1 Introduction

This study aims to analyze the current driver's eye height and suggest new values for it. Given that the driver's eye height values in the Hungarian Guidelines [1] have not been changed for nearly 40 years, and the automobile industry with its explosive growth contribute to finding cars with various dimensions that in turn affect the driver's eye height. These reasons together formed the motivation for conducting this study.

The height of the driver's eye is affected by human differences that include the height and gender of the driver, however in this study; the focus was on the height of the driver's eye without looking at these differences because they exist continuously and are not the focus of the study [2].

For this purpose, a sample of passenger cars of various shapes, sizes, and drivers (of both genders) was surveyed. Since current guidelines will be affected by the recent technology, autonomous vehicles must also be considered, which in turn will influence current driver eye height design values assigned to road design in the case of human drivers and their physical and mental capabilities.

The height of the driver's eye in Autonomous Vehicles (AVs) is represented by the height of the sensors installed on the self-driving cars.

Therefore, sight distances were tested on a vertical crest curve model using AutoCAD Civil 3D for several driver eye height values, which included camera height, LIght Detection And Ranging (LIDAR) height radar, and human driver eye height.

By comparing the values of resulted sight distances with their design values in the Hungarian Guidelines for road design, the minimum vertical curve radius corresponding to each sighting distance and design speed was found.

2 Background

By reviewing some of road design guidelines, it was found that the value of the driver's eye height has values that differ from one country to another. Some of these values have been fixed for decades and have not undergone any change, and some of them are constantly updating.

For example, the value of the driver's eye height suggested for the design in the first edition of American code [3] was 1,676 mm in 1920, then it was reduced in 1994 (i.e., after 70 years) to become 1,070 mm, passing by a value of 1,445 mm in 1936 and 1,295 mm in 1957, to keep up with changes in the vehicles fleet. After 2001 it has become 1,080 mm till now [3].

The height of the driver's eye is considered one of the parameters that enter into the calculation of the minimum radius of the vertical crest curve. Some studies [4] conducted surveys to determine an updated value for the driver's eye height in Italian standards [4] and investigated the effects of the difference in the driver's eye height. It was concluded that the current values of the driver's eye height are different, even from the updated values between 2003 and 2008 [4].

Based on the perception reaction time and sensor height of fully automated self-driving cars, the vertical and low vertical curve lengths and stopping visual distance were calculated and compared with the values for human drivers in the US's Green Book [3]. It was concluded that autonomous vehicles need Stopping Sight Distances (SSD) less than the required SSD in the case of human drivers, thus the lengths of the vertical curves of the sag and crest will be less in the case of AVs [5].

Using photogrammetry, was found that the driver's eye height should be greater than the current value in the United Kingdom Highway Standard [6], which equals 1.05 m, where all the driver's eye heights in the conducted survey were bigger than this value with the minimum value of the driver's eye height for any vehicle being 1.062 m [6].

A study [7] was conducted on a model of crest vertical curve using AutoCAD Civil 3D, tests were done using the checking visibility tool, and it was concluded that autonomous vehicles are able to obtain a sight distance higher than what that a human driver can obtain under the same geometric conditions of the vertical curve [7].

Magyari [8] used a laser scanner to assess the sufficiency of the visibility at a roundabout. They found that 3D models can describe objects more precisely than 2D views. The study also suggested that automated mobile laser scanners could be used for quick analysis of the visibility of various elements of the road network.

3 Aim of the study

The first aim of this study is to analyze the expected changes in the driver's eye height value. How it could be affected by the rapid development in the vehicle industry?

The second aim is to present and discuss the resulted radiuses of the vertical crest curve using AutoCAD Civil 3D visibility check model.

4 Methodology

4.1 Analyzing the changes in the driver's eye height

Due to the importance of the driver's eye height, and the essential updates on its value in the Hungarian Guidelines, a survey was conducted on Hédervári street (Győr, Hungary, July 19, 2022) that included a two-hours video recording.

4.1.1 Analyzing the video recording

This analysis included, counting the cars within the two hours recording, and exclude the inappropriate vehicles including buses, small trucks, or goods vehicles. The final number of the accepted cars (passenger cars) was 266.

4.1.2 Calculating the driver's eye height

From the actual value of the pole's height, the distance between the driver and the pole (pole's distance), and the distance between the driver and the camera (driver's distance), are driver's eye height can be calculated Fig. 1.

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Measurements in AutoCAD

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00808

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The concept of visual angle (or angular size) describes how the distant objects appear shorter and smaller, Fig. 2.

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Visual angle (distant objects)

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00808

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Also, the far end of roads seems narrower, Fig. 3.

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Visual angle (narrower roads)

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00808

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The calculated driver's eye height was determined for each car. Using AutoCAD software, the height of the pole, and the driver's eye height were possible to be defined as it is shown in Fig. 1. Based on the parameters illustrated in Fig. 4, Eq. (1) was extracted:

$H_c=\frac{D_d}{D_p}·h_{d,CAD}·\frac{h_p}{h_{p,CAD}}\text{,}$(1)

where H_c is the calculated eye height (m); D_d is the driver's distance (the distance between the camera and the driver), 15 m; D_p is the pole's distance, (the distance between the driver and the pole), 10 m; h_p is the pole's height, 2 m; h_p,CAD is the pole's height measured in AutoCAD, (m); h_d,CAD is the eye's height measured in AutoCAD, (m).

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Illustration of the used parameters

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00808

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4.1.3 Determine the driver's eye height by using one-sample t-test

In the Hungarian Guidelines, the driver's eye height is 1.1 m, in this study; the following hypothesis (null hypothesis) was examined:

• H₀: There is no significant difference between the mean of the driver's eye height in the studied sample and the driver's eye height in the Hungarian Guideline.

One-sample t-test was done using SPSS software and the results are in Table 1.

Table 1.

Measures of central tendency and dispersion

Descriptive Statistics
	N	Mean	SD	Standard error mean
Driver eye height	266	1.31100	0.20491	0.01256

To determine if the difference in eye height (calculated eye height - guideline eye height) is statistically different from zero (α = 5%), a 2-tailed, one-sample t-test was conducted. Table 2 shows the results:

Table 2.

2-tailed, one-sample t-test

One-sample test
	Test value = 1.1 m
	t	df	Sig. (2-tailed)	Mean difference (m)	95% Confidence interval of the difference (m)
					Lower	Upper
Driver eye height	16.79200	265	0.00000	0.21098	0.18620	0.23570

df: degrees of freedom; Sig. (2-tailed): significance value (2-tailed).

4.1.4 Other guidelines

To verify that the resulting range of the driver's eye height can be generalized and attempt to find an international interval based on the analysis of the same sample. Therefore, the same statistical analysis was repeated for the driver's eye height in the guidelines for the countries in Table 3. As its shown in Table 3, some countries have not changed this value over a long time and still use the old value.

Table 3.

Driver's eye height in other guidelines

Countries	Value (m)
Austria, France, Germany	1.00
Canada, England, Australia 2002	1.05
United States before 2001	1.07
United States after 2001	1.08
Italy, Netherlands, Sweden	1.10
Australia 1962÷2002	1.15
Japan	1.20

The results for each country's guidelines are illustrated in the following tables, from Tables 4 to 8.

Table 4.

Austria, France, Germany, 1 m

One-sample test
	Test value = 1.00 m
	t	df	Sig. (2-tailed)	Mean difference (m)	95% Confidence interval of the difference (m)
					Lower	Upper
Driver eye height	24.75100	265	0.00000	0.31098	0.28620	0.33570

Table 5.

Canada, England, Australia 2002, 1.05 m

One-sample test
	Test value = 1.00 m
	t	df	Sig. (2-tailed)	Mean difference (m)	95% Confidence interval of the difference (m)
					Lower	Upper
Driver eye height	20.77200	265	0.00000	0.26098	0.23620	0.28570

Table 6.

United States 2001, 1.08 m

One-sample test
	Test value = 1.08 m
	t	df	Sig. (2-tailed)	Mean difference (m)	95% Confidence interval of the difference (m)
					Lower	Upper
Driver eye height	18.38400	265	0.00000	0.23098	0.20620	0.25570

Table 7.

Australia 1962–2002, 1.15 m

One-sample test
	Test value = 1.15 m
	t	df	Sig. (2-tailed)	Mean difference (m)	95% Confidence interval of the difference (m)
					Lower	Upper
Driver eye height	12.81300	265	0.00000	0.16098	0.13620	0.18570

Table 8.

Japan, 1.20 m

One-sample test
	Test Value = 1.20 m
	t	df	Sig. (2-tailed)	Mean difference (m)	95% Confidence interval of the difference (m)
					Lower	Upper
Driver eye height	8.83300	265	0.00000	0.11098	0.08620	0.13570

In a similar way, it is found that the interval of driver's eye height = 1 + 0.2862, 1 + 0.3357 = 1.2862, 1.3357 m.

Driver's eye height = 1.05 + 0.2362, 1.05 + 0.2857 = 1.2862, 1.3357 m.

Driver's eye height = [1.08 + 0.2062, 1.08 + 0.2557 = 1.2862, 1.3357 m.

Driver's eye height = 1.15 + 0.1362, 1.15 + 0.1857 = 1.2862, 1.3357 m.

Driver's eye height = 1.2 + 0.0862, 1.2 + 0.1357 = 1.2862, 1.3357 m.

In case of Italy, Netherlands, and Sweden, the driver's eye height equals to 1.1 m, it is similar to its value in the Hungarian Guidelines, which means the interval of the driver's eye height is equal to 1.1 + 0.1862, 1.1 + 0.2357 m.

5 Results and discussion

Based on Table 1, it can be noted that the mean value of the measured driver's eye height for the 266 cars was 1.31 m with a standard deviation of 0.2049 and a standard error mean of 0.01256, this mean values is different from the driver's eye height used in the Hungarian Guidelines [1] which is 1.1 m.

From Table 2, the t-test value for the sample of 265 vehicles was t₂₆₅ = 16.792. Since the value of P (P = level of marginal significance) was equal to 0.000, which is less than the α (level of significance): i.e., P = 0.000 < α = 5%, therefore, it can be concluded that the sample mean is statistically significantly different, and the null hypothesis was rejected.

It can be estimated the 95% confidence interval of the driver's eye height as follows: driver's eye height = 1.1 + 0.1862, 1.1 + 0.2357 = 1.2862, 1.3357 m. This means that the driver's eye height should be modified to be 1.29 m at minimum and 1.34 m at maximum in the Hungarian Guidelines.

Based on the resulted radiuses, the following can be concluded:

• The minimum value of the sight distance 17 m or higher at any radius starting with radius 130 m can be reached in case of Avs, which is less than the minimum radius value in case of conventional vehicles;

• On the other hand, the minimum radius in case of human driver is 450 m, or even less than this value can be enough to get an adequate sight distance;

• At high speeds 110, 130 km h⁻¹, LIDAR sensor needs radiuses lower than the required ones in case of conventional vehicles to obtain an appropriate sight distance.

6 Conclusion and further steps

The interval of driver's eye height = 1.2862, 1.3357 m can be generalized to the guidelines mentioned previously.

This leads to new results represented in the need to modify the driver's eye height in the current guidelines and add new criteria in road design to involve the AVs as well, where the eye height can be higher than this range.

Add new values for the minimum radiuses of vertical crest curves to involve the autonomous vehicles requirements.

Some experiments at ZalaZone (vehicle test place) were conducted on an electric vehicle contains LIDAR sensor assembled on both sides of the vehicle. The objective is to measure the sight distance in case of LIDAR sensor and human's eye under the same circumstances of the road geometry and the existing obstacles. For this purpose, the most appropriate crest section was selected, and the obstacles were cubic boxes with different dimensions 10, 20, 30, 60 cm.

In these experiments, the sight distances for several positions of the objects right, left, and middle of the lane have been checked. Based on the car specifications and crest radius, it is expected to get sight distance values that can be compared with the values in the Hungarian guidelines for the same radius and vehicle speed.

Currently, the outcome from LIDAR sensor and the camera are analyzed using Foxglove Studio software.