area where the black line (SSDDEMAND) overlaps the dashed and grey ones [SSDPROVIDED (2D) and SSDPROVIDED (3D) respectively]. For example, in station 1290, the demanded SSD is 106m, where the provided SSD (for both 2D and 3D perspective) is 100m. In terms of quantifying the SSD safety violation area between the SSDDEMAND and the SSDPROVIDED (3D), the total SSD breakdown zone, or in other words the partial road disappearance, is approximately 80m (zone between st.1240 – st.1320).

As far as the SSDPROVIDED from a 3-D standpoint is concerned, the same figure reveals that, contrary to the relevant 2D SSDPROVIDED assessment, safety in emergency stopping conditions is ensured before the vertical vertex.

Commenting further on the SSD breakdown zone, it can be seen that the partial road disappearance (ch.1240 - ch.1320) is located inside a vertical transition area but in tangent horizontally. This finding is not surprising, since, according to AASHTO 2004 design guidelines, the formula applied for the vertical curve definition (Equation 1), which disregards the horizontal alignment, adopts SSD values extracted for 0% grade and not the unfavourable case of negative grade values (downgrade road sections). However, in design practice the “s” value in Equation 1 is taken into consideration as algebraic mean “s” values of the tangents preceding and succeeding a crest vertical curve. The consequence of AASHTO 2004 Design Guidelines to adopt minimum Crest Vertical Curve Rates (CVCR) based on 0% grade values is to produce SSD inadequacy when negative grades (downgrades) are utilized.

In order to ensure SSD sufficiency for AASHTO 2004 Design Guidelines and thus eliminate the SSD breakdown zones, formed by the overlap between demanded and provided in 3D perspective SSD respectively, the authors suggest a slight increase of the AASHTO vertical curvature rate (Figure 6) for the corresponding design speeds. The suggested CVCR are rounded values, calculated from Equation 1 where the most unfavourable grade rates (negative values) from Table 1 are exploited.

Fig. 6 - CVCR increment for SSD adequacy


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Note: Calculation Step = 50m, Vertical Curve Length = 98m ,

L: Length of Horizontal Spiral Curve, R: Radius of Horizontal Curve

Fig. 7 - SSD adequacy investigation chart for VDesign= 50km/h

Note: Calculation Step = 50m, Vertical Curve Length = 132m,

L: Length of Horizontal Spiral Curve, R: Radius of Horizontal Curve Fig. 8 - SSD adequacy investigation chart for VDesign=60km/h

Furthermore, in order the SSD adequacy analysis, as expressed in the present paper, to be more comprehensive and practical for implementation consistency, Figure 7 – Figure 11 illustrate the length of SSD breakdown for design speed values varying between 50km/h and 90km/h respectively. Through these figures, the authors intend to assess the effect of the crest vertical curve vertex arrangement on the horizontal alignment and thus investigate in more detail SSD sufficiency of compound alignments for the examined design speed values.

Figure 9a for example, shows once again the same compound alignment discussed in Figure 5 where a SSD adequacy investigation is performed for critical design values referring to 70km/h design speed. As already mentioned, the total SSD breakdown zone, or in other words the road length not visible to the driver, is approximately 80m (zone between st.1240 – st.1320).

Figure 9b illustrates the overall case of the same horizontal alignment and the same design speed (70km/h), where the shift of the vertical vertex (formed by s1= 6%, s2= -6% and CVCR=17) every 50m, produces different SSD inadequacy values. In the same Figure, it can be seen that when the vertical vertex is placed on station 1350, where the starting and ending points of the vertical curve are at station 1350-102 and station 1350+102 respectively, the partial road disappearance, as already stated above is 80m approximately. More specifically the vertical axis of Figure 7 – Figure 11 displays the length of the roadway that partially disappears from the driver’s view developed by positioning (“sliding”) the vertex of crest vertical curves in fixed distances along the horizontal alignments shown in the abscissa axis.


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Note: Dashed Line [SSDprovided (2D)]: SSD Available Based on Roadway’s Longitudinal Profile Grey Line [SSDprovided (3D)]: SSD Available Based on Suggested Approach Black Line [SSDdemand]: SSD Demand Based on Suggested Approach Vertical Lines: Boundary of SSD Breakdown Vertical Vertex Station: 1350

Fig. 9a - SSD adequacy investigation on compound road surface for 70km/h design speed and vertical vertex positioned at station 1350


L: Length of Horizontal Spiral Curve, R: Radius of Horizontal Curve Magenta Entry: SSD Breakdown when Vertical Vertex Positioned at Station 1350

Fig. 9b - SSD adequacy investigation chart for VDesign=70km/h



In other words the above mentioned figures aim to quantify the SSD inadequacy of compound alignments for a wide range of design speed rates based on minimum values of crucial design parameters as shown in Table 1.


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Note: Dashed Line [SSDprovided (2D)]: SSD Available Based on Roadway’s Longitudinal Profile

Grey Line [SSDprovided (3D)]: SSD Available Based on Suggested Approach Black Line [SSDdemand]: SSD Demand Based on Suggested Approach Vertical Vertex Station: 1800

Fig. 12 a - SSD adequacy investigation on compound road surface for 90km/h design speed and vertical vertex positioned at station 1800

Note: Horizontal nad Vertical Alignment Values are Shown in Figure 12a, Station of Vertical Vertex: 1800

Fig. 12b - Detail of SSD adequacy investigation for 90km/h design speed and vertical vertex positioned at station 1800

The general remark from the overview of Figure 7 – Figure 11 is that the SSD inadequacy

area decreases and even vanishes as the vertical vertex approaches the area of the horizontal curve, thus confirming a recent research study by Moreno et al. [17] according to which the location of the vertical midpoint that maximizes available sight distance is located before the horizontal vertex. Moreover, areas with abrupt label alternations referring to adjacent data series (Figure 11) are due to the existence of more than one overlapping zones between SSDPROVIDED and SSDDEMAND values.


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In order to unify such cases as SSD inadequate areas, the authors considered 30m as the least overlapping zone, where the distance between two adjacent SSD inadequate (overlapping) zones to be less than 100m. Such an example, shown in Figure 12a and Figure 12b, is drawn for the most critical illustration of Figure 11, representing the case for VDesign=90km/h and the vertical vertex positioned at station 1800 (Figure 12a), where the SSD inadequacy was considered 225.5m (Figure 12b).

6. Conclusions In this paper a SSD adequacy investigation is carried out for a wide range of design speed

values based on the difference between the provided and the demanded SSD. The SSDDEMAND is defined based on the point mass model enriched by the actual values of grade and friction variation due to vertical curves and vehicle cornering respectively. On the other hand the SSDPROVIDED is described as the driver’s line of sight towards the object height at a certain offset.

The crest vertical curve definition according to AASHTO adopts SSD values extracted for 0% grade and not the unfavourable case of negative grade values. As a result, although the SSD investigation revealed a satisfactory SSD reserve in areas of compound horizontal – vertical alignments, on tangents, the negative grade area revealed SSD inadequacy. The relevant SSD analysis as presented through Figure 7 – Figure 11, at least for right curved alignments, includes both direction of travel. Furthermore, the authors suggested an increase of the CVCR in order adequate SSDs to be provided at any point when road alignments are designed based on AASHTO guidelines. However, it must be stated that an improved accuracy (1m) regarding the SSDPROVIDED determination, which in the present analysis was set to 10m, will deliver more accurate SSD sufficiency control.

The SSD adequacy investigation approach as described in the present paper can be applied to any alignment, where further analysis seems necessary in order to include roadside formations where, for example in retaining wall areas, the sight distance is furthermore restricted.

The present paper identifies critical SSD situations based on the minimum geometric design parameter values. Further qualitative research is required in order to evaluate the influence of every parameter independently. It is evident that this kind of practice involves many constraints, rising from geometric arrangements, the topography as well as the road side environment given that the present procedure can be applied on existing road sections, left turns of divided highways as well as safety investigation on passing manoeuvres.

It is also necessary to underline the fact that the parameters used in the present paper (speed values, perception reaction time etc.) refer to daylight driving conditions, as the vehicle speed values in night time driving conditions are 6km/h – 15km/h less [14] on one hand and on the other the road view geometry changes.

Finally, it should not be ignored the fact that the human factor, in addition to perception – reaction procedure as well as the friction reserve utilized in the lateral direction during the braking process, might impose additional restrictions and consequently influence the braking process to some extent.

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continuous three-dimensional stopping sight distance control on crest vertical curves

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