Assessment of Driver’s Head Acceleration during a Possible Car Skidding Effect

Abstract

This document provides a design description of a data acquisition device that allows an alert to be issued to suggest to the driver to take a break after having subjected his body to a certain amount of acceleration and pressure changes after driving on a road with too many curves. The tests were carried out using sensors based on microelectromechanical systems. The system was strategically installed at specific points on the body of the driver and car. Several electronic arrays were carried out, like the design of a printed circuit board. The establishment of an inter-integrated circuit communication and its multiplexing to work with several devices with the same address simultaneously. Finally, in this context, the document also presents the critical velocity for each curve in the Hakone roadway, which was obtained by using a mathematical model and contrasted with data acquisition values for acceleration. The risk of skidding on a curve increases when the driver does not reduce driving velocity; only a slight variance in acceleration or environmental conditions is enough. The value of acceleration was acquired for the analysis of each curve; there is a greater possibility of skidding in curves 2 and 4 because their radius is smaller and the critical speed is approximately 60 km/h, which is very close to the driving speed. On the other hand, the deceleration value of −0.65 G read on the head accelerometer can increase fatigue symptoms such as blurry vision or dizziness.

1. Introduction

Across the globe, significant research is being conducted on drivers’ risks involving professionals, public transport, and individual drivers. The focus on distracted driving consistently ranks as a leading factor in traffic accidents, potentially leading drivers to make incorrect decisions and causing severe consequences [1]. Numerous studies have suggested that road accidents are more likely to happen on horizontal curves than on straight road sections for various reasons. The most significant factor is linked to the driver’s behavior on the curve, influenced by their perception of the road geometry [2]. The alignment of a road has a significant impact on the performance of drivers. Studies have determined that sharp curves and steep slopes increase the risk of accidents. In addition, there is an accelerated influence of factors such as traffic signs, fatigue behavior on drivers, and vehicle stability. Driving while fatigued is widely acknowledged as a significant factor contributing to both fatal and non-fatal road accidents globally. It is estimated that as much as 20% of severe crashes could be attributed to fatigued driving. Additionally, specific reports suggest that a considerable number of individuals are willing to persist in driving despite being too tired to do so safely [3]. Another aspect involves horizontal curves, which are well-known for being some of the most crash-prone areas on roads. For instance, in 2019, the Federal Highway Administration in the United States (FHWA), reported that the average crash rate on horizontal curves is roughly three times higher than on other types of highway sections and that over 25 percent of fatal crashes involve a horizontal curve. Consequently, this topic has garnered significant attention from researchers and highway authorities since the 1970s [4]. Variables that describe curve geometry and speed have been integrated into safety prediction methods. However, there has been relatively less research on how pavement friction and weather conditions impact safety [5].

The inadequate attention to safety in roadway geometry design has led to significant damage in recent years. Vehicle engineering and road design are two key factors that affect highway safety. With the rise in population and the increasing number of vehicles, traffic accidents have become a significant issue in the transportation sector [6]. The factors mentioned above can impact a driver’s sense of orientation, given the various moving objects in their environment and the accelerations and pressure changes affecting their vestibular organs. Jelica’s study [7] indicates that circadian rhythm, sleep, and work-related factors influence driver fatigue. Interestingly, the time spent going to sleep has no effect on sleep quality or fatigue. In Fanyu Meng’s study [8], a demographic questionnaire and the Brief Fatigue Inventory (BFI) were used to conduct a survey. Drivers participated in a braking simulator test session at two speeds (50 and 80 km/h) during three visits, with their brake reaction, lane control, speed control, and steering control performance recorded. Extended periods of driving may lead to loss of interest, causing the mind to wander and increasing the risk of accidents, not necessarily due to the driver’s tiredness but rather due to distraction from the road [9].

Various experimental, analytical, and simulation research studies have been carried out to discover the main relationship between vehicular accidents and their high incidence on rural roads with sharp curves. Samer [10] uses a driving simulator to conduct 76 driving experiments, simulating various road and weather conditions. The results show that drivers devote more attention and effort to overcoming road challenges than to weather conditions. The calibrated model can also simulate a road segment and predict changes in capacity and traffic disruptions due to different driving conditions. Srinivas [11], in their study, developed a crash modification factor (CMF) for skid number for all crashes, wet-weather crashes, runoff-the-road crashes, and wet-weather runoff-the-road crashes. A horizontal curve database from a southern state in the United States was used to achieve the study’s objective. It was found that the skid number variable is statistically significant, along with traditional variables such as traffic volume, curve radius, and cross-sectional widths. In the experimental study with people without any illness, they only underwent caloric stimulation, which showed that their reaction time was better. The researchers soon realized that the simulation’s fidelity mainly depended on how realistic the driving environment they intended to simulate [12]. Therefore, one of the main problems when conducting a driving simulation is to correctly emulate the passenger’s body’s main decelerations and pressure changes. Thus, they include actuators and motors to match the natural environment conduction [13]. This is due to research reports such as [14], which concluded that the driver determines the speed of the car based on acceleration changes sensed by its body.

In the same way, ref. [15] concluded that in a curve, the driver controls the car’s speed with an inverse relationship to the lateral accelerations and pressure changes that its body experiences. The reason for this is based on the results reported by different institutions around the world. It has been concluded that a driver experiences a series of acceleration and pressure changes when driving on a curved road [16]. Therefore, the driver’s driving ability and perception of movement and reaction time decrease, increasing the risk of an accident because driving on a curved road demands more attention and fatigue from the driver [17].

Furthermore, it has a high relation with pressure and acceleration changes by the driver’s vestibular organs [18]. Shauna [19] highlights the insufficient understanding of the interaction between the driver and the roadway environment, making it challenging to identify appropriate countermeasures. Using data from the S.H.R.P. 2 naturalistic driving study, they establish connections between the driver, roadway, and environmental characteristics and the risk of road departure in rural areas. The results indicate that roadway data, focusing on rural two-lane curves, encompass factors like geometry, shoulder type, and the presence of rumble strips.

Daniel [20] introduces an analytical approach to predicting driver fatigue based on a biomathematical model and estimating hard-braking events as a function of predicted fatigue. The analysis utilized de-identified data from a previously published naturalistic field study involving 106 U.S. commercial motor vehicle (CMV) drivers. The results demonstrate a proof of concept for a novel approach predicting fatigue based on drivers’ sleep patterns and estimating driving performance in terms of an operational metric related to safety. Hong Tao [21] develops an innovative real-time driving fatigue detection methodology using dry electroencephalographic (E.E.G.) signals. The study employs two methods for online detection of mental fatigue: power spectrum density (PSD) and sample entropy (S.E.). The results show the effectiveness of the proposed methods for fatigue detection. The prediction of fatigue aligns with the observed reaction time recorded during simulated driving, which is considered an objective behavioral measure.

Driving on curved roads is a routine task for many drivers, yet it has an underlying impact on both driver behavior and vehicle maneuverability. Previous research has highlighted the significance of driving performance (speed and acceleration) and visual performance (gaze and useful field of view (U.F.O.V.)) in curve analysis. However, as road conditions change, there is a growing concern for the safety of the driving environment, particularly in determining the vehicle’s maneuverability [22]. In this research, we specifically used the analysis of roll and skid on a highway segment through a mathematical model to define the critical speeds for each curve. Subsequently, the experimental development incorporates the instrumentation of the driver and the car into the data acquisition device. Six driving tests were conducted, obtaining acceleration results for both the car and the driver’s head and chest.

2. Materials and Methods

The experimental test integrates some characteristics that are necessary for each process. The experiment was carried out under a controlled environment, and the test subject’s safeguard was primary. The test was developed in a current commercial model vehicle on a curvy Japanese highway. At all times, the host country’s current traffic regulations, such as speed limits and signs, must be respected. The test subject must have a driving license and be a person who usually drives, not a professional or highly experienced driver. The D.A.D. did not alter the driver’s usual environment; in this instance, no significant modifications were made to the car. Further, objects should not be placed on the driver’s body, which could significantly impair its performance. In a general way, Figure 1 describes each process involved in a flowchart diagram.

2.1. Car and Human Considerations

A Japanese citizen conducted the driving test due to his anthropometric measurements according to The National Highway Traffic Safety Administration (NHTSA, 2019) guidelines of the United States of America [23] and the European New Car Evaluation Program (Euro NCAP, 2019) [24], which were consulted. Due to vestibular organs in the head [25], accelerations present in the torso and head are the study targets because they impair performance when driving. Therefore, measuring instruments were placed on the torso and head because the D.A.D. should not affect the driver’s performance. The research is limited to installing only two accelerometers in the driver’s body, placed strategically, as is shown in Figure 2 in red circles.

In addition, to establish a correlation of data between the driver and the vehicle’s accelerations, an accelerometer will also be arranged in the center of mass of the car and the front wheels, as is seen in Figure 3.

2.2. Forces, Momentum, and Reactions in the Car

As is well-known, curves are essential elements of highways whose design compromises the vehicle’s stability. Thus, their geometry must be adapted to vehicle dynamics to ensure the safety of the occupants in each possible climatic condition. Therefore, a detailed analysis of the different geometrical elements that influence vehicle dynamics, which transit through a circular alignment, is needed. The car behaviors in curves are a consequence of a system of forces acting on it, which is more unstable compared to when the vehicle circulates in a straight line. The main difference between both situations is the appearance in the first case of centrifugal force; this frictional force is nothing more than a consequence of the law of inertia—Newton’s first law—because when taking the curve, the vehicle is continually changing its direction. Several forces are acting on a vehicle (Figure 4), and these are mentioned below:

• Weight of the vehicle (W): vertical force in the car center of mass (c), which can be expressed in terms of acceleration, gravity (g), and mass of the vehicle (1506 kg, for Nissan note).
• Centrifugal force (Fc): This force is due to changes in the vehicle’s direction while taking a curve. This is proportional to the normal acceleration (an) of the car speed, v, and the radius curve (r).
• Friction force (R): a force due to the contact between the tire and road that depends on the normal reaction to the contact surface (N [N1, N2]) and coefficient of resistance to transverse slip (fs).

For vehicle stability, it is necessary to analyze the skidding hypothesis and the rollover hypothesis. The overturning of the vehicle would take place if the momentum produced by the force destabilizers or dumps exceeds the momentum generated by the force stabilizers that affect it. The critical points where rollover can occur are those that make contact with the vehicle and the firm, being able to cause tilt towards the outside or inside of the curve. The dump condition will occur if the value of any of the two vertical reactions, N1 or N2, is wholly canceled, which is the boundary condition that is obtained in both cases—overturn away from or overturn towards the inside of the curve. Figure 5 describes this behavior.

According to the forces shown in Figure 5, supposing a two-dimensional analysis, the weight of the car is divided equitably on the wheels (W [W1, W2]). Thus, the same happens with the normal forces (N [N1, N2]) and frictional force (R [R1, R2]). Notwithstanding, centrifugal force is kept in the center of the car’s mass (Fc). After Figure 6, several mathematical analyses can be developed to understand the possible reason for rolling over a car. First, notice that to avoid rollover, the reactions (N1, N2) must be over zero, and the best stability is when N1 = N2. On the other hand, rollover is going to happen when one reaction force turn equals zero, and then the other one holds the total weight of the car. To better understand this, momentum analysis is essential, and two momentums are responsible for car stability. The overturning momentum is the product of the centrifugal force (Fc) and the height of the car (h). The other one is known as the stabilizing momentum, which is the product of the reaction N2 (for this example, N1 = 0, N2 = W) and the half of the distance between the car’s wheel (d/2), Equation (1).

$$Fc\left(h\right)=N2{\displaystyle \frac{d}{2}},$$

(1)

Replacing all the factors of Equation (1), in the awareness, Fc is the product of the mass of the car (m) and the square of the speed (v), according to the guidelines of circular momentum.

$${\displaystyle \frac{m{v}^{2}h}{r}}={\displaystyle \frac{mgd}{2}},$$

(2)

In Equation (2), notice that the full is alien to the driver except for the speed; hence, it is important to establish a rollover speed condition, as shown in Equation (3).

$$v=\sqrt{{\displaystyle \frac{dgr}{2h}}},$$

(3)

Then, to raise the rollover speed, there are three possible factors: decreasing the car height (h), increasing the wheel distance (d), and increasing the curve radius (r). In real conditions, despite the rollover parameters mentioned above mention, most of the curved highways are banked, as represented in Figure 6. The angle (θ) has the aim to increase the car’s stability.

A trigonometrical analysis of forces is necessary to understand the interaction of forces better, as represented in Figure 6 (b). Hence, next, the angles are defined as the function of force, see Equation (4).

$$Sec\left(\varnothing \right)={\displaystyle \frac{R}{mg}},$$

(4)

Then,

$$\left(mg\right)Sec\left(\varnothing \right)=R=R1+R2,$$

(5)

In other way,

$$Tan\left(\varnothing \right)={\displaystyle \frac{\frac{m{v}^2}{r}}{mg}},$$

(6)

Finally,

$$Tan\left(\varnothing \right)={\displaystyle \frac{v^2}{gr}},$$

(7)

Expressing the same analysis of Equation (1), without turning N1 = 0, to better understand the model:

$$\left[\left({\displaystyle \frac{m{v}^2}{r}}\right)Cos\left(\varnothing \right)-\left(mg\right)Sin\left(\varnothing \right)\right]h=\left(N2-N1\right)\left({\displaystyle \frac{d}{2}}\right),$$

(8)

Then, simplified:

$$\left({\displaystyle \frac{2mh}{d}}\right)\left[\left({\displaystyle \frac{v^2}{r}}\right)Cos\left(\varnothing \right)-g Sin\left(\varnothing \right)\right]=\left(N2-N1\right),$$

(9)

Replacing Equation (5) (keeping N1) in Equation (9), then:

$$\left({\displaystyle \frac{2mh}{d}}\right)\left[\left({\displaystyle \frac{v^2}{r}}\right)Cos\left(\varnothing \right)-gSin\left(\varnothing \right)\right]-m\left[g Cos\left(\varnothing \right)+\left({\displaystyle \frac{v^2}{r}}\right)Sin\left(\varnothing \right)\right]=-2N1,$$

(10)

To analyze the rollover condition, N1 = 0 and simplify as much as possible, then:

$$\left({\displaystyle \frac{2v^{2}h}{dr}}\right)Cos\left(\varnothing \right)-\left({\displaystyle \frac{v^2}{r}}\right)Sin\left(\varnothing \right)=\left({\displaystyle \frac{2gh}{d}}\right)Sin\left(\varnothing \right)+gCos\left(\varnothing \right),$$

(11)

Multiplying full Equation (11) by (d/2 Cos θ).

$$\left({\displaystyle \frac{v^2}{r}}\right)\left[h-\left({\displaystyle \frac{d}{2}}\right)Tan\left(\varnothing \right)\right]=g\left[h Tan\left(\varnothing \right)+\left({\displaystyle \frac{d}{2}}\right)\right],$$

(12)

Finally, clearing v, Equation (13) shows the rollover speed condition in a banked highway.

$$v=\sqrt{gr{\displaystyle \frac{h Tan\left(\varnothing \right)+\left(\frac{d}{2}\right)}{h-\left(\frac{d}{2}\right)Tan\left(\varnothing \right)}},}$$

(13)

Skidding analysis: This condition depends on the camber’s values and the vehicle speed. Due to those parameters, there would be different movements of the vehicle, which could be towards the outside of the curve, caused by an excessive speed, due to insufficient camber or due to low pneumatic adhesion, or, conversely, a slide towards the inside of the curve, usually caused by an excessively pronounced camber. In Figure 7, it is possible to analyze how a car would slide when the resultant horizontal components of force became zero. First, it is necessary to understand that R1 and R2 are frictional forces acting on the car’s wheels. Who pushes the car towards the center of the highway while the centrifugal force pulls the vehicle outside the highway. Thus, to keep the car in its way, those forces must be different. The reaction force, always more significant than the centrifugal force, in Equation (14), shows the condition when the car would slide. Notice that both forces are precisely equal:

$${\displaystyle \frac{m{v}^2}{r}}=R1+R2,$$

(14)

After R1 = N1µ and R2 = N2µ, where µ is the friction coefficient, Equation (14) can be written as follows:

$${\displaystyle \frac{m{v}^2}{r}}=\mu \left(N1+N2\right),$$

(15)

Then, as N1 + N2 = W and W = N1 + N2, which at the same time is W = mg, finally.

$${\displaystyle \frac{m{v}^2}{r}}=\mu mg,$$

(16)

Clearing the speed (v) to find skidding speed:

$$v^2=\mu gr,$$

(17)

Then, given Equation (17), it could be seen that a car would slide as a function of the parameters of the highway and not of the car design. It is imperative to take into account the angle θ to attach with reality, as shown in Figure 5. According to this, after analyzing horizontal forces, Equation (15) would be the next.

$$m\left({\displaystyle \frac{v^2}{r}}\right)Cos\left(\varnothing \right)-mg Sin \left(\varnothing \right)=\mu mg Cos\left(\varnothing \right)+{\displaystyle \frac{\mu v2}{r}}Sin \left(\varnothing \right),$$

(18)

In order to clear v, divide the complete Equation (18) through Cos(θ) and simplify as much as possible, then:

$${\displaystyle \frac{v^2}{r}}\left[1-\mu Tan \left(\varnothing \right)\right]=g\left[\mu +Tan \left(\varnothing \right)\right],$$

(19)

Finally, clearing v:

$$V=\sqrt{\mu \left\{{\displaystyle \frac{gr\left[\mu +Tan\left(\varnothing \right)\right]}{1-\mu Tan \left(\varnothing \right)}}\right\}},$$

(20)

2.3. Driver Analysis

With dynamic equations, it is possible to study the behavior of the driver’s body. The equations of Euler–Lagrange apply well since these describe the evolution of a mechanical system. Figure 7 shows the human body presented as an inverted pendulum with a movable anchorage.

It is possible to determine the current position of the torso driver by using different parameters. Thus, given the above, the driver’s torso might experiment with rotational (Δϕ) and translational (Δx) movements. Those movements are the result of the driver’s anthropometric measures, such as the weight and the length of their torso, which are constant parameters. The temporal parameters are related to them because the final position of the moveable car and the pendulum are related. According to the open literature [26], an inverted pendulum with a moveable car is a no-line system. Due to this, is necessary to linearize around an equilibrium point. As Ref. [27] reported, an inverted pendulum with a moveable car has an equilibrium point around the angle zero, so for this research, ϕ will be considered ϕ = 0. Also, the inertial momentum can be considered as the nearest to zero. Finally, it is possible to establish Equations (21) and (22) to know the position of the driver’s body in the function of the input, force u(t):

$$\left(M+m\right)x″+ml\varnothing =u,$$

(21)

$$\left(l+{ml}^2\right)x″+mlx″=mlg\varnothing ,$$

(22)

To obtain the transfer function, it is possible to consider the inertial central force of Equation (22) to be close to zero, and then the transfer function of the driver’s body behaviors according to the system of Figure 6 can be as Equation (3) expressed:

$$\varnothing {\displaystyle \frac{s}{u\left(s\right)}}={\displaystyle \frac{1}{Ml{s}^2}}-\left(M+m\right)g,$$

(23)

The output of the system is the angle ϕ(s), while the input is the force u(s), which means that the final position of the driver’s body depends on the resultant force applied to it. It is commonly known that the force necessary to move somebody is directly proportional to the acceleration x″ and the mass of the body m. Then, the acceleration must be expressed as a Laplace function (s2).

$$U\left(s\right)=m{s}^2,$$

(24)

2.4. Experimental Test

A cycling helmet was used to install the accelerometer on the driver’s head, and the accelerometer was installed in its mass center. A vest was employed on the torso. The anchoring of the accelerometers in the helmet and vest must be carried out carefully. Any displacements or rotations can be experienced for the sensors. The conceptual acquisition system’s design to analyze the decelerations (G’s) of a driver’s body consisted of three stages. The first was the guidelines for instrumentation, followed by the acquisition of data through an embedded system, and the third was data processing and analysis. The necessary electronic devices and equipment include electronic materials such as accelerometers, D.C. adapters for cars, flat cables, cases for European fuses, Arduinos, USB wires, and laptops; for tools, include devices, tweezers, tm welding equipment, and cutters; for other miscellaneous items, include lifejackets, a cyclist helmet, scotch tape, and industrial glue.

The conceptual design of the D.A.D., including its limitations, was established. It is possible to scale to the implementation step. This section is divided into two. The prototype’s physical implementation and the set of electronic and programming tests to put the D.A.D. into operation. The MEMS used in this research (accelerometer ADXL345) combines a 3-axis gyroscope and a 3-axis accelerometer on the same printed circuit board (P.C.B.). Thus, in order to measure the complete data, it was necessary to implement an algorithm. Due to electrical noise in the sensors, digital Kalman filters were also implemented in the signals acquired. Owing MEMS communicate through inter-integrated circuits (I.I.C.s) communication. It was necessary to multiplex the MEMS’s signals using the integrated circuit ICA958a, connecting eight devices and the microcontroller. Finally, due to several components in the electronic circuit and minimizing the possibility of failure, a P.C.B. was designed. Therefore, a complex 3-axis motion in the three orthogonal directions was measured and registered, see Figure 8.

The experimental test was developed with several limitations that must be established before conducting the experimental test. First, the highway on which the study was carried out was selected. Subsequently, a significant amount of information about the study road including the testing section, driving time, number of tests, and speed must be collected. According to the traffic conditions on Japanese motorways at that stage of the year, it was decided to carry out the test drive on a road where car traffic was low. Therefore, according to the researchers’ experience, the Hakone-Shindo Highway (Figure 9), located in Kanagawa, was the most appropriate. Data acquisition began in the area with the most significant number of curves. Therefore, the driver would overcome six curves, covering a total distance of approximately 2.23 km.

It is necessary to know some measurements of the curves, such as the radius, the arc, lane width (3.5 m), and the angle with respect to the normal lane in each curve, which is approximately 4–6 degrees. These data will boost the result analysis. In

Table 1. Characteristic of each curve in Hakone’s segment highway.

I.D Curve.	Characteristics
1
2
3
4
5
6

, the measurements of the most significant curves are listed. It can be observed that the smallest radius is present in Curve 4, with a radius of approximately 43.84 m, and the biggest is in Curve 3, with a radius of roughly 185.16 m. In the case of the arcs, the biggest one is present in Curve 3, with a length of roughly 182.42 m, while the smallest one is in Curve 4, with a length of approximately 99.04 m.

With the purpose of analyzing the driver’s stress, fatigue, and vigilance to establish a relationship with the driver’s acceleration changes, previous research used questionnaires [27]. For anxiety and vigilance, the questions must relate to reactions, for example, exposing a hypothetical situation and asking the driver about its response. Also, ref. [28] has reported that there must be questions directly related to feelings. Finally, for fatigue, questions about pain in several parts of the body can be established, especially in those that might interfere with the driver’s performance, like the neck, head, eyes, arms, and calves.

Table 2. Test driver.

No.	Question
1	You are driving on the road, other motorists behind you whistle and change the light. A) Drive faster B) Go to your right and let them pass C) React D) Follow your pace are to import
2	Another driver makes you. He commits an evasive infraction or commits an infraction and does not apologize. A) He gets very angry and insults even if he hears B) He resigns without further C) He tries to reach it and accelerate D) He tries to write down his badge number and report it
3	At night, once you have advanced another vehicle it keeps the lights a long time: A) It signals him to realize that he is carrying the long lights B) he stops to realize that the lights are disturbed C) He lets him pass and does the same thing as
4	The driver goes ahead braking abruptly and you get into the back without being able to avoid it. A) Discuss the incident B) Discuss and let him know your discontent C) Recognize your distraction and accept your claims D) Claim The action of the other user
5	You drive quietly on the road, another vehicle passes him and joins his lane, causing you to brake abruptly. A) He goes down and insults him B) He insults him even if he doesn’t listen to him C) He lets him go quietly D) Write down his badge number and report it
6	Driving through the city a vehicle surpasses you and if it is placed in front of you and stops abruptly, you try to stop but it is impossible and collides in the back of the reckless vehicle A) Get off and dialogue on the subject B) Get off and try to intimidate him C) Get off and make him see his mistake that he is responsible D) Insults and physically assaults you
7	Blink for more than one second (Yes) (No)
8	Does the driver have dry eyes? (Yes) (No)
9	The driver yawns. (Yes) (No)
10	The behavior of the driver is? (Relaxed) (Animated)
11	Can the driver hold a conversation that demands mental dexterity? (Yes) (No)
12	Which numbers can the driver recognize?
13	Can you recognize or intuit what does is written into the red circle?
14	Does the driver experiment any paint? (Yes) (No)
15	How are the movements of the claves driver? (Skillful) (Awkward)

shows the main questions to know the driver’s state of mind and a test for a driver to apply before and after the experiment,

Once the experimental test boundaries were set, the researchers transported to Hakone Shingo Avenue to make the final test. Six driving tests were performed. Previously, all the accelerometers were fixed in their own places, and several tests with the D.A.D. were performed. The last was to certify the correct function of all the devices. A test driver holding a Japanese driver’s license drove three times. During all the experiments, data on the acceleration in the driver’s body and car were collected. The test was carried out in a Nissan Note model 2019. Once the D.A.D. was certificated and the test driving was carried out, several curves were registered. G’s were experienced in the driver’s body and those of the car. The two results will be analyzed subsequently, including the car axes’ accelerations in the geometrical aspects of the road. The second was planned to determine the injuries and fatigue in the driver’s body, owing to the accelerations experienced in the body. It must be considered that, firstly, the test was established to be performed in a safe environment. Thus, the result of this step must be those of safe driving. Furthermore, data acquisition was carried out to evaluate the D.A.D. system’s functionality, which was proposed in this research.

3. Results

After the above mathematical analysis, which allowed the establishment of a mathematical model for car skidding and rollover analysis, only the velocity factor was studied in each curve. According to the mathematical model, the first results are shown in

Table 3. Critical velocities in the car.

Curve	1 CR (m)	2 ROV (km/h)	3 SV (km/h)
1	70.16	300.80	78.98
2	50.15	243.65	66.19
3	185.16	468.17	127.18
4	43.84	237.77	62.43
5	35.80	214.87	56.41
6	82.45	312.41	84.86

¹ Curve ratio, ² rollover velocity, ³ skidding velocity.

, which describes critical velocities for rollover and skidding effects on a car in each curve.

The next step was to attach an experimental test. According to the knowledge of some parameters, the weight of the car (W) and the angle of the curve ϕ are constants, but the centrifugal force (fc) could be approximated by the accelerations experienced in the center of mass of the car (c). Tests were also done to know the behavior of the reaction’s forces in the wheels of the car and any consequent latch experimental and mathematical results to understand how safe Hakone Avenue is and how it impacts the driver’s performance. Figure 10 shows the data collected during the driving test performance by the driver. The accelerations experienced by the car in X-axis for each test and, for Figure 11, the accelerations observed on Y-axis during the tests. Each color is assigned for each test according to the following descriptions: blue, test 1; red, test 2; green, test 3; yellow, test 4; magenta, test 5; and cyan, test 6.

As with the D.A.Q. system implemented at the beginning, several data of acceleration in three axes, X, Y, and Z, have been collected. Thus, it is possible to analyze the response of the human body in the Y-axis and Z-axis. In Figure 12, the acceleration experiment in axes X, Y, and Z are shown. Through the data collected during the experimental test, it is possible to analyze the results using the mathematical models developed.

It is possible to identify the peak values for acceleration on the car, and those values are described in

Table 4. Maximum values for peak accelerations in car.

Test	* VP CM (G’s)		* V.P.P. (G’s)		V.P.C.P. (G’s)
	X	Y	X	Y	X	Y
1	−0.21/115 s	−0.28/45 s	−0.12/105 s	0.38/45 s	0.28/90 s	0.07/50 s
2	0.05/63 s	0.38/53 s	−0.25/65 s	0.34/70 s	0.23/50 s	−0.20/63 s
3	0.05/63 s	0.38/53 s	−0.25/65 s	0.34/70 s	0.23/50 s	−0.20/63 s
4	0.20/95 s	0.32/15 s	−0.35/95 s	0.32/30 s	0.23/80 s	−0.30/95 s
5	−0.18/117 s	0.33/40 s	−0.30/118 s	0.35/58 s	0.23/38 s	−0.27/118 s
6	−0.32/160 s	0.48/110 s	−0.12/110 s	0.30/65 s	0.23/118 s	−0.05/18 s

* Max refers to the maximum peak of acceleration in the center mass (CM), pilot position (P.P.), and copilot position (C.P.).

for each test.

The perspective between the center of mass and the head’s acceleration is described in Figure 13, where it is possible to show in terms of time the effects of drastic changes in velocity in the X-axis.

In general terms, Figure 12 and Figure 13 show all the acceleration behavior for all the tests. Just like the acceleration’s behavior on a car, it is possible to identify some peak values with respect to time. Applying the same context for each test,

Table 5. Maximum values of acceleration on head.

Test	* VP CM (G’s)		* V.H.P. (G’s)
	X	Y	X	Y
1	−0.21/115 s	−0.28/45 s	0.10/115 s	−0.18/45 s
2	0.05/63 s	0.38/53 s	−0.65/63 s	−0.10/53 s
3	0.05/63 s	0.38/53 s	−0.65/63 s	−0.10/53 s
4	0.20/95 s	0.32/15 s	0.10/95 s	−0.17/15 s
5	−0.18/117 s	0.33/40 s	−0.18/117 s	−0.13/45 s
6	−0.32/160 s	0.48/110 s	−0.70/160 s	−0.15/110 s

* Max refers to a maximum peak of acceleration at the center mass (CM) and head position (H.P.).

shows the results for this behavior.

4. Discussion

According to the results shown in Table 3, it can be observed that in Curves 2 and 4, the critical speed at which a skidding effect can occur is approximately 67 km/h, which is lower than the speed limit of Odawara-Atsugi highway, which is directly connected to Hakone Avenue and where the driving started. By comparing the peak acceleration values in each of the tests, it can be seen that the acceleration or deceleration values in that section fluctuate during the first minute, which resembles the results presented in the graphs associating acceleration in different cars in the work of Yang et al. [29], where a mathematical model estimates the safety velocity under similar condition in this research as radio curve, also considerate friction coefficient, Head acceleration in curves, specifically in curves with a longer radius than others, could drastically influence potential driver fatigue. If the driver does not follow the movement or maintain the same head position, it could lead to a dangerous situation. Even minimal acceleration in this kind of curve could be enough to cause the driver to lose all control of the vehicle.

The D.A.D. (driver assistance device) system plays a crucial role in this context. As a preliminary study, information about acceleration on the roadway could be obtained and contrasted with the results of a mathematical model of each curve. With the D.A.D. system, it could be possible to predict the likelihood of a skidding or rollover effect. An extrapolation could be associated with processing data at a constant velocity and identifying critical velocities that could pose risks. The information gathered could be precious for future studies and practical applications. For example, there is the potential to integrate this system into the highway’s database. By incorporating just one more variable, the safety of all passengers could be significantly enhanced. A sensor or command module could be associated with G.P.S. data to provide real-time recommendations or warnings. This could include advising drivers to reduce their speed when approaching a high-risk curve. Such integration would not only improve safety but also provide drivers with critical information to prevent accidents.

5. Conclusions

This document has presented a complete description of the acceleration and deceleration behavior that affect both the driver and the vehicle while driving on curvy roads. Several data points can be used to interpolate a function using numerical methods to obtain the force input functions, which are necessary to simulate the behavior of the torso impulse. Furthermore, as the head decelerations recovered, a more in-depth analysis was possible using the dynamic equation of an inverted double pendulum with a moving carriage during each driving test.

According to the results from the mathematical model, if the driver maintains the same velocity on all tracks, especially on Curves 2, 3, and 4, there is a significant possibility of skidding the vehicle because the critical velocity for the skidding effect on these curves is near to the driving velocity; an increase that environmental conditions, bad calibration of tires, and roadway conditions can exacerbate. A minimal increase in head acceleration during driving in curves with higher risk, considering these curves have a larger radius and a minimal angle with respect to normal, could be associated with increased driver fatigue, potentially resulting in an accident due to skidding or rollover effects. In summary, this research not only identifies specific risks related to driving at certain speeds on the Hakone roadway but also proposes practical solutions using advanced technology like the D.A.D. system. The aim is to ensure that these findings can be applied and tested in other contexts, ultimately leading to safer driving conditions for all.

There were some limitations associated with control variables during the development of this research, such as the friction coefficient and tests with different drivers. It is important to point out that, as a first attempt, the data acquisition system was evaluated in order to calibrate and identify all the main sections that provide enough information on acceleration during each test. In addition, it is of utmost importance to gather as much information as possible. This research is aimed at the future possibility of developing applications or emergency systems that can mitigate the risk of skidding and injuries to the human body, resulting from constant driving conditions.