 Original Paper
 Open Access
Sight distance restriction on highways’ horizontal curves: insights and sensitivity analysis
 Shy Bassan^{1}Email author
https://doi.org/10.1007/s1254401602086
© The Author(s) 2016
 Received: 6 November 2015
 Accepted: 14 July 2016
 Published: 3 August 2016
Abstract
Introduction
The study focuses on sight distance restrictions on horizontal curves in highway design. Barriers along open highways and walls on tunnels may restrict the available sight distance in the design of horizontal curves. The study aims to finalize a desirable horizontal radius by examining the equilibrium requirement of the centrifugal force vs. horizontal sight distance constraints.
Methods
The study examines these restrictions for the conventional case when the stopping sight distance lies within the length of the horizontal curve (case 1) and when the stopping sight distance lies outside the length of the horizontal curve (case 2). Also included in this study is a sensitivity analysis when the stopping sight distance is longer than the length of horizontal curve (case 2), based on the ratio between them.
Results
For the conventional case (case 1) the minimum horizontal radius that is based on the equilibrium of centrifugal force, is too small for the requirements of stopping sight distance when there are obstructions along the road that intrude on the line of sight. Sensitivity analysis results for case 2 show that the gap between the available horizontal stopping sight distance (for the minimum horizontal radius) vs. the design (demanded) stopping sight distance values and between the minimum horizontal radius vs. the desirable radius can be totally resolved when the ratio between stopping sight distance and the length of horizontal curve equals to 4.5 (for horizontal sightline offset of 4.8 m, i.e. shoulder width of 3.0 m plus half lane width of 1.8 m).
Conclusions
Practically, the resulted conditions of the ratio between stopping sight distance and the length of horizontal curve are not feasible in horizontal curve design especially when the horizontal sightline offset equals to 3.0 m. When the limitations of horizontal stopping sight distance are valid and the obstruction height is higher than the maximum, the highway engineer might consider a tradeoff by increasing the horizontal curve radius as well as adjusting the design to case 2.
Keywords
 Highway
 Sight distance
 Horizontal curve
 Equilibrium
 Restriction
1 Introduction
A major purpose in highway geometric design is to ensure that the driver is able to see any possible road hazard in sufficient time to take action and avoid an accident. Stopping sight distance (SSD) is the most important of the sightdistance considerations since sufficient SSD is required at any point along the roadway.
1.1 Stopping sight distance (SSD)
SSD is the distance that the driver must be able to see ahead along the roadway while traveling at or near the design speed and to safely stop before reaching an object whether stationary or not. SSD can be limited by both horizontal and vertical curves. The fact that it impacts the design radius of both curves makes SSD so fundamental in the highway design process. This study focuses on sight distance restriction on horizontal curves.
 SSD:

Minimum stopping sight distance (m)
 V_{d} :

Design speed (km/h)
 d:

Deceleration of passenger cars (m/s^{2}), equivalent to the longitudinal friction coefficient (f) multiplied by the acceleration of gravity (g)
 g:

Nominal gravitational acceleration of an object in a vacuum near the surface of the earth (g = 9.81 m/s^{2})
 t_{R} :

Perception reaction time (s), usually 2.5 s (AASHTO 2011).
The formula assumes level terrain. Ascending grade decreases the SSD, and descending grade increases the SSD.
The green book [1, 2] recommends on 3.4 m/s^{2} as a reasonable deceleration rate for obtaining the stopping sight distance and it no longer provides the tangent friction coefficient design values. Most vehicles are able to brake in this rate at least, under wet pavement conditions. The tangent friction coefficient in wet pavement surfaces and the modern vehicle braking capabilities typically enable larger equivalent friction coefficients than this deceleration rate.
1.2 Horizontal curve design: equilibrium concept
 R_{min} :

minimum radius of horizontal curve (m)
 V_{d} :

design speed (km/h)
 g·e_{max} = a_{e} :

superelevation acceleration
 g·f_{Rmax} = a_{fr} :

friction lateral acceleration
 a_{c} = a_{e} + a_{fr} :

centrifugal acceleration
 127:

conversion factor, taking acceleration of gravity as g = 9.81 m/s^{2}
Minimum horizontal radii (m) for emax = 0.08 [2]
Parameter  Design Speed (km/h)  

60  70  80  90  100  110  120  
e_{max} (max superelevation)  0.08  0.08  0.08  0.08  0.08  0.08  0.08 
f_{Rmax} max side friction  0.17  0.15  0.14  0.13  0.12  0.11  0.09 
R_{min} min horizontal radius (m)  113  168  229  304  394  501  667 
2 Stopping sight distance (SSD) restriction along horizontal curves and vertical curves: literature review
Arndt et al. [3] proposed the implementation of dry longitudinal friction coefficient of 0.61, utilizing high object height (e.g. 0.80 m), and reducing the design speed values based on speed prediction models, assuming that drives are prepared to slow prior to horizontal curves. They also proposed the perception reaction time value of 1.5 s of alert driving due to road environment and driving expectancy [8]. These less conservative criteria have been suggested to result in a lower but reasonable design value of stopping sight distance.
Still these criteria have been used in a case study of provision of sight distance around roadside safety barriers on freeways and interchanges by using a particular operating speed 80 km/h.
2.1 3D models combining horizontal and vertical alignments
Sarhan and Hassan [4] analyzed available stopping sight distance (SSD) on horizontal curves with roadside or median barriers in 3 Dimension (3D) combined alignments by using finite element technique software. Their analysis confirmed the dependency between the available SSD on horizontal curves (due to road barriers) and overlapping vertical alignment. They found that the available SSD increases as the overlapping crest vertical curve becomes flatter or as the overlapping sag vertical curve becomes sharper. The design aids presented in this research, which include available SSD, the horizontal sightline offset (HSO), and different alternatives of overlapping vertical curves, considered open roads SSD criteria where most range of horizontal sight line offset (HSO) is not practical for implementation in a bounded cross section or derives uneconomical wide shoulders which can mislead the drivers by using them as another travel lane or a parking laybay. Also, the design speed parameter was not included in these charts where the constraint of nonavailable horizontal sightline is not always accomplished.
Additional studies aimed to evaluate and optimize the actual sight distance in real driving conditions by 3D models. Nehate and Rys [9] examined the intersection of sightline with the elements representing the road surface by an algorithm which combines horizontal and vertical alignment and automatically calculate sightdistance profile along any given highway for which Global Positioning System’s (GPS’s) data are available. Results of actual data have shown the ability to identify sightdistance restrictions. Similarly, Kim and Lovell [10] used computational geometry and thin plate Spline interpolation to represent the road surface and eventually determine the maximum available sight distance.
Castro et al. [11] implemented a procedure supported by Geographic Information Systems (GIS) in order to determine highway distances visible to the driver in a twolane highway section. The GIS advantage in highway sight distance analysis is using data sources that besides the terrain include obstacles like trees or buildings that could reduce the driver sight distance. This procedure can perform highway sight distance analysis of existing highways where highway design information (tangents, horizontal and vertical curves) is not available or is not the latest (e.g. in many already built highways). Castro et al. [11] showed that sight distances obtained by GIS approach and the classic highway design approach are statistically the same.
Jha et al. [12] proposed a 3D design methodology which is capable of “efficiently measuring the sight distance for different superelevation, day and nighttime conditions, and obstructions”.
The methodology which utilizes triangulation techniques (Digital Terrain Model – DTM) consists of three stages: development of (a) the road surface, (b) virtual fieldofview surface, and (c) virtual line of sightplane. Moreno et al. [6] maximized the available stopping sight distance (SSD) at crest vertical curves overlapped with horizontal curves in two lane highways. They used a finite element method algorithm to generate an SSD profile. The available SSD profile indicated the available SSD of each evaluated position of the driver. The resulted available SSD could finalize certain alignment zones where vertical and horizontal curve could be improved if the minimum available SSD was lower than required among these curves. This study concluded that the vertical curve curvature in meters (K_{v} = L_{v}/A = R_{v}/100, i.e. the horizontal distance in meters needed to make a 1 % change in gradient, where: L is the horizontal length of vertical curve in meters, A is the algebraic difference of grade lines in percents, R_{v} is the vertical curve radius in meters), and the available horizontal radius (R_{h}) affect the available SSD. The optimal proportion of K_{v}/R_{h} (K_{v} and R_{h} were previously defined) which maximizes the available SSD is generally ranged between 0.05 to 0.15. The study also revealed a negligible impact of the offset between horizontal and vertical curves on available SSD. Additionally, the layout visibility got restricted to the point where the superelevation changed its sign [6].
Mavomartis et al. [5, 13] proposed an “accurate SSD control method” which relates the 3D alignment of the roadway (horizontal and vertical) to the dynamics of vehicle path along the roadway based on the difference between the available SSD and the “demanded” SSD. The method was applied to left turn horizontal curve divided highway. The SSD adequacy was evaluated by equalizing the available SSD and the demanded SSD and by identifying the zones where the sightline is obstructed by the median width. Their results have shown that by increasing the horizontal radius, inside the vertical curve transition area, the restricting area due to object height and blocked driver sightline (insufficient HSO) increases up to a certain point. As the horizontal radii increase more “the blocked sightlines decreases in advance of the object height amendment requirement”. This research finally suggested that by increasing the object height ( i.e. vehicle tail lights) to 1.08 m, the design consistency, and driver expectations can be satisfied by avoiding nonuniformed posted speed limits and uneconomical lateral road widening. Ismail and Sayed [14] presented a finite element approach of a 3D algorithm that calculates ASD for integrated vertical and horizontal alignments. This algorithm parameterizes horizontal elements such as pavement edge, median edge, and side slope relative to the centerline. Its final step similarly to other 3D methodologies is searching for the furthest object location that connects the driver location with an unobstructed sightline. The algorithm examined extreme cases of vertical and horizontal curvatures in order to validate them against available 2D models. The resulted 3D ASD was closed to the shortest of the 2D ASD sight distances (horizontal ASD, i.e. HASD and vertical ASD i.e. VASD). The 3D ASD resulted smaller than the critical 2D ASD if the 2D difference is positive (VASD > HASD). This case signified the necessity of 3D analysis.
2.2 Reliability analysis of sight distance in horizontal curves
Hussein and Sayed [7] applied reliability analysis (stochastic approach) to take into consideration uncertainty associated with geometric design parameters. They calibrated design charts for Horizontal Sightline Offset HSO, or in other words: the middle ordinate – M, at different probabilities of noncompliance (Pnc) levels. The HSO which is presented in Fig. 1 is the distance between the edge of median barriers and the centerline of the left traffic lane.
In highway geometric design the use of Pnc characterizes the probability that the design does not meet the standard design requirement. Hussein and Sayed used a limit state function which is the difference between ASD (available stopping sight distance) and the demanded stopping sight distance (SSD). The Pnc was generated from this function. SSD is presented in Eq. 1. ASD is the accurate horizontal sight distance formula assuming SSD is shorter than the horizontal curve length (L). Its approximate form is documented in the next section which is the background for the major objective of the current study to conduct a sensitivity analysis of R and HSO for SSD < L and SSD > L.
The preferred target Pnc is the road designer’s choice based on the design policy.
The calibration of horizontal radius and HSO for different Pnc’s showed that the current design guides are conservative especially at sharp radii and high design speed [7]. It appears that these results are somehow subjective because increasing the risk (i.e. increasing the target Pnc) can be performed by deterministic modifications such as reducing the perception reaction time (PRT) or increasing the friction coefficient (Eq. 1) based on the prevailing traffic and pavement conditions and specific driving behavior characteristics.
The reliability analysis approach was also implemented in other studies such as Ismail and Sayed [15] and Ibrahim et al. [16] in order to select a suitable combination of cross section elements with restricted sight distance to result in reduced collisions and acceptable risk levels.
3 Horizontal sightline offset (Hso): basic methodology
An approximate calculation of the minimum horizontal sightline offset (HSO) or the lateral clearance required between the centerline of the inside lane and a potential obstruction along the horizontal curve can be performed as a function of the sight distance, and the radius of the horizontal curve (R_{HSD}).
3.1 Horizontal sightline offset (HSO) for SSD ≤ L, case 1
3.2 Horizontal sightline offset (HSO) for SSD > L, case 2
When the sight distance lies outside the length of the horizontal curve (L) the analysis is slightly different. In this case, assuming two symmetrical tangent edges outside the horizontal curve, we can obtain the relationship between HSO, SSD, the horizontal curve radius (R_{HSD}), and the length of the horizontal curve (L).
After further algebraic arrangements the resulted relationship between HSO, SSD, the horizontal curve radius (R_{HSD}), and the length of horizontal curve (L) is as follows:
Further detail regarding sight distance on horizontal curves including: exact calculations of horizontal sightline offset (HSO), comparison between exact formulas and approximate formulas of HSO, and variation of sight distance according to the location of observer (driver) and object height along the horizontal curve, can be found in Olson et al. [17].
4 Sight distance restriction along the horizontal curve: insights
The sight along the inner side of the horizontal curve can be sometimes restricted by downhill excavations, retaining walls, structures, and other obstacles. On divided highways (multilane highways, freeways, etc) the driver sightline while driving along the lefthand side (LHS) horizontal curve is generally restricted by median safety barrier. The median safety barrier is usually closer to the left lane comparing to obstructions located beyond the right shoulder (typically safety barrier). The sightline problem is three dimensional and therefore, it is important to determine the height of its two edges (driver eye height and object height) by the type of sight distance considered. Additionally, the interaction between horizontal and vertical geometry parameters (especially vertical and horizontal curves, presented in section 2) are critical in addressing the available SSD.
Maximum obstruction heights for a clear sightline in horizontal curves
Sight Distance (SD) Type  Maximum Obstruction Height for Horizontal Curve Sightline (*), in meters 

Stopping SD (undivided highway)  (1.05 + 0.15)/2 = 0.60 m 
Stopping SD (twoway (divided) highway  (1.05 + 0.60)/2 = 0.825 ~ 0.80 m (rounding down) 
Decision SD  (1.05 + 0.60)/2 = 0.825 ~ 0.80 m (rounding down) 
Passing SD  (1.05 + 1.05)/2 = 1.05 m 
Every point along the inner side of the horizontal curve (and beyond) along the sight envelope (Fig. 4) should not incorporate an obstacle which prohibits the line of sight. If such an obstacle exists (typically, a safety barrier), its height should not exceed the critical obstruction’s height presented in Table 2. When the vertical alignment includes a tangent gradient, a profile sketch might be useful.
If the horizontal curve radius does not conform sight distance requirement for a specific design speed due to a local or continuous obstruction (vegetation, downhill excavation, retaining wall, and safety barrier along the median or beyond the right shoulder) whose height exceed the critical obstruction height, the highway engineer might consider increasing the horizontal radius or widening the shoulder without decreasing the design speed.
 (1)
On twolane highways, the inside barrier could restrict sight distance in the rightbound curve. The horizontal sightline offset (HSO) could be no more than 4.8 m (3 m of right shoulder plus 1.8 m of the distance between the centerline of the right lane and its right edge).
 (2)
On four (or six)lane divided highways, the median barrier could restrict sight distance in the leftbound curve. The HSO could be no more than 4.8 m (3 m of median/left shoulder width plus 1.8 m of the distance between the centerline of the left lane and its left edge). A typical cross section of six lanes divided highway is presented in Fig. 5. This cross section incorporates left shoulders of 3.0 m.
The concept of calculating the HSO (including conventional shoulder width of 3.0 m or narrower and the distance between the lane centerline and its edge) is documented in AASHTO [2] and in Austroads [8]. A typical graphical presentation of HSO on horizontal curves with median safety barrier in multilane highways is presented in Fig. 1.
The HSO could be even smaller (i.e. 3.0 m) if the median shoulder is reduced to 1.2 m (AASHTO [2], subsection 3.3.12 pp. 3–110).
The outside (median) barrier restriction on multilane divided highways is similar to twolane highways (HSO = 4.8 m); however, since design speed is usually higher, the stopping sight distance is even more restricted. This insight is more obvious in road tunnels, where continuous walls run along the sides.
Examples of SSD restrictions on horizontal curves, based on AASHTO SSD design values (SSD ≤ L), Case 1
SSD restrictions  Design speed, V_{d} (km/h)  

60  70  80  90  100  110  120  
Stopping sight distance, SSD (m), AASHTO [2]  85  105  130  160  185  220  250 
Calculated radius (m): desirable (HSO = 4.8 m)^{*}  188  287  440  667  891  1260  1628 
Calculated radius (m): desirable (HSO = 3.0 m) ^{*}  301  459  704  1067  1426  2017  2604 
Minimum radius, Rmin (m), equilibrium concept e(max) = 8 %, [2]  113  168  229  304  394  501  667 
AB: Available SSD (m), HSO = 4.8 m, R = Rmin **  66  80  94  108  123  139  160 
AB: Available SSD (m), HSO = 3.0 m, R = Rmin**  52  63  74  85  97  110  127 
Table 3 and Figs. 6, 7 emphasize the differences between the available horizontal SSD (for R = Rmin) vs. the design SSD values, and between Rmin (equilibrium concept) and the desirable horizontal radius (based on SSD design values). These differences increase as the design speed increases.
4.1 Sensitivity analysis for available horizontal sight distance and desirable radii (SSD > L), case 2
The gap between the available horizontal SSD (for R = Rmin) vs. the design SSD values and between Rmin (equilibrium concept) and the desirable radius (based on SSD design values) can be reduced when SSD > L (Eq. 10, 10a).
Examples of SSD restrictions on horizontal curves, based on AASHTO SSD design values (SSD = 2·L), Case 2
SSD restrictions  Design speed, V_{d} (km/h)  

60  70  80  90  100  110  120  
Stopping sight distance, SSD (m), AASHTO [2]  85  105  130  160  185  220  250 
Calculated radius (m): desirable (HSO = 4.8 m)^{*}  141  215  330  500  668  945  1221 
Calculated radius (m): desirable (HSO = 3.0 m) ^{*}  226  345  528  800  1070  1513  1953 
Minimum radius, Rmin (m), equilibrium concept, e(max) = 8 %, [2]  113  168  229  304  394  501  667 
AB Available SSD (m) HSO = 4.8 m, R = Rmin **  72  88  100  113  128  142  165 
AB Available SSD (m) HSO = 3.0 m, R = Rmin**  53  65  75  86  97  110  127 
Table 4 notifies that if SSD = 2·L, the gap is reduced but is still maintained i.e.:
AB_{Available} < SSD, and, R_{Desirable} > R_{min}.
Even if this gap is totally resolved the question is how practical is the ratio between SSD and L that is obtained for this optimal situation.
Sensitivity analysis of AB_{Available} (Available horizontal sight distance), HSO = 4.8 m, SSD > L, Case 2
Design speed (km/h)  60  70  80  90  100  110  120 

Stopping sight distance (m)  85  105  130  160  185  220  250 
AB (HSO = 4.8), R = Rmin  
S = 1.0·L  66  80  94  108  123  139  160 
S = 1.5·L  67  81  94  108  123  139  160 
S = 2.0·L  72  88  100  113  128  142  165 
S = 2.5·L  81  98  111  123  139  153  178 
S = 3.0·L  91  110  123  136  154  168  195 
S = 3.5·L  101  123  137  151  170  184  215 
S = 3.75·L  107  129  144  158  178  193  225 
S = 4.0·L  113  136  152  166  187  202  236 
S = 4.25·L  118  143  159  174  196  212  247 
S = 4.5·L  124  150  167  182  205  221  258 
S = 4.75·L  130  157  174  190  214  231  270 
S = 5.0·L  136  164  182  198  223  241  281 
S = 6.0·L  160  193  214  232  261  281  328 
S = 7.0·L  185  223  246  267  299  322  376 
S = 7.5·L  197  237  262  284  319  343  401 
Horizontal Rmin for emax = 8 %  113  168  229  304  394  501  667 
Sensitivity analysis of AB_{Available} (Available horizontal sight distance), HSO = 3.0 m, SSD > L, Case 2
Design speed (km/h)  60  70  80  90  100  110  120 

Stopping sight distance (m)  85  105  130  160  185  220  250 
AB (HSO = 3.0), R = Rmin  
S = 1.0·L  52  63  74  85  97  110  127 
S = 1.5·L  52  64  75  88  100  114  131 
S = 2.0·L  53  65  75  86  97  110  127 
S = 2.5·L  57  69  79  89  101  112  130 
S = 3.0·L  62  75  85  95  108  119  138 
S = 3.5·L  68  82  93  103  116  127  148 
S = 3.75·L  71  86  97  107  121  132  153 
S = 4.0·L  74  90  101  111  125  137  159 
S = 4.25·L  78  94  105  116  130  142  165 
S = 4.5·L  81  98  110  120  136  147  172 
S = 4.75·L  85  102  114  125  141  153  178 
S = 5.0·L  88  107  119  130  146  159  185 
S = 6.0·L  103  124  138  150  169  182  213 
S = 7.0·L  118  142  157  171  192  207  242 
S = 7.5·L  125  151  167  182  204  220  257 
Horizontal Rmin for emax = 8 %  113  168  229  304  394  501  667 
Sensitivity analysis of R_{Desirable}, HSO = 4.8 m, SSD > L, Case 2
Design speed (km/h)  60  70  80  90  100  110  120 

Stopping sight distance (m)  85  105  130  160  185  220  250 
R_{SSD} (HSO = 4.8)  
S = 1.0·L  188  287  440  667  891  1260  1628 
S = 1.5·L  167  255  391  593  792  1120  1447 
S = 2.0·L  141  215  330  500  668  945  1221 
S = 2.5·L  120  184  282  427  570  807  1042 
S = 3.0·L  105  160  245  370  495  700  904 
S = 3.5·L  92  141  216  327  437  617  797 
S = 3.75·L  87  133  203  308  412  583  752 
S = 4.0·L  82  126  193  292  390  551  712 
S = 4.25·L  78  119  183  277  370  523  676 
S = 4.5·L  74  113  174  263  352  498  643 
S = 4.75·L  71  108  166  251  336  475  613 
S = 5.0·L  68  103  158  240  321  454  586 
S = 6.0·L  57  88  134  204  272  385  497 
S = 7.0·L  50  76  117  177  236  334  432 
S = 7.5·L  47  71  110  166  222  314  405 
Horizontal Rmin for emax = 8 %  113  168  229  304  394  501  667 
Sensitivity analysis of R_{Desirable} , HSO = 3.0 m, SSD > L, Case 2
Design speed (km/h)  60  70  80  90  100  110  120 

Stopping sight distance (m)  85  105  130  160  185  220  250 
R_{SSD} (HSO = 3.0)  
S = 1.0·L  301  459  704  1067  1426  2017  2604 
S = 1.5·L  268  408  626  948  1268  1793  2315 
S = 2.0·L  226  345  528  800  1070  1513  1953 
S = 2.5·L  193  294  451  683  913  1291  1667 
S = 3.0·L  167  255  391  593  792  1120  1447 
S = 3.5·L  147  225  345  522  698  988  1276 
S = 3.75·L  139  212  325  493  659  932  1204 
S = 4.0·L  132  201  308  467  624  882  1139 
S = 4.25·L  125  191  292  443  592  837  1081 
S = 4.5·L  119  181  278  421  563  797  1029 
S = 4.75·L  113  173  265  402  537  760  981 
S = 5.0·L  108  165  254  384  513  726  938 
S = 6.0·L  92  140  215  326  436  616  796 
S = 7.0·L  80  122  187  283  378  535  691 
S = 7.5·L  75  114  175  265  355  502  648 
S = 8.0·L  71  108  165  250  334  473  610 
Horizontal Rmin for emax = 8 %  113  168  229  304  394  501  667 

For HSO = 4.8 m the ratio between SSD and L is 4.5.

For HSO = 3.0 m (more limited horizontal sight distance) the ratio between SSD and L is 7.5.
The critical design speed for meeting the horizontal sight distance criteria is approximately 110 km/h.

For HSO = 4.8 m, l = (SSDL)/2 = (4.5·LL)/2 = 1.75·L

For HSO = 3.0 m, l = (SSDL)/2 = (7.5·LL)/2 = 3.75·L
These resulted lengths of tangent edges, especially for HSO = 3.0 m, are much longer than the horizontal curve (L) itself.
This means that the highway engineer might consider increasing the horizontal curve radius as well as implementing limited dimensions of tangent edges (l). If the designed radius of the horizontal curve is larger than the minimum radius determined by Eq. 2, then the horizontal curve can be designed to a smaller superelevation rate than the maximum superelevation, e_{max}, and maintain less constrained and more comfort driving in addition to the basic advantage of less limited horizontal sight distance discussed in this study.
5 Summary and conclusion
Barriers along open highways and walls on tunnels may restrict the available sight distance in the design of horizontal curves. The minimum radius that is based on the equilibrium of the centrifugal force, is too small for the requirements of stopping sight distance when there are obstructions along the road (especially the median barrier on open roadways) that intrude on the line of sight. This study focuses on sight distance restrictions on horizontal curves.
The study examines these restrictions for the conventional case (case 1) when the stopping sight distance lies within the length of the horizontal curve (i.e. SSD ≤ L) and for the second scenario (case 2) when the sight distance lies outside the length of the horizontal curve (i.e. SSD > L).
When SSD ≤ L the differences between the available horizontal SSD (for R = Rmin) vs. the design (demanded) SSD values and between Rmin (equilibrium concept) vs. the desirable horizontal radius (based on SSD design values) are significant.
The sensitivity analysis results for SSD > L show that the gap between the available horizontal SSD (for R = Rmin) vs. the design SSD values and between Rmin vs. the desirable radius can be totally resolved when SSD/L equals to 4.5 for HSO = 4.8 m, and when SSD/L equals to 7.5 (for HSO = 3.0 m). Practically, in most cases, such conditions are not feasible in horizontal curve design, especially for HSO = 3.0 m.
The study also discusses the maximum obstruction height to ensure sightline while driving along a horizontal curve, for three types of sight distance (stopping SD, decision SD, passing SD) when the horizontal sight distance requirements are not applicable. The maximum obstruction height is assumed to be the average between the driver eye height and the object height.
When the limitations of horizontal stopping sight distance are valid and the obstruction height is higher than its maximum value, the highway engineer might consider a tradeoff by increasing the horizontal curve radius as well as adjusting the design to SSD > L and implementing limited dimensions of tangent edges (l). Additional improvements assuming that safety barriers intrude the sight distance could be: (1) reducing the design speed along the horizontal curve by no more than 10 km/h (accompanied by appropriate traffic signs) in order to maintain design consistency, (2) widening the left shoulder or right shoulder along the horizontal curve in order to achieve wider HSO, (3) Using less conservative stopping sight distance criteria such as reducing the equivalent deceleration rate (d) if weather conditions are regularly dry or reducing the perception reaction time design value according to driving behavior characteristics [3, 19].
Notes
Declarations
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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