The real impact of full hydroplaning on driving safety

Accident Analysis and Prevention 138 (2020) 105458

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The real impact of full hydroplaning on driving safety a

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Florian Spitzhüttl , Fabrice Goizet , Thomas Unger , Frederic Biesse * a b

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Institute for Traffic Accident Research (VUFO), Dresden University of Technology, France Michelin, Ladoux Research Center, Clermont-Ferrand, France

ARTICLE INFO

ABSTRACT

Keywords: Tire Hydroplaning Traffic accident Grip

Since its discovery at the end of the 1950′s, hydroplaning has been a matter of concern for drivers on wet roads because it can affect driver safety. Indeed, this phenomenon can lead to a complete loss of contact between the tire and the road caused by the layer of water that develops between them, resulting in a complete loss of longitudinal and lateral grip. Although the phenomenon of hydroplaning is about 60 years old, it is almost impossible to find any scientific estimation of how frequently vehicle accidents can be caused by hydroplaning, especially in Europe. To cover this gap, the well-known German In-Depth Accident Study (GIDAS) project has assisted to conduct a study. Thanks to GIDAS, it was possible to identify a sufficient number of cases on wet roads including a high accuracy of information about relevant parameters. With a physical analysis of all the cases, it was possible to compute the probability for an accident case to be in a full hydroplaning situation. This allowed for a precise estimate of the real importance of full hydroplaning situations on accident occurrence, which appears to be a much rarer accident cause than most drivers think.

1. Introduction Many drivers are anxious about hydroplaning, as they know it can impact their safety. This phenomenon is driven by a reduction of the contact surface between the tire and road due to the presence of water between them. This reduction of contact surface implies a reduction of tire grip, in some cases leading to a total loss of tire-road contact and removing any possibility for the driver to steer or brake. Drivers are generally aware about hydroplaning phenomenon. However, they don’t usually grasp the physical principle and many of them cannot distinguish the difference between pure hydroplaning (tire loses all contact with road) and lack of grip (tires stay in contact with the road but required steering or braking forces exceed the maximum available friction coefficient). The relation between hydroplaning and accidents is not so easy to establish, and drivers may confuse lack of grip with hydroplaning. Bibliography demonstrates a consensus that hydroplaning is a rare phenomenon and that the role of hydroplaning inside the accident scenario is difficult to quantify. As a consequence, the few existing studies on this question generally use subjective approaches to estimate the number of accidents due to hydroplaning. This study proposes a new approach to estimate the number of accidents related to hydroplaning for passenger cars (trucks do not

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encounter hydroplaning due to much higher tire inflation pressure and lower driving speed). By using GIDAS data (German In-Depth Accident Study), it is possible to access a sufficient number of cases on wet roads including a high accuracy of information about relevant parameters. Using this approach, it is feasible to compute the probability for an accident case to be in a full hydroplaning situation. In this paper, mechanisms of hydroplaning will first be reviewed, then details will be given on the available data and the process used to reach the calculation of the hydroplaning probability. Finally, results on the complete database will be detailed. This analysis is complemented by the accident data study of the Saxony police. This data source contains all accidents with personal or material damage that were reported to the police, but with the disadvantage of being generally less detailed than in-depth data and including no accident reconstruction. Thus, the secondary analysis will be broader in scope but with less depth. 1.1. Tire hydroplaning and tire grip Wet grip of tires has been the subject of research for decades. Many mechanisms have been identified concerning tire traction, such as hysteretic friction, viscous friction, adhesion, tread indentation, and hydroplaning. Illustrations of research on those topics can be found in

Corresponding author. E-mail address: [email protected] (F. Biesse).

https://doi.org/10.1016/j.aap.2020.105458 Received 10 September 2019; Received in revised form 8 January 2020; Accepted 27 January 2020 0001-4575/ © 2020 Elsevier Ltd. All rights reserved.

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Ignatyev Ripka et al. (2015). The design of the tread pattern to optimize the grip level has also been studied intensively (for example Hofstetter Grohs et al., 2006; Ripka Gäbel et al., 2009). In Todoroff, Paupy et al. (2019), it is proposed to group wet grip mechanisms into two families, namely rubber grip and hydroplaning. Rubber grip family groups in particular mechanisms of hysteretic friction (energy dissipation through the deformation cycle imposed to the rubber by the surface roughness), adhesion (molecular link between rubber au road surface, generally with low influence in case of wet road), viscous friction (generated by a small water layer remaining between the two bodies, which needs low roughness and high sliding speeds to appear). Hydroplaning family groups the mechanisms of water evacuation by the tire architecture and tread in front and inside the contact patch, until reaching a damp road – rubber contact. The strong influence of pavement texture on both rubber grip and hydroplaning is known since the 1960′s. A good example of the knowledge on this topic in 1970 can be found in Sabey Williams et al. (1970). For the rubber grip, the most impacting texture parameter is the micro-texture. Many publications detail this influence, the most known studies on this topic being Greenwood and Williamson (1966); Archard (1957), and since 2001 all the work developed by Persson (for example Persson, 2001; Persson Albohr et al., 2004). An example of comparative study can be found in Müser Dapp et al. (2017), a recent and very complete synthesis on the tribology is Vakis Yastrebov et al. (2018). The results indicate that a higher micro-texture level increases the hysteretic friction mechanism (which is key for wet grip), while reduces the efficiency of the adhesion mechanism (which is much less represented in wet grip than in dry grip). For the hydroplaning mechanism, the most influent parameter is the surface macro texture. As describe for example by Horne and Joyner (1966), by DeVinney (1967), and by Sabey Williams et al. (1970), macro texture has two effects on hydroplaning. The first effect is to store a certain amount of water in its cavities, which reduces the water quantity that the tire has to evacuate. The second effect is to enable water circulation within the ground cavities network, which can evacuate water when the contact patch applies a pressure on it. Thus, a higher macro-texture level will reduce the impact of hydroplaning

mechanism. Hydroplaning has been identified in the beginning of the 1960′s, Horne and Dreher, 1963; Horne and Joyner, 1966; Devinney, 1967, Sabey Williams et al., 1970, Allbert, 1968; Sinnamon and Tielking, 1974, being representative examples of the research. As described in Fig. 1, the hydroplaning phenomenon results in a reduction of the contact patch surface between the tire and road as the vehicle speed increases (cases A, B, C and D). This surface reduction is due to the presence of water between the tire and road, and is very progressive. The reduction of the contact patch also results in a reduction of tire grip level; the tire can transmit forces (see red arrow) to the road by rubber grip mechanism thanks to the surface of the tire in contact with the road. If the vehicle speed increases and exceeds a specific threshold (named hydroplaning speed - Vh) the tire completely loses its contact with the road (case E). In this case, a pure hydroplaning situation occurs, which inhibits any steer or brake force that may lead to a destabilization of the vehicle. Basically, hydroplaning is driven by the following elements:

• Speed of vehicle: an increase in vehicle speed will increase the water hydrodynamic pressure, until the hydroplaning speed is reached. • Volume of water on the road: The higher the water depth, the lower the hydroplaning speed. • Tire Pressure : a lower pressure results in a higher risk of hydroplaning (lower Vh) • Tire’s capacity to drain away water: in a first approach, drainage is led by void volume. The higher the void volume (due to the design of the sculpture and the tread depth), the higher the hydroplaning speed becomes. Note that the tire sculpture and its architecture can be optimized and thus the drainage efficiency may differ even if the void volume is equivalent.

1.2. Link between tire and road safety The main causes of accidents are often linked to human decision/ action/perception, as explained in the Trace project (Van Elslande Naing et al., 2008). Based on the chronological process proposed in

Fig. 1. Hydroplaning phenomenon.

2

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Fig. 2. Tire role in accident sequence.

their paper, the tire role can be highlighted relative to the different phases of an accident, as shown in Fig. 2. The phase 1 is the normal driving situation. Then a critical event occurs, which, in the vast majority of traffic accidents is caused by drivers/riders/pedestrians and their behavior (e.g. inappropriate speed, lack of safety distance, distraction, sleeping …). The occurrence of the critical event defines the entrance in the phase 2, where the incident participants will take action to try to avoid the accident (braking or steering for the vehicle drivers, moving for pedestrians, etc), or to mitigate the consequence of a possible accident. Those actions are named avoidance maneuvers. If those maneuvers are unsuccessful to avoid the accident, the crash becomes unavoidable, at a time noted tM, and we enter in the pre-crash phase, named phase 3. The participants still continue to take actions, which can hopefully results in minimizing the consequences of the crash (typically by reducing the vehicle speed). Then the collision occurs, with the crash phase (phase 4), and the postcrash phase (phase 5). In some cases, the tires are considered as an influencing factor and may have an effect during phase #2 and phase #3 (see in Fig. 2) depending on the accident context : the driver steers or brakes to avoid a collision through the action of the tires. These cases are named as “tire grip relevant”, because the real physical source of the tire’s influence is the available grip existing between the tire and the road (which is determined by numerous factors). In some rare cases, such as a blow out or sudden loss of grip due to hydroplaning, the tire may cause a “critical event” and generate entry into phase #2. These particular cases could be grip relevant or not, depending on the reaction of the driver. This study focuses on accidents caused by pure hydroplaning. In other word, the study will try to find road safety situations where hydroplaning has generated a “critical event”. However, other accidents where the tires play a role through grip request but without a link to a “critical event” will be also considered.

(2011), focus their study on ruts occurring in highway through the use of their numerical simulation tool on a tire at the minimum legal tread depth. Hydroplaning speeds found by their model are in between 72 km/h and 91 km/h. Those values are below the legal speed limit on highway which seem to show that hydroplaning is a phenomenon that can occur under those specific conditions. Yet, the results of those studies must be compared to speed and water depth distribution under rainy conditions to evaluate the real impact of the hydroplaning situation. Numerous studies have analyzed the evolution of vehicle speed under rainy conditions. Many authors have demonstrated that speed decrease compared to dry road condition is correlated to rain intensity (Sandor, 2013; Billot El Faouzi et al., 2009; Hartz, 2010; Gunaratne Lu et al., 2012). Biesse, 2019, synthetized multiple publications on this subject and highlights that under light rain (0−5 mm/h) speed decrease is in order of 10 % on motorways while under heavy or very heavy rain speed decrease can be as high as 30 % which would make the hydroplaning situation quite unlikely. The second external factor to cover is the water depth. Multiple publications have tried to correlate water depth on a road to rain intensity (Kang Nazari et al., 2019; Tang Anupam et al., 2019; Gallaway Ivey et al., 1979; Ross and Russam, 1968; Sheridan, 2014; Nygårdhs, 2003; Luo Wang et al., 2019). Yet, even if water depth is highly correlated to rain intensity it is also dependent on the geometric design of the road (Mean Texture Depth, cross slope, …) and it is therefore not possible to link the water depth and the rain intensity without a good definition of the road geometry. While it is interesting to gather data on external factors linked to hydroplaning, such studies do not try to evaluate the share of hydroplaning as a root cause of the accident. Kang Nazari et al. (2019), propose a theoretical framework based on a probabilistic approach to evaluate the hydroplaning risk. Their strategy relies on the determination of a hydroplaning occurrence knowing the type of ground, the water depth and the vehicle/tire pair. Theoretical equations are derived to estimate the hydroplaning risk of a specific condition (ground, water depth, vehicle/tire pair). Yet, in their paper, no quantitative results are given for now. Hydroplaning is a complex phenomenon, and its occurrence is an important subject of discussion inside the scientific community. This situation is clearly expressed in the introduction of Sheridan (2014) :

1.3. Literature review Since the 1960′s, significant research has been published related to braking under wet conditions. Both wet grip and hydroplaning mechanisms are combined in those situations (Ignatyev Ripka et al., 2015; Staughton, 1970). It has been demonstrated that the highest probability of experiencing a full hydroplaning situation is linked to high speed, low macrotexture of the road, low tread depth and high water depth. The focus on the hydroplaning of tires is still relevant today and numerous researches deal with this topic especially through numerical simulation of the phenomenon in order to predict the hydroplaning speed. Fwa Kumar et al. (2009), used their numerical simulation tool to evaluate the hydroplaning speed of tires with various tread patterns and tread depths on multiple water depths (1–10 mm). Fwa Pasindu et al.

“Opinions of aquaplaning vary greatly throughout the road industry with some believing that true aquaplaning does not exist at the speeds we travel at on our roadways whilst other believes the problem to be very common and occurs at mid to low speeds.” Bibliography demonstrates that authors are generally realistic about occurrence of phenomenon and studies converge to say that 3

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reconstruction in a simulation program is completed in order to encode 3500 pieces of information per accident on average into the data base. One limitation of this dataset is the focus on severe accidents. The two GIDAS investigation teams (located in Dresden and Hanover, Germany) only consider accidents with personal damage (slight, serious or fatal injuries). Material damage accidents or near accident cases are not considered, although they occur much more frequently than accidents including personal damages.

Table 1 Number of usable vehicles in the GIDAS database. Filtering step GIDAS Database : Passenger car vehicles Known tread depth Known initial speed Known location Known road condition Known tire type Known grip relevance Known season Filtering step 1 Known rain intensity Wet or damp road Final number of usable vehicles Vehicleswith speed > 60 kph

Nb of cases 2005–2017, fully completed cases ∈ [0 ; 20] mm ∈ [0 ; 400] km/h ∈ {urban, rural} ∈ {dry, damp, wet, snowy, icy} ∈ {summer, winter, all-season} ∈ {longitudinal, transversal, combine, non grip relevant} ∈ {summer, winter} All data available

38 22 16 21 22 22 18 20

668 783 386 142 783 733 158 649

2.2. Selection of usable cases As it will be explained in section 2.3.1, the methodology applied in this study requires the knowledge of several parameters. Thus, the first selection step is to look for accidents where all the necessary data are available:

22 781 13 781

Reference set

5 810 1 130 1 130

Potential hydroplaning

207

• Initial speed: initial speed is the vehicle’s speed at the moment of

Note about rain intensity: Rain intensity greater than 0mm/h is documented for 36 cases (17.4 % of 207). For the other cases, rain intensity is too low (< 0,2mm/h) and has been coded with 0mm/h. A possible explanation is that the road was wet/damp at the moment of the accident although the precipitation stopped before.

• •

hydroplaning is not a common occurrence (see for example Kolke, 2011). Regarding the link between hydroplaning and safety, we found only one study from Florida’s Department of Transportation (Gunaratne Lu et al., 2012) estimating an average crash rate for wet accidents that are linked to hydroplaning. This study takes into account relevant parameters like vehicle speed and driver comments. Unfortunately, this ratio cannot be proven as the following information is missing:

• Information about tire (tread depth, tire pressure) • Vehicle speed is estimated from posted speed limit.

•

It can be also noted that this study considers only accidents occurring in Florida, which is quite a severe location in terms of weather conditions (sub-tropical climate). Seeing the small number of scientific studies on this topic and the lack of objective and quantitative data on the importance of hydroplaning in road safety, this study was initiated to cover the gap.

•

the critical situation (end of normal driving phase). This information is derived from accident reconstructions done by accident engineers. The reconstruction take objective (e.g. traces) and subjective information (e.g. survey of participants) into account. The goal of reconstruction is to retrieve trajectories, speeds, acceleration and maneuvers of vehicles involved in accidents. Tread depth of tires: in the study, tread depth is considered for front axle or rear axle. Tread depth per axle is the average of left and right tire. Grip relevance: Grip relevance is determined from different information from the accident description. It indicates whether the driver solicited the tire grip by braking or steering during the emergency phase of the accident. Grip relevance is described in four categories in the GIDAS database : longitudinal (tire grip is solicited by braking or driving), transversal (tire grip is solicited by steering), combined (tire grip is solicited both in longitudinal and transversal) at no grip (tire grip is not solicited). Water depth: The exact water depth on the road is not available at the time of accident for most of the cases. However, it is possible to know the rain intensity at the time of the rescue call. Rain intensity (defined in mm/h) is noted by the operator when the GIDAS team is informed about the accident (usually within a timeframe of five to ten minutes). Other criteria (e.g. road condition, location, and tire type): these criteria are given only for information.

In a second step of selection, only wet and damp conditions are considered, as hydroplaning cannot occur on dry road. Finally, as shown in Table 1, a set of 1130 implied vehicles is usable for our study (only passenger cars are considered in this study, because trucks are generally not subject to hydroplaning due to much higher tire inflation pressure and lower driving speed). The classification of the 1130 vehicles by grip relevance gives about 59 % of grip relevant cases. This ratio is comparable to the ratio computed on all vehicles involved in wet/damp accidents, with a value of 64 % grip relevant cases. It confirms that the selection of 1130 vehicles is rather representative of all vehicles involved in wet and damp accidents. These 1130 vehicles are used as the reference number of cases for which hydroplaning has to be detected or not. Not every case will have hydroplaning as the main cause of the accident. Pure hydroplaning is very unlikely to occur at speeds below 60 kph, irrespective of the water depth and the tire tread depth. Fwa Pasindu et al. (2011), found hydroplaning speed in ruts for tire at the minimum legal tread depth of 72 kph for the deepest water depth. Horne and Joyner (1966), gives an analytical formula for the pure hydroplaning speed which is always greater than 60 kph if the inflation pressure is bigger or equal to 0.9 bar. In the model developed in section 2.3.2 and fitted on a set of measured tires, even a slick tire (0 mm tread depth) on 100 mm water depth and inflated at 1.05 bar has an hydroplaning speed greater than 60 kph. In

2. Analysis through GIDAS database 2.1. Description of GIDAS database As shown by the small amount of studies on this topic, it is a difficult task to estimate the share of accidents caused by hydroplaning. As hydroplaning sensors are not available at the place and time of the accidents, it is necessary to have access to several parameters in order to estimate the probability of hydroplaning in the situation (driving speed, water depth, tire pressure, tread depth). To access such accident data, the only solution is to use in-depth accident databases. GIDAS data are the most suited for our purpose, as they cover most of the needed parameters and contain a significant number of cases. GIDAS German In-Depth Accident Study is a joint venture between BASt and the Automotive Research Association FAT, initiated in July 1999. Approximately 2000 accidents involving personal injury are recorded in the areas of Dresden and Hannover Germany annually. The investigation team documents at the scene and later all relevant information on vehicle equipment, vehicle damage, injuries of persons involved, the rescue chain, as well as the accident conditions. Individual interviews of the people involved are conducted, detailed surveying of the accident scene is performed, and accident 4

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average with this model, when the tread is saturated with water, the hydroplaning speed is in the range [70–90] kph. Thus a lower limit of 60kph cover all the possible pure hydroplaning cases. This leads to the selection of 207 vehicles of potential hydroplaning (18 % of the 1130 cases) for the detailed analysis. For these 207 vehicles, the tread depth and pressure values are determined by the following rules:

considered) :

Pacc hydro | WD (i , WD) = Proba ( IS (i) > Vh (WD )| P (i), TD (i), Market ) (2) With those expressions, as WD is a continuous distribution, the result is a probability density function and not a discrete probability. As the water depths are known (see later) with a step of 0.1 mm, we will estimate WD as the water depth being inside an 0.1 mm interval, thus : n n+1 WD ; 10 with n . With this consideration, the equations are 10 real probabilities rather than probability density functions. The Bayes theorem of the conditional probabilities gives the following result :

• By default, tread depth and pressure associated to the front axle is used • In transversal grip situations, the minimum tire tread depth and pressure of front and rear axle is used.

Furthermore, the possibility of hydroplaning can be checked via other indications (driver interviews or VUFO (Verkehrsunfallforschung an der TU Dresden GmbH - Institute for Traffic Accident Research at Dresden University of Technology) analysis in the accident description, tire pressure, …) regardless of the initial speed. It appears that no additional case is detected using this approach (which argues in favor of the relevancy of the global process and the selection criteria).

Pacc hydro | WD PWD | acc hydro

Pacc hydro =

• Know the tire (size, manufacturer, brand, date of manufacturing), tire pressure, tread depth, and water depth on the road at the time of the accident Conduct a hydroplaning test with the same tire, in the same conditions (pressure, load, tread depth, water depth), and determine the full hydroplaning speed Vh in those conditions Compare this Vh with the initial speed of the accident.

Unfortunately, in addition to logistic, timing and cost difficulties, this procedure is simply not feasible. Because the accidents in the database might be up to 10 or 15 years old, it is possible that the corresponding tires are no longer produced nor sold. There is also no test result database gathering all hydroplaning results for all tires of all brands. These results would also need to correspond with the exact conditions (load, pressure, tread depth, water depth) of the accident. It is therefore necessary to use another procedure in order to overcome the impossibility of knowing the exact hydroplaning speed of each tire. There are two main unknowns in the question: the precise tire hydroplaning performance, and the exact water depth on the road. Thanks to a representative set of hydroplaning measurement of tires (see section 2.3.2 and Fig. 5), the distribution of the hydroplaning speed among tires on the market is known, if pressure (noted P), tread depth (noted TD) and water depth (noted WD) are known. From this distribution, it is possible to compute a hydroplaning probability by comparison with the accident initial speed. The probability for each accident to be caused by a full hydroplaning situation can be noted as follows:

Pacc hydro (i ) = Proba ( IS (i ) > Vh| P (i ), TD (i), WD (i), Market )

WD (with a 0.1mm interval)

PWD

Pacc hydro | WD × PWD PWD | acc hydro

WD

(3)

As it will be explained later, a global water depth probability distribution is known for Western Europe with mild climate, noted PWD Europe. We could imagine to use PWD Europe ≈ PWD in Eq. 3, but that implies an underlying hypothesis that the probability of water depth at the place of accident i exactly corresponds with the global knowledge of water depth PWD Europe. We have unfortunately no available information to corroborate this hypothesis (with the associated risk to under-estimate the real hydroplaning occurrence). In addition, it is possible to compute Pacc hydro | WD but not PWD | acc hydro . As it is not possible to compute Eq. 3, it was necessary to compute an upper bound for Pacc hydro (i) . A first way to do this is to consider that the water depth during accident i was at an upper bound value. We assumed an upper bound value of 8 mm in the scope of this study, which is the reference value used by many laboratories, prescribers and tire manufacturers for hydroplaning tests. This 8 mm value is also justified by the water depth measurements (see section 2.3.3), where no actual measurement gives a water depth higher than 8 mm. Using the mathematical fitting of the water depth distribution, the probability for water depth to be in the range [8 ; 100]mm is 6e-7 for the distribution fitted on measurements and 2e-5 for the worst case simulated distribution (see section 2.3.3). In addition, the hydroplaning speed model developed in section 2.3.2 presents a very low sensitivity for water depth above 8 mm (hydroplaning speed is already near to its asymptotic lower value). With this 8 mm water depth, we define :

2.3.1. Overview of the hydroplaning evaluation process To determine whether an accident was caused by full hydroplaning or not, the ideal method would have been the following, for each accident case analyzed in the accident database:

•

Pacc hydro

Thus

2.3. Methodology for hydroplaning evaluation

•

=

(4)

PMax hydro (i) = Pacc hydro | WD (i, WD = 8mm )

This 8 mm water depth value has an extremely low probability of occurrence, which leads to a huge over-estimation of the probability of the accident to be the result of hydroplaning. Given this over-estimation, the determination of a more appropriate upper bound of Eq. 3 was necessary. The principle of the revised approached is to replace Pacc hydro | WD × PWD by its maximum. The equation then becomes :

Pacc hydro

(1)

With : IS(i) = initial speed of the accident n°i Vh = hydroplaning speed P(i) = tire pressure of the accident n°i TD(i) = tread depth of the accident n°i WD(i) = water depth of the accident n°i Market = Vh distribution coming from the tire market knowledge In Eq. 1, with the accident database, the known parameters are IS(i), P(i), TD(i) and Market, while WD(i) is unknown. It is however possible to compute Pacc hydro (i ) for each possible WD (the [0 ; 8 mm] range is

max(Pacc hydro | WD × PWD ) PWD | acc hydro

WD

We define the most probable water depth (noted Most Prob. WD) by: (5)

Most Prob. WD = arg(max(Pacc hydro | WD × PWD )) Thus:

Pacc hydro

: 5

max(Pacc hydro | Most Prob . WD × PMost Prob. WD) PWD | acc hydro

WD

(6)

In particular, Eq. 6 is still valid for WD = Most Prob . WD , leading to

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Pacc hydro

Pacc hydro | Most Prob. WD × PMost Prob. WD PMost Prob. WD | acc hydro

(7)

In Eq. 7, it is reasonable to make the hypothesis that

PMost Prob. WD | acc hydro

PMost Prob. WD

And thus

PMost Prob . WD PMost Prob . WD | acc hydro

1

(8)

To justify our hypothesis, it is obvious that the hydroplaning mechanism has an increasing influence respective to a higher water depth. So for low water depth, we have P WD | acc hydro PWD , while for higher water depth we have P WD | acc hydro PWD . Thus the two probabilities curves are crossing at a given water depth. Considering the usual tread void ratio of tires, a worn tire will have its tread saturated by water at about 0.4 mm of water depth, and a midworn tire at about 1 mm of water depth (see section 2.3.2). As illustrated by Fig. 11, all the accident cases have their Most Prob. WD above 0.6 mm, and in average at 1.35 mm. Thus the hypothesis made for Eq. 8 appears to be relevant. By combining Eq. 7 and Eq. 8, we finally obtain :

Pacc hydro

Pacc hydro | WD

Fig. 3. Hydroplaning speed Vh as a function of water-absorption capability.

impacted by hydroplaning mechanism (low water depth, high tread depth for example). When 1 < 1, water remains in front of the tire and its pressure builds up in front of the tire to generate a lift force that decreases the load initially carried by the tire (the lift carries part of this load). Fig. 3 provides the experimental results obtained by varying sculpture saturation through tread depth and water depth changes. A total of 52 different tires have been measured with different water depth (to get several values of water absorption capacity), for a total of 177 tests conducted (tires × conditions). Hydroplaning speed Vh plotted as a function of 1 demonstrates a linear behavior. As a consequence, the model proposed in this paper to take into account the saturation is given by:

(9)

Finally, as an upper bound of Pacc hydro is now established, this value will be used for the estimation of the hydroplaning probability:

Pacc hydro est. (i) = Proba ( IS (i) > Vh| P (i), TD (i), Most Prob. WD (i ), Market )

(10)

All of those steps will be detailed and illustrated using an example in the following section. A case by case expert analysis will give a second estimation, which will be considered as the lower bound.

=

TD × TVR WD

(12)

Vh = 52 1 + K

Inflation pressure sensitivity was also tested for P = 1.8, 2.2 and 2.8 bars. To compare to theoretical studies we suppose that Vh is reached when the hydrodynamic pressure equals the inflation pressure, as explained by Horne and Joyner, 1966, ( is the fluid density).

2.3.2. Computation of hydroplaning speed distribution knowing pressure, tread depth and water depth As shown in the equations previously presented, the knowledge of the hydroplaning speed distribution Vh representative of the market is an important step. The aim of this section is to detail the computation of this Vh distribution. Vh distribution used in this study is derived from the analysis of loss of surface measured on a specific test track at Michelin’s test center in Ladoux. This track is composed of a straight road locally filled with a water film. The longitudinal and lateral slope of the road are zero, in order to ensure a constant water depth in the puddle. The water depth is regulated between 0.5 and 10 mm. An optical window is embedded in the ground and allows optical access from a room below the road where a camera is positioned and takes pictures of the tire rolling in the puddle. Post-processing of the pictures is then conducted to determine the contact patch as seen in Todoroff Paupy et al., 2019. The three main parameters that were tested for this study were the impact of tread depth (2 mm, 3 mm, 5 mm, and new tire), water depth (0.5, 1, 1.5, 3, and 8 mm) and pressure (1.8, 2.2, and 2.8 bars) on loss of surface. Instead of analyzing results in terms of sensitivity to tread depth or sensitivity to water depth, we analyze the results according to the water-absorption capability of the tread pattern (Sinnamon and Tielking, 1974). Water-absorption capability is determined in this paper by the ratio between the groove volume per unit of gross contact area and water depth that the tire sees : 1

1

1 Vh² = P 2

(13)

Doing a limited development around 2.2 bars gives the following equation:

Vh = 75.5 + 17.2 ×

P

(14)

The comparison between the experimental results and the theory is plotted on Fig. 4. We see that the slopes of ΔP/Vh for experimental and theoretical results are very similar (the vertical offset comes from the tread design effect). As a result, Vh sensitivity to 1 and pressure can then be written such as:

(11)

where TVR is the tread void ratio of the tire (typical value is 0.2). Water-absorption capability of the tread pattern is the key parameter to understand hydroplaning mechanism. In fact, while 1 > 1, the tire can evacuate water through the sculpture and is thus minimally

Fig. 4. Hydroplaning speed Vh in respect to delta pressure ΔP. 6

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Table 2 Water depth measurements on roads in Germany and France.

(15)

2.2) + K

K is the same tire constant than in Eq. 12, as the experiments used to build this relation between water absorption capability of the tread 1 and the hydroplaning speed Vh where conducted at 2.2 bar, and the pressure part in Eq. 15 equals zero at 2.2 bar. The results on Fig. 3 comes from a single tire to fit the pressure influence, and the corresponding test were conducted with an intermediate water absorption capability which leads to hydroplaning speed about 90 kph. The result with this tire gives a pressure sensitivity very similar to Horne’s theory. In order to determine the Vh distribution, we need to know the distribution of K values on the market. We expect K values to vary according to the dimension of the tested tire as well as certain tire characteristics such as void volume, the shape of the contact patch, the architecture stiffness, … To take into account the variability of tires on the market we tested 52 tires with various dimensions, brands and sculpture definitions. Results are plotted in Fig. 5 (blue dots). We see that there are some variations in Vh values for a given water-absorption capability. For example, when 1 = 0.2 there is less than 10 km/h differences between the various Vh plotted. When 1 = 1 variabilities are much higher, around 90 km/h for example. To consider this variability we define a standard deviation on Vh such as: Vh

=(

0

) × exp( 1.2/ 1) +

0

Germany, 587 road weather station

France, 17 road weather station

France, on-vehicle measurements

[0–1] mm ] 1–2] mm ] 2–3] mm ] 3–4] mm > 4 mm

99.17 % 0.32 % 0.14 % 0.19 % 0.18 %

98.69 % 1.09 % 0.17 % 0.03 % 0.02 %

99.50 % 0.49 % 0.0.6 % 0.002 % 0.003 %

water depth obtained through real measurement is available. The publication combines several measurement techniques, including road weather stations distributed along the roads in Europe and on-vehicle measurements with a dedicated water depth sensor. The measured values are reported in the Table 2. The road weather stations present the advantage of a refine time representativeness (measurement are taken every 15 min), but as they are on very localized points they present a lower geographical and road configuration representativeness (longitudinal slope and superelevation, importance of ruts or puddles are the ones resulting from the road design and maintenance state at the measurement place, which is assumed to be not statistically different from the other parts of the road network). The vehicle measurements have the reversed properties, a lower time representativeness and a very good geographical and road configuration one. The two approach (road weather station and vehicle measurement) are then very complementary, and it is noticeable that the water depth distribution of the two approaches are very similar. It is concluded in Biesse, 2019, that water depth on the road is inferior or equal to 1 mm during 99 % of the wet time, which is fully coherent with a previous German study (Vogt and Février, 2011) It is known that higher water depths are more likely to generate hydroplaning, thus it would be interesting to use refined data with a smaller sampling step and to include values higher than 4 mm of water depth. The raw data which where synthetized in Biesse, 2019, are available by 0.1 mm step. Thus a mathematical formula fitting the probability function of water depth was developed, resulting in a continuous formula respective to water depth. The resulting curve describing water depth during wet time is given in Fig. 6. Please note that this distribution is valid for Western Europe with mild climate (countries like Great Britain, Ireland, Netherland, Belgium, France, Denmark, Germany, Austria, Hungary, Poland, Czechia, Slovakia, Baltic countries, Belarus, Ukraine, etc). To validate the global approach in this study, it was decided to conduct a sensitivity study on the water depth by generating a worstcase for the water depth distribution. As high water depth generates

Fig. 5. Hydroplaning speed Vh model and comparison to experimental data.

Vh = 52 1 + 16.4 × (P

Water depth class

(16)

= 50 and 0 = 5 respectively the standard deviation at With high and low water-absorption capability. The exponential law represents the dynamic of the Vh as a function of the water-absorption capability. We assume that the CS distribution is a normalized Gaussian so 95 % of the population is in between I = [Vhmodel 1.96 × Vh; Vhmodel + 1.96 × Vh]. We see on Fig. 5 that 7 points are out of the interval, which represents 5.1 % of the population. On the same graph, we plot, in addition to our experimental data, the model defined in Eq. 15 where K = 79 (red line) as well as the interval I to define the expected limits of Vh (yellow area). We see that the model and standard deviation represents well the behavior of the tire population that we tested. The K = 79 value was fitted from the experimental data shown on Figs. 3 and Fig. 5. 2.3.3. Water depth distribution In reality, the exact water depth on the road at the time of the accident was not measured. To overcome this difficulty, as explained in the global process described in section 2.3.1, we use a water depth probability distribution for Western Europe with mild climate, noted PWD. Thanks to a recent study (Biesse, 2019), a statistical distribution of

Fig. 6. Probability of road water depth during wet time, for Western Europe with mild climate. 7

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Fig. 7. Numerical example to compute probability to be over hydroplaning speed for a given case.

more hydroplaning, the worst case scenario consists of an increased probability of high water depth multiplied by 10 compared to the fit on the actual data, but with nearly the same probabilities for water depth below 1 mm (99.16 % of time for the reference case, 99.05 % for the severized case). This severized water depth distribution could thus represent a road with much higher ruts or puddle occurrence. The two models are presented on in Fig. 6, in blue for the model fitted on measured data, in red for the severized one.

pressure and tire tread depth, the tread void ratio (TVR) is not known in the GIDAS database. With usual tire design, the value is in the range [20 % ; 30 %], and impacts the hydroplaning mechanisms (as described in section 2.3.2), but several other tire parameters influence hydroplaning performance, like tire architecture, contact patch shape, tread mix stiffness, etc. As those parameters are not available in the GIDAS database, their influence is taken into account through the standard deviation σ in the hydroplaning speed calculation. As we know the initial speed of the accident (IS(i)), the probability for the accident to be over the hydroplaning speed (considering its standard deviation) is simply the integral of Vh distribution on the interval [0 ; IS(i)]. A numerical example is given for a water depth of 1.0 mm in Fig. 7 : The probability to be over the hydroplaning speed can be computed for each water depth value within a range of 0–8 mm, with a 0.1 mm step. This results in a curve which givesthe probability to be over the hydroplaning speed as function of water depth (see Fig. 8), namely Pacc hydro | WD (i ) as given in Eq. 2. The next step, as described in section 2.3.1, is to determine what is the most probable water depth, Most Prob . WD (i ) . This value is defined by Eq. 5 as the X position of the maximum of the Pacc hydro | WD (i , WD) × PWD (WD) function. An illustration can be found on

2.3.4. Evaluation of hydroplaning probability for each case In this section, the details of the computation of Eq. 1 to Eq. 10 will be given, with an example to illustrate the process. The first step is to compute the probability to be over the hydroplaning speed for accident n°i (namely Pacc hydro | WD (i ) as given in Eq. 2), for each water depth in the calculation range (0–8 mm). In this step, for each accident, tire pressure (P(i)) and tire tread depth (TD(i)) are known, as well as the hydroplaning speed distribution of the tire market. This market hydroplaning speed distribution (noted Vh in section 2.3.1) is described by a normal law, from which the average and standard deviation ( x¯ & σ) are given by the hydroplaning speed calculation model (described in section 2.3.2). Contrarly to tire

Fig. 8. numerical example for Pacc hydro | WD (i) (probability to be over the hydroplaning speed as a function of water depth).

8

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Fig. 9. numerical example for.Pacc hydro est. (i )

the left part of the Fig. 9. Finally, four criteria were computed on the curve for each accident case i (see Fig. 9):

conclusion that one accident case is surely caused by hydroplaning. It is important to keep in mind that the computed rate, based on the proposed criteria, will be an upper bound of the hydroplaning accident rate. Indeed, many accident parameters have not been considered in this process, like driver distraction, sleeping, alcohol, … This is the reason why an expert case-by-case analysis was also made.

• Min Water Depth (Min WD): it corresponds to the water depth • • •

where probability starts to be greater than zero. This is the minimum water depth required to generate a chance to be over hydroplaning speed. Water depth linked to the maximum probability (Most Prob. WD): this water depth level represents the most probable water depth which can be found on road by assuming that the case is over the hydroplaning speed (see Eq. 5). From Most Prob. WD value, the probability to be over the hydroplaning speed is also given (named, Proba Hydro = Pacc hydro est. (i) ) (see Eq. 10). Probability to be over hydroplaning speed related to max water depth (here 8 mm). This criterion is named Max proba Hydro = PMax hydro (i) (see Eq. 4).

2.3.5. Validation of hydroplaning with other accident data An accident is most often the result of several factors. In the GIDAS process, many information are gathered for the analysis, leading to over 3 500 recorded parameters. In the current approach, only a very small number of those information have been used to obtain the objective evaluation of the hydroplaning accident rate. However, as explained previously, several factors of the accident have not been considered in our proposed process up to now. These include factors such as driver inattention, alcohol, and surrounding vehicles’ behavior. All relevant cases where validated through an expert evaluation in a case-by-case study. The main goal of this analysis was to read the accident description and attempt to estimate the probability of hydroplaning as a cause of the accident. The method used is to compare all the elements of the accident such as description, pictures, and technical elements (like road, presence of ruts, tires, behavior of other vehicles, …), and to compare them with all of the previously established criteria (Most Prob. WD, Proba hydro, …). Depending on the matching or not between all those technical information, the expert gives an estimated probability for the accident to be caused by hydroplaning (from 0 % to 100 %). Of course, contrary to the previous method, this evaluation contains a subjective component. Using the same approach as the Proba Hydro and max Proba Hydro calculations, all of the expert probabilities are summed to estimate the total number of accidents caused by hydroplaning (ten cases with a 10 % probability are equivalent to one case with a 100 % probability).

For the objective evaluation, only the Proba Hydro = Pacc hydro est. (i) will be used, the other criteria have been used for the expert evaluation of each case. The calculations have been made with the two water depth distributions, the measured one and the worst case one (see Fig. 6). The average difference between the two calculation were of less than 0.05 mm for the most probable water depth, and 8.6 % difference on the Proba Hydro criteria. This difference is small in comparison to the amplitude of the effect (ten times more occurrences of high water depth), which means that the result has a small sensitivity to the PWD data. As a consequence, an average of the two calculations (measured and severized water depth) has been used for the results. At the end of the process, we get two evaluations of the probability for each accident case to be caused by hydroplaning : Proba Hydro corresponding to the most probable water depth, and max Proba Hydro, corresponding to hydroplaning probability considering water depth = 8 mm. Our target is to determine an objective rate of accidents that have hydroplaning as a main cause, it was decided not to use any threshold (like 50 % probability), but rather to sum all the Proba Hydro and max Proba Hydro computed for all the accident cases. This means that if five accidents have a 20 % probability to be caused by hydroplaning, they will count as 100 % when summed, resulting in the

3. Results 3.1. GIDAS results In the previous steps, we selected 1130 wet or damp road cases in the GIDAS database where all the necessary information was available. The word “case” refers to a vehicle for which the grip situation was recorded. Among those 1130 cases, 207 were selected by the speed

9

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Fig. 10. Distribution of tread depth and initial speed for the 207 selected cases. Table 3 Comparison of the grip relevance of the 1130 selected cases and the 207 hydroplaning candidate cases. Grip request

Longitudinal Transversal Combine Non grip Total

GIDAS selected cases

Hydroplaning candidates

Nb vehicle

%

Nb vehicle

%

303 259 99 469 1130

27 % 23 % 9% 42 % 100 %

30 140 14 23 207

14 % 68 % 7% 11 % 100 %

filtering previously described. This represents around 18 % of vehicles involved in wet accidents. These 207 cases are considered as candidates for accidents where hydroplaning could be the main cause. Fig. 10 shows the distribution of tire tread depth and initial speed for those 207 cases. A further analysis of the 1130 selected cases versus the 207 hydroplaning candidates can be seen in the Table 3 through the grip relevance criteria. In the 1130 selected cases there is 27 % of longitudinal cases, 23 % of lateral, 9 % of combine and 42 % of non-grip relevant. For the 207 hydroplaning candidates, we observe 14 % of longitudinal case, 7 % of transversal, 68 % of combine and 11 % of non-grip relevant. It can be noted that the majority of the hydroplaning candidate cases (68 % of 207) are transversal, which differs from the nominal distribution (1130 cases), where transversal cases represent 23 % of wet and damp situations. This difference can be explained by speed threshold (60 kph) applied for the selection of the 207 cases. This speed threshold removes most of the urban cases where the majority of grip

Fig. 12. Objective criteria values for the 207 selected cases.

events involve longitudinal grip. It was explained on Eq. 8 that the hypothesis is reasonable for a water depth above 0.4 mm. We can see on Fig. 11 that all the cases have their Most Prob. WD above this limit: Two objective criteria were built in the section 2.3.4, to evaluate the hydroplaning probability for each case. Fig. 12 shows the results of those criteria over the 207 accident candidate cases (cases are ranked by decreasing order):

• Proba Hydro : Probability to be over hydroplaning speed related to most probable water depth (red curve). • Max Proba Hydro : Maximum of probability to be over hydroplaning speed (blue curve) by considering 8 mm of water depth on the road.

Basic results show that half of all cases (109/207, 52 %) have less than a 10 % chance to be over the hydroplaning speed when considering 8 mm of water depth on the road. The sum of all values related to Max Proba Hydro criteria gives 66.2. It means that 66 cases could be caused by hydroplaning which represents 5.9 % (66.2/1130) of all vehicles involved in wet accidents. However, as mentioned previously, this criterion is not realistic due to the assumption of 8 mm water depth required for each case (8 mm is an extremely rare situation according to observation and bibliography). The sum of all probability values related to Proba Hydro criteria gives 9.4. It means that around 9 cases are validated as an accident caused by hydroplaning and it represents 0.84 % (9.4/1130) of vehicles involved in wet accidents. Again, in both summations, all values of the criteria are considered, in other words, 10 cases with 10 % of probability is equivalent to 1 case with 100 % of probability. The first 30

Fig. 11. Distribution of the Most Prob. WD above for the 207 selected cases. 10

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Table 4 Details for the first 30 cases. (For interpretation of the references to colour in this Table legend, the reader is referred to the web version of this article)

Finally, we obtain an objective evaluation of the probability for a wet or damp accident to be caused by pure hydroplaning of 0.84 % (all the contact patch of the tire is lifted from the road by the water). This appears to be an upper bound, because this evaluation considers only some parameters and not the whole accident scenario. A case-by-case expert analysis gives a probability of 0.35 %. We may consider that the real figure should be in the range of 0.84 % - 0.35 %, with a central value of 0.6 %

Table 5 Analysis of the Saxony Police Data.

All cases Road condition Vehicle & road

07/2015 – 06/2016 Wet / damp Passenger car on wet/damp road keywords Hydroplaning Heavy rain Ponding water Rut Potential hydroplaning Confirmed hydroplaning

% of all

% of wet

223,791 cases 48,388 = 21.6% 44,582 = 19.9%

=100 %

81 = 0.036% 754 = 0.34% 0= 0% 22= 0.01% 332 = 0.15% 78 = 0.035%

3.2. Complementary analysis with Saxony police data =0.74 % =0.17 %

In the GIDAS database, only accidents with personal damages are registered, which naturally excludes all of the accidents with only material damages (material damage accidents occur about 20–25 times more frequently than personal damage accidents). Using another database that also includes accidents with only material damages would be very useful. In this study, it was possible to access to the Saxony reports (Saxony is one of the federated states of Germany, where the VUFO laboratory is installed). This database is much larger than GIDAS in quantity – in one year Saxony police reports accumulates more than 220 000 accidents or one hundred times the number of accidents than GIDAS database – but as a counterpart with less detail. Because this data is less detailed, the results of this analysis can only support previous statements and must not be considered standalone as a substantiated and valid analysis. The process involves selection of candidate cases by searching for keywords inside the accident descriptions. As a first step, candidate cases were selected by searching for accident descriptions containing “Hydroplaning” OR “heavy rain” OR “ponding water” OR “ruts”. 332 potential cases were found. Refinement was made by selecting cases where only the hydroplaning keyword is mentioned, leading to a selection of 78 cases (see Table 5).

cases are detailed in the Table 4. Inside this list, it is clear that two cases (#12 and #7) are very different than the other cases. For these two cases, hydroplaning could be a probable cause of accident. First, the rain intensity is not zero, resulting in the likelihood of higher real water depth compared to the other cases. In addition, no other cause seems to explain these situations, especially for case #7 where speed is very important under rainy conditions and the initial trajectory is a straight line. One explanation for the accident could be a loss of control due to pure hydroplaning phenomenon. The only doubt concerning case #7 is the presence of tire pattern rupture, which may have appeared during the pre-crash phase. Case #12 is very similar to case #7 (heavy rain, high speed and sudden loss of control of vehicle). The expert case-by-case analysis has shown that the number of hydroplaning cases is probably lower than the estimation given by objective criteria. From the case-by-case analysis, 4 cases are estimated with probable cause of hydroplaning. They represent 0.35 % (4/1130) of all vehicles involved in wet accidents. 11

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climate. To quantify the number of accidents caused by a full hydroplaning situation, detailed data are needed. The use of in-depth accident reports gives access to such data. In this study, the GIDAS database (German In-Depth Accident Study) with 22 783 passenger cars was used. Considering accident parameters such as rain intensity, vehicle initial speed, tire pressure, tire tread depth, and representative water depth data, it was possible to give a probability for a pre-selected number of accidents to have full hydroplaning as a main cause. An expert analysis of the most probable cases was also conducted in order to consider the complete context of the accident. This result was compared with a police accident database containing more than 220 000 accidents. An analysis of this database was performed using keyword searches of the accident reports, and results in a similar estimation of accident rates compared to the GIDAS-based analysis. The results of those two approaches are given in the Table 6. This study confirms that accidents caused by full hydroplaning situation do exist, even if they are rare. Full hydroplaning as an accident’s main cause represents 0.6 % of the wet and damp accidents. It would be interesting to apply the same approach to other geographical zones to determine if this result could be similar all around the world or may be influenced by weather conditions, road design, or local driving style. It should be emphasized also that this study was focused on full hydroplaning events. This refers to the situation where all tire-road contact is lost due to the water layer. Before arriving at this situation, partial hydroplaning is likely to occur. In this case, the result is a reduction of the tire grip level. Braking or steering still possible in this situation although less efficient. This study does not analyze the influence of partial hydroplaning on driving safety. It would be also an interesting topic for further research, as it is expected that partial hydroplaning occurs more frequently than full hydroplaning. In such situation, rubber grip and partial hydroplaning operate simultaneously, thus it would be interesting to model those situations with the two mechanisms together, in order to build a combined hydroplaning-andrubber-grip approach. The tire influences traffic safety through its ability to steer or brake sufficiently in response to the request of the driver in order to avoid a dangerous situation. This steering and braking response is directly linked to the grip level available at the time and place of the event. It is thus clear that the real descriptor of the accident risk (from a tire point of view) is the grip level. This grip level is influenced by the tire design itself (compound design, tread and tire design), by the driver’s influence (tread depth, tire pressure, speed), and by the environmental parameters (road grip level, quantity of water). Finally, the presence or absence of hydroplaning mechanism will modify the grip level; however, for road safety, the ability to generate steering or braking force is the important factor, and this is the definition of grip.

Table 6 Comparison of the rate of full hydroplaning as an accident main cause, for the two data sources. Data source

% of hydroplaning accidents in WET accidents

% of hydroplaning accidents in ALL accidents

GIDAS database Confidence interval Saxony police report Confidence interval

0.6 % [0.84 % - 0.35 %] 0.46 %

0.15 % [0.21 % - 0.09 %] 0.11 %

[0.74 % - 0.17 %]

[0.15 % - 0.04 %]

Note that the last filter (“confirmed hydroplaning”) is applied to the final count number of vehicles where hydroplaning is the probable cause of the accident. The way to confirm hydroplaning cases is based on the use of the specific word “hydroplaning” by police officers. It is of course a subjective estimation. In the analysis, 332 cases of potential hydroplaning were identified (keywords “Hydroplaning” OR “heavy rain” OR “ponding water” OR “ruts”, with wet or damp road), and 78 cases of hydroplaning were confirmed (keyword “Hydroplaning”). There is a total number of 44 582 accidents with passenger cars on wet or damp road. This results in 0.74 % occurrence of potential hydroplaning accidents and 0.17 % occurrence of confirmed hydroplaning accidents. 4. Discussion As synthetized in Table 6, the results are very similar between the two approaches, with a share of pure hydroplaning accident among wet ones in the [0.84 % - 0.35 %] interval with the GIDAS objective approach, and in the [0.74 % - 0.17 %] interval with the Saxony police report approach. As the two approaches are very different (based on a human evaluation by the police officer for the Saxony police data, and based on objective data and criteria for the GIDAS based approach), the very good alignment of the two approaches argues in favor of the robustness of the results obtained in this study. As mentioned during the literature review, only one study (Gunaratne Lu et al., 2012) has been found giving figures about accidents due to hydroplaning. Although hydroplaning crash rate are not directly calculated by Gunaratne in his report, we can compute from his data an hydroplaning crash rate in the range [1 % ; 5 %], the upper bound being the maximal value possible. This value is similar to our calculation with the maximal water depth (Max Proba Hydro criteria) giving a maximal upper bound of 5.9 %. It should also be noted that Gunaratne Lu et al. (2012), is concentrated on Florida, which has a subtropical climate contrary to Germany (mild climate), and that Gunaratne do not have information about tire (tread depth, tire pressure) and vehicle speed (which is estimated from posted speed limit). Even if no other direct estimation of the hydroplaning effect on accidents can be found in the scientific publications, the other related studies in the literature, with indications about water depth on the roads, water depth at the accident scene, speed reduction with rain, … (see the literature review) let us think that the share of full hydroplaning accident should be quite low compared to the other wet accidents, as confirmed by our study.

CRediT authorship contribution statement Florian Spitzhüttl: Methodology, Software, Investigation, Data curation. Fabrice Goizet: Conceptualization, Methodology, Software, Data curation. Thomas Unger: Validation, Supervision, Writing - review & editing. Frederic Biesse: Methodology, Formal analysis, Writing - original draft, Writing - review & editing.

5. Conclusion

Declaration of Competing interest

Even if hydroplaning has been studied for decades, it is very difficult to know the precise influence of this phenomenon on driving safety and, in particular, to determine the rate of accidents which have full hydroplaning as a main cause. This is proven by bibliography. This difficulty is mainly due to the rarity of the phenomenon and the difficulty to obtain the accident parameters influencing hydroplaning (like water depth on the road, vehicle speed, tire pressure, tire tread depth). This study proposed to fill this knowledge gap for mild European

The VUFO laboratory has been funded for this study by the Manufacture Française des Pneumatiques Michelin, Clermont Ferrand, France. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.aap.2020.105458. 12

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