## Abstract

This article represents an extensive literature on tire hydroplaning, specifically focusing on the assessment of real-time estimation methodologies and numerical modeling for both partial and total hydroplaning phenomenon. Hydroplaning still poses a significant challenge for contemporary passenger cars, even those equipped with state-of-the-art safety systems. The active safety features that equip the most technologically advanced passenger cars are unable to forecast and prevent the occurrence of hydroplaning. Total hydroplaning represents a phenomenon which occurs when the tire reaches a point where it can no longer expel the water from its tread grooves, leading to a complete control loss of the motor vehicle. This describes a scenario in which the entire contact patch is lifted from the ground due to the hydrodynamic forces generated at the contact between the tire and the layer of water formed on the road. Nevertheless, the decrease in contact between the tire and the road surface occurs gradually, a phenomenon which is presented in the literature as partial hydroplaning. The longitudinal speed that marks the transition from partial hydroplaning to total hydroplaning is defined as the critical hydroplaning speed. These principles are widely acknowledged among researchers in the hydroplaning field. Nonetheless, the literature review reveals variations for defining the critical hydroplaning speed threshold across different experimental investigations. In this article, past studies, and state-of-the-art research on tire hydroplaning has been reviewed, especially focusing on real-time estimation methodologies and numerical modeling of the partial and of the total hydroplaning phenomenon.

## 1 Introduction

Risk assessment of partial and total tire hydroplaning holds significant relevance for the future of autonomous vehicles. As self-driving cars become increasingly prevalent, understanding the risk associated with high-speed wet rolling conditions is crucial for assuring the safety of passenger car vehicles. For road condition perception, autonomous vehicles rely on different sensors such as cameras, lidar, and radar, however current sensing methodologies are not capable to assess in real-time the risk of total hydroplaning. In order to safely navigate through traffic, autonomous vehicles depend on complex control algorithms that can make decisions in real-time. Developing and integrating novel sensing methodologies of the hydroplaning phenomenon into the control algorithm of autonomous passenger cars can influence how the vehicle accelerates, brakes, and steers in wet conditions, improving their overall safety.

The physics that governs the hydroplaning phenomenon includes both dynamic and viscous effects. In wet rolling conditions, the tire tread will contact the rigid pavement only after it breaches through the layer of water. Therefore, the pavement macrotexture notably influences the type of hydroplaning. During partial hydroplaning conditions, a wedge of water is formed in front of the tire contact patch due to the hydrodynamic forces generated at the contact between the tire tread and the layer of water. The water edge effect, influenced by the hydrodynamic pressure of the water, causes a decrease in the contact area between the tire and the pavement [1]. Figure 1 illustrates the three important zones of tire–pavement interaction under partial hydroplaning conditions. Zone A represents the case where the hydrodynamic pressure of the water is greater than the contact pressure between the tire and the pavement, therefore the tire is lifted from the rigid surface and starts rolling on the layer of water.

The studies conducted by Hermange [2] are validating the three zones interaction model between the tire tread, the layer of water, and the rigid surface. The decrease in contact area between the tire tread and the road surface progresses gradually. With an increase in the longitudinal speed of the motor vehicle, assuming other hydroplaning factors remain constant, the tire gradually loses more contact area with the rigid surface until total hydroplaning occurs. In zone B, an intermediate region is apparent, marking the transition between the contact patch that runs on the layer of water and the contact patch that is maintaining full contact with the pavement. For this zone, the viscous effect of the hydroplaning is predominant, wherein the microtexture of the pavement acts to brake and expel the water layer from the contact area [1]. In his study, Mounce [3] indicated that viscous hydroplaning represents a phenomenon associated with low-speed operation on pavements with minimal or no microtexture. This phenomenon takes place between a thin film of water and a tire exhibiting a significantly worn tread pattern or no pattern at all. The study of viscous hydroplaning and its influencing parameters is relatively limited in the current research. Zone C represents the case where the tire and the hard pavement are in complete contact; nevertheless, with the increase in the longitudinal speed of the motor vehicle, zone C will gradually decrease until total hydroplaning takes place.

As presented above, total hydroplaning is initiated when the external pressure of water acting on the tire surpasses the contact pressure between the tire and the pavement. In Ref. [4], Horne provides a plot illustrating the ground hydrodynamic pressure in relation to the velocity ratio, defined as the longitudinal speed divided by the critical hydroplaning speed.

The data from Fig. 2 were collected using pressure plates positioned on the pavement beneath the water film. The study involved an aircraft rib tread tire with an inflation pressure of 90 psi and a vertical load of 10,500 lb, rolling on a water film with a depth of 1 in. At lower longitudinal speeds, the vertical pressure beneath the tread rib significantly exceeds the pressure under the center tread groove. With an increase in longitudinal speed, the hydrodynamic pressure beneath the center tread groove also increases. When the pressure measured in the tire tread groove matches the pressure under the tread rib, the critical hydroplaning speed is reached. By comparing these two pressure curves, an effective methodology for predicting the transition between partial and total hydroplaning phenomena can be developed [1].

This research article will introduce the most recent methodologies for real-time estimation of the total hydroplaning phenomenon. Also, a comprehensive study is performed on numerical modeling approaches employed in predicting the critical hydroplaning speed. Nevertheless, a novel study for estimating the rolling conditions of the tire using neural networks is included in a following section.

## 2 Methods of Predicting Hydroplaning

Total hydroplaning represents a dynamic phenomenon which is difficult to predict, therefore researchers have attempted to find a specific parameter solely affected by the presence of water on the road, varying in proportion to the risk of hydroplaning. This section presents various prediction methods for both partial and total hydroplaning. Given that hydroplaning is influenced by factors such as longitudinal speed of the motor vehicle, tire inflation pressure, tire tread wear, and water layer thickness, developing numerical models to estimate the critical hydroplaning speed represents an important aspect in this research domain. However, the accuracy of the empirical hydroplaning models depends on the accuracy of the data collected. This section also introduces several empirical and finite element (FE) models for estimating the critical hydroplaning speed [1].

### 2.1 Real-Time Sensing Methodologies.

In his research paper, Tuononen [5] has introduced an algorithm used to identify the critical hydroplaning speed, relying on measurements of the tire longitudinal and lateral acceleration. Figure 3 illustrates an instance of the lateral acceleration signal for both dry and wet pavement.

The vibration of the tire tread in the lateral direction is influenced by the presence of the water on the pavement. Compared to dry rolling conditions, when a layer of water was present on the hard surface, supplementary vibrations were measured for the lateral acceleration signal. However, using this sensing approach, it is hard to distinguish between partial and total hydroplaning phenomenon solely through the analysis of lateral acceleration signals. Additionally, other external factors may stimulate the contact patch similarly to hydrodynamic water pressure, potentially leading to false detection of the critical hydroplaning speed [1].

The same researcher has developed in Ref. [6] an intelligent tire system with the ability to instantly detect the onset of total hydroplaning rolling conditions using an optical sensor positioned inside the wheel. Figure 4 illustrates the principle of real-time hydroplaning estimation for a passenger car tire, leveraging data collected from the optical sensor.

_{100}= 174 deg and CM

_{0}= 180 deg.

While the suggested algorithm has demonstrated promising outcomes, its applicability is limited to situations where the longitudinal acceleration remains below 0.1 g. Consequently, the estimation of the critical speed can only be performed under constant rolling speed conditions [1].

Schmiedel presented in Ref. [7] a real-time methodology for estimating road wetness by analyzing the impact of tire water spray. In this study, accelerometers were installed beneath the passenger car for measuring vibrations resulting from the impact of water droplets originating from the tire–road interaction. Figure 5 illustrates an example of sensor positioning in the wheel arch.

The researchers classified the tire spray phenomenon into three primary categories: circumferential spray, torrent spray, and side splash. Among these categories, torrent spray is found to be appropriate for estimating medium and high road wetness conditions, whereas circumferential spray is suitable for identifying low road wetness conditions. In the specific test setup, the accelerometers were not placed in the wheel arch but underneath the underbody of the passenger car.

The measured data revealed a distinct shift in the acceleration signal under wet road rolling conditions; however, detecting the threshold between partial and total hydroplaning proves challenging. This paper does not attempt to formulate a direct methodology for estimating the critical hydroplaning speed, but the output signals from the accelerometers can offer valuable input for future hydroplaning detection algorithms [1].

Fichtinger [8] presented an algorithm designed to identify the critical hydroplaning speed by assessing the wheel spin-down and spin-up phenomenon, variations in rolling resistance, and variations in slip stiffness. Figure 6 illustrates an example of the change in rolling resistance when a tire encounters a layer of water.

The researchers found that the hydrodynamic pressure of the water acting on the exterior of the tire substantially amplifies the rolling resistance force. The computed resistance presented in the graph signifies the difference between the longitudinal acceleration recorded by the vehicle accelerometer and the theoretical longitudinal acceleration expected from the applied drive torque, considering all vehicle parameters (mass, aerodynamic drag, and nominal rolling resistance). The graph highlights that the calculated change in acceleration is approximately 0.4 m/s^{2} when transitioning from a dry surface to a wet surface, signifying a considerable magnitude. Through the analysis of data from sensors already integrated into a modern passenger car, the researchers have successfully developed an algorithm for detecting the hydroplaning phenomenon with a reasonable accuracy. However, the investigators acknowledged that external factors, such as misaligned concrete slabs on highways, could impact hydroplaning detection [1].

In Ref. [9], Maleska presents the influence of vehicle velocity, vertical load, tire inflation pressure, and water depth on critical hydroplaning speed, using the VDA (Verband der Automobilindustrie) testing procedure for hydroplaning measurments.

Figure 7 presents the main phases of the VDA test procedure to determine the longitudinal hydroplaning performance. For phase A, the passenger car is rolling with constant longitudinal speed on a dry pavement. For phase B, when the passenger car reaches the first light gate, two options for continuing the procedure are available: the longitudinal speed can be maintained approximately constant or the longitudinal speed can be increased by applying full throttle to achieve the maximum possible acceleration.

The researchers have completed the VDA test procedure with a front wheel drive passenger car using the full acceleration method when the vehicle reaches the first light gate. For phase C, the vehicle enters the wet pavement section which has a water film with controlled height. The driver will continue to apply full throttle until the vehicle passes the second light gate. The researchers stated that the critical hydroplaning speed can be estimated when the tire slip ratio reaches approximately 15% at the second light gate.

Hermange [2] has analyzed the images of partial and total hydroplaning using a high-speed camera mounted under the pavement. According to the researchers, the camera and the flash are synchronized with the tire velocity and position, in order to obtain quality image of tire–water interaction. The experimental setup is presented in Fig. 8.

The water film height is adapted according to the measurement plan and the vehicle is rolling on the measurement window at a constant longitudinal speed. Each test has to be repeated several times in order to get a good estimate of the actual contact surface “S.”

To capture the reference surface “S0,” the longitudinal speed is maintained constant at 30 km/h, where hydroplaning has almost no influence on the contact patch dimensions. The critical hydroplaning speed is found when the contact surface “S” between the tire and the measurement window tends to be zero. For these experiments, no driving/braking torque or transverse forces are applied to the tire. The results of the tests are discussed in Sec. 3.

In Ref. [10], Jansen presents a similar image analyzing methodology to estimate the contact area between the tire and the pavement when wet rolling conditions occur. In order to calculate the net contact area between the tire and the glass panel, the measurement system attributes different gray levels to each point on the captured image. The measurements were performed for free rolling tire case with the inflation pressure, the vertical load, and the water depth recorded for each test. The dry contact of the tire with the glass panel appears as a black area, the pure undisturbed water appears as a green area while the water infiltrating under the tread elements in partial hydroplaning condition appears as a gray area. Figure 9 presents an example of contact area variation with longitudinal speed for different types of tires.

The estimated contact area is measured in cm^{2} while the longitudinal speed is measured in km/h. With the increase of longitudinal speed, the measured contact area is reduced due to partial hydroplaning. The reference area when no hydroplaning occurs is calculated as the mean area of two images obtained for a longitudinal speed of 3.2 km/h. Researchers pointed out that the image analyzer is only sensitive to the gray scale and not the color spectrum, therefore the contact and non-contact areas between the tire and the glass panel can be better analyzed. The high-performance tire maintains the largest contact area while the ribbed tire presents the worst hydroplaning performance. Further results obtained are presented in Sec. 3.

D’Alessandro [11] presents a methodology for real-time estimation of the critical hydroplaning speed by analyzing the tire slip ratio variation, in a similar manner to Fichtinger [8]. The tire selected for the experiment is a new 2055/55R16 summer tire. The vehicle was instrumented with a dynamometric hub capable of measuring the longitudinal, lateral, and vertical interaction forces between the tire and the pavement. The signals acquired from the dynamometric hub are sampled at 2000 Hz. The 200 m length track used for the experiments was covered with a layer of water with a depth of 8.0 mm. In order to estimate the critical hydroplaning speed, the researchers performed longitudinal acceleration tests from different starting velocities. As the longitudinal speed of the vehicle increased, the hydrodynamic pressure of the water acting on the exterior of the tire carcass also increased, therefore the tire started to lose contact with the pavement. The investigators stated that during longitudinal acceleration tests, a sudden increase in the slip ratio occurs at the driving wheels when the critical hydroplaning speed is reached. Figure 10 shows the variation of the wheel angular velocity and slip ratio when the tire encounters a layer of water on the pavement.

For the longitudinal speed of 85 km/h, a sudden increase in the tire slip ratio was recorded, therefore the investigators stated that the critical hydroplaning speed can be estimated as being 85 km/h. The estimation of hydroplaning speed was based only on the analysis of the slip ratio and not on the force measured by the dynamometrical hub. This speed threshold is lower than a typically hydroplaning speed of 100–110 km/h for a new passenger car summer tire and a water depth of 8.0 mm, therefore the estimation process could be affected by errors.

Similar to Tuononen’s research [5], Cheli [12] has developed a methodology for real-time estimation of the hydroplaning phenomenon based on data collected from an accelerometer mounted inside the tire carcass. The accelerometer is capable of measuring acceleration on the three major axes: longitudinal, lateral, and radial. Figures 11 and 12 present the variation of longitudinal and radial acceleration measured by the Micro Electro-Mechanical Systems (MEMS) accelerometer during a complete tire revolution.

By analyzing the longitudinal acceleration signal, the moment when the accelerometer enters the tire contact patch is identified by a negative peak at the time value of 0.04 s and the moment when the accelerometer exits the tire contact patch is identified by a positive peak at the time value of 0.045 s.

According to the investigators, the negative values measured in the radial direction are recorded outside the tire contact patch and represent the centripetal acceleration. When the MEMS accelerometer is located in the tire contact patch during a complete wheel rotation, the radial acceleration has a value close to zero due to flattening phenomenon of the tire carcass. The high-frequency oscillations of both longitudinal and radial acceleration signals are attributed to the interaction between the tire and the pavement irregularities. The detection algorithm calculates a hydroplaning index that evaluates the risk of hydroplaning, based on the data obtained from the radial acceleration signal measured by the accelerometer positioned inside the tire. The investigators stated that the maximum value of the hydroplaning index indicates total hydroplaning rolling conditions and intermediate values indicate partial hydroplaning rolling conditions.

### 2.2 Empirical Hydroplaning Models.

Hydroplaning is a complex phenomenon which depends on a multitude of factors such as vehicle longitudinal speed, water film thickness, tread depth, inflation pressure, and tire vertical load. By definition, the critical hydroplaning speed defines the longitudinal velocity recorded when the tire completely loses the contact with the pavement and starts rolling on the layer of water. As discussed above, the actual measurement of the critical hydroplaning speed can be challenging, therefore the researchers have tried to develop empirical hydroplaning models which can estimate the hydroplaning speed. This approach has a lot of benefits in terms of cost and time reduction; however, the accuracy of the empirical hydroplaning models relies on the accuracy of the data collected.

The inflation pressure “*p*” is measured in kPa while the critical hydroplaning speed is measured in km/h [1].

For this equation, the inflation pressure is measured in psi and the critical hydroplaning speed is measured in mph. The “FAR” term represents the ratio of the tire footprint, calculated as width/length of the contact patch [1].

The lift coefficient “*C _{l}*” is dimensionless while the critical hydroplaning speed is expressed in km/h, the vertical load “

*Q*” is expressed in kg, the contact patch width “

*B*” is expressed in mm, and the water film thickness “

*t*” is expressed in mm [1].

*p*” is expressed in psi, and the tire tread depth “TD” is expressed in 1/32 in. while

*A*is a factor which signifies:

The “*t*” term signifies the water film thickness expressed in inches while the “TXD” signifies the pavement texture depth expressed also in inches [1].

*Q*,” inflation pressure “

*p*,” and water film thickness “

*t*” [1]. Similar to Horne equation, the “FAR” term denotes the ratio of the tire footprint (width/length). For light vehicles, the equation is

*V*,” was computed for water thickness “

_{p}*t*” levels below 2.4 mm using the equation:

*A*is calculated with the same formula proposed by Gallaway.

The minimum speed for viscous hydroplaning, denoted as “*V _{p}*,” is expressed in mph. The length of the tire footprint region, labeled as “

*L*,” is measured in inches, and the time needed for a substantial reduction of the fluid film to facilitate contact between the tread rubber and the pavement asperities, denoted as “Δ

*T*

_{sf},” is measured in seconds. It is important to note that this formula is not suitable for dynamic hydroplaning [1].

### 2.3 Water Film Thickness Models.

The water film thickness represents a critical hydroplaning parameter which is hard to measure in real-time conditions. Most of the hydroplaning experiments were conducted on special testing tracks which have good control on the water film depth, however, in a real-world scenario, the water film level could randomly vary on the surface of the road. In his hydroplaning research paper, Fichtinger [8] has used a special sensor named MARWIS for real-time measurement of the water film thickness. The MARWIS sensor can measure the water film thickness with a resolution of 1 *μ*m and an accuracy of 10% and can represent a good instrument for hydroplaning research purposes. However, this sensor is relatively large and expensive, therefore researchers have tried to develop empirical models to estimate the water film thickness using parameters which are much easier to measure in real-time.

*t*” is estimated from the top of asperities, the drainage length “

*L*” is measured in inches, the rainfall intensity “

*I*” is measured in in./h, the texture depth “MTD” is measured in inches, and the slope of pavement “

*S*” is measured in m/m. In the same research paper, the investigators also present an alternative equation to estimate the water film thickness, based on Manning's equation.

The parameters have the same definition as described above and the term “*n*” represents the Manning's roughness coefficient.

*t*” above the pavement texture.

In this numerical model, the drainage length “*L*” is measured in inches, rainfall intensity “*I*” is measured in in./h, and texture depth “MTD” is measured in inches.

In this numerical model, “*z*” represents a constant with a value of 0.01485, “*L*” represents the pavement flow path measured in meters, “*I*” represents the rainfall intensity measured in mm/h, “MTD” represents the pavement texture depth measured in mm, and “*S*” represents the pavement cross slope measured in m/m.

For analyzing surface water distribution, Chen [23] modeled porous asphalt layers under unsaturated seepage using the finite element method (FEM). Additionally, the critical rainfall intensity of porous asphalt pavements is compared with various design parameters while the coverage and depth of surface water at various locations are also analyzed. In this study, the material properties of the finite element model were based on a porous asphalt pavement constructed in Kunshan, China. The pavement structure consists of a 40 mm porous asphalt surface layer, a 60 mm asphalt base layer, a 180 mm cement-stabilized macadam base layer, and a 180 mm cement-stabilized macadam subbase layer. For studying the unsaturated flow behavior in porous asphalt pavements, the Richards equation was employed. Regarding the meshing of the porous asphalt pavements, a preliminary grid density sensitivity assessment was conducted and the optimal grid points were set at intervals of 1 m longitudinally, 0.5 m transversely, and 0.01 m vertically. The presented study offers a potential method to predict surface water distribution on porous asphalt pavement, enabling derivation of optimal geometric parameters, such as porous layer thickness and transverse/longitudinal slopes, for achieving maximum permeability.

The same researcher presented in Ref. [24] a study for predicting the spatial–temporal water film height on hard pavements under dynamic rainfall profiles, considering roadway slope and pavement surface texture effects. Initially, an analytical model was employed to predict the spatial–temporal distribution of the water film height. Subsequently, the critical hydroplaning speed was computed based on the tire–water–pavement interaction model using the obtained results. The analytical model for the water film thickness estimation was validated against measured data and the investigators found a maximum error of 1 mm for a measured water film thickness of 5 mm while the mean absolute error for all data points was 0.6 mm. Discrepancies were attributed to variations between the Manning's roughness coefficient used in the model and the actual measured values. After the dynamic water film depth was determined, the critical hydroplaning speed was computed using a finite element model developed by Ding [25].

Similar to other finite element models used for hydroplaning studies, the water domain is efficiently meshed using the Eulerian technique, while the tire structure employs conventional nonlinear Lagrangian analysis. The study clearly shows that significantly different hydroplaning speeds can be obtained for different driving lanes for the same rainfall intensities. At the same longitudinal speed, the risk of hydroplaning can differ from 2% to 3% for one driving lane to almost 50% for the next adjacent driving lane due to the uneven distribution of the water film thickness on the pavement.

### 2.4 Finite Element Method Hydroplaning Models.

As stated above, the hydroplaning phenomenon is influenced by a large number of factors; therefore the need to reduce cost and time has motivated researchers to develop novel hydroplaning models to estimate the risk of hydroplaning. Besides empirical models, investigators developed finite elements models to study the effects of all influencing factors on partial and total hydroplaning with minimum time and cost requirements.

In his research, Nazari [26] developed a coupled FEM-computational fluid dynamics (CFD) model to estimate the hydroplaning risk of passenger care tire. A 180/65R15 steel belted radial tire was modeled in two main steps using the FEM software abaqus. In the first step, a 2D cross section of the tire was modeled using SFMGAX1 elements for the belt and ply zones and CGAX4R elements for the rest of the tire components. The rubber material was modeled using a neo-Hookean hyper-elastic model and was assigned for the tread, sidewall, apex, and inner liner tire elements. In the next step, the 3D tire model was generated using the symmetric model generation tool. The 3D mesh uses C3D8R elements. The fluid was modeled using the computational fluid dynamics method in the commercial software star-ccm+ which allows the coupling between the fluid model and the abaqus FE model.

To model the flow of water and air around the tire, the volume of fluid (VOF) method is used, which tracks the volume fraction of each fluid through the domain. The shear-stress transport *k*–*w* turbulence model was coupled in the CFD model to estimate the onset and flow separation from surfaces. The FEM tire model and the fluid explicit finite volume method are coupled to estimate the tire and water interaction. This coupling allows information such as pressure and nodal coordinates to be transferred in both ways between the tire and the fluid model. Further results will be discussed in Sec. 3.

Ong [27] has developed an FE hydroplaning model for a truck tire which has the same dimensions with the tire used by Horne in his hydroplaning experiments. The goal of the research is to validate the hydroplaning model with the experimental results obtained by Horne. In order to simulate the hydroplaning phenomenon, the model developed has three main components, a pneumatic tire model, a pavement surface model, and a fluid model. Figure 13 presents the main components of the hydroplaning simulation model and the interaction between them.

The 10.00–20 pneumatic truck tire is modeled in the FE software adina using MITC4 single-layer interpolation of tensorial components shell elements. The thread and sidewall rubber are modeled using an orthotropic elastic material with the Young's elastic modulus *E _{a}* = 900 MPa,

*E*=

_{b}*E*= 700 MPa, and a shear modulus

_{c}*G*=

_{a}*G*=

_{b}*G*= 30 MPa. The subscripts

_{c}*a*and

*b*correspond to the in-plane orthogonal material axes and subscript

*c*is the third material axes, perpendicular on the plane described by

*a*and

*b*. These parameters are carefully chosen to simulate with good accuracy the dimensions and shape of the real stationary contact patch measured by Horne in his experiments under the same vertical load and inflation pressure. The mesh convergence was performed and the results for the contact patch length and width convergence study are presented in Fig. 14.

The investigators stated that 9700 shell elements for the tire model and 2400 elements for the pavement surface are sufficient for the model to offer accurate results. The pavement is modeled as a rigid surface with single-layer MITC4 shell elements. The fluid flow is modeled using the arbitrary Lagrangian–Eulerian formulation. The interaction between the pneumatic tire and the fluid requires a two-way coupling numerical method.

In Ref. [28], Kumar presented a study on hydroplaning risk for both rolling and sliding cases of a passenger car pneumatic tire. The tire model is an American Society for Testing and Materials (ASTM) E 524 standard smooth tire which has a belted bias ply construction. For the simulations, the inflation pressure varied between 110 and 260 kPa while the vertical load was maintained constant at 4800 N. The rubber material of the pneumatic tire is modeled as a Neo-Hookean hyperplastic formulation, similar to Nazari’s [26] research paper. The wheel load is applied at the center of the tire and acts in vertical direction, while the inflation pressure is applied on the inside of the tire. Both the rim and the pavement are modeled as rigid surfaces. The tire is modeled in the Lagrangian framework, and the fluid is modeled with Eulerian elements which are fixed in space. The interaction between the tire and the fluid is described using general contact coupling algorithm which allows the forces between the two different frameworks to be transferred from one to another. Similar to Ref. [26], the tracking of the interface is obtained using the VOF method. The wheel mesh contains 28,628 Lagrangian eight-node hexahedron solid elements for the tire and 7246 shell elements for the rim. The water part of the Eulerian grid is made of 21,220 elements and the void is made of 13,567 elements. As stated above, the Eulerian grid is fixed in space and the deformation and movement of the Lagrangian elements cause the water to flow through the fixed Eulerian mesh, therefore pressure gradients will be formed in the Eulerian grid.

Fwa [29] presents an analysis of tire tread pattern effectiveness in reducing the risk of hydroplaning. The tire modeled is an ASTM E 501 standard tire with a tread width of 148.6 mm and a cross-sectional radius of 393.7 mm. For this analysis, the 186.2 kPa inflation pressure and 2.41 kN vertical load were maintained constant. The critical hydroplaning speed was estimated for the locked wheel case for six different tread designs and six different tread depths varying between 0.5 and 9.8 mm, assigned for each tread design. Also, the water film thickness varied between 1.0 and 10.0 mm. The FEM model mesh uses six-node wedge elements and eight-node hexahedral elements. The model converged with an accuracy of 0.5% for the uplift force generated by the hydrodynamic pressure of the water that is acting on the exterior of the pneumatic tire carcass. The investigators stated that special attention was paid to design the elements size and shape in rib and groove areas and also for the water layer found between the tire and the pavement. The investigators assumed that total hydroplaning occurs when the average ground hydrodynamic pressure is equal to the pneumatic tire inflation pressure.

Ding [30] presents a method to investigate hydroplaning risk of truck tires using a three-dimensional fluid–structure interaction model. Three truck tires with the dimensions of 11R22.5, 425/60R22.5, and 445/50R22.5 have been modeled in the FEM software abaqus. The length of the elements in the contact patch varies from 6 to 11 mm while the width varies from 5 to 8 mm. The FEM pneumatic tire model has been validated by comparing the tire deflection under a certain load for a given inflation pressure with experimental data. Similar to other research papers presented above, the fluid is modeled using Eulerian coordinates while the solid domain consists of finite elements in Lagrangian description. For the hydroplaning simulation, the fluid is assumed to be incompressible and isotropic, with a constant viscosity. Investigators used the coupled Eulerian–Lagrangian (CEL) method to simulate the hydroplaning phenomenon. The fluid domain has been chosen to have a width of 560 mm, a length of 548 mm while the element size of the water layer should be less than one half of the tire groove width. To validate the simulated data, the researchers have compared the critical hydroplaning speed obtained from the FEM analysis with the results obtained from the empirical hydroplaning model developed by the Texas Transportation Institute.

In Ref. [31], Chen evaluates the effect of tire tread depth on skid resistance for wet rolling conditions using the finite element method. A computational model assessing aircraft tire skid resistance on runways with varying groove depths was developed and validated using full-scale testing results. The analysis employed a widely used 49 × 17 type VII tire found in the landing gear of wide-body Boeing 727 and Airbus A320 aircraft. In the described model, the tire is considered to be locked, neglecting the effect of centrifuge force due to wheel rotation. The air, water, and pavement surface move at the same longitudinal speed toward the tire and under the applied load, the tire deforms, generating hydrodynamic force. While assuming incompressible viscous turbulent flow without heat transfer, the interaction between the tire and the fluid is described using the turbulence *k*–*ε* model. For this study, the porous and the drainage effect of the pavement was neglected, the runway being considered impermeable. The model offers accurate results which were validated against field tests conducted by Federal Aviation Administration.

Similar to Chen’s research [31], Qian presented in Ref. [32] a finite element model used for studying the braking performance and skid resistance of a 49 × 17 aircraft tire running on a wet grooved pavement. The interaction between tire, water, and pavement was simulated in the FE model using the CEL method. Predictions and analyses of hydroplaning speeds were conducted to recommend the maximum approach speed for aircraft landings. The tire–pavement interaction was modeled in three steps: creating a 2D axisymmetric tire model, expanding it into a 3D symmetric model, and placing the 3D tire model in contact with the rigid pavement surface under a vertical load. Similarly to other FEM models developed for studying hydroplaning performance of tires, this simulation is employing the CEL method where the model captures water and air behavior, allowing the calculation of friction coefficients and braking distance when water flows under or alongside the tire. The water film on the pavement is modeled as an incompressible, isotropic, Newtonian fluid with constant viscosity, and gravity serves as the sole body force. The model was validated against full-scale tests performed at the Naval Air Engineering Center. The tire vertical load was 156 kN and the inflation pressure was 966 kPa. Both new and worn tires underwent testing in wet, puddled, and flooded conditions, with water depths of approximately 0.254 mm, 2.54 mm, and 6.35 mm, respectively. Testing speeds ranged from 61.1 to 276 km/h, with slip ratios between 10% and 20%. For this study, as a conservative approach, the critical hydroplaning speed was defined as the speed recorded when the longitudinal friction coefficient reaches a low value of 0.1. The investigators stated that the critical hydroplaning speed computed using the FE model for a worn tire and a 3.4 mm water film thickness closely aligns with the speed derived from field measurements.

### 2.5 Neural Networks for Estimating Rolling Conditions.

In recent years, there have been significant advancements in the development of neural networks driven by advances in hardware, algorithms, and data availability. Researchers have tried to estimate the risk of hydroplaning by analyzing the data coming from different transducers using the neural network technology. The development of machine learning methods in the hydroplaning research field could represent a major advancement toward enhancing the active safety of contemporary passenger vehicles.

Weyde [33] has developed an algorithm to predict the hydroplaning performance of a pneumatic tire by analyzing the tread pattern using machine learning. The database contains 21 tread pattern images divided into three groups, G1 with four images, G2 with nine images, and G3 with eight images. The input of the classification algorithm is represented by the grayscale pixel array of each image for different tread patterns. Based on the input data, the machine learning algorithm is trained using seven different features extracted from the tread pattern images (void volume, angular features, and cross-sectional features). Along with the tread pattern data, each tire had an experimentally measured hydroplaning performance value, known as the AQF value, provided as the target for the machine learning prediction. The AQF correlates with the longitudinal speed at which hydroplaning initiates. Additionally, the tire manufacturer supplied a predicted hydroplaning value, termed the FT value, determined by a heuristic formula based on tests and design experience. The researchers stated that the machine learning algorithm will estimate the risk of hydroplaning based on the information received from the image processing analysis and from the input information about the rubber stiffness using a standard feed-forward neural network with sigmoid activation functions. Experimental testing of new tread patterns in a controlled hydroplaning rig is costly and time-consuming, lasting several months, which significantly restricts the number of patterns that can be assessed. The researchers tried to avoid the experimental approach by developing a numerical model that correlates the tread pattern with the risk of hydroplaning. Therefore, the output of the supervised machine learning model is represented by the “FT” value which is proportional to the critical hydroplaning speed corresponding to a particular tread pattern.

Lee [34] proposed in his research paper a methodology to evaluate the pavement rolling conditions using a neural network algorithm. The neural network uses data collected from a three-axis accelerometer mounted on the inner side carcass of a pneumatic tire. This paper is not trying to estimate the hydroplaning risk of a passenger car tire; however the methodology presented could provide valuable information about the level of the water present on the road. Driving experiments were carried out at the Korea Intelligent Automotive Part Promotion Institute's proving ground to gather a database of signals from the tire accelerometers. The experiments were performed on five distinct road surface conditions, namely, dry asphalt, wet asphalt with a 1 mm water film height, wet asphalt with a 4 mm water film height, gravel, and unpaved road. For gathering the data points required to train the machine learning model, the driving experiments were conducted at different longitudinal speeds (10, 20, 30, 40, 50, 60, and 70 km/h) for each road surface. As presented above, the input of the neural network model is represented by the acceleration signals measured on the three main axes at different longitudinal speeds and road surfaces. To ensure a good accuracy of the model, for each combination of road surface and longitudinal speed, more than 400 contact points between the accelerometer and the pavement were measured. This represents a traveled distance of approximately 800 m for the tire at the given inflation pressure and vertical load. According to the investigators, the training set contains 100,000 samples with 20,000 samples divided for each pavement type. The testing data set contains 20,000 samples with 4000 samples divided for each pavement type. The data aquisition system samples the data from the accelerometer with a sample rate of 1000 Hz and then sends the digitized acceleration signals wirelessly to the computer. Investigators have used two types of neural networks, a fully connected neural network and a one-dimensional convolutional neural network. The output of the neural network is represented by the classification of the pavement into five main categories described above based on the acceleration signals measured by the intelligent tire system. Regarding real-time applications, the researchers stated that the trained neural network algorithm can classify the road conditions in less than 3 ms. Therefore, if the sampling rate for collecting the acceleration data is high enough, the proposed algorithm allows estimating road conditions in real-time, making it suitable for use in vehicle controllers.

## 3 Results and Discussion

In this section, the results of two different approaches for studying the phenomenon of hydroplaning are discussed. The first section presents the results of some of the most important experimental work documented in the literature focusing on both innovative approaches of detecting the critical hydroplaning speed and also the major influencing factors of the hydroplaning phenomenon. The second section presents the results obtained from modeling the hydroplaning phenomenon using the finite element method.

### 3.1 Results Obtained From Experimental Investigations.

Tuononen conducted in Ref. [5] hydroplaning research utilizing accelerometers mounted inside the tire carcass. The lateral acceleration signal demonstrated a strong correlation between acceleration amplitude and the quantity of water on the pavement. Nevertheless, as presented in the previous section, analyzing the lateral acceleration signal is not enough to distinguish between partial and total hydroplaning conditions. To determine the threshold between partial and total hydroplaning, the researcher analyzed the variation of the tire contact length based on the longitudinal acceleration signal. Figure 15 illustrates the variation in contact length as the tire encounters a water layer at different longitudinal speeds.

The plots illustrate the variation of the tire contact length measured over 22 consecutive rotations. The initial 13 rotations occur on dry pavement, while the subsequent rotations are performed on a layer of water which has a height of 8.0 mm. For partial hydroplaning conditions, the length of the tire contact with the pavement decreases as longitudinal speed increases. However, under total hydroplaning conditions (longitudinal speed exceeding 100 km/h), the contact length rises to a value close to that measured on dry pavement. These findings suggest that estimating the tire contact length could serve as an effective method for estimating both partial and total hydroplaning conditions [1].

In the preceding section, the real-time hydroplaning estimation using an optical method was introduced [6]. Utilizing data measured from an optical sensor mounted inside the tire carcass, a hydroplaning percentage was computed using Eq. (1). Figure 16 illustrates the hydroplaning percentage across various longitudinal speeds.

The data points were measured for the free rolling scenario with a water film height of 8.0 mm, a tire tread depth of 7.0 mm, and an inflation pressure of 2.5 bar. The algorithm successfully identified partial hydroplaning at a relatively low longitudinal speed (60 km/h). As expected, the hydroplaning percentage increases with the increase of the tire longitudinal speed until total hydroplaning occurs at around 100 km/h. For this real-time detection algorithm, the estimated hydroplaning percentage is computed once every tire rotation. The above-presented results indicate the successful detection of both partial and total hydroplaning using an optical sensor mounted inside the tire carcass. [1].

In Ref. [7], Schmiedel used three-axial accelerometers mounted under a passenger car body to detect the presence of the water on the pavement by analyzing the tire spray phenomenon generated by the interaction between the tire and the road. The methodology presented in the previous section cannot estimate the critical hydroplaning speed of a pneumatic tire, however it can predict with good accuracy the pavement rolling conditions, therefore the risk of hydroplaning can be further predicted. The sensors used are Bruel & Kjaer type 4397 and 4507 accelerometers and the signal processing is made by a band-pass filter with a center frequency of 5 kHz. The testing vehicle is a Porsche 911 type 991 Carrera 4S with 245/35R20 summer tires. The vehicle longitudinal speed is imported from the Controller Area Network (CAN) vehicle communication protocol while the water film thickness is measured in real-time using the MARWIS system. The water film thickness varies from 0.5 to 1.0 mm (wet rolling conditions) to almost 20 mm (very wet rolling conditions). An example of an acceleration signal for different types of rolling conditions is presented in Fig. 17.

The acceleration signals presented in Fig. 17 come from an accelerometer mounted near the side skirt of the passenger car. It can be observed that dry and moist conditions lead to very similar acceleration levels while the wet and very wet conditions lead to very different acceleration levels. Therefore, the methodology presented can predict with good accuracy the presence of water on the road. Also, the water film thickness on the road can be estimated from the output data of the measurement system, which can be further utilized to predict the risk of hydroplaning of a passenger car pneumatic tire.

In the previous section, a critical hydroplaning speed estimation methodology based on VDA test procedure was presented [9]. Maleska has performed several hydroplaning tests for different rolling conditions in order to analyze the longitudinal hydroplaning performance of a pneumatic passenger car tire. According to the investigators, the reduction of wheel traction force with the increase of the vehicle longitudinal speed can be attributed to the reduction of available time to eliminate the water film between the pneumatic tire and the pavement. Two different tire types, summer tire and winter tire, were tested following the VDA hydroplaning test procedure. For each tire type, two different water levels were chosen for the hydroplaning test. For the normal water depth test conditions, the water film thickness is set to be 7.0 mm while for the low water depth test conditions, the water film thickness is set to be below 7.0 mm. For each tire type and each water level, the load and inflation pressure were varied. The investigators described an initial vertical load and inflation pressure as *L*_{1} and *p*_{1}, without disclosing the absolute values. The next testing conditions describe a new vertical load *L*_{2} = *L*_{1} + 30 kg and a new inflation pressure *p*_{2} = *p*_{1} + 0.3 bar. The goal of this testing procedure is to reach the critical hydroplaning slip ratio of 15% as soon as possible. The investigators are not offering absolute values for the longitudinal speed, and the normalized vehicle speed is calculated as the ratio between the measured vehicle speed and the highest vehicle entry velocity in the pre-study test session. Figure 18 presents the variation of the critical hydroplaning speed for two different types of tires in normal water depth testing conditions.

Investigators stated that both tire types presented a significantly higher critical hydroplaning speed when the vertical load and the tire inflation pressure are increased. The influence of the wheel vertical load on the tire hydroplaning performance is attributed to the influence on the contact patch dimensions (length and width). Also, from Fig. 18, it can be observed that at the same vertical load and inflation pressure conditions, winter tires tend to have a better hydroplaning performance than summer tires.

Hermange [2] introduced a methodology for detecting both partial and total hydroplaning rolling conditions by analyzing images captured from a high-speed camera positioned beneath the road surface. In the experimental setup, a glass wall was mounted at the bottom of a water pool to facilitate filming of the tire–pavement interaction. These experiments measured the actual lifting of the contact patch from the pavement, offering reasonable accurate data about the critical hydroplaning speed. The researchers stated that partial and total hydroplaning could be distinguished by examining the ratio between the initial contact area “*s*_{0}” when no water was present on the pavement and the remaining contact area “*s*” under wet rolling conditions. Figure 19 illustrates the impact of water film thickness, tread depth, and inflation pressure on the estimated critical hydroplaning speed.

By analyzing the influence of the water film thickness, the investigators concluded that for a water film height exceeding 3.0 mm, the tire contact area with the pavement decreased as the longitudinal speed increased, eventually leading to no contact at all (total hydroplaning conditions). In contrast with the first scenario, the critical hydroplaning speed was not reached for water film heights with a value under 1.5 mm. The study of the tire tread depth influence on the hydroplaning phenomenon shows that the decrease in critical hydroplaning speed with the tread depth is not linear. Figure 7, phase B, illustrates that new tires retain nearly 80% of the initial contact area at longitudinal speeds below 80 km/h while worn tires with a tread depth below 3.0 mm will lose almost all the contact area at 80 km/h when rolling in a 3.0 mm water depth. Inflation pressure represents another influential parameter on the critical hydroplaning speed. The results from plot 7.c confirm that hydroplaning occurs when the hydrodynamic pressure of the water surpasses the contact pressure between the tire and the pavement (which is close to the inflation pressure). Hence, as inflation pressure increases, the critical hydroplaning speed also increases. It is important to note that these experiments could not account for the influence of pavement macrotexture because the glass wall had a very smooth surface compared to other pavement types. Additionally, the smooth surface posed challenges in generating significant longitudinal forces, limiting the tests to free rolling conditions only [1].

Similar to Hermange research, Jansen [10] has studied the contact patch features of a pneumatic tire when wet rolling conditions occur. The researchers have calculated both the average area and the percentage of reference area for each testing conditions. The average area represents the raw contact area measured by the camera while the percentage of reference area represents the ratio between the average area and the reference area measured at a longitudinal speed of 3.2 km/h, when no hydroplaning conditions occur. Figure 20 presents a plot for the variation of average contact area with the longitudinal speed, for different inflation pressures.

It can be observed from Fig. 20 that when the inflation pressure increases, the average contact area decreases at the same longitudinal speed. These results may indicate that the tires have better hydroplaning performance at a lower inflation pressure, completely opposite from the results obtained by other researchers. However, the investigators have plotted the average contact area not the percentage of reference area; therefore the performance of longitudinal hydroplaning cannot accurately be estimated from this type of plot. Also, from Fig. 20, it can be observed that at low longitudinal speed, there is a significant difference in the tire contact area among the three inflation pressures. However, with the increase of longitudinal speed, the difference is reduced, and two contact area curves (180 kPa and 207 kPa) actually cross each other.

In Ref. [11], D'Alessandro has measured the lateral response of a passenger car pneumatic tire in partial and total hydroplaning rolling conditions. As presented in the previous section, the vehicle was instrumented with a dynamometric hub capable of measuring the interaction forces between the tire and the pavement. In order to characterize the lateral response of the pneumatic tire, a series of swept sine maneuvers were performed with the longitudinal speed gradually increasing from 40 km/h to 95 km/h. Cornering stiffness represents the slope of the curve generated by the lateral force and the slip angle, therefore the investigators performed a curve fitting to the measured data in order to estimate the variation of cornering stiffness in hydroplaning conditions. Similar to Cheli’s [12] research paper, the investigators have calculated a hydroplaning index which is proportional to hydroplaning risk of the pneumatic tire. Figure 21 presents the variation of the cornering stiffness with the hydroplaning proximity for a pneumatic tire.

The “Ca +” represents the values of the cornering stiffness identified for positive slip angles while “Ca −” represents the values of the cornering stiffness identified for negative slip angles. Only when the hydroplaning index has a value over 80%, the cornering stiffness starts to drop significantly. This may indicate that even in rolling conditions close to total hydroplaning, the pneumatic tire still preserves capabilities to generate lateral forces. The investigators stated that the cornering stiffness curves can be exploited by a control system to estimate the cornering stiffness of the front tires while operating close to total hydroplaning conditions.

*I_Hd*which depends on the radial deformation of the contact patch. The equation for computing the hydroplaning index is

*I*_

*Hd*20 and

*I*_

*Hd*80 are the calculated hydroplaning indexes at 20 and 80 km/h. Figure 22 presents the variation of the hydroplaning index with the longitudinal speed. Each test was conducted by maintaining the tire at a constant longitudinal speed and the water film thickness at a value of 8.0 mm. At 20 km/h, no significant radial deformation of the contact patch was observed, resulting in an index value close to that measured for dry pavement. As the longitudinal speed increased to 80 km/h, approaching the critical speed, the hydroplaning index reached a value near 120. Using Eq. (16), the initial estimated hydroplaning index is scaled from 0 to 1, where 0 indicates no hydroplaning risk, and 1 indicates the maximum hydroplaning risk [1].

As presented above, investigators have developed different methodologies for detecting in real-time the transition between partial and total hydroplaning rolling conditions. However, those algorithms work for particular rolling conditions and have provided good results only for tests performed in controlled environments. As Chen presented in Ref. [24], the water film thickness can vary significantly from one driving lane to another, therefore the risk of hydroplaning for a passenger car can significantly shift only by performing a lane change maneuver. Therefore, one major recommendation for future research is developing and validating a system that can assess the risk of hydroplaning in real operation conditions.

### 3.2 Results Obtained From Finite Element Modeling.

In Ref. [26], Nazari presented a FEM modeling of hydroplaning phenomenon using both abaqus and star-ccm+ softwares. As presented in Sec. 1, total hydroplaning occurs when the hydrodynamic pressure of the water that acts on the exterior of the tire carcass overcomes the inflation pressure of the pneumatic tire. In the FEM analysis, total hydroplaning occurs when the lift force generated by the water overcomes the vertical load of the wheel. Investigators have used two different softwares to run the hydroplaning analysis. The variation of the lift force with the longitudinal speed is presented in Fig. 23 for a bald tire and a tread tire using both abaqus and star-ccm+ integration.

The investigators stated that the vertical lift force increases with the increase of the longitudinal speed for both bald and tread tire. As can be observed from Fig. 23, the results obtained from abaqus-cel, abaqus, and star-ccm+ integration are very similar, however the integration with star-ccm+ can offer more accurate results due to the turbulence model used to capture the behavior of the fluid. At the same longitudinal speed, the bald tire presents a significantly higher lift force due to the lack of tread pattern. The tread pattern of pneumatic tires allows the water to be better evacuated from the contact patch area. Therefore, the bald tire will reach the critical hydroplaning speed much sooner than the treaded pneumatic tire.

Ong [27] has described the fluid flow generated by the interaction with the pneumatic tire using an arbitrary Lagrangian−Eulerian formulation. The hydroplaning of a pneumatic 10.00–20 truck tire was studied using the FEM model for the locked wheel case. The pavement surface is assumed to be smooth and different vertical loads, inflation pressures, and water film thicknesses are considered in the simulation described by the investigators. The critical hydroplaning speed is found when the vertical lift force generated by the water hydrodynamic pressure overcomes the pneumatic tire inflation pressure. The wheel longitudinal speed is first increased with increments of 18 km/h until the vertical load is overcome by the water lift pressure. To improve the longitudinal speed resolution, after the first estimation of critical speed, the wheel speed is increased with a step of 0.36 km/h starting from a speed slightly lower than the one found in the first iteration. Figure 24 presents the influence of the wheel vertical load and the water film thickness on the critical hydroplaning speed of the pneumatic truck tire inflated with a pressure of 552 kPa.

According to the investigators, Fig. 24 shows that the critical hydroplaning speed is influenced significantly by the vertical wheel load and the water film thickness. As expected, with the increase of water film thickness, the critical hydroplaning speed decreases when the vertical load and the inflation pressure are maintained constant. Also, for the same water film thickness and the same inflation pressure, the critical hydroplaning speed is increasing with the increase of the wheel vertical load. The results for the critical hydroplaning speed obtained by the FEM model were validated with data obtained from the NASA hydroplaning equation for ASTM smooth tire.

Kumar [28] has described the interaction between the pneumatic tire and the fluid using the CEL formulation in abaqus. Similar to Ong’s [27] paper, the FEM model was validated using the NASA hydroplaning equation for smooth tires developed by Horne. Figure 25 presents the influence of inflation pressure on the hydroplaning speed for both rolling and locked wheel cases.

For this simulation, the water film thickness was kept constant at 7.0 mm and the vertical load was set to be 4800 N. The inflation pressure range between 110 kPa and 150 kPa represents an under inflated tire rolling condition and the risk of hydroplaning is considerably higher. It can be observed that the rise of inflation pressure from 110 kPa to 165.5 kPa can increase the critical hydroplaning speed by a factor of 1.25 for the rolling tire case and a factor of 1.18 for the sliding tire case. The hydroplaning speed difference between the sliding tire and the free rolling tire is relatively constant for the entire inflation pressure range. Investigators stated that the sliding tire case presents a higher hydroplaning risk than the free rolling tire case because it is more difficult for the entrapped fluid beneath the contact patch to escape when the pneumatic tire is locked and slides on the pavement.

Fwa [29] has studied the effect of the tread pattern on the critical hydroplaning speed for a locked wheel case. The pneumatic tire used for the simulation is a G78-15 tubeless tire of belted bias construction with the inflation pressure maintained constant at 186.2 kPa. The pavement was considered to be smooth. The width of each rib is 16.8 mm while the ribs are separated by grooves with width of 5.08 mm. The water film depth was maintained constant at 10.0 mm while the wheel vertical load was 2.41 kN. The investigators studied the effect of the tread grooves angle on the hydroplaning speed. Figure 26 presents the calculated critical hydroplaning speed for different inclination angles of the tread groove and different tread depths. According to the investigators, the groove inclination angle is defined as the angle between the centerline of the V-groove pattern and the centerline of tire circumference. Therefore, an inclination angle of 0 deg describes a tread pattern with longitudinal grooves while an inclination angle of 90 deg describes a tread pattern with transversal grooves.

From Fig. 26, it can be observed that the critical hydroplaning speed is gradually increasing when the inclination angle is increased from 0 deg to 20 deg. From an inclination angle of 40 deg, the critical hydroplaning speed is increasing at a higher rate with the increase of the groove inclination angle. As expected, when the tire tread depth is increased, the critical hydroplaning speed also increases for the same groove inclination angle. This is due to the improvement of water evacuation capabilities of the pneumatic tire. Researchers stated that with the increase of groove inclination angle, the longitudinal hydroplaning performance of the tire is improved; however the lateral hydroplaning performance is decreased. Therefore, tire manufacturers chose an inclination angle of 45 deg as a compromise between longitudinal and lateral hydroplaning performance.

Similar to other FEM hydroplaning research papers, Ding [30] has studied the hydroplaning performance of a pneumatic truck tire using the commercial software abaqus and the coupled Lagrangian–Eulerian (CEL) formulation. The researcher has found that the hydroplaning critical speed is increasing with the increase of wheel vertical load, the decrease of the water film thickness, and the increase of the inflation pressure. Another part of the research paper studies the effect of rain intensity and drainage path length on the water film thickness using an empirical equation developed by Gallaway in 1971. The equation used by the investigators and the meaning of terms are the same as Eq. (13) presented in Sec. 2. Figure 27 presents the effect of drainage path length and rain intensity on the water film thickness.

The Manning's roughness coefficient is chosen to have a value of 0.0327 and the mean texture depth (MTD) value of 0.91 mm, for typical dense graded asphalt. The light, moderate, and heavy rain conditions correspond to a rain intensity of 0.25, 1, and 5 mm/h. For this study, the slope of the drainage path was considered to be constant at 2%. As presented in Fig. 27, the water film thickness increases with the increase in drainage path lengths and rain intensities. In light rain conditions, the water film depth on the first lane can be estimated to have a value of 0.6 mm while the water film depth on the fourth lane can be estimated to have a value of 2.6 mm (the width of one lane is considered to be 3.66 m). In heavy rain conditions, the water film thickness varies from 8 mm in the first lane to 20 mm in the fourth lane. The investigators stated that these results are obtained for an even road surface, however if the uneven portions of the road surface are considered, the water film thickness can have a much higher value due to water ponding.

The specialized literature presents many definitions and assumptions for the critical hydroplaning speed. Several of the finite element models mentioned earlier also feature varying definitions of the critical hydroplaning speed. As a result, the outcomes presented could be influenced by a notable error stemming from these differing assumptions. A good recommendation for future research in modeling the hydroplaning phenomenon using the finite element method is to clearly define the critical hydroplaning speed as the longitudinal speed where the tire had completely lost the contact with the pavement. Another important consideration in the application of the finite element method to hydroplaning research involves the modeling of pavement texture. As detailed in Sec. 2.2, studies have identified pavement texture as a significant influencing factor in the overall hydroplaning phenomenon. Consequently, future research may require a heightened emphasis on modeling pavement texture to enhance result accuracy.

## 4 Conclusion

In order to enhance the active safety of passenger cars, researchers have attempted to develop methodologies for real-time estimation of both partial and total hydroplaning. A potential method to prevent total hydroplaning of a passenger car is to reduce the longitudinal speed of the tire. However, as presented in previous sections, the hydroplaning phenomenon depends on a multitude of factors, therefore establishing the critical hydroplaning speed can represent a challenging problem. The proposed real-time estimation methodologies could provide crucial insights for active safety systems such as electronic stability program (ESP) with respect to critical hydroplaning speed. Currently, these systems can decrease the longitudinal speed of the motor vehicle when there is a potential risk of losing the stability. However, the active safety systems lack adequate data to predict and prevent the occurrence of hydroplaning [1].

One of the common methods employed to estimate the risk of hydroplaning involved the utilization of axial accelerometers mounted to the inner carcass of the tire. In his study, for estimating the critical hydroplaning speed, Tuononen [5] analyzed the lateral and longitudinal signals from three accelerometers glued to the tire carcass. One major conclusion drawn from this study is that accelerometers are suitable to estimate the hydroplaning risk only for specific rolling conditions and cannot be used for commercial applications. Also employing accelerometers embedded within the tire, Cheli [12] developed a detection algorithm for estimating the threshold between partial and total hydroplaning based on the radial signal transmitted by the sensors. Tuononen [6] studied an alternative hydroplaning sensing technique which is based on measuring the deflection of the tire carcass. The detection algorithm relies on the signal obtained from an internal optical sensor mounted inside the motor vehicle wheel. The sensor accurately identifies the displacement of the maximum vertical deflection toward the front of the contact patch. As stated in a previous section, this phenomenon is attributed to the water wedge formation ahead of the tire due to the hydrodynamic pressure of the water. The system presented has proved to give accurate information about the hydroplaning risk for a free rolling tire case, however the investigators stated that false hydroplaning detection can be encountered when the longitudinal acceleration is above 0.1 g. Schmiedel [7] developed a method to quantify road wetness by analyzing the signal coming from accelerometers mounted under the body of a passenger car vehicle. The water particles from the tire spray are interacting with the accelerometers, thus generating a signal proportional with the amount of water on the pavement. The output of the detection algorithm is not directly related to the hydroplaning risk of the tire, therefore further research can be performed to corelate the tire spray phenomenon with the hydroplaning risk. Fichtinger [8] and D'Alessandro [11] have estimated the critical hydroplaning speed of a pneumatic tire only by analyzing the sensors output that already equips a modern passenger car; however the output of the detection algorithm can be affected by other external factors such as misaligned concrete slabs on highways, therefore the systems are not currently available for commercial applications. Maleska [9] has analyzed the hydroplaning performance of different pneumatic tires using the VDA test procedures, which also correlates the critical hydroplaning speed with the angular speed of the wheel. Hermange [2] and Jansen [10] have both studied the partial and total hydroplaning phenomenon of a pneumatic tire by analyzing the image of the contact patch between the tire and a glass panel in wet rolling conditions. Both studies have correlated the percentage of hydroplaning of a passenger car tire with the contact patch dimensions. The real-time hydroplaning estimation methodologies presented in this research paper are not designed for commercial applications and can detect the occurrence of total hydroplaning only for specific rolling conditions, therefore further research can be accomplished to develop a novel system that can detect and prevent the occurrence of hydroplaning in a real-world situation.

While many empirical models effectively predict the critical hydroplaning speed, their accuracy depends on the precision of the collected data. Some existing empirical models rely on data obtained several decades ago, and advancements in road and tire technology today may have improved the actual performance of modern tires, potentially surpassing estimations made by these empirical models. Another often overlooked aspect is the phenomenon of viscous hydroplaning. Mounce [3] highlighted that viscous hydroplaning becomes problematic during low-speed operation on pavements with minimal microtexture and for tires with severe worn tread pattern. This phenomenon may manifest at relatively low longitudinal speeds, such as those encountered in typical city driving scenarios [1]. Currently, there are almost no empirical models used to predict the critical hydroplaning speed for viscous hydroplaning conditions. Further development of empirical hydroplaning models can be accomplished using more recent and accurate experimental data. Also, in our literature review, we did not find any empirical hydroplaning model that quantifies the impact of the tread pattern design to the longitudinal hydroplaning speed, therefore significant research can be performed in this area.

In order to reduce the cost and time of hydroplaning experiments, different researchers have developed FEM models that simulate the interaction between the tire and the pavement in hydroplaning rolling conditions. Nazari [26] has developed the FE model of the tire in the commercial software abaqus and then he analyzed the hydroplaning performance of the modeled tire using star-ccm+ software. The critical hydroplaning speed was found by analyzing the vertical lift force of the water that acts on the exterior of the tire. Ong [27] has analyzed the hydroplaning performance of a truck tire by modeling the fluid flow using the arbitrary Lagrangian–Eulerian formulation. Similar to Nazari’s paper, Ong has found the critical hydroplaning speed by analyzing the vertical lift force generated by the tire and water interaction. Fwa [29] has analyzed the impact of the tire tread pattern on the critical hydroplaning speed of a pneumatic passenger car tire for different rolling conditions. The majority of the FEM hydroplaning models are validated using data obtained from the empirical hydroplaning models, therefore further improvements of the FEM hydroplaning models output can be accomplished using more recent experimental data.

## Acknowledgment

This work was supported by Terramechanics, Multibody, and Vehicle Systems (TMVS) Laboratory at Virginia Tech.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

No data, models, or code were generated or used for this paper.

## References

*Phenomena of Pneumatic Tire Hydroplaning*, National Aeronaustics and Space Administration, Washington, DC.