Research on driver injuries in vehicle rear-end collisions considering different overlap rate and speed difference

Abstract

Rear-end collisions involving passenger vehicles often result in significant injuries and fatalities, with the driver of the trailing vehicle being particularly vulnerable to severe harm. This study analyzes regulations related to rear-end collisions and their necessity, and develops finite element models of the vehicle, dummy, and airbags. The positioning of the dummy is based on C-NCAP standards, and the Primer software is utilized to model and integrate the seatbelt and airbags. Subsequently, the model is solved using LS-DYNA. Additionally, the study examines the effects of varying overlap rates and speed differences on the injuries sustained by the driver of the trailing vehicle. The research reveals that both overlap rate and speed difference have a significant impact on the extent of injury to the driver in rear-end collisions. Notably, in scenarios with low overlap and high speed differences, the driver experiences more severe injuries, particularly to the head, neck, and lumbar spine. Furthermore, the study demonstrates that, for the same speed, when the overlap rate exceeds 30%, the severity of the injuries to the driver increases as the overlap rate rises. In particular, at a 40% overlap rate, injuries to the neck, chest, and lumbar spine are most severe. Based on the simulation results, this paper validates the rationality of the current Chinese regulations concerning crash scenarios and proposes recommendations for revisions to improve traffic safety and reduce injury in rear-end collisions.

Introduction

According to the China Statistical Yearbook 2020 published by the National Bureau of Statistics, a total of 247,646 road traffic accidents occurred in China in 2019, resulting in 62,763 fatalities, 256,101 injuries, and direct economic losses amounting to 1.346 billion yuan^1,2. Among these accidents, automobile collisions accounted for 50–70%, with occupants of four-wheeled vehicles representing 25% of all traffic accident fatalities and those of large vehicles such as heavy trucks accounting for 19%³. These collisions not only inflict severe physical harm on victims but also lead to substantial economic losses, averaging 1–3% of global GDP, with China, as a middle-income country, experiencing losses of approximately 1.5% of its GDP⁴.Traffic accidents caused by automobile collisions can be categorized into three main types: head-on collisions, side collisions, and rear-end collisions. According to data from the National Highway Traffic Safety Administration (NHTSA) of the United States, head-on collisions are the most frequent among common accident types, accounting for approximately 28.7% of all accidents, with the highest fatality rate^2,5.Additionally, data from the China Traffic Accident Deep Investigation Study (CIDAS) reveals that over 60% of collisions are classified as full-frontal crashes⁶. Among these, small-offset frontal crashes are one of the most common forms. Research indicates that small-offset collisions make up about 25% of all head-on collisions, and due to the significant impact forces on the occupant compartment, the fatality rate is also extremely high, with fatalities from small-offset collisions accounting for approximately one-quarter of all head-on collision deaths^7,8. Furthermore, rear-end collisions are also a common type of automobile crash, and studies show that rear-end collisions account for more than 50% of all traffic accidents resulting in permanent disability⁹. As highway infrastructure develops rapidly towards higher-grade expressways, rear-end collisions have become a key area of research in accident prevention and control. Investigating the injuries sustained by drivers in rear-end collisions is of significant importance for improving the protection of vehicle occupants.

Research on rear-end collisions in passenger vehicles began in the 1970s, with researchers analyzing accident data and conducting dummy tests to lay the foundation for subsequent evaluations. Since then, numerous studies have explored the impact of different overlap rates on driver injuries, aiming to reveal how these variations affect injury mechanisms and severity. For instance, Shi et al.¹⁰ established multibody dynamics models and finite element simulations to identify injury risks in various collision scenarios. Xiao et al.¹¹ focused on active and passive safety simulations in typical accident scenarios to predict driver injuries and their influencing factors. Song et al.¹² used a random parameter bivariate Probit model to analyze truck-car collision data, exploring the correlation and heterogeneity of driver injury severity. Yang et al.¹³ assessed the effects of active versus traditional headrests on neck injury metrics in rear-end collisions, combining head and seat behavior analysis to evaluate the predictability of these metrics. Shi et al.¹⁴ found that chest stress and deflection are more sensitive to impact loads at higher overlap rates, with the highest risk of thoracic injury occurring during full-frontal collisions. Yang et al.¹⁵ validated seatbelt and airbag parameters using HyperMesh software and optimized restraint system performance using the NSGA-II genetic algorithm to enhance driver protection. These studies provide essential data and theoretical support for improving collision safety designs. Advancements in technology have enhanced the precision of collision simulations, while modern safety systems and intelligent vehicle interventions have been thoroughly investigated, further bolstering automotive safety design.

In summary, scholars have employed a variety of technical methods, including multibody dynamics models, finite element simulations, active and passive safety analyses, injury mechanism assessments, and genetic algorithms, to investigate the effects of different overlap rates and speed differences on the severity of injuries to key driver body regions. These studies aim to reveal injury patterns and provide theoretical support and data foundations for collision safety design. However, current research on driver injury patterns remains limited, with insufficient focus on strategies to reduce injury risks post-collision. To address this gap, this study analyzes the severity of injuries to key driver body regions based on variations in overlap rate and speed difference. Using the Toyota Yaris vehicle model provided by NHTSA, a rear-end collision model with a complete restraint system is established and validated. The three-dimensional model of the restraint system is meshed using Hyperworks finite element software, and the model is solved using LS-DYNA. The results offer fundamental data for enhancing the protection of drivers and occupants in vehicles.

Establishment and validation of the model

This section will provide a detailed explanation of how the model is constructed using scientific methods, and how the validation process ensures that it meets the intended objectives.

Collision test research methodology

Collision dummy tests are conducted to collect collision data. The dummy is made of metal, plastic, and foam materials, and is designed to mimic the shape and collision characteristics of the human body. Finite element simulation analysis is employed in the later stages of vehicle development, where finite element software is used to simulate collisions and accurately obtain data on vehicle structure deformation, occupant compartment intrusion, restraint system performance, and occupant injury. This provides crucial reference information for vehicle development and optimization. By modeling the collision dummy, it can be applied to the design of vehicle safety structures and devices, as well as accident reconstruction analysis. The computer simulation-based collision method allows for multiple modifications and optimizations of unreasonable design parameters, significantly shortening the development cycle and reducing costs, while also enabling numerous repeated tests to ensure high accuracy of results. Furthermore, this method can effectively handle the optimization of complex structures and components within the vehicle.

Establishment and verification of the full vehicle finite element model

The two simulation models used in this study are both based on the 10 Toyota Yaris sedan models released by NHTSA¹⁶. The 2010 Toyota Yaris model, as shown in Fig. 1, is used in this paper. The total vehicle mass of the simulation model is 1078 kg, with other parameters listed in Table 1.

Fig. 1.

FE model of a 2010 Toyota Yaris sedan.

Table 1.

Toyota Yaris vehicle finite element model information table.

Name	Number	Name	Number
Number of parts	917	Beam element connections	4425
Number of nodes	1,480,422	Nodal rigid body connections	727
Number of shells	1,250,424	Extra node set connections	20
Number of beams	4738	Rigid body connections	2
Number of solids	258,887	Spotweld connections	4107
Total number of elements	1,514,068	Joint connections	39

In accordance with the collision test conditions specified by the Insurance Institute for Highway Safety (IIHS), both LS-DYNA finite element simulation and real vehicle 40% offset frontal crash tests were conducted. The vehicle deformation results are shown in Fig. 2¹⁷.

Fig. 2.

Deformation comparison between real car and simulation model in IIHS ODB test.

As shown in Fig. 3, during the collision, although there is some discrepancy between the center-of-gravity acceleration curve from the finite element simulation and that from the real vehicle, the overall trend of variation is largely consistent. This confirms that the finite element model for the vehicle in the small offset collision is valid and can be used for subsequent simulation studies¹⁸.

Fig. 3.

Comparison of acceleration curve between real car and simulation model.

Modeling and validation of the frontal airbag system

In traffic accidents, the driver airbag can protect the head, chest, and abdomen of the driver. The airbag studied in this paper is the driver-side airbag (Driver Airbag, DAB), which is installed on the steering wheel. The performance of the airbag simulation model is influenced by parameters such as shape, inflation time, pressure, thickness, and vent holes. The deployed state of the airbag must be validated before use.

Figure 4 shows the basic mesh model of the airbag. The airbag cushion material is an orthotropic nylon fabric with a density of 603 kg/m³, Young’s modulus of 2.84 × 10⁸ Pa, and a thickness of 0.22 mm¹⁹. In this study, the Z-fold model of the driver-side frontal airbag was established using the Safety module of the Primer finite element analysis software. The gas flow rate, based on the curves obtained from the TANK test and gas chromatograph, is shown in Fig. 5 and is set using the NGAS and LCM keywords. The number of particles in the airbag particle method is 200,000 to enhance the realism and computational efficiency of the inflation process.

Fig. 4.

Airbag basic model.

Fig. 5.

Gas generator gas mass flow rate curve.

Establishment of the automotive collision simulation model

To ensure that the simulation results meet the requirements of real-world collision standards, the Hybrid III 50th percentile dummy model was positioned according to the 2018 version of the C-NCAP guidelines for a 100% frontal collision, as shown in Fig. 6. The specific parameter settings are detailed in Table 2²⁰.

Fig. 6.

Dummy’s relative position measurement diagram.

Table 2.

Dummy relative position measurement table.

Dimension code	Meaning of the code	Measurement value
		Length (mm)	Angle (°)
A	From the lower jaw to the steering wheel rim	549	5.5
B	From the nose to the top of the windshield	240	123
C	From the abdomen to the lower rim of the steering wheel	366	165
D	From the H-point to the threshold	198	− 90
E	From the knee joint to the upper edge of the threshold	218	− 90
F	From the knee joint to the edge of the dashboard	93	135
G	From the head to the roof of the vehicle	64	90

The Safety module in Primer software was then used to apply the seatbelt load to the Hybrid III 50th percentile dummy. The interference between the dummy and the seatbelt was adjusted to ensure there was no penetration in the model. Based on this, the Safety module was used to position the airbag, define its gas mass flow curve, exhaust hole area, and gas direction. Finally, the positions of the two vehicles were arranged and positioned according to the specified conditions. The frontal view is shown in Fig. 7, while the bottom view of the vehicle models is shown in Fig. 8.

Fig. 7.

Double car simulation model front view.

Fig. 8.

Double car simulation model bottom view.

Validation of the crash dummy model

After constructing the vehicle crash simulation model, the next step is to validate the accuracy and reliability of the model by verifying the dummy’s response during the collision process. In this study, the finite element model of the crash dummy provided by LSTC is used. The version utilized is the LSTC_NCAC Hybrid III 50th Dummy²¹.

As shown in Fig. 9, LSTC conducted a neck flexion limit test on the Hybrid III 50th dummy, and the limit position obtained is found to be consistent with that of the human neck in reality.

Fig. 9.

Neck flexion extreme position.

Figure 10 shows the chest calibration diagram of the Hybrid III 50th dummy. As indicated by the chest calibration force curve in Fig. 11, the dummy’s chest deforms smoothly under load and fully recovers after the force is applied, with no significant plastic deformation or permanent damage.

Fig. 10.

Chest calibration picture.

Fig. 11.

Chest calibration force defelction.

Figure 12 shows the Hybrid III 50th dummy’s lumbar rotation test at 45°. It can be seen that the lumbar behavior of the Hybrid III 50th dummy is in good agreement with that of a real human body.

Fig. 12.

Lumbar rotated 45 degrees.

The adjustment of the dummy driver and the posture of the dummy

The crash test dummy model used in this study is the Hybrid III 50th percentile male dummy. After importing the Deformable 50% dummy model into the PRESYS software, the engine compartment was hidden, and the posture of the dummy driver was adjusted using the transformation function cards to achieve optimal alignment of the head, back, and hips with the seat. Due to the mass of the Hybrid III 50th percentile dummy, which causes seat compression, the Primer software effectively simulates and calculates the deformation profile of the rear seat through the seat deformation function.

Validation of simulation results

The reliability of finite element simulations is influenced by factors such as initial kinetic energy, component mass configuration, and contact settings. By calculating the glastat option in the input glastat file or binout file, the variation curves of these factors involved in the model can be examined.

As shown in Fig. 13, the total energy of the system remains almost constant during the collision process. The mass increase curve reaches a maximum of 4.47%, with the mass increase rate being less than 5%. Additionally, the smooth transition of the curves in the figure further validates the reliability of the simulation results.

Fig. 13.

Simulation energy curve (left) and mass increase curve (right).

Design of the scheme and analysis of experimental results

This chapter will introduce the research plan applicable to the rear vehicle in rear-end collisions and discuss the analytical methods employed, providing foundational data for the protection of drivers and passengers.

Research plan design

To investigate the effects of overlap rate and speed difference on rear-end collision injuries to the trailing vehicle driver, this study established rear-end collision simulation models with five overlap rates and five speed differences, as detailed in Table 3. Scenarios 1–5, set at 50 km/h, align with C-NCAP frontal collision standards to analyze overlap rate impacts. Scenarios 6–9 focus on speed differences, tested at 30, 40, 60, and 70 km/h, as lower speeds (< 30 km/h) produce negligible collision effects. The overlap rate was fixed at 10% for speed difference analyses, as smaller overlap rates show more significant vehicle deformation and driver injuries.

Table 3.

Collision settings.

Operating condition number	Collision overlap rate (%)	Collision velocity difference (km/h)
1	10	50
2	20	50
3	30	50
4	40	50
5	50	50
6	10	30
7	10	40
8	10	60
9	10	70

Vehicle deformation and driver motion response analysis

This study uses finite element and simulation models to explore vehicle deformation in two scenarios: varying overlap rates with a speed difference of 50 km/h between sedans, and different speed differences with a constant overlap rate of 10% between sedans.

Vehicle deformation analysis

1. Vehicle Deformation at Different Rear-End Overlap Rates with a Speed Difference of 50 km/h

   As shown in Fig. 14, the deformation performance of vehicles varies significantly across different overlap rates in crash simulations. At a 10% overlap rate, the collision angle is small, and deformation is limited as the left front longitudinal beam absorbs energy. However, at a 30% overlap rate, deformation is most severe, with substantial front-end damage that reduces the driver’s survival space. In contrast, at a 50% overlap rate, the vehicle primarily experiences lateral forces, causing it to rotate around the Z-axis. This reduces front-end deformation and increases the driver’s survival space.

2. Vehicle Deformation at Different Speed Differences with a 10% Overlap Rate

   Figure 15 shows that as the speed difference between the two vehicles increases, the deformation of the left front section of the vehicle becomes more severe. The impact force exceeds the energy absorption capacity of the vehicle’s structural components, causing energy to be transferred to other parts of the vehicle. This aggravates the driver’s injuries.

Fig. 14.

Vehicle deformation characteristics under varying rear-end collision overlap rates.

Fig. 15.

Vehicle deformation characteristics under different speed differences in rear-end collisions.

Driver kinematic response

When the overlap rate is 30% and the relative speed difference is 50 km/h, the dummy motion is shown in Fig. 16. The motion analysis of the Hybrid III 50th percentile dummy during the collision process is as follows:

Fig. 16.

Dummy movement posture during the rear-end collision.

At the initial stage (T = 0 ms), the driver is in contact with the seat and undergoes inertial motion as the collision occurs, with the seatbelt restraining the driver at 2000 N. At T = 45 ms, the seatbelt releases, and the driver’s head moves away from the headrest. At T = 90 ms, the driver makes contact with the airbag, which provides protection. From T = 165 ms, the airbag gradually deflates, and the driver’s body continues to move forward, experiencing significant pressure. At T = 200 ms, the collision ends, and the head separates from the airbag.

Driver injury analysis

Head injury analysis

Based on a detailed analysis of the dummy’s motion, further analysis of driver injuries is conducted. The following sections present the head acceleration curves of the Hybrid III 50th percentile dummy in the X and Y directions under different overlap rates at a constant speed difference, or under different speed differences at a constant overlap rate.

1. Analysis of the Head Acceleration in the X and Y Directions of the Dummy at a 50 km/h Speed Difference

   This study focuses on how varying overlap ratios and speed differences affect drivers’ head injuries in rear-end collisions. In low-overlap rear-end collisions, head movements in the X and Y directions significantly impact injuries, while the Z-direction acceleration, much smaller than in the X and Y directions, has a relatively negligible effect and contributes less to head injuries. As shown in relevant literature, researchers generally exclude the Z-direction from core analyses in such cases, which gives us confidence that our approach is acceptable^22–25. Therefore, in Table 4, we respectively list the X-direction and Y-direction values of Head Injury Criterion (HIC36ms) without listing the Z-direction values.The HIC36ms value is computed using the following formula:

   1

   In this formula, and represent the starting and ending moments (in seconds) during the collision process, with their time interval constrained to no more than 36 ms, while denotes the acceleration of the dummy’s head (in meters per second squared, m/s²).

   The data in Table 4 shows that the HIC36ms value peaks at a 40% overlap. The curves in Fig. 17 indicate that at 40% overlap, the head’s X- and Y-direction accelerations rise markedly. This signifies a notable increase in the risk of head injury. HIC36ms is positively correlated with acceleration, as indicated by the HIC36ms calculation formula. This supports the rationale for the 40% offset collision condition in current Chinese regulations. Additionally, results indicate that higher overlap rates lead to more severe head injuries in the X direction. However, in the Y direction, the maximum head acceleration shows no clear trend with increasing overlap rate and remains relatively low. This suggests that at low overlap rates (e.g., 10%), the head acceleration curves in both X and Y directions exhibit unique patterns, especially with smaller and less consistent peak accelerations in the Y direction. This implies that low overlap rates may lead to different head loading patterns compared to typical offset collisions, affecting injury mechanisms. Therefore, existing collision standards may not adequately address head protection in small overlap scenarios, highlighting the need for improved design and standards for such conditions.

2. Analysis of the Head Acceleration in the X and Y Directions of the Dummy at a 10% Overlap Rate

   Table 5 and Fig. 18 indicate that as the speed difference increases, the maximum acceleration and HIC36ms values of the driver’s head also gradually rise. This suggests that under small overlap collision conditions, the driver’s head injury is significantly influenced by the collision speed difference. However, the current Chinese regulations specify only a 40% overlap collision scenario, which may not effectively ensure occupant safety in small overlap collisions. Additionally, the results show that as the speed difference increases, the HIC36ms value of the driver’s head in the X direction increases significantly, while the HIC36ms value in the Y direction exhibits more complex periodic fluctuations. The vehicle tends to rotate more around the Z-axis, and the overall variation in the Y direction remains relatively small. The primary influence of speed on the driver’s head acceleration remains concentrated in the X direction.From this, it can be concluded that under small overlap collision conditions (10% overlap), the acceleration of the driver’s head in the X direction shows significant variation, and as the speed difference increases, the maximum acceleration gradually rises. This indicates that the sensitivity of head impact forces is closely related to the collision speed difference, and the head’s motion pattern may exhibit different acceleration characteristics compared to conventional offset collisions. Therefore, existing collision test standards, which are based solely on 40% overlap collisions, fail to fully reflect the risk of head injury in small overlap collisions. This highlights the urgent need for a more thorough safety assessment and revision of standards for this scenario.

Table 4.

HIC36ms values of the dummy head in X and Y directions under a 50 km/h speed different.

	10%X	10%Y	20%X	20%Y	30%X	30%Y	40%X	40%Y	50%X	50%Y
HIC36ms	102.5	23.3	154.1	172.3	191.3	24.5	370.8	84.0	414.9	100.9
Max Acceleration (m/s2)	101.8	13.0	115.5	37.6	123.1	24.0	162.9	37.8	156.5	37.9

Fig. 17.

The acceleration of the dummy’s head.

Table 5.

HIC36ms values of the dummy head in X and Y directions under a 10% overlap rate.

	30 km/h X	30 km/h Y	40 km/h X	40 km/h Y	50 km/h X	50 km/h Y	60 km/h X	60 km/h Y	70 km/h X	70 km/h Y
HIC36ms	52.2	18.2	100.8	39.1	102.5	23.3	102.8	89.4	127.4	179.1
Max Acceleration (m/s2)	10.0	8.5	25.1	9.4	101.8	13.0	187.3	17.8	260.4	21.2

Fig. 18.

Acceleration analysis of the dummy’s head.

Neck injury analysis

1. Resultant Force on the Neck at Different Speed Differences under a 10% Overlap Rate

   Figure 19 shows the variation curve of the resultant force on the Hybrid III 50th percentile dummy’s neck under a 10% rear-end collision overlap rate. The dummy’s neck is connected using BEAM elements, and the History Beam ID is set in the DATABASE keyword card. This allows for the output of axial force, radial force, bending force, and moment on the dummy’s neck. In this study, the resultant force on the driver’s neck is extracted based on the Binout results output from the simulation.

   As shown in Fig. 19, under a 10% overlap, as the speed difference increases, the time for the neck’s resultant force to reach its maximum value gradually shortens. This indicates that the impact of the airbag on the head indirectly affects the neck, leading to an increase in the maximum resultant force on the neck and a decrease in the time to reach the peak value. This is inconsistent with the situation in Chinese collision regulations, which only test 40% offset collisions.

   Therefore, in small overlap (10%) collisions, the neck force response is closely related to the speed difference and exhibits rapid variations, indicating that the timing and magnitude of neck loading are unique. Compared to the conventional 40% offset collision standard, this condition has a more significant impact on the neck, suggesting that existing standards may underestimate the potential risk of neck injury in small overlap collisions.

2. Resultant Force on the Neck at Different Overlap Rates under a 50 km/h Speed Difference

   Figure 20 shows the variation curve of the resultant force on the Hybrid III 50th percentile dummy’s neck under a 50 km/h rear-end speed difference.

   As can be seen from Fig. 20, with the increase in collision overlap rate, the peak resultant force on the driver’s neck generally shows an increasing trend. Moreover, in the 40% offset collision, the force on the driver’s neck is maximized, which also validates the rationale behind the 40% offset collision requirement in Chinese regulations.

   Therefore, under small overlap (10%) collision conditions, the peak neck force does not show a significant increase compared to large overlap collisions, indicating a more gradual increase in neck loading. This finding reveals the distinct impact of small overlap collisions on the neck injury mechanism, suggesting that existing regulations may not fully address the safety risks associated with this scenario.

Fig. 19.

Driver’s neck force change diagram at different speeds.

Fig. 20.

Driver’s neck force change diagram at different overlap rates.

Chest injury analysis

1. Analysis of the Variation in Chest Combined Acceleration Curve at Different Speed Differences with a 10% Overlap Rate

   In the Federal Motor Vehicle Safety Standard (FMVSS) 208, chest acceleration is used as an index for evaluating chest injury²⁶. The formula is defined as:=,and , , represent the acceleration components of the chest center of gravity in the x, y, and z directions, respectively. As shown in Fig. 21, the results indicate that the combined chest acceleration increases gradually with the speed difference. When the speed difference reaches 60 km/h, the acceleration increases significantly, while the increase becomes smaller at 70 km/h (169 g). The current Chinese regulation specifies a collision speed of 64 km/h ± 1 km/h for 40% overlap frontal collisions, which is close to 60 km/h. This further validates the rationality of the Chinese regulation.

2. Analysis of the Variation in Chest Combined Acceleration Curve at a 50 km/h Speed Difference under Different Overlap Rates

   The results shown in Fig. 22 indicate that as the overlap rate increases, the maximum value of chest acceleration first increases and then decreases. This phenomenon can be attributed to the intense impact between the dummy driver’s chest and the left B-pillar, as well as the large restraining force momentarily applied by the seatbelt, which leads to a significant increase in chest acceleration. This further validates the rationality of setting the 40% overlap collision scenario in the regulations.

Fig. 21.

Dummy chest acceleration curve at different speeds.

Fig. 22.

Dummy chest acceleration curve at different overlap rates.

Lumbar spine injuries analysis

1. Variation of Lumbar Spine Force at Different Speed Differences under 10% Overlap Rate.

   As shown in Fig. 23, with the increase in the rear-end collision speed difference, the maximum resultant force on the dummy driver’s lumbar spine also increases. A larger speed difference exacerbates the relative motion between the upper and lower torso, generating greater shear forces, which may lead to lumbar spine fractures and increase the risk of paralysis or death.

2. Lumbar Spine Force at Different Overlap Rates with a 50 km/h Speed Difference.

   As shown in Fig. 24, within the overlap range of 10% to 40%, the lumbar spine force gradually increases. However, at 50%, the lumbar spine force decreases and shows no significant change. This indicates that as the collision overlap rate increases, the restraint force of the seatbelt and the vehicle’s Z-axis steering force gradually increase the lumbar spine moment.

Fig. 23.

Hysteresis lumbar force curve under different speeds of 10% overlap rate.

Fig. 24.

Lumbar force curve of 50 km/h driver at different collision overlap rates.

Leg injuries analysis

1. Leg Axial Force Variation at 10% Overlap with Different Speed Differences

   In the Federal Motor Vehicle Safety Standard (FMVSS) 208, the axial force of the leg is used as an index for evaluating leg injury²⁶. As shown in Fig. 25, with the increase in the speed difference of the rear-end collision, the axial force of both the left and right legs of the dummy driver increases. Under different speed differences, the force on the left leg is significantly greater than that on the right leg. This is mainly due to the collision being biased to the left side, resulting in more severe deformation and narrower space on the left side. Additionally, the vehicle’s rotation around the Z-axis enhances the inertia on the left side, further intensifying the force and injury on the left leg. Therefore, it is recommended to include an evaluation of the driver’s left leg injury in the C-NCAP occupant rating.

2. Leg Axial Force Variation at Different Overlap Rates with a 50 km/h Speed Difference.

   Figure 26a shows that at a collision speed difference of 50 km/h, the axial force of the driver’s right leg increases overall with the collision overlap rate, but the values are relatively small. In contrast, Fig. 26b shows that the axial force of the driver’s left leg also increases with the collision overlap rate and reaches a maximum value of 135 g at a 40% overlap rate. Additionally, under the same overlap conditions, the force on the left leg is always greater than that on the right leg.

Fig. 25.

Axial force curve change diagram at different speeds.

Fig. 26.

Axial force curve change diagram at different overlap rates.

Discussion

This study analyzed the impact of different overlap rates and speed differences on driver injuries in rear-end collisions using finite element modeling. It revealed significant effects on injuries to the driver’s head, neck, chest, lumbar spine, and legs. The results showed severe injuries under low overlap (10%) and high speed difference (50 km/h) conditions. These findings align somewhat with prior studies on overlap and speed effects but also show discrepancies.

Previous studies have generally indicated that collision overlap rate significantly affects driver injuries. For instance, Shi et al.¹⁴ found that in frontal collisions, chest stress and deflection are more sensitive to impact loads at higher overlap rates (e.g., 40%), with the highest risk of thoracic injury occurring during full frontal impacts. This study also observed a similar trend: at a speed difference of 50 km/h, the injury severity of the driver’s neck, chest, and lumbar spine increases with the overlap rate, especially at 40% overlap, where injuries are most severe. This indicates that overlap rate is one of the key factors affecting driver injuries, with higher overlap conditions posing greater injury risks. Additionally, Yang et al.¹³ pointed out that the risk of neck injury in low-speed rear-end collisions is closely related to collision overlap rate, which is consistent with this study’s finding that neck injuries worsen with increasing overlap rate. Teoh et al.¹⁷ further demonstrated that vehicle structural deformation and occupant motion responses in small overlap collisions are closely related to overlap rate, which further confirms the significant impact of overlap rate on occupant injuries. Previous research has predominantly employed methods such as biomechanical models, finite element analysis, and real-vehicle simulations to investigate the effects of collisions on occupant injuries. For example, Jiang et al.¹⁹ used finite element analysis to study the protective effects of airbags in frontal collisions and found that airbag design parameters (e.g., inflation time and pressure) significantly influence injuries to the head and chest. Similarly, Gabler et al.²⁷ analyzed the role of seatbelts in side collisions and found that the effectiveness of restraint systems is highly dependent on collision overlap rate, which aligns with this study’s findings on the variations in occupant protection provided by seatbelts under small overlap conditions. Furthermore, Rouhana et al^.28 indicated that the distribution of occupant injuries in side collisions exhibits similar asymmetric characteristics to those observed in small overlap collisions.

While prior studies and this research both emphasize the importance of overlap rate, there are differences in methodology and focus. Previous research has predominantly used biomechanical models, finite element analysis, and real-vehicle simulations. In contrast, this study analyzed specific collision conditions of two Toyota Yaris vehicles under varying overlap rates and speed differences, revealing a close link between key driver injuries and speed differences, especially in 10% overlap and 50 km/h speed difference scenarios. It also found more severe left leg injuries and suggested adding lumbar and left leg assessments to Chinese regulations, a perspective less explored in other studies. Jiang et al.¹⁹ noted that seatbelt and airbag configurations significantly affect occupant protection in small overlap collisions, aligning with this study’s findings on their role in small overlap crashes. However, this study further highlighted the greater impact of speed differences on occupant injuries in small overlap rates, a area less covered in prior research. Forman et al.²⁹ focused on optimizing seatbelt systems for rear-seat occupants, using cadaver experiments—a method distinct from this study’s finite element simulations. Shaw et al.³⁰ investigated seatbelt effects on bones via cadaver tests, whereas this study quantified collision parameters’ overall injury contributions through simulations. Bose et al.³¹ explored how pre-collision occupant parameters (e.g., posture) influence injuries, while this study focused more on the dynamic characteristics of collision scenarios, reflecting differing research perspectives.

This study found that in 10% overlap collisions, the driver’s head acceleration maxima rise with increasing speed differences, concentrated mainly in the X direction. This indicates a close sensitivity of head impact forces to speed differences in small overlap collisions. Teoh et al.¹⁷ also noted that head-airbag contact time is shorter in small overlap collisions, potentially increasing injury risks. In 40%-50% overlap collisions, the off-center collision forces cause yawing motions and significant lateral inertial forces on occupants’ heads, due to incomplete side collision effects. NHTSA and IIHS crash test data show that vehicle “fishtailing” in this overlap range increases peak lateral head acceleration by 20%-30% compared to full overlap collisions¹⁷. Thus, current crash standards based solely on 40% overlap don’t fully reflect head injury risks in small overlap collisions, necessitating further safety assessments and regulatory revisions.In terms of neck injuries, this study found that in 10% overlap collisions, neck resultant forces respond closely and rapidly to speed differences. This aligns with Yang et al.¹³ findings that cervical cortical bone yield stress is 1.8 MPa, suggesting seatbelt restraints can raise cervical injury risks. Therefore, using more optimal seatbelt restraint systems is crucial for protecting rear-impact occupants’ cervical vertebrae.

This study found that the combined chest acceleration increases with the speed difference, with the most severe injuries occurring in 40% overlap collisions. This shows that different crash conditions significantly affect chest injuries, and choosing the right crash conditions can reduce them. The results also show that the main cause of chest rib fractures is the seatbelt shoulder restraint and airbag deployment, which increase the risk of rib fractures. This means that when designing and selecting restraint systems, these factors need to be considered, and measures should be taken to reduce chest injuries. Shi et al.¹⁴ also found that the risk of chest injury increases significantly in large overlap collisions, which further confirms the conclusions of this study.

This study found that in rear-end collisions, the driver’s left leg axial force is greater than the right leg, and increases with the speed difference, making the left leg more prone to injury. So, it’s recommended to add left leg injury assessment in C—NCAP for better occupant protection. Jiang et al.¹⁹ also found a close link between leg injury risk and speed difference in small overlap collisions, which is in line with this study.

This study’s neck injury analysis shows that in 10% overlap collisions, the time to peak neck force shortens as speed difference increases. This indicates that rapid head forward movement under high-speed differences intensifies the instantaneous shear force and bending moment on the neck. Insufficient headrest contact area may reduce protection; thus, dynamically adjustable headrests are needed to accommodate asymmetric movements. Additionally, optimizing seatbelt pretensioner timing is crucial to prevent early restraint, which can increase inertial neck loads.

This study found that in rear-end collisions, the lumbar spine force increases linearly with the speed difference, especially when it exceeds 60 km/h. At 40% overlap, greater cockpit intrusion, combined with seatbelt restraint and seat reaction forces, subjects the lumbar spine to higher compression and bending moments. Unlike the thoracic spine stress concentration in full frontal collisions, vehicle rotation in small overlap collisions misaligns the seatbelt restraint direction, increasing lumbar torsional loads. Optimizing seatbelt anchor stiffness distribution is recommended to reduce these combined loading risks.

While this study revealed patterns of driver injuries across different overlap rates and speed differences, it has limitations. It mainly focused on injuries to the head, neck, chest, and legs, with limited analysis of other body parts like the abdomen. Also, it relied solely on finite element simulations without real-vehicle crash tests for validation.Future research could optimize restraint system parameters and explore interactions between various restraint factors. This would help develop more comprehensive strategies for different crash conditions. Additionally, research on collisions with smaller overlap rates (e.g., below 5%) is recommended. This would enhance the effectiveness of occupant protection systems and drive more precise safety innovations.

Conclusion

This study investigates the severity of driver injury at key body regions in two Toyota Yaris vehicles using finite element models under nine different conditions, including varying overlap rates and collision speed differences. The results are compared with C-NCAP ratings, leading to the following conclusions:

1. In the collision scenario with a 10% overlap, the severity of injury to the driver’s head, neck, chest, lumbar spine, and legs increases with the growing speed difference. In this scenario, the injury to the driver’s key body regions is more significantly affected by the speed difference. Therefore, it is recommended to include a small overlap collision scenario with a 10% overlap in Chinese regulations;

2. In collision scenarios with different overlap rates and speed differences, the driver’s lumbar spine and leg injuries are significantly influenced by both factors. Additionally, the injury to the driver’s left leg is more severe than that to the right leg. Therefore, it is recommended to include an evaluation of the driver’s lumbar spine and left leg injuries in the current Chinese crash regulations, in order to enhance occupant protection in future vehicle developments;

3. In collision scenarios with a 50 km/h speed difference and varying overlap rates, the driver’s neck, chest, lumbar spine, and left leg sustain the most severe injuries at a 40% offset collision overlap rate. Since the 40% overlap setting in offset collision tests is consistent between international and Chinese regulations, this directly validates the rationale behind the 40% overlap rate in both Chinese and international offset collision regulations.

4. Currently, there is a lack of systematic research on collisions with an overlap rate of less than 10%. Future work should focus on the impact of collisions with even smaller overlap rates (e.g., below 5%) on driver injury severity, particularly since, under such conditions, the vehicle’s structural and safety system responses may differ significantly from those observed in typical collision scenarios. Therefore, it is recommended that future safety regulations include assessments of collisions with overlap rates below 10% to enhance the effectiveness of occupant protection systems and promote more precise safety technology innovations.

Author contributions

H.L.: conceptualization, methodology, formal analysis, resources, writing—review and editing. D.Z.: visualiza tion, validation, writing—review and editing, software.Y.Z.: data curation, resources, writing—review.

Data availability

The datasets used and analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.