Keywords

1 Introduction

Hydroplaning is a critical factor for road safety, as underscored by alarming statistics on road accidents. According to [1], adverse weather conditions contribute to 10% of fatal road accidents, with 3% occurring on icy or snow-covered roads and the remaining 7% on wet roads. The phenomenon’s evolution was initially described by [2]. Tyre design, including tread grooves and sipes, plays a pivotal role in addressing hydroplaning by expelling water from the contact area and channeling it away. This design facilitates the tire’s ability to maintain direct contact with the road surface, thereby minimizing the risk of hydroplaning.

According to the definition in [3], hydroplaning speed is the velocity corresponding to the contact patch detaching from the ground; it is determined by factors such as water film depth, tread pattern design, and tire wear. The research [4] emphasizes the adverse impact of hydroplaning on vehicle responsiveness, caused by the wedge of water formed between the tire and the road surface. Previous research, including studies by [5] and [6], investigated hydroplaning’s effects on tire properties such as cornering stiffness, relaxation length, and friction coefficient. Road texture’s influence has also been examined by [7] and [8].

Furthermore, [9] explores how tread design affects a tire’s maximum volumetric flow rate, while [10] investigates the relationship between groove pattern and hydroplaning speed. The findings reported in [11] confirm that rear wheels develop tangential forces even when the front ones experience hydroplaning due to the cleaning effect of front tires.

Given the dangers associated with hydroplaning, various studies have sought to address it. The work [12] presents a control system based on a linear single-track model, while [13] suggests mitigating hydroplaning risk by using air streams to remove water ahead of the front tires. Detection of hydroplaning onset is crucial for activating control measures, as proposed by [14] through measurement devices and techniques.

Drawing from technical literature and experimental tests, researchers have developed a tyre model to simulate hydroplaning, incorporating scaling factors into the MFTyre model [15]. This model aims to replicate hydroplaning onset on a dynamic driving simulator [16] to evaluate a control logic designed to assist drivers in such hazardous situations.

2 Tyre Model Development

A tire model able to simulate hydroplaning was developed. Based on technical data, four scaling factors were introduced in the MFTyre model [15] to adapt the nominal conditions to the wet environment. The scaling factors modify cornering stiffness, longitudinal stiffness, relaxation length, and friction coefficient. They are obtained from experimental data available in [5, 6] as a function of the speed, considering specific tire dimensions and a 5mm-deep water layer (Fig. 1a).

Fig. 1.
figure 1

Technical data used to modify the MF model: (a) scaling factor obtained from [5, 6], (b) hydroplaning speed vs tire characteristics obtained in [4]

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To extend the range of possible scenarios, it is mandatory to relate the scaling factor with the maximum volumetric flow rate the tire can drain out. The research [3] provides the critical hydroplaning speed for different water layer depths and different tread tire characteristics (Fig. 1b). Thus, knowing the current tire and road condition and vehicle speed, it is possible to define an equivalent speed to be used in the experimental curves.

Moreover, the model includes the “cleaning effect” of the front tires: part of the water film is drained out by the front tires based on the maximum volumetric flow rate they can process. This phenomenon increases the critical hydroplaning speed for the rear axle. Research [11] relates the wedge of water under the front tires with the wedge of water under the rear tires, as a function of the speed. Knowing the speed, tire characteristics, and the amount of water, it is possible to scale the Pacejka’s curves also for the rear axle.

The proposed model was verified by comparing the outcomes of a sine sweep maneuver performed in [5]. Both sources exhibit similar trends in lateral forces. Figure 2 shows that the hydrodynamic interaction between the tyre and water leads to a more pronounced load shift asymmetry during turns, emphasizing the influence of the scaling factor on normalized cornering stiffness. The relaxation length significantly delays lateral force development, revealing a notable decrease in lateral force even at relatively low frequencies such as 2 Hz.

Fig. 2.
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Time histories of lateral force and slip angle during swept sine at 85 km/h.

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3 Off-Line Development of Control Strategy

A control strategy, aimed at enhancing safety, has been developed to counteract the hydroplaning phenomenon. The working principle is based on the reduction of the vehicle’s speed below the critical threshold to restore contact between tires and the road. Therefore, taking advantage of the cleaning effect, braking torque is applied to the rear axle.

Fig. 3.
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ADAS logic scheme.

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Concerning Fig. 3, the control logic activates independent braking of the rear tires taking advantage of the cleaning effect of the front ones; a yaw moment is generated, helping the driver to complete the maneouvre. The yaw moment depends on the steering wheel angle δ required by the driver. If the absolute value of δ crosses a given threshold and the car is not turning, the logic applies a different braking torque at the rear wheels (Mbr,l and Mbr,r). Lastly, activation of the logic is triggered assuming to use sensorized tires, able to detect hydroplaning onset.

The effectiveness of the logic was assessed through offline simulations and driving simulator tests. A double-lane-change maneouvre was considered and developed. It is typical of highways when it is necessary to move on the adjacent lane and come back to the original one and it can become dangerous if water is present on the ground and the speeds are high. The scenario has been simulated according to the scheme of Fig. 4a: cones were distributed over an artificial pool of water. Many tests with different conditions of water and speed have been considered to tune and calibrate the logic gains. Therefore, firstly, offline simulation with the ideal driver has been tested. For seek of brevity, a test characterized by 8-mm water film depth and 90 km/h speed is reported, to emphasize the effect of hydroplaning and evaluate the effectiveness of the control logic in a critical scenario. Results show the power of the control logic; the ADAS helps the driver stay focused on obstacles without worrying about reducing speed, as the system handles it for him.

Fig. 4.
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Double-Lane-Change offline simulation, 90 km/h and 8-mm water depth: (a) comparison of the vehicle trajectories, (b) steering wheel angle asked by the ideal driver with ADAS on and off.

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Figure 4a highlights the improvement in the vehicle’s trajectories when the ADAS is activated, while Fig. 4b shows the steering wheel angle asked by the ideal driver. With ADAS off, he saturates the maximum angle available.

Fig. 5.
figure 5

Double-Lane-Change offline simulation, 90 km/h and 8-mm water depth: braking torque applied by the logic to complete the maneouvre.

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Figure 5 shows the braking force on the rear axle, applied by the ADAS. First, the vehicle must turn to the left, thus a larger torque is applied to the rear left tire. In the second phase, the driver must turn to the right to avoid the second row of cones, coming back to the original lane. In this phase, a larger torque is applied by the logic to the rear right tire. Interesting to notice that the torque value starts oscillating; the vehicle speed is across the critical hydroplaning one, leading to ON-OFF the logic depending if the speed is lower or larger than the critical one. Finally, the torque value on the rear left tire becomes once again larger, since the driver is turning on the left again to get the original lane straight line.

Fig. 6.
figure 6

Double-Lane-Change offline simulation, 90 km/h and 8-mm water depth, lateral forces: (a) front left tire, (b) front right tire, (c) rear left tire, (d) rear right tire.

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Figure 6 shows the evolution of the lateral forces exchanged by the tires with the ground, on each corner. Without the control, front tires saturate the maximum lateral force exchangeable with the ground, colliding with the cones. Rear tires, thanks to the cleaning effect, can exchange larger amounts of force, but due to the presence of water and the loss of grip on the front axle, they undergo a delay, leading to a further decrease in the vehicle controllability.

4 On-Line Testing on the Driving Simulator

After completing the offline tuning, the model was implemented on the dynamic simulator of the Politecnico di Milano [6]. A panel of 37 volunteers (9 female and 28 male) was involved in an experimental campaign to assess the efficacy of the control logic. Users with different experiences, risk-taking attitudes, and genders had to drive the double lane change. This operating condition is rather typical when running on motorways. Tests were repeated changing the extension of the hydroplaning area, thus affecting the time of intervention of the control before the execution of the manoeuvre. Drivers were asked to control the vehicle with and without the assistance of the active control. The success rate in completing the manoeuvres determined the effectiveness of the proposed logic. The next figures compare the outcomes with and without the control logic. Figure 7 reports the average trajectory and the dispersion of trajectories (±1σ) considering all the 37 drivers. Drivers were asked to maintain a speed of 120 km/h while approaching the pool of water. A 5-mm water depth was assumed.

Fig. 7.
figure 7

Vehicle trajectories (average and dispersion) in double lance change at 120 km/h and 5-mm water layer: control logic OFF (a) and ON (b)

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Figure 7 clearly shows that the logic improves the possibility of avoiding the cones. More specifically, the success rate can be summarized as follows: without the assistance of the ADAS, none of the drivers was able to close the maneouvre without hitting the cones. With the assistance of the ADAS, 67% of the drivers were able to complete the maneouvre without contacting the cones, 15% of the drivers failed the test on the first lane change, while 18% failed the test on the second lane change. These two percentages are mainly associated with the lack of confidence of the drivers, depending on whether they experienced hydroplaning firstly without the logic or with the logic active. Drivers who tested firstly without logic had a delay in applying the right steering wheel angle, leading to manage to steer, but touching the cones. Nevertheless, all of them were able to steer during hydroplaning conditions.

5 Conclusions

The research yielded intriguing insights into the behavior of everyday drivers encountering hydroplaning. An innovative tire model was developed and integrated with a 14-degree-of-freedom vehicle model to replicate hydroplaning effects. Additionally, an ADAS system was designed to assist drivers in maintaining vehicle control. An offline simulation helped in tuning and calibrating the ADAS, and choosing the right gains. The results of the offline tests show that the developed system improves the vehicle’s drivability, allowing the ideal driver to avoid obstacles without knocking over the cones. Finally, the effectiveness of this control logic was evaluated using the dynamic driving simulator at the Politecnico di Milano. A critical highway scenario involving a 5-mm water layer during an overtaking maneuver was designed and tested, revealing that most drivers struggled to maintain control without ADAS assistance. The findings demonstrated that such a control system could greatly enhance vehicle controllability. Finally, the potential of the driving simulator was highlighted; it allows for a deeper study of environmental phenomena like hydroplaning, aiding in the improvement of ADAS systems by examining tire behavior, and facilitates an in-depth analysis of human reactions to hazardous conditions in a controlled environment, essential for developing autonomous driving systems.