Discussion on Humanistic Design of Intersection Curb Radius Based on Passenger Experience

Abstract

The huge waste of urban road resources caused by large turning radii of intersections has become a universal concern in traffic engineering. Here, an approach for determining curb radius at intersections is proposed using lateral acceleration to reflect ride perceptions, bringing human-oriented concepts into urban intersection design. First, we classified three kinds of ride perceptions into comfortable/uncomfortable but acceptable/unacceptable, after which the lateral acceleration and ride perceptions were obtained by ride perception experiments. The lateral acceleration critical values for each ride perception were obtained using the Raff critical gap method. Finally, we calculated the intersection curb radius based on the critical values, and verified vehicle safety under the recommended intersection curb radius. The results showed that the intersection curb radius based on the proposed approach was less than the specified value and safety was verified, indicating that enormous land resources could be saved were this methodology applied to intersection design.

Keywords

infrastructure roadway design performance effects of geometric design human factors human factors of vehicles human factors in roadway design

Increased travel demand has spurred the growth of urban roads, taking up more land resources. For example, urban roads in China in 2021 totaled 9.6 billion m², an increase of over 35% since 2015. However, increasing urban road land indefinitely to meet the unlimited growth of travel demand given the widespread concerns about urban land resources would be inappropriate. Consequently, urban designers and transport planners are pursuing approaches that will generate more efficient use of road resources. Operational management and improvements to road geometry are two approaches to promote efficiency. In relation to operational management of urban road sections and intersections, implementation of line- and surface- signal control programs, setting up exclusive lanes, and the organization of tidal lanes are commonly applied. However, the width of vehicle lanes, for example, can restrict the geometrical improvement and efficiency of roads. For instance, the width of a vehicle lane in certain road sections is 3.5 m, whereas it is only 2.8 m at some intersections.

Despite current methods having significantly improved the efficiency of road sources, there is still room for improvement. For example, given the complexity of geometrical design for urban intersections, additional approaches to improve their efficiency are required ( 1 ). It is clearly stated in the Urban road traffic engineering project specification (GB 55011-2021) ( 2 ) that the curb radius stipulated in the earlier CJJ152 ( 3 ) was too large, recommending it be reduced to some extent according to the designer’s experience ( 4 ). Excessive curb radii had led to poorly designed intersections, which had resulted in more conflict points and expansion of the conflict area. Furthermore, the elongated distance between the stop line and the center of the intersection, meant vehicles were taking a long time to traverse it. Over time, improvements in vehicle performance and driving technology have provoked consideration of the applicability of established turning radii.

Existing urban road design specifications for intersections and related provisions for curb radii are relatively standard: most focus on traffic volumes, vehicle types, and travel and pedestrian safety ( 5 ). Fei et al. constructed a microscopic simulation model for intersection turning radius design with the goals of minimum pedestrian delay and maximum safety at intersections ( 6 ). In A Policy on Geometric Design of Highways and Streets, AASHTO ( 7 ) recommends curb turning radii based on expected traffic volumes and vehicle types at intersections ( 6 ). Because of land use and travel safety concerns, the U.S. Urban Transportation Commission in the Urban Street Design Guide (7) proposed that the standard curb radius should be set at 10 to 15 ft, whereas the minimum curb radius of urban streets could be 2 ft. Intersection design in European industrial cities from the right angle to the rounded angle of the curb side sets the adjacent crosswalk line spacing to about 5 m, shortening the pedestrian crossing distance, thereby improving pedestrian safety. Intersection designers in China mainly select curb radii values based on previous urban road intersection specifications. The “urban road intersection planning and design specification” (GB50647-2011) ( 8 ) recommends providing a reference table indicating the minimum values of turning radii related to the speeds of right-turning vehicles.

The aforementioned urban intersection design coefficients overwhelmingly rely on traffic features and safety, ignoring road users’ perceptions, which directly affect driver behavior and ultimately influence vehicle movement trajectories. Road users’ perceptions are also overlooked in current transport facilities design processes, required for urban intersection geometrical design because of the expansion of human-oriented concepts. Human-oriented design was initially devised to elicit more quality-of-life benefits from urban design, and was found to be conceptually superior to conventional approaches having been applied to curb parking, sidewalks, and bicycle lanes. The smaller the radius of a curve, the smaller the plot area required. However, at the same time, a reduction in curve radius will increase road mileage, and if the radius is too small it will constitute a safety hazard. Taking passenger and driver feelings into account in the geometric design of intersections can better reflect human-oriented concepts and avoid the drawbacks of traditional vehicle-oriented intersection designs. Road users’ perceptions of urban intersections are likely to be wholly dependent on the geometric design parameters, especially the curb radius. Different curb radii for a given design speed will affect road users’ perceptions, which are usually embodied by lateral force coefficients, lateral acceleration, and lateral acceleration changes ( 9 ). Yang points out that when a car is driven on a curve, the main factor causing driving discomfort is the centrifugal force generated in the horizontal vertical direction ( 10 ), which acts at the vehicle’s center of gravity, off the level of the circular direction ( 5 ).Passengers will be affected by centrifugal force in the process of turning, and with increases in the force, feelings will gradually transition from comfortable to unbearable. The lateral force coefficient is defined as the lateral force per unit of vehicle weight, representing the stability of a vehicle running into curves and the associated passenger comfort. Lateral force coefficient values are generally under 0.15, 0.067 is used in the calculation of a general minimum radius, and 0.014 to 0.016 (2012) is used in the calculation of the ultimate minimum radius ( 9 ). However, to the best of our knowledge, the value of the lateral force coefficient reflecting road users’ perceptions is arbitrary and lacks a clear theoretical basis.

To this end, this study attempted to take road users’ perceptions related to lateral acceleration into urban intersection curb radius design, providing a theoretical basis for urban intersection design from a human-oriented perspective. The main objectives of this study were therefore to identify the relationship between lateral acceleration and road users’ perceptions, and to recommend values for safe intersection curb radii based on the relationship revealed. To achieve these objectives, three kinds of ride perceptions were classified following Gao ( 11 ) and the lateral acceleration and ride perceptions were obtained by designing ride perception experiments. The critical values of lateral acceleration for each ride perception were obtained using the Raff critical gap method, after which the intersection curb was calculated. Recommended values for different speeds are given and their safety verified. The findings could assist transport designers to archive human-oriented urban intersection designs by considering road users’ perceptions that reflect lateral acceleration, thereby contributing to meeting the ever-increasing demand for quality driving experiences.

Methodology

The basic pipeline architecture of this study is shown in Figure 1. There were three main stages: experimental design, experimental data and processing, and safety verification and application. In the first stage, after classifying the three types of ride perception—comfortable, uncomfortable but acceptable, and unacceptable—we loaded the MPU6050 inertial guidance gyroscope into the experimental vehicle and selected five curves as the experimental scenario. Each test required two volunteers to conduct the experiment. In the second stage, experimental data and processing, the Raff critical gap method was applied on the road users’ perception and the lateral acceleration obtained from the tests, thus calculating the critical values of the lateral acceleration for each road user’s perceptions. We then obtained the turning radius values for different ride perceptions based on the critical values. In the third stage, a lateral force factor was used for the safety verification to ensure that the vehicle did not tip over during driving. The verified radius was used to calculate the radius of the intersection’s curb.

Figure 1.

Methodology workflow: (a) Ride experience experiment, (b) data processing analysis, and (c) turning lane design.

Experimental Design

As stated with reference to the methodology of Lorenz ( 11 ) on lateral acceleration, the passengers’ feelings were divided into three states: comfortable, uncomfortable but acceptable, and unacceptable. Forty young people were selected as participants (30 adult males and 10 adult females who were in good health and fit to drive). A Shanghai Lavida 1.6-l automatic transmission vehicle was selected as the experimental vehicle. The geometric characteristics of the vehicle are given in Table 1.

Table 1.

Main Characteristics of the Experimental Vehicle

Length of the car (mm)	Width of the car (mm)	Height of the car (mm)	Wheelbase (mm)	Overall mass (kg)
4,650	1,765	1,460	2,610	1,245

The accelerometer (MPU6050), uses a high-precision inertial navigation module, with a resolution of 0.00006 g acceleration. In addition to use of accelerometry a questionnaire to capture road users’ subjective feelings during the experiment was designed by the research team and administered with time series for matching the analyses. The questionnaire also aimed to reveal the relationship between lateral acceleration and road users’ perceptions.

The sensor that measured the three-dimensional acceleration during the driving was installed on the underside of the experimental vehicle. The x-axis of the sensor was the direction of the vehicle, the y-axis was horizontal and perpendicular to the direction of the vehicle, and the z-axis was perpendicular to the xy plane. A high-precision GPS was fixed to the roof of the vehicle to record the vehicle’s speed and trajectory.

We selected five curved paths in Beijing’s South Fifth Ring Road as the experimental scenario. The main parameters of the experimental scenario are given in Table 2, and the specific route is illustrated in Figure 2.

Table 2.

The Main Parameters of the Experimental Scenario

Number	Name	Address	Radius(m)
1	R1	Luxi Road to Jingliang Road entrance	70
2	R2	South 5th Ring Road right-turn ramp on Jingliang Road	232
3	R3	First left-turn ramp off Jingliang Road on the South 5th Ring Road	234
4	R4	Second left-turn ramp off Jingliang Road on the South 5th Ring Road	99
5	R5	Left-turn ramp at Lu Xi Road on Jingliang Road	60

Note: R refers to the radius corresponding to each Address.

Figure 2.

Experimental driving route.

To analyze the correlation between the lateral acceleration and ride perceptions, we calculated the minimum sample size using Equation 1,

n = {(\frac{t δ}{E})}^{2}

(1)

where

n = minimum sample size to meet requirements,

t = distribution statistic at the constant confidence level of t,

$δ$ = standard deviation, and

E = allowable deviation.

When confidence is 95%, t = 1.96; acceleration standard deviation takes the general value of 0.5; and the acceleration allowable deviation is 0.1 m/s² ( 12 ).

Based on the above requirements, the minimum sample size calculated by the formula was 96. To make the experimental results more reliable by satisfying accuracy requirements, the sample size was 1,000. That is, for each of the five curves, several tests were conducted, and the 40 volunteers each filled out 25 ride “feelings,” giving a total of 1,000 copies.

Experimental Data and Processing

As stated, the Raff critical gap method ( 13 ) was used to determine the critical values of the three driving states; this is a commonly used method for determining critical values of gaps and widely used for the study of critical gaps in motor vehicle flows.

In addition to Raff, other methods of studying critical time intervals across the world include the Ashworth method, Harders method, maximum likelihood estimation method, and logit process calculation method, and the probit process meter ( 14 ). The advantage of the Raff critical gap method is that it is intuitive and therefore easy to operate and popular among researchers. According to the definition of the Raff gap critical value, the acceptable quantity less than a certain headway is equal to the rejected quantity greater than that headway. As shown in Figure 3, the intersection of the acceptance curve and the rejection curve is the gap critical value. Consequently, the Raff critical clearance method was used to determine the critical lateral acceleration values corresponding to the three ride perceptions.

Figure 3.

Raff critical gap method.

Measurement data for five curves were intercepted from successive lateral acceleration data based on relative time.

Analysis of the measured data revealed that the curve driving lateral acceleration data changed abruptly at the 90% level. Therefore, in this study, 90% lateral acceleration was used to match the ride perceptions. Sequential regression was conducted for each state using MATLAB, and the intersection of the regression equations was used as the critical value of the state experienced.

The design parameters of the curve mainly included the radius of the circular curve, the superelevation value, and the design speed. The critical values of lateral acceleration corresponding to the three ride perception states of comfortable, uncomfortable but acceptable, and unacceptable were determined. Although the determined radius and speed values can ensure driving comfort, it is not certain whether driving safety can be guaranteed. Therefore, this needed to be verified for safety reasons. Equations 2 to 6 are based on the safety of the right-turn lane radius derivation process.

Figure 4 shows the force analysis of the vehicle during the turn. In considering lateral superelevation, lateral acceleration was calculated according to Equation 2. From Equation 3, the right-turn lane radius was calculated.

a_{y} = \frac{V^{2}}{13 R} \cos i_{h} - G \sin i_{h}

(2)

R = \frac{V^{2} \cos i_{h}}{13 (a_{y} + g \sin i_{h})}

(3)

where

V represents travel speed (km/h),

R is radius of circular curve (m),

$i_{h}$ is value of superelevation, without superelevation, is the cross slope of road arch, which is taken according to the design specification for urban road engineering (CJJ37-2012 [ 2 ]), and

G is gravitational acceleration (m/s²), which can be taken as 9.8 m/s².

Figure 4.

Vehicle force analysis.

Road traffic design should comply with safety requirements, therefore, to ensure traffic safety, it was also necessary to verify the stability of the right-turn lane minimum radius. Currently, the lateral force coefficient is generally used for verification, which requires that the lateral force of the vehicle while driving on a curve is less than the adhesion force between the tire and the road. Vehicles are prone to lateral slip and rollover while driving on curves. In general, a slip precedes a rollover, therefore, it is vital that a vehicle does not slip to ensure that no rollover occurs ( 5 ).

The analysis showed that for a vehicle to avoid slipping, the lateral force must be less than the adhesion force between the tire and the ground, obtained by Equation 4, and giving Equation 5.

m \frac{V^{2}}{R} \cos i_{h} \leq G \cos i_{h} φ

(4)

R \geq \frac{V^{2}}{g φ}

(5)

where $φ$ = tire–road adhesion coefficient.

After verifying the safety, we applied the turning radius based on ride perceptions to the design of the intersection curb radius to provide a human-oriented approach to intersection design. In urban roads, intersections, as the convergence point of traffic flows in different directions, affect the traffic operation efficiency. Generally, traffic flows from various directions divide and merge at intersections, affecting each other and reducing traffic capacity. Intersections are therefore considered to be traffic bottlenecks, limiting capacity. The radius of an intersection curb angle is an important factor that affects the size of the intersection area (15, 16). Normally, as the radius of the curb angle increases, the intersection footprint also increases. Expression of the intersection curb corner radius, R₁, without considering motor vehicle widening, is shown by Equation 6,

R_{1} = R - (\frac{B}{2} + F)

(6)

where B represents the motorway width (m), generally using 3.5 m; and F is the width of nonmotorized vehicles at the turn (m) (the value is 0 when there is no nonmotorized lane).

Results and Discussion

Critical Value of Lateral Acceleration and its Distribution Interval

Based on the data recorded by the driver, a specific number of lateral accelerations was calculated for each curve at 90%. This value was matched with the ride perception at the corresponding moment. Based on the data series, the experimental data were sorted from the largest to the smallest values. The lateral acceleration data curves for the three ride perception states were plotted, as shown in Figure 5.

Figure 5.

Sequential distribution of lateral acceleration under three types of ride perception.

Applying MATLAB software to linearly fit the three types of lateral acceleration sequences, the results of the fit are shown in Equations 7 to 9,

y_{1} = 0.04168 x + 0.5267

(7)

y_{2} = - 0.03488 x + 5.60

(8)

y_{3} = 0.1168 x + 5.50

(9)

where

x = data sequence;

y₁ = acceleration when the ride feels comfortable (m/s²);

y₂ = acceleration when the ride feels uncomfortable but acceptable (m/s²); and

y₃ = acceleration when the ride feels unacceptable (m/s²).

Based on the above, R-square was used to evaluate the effect of fitting the data for the three ride perceptions. The R-square values corresponding to the experimental fitted equations $y_{1}$ , $y_{2}$ , and $y_{3}$ were 0.98, 0.96, and 0.91, respectively, each of which was close to the value of 1. Therefore, the experimental data were well-fitted and convincing.

As shown in Figure 6, the fitted line divided the lateral acceleration into three intervals, with the intersections at 3.294 and 5.585.

Figure 6.

Acceleration distribution for three kinds of ride perceptions.

The intersection of the straight lines represented the critical value of the corresponding ride perception. The lateral acceleration distribution areas corresponding to the three ride perceptions are shown in Table 3. When lateral acceleration was less than 3.294 m/s², the passenger felt comfortable; when it was between 3.294 and 5.585 m/s², the passenger felt it was uncomfortable but acceptable, that is, the passenger felt uncomfortable under the lateral acceleration, but confirmed it was an acceptable level of discomfort; when lateral acceleration was more than 5.585 m/s², the passenger felt the ride was unacceptable.

Table 3.

Lateral Acceleration Distribution Interval Under Three Kinds of Ride Perceptions

Feel of the ride	Lateral acceleration threshold(m/s²)
Comfortable	$a_{y} < 3.29$ 4
Uncomfortable but acceptable	$3.294 \leq a_{y} < 5.585$
Unacceptable	$a_{y} \geq 5.585$

Right-Turn Lane Radius Calculation

Based on the calculated critical ride perception value, that is, the maximum lateral acceleration of 3.294 m/s², using Equations 2 and 3, the calculation results of the right-turn lane radius can be obtained, as shown in Table 4. When the design speed was 40 km/h and the cross slope of the road surface was 0.02, the minimum radius obtained by the calculation method was 35.41 m, and the adopted value was 36 m; when the design speed was 30 km/h and the cross slope of the road surface was 0.02, the minimum radius obtained by the calculation method was 19.92 m, and the adopted value was 20 m; when the design speed was 20 km/h and the cross slope of the road surface was 0.02, the minimum radius obtained by the calculation method was 8.85 m, and the adopted value was 10 m; when the design speed was 15 km/h and the cross slope of the road surface was 0.02, the minimum radius obtained by the calculation method in was 4.59 m, and the adopted value was 5 m.

Table 4.

Right-Turn Lane Minimum Radius Calculation Table

Design speed (km/h)	40	30	20	15
Road surface cross slope	0.02	0.02	0.02	0.02
Calculated values (m)	35.41	19.92	8.85	4.59
Adopted value (m)	36	20	10	5

Verification of Vehicle Driving Safety in the Right-Turn Lane

Most urban roads are asphalt or concrete pavements and, according to the “Identification for the Speed of Vehicle Involved in Road Traffic Accident” (GB/T 33195-2016) ( 16 ). The tire–road adhesion coefficient under urban, wet conditions was taken as 0.40, and the calculated value of the curve radius considered from the aspect of traveling stability is given in Table 5.

Table 5.

Calculation Table of the Minimum Stability Radius of the Right-Turn Lane

Design speed (km/h)	40	30	20	15
Stable value (m)	31.49	17.72	7.87	4.43
Calculated minimum right-turn lane radius (m)	36	20	10	5

As can be seen from Table 5, when the design speed was 40 km/h, stability was 31.49 m, and the value selected in this study was 36 m, which met the requirement; when the design speed was 30 km/h, stability was 17.72 m, and the value selected in this study was 20 m, which met the requirement; when the design speed was 20 km/h, stability was 7.87 m, and the value in this study was 10 m, which met the requirement; and when the design speed was 15 km/h, stability was 4.43 m, and the value in the current study was 5 m, which met requirements. Therefore, the right-turn lane radius calculations based on ride perception met the stability requirements of vehicle driving.

Intersection Curb Radius Design

The minimum curb radius of intersections without nonmotorized vehicles were calculated according to Equation 6, as shown in Table 6.

Table 6.

Minimum Radius of Intersection Curb Corner

Design speed (km/h)	40	30	25	20	15
Calculated minimum right-turn lane radius (m)	36	20	15	10	5
Calculated minimum radius of the corner of the intersection curb (m)	33	18	13	8	4
Urban road intersection design regulations (m) ( 4 )	Not involved	25	20	15	10

It has been found that the radius of the intersection curb determined according to specifications produces various disadvantages by making the intersection area too large ( 15 ). When the design speed is 30 km/h, the intersection curb radius can be reduced from 25 (As mentioned in Table 6 Urban road intersection design regulations (m)) to 18 m (17, 18), and the intersection area is then reduced by about 945 m². Therefore, an appropriately reduced intersection curb radius can reduce the intersection area and improve the intersection capacity to some degree. At the same time, the area saved could be used for and thereby increase the area of urban greening ( 19 , 20 ).

Conclusion

The critical values of lateral acceleration under the three states of comfortable, uncomfortable but acceptable, and unacceptable were obtained through the ride perception experiments. When the lateral acceleration was less than 3.294 m/s², the ride was comfortable; when it was between 3.294 and 5.585 m/s², the ride was uncomfortable but acceptable; and when the lateral acceleration exceeded 5.585 m/s², the ride is unacceptable, most people finding it unbearable. As a result, the turning lane radius based on passenger comfort was determined, as was the intersection curb radius. The intersection curb radius derived in this study was significantly smaller than the normative value, but nonetheless passed the vehicle driving stability test, providing a theoretical basis for the adjustment of curb radii in urban intersection designs. If applied to actual intersection projects, the potential benefits include reducing the area of the intersection conflict zone and the interweaving that takes place within it; by reducing vehicle travel times ( 21 ) at intersections traffic capacity could be increased; and by reducing the area taken up by intersections, green areas of the city could be expanded.

This study adopted a new design concept to design urban intersections and applied the intuitive lateral acceleration index to measure ride perceptions—an active attempt to design urban intersections and achieve certain gains. However, as with all research, there were certain limitations to this work. The number of experimental sites, passenger age and gender, and vehicle type selection were limited by the number of experimental sites. In investigating lateral acceleration, the experiments did not consider variability in driver behavior (e.g., speed and turning rates), which could differ from the behavior observed at urban intersections. Therefore, further experiments are needed to obtain more accurate lateral acceleration intervals based on ride perceptions and to acquire more scientific intersection design indexes. Moreover, the research object of this paper was urban intersections that heavy vehicles are not allowed to traverse. Studies should be carried out on intersection curves where heavy vehicles are permitted to drive.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: C. J. Zhou, H. Li; data collection: H. Li, S. Y. Liu; analysis and interpretation of results: C. J. Zhou, H. Li, S. Y. Liu; draft manuscript preparation: C. J. Zhou, H. Li, S. Y. Liu. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the project “Intelligent Decision System for Highway Congestion Prevention and Control in Guangxi” and by the Beijing University of Civil Engineering and Architecture Post Graduate Innovation (projects nos. PG2022033 and PG2022026).

ORCID iD

Siyang Liu

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