Solar Energy Vol. 71, No. 1, pp. 23–31, 2001 2001 Elsevier Science Ltd  Pergamon PII: S0038–092X(01)00024–X All rights reserved. Printed in Great Britain 0038-092X / 01 / $ - see front matter www.elsevier.com / locate / solener EVALUATION OF PREDICTIVE MODELS FOR THE ANGLE-DEPENDENT TOTAL SOLAR ENERGY TRANSMITTANCE OF GLAZING MATERIALS , ² J. KARLSSON* , M. RUBIN** and A. ROOS* ˚ ¨ *Department of Materials Science, The Angstrom Laboratory, Uppsala University, P.O. Box 534, S-75121 Uppsala, Sweden **Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, USA Received 12 April 2000; revised version accepted 22 January 2001 Communicated by M.G. HUTCHINS Abstract—The predictions of angle-dependent optical properties of glazings are discussed. A categorisation of windows depending on the type of coating on the glazing is discussed as a way of improving the accuracy in the predictive models. Four approximate ways to predict the angle dependence of the total solar energy transmittance are compared. The impact on the energy performance of windows with different angle dependence is assessed in a heating and a cooling dominated climate, respectively. Results imply that by simply using the clear glass angular profile for all types of windows gives quite low errors in the angle dependence prediction, lower than some other previously proposed models. By using a model with window category as input, the errors in angle dependence prediction can be further reduced. The impact on the energy performance from incorrect angle dependence is considerable in some cases but not necessarily critical.  2001 Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION investigates the impact of failing accuracy in these data. In this study we focus the attention on Windows often play an important role in the the total solar energy transmittance, also known as energy system of a building. Large window areas the solar heat gain coefficient (SHGC) or here can increase the annual heating bill and / or cause referred to as the g-value. The different ap- considerable overheating during sunny periods. proaches to extract the angle-dependent properties Among the important properties that are required can briefly be summarised as; measurements to assess the impact of windows in buildings are (Roos, 1997), ‘exact’ Fresnel calculations (see for the optical properties, such as the transmittance instance: Born and Wolf (1980)), semiphysical averaged over the visual or solar spectral region. models (Rubin et al., 1999; Montecchi et al., These properties of a glazing are normally only 1999), empirical models (Montecchi and Polato, supplied for a near normal angle of incidence, but 1995; Karlsson and Roos, 2000a) and template are required for all angles of incidence. This models (see Section 3 below). All of these ap- problem has been addressed by several authors proaches have some advantages and drawbacks. (Pfrommer et al., 1995; Montecchi and Polato, Angle resolved measurements are very time con- 1995, 1998; Roos, 1997; Rubin et al., 1999; van suming and call for experts and expert equipment, Nijnatten, 1999; Montecchi et al., 1999; Karlsson but are always the ultimate way of confirming the and Roos, 2000a) and one of the purposes of the real angle-dependent properties. Fresnel calcula- European ADOPT project has been to find an tions would render accurate results but then the accurate algorithm or procedure to predict the exact physical properties of the coatings, such as angle-dependent integrated optical properties of thickness and optical constants, must be known windows. These properties are always used in which is often not the case. The semiphysical or building simulation models and their somewhat empirical models can be very simple and reason- complex feature may lead to errors in the calcu- ably correct, but do not always give the results lated energy use in buildings. This paper com- within a desired error limit. For the empirical pares and analyses some proposed algorithms and models, it is necessary to have the windows categorised in order to be able to get a good result ² (Karlsson and Roos, 2000a). Finally, the template Author to whom correspondence should be addressed. models utilise the known angular dependency for Tel.: 146-18-471-3134; fax: 146-18-500-131; e-mail: joakim.karlsson@angstrom.uu.se some specific glazing(s), usually uncoated float 23