JP4899054B2 - Method and apparatus for predicting sliding friction on road surface and program thereof - Google Patents

Description

  The present invention relates to a sliding friction prediction method and apparatus for predicting a road surface condition such as a road, and a program thereof.

  In the snowy area, the snow on the road becomes a snowy state due to the passage of vehicles, and it is easy to slip, so road management such as spraying of antifreezing agent is performed to prevent accidents. However, since the road surface condition changes variously depending on the time and place such as snowfall-snowfall-freezing-thawing, it is difficult to say that optimum road management is performed. For example, even if the road is patroled or the road condition is visually checked by fixed point observation, management is performed based on each person's experience, and is not based on objective situation judgment.

  For this reason, technological development for objectively predicting the road surface condition of such roads has been promoted, and a method using a statistical method has been proposed as one of the methods. Statistical methods include multiple regression analysis, discriminant function method, pattern analysis method, and method using neural network. However, these statistical methods are not versatile depending on regional characteristics, and they cover a wide range of roads. It is unsuitable for managing.

  As another method, a method using a heat balance has been proposed. This method predicts the road surface condition by quantitatively evaluating the heat flux across the snow and ice layer formed on the road surface. It is a natural method such as pavement structure and internal thermal factors such as weather and topography. Considering human factors such as factors and passing vehicles, it is possible to evaluate without depending on regional characteristics, and it is a method suitable for use in road management.

  The present inventors proceeded with research on a method using such a heat balance, proposed a heat balance model including vehicle bottom surface radiant heat, and verified the validity of the road surface temperature on dry, wet and snowy and ice road surfaces accompanying weather changes. (Refer nonpatent literature 1). In addition, based on the proposed heat balance model, quantitative evaluation of tire friction heat flux and vehicle bottom surface radiant heat flux was performed, and the influence on road surface temperature was examined (see Non-Patent Document 2).

  In addition, the present inventors have also studied the relationship between the snow / ice condition of the road surface and the sliding friction coefficient of the road surface along with a method for predicting the road surface state based on the heat balance model, and the sherbet road surface, the wet road surface and the ice plate road surface. The sliding friction coefficient was measured with a field test vehicle in Japan, and the sliding friction coefficient and the mass ice content, and the sliding friction coefficient and the sherbet thickness were analyzed (see Non-Patent Document 3).

As a method of predicting freezing of the road surface state using the statistical method and the heat balance method described above, for example, in Patent Document 1, the road surface state is predicted based on road surface state data, road surface temperature prediction data, and weather forecast data. A road surface condition prediction system is described. Further, in Patent Document 2, a plurality of road surface freezing detection devices are arranged along a route to measure the road surface temperature over the past several years, and the change patterns of the road surface temperature are classified according to the weather and the month. A road surface prediction method for extracting the most similar classification pattern and predicting the road surface temperature is described. In Patent Document 3, a short-term prediction of road surface condition is performed based on local data from a local meteorological data collection device equipped with a local road surface shape sensor and a weather sensor, and a medium- A road surface condition prediction system that performs long-term prediction is described.
JP 2006-30139 A JP-A-6-300860 JP 2002-196085 A Tomoyuki Arakawa and 4 others, "Analysis of road surface freezing by heat balance method-Thermal behavior on dry, wet and snowy roads", Cold Region Technical Papers, Vol.16, pp.389-395, 2000 Hiroshi Watanabe 2 people, “Modeling of heat supply from passing vehicles to road surface”, 21st Cold Region Technology Symposium, Cold Region Technology Papers and Reports, Vol.21, pp.195-200, 2005 Akihiro Fujimoto, 7 others, “Relation between sliding friction caused by MASS cars and road snow and ice”, Journal of the Japan Snow Engineering Society, October 2005, Vol. 21, No. 5, pp. 26-35

  As described above, in the past, the road surface temperature was predicted by the heat balance method, and the road surface state was classified according to the uneven shape classification, wetness, sherbet, snow pressure, etc., and the road surface state was grasped to predict the change in the road surface state. However, in order to judge how easy it is to slip a vehicle, etc., it is more efficient to predict the extent of the sliding friction coefficient of the road surface, such as spraying anti-freezing agents more efficiently. Can do.

  Therefore, as shown in Non-Patent Document 2, the present inventors have analyzed the relationship with the road surface state by paying attention to the sliding friction coefficient of the road surface, and based on the knowledge obtained from such analysis results, The present invention predicts the sliding friction coefficient of the road surface by modeling the road surface condition with the heat balance model of the road surface snow ice layer and the ice / water / air balance model and performing quantitative evaluation by simultaneous coupling analysis of each model. It is an object of the present invention to provide a method and apparatus for predicting sliding friction on a road surface and a program therefor.

The sliding friction prediction method for road surface according to the present invention uses road surface snow ice layer heat balance model , road surface snow ice layer ice mass balance model, road surface snow ice layer water mass prediction using weather and traffic condition prediction data . Calculates the snow / ice condition prediction data in the road / snow / ice layer based on the balance model and the volume / volume model of the snow / ice layer air volume, and determines the sliding friction coefficient of the road surface based on the calculated snow / ice condition prediction data. And

Another method for predicting sliding friction of a road surface according to the present invention is a heat balance model for a road surface snow ice layer, a mass balance model for the ice of a road surface snow ice layer using prediction data related to weather conditions and traffic conditions and dispersion data of an antifreezing agent. The snow ice condition prediction data in the road surface snow ice layer is calculated based on the mass balance model related to the water of the road surface snow ice layer and the volume balance model related to the air of the road surface snow ice layer, and the road surface based on the calculated snow ice condition prediction data is calculated. Determine the sliding friction coefficient, determine whether the determined sliding friction coefficient of the road surface is within a predetermined range, and if it is not within the predetermined range, the anti-freezing agent is added until the sliding friction coefficient of the road surface is within the predetermined range. The spray data is reset, the snow / ice condition prediction data is recalculated, and the spray data of the antifreezing agent within a predetermined range is determined.

  In the above-described road surface sliding friction prediction method, the snow and ice state prediction data is a mixing ratio of ice, water and air in the road surface snow and ice layer.

A road surface sliding friction prediction device according to the present invention includes a condition data setting unit for setting prediction data relating to weather conditions and traffic conditions, a heat balance model for a road surface snow ice layer, and a road surface snow ice layer using the set prediction data . A snow ice condition prediction unit that calculates snow ice condition prediction data in the road snow ice layer based on a mass balance model for ice, a mass balance model for water in the road snow ice layer, and a volume balance model for air in the road snow ice layer, and calculation And a sliding friction determining unit that determines a sliding friction coefficient of the road surface based on the snow and ice state prediction data.

Another apparatus for predicting sliding friction on a road surface according to the present invention uses a prediction data relating to weather conditions and traffic conditions and a condition data setting unit for setting anti-freezing agent spray data, and the set prediction data and spray data. Snow ice in the road surface snow ice layer based on the heat balance model of the road surface snow ice layer, the mass balance model for the ice of the road surface snow ice layer, the mass balance model for the water of the road surface snow ice layer and the volume balance model for the air of the road surface A snow / ice condition predicting unit that calculates condition prediction data, a sliding friction determination unit that determines a sliding friction coefficient of the road surface based on the calculated snow / ice condition prediction data, and the determined sliding friction coefficient of the road surface are within a predetermined range. As described above, the spray data is reset by the condition data setting unit and the snow / ice state prediction data is recalculated by the snow / ice state prediction unit. Characterized in that it comprises a spraying condition determining unit that determines the fabric data.

  In the above-mentioned road surface sliding friction prediction apparatus, the snow / ice state prediction data is a mixing ratio of ice, water and air in the road surface / snow / ice layer.

A program according to the present invention is a program for causing a road surface sliding friction prediction device to function by setting prediction data relating to weather conditions and traffic conditions and determining a road surface sliding friction coefficient, the road surface sliding friction prediction device The road surface snow ice layer heat balance model , the road surface snow ice layer ice mass balance model, the road surface snow ice layer water mass balance model and the road surface snow ice layer air volume balance using the set prediction data It functions as means for calculating snow / ice condition prediction data in the road surface snow / ice layer based on the model, and means for determining the sliding friction coefficient of the road surface based on the calculated snow / ice condition prediction data.

Another program according to the present invention is a program for functioning a road surface sliding friction prediction device that sets prediction data related to weather conditions and traffic conditions and dispersion data of an antifreezing agent to determine a road surface sliding friction coefficient. The road surface sliding friction prediction device using the set prediction data and the scattered data, a road surface snow ice layer heat balance model , a road surface snow ice layer mass balance model, a road surface snow ice layer water mass Means for calculating snow / ice condition prediction data in the road / snow / ice layer based on the volume / balance model of the snow / ice layer air volume, and means for determining the sliding friction coefficient of the road surface based on the calculated snow / ice condition prediction data Means for determining whether or not the determined sliding friction coefficient of the road surface is within a predetermined range, and if it is not within the predetermined range, the sliding friction of the road surface Factor to function as a means of determining a scatter data cryoprotectant to be within a predetermined range by re-calculating the snow and ice condition prediction data to reconfigure the scattered data cryoprotectant until within a predetermined range.

  In the above program, the snow and ice state prediction data is a mixing ratio of ice, water and air in the road surface snow and ice layer.

  The road surface sliding friction prediction method according to the present invention has the above-described configuration, whereby the road surface sliding friction coefficient can be quantitatively evaluated at each predicted point on the road, and the entire road can be evaluated. Detailed road management can be performed efficiently.

  That is, the prediction data related to weather conditions such as weather, temperature, wind direction, wind speed, precipitation (snowfall) amount of the predicted point can be set based on, for example, past observation data of the observation device installed at the predicted point, Moreover, the weather data provided from the local weather prediction model by GPV (Grid Point Value) of the Japan Weather Association can also be used. Prediction data related to traffic conditions such as the hourly traffic volume at the predicted point and the traveling speed of the vehicle can also be set based on, for example, past measurement data of a measuring device installed at the predicted point, and the Japan Road Traffic Information Center You can also use the data provided by or traffic survey data.

  In this way, high-precision prediction data regarding the weather conditions and traffic conditions at each prediction point is set, and using the prediction data regarding the set weather conditions and traffic conditions, the heat balance model of the road surface snow ice layer and ice / water / air If the snow / ice state prediction data in the road surface snow / ice layer is calculated by simultaneous coupled analysis based on the balance model, the accuracy of the snow / ice state prediction data closely related to the slipperiness of the road surface can be improved. Then, if the sliding friction coefficient of the road surface is determined based on more accurate snow and ice condition prediction data, it is possible to quantitatively evaluate the slipperiness of the road surface, and the road based on the data supported by the objective grounds Management can be performed accurately.

  Here, the simultaneous coupled analysis of each model mentioned above means an analysis method in which the models represented by different governing equations are associated with each other and analyzed simultaneously.

  The road surface sliding friction prediction apparatus according to the present invention has the above-described configuration, and the road surface sliding friction coefficient is quantified at each point of the road in the same manner as the road surface sliding friction prediction method described above. Evaluation can be performed efficiently, and detailed road management can be efficiently performed over the entire road.

  Another road surface sliding friction prediction method according to the present invention has the above-described configuration, so that it is possible to spray an appropriate amount of an antifreezing agent having a road surface sliding friction coefficient within a predetermined range. Slip generation due to insufficient spraying of the antifreezing agent and waste due to excessive spraying of the antifreezing agent can be suppressed to perform appropriate road management.

  In other words, when calculating the snow ice condition prediction data in the road surface snow ice layer based on the heat balance model of the road surface snow ice layer and the ice / water / air balance model, the spray surface of the anti-freezing agent is reflected to calculate the road surface after spraying. The sliding friction coefficient can be predicted. Therefore, by repeatedly calculating the snow and ice condition prediction data while changing the antifreeze spray data and observing the change in the sliding friction coefficient of the road surface, determine the spray data that the road sliding friction coefficient falls within the specified range. The antifreezing agent can be finely distributed according to the situation at each point on the road.

  Another road surface sliding friction prediction apparatus according to the present invention has the above-described configuration, so that the road surface sliding friction coefficient is appropriately set within a predetermined range in the same manner as the other road surface sliding friction prediction method described above. It becomes possible to spray an appropriate amount of antifreezing agent.

  And by calculating the mixing ratio of ice, water, and air in the road surface snow ice layer as snow ice condition prediction data, various state changes of the road surface snow ice layer such as snowfall state, compressed snow state, frozen state, sherbet state, and wet state Therefore, it is possible to obtain prediction data closely related to the above, and to predict the sliding friction coefficient with higher accuracy.

  Hereinafter, embodiments according to the present invention will be described in detail. The embodiments described below are preferable specific examples for carrying out the present invention, and thus various technical limitations are made. However, the present invention is particularly limited in the following description. Unless otherwise specified, the present invention is not limited to these forms.

FIG. 1 is a schematic block diagram of a road surface sliding friction prediction apparatus according to the present invention. The sliding friction prediction apparatus includes an information processing unit 1 that performs information processing necessary for determining a sliding friction coefficient, a setting data storage unit 2 that stores setting data related to a prediction point necessary for information processing, and is arranged along a road to be predicted. A transmission / reception unit 3 that transmits / receives data to / from the detection devices 30 ₁ to 30 _n , a storage unit 4 that stores programs and data necessary for information processing, a display unit 5 that displays prediction results, setting data, and the like An input unit 6 for inputting is provided. The prediction device is connected to a communication network 20 such as the Internet, and can transmit and receive data to and from an external server.

  The information processing unit 1 includes a condition data setting unit 10, a snow and ice state prediction unit 11, and a sliding friction determination unit 12.

  For example, the condition data setting unit 10 is connected to the server 21 of the Japan Meteorological Association, acquires the prediction data related to the weather condition of the predicted point from the prediction data DB 22 related to the weather condition, and stores it in the setting data storage unit 2. Similarly, by connecting to the server 23 of the Japan Road Traffic Information Center, the prediction data related to the traffic condition at the predicted location is acquired from the prediction data DB 24 related to the traffic condition and stored in the setting data storage unit 2. In addition, the detection data is acquired from the prediction point detection device via the transmission / reception unit 3, and the prediction data is created based on the detection data accumulated in the past and stored in the setting data storage unit 2. Further, the physical property value of the road surface layer (the road surface layer thickness, etc.) and the set value relating to the predicted point input from the input unit 6 are stored in the setting data storage unit 2, and the value of the sliding friction coefficient obtained from the experimental result etc. Is stored in the setting table 42.

  The snow and ice state prediction unit 11 reads out the data of the predicted point stored in the setting data storage unit 2 and based on the heat balance model of the road surface snow ice layer and the ice / water / air balance model, the snow and ice at the predicted point are analyzed by simultaneous coupling analysis. State prediction data is calculated.

  The road surface snow ice condition model is a combination of the road surface snow ice layer heat balance model and the ice / water / air balance model, and the volume change of the water, ice and air in the snow ice layer with temperature change (melting / freezing) ) Can be calculated, and the snow ice thickness and the mixing ratio (volume or mass) of water, ice and air in the snow ice layer can be calculated. Snow and ice conditions can be expressed by this mixing ratio. For example, when the volume ratio is water: ice: air = 1: 0: 0, wet state, water: ice: air = 0.3: 0.7: 0, sherbet state, water: ice: air = 0: 0.7 : It becomes a compressed snow state at 0.3.

Since the road surface snow ice layer is composed of water, ice particles and interstitial air except for impurities and antifreeze agents, the snow ice volume V _s (m ³ / m ² ) per unit area is expressed by the following equation (1). Thus, the water volume V _w (m ³ / m ² ), the ice volume V _i (m ³ (m ³ / m ² )), and the air volume V _a (m ³ (m ³ / m ² )).

Therefore, the volume ratios of water, ice, and air in the snow ice layer (volumetric water content θ _w , volumetric ice content θ _i, and volumetric air content θ _a ) are expressed by the following equation (2).

Further, the snow ice density ρ _s (kg / m ³ ) and the mass ice content Θ _i are obtained by the equation shown in Equation 3.

ここで、Ｍ_wは雪氷層中の水質量（ｋｇ／ｍ²）、Ｍ_iは雪氷層中の氷質量（ｋｇ／ｍ²）、ρ_wは水密度（ｋｇ／ｍ³）、ρ_iは氷密度（ｋｇ／ｍ³）、ρ_aは空気密度（ｋｇ／ｍ³）である。

Here, M _w is the mass of water in the snow and ice layer (kg / m ² ), M _i is the mass of ice in the snow and ice layer (kg / m ² ), ρ _w is the water density (kg / m ³ ), and ρ _i is Ice density (kg / m ³ ), ρ _a is air density (kg / m ³ ).

FIG. 2 is an explanatory diagram illustrating a water balance model and an ice balance model of a road surface snow and ice layer. As for the water balance (mass) of the road surface snow and ice layer, as shown in the left half of FIG. 2, the rainfall flux M _wf (kg / m ² / s), the evaporation / condensation flux M _wl (kg / m ² / s), Melting / solidification flux M _wi (kg / m ² / s), scattering flux M _ws (kg / m ² / s) associated with vehicle running, and drainage flux M _wd (kg / m ² / s) associated with road gradient The time change rate of the water mass M _w (kg / m ² ) of the snow and ice layer is defined by the equation shown in Equation 4. Here, t: time (s).

The rainfall flux M _wf is given by the product of the rainfall intensity v _fw (m / s) and the water density ρ _w and is expressed by the equation shown in Equation 5.

ここで、降雨強度ｖ_fwとしては、例えば、気象協会から提供される予想降水量を用いることができる。

Here, as the rainfall intensity v _fw , for example, an estimated precipitation amount provided by the Meteorological Association can be used.

The evaporation / condensation flux M _wl is given by the bulk formula shown in Equation 6.

ここで、α_wlは蒸発・凝結バルク係数（ｍ／ｓ）、ρ_vaは大気の水蒸気密度（ｋｇ／ｍ³）、ρ_vsは雪氷表面の水蒸気密度（ｋｇ／ｍ³）である。なお、ρ_va及びρ_vsは、世界気象機関で採用されている実験式を用いて求められる。

Here, α _wl is the evaporation / condensation bulk coefficient (m / s), ρ _va is the water vapor density (kg / m ³ ) of the atmosphere, and ρ _vs is the water vapor density (kg / m ³ ) of the snow ice surface. Note that ρ _va and ρ _vs are obtained using empirical formulas adopted by the World Meteorological Organization.

When the snow ice temperature T _s = 0 ° C. and the net heat balance flux Q _s (W / m ² )> 0 of the road surface snow ice layer described later, Q _s is consumed for melting the snow ice layer, and conversely, Q _s <0 Then Q _s is spent on coagulation. At that time, M _wi is given by the equation shown in Equation 7.

ここで、ｑ_mは融解及び凝固潜熱（ｋJ／ｋｇ）である。

Here, q _m is melting and solidification latent heat (kJ / kg).

The scattered flux M _ws can be estimated based on the result of an actual vehicle running experiment. Further, the drainage flux _Mwd can be obtained by using a known Manning formula or an average flow velocity formula, and a road gradient and a roughness coefficient necessary for the calculation may be set based on actual measurement values.

As shown in the right half of Fig. 2, the snow balance (mass) of the road surface snow ice layer is the snow flux M _if (kg / m ² / s), the sublimation flux M _il (kg / m ² / s), Time variation of ice mass M _i (kg / m ² ) defined by the solidification flux M _wi (kg / m ² / s) and the scattering flux M _is (kg / m ² / s) as the vehicle travels The rate is expressed by the equation shown in Equation 8.

The snowfall flux M _if is given by the product of the snowfall intensity v _fi (m / s) and the snowfall density ρ _si and is expressed by the equation shown in Equation 9.

ここで、降雪強度ｖ_fiとしては、例えば、気象協会から提供される予想降雪量を用いることができる。降雪密度ρ_siは、例えば、実際の測定結果に基づいて設定すればよい。

Here, as the snowfall intensity v _fi , for example, an expected snowfall amount provided by the Meteorological Association can be used. The snowfall density ρ _si may be set based on actual measurement results, for example.

The sublimation flux M _il is given by the bulk formula shown in Equation 10.

ここで、α_wlは昇華バルク係数（ｍ／ｓ）であり、ρ_va及びρ_vsは、世界気象機関で採用されている実験式を用いて求められる。

Here, α _wl is a sublimation bulk coefficient (m / s), and ρ _va and ρ _vs are obtained using an empirical formula adopted by the World Meteorological Organization.

The air balance (volume) of the snow and ice layer includes the snowfall air flux V _af (m ³ / m ² / s), the replacement air flux V _aex (m ³ / m ² / s), and the open air flux V _ao (m ³ / m). ² / s), and the time change rate of the air volume V _a (m ³ / m ² ) of the road surface snow ice layer is given by the equation shown in Equation 11.

The snowfall air flux V _af is the volume of air supplied along with the snowfall flux M _if and is given by the equation shown in Equation 12.

The replacement air flux V _aex is a volume per unit time / unit area of the air released from the snow / ice layer when the air inside the snow / ice layer is replaced with water by melting of ice, and is expressed by the following equation (13). .

The open air flux V _ao is the volume per unit time and unit area of the air released from the inside of the snow and ice layer by melting ice, and is expressed by the equation shown in Equation 14.

  FIG. 3 is an explanatory diagram illustrating heat balance components that affect the snow and ice layer on the road surface. First, as shown at the left end, a snow and ice layer is formed by snow on the paved road surface to form a snowy road surface. The formed snow and ice layer is mainly compressed by the running of the vehicle to become a compacted state and becomes a compressed snow road surface, but the running of the vehicle reveals radiant heat from the bottom of the vehicle, frictional heat from the tires, and wind induced by passing the vehicle. It is thought that heat balance components such as heat are generated. And it will be in the state melt | dissolved in the vehicle passage area | region of the snow-ice layer of the compaction state.

  In addition to the heat balance component due to such artificial factors, the heat balance component due to natural factors can be considered. In Fig. 3, pavement conduction heat transferred from the pavement surface to the snow and ice layer, sensible heat from natural wind, sensible heat from rainfall and snow removal, solidification latent heat due to freezing, radiant heat radiated from the sky to the snow and ice layer, and radiated from the snow and ice layer It is thought that long wave radiant heat is generated. And the water thawed on the surface of the snow and ice layer at night mainly freezes to become a frozen road surface. Further, during the daytime, it is considered that solar heat due to solar radiation and latent heat due to evaporation are generated, and the entire snow and ice layer becomes a sherbet road surface in a loose state like a sherbet.

FIG. 4 is an explanatory diagram illustrating the heat flux obtained by quantifying the heat balance components shown in FIG. As heat flux (unit: W / m ² ) due to natural factors, pavement heat flux G _sp , radiation flux R _sd , solar reflection flux R _su , solar transmission flux R _st , sky radiation heat flux R _ld , road surface The radiant heat flux R _lu , the sensible heat flux S _a due to natural wind, the sensible heat flux S _f accompanying rain-snowfall, the evaporation / sublimation latent heat flux _Le, and the melting / solidification latent heat flux L _m can be mentioned. As the heat flux due to human factors, the vehicle heat flux Q _v and the like. In this example, it is assumed that the heat transfer in the longitudinal direction of the road (x direction) is sufficiently small, and it is handled in two dimensions, the road crossing direction (y direction) and the vertical direction (z direction).

If the volumetric heat capacity of the snow ice surface layer is (ρc) _s (J / m ³ / K), the snow ice temperature is T _s (° C.), and the snow ice thickness is z _s (m), The heat balance Q _s is given by the equation shown in Equation 15.

体積熱容量（ρｃ）_sは、雪氷層中の水、氷及び空気の調和平均により数１６に示す式で与えられる。

The volumetric heat capacity (ρc) _s is given by the equation shown in Equation 16 based on the harmonic average of water, ice and air in the snow and ice layer.

ここで、（ρｃ）_w、（ρｃ）_i及び（ρｃ）_aは、それぞれ水、氷及び空気の体積熱容量（Ｊ／ｍ³／Ｋ）である。

Here, (ρc) _w , (ρc) _i and (ρc) _a are the volumetric heat capacities (J / m ³ / K) of water, ice and air, respectively.

The snow ice thickness z _s is given by the equation shown in Equation 17 as the sum of the water, ice and air volumes (V _w , V _i and V _a ) of the snow ice layer per unit area.

なお、θ_w、θ_i、θ_a、Ｖ_w、Ｖ_i及びＶ_aは、上述した氷・水・空気収支より求められる。

Note that θ _w , θ _i , θ _a , V _w , V _i and V _a are obtained from the ice / water / air balance described above.

The pavement heat flux G _sp is the amount of heat transfer between the snow ice layer and the pavement surface, and is given by the equation shown in Equation 18 using the contact thermal resistance R _c (m ² K / W).

ここで、λ_sは雪氷の熱伝導率（Ｗ／ｍ／Ｋ）、λ_pは舗装の熱伝導率（Ｗ／ｍ／Ｋ）、ｚ_psは舗装表層厚（ｍ）、Ｔ_sは界面からΔｚ_s／２上方の雪氷温度（℃）、Ｔ_psは界面からΔｚ_ps／２下方の舗装温度（℃）である。接触熱抵抗Ｒ_c（ｍ²Ｋ／Ｗ）は、θ_aの関数として数１９に示す式で表される。

Where λ _s is the thermal conductivity of snow and ice (W / m / K), λ _p is the thermal conductivity of the pavement (W / m / K), z _ps is the pavement surface thickness (m), and T _s is from the interface Snow and ice temperature above Δz _s / 2 (° C.), T _ps is the pavement temperature (° C.) below Δz _ps / 2 from the interface. The contact thermal resistance R _c (m ² K / W) is expressed by the equation shown in Equation 19 as _a function of θ _a .

なお、λ_sは、水、氷及び空気の熱伝導率の調和平均として与えればよい。

Note that λ _s may be given as a harmonic average of the thermal conductivity of water, ice, and air.

The reflected solar radiation flux R _su and the transmitted solar radiation flux R _st are given by the equations shown in Equation 20, respectively.

ここで、α_lはアルベドであり、アルベドモデルに基づいて理論的に求められる（例えば、近藤純正 外２名、「積雪面のアルベードのパラメータ化」、雪氷、Vol.50、No.4、pp.216-224、1988）。また、Ｔ_rは透過率であり、透過実験に基づいて決定することができる。

Here, α _l is an albedo and is theoretically obtained based on the albedo model (for example, two outside Kondo Jun, “parameterization of albedo on the snow cover”, snow ice, Vol.50, No.4, pp .216-224, 1988). Further, _Tr is a transmittance and can be determined based on a transmission experiment.

The road surface long wave radiation latex R _lu is given by the equation shown in Equation 21 according to the Stefan-Boltzmann law.

雪氷表面の射出率ε_sは、氷面と水面の面積率を重み係数とした調和平均で数２２に示す式で与えられる。

The injection rate ε _{s on the} surface of snow and ice is given by the equation shown in Equation 22 as a harmonic average using the area ratio of the ice surface and the water surface as a weighting factor.

ここで、σはＳｔｅｆａｎ−Ｂｏｌｔｚｍａｎｎ定数（５．６７×１０^-8Ｗ／ｍ²／Ｋ⁴）、ε_iは氷面の射出率（０．９８）及びε_wは水面の射出率（０．９６）である。

Here, σ is a Stefan-Boltzmann constant (5.67 × 10 ⁻⁸ W / m ² / K ⁴ ), ε _i is an ice surface injection rate (0.98), and ε _w is a water surface injection rate (0. 96).

Sensible heat flux S _a by natural wind, in accordance with the cooling law of Newton, given by the equation shown in Formula 5.

ここで、α_asは大気−雪氷層間の熱伝達率（Ｗ／ｍ²／Ｋ）であり、室内実験と伝熱解析から得られた値を採用し、数２４に示すような風速（Ｖ_w（ｍ／ｓ））の関数で与えられる。

Here, alpha _{the as} atmospheric - a heat transfer coefficient of the snow and ice layers ^{(W / m 2 / K)} , adopts the value obtained from the laboratory experiments and heat transfer analysis, wind speed, as shown in several 24 (V _w (M / s)).

気温（Ｔ_a）及び風速（Ｖ_w）は、条件データ設定部１０により日本気象協会から取得した予測データを用いればよい。取得した予測データに対応する地点が予測地点から外れている場合には、予測データに対応する地点の間を補間法により近似値を算出して予測地点の予測データとして用いてもよい。また、予測地点において観測された過去の蓄積データに基づいて作成された予測データを用いるようにしてもよい。

For the temperature (T _a ) and the wind speed (V _w ), prediction data acquired from the Japan Meteorological Association by the condition data setting unit 10 may be used. When the point corresponding to the acquired prediction data is out of the prediction point, an approximate value may be calculated between the points corresponding to the prediction data by an interpolation method and used as the prediction data of the prediction point. Moreover, you may make it use the prediction data produced based on the past accumulation data observed in the prediction point.

The sensible heat flux S _f accompanying the rainfall-snowfall is given by the equation shown in Equation 25 using the rainfall intensity v _fw or the snowfall intensity v _fi .

ここで、Ｔ_fは降雨−降雪温度である。降雨と降雪の区別は気温により判別する。

Here, T _f is the rain-snow temperature. The distinction between rainfall and snowfall is made by temperature.

Evaporation and sublimation latent heat flux L _e is given by the equation shown in Expression 26 by using the evaporation flux M _wl and sublimation flux M _il.

ここで、ｑ_eは蒸発潜熱（ｋＪ／ｋｇ）、ｑ_sは昇華潜熱（ｋＪ／ｋｇ）である。

Here, q _e is the latent heat of vaporization (kJ / kg), and q _s is the latent heat of sublimation (kJ / kg).

Melting and Solidification latent heat flux L _m is given by the equation of the equation 27 is multiplied by the latent heat of fusion q _m of ice melting and solidification flux M _wi.

融解・凝固潜熱フラックスＬ_mは、雪氷の変成に費やされて雪氷厚さｚ_sが増減するようになる。

The melting / solidifying latent heat flux L _m is consumed for the snow / ice transformation, and the snow / ice thickness z _s increases / decreases.

The vehicle heat flux Q _v is given as the sum of the tire friction heat flux _St , the vehicle bottom surface radiant heat flux R _v, and the vehicle induced sensible heat flux S _va , and is given by the following equation (28).

The tire frictional heat flux _St is given by an equation obtained by multiplying the temperature difference between the tire and the road surface by the heat transfer coefficient, as shown in Equation 29.

ここで、α_tpはタイヤ−乾燥路面間の熱伝達率（Ｗ／ｍ²／Ｋ）であり、室内実験と伝熱モデルから得られた６０Ｗ／ｍ²／Ｋを用いる（武士 俊也 外５名、「熱収支法による路面凍結解析−車両タイヤ−圧雪層−路面間の熱移動−、寒地技術論文・報告集、Vol.18、pp.71-76、２００２年）。また、タイヤ温度Ｔ_tは、気温（Ｔ_a）及び車両速度（Ｖ_vｋｍ／ｈ）の関数として数３０で示す式で計算される。

Here, α _tp is the heat transfer coefficient (W / m ² / K) between the tire and the dry road surface, and 60 W / m ² / K obtained from the laboratory experiment and the heat transfer model is used (Toshiya Takeshi and 5 others) , "Analysis of road surface freezing by heat balance method-Vehicle tire-Snow-capped layer-Heat transfer between road surface-, Cold district technical papers and reports, Vol.18, pp.71-76, 2002). _t is calculated by the equation shown in Equation 30 as a function of the temperature (T _a ) and the vehicle speed (V _v km / h).

車両速度（Ｖ_v）は、条件データ設定部１０により日本道路交通情報センターから取得された時間交通量に関する予測データや定期的な交通量調査結果に基づいて設定された予測データを用いて設定する。

The vehicle speed (V _v ) is set using the prediction data related to the hourly traffic volume acquired from the Japan Road Traffic Information Center by the condition data setting unit 10 and the prediction data set based on the periodic traffic volume survey results. .

The vehicle bottom surface radiant heat flux R _v is given by the equation shown in Equation 31.

ここで、ε_vは車両底面の射出率（０．８０）であり、Ｔ_vは車両底面の絶対温度（Ｋ）である。車両底面の絶対温度Ｔ_vは、図５に示すように、３つの領域に分けてそれぞれ数３２に示す式で与えられる。

Here, ε _v is an injection rate (0.80) on the bottom surface of the vehicle, and T _v is an absolute temperature (K) on the bottom surface of the vehicle. As shown in FIG. 5, the absolute temperature T _{v at the} bottom of the vehicle is given by the equations shown in Equation 32 divided into three regions.

ここで、Ｌ^*は、車両全長（Ｌ）を車両前方からの距離（ｘ）で除した無次元距離である。

Here, L ^* is a dimensionless distance obtained by dividing the total vehicle length (L) by the distance (x) from the front of the vehicle.

The vehicle-induced sensible heat flux S _va is given by the equation shown in Equation 33.

α_sは、数２４に示す式と同様に車両誘発風Ｖ_wの関数で与えられる。この場合、車両誘発風Ｖ_wは、実験結果に基づいて設定することができる。一例として、普通車両の通過に伴う場合では図６のグラフに示すような時間変化をするものとして設定することができる。

α _s is given as a function of the vehicle induced wind V _{w in} the same manner as the equation shown in Expression 24 In this case, the vehicle induced wind V _w can be set based on the experimental result. As an example, it can be set as a time change as shown in the graph of FIG.

  The snow and ice condition prediction unit 11 reads out necessary weather and traffic condition prediction data from the setting data storage unit 2 using the road surface snow and ice layer heat balance model and the ice / water / air balance model described above, and performs simultaneous coupled analysis. Thus, snow / ice state prediction data such as the snow / ice temperature, the snow / ice thickness and the mixing ratio (mass or volume) of water, ice and air in the snow / ice layer are calculated. Based on the calculated prediction data regarding the mixing ratio of water, ice and air in the snow and ice layer, data having a close relationship with sliding friction such as snow ice density and mass ice content can be obtained.

The sliding friction determination unit 12 determines the sliding friction coefficient of the road surface at each prediction point based on the snow and ice state prediction data calculated by the snow and ice state prediction unit 11. In the non-patent document 3, the present inventors have disclosed volume ratios of water, ice and air in the snow ice layer (volume water content θ _w , volume ice content θ _i and volume air content) when the snow and ice condition of the road surface changes. The correlation between the rate θ _a ) and the sliding friction coefficient μ is analyzed by experiment, and the analysis result is as shown in the graph of FIG. The data relating to the sliding friction coefficient thus obtained is registered in the setting table 42 in correspondence with the volume ratios of water, ice and air. The sliding friction determination unit 12 reads the corresponding sliding friction coefficient from the setting table 42 based on the calculated snow and ice state prediction data, and determines the temporal transition of the sliding friction coefficient at each prediction point.

  In addition to the volume ratios of water, ice and air described above, prediction data such as snow ice thickness, snow ice density, and mass ice content are related to tire slip. Evaluation may be performed. For example, if the thickness of snow and ice is less than 10 mm, the running tire will grip directly on the road surface, so the effect of the snow and ice layer on sliding friction will be less, but if it exceeds 10 mm, it will grip directly on the road surface. The sliding friction is influenced by the volume ratio of water, ice and air and the mass ice content.

  FIG. 8 is a flow relating to the prediction process of the sliding friction coefficient. First, necessary data relating to weather conditions and traffic conditions is stored in the setting data storage unit 2 as an initial state (S100). Next, parameters necessary for calculating the heat balance and the ice / water / air balance are set (S101). Examples of the parameters to be set include prediction data relating to weather conditions and traffic conditions at each prediction point. For example, as shown in FIG. 9, the temporal transition of parameters related to meteorological conditions such as snow data, rainfall data and temperature is set. As shown in FIG. 10, the parameters related to traffic conditions such as vehicle traffic data and vehicle speed data are set. Set temporal transition.

  Next, the snow / ice condition prediction unit 11 calculates the heat balance of the snow ice layer and the pavement layer using the heat balance model (S102), and also uses the ice / water / air balance model to determine the ice / water / air balance of the snow / ice layer. (S103) and simultaneous coupling analysis is performed between the models. Based on the analysis result, snow / ice state prediction data (volume ratio of water, ice and air, snow ice thickness, snow ice density, mass ice content, etc.) at each prediction point is calculated (S104).

FIG. 11 shows temporal transitions regarding the road surface temperature T _p , the snow ice temperature T _s, and the volume ratio of water, ice and air in the snow ice layer calculated based on the prediction data shown in FIGS. 9 and 10. In the time zone TA, a snow and ice layer in a compressed snow state is formed due to the accumulation of snow due to snowfall and the influence of traffic, and the thickness gradually increases and the ice content rate increases. And the remainder contains air and does not contain water. In time period TB, the temperature is ice melts the water content gradually increases in snow and ice layer the surface temperature T _p exceeds 0 ℃ to rise, changes in snow and ice layers sorbet state. In addition, the thickness of the snow and ice layer suddenly decreases due to the effects of solar radiation and rainfall. In the time body TC, the snow / ice temperature T _s becomes 0 ° C. or more, and all the ice melts and the snow / ice layer disappears to become a wet road surface. Thus, the change in the snow and ice condition on the road surface is quantified as the change in the volume ratio of water, ice and air.

  Based on the prediction data of the volume ratio of water, ice and air in the snow / ice layer calculated in this way and the sliding friction coefficient data stored in the setting table 42, the prediction data of the sliding friction coefficient is determined (S105).

  FIG. 12 shows the predicted sliding friction coefficient determined based on the predicted data shown in FIG. In the time zone TA, a snow and ice layer in a compressed snow state is formed and its thickness increases, so that the ice content increases and the sliding friction coefficient becomes 0.2 to 0.4, and the slippery road surface Is expected to be. In addition, in the state where the ice started to melt even in the time zone TB, the sliding friction coefficient is 0.4 because the ice content has not decreased so much, and the slipping state is still not resolved, It is predicted that the sliding friction coefficient increases to 0.6 as the ice content decreases and the water content increases.

  As described above, if the prediction data on the weather and traffic conditions at each point is used to calculate the snow / ice condition prediction data in the road / snow / ice layer based on the heat / snow model of the road / snow / ice layer and the ice / water / air balance model In addition, it is possible to improve the accuracy of snow and ice state prediction data closely related to the slipperiness of the road surface. Then, if the sliding friction coefficient of the road surface is determined based on more accurate snow and ice condition prediction data, it is possible to quantitatively evaluate the slipperiness of the road surface, and the road based on the data supported by the objective grounds Management can be performed accurately. In addition, safety management such as warning display and speed regulation for the driver can be performed at an optimal timing.

  Next, another embodiment relating to a sliding friction prediction device for a road surface will be described. In this embodiment, the sliding friction of the road surface when antifreezing agent is sprayed is predicted, and FIG. 13 is a schematic block configuration diagram thereof. In FIG. 13, in the schematic block configuration diagram shown in FIG. 1, a scatter condition determining unit 13 is provided in the information processing unit 1, and the other block configuration is the same.

  In the condition data setting unit 10, the type of the cryoprotectant input from the input unit 6, the melting rate data and the heat of fusion data obtained by the dispersion are stored in the setting table 42 as setting data.

The melt rate data for the cryoprotectant can be determined by experiment. For example, a predetermined amount of an antifreezing agent is sprayed on an ice plate at a constant temperature, and after a predetermined time has elapsed, the solution concentration and the amount of ice melt are measured to calculate the melting rate (g / m ³ / s). Then, by repeating the same experiment while changing the air temperature and the spraying amount, the fusion rate data corresponding to the air temperature and the spraying amount can be obtained.

  The heat of fusion of the antifreezing agent can be calculated by multiplying the melting speed by the latent heat of melting, and is set based on the obtained melting speed data.

In addition, the condition data setting unit 11 sets anti-freezing agent spray data (type of anti-freezing agent, spray amount per unit area (g / m ² ) and spray time) determined in advance as an initial setting.

  Antifreeze agents include inorganic salt substances such as sodium chloride and calcium chloride, and acetate substances such as calcium acetate, and are often used in the form of granules or powders. By spraying the antifreezing agent, the antifreezing agent dissolves on the surface of the snow and ice layer and the concentration of the solution increases, so that the freezing temperature is lowered and the snow and ice layer is difficult to freeze even when the road surface temperature becomes below freezing point. Therefore, a state close to a sherbet road surface with a lot of moisture occurs, and the volume ratio of water, ice and air changes, and as shown in FIG. 7, a decrease in the sliding friction coefficient can be suppressed. The action of such an antifreeze affects the above-mentioned ice / water / air balance model and changes the melting / solidification flux. In addition, since an endothermic reaction occurs due to the application of the antifreeze agent, the heat balance model is also affected, and the melting / solidification latent heat flux is changed.

  The spraying condition determining unit 13 determines whether or not the predicted data of the sliding friction coefficient determined by the sliding friction determining unit 12 is within the reference range based on preset reference range data of the sliding friction coefficient. If there is a time zone out of the reference range in the prediction data, the condition data setting unit 10 resets the scattered data, and the snow and ice state prediction unit 11 recalculates the snow and ice state prediction data. The dispersion data of the antifreezing agent is determined so that the predicted data of the friction coefficient falls within the reference range.

  The condition data setting unit 10 and the sliding friction determination unit 12 are the same as those described in FIG.

  FIG. 14 is a flow relating to the prediction process of the sliding friction coefficient when the antifreezing agent is sprayed. First, the type, application amount, and application time are set as application data of the antifreezing agent (S200). As the scatter data, data stored in advance may be automatically set, or may be input from the input unit 6.

  Next, necessary data regarding weather conditions and traffic conditions are stored in the setting data storage unit 2 as an initial state (S201). Then, parameters necessary for calculating the heat balance and the ice / water / air balance are set (S202). The parameters to be set may be set similarly to step S101 in the prediction process flow shown in FIG.

  Next, the snow / ice condition prediction unit 11 calculates the heat balance of the snow ice layer and the pavement layer using the heat balance model (S203), and also uses the ice / water / air balance model to determine the ice / water / air balance of the snow / ice layer. (S204), and a simultaneous coupling analysis is performed between the models. Based on the analysis result, snow / ice state prediction data (volume ratio of water, ice and air, snow ice thickness, snow ice density, mass ice content, etc.) at each prediction point is calculated (S205). Based on the snow / ice state prediction data thus calculated and the sliding friction coefficient data stored in the setting table 42, the sliding friction coefficient prediction data is determined (S206).

FIG. 15 is a prediction result of a sliding friction coefficient when sodium chloride is used as an antifreezing agent and sprayed at a spraying amount of 50 g / m ² before snowfall. When not sprayed as shown in FIG. 12, a snow and ice layer in a compressed snow state was formed, the sliding friction coefficient was reduced to 0.2, and a state where slipping was likely to occur was predicted. Therefore, the sliding friction coefficient is 0.4, and it can be seen that the reduction of the sliding friction coefficient is suppressed. This is because the formation of a snow and ice layer in a compressed snow state is suppressed by spraying the antifreezing agent, and the moisture content is increased, so that the reduction of the sliding friction coefficient is suppressed.

  It is determined whether or not the prediction result of the sliding friction coefficient thus determined is within the reference range (S207). If the prediction result is within the reference range, the application data set in step S200 is the optimum one. The spraying conditions are determined as follows (S208). If any part of the determined sliding friction coefficient prediction result is out of the reference range, the process returns to step S200, the scattered data is reset, and the calculation is repeated from step S201 to S206 to determine the sliding friction coefficient again. . Then, the optimum spraying condition is determined by adjusting the spray data of the antifreeze agent until the sliding friction coefficient determined again falls within the reference range.

  The reference range of the sliding friction coefficient is a sliding friction coefficient necessary for preventing slip at the lower limit, and may be set in accordance with a situation such as an inclined state of the road surface. In general, it is slippery at 0.4 or less, but it is desirable to set in consideration of road conditions. The upper limit may be set according to a normal wet road surface. Generally, it is 0.6 to 0.7, but it is desirable to set according to the road condition.

FIG. 16 is a prediction result of the sliding friction coefficient when the spray data in the case of FIG. 15 is reset and the spray amount is set to 100 g / m ² . Compared to the case of FIG. 15, it is predicted that the sliding friction coefficient increases to 0.5 and the road surface condition is further improved. However, when the lower limit of the sliding friction coefficient reference range is 0.4, the application condition is determined at an application rate of 50 g / m ² without excessive application based on objective data. Appropriate spraying conditions can be determined.

It is a schematic block block diagram regarding the sliding friction prediction apparatus of the road surface which concerns on this invention. It is explanatory drawing which illustrated the water balance model and ice balance model of the road surface snow ice layer. It is explanatory drawing which illustrated the heat balance component which affects a road surface snow ice layer. It is explanatory drawing which illustrated the heat flux which quantified each heat balance component shown in FIG. It is explanatory drawing which shows the dimensionless distance distribution of vehicle bottom face temperature. It is a graph which shows the time change of the vehicle induction wind accompanying a normal vehicle passage. It is a graph which shows the correlation between the volume ratio of water, ice, and air, and a sliding friction coefficient. It is the flow regarding the prediction process of a sliding friction coefficient. It is a graph which shows the time transition of the parameter regarding a weather condition. It is a graph which shows the time transition of the parameter regarding traffic conditions. It is a graph which shows the time transition regarding the road surface temperature, the snow ice temperature, and the mixing ratio of ice, water and air in the snow ice layer. It is a graph which shows the prediction result of a sliding friction coefficient. It is a schematic block block diagram regarding another sliding friction prediction apparatus which concerns on this invention. It is the flow regarding the prediction process of a sliding friction coefficient in the case of spraying an antifreezing agent. It is a graph which shows the prediction result of the sliding friction coefficient at the time of spraying with the application quantity of 50 g / m < ² >. It is a graph which shows the prediction result of the sliding friction coefficient at the time of spraying with the application quantity of 100 g / m < ² >.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Information processing part 2 Setting data storage part 3 Transmission / reception part 4 Storage part 5 Display part 6 Input part

Claims (9)

Using the prediction data on meteorological and traffic conditions, the heat balance model of the road surface snow ice layer, the mass balance model of the road surface snow ice layer ice, the mass balance model of the road surface snow ice layer water and the volume balance of the road surface snow ice layer air A method for predicting sliding friction of a road surface, comprising: calculating snow / ice state prediction data in a road surface snow / ice layer based on a model , and determining a sliding friction coefficient of the road surface based on the calculated snow / ice state prediction data. Predicted data on meteorological and traffic conditions and antifreeze spray data, heat balance model for road surface snow ice layer, mass balance model for ice of road surface snow ice layer, mass balance model for water of road surface snow ice layer and road surface snow ice The snow ice condition prediction data in the road surface snow ice layer is calculated based on the volume balance model of the layer air, the road friction coefficient is determined based on the calculated snow ice condition prediction data, and the determined road surface friction is determined. It is determined whether the coefficient is within a predetermined range. If the coefficient is not within the predetermined range, the spray data of the antifreezing agent is reset until the sliding friction coefficient of the road surface is within the predetermined range, and the snow / ice condition prediction data is re-established. A method for predicting sliding friction on a road surface, characterized by calculating and determining dispersion data of an antifreezing agent within a predetermined range.   3. The road surface sliding friction prediction method according to claim 1, wherein the snow / ice state prediction data is a mixing ratio of ice, water and air in the road surface snow / ice layer. A condition data setting unit that sets prediction data related to weather conditions and traffic conditions, and a heat balance model of a road surface snow ice layer, a mass balance model of ice on the road surface snow ice layer, and water of the road surface snow ice layer using the set prediction data. A snow ice condition prediction unit that calculates snow ice condition prediction data in the road surface snow ice layer based on a mass balance model related to mass and a volume balance model related to air on the snow surface of the road surface, and a slip of the road surface based on the calculated snow ice condition prediction data A sliding friction prediction device for a road surface, comprising a sliding friction determination unit for determining a friction coefficient. Prediction data related to weather conditions and traffic conditions, and a condition data setting unit for setting antifreeze spray data, a road surface snow ice layer heat balance model using the set prediction data and spray data , ice on the road surface snow ice layer A snow ice condition prediction unit that calculates snow ice condition prediction data in the road surface snow ice layer based on a mass balance model for the road surface snow ice layer water and a volume balance model for the road snow ice layer air. The sliding friction determination unit that determines the sliding friction coefficient of the road surface based on the predicted snow and ice condition prediction data, and the scatter data is reset in the condition data setting unit so that the determined sliding friction coefficient of the road surface is within a predetermined range. And a spraying condition determining unit for determining spraying data of the antifreezing agent by recalculating the snow / ice state prediction data in the snow / ice state prediction unit. Sliding friction prediction device of the road surface which is characterized in Rukoto.   6. The road surface sliding friction prediction apparatus according to claim 4, wherein the snow / ice state prediction data is a mixing ratio of ice, water and air in the road surface snow / ice layer. A program for setting a prediction data related to weather conditions and traffic conditions and determining a sliding friction coefficient of a road surface to function a sliding friction prediction device for a road surface,
A sliding friction prediction device for the road surface,
Using the set prediction data, the road surface snow ice layer heat balance model , the road surface snow ice layer mass balance model, the road surface snow ice layer water mass balance model, and the road surface snow ice layer air volume balance model Means for calculating snow and ice state prediction data in the road surface snow and ice layer,
A program for functioning as a means for determining a sliding friction coefficient of a road surface based on calculated snow and ice condition prediction data. A program for functioning a sliding friction prediction device for a road surface that sets prediction data on weather conditions and traffic conditions and dispersion data of an antifreezing agent and determines a sliding friction coefficient of the road surface,
A sliding friction prediction device for the road surface,
The heat balance model of the road surface snow ice layer, the mass balance model of the mass of the road surface snow ice layer, the mass balance model of the mass of the road surface snow ice layer and the volume of the air of the road surface snow ice layer using the set prediction data and the scattered data Means for calculating snow and ice condition prediction data in the road surface snow and ice layer based on the balance model of
Means for determining the sliding friction coefficient of the road surface based on the calculated snow and ice condition prediction data;
Means for determining whether or not the determined sliding friction coefficient of the road surface is within a predetermined range;
If it is not within the predetermined range, reset the antifreezing agent spray data until the sliding friction coefficient of the road surface is within the predetermined range, and recalculate the snow / ice condition prediction data to obtain the antifreezing agent spray data within the predetermined range. A program for functioning as a means for determining   The program according to claim 7 or 8, wherein the snow and ice state prediction data is a mixing ratio of ice, water and air in a road surface snow and ice layer.

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