Autonomous Vehicles and Vertical Road Design: A Parametric Assessment of Stopping Sight Distance and Vertical Curve Lengths

Abstract

Traditional road geometric design is based on assumptions regarding human perception and reaction, which directly influences Stopping Sight Distance (SSD) and the associated design parameters of vertical curves. Under a future scenario of full autonomous vehicle (AV) deployment, reduced perception–reaction times and modified sensing configurations may change visibility-controlled design requirements. This study presents a structured parametric assessment of SSD and vertical curve lengths under the assumption of full AV operation. Variations are considered in reaction time, sensor height, sensor inclination angle, longitudinal grade, and vehicle operating speed. Default parameter values derived from current design standards, together with ranges reported in the literature, are used to evaluate the geometric implications of full vehicle automation within a controlled analytical framework. The results indicate that reduced reaction times and increased sensor heights of AVs may decrease required SSD values and consequently shorten crest and sag vertical curve lengths compared to conventional human-driven vehicle assumptions. For sag curves in particular, headlight inclination angle is revealed as a significant geometric variable. Overall, the study proposes a framework for examining the interaction between AV sensing characteristics and vertical geometric design, thereby providing a basis for future evaluation of design standards without directly prescribing modifications to current practice.

1. Introduction

1.1. Study’s Motivation

For decades, the main axes of national and international road networks have been designed and constructed according to well-established methods, strict standards, as well as both empirical and analytical knowledge [1]. This was so far translated in the perception that the fundamental principles of road geometric design are considered essentially “research solved”. Design codes, such as the OMOE guidelines in Greece for example [2], provide clear instructions for horizontal and vertical alignment, minimum sight distances, and requirements for slopes and curves.

Although there is still margin for secondary roadway improvement, the core practice of road engineers has, for the most part, focused on the evaluation, maintenance, and optimization of existing pavements, as they comprise major transportation assets of the existing heavy-duty motorways. For more than two decades, much of road engineering research has identified new issues on aspects of pavement materials, pavement deterioration patterns or material performance modelling, asset condition assessment and maintenance planning [3,4,5].

However, in recent years, the introduction of autonomous vehicles (AVs) and the accelerating growth of the automotive industry pose new challenges and fundamentally reshape the landscape so far [6,7,8]. In more detail, the engineering community must now prepare road infrastructure to meet emerging challenges, thereby striving to answer open research questions like:

• How can road safety and operational efficiency be ensured when assumptions about human reaction and visual perception no longer apply?
• What adjustments may be needed in geometric features such as vertical curve lengths and minimum sight distances because of the different perceptions and reactions?
• How might qualitative factors, such as construction practices, signage materials, and operational requirements, be affected?

In this sense, a new research framework opens in the geometric design of future roads, where traditional knowledge and standards should be integrated with the technological possibilities offered by autonomous mobility [7,9,10]. The philosophy behind this emerging trend is that road design can no longer be considered a “solved problem”; it is rather a dynamic field that requires adaptation to new technologies. In this context, the way vehicles operate and interact with their road environment should be more gradually, yet informatively, transformed.

1.2. Core Aspects of Road Geometric Design

Geometric design comprises a structured framework towards the safe and efficient operation of roadways. Design principles consider vehicle dynamics and human factors to establish horizontal and vertical alignment, define cross-sectional elements, and meet sight distance requirements [11]. Established international standards, such as the AASHTO Green Book [12], or even national design guidelines (e.g., [2]), specify minimum values for horizontal curve radii, longitudinal and transverse grades, vertical curve lengths, and Stopping Sight Distance (SSD). The latter is traditionally considered based on human drivers’ perception and reaction characteristics as well as conventional vehicle performance [6].

Moving forward, the horizontal alignment includes the plan geometry of the road comprising tangents, curves and transition areas (e.g., spiral curves). Curve radii and superelevation are configured following speed and lateral stability criteria [13]. In the vertical road configuration, the longitudinal slope controls the travel path of a roadway at reasonable speeding, including crest or sag curves that both directly depend on SSD and headlight sight distance. Crest curves are typically controlled by day-time visibility constraints, while sag curves are governed by night-time illumination conditions [14]. The cross-sectional elements of roads include lane widths, and shoulders that ensure drainage efficiency, continuous vehicle stability through superelevation adjustments and operational safety margins.

From the above, it appears that sight distance remains a central parameter in both horizontal and vertical design, incorporating reaction time, braking capability, and grade effects. Reaction time for human-based driving has been reported to range from 1.5 to 2.5 s [9]. A more conservative approach is followed in [12], where a reaction time of 2.5 s is assumed, whereas in [2] it is suggested to use the value of 2 s. In addition, based on the SSD dependence of vertical curve lengths, it appears that the considered reaction time induces practical constructability issues, as it affects earthwork volumes and the overall road’s adaptation to the natural landscape [8,9]. Of course, earthworks do also depend on the lateral extension of a particular section of the road, as a road often consists of cut-and-fill segments. Drainage is still an important aspect to consider.

Overall, the traditional or human-based geometric design represents a conservative balance between safety, operational efficiency, and construction feasibility, as it is grounded in the interaction between the drivers of human-driven vehicles (HDVs) and their surrounding environment.

1.3. Road-Related Challenges from AV Deployment

Compared to conventional vehicles, AVs are anticipated to have lower accident rates, quicker reaction times, and less driver behavior variability [15]. Additionally, it is believed that AVs will boost capacity, enhance traffic flow, reduce congestion, and improve the efficiency of the transportation network [16]. By eliminating the human factor, one of the major AV advantages is safety, considering that nearly 80% of road accidents are caused by human errors, like over-speeding, distracted driving, etc. [17]. Of course, the infrastructure status is also critical for road safety [18,19,20].

Given the above rationale, the introduction of AVs definitively questions some of the traditional assumptions in road design. Operating with faster and more consistent perception, and being supported by advanced sensors, AVs are able to efficiently interact with the surrounding environment. Figure 1 graphically illustrates the capabilities of AV communication with pedestrians, vehicles, infrastructure components, and the overall road network [10,21,22].

Therefore, it comes as a rational remark that in a fully AV road environment, the improved reaction capabilities could reduce the necessary stopping distances for safe vehicle maneuvering leading to substantial crash reduction rates [9]. Recall that SSD is the sum of perception–reaction distance and braking distance. So, even if braking distance remains the same, as it practically depends on speed values and the speed change rates (i.e., deceleration), a reduction in the first part of the SSD definitively reduces the whole SSD of AVs, thereby indicating better and more efficient obstacle detection ability (Figure 2).

Indeed, the reaction times of AVs have been reported to range from 0.1 to 0.5 s for full AV deployment [7,9,23,24], whereas for mixed traffic conditions, including both conventional vehicles and AVs, the reaction time of AVs is higher (e.g., 1 s [25]), but still lower than conventional ones. In terms of road geometric design, once the SSD controls the value of vertical curve radii, vertical curve lengths highly depend on the variation in the considered reaction time. In addition, AV deployment could also introduce new considerations, including sensor capabilities and requirements, vehicle-to-infrastructure communication challenges, and environmental/weather factors that could affect system reliability and require attention. However, such issues fall outside the interest of road design.

Aspects of horizontal alignment including curve radii and spiral curve lengths do not depend on the perception–reaction time. Thus, being more dependent on basic principles of vehicle dynamics (recall the fundamental relationship linking side friction coefficient, speed, curve radius and superelevation), the requirements for the minimum horizontal curve radii remain constant [8]. Spiral curve lengths also depend on the curve radius, the design speed and the rate of increase in lateral acceleration, linked to comfort levels, and thus are independent of drivers’ performance metrics, like reaction time.

Another important factor of AV movement patterns is their improved lane positioning thanks to accurate radar systems and sensors. A consistent lateral vehicle control may permit narrower lane widths without considering the necessary lateral driving variability [10]. Most importantly, safety and traffic flow efficiency are not compromised through this reduction trend. While standard lane widths range from 3 to 3.7 m [10,26], lane width for AVs can become 2.5 m or even lower [8,27]. The reduction rate is not guaranteed for mixed traffic scenarios, since the existence of human-based vehicles require the necessary tolerance of drivers’ behavior [10]. A dedicated lane for AVs only could be a solution for these real-case scenarios.

No matter the reduction rate, a smaller lane width also exhibits technoeconomic implications for road pavement construction, since narrower lanes could be cheaper. Nevertheless, a narrower lane could accelerate pavement deterioration and maintenance needs because of the nearly identical wheel paths. Therefore, a balance between the achieved safety levels and the infrastructure condition status is needed, thereby making the issue of lane width an open aspect of future road design.

Because of AV deployment, qualitative effects must be taken into account in addition to quantitative modifications. Improved road markings, signage, reflective materials, or integrated communication systems embedded within the road infrastructure may be necessary for AV operation [28,29]. These issues can definitively affect material selection and road building methods. For example, the utility of embedded sensors may be hampered by regular pavement reconstruction activities.

Furthermore, machine-readable standards may replace driver-centric visual signals in signage design [30]. AV traffic domination may also have an impact on operational procedures including intersection control, speed harmonization, and lane utilization [31]. These modifications highlight the necessity of considering the wider interactions between automobiles, control systems, and infrastructure components when assessing roadway design, in addition to the physical geometry.

1.4. Aim and Objectives

Until now, several recent studies have examined the implications of autonomous vehicles on roadway geometric design. For instance, Welde and Qiao [32] investigated the effects of AVs on SSD and vertical curve lengths through a comparative computational approach. Zhao et al. [33] proposed revised design standards for freeways under a full autonomous driving scenario, focusing on recommended design values across multiple geometric elements. Most recently, Birhane et al. [34] provided a comprehensive review of next-generation road design, addressing broader infrastructure adaptations required for AV deployment, including alignment design, intersection design, signal and communication attributes, pavement and structure status, etc.

It appears that the existing studies either adopt a normative perspective with the focus being put on the proposal of design values, or a conceptual approach, where the emphasis is on a broader infrastructure transformation. Contrariwise, the development of a structured parametric framework that systematically captures the interaction between AV sensing characteristics and geometric design parameters has not been systematically explored.

In this context, the present study contributes by developing a multiparametric analytical framework that integrates the following parameters: (i) reaction time, (ii) operating speed, (iii) longitudinal grade, and (iv) sensor-related characteristics (height and inclination angle). Their impact on SSD and vertical curve requirements is quantified. Rather than proposing immediate modifications to existing standards, the study aims to provide a consistent basis for assessing how AV-related parameters may influence geometric design under fully autonomous conditions. To meet the research aim, the following objectives were set:

• To present the necessary design background on SSD and vertical alignment based on both international and national standards.
• To quantify the potential effects of AV deployment on these design parameters, considering changes in vehicle perception–reaction time, and sensor layout for obstacle identification based on literature observations.
• To compare the resulting SSD values and corresponding vertical curve length requirements under HDV and AV assumptions.

Ultimately, the study provides a comparative framework of how current design standards for HDVs could apply to AVs, which will be useful for engineers, and road planners. The rest of the paper is organized as follows: Section 2 includes the description of the methodology followed, with the necessary background of the Greek standards for road design. Section 3 includes the results of the structured framework, with relevant discussion points being provided in Section 4. Finally, Section 5 includes the concluding remarks of the study.

2. Methodology and Assumptions

2.1. Stopping Sight Distance

The first part of this study focuses on the SSD. Perception–reaction distance and the braking distance are the two primary distances that make up the SSD. The driver’s focus and response are the main determinants of the perception–reaction distance. Conversely, the vehicle’s mechanical properties determine the braking distance. Assuming identical mechanical behavior of HDVs and AVs, as well as identical surrounding conditions, like weather, grade, pavement surface status, etc., it occurs that the braking distance remains constant. Given these remarks, when considering different reaction times for HDVs and AVs, only the first part of the SSD differentiates.

Although deceleration rates for AVs are assumed to be similar to those of HDVs to isolate the influence of perception–reaction time on SSD, AV control systems in real life may adopt advanced braking strategies. A smoother or more optimized deceleration profile could influence SSD values, particularly at higher speeds. Therefore, the calculation and interpretation of the SSD should be made under the assumption of comparable braking performance, while acknowledging that alternative control strategies may further affect stopping requirements. In this context, the SSD in [2] is mathematically calculated in m as:

$$\mathrm{S}\mathrm{S}\mathrm{D}={\mathrm{S}}_1+{\mathrm{S}}_2={\displaystyle \frac{\mathrm{V}}{3.6}}\times {\mathrm{t}}_{\mathrm{p}-\mathrm{r}}+{\displaystyle \frac{{\left(\frac{\mathrm{V}}{3.6}\right)}^2}{2 \ast (\mathrm{a}+\mathrm{g}\times \mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e})}}$$

(1)

where:

• ${\mathrm{S}}_1$: perception–reaction distance (m);
• ${\mathrm{S}}_2$: braking distance (m);
• V: design speed (km/h);
• ${\mathrm{t}}_{\mathrm{p}-\mathrm{r}}$: perception–reaction time (s);
• a: vehicle deceleration (m/s²);
• g: acceleration due to gravity, equal to 9.81 m/s²;
• slope: longitudinal grade (m/m), positive for ascending segments and negative for descending segments.

For the parametric evaluation of the perception–reaction time, the considered values for HDVs were 2 s [2] and 2.5 s [12]. Following literature suggestions, two values were considered for the case of AVs [7,9,23,24], namely 0.2 s and 0.5 s.

As per the considered speed, it has to be clarified that national guidelines [2] differentiate the role of speed in SSD estimation. While in [12], the design speed is used, or else, the speed at which the road is intended to be safely navigable, the operation speed, known as V₈₅, is considered in [2]. V₈₅ represents typical driver behavior, corresponding to the 85th percentile of observed speeds, thereby reflecting real-world (i.e., measurable) traffic flow conditions. Normally, V₈₅ exceeds the design speed. Nevertheless, AASHTO makes more conservative assumptions for the reaction time, thereby counterbalancing to some extent potential differences in the SSD calculations. Since readily calculated SSDs are already tabulated in [12] for several design speeds, in this study the concept of V₈₅ was used in both approaches for comparability purposes. Assuming a higher speed is more conservative in terms of the SSD, as it becomes feasible to indirectly consider various factors that could limit the braking capability of a vehicle, like rainy road surfaces, poor tire–pavement interaction, and a distressed pavement condition status.

Assuming travelling on highway dual carriageways, the national guidelines propose the following formula to estimate V₈₅ (km/h) for new roads based on the design speed V (km/h) [2]:

$$\begin{array}{c}{\mathrm{V}}_{85}=\mathrm{V}+20,\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n} \mathrm{V}\ge 100{\displaystyle \frac{\mathrm{k}\mathrm{m}}{\mathrm{h}}}\\ {\mathrm{V}}_{85}=\mathrm{V}+30,\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n} \mathrm{V}<100{\displaystyle \frac{\mathrm{k}\mathrm{m}}{\mathrm{h}}}\end{array}$$

(2)

Deceleration in [12] is assumed to be 3.4 m/s², whereas variable deceleration is considered against operation speeds in [2], according to

Table 1. Deceleration values for various operation speeds [2].

V85 (km/h)	a (m/s2)
50	4.4
60	4.2
70	4.0
80	3.8
90	3.6
100	3.4
110	3.3
120	3.1
130	3.0

.

Regarding longitudinal grade considerations, the maximum allowable grades were adopted according to [2], as a function of design speed and terrain classification (i.e., level, rolling, and mountainous). In the present study, rolling terrain was assumed, leading to maximum absolute grades of 8% (50 km/h), 7% (60 km/h), 6% (70 km/h), 5% (80–90 km/h), and 4% (≥100 km/h).

However, in order to develop a generalized parametric framework for SSD sensitivity analysis, grade values of 0%, ±1%, ±3%, ±5%, and ±7% were examined independently of the speed–grade regulatory coupling. This approach allows the isolated assessment of the influence of longitudinal grade on SSD. The regulatory maximum grade constraints were strictly applied in the subsequent vertical alignment analysis (Section 2.2).

2.2. Length of Vertical Curves

Building upon the design interdependency between SSD and vertical curves, this subsection gives the mathematical background for determining the length of the vertical curves, which is associated with the related earthworks during road construction, thereby exhibiting technoeconomic implications.

For the case of a crest curve (Figure 3a), the main difference between the consideration of HDVs versus AVs lies upon the height of the one being responsible for vehicle controlling: the driver’s eye height in HDVs, and the sensor’s height in AVs (Figure 3b). This means that the traditional “eye height” in the case of the AVs will depend on the LiDAR sensor configuration and setup of the AV, which is usually on the top of a vehicle, and thus higher than the classical driver’s position.

Mathematically, the length L of the crest curve in m and the necessary SSD in m are linked through the relationship (assuming that L > SSD):

$$\mathrm{L}=2\times \left({\displaystyle \frac{\mathrm{H}}{2}}\times \mathsf{\Delta }\mathrm{s}\right)=\mathrm{H}\times \mathsf{\Delta }\mathrm{s}={\displaystyle \frac{{\mathrm{S}\mathrm{S}\mathrm{D}}^2}{2\times {\left(\sqrt{{\mathrm{h}}_1}+\sqrt{{\mathrm{h}}_2}\right)}^2}}\times \mathsf{\Delta }\mathrm{s}$$

(3)

where:

• $\mathrm{H}$: radius of the vertical curve (m);
• $\mathsf{\Delta }\mathrm{s}$: the algebraic difference in grade of two successive segments (dimensionless); for example, assuming two segments with grades +5% and −3% yields a $\mathsf{\Delta }\mathrm{s}$ of 0.08;
• ${\mathrm{h}}_1$: eye/sensor height (m);
• ${\mathrm{h}}_2$: obstacle height (m).

For HDVs, AASHTO [12] suggests using the values ${\mathrm{h}}_1$ = 1.08 m and ${\mathrm{h}}_2$ = 0.60 m. Greek guidelines [2] consider the value ${\mathrm{h}}_1$ = 1.06 m for eye height, whereas variable obstacle heights are considered depending on the value of operation speed. In more detail, obstacle heights range from 0.07 to 0.42 m, with the lower values corresponding to lower operation speeds that probably ensure more accurate obstacle detection ability. As the speed increases, so does the obstacle height to ensure timely detection and efficient stopping.

To complete the parametric study of crest curve lengths, the sensor height for AVs is needed. Prior studies indicate that sight distance improves as sensor elevation increases, thereby rendering the positioning of the LiDAR system a decisive factor in determining the required vertical curve length [9]. From documented AV configurations, a conservative sensor height of 1.84 m was adopted elsewhere, although differentiations because of evolving manufacturing patterns was acknowledged [8]. Following the parametric nature of this study, three values, namely 1.6, 1.8 and 2 m, were assumed for the AV’s sensor height. These values are representative of typical LiDAR sensor placements reported in the literature, e.g., [8,32,34], where sensing systems are commonly mounted on the vehicle roof or upper body of smart cars to enhance the visibility and detection range.

Sag curve design (Figure 4) is traditionally controlled by night-time visibility, which depends on headlight height and beam inclination angle. In AVs, LiDAR sensors replace headlights, providing higher observation height and, thus, a wider beam angle. The mathematical expression of a sag curve length L in m is as follows (assuming that L > SSD):

$$\mathrm{L}=2\times \left({\displaystyle \frac{\mathrm{H}}{2}}\times \mathsf{\Delta }\mathrm{s}\right)=\mathrm{H}\times \mathsf{\Delta }\mathrm{s}={\displaystyle \frac{{\mathrm{S}\mathrm{S}\mathrm{D}}^2}{2\times \left(\mathrm{h}+\mathrm{S}\mathrm{S}\mathrm{D}\times \sin \mathsf{\epsilon }\right)}}\times \mathsf{\Delta }\mathrm{s}$$

(4)

where:

• $\mathrm{H}$: radius of the vertical curve (m);
• $\mathsf{\Delta }\mathrm{s}$: the algebraic difference in grade of two successive segments (dimensionless); for example, assuming two segments with grades −2% and +5% yields a $\mathsf{\Delta }\mathrm{s}$ of 0.07;
• $\mathrm{h}$: headlight/sensor height (m);
• $\mathsf{\epsilon }$: inclination angle of the headlight beam or LIDAR sensor (in degrees).

For HDVs, AASHTO [12] suggests using the values $\mathrm{h}$ = 0.60 m and $\mathsf{\epsilon }$ = 1 degree. For the h values of AVs, the same height as in crest curves is used, whereas for the angle $\mathsf{\epsilon }$, values ranging from 13 to 27 degrees have been reported elsewhere [8,23]. Since AV manufacturing is evolving, the exact values right now may vary. Thus, following the parametric nature of this study, two angles were considered, namely 5 and 10 degrees. The sensor height was assumed to be equal to 1.6 m.

It should be acknowledged that the selected inclination angles, as well as the previously assumed sensor height range, may represent a limited, yet representative, subset of the ranges reported in the literature. These values were chosen to enable a structured and consistent parametric analysis, while reflecting the typical configurations of current AV sensor systems.

However, especially for the case of sag curves, vertical road design is particularly sensitive to variations in beam inclination angle and sensor placement. A broader range of inclination angles and sensor heights, as documented in previous studies [8,23], can probably lead to different SSD and vertical curve length requirements. Therefore, the results of this study should be interpreted within the context of the selected parameter range.

Furthermore, there is an additional empirical check of the vertical curve length according to [2]. In particular, to prevent the visual perception of abrupt changes in the longitudinal profile at crests or sags, the vertical tangent length, or else the half curve length, should be (at a minimum) equal to the design speed [2]. For example, for a segment with a design speed of 80 km/h, the minimum crest or sag curve length should be 2 × 80 = 160 m.

As per the considered speeds in the evaluation of vertical curve lengths, design speeds falling in the range of 70–110 km/h were chosen that are indicative for high-speed dual carriageways. As illustrated in Figure 5, the selected speed range corresponds to posted speeds commonly observed on motorways with pronounced vertical alignment variations. So, for the design speeds 70, 80, 90 and 110 km/h, the operation speeds were calculated as 100, 110, 120, and 130 km/h, respectively, according to Equation (2).

Finally, the maximum grade values were considered according to [2] as previously explained. Based on this, for the assumed speeds, two cases of $\mathsf{\Delta }\mathrm{s}$ were considered; one corresponding to an abrupt slope change, and one corresponding to a smooth slope change. The abrupt slope change (high $\mathsf{\Delta }\mathrm{s}$) was assumed as 0.10 and 0.08 for operation speeds in the range of 100–120 km/h, and 130 km/h, respectively. The smooth slope change (low $\mathsf{\Delta }\mathrm{s}$) was assumed as 0.07 and 0.05 for operation speeds in the range of 100–120 km/h, and 130 km/h, respectively.

3. Results

3.1. Calculation of SSD

This part of the investigation includes the parametric SSD calculation for HDVs and AVs. Gathering all SSDs for all combinations of speeds and grades, there is a sample of 81 cases. SSD is first presented in Figure 6 for HDVs including OMOE and AASHTO assumptions for the perception–reaction time. Recall that the concept of operation speed was followed in both cases.

From Figure 6, it appears that for SSDs up to the range of 200–250 m, the considered perception time dominates, as the AASHTO leads to higher SSD values. On the other hand, for SSDs higher than 250 m, speed probably becomes more dominant in conjunction with the considered longitudinal grade.

Thereafter, calculated SSDs according to [2] were compared as an overview in the form of boxplots (Figure 7). The three boxplots correspond to a perception–reaction time of 2 s (HDVs), 0.2 s (AVs—first case), and 0.5 s (AVs—second case).

Profoundly, the consideration of lower perception–reaction times for AVs lowers the necessary SSD. Recall that the concept of the operation speed was adopted herein to ensure comparability. This implies that using the design speed for AVs where the human factor is fully eliminated could have led to even more pronounced differences in the SSD comparison. This is a rather important note, since in the era of full AV deployment, vehicles traveling at higher speeds than the design value might not be as usual a case as nowadays.

In terms of the impact of speed and longitudinal grade on the produced SSD values, Figure 8 presents the parametric evaluation in the form of surface plots. All of the investigated cases are considered, i.e., two perception–reaction times for HDVs and two for AVs. The joint impact of speed and grade can be assessed from Figure 8.

The worst case for an emergent stopping process happens at the lowest negative slope and the highest speed. In contrast, a vehicle moving uphill with the highest positive slope and the lowest speed can successfully stop under the most favorable conditions, which means it has the smallest required SSD. Indeed, from all subfigures, the maximum SSD was calculated to be equal to 355, 335, 290, and 300 m, whereas the minimum SSD was calculated to be equal to 50, 60, 25, and 30 m.

For all other scenarios, the trends in SSD show that speed plays a crucial role because it is known that it has a squared effect on braking distance. The impact of the road grade is also distinguishable. Descending grades, or negative values, consistently require a longer SSD than ascending grades of the same size, as a downhill slope decreases effective deceleration. This combined effect becomes more significant at higher speeds, where the need for braking is already greater.

The additional comparison of subfigures (a) to (d) shows a downward shift in the surface plots because of the reduced reaction time. This shift reflects the role of the perception–reaction component in the total SSD. The reduction is more noticeable at lower and intermediate speeds, where the reaction distance is a larger part of the total stopping distance. This is a rather important aspect of AVs especially when traveling in urban and suburban areas, where lower speeds dominate. These findings indicate that, under reduced reaction time assumptions, geometric visibility requirements decrease, which may complement the broader safety improvements attributed to AV technology according to the literature [35,36]. At higher speeds, even though the absolute differences are significant, the braking part increasingly affects the total value of SSD, thereby shortening the impact of reaction time when moving on highways, where higher speeds are met.

3.2. Calculation of Vertical Curve Lengths

Given all the assumptions described in Section 2.2, the length of the crest and sag curves is calculated in this section. Initially, some representative cases are presented in

Table 2. Representative scenarios for crest curve length data.

Vehicle Type (Reaction Time, Sensor Height)	Operation Speed (km/h)	Slope Change Δs	Length of Crest Curve (m)	% Change in Length of Crest Curve
HDV (t = 2 s, ${\mathrm{h}}_1$ = 1.06 m)	100	0.10	618	-
AV (t = 0.5 s, ${\mathrm{h}}_1$ = 1.6 m)	100	0.10	271	−56%
AV (t = 0.5 s, ${\mathrm{h}}_1$ = 1.8 m)	100	0.10	249	−60%
AV (t = 0.5 s, ${\mathrm{h}}_1$ = 2 m)	100	0.10	231	−63%
HDV (t = 2 s, ${\mathrm{h}}_1$ = 1.06 m)	130	0.05	747	-
AV (t = 0.5 s, ${\mathrm{h}}_1$ = 1.6 m)	130	0.05	393	−47%
AV (t = 0.5 s, ${\mathrm{h}}_1$ = 1.8 m)	130	0.05	364	−51%
AV (t = 0.5 s, ${\mathrm{h}}_1$ = 2 m)	130	0.05	339	−55%

and

Table 3. Representative scenarios for sag curve length data.

Vehicle Type (Reaction Time, Headlight Height and Angle)	Operation Speed (km/h)	Slope Change Δs	Length of Sag Curve (m)	% Change In Length of Sag Curve
HDV (t = 2 s, $\mathrm{h}=0.6$ m, ε = 1°)	100	0.10	405	-
AV (t = 0.5 s, h = 1.6 m, ε = 5°)	100	0.10	65	−84%
AV (t = 0.5 s, h = 1.6 m, ε = 10°)	100	0.10	35	−91%
HDV (t = 2 s, $\mathrm{h}=0.6$ m, ε = 1°)	130	0.05	371	-
AV (t = 0.5 s, h = 1.6 m, ε = 5°)	130	0.05	64	−83%
AV (t = 0.5 s, h = 1.6 m, ε = 10°)	130	0.05	33	−91%

, where the aim is to support the interpretation of the full parametric results. A clear reduction in the lengths of both types of vertical curves is shown for the typical HDV and AV configurations assumed in this paper, including their relative differences. Noticeably, a dramatic reduction in the sag curve length governed by SSD is observed (Table 3), raising concerns regarding the practical feasibility of these estimates—an issue that will be discussed later. Similar trends are consistently observed across all examined cases, as illustrated in Figure 9 and Figure 10.

In particular, Figure 9 shows the required crest curve length for different operating speeds and two slope changes. In all different cases (HDVs, and AVs with variable sensor heights), the curve length increases with operating speed, which is justified by the quadratic effect of speed on SSD. This trend is more pronounced for HDVs that have longer perception–reaction times. As per the considered slope changes, it was rationally found that for higher or more abrupt variations in the vertical road alignment, there is a demand for higher vertical transition curves. In contrast, a smoother geometric transition (i.e., low slope change) mitigates the visibility constraint by reducing the required vertical curve length.

Furthermore, following the representative examples shown in Table 2 and having as reference the “OMOE” case for HDVs (i.e., reaction time = 2 s), the required length of the crest curves is reduced by 47–56%, 51–60%, and 55–63% in the case of AVs, when considering sensor heights of 1.6, 1.8, and 2 m, respectively. A higher sensor position increases the available sight distance, thereby reducing the required SSD values. Nevertheless, even under AV assumptions, high-speed conditions (V₈₅ ≥ 120 km/h) still require substantial curve development, especially in abrupt transitions.

Overall, the results demonstrate that operating speed is the dominant controlling parameter. Reaction time (HDVs versus AVs) produces a systematic downward shift in the required vertical curve lengths, while the magnitude of slope change significantly influences crest curve length. These effects also have constructability implications, particularly at higher speeds, where the calculated lengths increase substantially.

Figure 10 shows the required sag curve lengths under the slope change scenarios, considering different reaction times (HDVs versus AVs), as well as sensor height and headlight inclination angle. For HDVs, the required lengths remain substantial, ranging approximately from 400 m to over 630 m in the case of abrupt slope change.

For AVs, sag curve lengths are dramatically reduced if the SSD criterion is to be met (recall the examples shown in Table 3 too). When the headlight inclination angle increases from 5 to 10 degrees, the required lengths decrease further, highlighting the strong geometric influence of sensor orientation in night-time or headlight-controlled visibility conditions. Recall that the sag curve length is very sensitive to the selected inclination angle. Even higher angles could further relax the requirements for the sag curve length; however, such higher values were not selected in the current parametric analysis.

As per the slope, AV-related lengths remain below 100 m even at high speeds for the abrupt case, whereas lengths are even more reduced (i.e., less than 80 m) in the smooth case of slope changes, as visibility may not be so critical in such cases. Overall, the results suggest that sensor configuration and slope affect geometric SSD requirements, particularly when compared to conventional HDV assumptions.

Furthermore, it is observed that, for AV scenarios, the calculated sag curve lengths in several cases (right part of Figure 10) fall below the typical minimum values adopted in current design practice. These findings highlight that, under improved perception and reduced reaction times, SSD may no longer be the governing criterion for sag curve design. Nevertheless, in sag curves there are additional issues to consider beyond the fulfillment of the SSD criterion, including riding comfort and adequate water drainage. Thus, even if lengths of approximately 50 m were theoretically calculated for AVs, these may be practically infeasible. Accordingly, the results from Figure 9 and Figure 10 are just indicative of the potential minimized geometric demand under full AV deployment.

In real-scale highway design, vertical curves are typically selected with radii exceeding the minimum visibility requirements in order to ensure riding comfort, drainage efficiency, and construction feasibility, thereby leading to higher curve lengths. Therefore, the presented results should be interpreted as lower-bound theoretical estimates of geometric demand under full AV deployment, rather than as directly applicable design values. This is an important aspect to clarify, as theoretical calculations must be clearly distinguished from real-world practice, where some of the derived sag curve lengths may prove unrealistic.

4. Discussion

4.1. Practical Study’s Implications

The parametric evaluation yielded reductions in SSD in the case of AVs because of the assumption of lower reaction times. Differentiated sensor characteristics in AVs may additionally translate into shorter required vertical curve lengths under visibility-controlled design. From a geometric standpoint, this has direct consequences for vertical road alignment and the associated earthworks. Shorter crest and sag curves can reduce excavation and embankment volumes, particularly in rolling or mountainous terrain. In those cases, grade changes are more pronounced and vertical road alignment can generate substantial earthwork quantities. Thus, even moderate reductions in the required curve length can influence cut–fill balance, and overall road construction cost. A quantitative example of a possible reduction in earthwork volumes is illustrated for the case of HDV-based and AV-based sag curves in Figure 11. On the contrary, in flat terrain, the algebraic grade differences are limited; thus, the geometric and earthwork benefits are expected to be marginal.

While the present study does not include a quantitative cost–benefit analysis, the reduction in vertical curve lengths and associated earthwork requirements suggests potential construction cost savings. Future research could extend this work by integrating earthwork quantities, unit construction costs, and lifecycle considerations to evaluate the economic implications of AV-based geometric design.

It should be emphasized, however, that visibility-controlled minimum radii for vertical curves are rarely adopted directly in practice, because of other factors (e.g., comfort criteria and drainage requirements) that are to be considered too. Consequently, the curve length reductions identified in this parametric study should be interpreted as potential geometric flexibility margins rather than immediate prescriptions for vertical profile modification.

From a broader perspective, the potential magnitude of the identified geometric adjustments strongly depends on the penetration rate of autonomous vehicles within the traffic fleet. This study considered the case of fully autonomous conditions, where human-based variability, including perception–reaction time, fatigue, risk tolerance, and behavioral dispersion is expected to diminish significantly. In such an environment, the concept of operating speeds, currently adopted in [2], may have a reduced statistical relevance given the increased conformity rate of AVs.

Nevertheless, in the present analysis full AV penetration was intentionally assumed to isolate the potential effects of autonomous driving on geometric design parameters under idealized conditions. In real-world applications, a long transition period with mixed traffic conditions is expected, where HDVs and AVs will coexist. Under such conditions, geometric design requirements are likely to remain governed by conservative assumptions associated with human driving behavior. Therefore, the magnitude of the reductions in SSD and vertical curve lengths identified in this study should be interpreted as an upper-bound estimate of the potential impact of AV deployment. In other words, the shortening of road geometric requirements will not be technically justified. Accordingly, potentially revisiting geometric design aspects is shifted to the period where high levels of AV adoption (if not 100%) will be met.

4.2. Study’s Limitations and Prospects

As previously said, this study was based on a fully automated traffic assumption, which does not reflect current or near-future mixed traffic conditions. Additionally, identical braking performance was assumed for HDVs and AVs in order to isolate the influence of the perception–reaction time. In reality, AV systems may exhibit different deceleration profiles depending on control algorithms and safety protocols.

The parametric evaluation also focused exclusively on visibility-based geometric constraints and did not consider riding comfort, vehicle dynamics, or drainage requirements. For sag curves in particular, very short theoretical lengths may not be practically desirable because of constructability and drainage issues, despite satisfying visibility criteria.

Furthermore, apart from the ideally controlled parameters of sensor performance (i.e., heights and inclination angles), other real-scale factors like adverse weather conditions (e.g., rain, fog, and snow), sensor occlusion due to dirt or obstacles, and glare from sunlight or oncoming headlights were not explicitly modeled. Consequently, the calculated reductions in SSD and vertical curve lengths may be overestimated compared to real-world driving conditions, where sensor effectiveness can be compromised to some extent.

On the same context, additional operational factors that could affect AV perception capabilities were not explicitly considered in this study. These include low-visibility night-time conditions, temporary roadwork zones, sensor calibration drift, and potential failures in V2V communication systems. Such conditions may further reduce AVs’ detection performance, so a technically feasible SSD might appear higher.

These aspects further reinforce the distinction between idealized theoretical estimates and real-world design applicability. In other words, the SSD reductions estimated under idealized conditions may be less pronounced in practice. Future research should investigate the combined effects of environmental and operational factors to provide a more comprehensive assessment of AV performance under more realistic driving conditions.

5. Conclusions

This study reassessed selected elements of road geometric design under the assumption of full AV deployment, focusing primarily on SSD and its implications for vertical curve design. The main remarks are as follows:

• The parametric investigation confirms that modifications in reaction time directly affect the perception–reaction component of SSD and, consequently, the geometric control parameters governing crest and sag vertical curves. While speed remains the governing variable in high-speed environments due to braking dominance, reduced reaction time can induce design sensitivity primarily in low and intermediate speeds.
• For crest curves, increased sensor height in AVs combined with reduced reaction time leads to shorter curve lengths compared to HDVs. For sag curves, the sensor inclination angle emerges as a critical geometric parameter influencing visibility-controlled design limits. Nevertheless, vertical curve design is not governed solely by visibility criteria.

It should be noted that the findings of this study are primarily based on analytical and parametric evaluations and are not supported by validation using real-world roadway data, measured SSD values, or crash records. As such, the results should be interpreted as indicative of general geometric trends under full AV deployment rather than as directly validated design outcomes. Future research could enhance the practical relevance of the present work by applying the proposed methodology to real roadway case studies, or by comparing the derived SSD and vertical curve requirements with empirical data from field measurements or safety analyses.

Overall, the parametric study suggests that AV deployment does not invalidate geometric design theory, but it provides a framework for integrating AV capabilities into future road geometric design. From that perspective, road geometric design proves its dynamic nature under the evolving trends in the automotive industry and vehicle dynamics. Systematic research is needed to capture the impact of HDV–AV coexistence in road geometric design.