# 平均輻射溫度

## 計算方式

（1）${\displaystyle MRT=T_{1}A_{1}+T_{2}A_{2}+...+T_{n}A_{n}}$  此處：

${\displaystyle MRT}$  是平均辐射温度；
${\displaystyle T_{n}}$        是表面温度，以絕對溫標為單位，以下標n為各個表面編號；
${\displaystyle A_{n}}$   是各個表面的面積。

（2）${\displaystyle MRT^{4}=T_{1}^{4}F_{p-1}+T_{2}^{4}F_{p-2}+...+T_{n}^{4}F_{p-n}}$  此處：

${\displaystyle MRT}$  是平均辐射温度；
${\displaystyle T_{n}}$        是表面温度，以絕對溫標為單位，以下標n為各個表面編號；
${\displaystyle F_{p-n}}$   是人与表面n之间的角度因子。

（3）${\displaystyle MRT=T_{1}F_{p-1}+T_{2}F_{p-2}+...+T_{n}F_{p-n}}$

## 測量方式

（4）${\displaystyle MRT=\left[\left(GT+273\right)^{4}+{\frac {1.1\cdot 10^{8}\cdot v_{a}^{0.6}}{\varepsilon \cdot D^{0.4}}}(GT-T_{a})\right]^{1/4}-273}$

${\displaystyle MRT}$ 是平均辐射温度（°C）；
${\displaystyle GT}$      是地球温度（°C）；
${\displaystyle v_{a}}$        是地球高度的风速（m / s）；
${\displaystyle \varepsilon }$          是球體的发射率（無單位）；
${\displaystyle D}$         是地球仪的直径（米）；
${\displaystyle T_{a}}$        是气温（°C）;

（5）${\displaystyle MRT=\left[\left(GT+273\right)^{4}+2,5\cdot 10^{8}\cdot v_{a}^{0,6}(GT-T_{a})\right]^{1/4}-273}$

## 参考資料

1. ISO 7726. Ergonomics of the thermal environment - Instrument for measuring physical quantities. Geneva, Switzerland: International Organization for Standardization. November 1998.
2. ^ ScienceDirect Topics. www.sciencedirect.com. [2020-12-24].
3. ^ Walikewitz, Nadine; Jänicke, Britta; Langner, Marcel; Meier, Fred; Endlicher, Wilfried. The difference between the mean radiant temperature and the air temperature within indoor environments: A case study during summer conditions. Building and Environment. 2015-01-01, 84: 151–161. ISSN 0360-1323. doi:10.1016/j.buildenv.2014.11.004 （英语）.
4. ^ Fanger, P.O. Thermal Comfort: Analysis and Applications in Environmental Engineering. New York: McGraw Hill. 1970.
5. ^ Matzarakis, Andreas. Estimation and Calculation of the Mean Radiant Temperature within Urban Structures.
6. ^ Mclntyre and Griffiths, D.A. and I.D. Subject Response to Radiant and Convective Environments. 1972.
7. ^ Indoor Environmental Quality with Energy Efficiency. www.healthyheating.com. [2020-12-24].
8. 2009 ASHRAE Handbook Fundamentals, ASHRAE, Inc., Atlanta, GA.