# Estimation of Thermal Radiation in Bed Mattresses
## 1 Introduction  
In current times, industries are developing, building materials are becoming more diversified and customized, and the population density of cities is increasing, leading to more frequent accidents. Particularly, building fires in large cities with high population density can cause extensive damage in a single accident. Moreover, when designing buildings, the thermal radiation generated in a fire and the intensity of the fire source are not estimated in advance, and design measures to reduce the impact of flames on the surroundings are not considered. As such, governments and organizations related to fire protection and safety are dedicating efforts and steadily developing technologies to prevent accidents and minimize damage from fires, but their implementation is inadequate in practice.  
The thermal radiation emitted by a flame is an important parameter that determines the flame's future conditions, and the thermal radiation loss can lead to fire extinguishment [1]. In a fire, thermal radiation is generated from flames; moreover, research on heated architectural members, the smoke layer, and thermal radiation is underway. For example, when measuring the amount of radiation generated by a fire source in a compartment, [PERSON] estimated thermal radiation by considering not only the thermal radiation of theflame itself but also the thermal radiation feedback generated from the ceiling, walls, and the smoke layer [2]. Additionally, to estimate the constant of the radiative fraction in turbulent fires, [PERSON] and [PERSON] obtained the radiative fraction constant from methane burning [3], [PERSON] estimated the radiative fraction constant from liquid fuel through experiments [4], and [PERSON] obtained the flame radiative fraction constant from burning solid materials [5]. Furthermore, [PERSON] [6] calculated thermal radiation using the flame height equation of [PERSON] [7] in a windless environment, and [PERSON] [8] estimated thermal radiation using the flame height equation of [PERSON] [9]. Based on these prior research results, in ISO 24678-7, the existing thermal radiation estimation models are applied based on constituent factors for estimating thermal radiation (the combustion area and the heat release rate) to establish the thermal radiation estimation algorithm as an international standard [10].  
Meanwhile, the Korean market for bed mattresses (hereinafter referred to as mattresses) that are widely used in residential spaces has grown at an annual average of 17.17%, from KRW 211.5 billion in 2014 to 398.6 billion in 2018, and is projected to reach KRW 589.8 billion in 2023 [11]. The frequency of mattresses-related fires increases with the growth of the mattress market. Mattress-based fires in South Korea were responsible for an annual average of 312 deaths over the past five years (2015-2019), with bedrooms being the most common place of death, with an average of 70 people (22.4%) [12]. In the United States, it was reported that half of the deaths and injuries caused by bedroom fires were due to mattresses and bedding, and one-third of bedroom fires were related to mattresses and bedding [13; 14; 15]. Hence, the fire risk of mattresses increases as the mattress market grows, but there is low public awareness of the risk, and sufficient preventive measures based on scientific findings have not been established yet.  
Accordingly, this study confirmed thermal radiation measurements through a real-scale model experiment on mattresses at different installation heights and compared the experimental results and the predicted calculation results. Specifically, when a mattress was ignited in an open environment at different installation heights (0-515 mm), the measurements from a heat flux meter and the calculated thermal radiation were compared, and a comparative analysis was conducted using the existing prediction formulas described in ISO 24678-7.