JP2002181636A - Method for estimating road surface temperature - Google Patents

Method for estimating road surface temperature

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Publication number
JP2002181636A
JP2002181636A JP2000380486A JP2000380486A JP2002181636A JP 2002181636 A JP2002181636 A JP 2002181636A JP 2000380486 A JP2000380486 A JP 2000380486A JP 2000380486 A JP2000380486 A JP 2000380486A JP 2002181636 A JP2002181636 A JP 2002181636A
Authority
JP
Japan
Prior art keywords
road surface
temperature
surface temperature
road
heat
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP2000380486A
Other languages
Japanese (ja)
Other versions
JP3690275B2 (en
Inventor
Teruyuki Nakamura
晃之 中村
Hiroaki Kitagawa
博朗 北川
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hitachi Cable Ltd
Original Assignee
Hitachi Cable Ltd
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Filing date
Publication date
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Priority to JP2000380486A priority Critical patent/JP3690275B2/en
Publication of JP2002181636A publication Critical patent/JP2002181636A/en
Application granted granted Critical
Publication of JP3690275B2 publication Critical patent/JP3690275B2/en
Anticipated expiration legal-status Critical
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Abstract

PROBLEM TO BE SOLVED: To provide a road surface temperature estimating method that can accurately estimate road surface temperature distribution without using meteorological data. SOLUTION: Earth temperature distribution is measured by an optical fiber 2 buried under a road 1 along the longitudinal direction of the road, and road surface temperature distribution is estimated using the earth temperature distribution and an earth heat constant such as heat conductivity and heat capacity.

Description

【発明の詳細な説明】DETAILED DESCRIPTION OF THE INVENTION

【0001】[0001]

【発明の属する技術分野】本発明は、地中温度から路面
温度を推定する方法に係り、特に、気象データを使わな
くても正確に路面温度分布を推定することができる路面
温度推定方法に関するものである。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for estimating a road surface temperature from an underground temperature, and more particularly to a method for estimating a road surface temperature accurately without using weather data. It is.

【0002】[0002]

【従来の技術】従来、一般に、路面温度は、気象データ
と熱伝導率、熱容量などの地中熱定数(地中内部定数と
もいう)とによって求められている。以下に、その詳し
い方法を説明する。
2. Description of the Related Art Conventionally, a road surface temperature is generally obtained from weather data and an underground heat constant (also referred to as an underground internal constant) such as heat conductivity and heat capacity. Hereinafter, the detailed method will be described.

【0003】まず、熱量が路面(地表面)へ流入する概
念を説明する(なお、ここでは熱量が出ていくことも含
めて流入と表現している)。図4に示されるように、地
表面へ流入する熱量は、太陽からの輻射熱Ws、雲から
の輻射熱Wc、大気からの流入熱Wa(輻射熱Warと
対流熱Wαとの和)、地表面からの放射熱Wre、地中
からの流入熱W2からなる。大気側から地表面へ流入す
る各熱量の総計をW1 とする。このとき、(1)式、
(2)式が成立する。
[0003] First, the concept of the flow of heat into the road surface (ground surface) will be described (herein, the term "inflow" includes the flow of heat). As shown in FIG. 4, the amount of heat flowing into the ground surface is radiant heat Ws from the sun, radiant heat Wc from the clouds, inflow heat Wa from the atmosphere (sum of radiant heat War and convective heat Wα), and heat from the ground surface. radiant heat Wre, consisting inflow heat W 2 from the ground. The total of each heat flowing from the atmosphere side to the ground surface and W 1. At this time, equation (1)
Equation (2) holds.

【0004】 W1 +W2 =0 (1) W1 =Ws+Wc+Wa+Wre (2) 次に、大気側からの流入熱と気象データとの関係を説明
する。
W 1 + W 2 = 0 (1) W 1 = Ws + Wc + Wa + Wre (2) Next, the relationship between the inflow heat from the atmosphere side and weather data will be described.

【0005】 Ws=(1−Ae) Wc=Ee・σ・Tc4 ・f(ηc) Wre=Ee・σ・Te4 Wα=α(Ta−Te) War=Ee・σ・Ta4 α=α0 +β・V・f(H) (3) 但し、 Ae:アルベド数(定数) Wso:太陽からの輻射熱(日射量) Ee:地表面の輻射率(定数) σ:ボルツマン定数 Te:地表面温度(K) Tc:雲の温度(K)(ほぼ一定) ηc:雲量比率 α:対流による熱伝導率 Ta:大気温度(K) V:風速(m/s) α0 、β、f(H):温度依存係数 である。これらの量を計測して(2)式、(3)式に代
入することにより、大気側からの流入熱W1 を求めるこ
とができる。
[0005] Ws = (1-Ae) Wc = Ee · σ · Tc 4 · f (ηc) Wre = Ee · σ · Te 4 Wα = α (Ta-Te) War = Ee · σ · Ta 4 α = α 0 + β · V · f (H) (3) where Ae: Albedo number (constant) Wso: radiant heat from the sun (solar radiation) Ee: emissivity of the ground surface (constant) σ: Boltzmann constant Te: ground surface temperature (K) Tc: Cloud temperature (K) (almost constant) ηc: Cloud volume ratio α: Thermal conductivity due to convection Ta: Atmospheric temperature (K) V: Wind speed (m / s) α 0 , β, f (H) : Temperature-dependent coefficient. By measuring these quantities (2), by substituting the equation (3), it can be determined inflow heat W 1 from the atmosphere side.

【0006】次に、地中からの流入熱について説明す
る。地中からの流入熱W2 は、地中内部の温度分布から
求まる。ここでは、基底温度T0 から求める方式で説明
する。基底温度を利用する方式は、地中深い所(数10
m程度の深さ)の温度が年間を通じてほぼ一定となると
いうことを利用するものであり、この温度を基底温度T
0 とする。図5に示したように、路面から基底までにn
個の位置をとると、路面から基底までの熱等価回路は、
熱抵抗R1 ,R2 ,…,Rn 及び熱容量C1 ,C 2 ,…
Cnで構成した梯子状回路となる。
Next, the inflow heat from the ground will be described.
You. Inflow heat W from undergroundTwo From the temperature distribution inside the ground
I get it. Here, the base temperature T0 Explain in the method required from
I do. The method using the base temperature is used in deep underground (Equation 10).
(depth of about m) becomes almost constant throughout the year
This temperature is used as the base temperature T.
0 And As shown in FIG. 5, n from the road surface to the base
Taking this position, the heat equivalent circuit from the road surface to the base is
Thermal resistance R1 , RTwo , ..., Rn And heat capacity C1 , C Two ,…
It becomes a ladder-like circuit composed of Cn.

【0007】この熱等価回路における温度計算は、時間
Δtごとに行う。
The temperature calculation in this heat equivalent circuit is performed for each time Δt.

【0008】k番目の位置での地中温度Tk は、(5)
式で表される。
The underground temperature T k at the k-th position is given by (5)
It is expressed by an equation.

【0009】 (Tk −Tk-1 )/Rk-1 +(Tk −Tk-1 )/Rk +Ck-1 ・Tk /Δt=0 (5) ここで、n個の位置を等間隔にとると、各間隔における
熱抵抗及び熱容量について、 Rk =Δh/λkk =ρk ・Cpk ・Δh となる。但し、 Δh:道路下深さ方向の刻み幅 λk :各間隔における地中の鉛直方向の熱伝導率 ρk :各間隔における地中構成物質の密度 Cpk :各間隔における地中構成物質の密度当り熱容量 そこで、(5)式にRk の式を代入すると、 (Tk −Tk-1 )・λk-1 /Δh +(Tk −Tk-1 )・λk /Δh +Ck-1 ・Tk /Δt=0 (5)´ となる。
[0009] (T k -T k-1) / R k-1 + (T k -T k-1) / R k + C k-1 · T k / Δt = 0 (5) here, the n taking positions at equal intervals, the thermal resistance and heat capacity at each interval, the R k = Δh / λ k C k = ρ k · Cp k · Δh. However, Delta] h: stride of the road under depth lambda k: thermal conductivity in the vertical direction in the ground in each interval [rho k: Density Cp k underground constituents in each interval: the ground constituents in each interval Heat capacity per density Then, when the equation of R k is substituted into the equation (5), (T k −T k−1 ) · λ k−1 / Δh + (T k −T k−1 ) · λ k / Δh + C k−1 · T k / Δt = 0 (5) ′

【0010】また、(5)式にCk の式を代入すると、 (Tk −Tk-1 )/Rk-1 +(Tk −Tk-1 )/Rk +ρk-1 ・Cpk-1 ・Δh・Tk /Δt=0 (5)´´ となる。実際には、(5)式にRk の式とCk の式とを
両方とも代入することになる。
Further, when the equation of C k is substituted into the equation (5), (T k −T k−1 ) / R k−1 + (T k −T k−1 ) / R k + ρ k−1. Cp k−1 · Δh · T k / Δt = 0 (5) ″ Actually, both the expression of R k and the expression of C k are substituted into the expression (5).

【0011】境界条件は、(6)式、(7)式で表され
る。
The boundary condition is expressed by the equations (6) and (7).

【0012】 (T1−T2)/R1 =W1 (6) Tn =T0 (7) 従って、(5)式、(6)式、(7)式を計算すると、
1 すなわち路面温度(地表面温度)Teが求まる。
(T1−T2) / R 1 = W 1 (6) T n = T 0 (7) Therefore, when the equations (5), (6) and (7) are calculated,
T 1 ie, the road surface temperature (surface temperature) Te is obtained.

【0013】[0013]

【発明が解決しようとする課題】しかしながら、従来の
路面温度算出方法では、以下のような問題があった。
However, the conventional road surface temperature calculation method has the following problems.

【0014】(1)日射、気温、風速、湿度等を計測す
る気象センサが必要であり、気象センサを設置していな
い箇所では、路面温度の精度が悪くなる。
(1) A weather sensor for measuring solar radiation, air temperature, wind speed, humidity, and the like is required, and the accuracy of the road surface temperature is deteriorated in places where no weather sensor is installed.

【0015】(2)道路長手方向の路面温度分布を算出
しようとすると、予め地形データ等の周囲環境のデータ
を把握しておく必要があり、このデータを収集するのに
非常に手間がかかる。また、予めデータを把握できたと
しても、そのデータをもとに道路長手方向の気象量を補
正しており、路面温度の精度が悪くなる。気象センサを
道路長手方向に多数設置する案もあるが、気象センサを
道路長手方向に多数設置すると非常にコストが高くな
る。
(2) In order to calculate the road surface temperature distribution in the longitudinal direction of the road, it is necessary to grasp the surrounding environment data such as terrain data in advance, and it is extremely troublesome to collect this data. Even if the data can be grasped in advance, the weather amount in the longitudinal direction of the road is corrected based on the data, and the accuracy of the road surface temperature is deteriorated. There is a plan to install a large number of weather sensors in the longitudinal direction of the road. However, if a large number of weather sensors are installed in the longitudinal direction of the road, the cost becomes extremely high.

【0016】(3)路面状態(特に凍結、積雪)毎に、
(3)式のアルベド数Aeが変化するため、正確に路面
温度を推定することは困難である。また、正確に路面温
度を推定するためには、路面状態センサを設置する必要
があり、路面状態センサを設置するとコストが高くな
る。
(3) For each road surface condition (especially freezing, snow cover)
Since the albedo number Ae in the equation (3) changes, it is difficult to accurately estimate the road surface temperature. Further, in order to accurately estimate the road surface temperature, it is necessary to install a road surface state sensor, and if the road surface state sensor is installed, the cost increases.

【0017】そこで、本発明の目的は、上記課題を解決
し、気象データを使わなくても正確に路面温度分布を推
定することができる路面温度推定方法を提供することに
ある。
An object of the present invention is to solve the above problems and to provide a road surface temperature estimation method capable of accurately estimating a road surface temperature distribution without using weather data.

【0018】[0018]

【課題を解決するための手段】上記目的を達成するため
に本発明は、道路下に道路長手方向に沿って埋設した光
ファイバにより地中における道路長手方向の温度分布を
計測し、この地中温度分布と熱伝導率、熱容量などの地
中熱定数とを用いて路面温度分布を推定するものであ
る。
In order to achieve the above object, the present invention measures the temperature distribution in the longitudinal direction of the road under the road by using an optical fiber buried under the road along the longitudinal direction of the road. The road surface temperature distribution is estimated using the temperature distribution and the underground thermal constants such as thermal conductivity and heat capacity.

【0019】上記地中熱定数は、深さ方向に所定の間隔
刻みで設定してもよい。
The underground thermal constant may be set at predetermined intervals in the depth direction.

【0020】上記地中熱定数は、地中構成成分に応じて
設定してもよい。
The underground heat constant may be set according to the underground constituent components.

【0021】[0021]

【発明の実施の形態】以下、本発明の一実施形態を添付
図面に基づいて詳述する。
An embodiment of the present invention will be described below in detail with reference to the accompanying drawings.

【0022】図1に示されるように、本発明の路面温度
推定方法を実施するために、道路1の道路表面下に道路
長手方向に沿って光ファイバ2が埋設されている。この
光ファイバ2の一端には光ファイバ長手方向の温度分布
を計測する光ファイバ温度計測装置3が設けられてい
る。そして、この温度分布から路面温度分布を推定する
路面温度推定装置4が設けられている。
As shown in FIG. 1, an optical fiber 2 is buried under a road surface of a road 1 along a longitudinal direction of the road to implement the road surface temperature estimating method of the present invention. At one end of the optical fiber 2, an optical fiber temperature measuring device 3 for measuring the temperature distribution in the longitudinal direction of the optical fiber is provided. A road surface temperature estimating device 4 for estimating the road surface temperature distribution from the temperature distribution is provided.

【0023】以下、本発明の路面温度推定方法を詳しく
説明する。
Hereinafter, the road surface temperature estimating method of the present invention will be described in detail.

【0024】図2に示されるように、光ファイバ2の埋
設位置(深さ)fを含んだ熱等価回路を考える。光ファ
イバ2の埋設位置fを、例えば、道路表面下3cmとす
る。この埋設位置の温度変化量(過去から現在までの温
度変化量)と、その埋設位置から鉛直方向に道路表面に
向かっての熱伝導率及び熱容量とを使用し、道路表面に
流入する熱量の変化量を求める。次に、この熱量の変化
量に見合った道路表面の温度変化量を求め、この温度変
化量を予め測定した初期の路面温度に加えることによ
り、現在の路面温度を推定する。
As shown in FIG. 2, a heat equivalent circuit including the embedded position (depth) f of the optical fiber 2 is considered. The embedding position f of the optical fiber 2 is, for example, 3 cm below the road surface. Changes in the amount of heat flowing into the road surface using the temperature change amount at this buried position (the temperature change amount from the past to the present) and the heat conductivity and heat capacity from the buried position toward the road surface in the vertical direction Find the quantity. Next, the amount of temperature change on the road surface corresponding to the amount of change in the heat amount is obtained, and the current amount of road surface temperature is estimated by adding the amount of change in temperature to the previously measured initial road surface temperature.

【0025】実際の大気側から路面への流入熱の変化量
ΔWがΔW* のとき、光ファイバ2で計測した地中温度
f が時間Δt当たりΔTf だけ変化したとする。この
とき、ΔTf は、ΔW=0のときの光ファイバ埋設位置
fでの温度変化量δTf0と、大気側から路面へΔW*
流入してきたときの温度変化量δTf との和で表される
((101)式)。
The actual variation [Delta] W inflow heat from the atmosphere side to the road surface when the [Delta] W *, and underground temperature T f measured by the optical fiber 2 is changed by the time Δt per [Delta] T f. In this case, the table by the sum of the [Delta] T f is the temperature change amount? T f0 of the optical fiber embedded position f in the case of [Delta] W = 0, the temperature change amount? T f at which the road surface is [Delta] W * has flowed from the atmosphere side (Equation (101)).

【0026】 ΔTf =δTf0+δTf (101) ΔW=0のときの光ファイバ埋設位置fでの温度変化量
δTf0は、(6)式のW1 を0とし、(5)式、(7)
式より求まる。
The temperature change amount? T f0 of the optical fiber embedded position f in the case of ΔT f = δT f0 + δT f (101) ΔW = 0 is set to 0 W 1 of (6), (5), ( 7)
Obtained from the formula.

【0027】次に、図3に示すように、熱量の変化と温
度の変化との関係が直線で近似される範囲内で、大気側
から路面への流入熱の変化量ΔWを任意にΔWz として
与える。このとき、光ファイバ埋設位置fでの仮の温度
変化量ΔTfzは、(6)式のW1 をΔWz とし、(5)
式、(7)式より求まる。温度変化量ΔTfzは、ΔW=
0のときの光ファイバ埋設位置fでの温度変化量δTf0
と、任意に定めた大気側から路面へΔWz が流入してき
たときの温度変化量δTfzとの和で表される((10
2)式)。
Next, as shown in FIG. 3, within a range in which the relationship between the change in the amount of heat and the change in the temperature is approximated by a straight line, the amount of change ΔW in the heat flowing into the road from the atmosphere side is arbitrarily set to ΔW z Give as. At this time, the temperature change amount [Delta] T fz provisional optical fiber embedded position f is a [Delta] W z the W 1 of (6), (5)
It can be obtained from the equation (7). The amount of temperature change ΔT fz is ΔW =
Temperature change amount δT f0 at the optical fiber embedding position f when 0
When, as represented by the sum of the temperature change amount? T fz when [Delta] W z from the atmosphere side to arbitrarily determined to road surface has flowed ((10
2) Formula).

【0028】 ΔTfz=δTf0+δTfz (102) よって、ΔW=0のときの光ファイバ埋設位置fでの温
度変化量δTf0と、仮の温度変化量ΔTfzとが上記まで
に求められるので、温度変化量δTfzが求まる。
ΔT fz = δT f0 + δT fz (102) Therefore, the temperature change amount δT f0 at the optical fiber embedding position f when ΔW = 0 and the temporary temperature change amount ΔT fz are obtained as described above. , The temperature change amount δT fz is obtained.

【0029】次に、図3より(103)式が得られる。Next, equation (103) is obtained from FIG.

【0030】 δTf /ΔW* =δTfz/ΔWz (103) (103)式より、実際に路面に入ってくる熱量変化Δ
* は、 ΔW* =(ΔWz /δTfz)・δTf (104) (104)式において、δTf は実際の光ファイバ埋設
位置fでの温度変化量から得られ、、δTfzは(10
2)式から得られ、また、ΔWz は任意に定めることが
できる値であることから、実際の熱量変化ΔW* が分か
る。
ΔT f / ΔW * = δT fz / ΔW z (103) From the equation (103), the change Δ in the amount of heat actually entering the road surface
W * is, [Delta] W * = In (ΔW z / δT fz) · δT f (104) (104) Formula,? T f is obtained from the temperature variation in the actual optical fiber embedded position f ,,? T fz is ( 10
2) obtained from the equation, also, [Delta] W z from it is a value that can be determined arbitrarily, the actual heat quantity change [Delta] W * is found.

【0031】このようにして求まったΔW* を(6)式
に代入し、(5)式、(7)式から、路面温度の変化量
ΔTe が求まる。
The ΔW * obtained in this way is substituted into the expression (6), and the amount of change in the road surface temperature ΔT e is obtained from the expressions (5) and (7).

【0032】初期の路面温度Te0は、予め熱電対等で測
定しておけば、下記(105)式のようにして、路面温
度が算出できる。
If the initial road surface temperature T e0 is measured in advance with a thermocouple or the like, the road surface temperature can be calculated as in the following equation (105).

【0033】 Te =Te0+ΔTe (105) 初期の路面温度Te0は、道路長手方向の一箇所で測定す
ればよく、その測定点における路面温度Te0と光ファイ
バ埋設位置fでの温度との差(初期温度差)を求め、こ
の初期温度差を道路長手方向各測定点における光ファイ
バ埋設位置fでの温度に加算して初期路面温度分布とす
る。爾後、各測定点について、それぞれ(105)式に
より路面温度を算出することになる。
[0033] T e = T e0 + ΔT e (105) the initial road surface temperature T e0 may be measured at one location of the road longitudinal, temperature at the surface temperature T e0 and an optical fiber embedded position f at the measuring point (Initial temperature difference), and the initial temperature difference is added to the temperature at the optical fiber embedding position f at each measurement point in the longitudinal direction of the road to obtain an initial road surface temperature distribution. Thereafter, the road surface temperature is calculated for each of the measurement points by using the equation (105).

【0034】刻み幅Δhは、例えば、0.5mmとす
る。地中構成物質が道路表面より順にアスファルト(又
はコンクリート)、砕石、土となっており、刻み幅Δh
毎の熱抵抗Rk =Δh/λk は、これらの地中構成物質
の熱伝導率λk により定めることになる。また、刻み幅
Δh毎の熱容量Ck =ρk ・Cpk ・Δhは、地中構成
物質の密度ρk 及び密度当り熱容量Cpk により定める
ことになる。
The step width Δh is, for example, 0.5 mm. Underground constituent materials are asphalt (or concrete), crushed stone, and soil in order from the road surface, and the step width Δh
Each thermal resistance R k = Δh / λ k is determined by the thermal conductivity λ k of these underground constituent materials. Moreover, the heat capacity C k = ρ k · Cp k · Δh for each stride Delta] h will be determined by the density of underground construction materials [rho k, and density per heat capacity Cp k.

【0035】図1の場合、埋設する光ファイバを1本と
したが、深さ方向、道路幅方向に複数本の光ファイバを
埋設してもよい。
In FIG. 1, one optical fiber is embedded, but a plurality of optical fibers may be embedded in the depth direction and the road width direction.

【0036】[0036]

【発明の効果】本発明は次の如き優れた効果を発揮す
る。
The present invention exhibits the following excellent effects.

【0037】(1)日射、気温、風速、湿度等を計測す
る気象センサがなくとも、光ファイバで計測した地中内
部温度と道路下の地中内部定数(熱伝導率など)とだけ
で、路面温度を正確に推定できる。
(1) Even if there is no weather sensor for measuring solar radiation, air temperature, wind speed, humidity, etc., only the underground internal temperature measured by an optical fiber and the underground internal constant (thermal conductivity, etc.) under a road, The road surface temperature can be accurately estimated.

【0038】(2)地形データ(山、建物等)による情
報を処理する必要がなく、システムの構築が容易であ
る。
(2) There is no need to process information based on terrain data (mountains, buildings, etc.), and system construction is easy.

【0039】(3)簡素なシステムで実施できるので、
コストが安い。
(3) Since it can be implemented with a simple system,
Cost is low.

【図面の簡単な説明】[Brief description of the drawings]

【図1】本発明の路面温度推定方法を用いたシステムの
構成図である。
FIG. 1 is a configuration diagram of a system using a road surface temperature estimation method of the present invention.

【図2】本発明に利用する熱量変化対温度変化の特性図
である。
FIG. 2 is a characteristic diagram of a change in calorific value versus a change in temperature used in the present invention.

【図3】本発明における地中の熱等価回路の図である。FIG. 3 is a diagram of an underground heat equivalent circuit according to the present invention.

【図4】地表面へ流入する熱量の概念図である。FIG. 4 is a conceptual diagram of the amount of heat flowing into the ground surface.

【図5】地中の熱等価回路の図である。FIG. 5 is a diagram of an underground heat equivalent circuit.

【符号の説明】[Explanation of symbols]

1 道路 2 光ファイバ 3 光ファイバ温度計測装置 4 路面温度推定装置 Reference Signs List 1 road 2 optical fiber 3 optical fiber temperature measuring device 4 road surface temperature estimating device

Claims (3)

【特許請求の範囲】[Claims] 【請求項1】 道路下に道路長手方向に沿って埋設した
光ファイバにより地中における道路長手方向の温度分布
を計測し、この地中温度分布と熱伝導率、熱容量などの
地中熱定数とを用いて路面温度分布を推定することを特
徴とする路面温度推定方法。
An optical fiber buried under the road along the longitudinal direction of the road measures a temperature distribution in the longitudinal direction of the ground in the ground, and calculates the underground temperature distribution and the underground thermal constant such as thermal conductivity and heat capacity. A road surface temperature estimating method characterized by estimating a road surface temperature distribution by using a method.
【請求項2】 上記地中熱定数は、深さ方向に所定の間
隔刻みで設定することを特徴とする請求項1記載の路面
温度推定方法。
2. The road surface temperature estimating method according to claim 1, wherein the underground thermal constant is set at predetermined intervals in a depth direction.
【請求項3】 上記地中熱定数は、地中構成成分に応じ
て設定することを特徴とする請求項1又は2記載の路面
温度推定方法。
3. The road surface temperature estimating method according to claim 1, wherein the underground thermal constant is set according to an underground component.
JP2000380486A 2000-12-14 2000-12-14 Road surface temperature estimation method Expired - Fee Related JP3690275B2 (en)

Priority Applications (1)

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Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
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JP3690275B2 JP3690275B2 (en) 2005-08-31

Family

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Family Applications (1)

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Country Status (1)

Country Link
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2003240867A (en) * 2002-02-20 2003-08-27 Natl Inst For Land & Infrastructure Management Mlit Road surface condition estimation method

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2003240867A (en) * 2002-02-20 2003-08-27 Natl Inst For Land & Infrastructure Management Mlit Road surface condition estimation method

Also Published As

Publication number Publication date
JP3690275B2 (en) 2005-08-31

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