Numerical derivation and validation of the angular, hemispherical and normal emissivity and reflectivity of common window glass

D. Rüdisser*, R. S. McLeod, W. Wagner, C. J. Hopfe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The thermal radiative properties of glazing materials are fundamental inputs for evaluating the energetic performance and thermal behaviour of buildings. These properties are required for many practical applications ranging from infrared thermography to building performance simulation and thermal comfort evaluations. Soda–lime–silica glass is the most widely used glass, worldwide, for glazing and the derivation of its thermal and optical properties are the subject of this work. Based on experimentally acquired spectral reference measurement data for soda-lime glass, the complex-valued Fresnel equations are solved and Monte-Carlo integration is carried out over the black-body spectrum, as well as over the hemisphere. These calculations are performed for various radiative temperatures to establish their temperature dependencies, and additionally the temperature-dependent transmittance of soda-lime glass was analysed. By applying a non-linear optimisation algorithm, computationally efficient practical fitting formulae for the angular reflectivity, emissivity and absorptivity are derived. All equations are numerically solved with a high degree of accuracy. The determination of the hemispherical total emissivity for this type of glass confirms the current accepted value (∼0.2%) originally derived by Rubin (1985). A simple yet robust experimental design, based on thermography, is used to validate the results of the numerical reflectivity model. Additionally, we provide angular functions, fitting functions and additional constants that were hitherto unavailable. The practical benefits of the fitting formulae provided are considerable in relation to modelling the reflection of thermal radiation on glazed surfaces, and are demonstrated in two case-study applications in the appendix.

Original languageEnglish
Article number108536
JournalBuilding and Environment
Publication statusPublished - Jan 2022


  • Angular, normal and hemispherical emissivity
  • Emissivity
  • Measurement of glass temperature with pyrometer or thermography
  • reflectivity of thermal radiation
  • Thermal radiation
  • Window glass, i.e. soda-lime glass

ASJC Scopus subject areas

  • Environmental Engineering
  • Civil and Structural Engineering
  • Geography, Planning and Development
  • Building and Construction


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