## 3 Results and Discussion  
### Burning Characteristics of Black Acrylic According to External Heat Flux  
To evaluate the relevance of experimental methods and the setup of a cone calorimeter, Figure 3 illustrates the ignition time according to the external heat flux under auto and spark ignition conditions. Quantitative errors that may be generated owing to the specimen components were verified by comparing standard PMMA and black acrylic applied in this study. In addition, the ignition time of PMMA was compared with the findings of previous studies [33; 37]. Figure 3a shows the experimental results obtained where the auto-ignition method was applied; all conditions below 40 kW/m\({}^{2}\) were excluded where ignition did not occur during an exposure time of external heat flux for 30 min or longer [2]. The ignition time gradually decreased with the external heat flux, and there was almost no quantitative difference between black acrylic and standard PMMA. Moreover, the relative error between the measurements in this study and the previous study [37] is very similar, about 3.5%. Figure 3b shows the results obtained within an external heat flux range of 15-65 kW/m\({}^{2}\) under the spark ignition condition. The results of this are quantitatively very similar to those of a previous study conducted under identical experimental conditions. The standard deviation (vertical error bar) from repeated experiments was largest under the condition of 15 kW/m\({}^{2}\), while the reproducibility of measurements was fairly high under the condition of 30 kW/m\({}^{2}\) or greater. The relative error between the measurements with the previous study [33] is very similar, about 9.5% at 15 kW/m\({}^{2}\) and about 4.8% above 30 kW/m\({}^{2}\). Thus, the reliability of the experimental methods and cone calorimeter apparatus applied in this study is guaranteed, while the results of black acrylic are quantitatively very similar to the results of standard PMMA, as shown in Figure 3.  
Figures 4 and 5 illustrate the changes in MLR and HRR of black acrylic with respect to time under various external heat fluxes. Time from ignition may be generally used as the title of the \(x\)-axis. However, to examine the ignition phenomena in detail according to an ignition method, the time in the \(x\)-axis was proposed as the time at which the external heat flux is exposed to the specimen. The results illustrated in Figure 4 show that the MLR was higher after ignition as the external heat flux was higher, regardless of the ignition method, while the time to reach the maximum MLR was reduced. The difference in MLR in terms of the ignition method was clearly shown under the condition of an external heat flux of 40 kW/m\({}^{2}\), which is relatively low. In other words, the MLR value between 50 and 140 s was approximately 0.05 g/s when auto-ignition was applied, where MLR increased sharply for an ignition time of 140 s, as shown in Figure 3. On the contrary, MLR increased sharply after 25 s, which corresponds to the ignition time when spark ignition was applied. Specifically, under the auto-ignition condition, even if pyrolysis by external heat flux proceeds and combustible gas reaches the lower flammability limit, ignition would not occur if insufficient thermal energy is provided to initiate the gas-phase reaction. This moment is marked as the \"only pyrolysis period\" in Figure 4a. In contrast, forced ignition occurs when the lower flammability limit is reached through pyrolysis under the spark ignition condition [36]. Under the condition of a relatively lower external heat flux, excluding the delay in ignition time due to the inactivation of the gas-phase reaction that can occur in the initial phase of pyrolysis, the changes in HRR with respect to time showed very similar behaviors when compared to MLR, as illustrated in Figure 5.  
Figure 4: Time histories of mass loss rate under the conditions of various external heat fluxes for the auto and spark ignitions.